Mineral Processing: Beneficiation Operations and Process Optimization through Modeling [1 ed.] 0128231491, 9780128231494

Citation preview

Mineral Processing Beneficiation Operations and Process Optimization through Modeling

This page intentionally left blank

Mineral Processing Beneficiation Operations and Process Optimization through Modeling

Edited by

Sripriya Rajendran Tata Steel Europe, Ijmuiden, The Netherlands

Ch. V.G.K. Murty Natural Resource Division, Adani Group, Ahmedabad, Gujarat, India

Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, Netherlands The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States Copyright © 2023 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. ISBN: 978-0-12-823149-4 For Information on all Elsevier publications visit our website at https://www.elsevier.com/books-and-journals

Publisher: Matthew Deans Acquisitions Editor: Dennis McGonagle Editorial Project Manager: Dan Egan Production Project Manager: Surya Narayanan Jayachandran Cover Designer: Miles Hitchen Typeset by MPS Limited, Chennai, India

Dedication Dedicated to my parents, my in-laws, my husband (R. Rajendran), and my son (R. Aniruddh) for helping me become what I am today
Dr. Sripriya Rajendran Dedicated to my wife, C. Anuradha Devi, my son, Krishna Chaitanya, and my daughter, C. Valli Niharika. I could not have contributed in writing this book without their cooperation.
Dr. Ch. V.G.K. Murty

This page intentionally left blank

Contents List of contributors Foreword Preface Acknowledgment

1.

Coal beneficiation: theory and practice

xvii xix xxi xxiii 1

I.N. Bagchi 1.1 Introduction 1.2 Geology and occurrence of coal 1.3 Formation of coal 1.3.1 Depositional environments 1.3.2 Time 1.3.3 Temperature 1.4 Coal rank 1.4.1 Lignite 1.4.2 Subbituminous 1.4.3 Bituminous 1.4.4 Anthracite 1.5 Coal beds 1.6 Coking and noncoking coal 1.7 Metallurgical coal blends 1.8 Coal mining and the environment 1.8.1 Mining methods 1.9 Modes of coal transport 1.9.1 Trucks 1.9.2 Trains 1.9.3 Bulk carrier 1.9.4 Storage 1.10 General testing procedure for coal pertaining to beneficiation 1.10.1 Typical results from laboratory testing of different coals 1.11 Coal beneficiation 1.11.1 Coal sizing 1.11.2 Blending of coal 1.11.3 Coal Preparation 1.12 Generic description of coal preparation plant

1 1 1 2 2 2 2 3 3 3 3 3 4 5 6 6 8 8 9 9 9 9 10 14 19 20 20 30

vii

viii

2.

Contents

32 32 32

1.13 Broad input and output design parameters in coal washery 1.13.1 Raw coal section 1.13.2 Washing section 1.13.3 Loading section of clean coal, middlings and rejects 1.14 Brief system description of high/medium coking coal washery 1.14.1 Raw coal section 1.14.2 Washing section 1.14.3 Post washing section 1.14.4 Utilities 1.15 Environment management 1.15.1 Dust pollution 1.15.2 Rain water treatment 1.15.3 Slurry/effluent water treatment 1.15.4 Noise pollution 1.16 Quality monitoring and control 1.17 Instrumentation and control systems 1.17.1 Monitoring and control system for dense medium cyclones 1.17.2 Instrumentation and control in fine coal flotation circuit 1.18 Guideline to plant availability, material and power consumption in a coal beneficiation plant 1.19 Operational problems and mitigating measures in a coal washing plant 1.19.1 Dense medium cyclone separation 1.19.2 Froth flotation 1.19.3 Spirals 1.19.4 Thickeners 1.19.5 Trouble shooting guide 1.19.6 Horizontal belt filters 1.19.7 Wet drum magnetic separator 1.19.8 Troubleshooting 1.20 Conclusions References

41 42 44 45 46 48 49 49 51 52 53

Iron ore beneficiation: an overview

55

32 32 32 34 35 36 36 36 36 36 37 37 38 39 39 40

N.D. Rao, D.P. Chakraborty, Vishal Shukla and Neeraj Kumar 2.1 Introduction 2.2 Geology and occurrence 2.2.1 Indian iron ore resources 2.2.2 General geology 2.3 Mining methods 2.4 Beneficiation methods 2.4.1 Selection of beneficiation flowsheet

55 56 56 56 58 60 60

Contents

2.5 Operating practices 2.5.1 Processing of high-grade ore 2.5.2 Processing of low-grade ore 2.5.3 Processing flowsheet of beneficiation plant of Tata Steel Minerals Canada 2.5.4 Processing flowsheet of beneficiation plant of Tata Steel Long Products Ltd 2.5.5 Processing route followed across other beneficiation plants 2.6 Summary References

3.

Chromite ore beneficiation: prospects and challenges

ix 70 70 73 73 74 75 76 77

79

C. Raghu Kumar, Y. Rama Murthy and Sharath Kumar Bhoja 3.1 Introduction 3.2 Ore genesis 3.2.1 Occurrence 3.2.2 Reserves of chromite deposits 3.3 Mining 3.3.1 Underground mining methods 3.4 Characterization 3.4.1 Physical properties 3.5 Beneficiation 3.5.1 Kemi chromium concentrator (Finland) flowsheet 3.5.2 Turkish chromite concentrator flowsheet 3.5.3 Chrome ore beneficiation plant, Sukinda, India 3.5.4 Challenges in chrome ore gravity concentrator 3.6 Research & development 3.6.1 Reduction of tailing losses 3.6.2 Beneficiation of low and subgrade chromite ore 3.6.3 Reprocessing of stockpiled tailings 3.6.4 Processing/recovery of ultrafine size particles: world 3.7 Effluent treatment processes 3.7.1 Chromium existence 3.7.2 Chromium chemistry in water treatment and distribution 3.7.3 Formation of hexavalent chromium 3.7.4 Effluent treatment methods 3.7.5 Adsorption 3.8 Cost structure for the chromite ore beneficiation plant 3.8.1 Processing cost 3.8.2 Capital cost 3.8.3 Operating cost 3.8.4 Mineral value per ton (or concentrate selling cost) References Further reading

79 80 81 83 84 84 87 88 88 90 90 92 92 94 94 94 95 95 96 97 98 98 99 100 108 108 108 108 110 111 112

x

4.

Contents

Beneficiation of bauxite ores

117

Pradip Kumar Banerjee, Amol Udaram Mankar and Vivek Kumar Introduction Refining of bauxite ore for alumina production Bauxite ore resources Bauxite mining practices 4.4.1 Manually operated mines 4.4.2 Semimechanized mines 4.4.3 Mechanized mines 4.5 Geology of bauxite deposits 4.6 Characterization of bauxite ores 4.6.1 Gibbsite-boehmite mix ore (central Indian deposits) 4.6.2 Low-grade bauxite ores (East Coast deposits in India) 4.7 Beneficiation of bauxite ores 4.7.1 Gibbsite
Boehmite mix type ore (Central Indian deposits) 4.7.2 Low-grade bauxite ores 4.8 Pilot trials for developing beneficiation flowsheet 4.9 Impact of different bauxites on the Bayer process 4.10 Major alumina refinery plants in India and abroad 4.11 Bayer process technology 4.12 Capital investments, Operating cost, and techno-economical viability for green-field refinery 4.13 Sustainability challenges 4.13.1 Bauxite residue management 4.13.2 Effluent management 4.14 Concluding remarks Acknowledgments References

117 119 120 122 122 123 123 124 125 126 132 136

Beneficiation of mineral sands: a practical outlook

167

4.1 4.2 4.3 4.4

5.

136 146 150 153 154 156 159 160 160 162 164 165 165

Ch. V.G.K. Murty, Jaisankar Natarajan and Jagadeswara Rao N. 5.1 Introduction 5.2 Geology 5.2.1 What are mineral sands? 5.2.2 Formation of mineral sands 5.2.3 Composition of Mineral sands 5.2.4 Texture and transport of Mineral sands 5.3 Mining 5.3.1 Mining technologies 5.3.2 Mine planning 5.3.3 Mining activities 5.4 Processing 5.4.1 Mineral sands concentration 5.4.2 Mineral separation equipment used in heavy mineral sands industry

167 169 169 169 170 170 173 173 180 181 182 182 182

Contents

5.5 Processing of heavy mineral ore 5.5.1 Pre concentration plant 5.5.2 Mineral Separation Plant (MSP) 5.6 Factors influencing mineral sand processing 5.7 Tailing’s disposal 5.8 Metallurgical accounting system 5.8.1 Measurement system 5.9 Data collection, validation, and management 5.10 Reconciliation, balancing and reporting 5.11 Metal accounting system 5.11.1 Procedure 5.12 Record keeping 5.13 Methodology to develop a mineral sands project 5.14 Economic uses 5.14.1 Ilmenite and Rutile 5.14.2 Zircon 5.14.3 Sillimanite 5.14.4 Garnet 5.14.5 Monazite 5.14.6 Cost considerations 5.15 Resource characteristics 5.15.1 Grade 5.15.2 Proportion of slimes 5.15.3 Overburden 5.15.4 Mineral assemblage 5.16 Availability and cost of utilities 5.16.1 Power tariff 5.16.2 Water 5.16.3 Fuel 5.16.4 Location, which affects infrastructure and transport costs 5.17 Conclusion Acknowledgements Further reading

6.

Addressing an inverse problem of classifier size distributions

xi 199 200 204 207 207 209 209 209 210 210 210 212 212 213 213 213 213 214 214 214 216 216 216 216 216 217 217 217 217 217 218 219 219

221

B. Venkoba Rao 6.1 Introduction 6.1.1 Evaluation of size classifier performance 6.2 Analytical solution to the Classifier product size distributions 6.2.1 Classifier analytical expressions for Plitt’s efficiency curve 6.2.2 Classifier analytical expressions for the logistic efficiency curve

221 223 225 226 227

xii

7.

Contents

229 233

6.3 Validation of the proposed analytical expressions 6.3.1 Estimation of solid flow split to coarse product 6.4 Pivot phenomenon and difference similarity of the classifier distributions 6.5 Classifier inverse problem 6.6 Parameter sensitivity analysis 6.6.1 Case 1: Plitt efficiency curve approach 6.6.2 Case 2: Logistic efficiency curve approach 6.7 Conclusions Acknowledgments References

234 239 244 246 247 249 249 249

Numerical methods in mineral processing: an overview

251

Sripriya Rajendran, Teja Reddy Vakamalla and Narasimha Mangadoddy

8.

7.1 Introduction 7.2 Discrete Element Modeling (DEM) 7.2.1 Milling/grinding 7.2.2 Screw conveyor/mixer 7.2.3 Jigs 7.3 Population Balance Modeling (PBM) 7.3.1 Milling/grinding 7.4 Computational Fluid Dynamics (CFD) modeling 7.4.1 Hydrocyclones 7.4.2 Dense medium cyclones 7.5 Conclusions References

251 252 253 255 257 260 261 263 264 274 277 278

Computational fluid dynamic modeling of hydrocyclones

287

Teja Reddy Vakamalla, Sripriya Rajendran, Mandakini Padhi and Narasimha Mangadoddy 8.1 Introduction 8.2 Computational methodology 8.2.1 Turbulence modeling 8.2.2 Multiphase modeling 8.2.3 Rheology modeling 8.2.4 Details of simulation 8.3 Two-phase flow predictions 8.3.1 75 mm hydrocyclone 8.3.2 75 mm laboratory hydrocyclone 8.4 Multiphase flow predictions 8.4.1 Conventional hydrocyclone: homogeneous feed 8.4.2 Laboratory hydrocyclone: homogeneous feed 8.4.3 Laboratory hydrocyclone—heterogeneous feed

287 290 290 292 295 296 298 298 299 306 306 306 313

Contents

9.

xiii

8.4.4 Analysis of the effect of turbulence on particles 8.5 Conclusions Acknowledgements Abbreviations References

316 320 321 321 321

Numerical modeling of dense medium cyclones

325

Teja Reddy Vakamalla and Narasimha Mangadoddy 9.1 Introduction 9.2 Computational fluid dynamics approach for dense medium cyclone modeling 9.2.1 Governing equations 9.2.2 Turbulence modeling 9.2.3 Multiphase modeling 9.3 Rheology modeling 9.3.1 Granular Viscosity (MASM 1 GV) model 9.3.2 Newtonian viscosity model with total feed solids correction (MASM 1 Nfs) 9.3.3 Newtonian model with total solids and fines correction (MASM 1 Nfsfc) 9.3.4 Non-Newtonian Herschel
Bulkley (MASM 1 HB) model 9.4 Numerical modeling 9.5 Results and discussion 9.5.1 Mean flow field analysis and grid independence study 9.5.2 Magnetite medium segregation prediction and validation 9.5.3 Medium segregation predictions by standard Algebraic Slip Mixture and Modified Algebraic Slip Mixture models 9.5.4 Prediction of viscosity levels by different rheology based CFD models 9.5.5 Simulating coal particle dynamics using Discrete Particle model 9.5.6 Simulating coal particle dynamics using Algebraic Slip Mixture model 9.6 Using computational fluid dynamics to improve dense medium cyclone performance 9.6.1 Sources of inefficiencies in conventional dense medium cyclones 9.6.2 Scope to improve the performance of different dense medium cyclone designs 9.6.3 Prediction of the performance of novel dense medium cyclone designs using CFD 9.7 Conclusions Acknowledgments

325 326 326 327 329 332 332 333 333 334 334 335 335 336

340 343 344 349 352 352 353 354 360 360

xiv

Contents

Abbreviations References

10. Froth flotation and its modeling aspects

361 361

365

B. Venkoba Rao 10.1 Introduction 10.2 A brief description of flotation reagents 10.3 Concepts of grade and recovery 10.3.1 Effect of head grade on mineral upgradation 10.4 Smelter contract and economic sustenance 10.5 Flotation kinetics 10.5.1 First-order kinetics 10.5.2 Modified first-order kinetics 10.5.3 Higher-order flotation kinetics 10.5.4 Kinetic models with distributed rate constants 10.6 Some standard flotation testing procedures 10.6.1 Release analysis 10.6.2 Advanced flotation washability 10.6.3 Flotation tree analysis 10.6.4 Locked cycle test 10.7 Data reconciliation 10.8 Residence time distribution 10.8.1 Dimensionless residence time distribution 10.8.2 Plug flow 10.8.3 Perfect mixing 10.8.4 Perfectly mixed flotation cells in series 10.8.5 Large and Small Tanks in Series (LSTS) model 10.8.6 Hydrodynamics of scaled up cells 10.8.7 Particle size effects on residence time distribution 10.8.8 Reflection of process issues through residence time distribution measurements 10.8.9 Residence time distribution of column flotation cell 10.8.10 Kinetics of flotation in a continuously operated flotation cell 10.9 Entrainment 10.10 Industrial mechanical cells 10.10.1 Power input parameters 10.10.2 Gas dispersion parameters 10.10.3 Selection tips for mechanical flotation cells 10.10.4 κ
Sb relationship 10.10.5 Pulp-froth multiphase model 10.10.6 Neethling and Cilliers model on grade-recovery curve 10.11 Effect of mechanism profile on the mineral upgradation

365 369 370 373 377 382 382 383 388 388 390 390 392 394 397 399 400 403 403 404 405 408 410 410 411 412 412 413 413 414 415 417 417 419 420 421

Contents

10.12 Brief description on flotation circuit process modeling 10.12.1 Steady-state process model 10.12.2 Transient-state process model 10.12.3 Dynamic process model 10.13 Final remarks Acknowledgments References

11. Mathematical modeling of mineral jigs

xv 422 422 426 432 432 433 433

437

B. Venkoba Rao 11.1 11.2 11.3 11.4 11.5 11.6

11.7 11.8 11.9 11.10 11.11 11.12 11.13 11.14

11.15

Introduction Test work and grade-yield-recovery curves Effect of head grade on the jig performance Timed batch jig tests and attainment of dynamic equilibrium of particles in the jig bed Jig Stratification Index Jig bed kinetics and bed assay evolution 11.6.1 Particle segregation in a continuous Baum jig operation Kinetics of particle size segregation in a batch jig Jig types Jig wave forms King’s stratification model Application of King’s stratification model to the continuous performance of an industrial jig Simulation studies of King’s stratification model for batch jig operation Simulation studies of King’s stratification model for continuous jig operation Partition surface 11.14.1 Mathematical representation of the partition surface 11.14.2 Generation of partition coefficients for the partition surface representation 11.14.3 Partition surface visualization using key parameter indices Size-density bivariate distributions and their characteristics 11.15.1 Difference similarity among bivariate distributions 11.15.2 Sink and float distribution predictions from the feed distribution and partition surface concept 11.15.3 Multistage separations 11.15.4 Circuit sensitivity analyses of two-stage circuits for a fluctuating feed composition and varying operational variables

437 438 440 444 445 447 447 449 450 453 454 460 460 463 466 468 472 473 475 482 484 486

493

xvi

Contents

11.15.5 Data reconciliation of bivariate distributions of a separator using the concept of partition surface 11.16 Extended King’s stratification model 11.16.1 Comparison of the two jig models that define partition surfaces at various slice positions 11.17 Control of industrial Batac jig performance 11.17.1 Feed composition control 11.17.2 Additional operational control aspects related to the feed material 11.17.3 Pulse control 11.17.4 Gate operation control 11.17.5 JigScan 11.17.6 Factors affecting jig operation 11.18 Challenges ahead Acknowledgments References Index

495 501 508 510 511 511 512 512 513 513 515 516 516 519

List of contributors I.N. Bagchi Planning, Design & Engineering, Coal Washery EPC Division, ACB India Limited, Gurugram, Haryana, India Pradip Kumar Banerjee Hindalco Industries Ltd, Mumbai, Maharashtra, India Sharath Kumar Bhoja Raw material Technology, Process Technology Group, Tata Steel Ltd, Jamshedpur, Jharkhand, India D.P. Chakraborty Iron Making Technology Group, Process Technology Group, Tata Steel, Jamshedpur, Jharkhand, India C. Raghu Kumar Raw material Technology, Process Technology Group, Tata Steel Ltd, Jamshedpur, Jharkhand, India Neeraj Kumar Coal Beneficiation Technology Group, Process Technology Group, Tata Steel, Jamshedpur, Jharkhand, India Vivek Kumar Hindalco Industries Ltd, Lohardaga, Jharkhand, India Narasimha Mangadoddy Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Sangareddy, Telangana, India Amol Udaram Mankar Hindalco Industries Ltd, Belagavi, Karnataka, India Ch. V.G.K. Murty Natural Resource Division, Adani Group, Ahmedabad, Gujarat, India Y. Rama Murthy Ferro Alloys and new minerals research group, Research & Development, Tata Steel Ltd, Jamshedpur, Jharkhand, India Jaisankar Natarajan Kenmare Moma Resources, Maputo, Mozambique Mandakini Padhi Pfizer Healthcare India Pvt Ltd, IIT Madras Research Park, Chennai, Tamil Nadu, India Sripriya Rajendran Tata Steel Europe, Ijmuiden, Noord Holland, The Netherlands B. Venkoba Rao DELKOR, Takraf India Private Limited, Bengaluru, Karnataka, India N.D. Rao Projects, Atha Group, Bhubaneswar, Orissa, India Jagadeswara Rao N. Natural Resource Division, Adani Group, Ahmedabad, Gujarat, India Vishal Shukla Ore Beneficiation Technology Group, Process Technology Group, Tata Steel, Jamshedpur, Jharkhand, India Teja Reddy Vakamalla Department of Chemical Engineering, National Institute of Technology Calicut, Kozhikode, Kerala, India

xvii

This page intentionally left blank

Foreword As I write the foreword for this book, I remember the interactions I have had with the editors over the last few decades in connection with multiple projects on mineral beneficiation. These interactions had enlightened me with a general understanding of various unit operations employed in beneficiation. Over the years, the authors have used their expertise to develop and optimize new processes for mineral beneficiation plants treating iron ore, coal, chromite ore, and other minerals. Textbooks currently available on mineral beneficiation provide information of unit operations and explain the separation aspects of beneficiation process through first principles. However, practicing mineral engineers need to make practical use of this knowledge on the field. A deep understanding of the variability in mineralogical and chemical composition of individual mineral resources is needed. The interaction of different feed types with unit operations will influence both the selection and the sizing of equipment. Practicing engineers should be able to apply this knowledge in designing process flow diagrams for a new deposit, or in modifying a process flow diagram of an existing plant, as the characteristics of the deposit change with mine site, mine face or depth. Modification of existing processes and development of new ones are also needed to conserve natural resources and to meet environment targets. Currently, this knowledge is mostly in tacit form due to absence of books that deal with these attributes in detail. This book provides a practitioner’s view on mineral processing that will help readers gain information and knowledge on practical aspects of mineral beneficiation, and in developing process flowsheets for complex low quality raw materials. The numerical modeling chapters will help gain further insight into understanding the influence of the process variables on equipment efficiency and in developing optimization strategies. Wishing the readers an instructive read! Debashish Bhattacharjee Vice President, Technology and New Materials Business, Tata Steel Limited, Jamshedpur, Jharkhand, India

xix

This page intentionally left blank

Preface New entrants in manufacturing companies face difficulties in understanding the operating and control philosophy of an operating plant. Books available in the market today lack clarity in these concepts and supporting data as they were written for a different purpose. This book is an essence of more than 70 years of combined experience of the authors as a shop floor operator, researcher, and a senior executive, leading various cross functional teams in mineral and metal industries. Various aspects of mineral processing have been dealt with and explained in an easyto-understand manner. Simple numerical calculations necessary for evaluation of different processes have also been incorporated. Numerical models for better understanding of unit operations have been explained. The book will be of great use, not only for beginners but also for operating personnel, design engineers, and researchers. We sincerely hope that the contents of the book are useful and welcome any comments and feedback on the book. Any suggestions for improvement will be appreciated, acknowledged, and implemented in the right spirit. Sripriya Rajendran Ch. V.G.K. Murty

xxi

This page intentionally left blank

Acknowledgment This book wouldn’t have been possible without the encouragement and support of my superiors, Dirk van der Plas and Tim Peeters, Tata Steel Europe. I am also immensely thankful to Elsevier publishers for this opportunity. Special note of thanks to Dr. Hilary Carr, Elsevier publications USA for her wonderful editorial support and guidance. I owe an enormous debt of gratitude to the authors of various chapters who discussed nuances of the text and clarified concepts, explored particular facets of insight work, and explained the rationales for specific recommendations. Thanks to Dr. Debashish Bhattacharjee for having been an unrelenting source of inspiration and for agreeing to write the foreword. My coeditor, Dr. Ch. V.G.K. Murty deserves a special word of appreciation for his vision to write the book. Finally, I want to thank my husband, R. Rajendran, for tolerating my incessant disappearances into my home office. A lifelong partner makes both the journey and destination worthwhile. And many thanks to my son, R. Aniruddh, who, though unaware of the subject, kept tabs on my delivery schedule and motivated me to complete the book on time. Thank you both! Without you, I wouldn’t have accomplished this feat. Support and help from my vast extended family while preparing this book is invaluable. Sripriya Rajendran This book wouldn’t have been possible without the encouragement and support of all my colleagues in my present organization of Natural Resource Division, Adani Group, Mr. Rahul Saraf CMD of M/s. Saraf Agencies and Mr. Pradeep Koneru, MD of M/s. Trimex Sands Private Limited. I am also immensely thankful to Elsevier publishers for this opportunity. Special note of thanks to Dr. Hilary Carr, Elsevier publications USA for her wonderful editorial support and guidance. I also want to thank Mr. Amit Gautam, a colleague of mine in the present organization, for his continuous support. I also want to thank Mr. Deepak Rathod, Mr. N. Jagadeeswara Rao, Mr Jaisankar Natarajan and Mr. R. Narayanan for their immense support and their valuable suggestions. I owe an enormous debt of gratitude to the authors of various chapters, who readily agreed to contribute when I approached them. Their combined xxiii

xxiv

Acknowledgment

knowledge operations and research was very well reflected in their respective chapters. Thanks to Dr. Debashish Bhattacharjee for having been an unrelenting source of inspiration and for agreeing to write the foreword. My coeditor, Dr Sripriya Rajendran deserves a special word of appreciation for her relentless efforts not only to translate a concept into a book but also to motivate me at all times. Finally, I want to thank my wife, C. Anuradha Devi, for her continuous support and motivation. I also want to thank my son, Krishna Chaitanya, who supported me with continuous encouragement. I want to thank my daughter, C. Valli Niharika for her inspirational words throughout the preparation of the book. Without you all, I wouldn’t have accomplished this herculean task. Support and help from my vast extended family while preparing this book is invaluable. Ch. V.G.K. Murty

Chapter 1

Coal beneficiation: theory and practice I.N. Bagchi Planning, Design & Engineering, Coal Washery EPC Division, ACB India Limited, Gurugram, Haryana, India

1.1

Introduction

Coal washing technologies vary widely due to wide variations in the properties and uses of coal. When selecting the process equipment for a particular washing technology, many operational factors play a vital role, which, if ignored, can lead to chronic operational problems. Some documented guidelines to provide conceptual plant operation strategies for different circuit configurations are needed to bridge the gap between fresh mineral graduate engineers entering the beneficiation industry and manufacturing, sales, R&D, operation, and maintenance. The chapter discusses the most prevalent and widely used modern circuits in coal washing.

1.2

Geology and occurrence of coal

Coal formation occurred as far back as 350 million years ago and as recently as 2 million years ago. Coal is a heterogeneous mixture of organically derived plant remains, which have undergone chemical and physical changes in response to biologic and geologic processes. The right conditions must exist for plant materials to undergo these physical and chemical changes.

1.3

Formation of coal

Coal is a sedimentary deposit comprising the remnants of decayed plants, in contrast to minerals, which are building blocks of rocks. The plant remains that contribute to coal deposits depend on the type of plants that existed at the inception of coal formation. The depositional environment determines the chemical, physical, and biological changes to the accumulated plant remains over time. Like minerals found in rocks, the preserved plant remains Mineral Processing. DOI: https://doi.org/10.1016/B978-0-12-823149-4.00007-7 © 2023 Elsevier Inc. All rights reserved.

1

2

Mineral Processing

are metamorphosed over millions of years by pressure and temperature into various kinds of coal. For coal to be preserved in the geologic record into a merchantable and mineable commodity, the seam thickness requires a depositional environment where plant debris can accumulate faster than it decays.

1.3.1

Depositional environments

A thick, mineable accumulation of coal requires a depositional environment or geographic setting with rapid plant growth. Plant material and debris are preserved by accumulating faster than they decay. Tropical rainforests or swamps on the low-lying ground in deltas, alluvial plains, and coastal areas are all examples of depositional environments. The precursor to coal is peat. Peat is a soft, organic material consisting of partly decayed plant and mineral matter. When peat is placed under high pressure and heat, it undergoes physical and chemical changes (coalification) to become coal.

1.3.2

Time

Accumulations of plant material that have become coal are found in sedimentary rock layers worldwide that are ,350 million years old. Coals are classified basis on rank, type, and grade. Older deposits are more likely to be higher in rank as their biologically digested plant remains were buried deeper, exposing them to higher temperatures and pressures, which advance the coalification process. Rank refers to the degree of alteration or metamorphism of the plant remains. Type, refers to the variety of plant remains preserved, known as macerals, and grade refers to the minerals associated with or accompanying the plant remains during the inception of coal formation.

1.3.3

Temperature

As the peat becomes more deeply buried, it becomes heated due to the geothermal gradient. Geothermal gradient is the rate of temperature increase with increasing depth from the earth’s surface. In tectonically stable sedimentary rock areas, the geothermal gradient starts at B400 ft deep and is B1  F for every 100 feet depth.

1.4

Coal rank

Coal rank (Abbott, 1982) describes the amount of metamorphosis the coal has undergone and is used by industries to classify coals for certain uses. The coal rank properties include carbon content, volatile matter content, moisture, and heating value.

Coal beneficiation: theory and practice Chapter | 1

1.4.1

3

Lignite

Commonly referred to as brown coal, lignite is soft and brownish-black in color. Lignite represents the largest portion of the world’s coal reserves. This geologically young coal has the lowest carbon content of all coal ranks, offering a low heat value of 4000
8300 Btu/lb on a moist, mineral matter free (mmmf) basis. Lignite is used mainly for electric power generation.

1.4.2

Subbituminous

This dull black coal gives off more heat than lignite (8300
11,500 Btu/lb) and is cleaner burning than other coal due to its lower sulfur content. With a highly variable sulfur content and usually a high heat content ( . 10,500
14,000 Btu/lb), it is used for power generation, coke making, and other industrial uses.

1.4.3

Bituminous

Bituminous coal is a sedimentary deposit comprised of the remnants of decayed plants, in contrast to minerals which are the building blocks for rocks.

1.4.4

Anthracite

Anthracite coal has the highest ranking, and after undergoing significant metamorphosis, it contains the highest fixed carbon content. Anthracite coal is a tiny component of coal production nationwide, used mostly for home heating. Anthracite coal contains heat values of 12,500 1 Btu/lb. It is a misconception that anthracite coals contain the highest heat value due to their rank. The highest rank bituminous coals contain the highest heat values.

1.5

Coal beds

A coal bed is simply a stratum layer of coal peat. This, along with fluctuating sea levels allows sand, silt, and clay to be deposited on top of the peat. This sediment accumulates causing pressure that, along with the heat generated by depth of burial, results in chemical and compositional changes, turning peat into lignite. Additional pressure turns lignite into bituminous coal, and then into anthracite coal, a process called coalification. Beds vary from a few inches to 100 ft’ or more. The rock layers on top of a coal bed are called “overburden.” The rock layers between coal beds are called “interburden.” The rock layers below a coal bed are called “floor rock.” Coal is comprised of three major maceral groups—vitrinite, inertinite, and liptinite—which proceeded along distinctly different metamorphic paths. Vitrinite is the predominant maceral constituent in nearly all coals, originating from the woody tissue of plants. It is the most abundant of the

4

Mineral Processing

macerals and matures the most uniformly throughout the coalification process. Its reflectance in plain polarized light is often used as the ultimate indicator of rank. In terms of coking properties, vitrinite is the predominant reactive binder forming the wall and pore structure of coke and acting as the cement necessary to assimilate and bond the aggregate, which originates with the inertinite group. Inertinite comprises various plant remains, which had achieved a high rank early in the coalification process such as fusinite and semifusinite, which originated from woody tissue exposed to fire and converted to charcoal, or macrinite, which is believed to be the product of accelerated decay of various plant tissues during the inception of coal formation. Most inertinite, as the name implies is inert. Liptinite comprises spores, resins, and cuticles of the preserved plant remains and is also very reactive. In terms of coking properties, members of the liptinite group have much lower coke yields than their associated vitrinite and contribute more heavily to the by-products during coke making (i.e., gas, tars, and light oils). Liptinite matures much more slowly than its associated vitrinite in the early stages of coalification, up through high volatile bituminous in rank, and then very quickly in the medium volatile rank range where it becomes optically indistinguishable from vitrinite. Mineral matter, which comprises the ash and sulfur found in the coal, can be quite variable depending on its origin, and its concentration level can impact the utilization potential. The inherent ash-forming minerals that contribute to a plant’s nutrients represent the more fundamental components in the ash, while its inherent sulfur is of the organic variety. Ash-forming minerals added later as impurities during or after the biochemical stage can be basic or acidic depending on their origin. Pyritic sulfur can also be of primary or secondary origin from bacterial action or precipitation from sulfurbearing waters.

1.6

Coking and noncoking coal

The unqualified term “coke” usually refers to the product derived from lowash and low-sulfur bituminous coal by coking. A similar product called petroleum coke, or pet coke, is obtained from crude oil in oil refineries. Coke may also be formed naturally by geologic processes Noncaking coal on heating without air does not form a coherent residual mass. Coking coal on heating without air leaves a solid residue. Noncoking coal also leaves a solid coherent residue, which may not possess the physical and chemical properties of the coke. Metallurgical coal (coking coal) is used to produce hot metal used for steelmaking, whereas thermal coal is used to make steam that generates electricity. Other terms used to describe metallurgical coals are hard coking, semisoft, and Pulverized Coal Injection (PCI). Coking coal, by definition,

Coal beneficiation: theory and practice Chapter | 1

5

must be hard, and the term hard coking coal (HCC) is a general term used to describe coking coals with superior coking properties relative to their semisoft counterparts. Hard coking coal (HCC) represents the premium band of coking coals used solely for steel production through the blast furnace process. These coals range from high volatile through low volatile bituminous in rank and can soften and re-solidify into a coherent, porous mass when heated from 300 C to 550 C in the absence of air in a confined space. The conversion from coal to coke occurs in long, tall, slender chambers called coke ovens where the volatiles from the coals escape, leaving behind metallurgical coke, which reaches a temperature of approximately 1000 C before being removed from the ovens. The coking cycle normally takes 18 h in an oven width of 18", or 1"/h. Coke is used primarily as a fuel and a reducing agent in a blast furnace during the smelting of iron ore into iron before it is converted into steel. Coking properties are rank dependent and the term semisoft normally applies to lower rank high volatile coals. PCI coal is injected directly through tuyeres in the blast furnaces and is used as a substitute for the coking coal. Metallurgical coal, and the resulting coke, must have low ash and sulfur content for it to be used in the steelmaking process. The amount of volatile matter in metallurgical coal impacts coke yield - the amount of coke and byproducts produced per ton of coal charged. Increased moisture has a comparable impact on coke yield and can also impact bulk density in the ovens and the under firing requirements in terms of heating value, btu/lb of coal carbonized. Metallurgical coal is usually classified as high, medium, and low volatile based on its dry, mineral matter, free volatile matter (dmmf VM). High volatile coals are typically between 31% and 38%, medium volatiles are between 22% and 31%, and low volatiles are between 17% and 22%. There is usually a strong inverse relation between vitrinite reflectance and dry ash free volatile content.

1.7

Metallurgical coal blends

Metallurgical coal blends are generally formulated from various different ranks, types, and grades of coals sourced from different geographic regions with the purpose of producing the highest quality coke at the lowest possible cost while protecting the ovens in which those blends will be carbonized. Coal blends must perform optimally in the confined space of the ovens in which they are carbonized while at the same time ensuring oven safety. The coking pressure of the coal blend being carbonized must be kept within strict limits based on the age and height of the ovens to avoid undue pressure on the walls, which can lead to their premature failure. The coal blend which initially expands during its conversion to coke must also contract sufficiently away from the oven walls to allow easy discharge from the oven.

6

Mineral Processing

Other process variables in the coking process that must be controlled include coal blend moisture, pulverization, charge bulk density, and coking rate. The coal charge bulk density, measured in pounds per cubic foot, must be controlled to maximize oven productivity and coke stability while maintaining safe coking pressure and blend contraction. Increased coal pulverization increases coke strength and blend homogeneity, however, too finely ground coal is more difficult to handle and often leads to lower oven bulk densities and more problems with emissions and carryover in the by-product collection system during oven charging. The coking or heating rate of the coal charge, as measured in inches per hour, impacts coke strength, coke pressure, blend contraction, carbon formation, and oven productivity. The heat of carbonization and coking times, which are more coal-blend related, are also impacted by changes in operating practice.

1.8

Coal mining and the environment

The environment’s health is always analyzed before mining through baseline monitoring and analysis. Then, based upon proven engineering principles, data, and experience, engineers can prepare mine plans that eliminate or minimize the impacts of mining. Mine planning must mitigate those impacts. Before any mining begins, the post-mine land use must be addressed so that the operator restores the land to a condition capable of supporting the uses it could support before mining, to higher or better uses. The quality and quantity of surface water and groundwater can be protected both within a mine and surrounding areas if modern mining techniques and procedures are followed. Unfortunately, many sites were abandoned with inadequate reclamation measures in the past, leaving a legacy of contaminated drainage and water pollution. However, today’s mitigation technologies offer solutions to past problems caused by out-of-date mining practices.

1.8.1

Mining methods

1.8.1.1 Open cast mine Open cast mining refers to mining at the surface rather than underground. The mineral deposit is covered by soil, which is removed and stored for use after mining by large machines, and then explosives break up the overburden and ore deposit. Overburden is the layers of soil and rock that cover a coal seam. Globally, about 50% of coal production involves surface mining. 1.8.1.2 Shaft mine The ground surface is the top of a vertical excavation, referred to as a shaft, hence the term “shaft mining.” Shaft mining uses a vertical mine shaft, a tunnel where miners travel up and down in an elevator. Mine ventilation is also

Coal beneficiation: theory and practice Chapter | 1

7

provided through the shafts. Tunnels are dug out from the mine shaft into the mine seam. Once the coal is mined, it is transported to the surface through a second vertical shaft.

1.8.1.3 Slope mine Slope mines are another kind of underground mines. Slope mining uses shafts that are slanted down to the coal or mineral bed, in lieu of drilling shafts straight down. G G G

Slope mines are usually not as deep as shaft mines. Conveyors bring the coal out of the mine using the slope tunnel. Sometimes there are three slopes—one takes workers in and out of the mine and provides an intake for fresh air, the second takes coal out on a belt and the third provides an exhaust for returned or used air.

1.8.1.4 Drift mine Drift mining is used when the coal or mineral is accessed from the side of a mountain. The opening to the mine is dug from a bench to the coal or mineral vein. G

G

Drift mines have horizontal entries, called adits, in the coal deposit from a hillside. Conveyance/transportation equipment often contains conveyor belts, rubber-tired equipment, or track equipment.

1.8.1.5 Long wall mining This highly productive underground coal mining technique occurs when a long wall, about 250
400 m long of coal, is mined in a single slice, typically 1
2 m thick. Long wall mining machines consist of multiple coal shearers mounted on a series of self-advancing hydraulic ceiling supports. Long wall miners extract “panels,” or rectangular blocks of coal as wide as the mining machinery and as long as 12,000 ft. 1.8.1.6 Short wall mining Similar to the longwall method, except that the blocks of coal are no longer than 100 m wide and removed by a continuous miner. The roof support also operates similarly to long wall shields, allowing it to collapse once the miner has advanced. It currently accounts for ,1% of deep coal production. Coal panels are 150
200 ft wide and .0.5 miles long. 1.8.1.7 Room and pillar mining The most common type of underground coal mining involves excavating a room or chamber while leaving behind pillars of coal to support the roof.

8

Mineral Processing

Coal seams are mined using a continuous miner, a machine that extracts the coal without interrupting the loading process. Excavation is carried out in a pattern advancing away from the entrance of a mine. Once a deposit has been exhausted, pillars may be removed or pulled in a pattern opposite from which the mine advanced, known as retreat mining.

1.8.1.8 Mountaintop mining This is used where multiple coal seams allow for coal extraction across the entire area rather than around edges as in contour mining. Large-scale equipment is used to move overburden from above coal seams and extract coal. 1.8.1.9 Contour mining Contour mining follows the contours of one or more coal seams around a hillside where these are exposed. Overburden is excavated and the coal is removed, creating a working bench referred to as a “contour bench.” When mining is finished, the contour bench is filled in. 1.8.1.10 Highwall mining Holes or entries are excavated up to 1000 ft into a coal seam. A special highwall mining machine advance into the coal seam. Its cutting head removes the coal and moves it to conveyor cars attached to the machine. 1.8.1.11 Auger mining Working on a contour mining bench, or in an open mine pit, horizontal holes are drilled up to a distance of 300 ft into a coal seam. The coal is removed by a special auger through a screw-like action. 1.8.1.12 Open-pit mining Appropriate only where the terrain is flat or only slightly rolling and where coal seams are very thick. An open pit is excavated with terraces or benches that expose the coal seam for extraction.

1.9 1.9.1

Modes of coal transport Trucks

For shorter hauling distances, smaller quantities, and access to certain loading points, trucks meet the need. They are used mainly in short hauls to nearby electric and industrial plants. Multimodal deliveries can include trucks, railcars, and barges. Trucks are often the quickest and easiest way to move product and are able to be scaled up or down as needs change. Highway trucks haul coal in loads typically under 25 tons.

Coal beneficiation: theory and practice Chapter | 1

1.9.2

9

Trains

Rail is an effective way to move large quantities of coal over long distances. Nearly three-fourths of the coal produced annually in the India moves by rail. A typical coal train travels over 800 miles from a mine to a plant or terminal, carrying about 4800 tons of coal in 600 cars. Railroads carry more coal than any other commodity. Coal is about 40% of the annual volume hauled by rail in the India.

1.9.3

Bulk carrier

Single deck ship designed to carry homogeneous dry cargoes, such as coal, ores, grains, etc.

1.9.4

Storage

Coal is often stored at a plant, river port, or import/export terminal. Without some type of storage, the logistics of supplying coal would be far more difficult and costly. This also allows the blending of different coal products to better meet customer needs while optimizing the value received by the mine operators. Coal storage must be managed and controlled using proven practices, since some coals, especially lower rank coals, have a natural tendency to heat through spontaneous combustion

1.10 General testing procedure for coal pertaining to beneficiation The coal samples require analysis at the laboratory. The coal samples are subjected to some or all of the following tests depending upon its end use: 1. Screening of coal sample (as received in laboratory) at 200, 100, 50, 25, 13, 6, 3, and 0.5 mm screen aperture and determination of ash% and moisture% of each screened fraction. Typical test results are shown in Table 1.1 2. Proximate analysis of as-received coal sample under equilibrated condition, that is, 60% Relative Humidity (RH) and 40 C including Gross Calorific Value (GCV) & Hardgrove Grindability Index (HGI). 3. Crushing of as received coal sample down to 50 mm size and screening at 25, 13, 6, 3, and 0.5 mm screen apertures and determination of ash% and moisture% of each screened fraction. 4. Float and sink test of 50
25, 25
13, 13
6, 6
3, and 3
0.5 mm size fractions of crushed coal and determination of wt.% and ash% at each specific gravity (from 1.4 to 1.9 at an interval of 0.1).

10

Mineral Processing

TABLE 1.1 Grade-wise calorific value of a typical Indian coal. Grade

Calorific value range (in kcal/kg)

A

Exceeding 6200

B

5600
6200

C

4940
5600

D

4200
4940

E

3360
4200

F

2400
3360

G

1300
2400

5. Crushing of 50
13 mm coal to (2) 13 mm and screening at 6, 3, and 0.5 mm screen apertures and determination of ash% of each screened fraction. 6. Float and sink test of 13
6, 6
3, and 3
0.5 mm size fractions of 50
13 mm crushed down to 13 mm and determination of wt.% and ash % at each specific gravity (from 1.4 to 1.9 at an interval of 0.1). 7. Wet sieving of 20.5 mm size fraction at 72# (mesh), 100# (mesh), 200# (mesh), and 300# (mesh) obtained at (4) and (6) and determination of wt.% and ash% of each size fraction. 8. Proximate analysis of crushed Raw coal. 9. Petrographic analysis of Raw coal. 10. Determination of Low Temperature Gray King Coke Type (LTGK), Swelling Index, HGI and GCV of raw coal. 11. Flotation test of entire 20.5 mm coal. 12. Filtration test. 13. Sedimentation test.

1.10.1 Typical results from laboratory testing of different coals This section discusses the results from lab testing of different coal samples. Representative Run-Of-Mine (ROM) coal samples are drawn after coning and quartering and are subjected to screen analysis at various aperture screens. Weight%, ash%, and moisture% are determined for respective size fractions. The test results for a medium volatile subbituminous/bituminous coal are given in Table 1.2. Sometimes the coal is crushed to 250 mm and screened at 25, 13, 6, 3, and 0.5 mm screen apertures. Weight%, ash%, and moisture% are determined for respective size fractions. Typical test results for a low-rank bituminous coking coal are given in Table 1.3. The results of the proximate, ultimate analysis, ash fusion temperature, other coking

Coal beneficiation: theory and practice Chapter | 1

11

TABLE 1.2 Screen-cum-ash & moisture analysis of a ROM medium volatile bituminous/subbituminous coal. Size (mm)

Wt.%

Ash%

Moisture%

200
100

25.6

32.5

1.2

100
50

20.6

30.4

1

50
25

17.2

27.9

1.2

25
13

15.2

22.8

1.3

13
6

6.9

22.1

1.3

6
3

6.1

21.5

1.3

3
0.5

3.8

20.6

1.3

2 0.5

4.6

19.8

1.4

Total

100

27.4

1.2

TABLE 1.3 Screen-cum-Ash and moisture analysis of Run of Mine low rank bituminous coking coal crushed to (2) 50 mm. Size (mm)

Wt.%

Ash%

Moisture%

50
25

40.4

30.1

1

25
13

23.2

27.7

1.1

13
6

11.1

26.2

1.2

6
3

7.3

25.3

1.1

3
0.5

9.8

23.3

1.3

2 0.5

8.2

21.7

1.2

Total

100

27.4

1.2

parameters and petrographic analysis of raw coal are given in Tables 1.4
1.8. The tables show the values for different kinds of coals. Sometimes, the (2) 0.5 mm size fraction of coal is subjected to wet sieving at 72#, 100#, 200#, and 300# mesh. Weight% & ash% are determined for respective size fractions. Typical results for a medium volatile prime coking coal are given in Table 1.9. Froth flotation test results carried out for (2) 0.5 mm fraction of medium coking coal at 10% & 15% concentration with conditioning time of 2 min are given in the Table 1.10. Results of float and sink test of different size fractions of medium coking ROM coal in the 50
0.5 mm are given in Table 1.11. Sedimentation test results with and

12

Mineral Processing

TABLE 1.4 Proximate analysis of a typical prime coking coal. Sl. no.

Particulars (%)

1

Moisture

1.2

2

Ash

24.4

3

VM

24

4

Fixed carbon

50.4

TABLE 1.5 Ultimate analysis of a typical bituminous noncoking coal. Sl. no.

Particulars (%)

Typical value for illustration

1

Carbon

63.96

2

Hydrogen

3.95

3

Nitrogen

0.89

4

Sulfur

0.62

TABLE 1.6 Ash fusion temperatures of a typical subbituminous noncoking coal. Sl no.

Particulars ( C)

Typical value for illustration

1

Initial deformation temperature

1080

2

Sphere temperature-ST

1148

3

HT: Hemisphere temperature-HT

1174

4

FT: flow temperature

1189

TABLE 1.7 Other coking parameters of bituminous noncoking coal. Values given here for Illustration purpose Sl. no.

Particulars

Raw coal

1

GCV (kcal/kg)

6280

2

HGI

79

3

LTGK

F

4

Swelling Index

2

TABLE 1.8 Petrographic analysis of a typical subbituminous medium volatile noncoking coal. Maceral composition (%)

Maceral composition (%) [visible mineral matter free area basis (%)]

Particulars

Vitrinite

Liptinite

Intertinite

Visible mineral matter

Vitrinite

Liptinite

Intertinite

Raw coal

48

0

39.2

12.8

55

0

45

Random vitrinite reflectance Rr (%)

1.17

14

Mineral Processing

TABLE 1.9 Wet Sieve analysis of 20.5 mm medium volatile prime coking coal. Values given here for illustration purpose Size (mesh)

Wt.%

Ash%

72

52

17

72
100

8.1

19.1

100
200

13.4

26.1

200
300

8.2

28.4

2 300

18.3

32.5

Total

100

22.2

without flocculant for high volatile prime coking coal are shown in Table 1.12. Filtration Test results for (2) 0.5 mm size high volatile coking coal is tabulated in Table 1.13. It is to be noted that the values in the mentioned tables are representative of the type of coal treated and are not specific to any particular coal.

1.11 Coal beneficiation After mining, coal is washed to remove impurities including ash and to increase its heating value. Preparation plants remove rock, sulfur, and other particulates from the run-of-mine coal. These plants also allow mining companies to sort coal based on quality, enhancing their ability to serve customers’ various specifications. Some of the benefits of washing could be: G G G G

Boost the heat content of the coal. Improve power plant capacity. Reduce maintenance costs at the power plant and extend plant life. Reduce potential air pollutants, especially sulfur dioxide.

The coal preparation plant design can be influenced by several factors including coal characteristics, market requirements, local infrastructures, and regional preferences. Accordingly, there is a considerable regional variation among coal producers in their design philosophy. However, two major plant categories can be identified. In applications where a premium product range is required, total washing is normally carried out using several technologies in a relatively complex flowsheet. Where the main product is fuel for a power station, that is, Power Station Fuel (PSF), dry fines are often extracted from the ROM coal by screening, and a relatively simple partial-washing process is applied. The cleaned coal from the washery is then blended with the untreated fines to achieve the required PSF specification.

TABLE 1.10 Froth flotation test results of medium coking coal fines. Sr no

Solid concentration %

RPM

Diesel oil (kg/t)

Pine oil (kg/t)

Mixing time, min.

Conditioning time, min

Collection time, min

1

10

1300

1

0.2

2

2

2

10

1300

2

0.4

2

3

10

1300

3

0.6

4

10

1300

4

5

10

1300

6

Froth

Tailings

Overall

Wt. %

Ash %

Wt. %

Ash %

Ash%

3

33.8

9.9

66.2

30.3

23.4

2

3

38.4

11.9

61.6

32.1

24.3

2

2

3

80.7

14.3

19.3

48.5

20.9

0.8

2

2

3

84.3

16.9

15.7

52.5

22.5

1.2

2

2

3

91.1

17.2

8.9

54.1

20.5

TABLE 1.11 Float and sink test results of medium coking coal. Size fraction, mm Wt.%

50
25

25
13

13
6

3-Jun

3
0.5

50
0.5

44.2

26.1

13.2

7.7

8.8

100

Sp.gr.

Wt. %

Ash %

Wt. %

Ash %

Wt. %

Ash %

Wt. %

Ash %

Wt. %

Ash %

Wt %

Ash %

,1.40

39.5

11.2

47.3

10.9

55.4

11.6

47.6

7.9

61.8

5.8

46.2

10.3

1.40
1.50

23.5

17.7

28.6

18.8

22.3

19.7

30.3

17.1

18.1

16.2

24.7

18.1

1.50
1.60

6.8

27.5

6.8

26.9

6.7

30.7

6.6

26.8

6.4

25.5

6.7

27.5

1.60
1.70

3.7

34.9

2.5

38

2.1

36.5

2.9

32.7

2.3

33.7

3

35.5

1.70
1.80

5.5

41.2

3.2

43.4

2.6

42.4

2

41.3

1.9

37.5

3.9

41.6

1.80
1.90

2.1

45

1.1

46.3

1.3

44.9

2

44.5

1.3

46.3

1.7

45.3

.1.90

18.9

56.5

10.5

58.4

9.6

54.8

8.6

58.8

8.2

58.5

13.7

56.9

Total

100

25.6

100

21.3

100

20.6

100

18.4

100

15

100

22.4

Coal beneficiation: theory and practice Chapter | 1

17

TABLE 1.12 Sedimentation test results with and without flocculant for high volatile prime coking coal fines. Settling rate (m/h) Particulars

Without flocculants

With flocculants

Raw coal fines

0.9

2.5

Flotation tailings

1.3

3.4

TABLE 1.13 Filtration test data for high volatile coking coal. Particulars

Test 1

Test 2

Solid concentration (%)

15

20

Size (mm)

2 0.5

2 0.5

Beaker capacity (liter)

2

2

Area of filter (sq. cm.)

10 3 10

10 3 10

Initial pressure (inch/mm Hg)

11/275

11/275

Final pressure (inch/mm Hg)

19.5/490

20.5/515

Dipping time (min)

2.2

2.2

Drying time (min)

1.6

1.8

Av. cake thickness (cm)

16.4

18.5

Surface moisture of cake (%)

14

18

In the coal preparation plant design, there is a clear trend toward a simpler process flowsheet employing larger equipment in single-unit processes. This trend has been driven by the need to reduce coal preparation costs while maintaining an acceptable process performance. There is also a trend toward modular preparation plant designs, which allows greater flexibility in operation and can be readily dismantled and relocated. Coal preparation, in its earliest forms, dates to medieval times. However, the major coal preparation stimulus came in the 1960s with the deterioration in ROM quality as more-productive but less selective, mechanized mining methods were adopted. In some coalfields, the trend toward higher productivity and increased mechanization has also been accompanied by deteriorating quality of coal reserves. In general, these changes have led to an increase in the ash and moisture content and decrease in the average particle size of ROM coal (Figs. 1.1 and 1.2).

18

Mineral Processing

FIGURE 1.1 Process flow diagram: heavy media bath At PT CIB services, Indonesia.

DESLIMING CYCLONE

MAGNETIC SEPARATOR

ROM COAL 60 T INFEED HOPPER

CLEAN WATER FROM LAGOON

CRUSHER

SIZING SCREEN

TO TAILINGS DISPOSAL PUMP TANK

DREWBOY HEAVY MEDIUM BATH

DRAIN & RINSE SCREEN

DESLIMING SCREEN

PRODUCT SCREEN

2 OFF ø 380 MM PARNABY CYCLONES

DISCARD

DISCARD

FLOATS

PRODUCT

FINES TANK

CIRCULATING MEDIUM TANK

DILUTE MEDIUM TANK

PROCESS FLOW SHEET OF DENSE MEDIUM BATH COAL WASHERY IN INDONESIA

FIGURE 1.2 Process flow-sheet of DM bath coal washery in Indonesia. DM, Dense Medium.

19

Coal beneficiation: theory and practice Chapter | 1

Coal preparation practice has had to adapt to these changes in ROM quality while at the same time responding to changing market requirements. The flow sheet of a typical coking coal preparation plant in India is given in Fig. 1.3. Each coal preparation plant has three primary sections:

1.11.1 Coal sizing Sizing coal is the process of segregating coal lumps that are similar in size. Coal passes over one or more vibrating screens/grates and the larger sizes not passing through each screen are separated. Coal is usually separated using grates of three sizes: coarse, intermediate, and fine. Each size follows a different path through the plant. The sizes of coal produced may vary depending on customer needs and coal type. Most utility coal specifications will require a 2" 3 0 (2" or less) product with a maximum percentage of fines. This allows for efficient shipping and handling of the coal before being pulverized for combustion. Some customers, especially in the industrial sector, request stoker coal, which is smaller and relatively uniform in size, as it will not be crushed again.

TRACK HOPPER BOBR WAGONS

RAW OCIAL-400M

PRIMARY SCREEN PICKING CONV.

BURGE HOPPER V.FEEDER DOUBLE STAGE ROLL CRUSHER

SECONDARY SCREEN

OVER HEAD SURGE HOPPER

SIEVE BEND

DESLIMING SCREEN

PRIMARY HEAVY MEDIA PUMP

CLASSIFYING PUMP

HEAVY MEDIA PUMP D & R SCREEN PRIMARY-H.M CYCLONE SECONDARY HM PUMP

PRIMARY-H.M CYCLONE

CLASSIFYING PUMP

BASKET CENTRIFUGE CLASSIFYING CYCLONE-BANK

MAGNETIC SEPARATOR

FINES THICKENER

SPIRALS - BANK

HM PUMP

D&R SCREEN

D&R. SCREEN

BASKET CENTRIFUGE

FORTH FLOTATION CELL

CONDITIONING TANK-2

H F SCREEN BASKET CENTRIFUGE

SECONDARY HM CYCLONE MAGNETIC SEPARATOR

CONDITIONING TANK-1

HORIZONTAL BELT FILTER PRESS

MAGNETIC SEPARATOR

SCREEN BOWLCENTRIFUGE

SIEVE BEND

TAILINGS THICKENER

BELT PRESS -MULTIROLL TAILINGS POND

REJECT BUNKER -4000 t

PREWEIGH HOPPER (REJECTS)

WASHED COAL(POWER) BUNKER -6000 t

CLEAN COAL BUNKER -4000 t cap.

PREWEIGH HOPPER PREWEIGH HOPPER (CLEAN COAL) (WASHED POWER COAL)

PROCESS FLOW DIAGRAM FIGURE 1.3 Process flow diagram of typical Indian Coal Washery.

20

Mineral Processing

1.11.2 Blending of coal Blending is the process of mixing two or more coal types. This provides, for example, the potential to mix low-cost or low-quality coals with higher-cost or higher-quality coals and reduce the overall cost of the final blend. Blending two or more coal types into a shipment provides a seller the opportunity to mix complementary products having different mining costs such that the final product can achieve a customer’s price and quality objectives. Coal blending helps reduce: plant fuel usage, and control coal quality while maximizing fuel efficiency in response to forecasted generation needs; and minimizing coal quality events like reducing fouling, slagging, and emission occurrences.

1.11.3 Coal Preparation Coal preparation conventionally involves cleaning coal by separating coalrich from mineral-matter-rich particles in different size ranges. Typically, the processes may include: G G G G G

Raw coal pretreatment. Coal sizing and classification. Coal cleaning. Coal dewatering. Tailings treatment and water clarification.

1.11.3.1 Raw coal pretreatment ROM coal characteristically varies in size, moisture, and ash content, with differing amounts and types of other contamination from the mining operation. The basic equipment in general use worldwide for the dry ROM coal screening is a vibrating screen in various forms. Multiangle deck screens (banana screens) were first conceived to achieve high throughput, high screening efficiency, and low power consumption. This technology has proven popular and reliable for untreated fines extraction, and banana screens are now found in most modern high-technology coal preparation plants globally. An interesting departure from this trend is South Africa, where roller screens have been used for some applications instead of banana screens. In this screening technology, the screen bed is kept alive using elliptical rolls, which rotate to prevent pegging and blinding. For dry coal screening, roller screens have been reported to achieve high efficiency down to 6 mm. For precrushing of raw coal, there has been a gradual move toward using twin-scroll sizers and many major coal producers worldwide apply this technology. The twin-scroll sizer allows the selection of a wide range of

Coal beneficiation: theory and practice Chapter | 1

21

capacities, up to 5000 t/h, and product sizes. Twin-scroll sizers also generate less fine material than crushers and the trend toward their use appears likely to continue and increase.

1.11.3.2 Coal sizing and classification Classification by size is one fundamental operation of coal preparation. Screens can classify a broad range of sizes and are used for various applications throughout the coal preparation plant, including raw coal pretreatment and dry fines extraction, presizing of feeds to separation processes, recovery and dewatering of products after separation processes, and sizing of washed coal to meet market requirements. The main screen types currently in use are static or vibrating screens. The most common application of a static screen is the sieve bend, constructed as an arc or a bend with the sieve surfaces offering very steep to progressively lower angles to the material flow. The most common application of sieve bends is to remove large volumes of water before the material passes into a vibrating dewatering screen. Vibrating screens are widely used to size and dewater coal in the range of 200
0.25 mm. A wide range of screen sizes and designs are available to meet the specific requirements of each application. One significant development in screening technology in recent years has been the introduction of new materials for screen decks to reduce wear, increase screening performance, and reduce noise at the coal preparation plant. Vibrating screens become less effective as the particle size decreases, and accurate size classification of fine and ultrafine coal remains a problem. These sizes tend to be classified using the differential settling velocity principle. In the past, a range of classifiers operating on this principle have been applied, including hydrocyclones, spiral classifiers, and settling towers. Settling towers are still commonly used to classify the process water for a jig-washing plant. However, a major feature in recent years has been the increasing use of hydrocyclones in coal preparation. Hydrocyclones are used for many applications, including controlling fine solids, recirculating process water, classifying fine from ultrafine coal before further cleaning, and preconcentrating fine coal before dewatering. Over the years, there has been considerable R&D into improving the accuracy of separation in hydrocyclones, and, currently, several highly efficient units are available. However, hydrocyclones suffer from an inherent problem of some ultrafines (or slimes) always reporting to the coarse product. The misplacement of slimes can be minimized by optimizing the hydrocyclone design to minimize water flow, and hence the entrainment of slimes, to the underflow and injection of clean water close to the cyclone underflow spigot. A recent interesting approach has been to use multiple-stage

22

Mineral Processing

hydrocyclone circuits to increase the overall separation accuracy. In Australia, a three-stage hydrocyclone system has been tested recently. The circuit and produced a much sharper separation, improving coarse coal recovery, and minimizing slime misplacement. However, despite the improved performance, multiple-stage hydrocyclone systems are relatively expensive to install and operate, and their use will be limited to applications where the additional cost can be justified.

1.11.3.3 Coal cleaning For coal cleaning, two main separating principles predominate: 1. Separation based on differences in Relative Density (RD) between coal and associated mineral matter; pure coal has an RD of B1.3 and associated mineral matter commonly has an RD .2.2 2. Separation based on differences in surface properties between coal and associated mineral matter; coal is hydrophobic, whilst associated mineral matter is generally hydrophilic. The processes in coal cleaning are determined largely by the variability in size of the coal feed and the size range desired in the final products. RD difference of Separation of one type or another, are normally restricted in application to particle size ranges above B0.1 mm although recent developments are extending this lower size limit further toward “zero size.” Processes based on surface properties, such as froth flotation, can normally be applied to particle sizes below B0.6 mm. Coal cleaning methods are often categorized by the coal size range for which they are designed, that is, coarse, small, fine, and ultrafine coal. These terms can cause confusion because many of the principal methods and much of the equipment used for cleaning coal have significant overlap in the particle size ranges they can treat. Commonly accepted nominal size definitions, as used in this report, are as follows: G G G G

Coarse coal ( . 25 mm) Small coal (25
3 mm) Fine coal (,3 mm) Ultrafine coal (,0.15 mm).

1.11.3.4 Coarse coal Coarse coal has always been in demand for burning on less sophisticated grates and combustion systems and for domestic use. Although the traditional use of larger coal (e.g., for railways and household use) has virtually disappeared as a significant market in many economies, there remains a small but important demand for larger coal for industrial applications. For these applications, a significant price premium is often payable.

Coal beneficiation: theory and practice Chapter | 1

23

For coarse coal cleaning, two main processes are used: Dense Medium (DM) separation, which simulates the effect of using a heavy liquid of the appropriate density to effect a float/sink separation of coal from associated mineral matter. In commercial practice, this is achieved by using a suspension of finely ground dense solids (e.g., magnetite with specific gravity 5.2) in water. Jig washing, which is a water-based process that relies on the pulsation of water through the particle bed to stratify particles of different density. The higher-RD shale particles, forming the lower layers, are separated from the clean coal using a shale discharge system. Both processes have found wide application throughout the world. The choice is often made according to regional preferences for particular processes, which only in part reflect the washability characteristics of the coal. Jig washers, such as the Baum jig, have been developed to accept a wide range of sizes up to a top size of 150 mm in a single process. The jig is a relatively low-cost, simple washing system generally considered efficient only for coals that are relatively easy to clean. However, jig washing technology has been subject to continuous improvement since the 1970s, and several improved jigs (e.g., the Batac jig and the Fisher Cails Babcock jig) have found wide application, particularly in Germany, India, and China. Much of the present R&D effort in this area is aimed at developing improved jig control systems. An example is the JIGSCAN online control system developed by the Julius Kruttschnitt Mineral Research Centre, which uses nucleonic density gauges to monitor jig bed density. The signal is then used to control the jig density cut-point. As quality requirements for coarse coal have become more rigorous, the DM static bath has become the predominant technology for cleaning larger coal, that is, up to 250 mm. A wide range of DM baths is available, the main differences being the method of extraction of the separation products. Figs. 1.1 and 1.2 show the process flow diagrams of heavy media baths in Indonesia. DM cyclones, which use high centrifugal forces, are commonly used for the finer size ranges of coarse coal cleaning. Coal particles with a specific gravity less than that of heavy media will report cyclone overflow and the particles with a specific gravity more than that of heavy media will report the underflow of the cyclone. The DM overflow is clean coal and the underflow is called discard/cyclone rejects. DM cyclones are frequently installed in banks of two or more parallel units or in parallel with other separators (such as DM vessels) to meet the production requirements of a plant. Theoretical analyses show that the clean coal yield from these parallel circuits is maximized when all separators are operated at the same specific gravity cut-point (Abbott, 1982; Edward and Clarkson, 1999; Clarkson & Wood, 1991; Luttrell et al., 2000). This optimization principle is valid regardless of the desired quality of the total clean coal product or the ratios of different coals passing through the circuits.

24

Mineral Processing

To illustrate the importance of this optimization concept, consider a 500-tph circuit consisting of two identical DMCs operating in parallel (Luttrell et al., 2003). Both DMCs are capable of producing an 8% total ash product when they operate at the same cut-point of 1.55 Specific Gravity (SG). The overall yield from these two DMCs is 68.2%. However, the two units can also produce combined clean coal ash of 8% by operating the first DMC at 1.59 SG (produces 8.5% ash) and by operating the second cyclone at 1.51 SG (produces 7.5% ash). Although the combined product is still 8% ash, operation at a cut-point difference of 0.08 SG units reduces the overall yield from the combined circuit from 69.6% to 68.2% (i.e., 1.4% reduction). If the cyclones are operated for 6000 h/yr, the annual revenue lost due to the cut-point difference is $2.1 MM annually (i.e., 1.4% 3 500 tph 3 6000 h/yr 3 $50/ton 5 $2,100,000). Therefore, it is important that all DM circuits (vessels and DMCs) be operated at the same SG cut point to optimize total plant profitability. The industrial application of cut point optimization is relatively straightforward for DM vessels. Vessels tend to operate at a predictable density cutpoint based on the SG of the feed medium. On the other hand, the segregation of medium by the centrifugal field within a DMC makes it very difficult to estimate the true SG cut point for cyclones. Typically, the underflow medium from a DMC has a substantially higher SG than the overflow medium due to the preferential classification of the magnetite particles used to create the artificial medium. The thickening of the medium tends to increase the SG cut point for the DMC above that of the feed medium SG. Because of this phenomenon, the actual cut point of the DMC is about 0.05
0.10 SG units higher than that of the measured SG of the feed medium. This “offset” between true and measured density can vary substantially depending on the feed medium density, extent of cyclone wear, and characteristics of the feed coal. In some cases, negative offset values have even been reported from plant studies due to the use of poor grades of magnetite. As a result, the normal practice of monitoring the feed medium SG online using nuclear density gauges, cannot be used to estimate the true cut point for DMCs accurately. As discussed previously, this inability to estimate and maintain the SG cut point can result in coal losses that have a tremendous impact on plant profitability. Until recently, the application of DM cyclones had been restricted to particle sizes ,35
40 mm. However, the introduction of larger-diameter DM cyclones has now allowed the treatment of a much wider feed-size range, and larger cyclone units are now capable of accepting top sizes up to 80 mm, depending on feed inlet configuration (i.e., tangential, involute, or cycloidal). The largest DM cyclones in commercial operation are 1.25 m in diameter with feed capacities of 300
350 tph/unit. However, technical issues are still to be resolved concerning the performance of the large-diameter cyclones in the finer sizes, where some misplacement of low-density material to reject has been reported.

Coal beneficiation: theory and practice Chapter | 1

25

One of the earliest coarse coal separators, the barrel washer, has also reemerged as an option for upgrading coals for applications where it is less important to achieve high separation accuracy. Traditionally, the barrel washer has been used as a semi-portable method for recovering coal from waste tips, but in recent years it has also found some applications as a simple, cost-effective method of destoning ROM coal. An example is the Lodna washery in India, which incorporates barrel washers and cyclones to produce coal for the cement market.

1.11.3.5 Small coal Jig washing systems can treat both large and small coal in a single unit. Over the years, jig washers have shown a significantly improved performance, particularly in cleaning small coal. One of the most notable developments in this area has been the Batac jig, which in some forms, is claimed to be capable of washing coal down to 3 mm. However, the DM cyclone is now probably the most widely used system for processing coal in the 13.0
0.5 mm size range. As mentioned earlier, the most notable recent development has been the introduction of large-diameter DM cyclones, capable of accepting particles up to 75 mm in size and allowing both small and large coal to be treated in a single unit. 1.11.3.6 Fine coal Coal producers worldwide have debated the pros and cons of fine coal treatment and recovery for long. In the past, arguments for discarding fines directly to lagoons have been based on the cost of fines recovery and the increased difficulty this causes with product handling. Current coal preparation practice tends to place primary importance on maximum recovery of coal, which favors fines treatment. The requirement to maximize coal yield, together with a growing emphasis on improving product quality, has redefined the scope of fine coal cleaning, and, nowadays, a wide range of process designs is available (Fig. 1.4). Froth flotation is the most preferred process for preparing coal below B0.6 mm in size. In a froth flotation circuit, conditioned slurry is introduced into the tank through the feed box by gravity. Flotation banks are installed to facilitate easy gravity flow in downstream equipment. Flotation air is uniformly dispersed into the slurry through the slots in the rotor. The air bubble breaks into smaller sizes and are dispersed throughout the cell, maximizing the probability of contact with the particle, and thus increasing recovery. Air feed to the rotor takes place through the hollow lower shaft. Particles with an affinity to air rise to the surface carried by air bubbles and form a froth, which flows over the froth lip provided on either side of the tank through the launders (Fig. 1.5).

26

Mineral Processing Dense Medium Cyclones D&R Screen

D&R Screen

Refuse

Clean Bleed

Magnetic Separator

Magnetite Bin

To Fines Circuit Circuit Feed

Water Medium Sump

Dilute Sump

Density Gauge Plant

Water

Control System

FIGURE 1.4 Typical heavy media cyclone circuit.

Mechanical flotation cells, where impellers are used to disperse air bubbles within the fine coal slurry, are used in all the coal-producing countries and can be highly efficient in terms of recovery. Perhaps a significant development in this area in recent years has been the increase in the size and capacity of the individual flotation cells that are combined to form a flotation bank, usually containing four or more cells. For mineral applications, mechanical flotation cells are now available with volumetric capacities up to B120 m3. For coal applications, however, where much of the flotation feed is removed as froth concentrate, the maximum practical size is considered closer to B40 m3/cell. Fig. 1.6 shows a typical bank of mechanical flotation cells. Although mechanical flotation cells are still widely used, in the past decade, a range of selective flotation technologies, such as column flotation, has become increasingly popular. Mechanical agitation is not used in these systems, and selectivity is increased for the smallest particle sizes by producing much smaller bubbles than possible with mechanical flotation cells. In addition, water sprays are often used to rinse entrained mineral matter from

Coal beneficiation: theory and practice Chapter | 1

27

FIGURE 1.5 Flow-sheet of a typical thickener section.

the froth concentrate. There are now many types of column flotation cells commercially available. In Australia, the preference for column flotation over mechanical systems has focused particularly on Jameson cells, in which coal particles and bubbles collide and attach in a downcoming feed and air tube. Another notable development in fine-coal treatment is the widespread application of fine-coal density separation techniques, such as spiral concentrators and teeter-bed separators to clean the B3.0
0.1 mm size range. Teeter-bed separators (upward current separators or hydrosizers) have found widespread use in the Northern hemisphere, for example, in the United Kingdom, the United States, Russia, and eastern Europe. A major advantage is their potential to achieve a low-RD cut-point in a single pass, high unit capacity process. However, there is a perceptible tendency to prefer spiral concentrators in new coal preparation plants because of their ease of operation. Spirals, though, have the disadvantage that they can only separate at B1.7 RD or above, and, because of their relatively low selectivity, they are often used as two-stage units to meet product requirements. Recent R&D has been aimed at lowering the RD cut-point and improving selectivity, One notable development has been the introduction of compound spiral concentrator systems. In these systems, two “short-turn” spirals are mounted serially on a common spiral column to achieve a two-stage separation in a single unit. Compound spirals are now finding increasing applications for the treatment of fine coal.

28

Mineral Processing

FIGURE 1.6 Typical froth flotation unit with mechanical flotation cells.

Interest has also continued in the use of small DM cyclones for the separation of fine coal. A recent example is a 500 mm cyclone circuit in Australia in the 1990s to treat coal down to 0.15 mm. However, while separating performance met or even exceeded expectations in the targeted size range, the application was limited by difficulties in desliming the feed and products, resulting in the carryover of high-ash slimes with the clean coal.

1.11.3.7 Coal dewatering The difficulty of dewatering increases as the diameter of the particle decreases, as the total surface area of the particles to which water can attach increases significantly (by the cube of the diameter). Fine coal is far more difficult to dewater than coarse or small coal because the surface area of the particle is significantly larger for the same tonnage. The tendency for water to be trapped on porous surfaces and between particles increases as the size of particles decreases. Water also has greater difficulty in passing through the interstitial voids when the particle diameter decreases. Coal particles vary widely in terms of size, shape, and composition. A bed of coal slurry particles also consists of other species such as clays and shales. Generally, coarse coal is adequately dewatered using conventional screens and small coal is dewatered using conventional screens with vibrating basket centrifuges. Water in coal can be considered a contaminant like ash. It reduces the effective heating value of coal, increases transport costs, and can cause difficulty handling. Depending on the type of contracts, there may be penalties due to excess moisture and sometimes even rejection clauses. The plant moisture balance is also important and water lost on the products must be replaced.

Coal beneficiation: theory and practice Chapter | 1

29

Fine coal dewatering should produce a product with as low a moisture content as the selected equipment can produce. This should be done while also recovering a high percentage of the feed, unless the poor quality of the finer coal dictates that it should be discarded if possible. While dewatering sizes above B0.5 mm have generally presented few problems, the dewatering of finer coal, particularly by vacuum filtration, has always been more difficult. Dewatering of fine coal continues to be the subject of considerable R&D. Traditionally, rotary vacuum filters, either disk or drum, have been used. A more recent addition to filtration technology has been the horizontal belt filter, which is now gaining popularity. Screen bowl centrifuges are expensive, and their use is limited to applications where their cost-effectiveness can be demonstrated. In general, compared with disk and drum filters, the HyperBaric disc Filter (HBF) has demonstrated improved dewatering performance and ease of operation and maintenance. During the 1990s, the HBF was the main type of vacuum filter installed in the Australian coal industry, totaling more than 15 units. One possible disadvantage of the HBF is its requirement for a large floor area to accommodate the horizontal belt. For some applications, high-pressure filters have also been considered for fine coal dewatering to increase filter throughput and produce low-moisture filter cakes. Several variants have been investigated, including tube presses, air-blown filter presses, and hyperbaric filters, where a vacuum drum or disk filter is installed inside a pressure vessel. However, although these devices can demonstrate much improved dewatering performance compared with conventional vacuum filtration, they are expensive and commercial application is restricted to special cases where the additional costs can be justified. For fine coal dewatering, various designs of scroll centrifuges have also been introduced in the last decade, and these are finding increasing application in coal preparation. Generally, these centrifuges operate at a higher speed and can generate greater dewatering forces than the more traditional vibrating centrifuges used for coarser coal. In this type of centrifuge, the inner scroll rotates slightly slower than the centrifuge basket to discharge the dewatered coal. Typically, scroll centrifuges dewater coal up to a top size of 1
1.5 mm. Overall, reduced product moisture is achieved not only through improved dewatering of this finer fraction but also through the decreased solids loading on the coarse coal centrifuges. Screen bowl centrifuges operate at even higher speeds than scroll centrifuges and are capable of dewatering coal down to ultrafine sizes. This type of centrifuge has found application, particularly for the dewatering of froth concentrates. Tailings treatment and water clarification remain the most difficult and costly areas of coal preparation. Current practice now favors using modern, “high-rate” thickener/clarifier designs, enhanced using advanced chemical

30

Mineral Processing

reagent systems. For applications where further dewatering of thickened tailings is necessary, the traditional method has been the recessed-plate filter press. However, for some applications, the multiroller filter can offer acceptable dewatering performance in a continuous process at a lower capital cost, and is now challenging the predominance of the filter press. The level of automation and control in coal preparation globally varies considerably. Although sophisticated technology is now available for online process monitoring, coal preparation plant, even of recent construction, still employ a mixture of conventional manual and automated monitoring and control. One of the major R&D issues currently facing plant automation is the need for improved sensors to monitor process stream qualities. Recent attention has also focused on developing advanced control systems using fuzzy logic and neural networks. However, commercial applications of these advanced systems in coal preparation are unlikely in the near future.

1.11.3.8 Dry coal beneficiation Dry coal beneficiation processes were widely applied in Europe and the United States during 1930
65. However, they were later abandoned largely because the separation was not accurate, the available technology severely restricted feed size and throughput, and moisture presented a major inhibiting factor on performance. During that period, the main processes used were pneumatic table- or jigbased designs, the latter being more common. There remain a small number of units in operation, particularly in some areas of China where water is scarce, although the throughput can be considered currently insignificant. However, increasing economic and environmental pressures to expand the use of coal preparation in some of the largest coal-producing nations, where some key production areas are in arid regions (e.g., in China, India, and Kazakhstan), has revived interest in dry coal beneficiation processes.

1.12 Generic description of coal preparation plant The world’s coal resources are not abundant hence there is a need to use the available coal resources effectively. Therefore, there is a requirement of new coal washeries, with improved washing technologies. This section provides the description of typical noncoking & coking coal washeries. In modern Washeries, the top size of ROM coal is 200 mm (max). The Coal washery Complex generally starts from receipt of ROM coal (size ,200 mm) through Bottom Open Bottom Discharge (BOBR) wagons at track hopper or truck to truck dump hopper at the washery. ROM coal is crushed from (2) 200 mm size to (2) 50 mm for noncoking coal and (2) 13 mm for coking coal washery and carry out beneficiation in multiple streams.

Coal beneficiation: theory and practice Chapter | 1

31

The typical coking coal washery has three main sections for flow/handling of solid material as follows: G G G

Raw coal section; Main washing plant; Wash/clean coal, wash coal (power) and rejects storage and wagon loading section. A typical coking coal washing plant has the following sections:

G G G G

Treatment of (2) 13 mm to (1) 2 mm size fractions by heavy media cyclone. (2) 2 mm to (1) 0.5/0.15 mm coal in spirals or reflux separators. Rest (2) 0.5 mm / (2) 150 μm goes to froth Flotation. Products of the above size fractions are mixed to get the required quality and yield of coal. A representative noncoking coal washery has the following sections:

G G G

Treatment of (2) 50 mm to (1) 2 mm size fractions by heavy media cyclone. (2) 2 mm to (1) 0.150 mm coal in spirals or reflux separators. (2) 150 mm is tailings and mixed with coarse rejects.

The products, middlings, and rejects are evacuated in the rail wagons through the preweigh hopper system in a rapid loading system. In addition, the plant will also consist of the following auxiliary services: G G G G G G G

G G G G G G G G G G G

Fresh water distribution system; Firefighting system; Chemical dozing system; Dust extraction and dust suppression system; Compressed air system; Thickeners and slime ponds; Weighing arrangement (belt weighers, in-motion weighbridge, and road weighbridge); Auto samplers and online ash and moisture monitoring devices; Power supply arrangement; Illumination, earthing and lightning arrangements; Plant control system; Communication arrangement; Air conditioning; Stores; Workshop; Laboratory; Required service buildings; Roads and drains.

Generally, the following parameters are monitored in a coal washery: (1) quality of raw coal: (ash); (2) range of day-to-day basis ash; (3) size of raw

32

Mineral Processing

coal; (4) quality of product coal: (ash); (5) targeted monthly average ash; (6) clean coal; (7) middlings; and (7) rejects.

1.13 Broad input and output design parameters in coal washery 1.13.1 Raw coal section G G

Rate of receipt of coal at washery. Design capacity.

1.13.2 Washing section G G

Annual effective working hours of operation. Design capacity.

1.13.3 Loading section of clean coal, middling’s and rejects G G

Loading capacity. Loading of wagons.

1.14 Brief system description of high/medium coking coal washery 1.14.1 Raw coal section This section will comprise the portion between the raw coal receipt point and the main washing unit as per generic process description given next:

1.14.1.1 Raw coal receipt section Raw coal is received through wagons in track hopper. Rotary Plow Feeders within built dust suppression system is installed in the tunnel below the track hopper for reclaiming coal from the track hopper and load on to belt conveyor. 1.14.1.2 Raw coal storage The reclaimed coal from the track hopper/truck dump hopper is transported by a series of belt conveyors and spread on the ground to form a raw coal stock of required capacity over a tunnel. Raw coal from the stock may be reclaimed with the help of vibratory feeders or plow feeders and loaded on a belt conveyor for discharging on double deck scalping primary screen. Rack and pinion gate with vibratory feeder are provided for reclamation of raw coal from the raw coal stockpile.

Coal beneficiation: theory and practice Chapter | 1

33

1.14.1.3 Primary screening and manual picking arrangement Double deck primary screens are suitable to receive even (2) 200 mm lumps. The primary screen generally has 150 mm openings in the top deck and 50 or 13 mm openings in the bottom deck. The (1) 150 mm size coal fractions from top deck will be received on a slow-moving picking belt conveyor (this size fraction mainly consists of shales and stones). Stones and oversize coal lumps picked from the picking belt conveyor are discharged on a belt conveyor after crushing down to (2) 50 or (2) 13 mm), as the case may be. They are in turn discharged to a small overhead hopper for loading them in a truck as and when required. The (2) 50 or (2)13 mm, will be collected on a belt conveyor. The (1) 50 or (1) 13 mm coal from the primary screen and (1) 150 mm coal from the picking belt conveyor, are recirculated to a hopper in the Crusher House. This recirculation system provides correct sized coal for upstream washing process. Metal Detectors are provided for identification and removal of nonferrous metal pieces. Electromagnetic Separator is provided at the discharge end of belt conveyor to remove tramp iron. 1.14.1.4 Crusher house Raw coal from the hoppers is generally reclaimed by vibratory feeders and fed to roll crushers for crushing coal to (2) 50 or (2) 13 mm size fraction. 1.14.1.5 Secondary screening The roll crusher product (1) 50 mm or (1) 13 mm is fed to secondary screen. After screening at 50 or 30 mm, the oversize (1) 50 or (1) 13 mm from the secondary screen is recirculated to the surge hopper of primary sizing screen. The (2) 13 mm product of secondary screen is taken to main overhead bunker of the washery section. 1.14.1.6 Crushed coal storage A suitable capacity overhead steel bunker is provided for storing the excess (2) 50 or (2) 13 mm coal to regulate the flow to the washing plant. A reversible drive belt conveyor spreads the crushed coal over the bunker. Suitable vibrating feeders reclaim the coal and load them onto conveyor belt. The (2) 50 or (2) 13 mm coal is fed to a feed box located in the main washery building. In this feedbox, generally called the mixing box, process water is added for desliming purposes. This is the beginning of the wet process.

34

Mineral Processing

1.14.2 Washing section 1.14.2.1 Desliming operation The coal is mixed with water in mixing boxes and is discharged on to sieve bend(s) before being fed on to desliming banana screen(s). In the desliming screen, water is sprayed through nozzles on the coal bed for removal of slimes and fines from coarse coal. The screen deck of the banana screen uses 2/1/0.5 mm aperture depending upon the upstream fine coal washing scheme. The coal fraction retained over the desliming screen is carried to the primary heavy media sump/tank. The water along with coal fines from the underflow of the desliming screen reports to the fine coal tank. 1.14.2.2 Heavy media beneficiation circuit and media recovery circuit A typical heavy media cyclone circuit is shown in Fig. 1.4. The required quantity of media is added in the primary heavy media sumps/tank to maintain the required specific gravity of heavy media. Heavy media along with the deslimed coal from the heavy media sump/tank is pumped to the primary heavy media cyclones. The density of media is adjusted automatically through the density compensation system as per requirement, to produce products depending upon the raw coal quality. The overflow from the primary heavy media cyclones reports to a drain and rinse (D&R) screen. The D&R screen deck can have 2/1/0.5 mm aperture as per process requirement. The (1) 2 mm/(1) 1 mm/(1) 0.5 mm size coal retained over the screen is taken to a vibrating basket type centrifuge for removal of moisture and then discharged on to a clean coal belt conveyor. The dense media (drained media) collected in the underpan of the above screen will be taken to primary heavy media sump/tank. At the discharge end of the D&R screen, there is a provision for spray water to rinse off the adhered media. The rinsed dilute media is collected and this rinsed media/dilute media is taken to a wet low magnetic separator for removal of media. The wet low-intensity magnetic separator produces a high-density magnetite slurry concentrate and nonmagnetic tailing. The recovered overdense media is taken to the dense heavy media sump/tank. The nonmagnetic tailings report to the fine coal tank. The underflow from the primary heavy media cyclones after passing over the sieve bend is taken to secondary heavy media sump/tank. The mixture of coal and the heavy media from the secondary heavy media sump/tank is pumped to secondary heavy media cyclone. The secondary heavy media cyclone circuit is very similar to the primary circuit. Nucleonic density gauges are fitted for controlling the addition of media in the primary and secondary heavy media sumps and for monitoring the density of the pulp. Level monitoring and transmitting units are provided to monitor the

Coal beneficiation: theory and practice Chapter | 1

35

level in the primary and secondary heavy media sumps/tanks. Level monitoring/ transmitting units will also be provided at the fine coal tank.

1.14.2.3 Fine coal circuit From fine coal sump pump, the slurry is fed to a cluster of raw coal classifying cyclones. In coking coal washeries, the overflow from the classifying cyclones is sent to froth flotation cells. However, in noncoking coal washery, the cyclone overflow is sent to the tailings thickener. The underflow from the classifying cyclones reports to a bank of spirals. Heavy particles/middlings from the spirals will be collected and sent to high frequency screens. The solid particles from the high frequency screens will be discharged on the middling’s conveyor and the underflow slurry from the high frequency screen will be taken to raw coal thickeners. The lighter particles from the spirals will be taken to screen bowl centrifuges or a screen scroll centrifuge after passing through a sieve bend for removal of moisture. The treated particles from a screen bowl centrifuge will be discharged onto a clean coal conveyor. The overflow fines from the classifying cyclone, as mentioned before, are treated in froth flotation cells. Older coal washeries use two different reagents (a collector and a frother) for coal flotation. However, more recent washeries use a single reagent. In some plants, along with collectors and frothers, surface modifiers are also used because of partially oxidized coal surface. The froth from the froth flotation cell is taken to a raw coal fines thickener. The thickened underflow is pumped to a horizontal traveling vacuum belt filter for further moisture removal. The practice is in vogue in many of Indian coal washeries. After removal of moisture, the solid particles are taken to a clean coal conveyor. The tailings from the flotation cells report to the tailing thickener. The underflow form the tailings thickener discharge the slurry to a mixture box where flocculant is added to agglomerate the fine particles for efficient liquid
solid separation when the slurry passes through multi roll belt presses. In the above belt presses, the material will be pressed to squeeze the water. Afterwards the cake will be discharged on the rejects belt conveyor and the water will be taken back to a tailings thickener. Flocculant is added to the thickener feed slurry to accelerate settling of solid particles. The clarified water from the thickener overflow is laundered down to clarified the water tank. 1.14.3 Post washing section Conveyors are provided in the washing plant for receiving the respective products. All three products are transported by belt conveyors to their respective product storage bunkers.

36

Mineral Processing

From product storage bunkers, plow feeders/vibro feeders finally transport coal to rapid loading system.

1.14.4 Utilities G

G

G

Water required for the washing plant is supplied from the nearby rivers or lagoons to a reservoir at the washery. Air compressors with all accessories is provided for arranging compressed air to operate various control valves, pneumatically operated actuators, for agitating the media in the media storage tank, and for belt presses. Chemicals are used at various stages of washing/dewatering.

1.15 Environment management 1.15.1 Dust pollution In a raw coal circuit, dust is created at all transfer points and is a major source of environmental pollution. To control the environment pollution and the pollution levels within the prescribed norms, following measures should be adopted. A dust extraction system should be provided in the tunnel below the track hopper, screening, and crusher houses for extraction of coal dust crated during handling. The system generally consists of a blower, cyclones, screw feeder, chimney, hoods, ducting, etc. The dust generated at the transfer points (except screening and crusher house) in the raw coal circuit should be suppressed by spraying water in an atomized condition with the help of spray nozzles At the Raw coal stock/ ground stock, nozzles of higher capacity should be provided for suppression of dust. The dust suppression system will consist of pump, GI pipes, nozzles, manual sluice valves, solenoid valves, header pipes, etc. An exhaust fan of required size should be provided at the mouth of each escape tunnel to provide proper ventilation in the tunnel below the raw coal stockpile and tunnel below the track hopper.

1.15.2 Rain water treatment Rain water should be diverted to settling/slime ponds through drains. After settlement of suspended particles, the clarified water will then be discharged to natural drainage or pumped to a fresh water tank.

1.15.3 Slurry/effluent water treatment When a thickener malfunctions, it is advisable to divert the effluent to slime ponds. Water from surface drains can also be taken to these slime ponds.

Coal beneficiation: theory and practice Chapter | 1

37

The clarified water from the slime ponds can then be recycled for use in the plant. The tailings from the slime ponds can be excavated with the help of excavators, and loaded in the trucks for onward transportation.

1.15.4 Noise pollution Noise pollution is another major source of pollution in coal washeries. The noise is created due to the operation of crushers, screens, blowers, screen bowl centrifuge, etc. Suitable noise reduction devices and vibration dampening accessories should be provided and persons working near the above equipment should be provided with the necessary personal protection equipment.

1.16 Quality monitoring and control In-house facilities for sample collection and adequate number of automatic samplers complete with all required accessories are generally available to test the quality of raw coal, clean coal, middlings, and reject those produced at the washery and delivered to customers. An online ash and moisture analyzer for raw coal, clean coal, middlings, and reject conveyors provide a tool to control the operation of the washery. In addition to instantaneous monitoring, all of the above parameters are recorded and displayed in a control room, where online analyzers store all data on a time scale basis. All coal washeries also have their laboratory for testing and analysis of various samples collected during plant operation. The laboratory test results guide the plant operation and input/output product specifications. A typical coal washing laboratory has the following equipment: Sl. no.

Equipment

A B C D E F

Jaw crusher (250 to 50 mm); 1 tph Jaw crusher (50 to 13 mm); 0.5 tph Double roll crusher/cone crusher (23 mm), 0.2t RH cabinet; temperature: 27 C
98 C humidity: 50%
98%. Ash furnace, temperature of 815 (1/ 2 10%) deg C, lined with required controls. Volatile matter furnace, maximum temperature will be 900 C, lined along with required controls. Moisture testing oven, maximum temperature of furnace/hot air oven will be 108 C (1/ 2 2%) HGI testing machine; 30
90. Pulverizer, (2) 3 mm to 212 μm, approximately 100 g sample at a time along with the motor. Bomb calorimeter.

G H I J

(Continued )

38

Mineral Processing

(Continued) Sl. no.

Equipment

K

Sieve shaker, sieve shaker, electrically operated along with screens (50, 30, 20, 16, 13, 6, 3, 2, and 0.5 mm). Weighing machine
300 kg. Electronic balance, capacity 5 kg. Electronic balance, capacity 100 g. Desktop computer with printer and allied accessories. Bar magnet of 700 gauss for magnetite testing. Mercy balance for specific gravity of any slurry. Laboratory froth flotation cells. Jar testing apparatus for sedimentation testing. Digital pH meter. Digital TDS meter. Other Miscellaneous equipment: silica crucible, glass crucible, volatile matter crucible, aluminum tray, hydrometer, measuring cylinder, laboratory chemicals, measuring cylinder, beaker, weight box, desiccator, funnel, litmus paper, tong, spatula, flask, and thermometer.

L M N O P Q8 R9 S0 T U W

1.17 Instrumentation and control systems Effective monitoring and control systems are recognized as being essential for the efficient performance of a coal preparation plant. A wide range of techniques are now available for online process monitoring, including nucleonic density gauges, magnetic flowmeters, ultrasonic level detectors, and mechanical belt weighers. However, it is still common, particularly in older plants, for at least some of the processes to be monitored and controlled by operators relying on manual measurement of process parameters. For online quality monitoring, several techniques are used, including measurement of response to electromagnetic radiation, emission of natural gamma radiation, and variation of capacitance recorded between two charged plates. In both monitoring systems, the measurement technique produces an electronic signal that can be used for control purposes. Conventional control systems use either traditional a hardwired technology or computer-based Programmable Logic Controller (PLC) systems for the stop
start sequencing and control of equipment speed and feed rates. PLC control supports individual control loops to allow constant monitoring and adjustment of processes. However, PLC control is limited by the rule-based logic that is applied and by the inconsistencies of applying this logic to processes in which the dynamics are, as yet, ill defined. Recent R&D in this field has included investigations into the application of advanced control systems using fuzzy logic and neural networks. However, although both systems have been employed in grinding and froth flotation circuits for base metals and industrial minerals, there is, as yet, no known commercial application for coal preparation.

Coal beneficiation: theory and practice Chapter | 1

39

In the western industrialized economies, automatic weighing systems are used in majority of plants, while only half of the plant uses ash monitors and use automatic samplers. For process control, almost 90% of plants have PLC systems installed. The instrumentation and control of coal preparation plants aims to achieve the following: G G G

G

Maximizing coal recovery; Improving the efficiency and quality parameters of products; Increasing the efficiency of machines along with production costs reduction; Adaptation to market demands, increasing work safety and minimizing negative impact on the environment.

Currently DM cyclone and froth flotation are the major unit operations which require state-of-the-art instrumentation and control, which will be discussed next.

1.17.1 Monitoring and control system for dense medium cyclones DM cyclones (DMCs) have high efficiency, large capacity, small footprint and low maintenance requirements. Although the advantages of DMCs make them highly desirable, size-by-size partitioning data collected from industrial operations suggest that DMC performance can suffer in response to fluctuations in feed coal quality. In light of this problem, a monitoring system that measures the densities of the feed, around a DMC circuit is used. The data obtained from the real-time data acquisition systems indicate that serious shortcomings exist in the methods commonly used by industry to monitor and control DMC circuits. This insight, together with size-by-size partition data obtained from in-plant sampling campaigns, can be used to develop an improved control algorithm that optimizes DMC performance over a wide range of feed coal types and operating conditions.

1.17.2 Instrumentation and control in fine coal flotation circuit In flotation cells, the flotation air from dedicated air blower is introduced to a hollow rotor shaft that comes out at the bottom slot of a rotor to get dispersed in the coal water slurry. Generally, each individual cell has one butterfly valve to control the air flow rate. In addition, there is one butterfly valve at the main airline header for manual control. The mean diameter of a bubble varies from 500 μm to 2 mm. The level control in the flotation cell is maintained automatically by an automatic level control system. The intermediate or discharge boxes are supplied with one manually operated valve assembly and the others with automatic level control assembly. The automatic level control assembly has a

40

Mineral Processing

pneumatically operated cylinder with positioner fitted to the dart valve shaft assembly, which accepts the level signal from an ultrasonic level transmitter. The ultrasonic level transmitter is installed at the preceding cell to the intermediate and discharge box to sense the level in flotation bank. The ultrasonic level sensor gives signal (4
20 mA) to the positioner of the pneumatic cylinder to open/close by maintaining the level in the flotation cell banks. The feed and flotation tailings continuously pass through the coal slurry analyzer, which is an online ash monitor. Depending on the tailings ash, the froth depth, air flow, and reagent addition is adjusted to correct the loss of combustibles. In operation, the use of reagents should always be investigated ahead of process parameters such as air flow rate and froth depth as these variables are secondary to controlling performance compared to reagents. In addition, froth washing should only be used if the target concentrate quality cannot be achieved. It is not mandatory to the flotation process itself, but simply an additional tool, albeit an extremely effective one that can be used for controlling concentrate grade.

1.18 Guideline to plant availability, material and power consumption in a coal beneficiation plant An efficient coal washing plant having a good operating practice can aim to maintain its materials and power consumption as discussed in this section. Major input raw materials required for coal beneficiation plant are: G G G G G G G G G

Power. Water. Magnetite powder. Anionic or neutral flocculant. Cationic coagulant. Frother. Collector. Oil for lubrication. Grease for lubrication.

The consumption of these input variables is dependent on plant availability and plant use. These two factors are generally in the following ranges: G G

Plant availability must be maintained $ 85%. Plant use must be maintained $ 95% of plant availability. The general consumption norms for inputs other than raw coal is given next:

G G

Magnetite consumption # 0.8 to 1.0 kg/t of raw coal treated. Magnetite specification should be 195% magnetic content with 90% 45 μm

Coal beneficiation: theory and practice Chapter | 1

41

with specific gravity of 4.6
5.0. G G G G G

Anionic (flocculant) consumption # 8 g/t of raw coal treated in the process. Cationic (Coagulant) consumption # 4 g/t of raw coal treated in the process. Flotation Reagent consumption # 600 g/t of raw coal treated. Power consumption # 6.0
8.0 kwh/t of taw coal treated. Water consumption # 0.11
0.12 m3/t of raw coal treated.

Tentatively, at the current market price, the operating cost for a washery with a capacity of 2.5
5.0 MTPA is approximately INR 150 crores/1 million tons/year capacity of raw coal treatment. Tentative operating expenditure are tabulated in Table 1.14.

1.19 Operational problems and mitigating measures in a coal washing plant This section outlines operational problems encountered in a coal washing plant. their causes and possible remedial measures. The discussion will focus on the following equipment: TABLE 1.14 Typical expenditure in a coal washery. Particulars Tentative consumption charges (INR/ton) Power

60
65

Stores

14
18

Chemicals

8
10

Magnetite

7
8

HSD

16
20

Tentative plant and machinery expenses (INR/ton) Repair/maintenance

4.8
5.5

Hiring charges

3.5
4.0

Misc. expenses

5
7

Man power cost (INR/ton) Salary department

10
15

Cont. M/P

14
18

Security

3.0
4.0

Welfare expenses

2

Notes: Misc. exp includes—(1) rep.and maint. buildings, (2) running maint. others, (3) environmental protection, (4) lease rent free hold land, (5) siding rent, (6) insurance charges, (7) printing and stationary, (8) sampling and testing exp., (9) telephone exp., (10) fees and taxes, (11) legal and professional consultancy charges, (12) light vehicle maintenance cost.

42 G G G G G G

Mineral Processing

DMC. F F Cell. Spirals. Thickener. HBF. Wet LIMS.

1.19.1 Dense medium cyclone separation Observation

Possible problem

Action

Feed to the preparation screen is fluctuating Not enough water on screen

Inconsistent feed rate from coal preparation section Water pressure too low, water not open, spray nozzle blocked.

Screen blockage, water does not drain properly

Type of material treated, contaminated with vegetation, require different type of screen panel, screen motion Prevent contamination of medium

Coarse material in effluent and medium Fluctuating cyclone pressure

Holes in screen panels

Investigate problem and rectify Verify water pressure, ensure water valves are open, unblock spray nozzle, add sufficient water to remove clay. Minimize clay balls and cyclone blockages by ensuring the spray nozzles on the spray bars are open. Is better to have too much water than too little De-blind where required, maintain aperture size, verify correct panels are provided for the application, ensure screen stroke is sufficient Provide a weir bar between drain and rinse to prevent medium carryover to rinse section, use enough water on the rinse section to minimize adhering medium loss Check condition of screen panel & rectify Ensure header tank level is correct Check correct medium sump level and add medium if required Maintain level in mixing box, open medium flow to mixing box. Check for obstructions in medium flow to mixing box Low pumping efficiency, check condition of medium pump, make sure coal feed

Mixing box level not constant, insufficient medium in circuit Medium to mixing box is fluctuating

Poor cyclone efficiency

(Continued )

Coal beneficiation: theory and practice Chapter | 1

43

(Continued) Observation

Possible problem

Accelerated Wear Cyclone pressure increase

Pressure decrease

Blocked cyclone inlet (product disappear from screens) increase in medium density mixing box level too high Cyclone feed pump speed is too high density in medium density Partial blockage in cyclone feed hose mixing box level too high

excessive concentrate

cyclone feed pump impeller blocked Cyclone feed pump speed is too low drop in medium density excessive medium contamination excessive medium magnetization worn spigot Worn vortex finder

reduction in concentrate, possible clean coal loss

Inadequate densification (cannot maintain circulating medium density)

change in ore characteristics

High medium density excessive cyclone pressure Change in medium grading Change in ore feed characteristics Densifying cyclone defective. Insufficient level in dilute media sump. Insufficient bleed from floats drain panel

Action rate is constant. Operate as consistently as possible Cyclone pressure to be in the specified range Stop plant & unblock inlet/ check for source of oversize Check density & rectify Adjust level by restricting medium flow to box Check speed indication/VSD malfunctioning Check density and rectify, may require magnetite Clear out cyclone feed hose Open medium flow to box, check sump level open Impeller and clear obstruction Check speed indication/VSD malfunctioning check density on pulp density scale check viscosity, clear medium by running without feed excessive quantity passing through magnetic separator— check demagnetizing coil. Check monthly and replace when worn by 10% Check monthly and replace when worn by 10% Investigate increasing separation density check mixing box density check pressure indication check medium—coarse/fine Investigate and change medium density if required Check cyclone for wear and blockages. Check sprays and rectify. Increase bleed to dilute media side

44

Mineral Processing

1.19.2 Froth flotation Some of the typical problems in a flotation circuit are: G

G

G

G G G G G G G G

G G G G G G

G

G

Low recovery of ultrafine coal particles due to slime coating by ashforming minerals. Slime coating on both valuable ore and gangue inhibits bubble-particle resulting in reduction in flotation recovery. Lack of selectivity, which results in the flotation of middlings and entrainment of mineral fines in the froth. In this case mineral matter may be degraded to extremely fine or colloidal sizes thereby creating difficulty in flotation. The presence of slimes in the flotation circuit also leads to high consumption of reagents due to their increase in the solid/liquid interfacial area, colloidal size and high ion exchange capacity. High consumption of reagents due to presence of slimes coating cause a problem in the floatation circuit as it reduces the availability of reagents for targeted minerals (coal particles). Presence of 10.5 mm coal fines in tailings Variation in the nature of feed coal Variation in pulp density of feed slurry Variation in quantity of slurry from thickener underflow Improper conditioning Absence of split dozing / multiple dozing of reagents Inconsistency and poor quality of frother Less solids content and higher proportion of ultrafines (20.053 mm) in concentrate Froth depth control Tailings discharge control Poor recovery in dewatering equipment. Oxidation of fine coal Requirement of constant monitoring for reagent dosages. Even though flotation is the “separation process”, the overall peformance of the fines circuit is often dictated by concentrate and/or tailings dewatering or treatment capacity as this often proves to be the bottleneck in the process. Many flotation circuits have to be “scaled back” to suit the capacity of the dewatering device leading to large losses in coal fines which in turn may then lead to issues in the tailings thickener. Another area to address is the type of dewatering device used for concentrate dewatering. The technology chosen needs to be carefully considered to suit the particle size and type of coal treated. One of the most important characteristics of any flotation technology is air bubble generation and the size of air bubbles produced as this controls flotation kinetics and also dictates the carrying capacity of the machine. Another crucial component is the effectiveness of machine design in creating collision and contact between air bubbles and particles.

Coal beneficiation: theory and practice Chapter | 1

45

There are no specific guidelines available for troubleshooting the froth flotation circuit. With a low level of instrumentation, controlling the froth floatation circuit is still an “art.” The operator must understand the whole process and take necessary steps as deemed appropriate for the situation. In practice, the recovery and ash of the concentrate is affected by the variables in the following order G

G

the recovery of the concentrate: pulp density . frother dosage . collector dosage the ash percent of the concentrate: frother dosage . pulp density . collector dosage

With increase in solids concentration and collector oil dosage, the hydrophobicity and floatability of coal particles increases thereby resulting in an increased recovery of clean coal at acceptable ash levels.

1.19.3 Spirals Total mass and volumetric flow rate are the two most important factors affecting the capacity and efficiency of a spiral in cleaning fine coal. As the volumetric feed rate increases, the number of entrained materials reporting to the outer wall increases, resulting in a decrease of separation efficiency. The misplaced coal particles have little chance to escape the high velocity flow regime at the outer zone and ultimately report to the clean coal product. Feed rate and feed solids have a greater effect on separation cut-points than the position of splitter. The volumetric velocity of slurry down the spiral increases if the feed rate was increased with a constant percentage of solids. The increased velocity increases centrifugal force exerted on the slurry particles, forcing more material to move toward the clean coal launder. The relationship between the feed rate and cut-point of a spiral separation depends on the effect of three key operating variables and their interactive relationships when treating coal in the size range of 2210 1 44 μm. The three key parameters include the volumetric feed rate, feed solids concentration, and splitter position. The volumetric feed rate plays a critical role in the combustible recovery and product ash. The feed solid concentration also has a significant effect on the product ash content. Splitter position and volumetric flow rate jointly influence the product grade. Maximum recovery is possible at the highest volumetric feed rates and lowest feed solid concentration, whereas the minimum product ash content is realized at the opposite end of the parameter value ranges. As opposed to the solids concentration, the flow rate has a greater effect on the variation of yield and ash values. As the flow rate decreases, the yield and ash value of the clean coal reduces, resulting in increased yields of the middlings and refuse. Typical results in a coal beneficiation plant using spirals to treat fine coal indicated very little deterioration in performance with

46

Mineral Processing

the under-slimed and deslimed feed material (2500 mesh) even when the feed contained B50% of 2500 mesh material. However, the clean coal ash reduced when the 2500 mesh material was removed. Zhuping et al. (Department of Mining) noticed that a Multotec SX7 twostage spiral showed good performance when treating three different feed with widely varying characteristics. Fine anthracite refuse, the thickener feed slurry (nominal 21.2 mm) and the thickener underflow slurry were deslimed using a 102-mm diameter Krebs cyclone and the 21.2 1 0.025 mm feed was fed to the spirals. The feed ash could be reduced from 71% to 21% for the 10.025 mm material and the ash value of the refuse was 91%. Regardless of the deslime, the 10.025 mm material could be cleaned very well. The separation occurred even with the thickener underflow, which had been treated with flocculant. The 20.025 mm material reported in clean coal and refuse was proportional to the water content (Zhuping et al., Department of Mining). When correctly configured and properly operated, fine spirals are generally capable of maintaining good recoveries of clean coal. However, the shortcomings of industrial spiral circuits are that they are ineffective for small particles (,0.15 mm), have a low unit throughput capacity (,3.5 tph/start), have a high specific gravity cut-point ( . 1.9), there is misplacement of rock to clean coal, sensitive to feed distribution and solids loading, and require desliming of clean coal. The performances of fine spirals can be improved by optimizing the solids mass rate, slurry flow rate, feed solids content, splitter positions, feed distribution, and circuit configuration.

1.19.4 Thickeners In the coal washing process, huge quantity of water is used in fines classification and separation process. Bulk of the water that is used in the process needs be reduced before start of downstream operations. The separation of solids from liquids is done by gravity sedimentation in thickeners. In general, 70%
80% of the water can be separated and removed by thickeners. For further removal of water, filters are used. Industrial sedimentation is conducted as a continuous process in a thickener. It receives the slurry at the center, permits the overflow of the supernatant liquid through over weirs in periphery, and discharges a thick slurry from the bottom. The tank bottom is conical to facilitate the discharge of the underflow slurry. The tank is fitted with rakes, which are rotating railings with fixed vertical plates and positioned slightly above the tank bottom. These rakes scrap the concentrate slurry toward the central discharge. When the particles are finer or charged particles, the settling rate is extremely low. By adding a flocculant, the settling rate can be enhanced.

Coal beneficiation: theory and practice Chapter | 1

47

A thickener consists of the following sections: G G G G

Tank: The thickener tank can be of RCC or Mild steel construction. Rake drive mechanism. Underflow discharge removal. Flocculant and coagulant addition system.

However, it is important to check the following before operating a thickener: G G

G G G

G

If all the overflow V-notches are in one level. If the gaps (if any) between the V-notch plates and concrete are sealed. If the feed well and the deflector cone are leveled. If the feed well weir plates are leveled properly. It is also important to ensure that: The feed well weir plate to be only 10
25 mm lower than the overflow weir plates for smooth autodilution. Underflow arrangement: It is important that the underflow piping is correctly sized and for most of the applications, it is safer to size this at a velocity of 1.2 m/s. Oversized underflow pipes will create a major problem in operations, particularly for the fast-settling solids like Iron ore concentrate. The cross-sectional velocity of the underflow slurry should be always higher than the critical settling velocity of the particle and if this condition is not met, the solids start to settle during pumping and the pipelines get choked over a period. Typical process parameters in thickening operation are:

G G G G G G G G G

Flow rate of feed, solids and liquid. Overflow water flow rate. Overflow turbidity. Underflow density of thickened sludge. Underflow sludge flow rate. Rake position. Rake power and torque. Flocculant dosage rate Bed mass and its level.

The drawing of a control system for a thickener section is shown in Fig. 1.5. Usually the following control loops exist to control thickener performance: 1. Bed level with flocculant dosage. If bed level is higher, flocculant dosage is increased and vice versa. 2. Bed mass pressure with the speed of underflow pump rpm. It is also required to monitor underflow density and flow, and torque.

48

Mineral Processing

1.19.5 Trouble shooting guide Underflow density

Bed level

Bed pressure

Polymer addition

Underflow pump speed

Above target

Rising

Increase

Increase

Steady

Increase

Increase

Falling

Increase

Increase slightly

Above target

Above target Above target Above target On target

Rising

Increase

Above target

On target

Steady

Above target Above target

On target Below target Below target Below target Above target Above target Above target On target

Falling Rising

Decrease slightly Decrease slightly No action Decrease

No action Increase

Steady

Decrease

Increase slightly

Falling

No action

Rising

Decrease slightly Increase

Increase

Steady

Increase

No action

Falling

Increase

Decrease slightly

Rising

Increase

On target On target Below target Below target Below target Above target Above target Above target On target On target

Steady Falling Rising

Decrease slightly No action No action Decrease

No action Decrease slightly Increase

Steady

Decrease

No action

Falling

Decrease slightly

Rising

Decrease slightly Increase

No action

Steady

Increase

Decrease

Falling

Increase

Decrease

Steady Falling

Decrease Decrease

Below target Below target

Steady

No action Increase slightly Decrease slightly No action

Above target Above target

Above target Above target On target On target On target On target On target On target On target On target On target Below target Below target Below target Below target Below target Below target Below target

Falling

Increase slightly

Decrease Decrease

Coal beneficiation: theory and practice Chapter | 1

49

1.19.6 Horizontal belt filters Problems associated with HBF: G G

Partial blinding of filter belt. Choking or inoperative spray bar nozzles at both the front end (before slurry addition) and midway along the belt filter.

This indicates poor performance of belt filter with a large variation in moisture across the width of the filter. There is a clear relationship that the cake depth has with moisture content. Apart from cake depth, use of calibrated and verified moisture analyzer is essential. Belt speed also has a major effect on online moisture control. A 0% speed represents minimum belt speed, while 100% represents the maximum speed. As the belt speed increases the bed depth of coal fines decreases. As the belt speed approaches 35% of its maximum speed, the moisture content can be seen rising rapidly. Therefore, belt speed and bed depth parameters are to be judiciously adjusted for improved moisture content. Apart from the belt parameters, addition of flocculant- also has some positive effect on reducing moisture content. Both manual sampling and online moisture analyzers are in use to measure the moisture content of the discharge cake. There is currently no easy way to know the best approach for moisture analysis. Traditional practices usually involve a manual sample being taken directly from the belt discharge every two hours. Not only is the sample a “snap-shot” sample, but the analysis results can take up to 4 h to be received by the operator. By this time, the operation of the belt filter can and usually does change considerably. However, online instrument measuring belt filter moisture provides effective control strategies. The standard moisture analyzer is a low level nonionizing microwave radiation. The microwave power emitted is less than 10 mW (10 dBm), which complies with AS/NZS 4268 (specifies the maximum equivalent isotopically radiated power for short range radio equipment). The analyzer could be used in industry for more effective means to monitor product quality and efficient use of flocculant. The control strategies for optimum belt filter control will vary considerably depending upon the objectives of each operation. Not all plants may require the lowest moisture possible, as some operations will consider throughput and flocculant usage as equally important parameters. There may even be the case of wanting the product to be of higher moisture content to meet client specifications.

1.19.7 Wet drum magnetic separator Feed preparation and characterization is critical to the optimal operation of wet drum magnetic separator. When considering feed preparation and characterization, the following parameters have the greatest impact:

50 G G G G

Mineral Processing

Feed slurry density. Feed particle size distribution. The proportion of magnetic material in the feed solids. The distribution of the feed slurry to the magnetic separator.

1.19.7.1 Feed slurry density Feed slurry density affects volumetric capacity, viscosity, and magnetic flocculation. If the feed slurry density is too low, then the volumetric capacity of the wet drum magnetic separator is likely to be exceeded. Another impact of low slurry density is on magnetic flocculation. Low density means fewer particles present in the slurry, which in turn reduces the probability of magnetic flocculation for ferromagnetic particles. This is critical for dense media recovery, which relies on the magnetic flocculation for the recovery of the very fine magnetite and ferrosilicon particles. A high-feed slurry density increases slurry viscosity. The impact of increased viscosity is an increase in entrainment of nonmagnetic particles in the magnetic concentrate Therefore, if a clean magnetic concentrate is required then lower feed slurry densities will be required. In dense media recovery, the magnetite and ferrosilicon slurries have a high viscosity, which is why the maximum allowable density is relatively low. 1.19.7.2 Magnetics content of feed particles The proportion of magnetic material in the feed solids has a great impact on the performance of wet drum magnetic separator. The capacity to remove the magnetic concentrate is directly related to the magnetics content in the feed and this needs to be balanced to prevent loss of magnetics. In the case of dense media recovery, with magnetite and ferrosilicon being ferromagnetic, the high magnetic content in the feed ensures a high probability of magnetic flocculation, which ensures high recovery. If the maximum feed slurry densities are not exceeded, then magnetic removal will not be a problem, provided the overall solids and volumetric capacities are not exceeded. There must be .50% magnetics in the feed, otherwise there will be insufficient magnetic flocculation. Insufficient flocculation results in loss of high magnetics which is generally ,2% in dense media circuits. 1.19.7.3 The distribution of the feed slurry to the magnetic separator The capacity of a wet drum magnetic separator is fundamentally a function of drum diameter and drum width. Full capacity utilization then depends on distributing the feed across the full width of the drum. This means that if the full drum width is not used, it will affect the performance of the magnetic separator as a part of the drum will be overutilized. To ensure even distribution of feed over the drum, the feed manifold needs to be fully opened. This

Coal beneficiation: theory and practice Chapter | 1

51

ensures that the slurry velocity inside the manifold is sufficient to prevent settling out of solids, which is particularly critical for magnetite and ferrosilicon.

1.19.7.4 Dense media recovery: single stage versus two stages Where two stage circuits are installed, it would make more sense to split the feed between the primary and secondary separators. This way, both separators would contribute to media recovery effectively and the volumetric feed flow rate to both separators would have been essentially halved. Both separators will have increased volumetric capacity, with more flexibility to cope with feed volume fluctuations. The case for single stage dense media recovery circuits is further supported by using wet drum magnetic separators with a counter-rotation tank configuration together with a radial magnet assembly configuration in the drum. These two aspects further maximize recovery of the magnetics. 1.19.8 Troubleshooting 1. Low recovery of magnetite Low Level of magnetite slurry Decrease tails discharge diameter until approximately 1/4" flows over the overflow weir. 2. Very dry concentrate If concentrate is dry, rotate magnet toward discharge. If concentrate is dilute, rotate magnet toward feed end. 3. Operating gap too large Readjust drum positioning to correct gap. 4. Low magnetite content in feed Cannot normally be adjusted (common secondary separators). 5. Flooding over sides of tank: Too small tails discharge diameter. Increase tails discharge diameter until approximately 1/4" flows over overflow weir. 6. Feed solids too high Increase the operating gap and recheck overflow. 7. Drum positioned too near feed end Reposition the drum. 8. Blockage under the drum Can be checked by passing a piece of rubber belt under drum and moving it from side to side. If blockage is found, raise drum and remove. 9. Low concentrate gravity In this case, just by pass the slurry to feed tank of magnetic separator and add more magnetite powder to the system.

52

Mineral Processing

10. Magnet position too high Reposition the magnet. 11. Water level high Readjust the tail bushings size. 12. Discharge gap too wide Move the drum forward. 13. Uneven distribution of magnetics on discharge Drum is not parallel to discharge gap. 2 2 2

Readjust the drum position. Tank and drum are not at the same level. Shim the legs until level. Blockage under the drum. Check and remove.

1.20 Conclusions In summary, for coarse coal cleaning, the two main processes are DM separation and jig washing. DM processes are capable of very accurate separation and are favored in many western industrialized countries. A Large-diameter DM cyclones, as mentioned earlier are capable of treating a wide range of sizes in a single unit. This has helped simplify the operation and reduce the costs of DM plant. However, jig washing also remains popular because of its low capital cost and perceived ease of operation. Another notable development has been the ROM jig, which has attracted interest, particularly in India, for the deshaling of large coal. Perhaps the most significant development in fine coal cleaning has been the introduction of fine-coal density separators. Two processes now predominate, spiral concentration and teeter-bed separation. Both processes are finding wide applications globally and continue to be subjects for considerable R&D effort. Froth flotation continues to be a major processing technique for coal below B0.6 mm and is particularly predominant for the cleaning of ultrafine coal. The major development in this area has been the introduction of more selective flotation systems, including variants of column flotation and the Jameson cell. Several enhanced density separators have also attracted interest for ultrafine coal cleaning. However, although these have been applied commercially in the minerals industry, further development is required before they can gain commercial acceptance in coal preparation. One of the most significant recent developments in fine coal dewatering has been the introduction of high-speed scroll centrifuges. Vacuum filtration also remains a major dewatering option for coal below B0.5 mm and, in this area, HBFs have been gaining increasing popularity. Tailings treatment has seen a major improvement through the introduction of high-rate thickener/clarifiers, supported by the use of advanced

Coal beneficiation: theory and practice Chapter | 1

53

synthetic polymers to improve performance. Where further dewatering of tailings is required, the traditional choice has been the plate and frame filter press. The past decade has seen the increasing use of online monitoring and PLC systems for plant control. However, the majority of coal preparation plant still employ a mixture of manual and automatic monitoring and control. Further scope for automation is constrained by the need for improved sensors for online quality monitoring and by the need for improved logic-based control systems. One noteworthy addition in this respect is online washability analyzer with density tracers and Radio Frequency Identification (RFID) Detectors in Australia. Several development issues still face the coal preparation industry. These include the cleaning and dewatering of ultrafine coal, desulfurization of high-sulfur coals, development of reliable and accurate sensors for coal quality monitoring, and application of dry coal beneficiation processes for arid regions. With world coal production and use predicted to increase in the coming years, the indications are that the present level of R&D effort in coal preparation will continue or, indeed, increase in the future.

References Abbott, J., 1982. The optimisation of process parameters to maximise the profitability from a three-component blend. In: 1st Australian Coal Preparation Conference, Newcastle, Australia, April 6
10, 87
105. Clarkson, C.J., Wood, C.J., 1991. A model of dense medium cyclone performance. Coal Prep. 12(1
4), 101
115. Edward, D., Clarkson, C., 1999. Sampling statistics toolkit. ACARP Project C3090. Australian Coal Research Pty Ltd. Luttrell, G.H., Barbee, C.J., Wood, C.J., Bethell, P.J., 2003. Operating guidelines for heavymedia cyclone circuits. Coal Age 108 (4), 30
34. Luttrell, G.H., Catarious, D.M., Miller, J.D., Stanley, F.L., 2000. An evaluation of plantwide control strategies for coal preparation plants. In: Herbst, J.A. (Ed.), Control 2000. SME, Littleton, CO, pp. 175
184. Zhuping, C., Felicia, F.P., Syd S.P., Yi L., 2009. Application and Evaluation of Spiral Separators for Fine Coal Cleaning. West Virginia University, Morgantown.

This page intentionally left blank

Chapter 2

Iron ore beneficiation: an overview N.D. Rao1, D.P. Chakraborty2, Vishal Shukla3 and Neeraj Kumar4 1

Projects, Atha Group, Bhubaneswar, Orissa, India, 2Iron Making Technology Group, Process Technology Group, Tata Steel, Jamshedpur, Jharkhand, India, 3Ore Beneficiation Technology Group, Process Technology Group, Tata Steel, Jamshedpur, Jharkhand, India, 4Coal Beneficiation Technology Group, Process Technology Group, Tata Steel, Jamshedpur, Jharkhand, India

2.1

Introduction

The global steel industry is going through a development phase due to the increasing demand for steel. In India, at the current rate of GDP growth, the demand will increase and reach up to 300 MT by 2030. Yet, India’s per capita consumption would reach only 160
180 kg (current approximately 69 kg), which will be lower than the current global average of 208 kg. Hence, to meet the growing steel demand, the demand for iron ore is also increasing. While, on one side reserves of good quality iron ore are depleting, on the other side the steel companies require better quality of iron ore with lower gangue content due to the addition of higher capacity blast furnaces for higher productivity, lower hot metal cost, and lower CO2 footprint for sustenance. For example, if alumina content (gangue) in the blast furnace burden increases due to the inferior quality of iron ore, the slag viscosity increases, leading to higher fuel and flux demand, resulting in increased operating cost along with lower productivity and a higher carbon footprint. Currently, the general practice adopted by majority of steel companies has been the utilization of medium- to high-grade ore for iron-making process. This is mainly achieved by selective mining of high-grade ore, keeping the cut-off to approximately 55% Fe. However, due to the growing demand for iron ore, this is not sustainable; in India, the cut-off grade is now revised to 45% Fe by the Indian Bureau of Mines for hematitic and geothitic ores. Hence, the low-grade iron ore needs to be beneficiated to make the iron ore concentrate suitable for iron-making process. Thus, the main objective of processing/beneficiation is Fe enrichment, thereby reducing gangue content, especially alumina, which occurs in iron ore deposits across many conuntries like India. Mineral Processing. DOI: https://doi.org/10.1016/B978-0-12-823149-4.00003-X © 2023 Elsevier Inc. All rights reserved.

55

56

Mineral Processing

This chapter briefly discusses the current scenario of the following: iron ore resources in India, iron ore mining methodology, beneficiation techniques for various ore sizes, beneficiation tests and results for a typical Indian iron ore deposit and the current operating practices for achieving sustainable growth in the iron and steel industry.

2.2

Geology and occurrence

2.2.1

Indian iron ore resources

India is endowed with large resources of iron ore, which is estimated to be about 33.27 billion tonnes (as per the National Mineral Inventory, NMI) of both hematite and magnetite ores (Table 2.1). More than 95% of the total hematite resources of India are distributed in five states (Odisha, Jharkhand, Chhattisgarh, Karnataka, and Goa) with the balance in other states (Maharashtra, Madhya Pradesh, etc.). The state-wise distribution of major resource as per the NMI as on April 01, 2015 is given in Table 2.2, in their order of abundance. India is currently ranked fourth in terms of production of iron ore. Country-wise iron production figure (as per Mineral Commodity summaries, United States geological survey) is given in Table 2.3.

2.2.2

General geology

The Indian iron ore deposits can be broadly divided into the following six groups based on mode of occurrence and origin. 1. 2. 3. 4. 5. 6.

Banded iron formations (BIF) of Pre-Cambrian age Sedimentary iron ore deposits of siderite and limonitic composition Lateritic ores derived from the subaerial alternations Apatite-magnetite rocks of Singhbhum copper belt Titaniferous and vanadiferous magnetite Fault and fissure filling deposits

TABLE 2.1 Iron ore resources (approximate) as on 01.04.2015 (in billion tonnes) [7]. Ore

Reserves

Remaining resource

Total

Hematite

5.4

17.10

22.50

Magnetite

0.05

10.74

10.79

Total

5.45

27.84

33.29

Iron ore beneficiation: an overview Chapter | 2

57

TABLE 2.2 Statewise distribution(approximate) of hematite reserves/ resources of India (in million tonnes) [9]. State

Reserves

Remaining resources

Total resources

Odisha

2572

4987

7559

Jharkhand

439

4847

5287

Chhattisgarh

1387

3471

4858

Karnataka

550

1917

2467

Goa

358

831

1189

Andhra Pradesh

30

311

341

Madhya Pradesh

62

268

330

Maharashtra

17

277

294

Uttar Pradesh

0

58

58

Telangana

1

53

53

Rajasthan

5

34

38

Assam

0

13

13

Total

5422

17,065

22,487

Source: NMI as on 01.04.2015.

The most important hematite iron ore deposits of economic importance belong to Pre-Cambrian iron ore series. These occur in massive, laminated, friable, and powdery form and are within the BIF. BIF is found in the states of Odisha, Jharkhand, Madhya Pradesh, Chhattisgarh, Maharashtra, Karnataka, and Goa. The Pre-Cambrian banded iron ore formations are grouped into five major zones (refer Table 2.4). The quality of Indian iron ore resources is generally good with high iron content and high percentage of lumpy ore. More than 85% of the hematite ore reserves are of medium- to high-grade (162% Fe) and are directly used in blast furnace and in direct-reduced iron (DRI) plants in the form of sized lump ore, agglomerated sinter, and agglomerated pellets (Iron and SteelVision, 2020). However, the quality is gradually deteriorating (the iron content is decreasing while the gangue content is increasing) due to the high demand for iron ores and mechanized mining. Moreover, there are statutory guidelines to utilize all resources above 45% Fe. In the low-grade iron ore deposits (45%
55% Fe), there is a complex association of gangue mineral with Febearing minerals, which makes it challenging to beneficiate the iron ore concentrate as per downstream requirement.

58

Mineral Processing

TABLE 2.3 World Mine Production and Reserves [8] (approximate)—US Geological Survey, Mineral Commodity Summaries, January 2022. Country

Mine production Usable ore

Reserves

Iron content

(Billion metric tons)

2020

2021e

2020

2021e

Crude ore

Iron content

Australia

912

900

565

560

51

25

Brazil

388

380

247

240

34

15

China

360

360

225

220

20

7

India

204

240

127

150

6

3

Russia

100

100

70

71

25

14

Ukraine

79

81

49

51

7

2

Kazakhstan

63

64

13

13

3

1

Canada

60

68

36

41

6

2

South Africa

56

61

35

39

1

1

Iran

50

50

33

33

3

2

United States

38

46

24

29

3

1

Other countries

165

198

102

129

22

12

World total

2474

2548

1526

1576

179

85

2.3

Mining methods

Generally, a mechanized method of open-cast mining has been adopted for mining iron ore in a series of 12-m-high benches with the help of a shovel
dumper combination. The minimum bench width is maintained at 25 m in the working benches while the bench width shall be reduced to 12 m in the ultimate stage, thus having a final pit slope, which is less than 45 degrees due to strata conditions. The bench height depends on various factors such as production required, disposition of ore-body, geological disturbances, machinery sizes to be deployed, etc. The bench width depends mainly on the size of the machinery deployed and is approximately three times the width of dumper. The length of face is dependent on factors such as output required, variation in grade, blending requirement, contours of the deposit, etc. (Challenges of Indian iron ore industry, geology).

Iron ore beneficiation: an overview Chapter | 2

59

TABLE 2.4 Zone-wise characterization of Indian iron ore [1]. Zone

Location

Nature of mineralization

A

Bonai Iron ore ranges in Jharkhand and Orissa and in adjoining areas in eastern sector

G

N-S trending linear belt in Central India in the States of Chhattisgarh, MP and East MS

G

Bellary
Hospet region of Karnataka

G

B

C

G

G

G

BHQ/BHJ formations Mineralization occurs as massive ore (58%
66% Fe), laminated ore, shaly ore, and blue dust (64%
68% Fe). Associated with BHQ Mainly laminated and massive ore of high-grade hematite (64%
68% Fe) BHQ/BHJ intercalations of ferruginous shale Long, narrow, and scattered patches of hematite (58%
64% Fe)

D

Goa and west Maharashtra

G

Predominantly (nearly 80%) blue dust (63%
64% Fe) and fines (59% Fe) with little lumps (57%
58% Fe)

E

Magnetite deposits of Karnataka

G

Occurs as thick bands and lenses of hematite/magnetite in BHQ/ BMQ formations (57%
62% Fe) Quartz is associated gangue

G

Drilling is done generally using 150/165 mm diameter drills with 10% subgrade drilling. The pattern of blast holes is governed by the hole diameter, bench height, drilling machinery, nature of the rock, and the type of explosives used (Srivastava and Chikhale, 2013) based on powder factor required by the lessee. Blasting is performed by adopting the state-of-art technology by mostly using site mixed emulsion explosives. Nonel (nonelectric initiation) and electronic detonators are used for blasting. The blasted material is transported using shovel
dumper combination. Rock breaker is utilized to break the oversize material [more than 500
1000 mm guided by primary crusher design for run of mine (ROM) crushing] generated during blasting into smaller fragments. Rigorous quality control procedure is adopted in the mine to avoid mixing of ore, subgrade, and waste. Blasthole drill cuttings are sampled and analyzed in the laboratory using inductively coupled plasma spectrophotometer/X-ray fluorescence spectroscopy for determining iron and other elements. Depending on the analysis results, mine face is demarcated as ore, subgrade or lean grade, and waste (ore burden) zones and daily schedule for the material hauling is prepared accordingly. The subgrade ore is stacked separately at the earmarked place. Waste rocks encountered during mining are handled separately and used for bench

60

Mineral Processing

floor leveling, making berms, etc. The ore is transported from different mining faces in a predetermined proportion (for blending different qualities of ore) and delivered it to the processing plant. The haul roads are maintained with a gradient of less than 1 in 16, except for short ramps, which have a maximum gradient of 1 in 10. The floor level of each bench is maintained by employing graders and dozers. This helps in the easy, safe, and efficient mobility of heavy earth-moving machinery. Dust suppression in haul roads is done with the help of mobile water sprinklers and/or with fixed water sprinklers of approximately 1.5 km in length. Drills are operated with in-built dust extraction/suppression system.

2.4

Beneficiation methods

Beneficiation is a process where ore is reduced in size and valuable minerals are separated from the gangue minerals. Separation of valuable minerals from gangue minerals can be efficiently achieved by taking advantage of the differences in physical, surface, and magnetic properties. Suitable beneficiation methodology for iron ore is mainly dependent on its mineralogy and its nature. However, due to specific mineralogical characteristics (varies significantly with deposit), beneficiation process may differ for different type of deposits. Several techniques, such as wet-scrubbing, jigging, magnetic separation, gravity concentration, froth-flotation, selective flocculation, etc. are used to enhance the Fe content and reduce the gangue content of the ore. These techniques are employed in varying combinations to beneficiate iron ore to the required grade in order to develop a cost-effective process flowsheet. While selecting a proper flowsheet, emphasis is usually to maximize the recovery at the coarsest possible size. This is mainly because of the following two reasons: G G

Processing cost is generally inversely proportional to the liberation size Ease of transportation (for very finer size slurry transportation is required)

2.4.1

Selection of beneficiation flowsheet

The steps involved in the selection of beneficiation techniques are described below. For better understanding, a typical test work result is given as an example. G

Characterization study: The first step in the selection of a beneficiation flowsheet involves the detailed characterization study of the iron ore deposit for which beneficiation flowsheet is being developed. This study investigates the composition/distribution, texture, elemental distribution, liberation study of the minerals, and comminution and physical competency tests of ore.

Iron ore beneficiation: an overview Chapter | 2

61

TABLE 2.5 Mineral abundance of iron ore deposit.

G

Mineral

Mass percentage

Hematite

58
89

Goethite

8
26

Magnetite

0

Quartz

2

Kaolinite

0.5
3

Limonitic material

1
12

Gibbsite

1

Study of minerals composition/distribution: The second step indicates proportion of the desired and undesired minerals in the ore. It also provides the mode of association between gangue and the desired minerals. The mineral distribution of a typical iron ore deposit in Eastern India is given in Table 2.5.

From Table 2.5, it can be seen that the major iron-bearing minerals are hematite and goethite. Among these, hematite is the most prominent iron-bearing mineral followed by Goethite. The gangue minerals are mainly kaolinite, gibbsite, and quartz. They are associated mostly with goethite and limonite. Limonite is present as an amorphous clay coating surrounding other minerals with high iron content. It was also noted that the kaolinite that is present has varying iron content (from 4% to 16%). In this type of iron ore deposit, the focus is mainly to economically reduce alumina to the maximum possible extent. Hence, the distribution of the minerals was also studied. This also iron ore samples to be identified as low, medium, and high alumina grades. The study indicated that when kaolinite and limonitic material were removed, the alumina grade would remain below 2%, which would meet the customer requirement. However, for ironmaking, the preferred alumina grade is below 0.5%.

2.4.1.1 Liberation study The next step was to identify the size at which valuable minerals would be free of association with gangue minerals. The above-mentioned iron ore samples were subjected to a liberation study. The iron samples were found to be approximately 85% liberated at 1 mm size. The nonliberated particles predominantly contained a matrix of limonitic material impregnated with hematite, goethite, kaolinite, and gibbsite (refer Fig. 2.1).

62

Mineral Processing

FIGURE 2.1 QEMSCAN image (Limonite).

Limonitic material was found to be easily washable as cracks/pores could be seen within the particles. Scrubbing or attrition would break down the clays and enrich the concentrate. No goethite mineral was found to be liberated above 50 μm as it was mostly finely disseminated within hematite particles. Hence, to significantly reduce alumina below 2%, alumina-bearing goethite mineral had to be liberated, which required grinding below 50 μm. It was found that a target alumina of approximately 2% can be achieved by the removal of kaolinite and limonite minerals only.

2.4.1.2 Comminution and physical competency tests This study is needed for selection of size-reduction equipment such as crushers and grinding mills. It includes abrasion test, bond work index tests, and tumble test. G

G

Abrasion and impact crusher work index test: Test work was conducted with the iron ore samples from the same mines with the results displayed in Table 2.6. Tumble test work: Test work was performed on the 5
18 mm (CLO for DRI making) or 8
32 mm lump product and determine whether it could be classified and processed as lump iron ore. Tumbler index for friable ore sample was found to be 72 and the results were less than the required

Iron ore beneficiation: an overview Chapter | 2

63

TABLE 2.6 Abrasion and crusher work index results. Tests

Results

Abrasion index

0.07

Bond impact crusher work index

5.1

tumbler index of more than 85 (suitable for blast furnace burden). Hence, it was decided that the lump ore from the deposit was not suitable for use.

2.4.1.3 Beneficiation study The beneficiation methodology includes processes that improve the physical, chemical, and metallurgical characteristics of iron ore concentrate that makes it desirable for iron-making processes. Such methods include size reduction or comminution, scrubbing, classification, gravity concentration, magnetic separation, flotation, dewatering-filtration, etc. 2.4.1.4 Crushing and grinding First step in the process is crushing and grinding coupled with wet or dry size-classification of run of mine (ROM) ore. This is required to prepare feed for beneficiation of ore. Final product size may depend on ROM characteristics (obtained by characterization study) and the requirement of iron
steel making process both in terms of size and quality. In this iron ore deposits (mentioned above), the iron ore was crushed using three stages of crushing to a size below 32 mm and then was subjected to beneficiation. Primary and secondary crushing was done by gyratory crushers. For sticky iron ores with a high clay content, primary and secondary sizers were also used instead of gyratory crushers. Tertiary crushing was done utilizing short-head cone crushers in a closed circuit. Generally, grinding to a very fine size, below 150 μm using a combination of rod and ball mills may be required if the liberation size was very fine to achieve the desired product quality, which was not the case with this iron ore deposit. However, for friable/soft, where the bond work index is below 10 KWh/s Ton, prevention of ultra-fines generation is very challenging. Unlike the harder ores, where throughput of the grinding mills is a challenge, for softer ores (e.g. Odisha & Jharkhand regions of India) overgrinding is a challenge resulting in excessive generation of ultra-fines with very high Blaine nos. This also has to be taken into account during the selection and design of grinding mills. The capital and operational costs of crushing and grinding processes are substantial. Hence, economics play an important role in determining the extent of crushing and grinding to be carried out on the ore for beneficiation.

64

Mineral Processing

Along with this, for very fine products, slurry pipeline is the only suitable option for transportation of ore from mine site to steel plant. For slurry transportation of iron ore, 100% of particles must be ground below 225 μm and 60%
90% of particles must be ground below 40 μm. Percent solids (w/w) of the slurry should be in the range of 60%
70%.

2.4.1.5 Beneficiation test The main objective of a test work program is to develop a process flowsheet that would be flexible enough to accommodate variations in ore feed grade as well as ore type and to maximize recovery at targeted grade of concentrate with the coarsest possible particles size. Ore from the mines is generally crushed, scrubbed and its assay analysed. For example, for a typical Indian iron ore that is used in ironmaking, the ore is a. Crushed below 32 mm size and subjected to wet-scrubbing (for 3 or 5 min) to segregate adhered clay particles from the coarser fractions. Then, assay analysis was conducted on different size fractions. The measured head grades of the samples analysed FeB55%, Al2O3B8%, and SiO2B7.5%. Beneficiation process generally differs for different size fractions.

2.4.1.6 Beneficiation of coarser (11 mm) fraction Coarser fraction (i.e., 11 mm fraction) is generally beneficiated using gravity concentration process. The process utilizes difference in gravity of the gangue minerals and valuable minerals for beneficiation. However, due to the prevalent-hindered settling condition, the size range of the particles has a very high impact on separation efficiency through gravity concentration. Hence, lighter gangue minerals of coarser size may report to concentration despite differences in density. Because of this potential problem, particle sizes must be kept in a narrow band range to minimize any potential misplacements due to differences in size and maximize the effect of density during the concentration process. Several gravity concentration methods have historically been used for beneficiation of coarser fraction in iron ore namely (1) jigging and (2) heavy-media separation. 2.4.1.7 Jigging This is a process in which particles of different densities are stratified by the repetitive pulsation of water, owing to the difference in a relative velocity of particles in water. Heavier iron ore minerals move down the deck and the lighter gangue particles move to the top of the bed. Bed height is adjusted based on the cut density or desired product quality. Jigging tests are conducted in Mineral

Iron ore beneficiation: an overview Chapter | 2

65

Density Separator (MDS) or laboratory jigs to establish the amenability of beneficiation through jigs.

2.4.1.8 Heavy-media separation This is a process in which particles of different densities are stratified based on the “sink
float” principle in a suspension of fine ferrosilicon as a separation medium. Lighter gangue mineral particles report to “float” whereas denser iron-bearing minerals settle in “sink.” The separation vessels are selected based on the liberation size and capacity. Commonly used heavymedia separators are dense medium drum and dense-media cyclones. Media are recovered utilizing magnetic separators from the sink and float products. Recovered media are recirculated to the system. Test work for these separators is done using Heavy Liquid Separations (HLS) test. 2.4.1.9 Beneficiation test of coarse (e.g., 232 1 8 mm) material Beneficiation test for this fraction is done separately using MDS and HLS keeping in mind the targeted product Fe percentage and alumina in the coarse product. The results obtained in one of these tests are provided in the diagram below for reference (Fig. 2.2). From the above diagram, it can be observed that HLS test results were marginally better than the MDS test results. In this scenario, jigging is a preferred process route, because of lower operating costs and ease of operation. The tailings produced during jigging of this fraction can be reprocessed through crushing
grinding, thus improving the liberation size and retreating in the fines circuit to increase the overall yield.

4.0

70

3.5

60

3.0

50

2.5

40

2.0

30

1.5

20

1.0

10

0.5

0

0.0 3.4

3.6

3.8

4

4.2

cut s.g. Jig yield

DMS yield

Jig product Fe grade

DMS product Fe grade

Jig product Al2O3 grade

DMS product Al2O3 grade

FIGURE 2.2 Jigging and DMS test results on 8
32 mm fraction.

4.4

Al2O3 grade (%)

Mass yield/Fe grade (%)

8-32mm results 80

66

Mineral Processing

Generally, Dense Media Separation (DMS) process is more efficient, but is less preferred owing to operation difficulty and higher operating cost (increased media consumption in Indian iron ore due to higher porosity). They are generally preferred over jigging if gain in yield offsets the high operating cost in DMS operation. For one of the flowsheets, it was observed that with 4% extra yield, DMS process could become economically viable over than the jigging process.

2.4.1.10 Beneficiation test of intermidate size (28 1 1 mm) material Beneficiation test for this fraction can be conducted using MDS and HLS tests. A typical test resut on an Indian ore showed that it was possible to obtain a product with the desired Al2O3 grade during MDS as well as HLS tests. HLS test work was conducted on a 28 1 1 mm sample whereas MDS test work was conducted on a 28 1 3 mm as well as a 23 1 1 mm size fraction to increase the efficiency of the jig (maximize recovery). Some reference cumulative results obtained on these fractions are given in Fig. 2.3. The results thus obtained were compared in terms of overall grades, recoveries, and yields. It can be observed that the difference in yields between DMS and jigs are higher than for the lumpy fraction. 2.4.1.11 Beneficiation of finer (21 mm) fraction In such type of deposit, finer fraction is generally beneficiated using combination of gravity concentration, magnetic separation, flotation, selective flocculation, etc. Decision is taken based on the ore characteristics, liberation study, and targeted product quality. Spirals and teeter-bed separators (TBS)

FIGURE 2.3 Jigging and DMS test results on 1
8 mm fraction.

Iron ore beneficiation: an overview Chapter | 2

67

are generally preferred for gravity concentration. Wet high-intensity magnetic separators (WHIMS) and high-gradient magnetic separators (HGMS) are used for magnetic separation. Reverse flotation is generally used for siliceous type ores. Ultra-fine magnetic separators and selective flocculation are selected in a special case for iron recovery from ultra-fine particles (210 μm) when there is a significant iron loss in this size fraction even after adopting the conventional beneficiation process routes.

2.4.1.12 Spirals Spiral concentrators are flowing film separation devices. General operation is a continuous gravitational laminar flow down on an inclined surface. The mechanism of separation involves primary and secondary flow patterns. The primary flow is essentially the slurry flowing down the spiral trough under the force of gravity. The secondary flow pattern is radial across the trough. Here, the upper-most fluid layers comprising higher-density particles move away from the center, while the lower-most concentrate layers of higherdensity particles move towards the center. A band of iron mineral forms along the inner rim, and the gangue forms bands toward the outer rim. Splitters are adjusted along the inner rim to collect and remove the heavier iron minerals. The lighter gangue minerals remain in the spiral and discharges at the bottom (https://www.ispatguru.com/processes-for-beneficiation-of-iron-ores/) (Fig. 2.4).

FIGURE 2.4 Distribution of iron and gangue bearing particle on spiral concentrator.

68

Mineral Processing

2.4.1.13 Teeter Bed Separator (TBS) TBS is a kind of hydro-classifier wherein feed settles against an evenly distributed upward current of water. The feed material builds into a bed within the cell, creating a teeter zone. The lighter material overflows into the upper launder while heavier particles are not supported by the upward current water settles out of the teeter zone and is discharged at the bottom of the cell. 2.4.1.14 Wet High Intensity Magnetic Sseparators (WHIMS) It utilizes difference in magnetic susceptibility of valuable minerals and gangue minerals for separation. Magnetic susceptibility test is first conducted in Davis tube or Frantz isodynamic magnetic separator before selecting the equipment for flowsheet development. In WHIMS/HGMS iron ore slurry is introduced to a matrix (selected based on feed particle size distribution) where the paramagnetic particles are entrapped and are subsequently demagnetized and flushed with clear water to the magnetic concentrate trough. The nonmagnetics pass through the matrix to the nonmagnetics collection hoppers (Fig. 2.5). 2.4.1.15 Multigravity separator (MGS) Multigravity separator (MGS) can be visualized as rolling the horizontal surface of a conventional shaking table into a drum, then rotating it so that many times the normal gravitational pull can be exerted on the mineral particles as they flow in the water layer across the surface. High revolutions per minute ranging between 90 and 150 rpm, enable forces of between 5 and 15 g to be generated at the drum surfaces (Wills and Napier-Munn, 2016), leading to an efficient separation of the heavier particles from the lighter particles even for very fine particles.

FIGURE 2.5 Schematic and the pilot set up of the HGMS test work at Tata Steel Ltd.

Iron ore beneficiation: an overview Chapter | 2

69

2.4.1.16 Reverse flotation Flotation utilizes the difference in surface properties of gangue and concentrate minerals for separation. For iron ore floatation, reverse flotation is generally preferred where siliceous minerals are floated and iron-bearing minerals are generally depressed. Flotation process is generally less costeffective and more operationally challenging than the magnetic separation process. Reverse floatation is generally not preferred for the iron orecontaining gibbsite as the major gangue mineral (Fig. 2.6). 2.4.1.17 Beneficiation test of 21 mm fraction For beneficiation of 21 mm fraction wide combination of processing equipment can be a possibility. The 21 mm material (natural fines and the ground products from the jig reject generated from the beneficiation test of 11 mm fraction) was first subjected to a TBS test. Since the targeted product grade was achieved, it was decided to use a TBS as the primary processor. The TBS overflow and underflow were then subjected to various laboratory-scale processes such as spirals, MGS, WHIMS, flotation, etc. From the results, a combination of TBS and spirals was found to be the most suitable option for beneficiation of the 21 mm 1 75 μm fraction. Rejects from the TBS- spiral units were ground to the required liberation size and were mixed with the naturally generated 275 μm fraction for beneficiation in magnetic separators. The results from flotation tests on the sample were not encouraging and hence were not selected. Dewatering tests were then conducted on the final concentrate and tailings for selection of thickeners and filters. The final conceptual process flowsheet based on the results of the test work is shown in Fig. 2.7.

FIGURE 2.6 Column flotation pilot set up for iron ore beneficiation at Tata Steel Ltd.

70

Mineral Processing

FIGURE 2.7 Final conceptual flowsheet developed after beneficiation test.

2.5

Operating practices

Iron ore processing operating practices vary depending upon the the quality of iron ore deposit. For high-grade ore, dry- or wet processing can carried out and for low-grade ore beneficiation is needed to make it suitable for iron making. Typical flowcharts for processing different types of deposits and their usage is given in Fig. 2.8.

2.5.1

Processing of high-grade ore

The high-grade iron ore is defined in terms of iron content. In general, cutoff iron content of ROM for such type of ore is kept at approximately 55%, which is obtained by selective mining. The ROM ore is subjected to dry/wet processing through multistage crushing and screening for production of lumps (240 1 10 mm) and fines (210 mm). In the Indian scenario, the processing cost of high-grade ore, including mining varies from Rs. 400
500 per ton of product. This excludes the government levies and logistics costs. The production cost depends on many factors such as stripping ratio, degree of processing, plant yield, etc. 1. Dry processing of iron ore: In dry processing of iron ore, ROM is generally crushed below 40 mm through three-stage crushing and thus segregated by screening into 10
40 and 210 mm fractions. For softer ore, tumbler index is generally low and hence lump ore is crushed below

Iron ore beneficiation: an overview Chapter | 2

ROM

Magnetite

-

Hematite

High Grade Ore

-

71

Limonite

Low Grade Ore

Beneficiation

Crushing Screening

Comminution Screening Desliming Dewatering

Comminution Upgrading Dewatering

Products

Lump

Fines

Concentrate

Agglomeration

Sinter

Pellete

Iron Making

Blast Furnace

Direct Reduction

FIGURE 2.8 Flowchart for processing of High-Grade and Low-Grade Ore.

10 mm to produce 100% fine product. Yield from the plants has been generally 100% as no waste is discarded from such plants. Hence, the product grade is equivalent to the feed grade. Dry-processing flowsheet of dry plant of Joda iron ore mines, Tata Steel Ltd is depicted in Fig. 2.9. 2. Wet processing of iron ore: The ROM is crushed below 40 mm through three stages of crushing. Primary and secondary circuits are open circuits and generally utilize gyratory crushers for crushing, while tertiary crushing is through the short-head cone crusher, which generally operates in the closed circuit. This ore is processed in a wet drum scrubber. The 240 1 10 mm fraction is recovered as sized ore. The 210 mm fraction of the tertiary crushed product is sent to screw classifiers. In the screw classifier, the 210 mm fraction is classified to yield two products viz 210 1 0.15 mm (as underflow) and 20.15 mm (as overflow). The coarser fraction (i.e., 210 1 0.15 mm) is then sent to dewatering screens to drain off the excess moisture in the fines. The 210 1 0.15 mm product after screening is sent for jigging or may be taken out as a product directly depending on the feed grade. Jigging concentrate is taken as fines concentrate. The finer fraction (i.e., 20.15 mm) as classifier overflow is sent to the hydrocyclones for further classification. Hydrocyclones underflow (20.15 1 0.05 mm) is mixed in the fines concentrate. Hydrocyclone overflow is then sent to the thickeners. The slurry is thickened in the thickener and pumped to the tailings dam. Wet-processing flowsheet of wet plant of Noamundi iron ore mines, Tata Steel Ltd is depicted in Fig. 2.10.

72

Mineral Processing

FIGURE 2.9 Dry plant process flowsheet of Joda iron ore mines.

FIGURE 2.10 Wet plant process flowsheet of Noamundi iron ore mines.

Iron ore beneficiation: an overview Chapter | 2

2.5.2

73

Processing of low-grade ore

Flow-sheets for low-grade ore processing of different iron ore mines vary significantly; however, the underlying principle of operation is very similar. Methodology for selection of beneficiation flowsheet is already defined in the above sections. For beneficiation of coarser fraction (11 mm), jigging is widely used. However, in some cases, dense media separators are also deployed. For 21 mm fraction, different combination of spirals, hydrosizers, WHIMS, etc. is generally used. Rejects generated from the 11 mm circuit are generally ground to improve liberation, and beneficiated in 21 mm circuit to maximize recovery. Typical beneficiation flowsheets of two different beneficiation plants have been provided below for reference.

2.5.3 Processing flowsheet of beneficiation plant of Tata Steel Minerals Canada Simplified processing flowsheet of concentrator of Tata Steel Minerals Canada (TSMC) has been given in Fig. 2.11. At the TSMC beneficiation plant, ROM is crushed below 8 mm using a combimation of sizers and cone crushers. The scrubbed ore is then fed to the beneficiation circuit. Coarser fractions (28 1 1 mm) are beneficiated in jigs. The circuit utilizes two jigs operating in parallel with a capacity of 150 t/hours each. They are designed to operate at an air pressure of approximately 0.5 bar and a water flow rate of approximately 900 m3/hr. Jig concentrate is then

FIGURE 2.11 Simplified processing flowsheet of Tata Steel Minerals Canada (TSMC) beneficiation plant.

74

Mineral Processing

dewatered in a centrifuge and considered as sinter fines. Rejects from the jigging are crushed in rod mills to below 1 mm. 1 mm fractions are beneficiated in the fines circuit, which consists of spiral and hydro-classifiers. Firstly, 21 mm fraction is fed to spirals, concentrate of which is fed to a hydro-classifier. Concentrate from the spiral hydro-classifier circuit is dewatered in a pan filter and is mixed with the sinter fines. Rejects from the spiral hydro-classifier circuit are ground in a ball mill and then beneficiated in WHIMS and this concentrate is dewatered in the drum filters and is used as pellet fines. WHIMS rejects are then discharged to a tailings thickener and the thickened slurry is discarded as tailings.

2.5.4 Processing flowsheet of beneficiation plant of Tata Steel Long Products Ltd Simplified processing flowsheet of beneficiation plant of Tata steel long products is given in Fig. 2.12. The beneficiation plant is designed to process less than 10 mm of low-grade iron ore fines. Low-grade fines fed to the plant are scrubbed and then classified into two size fractions, that is, 10.5 and 20.5 mm utilizing vibratory screens. The 20.5 mm fraction is deslimed in two stages using a combination of screw classifier and hydrocyclone in series to produce 2150 1 20 μm fraction (natural 200 TPH -10 mm

ROM FINES GROUND HOPPER

DAY BIN FINE SCREEN (present: 2 Nos.); O/S

REJECTS FROM JIGGING PLANT

SCRUBBER (2 Nos.)

40 TPH -10+0.5 mm

CYCLONE OVERFLOW FROM WASHING PLANT

U/S PRIMARY MILL (2 Nos.)

O/S

120 TPH -0.5 mm

SPIRAL STAGE - 1

VIB. SCREEN (2 Nos.) O/F IOWP

PRE CONC

TAILS

U/S SPIRAL STAGE - 2

O/F PMC (2. Nos.)

U/F

TAILS

U/F

CONC O/F

O/S

DSC (2 Nos.)

U/S

U/F

O/F

U/F

INTERMEDIATE THICKENER O/F

TAILS

TAILING THICKENER

HGMS (4 Nos.)

CONC U/F

SMC (2 Nos.) SECONDARY BALL MILL (2 Nos.)

O/F U/F CONCENTRATE THICKENER

FILTER (OPTIONAL) O/F

U/F

175 TPH: 63.5 a 64%Fe FILTER

SLURRY TANK (OPTIONAL)

FILTRATE

TAILINGS DUMP

SLURRY TANK

FILTRATE

BENEFICIATED ORF 1.30 MTPA PRODUCTION

WATER TANK FOR RECIRCULATION

FIGURE 2.12 Simplified processing flowsheet of Tata Steel long products Ltd beneficiation plant.

Iron ore beneficiation: an overview Chapter | 2

75

fines), 2500 1 150 μm fraction, and less than 20 μm fraction(tailings). Tailings are then discharged into a tailing thickener and the thickened slurry is discarded into the tailing pond. Oversize of the vibratory screen (i.e., 10.5 mm fraction) and 2500 1 150 μm fraction produced in screw classifier is processed through a closed circuit grinding mill to produce a product (size; 2250 μm). The 150
250 μm fraction material is beneficiated in the spirals. The 2150 μm fraction from the spiral rejects and naturally occurring 2150 μm fraction (produced as screw classifier overflow) is beneficiated in a HGMS. Concentrate from spirals and HGMS is then ground below 45 μm in a closed circuit secondary ball mill. The ground product is dewatered in disk filters and then the filter cake is sent to the pellet plant.

2.5.5

Processing route followed across other beneficiation plants

The selection of processing route depends on mineralogy of iron ore deposit and customer requirement. Benefications processes employed in iron ore beneficiation plants treating different iron ores are given in Table 2.7.

TABLE 2.7 Processing route followed across different beneficiation plants. S. no.

Mine

Mineral type

Process

1.

Meghataburu, Boiani (Jharkhand)

Hematite

Crushing (four stage), scrubbing, rinsing (four stage), classification, dewatering, cycloning, thickening & filtration

2.

Kiriburu, Bolani (Jharkhand)

Hematite

Crushing (four stage), scrubbing, rinsing (four stage), classification, cycloning, & thickening

3.

Barsua, Keonjhar (Orissa)

Hematite

Crushing (two stage), scrubbing, rinsing (two stage), screening & classification, jigging, dewatering, & thickening

4.

Donimalai (Karnataka)

Hematite

Crushing (three stage), rinsing (two stage), classification, dewatering, thickening, & filtration

5.

Essar Dabuna, (Orissa)

Hematite

Crushing, grinding, magnetic separation (HGMS), & allflux

6.

Bailadala No.14. Bastar (Chhattisgarh)

Hematite

Crushing (two stage), rinsing (two stage), classification, dewatering, & thickening (Continued )

76

Mineral Processing

TABLE 2.7 (Continued) S. no.

Mine

Mineral type

Process

7.

Dhaili, Durg (Chhattisgarh)

Hematite

Dry process, crushing & screening (two stage) followed by blending

8.

Rajhara, Durg (Chhattisgarh)

Hematite

Dry process, crushing & screening (two stage)

9.

Kudremukh (Karnataka)

Magnetite

Crushing, grinding, magnetic separation (LIMS), spirals, flotex density separation, & column flotation

10.

Sarda mines, JSPL

Hematite

Crushing, jigging, & magnetic separation

11.

Fomento, Goa

Hematite and magnetite

Crushing, log washer, & magnetic separation (LIMS, MIMS, & HGMS)

12.

Sesa Goa

Hematite

Crushing, log washer, & magnetic separation (WHIMS)

13.

Sishen mines and Kumba iron ore mines, South Africa

Hematite

Crushing, jigging, dense-media separation (cyclones and baths), & allflux

14.

LKAB iron ore mines, Sweden

Magnetite

Grinding, magnetic separation, & flotation for removal of apatite

15.

Mount Whaleback mine, Newman, Australia

Hematite

Crushing, dense-media separation (cyclones and baths), and spirals

16.

Tilden mine (Cleveland cliff), Michigan, United States

Silicious hematite

Grinding, selective flocculation, and flotation

2.6

Summary

This chapter briefly discusses the current scenario of iron ore resources in India and future challenges emerging due to the depletion of high-grade ore reserves and a change in the ore cut-off grade to 45% Fe. Mining methodology for open-cast iron ore mine is also covered. Special focus has been given on the selection of beneficiation processes routes based on mineralogy for processing of low-grade iron ore, various steps involved in the test work along with the commonly used equipment in a commercial set up. A final recommended and operating process flowsheet for an iron ore deposit is also

Iron ore beneficiation: an overview Chapter | 2

77

provided. Moreover, current operating practices for processing of different types of iron ore have also been provided.

References Indian Bureau of Mines. Statistical Profiles of Minerals 2019
20. Mining & Mineral Statistics Division, Indian Bureau of Mines https://ibm.gov.in/writereaddata/files/ 12092021164614Statistical_Profile_2019-20.pdf. Iron and Steel-Vision, 2020. Ore Dressing Division, Indian Bureau of Mines https://ibm.gov.in/ writereaddata/files/06062017100713Iron%20and%20Steel%202020_2.pdf. National Mineral Inventory - An Overview- https://ibm.gov.in/writereaddata/files/04202018152229chapter%202_NMI.pdf. Srivastava, S., Chikhale, M. Challenges of Indian iron ore industry—geology, mining and processing perspective. In: 12th Brazilian Symposium on Iron Ore and 1st Brazilian Symposium on Agglomeration of Iron Ore, Belo Horizonte, Brazil, September 1
4, 2013. U.S. Geological Survey, 2022. Mineral Commodity Summaries. https://pubs.usgs.gov/periodicals/mcs2022/mcs2022.pdf. Wills, B.A., Napier-Munn, T., 2016. Mineral Processing Technology: An Introduction to the Practical Aspects of Ore Treatment and Mineral Recovery, seventh ed. ButterworthHeinemann, Oxford.

This page intentionally left blank

Chapter 3

Chromite ore beneficiation: prospects and challenges C. Raghu Kumar1, Y. Rama Murthy2 and Sharath Kumar Bhoja1 1

Raw material Technology, Process Technology Group, Tata Steel Ltd, Jamshedpur, Jharkhand, India, 2Ferro Alloys and new minerals research group, Research & Development, Tata Steel Ltd, Jamshedpur, Jharkhand, India

3.1

Introduction

Chromium is one of the most versatile and widely used elements. Its use in the metallurgical (about 50%), chemical (about 15%), and refractory (about 35%) industries is well known. It is an essential element in the production of a wide variety of stainless steels, tool, and alloy steel, nickel
chromium heating elements, and plating metals. Its widespread use in the metallurgical industry is attributed to its capability of enhancing properties such as resistance to corrosion or oxidation, creep and impact strengths, and hardenability. Chromium is one of the transition metals in Group VI of the periodic table. It is a very hard, crystalline steel-gray metal with an atomic number of 24 and a molecular weight of 528 g/cm3. Chromium has three common oxidation states, two of which Cr(II) and Cr(III) are basic and the other Cr(VI) is acidic. Chromium metal is an essential trace element, however, hexavalent chromium [Cr(VI)] is toxic and carcinogenic. Chromite is an important commercial chromium-bearing mineral. It is an oxide of chromium and iron (FeO, Cr2O3, or FeCr2O4). A complex mineral containing magnesium, iron, aluminum, and chromium in varying proportions depending upon the deposit. Iron is replaced by magnesium, similarly chromium by ferric iron and aluminum. The chromite mineral theoretically comprises 68% Cr2O3 and 32% FeO, however, Al2O3, Fe2O3, MgO, CaO, and SiO2 may displace some Cr2O3 content reducing as low as 40%. The chrome
iron ratio should be above 1 to 2.5 for the metallurgical grade. Chromium is an important metal, however, the pure metal is neither used by the stainless steel industry nor traded. Elemental chromium (Cr) does not occur in nature but is present in ores, primarily as chromite (FeOCr2O3). Around 90% of the mined chromite ore is converted into different grades of Mineral Processing. DOI: https://doi.org/10.1016/B978-0-12-823149-4.00004-1 © 2023 Elsevier Inc. All rights reserved.

79

80

Mineral Processing

ferrochrome, while about 80% ferrochrome produced of mainly high-carbon or charged chrome grade are consumed by stainless steel industry. Chromium imparts to alloys strength, toughness, hardness, and resistance to oxidation, corrosion, abrasion, chemical attack, electricity, and high-temperature breakdown. Consequently, it finds diverse applications. The great strength of chrome steel allows weight reduction of metal in automobiles, airplanes, trains, etc. Special chrome alloys yield hard, high-speed tool steel. Chromium plating has gaining more popularity than nickel plating. The chromite mineral is widely used in the furnace linings as refractory and is also used as chemical compound for dyeing, tanning, bleaching pigments, and oxidizing agent.

3.2

Ore genesis

The mineral deposits are of different types of complex formations and generally containing several ore and gangue minerals with difference in mineralogy, texture, size, and other features. The various processes knowledge that yield mineral deposits are fundamental to an understanding of mineral deposits and are susceptible of field classification according to the processes (Bateman and Jensen, 1981). The processes that have given rise to mineral deposits are 1. 2. 3. 4. 5. 6. 7. 8. 9.

Magmatic concentration Sublimation Contact metasomatism Hydrothermal processes Sedimentation Evaporation Residual and mechanical concentration Oxidation and supergene enrichment Metamorphism

Two or more of these processes together (either concurrently or at different times) form mineral deposits. Certain scarce constituents of magma may become concentrated into bodies of sufficient size and constitute valuable mineral deposits. Magmatic ore deposits are characterized by their close relationship with intermediate- or deep-seated intrusive igneous rocks and constitute either the whole igneous mass or form offset bodies. These deposits are also termed magmatic segregations, magmatic injection, or igneous syngenetic deposits. The early magmatic deposits resulted from straight magmatic processes have been formed by (1) simple crystallization without concentration, (2) segregation of early formed crystals, and (3) injections of materials concentrated elsewhere by differentiation. The primary magmatic segregations are early concentrations of valuable constituents of the magma that have taken place because of gravitative crystallization differentiation. The segregation may take place by the sinking of heavy early formed crystals to the lower part of the magma chamber or by

Chromite ore beneficiation: prospects and challenges Chapter | 3

81

constructional flowage. Chromite deposits have long been considered an impeccable illustration of early magmatic segregation and are generally lenticular and of relatively small size. Usually, they are disconnected pod-shaped lenses, stringers, and bunches. Unusually, they form layers in the host rock, and notably the case in the bushveld igneous complex of South Africa, where stratiform bands of chromite of remarkably uniform thickness lie parallel to the pseudostratification of the enclosing basic igneous rocks and can be traced for miles. Even more remarkable are other thin bands of chromite in the Merensky Reef horizon that contains economic quantities of platinum. The ore mineral of late magmatic deposits is later than the rock silicates, reacts with them and forms into a bay, and these ore bodies yielded before the final consolidation of the igneous body. The late magmatic deposits are predominantly combined with basic igneous rocks resulted from variety of crystallization differentiation, gravitative accumulation of a heavy residual liquid, liquid immiscibility, or other modes of differentiation. Chromite is also found in peridotite, anorthosite, and similar basic rocks. Chromite deposits formed at this late magmatic stage and crystallized with the silicates like plagioclase. According to Thayer (1956), all the early magmatic chromite deposits are of sufficient size to be of economic interest. He believed that primary chromite separated from a magmatic body with the first minerals to crystallize out and the formation of the late chromium-rich magmatic differentiates cannot easily be explained based on the available field data. The formation of a chromiumrich late magmatic liquid fraction is not possible according to the normal course of magmatic differentiation as evident from the order of isomorphs substitution in magmatic minerals. This is supported by Goldschmidt who stated, “when different ions of similar size and of the same charge (valency) substitute each other during the crystallization of minerals from cooling igneous rocks, the sequence for entrance of the various ions into the crystal lattices is generally the sequence of decreasing bond strength. The electrostatic bond strength in the case of identical electric charge is inversely proportional to the squares of the interionic distances; thereby, the smallest ion is bounded preferentially. Thus, magnesium ions are bonded before the somewhat larger ferrous ions. In those cases where electronic bonds are present besides ionic bonds, the integral sum of bond strength is decisive. Therefore, nickel is concentrated in the earliest fraction of magnesium silicates from magmas, even though nickel and magnesium have virtually identical ionic radii, and chromium spinel crystallized before other spinel minerals because of the contribution of electronic bonding in the minerals of trivalent chromium.”

3.2.1

Occurrence

Chromite, the only commercial source of chromium, is a spinel group mineral that occurs in ultramafic igneous rocks and further occurs exclusively in rocks formed by the intrusion and solidification of molten lava or magma,

82

Mineral Processing

which is very rich in the heavy iron-containing minerals such as pyroxenes and olivine. In addition, it is also found in metamorphic rocks such as some serpentinites. Pure chromite is a double oxide of iron and chromium with the formula FeO. Cr2O3. Considerable variation in composition occurs, however, due to partial substitution of divalent iron by magnesium and trivalent chromium and iron by aluminum. The chromium spinel may be described as (Fe, Mg)O. (Cr, Fe, Al)2O3. The chromium spinel is a heavy mineral and it is concentrated through gravity separation from most of the other molten material in the magma during the crystallization. Commercial chromite deposits are found mainly in two forms namely stratiform and podiform. G

G

G

G

Stratiform seams in basin-like intrusions, often multiple seams through repeated igneous injections. The best-known example of a stratiform deposit is the Bushveld igneous complex of South Africa. This complex contains most of the world’s chromite reserves. The stratified bands within the Bushveld igneous complex around Rustenburg and Lydenburg dip gently. The chromite stretch can be of kilometers and huge tonnages are present. The average grade is only 43% Cr2O3. The Great Dyke of Zimbabwe, traversing nearly the length of the country, is very similar and has been linked to the Bushveld in geological history. Other stratiform deposits occur in Madagascar and in the Odisha district of India. The high-grade deposits at Gwelo (includes Selukwe and Victoria, Lomagundi and Hartley) of Rhodesia occur near the amazing Great dyke, which is around 530 km long, averages 6.5 km in width and consists of layers of ultrabasic rocks now largely altered to serpentine. These layers dip toward the center from both sides and are having chromite bands of about 0.2 m thick that are analogs to the pseudostratification. Whereas, the deposits outside the dike are lenses in talc schists and serpentine. The podiform deposits are generally smaller but richer in chromium than the stratiform deposits and have high Cr: Fe ratios. The important deposits are around the Sverdlovsk region on the East side of the Urals, where they occur as magmatic segregation of lenses, stringers, and disseminations in serpentine and soapstone. Further, Turkey also contains several disseminated deposits, the most important ones occurring near Bursa (south of the Sea of Marmora) and along the south Mediterranean coast and are associated with altered ultrabasic intrusive. These ores are hard and of high quality (average 50%
52% Cr2O3). In Cuba, important refractory ores carrying 33%
43% Cr2O3 are found in Camaguey, Oriente, and Matanzas. There are also huge tonnages of low-grade chromiferrous nickel-iron ores in Mayari and Mao Bay. Small deposits of high-quality ore occur in the Mysore and Odisha states of India. The eluvial deposits have been formed by weathering of chromite-bearing rock and release of the chromite spinels with subsequent gravity concentration by flowing water (e.g., Andersons Creek, Beaconsfield district, West Tamar municipality, Tasmania, Australia) (Bateman and Jensen, 1981).

Chromite ore beneficiation: prospects and challenges Chapter | 3

3.2.2

83

Reserves of chromite deposits

World reserves of shipping-grade chromite are about 570 million tonnes in terms of chromite ore. Countries that possess sizeable quantities of reserves are Kazakhstan (40%) and South Africa (35%). These two countries together hold about 75% of the World’s chromite reserves. India possesses 18% and while the United States accounts for 5% of the world reserves of chromite. The available data on world reserves of chromite (shipping grade) is shown in Table 3.1 and the World shipping grade of chromite volumes by principal countries is tabulated in Table 3.2.

TABLE 3.1 Global chrome ore reserves (Mt). Country

Mt

1

South Africa

7340

2

Zimbabwe

930

3

Kazakhstan

387

4

Turkey

220

5

Finland

120

6

India

66

7

Brazil

17

Others

577

Source: Pariser, H.H., Indian Bureau of Mines, South Africa Department of Mineral Resources, Alloy Metals & Steel Market Research, Department of Mineral Resources, South Africa.

TABLE 3.2 Country wise shipping grade of chromite volumes. Country

Reserves (‘000 tons)

World: Total (rounded off)

5,70,000

Finland

13,000

India

1,00,000

Kazakhstan

2,30,000

South Africa

2,00,000

Turkey

26,000

United States

620

84

Mineral Processing

3.3

Mining

Owing to the stringently enforced laws for the conservation of depleting mineral resources, conservation has been the focus of the mining and mineralprocessing industry. Mining of chromite deposits is being carried out both by open-pit and underground mining. Early mining of chromite was on a smallscale and was relatively straightforward from outcrops or to shallow depths followed by hand sorting. With the increased demand, conventional open-pit mining and mechanical underground mining became necessary. Underground mining of stratiform deposits is most often required but can be particularly difficult due to the narrow seam thickness (less than 1.5 m), weathering close to the surface, and faulting and steep ore body. Open-pit mining is generally applied to the podiform ores at first but this progresses to underground mining as deeper levels of the deposit are reached. Huge quantity of raw chromite ore is being mined and beneficiated in various chrome ore beneficiation plants throughout the world to cater the customized needs of various end users. The mined high-grade lumpy ores are directed to Ferro chrome plant after sizing to the requirement of the metallurgical operation, while the lowgrade ore is processed through beneficiation plant/agglomeration plants. Deposit characteristics like ore strength, rock strength, deposit shape, deposit dip, deposit size, depth, ore grade, and ore uniformity determine the choice of mining method amongst other factors like production rate, relative cost sequence of development, cycle of operations, etc.

3.3.1

Underground mining methods

3.3.1.1 Unsupported methods Room and pillar mining, stope and pillar mining, shrinkage stoping, and sublevel stoping—in these methods, rock is self-supporting and for which no major artificial support is necessary to carry the load of the overlying rock. The weight of overlying rock plus any tectonic forces is generally called the superincumbent load. This load will be too high on many rock masses, but for the unsupported methods, geologic materials can sustain the load. Theoretically, unsupported methods can be used in any type of mineral deposit by varying the ratio of opening to the width of the pillar. However, on a practical basis, it depends on economic basis. Hence, the ratio of span to width of the pillar is limited to results in favorable productivity Table 3.3. 3.3.1.2 Supported methods: cut-and-fill stoping, stull stoping, square-set stoping The supported class of methods is intended for application to rock ranging in competency from moderate to incompetent. Three methods are in this class:

Chromite ore beneficiation: prospects and challenges Chapter | 3

85

TABLE 3.3 Brief comparison of each unsupported methods. Method

Type of deposits— applicability

Brief description of method

Room and Pillar

Horizontal or nearly horizontal deposits e.g., coal, potash, trona, and limestone

Openings are driven orthogonally and at regular intervals in a mineral deposit— forming rectangular or square pillars for natural support

Stope and Pillar

Horizontal or nearly horizontal deposits Mineral deposit is ,6 m in thickness. e.g., commodity being exploited is mineral other than coal

Like room and pillar mining, in which openings are driven horizontally in rectangular or random patterns to form pillars for ground support

Shrinkage stoping

Vertical stoping method Suitable for deposits of vertical or near-vertical plane at an angle .angle of repose of broken ore. e.g., chromite ore, copper, lead, zinc, etc.

It is an overhand method in which ore is mined in horizontal slices from bottom to top and remains in the stope as temporary support to the walls and to provide a working platform for the miners Ore swells when the breakage occurs, about 30%
40% of broken ore in each stope must be evacuated during mining to provide sufficient working space in the stope, means 60%
70% ore must be left in the stope as working platform. However, this tied-up ore may be extracted further by filling the stopes with suitable filling material to provide ground support Rock mechanics will determine the size of the stope

Sublevel Stoping

Vertical mining method in which a large open stope is created within the vein e.g., steep deposits like copper, chromite, lead, zinc, etc.

Open stope is not meant to be occupied by the miners; all work of drilling and blasting must be performed from sublevels within the ore block Three different variations of sublevel stoping are practiced a. blast hole method b. open-ending method c. vertical crater retreat method

1. 2. 3. 1.

Cut and-fill stoping Stull stoping Square-set stoping Cut and fill stoping: Ore is extracted in horizontal slices and replaced with backfill material. The backfilling operation is normally performed after

86

G G G G G

Mineral Processing

each horizontal slice is removed. The fill material used in this method varies, depending on the support required and material that may be available to the mine operator. The major types of fill material are: Waste fill Pneumatic fill Hydraulic fill with dilute slurry High-density hydraulic fill Paste fill

This method is commonly used for moderate to steep deposits ( . 450) like chromite ore. The major advantages of this method are: G G G G G G G G G

Moderate productivity Moderate production rate Permits good selectivity Low development cost Moderate capital investment Versatile, flexible, and adaptable Excellent recovery if pillars are recovered (90% to 100%) Low dilution (5% to 10%) Surface waste can be used as fill material. The disadvantages of this method are (Table 3.4)

Fairly high mining cost Handling of fill may increase mining cost G Filling operations interfere with production G Compressibility of fill may cause some ground settlement. 2. Stull stoping: Infrequently used and relatively unimportant today. Suitable for tabular deposits. 3. Square-set stoping: Least used method and suitable for worst ground conditions when caving and subsidence are not permitted. G G

3.3.1.3 Caving methods: longwall mining, sublevel caving, block caving Longwall mining, sublevel caving, and block caving are considered as caving methods. These methods are not suitable for chromite deposits as openings are designed to collapse, which is not practicable in Sukinda valley. Since the width of chromite ore body typically varies from 2
8 m in Sukinda valley region and at some quarries it is even less than 2 m, it is always advisable to go for shrinkage stoping with a backfilling or cut-andfill method or sublevel stoping. Chromite underground mines in India are confined to Byrapur in Karnataka and Boula & Kathpal mines in Odisha (Table 3.5).

Chromite ore beneficiation: prospects and challenges Chapter | 3

87

TABLE 3.4 Advantages and disadvantages of shrinkage & sublevel stoping methods for vertical deposits. Method

Advantages

Shrinkage stoping

G G G

G

G

G G

G G

Sublevel Stoping

G G G G

G G

G G

Disadvantages

Small to moderate scale operation Ore is drawn down by gravity Method conceptually simple and can be used for a small mine Low capital requirement, little equipment required for the basic method Little ground support is required in the stope Stope development is moderate Works very well in veins with the widths of ,3 m Fairly good recovery (75%
85%) Low dilution (10%
20%)

G

Moderate to high productivity Moderate mining cost Moderate to high production rate Low breakage cost, low handling cost Easy to ventilate Unit operations can be carried on simultaneously Fair recovery Modest dilution

G

G

G

G

G

G

G G

G

Low to moderate productivity range Moderate to high mining cost Rough footing in stope, unergonomic working conditions Most of ore tied-up in stope ( . 60%) if backfill methods are not deployed Ore is subject to oxidation, packing, and spontaneous combustion Selectivity is only fair Fairly complicated and expensive development Inflexible in mining plan Long hole drilling requires precision (, 2% deviation) Large blasts can cause significant vibration, air blast, and structural damage

TABLE 3.5 Underground mining of India. Mine/State

Depth

Underground method deployed

Byrapur, Hassan District, Karnataka

300 m

Cut and fill method

Boula and Kathpal, Odisha

200 m

Sublevel stoping with parallel/ring hole blasting

3.4

Characterization

Chromite is a member of the spinel group of minerals and consists essentially of ferrous and chromic oxides—FeO, Cr2O3, analogous to aluminates. Ferrous oxide is, however, often partly replaced by magnesia and chromic

88

Mineral Processing

oxide by alumina so that there is a transition to chrome spinel or picotite (MgFe)O. (AlCr)2O3. Further, with the replacement of chromic oxide by ferric oxide, there may be a transition to magnetite, Fe3O4. Thus, chromite is represented by the general formula R2O.R32O3 where R2 stands for a bivalent metal, mainly magnesium, ferrous iron with minor amounts of zinc, manganese, and nickel, and R3 represents a trivalent metal, that is, chromium, aluminum, or iron. This chromite mineral contains gangue, which is generally orthopyroxene, olivine, calcic plagioclase, and their hydrous products such as serpentine, chlorites, and talc. In fact, the hydrous-altered magnesium silicates are probably more commonly present than the original minerals (although they may reveal the original silicates from which they were derived) other less common to rare gangue minerals that have been found in various deposits, which include dolomite, magnesite, brookite, chromite tourmaline, uvarovite (Chrome garnet) kaolin, pyrite, mica, and goethite. Chromite mineral is belonging to the spinel group, the crystals are uncommon, but when found they are octahedral of cubic crystal. Generally, the chromite is usually massive or in the form of lenses and tabular bodies, or it may be disseminated as granules. Chromite is dark brown to black in color and can contain some magnesium and aluminum. Chromite is most commonly found as an accessory mineral in iron and magnesium-rich igneous rocks or concentrated in sediments derived from them. It occurs as layers in a few igneous rocks that are especially rich in iron and magnesium. Almost pure chromite is found in similar layers in sedimentary rocks. The layers are preserved when the sedimentary rocks metamorphose to form serpentinite and these rocks are the most important ores of chromium. The weathering of chromite ore bodies can also lead to its concentration in placer deposits.

3.4.1

Physical properties

Chromite mineral is having cubic crystal structure and occurs in octahedra, however, commonly found massive, having a granular or compact structure. The chromite mineral is having iron-black and brownish-black color whereas streak is brown and possesses submetallic luster but often faint. The fracture is uneven, sometimes flat. The Mohr’s hardness is about 5.5 and specific gravity is 4.5 to 4.8. The chromite mineral exhibits high relief and nonpleochromism under optical microscope. The chemical, physical, and optical properties are tabulated in Table 3.6.

3.5

Beneficiation

The purpose of beneficiation is to concentrate the ore mineral physically and chemically suitable for subsequent applications. The gravity concentration is

Chromite ore beneficiation: prospects and challenges Chapter | 3

89

TABLE 3.6 Chemical, physical, and optical properties of chromite. 1

Chemical properties

a

Chemical classification

Oxide minerals, spinel group

b

Formula

(Fe, Mg)Cr2O4

c

Common impurities

Mg, Mn, Zn, Al, Ti

2

Physical properties

a

Crystal habit

Octahedral rare, massive to granular

b

Color

Black to brownish black, brown to brownish black on thin edges in transmitted light

c

Streak

Brown

d

Luster

Resinous, greasy, metallic, submetallic, dull

e

Cleavage

None observed

f

Diaphaneity

Translucent, opaque

g

Mohs hardness

5.5

h

Crystal system

Isometric

i

Tenacity

Brittle

J

Density

4.5
4.8 g/cm3 (measured) 5.12 g/cm3 (calculated)

k

Fracture

Irregular/uneven, hackly, subconchoidal

l

Parting

Parting may develop along {111}

m

Magnetic property

Weakly magnetic

3

Optical properties

a

Type

Isotropic

b

Color/pleochromism

Nonpleochroic

c

RI values

n 5 2.08
2.16

d

Twinning

On {111}

e

Relief

Very high

a well-established and widely accepted technique for chrome ore beneficiation due to the density difference between the chromite mineral and other associated gangue-bearing minerals. The beneficiation circuit includes comminution operations such as crushing and grinding operations to liberate the ore particles from gangue-bearing particles and produce uniform size fractions for subsequent concentration techniques (generally, wet concentration techniques) such as gravity concentration, magnetic separation, flotation, etc.

90

Mineral Processing

In general, the beneficiation process circuit design varies from deposit to deposit and is tailored based on the mineral characteristics like mineral assemblage, degree of dissemination of constituent mineral, and the end-use requirements. The Kemi chromium concentrator (Finland), Turkish chromite concentrator, and the Sukinda chromite ore beneficiation circuits (India) were depicted in the following sessions.

3.5.1

Kemi chromium concentrator (Finland) flowsheet

The chromium ores at Kemi are associated with a mafic-ultramafic layered intrusion within the contact between migmatite granite and schist. The formation starts at the town of Kemi and extends approximately 15 km NE, with a maximum width of 1500 m. The compact chromite-rich horizon appears 50
200 m above the bottom of the formation. The thickness of the continuous chromite horizon varies from a few millimeters to a couple of meters, but in the Nuottija¨rvi-Elija¨rvi area, the chromite layer contains eight layers, which are economically viable over a distance of 4.5 km. Both host rock is serpentinite and talc-carbonate rock. Idiomorphic chromite is the only ore mineral appearing in economic quantities. The average content of the ore is 26% Cr2O3 and the Cr/Fe ratio is 1.55. The Kemi chromium mine is an open-pit mine with a waste rock to ore ratio of 5.5:1. At Kemi, the ore from the mine contains 11% iron and 25.5% Cr2O3. After beneficiation, the concentrate contains between 35% Cr2O3 in the coarse fraction (lumps) and 44% of Cr2O3 in the fines. The process steps will be explained in the following sections in more detail. The mineral-processing plant operates at 207 t/hours. Size reduction at Kemi is carried out as follows: crushing in three stages with a jaw crusher and two-cone crushers, grinding in two stages with a rod mill (Ø 3.2 3 4.5 m) and a ball mill (Ø 2.7 3 3.6 m). The equipment and techniques used at Kemi to separate the chromite mineral from the gangue are two-drum separators and three dewatering screens in a dens-medium separation plant for lumps and nine-cone separators and a high-gradient magnetic separator in the concentrating plant for fine material. The flowsheet is depicted in Fig. 3.1.

3.5.2

Turkish chromite concentrator flowsheet

The worlds fourth-highest reserves in terms of total chromite reserves are at Turkey with 31.14 million tons. There are 13 chromite concentration plants, which are in operation to produce chrome concentrate for metallurgical purpose. All the plants except the Kef concentrator are adopted with the gravity concentration technique and are employing many spirals, jigs, and shaking tables. The Kef concentrator, where low and high-intensity magnetic separators have been used, was revised and a new flowsheet was developed. The new flowsheet consists of Reichert cones, spirals, shaking tables, and high-intensity

Chromite ore beneficiation: prospects and challenges Chapter | 3

91

FIGURE 3.1 Kemi (Finland) chromium concentrator flowsheet.

FIGURE 3.2 Turkish chromite concentrator flowsheet.

magnetic separator. The beneficiation flowsheet of Kef chromite ore concentrator, Turkey is given in Fig. 3.2. Reichert cones, spirals, shaking tables, and workplace hazardous materials information system are the principal concentrating unit operations in the plant. The concentrator was designed to treat

92

Mineral Processing

28%
32% Cr2O3 at 84 t/hours capacity and was intended to produce concentrate of two grades as high- and low-grade concentrate with 44% and 40% Cr2O3 respectively and the plant was designed to generate tailings of 16% Cr2O3 at maximum.

3.5.3

Chrome ore beneficiation plant, Sukinda, India

The mining process generates two types of ore—hard/lumpy and soft/friable. The mined high-grade lumpy ores are directed to ferro chrome plant after suitable sizing in the lump ore-processing plant while the low-grade ore (soft/friable) to the beneficiation plant. The beneficiation circuit consists of two major operations, that is, comminution (for preparing the material to the subsequent unit operations) and concentration. The run-off-mine ore (ROM) is crushed to 75 mm from 2220 mm followed by two-stages crushing (primary and secondary crusher) and screening to produce less than 3 mm size fraction. This fraction is further ground to less than 1 mm size in the variable speed ball mill and then sent to beneficiation circuit for upgradation or concentration. The chrome ore beneficiation circuit, Sukinda is shown in Fig. 3.3. The plant is designed to produce concentrate of three different size ranges, that is, coarse (21 mm 1 106 μm), fine (2106 μm 1 70 μm), and ultrafine (270 μm 1 25 μm). The beneficiation circuit comprises of a combination of hydrocyclone, floatex density separator, spiral concentrator, and wet-shaking tables. Where the segregation of chromite minerals from the gangue-bearing minerals takes place based on the specific gravity difference.

3.5.4

Challenges in chrome ore gravity concentrator

Particle density-based separations are commonly used to concentrate minerals like chromite, tin, heavy mineral sands, iron ore coal, etc. These processes operated in parallel or multi-stage circuits. In case of chrome ores, where the quality of the ROM and physical parameters vary within the deposit, the operators need to modify the critical-operating parameters on a continuous basis, which is very difficult and tiresome. These variations in ROM impact the efficiency of the beneficiation circuit thereby affecting the overall performance of the operating plant in terms of quality and quantity of concentrate fraction also loses of valuable minerals into tailing fraction. A typical gravity concentration circuit comprises of two or more stages of spiral circuit such as roughing, cleaning, and recleaning with various configurations around scavenging circuit to overcome the inherent efficiencies created by the random misplacement and/ or bypass of particles in density-based separation process (Luttrell et al., 2003). In last two decades, enough literature was published on chromite ore beneficiation in the form of research papers, technical reports, and

Chromite ore beneficiation: prospects and challenges Chapter | 3

93

FIGURE 3.3 Sukinda flow sheet for chromite ore beneficiation.

reviews. However, none was on the performance evaluation of concentrators with respect to size and liberation of particle. Process control systems and related applications have been reported over the years in mineral-processing plants. However, the beneficiation plants that make use of gravity-based unit operations have the potential to improve through proper application of existing process control and improve incremental quality concept and linear circuit analysis are often overlooked. Such process control systems are generally developed from the huge database that has been generated in the past from the various operating parameters of the plant. In practice, the performance of a system deteriorates with time but such situations are rarely discussed in the literature, however, the recent research works have shown that it is possible to evaluate the performance of the gravity separation circuits based on the mineralogical and particle granulometry data. Whereas, the research works of Pascoe et al. (2007) show that it is possible to make a sensible selection of gravity unit operations on particle size and the mineralogy of the ore.

94

Mineral Processing

3.6

Research & development

Globally, several investigations have been made to determine the most economic processes applicable to reduce the tailing losses or to recover the fine chrome particles from the stockpiled gravity concentration plant tailings and to process the low and subgrade fines are critically discussed.

3.6.1 G

G

G

Due to the variation in ore characteristics, the mesh of grind tends to vary, which ultimately affects the efficiency of the gravity concentration circuit, resulting in the loss of fine chromite to the tailing fraction. The studies of C¸ic¸ek and Co¨cen (2002) reveal that Mozley’s multi gravity separator (MGS) can be employed to reduce fine chromite losses in the tailings of Turkish chromite gravity concentration plants. His work established that by integrating MGS into the existing chromite circuit the concentrate yield can be improved by 11%, that is, the MGS could recover less than 106 μm size fraction, which is being lost in the tailing fraction. To recover the ultrafine chromite particles, flotation technique is also an alternative method. Abundant research work illustrated that the chromite particles could be concentrated with cationic and anionic collectors. The research work of Sysila¨ et al. (1996) shows that by treating slimy feed in flotation circuit the Cr2O3 losses can be reduced to less than 10% Cr2O3 in tailing fraction.

3.6.2 G

G

G

G

Reduction of tailing losses

Beneficiation of low and subgrade chromite ore

The beneficiation studies of Suresh (1981) illustrate that low-grade chromite ore of 16%
25% Cr2O3 of Sitampundi area of India, cannot be upgraded by using conventional physical beneficiation techniques like gravity and flotation, due to the intimate association of iron in the lattice of chromite particle. However, they have demonstrated that chemical or thermochemical treatment is essential to achieve the metallurgical grade. The research work of Rao et al. (1987) reveals that low-grade chromite ore of about 20%
30% Cr2O3 of Sukinda region, India can be upgraded to 50% Cr2O3 with a recovery of about 70% by using different gravity concentration unit operations such as spirals and tables. Maulik et al. (1997) work reveals that low-grade chromite ore/waste dump samples of about 10%
20% Cr2O3 of Sukinda, India can be beneficiated to 50% Cr2O3 with recovery of 50%
80% by using spirals and table combination. Considering the tailing disposal problems of chromite gravity concentration plants, the research works of Amer and lbrahim (1996) on hydrometallurgical processing of low-grade chromite ore (Barramiya, Egypt),

Chromite ore beneficiation: prospects and challenges Chapter | 3

95

using mechanical alkaline treatment in an attritor followed by oxidative leaching in an autoclave reveals that single-stage leaching at 240 C, with an oxygen partial pressure of 10 bar can extract about 90% Cr2O3.

3.6.3 G

G

G

Reprocessing of stockpiled tailings

The research work of C¸ic¸ek and Co¨cen (2002) evident that the fine chromite particles can be recovered using MGS as an enhanced gravity concentrator and can produce chrome concentrate of around 48% of Cr2O3 with a recovery of 51.6% from the stockpiled tailings of Turkish chromite gravity plants with a Cr2O3 of about 8%
14.4%. The investigation result of Gu¨ney et al. (2001) depicts that the chrome concentrate of 45%
48% Cr2O3 and a tailing loss of below 7% Cr2O3 with an overall plant recovery of 60%
65% can be recovered by introducing shaking table for 0.1
1.0 mm size fraction and high-intensity wet magnetic separator and column flotation for treating less than 0.1 mm size fraction that is present in the gravity tailings of Turkish chromite gravity concentration plants having 20%
22% of Cr2O3. The research work of Murthy et al. (1994) illustrates that a combination of gravity concentration and wet high-intensity magnetic separator can produce a consistent concentrate grade of 50%
52% Cr2O3 and 2.8 Cr/Fe ratio with a recovery of 38%, from a feed grade-containing 25% Cr2O3 and 0.8
1 Cr/Fe ratio.

3.6.4

Processing/recovery of ultrafine size particles: world

Unsteady operation of beneficiation units in the process circuits often arises especially in the gravity-operated circuits due to numerous changes in the input to the plant such as feed (ROM) properties to the circuit, overall flow rate, mineral composition, percent solids, size distribution of the feed, etc. This variability affects the overall performance of the beneficiation circuit in terms of grade, recovery, and throughput, including loss of valuable mineral into tailing fraction. Increased mechanization in mining to substantiate the need for higher production rates has resulted in the generation of higher quantities of fines. Further, due to the indiscriminate nature of the breakage process, conventional comminution methods that lead to high energy consumption and the generation of difficult to recover ultrafine particles. The recovery of fine particles is becoming increasingly important as many newer ore deposits require fine grinding of the ore due to the complexity of the mineral assemblage and their liberation characteristics. Finer grinding leads to increased costs not just in the grinding stage but also in flotation where the slower flotation kinetics of fine minerals require greater flotation capacity. These ores contain valuable minerals in finely disseminated form resulting in the recovery of these fine mineral particles

96

Mineral Processing

exceedingly difficult. In the last two decades, many processes for the recovery of chromite values have been claimed and reported in the form of technical reports, papers, and reviews to economically recover these lower-grade deposits, separation circuits must be optimized. Huge quantity of fine-sized chromite tailings is naturally generated during the production or processing and causes severe environmental hazards as well as resource losses due to the high chromite content. Generally, after crushing and grinding, spirals and shaking tables are used as the concentrators, therefore, fine-sized chromite particles (20.038 μm) are removed as tailings. The beneficiation of these ultrafine valuable minerals is intricate problem in mineral processing, in particular, gravity concentration. The fines below 100 μm are generally discarded as gangue from gravity concentration processes, which ultimately report to tailing fraction along with the processed water stream. To recover these fines, Feng and Aldrich (2004) worked on the Western chromite mines at South Africa and illustrated that maximum of 95.6% of chromite fines can be recovered by using column flotation technique. Further, the studies of Akdemir and Hic¸yilmaz (1996) that shear flocculation of chromite is possible in aqueous solution of sodium oleate to recover the ultrafine (,10 μm) chromite particles. However, all these investigations require technoeconomic viability otherwise these ultrafine valuable chromite could not be realized for metallurgical purpose.

3.7

Effluent treatment processes

Water is an essential resource for mining, beneficiation, and metallurgical operations. However, the industrial development has been a major contributor to the dilapidation of water quality, both through negligence in treatment of wastewater before discharge and accidental pollutant spills in an aquatic environment. Processed water from mining and metallurgical operations is contaminated by various pollutants like chemicals, metal ions, oils, organic, and others, sometimes rendering the water useless for recycling as processed water, often dangerous for the environment. In the recent past, to substantiate the demand from metallurgical industries and depletion of the high-grade ores, the processing of low-grade deposits has been started, which substantially generating huge quantities of waste owing to high production rates and large waste to product ratios. Mining waste includes topsoil, overburden, waste rock, and fine tailings/slimes in processed water and metallurgical waste such as flue dust, leach residues, precipitates, etc. and these effluents require treatment by means of physical, chemical, and/or biological to minimize or eliminate their potential impact on environment. In a mineral-processing plant, waste (gangue/tailing) generated after separation of valuable mineral as concentrate from an integrated series of unit operations, including crushing and grinding for liberation of mineral grains, screening and hydrocyclone for particle size classification, and gravity

Chromite ore beneficiation: prospects and challenges Chapter | 3

97

FIGURE 3.4 Overall waste generation in process industries.

concentration, flotation, magnetic separation, or analogous techniques for mineral separation. The characteristics of tailings vary according to mineralogical and geochemical compositions, specific gravity of particles, settling behavior, permeability, consolidation behavior, rheology/viscosity, pore water chemistry, and leaching properties. A general view on the source of waste generation from mining and mineral-processing industries is outlined in the Fig. 3.4. In majority of the cases, ores treated in mineral processing are through wet methods. The tailing (or waste) of such processing plants is disposed-off through suitable systems and the water is recovered back into the system for reuse. Water purification and disposal are expensive operations and usually are influential factors about location and design on processing plants. In view of the above, the focus is given on various techniques and processes available for the remediation of effluents contaminated by different chromite-processing industries.

3.7.1

Chromium existence

Chromium in nature comes directly from mining and indirectly from tannery, chrome-plating industries, chemical industries, etc. Chromium exists in two stable oxidation states, that is, trivalent [Cr(III) or Cr13] and hexavalent [Cr(VI) or Cr16] in aqueous systems. At trace level, the trivalent form is considered as an essential nutrient, however, hexavalent form of chromium is toxic, carcinogenic, and mutagenic in nature. Cr(III) does not readily migrate in groundwater since it usually, precipitates as hydroxides, oxides, or oxyhydroxides. Whereas Cr(VI) is soluble in aqueous phase over almost the entire pH range, thus it is quite mobile in the natural environment. Considering its toxicity and carcinogenic nature, the maximum levels permitted for trivalent chromium in wastewater is 5 mg/L and for hexavalent chromium as 0.05 mg/L. Therefore, reduction of Cr(VI) to Cr(III) is beneficial for the environment and is a feasible method.

98

Mineral Processing 100 Cr2O72-

10 1 g/L Cr .1

HCrO4-

H2CrO4

.01

CrO42-

.001 .0001 -2

-1

0

1

2

3

4 pH

5

6

7

8

9

10

FIGURE 3.5 Speciation diagram of Cr(VI) (Dionex, 1996).

3.7.2

Chromium chemistry in water treatment and distribution

Thermodynamically Cr (III) is the most stable oxidation state under reducing conditions. Cr(III) predominates at pH , 3.0 and at pH . 3.5, hydrolysis of aqueous Cr(III) yields trivalent chromium hydroxy species [CrOH21, Cr(OH)21, Cr(OH)30, and Cr(OH)42]. Cr(OH)30 is the only solid species existing as an amorphous precipitate. Hexavalent chromium exists primarily as salts of chromic acid (H2CrO4), hydrogen chromate ion (HCrO42), and chromate ion (CrO422) depending on the pH. H2CrO4 predominates at pH less than about 1.0, HCrO42 at pH between 1.0 and 6.0, and CrO422 at pH above about 6.0 as shown in Fig. 3.5. The dichromate ion Cr2O722, a dimer of HCrO42, minus a water molecule, forms when the concentration of chromium exceeds approximately 1 g/L.

3.7.3

Formation of hexavalent chromium

From a practical perspective, Cr(III) presence is not a health concern at levels encountered in potable water. In each water sample, Cr(III) can be presented in five forms (Fig. 3.6): G G G G

G

as soluble Cr(III) species, as a precipitated Cr(OH)3 solid, sorbed to the surface of Fe(OH)3 and other oxides, "fixed" inside oxides in a form that is relatively inaccessible from solution, and complexed with naturally occurring organic matter such as humic and fluvic acids (Icopini and Long, 2002).

Chromite ore beneficiation: prospects and challenges Chapter | 3

99

FIGURE 3.6 Dissolved or soluble Cr(III) in water.

Although Cr(VI) can undergo similar reactions, it is much more likely to remain soluble. These different types of chromium are the issues to understand the importance in analytical chemistry, water treatment, and distribution. In Fig. 3.6, dissolved or soluble Cr(III) in water can sorb to oxide surfaces, complex with natural organic matter, form precipitated solids such as Cr(OH)3, or be trapped in solids relatively inaccessible from the water as "fixed" Cr(III). In aquatic environment, manganese oxide is responsible for oxidation of trivalent chromium, which is accomplished in three steps adsorption of Cr (III) onto MnO2 surface sites followed by oxidation of trivalent to hexavalent chromium by surface Mn(IV) and then the desorption of reaction products, Cr(VI) and Mn(II) as illustrated by Amacher and Baker (1982). 21 1987Cr31 1 3=2MnO2 ðsÞ 1 H2 O-HCrO2 1 H1 4 1 3=2Mn 1 CrðOHÞ21 1 3MnO2 ðsÞ 1 3H2 O-HCrO2 4 1 3MnOOHðsÞ 1 3H

Chromium and manganese form a pair of chemical elements with contrasting characteristics. Under oxidizing condition, Cr(VI) is soluble as CrO422 and Mn(IV) is scavenged as MnO2 whereas under reducing condition Cr(III) is removed as Cr(OH)3 and Mn(II) is soluble as Mn21. Magnesium release during alteration of ultramafic rocks leads to the generation of Cr(VI) from inert chromite.

3.7.4

Effluent treatment methods

Numerous effluent treatment techniques are being in practice for industrial wastewater and effluent treatment all over the world however it needs to be

100

Mineral Processing

FIGURE 3.7 Various effluent treatment methodologies.

established in the field of mining and mineral processing. Effluent treatment process selection for a complete wastewater management system should be technically, economically, and ecologically viable solution is the need of the hour. Broadly, the different waste/effluent treatment technologies can be categorized as shown in Fig. 3.7. Several approaches such as adsorption, biosorption, ion exchange, chemical precipitation, and electrochemical methods like electrowinning, electrodialysis, electrodeionization, membrane-less electrostatic-shielding electrodialysis/electrodeionization, and electrocoagulation have been studied by researchers for the development of cheaper and more effective technologies, both to decrease the amount of wastewater produced and to improve the quality with reference to removal of heavy metals from the treated effluent. The selection of suitable techniques is dependent on the source water chemistry, chromium concentration, the origins of the Cr(VI), preexisting treatment processes and facilities, water scarcity, residuals handling concerns, etc. Hence the focus is given on those techniques like adsorption methods, electro methods, bioremediation methods, etc. that are convenient to install in any operating plant followed by chromium concentration and economics.

3.7.5

Adsorption

In recent years, adsorption has one of the alternative and versatile methods for effective removal of chromium. Adsorption by activated carbon is one of the effective techniques for chromium removal from wastewater because of high surface area, highly porous character, and relatively low cost. Selomulya et al. (1999) used different types of activated carbons, produced from coconut shells, wood, and dust coal to remove Cr(VI) from synthetic wastewater. Whereas, Karthikeyan et al. (2005) used rubber wood sawdust-activated

Chromite ore beneficiation: prospects and challenges Chapter | 3

101

TABLE 3.7 Various adsorbents used for the removal of chromium. Adsorbent

Adsorption capacities (mg/g)

pH isotherm

Activated carbon

Cr(VI) 315.6

3.0

Chitosan

Cr(VI) 273

4.0

Flyash

Cr(VI) 1.4

2.0

Fly ash impregnated Aluminum

Cr(VI) 1.8

2.0

Flyash-impregnated iron

Cr(VI) 1.7

2.0

Japanese ceder

Cr(VI) 80.0

3.0

Sawdust

Cr(VI) 45

3.0

carbon for removal of Cr(VI) in a batch system and was established that Cr (VI) removal is pH dependent, that is, maximum at pH 2.0. However, the search for low-cost adsorbents that have metal-binding capacities have intensified. The available adsorbents may be of mineral or biological origin, zeolites, industrial byproducts, agricultural wastes, biomass, and polymeric materials, the bentonite is considered by many authors as main possible choice in the treatment of detrimental metal ions, because of its large-specific surface area along with high adsorption capacity. The natural zeolites also gained a significant interest, mainly due to their valuable properties such as ion exchange capability. There have been numerous tests by using different adsorbents tabulated in the Table 3.7.

3.7.5.1 Electro methods Electro flotation is extensively used in the mining industries and is finding increasing applications in wastewater treatment due to electrically generated tiny and uniform-sized bubbles giving much better performance than the air flotation, sedimentation, or even impeller flotation. Further, electrocoagulation has been used industrially and demonstrated its superior performances in treating effluents containing suspended solids, oil, and grease, and even organic or inorganic pollutants that can be flocculated. The direct anodic oxidation represents one of the simplest technologies in the pollutant mineralization provided the anode materials are stable and have a high overpotential of oxygen evolution. The investigation of various materials so far shows that titanium or other noble metalbased boron-doped diamond film is the suitable for industrial application for water split and is inert in tough situations. Some of the results of research work are tabulated in Table 3.8 below.

102

Mineral Processing

TABLE 3.8 Electrochemical treatment technologies used for removal of chromium. Electrolytes employed

Chromium concentration

Experimental conditions

Removal efficiency

Carbon aerogel electrodes

8 mg/L

pH 2.0

98.50%

Iron rotary

130 mg/L

pH 8.5

99.60%

21

Aluminum or iron electrodes

Al 5 335.6 mg (Ah) , iron 5 1041 mg(Ah)21

I 5 20
25Am-2

—

Aluminum electrodes

50
5000 mg/L

—

—

Stainless steel electrodes

1470 mg/L

I 5 7.4 A, applied time 5 70 min., pH 1.8

100%

Electrochemical precipitation units having six plates

215
3860 mg/L

I 5 3
6 A, EP 5 30
75 V, pH . 3.2

100%

Titanium electrodes

4056 mg/g

pH , 4

27% at 15 V, 87% at 30 V

3.7.5.2 Electrolytic treatments Electrolytic wastewater treatment is rarely used in comparison to chemical treatment. However, this treatment is convenient and more efficient to produce high-quality water. The electrodes with aluminum (Al), iron (Fe), steel, and graphite are generally best suited to electrochemical water treatment. Electrolytic technology is an essential and significant discipline in many sectors of wastewater treatment, including clean synthesis, monitoring of removal efficiency of contaminants, water sterilization, clean energy conversion, and the efficient storage and utilization of electrical energy. Electrolysis has significant advantages such as its simple equipment, convenient operation, and nonrequirement of chemical substances for the sedimentation and floc generation. It allows the wastewater treatment to electrochemically oxidize or reduce the organic contaminants to nonhazardous inorganic substances. Chopra et al. (2011) and Chen (2004) published an exhaustive review on electrochemical methods and summarized that further improvement in the stability of electrochemical application is required before commercialization. Electrocoagulation (EC) is an electrochemical wastewater treatment technology that is currently experiencing both increased popularity and considerable technical improvements. It is still an empirically optimized process that

Chromite ore beneficiation: prospects and challenges Chapter | 3

103

requires more fundamental understanding for improved engineering design. The EC comprises complex chemical and physical processes involving many surface and interfacial phenomena. There is, however, a paucity of scientific understanding of these phenomena, which limits the engineering design of EC reactor for optimum performance and future progress of this novel and innovative technology. The EC is a complicated process involving many chemical and physical phenomena that use consumable electrodes to supply ions into the wastewater stream. In an EC process, the coagulating ions are produced “in situ” and it involves three successive stages: 1 Formation of coagulants by electrolytic oxidation of the “sacrificial electrode,” 2 Destabilization of the contaminants, particulate suspension, and breaking of emulsions, and 3 Aggregation of the destabilization mechanism of the contaminants, particulate suspension, and breaking of emulsions has been described in broad steps and may be summarized as follows: a. Compression of the diffuse double layer around the charged species by the interactions of ions generated by oxidation of the sacrificial anode. b. Charge neutralization of the ionic species present in wastewater by counter ions produced by the electrochemical dissolution of the sacrificial anode. These counter ions reduce the electrostatic interparticle repulsion to the extent that the van-der Waals attraction predominates, thus causing coagulation. A zero net charge results in the process. c. The floc formed because of coagulation creates a sludge blanket that entraps and bridges colloidal particles remaining in the aqueous medium.

3.7.5.3 Ion exchange Among the physicochemical methods developed for chromium removal from wastewater, ion exchange processes have been widely used to remove heavy metals due to their many advantages, such as high treatment capacity, high removal efficiency, and fast kinetics. This is a promising technique based on adsorption/exchange of cations or anions on synthetic resins with essential characteristics of its regeneration after elution/release of ions. The most common cation exchangers are strongly acidic resins with sulfonic groups (2SO3H) and weakly acid resins with carboxylic acid groups (2COOH). Hydrogen ions in the sulfonic group or carboxylic group of the resin can serve as the solution containing heavy metal passes through the cations column; metal ions are exchanged for the hydrogen ions on the resin with the following ion-exchange process given in Table 3.9. 3.7.5.4 Membrane separation A membrane is a semipermeable barrier between two phases, which restricts the movement of ions/molecules in a very specific manner. These

104

Mineral Processing

TABLE 3.9 Comparative performance of various ion exchangers in remediation of chromium. Membrane characteristics

Chromium concentration

Experimental conditions

Removal efficiency

Ultrafiltration, UF carbon membranenitrated and aminated

—

—

96% rejection (unmodified) 84% rejection (nitrated)

Zn Al2O4-TiO2 Uf membrane

10
3 mol/L

pH 3.6

96% rejection

CMC and polyether sulphion-UF membrane

100 mg/L

pH $ 7

99.1% rejection

UF made from poly acrylonitrile

0.07 mg/dm3

17.6% PA, pH 6.0

98% retention

Liquid membrane Nanofiltration membrane NF-I NF-II

5
2000 mg/L

pH 2
11

84%
99.7% rejection (NF-I) 47%
94.5% rejection (NF-II)

movements are based on size exclusion, differences in diffusion coefficients, electrical charge, and solubility. Membrane processes are often governed by driving forces to effect separation like micro, ultra, and nano-filtrations and reverse osmosis by hydrostatic pressure, dialysis by concentration gradient, electrodialysis by electric potential, and gas permeation by pressure and concentration gradients. The various membrane separation processes are tabulated in Table 3.10.

3.7.5.5 Bioremediation The processes that control the environmental chemistry and fate of Cr include adsorption, redox transformations, and precipitation reactions by utilizing microorganisms offer the potential for a highly selective removal of toxic metals coupled with considerable operational flexibility, hence they can be both in situ or ex situ in a range of bioreactor configurations. Microbes, especially bacteria, capable of Chromium (VI) reduction exhibit plasmid-mediated chromate resistance and the reduction is enzymatically mediated. 3.7.5.6 Phytoremediation Phytoremediation is an ecofriendly approach for remediation of contaminated soil and water using plants comprised of two components, one by the rootcolonizing microbes and the other by plants themselves, which accumulate

Chromite ore beneficiation: prospects and challenges Chapter | 3

105

TABLE 3.10 Removal of chromium by various membrane separation processes. Ion-exchangers

Chromium concentration

Experimental conditions

Removal efficiency

Indion-790

500 mg/L

Acidic

100% removal

Chelax-100

2 mM

Basic, saline

100% removal

Dowex 2-X4

9.8 mg/L

Strongly basic

100% removal

Solvent impregnated resin (Sir) with aliquot 336

0.1 mg/L

Acidic resin based on hydrophilic polymer

99.5% removal

Ambersep 132

750 mg/L

Strongly basic

—

the toxic compounds to further nontoxic metabolites. Phytoremediation is the emerging technology for cleaning up contaminated sites, which combine the disciplines of plant physiology, soil chemistry, and soil microbiology. It is cost effective and has esthetic advantages and long-term applicability. It is best applied at sites with shallow contamination of organic, nutrient, or metal pollutants that are amenable to one of the five applications: phytotransformation, rhizosphere bioremediation, phytostabilization, phytoextraction, and rhizofiltration. After sufficient plant growth and metal accumulation, the above-grounded portion of the plant is harvested and removed, resulting in permanent removal of metals from the site. An overall comparative performance characteristic, advantages, and disadvantages of various methods in remediation of chromium are presented in Table 3.11.

3.7.5.7 Summary on Cr(VI) remediation G There are many treatment technologies available for chromium remediation but the suitability/applicability of each method or technique is dependent on the quality of contamination. G The major objective of these should be not only suitable, appropriate, and applicable to the local conditions but also able to meet the maximum contaminant level (MCL). [MCL for Cr(IV) 5 0.05 mg/L] standards established. G All the techniques are well established in the other area of processing, in the mineral industries particularly in India it must be established yet in the plant scale.

TABLE 3.11 Comparative performance characteristics, advantages and disadvantages of various methods in remediation of chromium (Madhavi et al., 2013). Performance characteristics

Advantages

Disadvantages

pH range

Metal selectivity

Influence of suspended solids

Tolerance of organic molecules

Working level (ppm)

Chemical Precipitation Hydroxide

Tolerant

Nonselective

Tolerant

Tolerant

.1000

Low capital cost, simple operation

Sludge generation, extra operational cost for sludge disposal

Sulfide

Limited tolerant

Limitedselective, pH dependent

Tolerant

Tolerant

.10

No secondary waster generation

Toxic gas intermediate, gas delivery to aquifer is difficult

Adsorption

Limited tolerant

moderate

fouled

Can be poisoned

,10

Wide variety of target pollutants, low cost, fast kinetics

Performance depends on type of adsorbent, production of waste products

Electro chemical treatment

Tolerant

moderate

Can be engineered

Can be accommodated

.10

No additional chemical reagents required, high selectivity, low cost

Spongy deposit, production of sludge, filtration process for flocs

Photocatalysis

Limited selective

Tolerant and removed

Membranefiltration

Limited tolerant

Nonselective

fouled

Bioremediation

Limited tolerant

Nonselective

Tolerant

Phyto remediation

tolerant

Non selective

.100

removal of metals & organic pollutants simultaneously, less harmful byproducts

Long duration time, limited applications

.10

Low solid generation, low chemical consumption, small space requirement

High initial capital cost, high maintenance cost, limited flow rate

High initial capital cost, high minimization of chemical mud, heavy metal recovery

Not applicable to synthetic waste, no recycling

eco-friendly, high accumulation rate

Long duration time, phytotoxic at high Concentrations

Tolerant & degrade

tolerant

.100

108

Mineral Processing

Most of these methods suffer from technical and/or economic shortcomings such as high capital and/or operationa1 cost and/or the problems associated with the disposal of the residual metal-containing sludge.

3.8

Cost structure for the chromite ore beneficiation plant

The economics of any mineral-processing plant depends on the economics of the mineral under separation, which can be ascertained using the below thumb rule mineral value per ton is greater than processing costs per ton.

3.8.1

Processing cost

The major governing factor, in this case, is the size of the plant, which is taken into consideration. If the plant is a simple ore beneficiation (crushing followed by screening), then major cost part of the total processing is mining and logistics and this can vary enormously, from only a few tons of ore to well over high-tonnage operations. When the deposit is of higher reserves, higher volume can be treated and accordingly, operation becomes cheaper but also it attracts higher capital expenditure. For a bigger beneficiation plant, the processing cost can be viewed into two major categories. 1. The capital costs 2. The operating cost.

3.8.2

Capital cost

The capital component indicates the first cost or the amount of money required for procuring necessary plant equipment, auxiliaries, and related off-site facilities. This capital expenditure must be recovered eventually within the stipulated period. The typical capital expenditure considering the essential installation can be depicted below Table 3.12.

3.8.3

Operating cost

These are the elements that indicate the funds that should be available to commence the plant production. Typical overall operating cost structure of the chromite beneficiation plant is depicted in the Fig. 3.8. It can be observed that the major operating cost element is the fixed cost of around 38%, which covers the elements like wages and contracts that are fixed irrespective of the production volume. Raw material cost accounts for only 25% of the overall operating cost whereas the operation cost such as equipment maintenance costs, stores inventory, and electrical cost are major elements of variable operating cost as they keep changing dynamically and do not remain constant. If the operating cost structure is visualized from only process point of view, then the percent contribution of the different elements is depicted in Table 3.13.

Chromite ore beneficiation: prospects and challenges Chapter | 3

109

TABLE 3.12 Typical capital expenditure considering the essential installation. Si. No

Description

% cost of capex

1

Platform & general instrumentation shed, electrical transformer

19

2

Cost of land

17

3

Plant shed

16

4

Spirals

13

5

Weigh bridge

10

6

Hydrocyclone

4

7

Settling tank & reservoir

4

8

Vibrating screen

4

9

Wet grinder

4

10

Civil foundation

3

11

Accessories

2

12

Slurry pump

2

13

Packing & stitching machine

1

14

Table weighing machine

1

15

Water pumps

1

Total

100

FIGURE 3.8 Typical overall operating cost structure of a chromite beneficiation plant.

110

Mineral Processing

TABLE 3.13 Cost breakup of various elements in the process plant. Si. no

Cost element

% of Cost

1

Grinding

47

2

Crushing

12.6

3

Water

8

4

Filtration

7.4

5

Mining

7.1

6

Tailings

5.1

7

Laboratory

4.5

8

Thickening

3.5

9

Reagents

3.1

10

Management support

1.7

Total

100

TABLE 3.14 Chrome concentrate specifications and price. Cr2O3

SiO2

Price/ Ton ($)

Price/ton (as on Feb’2021 conversion)

Normal silica (48%
50% Cr)

upto 4%

157

₹11,398

Low silica (52%
54% Cr)

upto 2%

281

₹20,401

Ultralow silica (54%
56% Cr)

less than 0.5%

345

₹25,047

The most cost-intensive process as observed is commination circuit and it is dominated by grinding area. Water pumping is also cost sensitive, whether it is freshwater or the processed water, circulation is being essential for continuous process.

3.8.4

Mineral value per ton (or concentrate selling cost)

The mineral value or in other words, the selling value of mineral is mostly governed by the quality and the specification of the concentrate and depends on the demand and supply of the mineral in the market. The chromite concentrates of different quality are tabulated in the Table 3.14.

Chromite ore beneficiation: prospects and challenges Chapter | 3

111

For any said capacity, the selling cost is more than the installation cost and processing cost then the beneficiation plant can be operated profitably.

References ¨ ., Hic¸yilmaz, C., 1996. Shear flocculation of chromite fines in sodium oleate soluAkdemir, U tions. Colloids Surf. A Physicochem. Eng. Asp. 110 (1), 87
93. Amacher, M.C., Baker, D.E., 1982. Redox reactions involving chromium, plutonium and manganese in soils. Final Report DOE/DP/04515-1, Pennsylvania state university, Institute for Research on Land and Water Resources, 166
170. Amer, A.M., lbrahim, I.A., 1996. Leaching of a low grade Egyptian chromite ore. Hydrometallurgy 43, 307
316. Chopra, A.K., Sharma, A.K., Kumar, V., 2011. Overview of Electrolytic treatment: An alternative technology for purification of wastewater. Arch. Appl. Sci. Res 3 (5), 191
206. C¸ic¸ek, T., Co¨cen, I., 2002. Applicability of Mozley multigravity separator (MGS) to fine chromite tailings of Turkish chromite concentrating plants. Miner. Eng. 15 (1
2), 91
93. Available from: https://doi.org/10.1016/S0892-6875(01)00195-9. Dionex, 1996. Determination of Cr(VI) in water, wastewater and solid waste extracts, Technical Note 26. https://assets.thermofisher.com/TFS-Assets/CMD/Technical-Notes/TN-26-LC-ChromiumWater-Wastewater-Waste-TN71432-EN.pdf. Feng, D., Aldrich, C., 2004. Recovery of chromite fines from wastewater streams by column flotation. Hydrometallurgy 72 (3
4), 319
325. ¨ nal, G., Atmaca, T., 2001. New aspect of chromite gravity tailings re-processing. Miner. Gu¨ney, A., O Eng. 14 (11), 1527
1530. Available from: https://doi.org/10.1016/S0892-6875(01)00165-0. Icopini, G.A., Long, D.T., 2002. Speciation of aqueous chromium by use of solid-phase extractions in the field. Environ. Sci. Technol. 36 (13), 2994. Luttrell, G.H., Honaker, R.Q., Bethell, P.J., Stanley, F.L., 2003. Operating guidelines for coal spiral circuits. Coal Age 108 (8), 26
29. Madhavi, V., Reddy, A.V.B., Reddy, K.G., Madhavi, G., Prasad, T.N.V.K.V., 2013. An overview on research trends in remediation of chromium. Res. J. Recent. Sci. 2 (1), 71
83. Maulik, S.C., Bhattacharyya, K.K., Singh, R., 1997. Gravity concentration of fines and ultrafines. Conference proceedings of PROF-97,NML. JAMSHEDPUR: 40
56. Murthy, Sripriya, Rao, 1994. Enrichment of Cr/Fe ratio in chromite concentrate produced in chromite beneficiation plant at Tata Steel. Trans. Indian Inst. Met. 47 (6), 413
416. Pascoe, R.D., Power, M.R., Simpson, 2007. QEMSCAN analysis as a tool for improved understanding of gravity separator performance. Miner. Eng. 20, 487
495. Rao, Bhima R., Reddy, S, Prakash, Ansari, M.I., 1987. Recovery of chromite values from chromite ore beneficiation plant tailings. Trans. IIM 40 (3), 203
206. Suresh, 1981. report on chromite beneficiation. Unpublished. Sysila¨, S., Laapas, H., Heiskanen, K., Ruokonen, E., 1996. The effect of surface potential on the flotation of chromite. Miner. Eng. 9 (5), 519
525. Available from: https://doi.org/10.1016/ 0892-6875(96)00040-4. Thayer, 1956. Chromium, Mineralogy and Geology. Monograph No. 132. Reinhold Publishing Corporation, New York. Yang, Y. (Ed.), 2003. Adsorbents: Fundamentals and Applications. Wiley/Interscience.

112

Mineral Processing

Further reading Acar, F.N., Malkoc, E., 2004. The removal of chromium (VI) from aqueous solutions by fagusorientalis L. Bioresour. Technol. 94, 13
15. Alloway, B.J., 1995. Heavy Metals in Soils, second ed. Blackie Academic and Professional, London, p. 368. Al-Qunaibit, M.H., Mekhemer, W.K., Zaghloul, A.A., 2005. The adsorption of Cu(II) ions on bentonite-a kinetic study. J. Colloid Interface Sci. 283, 316
321. Amacher, M.C., Baker, D.E., 1982. Redox reactions involving chromium, plutonium and manganese in soils. DOE/DP/04515-1, Pennsylvania State University, Las Vegas, USA. Aroua, M.K., Zuki, F.M., Sulaiman, N.M., 2007. Removal chromium ions from aqueous solutions by polymerenhanced ultra filtration. J. Hazard. Mater. 147, 752
758. Babel, S., Kurniawan, T.A., 2003. Low cost adsorbents for heavy metals uptake from contaminated water: a review. J. Hazard. Mater. B. 97, 219
243. Barakat, M.A., 2008. Removal of Cu(II), Ni(II), and Cr(III) ions from wastewater using complexation
ltrafiltration technique. J. Environ. Sci. Technol. 1 (3), 151
156. Basaldella El, I., Va
zquez, P.G., Iucolano, F., Caputo, D., 2007. Chromium removal from water using LTA zeolites: effect of pH. J. Colloid Interface Sci. 313 (574
578), 569
573. Bateman, Alan M., Jensen, Mead L., 1981. Chapter 5. In: Economic Mineral Deposits, 2nd Edition John Wiley & Sons, pp. 72
75. Bohdziewicz, J., 2000. Removal of chromium ions (VI) from underground water in the hybrid complexationultrafiltration process. Desalination 129 (3), 227
235. Bolger, P.T., Szlag, D.C., 2004. Electrochemical treatment and reuse of nickel plating rinse waters. Environ. Prog. 21, 203
208. Bureau of Indian Standards, 1991. Indian Standard for drinking water as per BIS Specifications, IS: 10500. Castillo, A.M.N., Soriano, J.J., Garcy´
a-Delgado, R.A., 2008. Changes in chromium distribution during the electrodialytic remediation of a Cr (VI)-contaminated soil. Env. Geochem. Health 30, 153
157. Chanda, M., Rempel, G.L., 1997. Chromium(III) removal by epoxy-crosslinked poly (ethyleneimine) used as get-coated on silica, 1. sorption characteristics. Ind. Eng. Chem. Res. 36, 2184
2189. Chen, G.H., 2004. Electrochemicals technologies in wastewater treatment. Sep. Purif. Technol. 38 (1), 11
41. Chen, J.M.N., Hao, O.J.N., 1998. Microbial chromium(VI) reduction. Crit. Rev. Environ. Sci. Technol. 28 (3), 219
251. Chen, G., 2004. Electrochemical technologies in wastewater treatment. Sep. Purif. Technol. 3, 11
41. Chopra, A.K., Sharma, A.K., Kumar, V., 2011. Overview of electrolytic treatment: an alternative technology for purification of wastewater. Arch. Appl. Sci. Res. 3 (5), 191
206. Cieslak-Golonka, M., 1995. Toxic and mutagenic effects of chromium (VI) a review. Polyhedron 15, 3667
3689. Cook, K.R., 2000. In-situ treatment of soil and groundwater contaminated with chromium, Technical Resources Guide, United States Environmental Protection Agency, US EPA/625/ R-00/005. Dermentzis, K.I., Davidis, A.E., Dermentzi, A.S., Chatzichristou, C.D., 2010. An electrostatic shielding based coupled electrodialysis/electrodeionization process for removal of cobalt ions from aqueous solutions. Water Sci. Technol. 62, 1947
1953.

Chromite ore beneficiation: prospects and challenges Chapter | 3

113

Dudeney, A.W.L., Chan, B.K.C., Bouzalakos, S., Huisman, J.L., 2013. Reclamation and environment management of waste and wastewater from mineral industry processes, especially leaching of sulphide resources: state of the art. Int. J. Min. 27 (1), 2
37. Dupont, I., Guillon, E., 2003. Removal of hexavalent chromium with a lignocellusic substrate extracted from wheat bran. Environ. Sci. Technol. 37, 4235
4241. Eary, L.E., Rai, D., 1987. ‘Kinetics of Chromium(III) oxidation to chromium(VI) by reaction with manganese dioxide’. Environ. Sci. Technol. 21, 1187
1193. Ghosh, G., Bhattacharya, P.K., 2006. Hexavalent chromium ion removal through micellar enhanced ultrafiltration. Chem. Eng. J. 119 (1), 45
53. Gode, F., Pehlivan, E., 2007. Sorption of Cr(III) onto chelating b- DAEG
sporopollenin and CEP
sporopollenin resins. Bioresour. Technol. 98, 904
911. Godgul, G., Sahu, K.C., 1995. Chromium contamination from chromite mines. Environ. Geol. 25, 251
257. Gupta, V.K., Ali, I., 2003. Adsorbents for water treatment: development of low cost alternatives to carbon for the updated. In: Somasundaran, P. (Ed.), Encyclopedia of Surface and Colloid science. Marcel Dekker, New York, pp. 1
34. Gupta, V.K., Srivastava, S.K., Mohan, D., 1997. Design parameters for fixed bed reactors of activated carbon developed from fertilizer waste for the removal of some heavy metal ions. Waste Manage 17 (8), 517
522. Gupta, V.K., Park, K.T., Sharma, S., Mohan, D., 1999. Removal of chromium(VI) from electroplating industry wastewater using bagasse flyash—a sugar industry waste material. Environmentalist 19, 129
136. Gupta, V.K., Gupta, M., Sharma, S., 2001. Process development for the removal of lead and chromium from aqueous solutions using red mud—an aluminium industry waste. Water Res. 35 (5), 1125
1134. Heidmann, I., Calmano, W., 2008. Removal of Zn(II), Cu(II), Ni(II), Ag(I) and Cr(VI) present in aqueous solutions by aluminium electrocoagulation. J. Hazard. Mater. 152, 934
941. Herrmann, J.M., 1999. Heterogeneous photocatalysis: fundamentals and applications to the removal of various types of aqueous pollutants. Catal. Today 53, 115
129. Inglezakis, V.J., Loizidou, M.D., Grigoropoulou, H.P., 2003. Ion exchange of Pb2 1 , Cu2 1 , Fe3 1 and Cr3 1 on natural clinoptilolite: selectivity determination and influence on activity on metal uptake. J. Colloid Interface Sci. 261, 49
54. Kabay, N., Arda, M., Saha, B., Streat, M., 2003. Removal of Cr(VI) by solvent impregnated resins (SIR) containing aliquat 336. Reactive Funct. Polym. 54 (1
3), 103
115. Kapure, G., Mohan Rao, S., 2008. Application of terminalia chebula for removal of hexavalent. ISIJ Int. 48 (6), 868
874. Karthikeyan, T., Rajgopal, S., Miranda, L.R., 2005. Chromium(VI) adsorption from aqueous solution by Heveabrasiliensis sawdust activated carbon. J. Hazard. Mater. 124 (1
3), 192
199. Karthikeyan, T., Rajgopal, S., Miranda, L.R., Chromium(VI) adsorption from aqueous solution by Heveabrasiliensis sawdust activated carbon. J. Hazard. Mater., 124(1
3), 192
199. Khezami, L., Capart, R., 2005. Removal of chromium (VI) from aqueous solution by activated carbons: kinetic and equilibrium studies. J. Hazard. Mater. 123, 223
231. Khezami, L., Capart, R., 2005. Removal of chromium (VI) from aqueous solution by activated carbons: kinetic and equilibrium studies. J. Hazard. Mater. 123, 223
231.

114

Mineral Processing

Kozlowski, C.A., Walkowiak, W., 2002. Removal of chromium(VI) from aqueous solutions by polymer inclusion membranes. Water Res. 36, 4870
4876. Kurniawan, A., Chan, G.Y.S., Lo, W.-H., Babel, S., 2006. Physico-chemical treatment techniques for wastewater laden with heavy metals. Chem. Eng. J. 118, 83
98. Lazaridis, N.K., Bakayannakis, D.N., Deliyianni, E.A., 2005. Chromium (VI) sorptive removal from aqueous solution by nano crystalline akaganeite. Chemosphere 58, 65
73. Lee, M.Y., Hong, K.J., Shin-Ya, Y., KajiuchiT, 2005. Adsorption of Cr(VI) by chitosan-based polymeric surfactants. J. Appl. Polym. Sci. 96 (1), 44
50. Lin, S.H., Juang, R.S., 2002. Heavy metal removal from water by sorption using surfactantmodified montmorillonite. J. Hazard. Mater. 92, 315
326. Liu, Y.-X., Yuan, D.-X., Yan, J.-M., Li, Q.-L., Ouyang, T., 2011. Electrochemical removal of chromium from aqueous solutions using electrodes of stainless steel nets coated with single wall carbon nanotubes. J. Hazard. Mater. 186, 473
480. Lottermoser, B.G., 2010. Mine Wastes: Characterisation, Treatment and Environmental Impacts, third ed. Springer, Heidelberg, Dordrecht, London, New York. Lu, H., Wang, J., Yan, B., Bu, S., 2010. Recovery of nickel ions from simulated electroplating rinse water by electrodeionization process. Water Sci. Technol. 61, 729
735. Marder, L., Bernardes, A.M., Ferreira, J.Z., 2004. Cadmium electroplating wastewater treatment using a laboratory-scale electrodialysis system. Sep. Purif. Technol. 37, 247
255. Martinez, S.A., Rodriguez, M.G., Aguolar, R., Soto, G., 2004. Removal of chromium hexavalent from rinsing chromating waters electrochemicals reduction in a laboratory pilot plant. Water Sci. Technol. 49 (1), 115
122. Matis, K.A., Mavros, P., 1991. Recovery of metals by ion flotation from diluteaqueous solutions. Sep. Purif. Meth. 20, 1
48. McNeill, L., McLean, J., Edwards, M., Parks, J., 2012. State of the Science of Hexavalent Chromium in Drinking Water, Water Research Foundation, Denver, pp. 1
13. Mohammadi, T., Moheb, A., Sadrzadeh, M., Razmi, A., 2005. Modeling of metal ion removal from wastewater by electrodialysis. Sep. Purif. Technol. 41 (1), 73
82. Mohan, D., Singh, K.P., Singh, V.K., 2005. Removal of hexavalent chromium from aqueous solution using low-cost activated carbons derived from agricultural waste materials and activated carbon fabric cloth. Ind. Eng. Chem. Res. 44, 1027
1042. Mohan, D., Singh, K.P., Singh, V.K., 2006. Trivalent chromium removal from wastewater using low cost activated carbon derived from agricultural waste material and activated carbon fabric cloth. J. Hazard. Mater. 135, 280
295. Mollaha, M.Y.A., Morkovskyb, P., Gomesc, J.A.G., Kesmezc, M., Pargad, J., Cockec, D.L., 2004. Fundamentals, present and future perspectives of electrocoagulation. J. Hazard. Mater. 114 (1
3), 199
210. Murray, J.W., Spell, B., Paul, B., 1983. The contrasting geochemistry of manganese and chromium in the Eastern Tropical Pacific Ocean. In: wong, C.S., Boyle, E., Bruland, K., Burton, J.D., Goldberg, E.D. (Eds.), Trace Metals in Seawater. Plenum Press, New York, pp. 643
670. Muthukrishnan, M., Guha, B.K., 2008. Effect of pH on rejection of hexavalent chromium by nanofiltration. Desalination 219, 171
178. Myers, C.R., Myers, J.M., Carstens, B.P., Antholine, W.E., 2000. Reduction of chromium (VI) by human microsomal enzymes: effects of iron and quinines. Toxic. Subst. Mech. 19, 25
51. Norseth, T., 1981. Cancer hazards caused by nickel and chromium exposure. J. Toxicol. Environ. Health. 40, 121
130.

Chromite ore beneficiation: prospects and challenges Chapter | 3

115

¨ lmez, T., 2009. The optimization of Cr(VI) reduction and removal by electrocoagulation using O response surface methodology. J. Hazard. Mater. 162, 1371
1378. Ozaki, H., Sharma, K., Saktaywin, W., 2002. Performance of an ultra-low pressure reverses osmosis membrane (ULPROM) for separating heavy metal: effects of interference parameters. Desalination 144, 287
294. Parga, J.R., Cocke, D.L., Valverde, V., Gomes, J.A.G., Kesmez, M., Moreno, H., et al., 2005. Characterization of electrocoagulation for removal of chromium and arsenic. Chem. Eng. Technol. 28 (5), 605
612. Paterson, J.W., 1975. Wastewater treatment technology. Ann. Arbor Mich, 12, 43
58. Petruzzelli, D., Passino, R., Tiravanti, G., 1995. Ion exchange process for chromium removal and recovery from tannery wastes. Ind. Eng. Chem. Res. 34, 2612
2617. Rengaraj, S., Joo, C.K., Kim, Y., Yi, J., 2003. Kinetics of removal of chromium from water and electronic process wastewater by ion exchange resins: 1200H, 1500H and IRN97H. J. Hazard. Mater. 102 (2/3), 257
275. Rengaraj, S., Yeon, K.-H., Moon, S.-H., 2001. Removal of chromium from water and wastewater by ion exchange resins. J. Hazard. Mater. 87 (1
3), 273
287. Rengaraj, S., Yeon, K.-H., Kang, S.-Y., Lee, J.-U., Kim, K.-W., Moon, S.-H., 2002. Studies on adsorptive removal of Co(II), Cr(III) and Ni(II) by IRN77 cation-exchange resin. J. Hazard. Mater. 92 (2), 185
198. Rojas, G., Silva, J., Flores, J.A., Rodriguez, A., L’Maldonado, M., 2005. Adsorption of chromium onto cross-linked chitosan. Sep. Purif. Technol. 44, 31
36. Roundhill, D.M., Koch, H.F., 2002. Methods and techniques for the selective extraction and recovery of oxoanions. Chem. Soc. Rev. 31, 60
67. Saffaj, N., Loukil, H., Younssi, S.A., Albizane, A., Bouhria, M., Persin, M., et al., 2004. Filtration of solution containing heavy metals and dyes by means of ultrafiltration membranes deposited on support made of Morrocan clay. Desalination 168, 301
306. Sahu, S.K., Meshram, P., Pandey, B.D., Kumar, V., Mankhand, T.R., 2009. Removal of chromium(III) by cation exchange resin, Indion 790 for tannery waste treatment. Hydrometallurgy 99 (3
4), 170
174. Salazar, E., Ortiz, M.I., Urtiaga, A.M., 1992. Equilibrium and kinetics of Cr(V1) extraction with Aliquat 336. Ind. Eng. Chem. Res. 31, 1516
1522. Sanjay, K., Arora, A., Shekhar, R., Das, R.P., 2003. Electroremediation of Cr (VI) contaminated soils: kinetics and energy efficiency. Colloids Surf. A: Physicochem Eng. Asp. 222, 253
259. Sapari, N., Idris, A., Hisham, N., 1996. Total removal of heavy metal from mixed plating rinse wastewater. Desalination 106 (1
3), 419
422. Selomulya, C., Meeyoo, V., Amal, R., 1999. Mechanisms of Cr(VI) removal from water by various types of activated carbons. J. Chem. Technol. Biotechnol. 74 (2), 111
122. Senthikumar, R., Vijaraghavan, K., Jegan, J., Velan, M., 2010. Batch and column removal of total chromium from aqueous solution using Sargassum polycystum. Environ. Prog. Sustain. Energy 29, 334
341. Shaalan, H., Sorour, M., Tewfik, S., 2001. Simulation and optimization of a membrane system for chromium recovery from tanning wastes. Desalination 14, 315
324. Song, Z., Williams, C.J., Edyvean, R.G.J., 2000. Sedimentation of tannery wastewater. Water Res. 34 (7), 2171
2176. Tels, M., 1987. Advances in treating heavy metals containing wastes. Resour. Conserv. 14, 71
92. Tiravanti, G., Petruzzelli, D., Passino, R., 1997. Pretreatment of tannery wastewaters by an ion exchange process for Cr(III) removal and recovery. Water Sci. Technol. 36, 197
207.

116

Mineral Processing

Tsai, S.C., Ouyang, S., Hsu, C.N., 2001. Sorption and diffusion behavior of Cs and Sr on JihHsing bentonite. Appl. Radiat. Isot. 54, 209
215. Udaybhaskar, P., Iyengar, L., Rao, A.V.S.P., 1990. Cr(VI) interaction with chitosan. J. Appl. Polym. Sci. 39 (3), 739
747. US Department of Health and Human Services (USDHHS), 1991. Toxicological Profile for Chromium, Public Health Services Agency for Toxic Substances and Diseases Registry. Washington, USDHHS. Vasudevan, S., Lakshmi, J., Vanathi, R., 2010. Electrochemical coagulation for chromium removal: process optimization, kinetics, isotherms and sludge characterization. Clean Soil Air Water 38, 9
16. Yeon, K.H., Seong, J.H., Rengaraj, S., Moon, S.H., 2003. Electrochemical characterization of ionexchange resin beds and removal of cobalt by electrodeionization for high purity water production. Sep. Sci. Technol. 38, 443
462. Zhitkovich, A., Quievryn, G., Messer, J., Motylevich, Z., 2002. Reductive activation with cysteine represents achromium(III)-dependent pathway in the induction of genotoxicity by carcinogenic chromium(VI). Environ. Health Persp. 110 (S9), 729
731.

Chapter 4

Beneficiation of bauxite ores Pradip Kumar Banerjee1, Amol Udaram Mankar2 and Vivek Kumar3 1

Hindalco Industries Ltd, Mumbai, Maharashtra, India, 2Hindalco Industries Ltd, Belagavi, Karnataka, India, 3Hindalco Industries Ltd, Lohardaga, Jharkhand, India

4.1

Introduction

Approximately 8% of the earth’s crust comprises aluminum, the most abundant metal in the world. It is considered a metal for the future for its strategic significance. Fig. 4.1 shows many important properties, such as light weight, high durability, corrosion resistant, non-toxic, high thermal, and electrical conductivity, and high strength-to-weight ratio. The metal can be recycled several times without losing its inherent properties, which makes it truly a green metal. The metal’s potential is yet untapped in various parts globally. The production and consumption of the metal has grown steadily over the last several years. Most consumption is yet at the lower end of value, for example, power, infrastructure, durable goods, building and construction. With increased focus on its usage in the areas of packaging, transportation, aerospace, defense, the industry is ready for rapid growth in the future. Aluminium

Light Weight

Aids in fuel efficiency in Transportaon (Auto, Aviaon) and Defense sectors

Electrical Conducvity

Reduced energy losses while transmission in electrical conductors and cables

Durability

High durability Ideal for applicaons requiring sturdy and robust structures, e.g. construcon

Thermal Conducvity

Quick heat transfer

Corrosion Resistant

An-corrosive properes due to oxide surface layer

Strength

High, in alloyed forms High strength to weight rao

Non-Toxic

Preferred for packaging soluon (food, pharma)

Recyclable

Known as “Green Metals” Can be recycled number of mes without loosing its inherent properes.

FIGURE 4.1 Properties of aluminum metal. Mineral Processing. DOI: https://doi.org/10.1016/B978-0-12-823149-4.00014-4 © 2023 Elsevier Inc. All rights reserved.

117

118

Mineral Processing

The aluminum industry is quite resource intensive. Bauxite is the only ore commercially used for extracting aluminum metal. The complete value chain for aluminum production is depicted in Figs. 4.2 and 4.3, which shows the raw materials needed for the metal production. The ore is processed to produce alumina by the Bayer process. Alumina is then converted to a metal through electrolysis in aluminum smelters. The downstream plants produce end products through various processes, such as hot and cold rolling, extrusions. For 1 t of metal production, approximately 2 t of alumina is required, which is obtained through processing 5
6 t of bauxite ore. Large amount of power is consumed for smelting of aluminum, which is mostly provided by coal-based power plants. For this, about 8
12 t of coal is needed per ton of aluminum produced. In addition, large volume of by-products generated through this process accounts for about 3
4 t of bauxite residue (red mud) and 2
5 t fly ash. Bauxite ore plays a key role in the sustainability of primary aluminum production. The ore quality determines the performance of the Bayer’s process. The process is uneconomical if the reactive silica content in the ore is

FIGURE 4.2 Aluminum value chain.

FIGURE 4.3 Major raw materials and by-products generation for 1 ton of aluminum production.

Beneficiation of bauxite ores Chapter | 4

119

.5%. This is mainly due to excessive soda consumption in the process. The other problem associated with low-grade bauxite ore is the generation of large volumes of bauxite residue. Bauxite residue is very fine and alkaline in nature, which is a potential pollution threat to water, land, and air. The safe storage and utilization are major problems for alumina plants worldwide. It is, therefore, necessary to develop efficient technologies to reduce reactive silica and other gangue materials from the ores and simultaneously establish value-added uses of the bauxite residue generated from the process for the sustainability of the aluminum industry (Kumar et al., 2013; Banerjee, 2018; Buntenbach, 2008). There is no substitute for bauxite as source for aluminum extraction conducted on a large scale. However, calcined clay can be substituted for refractory bauxite but only with reduction in time and stock resistance. Sillimanite, alumina, silicon carbide, magnesite-chromite, and carbon-magnesite refractories are the other alternatives for high alumina material, but these would entail higher costs. Silicon carbide and diamonds can substitute for fused aluminum oxide in abrasive use but these would entail again a higher cost. Synthetic mullite is a probable substitute for bauxite-based refractories. Silicon carbide and alumina-zirconia are costlier substitutes for bauxitebased abrasives. The raw material like alunite, anorthosite, coal wastes and oil shales are other potential sources of alumina. The extraction, however, would require development of cost-effective technologies.

4.2

Refining of bauxite ore for alumina production

Alumina produced commercially from bauxite ore is primarily through a refining process patented by Karl Josef Bayer in 1887. In the Bayer process, alumina-bearing minerals in bauxite, that is, gibbsite, boehmite, and diaspore, are selectively extracted from the insoluble components by dissolving them in a solution of sodium hydroxide at temperatures ranging from 120 C to 270 C, depending on the form of alumina-bearing mineral present in the ore. The solution is separated from digested slurry by different methods, which contain sodium aluminate and then the solute of the solution precipitates to aluminum hydroxide. The hydrate is calcined to produce metallurgical grade alumina, which is used to produce aluminum through Hall-Heroult smelting process. The digestion of bauxite involves not only dissolution of most alumina but also the silica present as kaolinite and quartz. It is generally considered uneconomical to treat bauxites containing highly reactive silica. It has been estimated that about 1.2 t of soda is consumed for dissolving 1 t of silica during the digestion of the ore. The resultant insoluble product, commonly known as desilication product (DSP), reports to bauxite residue leading to its increased generation. The actual processing conditions within the digester,

120

Mineral Processing

such as the caustic concentration, leaching temperature and pressure, and the operating costs, are greatly influenced by the type of bauxite ore. Ores with high gibbsite content can be processed at about 140 C. Processing of boehmite contrarily requires 220
270 C. Complete extraction from diaspore bauxite requires stronger caustic solutions in addition to higher temperature and pressure. In general, the reaction equilibria move to the right with increase in caustic soda concentration and temperature as in Eq. 4.1. However, the reaction rate of reactive silica is faster than bauxite minerals. To recover the caustic soda, it is allowed several hours for storage during digestion period at nearing atmospheric boiling to make re-precipitation of the solubilized silica to DSP as per given in Eq. 4.2. 3Al2 SiO5 ðOHÞ4 1 18NaOH-6Na2 SiO3 1 6NaAlðOHÞ4 1 3H2 O 6Na2 SiO3 1 6NaAlðOHÞ4 1 Na2 X-Na6 ½Al6 Si6 O24 Na2 X

ð4:1Þ ð4:2Þ

X represents a variety of inorganic anions, most commonly sulfate, carbonate, chloride, aluminate and hydroxide. Since DSP is usually discarded with the bauxite residue as per above two equations, loss of sodium hydroxide is at least one mole of NaOH per mole of reactive silica. This loss of soda in bauxite residue is the source of the economic penalty and is linear with the reactive silica content in the bauxite. The reduction of reactive silica and other gangue minerals present in bauxite ore is the major concern for any alumina processing industries today. The above problems will be amplified with further increase in the use of low-grade ores. It is, therefore, necessary to understand the mineralogical characteristics of the ores and develop beneficiation technologies for removal of reactive silica and other gangue minerals from the ores.

4.3

Bauxite ore resources

Bauxite ore is basically an aluminous rock that contains hydrated aluminum oxide as the main constituent and iron oxide, silica and titania as minor constituents present in varying proportions. Hydrated aluminum oxides present in the bauxite ore are diaspore and boehmite, Al2O3  H2O (Al2O3% 85%, Al 45%); gibbsite or hydrargillite, Al2O3  3H2O (Al2O3% 65.4%, Al 34.6%), and bauxite (containing colloidal alumina hydrogel), Al2O3  2H2O (Al2O3% 73.9%, Al 39.1%). The iron oxide in bauxite ore is present as hematite or goethite; silica as clay; and free quartz and titania as leucoxene or rutile. Bauxite is the principal ore of aluminum which is one of the most important nonferrous metals used in the modern industry. It is also an essential ore for refractory and chemical industries. The world bauxite reserves are estimated at 30 billion tons and are located mainly in Guinea (25%), Australia (20%), Vietnam (12%), Brazil (9%), Jamaica (7%), Indonesia, Guyana, and China (3% each). The world

Beneficiation of bauxite ores Chapter | 4

121

production of bauxite was estimated at 304 million tons in 2017. Australia continued to be the major producer and accounted for about 29% share in total production, followed by China (21%), Guinea (15%), Brazil (13%) and India (7%) (Indian Minerals Yearbook, 2018). China is undoubtedly the biggest consumer of bauxite and some alumina refineries have been built in the recent past based on imported gibbsite bauxite of Guinea. According to Antaike, the research arm of the China Nonferrous Metals Industry, China is expected to add 4.7 million tons of alumina production capacity in 2020 and China’s total production may rise by 3.3% to 73.98 million tons per annum (Nandi, 2021). Bauxite resources in China are concentrated in regions such as Guangxi, Guizhou, Henan, and Shanxi. Chinese origin bauxite supply becomes tight because of strict environmental protection policy and the local bauxite is at present costlier than the imported ore of Guinea. Alumina refineries in Henan and Shanxi have also started using imported bauxite. Demand for imported bauxite will continue to rise and Guinea will be major contributor (Nandi and Bangoura, 2020). Chinese domestic bauxite production peaked in 2018 and is now declining on depleting reserves, lower grades, and environmental constraints. China’s declining bauxite output continues to accelerate bauxite imports. It is estimate that in 2020
21, only 70 million tons of domestic bauxite will be used. Keeping in view the total alumina production in China as 74 million tons with an average bauxite consumption of about 2.6 t, the bauxite requirement in China may be in the range of 190 million tons and out of this, about 70 million tons will be sourced from domestic mines. This will lead to import of about 120 million tons bauxite by China and majority of this will be sourced from Guinea thanks to superior bauxite quality and fast developing infrastructure. According to Asian Metal report, China imported about 100.6 million tons of bauxite during 2019, out of this 70.7 MT was gibbsitic ore (i.e., bauxite from Guinea, Indonesia, Brazil, Malaysia, and India) and about 29.9 MT boehmitic ore (i.e., bauxite from Australia and other countries). Guinea exported about 44.4 million tons of bauxite to China during 2019 and remaining 25.9 MT ore was exported to all over the world. The proportion of Guinea bauxite to China may further increase in 2020 as observed in the present trend of this year. In 2019, Guinea, Australia and Indonesia remained the top three bauxite exporters to China with their combined volume of 94.9 Mt. Bauxite production in Indonesia was 1.4 million tons compared with 4,72,000 tons in 2015, 2.56 million tons in 2014, and 57 million tons in 2013, as mines that supplied two alumina refineries ramped up production. A ban on exporting bauxite and other unprocessed mineral ores took effect on January 12, 2014. The export ban was part of the 2009 Mining Law and was intended to increase economic development in the country through investment in mineral processing facilities. The Government proposed to change the bauxite export ban by establishing a system to issue 5-year bauxite

122

Mineral Processing

export permits to companies building alumina refineries in Indonesia (Indian Minerals Yearbook, 2018). In Malaysia, bauxite production decreased to 1 million tons in 2016 from 35 million tons in 2015 and 3.67 million tons in 2014. In January, the Government temporarily banned bauxite mining in response to illegal mining and pollution at ports from bauxite stockpiles. The initial mining ban was for 3 months but was extended until at least March 2017. Exportation of bauxite was still allowed in order to remove uncovered stockpiles at ports. When mines increased production in 2015, storage facilities and other infrastructure were inadequate for handling and storing bauxite, leading to water pollution. Production in Malaysia increased in 2015 to supply alumina refineries in China after Indonesia implemented a ban on exporting bauxite and other mineral ores in 2014 (Indian Minerals Yearbook, 2018). The bauxite demand in India will grow albeit at a slow pace as alumina industry is growing at slower rate and the country has its own mines of medium grade bauxite. However, some good bauxite deposits are located in deep forest and ecologically sensitive areas with population of tribes. Presently, few Indian alumina refineries are importing bauxite from Guinea and Sierra Leone and total may reach maximum to 10 million tons in the future (Nandi, 2021). Reserves/resources of bauxite in India as on April 01, 2015, as per NMI database, based on UNFC system have been placed at 3,896 million tons These resources include 656 million tons reserves and 3,240 million tons remaining resources. By grades, about 77% resources are metallurgical grade. The resources of refractory and chemical grades are limited and together account for about 4%. State-wise, Odisha alone accounts for 51% of country’s resources of bauxite followed by Andhra Pradesh (16%), Gujarat (9%), Jharkhand (6%), Maharashtra (5%), and Madhya Pradesh and Chhattisgarh (4% each). Major bauxite resources are concentrated in the East Coast bauxite deposits in Odisha and Andhra Pradesh (Indian Minerals Yearbook, 2018).

4.4

Bauxite mining practices

The mining of bauxite is carried out by opencast method. The mines are classified in the following three categories depending upon the level of mechanization: G G G

Manually operated mines. Semimechanized mines. Mechanized mines.

4.4.1

Manually operated mines

Many bauxite mines are small and produce less than 25,000 tpy. The entire work of overburden removal, extraction of bauxite and loading of bauxite

Beneficiation of bauxite ores Chapter | 4

123

onto trucks is conducted manually and the bauxite is transported to respective railway siding or plants by road.

4.4.2

Semimechanized mines

In semimechanized mines, mining operations are carried out by jack hammer drilling and normally ANFO mixture is used as an explosive for blasting in mineralized zone as well as in overburden, if required. Loading of mineral on to trucks or dumpers is done by payloaders or manually. Since bauxite occurs as small lenses or pockets or boulders or as segregations in laterite, it is difficult to mechanize the mining operations.

4.4.3

Mechanized mines

Mechanized mining operations are carried out in a few captive mines of the alumina/aluminum plants. These mines use compressed-air drills for drilling blastholes. Sometimes, compressed-air jack hammer drills are also used for drilling blastholes for secondary blasting of boulders and also for the drilling in irregular bauxite faces caused due to improper fragmentation of bauxite. The blasted overburden/ore materials are handled and transported separately by using shovels or excavators and trucks /dumpers. Separate benches are maintained for overburden and ores. The height of benches in ore varies from 1.5 to 7.5 m. Hindalco had done away with drilling and blasting at its west coast mines in Maharashtra and instead had adopted the state of-the-art ripper dozer which is regarded as “Miner’s Plow.” The ripper dozer silently plows the mine surface to extract the mineral. It eliminated ground vibrations and air pollution normally caused by dust, gases, and noise. In Central India, mines of Hindalco in Jharkhand, the blasted bauxite is being transported with the help of dumpers to the crusher. The 4-inch crushed bauxite is then transported to nearby railway station by a monocable aerial ropeway. Balco also had monocable ropeway for transporting bauxite from its captive mines to the alumina plant at Korba in Chhattisgarh. Computerized mine planning, use of mobile crusher, simultaneous land reclamation, restricting operations to small portions of mining area at a time, etc. have greatly helped in conserving energy and faster land rehabilitation. In East Coast mines of Odisha, Nalco has adopted the mechanized “Trench method” of opencast mining. In this method, a pilot trench is driven through the middle of the deposit and several other trenches are opened on both sides in a staggered pattern exposing and creating more number of working faces. Transportation of ore to alumina refinery has been done through a 14.6 km long single-flight, multi curve cable belt conveyor of 1800 tph capacity. The mining operations involve dozing aside the top fertile soil which is usually preserved and hard laterite of 3 m thickness is drilled and blasted. The overburden is removed using higher capacity mobile

124

Mineral Processing

equipment like dumpers and wheel loaders to expose the bauxite bed. The top slice of bauxite having 8
10 m thickness is loosened by drilling and blasting and the bauxite of 3
4 m thickness at the bottom contact is removed selectively using backhoe shovels. The higher capacity mobile equipment like dumpers, wheel loaders, ripper dozers and faster drills had been introduced in newer mines.

4.5

Geology of bauxite deposits

The bauxite ore is a hydrated aluminum oxide with associated impurities like iron oxide, titanium dioxide and silicon dioxide. When alumina-rich igneous rock or metamorphic rocks weather, the feldspars of such rocks are usually kaolinized, but under tropical monsoonal condition, the weathering goes a step further and results in residuum rich in hydroxide of aluminum together with oxides of iron, manganese and titanium. The deposit gets economically viable for alumina extraction when sufficient concentration of the aluminum hydroxides is reached in the deposit (Bhukte et al., 2017a,b; Bhukte and Chadda, 2014; Rao and Ramam, 1979). Bauxites are considered to be of two major types: (1) lateritic bauxite and (2) karst bauxites. Lateritic bauxites are primarily alumina-silicate rocks, whereas karst bauxites are from inter bedded carbonate and alumina-silicate rocks (Bhukte et al., 2017a,b). Bauxite is composed of one or more aluminum hydroxide minerals, including primarily gibbsite [Al(OH)3], boehmite [AlO(OH)] and diaspore [AlO(OH)]. Based on the presence of aluminabearing minerals, bauxite ores are classified as: (i) pure gibbsite, (ii) gibbsite having quartz, (iii) gibbsite-boehmite mix, (iv) boehmite, and (v) diaspore. There are also other compounds in bauxite, such as hematite (Fe2O3), goethite [FeO(OH)], quartz (SiO2), rutile/anatase (TiO2), kaolinite [Al2Si2O5 (OH)4] and other impurities in minor or trace amounts. In lateritic ore, the main silicate mineral is kaolinite and often associated with goethite. The other common silicate mineral in bauxite ore is quartz. Hematite and goethite are the main iron bearing gangue minerals present in bauxite ore. The India deposits are mostly associated with laterite capping occurring as blankets on the plateau and hill ranges of the coastal and peninsular regions. However, occurrence at lower level is also common, especially on the Western and Central part of India. These bauxites are hard and massive in the top 1
3 m thickness and moderately hard and spongy below (Choudhuri and Mukherjee, 1992). The common types include reddish brown, pink, cream and yellowish-brown colored bauxites with crystalline, cryptocrystalline textures where dense gibbsite occurs in varying proportions. The pink, cream, ash and yellow types are invariably of good quality and are characterized by high alumina and low iron. Deepening of the color to red and allied shades signifies decrease in alumina and increase in iron content.

Beneficiation of bauxite ores Chapter | 4

125

Vesicular, Vermicular, and spongy textures are very common. Spongy texture is common in all sections of the profiles whereas the other textures are restricted to the top section (3
5 m) in general. Bauxite/Laterites derived from the charnockite are usually very hard and dark red colored with no trace of any relict structure of the parent rock. Bauxite capping overlying charnockite are relatively flat whereas those of khondalite are slopping. Dense gibbsite is in greater proportion in the bauxite overlying the charnockite whereas crystalline and partly crystalline gibbsite is common in the khondalitic bauxite. Vermicular and spongy textures are very common and outlines of relict garnets are discernible even to the naked eye in bauxite derived from the khondalitic gneisses. The specific gravity of bauxite ranges between 2.1 and 2.3 while the porosity and moisture contents are highly variable. In India, a vast area of west-central part covering states of Maharashtra, parts of Madhya Pradesh, Gujarat, Jharkhand, and Chhattisgarh is underlain by continental flood basalts of Paleocene age (Deccan Traps), which host numerous important bauxite deposits, resulting from lateritization processes. The ore is widely developed in the form of pockets and lenses within extensively developed laterite over the Deccan basaltic plateau. Bauxite was formed due to subaerial weathering and lateritization of Deccan basalt under intense weathering conditions with very good drainage. This enables the dissolution of the kaolinite and the precipitation of the gibbsite. Zones with highest aluminum content are usually found below the ferruginous surface layer. Presence of boehmite and goethite are evidences of intense weathering during the formation of the bauxite deposits. A generalized lateritic profile of the area is as follows: G G G G G G G G

Topsoil Aluminous and ferruginous Laterite Aluminous laterite Bauxite Aluminous and ferruginous Laterite Lithomarge clay Altered trap Deccan trap

4.6

Characterization of bauxite ores

Indian bauxite deposits have been categorized into three types based on the regions: East Coast, Central India, and West Coast bauxite. Generally, Central Indian bauxites contain high boehmite content, which require high temperature and high-pressure digestion technology (Kumar et al., 2020). As shown in Fig. 4.4, these deposits are mostly boulder type formation with high total available alumina (TAA) and high silica content; occasionally

126

Mineral Processing

FIGURE 4.4 Classification of Central India Bauxite Ores based on geological background.

found in continuous layers which are high TAA and low silica. The East Coast bauxites are mainly gibbsite with high iron content. These are easy to digest and are main sources for alumina production in the country. The quality of West Coast bauxite varies quite significantly with location of mines. These are mainly gibbsitic. Some of these ores are low in iron content and being used as raw materials for the refractory industries. The mining of bauxite is carried out by opencast method because of its formation in shallow depth. These result in high level of contamination in the ore being mined leading to its high transportation and processing cost. Detailed studies were conducted with a typical gibbsite-boehmite mix type bauxite ore from Central Indian deposits and with low or sub-grade ores, namely, aluminous lateritic and partially kaolinized khondolite (PKK) samples from East Coast deposits of India.

4.6.1

Gibbsite-boehmite mix ore (central Indian deposits)

Following studies were carried out to understand the characteristics of the ore (Biswal et al., 2021): G G

G

Size-wise wt.% and chemical analysis. Mineralogical studies: associated minerals, quantification, color, and textures. Liberation studies: grain sizes of key minerals and gangue minerals, locking pattern and quantification and liberation sizes for gangue minerals.

4.6.1.1 Sample collection and chemical analysis About 10 t representative sample of the ore was collected from the mines for the studies. The sample was first reduced to 100 mm size. The reduced sample was mixed thoroughly, and a representative sample of 400
500 kg was collected by following the standard cone and quartering technique. The representative samples were subjected to detail characterization, crushing and liberation, classification and beneficiation studies, such as scrubbing,

Beneficiation of bauxite ores Chapter | 4

127

TABLE 4.1 Bulk chemical analysis of a typical Central India Gibbsite & Boehmite mix Bauxite sample. Type of Sample

Moisture, %

Fe2O3, %

Al2O3, %

LOI, %

SiO2(T), %

SiO2 (R), %

TiO2, %

Central India (gibbsite 1 boehmite)

6.9

17.6

41.3

22.8

4.6

3.6

7.4

hydrocyclone, magnetic separation and flotation. The bulk analysis of as received bauxite samples is given in Table 4.1. The as received bauxite ore samples crushed to below 100 mm were subjected to further size reduction by using a jaw crusher and roll crusher. The run of mine (ROM) sample was reduced to 225 mm. A representative sample was prepared by following coning and quartering technique. The crushed products were classified into different size fractions such as 225 1 10, 210 1 3.35, 23.35 1 1, 21 1 0.5, 20.5 1 0.25, 20.25 1 0.15, 20.15 1 0.1, 20.1 1 0.075, 20.075 1 0.045, and 20.045 mm using both dry and wet sieving process. Each size fraction was subjected to wet chemical analysis to evaluate the Fe2O3, Al2O3, SiO2 (total silica, reactive silica); TiO2 and loss on ignition.

4.6.1.2 Petrographic characterization Representative samples were collected and polished sections were prepared in cold mounting medium of epoxy araldite for optical microscopy. Powdered samples were characterized by XRF and XRD methods. Characterization of the selected samples of bauxite was performed using the following methods: G G G G

Physical characterization. Optical microscopy. X-ray diffraction. X-ray fluorescence.

4.6.1.2.1 Megascopic studies Five representative bulk bauxite samples were taken for the mineralogical study based on their typical morphological features, such as oolitic, pisolitic, spotted, dispersed, disseminated and massive varieties (Fig. 4.5). The spongy nature of all the samples is due to the laterite capping over bauxite. The pisolitic bauxite of the studied area is reddish to off white in color, consisting dominantly of pellet shaped pisolites/oolites. The bulk density and the

128

Mineral Processing

FIGURE 4.5 Hand specimens and morphological varieties of bauxite ore collected from mines. (A) Bauxite showing well-developed pisolites in a red color fine matrix of iron oxide. (B) Pisolitic bauxite showing small, spherical, concentrically layered structure. (C) Fine disseminated bauxite minerals are in iron matrix. (D) Bauxite showing spotted white oolites in iron and clay matrix. (E) Porous, spongy bauxite.

porosity of the representative samples have been measured and shown in Table 4.2. 4.6.1.2.2 X-ray fluorescence study The chemical analysis of five powdered bauxite samples was carried out by X-ray fluorescence method to obtain the major elements in the oxide form as shown in Table 4.3 showing presence of Al2O3, Fe2O3, SiO2, TiO2, and LOI at varying concentrations. The major constituents are aluminum and iron with titanium and minor silica. The LOI varies from 16% to 27%.

Beneficiation of bauxite ores Chapter | 4

129

TABLE 4.2 Bulk density and porosity of different specimen of Central India bauxite ore. Sample

Bulk density (g/cm3)

Porosity (%)

1

2.56

4.57

2

2.27

4.48

3

2.40

7.35

4

2.39

4.25

5

2.62

19.64

TABLE 4.3 Chemical composition of bauxite sample obtained from XRF data. Sample name

Al2O3, %

Fe2O3, %

SiO2, %

TiO2, %

LOI, %

Sum

1

41.9

19.4

0.8

7.5

23.7

93.3

2

69.7

4.5

0.9

8.8

16.1

100.0

3

53.3

16.1

1.0

8.7

20.7

99.8

4

52.3

6.3

1.0

9.7

27.5

96.8

5

48.8

21.4

1.2

8.5

19.7

99.6

4.6.1.2.3

Mineralogy

Mineralogical variations in different morphologies of bauxite ore are observed from their respective XRD (Fig. 4.6, Table 4.4) and textural pattern under optical and stereo microscope. Major minerals present in the lateritic zone are gibbsite, goethite, boehmite, and hematite. Irrespective of morphotypes, gibbsite dominates in the bauxite zone along with small amounts of anatase. Minor amounts of quartz are observed in all types. All samples contain iron oxide phases like hematite and goethite. The XRD analysis revealed the presence of gibbsite, boehmite, hematite, goethite, anatase, and quartz mineral phases in the rock samples. 4.6.1.2.4

Optical microscopy

The petrographic investigation under reflected light microscope (Figs. 4.7 and 4.8) suggests that the samples consist of mostly gibbsite, hematite, goethite, anatase, and silica. During the process of lateritization/bauxitization, a

130

Mineral Processing

140000 Gibbsite Boehmite

100000

Gibbsite Anatase Boehmite

140000

Anatase Hematite Goethite Quartz

120000 Intensity counts, a.u

Intensity counts, a.u

120000

80000 60000 40000

-Quartz Hematite

100000 80000 60000 40000 20000

20000

0 0 10

20

30

40

50

60

70

80

10

20

30

Position, 2θ

40

50

60

70

80

Position, 2θ

90000 Gibbsite Boehmite

80000

Intensity counts, a.u

70000 60000

Intensity counts, a.u

Anatase Hematite Goethite Quartz

50000 40000 30000 20000

70000

Gibbsite Boehmite

60000

Anatase Hematite Goethite Quartz

50000 40000 30000 20000 10000

10000 0

0 10

20

30

40

50

60

70

80

10

20

30

Position, 2θ

40

50

60

70

80

Position, 2θ

FIGURE 4.6 X-ray diffraction patterns of selected bauxite representative samples showing different mineral phases.

TABLE 4.4 Quantitative analysis from XRD. Sample

Gibbsite

Boehmite

Goethite

Hematite

Anatase

Quartz

1

68.6

6.7

19.7

4.0

0.6

0.5

2

88.8

8.6




1.6

0.6

0.4

3

71.2

6.1

19.3

2.4

0.5

0.6

4

90.7

2.2

4.2

2.0

0.9




5

72.5

5.0

17.1

4.2

0.7

0.5

lot of change took place; some elements like Si and Fe are leached out. Enrichment of Al is due to its residual concentration. The pisolitic morphology dominating over the samples caused by sequential Al migration, both laterally and vertically. 4.6.1.2.5

Stereomicroscopic studies

Different size classified fractions from 25 mm to 45 microns were studied under stereo microscope to find out their liberation pattern (Fig. 9A and B).

Beneficiation of bauxite ores Chapter | 4

131

FIGURE 4.7 Microphotographs of bauxite samples (Gi-gibbsite, Go-goethite, H-hematite, Aanatase). (A) Gibbsite grains are enclosed within silicate oolites surrounded by iron rich matrix. (B) Gibbsite grains are pocketed in clay rich groundmass. (C) Well-developed pisolitic and oolitic grains of gibbsite in goethite and hematite matrix. (D) Large pisolites of gibbsite embedded in clay matrix. (E) Microcrystallites of anatase found disseminated in gibbsite grains along with hematite and goethite crystals.

Most of the samples consist of aluminum minerals (mostly gibbsite with minor amount of boehmite), iron bearing minerals (hematite, goethite), titanium bearing minerals (anatase), and quartz. The XRD analysis of different size fractions and the quantitative analysis is shown in Fig. 4.10 and Table 4.5, respectively. The photo micrographs are shown in Figs. 4.11A and B.

132

Mineral Processing

FIGURE 4.8 Microphotographs of bauxite samples (Gi-gibbsite, Go-Goethite, H-hematite, and A-Anatase). (A) Hematite and goethite rims around the silicate grains. (B) Microcrystallites of anatase and crystals of hematite and goethite are found disseminated in clay matrix. (C) Rims of hematite and goethite around gibbsite grains. (D) Large grains of silicate oolites and gibbsite grains found in aluminous rich matrix. (E) Gibbsite grains are enclosed within silicate oolites surrounded by rims of hematite and goethite.

4.6.2

Low-grade bauxite ores (East Coast deposits in India)

4.6.2.1 Aluminous laterite sample The size analysis of the representative sample was carried out by the standard wet sieving methods down to micron size (Rao and Das, 2014; Rao, 2016). Different standard sieves down to below 45 microns, for the sample and were subjected to size analysis. The complete chemical analysis of the

133

Beneficiation of bauxite ores Chapter | 4

FIGURE 4.9 (A) Stereo-micrographs of wet size classified fraction. (a) 25 1 3 mm, (b) 23 1 2 mm, (c) 22 1 1 mm, (d) 21 1 500 μm. (B) Stereo-micrographs of size classified fraction. (a) 2500 1 250 μm, (b) 250 1 150 μm, (c) 2150 1 75 μm, (d) 275 1 45 μm.

Gibbsite Boehmite

Anatase

Hematite

Goethite

Gibbsite

Quartz

Boehmite

Anatase

Hematite

Quartz

Goethite

-75+45μm -150+75μm -250+150μm -500+250μm

Intensity counts, a.u.

Intensity counts, a.u.

-1mm+500μm -2mm+1mm -3mm+2mm -5mm+3mm

20

40

60

20

80

40

60

80

Position 2θ

Position 2θ

FIGURE 4.10 X-ray diffraction pattern of wet size classified fraction showing mineral phases of gibbsite, boehmite, anatase, goethite, hematite, and quartz.

TABLE 4.5 Quantitative analysis from XRD. Size, mm

Gibbsite

Boehmite

Goethite

Hematite

Anatase

Quartz

25 1 3

70.5

5.4

20.5

2.5

0.5

0.6

23 1 2

69.3

5.3

21.8

2.5

0.5

0.6

22 1 1

68.7

5.8

21.6

3.0

0.4

0.6

21 1 0.5

63.3

6.4

24.1

2.7

0.7

0.8

20.5 1 0.25

68.4

6.7

21.4

2.4

0.5

0.7

20.25 1 0.15

75.3

5.8

15.9

1.8

0.7

0.5

20.15 1 0.075

76.5

4.6

15.8

2.0

0.6

0.6

20.075 1 0.045

76.4

4.7

15.9

2.0

0.5

0.6

134

Mineral Processing

FIGURE 4.11 (A) Microphotographs of wet size classified samples. (a) 2 5 1 3 mm, (b) 23 1 2 mm, (c) 22 1 1 mm, (d) 2 1 1 0.5 mm, (B) Microphotographs of wet size classified samples. (a) 20.5 1 0.25 mm, (b) 20.250 1 0.150 mm, (c) 20.150 1 0.075 mm, (d) 20.075 1 0.045 mm. (A: Anatase, Go: Goethite, H: hematite).

different size fractions obtained from the size analysis were determined by X-ray florescence technique against the known standards. The complete chemical analysis of the representative sample and different process products were conducted after grinding the sample to a very fine size. The weight percentage data of the size classified fractions along with their alumina, silica, iron oxide, and titania is reported in Table 4.6. The data reveals that there is no significant variation in the alumina, silica and iron oxide content in any size classified fractions. All the size classified fractions show more or less similar levels of alumina, silica, and iron oxide content. Quantitative mineralogy of aluminous laterite sample is shown in Fig. 4.12. Typical mineral phases present in the aluminous laterite samples are shown in Fig. 4.8.

4.6.2.2 Partially kaolinized khondalite sample The size analysis of the representative sample was conducted by the standard wet sieving methods down to micron size (Rao and Das, 2014; Rao, 2016). Different standard sieves down to below 45 microns were used for the size analysis. The complete chemical analysis of the different size fractions obtained from the size analysis were determined by X-ray florescence technique against the known standards. The complete chemical analysis of the representative sample and different process products were carried out after grinding the sample to a very fine size. The weight percentage data of the size classified fractions along with their alumina, silica, iron oxide, and titania is reported in Table 4.7. The size classification data along with their respective analysis indicates that the 110 mm size classified fraction sample is approximately 16% and shows improvement in alumina content (from 40% in the feed to 45% in 110 mm size) and decrease in iron and silica content also.

Beneficiation of bauxite ores Chapter | 4

TABLE 4.6 Size classification of the as received laterite sample. Size

Weigh in %

Laterite sample Al2O3 (%)

Fe2O3 (%)

SiO2 (%)

TiO2 (%)

140 mm

9.67

41.18

27.91

5.79

2.12

240 1 20 mm

45.85

40.41

32.51

4.22

1.91

220 1 10 mm

18.65

38.18

32.92

6.91

1.84

210 1 5.6 mm

8.33

38.50

31.93

7.04

1.91

25.6 1 3.35 mm

3.19

38.72

33.05

6.80

1.85

23.35 1 2 mm

1.68

38.09

32.69

7.10

1.94

22 1 1 mm

3.12

38.96

31.19

7.21

1.93

21000 1 500 μm

1.86

38.58

31.06

8.35

2.01

2500 1 250 μm

2.01

37.99

30.92

9.23

2.14

2250 1 150 μm

0.36

37.68

32.87

8.31

2.73

2150 1 100 μm

0.47

36.91

33.42

8.95

2.73

2100 1 75 μm

0.43

36.97

33.24

8.02

2.85

275 1 45μm

0.17

36.32

34.52

7.81

2.85

245 μm

4.21

36.08

32.46

11.07

2.71

FIGURE 4.12 Quantitative mineralogy of aluminous laterite sample.

135

136

Mineral Processing

TABLE 4.7 Size classifications of the as received PKK sample. PKK sample Wt.%

Al2O3(%)

Fe2O3(%)

SiO2(%)

TiO2(%)

115 mm

6.91

47.11

12.02

14.61

0.83

215 1 10 mm

9.52

44.22

13.87

19.42

1.06

210 1 6 mm

3.99

38.82

18.61

20.26

1.43

26 1 3 mm

2.78

41.24

14.91

19.97

1.08

23 1 2 mm

3.73

40.96

14.41

23.46

1.12

22 1 1 mm

4.13

39.53

18.30

22.70

1.06

21 1 500 μm

4.26

38.79

21.20

22.16

1.06

2500 1 300 μm

4.62

37.44

23.19

22.73

1.05

2300 1 210 μm

4.35

38.01

21.18

24.46

1.15

2210 1 150 μm

2.69

38.29

19.63

25.27

1.43

150 1 100 μm

5.92

38.03

20.03

25.13

1.69

2100 1 75 μm

4.08

38.51

18.02

26.84

1.58

275 1 45 μm

4.35

37.98

19.18

26.27

1.52

2C45 μm

38.64

38.04

19.75

26.03

1.41

4.7 4.7.1

Beneficiation of bauxite ores Gibbsite
Boehmite mix type ore (Central Indian deposits)

Amenability of the ore towards physical beneficiation was studied through the following studies (Biswal et al., 2021): G G G G G

Impact of crushing and grinding on mineral liberation. Dry beneficiation processes. Wet scrubbing and separation processes. Gravity, magnetic, and flotation. Proposed beneficiation flowsheet with grade and recovery data.

4.7.1.1 Size classification and scrubbing studies 4.7.1.1.1 Dry and wet sieving of the samples crushed to 25 and 100 mm top sizes Size-wise chemical analysis was carried out with as-received sample crushed to below 10 and 25 mm sizes. Wet sieving was adopted for both the samples.

Beneficiation of bauxite ores Chapter | 4

137

TABLE 4.8 Bulk analysis of bauxite ore. Composition

Al2O3

Fe2O3

SiO2 (T)

SiO2 (R)

SiO2 (NR)

TiO2

LOI

Percentage

41.27

17.61

4.16

3.42

0.74

7.38

22.86

Dry sieving was also carried out with 225 mm size ore for comparison between dry and wet sieving. The detailed chemical analysis of the sample studied is presented in Table 4.8. The chemical composition of the sample are 17.61% Fe2O3, 41.27% Al2O3, 4.16% SiO2, 7.38% TiO2, and 22.86% LOI. The reactive silica present in the sample is 3.42%. The nonreactive silica content is 0.74% and less than the reactive silica. From the point of cost reduction and to reduce the reactive silica content, it is worth pursuing the removal of reactive silica from the ore by a physical and physio-chemical beneficiation process. The 225 mm bauxite ore is classified into different size fractions by wet and dry sieving methods (Tables 4.9 and 4.10). Size-wise analysis for 2100 mm sample was carried out through wet method as given in Table 4.11. Size distribution of all the three samples is shown in Fig. 4.13. The d80 of the 225 mm sample is 20 mm. The d80 of 2100 mm sample is 70 mm. The size distribution suggests that the undersize percentage obtained by wet sieving is slightly higher than the dry sieving. The effect of size classification on the silica removal of the 225 mm ore for both dry and wet methods is shown in Fig. 4.14. The result indicates that the total and reactive silica removal are higher in wet than the dry classification at any given classification. The result suggests that by wet classification at 0.5 mm, it is possible to achieve 26% and 15% total and reactive silica removal, respectively at 95% yield. The result indicates wet sieving is more efficient to remove the reactive silica than dry sieving. About six times more silica content is reduced in wet sieving. The effect of size classification on the silica removal of 2100 mm bauxite ore is shown in Fig. 4.15. The result indicates that by wet classification at 0.5 mm it is possible to achieve 33% total silica removal with 93% yield. 4.7.1.1.2

Scrubbing followed by hydrocyclone of 20.5 mm fraction

The 225 mm crushed bauxite sample of 5 kg was subjected to scrubbing in a standard ball mill of 300 mm 3 300 mm dimension without any grinding media, which is similar to a commercial scrubber in laboratory scale. The scrubbed product was screened at 0.5 mm sieve to have the 10.5 fraction as the concentrate product. The 20.5 mm fraction was further subjected to classification in a hydrocyclone to have the underflow as a secondary product. The hydrocyclone overflow was the final rejects.

TABLE 4.9 Size-wise wet classification and chemical analysis of 225 mm bulk bauxite ore. Size, mm

Wt.%

Cum. Wt, %

Al2O3, %

Fe2O3,%

SiO2 (T), %

SiO2(R), %

TiO2, %

LOI, %

- 2 25 1 10

69.05

69.05

42.13

17.94

2.63

2.07

7.70

21.33

210 1 5.6

12.24

81.29

41.10

18.58

4.92

4.40

7.19

20.52

25.6 1 3

3.24

84.53

41.11

18.75

5.53

4.99

7.19

20.46

23 1 2

2.73

87.26

41.30

17.35

4.72

4.48

7.24

21.41

22 1 1

2.28

89.54

41.43

16.90

4.33

3.84

7.31

19.19

21 1 0.5

3.10

92.64

41.96

15.65

4.83

4.15

7.48

18.36

20.5 1 0.25

1.75

94.39

41.49

14.17

6.81

4.85

7.79

15.87

20.25 1 0.15

0.29

94.68

40.66

14.41

7.25

4.09

7.62

16.29

20.15 1 0.075

0.49

95.17

41.31

14.82

7.37

5.18

7.51

19.05

20.075 1 0.045

0.49

95.66

39.95

15.30

10.12

5.88

6.80

15.81

20.045

4.34

100.00

35.15

13.34

25.85

14.49

5.57

11.17

41.59

17.63

4.32

3.25

7.49

20.47

100

TABLE 4.10 Size-wise dry classification and chemical analysis of 225 mm bulk bauxite ore. Wt., %

Cum. Wt., %

Al2O3, %

Fe2O3, %

SiO2 (T), %

SiO2 (R), %

TiO2, %

LOI, %

225 1 10

72.34

72.34

42.46

16.41

2.82

2.15

7.76

23.18

210 1 5.6

12.15

84.49

41.46

17.63

4.35

3.79

7.34

22.58

25.6 1 3

4.04

88.54

41.11

17.80

4.56

3.97

7.28

22.45

23 1 2

2.25

90.79

40.99

17.55

4.94

4.11

7.21

22.48

22 1 1

1.63

92.42

41.24

16.98

5.54

4.16

7.17

21.93

21 1 0.5

2.86

95.28

40.79

15.31

8.49

6.35

6.96

21.42

20.5 1 0.25

1.95

97.24

39.93

14.31

11.77

8.07

6.89

20.69

20.25 1 0.15

0.23

97.46

40.00

14.14

11.08

7.67

7.07

20.61

20.15 1 0.075

0.59

98.06

39.00

14.58

13.35

9.5

6.76

19.75

20.075 1 0.045

1.54

99.60

36.47

14.02

20.58

11.24

6.05

17.52

20.045

0.40

100.00

36.49

14.04

20.11

11.44

6.15

17.52

41.99

16.51

3.93

2.97

7.59

22.81

100.00

140

Mineral Processing

TABLE 4.11 Size-wise wet classification and chemical analysis of 2100 mm bulk bauxite ore. Size, mm

Wt. %

Cum. Wt., %

Al2O3, %

Fe2O3, %

SiO2 (T), %

TiO2, %

2100 1 50

55.47

55.47

45.049

13.359

1.849

8.503

250 1 25

19.53

74.99

41.346

18.49

2.775

7.796

225 1 10

9.31

84.31

40.884

18.415

3.84

7.631

210 1 5.6

2.69

86.99

41.541

17.509

3.389

7.575

25.6 1 3

1.88

88.88

38.773

20.958

5.843

6.495

23 1 2

1.51

90.38

38.851

20.793

6.311

6.368

22 1 1

1.30

91.69

40.174

18.441

5.84

6.566

21 1 0.5

1.36

93.05

40.79

17.202

6.156

6.709

20.5 1 0.25

1.14

94.20

35.448

13.457

6.005

5.596

20.25 1 0.15

0.91

95.10

41.366

14.223

8.788

6.868

20.15 1 0.075

0.34

95.45

40.936

15.392

8.732

6.489

20.075 1 0.045

0.25

95.70

38.104

14.502

15.54

5.188

20.045

4.30

100.00

32.951

12.857

29.656

4.162

Total

100

42.82

15.31

3.8741

7.89

100 -25 mm wet sieving

Cum. Undersize, %

90

-25 mm Dry sieving

80

-100 mm Wet sieving

70 60 50 40 30 20 10 0 0.01

0.1

1 Size, mm

10

FIGURE 4.13 Particle size classification of 225 and 2100 mm bauxite ore.

100

Beneficiation of bauxite ores Chapter | 4

141

-25 mm bauxite ore classification 45

SiO2 (T) Removal, %: wet sieving SiO2 (R) Removal, %: Wet sieving Yield: Wet sieving

40

100

SiO2 (T) Removal, %: Dry sieving SiO2 (R) Removal, %: Dry sieving Yield: Dry sieving

95 90 85

30

80 25 75

20 70 15

Yield, %

Silica removal, %

35

65

10

60

5

55

0

50 0

2

4

6

8

10

12

Size classification

50 45 40 35 30 25 20 15 10 5 0

-100mm wet siving (SiTR)

0 10 20 30 40 50 60 70 80 90 100

Yield

Yield

Total silica removal, %

FIGURE 4.14 Effect of size classification on the silica removal of 225 mm bauxite ore.

0

10

20 30 40 Size classification, mm

50

FIGURE 4.15 Effect of size classification on the silica removal of 2100 mm bauxite ore.

The effect of scrubbing time on the silica removal was studied as shown in Fig. 4.16. Fig. 4.16 indicates that the silica and total silica removal increases with an increase in scrubbing time till 3 minutes. With a further rise in scrubbing time, the total and reactive silica removal decreases. Based on these results, a process flowsheet has been developed as shown in Fig. 4.17. The result shows that it is possible to achieve a bauxite

142

Mineral Processing

45

SiO2 (T) Reduction %:1 mm

SiO2 (R) Reduction %:1 mm

SiO2 (T) Reduction %: 0.5 mm

SiO2 (R) Reduction %: 0.5 mm

Yield, %: 1 mm

Yield, %: 0.5 mm

60 65

35

70

30 25

75

20

80

15

Yield, %

Silica removal, %

40

85

10 90

5

95

0 0

2

4

6 Time, min

8

10

12

FIGURE 4.16 Effect of scrubbing time on the silica removal from 225 mm bauxite ore.

FIGURE 4.17 Process flowsheet of bauxite ore to remove silica and reactive silica from the ore.

concentrate of 3.08 from feed silica content of 4.43% at 88% yield. The reactive silica content of the scrubbed product is 2.62%. The tailings contain 14.6% total silica. After hydrocyclone separation of the tailing, a second product is possible to achieve with 5.67% reactive silica with an 8.12% yield.

4.7.1.2 Magnetic separation of the bauxite ore Magnetic separation had shown promises for some of the bauxite ores (Bhagat et al., 2001, 2006). In this study, magnetic separation studies were carried out using a dry perm roll magnetic separator as shown in Fig. 4.18. Different size fractions of bauxite ore were subjected to perm roll at different belt speed at fixed splitting angle and feed rate. There were three products generated during perm roll experiment such as magnetic, middling and

Beneficiation of bauxite ores Chapter | 4

143

FIGURE 4.18 Dry magnetic separator.

40

Silica removal, %

70

Yield, %

60

30

50

25

40

20 30

15

Yield, %

Silica removal, %

35

20

10

10

5

0

0 0

20

40

60

80

100

120

Belt speed, rpm FIGURE 4.19 Effect of belt speed on the dry magnetic separation of 2300 μm bauxite ore.

nonmagnetic. Each of these product fractions were weighed and analyzed for silica and iron content. The result shows that the mag and a middling fraction has more silica content than the non-mag fractions. The belt speed also has a significant effect on the removal of iron and silica content from the ore. The effect of belt speed on the dry magnetic separation of 0.3 mm bulk bauxite ore is shown in Fig. 4.19. The results indicate that as the belt speed increases the yield of non-mag fraction increases and silica removal decreases. The studies had shown that the mag and a middling fraction had more silica content than the non-mag fractions. At 66 rpm belt speed it is possible to remove 21% total silica with 42% yield.

144

Mineral Processing

4.7.1.3 Flotation studies Flotation process was explored to reduce the reactive silica in the ore. Oleic acid and sodium hexametaphosphate (SHMP) were used as collector and depressants, respectively. Tap water was used throughout the flotation experiments. Conventional flotation experiment methodology was adopted for carrying out the studies. Denver D-12 sub-aeration flotation cell having a 3 L capacity was used for the studies (Fig. 4.20). Collector dosage and pH were varied for these experiments as shown in Table 4.12.

FIGURE 4.20 Flotation cell.

Beneficiation of bauxite ores Chapter | 4

145

TABLE 4.12 Influence of the oleic acid dosage and pH on the bauxite flotation performance (SHMP dosage 5 2 mL/kg). Collector dosage (μL/kg)

Product

Concentrate (wt.%)

Al2O3 (%)

Fe2O3 (%)

SiO2 (%)

TiO2 (%)

pH 5 5.10 300

500

Concentrates

4.00

43.40

12.78

3.13

5.33

Tailings

96.00

39.96

16.87

4.91

7.25

Feed Ore

100.00

40.10

16.71

4.84

7.17

Concentrates

18.00

46.91

15.61

2.73

6.42

Tailings

82.00

38.97

16.53

5.12

7.34

Feed Ore

100.00

40.40

16.36

4.69

7.18

pH 5 9.93 200

500

Concentrates

1.51

43.16

11.70

4.09

6.09

Tailings

98.49

40.53

16.86

4.62

7.18

Feed Ore

100.00

40.57

16.78

4.61

7.16

Concentrates

14.50

45.95

14.52

3.11

6.92

Tailings

85.50

39.73

16.77

5.22

7.23

Feed Ore

100.00

40.64

16.44

4.92

7.18

The oleic acid and SHMP were used for direct flotation of bauxite ore. The depressant solution contains 16.67% SHMP (50 g in 250 mL water). The dosage of oleic acid is varied between 200 μL/kg to 500 μL/kg at constant SHMP dosage (2 mL/kg). Flotation was not responding at 100 μL/kg collector dosage. Table 4.12 shows the results of flotation study performed at pH 5.10 (normal water pH). The concentrate wt.% was found to be very low nearly to value of 1%, however, the wt.% of the concentrate increased to 18% with increased oleic acid dosage (500 μL/kg). As seen from the Table 4.12, the Al2O3% in the concentrate increased from 40.66% to 46.91% with increased in the collector dosage. Though the yield achieved in flotation experiments were quite low, the oleic acid dosage is quite affecting for the recovery of Al2O3% in the concentrate. Table 4.12 shows that higher collector dosage of 500 μL/kg and lower pH of 5.10 gave better results. Concentrate with 18% yield and 46.91% Al2O3 and 2.73% SiO2 could be recovered at this condition. However, the yield is quite low for economical viability of the process while compared to scrubbing and classification process described in earlier section.

146

Mineral Processing

Reverse flotation technique was also attempted to float silica from the ore. In the flotation study, SOKEM 565 and starch (potato derived starch purchased form Merck) were used as silica collector and iron depressant, respectively. The experiments were conducted varying collector dosage and pH at a fixed starch dosage (2 mL/kg). Results of these experiments were also not very attractive. A concentrate with 12.37% yield and 7.96% silica could only be achieved at 500 μL/kg collector dosage and 4.8 pH.

4.7.2

Low-grade bauxite ores

4.7.2.1 Aluminous laterite sample 4.7.2.1.1 Wet high intensity magnetic separation studies Beneficiation studies were carried out using laboratory model wet high intensity magnetic separator (WHIMS) supplied by Box Mag Rapid, England (Rao, 2016). The objectives of the studies are to remove the silica as well as iron phases present in laterite sample. A desired concentration of solids was maintained during the experiment and then passed through the magnetic separator. A standard grove plate based on the particle size was used for the separation and the required current was applied to evaluate the effect of magnetic intensity. The products, magnetic and nonmagnetics, were collected and weighed. The weight of the magnetic fractions from these experiments were found too low and therefore, it was concluded that magnetic separation was not effective in beneficiating such low-grade ores. 4.7.2.1.2

Reduction roasting followed by magnetic separation

As the sample had not responded to the wet high intensity magnetic separation, reduction roasting experiments were conducted for 210 mm particle size of the sample. Tests were conducted under different temperature, time of roasting and percentage of the reductant that is activated charcoal. The sample was first mixed with the desired quantity of activated charcoal then placed in the furnace. The temperature of the furnace was raised to the desired experimental temperature and maintained at that temperature. As soon as the temperature of the charge attained the reaction temperature, the experiment was deemed to be started. Two different temperatures were considered for the reduction. After keeping the mixed charge at the reaction temperature for a predetermined period, the furnace was put off. The hot charge was either discharged after cooling to 50 C or quenched in cold water. The reduced ore was then ground to below 75 microns and subjected to WHIMS. The ground reduced products were subjected to two different levels of current intensity. The products/fractions of the WHIMS were then dried in a hot air oven and then subjected to analysis for determining their grade and weight percentage recovery. The details of the experimental

Beneficiation of bauxite ores Chapter | 4

147

TABLE 4.13 WHIMS of reduced laterite sample. Current (Amps)

Weigh %

Sample nature

Al2O3(%)

Fe2O3(%)

SiO2(%)

TiO2(%)

Conditions of reduction 850 C 1 6 C 1 120 min 7.5

52

Mag

38.4

44.1

3.8

2.2

7.5

48

N.Mag

56.2

16.8

2.9

1.7

12.5

60

Mag

38.8

42.8

3.8

2.2

12.5

40

N.Mag

55.6

16.7

2.8

1.7





Conditions of reduction 950 C 1 6 C 1 120 min 7.5

50

Mag

36.1

43.6

4.9

2.3

7.5

50

N.Mag

55.9

17.4

2.7

1.8

12.5

57.7

Mag

38.2

40.9

4.7

2.2

12.5

42.3

N.Mag

59.1

13.9

2.2

1.6

conditions, with percentage of reductant and temperature are presented in Table 4.13. Hence reduction roasting studies were carried out and a product having 59.1% Al2O3, 13.9% Fe2O3, 2.2% SiO2, and 1.6% TiO2 was obtained at conditions of reduction 950 C 1 6% C 1 120 minutes of reduction roasting time. The performance at a lower temperature of 850 C was equally attractive. The yield of this nonmagnetic fraction was about 40%, which could be a very good input raw materials for refractory and other applications.

4.7.2.2 Partially kaolinized khondalite sample 4.7.2.2.1 Wet high intensity magnetic separation studies As attempted for lateritic sample, beneficiation studies were also carried out using laboratory model WHIMS. The objectives of the studies were to remove the silica as well as iron phases present in PKK sample. A desired concentration of solids was maintained during the experiment and then passed through the magnetic separator. A standard grove plate based on the particle size was used for the separation and the required current was applied to evaluate the effect of magnetic intensity. The products viz. magnetic, and nonmagnetics were collected and analyzed by wet chemical and instrumental techniques. The PKK sample was ground to different size fractions: 2500, 2250, 2106, and 275 microns and were subjected to WHIMS. Each size fractions were subjected to 7.5, 10, and 12.5 A. The data of WHIMS magnetic separation is reported in Table 4.14.

148

Mineral Processing

TABLE 4.14 Magnetic separation studies of the PKK rock at different grinds as well as different magnetic intensity HIMS. Sample description

Weight %

Al2O3(%)

Fe2O3(%)

SiO2(%)

TiO2 (%)

LOI (%)

PKK 2 500 µm sample PKK 7.5 Amps, Mag

2.9

19.9

47.7

15.4

2.4

PKK 7.5 Amps, N. Mag

97.1

40.9

15.2

27.7

1.4

PKK 10 Amps, Mag

6.4

20.2

47.7

15.4

2.3

PKK 10 Amps, N. Mag

93.6

41.2

14.4

27.5

1.4

PKK 12.5 Amps, Mag

5.1

19.9

47.7

15.4

3.0

PKK 12.5 Amps, N. Mag

94.9

41.0

14.7

27.5

1.4

Head

100.0

40.3

16.4

27.4

1.4

12.3

12.4

PKK 2 250 µm sample PKK 7.5 Amps, Mag

9.9

19.3

46.5

16.1

2.5

PKK 7.5 Amps, N. Mag

90.1

41.9

13.3

26.9

1.4

PKK 10 Amps, Mag

10.0

19.4

46.5

16.4

2.5

PKK 10 Amps, N. Mag

90.0

41.8

13.3

26.6

1.3

PKK 12.5 Amps, Mag

10.7

19.8

44.5

16.5

2.8

PKK 12.5 Amps, N. Mag

89.3

42.1

13.0

26.7

1.4

Head

100.0

40.8

16.2

26.6

1.4

13.0

12.9

13.1

(Continued )

Beneficiation of bauxite ores Chapter | 4

149

TABLE 4.14 (Continued) Sample description

Weight %

Al2O3(%)

Fe2O3(%)

SiO2(%)

TiO2 (%)

LOI (%)

12.7

PKK 2 75 µ sample PKK 7.5 Amps, Mag

2.0

19.7

48.5

14.6

3.0

PKK 7.5 Amps, N. Mag

98.0

40.6

16.4

26.4

1.4

PKK 10 Amps, Mag

2.5

20.2

48.5

14.5

2.9

PKK 10 Amps, N. Mag

97.5

40.8

16.2

26.6

1.4

PKK 12.5 Amps, Mag

2.9

20.2

48.5

14.3

3.0

PKK 12.5 Amps, N. Mag

97.1

40.5

16.1

26.6

1.4

Head

100.0

40.1

17.4

25.4

1.3

12.3

12.3

The results indicated that the magnetic products show enhanced iron content and reduced in silica and alumina content. However, the nonmagnetic product did not give significant enrichment in alumina content. This trend was observed for all the ground fractions: 2500, 2250, and 275 microns. The primary reason for this observation was due to low yield of the magnetic fraction even at enhanced magnetic intensity. It was concluded that WHIMS is not a viable option for treating such PKK materials. 4.7.2.2.2

Scrubbing and hydrocyclone studies

Scrubbing study was carried out in 600 3 600 mm ball mill. Approximately 100 kg of the representative sample of 225 mm size was taken in a semi batch-scrubbing unit provided with continuous input and output of the materials. The wash water used for the scrubbing was continuously fed into the scrubbing unit at a predetermined rate. The scrubbed slurry obtained from the scrubbing unit was continuously fed to 1 mm sieve attached to a CTS sieve bend. The products obtained from the sieve bend were kept separately for further processing. At the end of the experiment, the entire material from the unit was taken out and subjected to screening at 1 mm size. The screen undersize and oversize products were separated out. The screens undersize along

150

Mineral Processing

TABLE 4.15 Scrubbing and hydrocyclone studies of the PKK sample. Process

Sample

Al2O3, %

Fe2O3, %

SiO2, %

TiO2, %

Scrubbing and screening

11 mm

43.07

14.67

20.05

1.03

21 mm

37.04

21.09

24.64

1.84

Hydrocyclone OF

36.57

14.21

28.76

2.12

Hydrocyclone UF

36.38

16.26

28.12

1.94

Hydrocyclone of -1 mm fraction

with the sieve bend products were mixed. The two products thus obtained from the scrubbing unit were subjected to complete chemical analysis. The
1 mm fraction generated during scrubbing was used for possible enrichment of alumina value through classification. A standard 125 mm hydrocyclone was used for the classification studies. The experiments were carried out at B25% solid by weight and at a pressure of 15
20 psi. The underflow and overflow materials were collected at steady state, dried, weighed and analyzed for different constituents. The objective of the hydrocyclone studies was to enrich the alumina content from the finer fraction obtained after scrubbing the ROM from the bulk ore. The results of the scrubbing and classification studies of the PKK sample is presented in Table 4.15. The studies shows that some enrichment on the material in terms of Al2O3 took place through scrubbing and rejecting the 21 mm fraction. The 11 mm fraction of the scrubbed material had an Al2O3 content of 43.1% as against 37.0% Al2O3 for the 21 mm fraction. However, further recovery of Al2O3 rich material from the 21 mm fraction through hydrocyclone classification did not give any encouraging results. Therefore, scrubbing and screening or scrubbing, screening and classification routes were not proven to be attractive for the beneficiation of this low-grade material.

4.8

Pilot trials for developing beneficiation flowsheet

Based on encouraging laboratory results for the silica reduction of the gibbsite-boehmite mix types of bauxite ores of Central Indian origin, pilotscale studies were undertaken to develop a cost-effective beneficiation flowsheet (Rath et al., 2020; Kumar et al., 2020; Banerjee, 2020). Table 4.16 shows the size-wise chemical analysis of the sample used for these trials. The table shows that the reactive silica content increases with decrease in size. Significant amount of clay minerals was also found adhered to large

TABLE 4.16 Size-wise chemical analysis of a typical Bauxite Ore sample from Central India. Size (mm)

Wt.%

TAA%

R-SiO2%

Al2O3%

Fe2O3%

SiO2%

TiO2%

LOI %

2 200 1 150

7.2

48.95

2.57

53.85

9.12

2.79

9.66

23.70

2 150 1 100

24.9

47.95

2.77

52.85

9.62

3.04

9.25

24.25

2 100 1 50

25.6

47.25

3.21

51.25

11.02

3.55

8.84

24.36

2 50 1 20

15.8

36.05

6.69

43.95

18.52

7.28

7.16

22.18

2 20 1 10

9.2

25.35

11.48

39.05

23.72

11.81

5.61

18.90

2 10 1 05

4.2

22.35

12.58

38.35

23.52

13.11

5.03

18.99

2 05 1 01

7.7

22.05

14.26

38.35

20.32

16.35

4.79

19.15

2 01 1 0.5

2.0

17.35

19.39

38.65

15.32

22.85

4.32

17.96

2 0.5 1 0.15

2.0

16.65

19.69

38.15

15.72

23.36

4.36

17.48

2 0.15

1.4

11.45

20.72

36.75

17.32

24.95

4.13

15.91

Feed (Cal.)

100.0

39.05

6.51

47.30

14.40

7.20

7.72

22.42

152

Mineral Processing

alumina-rich particles. Based on these observations, two processing schemes comprised crushing, screening, wet scrubbing followed by classification were developed for the beneficiation of the ores (Figs. 4.21 and 4.22). Detailed pilot scale studies were conducted with the two schemes and the results are shown in Table 4.17. The studies established that the reactive silica could be reduced from about 6.5% to 3.3% and the TAA increased from 39% to about 46% with a yield of about 70%. Comparison between two schemes shows that, Scheme-I was slightly better than Scheme-II in terms of yield for similar reduction in reactive silica. Also, the operating cost for Scheme-I is expected to be lower due to lower consumption of water and power. The product from Scheme-I will have lower moisture than the product from Scheme-II. Based on this encouraging result, a plant-based demonstration on Scheme-I has been recommended.

ROM (-200 mm)

Screen

-200 + 100 mm

Product I

-100 mm

Water -100 + 20 mm

Screen

Scrubber

Water

- 20 mm

+ 20 mm

Vibrating Screen

Product II

Reject I

- 20 mm

Reject II

FIGURE 4.21 Conceptual beneficiation flowsheet for a typical Central Indian bauxite ore.

ROM (-200 mm) -200 + 100 mm Screen Crusher -100 mm -100 mm Screen

-100 +20 mm

Water

Scrubber Water

- 20 mm

Reject I

Vibrating Screen

+ 20 mm

Product

-20 mm

Reject II

FIGURE 4.22 Conceptual beneficiation flowsheet for a typical Central Indian bauxite ore.

Beneficiation of bauxite ores Chapter | 4

153

TABLE 4.17 Comparison of two schemes in terms of reduction in reactive silica content. TAA

R.SiO2, %

Product Range Wt, %

TAA, % (increment)

Reduction in R.SiO2%

Head feed sample

39.1

6.5

100







Scheme-I

46.7
45.6

3.1
3.5

65.2
71.7

6.6
7.7

3.0
3.4

Scheme-II

45.7
47.2

3.5
2.9

70.0
57.6

6.7
8.2

3.0
3.6

4.9

Impact of different bauxites on the Bayer process

The Bayer process is basically used for the extraction of aluminum hydrate from the bauxite ores with the mass ratio of alumina to silica (A/S) above nine (Tabereaux and Peterson, 2014). The sinter process is widely used to process the poor-grade diasporic bauxite ores with A/S below seven, in China and Russia, by sintering the bauxite ore with sodium carbonate and limestone to form sodium aluminate and calcium silicate. Before the 1970s, alumina was produced in two different grades, that is, floury and sandy. During the past decades, the sandy alumina, with low fine content (90% greater than 45 μm), was more desirable because of the increased concerns of the environmental influence and energy costs. Sandy alumina can be obtained by the Bayer process, with adjustments in the precipitation step. However, it is difficult to produce sandy alumina with a low fine particulate content and narrow size distribution by the sinter process. Ores that contain high concentrations of aluminum hydroxide minerals .35%, are called bauxite. It is the raw material for almost all production of alumina. Bauxite occurs in three main forms depending on the number of molecules of water of hydration and the crystalline structure. The three structures are gibbsite, boehmite, and diaspore. The major difference between them is that boehmite and diaspore have a different crystalline structure that requires even higher temperatures and pressures for complete dehydration than gibbsite as shown in Table 4.18. Gibbsitic ores are plentiful in a number of countries such as Australia, Brazil, Guinea, Guyana, India, Jamaica, Surinam, and Venezuela. Recent discoveries of bauxite have been found in Cambodia, Saudi Arabia, and Vietnam. More than 99% of the bauxite ores in Russia and China are boehmitic and diasporic ores that are characterized by challenging processing demands, high alumina and silica content, and low A/S mass ratios. The energy usage for the low temperature digestion of gibbsite bauxite is 7.5
12 GJ/t, and the hightemperature digestion of boehmite and/or diaspore bauxite is 11
18 GJ/t.

154

Mineral Processing

TABLE 4.18 Composition and process differences in bauxites ores. Characteristics

Unit

Gibbsite

Boehmite (gibbsite
boehmite mixtures)

Diaspore

Process

Bayer

Bayer

Sonda-Lime Sinter

Composition

α-A12O3  H2O

α-A12O3  H2O

β-A12O3  3H2O

Alumina content

%

45
65

47
85

47
85

Silica

%

1
5

2
5

4
16

19

12

B4

Alumina/silica ratio Crystal system

Monoclinic

Orthorhombic

Orthorhombic

Density

g/cm3

2.42

3.01

3.44

Temperature, rapid dehydration



150

200
250

B450

Na2O in liquor

g/l

120
150

205
245

240
360

Pressure

MPa

1

1

B3.5

Energy

Gj/t

7.5
12

11
16

34
45

Sandy alumina, lower soda loss, normal organics

Floury alumina, high soda loss with DSP, high organic oxalate

Floury alumina, high fines, high 245μm

Comments

C

4.10 Major alumina refinery plants in India and abroad Alumina refining is a capital-intensive process and this is very much concentrated into selective countries and with few companies. There are only 20 countries in the world that has alumina refineries with a total installed annual capacity of over 130,000 kt. China is the leading country with more than 65,000 kt of installed capacity and over 50% of the total share. Australia and Brazil are the next two countries with in terms of installed capacity and producing more than 20% of total share. North America and Europe do not do much alumina refinery and mostly rely upon importing primary aluminum for domestic consumption. There are around 75 operational alumina refineries in the world (as on 2020). Hydro Alunorte is the world’s largest alumina refinery plant and it is located in Par´a, Brazil, in the industrial park of Barcarena. It has a total

Beneficiation of bauxite ores Chapter | 4

155

installed capacity of 6300 kt. China has the highest number of active refineries (27) and Chinalco is the company, which is having the most holding shares among them. Some of the leading alumina refineries across the world and in India are given in Tables 4.19 and 4.20.

TABLE 4.19 Major alumina companies and technology in the world Name of refinery

Production capacity (Mtpa)

Digestion Technology

CHALCO

17

Bayer sinter process

Alcoa and Alumina limited

12

low temp digestion

Rio Tinto(Australia)

7.9

high temp sweetening, tube digestion

Rusal

7.7

Bayer sinter process

Norsk hydro (Norway)

6.2

low temp digestion

Nalco India

2.1

Atmospheric low temp digestion

EGA

2.0

Tube digestion

TABLE 4.20 Major alumina companies and technology in India. Name of the refinery

Present installed capacity (Mtpa)

Digestion technology

NALCO, Damanjodi

2.275

Atmospheric low temp digestion

HINDALCO, Renukoot

0.7

High temp Double digestion

HINDALCO, Belgaum

0.32

Low temp digestion

HINDALCO, Muri

0.35

High temp Double digestion

Utkal Aluminia international, Rayagada

2.1

Low temp digestion

Vedanta, Lanjigarh

2.0

Low temp digestion

ANRAK, Visakhapatnam (NIO)

1.4

Low temp digestion

BALCO, Korba (NIO)

0.2

High temp digestion

MALCO (NIO)

0.07

Low temp digestion

NIO,- Not in operation.

150

500

120

400

90

300

60

200

30

100

0

US$ a tonne (FOB Australia)

Mineral Processing

Million tonnes

156

0 2013

2015

Production

2017

Consumption

2019

2021

2023

FOB Australia alumina prices (rhs)

Source: International Aluminium Institute (2021); World Bureau of Metal Statistics (2021); Department of Industry, Science, Energy and Resources (2021)

FIGURE 4.23 World alumina production, consumption, and prices.

World alumina consumption is forecast to rise at an average annual rate of 1.5% in 2022 and 2023, reaching 135 million tons in 2023 (Fig. 4.23). Alumina demand is driven by primary aluminum production, which is forecast to increase by 1.8% a year in 2022 and 2023. World bauxite consumption is forecast to grow at an average annual rate of 3.9% in 2022 and 2023, reaching 346 million tons in 2023. This is expected to be driven by new alumina capacity in China and India.

4.11 Bayer process technology Based on available geological exploration data and chemical analysis of bauxite average compositions of bauxite is considered for design of alumina refinery. With available mineralogical composition of bauxite, various technological options can be worked out to arrive at the best-suited process technology to be adopted for new alumina refinery. Various technological options considered for associated major unit operations and unit processes are outlined below: Bauxite crushing: As per predominant practices, secondary crushing of bauxite from around 120 to 20 mm is done using following types of crushers: G G G

Hammer crushers. Impactors. Double roll crushers.

Availability and operational reliability of such equipment are the basic consideration for their selection. Comparatively the availability and reliability of double roll crusher is much more than hammer crushers and impactors for the required duty.

Beneficiation of bauxite ores Chapter | 4

157

Bauxite Grinding: Crushed bauxite is ground to increase the surface area of bauxite resulting in improvement in its reactivity with caustic soda. Following are the various ways for grinding of bauxite: G G G

Dry grinding. Closed circuit wet grinding. Open circuit wet grinding.

Earlier, Alumina Refinery had dry grinding system using Ball mills as the main equipment. Dry grinding of bauxite causes dust generation affecting the working environment and hence the dry grinding system was modified to wet grinding system. Under wet grinding, following types/combinations are used: G G G

Single-stage closed circuit wet grinding. Two-stage closed circuit wet grinding. Single-stage open circuit wet grinding.

Generally, Rod mills/Ball mills are used as grinding equipment for bauxite in Alumina refineries in above-mentioned types of combinations. Out of the above-mentioned grinding system, single-stage open circuit grinding is considered to be an appropriate grinding technique for green-field Alumina Refinery. Digestion (Sankar Sankaranarayanan, 2020) Under mentioned digestion processes have been adopted in various Alumina refineries: G G G G G G

Atmospheric digestion. Low temperature digestion. High temperature digestion. Double digestion (co-current and counter current). Tube digestion. Two-step digestion.

Atmospheric and low temperature digestion methods are considered for gibbsitic alumina however high temperature and two-step digestion techniques are adopted in case of boehmitic bauxite. Atmospheric digestion technology has following advantages over low temperature digestion technology: G

G G

Lower capital investment as it does not require pressure vessels and slurry flash tanks. Ease in operation. Lower process steam requirement.

In spite of above advantages of atmospheric digestion, lower alumina recovery is its main disadvantage which causes higher consumption of bauxite per ton of alumina and hence under-utilization of natural resources. In addition, lower alumina recovery requires high flow of plant liquor. Hence low temperature digestion is considered to be most appropriate technology for gibbsitic bauxite.

158

Mineral Processing

For the boehmite-gibbsite mixed bauxite, double digestion, tube digestion and two-step digestion technology are adopted. Two-step digestion (atmospheric followed by high temp) Digestion shall be most efficient and economical for processing the gibbsite-boehmite mixed bauxite. Residue thickening, washing and disposal The undesired oxide of iron, titanium, silicon and other minor metals is termed as residue. The separation of residue from saturated aluminate liquor is carried out using gravity settlers/decanters. Earlier the concept was to use the large diameter settlers for the purpose but over a period of time lot of technological advancement has taken place in this area and smaller diameter deep thickeners have been developed as efficient equipment for residue settling and washing. The disposal of washed residue from alumina refinery to residue pond is achieved by two ways: G G

Wet residue ponding. Dry residue stacking.

As per latest guidelines of environmental control authority, wet residue ponding method is not permitted for green-field alumina refineries. Hence disposal of residue at higher solids at approximately 55%
65% is done which is popularly known as dry residue stacking technique. Polishing Filtration Supernatant overflow liquor collected from decanters are polished in security filtration unit of alumina refinery. Horizontal leaf filters having manual removal of residue sludge were operative in most alumina refineries of the world. Now, almost all new alumina refineries are preferring the installation of auto-dumping vertical security filters. Heat Interchange There are two methods for recovery of thermal energy from filtered aluminate liquor going to crystallizers: (i) liquor flashing system and (ii) plate heat exchangers. The heat recovery system employs a battery of flash tanks and shell and tube heat exchangers. Liquor flashing system requires more space; however, PHEs need small space and ease in operation. Both techniques are used in alumina refineries but most of the existing alumina refineries have plate heat exchanger system. Precipitation Three types of precipitation technologies are normally used in most of the alumina refineries of the World. G G G

Batch precipitation. Single-stage continuous precipitation. Two-stage continuous precipitation.

Because of higher liquor productivity and consistency in coarseness of product alumina, two-stage continuous precipitation technology is preferred over batch precipitation technology. Two-stage continuous technique is based on controlled precipitation of alumina hydrate adopting agglomeration and crystal growth principles.

Beneficiation of bauxite ores Chapter | 4

159

Calcination Calcination is the last unit step of Alumina Refinery. Two types of equipment are used for producing metallurgical grade calcined alumina: G G

Horizontal rotary kiln. Stationary calciner.

Stationary calciner is thermally efficient and hence requires less fuel per ton of alumina production. Hence stationary calciner is a preferred choice over rotary kilns. Target efficiency figures Following efficiency figures are achievable with selected process route and equipment: G G G G G

Overall alumina recovery: 94%. Liquor productivity: 90 g/L Al2O3. HFO requirement: 73 kg/t Al2O3. Process steam requirement: 1.85 t/t Al2O3. Total energy requirement: 8.5 GJ/t Al2O3.

4.12 Capital investments, Operating cost, and technoeconomical viability for green-field refinery Capital investments (CAPEX), operating cost (OPEX), and techno-economic viability aspects for setting up new alumina refineries in India are given in this chapter. The capital expenditure data analysis clearly reveals that specific capital investment in setting up alumina refineries in India varies from US$650 to US $1000 per ton of calcined alumina depending on geographic location of the plant in the country. The CAPEX will be lowest for the plant in Orissa, Gujarat, and Jharkhand whereas the same will highest in Gujarat. In addition, the OPEX will be higher mainly because of poor plant efficiency figures due to wide variation in mineralogical and chemical composition of basic input material, Bauxite. In addition, the volume effect of plant capacity because of low reserve of Bauxite in Gujarat is the other reason. It will be prudent to mention that comparatively lower grade of bauxite, nonavailability of desalinated water, availability of low calorific value solid fuel source (Lignite) for cogeneration plant are the main reasons for highest capex. Again, on opex part, the same will be abnormally high because of poor plant efficiency figures coupled with low grade of bauxite in Gujarat. At current price level of Caustic soda, Heavy furnace oil (HFO) and Lignite, even the economic viability for Alumina refinery in Gujarat is a question mark because of high specific capital investment of around US$1000 per ton and estimated operating cost excluding financing charges (interest and depreciation) at around US$200 per ton of calcined alumina as per preliminary estimates. However, the actual figures of CAPEX and OPEX can be ascertained by the project owner with detailed studies before taking financial decision on the matter. In spite of all these facts stated above, green-field alumina refineries will

160

Mineral Processing

be installed mostly in India and Vietnam in coming decade because of huge bauxite reserves of comparatively improved quality than other countries across the globe. In other words, India and Vietnam are the future destinations for green-field alumina refineries in years to come. The above deliberation will give a glimpse of required CAPEX, OPEX, and economic viability aspects for setting up green-field alumina refinery to one and all across the globe.

4.13 Sustainability challenges 4.13.1 Bauxite residue management Bauxite residue is a perennial problem to the primary aluminum producers (Banerjee, 2017; Gupta, 2020). The problem is more while processing lowgrade bauxite ores. The residue generation increases as the iron and silica bearing gangue minerals present in the ore increases. For overcoming this challenge, a 5R 1 1S bauxite residue management strategy has been adopted by Hindalco (Fig. 4.24). The key focus areas are: (i) Reduce: reduction in the generated waste through beneficiation, (ii) Redesign: modification of refining process for improvement of residue quality, (iii) Recover: extract valuable materials from residue, (iv) Storage: taking suitable steps to reduce impact of stored waste materials on environment, (v) Rehabilitate: converting exhausted bauxite residue storage areas into green areas, and (vi) Recycle: cement industries, construction works, and mine backfilling followed by rehabilitation of the mines. Hindalco has become the world’s first company to achieve 100% red mud utilization across three of its bauxite refineries. This is a major step in reducing cement industry’s dependence on mined material; replaces up to 3% of the clinker raw mix. Bauxite residue is rich in iron oxides, along with alumina, silica, and alkali. The cement industry has developed the capability to process this as a replacement for mined minerals such as laterite and lithomarge in its process. Use of bauxite residue reduces the cement industry’s dependence on natural

FIGURE 4.24 Bauxite residue (red mud) management at Hindalco.

Beneficiation of bauxite ores Chapter | 4

161

resources and promotes a circular economy. Hindalco’s alumina refineries are currently supplying 250,000 MT of bauxite residue to .20 cement companies every month, making Hindalco the world’s first company to have enabled such large-scale commercial application of bauxite residue. In the current year, Hindalco aims to achieve 2.5 million MT of bauxite residue utilization, which will be another global milestone (Verma et al., 2021; Gupta, 2020). The proximity of cement plants near the alumina plants is the key driver for its use in cement making, primarily due to high transportation cost. Unfortunately, most of the bauxite refineries in India are in Odisha which are far away from the cement plants. Alternative uses, such as, construction of roads, embankments, and mine backfilling, are to be pursued on priority to address the issues faced by east coast refineries. Hindalco along with IIT Bombay has developed and patented a process for large-scale use of bauxite residue for road subbase construction. This is being demonstrated at our Utkal alumina plant. Detailed studies have also been conducted for developing an environmentfriendly process for mine backfilling with bauxite residue. This is being piloted in our Baphlimali mines in collaboration with NEERI Nagpur, IIT Bombay, IBM Nagpur, Odisha State, and Central Pollution Control Boards and MoEFCC. As a long-term strategy, a research project has been initiated to recover metallic values from bauxite residue. Iron, aluminum, and titanium are the major metals present in bauxite residue. The presence of rare earth elements (REE) is the main attraction for value recovery from the residue. Under the guidance of Niti Aayog, a research consortium has been formed to develop technology for recovering these values from bauxite residue including the end residue utilized for construction applications. All three primarily aluminum producers (Nalco, Vedanta, and Hindalco) and three research laboratories (NML Jamshedpur, IMMT Bhubaneswar, and JNARDDC Nagpur) are members of this research collaboration. The broad conceptual processing routes for holistic use of bauxite residue is shown in Fig. 4.25.

Bauxite Residue

Construcon Materials

Products to Market

BR Beneficiaon

I. Smelting Route

Thermal Insulaon

Pig Iron

Electric Arc Furnace Soda-ash Roasng

Leachate

Water Leaching

Alumina Recovery

Chemical Treatment

Slag

Pellesing / Granulaon

Fe-Rich Fracon

Reducon Kiln

REE / Sc Recovery

Magnec Separaon

II. Reducve Roasng Route

Soda-ash + Reductant in Kiln

Non-Magnec Fracon

Chemical Treatment

Alumina Recovery

Recovery

Water Leaching

Tio2

III. Reducve Roasng with

Sodium Salts Route

FIGURE 4.25 Conceptual processing routes for total value recovery from bauxite residue with zero waste.

162

Mineral Processing

4.13.2 Effluent management Management and treatment of liquid effluents are determining factor in the design of alumina refineries (Lucy and Steven, 2011). Rainfall, evaporation rate, proximity to the coast, process design and layout, ore mineralogy, the local environment, and potential impact on neighboring communities are all integral to the development of an appropriate refinery water management strategy. An alumina refinery will generate large volumes of liquid and solid phase alkaline effluent from a variety of sources, predominantly waste mud, and other process by-products discharged with the mud, including: G G G G

Diluted process liquor entrained with the bauxite residue (red mud). Insoluble fraction of the bauxite (iron and titanium oxides). DSP—hydrated sodium aluminum silicates. Calcium compounds, for example, tricalcium aluminate and calcium oxalate.

The other effluent streams will be generated by contamination of rainfall runoff from the refinery site, and possible spillage and release of process materials to impoundments. Effluent that is released from the waste mud stream will invariably exhibit pH levels above 12. Both the liquid and the solid phase sources of alkalinity (hydroxide ions) must be reacted with a neutralizing agent. The rate at which the neutralization reaction proceeds will vary greatly depending upon the reactants involved, the pH, concentration, and temperature.

4.13.2.1 Principles of effluent treatment The primary objective is to reduce the immediate and longer-term environmental risk of the (solid or liquid) waste stream by reducing the alkalinity to the minimum practicable level. However, low alkalinity is not the only consideration. Potentially serious soluble pollutants such as aluminum and other elements (e.g., molybdates, vanadates, and arsenates) must also be targeted. Options for neutralization include reaction with seawater, dilute sulfuric acid (or a combination of both), and carbon dioxide. A third option, carbonation, is in the early stages of development and little process performance data is available to suggest this as a viable option at this phase of development. Application of either seawater or acid neutralization must recognize that a certain fraction of solid phase alkalinity is released over long periods, weeks or months, depending upon the prevailing conditions and the composition of the residue. In practical terms, there is no such thing as complete neutralization, due to the limited treatment time available. Treatment with sulfuric acid invariably involves the utilization of spent dilute acid used for cleaning refinery heat exchangers. During the cleaning process, the acid dissolves scale deposits which may contain additional pollutants. A corrosion inhibitor will also be

Beneficiation of bauxite ores Chapter | 4

163

employed, the nature of which must be assessed if the reacted acid is to be released into the environment. The chemical and physical properties of the particular bauxite to be processed have a determinant impact upon the process design of the red side of the refinery, upon the bauxite residue disposal area (BRDA) design, and upon the technology selected for effluent treatment. Significant effort and cost must be invested in the characterization of the bauxite, and the same attention must be paid to the environmental control requirements.

4.13.2.2 Acid neutralization Residue is mixed with dilute acid which reacts immediately with soluble alkalinity, producing a rapid but temporary drop in pH. This is commonly achieved by adding (waste) acid after the last mud washing stage. Attack by residual acid (if any) on the solid phase alkaline content occurs over a much longer time frame and may lead to a gradual increase in pH. It is therefore impractical to neutralize the solid phase component prior to residue disposal. Postneutralization of waters released from the BRDA may be necessary. Acid neutralization produces a dilute sodium sulfate solution, which, if released, may give rise to environmental impact in its own right, such as algal blooms or local concentrations exceeding background levels, or that specified for potable water (,250 mg/L). Careful assessment must be made to establish that sufficient acid will be available for primary/secondary residue or effluent treatment, that probable peak effluent discharge rates can be handled, and potential heavy metal contamination of spent acid is acceptable. 4.13.2.3 Seawater Neutralization The important reaction in seawater neutralization is the precipitation of hydroxyl ions by reaction with magnesium (Mg21) ions present in the seawater. Again, the rate of reaction varies greatly - rapid in the liquor phase, much slower with calcium compounds and DSP. The presence of sulfate ions will inhibit the reaction with DSP. A major advantage of seawater neutralization is the precipitation of aluminum ions during the formation of hydrotalcite, the primary reaction product from the soluble alkalis and magnesium. Hydrotalcite formation has also been shown to remove vanadium, molybdenum and phosphorus provided that the pH is in the range 8.0
10.0. Seawater neutralization of residue allows immediate effluent discharge, provided turbidity criteria can be attained, eliminating the need for separate containment and management of liquor. By providing excess seawater, alkaline runoff generated by the slow dissolution of alkaline compounds can be neutralized and released. System design must ensure that the seawater supply and discharge capacity always exceeds the magnesium demand of excursions in residue alkalinity, due to process problems. If the pH is allowed to rise,

164

Mineral Processing

some of the trace metals in the hydrotalcite will revert to the soluble phase and impact on receiving water quality. If excess alkalinity cannot be precipitated within the BRDA, additional hydrotalcite precipitation will occur at the outfall, creating a visible plume. It should be noted that attempts have been made to augment seawater neutralization with sulfuric acid. This significantly alters the chemistry such that a much lower pH is necessary to remove aluminum from the solution. Removal of oxalate is favored at high pH values, so that the addition of acid may be counterproductive and costly.

4.13.2.4 Alternative technologies Other technologies for industrial water treatment, such as membrane treatment and ion exchange, are untested on alumina wastewater chemistry and at the scale discussed in this paper. If these technologies were proven to be effective, the volumes that would require treatment in tropical and subtropical locations would result in significant increases in capital and operating costs for these facilities. In tropical and subtropical climates, coastal and inland refineries will discharge effluent under normal and extreme circumstances. To minimize the amount of effluent requiring treatment and discharge, the environmental design features and operational controls for management of raw water intake, and the water balance detailed in this paper should be incorporated into the alumina refinery design.

4.14 Concluding remarks Aluminum metal is well positioned to witness a rapid growth in the coming years. Bauxite ore is the only raw materials for the production of the metal. While the world has good amount of bauxite ore, the reserve of the good quality ore is limited. Also, the quality varies widely from region to region and country to country. The quality of the ore plays a critical role for the economics as well as sustainability of the aluminum industry. Excessive quantity of gangue bearing minerals lead to high refining cost and generation of bauxite residue which is a major environmental challenge to the industry today. The cost of refining further increases with increase in the proportion of boehmitic or diasporic alumina minerals in the bauxite ore. Various attempts had been made to characterize and beneficiate bauxite ores from different origins. Studies conducted with typical bauxite ore from Central Indian deposits have revealed that such ores are amenable to simple beneficiation process to reduce the reactive silica content to some extent. More research has to be conducted to improve the liberation and separation of gangue mineral from the alumina-bearing minerals. However, the lowgrade lateritic ores of PKK ores were found very difficult to beneficiate.

Beneficiation of bauxite ores Chapter | 4

165

Reduction roasting followed by magnetic separation has shown promises for the utilization of aluminous lateritic ores present in East Coast deposits of India. The other challenge faced by the industry is the management of large volume of bauxite residue generated from processing of bauxite ores. Hindalco has become the world’s 1st company to achieve 100% red mud utilization in cement plants across three of its bauxite refineries. Unfortunately, most of the bauxite refineries are far away from the cement plants and therefore, this application may not always viable from cost point of view. Alternative uses, such as construction of roads, embankments, mine backfilling are to be pursued on priority to address the issues faced by bauxite refineries. Simultaneously, technology to be developed for metallic value recovery from the residue, especially REE, iron, and titanium, for holistic use of the residue.

Acknowledgments The author would like to thank his colleagues from Mines and Minerals division, Alumina plants, Innovation centers and Sustainability division for their help in preparing this paper. Also, the contributions of scientists from research labs, especially, IMMT Bhubaneswar, NML Jamshedpur, JNARDDC Nagpur and Aditya Birla Science and Technology Centres, in carrying out these studies are thankfully acknowledged.

References Banerjee, P.K., 2020. Bauxite ore quality
a key to the sustainability of aluminum industry. In: Webinar on Raw Material Security for Mineral Based Industries, Society of Geoscientists and Allied Technologists, Bhubaneswar, India, December 2020. Banerjee, P.K., 2018. Resource efficiency: key to the sustainability of the Indian aluminum and copper industry. In: 22nd International Conference on Nonferrous Minerals and Metals (ICNFMM-2018), Ranchi, India, 6
7 July 2018. Banerjee, P.K., 2017. Sustainability of the Indian aluminum industry: challenges and opportunities, Travaux 46. In: Proceedings of 35th International ICSOBA Conference, Hamburg, Germany, 2
5 October 2017, pp. 37
51. Bhagat, R.P., Banerjee, B., Kunwar, R.K., Dey, S., 2001. Metallurgical & materials and mining engineering, beneficiation tests on an Indian bauxite incorporating magnetic separation. Trans. Inst. Min. Metall. Sect. C. 110, C165
C168. Bhagat, R.P., Banerjee, B., Saha, P., Mukherjee, B.C., 2006. Dry magnetic separation of bauxite ore. In: Proceedings of the International Seminar on Mineral Processing Technology: 2006, Chennai, India, pp. 328
333. Bhukte, P.G., Chadda, M.J., 2014. Geotechnical evaluation of Eastern Ghats bauxite deposits of India. J. Geol. Soc. India 84, 227
238. Bhukte, P.G., Puttewar, S.P., Agnihotri, A., 2017a. Evaluation and beneficiation of lateritic bauxite deposits of India. J. Geosci. Res. Spec. 1, 251
256.

166

Mineral Processing

Bhukte, P.G., Puttewar, S.P., Daware, G., Agnihotri, A., Thakre, G.P., 2017b. Status of lateritic bauxite deposits of India for non-metallurgical applications. J. Ind. Geol. Cong. 9 (2), 71
79. Biswal, S.K., Dwari, R.K., Rath, S.S., Eswaraiah, C., Nayak, D., Deb Berma, S., et al., 2021. Internal Report on Characterization and Beneficiation Studies of Bauxite Ores to Develop Process Flowsheet. Institute of Minerals and Materials Technology and Hindalco Industries Ltd, Bhubaneswar, pp. 1
83. Buntenbach, S., 2008. Mineral processing technologies in the bauxite and alumina industry. In: 8th International Alumina Quality Workshop, Darwin, Australia, January 2008, pp. 1
5. Choudhuri, S.K., Mukherjee, M., 1992. Monograph on Bauxite, Indian Bureau of Mines. Ministry of Mines, Nagpur, pp. 1
461. Gupta, R., 2020. Utilization of bauxite residue in different applications
a review. In: Internal Report No. HICA-2020/02, Hindalco Innovation Centre
Alumina. Indian Minerals Yearbook, 2018. Part-III: Mineral Reviews, 57th (ed.). Bauxite (Final Release). Government of India, Ministry of Mines, Indian Bureau of Mines, Nagpur, India, November, 2019. Kumar, V., Mankar, A., Parida, D.K., 2020. Beneficiation of bauxite ore: an approach towards sustainability of Indian aluminum industry. In: 24th International Conference on Nonferrous Metals, 15 December 2020. Kumar, M., Senapati, B., Kumar, C.S., 2013. Beneficiation of high silica bauxite ores of India an innovative approach. Light. Met. 2013, 187
190. Lucy, M., Steven, H., 2011. Alumina refinery wastewater management: when zero discharge just isn’t feasible. Light. Met. 1, 679. Nandi, S.K., 2021. Alumina Production in India
can it reach 20 Million tons by 2030? Personal. Commun. . Nandi, A., Bangoura, A.Y. A booming bauxite mining industry of guinea and future prospects. In: International Bauxite, Alumina and Aluminum Society (IBAAS), 2 December 2020. Rao, D.S., 2016. Internal Report on Characterization and Beneficiation Study of Low Grade Bauxite and Partially Kaolinized Khondolite Samples. Institute of Minerals and Materials Technology and Hindalco Industries Ltd. Rao, D.S., Das, B., 2014. Characterization and beneficiation studies of a low grade bauxite ore. J. Inst. Eng. D. 95, 81
93. Rao, M.G., Ramam, P.K., 1979. The east coast bauxite deposits of India. Bull. Geol. Surv. India, Series A—Econ. Geol. 46, 1
24. Rath, R.K., Swain, A.K., Singh, R.K., Ruby, K., Singh, R., 2020. Internal Report on “Studies on Beneficiation of Bauxite Sample for Reduction of Reactive Silica”. National Metallurgical Laboratory and Hindalco Industries Ltd, pp. 1
28. Sankaranarayanan, S., 2020. AA02-technology options for mixed bauxites. In: Proceedings of the 38th International ICSOBA Conference, Virtual, 16
18 November 2020. Tabereaux, A.T., Peterson, R.D., 2014. in Treatise on Process Metallurgy. Industrial Processes. Verma, A., Ashok, V., Varshney, S., 2021. Large scale use of bauxite residue in cement plants: Renukoot experience. In: 25th International Conference on Nonferrous Metals, New Delhi, August 2021, pp. 55
62.

Chapter 5

Beneficiation of mineral sands: a practical outlook Ch. V.G.K. Murty1, Jaisankar Natarajan2 and Jagadeswara Rao N.1 1

Natural Resource Division, Adani Group, Ahmedabad, Gujarat, India, 2Kenmare Moma Resources, Maputo, Mozambique

5.1

Introduction

Mineral sands are classes of ore deposits containing valuable heavy minerals that commonly include titanium-bearing minerals like, zircon, garnet, and sillimanite. The source rocks which provide the heavy mineral sands determine the composition of the economic minerals. These are formed mostly in current or old beach environments by concentration due to the specific gravity of the mineral grains. Exploration for heavy mineral sands has intensified in the recent years due to the increasing use of and demand for titanium oxides, metals, and alloys. Zircon formerly viewed as a by-product has more recently gained importance in the construction industry. Some well-known examples of heavy mineral sand (HMS) deposits are in countries such as Australia, Canada, the United States, Madagascar, Mozambique, Ukraine, South Africa, West Africa, India, and Kenya. HMS deposits are generally present as black concentrates composed of ilmenite (4.5–5.0 specific gravity), the most abundant mineral of titanium on earth, rutile (4.25 specific gravity), a high-grade titanium mineral, and zircon (4.6–4.7 specific gravity) which is used in ceramic opacifiers, frits, tiles, etc. Other heavy minerals that may occur are magnetite, kyanite, sillimanite, and garnets which hold their market segment as industrial minerals. Monazite (4.6–5.4 specific gravity), with thorium as its principal component, is a rare earth phosphate. The principal mineral sources of titanium are Rutile and Anatase (both are TiO2), Ilmenite (FeTiO3), and Leucoxene/Brown Ilmenite(Fe2Ti3O9). These titaniferous minerals with their value-added products like Synthetic Rutile and TiO2 slag constitute “titanium feedstocks” for TiO2 pigment, titanium metal, and welding electrode industries. Rutile and Anatase have high TiO2 ( . 95%) content but are found comparatively rarely in economic deposits. Ilmenite and Leucoxene more prevalent heavy mineral deposits Mineral Processing. DOI: https://doi.org/10.1016/B978-0-12-823149-4.00005-3 © 2023 Elsevier Inc. All rights reserved.

167

168

Mineral Processing

FIGURE 5.1

across the world (rock, beach and inland deposits), along with Zircon (ZrSiO4), Sillimanite (Al2O3SiO2). The material flow in the titanium industry is shown in Fig. 5.1. The ilmenite of ,58% TiO2 can be used for producing TiO2 slag or TiO2 pigment through the sulfate route The TiO2 content will largely determine the relative values of titaniferous feedstocks, and the more TiO2 there is in the material the greater its value. For comparison, the value of ilmenite is US $150
160/MT, where the value of synthetic rutile (92% TiO2) is about US $900/MT and the value of TiO2 pigment is US$3000
3300/MT. VALUE CHAIN (USD/MT)

TITANIUM INDUSTRY FEEDSTOCK FLOW MINERAL PRODUCTS

BENEFICIATED PRODUCTS

ILMENITE

SULFATE

45-50% TIO 2

ILMENITE 45-57% TIO 2

CHLORIDE ILMENITE

LEUCOXENE

58-63% TI O 2

65-91% TIO 2

TITANIUM SLAG

SYNTHETIC RUTILE

75-86% TIO 2

90-95% TIO 2

Ilmenite

Rutile

150 -160

1400-1600

TI Slag

S.R.

1434

900

RUTILE

92-96% TI O 2

TI Pigment 3300 SULFATE PIGMENT PRODUCTION

CHLORIDE PIGMENT PRODUCTION

TI Sponge

FINAL PRODUCTS TITANIUM SPONGE PRODUCTION

13000

Beneficiation of mineral sands: a practical outlook Chapter | 5

5.2

169

Geology

Mineral Sands are quaternary beach deposits that have been partially to completely reworked by the wind to form aeolian heavy mineral sand deposits. The origin of mineral sands can be attributed to the deep weathering of the abundant precambrian age crystalline rocks, such as khondalites and garnet quartz-sillimanite rocks. More resistant minerals such as Ilmenite, Rutile, Zircon, Monazite, Sillimanite, and Garnet get disintegrated from the parent rock. Erosion and river transport begin a process of selective concentration of the heavy resistant minerals in the sea, where they are further selectively concentrated on beaches by the long-shore currents and the action of waves. Further, these minerals deposited on the beaches get carried away by the winds and deposited on the land sides near the beaches to form inland dune deposits which could be Upper Sand: An upper fine- to medium-grained homogeneous ore body that is brown in color and has possibly been reworked and redeposited by the coastal winds, commonly known as an upper ore body having less slime content. Lower Sand: Lithologies, i.e., clayey sand and sandy clay, are defined as lower sand. A coarse- to fine-grained homogeneous ore body, brown in color, and is possibly alluvial sediment from the most recent deltaic progradation, commonly known as a lower ore body having high slime content. Clay: A fine-grained homogeneous ore body, brown or dark gray, possibly alluvial sediment deposited by deltaic progradation having meager THM content and very high slime content.

5.2.1

What are mineral sands?

Most sands on beaches consist of mineral quartz (SiO2) grains. Mineral sands are old beach, river, or dune sands containing concentrations of important minerals, such as rutile, ilmenite, zircon, and monazite. These “heavy” minerals have a relative density between 4 and 5.5 g/cm3 and are much heavier than common sand minerals, such as quartz, which has a density of around 2.65 g/cm3. Garnet, magnetite, sapphire, diamond, and staurolite are also mined from some mineral sand deposits.

5.2.2

Formation of mineral sands

Mineral sands form mostly by a chemical or physical breakdown of rocks, collectively known as weathering. Physical and chemical weathering are usually treated separately, but in reality, they usually go hand-in-hand and are often difficult to separate one from the other, as they tend to support each other. Chemical weathering is a more important overall sand-producing factor. It operates most efficiently in humid and hot climates. Physical weathering

170

Mineral Processing

dominates in cold or dry areas. Weathering of bedrock, which produces sand, usually occurs in the soil. Soil covers bedrock as a thin layer, providing moisture for the disintegration of rocks. Rutile, Ilmenite, Zircon, Garnet, Magnetite, and Monazite are hard minerals resistant to weathering. They all originally grow as crystals in igneous rocks such as granite or basalt and some metamorphic rocks. Over millions of years, these rocks get weathered and eroded. The harder minerals, including quartz, are washed down to the sea by heavy rainfall and fast flowing streams. The minerals are then carried back onto the beach by waves. As the waves wash up and down the beach, they carry the lighter quartz grains back into the sea, leaving the heavy mineral grains behind on the beach. Wind also helps concentrate the heavy minerals by blowing away the lighter quartz sand. These processes are repeated over millions of years, eventually creating a large deposit of mineral sands on the beach. As the sea levels rise and fell over geological time, shorelines also move. As this happens, more sand buildup cover the mineral sand deposits and they are eroded and redeposited elsewhere. This is why we sometimes find mineral sand deposits many kilometers inland and maybe as deep as 50 m below the surface.

5.2.3

Composition of Mineral sands

Mineral sand is a residue of preexisting rocks. It is therefore composed of minerals already in the rocks before the disintegration commenced. However, one important aspect—sand occurs in a harsh environment where only the strongest survive. By “strongest,” we mean the most resistant to weathering. Quartz is one of these minerals (list of minerals in sand). It is dominant in most sand samples because it is abundant. Twelve percent of the crust is composed of quartz. Only feldspars are more abundant than quartz. Relatively rare minerals like Ilmenite, Zircon, Monazite and Rutile are also highly resistant to weathering, but they rarely constitute more than a few percentage of sand. These minerals are collectively referred to as "Heavy Minerals". Heavy minerals sometimes occur in sands in higher concentrations. This is usually due to hydrodynamic sorting. Sea waves or river flow sort out heavier grains and carry lighter grains. Such occurrences are known as placers and are often valuable mineral resources. Minerals often extracted from placer deposits are gold, cassiterite, ilmenite, monazite, magnetite, zircon, and rutile.

5.2.4

Texture and transport of Mineral sands

Geologists describe sand by measuring the grain roundness and grain size distribution. By doing so, they hope to shed some light on the origin of the measured grains. Roundedness usually provides information about the length

Beneficiation of mineral sands: a practical outlook Chapter | 5

171

of the transport route and the distribution of grain sizes helps determine from which environment these grains come from. River sand is usually poorly sorted and compositionally immature. Beach sands are more rounded, and aeolian dune sands are generally well sorted. The average grain size is determined by the transport medium energy. Higher current velocity (stream flow or sea waves) can carry heavier loads. Hence most sand sediments are coarse-grained while finer materials are carried away. Sand is mainly transported by rivers, but average sand grains are too large or heavy for an average river to carry them in suspension. Hence, sand grains tend to move in “jumps”. They are lifted by more energetic currents and settle down when the current velocity decreases and then wait for the next jump. This movement mode is known as saltation. Average silt grains move differently. It is light enough to be carried in suspension for a long time and is actually one of the most important reasons why silt is treated separately from the sand. Most sand grains carried by the rivers are eventually deposited at the river mouths, where the current velocity suddenly drops. Then, sea waves (long-shore currents) take over and carry sands along the coastline. Sand grains carried by the rivers are also deposited on alluvial flood plains and point bars (inside bends of streams where current flow is the slowest). Sand is also transported by the wind, ocean currents, glaciers, turbidity currents, moving sand forms, and landforms like ripples and dunes. The following is a list of minerals in a beach sand

5.2.4.1 Quartz No other mineral is as important in the sand as quartz. It occurs almost everywhere and forms the bulk of sand composition in most cases. Pure quartz is transparent, but quartz can have almost any color. The grains are usually rounded and may be covered by a very fine hematite pigment giving them a rust-colored appearance. Why is quartz so common in sand? It is a widespread rock-forming mineral and extremely resistant to weathering. Quartz has no cleavage. So, we never see planar surfaces on freshly fractured grains. Rocks that contain much quartz are sandstone, quartzite, gneiss, granite, and many others. 5.2.4.2 Garnet Garnet is a very common heavy mineral group in many sand samples. Most garnets are pink, orange, or red. Garnets have isometric crystal structures that are very rarely elongated. Garnets are formed in metamorphic (schist, amphibolite, and eclogite) and igneous (some granites and peridotite) rocks. When sand contains an abundance of garnets, it usually contains epidote and magnetite as well. Some garnets (pyrope) are useful index minerals when

172

Mineral Processing

searching for diamond-bearing kimberlite pipes. Sometimes Staurolite grains (deeper red color) may be misidentified as garnets.

5.2.4.3 Sillimanite Sillimanite is a metamorphic mineral occurring mostly in schist and gneiss. It may be present in lesser amounts in some granites as an accessory mineral. As a sand grain, it usually is accompanied by other metamorphic minerals like kyanite, staurolite, mica, and garnet. It is usually colorless or light brown. Sillimanite grains are mostly elongated. 5.2.4.4 Kyanite Kyanite is closely related to sillimanite. Together with andalusite, these two have the same chemical composition but are different structurally. Kyanite is blue or gray and bladed. It is also a metamorphic mineral, like sillimanite. 5.2.4.5 Zircon Zircon is one of the most resistant minerals. The oldest zircon crystals are almost as old as the earth itself. These crystals are the oldest earth materials we know. Meteoritic materials are older but extraterrestrial in origin. Zircon crystals are generally very small and elongated. They are usually transparent and contain inclusions. It is easy to identify them using high magnification and illumination below the sample. Zircons are highly resistant but as time goes by, they tend to partly destroy themselves by internal radiation. They contain a small amount of uranium, which may replace zirconium in the crystal structure. This fact makes zircon grains highly valuable to geologists as a geological chronometer. 5.2.4.6 Apatite Apatite is present in small quantities in many igneous and metamorphic rocks. It is also an important biomineral. This mineral is principalm component of the teeth. Apatite crystals are usually elongated and are colorless or have pale shades of blue, green, or yellow. 5.2.4.7 Monazite Monazite is an igneous and metamorphic mineral. Monazite grains are usually very small and not easily spotted. They are mostly pale yellow or colorless. Monazite is a valuable mineral resource. It is mined because it contains some rare and valuable chemical elements (cerium, lanthanum, and thorium). 5.2.4.8 Rutile Rutile occurs in small amounts in igneous and metamorphic rocks. It is a common heavy mineral in sand because it is very resistant to weathering.

Beneficiation of mineral sands: a practical outlook Chapter | 5

173

Rutile is reddish-brown and usually elongated. It is easier to spot when the sample is illuminated from below. Rutile is an oxide of titanium. It is mined for its titanium content.

5.2.4.9 Ilmenite Ilmenite is a widespread mineral accessory in many igneous and metamorphic rocks. It is opaque and has a metallic black color. It is weakly magnetic due to intergrown magnetite. Ilmenite grains tend to be somewhat tabular. Ilmenite is mined for its titanium content. 5.2.4.10 Magnetite Magnetite is easy to identify because it is highly magnetic. Magnetite grains are generally small and equant. Some grains may have well-developed octahedral crystal faces. Magnetite occurs in igneous and metamorphic sources. Mode of Occurrence of Heavy Mineral Sands

5.3 5.3.1

Mining Mining technologies

Worldwide, mineral sands are mined using various mining technologies. These are generally selected to suit the deposit characteristics, along with the scale of operations. Other criteria are geographical and infrastructure aspects of the deposit and corporate history and opportunistic use of conveniently available equipment. Very high-grade deposits should favor mining systems to ensure selectivity and high resource recovery. Conversely, large low-grade resources require bulk mining techniques with a low unit cost. Low unit value deposits

174

Mineral Processing

also require short transport distances between the mine and concentrator, and then to the tailing’s disposal site. Large dune systems (1100 m height) with very low grades have been economically exploited using hydraulic dredge systems coupled to floating concentrators. Where the excavation characteristics, water availability, and power costs are favorable, dredge mining with adjacent floating concentrator can deliver very low unit costs. For this reason, project developers often view dredging as the first-choice mining technique. There are many reasons why dredging may not be appropriate, including some circumstances where it is more costly than alternative dry mining methods. Nevertheless, in a medium unit value resource, such as that being considered by the Tata group, the various dredge types and options should be reviewed. Dry mining techniques are also widely used in the mineral sands industry. Again, dependent upon the unit value, complexity, and other attributes of the resource, there are various dry mining and ore delivery techniques used. Mineral sands are mined by surface mining methods including open cut mining, suction dredging, and hydraulic mining. The first stage of the mining process is to remove all timber and topsoil from the mine site. The topsoil is stockpiled for later rehabilitation of the site after mining has been completed.

5.3.1.1 Dredging A dredge lifts the ore from the bottom of an artificial pond created over lowgrade deposits to allow rapid movement of large amounts of sand through a large suction pipe, which carries it to a separation plant. The dredge continues to slowly advance across the pond, whereas the clean sand tailings are spread behind the pond, where they will be revegetated later (Fig. 5.2). Dredge mining is invariably associated with a floating concentrator and occurs in an operating lake or “pond.” While dredge mining, it is important

FIGURE 5.2 A typical dredge plant.

Beneficiation of mineral sands: a practical outlook Chapter | 5

175

to pay attention to the prevailing water table levels with respect to the ore sequence and water supply or disposal issues. The pond surface must be maintained at a sufficiently high elevation for the dredge and concentrator to safely navigate without running aground. Where there is an elevated water table, disposal of excess water may be required, such that the dredge maximum digging depth can access the lowest ore materials. Usually, mineral sand dredging operations require supplementary water supply to maintain the pond level. Contrary to popular belief, most water consumed in mineral sand operations do not seep out or evaporate from the dredge pond but is trapped in the tailings mound. Accordingly, a lack of water supply is just as likely to affect a dry mining project as a dredge mining one. Seepage into or out of the pond is directed by the relative regional water table and pond surface levels. The water transfer rate is mainly affected by the permeability of the enclosing soils and rock. Obviously, impervious side walls and the pond floor will provide the best containment characteristics. A strong correlation exists between the imperviousness and soil clay content. The fine material component of the soil near the base of the Tamil Nadu (India) deposits range from 10% to 20% and averages about 16%. Therefore, these soils would be expected to have relatively high transmissivity. The regional water table is below the mineralized sand, so a dredge pond in this area would require constant water input to maintain its elevation, irrespective of evaporative and tailings entrapment losses. Dredges typically excavate the ore by the mechanical cutter action, bucketwheel, or bucket chain. The cutting tool is engaged in the mining face by maneuvering the entire dredge, which continues to move across the face to engage successive slices of new ore. Once the edge of the ore body or current dredge path is reached, the dredge direction is reversed and the recently created face is re-engaged by the cutting tool now approaching from the opposite direction (Fig. 5.3). 5.3.1.1.1

Maneuvering

The dredge is moved and held in place by steel cables anchored to the shore, and sometimes by the use of steel “spuds” embedded in the pond floor, around which the dredge may swivel. Spuds can be attached to a fixed position on the dredge or to a spud carriage that enables concentric arcs to be dredged between each spud “reset” operation. The engagement of the digging tool is very positive when spuds are employed, but more “elastic” when only using positioning cables (Fig. 5.4). 5.3.1.1.2

Operation

A typical mineral sand dredging operation uses a bucketwheel excavator and a working spud on a sliding carriage. Two maneuvering cable winches slew

176

Mineral Processing

Bucketwheel

C u t t e r s uc t i o n

B u c k e t l ad de r

FIGURE 5.3 Bucketwheel, bucket ladder, and cutter dredge.

FIGURE 5.4 Diagram of dredge movement.

the dredge about the spud via fairlead sheaves mounted on the bow. The size of the “bite” is controlled by moving the spud carriage such that the excavating wheel advances the required amount into the face at the start of the traverse. The winches then operate to pull the excavator across the face in an arc, centered by the spud. As the ore is loosened, the influence of the dredge pump sucks the ore and pond water into the suction mouth. The pump speed is controlled to provide the optimum slurry density, consistent with the rate of excavation, which in turn is controlled by the slewing winch speed. If the ore is sufficiently unconsolidated, it may be possible to excavate in a single horizontal pass, positioning the excavator at the base of the orebody and allowing ore from above to fall into the excavator. Such ore is termed

Beneficiation of mineral sands: a practical outlook Chapter | 5

177

“free digging” and is ideal for low unit cost dredge mining. Otherwise, in a more competent ore, it may be necessary to excavate in benches. Winching speeds and bucketwheel power are usually much higher where bench dredging is necessary. Very competent ore or even quite hard rock can be excavated provided the dredge has enough mass, power, and breakout force. If an orebody contains more than a very minor amount of hard rock, wear rates, maintenance downtime and operating costs will increase drastically making dry mining more attractive. 5.3.1.1.3 Pond bottom losses All dredge operations leave spillage above the excavated floor. Where this loss is extensive and worth recovering, it is usual to back away from the face for a period to “sweep” the spillage. Even after sweeping, there inevitably remains some spillage and eventually the production level falls so much that further sweeping is abandoned. A typical final pond bottom loss of about 1 m depth of material could be expected from a 2000 to 3000 tph dredge. Smaller operations may lose less, but rarely ,0.5 m. This level of pond bottom loss is effectively irrelevant in a 100 m high sand dune deposit but becomes extremely important in shallow deposits. Normally, the pond loss material has a grade which is roughly the average of the ore sequence. This will not be the case if there is a high-grade strand overlain by lower grade ore and the sequence is mined in benches. 5.3.1.1.4

Operating cost drivers

The nature and geometry of deposits are the most significant factors affecting unit costs for dredge mining. A deep sequence of free-flowing sand, such as that found at the Richards Bay Minerals and Consolidated Rutile Limited, provides the most advantageous conditions for dredging. The dredges typically move only small distances and the ore flows under gravity to the virtually idling cutter. High delivery densities are available and the percentage of time spent in low productivity sweeping is minimal. Low fines content is important, both for pond quality and soil competence. TZ Minerals International(TZMI) considers 10% slimes (slime definition varies from 45 μm to 63 μm) content ,63 μm to be a threshold, above which dredge mining is unlikely to be a suitable choice. Those projects where higher fines content ores have been dredged have much higher unit mining costs. In such cases, it would be preferable to use conventional surface mining equipment. Due to depletion of resources, some operators still mine ore with .30% slimes using advanced mining technologies. Dredging uses water to transport the ore and delivers it in a less concentrated form compared to a truck or conveyor. Circulation of large volumes of water consumes considerable power, so pumping is more suited to a location

178

Mineral Processing

where power costs are low. Some remote, otherwise perfect dredge targets, can be dry mined more economically because the power has to be locally generated at a high cost. Recovery of seeped water, either for environmental protection or simply to keep the dredge afloat, can become a large part of the operating costs. The ideal situation is to have the local water table about the same level as the dredge pond. The presence of rocks, indurated layers, or tree roots can hinder production and in extreme cases stop the dredge. Maintenance costs invariably increase and the production level decreases. Unit costs are therefore much lower in the absence of such impediments. The dredging characteristics of a typical deposit when compared to ideal dredging attributes are shown in Table 5.1. Unless seawater can be used as a water source, there is probably insufficient water available to allow for the seepage and evaporation that could be expected in addition to tailings mound losses. Though not ideal, it would be possible to dredge a deposit with an average depth of 8 m, At the projected 8
10 million tph mining rate, it would be frequently required to relocate the pond bank. Again, as previously stated, the pond bottom losses could represent about 10% of the resource. Power costs would also not be favorable compared to other dredge mining projects. In the initial assessment of the one of the deposits, it had been assumed that the fines level was below 10% (about 5%
7%). In the event the fines content was double this amount, it would ordinarily disqualify dredging as an option. However, some higher fines deposits have been successfully dredged with very careful attention to removing fines from the operating pond, and maintaining pond water quality. High fines content would mean lower seepage, as the otherwise porous pond bottom would get quickly clogged. However, the loss of water into the tailings mound would be higher,

TABLE 5.1 Ideal dredging conditions of a typical deposit. Attributes

Typical deposits

Deep deposit

Very favorable

Free flowing sand

Fair

Low fines content

Good

No rocks or indurated layers

Good

No tree stumps

Fair

Low Water table near operating pond level

Poor

Low-cost power

Good

Beneficiation of mineral sands: a practical outlook Chapter | 5

179

given the water holding properties of clay and silt. Higher fines ore, would lead to higher evaporation losses and increased tailings pumping distances. Despite the issues, it may still be technically possible to mine the deposits using a dredge, provided enough water is available.

5.3.1.2 Dry mining Higher grade deposits containing moderately hard material or layers are mined using scrapers and bulldozers. Scrapers mine the ore from the top of the face to the bottom and progressively mine across the whole face. This ensures that the ore being mined is a constant blend on a day-to-day basis. The scraper carries the ore to a screening plant where the ore is broken down into grains no larger than 2 mm. The screened ore then proceeds through an intricate series of spirals to remove tailings and excess clay fines. The concentrate is stockpiled for separation and treatment. Many mineral sand operations use standard earthmoving equipment to excavate and transport ore to a land-based concentrator. This typically requires a relocatable concentrator to manage haulage distances, although conveyor and slurry pumping systems extend the economic distances that dry mining can be used. Advantages of dry mining systems compared to dredging include ease of fines management and high mining recovery. Hard ore can be readily managed and multiple dry mining units have the flexibility to manage the blending of ore from more than one mining area if required. Direct use of hydrocarbon fuel and transport of dry ore can be an economic advantage where electric power costs are high or where electric power needs to be locally generated from fuel oil. Disadvantages compared to dredge mining include the need for several equipment; providing and maintaining haul roads; ongoing replacement cost; and interfacing discrete haulage loads into a continuous concentrator feed stream. Relocating the concentrator can be a costly affair and production ceases during plant movement. Typical dry mining/ore transport systems used in the mineral sands industry include the equipment shown in Table 5.2. The cost of mining and transporting large tonnages of ore over increasing distances influences the choice of transport systems. To exploit lower cost transport, the mining interface must suit the transport mode. Following is a table of the types of mining equipment suitable for mineral sands excavation and loading with comments on appropriate transport systems (Table 5.3). 5.3.1.3 Hydraulic mining With this technique, the ore body is washed down using a water cannon. The ore is then pumped as a slurry to a wet concentrator, which separates the valuable minerals from the waste (Fig. 5.5).

180

Mineral Processing

TABLE 5.2 Transport systems. Pros

Cons

Suggested limits

Scrapers

Excavates and hauls in single unit. Useful for blending.

Effective limit 800 m. High tonnage fleets expensive.

2800 m 2 10 mtpa

Conveyors

Long haulage distances at low unit cost.

Relatively immobile; interface with orebody; capital cost.

12000 m 1 10 mtpa

Pumping

Most mineral plants have “wet” section. Slurrying facilitates liberation of mineral. Relatively mobile. Moderately long distances.

Pre-screening essential; moderate transport cost; maximum 4 km.

24000 mNo rockFines help

Haul trucks

Versatile, robust, reliable and large tonnage range. Moderate to long distances.

Road surface limits. Expensive in short haul.

11000 m Dry roads

TABLE 5.3 Mining and transport interface. Mining equipment

Transport interface

Comment

Scrapers

Drive-over dump hopper.

Rocks must be screened.

Bulldozers

Buried loaders—pumping or conveying.

Regular relocation necessary. Deals with hard digging.

Front-end Loaders

Dump hopper, can be small scale, easy to relocate—pumping or conveying.

Easier to move than driveover dump station.

Excavator

Direct into haul trucks or dump hopper for pumping.

High volume, low unit cost. Handles harder digging.

Bucketwheel Excavator

Ideal for pumping or conveying.

High, steady productivity. Limited mobility or blending.

5.3.2

Mine planning

Mine planning activities cover two important aspects in the total mining operation. The first aspect deals with the prospection, exploration, and deposit evaluation. The selection of equipment, sequence of minerals extraction in the

Beneficiation of mineral sands: a practical outlook Chapter | 5

181

FIGURE 5.5 Hydraulic mining.

short- and long-term are determined from the data obtained during preliminary investigation. The second aspect covers wide range of current mining activities such as providing support facilities to the operating personnel guiding the operating personnel by providing information related to production activities, rehabilitation of the mined-out area by systematic plantation. Laying roads and power lines ahead of the dredge movement is also an important planning function. Planning the dredge—the path is a very important activity which helps the operating people in monitoring the production schedule monthly and yearly. Dredge—the path planning is based upon several data such as production target, dredging area, height of the deposit, dredging depth desired, grade of minerals available in the area, and behavior of the ground water table. The focus of the planners is always to use the maximum land available and guide the dredging personnel to minimize losses that may arise due to encroachment of tailings on the virgin area and between successive runs that the dredge takes in the deposit.

5.3.3

Mining activities

The wet mining method is usally adopted for extracting heavy minerals as it is more advantageous to deal with wet processes in slurry form. Dredging is the most suitable wet mining method of beach sand. The dredge consists of a cutter-ladder unit, dredge pump, and all ancillary equipment mounted on a floating pontoon. The dredge operation is conducted along the front hank of the pond and the tailings of the dredge sand, after processing is directed back into the rear portion of the pond for backfilling of the mined out area. The dredged sand in slurry form is pumped to a trommel screen to remove any oversized material including roots, pebbles, stones encountered while dredging. The screened material is collected in a surge bin mounted on a floating pontoon. The surge bin ensures that a constant pulp density is maintained at the concentrator unit.

182

Mineral Processing

5.4

Processing

Minerals rarely occur in their pure form, but occur in the form of ores, homogeneous mixtures of rocks, minerals) and are seldom used directly. Most of the nonmetallic and all metallic ore bodies contain valuable elements in widely varying states between parts per million and percentage. The ore produced from the mine head needs to be beneficiated or upgraded to an intermediate stage or final form for industrial, end uses. Heavy mineral sands processing is also not an exception to the same. The upgradation process is called concentration/beneficiation and the upgraded product is called the concentrate. Ore, whether mined by dry or wet methods, is processed in two stages. During the wet stage, differences in particle size, density, and amenability for flotation are used to separate heavy minerals from quartz sand and clay. In the wet stage, hydrocyclones remove the clay-sized fraction, and then the underflow (heavy minerals plus quartz sand) is passed through several stages of spiral separators, wet tables, and hydosizers, where the heavy minerals are separated from the sand by using their differences in density. After separation, the clay-silt-sized fraction (slimes below 45
75 μm) is generally mixed with a flocculent in a thickener, and the thickened underflow is mixed with the quartz sand tailings from the spiral separators, and pumped back into already mined out pits. Subsequently, during the dry stage, differences in magnetic and electrical properties and sizes are used to separate heavy minerals. Dry processing involves several stages of magnetic and electrostatic separation. Strong magnets remove most of the ilmenite from the feed. In the past, electromagnets were used, but currently (2013) permanent rare-earth drum/roll magnets are used to save on power costs. The nonmagnetic minerals are then subjected to electrostatic separation that divides the nonconductive minerals (zircon, kyanite, quartz, monazite, and staurolite) from the conductive minerals (rutile and leucoxene).

5.4.1

Mineral sands concentration

Concentration is performed by various methods of exploiting the physical and chemical behaviors of the feed materials to the process plant. Beneficiation processes mainly used for heavy mineral sand deposits are: (1) gravity separation, (2) magnetic separation, (3) electrical separation, (4) hindered settling, and (5) flotation (Table 5.4).

5.4.2 Mineral separation equipment used in heavy mineral sands industry 5.4.2.1 Gravity concentrators Gravity concentration is a proven process for mineral beneficiation. Gravity concentration techniques are often considered where flotation is less efficient

Beneficiation of mineral sands: a practical outlook Chapter | 5

183

TABLE 5.4 Physical properties and chemical composition of beach sand minerals. Mineral

Magnetic susceptibility

Electrical conductivity

SG

Chemical formula

Ilmenite

High

High

4.5
5

Fe.TiO3

Rutile

Low

High

4.2
4.3

TiO2

Zircon

Low

Low

4.7

ZrSiO4

Leucoxene

Semi

High

3.5
4.1

Fe.TiO3.TiO2

Monazite

Semi

Low

4.9
5.3

(Ce,La,Th,Nd,Y)PO4

Sillimanite

Low

Low

3.6
3.7

Al2SiO5

Garnet

Semi

Low

3.4
4.2

(Fe,Mn,Ca)3.Al2(SiO4)3

Quartz

Low

Low

2.7

SiO2

and operational costs are high due to extremely complicated physical, chemical, and mechanical considerations. Gravity separations are simple and separate mineral particles of different specific gravities. This is conducted by their relative movements in response to gravity along with one or more forces adding resistance to the motion offered by viscous media, such as air or water. Particle motion in a fluid depends on specific gravity, size, and shape of the moving material. Efficiency increases with coarser size to move adequately but becomes sensitive in the presence of slimes. There are many types of gravity separators suitable for different situations and many devices for gravity concentration. The common method is panning. Panning as a mineral/metal recovery technique was known to many ancient civilizations. Gold panning was popular and extensively practiced in California, Argentina, Australia, Brazil, Canada, South Africa, and India during the 19th century. Panning is the manual shaking of a tray containing river bed sand and gravel, and alluvial soil containing precious metals like gold, silver, tin, tungsten, and native platinum. The shaking tray separates sand, stones, and fine-grained metals into different layers by differential gravity concentrations. The undesired materials are removed. This is a primitive practice used by remote tribal people on a small scale and at low cost (Fig. 5.6). It is extensively practiced for a quick assessment of HM content in the deposits during site visits and also as a tool for quality control in a primary concentration plant. 5.4.2.1.1

Spiral concentrator

The spiral concentrator is developed for concentration of low-grade ores and industrial minerals in a slurry form. It works on a combination of solid

184

Mineral Processing

FIGURE 5.6 Panning of raw sand containing heavy minerals.

particle density and its hydrodynamic dragging properties. The spirals consist of a single, double or triple helical conduit or sluice wrapped around a central collection column. The device may have a wash water channel and a series of concentrate removal ports placed at regular intervals. Separation is achieved by stratification of material caused by a combined effect of centrifugal force, differential settling, and heavy particle migration through the bed to the inner part of the conduit (Fig. 5.7). Extensive application is the treatment of heavy mineral beach sand consisting of monazite, ilmenite, rutile, zircon, garnet, and upgrade chromite concentrate. Two or more spirals are constructed around one central column to increase the amount of material that can be processed by a single integrated unit. Operating parameters Feed rate of 21 to 2.0 tph per start depending on the heavy minerals content in the feed % Solids—20%
40% Splitter positions-adjustable based on the concentrate yield, Heavy Mineral (HM) grade in the products viz, concentrate. middling’s and Tails (Figs. 5.7 and 5.8). 5.4.2.1.2 Shaking table The shaking table consists of a sloping deck with a rifled surface. A motor drives a small arm that shakes the table along its length, parallel to the rifle pattern. This longitudinal shaking motion drives at a slow forward stroke followed by rapid return strike. The riffles are arranged such that heavy materials are trapped and conveyed parallel to the direction of oscillation. Water is added to the top of the table and perpendicular to table motion. The heaviest

Beneficiation of mineral sands: a practical outlook Chapter | 5

185

FIGURE 5.7 (A) A spiral trough with operation. (B) Cross-section of the spiral trough.

FIGURE 5.8 A typical spiral concentrator plant.

and coarsest particles move to one end of the table. The lightest and finest particles tend to wash over the riffles and to the bottom edge. The intermediate points between these extremes provide recovery of middling (intermediate size and density) particles. Shaking tables find extensive use in concentrating gold, tin, and tungsten. These devices are often used downstream of other gravity concentration equipment such as spirals, Reichert cones, jigs, and centrifugal gravity concentrators for final cleaning prior to refining or sale of product. A typical model diagram of a shaking table (Fig. 5.9). The optimum capacity of fine circuit wet tables is 0.5 tph and the capacity for coarse circuit tables is up to 1 tph. The particles of mineral fed onto the table form a layer behind the riffles. The table’s motion causes the lighter, larger particles to layer above the

186

Mineral Processing

Feed Dressing water

Feed box Riffles

Heavy mineral discharge

Motor drive

Middling Light mineral discharge

(A)

(B)

FIGURE 5.9 (A) Wet shaking table principle. (B) Wet shaking table with feed.

heavier, smaller particles. The action of the wash water carries the lighter, larger mineral layers over the top of the riffles where they again segregate depending on size and weight. At the discharge end of the wet table, an overlapping band of lighter, smaller particles and heavier, larger particles is formed. Optimum performance of a wet table will result from a wide band of mineral at the discharge end of the table offering a definite separation point. This will be achieved by keeping the angle of the table as low as practical and ensuring the amount of wash water used is sufficient to spread across the whole surface of the table. The flow should be great enough to carry the larger, lighter particles (kyanite and silica) across the table to tails. Operating parameters G Feed rate 20.5 to 1.0 tph per start depending on the heavy minerals content in the feed. G % Solids 220% to 25%. G Splitter Positions-Adjustable based on the concentrate yield, HM grade in the products viz, concentrate, middlings and tails. 5.4.2.1.3

Hydrosizers

This is another form of classifier used to separate the fines, low specific gravity particles from the coarse, high specific gravity particles from downstream equipment, such as spirals and shaking tables can separate more effectively. The hydrosizer is a large tank in the bottom of which is a valve to release slurry falling to the bottom of the tank. Slurry enters the tank through a feed well below the slurry level in the tank. Around the lip of the tank is a launder into which water can overflow from the tank as more slurry enters. At the bottom of the tank are two rings, through which process water is pumped into the teeter pipes which has inverted perforations through which water rises through the slurry in the tank towards the top, causing an upcurrent. The slurry entering the tank contains fine and coarse particles and the fine

Beneficiation of mineral sands: a practical outlook Chapter | 5

187

FIGURE 5.10 (A) Density separator principle. (B) Hydrosizer separators in the plant.

and low specific gravity particles are caught in the upcurrent and move with the water to the top of the tank, eventually overflowing into the launder. The coarse and high specific gravity particles are too heavy to be carried by the upcurrent and fall to the bottom of the tank to form a dilated bed of material (Fig. 5.10). The dilated bed has the upcurrent flowing through it and the finer and lighter particles tend to stay at the top of the bed, whereas the coarser and heavier particles tend to work their way to the bottom. A pressure sensor in the bottom of the tank monitors the depth of the bed, and when there is sufficient depth, operates the valve in the base of the tank to release the lower part of the bed downstream (Fig. 5.11). Operating parameters of the Hydrosizer are: 1. Feed rate and percentage solids. 2. Differential pressure across the bed. 3. Volume of teeter water. 5.4.2.1.4 Magnetic separators Magnetic separation takes advantage of natural magnetic properties between minerals in the feed. The separation is between economic ore constituents, noneconomic contaminants, and gangue. Magnetite and ilmenite can be separated from their nonmagnetic rock-forming minerals of host rock as valuable products or contaminants. The technique is widely used in the beneficiation of beach sand. All minerals will have one of the three magnetic properties: ferromagnetic (magnetite and pyrrhotite), paramagnetic (monazite, ilmenite, rutile, chromite, wolframite, hematite), or diamagnetic (plagioclase, calcite, zircon, and apatite). Commercial magnetic units follow a continuous separation process on a moving stream of dry or wet particles passing through a low or high magnetic field. The various magnetic separators are drum, disc, cross belt, roll, high gradient magnetic separation, high-intensity magnetic separation, and low-intensity magnetic separation types.

188

Mineral Processing Pre Concentrate Plant

Feed

Cons

Tails

Rougher Spiral M230 Cons

Tails

Mids Spiral Mids

Feed Cons

Cleaner Spiral

Tails

Classifier

Overflow

Underflow

Density Classifier

Overflow Feed

Underflow Cons

Spiral

Tails

Mids

Cons

Spiral Mids

Tails

Condioning

Soda Ash, Sodium silicate, Oleic Acid, MIBC Frother

Feed

Flotaon

Sink/Tails

Froth/Cons

IRZ Cons

Garnet Cons

Sillimanite Cons

Final Tails

FIGURE 5.11 Typical flow sheet for Heavy Mineral Concentration.

Disc Magnetic separator/cross belt magnetic separator A disc magnetic separator or cross belt magnetic separator was used to separate paramagnetic titanium bearing minerals from other minerals. A magnetic field strength up to 0.8 Tesla was attainable in the air gap between disc and flat pole stationary magnets placed below the disc/cross belt running across the main belt. Magnetic minerals were picked up and transported by the revolving disc/

Beneficiation of mineral sands: a practical outlook Chapter | 5

189

FIGURE 5.12 WHIMS.

cross belts and deposited as a magnetic fraction, whereas nonmagnetic materials followed the path of the feed and were discharged by gravitational force. Presently, these equipment are not being utilized in plants due to its low feed capacity. Wet High Intensity Magnetic Separator(WHIMS) WHIMS are suitable for applications requiring higher magnetic field gradients to remove weakly magnetic particles from nonmagnetic concentrates (Fig. 5.12). High intensity magnetic separators focus on the separation of very fine particles that are paramagnetic. They utilize magnetism, rotating matrix and gravity to separate the minerals. WHIMS is suitable for applications requiring higher magnetic field gradients to remove weakly magnetic particles from nonmagnetic concentrates. The feed is fed through the rotating matrix in slurry form, where in the magnetic minerals stick to the poles and are washed to the magnetic port while the nonmagnetic mineral passes through the matrix. The WHIMS range includes 2, 4, 8, 16, 24 and 48 pole machines with either 68 or 120 mm separation matrix widths. WHIMS separators are suitable for applications requiring higher magnetic field gradients to remove weakly magnetic particles from nonmagnetic concentrates. Rare earth drum magnetic separator The drum separator consists of a nonmagnetic drum fitted with 3% to 6% magnets composed of ceramic or rare earth magnetic alloys in the inner periphery. The drum rotates at uniform motion over a moving stream of preferably dry feed. The ferromagnetic and paramagnetic minerals are picked up by the rotating drum which is fixed on a shaft where the rare earth magnets and pinned to the outer surface of the drum. Drum rotation can be clockwise or counter-clockwise and the collection of concentrate is designed accordingly. A drum separator produces extremely clean magnetic concentrate. It is suitable for the recovery of precious minerals from beach sand.

190

Mineral Processing

The separation efficiency is further enhanced by the alternating north/ south polarity of the magnets in the array. The magnets are arranged so that the polarity of the field changes every 80 mm or so. This causes a tumbling effect on the magnetic particles, allowing any nonmagnetic material trapped against the drum to be freed. To protect the integrity and efficiency of the natural magnets it is recommended that the run temperatures remain less than 80 C (Figs. 5.13 and 5.14). Rare earth roll magnet separator Feed material consists of magnetic and nonmagnetic minerals will be fed on a belt in a form of thin layer. The permanent magnetic roll consists of alternate layers of rare earth magnet and mild steel. The rare earth magnet produces magnetic field that converges at the mild steel layers and the magnetic minerals on the belt is drawn

FIGURE 5.13 Rare earth drum magnetic separator.

Feed Rare Earth Roll

Idler roller N Magnec

Magnec

FIGURE 5.14 Rare earth roll magnetic separator.

Beneficiation of mineral sands: a practical outlook Chapter | 5

191

towards the steel layers and pinned to the belt whilst non magnetics not influenced by the field and are thrown due to centrifugal force away from the roll. Feed rate control and usage of right thickness of the belt, splitter position, and speed of the roll are the influencing factors to achieve the necessary grade and recovery of the products. Induced roll magnetic separator Magnetic and nonmagnetic minerals are separated as they pass through a magnetic field generated between a rotating roll and an adjacent nose piece. Feed material from the hopper is passed through a rotating roll where in magnetic field is induced. Magnetic particles remain pinned to the roll until they are removed by a fiber brush at the back of the roll. Nonmagnetic particles are unaffected by the magnetic field and are thrown by centrifugal force into the nonmagnetic fraction (Fig. 5.15). Following are the operating parameters of the induced roll magnetic separator Feed rate 3 to 4 tph per machine. Overfeeding will result in multilayer feeding resulting in poor separation Field intensity 12,000 to 15,000 gauss. The magnetic field intensity can be altered by using the controller. Splitter position Depending on the separation trajectory, position of the splitters can be set and the same can be altered based on the separation requirement.

FIGURE 5.15 Induced roll magnetic separator.

192

Mineral Processing

Roll speed This is a critical operating parameter and is being used in order to ensure grade and recovery of the product. 5.4.2.1.5

Electrostatic separation

Electrostatic separation works on the natural conductivity properties between minerals in feed. The common units are high-tension roll and electrostatic plate separator. It is used for separating monazite, spinel, sillimanite, tourmaline, garnet, zircon, rutile, and ilmenite from heavy beach/stream placer sand. The electrostatic technique is extensively used in Australia, Indonesia, Malaysia, and India bordering Indian Ocean for separation of mineral sands. High tension roll separators High tension separation is a process which uses the difference in electrical conductivity of the surface of particles. A DC electrode running parallel to the roll generates a corona charged electrostatic field between itself and the earthed roll. Mineral is fed onto the rotating roll at about the top dead center position and is carried into the zone of influence of the ionizing wire. All particles passing through this zone receive an electrical surface charge sufficient to pin them to the earthed roll. As the particles leave the ionizing zone, they are treated according to their surface charge. Conducting particles quickly lose their charge to the earthed roll and are thrown out due to centrifugal force whilst the nonconductors will get pinned along with the roll surface and are brushed aside (Fig. 5.16). New generation machines such as Coronastat and Carrara High Tension Roll (HTR) in the market have added features such as larger diameter of the separation roll, capacitance electrodes (III electrode) which are used to get the improved performance of the plant (Figs. 5.17 and 5.18). Operating parameters The following adjustments are made while the plant is operating to ensure that product grades meet the customer specification and that recirculating loads of mineral do not build-up within the separating circuit. Feed rate control Feed rates should be kept to a minimum without causing build-ups upstream of the HTR. Decreasing the feed rate reduces the thickness of feed on the roll and gives the conductive minerals the maximum possible chance to lose their charge through the surface of the roll. Electrode position The air gap between the roll and the glass electrode can be adjusted to achieve the desired result. DC electrode voltage The electrostatic force applied to a particle is proportional to the surface charge of the particle. Increasing the voltage increases the pinning effect on the roll and as a result a clean conducting product can be produced and this also will be useful when the recovery of nonconductors is required. Adjustments to the voltage of DC electrode are made either on the scan or at the rectifier cabinet. Arcing causes the temporary loss of the

Beneficiation of mineral sands: a practical outlook Chapter | 5

193

FIGURE 5.16 HT roll separator working principle.

ionizing field and therefore results in all particles being thrown from the roll into the conductor fraction. Voltage will be decreased if the requirement is to have less pinning effect. Achieving a clean non conducting product requires less voltage. Usual range of voltage will be 25
30 kV. Product splitters The movement of splitters on high tension roll machines has the greatest immediate impact on the product splits produced. Moving any HTR splitter toward the roll improves the quality of the nonconductor fraction at the expense of the conductor grade. The reverse applies if the splitter is moved away from the roll, i.e., conductor quality improves at the expense of nonconductors. Feed temperature The temperature of the feed is critical, especially in times of wide dew point changes. If mineral feed temperature approaches room temperature, the ability of particles to adsorb moisture increases, and the effect of dew point on HTR performance also increases. By heating the mineral, most of the adsorbed water is driven off and the true conductive properties of the particles are revealed. Hence, mineral feed temperatures are normally maintained above 75 C to nullify most of the effects of dew point. However, feed temperature can be varied to aid the HTR separation.

194

Mineral Processing

FIGURE 5.17 Carrara HT roll separator.

On days of low dew point it is common to operate at reduced feed temperatures to allow adsorption of moisture onto particle surfaces. Lower mineral feed temperatures are also used on very hot days as the loss of heat from the mineral is reduced. Consequently, mineral feed temperatures throughout the separating circuits will be maintained. Mineral feed temperature is controlled by regulating the discharge temperature of the relevant dryer or reheater. The following long-term adjustments can be made when the HTR has been isolated electronically. Roll speed Roll speed may be changed to improve the grade or recovery of either the conductor or nonconductor fraction. An increase in roll speed increases the centrifugal force applied to all particles. Electrostatic plate separation Electrostatic Plate Separators (EPS) are generally used to complement high tension roll machines, where fine conductor particles have been pinned to nonconductors and larger nonconductor particles have been thrown from the roll into the conductor product. Electrostatic plate separation is a process, which uses the difference in surface electrical

Beneficiation of mineral sands: a practical outlook Chapter | 5

195

FIGURE 5.18 Coronastat HT roll separator.

conductivity of particles. Feed is presented as a thin film, which gravitates down an earthed plate into an electrostatic field induced by large curved electrode. A conductive particle in contact with the earthed plate will lose the charge and will be attracted towards the electrode which has opposite polarity. A nonconductive particle cannot lose its charge to the earthed plate and is left with an overall zero charge. Consequently, the particle is unaffected by the electrostatic field and it continues to slide down the earthed plate under the influence of gravity (Fig. 5.19). Operating parameters Feed rate 2 to 3 tph depending on the feed configuration and the presence of nonconductor in the feed. Overfeeding results in misreporting of nonconductors to conductors and vice versa in case of underfeeding. Electrode voltage An increase in electrode voltage increases surface charge of particles, resulting in greater electrostatic forces being applied to the conductor minerals, allowing them to overcome gravity more easily and lift into the conductor fraction. Typically, 25
30 kV is maintained in the plant.

196

Mineral Processing

FIGURE 5.19 Electrostatic plate separator.

Feed temperature Desired temperature of feed is about 60 C
90 C to nullify the impact of dew point The temperature of the feed is critical especially in times of widespread dew point changes. As mineral feed temperature approaches the room temperature, the ability of particles to adsorb moisture increases, and the effect of dew point on EPS performance also increases. By heating the mineral, most of the adsorbed water is driven off and the true conductive property of the particles is revealed. Product splitters Adjustment of product splitters at the bottom of the machine will assist to ensure product grade and recovery. Poor particle surface cleanliness will also result in surface coatings building up on the EPS plates which will result in poor separator performance. Regular cleaning of plate and electrodes will assist to achieve an improved performance. 5.4.2.1.6 Screens The sizing of products in the mineral sands industry is an integral part of the production process. Screening is generally conducted on relatively coarse material as screening efficiency decreases rapidly as finer screening meshes are used. Fine screens tend to be very fragile and become blinded more easily. The screen cloth is most commonly a stainless-steel wire surface with a large number of apertures of a given dimension (Fig. 5.20). There are a number of factors common to all types of screens that will affect the screening performance. These factors reduce the efficiency of screening and may be present singular or in combination. When problems occur in the plant, a systematic check should be made of each of the following items so that the problem is identified and quickly rectified. Feed rate Screening works most effectively at lower feed rates with a long screening time. High-capacity screening is generally not conducive to good

Beneficiation of mineral sands: a practical outlook Chapter | 5

197

FIGURE 5.20 Derrick screen.

screening efficiency. Whenever the situation permits, the feed rate to all screens in the plant should be reduced. High screen efficiency leads to a greater degree of product control within the plant. Screen blinding Screen blinding leads to reduced undersize fraction from a screen operation. Blinding can be controlled by increasing the vibration of the screens. This will reduce the mineral bed thickness on the screen. Screen open area The percentage of screen area, which comprises the holes or apertures is termed the open area of the mesh. The ability of fines to pass through the mesh increases as its open area increases. Open area decreases as the wire diameter of the mesh, in comparison to the aperture size, is increased. 5.4.2.1.7 Dense medium separation Dense medium separation (DMS) or heavy medium separation works on the principle of sink-and-float when treating minerals with variable specific gravities as in the case of coal and shale, and sulfide ore in carbonaceous host rock. DMS in industries uses organic liquids, aqueous solutions, and thick suspensions in water or the pulp of heavy solids in water. This is the simplest method following wet gravity separation. Minerals lighter than the liquid medium will float and those denser will sink. 5.4.2.1.8

Froth flotation

The froth flotation process produces froth of selective mineral agglomerates and separates them from other associated metallic components and gangue

198

Mineral Processing

minerals. The physical and chemical surface properties of certain fine size fractions make their surfaces hydrophobic. The particles become water repellent by coming in contact with moving air bubbles in the presence of certain reagents. The froth moves up leaving the gangue (tailing) below, and collects as concentrate for further cleaning. The mineralized froth (concentrate) stabilizes for a while at the top of the cell (Fig. 5.21), overflows, and moves to a cleaner cell. It is then filtered, and driede to form a mature saleable product. The concentrate is the raw material that can later be used for for extracting metals by smelting and electro- and chemical refining. The continuous process of separation in commercial plants occurs in a series of containers called flotation cells forming a bank (Fig. 5.21). The final products of the grinding mill pass through a conditioner tank where the pulp is conditioned from a few seconds to a couple of minutes in the presence of xanthate and methyl isobutyl carbinol (MIBC). The conditioned pulp enters the first few cells (“rougher cells”) charged with reagents. Some of the hydrophobic ore minerals attach to air bubbles and move up as rich froth (concentrate). Rougher concentrate moves downstream to cleaner cells to produce the highest-grade concentrate. The last few cells in the bank (scavengers) process low-grade pulp along with gangue and recover the remaining mineral froth and clean it. The bank of flotation cells is placed in rows on the floor of the oredressing plant in close circuit to recover multiple concentrates of respective

FIGURE 5.21 Floatation working principle.

Beneficiation of mineral sands: a practical outlook Chapter | 5

199

Cells Feed

Conditioner

Roughers

Scavengers

Cleaners

Tailings

Cleaner tailings

Final concentrate FIGURE 5.22 Schematic diagram of process flow sheet illustrating conditioner-rougherscavenger-cleaner cells, including formation of concentrate and reject.

minerals (Fig. 5.22). Three main group of reagents used in flotation are collectors, frothers, and regulators. Each set of reagent plays a specific role in mineral processing (Fig. 5.21). Schematic diagrams showing the principle of froth flotation and total function inside a flotation cell.

5.5

Processing of heavy mineral ore

Ore, whether mined by dry or wet methods, is processed in two stages. Wet separation (primary concentration) and dry separation (mineral separation). During the wet stage, differences in particle size and density are employed to separate heavy minerals from quartz sand and clay. Subsequently, during the dry stage, differences in magnetic and electrical properties are used to separate heavy minerals from each other. In the wet stage, hydrocylones remove the clay-sized fraction, and then the underflow (heavy minerals plus quartz sand) is passed through several stages of spiral separators, where the heavy minerals are separated from the sand by using their differences in density. After separation, the clay-siltsized fraction (slimes) is generally mixed with a flocculent/thickener, mixed with the quartz sand tailings from the spiral separators, and pumped back into the pit void. Dry processing involves several stages of magnetic and electrostatic separation. Strong magnets remove most of the ilmenite from the feed. In the past, electromagnets were used, but in the recent days permanent rare-earth drum magnets are employed to save on power costs. The nonmagnetic minerals are then subjected to electrostatic separation that divides the nonconductive minerals (zircon, kyanite, quartz, monazite, and staurolite) from the conductive minerals (rutile and leucoxene).

200

Mineral Processing

5.5.1

Pre concentration plant

A typical process flow sheet is shown below Fig. 5.23. In this stage, the amount of heavies is upgraded up to 90%. Then, it is sent to Heavy Upgradation Plant (HUP) for further treatment. The ROM sand is pumped or conveyed through conveyor belts or trucks to the trommel with aperture size is 2
4 mm, which rotates at 5
6 rpm. The undersize of Pre Concentrate Plant

Feed

Cons

Tails

Rougher Spiral M230 Cons

Tails

Mids Spiral Mids

Feed Cons

Cleaner Spiral

Tails

Classifier

Overflow

Underflow

Density Classifier

Overflow Feed

Underflow Cons

Spiral

Tails

Mids

Cons

Spiral Mids

Tails

Condioning

Soda Ash, Sodium silicate, Oleic Acid, MIBC Frother

Feed

Flotaon

Sink/Tails

Froth/Cons

IRZ Cons

FIGURE 5.23 Pre-concentrate plant.

Garnet Cons

Sillimanite Cons

Final Tails

Beneficiation of mineral sands: a practical outlook Chapter | 5

201

the trommel is sent to bins from where it is sent to the spirals for concentration and the oversize usually containing pebbles, grass and other waste materials. In spirals 4-stage of cleaning takes place, i.e., rougher, cleaner, recleaner, and scavenger. Concentrate from the rougher spirals usually is sent to cleaner spirals, then middlings to scavenger spirals and the tailings to the hydrocyclone from where the overflow (water) is sent to the trommel discharge and the underflow is the rejects (sand), which is used for backfilling of the pits. Cleaner concentrate is sent to the recleaner, the middlings are recirculated and tailings are sent to to the scavenger. Recleaner concentrate is final concentrate, which is sent to an HUP, middlings are recirculated, and tailings are sent to cleaner. The scavenger concentrate is sent to a cleaner circuit, its middlings are recirculated, and its tailings are sent to a hydrocyclone. By this process, the recovery of heavies improve to 90%
92%. Spirals: Spirals are gravity separators where slurry is fed at a pulp density of about 20%
40%. The size range is commonly 3 mm to 75 μm and as the slurry flows down the curved channel, lighter particles due to the action of centrifugal forces report to the outer area of the spirals as tails, whilst the heavier particles are pulled inward due to drag force and report to the inner area of the spiral as concentrate, thus effecting the separation. Modern spirals are constructed from fiberglass and polyurethane and can treat 1
3 tph of feed effectively. The operating parameters are feed rate, pulp density, feed grade, splitter openings, position of distributors, diameter of spirals etc. The operating range of these operating parameters and their influence on control of the grade and recovery are given below (Table 5.5).

5.5.1.1 Process flow circuits 5.5.1.1.1 Mineral concentration The basic units of mineral sand concentrators are feed preparation, sand separation, and tailings disposal and water recovery. Where a concentrator is fed by a dredge or directly by a mobile earthmoving equipment, an important duty of the feed preparation section is to provide surge capacity to convert cyclical mine production into steady flow feed to the downstream processes. TABLE 5.5 Spiral operating parameters. Rougher (tph)

Scavenger (tph)

Cleaner

Remarks

Feed Rate

2
3

2
2.5

1
1.5

To increase grade, to increase recovery

Pulp density (%)

35
40

35
40

30
35

202

Mineral Processing

Dredge or dry mining delivers the ore in a slurry form, which is very convenient as the concentration steps are all wet processes. The first step in a feed preparation plants. A dry mining operation feed preparation plant’s first duty is to slurry the ore stream, after which the downstream processes are common for both dredge and dry mining operations. Ore slurry usually is screened to remove coarse particles, usually at about 2 mm. Coarser oversize, e.g., 110 mm, is hauled away from landbased concentrators by truck and often used as road base or in other mine site construction jobs. The finer oversize may be joined to concentrator sand tailings for disposal in the mine void backfill. Floating concentrator oversize is typically chuted directly into the operating pond and plays no further part, unless as a navigating hazard, where oversized content of the ore is significant. Some mineral sand ore bodies contain slightly indurated ore formations, or clay-bound valuable minerals, which need to be liberated in the feed preparation section. In such cases, it may be necessary to reprocess the initial oversize, typically in a rotating scrubber, log washer, or similar type of mild comminution device. Following the removal of the oversized material, the final feed preparation task is desliming. This is usually performed by hydrocyclones, aiming to remove material finer than the valuable mineral size (finer than 45
75 μm). Mineral sand resources often contain clay minerals, which can prove troublesome in effective separation from the process water stream. It is thus usually necessary to process the desliming cyclone overflow in a thickener to recover the considerable volumes of process water for reuse. In some cases, where the fines content of ore is low, it may be possible to use natural settling to recover the water. Most dredge operations employ this system using the dredge pond as a “natural thickener” by allowing the fines to settle on the pond floor. Before this type of operation is considered, the project owner must be absolutely certain that a buildup of fines will not occur in the circulating dredge pond water. Spectacular failures of major projects have occurred in quite recent times as a result of this factor being overlooked. In recent years, dredge mining operations have used floating thickeners to recover water while allowing slimes to be pumped in a concentrated form from the dredge pond. The deslimed sand is stored in a surge bin in readiness for introduction to the spiral concentrator circuit. It is usual for dry mining projects to maintain a reservoir of process water, as the flow rates to the plant are many times the required made-up volume. Some primary concentrators use seawater for their main process water, either because a dredge mine is operating near the ocean and fresh water is not able to be quarantined from the sea, or because there is insufficient local supply of nonsaline water. It is an important requirement for the performance of a spiral plant that sufficiently clean process water is available. A combination of process water quality and desliming efficiency must result in the process flow to the first

Beneficiation of mineral sands: a practical outlook Chapter | 5

203

stage of spirals having a carrier fluid (water) quality well below 4% fines, otherwise separation efficiency will be impaired. Figure below shows the impact of slime (fines) in spiral feed water on the recovery of valuable heavy minerals (VHM). Although this is a generic depiction of the impact, it is a very common industry experience (Fig. 5.24). 5.5.1.1.2

Mineral recoveries

Recoveries of individual minerals is largely dictated by extent of processing, type of equipment used, mineral assemblages and the THM grade, the range of recoveries of various heavy minerals at the stage of Primary Concentration is as follows (Table 5.6).

FIGURE 5.24 Recovery versus percenteage of fines.

TABLE 5.6 WCP mineral recoveries. Recoveries (%)

Bench Marks (%)

Ilmenite

90
95

95

Rutile

85
90

90

Zircon

90
95

95

Garnet

40
50

50

Monazite

90
95

95

Sillimanite

40
50

45

204

5.5.2

Mineral Processing

Mineral Separation Plant (MSP)

In the mineral separation plant (MSP), the heavy minerals like ilmenite, rutile, monazite, zircon and sillimanite are separated from the upgraded feed minerals based on their physical properties like electrostatic and magnetic property, surface characteristics and specific gravity. The plant is equipped with different material handling equipment like bucket elevators, belt conveyors, screw conveyors, drag conveyors to facilitate smooth transport of materials to the desired machines, e.g., rotary dryer, high tension separators, magnetic separators, shaft dryers, electrostatic separators. Besides, there is a wet processing circuit which comprises spirals, floatex, wet tables and flotation cells, and slurry pumps are used to transport materials from one point to another. The only chemical processes employed are in cleaning mineral surfaces and even this is often not necessary. In the case of surface coatings, minerals may be somewhat intractable, requiring strong cleaning processes. There are various physical separation equipment available for mineral sand processing, and a wide range of possible flowsheets deploying the various separating processes. Typically, a high ilmenite HMC will be subjected initially to magnetic separation, which in ideal circumstances may isolate a final product ilmenite in a single pass. However, the presence of moderately magnetically susceptible minerals like monazite, garnet, and staurolite may require subsequent electrostatic separation to purify the ilmenite product. This requirement has resulted in some plants choosing an alternative first stage, where electrostatic separation is followed by magnetic separation. Selection of the best flow sheet and type of equipment will have a very positive impact on capital cost as well as recovery and ease of operational control. The process involved in the mineral separation plant are: (1) dewatering, (2) drying, (3) electrostatic separation, (4) magnetic separation, and (5) sizing.

5.5.2.1 Dewatering Dewatering is done either through a hydrocyclone with natural sun drying or a hydrocyclone with horizontal belt filters to ensure that the moisture content in the HMC fed to the dryers is ,6%. 5.5.2.1.1

Horizontal belt filters

Horizontal belt filters are, in broad terms, the most commonly used vacuum filters in the industry due to their flexibility of operation, adaptation to corrosive slurries and suitability to handle large throughputs. The components of horizontal belt filters are main belt, filter cloth, feed box, wash box, vacuum box, cloth wash box, discharge roll, aligning roll, take-up roll, and cloth form roll. A typical process flow sheet is shown below Fig. 5.25.

Beneficiation of mineral sands: a practical outlook Chapter | 5

205

Concentrate from PCP

DRYING (FLUIDISED BED DRYERS)

ELECTROSTATIC SEPERATION ( HT ROLL SEPERATORS & ES PLATE SEPARATORS )

N Con 1

Cond MAG SEPARATION (RED’S)

HI MAG SEPARATION (RER’S )

N.Mag

Mag

N Con2

MAG SEPAR ATION (RED SEPARATORS)

Mag & N/mag

N Con 3

HI MAG SEPARATION (RER SEPARATORS)

Mid

N.Mag Mag

N.Mag

WET GRAVIRTY SEPERATION (SHAKING TABLES)

SIZE SEPERATION (SCREENS)

REJECTS ILMENITE

RUTILE

ZIRCON

GRADED GARNET

SILLIMANITE

BACK FILLING

FIGURE 5.25 Concentrate from PCP.

5.5.2.2 Drying Drying is done either through a rotary dryer or a fluidized bed dryer to maintain the temperature of the feed to electrostatic separation above 100 C for effective separation. 5.5.2.2.1

Rotary drier

The main components of the rotary dryer are the Hot Air Generator unit (HAG), burner, blower, rotating shell, exhaust blower, and discharge unit. First is the hot air generator where hot air is produced. The burner is inside this portion. The fuel for the burner is usually heavy fuel oil. To be able to generate enough heat to dry, the concentrate air must be added by way of a blower. The wet concentrate enters the drier in front of the HAG. It is a revolving shell that is on a slight incline. As the concentrate travels down this incline to the exit of the drier, it is dried. At the discharge end, the exhaust blower would need to be installed to remove the flue gas through a chimney.

206

Mineral Processing

FIGURE 5.26 Rotary drier.

A typical drawing of the rotary dryer is given below (Fig. 5.26). 5.5.2.2.2 Fluidized Bed Dryer (FBD) Fluid bed dryers work on the principle of fluidization, a process where a material is converted from a static solid-like state to a dynamic fluid-like state. In this process, hot gas or air is introduced through a perforated distribution plate into the area holding the material. This hot gas pumps through the spaces between solid particles. As the velocity of the gas or air increases, the upward forces on the particles increase, causing them to equal the gravitational forces below. This creates a state of fluidization where the particles are suspended in what appears to be a boiling bed of liquid. Each particle is in direct contact with, and surrounded by, the hot gas or air—creating an efficient and uniform drying process. The main parts of the FBD are: (1) feed chute, (2) wind box; (3) hot air distributor plate with tuyers, (4) expansion chamber, (5) discharge chute, (6) exhaust chamber with cyclones, and (5) exhaust blower and chimney. The burner is mounted on the wind box and the hot air is produced in the wind box. The hot air along with the dilution air is passed through the distributor plate with tuyers for even distribution of the air across the expansion chamber. The wet feed is fed through the feed box, which is located just above the expansion chamber and after drying, the dried material is discharged through the discharge chute, which is located at the bottom of the expansion chamber. The exhaust blower sucks the flue gas and discharges through the chimney to the atmosphere. The advantages of the FBD are: G G G G G

It It It It It

occupies less space is energy efficient.-Heat transfer with minimal energy consumption is multi-functional: capable of heating, drying, and more. is adaptable to continuous or batch processing. has no moving parts and hence requires less maintenance.

Beneficiation of mineral sands: a practical outlook Chapter | 5

207

Flue Gas Feed Inlet Bag Filters

Expansion chamber Stack

Tuyers Product Outlet

'Pbcd

Tbcd

Conical chamber

Fuel

Windbox Bypass value

Burner

Flow meter

Air heater Roots blowe

FIGURE 5.27 Fluidized bed drier.

A typical FBD drawing is given below (Fig. 5.27).

5.6

Factors influencing mineral sand processing

Production of mineral products can be broadly considered in two stages. The ore is upgraded to a mixed Heavy Mineral Concentrate (HMC) in the first stage and HMC is then split into individual mineral products at the Mineral Separation Plant (MSP). It is usually convenient to consider both physical processes and costs of mineral production in these two components. The production and cost of landing HMC at the MSP is a standard point of comparison with competitor projects, whereas the intrinsic value of the concentrate and MSP conversion costs are a measure of the second stage. Mining and primary concentrator plant costs are largely driven by ore grade, whereas MSP costs are mainly affected by the mixture of minerals in the HMC. Transport distances and energy costs are also very significant for both waste ceramic tile powder (WCP) and MSP. The types of separation equipment used in the mineral sands industry are well established and generally do not affect operating costs too greatly. However, the efficiency of separation can vary considerably, so the correct selection of flow sheet items and philosophy are important to optimize product quality and recovery. Judicious use of some recently developed separation equipment items could significantly reduce the capital cost, especially in the MSP.

5.7

Tailing’s disposal

The planning and execution of tailings disposal is one of the most important activities of the mine site. Without secure storage available to dispose off the vast quantities of tailings and an effective water recovery regime, operations

208

Mineral Processing

can grind to a halt very quickly. The temptation to carry on operations when tailings activities are in jeopardy has resulted in environmental and safety disasters in the past, and must be avoided at all costs. The simplest tailings operations occur in low fines dredge deposits, where the concentrator sand tailings are discharged directly behind the floating concentrator. Where the dredge face is about ,10 m higher than the pond level it is possible to directly stack all the sand tailings. If there are fines in the circuit water, or the tails needs to be stacked higher, then it will be necessary to pump tailings further away, and possibly use dewatering cyclone stackers. As any of tailings stack height, fines content of ore, or dry mining haulage distances increase, the pumping duty will also increase. Power consumption of the tailings pump can be higher than the rest of the WCP in some circumstances. A critical aspect of the operation is water recovery. Pure quartz sand allowed to settle in water will achieve a pulp density of about 80% solids. Most of this water will remain in the tailings mass and represents a significant water loss to the operation. Pumping of sand tails is generally carried out at slurry densities of 35%
45% solids and the difference between this hydraulic transfer medium volume and the sand must be recovered as effectively as possible for return to the plant. Where cyclone stackers are employed, the overflow water can usually be collected and pumped directly back to the plant. Cyclone underflow densities achieved are usually around 75% solids, so some water will be displaced from the settling tails stack as it densifies to 81% solids. Collection of this “bleed out” water is more difficult than the cyclone overflow and some of it is unavoidably lost. Water recovery from tailings can be vastly more complicated when significant fines are co-disposed with the sand tailings. Co-disposal can be necessary for environmental reasons, or simply due to available land limitations. It is preferable for the top meter or so of the final land form to contain a reasonable proportion of fines within the soil mass for nutrient and moisture retention. The ingredients for creating such a growing medium are readily to hand during the replacement of sand and fines tailings and the challenge is to develop an effective method to mix the two, without creating operational cost or safety problems. If the resource being mined has a fairly high fines content, co-disposal is required because of the sheer volume of fines that would otherwise occupy vast areas of tailings impoundments as a post-mining legacy. Mixing thickened fines from the water recovery thickeners with cycloned sand tails results in a pulp that can be pumped to the tailings area. Unlike sand tailings, this mixture does not stack, and only dewaters by settling. Water recovery, while avoiding recirculating thickened fines, is therefore much more difficult to achieve. Such mixed tailings are also far less stable than sand stacks, so must be adequately retained. This is typically achieved by the edges of the ore body and cross-wall construction at judicious intervals to isolate the tailings from the current extraction operations (Table 5.7).

Beneficiation of mineral sands: a practical outlook Chapter | 5

209

TABLE 5.7 Mineral Recoveries at MSP. Recoveries (%)

Bench marks (%)

Ilmenite

94
96

95

Rutile

85
88

85

Zircon

65
70

68

Garnet

65
75

75

Monazite

65
70

70

Sillimanite

80
82

80

5.8

Metallurgical accounting system

Metallurgical accounting is an ongoing process that involves sampling, analyzing, and accounting for the minerals that are part of the metallurgical circuit. Just as financial accounting provides the necessary framework for financial decisions; metal accounting provides the diagnostic information required for effective metallurgical decisions. Well-designed metal accounting procedures are a powerful tool that can provide insight, help monitor and address remedial measures for: 1. 2. 3. 4.

Production variability. Unexplained material losses and gain. Process inefficiencies. Production forecasting problems.

5.8.1

Measurement system

Critical to every metallurgical accounting system is mass and assay of key streams in each processing unit to arrive at process recovery. The metallurgical accounting process mass measurement is carried out through production meters, weightometers, weighbridge, and wet/dry stockpile and mined out area surveys while assay samples are collected and conveyed to the laboratory for subsequent analysis. The laboratory receives, prepares, analyses and reports all samples taken from the different plants.

5.9

Data collection, validation, and management

At the end of each month, data is collected from three key sources indicated above G

Concentrator throughputs and grades: Mine planning/survey reconciliation report.

210 G

G G G

Mineral Processing

Concentrator HMC Production: Weighbridge and moisture reports and HMC stockpile survey report. Stage recovery performance: Plant records and lab assays. MSP Production: Final product report. Final Products: Lab assays.

The above data is required as key input to the metal balance and is validated before it is used in the metal balance. The entire set of data collected and validated is then stored in the SRL Met network drive for later use as input to the metal balance.

5.10 Reconciliation, balancing and reporting The data is input into the accounting spreadsheet. Reconciliation is done betweeen the mined HMC and what was treated and produced by the MSP. A balance is achieved if there are no closure errors across the entire process.

DATA COLLECTION, VALIDATION

•Mass Measurement •Sampling Process •Sample Analysis MEASUREMENT SYSTEM

•Plant Records, Mine Planning Recon, MSP Stock Take & Weighbridge •Laboratory Assays

•Metal Balancing Process •Reporng & Record Keeping METAL RECONCILIATION, BALANCING & REPORTING

5.11 Metal accounting system 5.11.1 Procedure G

G

G

G

Feed tonnage and Grade of HM and minerals calculated based on the inpit survey and the mine block/resource model and composite grades of Feed, HMCs and final products from quality control Lab. Validate all these data and input into the accounting spread sheet as per the prescribed format. Calculate the recovery for each plant and pit-to-product on "tons in" and "tons out" basis and arrive the balance and accountability. Details of the recovery formulae and the sources of data for each plant are given below (Table 5.8).

Beneficiation of mineral sands: a practical outlook Chapter | 5

211

TABLE 5.8 Mineral recovery calculations are given here under. Sl no

Plants

1

Wet Plant

2

Units

Source of data/recovery formula

ROM Feed

MT

Feed tonnage

Grade of target mineral in feed

%

Weighted average grade

HM input

MT

Contained HM

Heavy minerals concentrate production

MT

Weightometer/Densitometer

HM output

MT

Contained HM in HMC

Grade of target mineral in HMC

%I

Weighted average grade

Wet plant HM recovery

%

HMC production x HM grade/Feed tonnage Feed HM grade

Recovery of target mineral

%

HMC production Ilmenite grade/Feed tonnage ilmenite grade in the feed

Mineral Separation Plant MSP feed

MT

Feed tonnage

Grade of target mineral

%

Weighted average grade

Production

MT

Weightometer of the product conveyor/time weights

%Ilmenite

Weighted average grade

%Rutile

Weighted average grade

%Zircon

Weighted average grade

%Garnet

Weighted average grade

%Sillimanite

Weighted average grade

Ilmenite Rutile Zircon Garnet Sillimanite Product grade

(Continued )

212

Mineral Processing

TABLE 5.8 (Continued) Sl no

3

Plants

Units

Source of data/recovery formula

Product recovery

%

Production of target mineral 3 Grade/ MSP Feed tonnage X grade of target mineral in the MSP Feed

Ilmenite

%

Ilmenite recovery at Wet Plant 3 Ilmenite recovery at MSP

Rutile

%

Rutile recovery at Wet Plant 3 Rutile recovery at MSP

Zircon

%

Zircon recovery at Wet Plant 3 Zircon recovery at MSP

Garnet

%

Garnet recovery at Wet Plant 3 Garnet recovery at MSP

Sillimanite

%

Sillimanite recovery at Wet Plant 3 Sillimanite recovery at MSP

Overall recovery

Loss point analysis Total loss percentage

%

Scrubber oversize

Ore mined-screen feed

Screen oversize

Screen feed-cyclone feed

Cyclone overflow

Cyclone feed-spiral feed

Spiral tails

Spiral feed-spirals HMC

MSP tails

MSP feed
(final 1 intermediate products)

Total

5.12 Record keeping Reports from weighbridge, laboratory assay, stockpiles from surveys, head feed grade from mine planning, daily production report and weekly reconciliations are all put together in the metallurgical balance and released every month, which is being saved in the met drive.

5.13 Methodology to develop a mineral sands project 1. Identification of geological domains. 2. Laboratory scale tests with different geological domain samples— Preliminary flow sheet.

Beneficiation of mineral sands: a practical outlook Chapter | 5

213

3. Pilot scale test work with a bulk sample (from a representative sample from pit). 4. Sample testing at pilot scale. 5. Finalization of flow sheet. 6. Basic engineering leading to estimates of Capital expenditure(Capex) and Operating expenditure(Opex). 7. Detail engineering. 8. Construction and commissioning.

5.14 Economic uses Strategic and economic applications which are mostly dependent on titanium, zirconium, and rare earths, in the form of their metals/compounds or alloys. The placer deposits are the treasure houses for ilmenite, rutile, leucoxene—all titanium minerals, zircon—ore for zirconium and hafnium, monazite—source for cerium and other light rare earths, garnet—the most preferred abrasive and sillimanite—an excellent refractory mineral. The economic importance of the minerals has prompted the whole world to start exploring heavy minerals.

5.14.1 Ilmenite and Rutile As Titanium (TiO2) white pigment: Used in paints/varnishes, plastic, paper, rubber, printing ink, coated fabric textiles, cosmetics, sun protection creams and pharmaceuticals. As Titanium (Ti) sponge/metal: Used in chemical, aerospace and aviation industry, surgical equipment, electrical turbines tubing, bullet proof vests, different alloys in iron and steel industry, immersion heater tubes, consumer goods, spectacle frames, golf clubs. Used for coating of welding electrodes.

5.14.2 Zircon Zircon is used in ceramics, foundries, refractories, glazing tiles, television and computer monitors and white wars. It is also used in manufacture of zirconium chemicals/metal, american diamond, scratch free bracelets, cutting tools, yttria zirconia as oxygen sensors. Zircon free from hafnium is used in nuclear reactors as cladding tubes to hold nuclear fuel.

5.14.3 Sillimanite Sillimanite is mainly used for the manufacture of high-grade refractory bricks, high alumina refractories, cement kilns and heat treatment furnaces.

214

Mineral Processing

5.14.4 Garnet Garnet is used for manufacturing blasting media, abrasives, grinding wheels, mosaic cutting stones, decorative wall plasters, ceramics, polishing of picture tubes, glass polishing and antiskid surface for roads, air strips, runways, water filter, water jet cutting, Artificial granite tiles/heavy duty floor tiles, cleaning of casings/pipes in petroleum industry and as a gemstone.

5.14.5 Monazite Monazite is used in the extraction of thorium concentrate and rare earth compounds. Rare earth chlorides are widely used in the manufacture of misch metal used for lighter flints, for the production of catalysts for cracking, for the manufacture of metallic soaps which are used as dryers in paints, starting material for the production of pure rare earths and rare earth compounds, removal of organic impurities and decolorization of effluents from paper mills and for the manufacture of special ferrous casting. Rare earth oxides are used in the arc carbon industries to increase the arc intensity by a factor of ten, for glass polishing in optical industries. For e.g., cerium oxide is used in polishing optical lenses, plate glasses, television tube face plates;, as a prism finds application in semiconductor devices, as a ultra-viloet absorber in glasses, as radiation protective glasses, and decolorizing. Thorium nitrate is used in the gas handling industry. Thorium oxide is used in fluorescent tubes and starters and as a catalyst for petroleum industry. Uranium oxide is used in the nuclear industry. Tri sodium phosphate is used in descaling, degreasing, detergents.

5.14.6 Cost considerations An analysis of the cost of production of heavy mineral sands is significantly complicated by their multi-product nature. Due to differing resource compositions and mineral quality, the volume of products from each of the major operation varies. This factor makes it difficult to compare the costs of production from one operation to another. An additional complication is the wide difference in product values (e.g., rutile compared with ilmenite), which means that cost alone is not an adequate measure of the relative competitiveness in this industry. Account must also be taken of the differing revenues achievable from the differing mix of products in order to establish a realistic assessment of relative competitiveness. Because of the differences in product mix, the relative importance of the various products and their differing values, the method of internal cost allocation used by different producers varies significantly. Each producer tends

Beneficiation of mineral sands: a practical outlook Chapter | 5

215

to use a method for allocating costs that reflects the nature of its particular operation or the corporate culture of the parent entity, but this does not necessarily generate the cost information that is comparable with that from other producers. The cash operating costs include the following: HMC costs G G G G G G G G G G

G G

Cleaning and removing of vegetation Overburden Removal Drilling and blasting (in case of rock deposit or where necessary) ROM sand excavation Transport of the ROM sand to PCP All costs incurred in the PCP Tailings disposal costs Thickener operating cost and slime disposal cost Rehabilitation costs The cost of mine site accommodation and township administration in those instances where the mine site is remote from the mineral separation plant (MSP) site. Costs incurred in the transport of HMC to the MSP HMC stock adjustment MSP costs

G G G G G

Ilmenite roasting (where applicable) HMC leaching (where applicable) All costs incurred in the MSP. Transport of Mineral Products to Shipping Port Costs incurred in product storage and ship loading to FOB Vessel (or costs to FOR/FOT transportation in the case of sales to domestic consumers). Administration, marketing and royalties

G

G

G

Site administration costs, including centralized costs incurred on behalf of operating sites, but not corporate overheads Costs associated with marketing mineral products, including commissions (which are included as a cost, rather than being deducted from revenues) Government and landholder royalties payable on mineral products.

Actual costs for any particular project will be influenced by project—specific factors such as: G

G G

Resource characteristics—for example grade, mineral suite, overburden, and slime content; Location, which affects infrastructure and transport costs; Availability and cost of utilities, particularly electric power.

216

Mineral Processing

5.15 Resource characteristics 5.15.1 Grade The costs are heavily dependent on total HM grade and scale of operations. As a result, it can vary from US$12/MT to US$127/MT. It is notable that those operations with very low cost of HMC production are all favored by high grade ore bodies, with little or no overburden and higher thickness of deposits. Additionally, those based on ilmenite dominated resources have lower HMC costs than those with high rutile zircon contents. However, this reflects more on the economic necessity for high HM grades with low value mineral assemblages than on any cost effect. Higher product revenues available from zircon and rutile rich assemblages enable some deposits to be economically mined with a lower total HM grade. This results in a higher mining and concentrating cost per ton of HMC compared with ilmenite rich assemblages. A case in example is the operation of Sierra rutile. Despite the THM grade of 2.0% max, the operation is highly economical and viable because its 2.0% THM is of rutile only, which is of very high value. Similarly Australian zircon is running profitably though the THM grade is not more than 2%
3% (to be checked) since majority of the THM is Zircon, which is again of high value.

5.15.2 Proportion of slimes When the slimes (below 45 μm) in the deposit is .5%, the ROM sand needs desliming since the presence of slimes increases the viscosity of the slurry thereby reducing the sharpness of the separation in all gravity separators. The desliming is traditionally carried out using a set of hydrocyclones and the slimes thus separated will be mixed with coarse tailings and will be dumped back into the mined-out pits. The rheology of slimes dictates the loss of water and types of chemicals required for their settling and thus disposal of slimes adds to the costs significantly.

5.15.3 Overburden Removal of overburden adds to costs and with the increase in the thickness of overburden, its removal costs increase proportionately.

5.15.4 Mineral assemblage With the number and types of minerals in the mineral suite, processing and separation costs at PCP and MSP will vary. The costs involved in a threemineral suite will be less compared to those of a 5-mineral suite. The traditional 3 mineral suite consists of ilmenite, rutile and zircon while in a fivemineral suite, two more minerals, i.e., sillimanite and garnet will be present.

Beneficiation of mineral sands: a practical outlook Chapter | 5

217

Though the separation of sillimanite and garnet will necessitate additional processing circuits including flotation, additional revenues accrued from the sale of those minerals will compensate the same. The presence of iron oxide coatings on zircon and rutile particles necessitate HCL leaching, which would add to costs. Similarly, the presence of chromium leads to roasting thereby leading to increase in costs.

5.16 Availability and cost of utilities 5.16.1 Power tariff The power tariff plays a significant role in operating costs of a heavy mineral sands industry particularly so in the case of high-power tariff countries such as India. Lower power tariff would always help the cause in the case of processing of low-grade deposits.

5.16.2 Water Since the operation of PCP is primarily a wet operation and requires about 0.6
0.7 m3 of water per MT of ROM feed, the cost of water assumes immense significance. In addition to the same, the mining is a dredge operation, it will add the requirement of water. If adequate ground water is available and can be used, the water costs will be minimal. However, if the water has to pumped over a significant distance, the water costs would be significantly high. The water costs for mineral sands operations over in the range of INR10 per m3.

5.16.3 Fuel The fuel consumption is mainly for drying of HMC in MSP and also for the operation of heavy earth moving equipment for mining operations. The cost of fuel plays an important role in dictating the costs of per MT of Mineral.

5.16.4 Location, which affects infrastructure and transport costs The distance between the seaport and the plant site dictate transportation costs. Well-developed seaports and rail lines being nearby would reduce transportation costs significantly. The cash costs based on the above-mentioned factors vary significantly from one deposit to another deposit. The contribution of various cost drivers of these costs varies depending deposit characteristics, unit costs, logistics, etc., as shown below (Table 5.9).

218

Mineral Processing

TABLE 5.9 Cost driers for different types of operations. Cost drivers

Deposit of 3 mineral suite, no slimes, no overburden (%)

Deposit of 2% HM (%)

Deposit of 4 mineral suite, no overburden, 15% slimes (%)

Deposit of 5 mineral suite with 15% slimes, no overburden (%)

Labor

19

30

4

6

Electric power

9

13

19

17

Materials (handling and consumption)

28

22

9

11

Contract Services

29

14

22

32

16

0.3

Water Other (including royalties)

15

21

30

34

100

100

100

100

5.17 Conclusion Titanium is the 9th most abundant element, making up about 0.6% of the earth’s crust. It occurs naturally in chemical combinations, usually with oxygen and iron. Because of the high strength-to-weight ratio of its alloys and resistance to corrosion, titanium is an important strategic and critical material used widely in high-performance military and civilian aircraft in both engines and airframes. Having understood the importance of titanium and its alloys, the gainful and meaningful exploitation of resources of titanium namely ilmenite, rutile and leucoxene assumes immense significance. It may be noted that all the techniques of physical processing viz. screening, washing, gravity concentration, flotation, dewatering and filtering, drying, electrostatic separation, magnetic separation, grinding, are employed in concentration, separation and production of heavy minerals including ilmenite, rutile, zircon, sillimanite, and garnet. The separation of heavy minerals is a challenging one, as more than five minerals of varying characteristics (both physical and chemical) are to be concentrated and separated with optimum recovery from a source of an ROM sand, which consists of varying proportions of THM from 1% to 60%.

Beneficiation of mineral sands: a practical outlook Chapter | 5

219

Ilmenite is the main source of TiO2, which is the base for pigment industry without which there is no snow-white paint. Zircon is essential for making the control rods for nuclear reactors. With development in infrastructure, aviation industry, medical sciences, steel making industry, the advancement in oil, cutting & polishing industries, the requirement of not only ilmenite but all heavy minerals like zircon, garnet, sillimanite are inevitable. Keeping pace with the development of new techniques and machines, is the mantra for optimal exploration of heavy mineral sands deposits, which is going to play an important role in the all-round growth globally.

Acknowledgements The authors thank Mr. R Narayanan and Mr. Deepak Rathod for his assistance in preparing and compiling this chapter. The authors thank Mineral Technologies Ltd., Derrik Corporation, Ore Kinetics Pty Ltd., for according permission to use the pictures of their machines etc. The authors thank the Dr. Sripriya Rajendran for giving an opportunity for presenting this chapter. The authors thank their family members for their full support in preparation and shaping this chapter. The authors thank the publishers for their guidance in presenting this chapter.

Further reading Gujar, A.R., 2004. Placer mineral exploration: contribution and future projection of MO. In: Loveson, V.J., Misra, D.D. (Eds.), Placer 2004. Allied Publishers PVT Ltd, Bengalure. Hubert, J.F., 1962. A zircon-tourmaline-rutile maturity index and the interdependence of the composition of heavy mineral assemblages with the gross composition and texture of sandstones. J. Sediment. Res. 32 (3), 440
450. Indian Bureau of Mines, 2020. Indian Minerals Yearbook 2020. (Part- III: Mineral Reviews) 59th (ed.)., The Indian Bureau of Mines. Mohan, P.M., Rajamanickam, G.V., 2014. Indian Beach Placers- A Review, hand book of placer mineral deposits,151th ed. Rajamanickam, G.V. (Ed.). New Academic Publishers, New Delhi. Mukherjee, T.K., 1998. Mining and processing of titanium minerals in India. Met. Mater. Process. 10, 85
98. Prothero, D.R., Schwab, F., 1996. Sedimentary Geology, p. 460, ISBN 0-7167-2726-9. Rao, A.Y., Nagabushanam, B., Dash, A.K., Ratul Paul, Ravi, G.S., 2001. Present exploitation status and future prospects of beach placers and their industrial applications. In: Subba Rao, K.V., Rajasekhar Reddy, D. (Eds.), Some Aspects of Mineral development in India. GSI and Andhra University. Ravishankar, S., 2019. Mining the Coasts of Tamil Nadu. Rozendaal, A., Philander, C., Carelse, C., 2010. Characteristics, recovery and provenance of rutile from the Namakwa Sands heavy mineral deposit, South Africa. J. South Afr. Inst. Min. Metall 110, 2, 67
74. https://en.wikipedia.org/wiki/Heavy_mineral_sands_ore_deposits. https://www.amd.gov.in/app16/contentpage.

220

Mineral Processing

https://crirsco.com/docs/17_Mineral_Sands_Deposits_their_complexity-DRathod.pdf. http://earthsci.org/mineral/mindep/minsand/minsand. https://www.cdeglobal.com. https://www.tenova.com/products-technologies/mining-technologies/. http://ethesis.nitrkl.ac.in/4783/1/109MN0585.pdf. https://www.911metallurgist.com/blog/wp-content/uploads/2015/12/Recovery-of-titanium-frombeach-sand-by-physical-separation.pdf. https://tio2.info/2021/06/11/International-rutile-prices-rose-in-the-third-quarter/. https://tio2.info/2021/10/28/LB-group-rutile-tio2-latest-price-offer-26th-Oct/. tio2.100ppi.com. http://www.alsglobal.com. http://www.mineraltechnologies.com. http://www.multotec.com. http://www.indiawijzer.nl/index. http://www.tailings.info/technical/hydraulic.htm. http://www.imsc-group.com/spiral-concentrators. http://www.trimexsands.com. http://www.britannica.com/technology/flotation-ore-dressing. http://www.derrick.com. http://www.mogroup.com. http://www.holmanwelfley.co.uk.

Chapter 6

Addressing an inverse problem of classifier size distributions B. Venkoba Rao DELKOR, Takraf India Private Limited, Bengaluru, Karnataka, India

6.1

Introduction

Particle size separations for the industrial unit operations are addressed using various types of size classifiers wherein the separations are based on mechanical and/or centrifugal forces applied to the crushed and ground feed particles. The size classification of particles can be achieved on dry or wet particle streams using suitable equipment depending on the process requirements. Frequently, the size classifiers are placed in closed circuit configurations with the crushers or with the grinding mills that reroute back the escaped particles of higher size from the “open side setting” of the crusher or due to inadequate residence time in the grinding mills. While these size reduction equipment (i.e., crushers and mills) reduce the particle sizes to smaller sizes to liberate the valuables from their associated gangue matrix, the classifiers remove those particles that have already attained the required “sieve-opening size” or the “mesh of grind” from the crushing/grinding circuit from the viewpoint of process needs. The over-grinding of particles in mills increases the energy consumption of the plant operations and creates problems for the fine particle recovery in the downstream upgradation operations. In a way, the classifiers reduce the energy consumption for size reduction and also give the correct sized material for the downstream process separations. The classifier particle size distribution is an important factor influencing the performance efficiency of the downstream mineral separators. For a good and consistent performance of the plant, the size distribution from the mill output needs to be controlled within a stipulated narrow band of variation. The wet classifiers also find application in dewatering circuits to aid solid
liquid separations. In a classifier, the settling and recovery of solid particles more to the coarse particle stream and the recovery of water more to the finer particle stream aid solid
liquid separation. Upgradation of China Mineral Processing. DOI: https://doi.org/10.1016/B978-0-12-823149-4.00008-9 © 2023 Elsevier Inc. All rights reserved.

221

222

Mineral Processing

clay uses a multistage bank of small diameter hydrocyclones, as these units also help in gravity concentration. Similarly, hydrocycles, water-onlycyclones/stub-cyclones find application in the beneficiation of coal and iron ore, as higher density particles report more to the underflow stream and enrich their concentration in the underflow stream. Several units such as vibrating screens, screw classifiers, rake classifiers, air cyclones, hydrocyclones, hydrosizers, sieve bends, Derrick screens, etc. are employed industrially to classify the particles. The selection of these units depends on the size of the particles to be separated, the dry/wet process, and the tonnage to be handled. The assessment of the size classifiers is done using particle size distributions of the feed and product streams. The separation of the feed size distributions at the desired particle size of interest is never perfect. The cut size represents the size that has a 50% probability of reporting to the oversize and the undersize streams. The cut size of the particles varies based on the type of classifier and the nature of the feed distribution. For example, the vibrating screens have a coarse cut size range followed by the cut sizes of rake and spiral classifiers, which are followed by the cut sizes of cyclones. This is mainly due to the size range of the feed particle size distributions that these units treat. Fig. 6.1 shows a schematic diagram of some of the size classifiers generally used in the mineral-processing industry. A classifier has one input feed stream, which is split into two output product streams, i.e., coarse and fine size distribution streams. A few classifiers can split particles into more than two streams. Such equipment can in turn be viewed as a series of one-input two-output devices connected together (Tarjan, 1981; Wills, 1997).

FIGURE 6.1 Schematic diagram of various size classifiers generally used in mineral processing.

Addressing an inverse problem of classifier size distributions Chapter | 6

6.1.1

223

Evaluation of size classifier performance

The efficiency of particle separation in size classifiers is generally measured in terms of partition coefficent as a function of particle size. The partition coefficients indicate the recovery of the feed particles of a given size to one of the product streams, generally to the coarse stream. During classification, each size has a probability of being recovered either in the coarse stream or in the fine stream. These probabilities are size-dependent and when plotted as a function of particle size will produce a smooth sigmoid curve of separation. The size attribute which is plotted on the abscissa is either the passing size or the average size of the size class from the sieve analysis. The classifier performance is never perfect in that they account for some misclassification of particles to either of the product streams. It is essential to understand the behavior of a classifier in terms of the overall mass split of particles to each of the product streams and also the profile of the efficiency curve (also called the partition curve) that the unit produces. Fig. 6.2 represents a schematic diagram of the split of particles in a size classifier, where F; O; and U represent the solids flow rate of the feed stream, the fine stream, and the coarse stream respectively. Also, f ðd Þ; oðd Þ; and uðd Þ represent the size distributions of the feed stream, the fine stream, and the coarse stream respectively in the density form, where d is the particle size. The density form of the distribution represents the fraction of material present in the size range d to d 1 dd in that stream. Under steady-state operation, the mass balance of the classifier unit can be written as F5O1U

ð6:1Þ

F f ðd Þ 5 O oðdÞ 1 U uðd Þ

ð6:2Þ

FIGURE 6.2 Schematic diagram of the split of particles in a size classifier.

224

Mineral Processing

Discretization of the size distributions as the sieve size-classes, Eq. (6.2) can be expressed as F f ðdi Þ 5 O oðdi Þ 1 U uðdi Þ

ð6:3Þ

Where di denotes the representative size of the ith size class of particles and f ðdi Þ; oðdi Þ; and uðdi Þ respectively represent the mass fraction of particles retained in the ith size class of the feed, the fine, and the coarse streams. In terms of the mass split of particles to the coarse stream, Eq. (6.3) can be expressed as
 f ðdi Þ 5 Ssplit uðdi Þ 1 1 2 Ssplit oðdi Þ ð6:4Þ Where Ssplit represents the mass split of the overall solid particles flowing from the feed stream to the coarse stream. With the rearrangement of Eq. (6.4), we can express mass split of particles to the coarse stream as
Ssplit 5

U f ðdi Þ 2 oðdi Þ 5 F uðdi Þ 2 oðdi Þ

ð6:5Þ

Eq. (6.4) suggests that Ssplit can be calculated from all the sieve size classes, and this redundant information is useful for data reconciliation of the classifier size distributions (Wills, 1997). The partition coefficients, also called the actual separation efficiency for various size classes can be calculated from Ea ðdi Þ 5 Ssplit

uð di Þ f ðdi Þ

ð6:6Þ

Where Ea ðdi Þ represents the actual efficiency of separation for the ith sizeclass fractions. The actual efficiency of separation can be calculated from reconciled data of experimental size distribution measurements. The actual efficiency of separation that shows the by-pass of very fine particles to the coarse stream, can be expressed in terms of the corrected efficiency curve as
Ea ðdi Þ 5 ð1 2 Rf Þ Ec ðdi Þ 1 Rf

ð6:7Þ

Where Ec ðdi Þ represents a corrected efficiency of separation for the ith sizeclass particles and Rf represents the by-pass of very fine particles reporting to the coarse stream. The by-pass fraction is proportional to the water/fluid recovery to the coarse stream during the classification of particles. The corrected efficiency of separation for the various size classes, di , which spans between [0, 1] shows a sigmoidal curve and can be mathematically expressed in several forms. Plitt (1971) proposed the corrected efficiency of separation as
    di m Ec ðdi Þ 5 1 2 exp 2 ln ð2Þ ð6:8Þ d50c

Addressing an inverse problem of classifier size distributions Chapter | 6

225

Where d50c represents the corrected cut size of the separation and m represents the sharpness of separation. Austin et al. (1984) and King (2001) represent the corrected efficiency of separation in logistic form as Ec ðdi Þ 5

11

1  2r di d50c

ð6:9Þ

Where d50c represents the corrected cut size of the separation and r represents the sharpness of separation. Eqs. (6.8 or 6.9) can be combined with Eq. (6.7) to get the actual efficiency of separation in terms of particle size, which then can be fit to partition coefficient data from the measured/reconciled size distributions, to evaluate the three parameters, namely the by-pass fraction, the cut-size, and the sharpness of separation through optimization routines. It should be noted that the actual efficiency of separation for the classifier is a function of the process-operating conditions such as pulp density (or the percentage of solids), flow rate, particle size distribution, etc. of the feed stream as well as the design variables of the equipment. So, by suitably controlling the possible variables of influence, the efficiency of separation can be improved for any given operation. Such relations have been well established in the literature for hydrocyclones (Lynch et al., 1974; Nageswararao et al., 2004). It has been discussed in the literature that hydrocyclones and vibrating screens sometimes in their operation show a fish-hook effect and a piggyback effect in their actual efficiency curve in the fine size range, where the recovery of very fine particles to the coarse stream increases drastically. However, for simplicity, these aspects are not considered in this chapter. The efficiency curve representation here is based on Eqs. (6.7
6.9).

6.2 Analytical solution to the Classifier product size distributions Typically, the shape parameters of the efficiency curves namely, the by-pass fraction, the cut-size, and the sharpness index are evaluated from the established empirical relationships involving design and process variables. An actual efficiency curve can be constructed easily from the thus obtained classifier parameters. A transformation of the feed size distribution with the actual efficiency curve simulates the coarse and fine product size distributions of the classifier (Kawatra and Seitz, 1985; Heiskanen, 1993; King, 2001; Venkoba Rao, 2005, 2007a, 2007b). The discrete density functional form for the classifier fines stream, oðdi Þ; and the coarse stream, uðdi Þ; can be evaluated from the actual

226

Mineral Processing

efficiencies of separation, Ea ðdi Þ; and the discrete feed density function, f ðdi Þ; as ð1 2 Ea ðdi ÞÞf ðdi Þ oð di Þ 5 P i ð1 2 Ea ðdi ÞÞf ðdi Þ

ð6:10Þ

Ea ðdi Þf ðdi Þ uð di Þ 5 P i Ea ðdi Þf ðdi Þ

ð6:11Þ

The classifier product size distributions in Eqs. (6.10 and 6.11) can be expressed as continuous functions of particle size in percent cumulative form as Ðd ð1 2 Ea ðdÞÞf ðd Þdd Oðd Þ 5 100 Ð d0max ð6:12Þ ð1 2 Ea ðdÞÞf ðdÞdd 0 Ðd

Ea ðdÞf ðd Þdd U ðd Þ 5 100 Ð d0max Ea ðd Þf ðdÞdd 0

ð6:13Þ

Where OðdÞ and U ðdÞ respectively represent the fine and the coarse cumulative product size distributions of the classifier passing particle size, d; and dmax represents the maximum particle size of the classifier feed distribution. Suppose we define the feed size distribution of the classifier in terms of the Gates-Gaudin-Schumann (GGS) function, we can combine it with the Plitt’s efficiency curve (i.e., Eq. 6.8) or the logistic efficiency curve (Eq. 6.9) to obtain analytical expressions for the product size distributions, which then will help to solve the inverse problem of the size separations, which will be discussed in the subsequent sections of this chapter. The density and cumulative from of the feed distribution by the GGS function are respectively expressed as 80 10 1n21 > > < @ n A@ d A for 0 # d # dmax ð6:14Þ f ðd Þ 5 dmax dmax > > : 0 for d . dmax 80 1n > > d >

> > : 0 for d . dmax

6.2.1

Classifier analytical expressions for Plitt’s efficiency curve

Substituting the values of Ea ðdÞ; Ec ðdÞ; and f ðdÞ from Eqs. (6.7, 6.8, and 6.14), respectively into Eqs. (6.12 and 6.13) and simplification of the terms

227

Addressing an inverse problem of classifier size distributions Chapter | 6

yields (Venkoba Rao, 2005)0 1 8 > > n > > γ@ ; K A > > m > > < 1 for 0 # d # dmax 100 0 OðdÞ 5 > n > > γ @ ; Kmax A > > m > > > : 100 for d . dmax

U ðd Þ 5

8 > > > > > > > > > > > > < 100 > > > > > > > > > > > > :

  mK

n m

0 1 @nA m m Kmax




2 n 1 2 Rf



ð6:16Þ

0

1 n γ@ ; K A m for 0 # d # dmax 0

1

ð6:17Þ


 n 2 n 1 2 Rf γ @ ; Kmax A m for d . dmax

100

Where the values of K and K max are given by
  d m K 5 lnð2Þ d50c Kmax 5 lnð2Þ

  dmax m d50c

ð6:18Þ ð6:19Þ

Eqs. (6.16
6.19) represent the product distributions of the classifier in terms of incomplete gamma distributions. The parameters involved namely, m; d50c ; and Rf are Plitt’s actual efficiency curve parameters, and the parameters n and dmax are the GGS feed distribution parameters. The flow split of solid particles to the coarse stream from the feed can be calculated by integrating the denominator of Eq. (6.13), which is given by !  n 
1 2 R   d  n  n  f 50c Ssplit 5 1 2 ; Kmax γ ð6:20Þ m ðlnð2ÞÞðn=mÞ m dmax

6.2.2 Classifier analytical expressions for the logistic efficiency curve Substituting the values of Ea ðdÞ; Ec ðdÞ; and f ðdÞ from Eqs. (6.7, 6.9, and 6.14), respectively into Eqs. (6.12 and 6.13) and simplification of the terms

228

Mineral Processing

yields (Venkoba Rao, 2007b) 0

1  r n n 1 r d @ A  n 2 F 1 1; r ; r ; 2 d50c d 0 1 for 0 # d # dmax 100 dmax  r O ðd Þ 5 > n n 1 r > @ A > ; ; 2 ddmax > 2 F 1 1; > 50c r r > > > : 100 for d . dmax 8 > > > > > > > >
n n 1 r > d @ðRf 2 1Þ F @1; ; A 1 1A > ; 2 dmax > 2 1 > 50c r r > > > : 100 for d . dmax 8 > > > > > > > >
n d > 2 d > m > 50c > > 2 m ln ð 2 Þ dn21 > < 0 1 for 0 # d # dmax oð d Þ 5 n > n γ@ ; K A > d50c > max > m > > > : 0 for d . dmax

ð6:25Þ

0    m 1 8 > n d > > B
 2 d50c C m > > n21 B C > d mn lnð2Þ > @1 2 1 2 R f 2 A > > > < uð d Þ 5 0 0 11 for 0 # d # dmax > >
 > n > dn @m K n=m 2 n 1 2 R γ @ ; K AA > > max f max > m > 50c > > : 0 for d . dmax ð6:26Þ Similarly, differentiating Eqs. (6.21 and 6.22) with respect to particle size, d; yields (Venkoba Rao, 2007b):

oðd Þ 5

8 > > > >
> > > :



r  d d50c

n d n21 0 11 for 0 # d # dmax  r n n 1 r d max @ F @1; ; ; 2 d50c AA 2 1 r r 0

for d . dmax

0

ð6:27Þ

u ðd Þ 5

8 > > > > > >
dmax 11 > > > > > : 0



r  d d50c

r d d50c

 1 Rf

0 1 for 0 # d # dmax 0 1  r
 n n 1 r d @ Rf 2 1 F @1; ; A 1 1A ; 2 dmax 2 1 50c r r for d . dmax

ð6:28Þ The area under these particle distributions expressed in density form sums to 1 when integrated over the entire particle size range ½0; dmax . Since the feed particles get separated in the classifier into coarse and fine particle distributions, the feed distribution in density form always intersects both the product distributions. The size at which the feed distribution intersects with the overflow and the underflow distributions (in the density form) can be obtained by equating Eq. (6.14) with Eqs. (6.25 and 6.26). Solving

236

Mineral Processing

for the intersecting particle size, d ; for both the product distributions yields (Venkoba Rao, 2006) 

d 5 d50c

!!1=m  
n d50c n γ mn ; Kmax 21:4427 ln n m dmax lnð2ÞðmÞ

ð6:29Þ

Similarly, equating Eq. (6.14) with Eqs. (6.27 and 6.28) and solving for the intersecting particle size, d ; for both the product distribution yields (Venkoba Rao, 2007b): 0 11=r B d 5 d50c @



1



dmax n n1r 2 F 1 1; r ; r ; 2 d50c

r



21

C A

ð6:30Þ

The parameter, d ; is called the pivot particle size, where all the classifier distributions in density form meet and is a characteristic size of the classifier separation. This is the size where the cumulative size distributions show the maximum separation. Fig. 6.6 shows a plot of classifier distributions using data set: #2 in both cumulative and density form for the Plitt efficiency curve based analytical solution. It shows that the pivot size, d corresponds to 43 μm, where the distributions intersect in density form and where the corresponding cumulative distributions have the maximum separation in terms of the percentile differences for any two combinations of the classifier distributions. A similar plot can be shown for the analytical solution obtained from the logistic efficiency curve as well. The pivot phenomenon in classifiers has been noticed in the works of Roldan Villasana and Williams (1991), Kapur (2000), and Kraipech et al. (2002) but with no explanation. The above discussions explain the reasons for the pivot phenomenon using the derived closed form solution to the classifier distributions. Kraipech et al. (2002) report that the distributions in their research were measured using the laser diffraction technique, and the feed particles were not agglomerated. From the rearrangement of mass balance terms in Eq. (6.5) with respect to Ssplit , it can be shown that there exists a proportionality between absolute differences of the classifier distributions over the entire size range, ½0; dmax ] (Venkoba Rao, 2006; 2007b) as: Absðf ðdÞ 2 oðdÞÞ ~ Absðoðd Þ 2 uðdÞÞ ~ Absðuðd Þ 2 f ðd ÞÞ

ð6:31Þ

Fig. 6.7 shows the absolute difference among the feed and product distributions of the classifier using the density forms for the data set: #2. The curves meet the abscissa at the pivot size, d ; indicating that all three distributions in density form have the same value at the pivot size.

FIGURE 6.6 Classifier feed, fine and coarse size distributions expressed in cumulative finer as well as in density forms for the data set: #2 (Note: d 5 43 μm).

FIGURE 6.7 Absolute differences among classifier distributions in density form for the data set: #2.

238

Mineral Processing

Eq. (6.31) can be expressed using cumulative finer distributions over the entire particle size range, ½0; dmax ] as AbsðF ðdÞ 2 OðdÞÞ ~ AbsðOðdÞ 2 U ðd ÞÞ ~ AbsðU ðdÞ 2 F ðdÞÞ

ð6:32Þ

Fig. 6.8 shows absolute differences among the cumulative distributions for classifier data set: #2. When the absolute differences of the cumulative fine distributions are scaled with corresponding reciprocals of their maximum distribution difference values, the resulting curves collapse onto a single curve. The difference
similarity is a generic phenomenon of the classifiers. The maximum value of the difference
similarity happens at the pivot size, d  :

FIGURE 6.8 Cumulative finer distributions are expressed as: (A) absolute differences among the cumulative finer size distributions and (B) difference
similarity arising from these absolute differences for the data set: #2.

Addressing an inverse problem of classifier size distributions Chapter | 6

6.5

239

Classifier inverse problem

Inverse problems mainly identify the cause from the effects that can be measured. Inverse problems are generally ill-posed problems. Inverse problems may not have a solution in the strict sense or the solution may not be unique. We know that the feed distribution of the classifier can be combined with the actual efficiency curve to get the classifier’s fine and coarse product distributions. However, if the product distributions only are known, the question is to identify the feed distribution and the actual efficiency curve, from the product distributions. Eq. (6.4) suggests that the feed distribution can be calculated from the product distributions if the solid particle split to one of the product streams is known. However, in the absence of this solid particle split information, the problem is an ill-posed one. Fig. 6.9 shows that there exist infinitely many solutions to this inverse problem. It shows that the same fine and coarse product distributions in Fig. 6.9(A) can be obtained by combining feed distributions (i), (ii), and (iii) in Fig. 6.9(A) with corresponding actual efficiencies (i), (ii), and (iii) represented in Fig. 6.9(B) respectively. These are only a few cases of the many such combinations (proposed here for argument’s sake). Among these many solutions, we have to identify the solution, which represents a more realistic scenario of the combination of the feed and actual efficiency curve, from which the product distributions were produced. To resolve this problem, we can resort to functional forms of the feed and actual efficiency curves, which help us to identify a closer solution to reality Eqs. (6.16 and 6.17) as well as Eqs. (6.21 and 6.22) represent the analytical solutions of fine and coarse classifier distributions by considering specific functional forms for the feed and the actual efficiency curve. The five parameters in these functional forms are practically embedded in the product distributions represented by the analytical approaches. Therefore, if the five parameters that closely represent the product distributions are evaluated by the optimization routines using the analytical forms of the product size distributions, then these five parameters also represent the feed and the actual efficiency curve, from which the product distributions have been obtained. The errors associated with the product size distribution measurements influence the solution by this approach. This aspect will be discussed in the next section of parameter sensitivity analysis. Moreover, using the cumulative finer distribution form helps to build a more robust solution than considering the density form of the distributions. Tables 6.3 and 6.4 represent the classifier parameters estimated for the inverse problem using the cumulative product size distributions respectively for the Plitt efficiency curve and the logistic efficiency curve approaches. For the inverse problem solutioning, the feed distribution is excluded from the parameter estimation scheme and the model parameters are only evaluated from the measured product size distributions. It can be noticed that these parameters are quite close to those in Tables 6.1 and 6.2 respectively, which were evaluated by using all the three classifier distributions.

240

Mineral Processing

FIGURE 6.9 Characterization of the classifier inverse problem: the same classifier fine and coarse distributions in (A) (in pink and blue lines) can be obtained by combining feed distribution (i), (ii), and (ii) in (A) with corresponding actual efficiency curves (i), (ii), and (ii) in (B). There exist many such combinations, which make it an ill-posed problem.

Figs. 6.10 and 6.11 represent the feed and product size distributions from the parameters in Tables 6.3 and 6.4 respectively. The identified feed distribution is represented by the blue line for the Plitt efficiency curve approach and by the red line for the logistic efficiency curve approach. The identified feed distributions are quite close to the measured feed distributions despite avoiding them in the parameter estimation scheme. The absence of measured flow split factor also has negligible influence. We can thus identify the feed distributions quite closely to the real values using the inverse problem framework that captures feed distribution parameters as part of the product size distribution representation.

TABLE 6.3 Summary of best-fit parameters for the classifier product distributions estimated using the analytical solutions from the Plitt efficiency curve (Venkoba Rao, 2007a). Sl no

Classifier type

Model parameters n

m

Rf, %

dmax, μm

d50c, μm

SSE

References

1

Hydrocyclone

0.229

3.018

14.944

899

298

0.001

Lynch et al. (1974)

2

Air cyclone

0.773

2.451

60.274

105

41

0.021

Austin et al. (1984)

3

Dry screen

0.541

3.884

0.468

40,899

17,297

0.023

Austin et al. (1984)

4

Sieve bend

0.567

1.664

24.593

976

245

0.001

Austin et al. (1984)

5

DSF Dorr classifier

0.746

1.699

30.473

702

182

0.010

Austin et al. (1984)

6

Hydrocyclone

0.409

1.516

15.856

269

143

0.003

Napier-Munn et al. (1996)

7

Hydrocyclone

0.662

1.172

56.693

1053

165

0.009

Fuerstenau & Han (2003)

8

Dry screen

0.632

13.323

0.56

17,220

15,764

0.017

Napier-Munn et al. (1996)

9

Dry screen

0.537

12.377

0.927

17,026

15,354

0.008

Napier-Munn et al. (1996)

10

Dry screen

0.558

11.188

1.39

17,600

14,026

0.007

Napier-Munn et al. (1996)

11

Hydrocyclone

0.52

2.134

56.592

1151

245

0.022

Wills (1997)

TABLE 6.4 Summary of best-fit parameters for the classifier product distributions estimated using the analytical solutions from the logistic efficiency curve (Venkoba Rao, 2007b). Sl no

Classifier type

Model parameters n

r

Rf, %

dmax, μm

d50c, μm

SSE

References

1

Hydrocyclone

0.229

4.953

15.294

901

284

0.001

Lynch et al. (1974)

2

Air cyclone

0.765

4.125

59.099

105

40

0.019

Austin et al. (1984)

3

Dry screen

0.546

11.903

2.119

41,119

16,790

0.02

Austin et al. (1984)

4

Sieve bend

0.541

3.105

25.128

977

256

0.002

Austin et al. (1984)

5

DSF Dorr classifier

0.686

3.468

29.483

702

205

0.01

Austin et al. (1984)

6

Hydrocyclone

0.405

2.056

16.466

271

140

0.003

Napier-Munn et al. (1996)

7

Hydrocyclone

0.605

2.485

49.023

1053

205

0.01

Fuerstenau & Han (2003)

8

Dry screen

0.634

14.936

0.646

17,426

15,625

0.017

Napier-Munn et al. (1996)

9

Dry screen

0.538

13.878

1.028

17,201

15,211

0.008

Napier-Munn et al. (1996)

10

Dry screen

0.559

13.996

1.457

17,755

13,771

0.007

Napier-Munn et al. (1996)

11

Hydrocyclone

0.495

4.06

52.414

1149

252

0.022

Wills (1997)

Addressing an inverse problem of classifier size distributions Chapter | 6

243

FIGURE 6.10 Feed distribution identification (as indicated by the blue line) from the measured product size distributions using the Plitt efficiency curve approach.

Fig. 6.12 represents the Plitt and logistic actual efficiency curves identified from the parameters estimated using the inverse approach. These are shown by blue line and red lines in Fig. 6.12. The dots represent the actual efficiency values as function of particle size, which are estimated from the reconciled data of the three-classifier distributions, namely, the feed, the fine product, and the coarse product. Fig. 6.12 indicates that the logistic efficiency curve method identifies the actual efficiency curves better than the Plitt efficiency curve approach. The small deviations of the estimated efficiency curves from the measured efficiency values are attributed to inaccuracies in the parameter estimation from the product distributions. Fig. 6.13 compares the solid split factors estimated from the inverse model with those

244

Mineral Processing

FIGURE 6.11 Feed distribution identification (as indicated by the red line) from the measured product size distributions using the logistic efficiency curve approach.

of the actual separations. The solid flow splits are predicted fairly well by the inverse model (except for data #6, which shows some deviation).

6.6

Parameter sensitivity analysis

As the parameter estimation in the inverse model is highly influenced by the errors in the measurement of product size distributions, a sensitivity analysis is carried out in this section to identify those parameters that affect the feed and the efficiency curve. In other words, the uncertainty in the estimation of the feed and actual efficiency curve is attributed to the uncertainty in the

Addressing an inverse problem of classifier size distributions Chapter | 6

245

FIGURE 6.12 Identification of the Plitt efficiency curve and the logistic efficiency curve from the product size distributions.

estimation of the model parameters that represent these curves. Assuming that these parameters are independent of one another, the variances of the feed distribution and the efficiency curve for a given particle size due to variances in their parameter estimation are given by Venkoba Rao (2007a, 2007b).     @FðdÞ 2 @FðdÞ 2 Vn 1 Vdmax ð6:33Þ VFðdÞ 5 @n @dmax and

 VEa ðdÞ 5

@Ea ðdÞ @Rf

2

 VR f 1

@Ea ðdÞ @d50c

2 Vd50c 1

  @Ea ðdÞ 2 Vm @m

ð6:34Þ

246

Mineral Processing

FIGURE 6.13 A comparison of the solid flow split factor to the coarse stream estimated from the model parameters using closed-form solution of the product size distributions with those estimated from the reconciliation of classifier-measured distributions.

Where VFðdÞ ; Vn ; Vdmax ; VEa ðdÞ ; VRf ; Vd50c ; and Vm respectively represent the variances in F ðd Þ; n; dmax ; Ea ðd Þ; Rf ; d50c ; and m; respectively. Eqs. (6.33 and 6.34) suggest that the overall variance of the feed distribution and the efficiency curve is related to the sum of variances of individual parameters multiplied by their respective sensitivity coefficients. Therefore, sensitivity coefficients play a vital role in determining the overall variance of the feed distribution and efficiency curve representation.

6.6.1

Case 1: Plitt efficiency curve approach

The sensitivity coefficients are evaluated from the squares of the partial derivatives by partial differentiation of Eqs. (6.15) and (6.7) with respect to the

Addressing an inverse problem of classifier size distributions Chapter | 6

247

parameters contained in them. The following Eqs. 6.35
6.39 give the partial derivatives for the feed distribution and the Plitt efficiency curve representations, which when substituted in Eqs. (6.33 and 6.34) to enable the overall variance estimation for VFðdÞ and VEa ðdÞ :     @FðdÞ d n d 5 100 ln ð6:35Þ @n dmax dmax    @FðdÞ d n n 5 2 100 ð6:36Þ @dmax dmax dmax  m 2 dd @Ea ðdÞ 5 100 2 50c ð6:37Þ @Rf  m   
2 dd @Ea ðdÞ d m 1 2 Rf 50c 5 2 100 2 m lnð2Þ ð6:38Þ @d50c d50c d50c  m      2 dd @Ea ðdÞ d m
d 50c 5 100 2 1 2 Rf lnð2Þln ð6:39Þ @m d50c d50c

6.6.2

Case 2: Logistic efficiency curve approach

The sensitivity coefficients for the feed distribution are given by the same Eqs. (6.35 and 6.36), which are obtained by partial differentiation of Eq. (6.15). However, the partial differentiation of Eq. (6.7) by the substitution of Eq. (6.9) gives actual efficiency curve sensitivity coefficients for the logistic curve representation as: @Ea ðdÞ 100  r 5 @Rf d 1 1 d50c 

@Ea ðdÞ 5 @d50c

100

r

d50c ðRf 2 1Þ   r 2 d 11 d50c d50c

r

 @Ea ðdÞ 100 5 @m

ð6:40Þ

r

d

ðRf 2 1Þ ln   r 2 d 11 d50c

d d50c

ð6:41Þ



d d50c

 ð6:42Þ

Tables 6.5 and 6.6 give the estimated sensitivity coefficients for the evaluated model parameters for data set: #5 of Table 6.3 and data set: #4 of Table 6.4 respectively as a function of particle size. The trend in the results hold good to most data sets (some not discussed here). These results

248

Mineral Processing

TABLE 6.5 Estimated sensitivity coefficients for model parameters as a function of particle size for data set #5 of Table 6.3 (Venkoba Rao, 2007a). Size class

Particle size, d

Sensitivity coefficients as a function of particle size for the estimated model parameters of the inverse problem Rf

n

m

d50c

dmax

1

86.3

6775.81

1923.87

69.37

1.08E-02

4.95E-04

2

76

7307.77

1790.3

66.5

7.54E-03

4.09E-04

3

57.7

8216.55

1499.11

50.7

3.33E-03

2.71E-04

4

43.5

8855.32

1218.32

32.47

1.37E-03

1.78E-04

5

32.8

9275.07

969.93

18.67

5.51E-04

1.17E-04

6

26.7

9483.27

812.52

11.9

2.80E-04

8.59E-05

7

22.1

9622.5

685.66

7.67

1.50E-04

6.48E-05

TABLE 6.6 Estimated sensitivity coefficients for model parameters as a function of particle size for data set # 4 of Table 6.4 (Venkoba Rao, 2007b). Size class

Particle size, d μm

Sensitivity coefficients as a function of particle size for the estimated model parameters of the inverse problem Rf

n

r

d50c

dmax

1

840

5.94

193.84

4.48

4.66E-04

2.60E-03

2

590

48.47

1473.96

16.4

3.46E-03

1.78E-03

3

420

313.08

2858.99

29.14

1.75E-02

1.23E-03

4

297

1495.26

3909.32

6.96

4.64E-02

8.45E-04

5

210

4213.08

4478.55

11.41

4.28E-02

5.81E-04

6

149

7106.05

4622.61

28.77

1.44E-02

4.01E-04

7

105

8852.53

4453.23

13.78

2.55E-03

2.74E-04

8

74

9589.07

4081.54

3.57

3.41E-04

1.88E-04

portrayed in Tables 6.5 and 6.6 indicate that for a given particle size, the feed distribution is most sensitive to the estimation of the distribution parameter, n; while the efficiency curve is most sensitive to the estimation of

Addressing an inverse problem of classifier size distributions Chapter | 6

249

by-pass fraction, Rf : The results also indicate that for a given particle size, the feed distribution is least sensitive to the estimation of size modulus, dmax , while the efficiency curve is least sensitive to the estimation of cut size, d50c :

6.7

Conclusions

This chapter addresses an inverse problem of identifying classifier feed size distribution and actual efficiency curve from closed-form solution to classifier size distributions. The estimated parameters describe the efficiency curve accurately and retain the mass balance over the entire size range of the distributions. The estimated parameters enable the calculation of the flow split to the coarse stream, which are quite close to the real values. The classifier distributions in density form pivot at a size, where the cumulative distributions of the classifier have the maximum separation. The cumulative distributions of the classifier show “difference similarity”, when the absolute differences of the distributions are scaled by the reciprocal of the maximum value of the absolute differences.

Acknowledgments BVR acknowledges friends at M/s DELKOR who supported and encouraged this contribution.

References Abramowitz, M., Stegun, I.A., 1972. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. US Government Printing Office, Washington, DC. Austin, L.G., Klimpel, R.R., Luckie, P.T., 1984. Process Engineering of Size Reduction: Ball Milling. SME, New York. Forrey, R.C., 1997. Computing the hypergeometric function. J. Comput. Phys. 137, 79
100. Fuerstenau, M.C., Han, K.N., 2003. Principles of Mineral Processing. SME, Littleton. Heiskanen, K., 1993. Particle Classification. Chapman and Hall, London. Kapur, P.C., 2000. Analysis of Particle Size Distributions in Mathematica, Instructional Module on Particle Science & Technology, NSF Engineering Resource Center for Particle Science & Technology. University of Florida. Kawatra, S.K., Seitz, R.A., 1985. Calculating the particle size distribution in a hydrocyclone overflow product for simulation purposes. Miner. Metall. Process. 2, 152
154. King, R.P., 2001. Modeling and Simulation of Mineral Processing Systems. ButterworthHeinemann, Oxford. Kraipech, W., Chen, W., Parma, F.J., Dyakowski, T., 2002. Modelling the fish-hook effect of the flow within hydrocyclones. Int. J. Miner. Process. 66, 49
65. Lynch, A.J., Rao, T.C., Prisbrey, K.A., 1974. The influence of hydrocyclone diameter on reduced efficiency curves. Int. J. of Miner. Process. 1 (2), 173
181. Nageswararao, K., Wiseman, D.M., Napier-Munn, T.J., 2004. Two empirical hydrocyclone models revisited. Miner. Eng. 17 (5), 671
687.

250

Mineral Processing

Napier-Munn, T.J., Morrell, S., Morrison, R.D., Kojovic, T., 1996. Mineral comminution circuits
their operation and optimization, JKMRC Monograph Series, Julius Kruttschnitt Mineral Research Centre, University of Queensland. Plitt, L.R., 1971. The analysis of solid-solid separations in classifier. CIM Bull 64, 42
47. Roldan Villasana, E.J.R., Williams, R.A., 1991. Calculation of steady state mass balance for complex hydrocyclone networks. Miner. Eng. 4 (3/4), 289
310. Tarjan, G., 1981. Mineral Processing: Fundamentals, Comminution, Sizing, and Classification, Vol. 1. Akademiai Kaido, Budapest. Venkoba Rao, B., 2005. Analytical expressions for classifier product size distribution. Miner. Eng. 18, 557
560. Venkoba Rao, B., 2006. The pivot phenomenon and difference-similarity of classifier particle distributions. Powder Technol. 168, 152
155. Venkoba Rao, B., 2007a. Addressing an inverse problem of classifier size distributions. Powder Technol. 176, 123
129. Venkoba Rao, B., 2007b. Representation of classifier distributions in terms of hypergeometric functions. China Particuology 5, 274
283. Venkoba Rao, B., 2008. Reconciliation of size-density bivariate distributions over a separating node. Particuology 6, 167
175. Wills, B.A., 1997. Mineral Processing Technology. Butterworth-Heinemann, Oxford.

Chapter 7

Numerical methods in mineral processing: an overview Sripriya Rajendran1, Teja Reddy Vakamalla2 and Narasimha Mangadoddy3 1

Tata Steel Europe, Ijmuiden, Noord Holland, The Netherlands, 2Department of Chemical Engineering, National Institute of Technology Calicut, Kozhikode, Kerala, India, 3Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Sangareddy, Telangana, India

7.1

Introduction

The mineral industry has developed into a “technology” industry. The technology includes various processes and unit operations. Particle flow, turbulent fluid flow, their interactions (solid
liquid, solid
solid, and solid
gas interactions), the transport of bubbles and inclusions, and multiphase flow— all exist in different stages of mineral processing, starting from size separation to filtration. Wet grinding, filtration, hydrocyclone, and thickening are some examples of processes that include solid
liquid interaction. Magnetic and electrostatic separators are processes that involve solid
solid interaction. Flotation is a process that involves three phases: solid, liquid, and gas. Such multiphase systems and interactions are opaque and quite difficult to study and hence quite challenging to optimize. Numerical methods offer an excellent solution to studying these systems. Various molecular, empirical, and numerical models can be developed that can give a better insight into the process phenomena. Molecular models look at atomic/molecular levels; they are mainly used to develop new reagents/chemicals for specific purposes or to understand reagent mineral interaction. On the other hand, empirical models suffer from an inherent drawback of not being useful beyond the range of conditions for which they are developed. This has made the use of first principle computational methods, such as discrete element modeling (DEM), computational fluid dynamics (CFD), and population balance modeling (PBM), very popular. These modeling techniques play a very critical role in gaining insight into unit operations. These can also be used (1) to optimize the process leading to process improvements or (2) to help in developing new designs. Mineral Processing. DOI: https://doi.org/10.1016/B978-0-12-823149-4.00012-0 © 2023 Elsevier Inc. All rights reserved.

251

252

Mineral Processing

This chapter describes the principles behind these commonly used numerical modeling tools; Though these tools have been widely used in many mineral-processing areas, this chapter mainly gives an overview of their application in mixing, classification, grinding, and heavy media separation.

7.2

Discrete Element Modeling (DEM)

DEM developed by Cundall and Strack (1979) is based on Sir Isaacs Newton’s law of motion. This numerical method has successfully been used to simulate particulate/granular systems and is used to model their mechanical behavior. As the name indicates, the method considers the particles not as a continuum but as an assemblage of individual particles. Assuming that laws of physics and mechanics govern the particles, the velocities, position, and acceleration of individual particles are tracked over a period of time, and the total forces between particles such as the contact force (particle/particles and particle/boundary) and the body forces such as drag/gravity, magnetic, and electrostatic forces are modeled. There is no limit or restriction imposed on the mode of deformation or the amount of displacement of each particle. The method can predict the macroscopic behavior of solid particles, that is, the stress/strain relationship, fracture, etc. DEM has been used in a wide range of applications: 1. Soils—In studying soil stability, its subsidence, and in the development of avalanches, creep. 2. In powder and bulk solids handling and storage—To understand the behavior of particles in chutes, bins (in transfer chute designs) in crushing and grinding in mills, etc. 3. To study rock structure and fragmentation—especially important while building tunnels, dams, and bridges. 4. In pneumatic conveying 5. Sorting and screening systems in mining and agriculture 6. Granular mixing and drying in the food and pharmaceutical industries The first step in modeling involves importing/creating the geometry and defining the boundary motion of the moving parts. Particles are then generated, which are assigned to grids. If the particles touch each other, then contact forces are included. The body force in the model can include gravity, fluid drag, adhesion/cohesion due to liquid bridging, electrostatics, and magnetic forces. The total force “F” acting on the particle will be the sum of the body (Fbody) and contact (Fcontact) (mechanical) forces. As mentioned earlier, the velocity and acceleration of particles are calculated using a time integration scheme. X F 5 Fcontact 1 Fbody 5 ma ð7:1Þ

Numerical methods in mineral processing: an overview Chapter | 7

253

It is possible to predict some key parameters like flow patterns and rates, wear and stress patterns, dead and velocity zones, impact and abrasive forces on particles and equipment, patterns of mixing and segregation, force, torque, and power consumption of equipment, etc. In mineral processing, the method is widely used in modeling crushing and grinding mills, screw and rake mixers, and particle stratification in jigs.

7.2.1

Milling/grinding

DEM was first used in the milling process by Rajamani and Guo (1992). The package Milsoft based on DEM could predict the power drawn by a 2D rotary grinding mill when its critical speeds were between 0
80% (Moys et al., 2005). Mishra & Rajamani (1992); Cundall and Strack (1979); Djordjevic et al. (2003); Djordjevic (2005); Kalala et al. (2007); Powell et al. (2011) have used DEM to model particle dynamics in milling and have shown that the results from simulations are valid over a wide range of operating conditions. In grinding/tumbling, the fineness of the product and the wear on the shell liners are determined by the speed of the mill. The speed of the mill should be such that the balls fall on the charge and not on the liner; if not, the balls can impact the shell liners increasing its rate of wear. Also, the energy of the mill is transmitted to the charge through the liners. Hence, it is essential to know the trajectory of the balls in the mill and its linear wear profile for which DEM can be used. DEM can help understand the relationship between the lifter profile, the power draw, and the behavior of charge (e.g., Powell, 1991; Cleary, 2001). Makokha & Moys (2006) modified the lifter design in a SAG mill, which increased the power draw and mill throughput. The modified design was based on a 3D DEM modeling study that was carried out to study the effect of two lifters on load behavior. The modification increased the life of the lifters at no extra cost. Dahner & Bosch (2010) showed that total milling cost and energy consumption can be reduced if the lifter profiles were optimized a priori using DEM. DEM was also used to predict the mixing behavior in the mill. Moys et al. (2005) noticed that the balls follow the same trajectory over a period of time (observed over 20 revolutions of the mill), implying that there will be no mixing of material across trajectories. The coarser material would not be able to penetrate the mix, while the finer material caught in the center would be overground. So, they predicted that such a rotary mill would draw 80% more energy (kWh/tonne of the desired product) than other mills like the vertical spindle mill. They also found that DEM models can be used to analyze the effect of liner profile on the behavior of load in the mill. They compared the average behavior of load in the mill over several mill revolutions for unworn and worn lifters. The unworn lifters lifted a portion of the grinding media up into the air above the bulk of the media, allowing the

254

Mineral Processing

media to then cataract; With worn lifters, very little cataracting was noticed. So, there would be a minimal lifting of the balls leading to minimum interaction between the classifying air and the finer material. This, in turn, would affect the kinetics of milling and its removal rate from the mill. Mishra and Rajamani et al. (1992) used DEM to model the motion of balls in a tumbling mill and developed a code to calculate the torque and hence the power required by the mill. They found that the predicted values matched well with experiments when a particular value for the coefficient for friction was used. They also modeled a SAG mill in 2 dimensions. The model was then used in industrial SAG mills to assess liner wear and to determine the extent of ball breakage. The model was also used to compare and evaluate different lifter designs and to identify the most suitable design for a particular process. Cleary (2001a) studied the effect of lifter shape on the motion of charge in a 5-m diameter semi-autogenous grinding (SAG) mill using two-dimensional (2D) DEM modeling. Later, Cleary (2001b) and Herbst and Nordell (2001) modeled a thin central slice of the mill in 3D; that has now become the most widely used technique in the last few years. The model gives a better understanding of the particle motion in the mill center. Cleary et al. (2003) also developed and compared different 3D DEM models for a 600-mm diameter AG mill for several mill speeds and a wide range of conditions. Over the last decade, many such 3D DEM models have been developed for pilot scale SAG mills (Cleary, 2004, 2009a; Morrison and Cleary, 2008). Cleary (2006, 2009b) also used the model in ball mills for studying axial flow of the charge. While studying the motion of particles in the mill, it is also important to understand the slurry flow inside the mill as it passes through hundreds of grate holes. This could be difficult with grid-based normal Eulerian flow solvers since it requires a free surface flow in a rotational geometry. Smoothed Particle Hydrodynamics (SPH) modeling can predict splashing and fragmentation of free surface flows in rotating geometries. Cleary et al. (2007) used the SPH to model the free fluid flow within the SAG mill, flow through the grate, and along the lifters. Cleary et al. (2006) also used a combined DEM
SPH 2D model to model a mill where slurry flow did not dominate. One-way coupled model was used, and the media was assumed to be porous. The model then used an appropriate interphase drag, dependent upon the porosity calculated from the DEM model. The model identified slurry pooling at high slurry loads and predicted dry regions when the slurry loads were less. Sinnott et al. (2011) used the same technique to develop a 3D model and predicted the slurry flow in a tower mill. The method was also used to predict slurry flow on double-deck banana screens (Fernandez et al., 2011a,b). Paul and Rob (2012) used the three-dimensional SPH
DEM model to analyze the slurry flow within an industrial SAG pilot. DEMs have also been extensively used to model jet mills. Jets mills are known to produce micron to submicron size particles. Bria et al. (2020) used

Numerical methods in mineral processing: an overview Chapter | 7

255

a CFD
DEM coupled technique to model the jet mill. They outlined the limitations of the technique while simultaneously mentioning ways to overcome them. Many authors have used DEM to investigate the effect of the lifter profile on the charging behavior and power draw within industrial mills (Powell, 1991; Cleary, 2001a). Lifters play a key role in ball milling by giving the best energy transmission to the load and the media when the mill is rotating. Cleary (2001a) investigated the influence of lifter shape on charge motion for a 5-m diameter semiautogeny- nous grinding (SAG) mill using 2D DEM modeling. Makokha and Moys (2006) assessed the effect of two lifters. In most DEM models, the effect of fluid is generally accounted for by using a coefficient of viscous dissipation. Jaysasundra et al. (2009, 2011) found that the density and viscosity of the fluid/slurry had a profound effect on the charge motion in their combined CFD
DEM model. They simulated the trajectories of particles while simultaneously solving for fluid flow. Mayank et al. (2015) used a CFD
DEM coupled approach to model the charge and slurry dynamics in a tumbling mill. They modeled the free surface profile of the slurry in the system and looked at the effects of the solid on the fluid phase. They found that the one-way coupled CFD
DEM model could predict the tangential velocity profiles more accurately (Fig. 7.1A and B). It could also predict the complex multiphase dynamics of charge, air, and slurry inside the mill.

7.2.2

Screw conveyor/mixer

A screw conveyor is an equipment used to transport the solids that can simultaneously convey and mix. They have a helical screw that rotates in a U-shaped trough. Otherwise, called worm conveyors, they are not as efficient as belt conveyors but they are useful in conveying through short distances at steady rates. They can be operated at an incline and hence can be used to lift materials. The inefficiency of the screw conveyors is due to the friction between the solids and the flights of the screw and hence are generally used to transport materials that are free flowing. They find wide applications in food and process industries, mining, agriculture, and construction. In the food industry, these are typically used to convey grains from silos to hoppers and then to mixers. Typically, before transporting to the mixers, the grains are premixed in the modified types of screw conveyors. Despite being very simple in design, there are many variables that affect the performance of the screw conveyor. The performance is greatly influenced by the rotational speed of the screw, its inclination, length, and the volumetric fill level of the trough. Other variables such as the design of the screw conveyor (same or variable/) and the shape of the blades are also important. An improper design of the screw conveyor could degrade the product such as deformation and melting of granules, improper mixing and

256

Mineral Processing 8.00E-01

6.00E-01

4.00E-01

Tangenal Velocity(m/s)

2.00E-01

0.00E+00 -1.00E-02 0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

6.00E-02

7.00E-02

8.00E-02

9.00E-02

One Way Coupled Pure DEM

-2.00E-01

Pure CFD -4.00E-01

PEPT

-6.00E-01

-8.00E-01

-1.00E+00

-1.20E+00

Length(m)

(A)

(B) FIGURE 7.1 (A) A comparison of tangential velocity along the line joining the center of circulation to the center of the mill with experimental results (red points). (B) Velocity vector plot of the slurry inside the mill from the coupled DEM
CFD model.

segregation, power surges due to excessive power draw, abnormal wear of equipment, high start-up torques, and a lesser quality of the final product. Numerical modeling techniques such as DEM have proven to be quite effective in understanding the interaction between particles and their mixing

Numerical methods in mineral processing: an overview Chapter | 7

257

behavior. Shimizu and Cundall (2001) developed the first DEM model for the screw conveyor and used it to compare the performance of horizontal and vertical screw conveyors. A periodic slice model was used by Owen et al. (2003) to study the performance of the screw conveyor. Cleary (2004, 2007) have modeled the screw conveyors, extensively using DEM. Cleary and Sawley (2002) used DEM to study the flow of material from a hopper. The material was transported through a 45 degrees inclined screw conveyor. He (1994) studied the effect of particle shape on the flow of material from the hopper and its transport characteristics. Cleary (2007) also studied the effect of cohesion between particles and its effect on transportation. He also studied the effects of (1) the rotational speed of the screw and (2) the effect of the screw length in container design. Zhong and O’Callaghan (1990) and Fernandez et al. (2011a,b) studied the effect of different variables on the performance of horizontal screw conveyors. While the former looked at the effect of the shape of the feed opening on the performance, the latter studied the effect of screw design on the flow of spherical particles in the conveyor. The effect of other variables such as variable screw design, variable screw pitch, and variable core diameters on particle transport was also studied using DEM. The model could also show how evenly the particles flowed down the hopper, the effect of screw design on the mass flow rate of particles, the screw wear, and the amount of power consumed. Cleary (2013) investigated particle flow in a plowshare mixer using realistic-shaped particles. Since the particles were of a more realistic shape, the DEM could model the contacts between particles more realistically and give a closer prediction regarding the strength of the bed and its failure. Moysey and Thompson (2007) developed a nonisothermal threedimensional DEM technique to model the flow of solids within an extruder. They also used the model to evaluate the contact mechanism of commonly used polymers. Segregation of spherical particles on a packed bed was studied by Moysey and Baird (2009) using DEM. Lato Pezo et al. (2015) used DEM to compare the premixing action of 15 different designs of screw conveyor premixers with experimental results. He studied the effect of different variables of the screw conveyor, such as the screw length on particle transport. A modified geometry of the screw conveyor with three extra complementary helices could improve mixing quality.

7.2.3

Jigs

Jigging is a process in which a pulsating bed of water is used to stratify minerals based on their specific gravity. Though jigging is widely employed in the mineral industry, very little is known about the actual stratification of particles in jig beds. King’s stratification model, developed in 1987, was one of the first models to predict the stratification in jigging process. Venkoba Rao et al. have extended the model and used it to understand the segregation

258

Mineral Processing

of particles across the jig bed. Details of the improved stratification model are presented in Chapter 6. In this chapter, the focus will be on the use of the DEM/CFD technique to model the jigging process. Mishra and Mehrotra (1998a,b, 2001) have pioneered DEM and developed reliable models that can accurately predict the stratification process in a jig. They studied the effect of the amplitude and frequency of pulsion on stratification and determined the optimal conditions for good stratification. They also used the Marker cell technique to study fluid flow (1998). Their 3D DEM model (2001) could predict the concentration of each particle type across the jig bed. The model was coupled with a simple fluid model and was validated against experimental results. A good agreement was found between the experiment and the simulated results. On the other hand, Solnordal et al. (2009) used only a single-phase CFD model to model the jig (no DEM), considering the slurry as a single phase. In most DEM-CFD models, while the motion/collision of particles is simulated by the discrete element, the fluid flow model is a simple model that doesn’t consider the variations in fluid velocity. The fluid models assume a uniform flow fluid (Beck & Holtham, 1993; Mishra & Mehrotra, 1998, 2001; Srinivasan et al., 1999; Mukherjee & Mishra, 2006, 2007). Viduka et al. (2011) used a combination of 2D CFD and 3D DEM models to study the movement and stratification of particles for five different pulsation profiles (Fig. 7.2). The model showed a significant difference in the rate of segregation of particles and the energy used. The Euler
Lagrange (CFD
DEM) model, first proposed by Tsuji et al. (1993), solves (1) the fluid flow using the Navier
Stokes equation, (2) the motion of particles using Newton’s second law of motion, and (3) the solid
fluid interaction using Newton’s third law. The model could capture particle physics better and could predict the transient forces between the solid and liquid. The model used much lesser computational resources as opposed to DNS and gave reliable particle trajectories. The DEM
CFD approach has been used by few others too (Asakura et al., 2007; Xia and Peng, 2007; Dong et al., 2009). The models differ in the way the particle forces have been accounted for. For example, Asakura, and Xia and Peng (2007) used a two-way coupled model that included drag and virtual force but excluded porosity. Their other models included the Magnus (Rubinow and Keller, 1961) force and the Saffman (1965, 1968) lift force. The effect of amplitude and frequency of sinusoidal pulsion on particle separation was studied and the importance of different forces in jigging was also analyzed. Subsequently, a 3D column model was developed by Asakura et al. (2007), in which he modeled a single particle and studied its trajectory and response time. The model included the Basset force (Basset, 1961). Dong et al. (2009) used a sawtooth-forward leaning jigging profile instead of a sinusoidal pulsion cycle and studied the effect of vibration frequency, amplitude of pulsion, and the size and density of ragging particles on

Numerical methods in mineral processing: an overview Chapter | 7

259

FIGURE 7.2 Solid flow patterns shown by particle positions under different pulsation profiles at 1st, 3rd 4th, and 6th cycles. Heavy and light particles are colored gray and black. Pulsation profiles: Sawtooth-forward (A), Tabletop(B).

separation in the jig. The model was a one-way coupled 3D model. They found that the power to the jig increased during the suction part of the cycle when porosity was locally developed. Their work showed the usefulness of the DEM
CFD model in understanding the segregation and stratification in jigging. As can be seen, consistent efforts have gone into improving the discrete element models over the years, thus providing new insights into the process operations, and opening avenues to improve and optimize the processes. For example, discrete element models in milling have allowed us to understand the effect of various operational parameters on milling such as the operational speed, size of the grinding media, lifter wear and its effects, and

260

Mineral Processing

different lifter shapes and designs. The DEM
CFD models in jigging have helped improve the knowledge of the actual jigging process.

7.3

Population Balance Modeling (PBM)

Generally, a population can be made of entities (bubbles, crystals, granules, powder, cells, etc.). These entities could react with the environment (e.g., precipitation) or with one another (aggregation and coalescence). This exchange is mainly a function of the property of the entity (specific gravity/ density, weight, size, etc.). The exchange might result in the birth of a new entity/death of a specific entity. The population balance model consists of integro-partial differential equations that define the reaction of these individual particles/entities with the environment over a specific period of time. From this, the mean-field behavior of a population of particles is deduced. Monte Carlo methods/discretisation or moment end methods are used to solve the equation depending upon the application and the availability of computing resources. For example, let (x, r) be a particle state vector denoting the particle properties of an average number of particles in a population. Here “x” corresponds to particle properties or internal coordinates such as size, density, etc., and “r” to the spatial position or the external coordinates. The spatial positions are assumed to be dispersed in a continuous phase, which is represented by vector y(r, t). Then f(x, r, t) represents the function of many such vectors, which represent the particle properties distributed in the continuous phase at various locations. Now, if the birth rate of particles per unit of volume space can be defined by h(x, r, y, t), the PBE then is ð ð ð ð dd=dt dVx dVrf ðx; r; tÞ 5 dVx dVrhðx; r; y; tÞ ð7:2Þ ΩxðtÞ

ΩrðtÞ

ΩxðtÞ

ΩrðtÞ

[5]

This is a generalized form of PBE. In engineering, population balances have been used in the following areas: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Crystallization and precipitation Dissolution Deposition (e.g., chemical vapor deposition and electrodeposition) Granulation, aggregation, and flocculation Milling Drying Mixing Pneumatic conveyance Polymerization Multiphase flow and reaction (e.g., fluidized bed reactor, flame, and micellar synthesis of nanoparticles).

Numerical methods in mineral processing: an overview Chapter | 7

261

11. Fermentation 12. Cell growth, division, differentiation, and death.

7.3.1

Milling/grinding

Population balance models have been widely used to simulate and modelgrinding mills since the early 1980s. (Prasher, 1987; Austin, 1971; Austin et al., 1981; Austin and Bagga, 1981; Heim and Leszczyniecki, 1985; Hennart et al., 2009). The first PBM models for milling were developed by Sedlatschek and Bass (1953). They were first-order rate models and assumed that the disappearance of a particular size range of particles is proportional to the weight of the particles of that size present. Broadbent and Callcott (1956a,b,c and 1957) assumed the grinding to happen in stages. They also introduced the concept of breakage distribution and the probability of selection for breakage. The equations were further developed by Gaudin and Meloy (1962) who used the time and size-dependent mass density form of the equation. The time and size-dependent discrete form of the equation, also known as the linear time-invariant model, is i21 X dMiðtÞ 5 2 SiMiðtÞ 1 bijSjMjðtÞ dt j51

N $i$j$1

with

ð7:3Þ

Mið0Þ 5 Mini

In Eq. (7.3), Mi represents the mass fraction of particles in size-class i, Si is the specific breakage rate parameter, and bij is the breakage distribution parameter. This parameter describes the distribution of particles formed when a particle of size class j is broken, i and j are the size-class indices and extend from size class one containing the coarsest particles to size class N containing the finest particles usually in a geometric progression. It is called the time-invariant linear model since the specific breakage rate is independent of time, and only the particle size of a given class size determines the discretized value. The following constraints also apply to Eq. (7.3) due to the conservation of mass: SN50 ;

N X

bij 5 1; bii 5 0

i5j11

The parameters S and b are usually determined either by experiments or by back calculation. It was found that the model failed in predictions (Austin, 1971; Austin et al., 1981; Rajamani and Guo, 1992; Meloy and Williams, 1992), especially during long milling times or when there were excessive fines. Austin and Bagga (1981) investigated this and noted that the specific breakage rate decreases with increased fines. A similar phenomenon

262

Mineral Processing

was noted by many authors, especially when different types of particles with the same size or particles with different coarse/fine ratios were ground. They also found that the fine fractions slowed down the breakage rate of coarse fractions. They concluded the non first effect could be due to the cushioning effect of fine particles and introduced a time-dependent specific breakage parameter. A false or equivalent first-order grind time, θ, was used. They assumed that the specific breakage parameter for all particle sizes changed in line with the milling environment according to an acceleration
deceleration function κ(t). Both the parameters had to be determined from experiments with mono-sized feed. Population balance models could successfully simulate grinding of homogenous (pure) minerals (Herbst and Fuerstenau, 1968; Herbst et al., 1973). Austin and Bagga (1981), Woodburn and Kalligeris-Skentzos (1987), Celic (1988), and Fuerstenau et al. (1986, 2010) studied the effect of mill environment on the kinetics and breakage of coarse particles in the mill using PBM. They used a mixture of coarse/fine material as feed material in the mill. Venkataraman and Fuerstenau (1981) were the first to simulate the grinding behaviour of heterogeneous materials in a grinding mill. The materials differed from each other in their physical properties. Austin and Bagga (1981); Gupta (1986); Celic (1988); Woodburn and Kalligeris-Skentzos (1987) studied materials that had different feed size distributions. Venkataraman and Fuerstenau (1984), Fuerstenau et al. (1986), and Kanda et al. (1989) used the model to study single-size fractions of different mineral mixtures. The aim was to understand the effect that the different physical properties of the feed constituents had on the grinding kinetics. It was noticed that in all the above cases., that is, when the same size fractions of two different minerals were ground, the population balance model predicted an increase in the breakage rate of softer fractions and a decrease for the hard components. Celic (1988) and Fuerstenau et al. (1986, 2010) compared the breakage rate of the coarse size fraction in a coarse/fine fraction mix with the breakage rate of the same size fraction of a pure mineral. They observed that the breakage rate of the coarser fractions increased with a decrease in its volume ratio compared with the latter. Bilgili and Scarlett (2005) developed a population balance model to take care of the non first-order effects. They split the specific breakage rate parameter into two parts (1) an apparent breakage rate and (2) a population balance-dependent function that can describe the non-first-order breakage kinetics. Fuerstenau et al. (2011) used the population balance model to study a mixture of quartzite, dolomite, and limestone with different hardness indices and coarse/fine ratios. A modified breakage function was used. They found that the mixture composition of the three materials had a negligible impact on the cumulative breakage distribution function of the three minerals. However, it was found that the increase of fines in the mixture increased the breakage rate of the coarse particles.

Numerical methods in mineral processing: an overview Chapter | 7

Cumulative Mass Fraction Undersize

1.0

0.8

0.6

263

Feed 1 min 3 min 7 min 15 min 31 min 127 min 255 min 511 min Non-Linear Model

0.4

0.2

0.0 0.1

1

10

100

Particle Size (μm) FIGURE 7.3 Comparison of the experimental batch milling data and the two-aprameter nonlinear modelpredcition. Back calculated model parameters A 5 1.369 min^-1, m 5 1.091, μ 5 0.816, ɸ 5 0.522, λ 5 3.392, α 5 7.327, and ν 5 3.195.

Maxx et al. (2011) used a back-calculation method to determine the nonlinear model parameters using Matlab and found that the simulated results matched well with the experimental results (Fig. 7.3). Bu¨rger et al. (2018) used the experimental data in their population balance model to predict the ball recharge and wear in a ceramic ball mill. A part of the population balance function is partly empirical and is determined by mill type, design variables, operation mode, operating variables, and material properties. Determining these nonlinear functional parameters is of utmost importance if PBM is to be used effectively to model the grinding process. Determining these non first-order terms in the population balance model has posed the biggest challenge in developing a good model to simulate the grinding phenomenon. Efforts are continuously on to develop a robust model that can give a good insight into the phenomenon happening in the grinding mills.

7.4

Computational Fluid Dynamics (CFD) modeling

CFD generally uses the finite volume method for modeling the flow field. In the finite volume method, the entire computational domain is divided into

264

Mineral Processing

several control volumes, also known as the computational cell/grid. At each computational cell, the flow field equations are discretized and solved such that mass, momentum, and energy are conserved. For example, in a hydrocyclone that is operated at isothermal conditions, the energy equation is not considered. Mass conservation or continuity equation for an incompressible fluid in Cartesian coordinate is @ρ @ðρui Þ 1 50 @t @xi

ð7:4Þ

Momentum conservation equation for an incompressible fluid is @ @ @p @2 u i ðρui Þ 1 ðρui uj Þ 5 2 1 μ 2 1 pgi @t @xj @xi @xj

ð7:5Þ

Momentum conservation is popularly known as Navier
Stokes equation.

7.4.1

Hydrocyclones

Normally called a cyclone, it is a classifying device that utilizes centrifugal force to accelerate the settling rate of slurry particles and separate particles according to size, shape, and specific gravity. It has numerous advantages: (1) it has no moving parts, (2) it requires little maintenance, (3) it can be operated continuously, (4) it has high efficiency, (5) it saves energy, and (6) it is low in cost and hence, highly economical. The operating principle is simple: the feed slurry enters the cyclone under pressure through a tangential inlet. As it flows down the cyclone, due to the high centrifugal forces, the coarse and heavier particles/faster settling particles are pushed to the outside, closer to the walls of the cyclone where the velocity is the lowest and flow downwards, creating the outer vortex. Due to the limited area of the spigot, a portion of the slurry close to the center of the cyclone reverses its flow and travels upwards. Due to the drag forces, the finer and lighter particles move to the center of the cyclone and are carried into the vortex finder along with the upward-flowing liquid. This forms the inner or the forced vortex, enveloping a low-pressure air core at the center. The air core is connected to the atmosphere through the spigot. The equipment itself is quite simple to operate and maintain while the flow inside is quite complex. Various models have been developed to predict the performance of hydrocyclones—from simple models that are based on correlations between static pressure drop and predicted cut size to complicated numerical models. The models, in short, can be classified into the following categories: G G

Simple theory-based phenomenological models. Empirical and semiempirical models.

Numerical methods in mineral processing: an overview Chapter | 7 G

265

Fluid flow-based numerical models.

The simple theory-based models are derived from one of these theories (Svarovsky, 1984): G G G

The equilibrium orbit. The retention-time hypothesis. The crowding theory.

The equilibrium orbit theory assumes that the particles reach an equilibrium radial position in the hydrocyclone. Smaller and fine particles reach equilibrium at smaller radii, while the coarser particles reach equilibrium at larger radii. Hence, the smaller and finer particles are carried upwards with the flow at the top and discharged through the vortex finder, while the coarser and bigger particles are transported along with the fluid discharging through the spigot. The particles that lie in the Locus of Zero Vertical Velocity (LZVV) have an equal chance of reporting either to the overflow or the underflow. The drag force (FD) experienced by the particle can be calculated using
2  ð7:6Þ FD 5 0:5 ρf  Uf 2Up Cd  Ap Here, Cd is the drag coefficient, Uf is the radial velocity of the fluid, Up is the radial velocity of the particle, ρf is the density of the fluid, and Ap is the cross-sectional area of the particle. The centrifugal force (FC) of the particle is a function of the tangential velocity component (Vt), the volume fraction of the particle (Vp), and the difference in densities between the fluid and the particle. FC 5 Vt 2 =r  ðVp  ðρp 2 ρf ÞÞ

ð7:7Þ

The particles that have a drag force equal to that of the centrifugal force are the particles that are caught in the LZVV and have a good chance of misplacement. The equilibrium orbit theory had two drawbacks 1. It does not consider the residence time of the particles. 2. It does not consider the effect of turbulence on particles. The residence time theory is based on the nonequilibrium assumption. For 50% collection efficiency, a particle should reach the wall from the center of the inlet after entering the cyclone within the particles’ residence time. So, the cut size of the cyclone will be the size of the particle that can reach the cyclone (Rietema, 1962) wall within its residence time. The model does not consider the size distribution of the particles and the solids concentration. So, it is most suitable for dilute flow (,2% solids concentration). Using empirical equations, Rietema developed a characteristic cyclone number that he recommended for optimum hydrocyclones design. Again, Rietema’s design does not consider fluid turbulence, inertial effects, and radial fluid velocity.

266

Mineral Processing

The crowding theory assumes that at high solids concentration of feed, the cut size is mainly determined by the discharge capacity of the spigot and feed-size distribution The second set of models, that is, the empirical and semiempirical models, can be classified into two types: one for the Newtonian fluids and the other for non-Newtonian. The Newtonian models are regression equations that correlate the physical properties of the particle system (e.g., solid and fluid densities, fluid viscosity, and particle size distribution), and the operational conditions (e.g., fluid flow rate and feed solids concentration) to the separation cut diameter, the total and grade efficiencies, and the relation between flow rate and pressure drop (Bradley, 1965; Svarovsky, 1984). The models by Rao (1966); Plitt (1976); Napier-Munn (1980); Horsley et al. (1992) all belong to the first group. Here, results from experiments are used to develop empirical equations. The earliest in this category was by Lynch and Rao, who developed the first comprehensive model to predict the performance of industrial cyclones at the University of Queensland (Rao, 1966). They carried out numerous trials to understand the effect of operational and design parameters and used them to develop empirical equations to predict the performance of the cyclone at Mount Isa Mines, Australia. The methodology has since been successfully adopted in the minerals industry. However, the disadvantage of these models is that they do not give acceptable results when used outside the range of conditions under which they were developed. Also, the models use a solids concentration term to account for viscosity; there is no explicit viscosity term. Hence, any change in slurry rheology due to changes in temperature, the size distribution of solids, and a different chemical environment cannot be studied by these models (Shi and Napier-Munn, 1996). However, the later models have used online viscometers to measure slurry viscosities at high shear rates (Kawatra et al., 1996; Asomah and Napier-Munn, 1997). Such models have materialspecific constants and are more generic. These models can be used to predict equipment performance under different operating and design conditions. No additional experiments need to be carried out to refit the model parameters for the new operating and design conditions (Plitt, 1976; Flintoff et al., 1987); Nageswararao (1978, 1995); Svarovsky (1984); Asomah (1996); Asomah and Napier-Munn (1997). Similar hydrocyclone models have also been developed by Asomah (1996); Castro (1991); Kojovic (1988); Tavares et al. (2002). All these models are again empirical and are application and design specific. Because of this shortcoming, inputs from mathematical models based on fluid mechanics are highly desirable. In recent times, numerical methods have proven to be quite reliable in understanding the internal fluid dynamics in hydrocyclones. They spread over a wide spectrum and include finite volume, finite element finite difference, Smooth Particle Hydrodynamics (SPH), and Discrete Element Methods

Numerical methods in mineral processing: an overview Chapter | 7

267

(DEM), as well as many others. CFD, DEM, and CFD
DEM coupling approaches can resolve fluid and particle behaviors at high feed solids loading Chen et al. (2012); Chu et al. (2009a,b); Mangadoddy et al. (2020); Narasimha et al. (2005), (2006a,b), (2007a,b), (2012); Vakamalla and Mangadoddy (2019); Ghodrat (2014). The parametric studies on different equipment and their effects on flow dynamics have been actively undertaken in recent years using CFD and coupling techniques (Chen et al., 2012; Swain and Mohanty, 2013; Murthy and Bhaskar, 2012; Bhaskar et al., 2007; Delgadillo and Rajamani, 2005; Vakamalla and Mangadoddy, 2017; Cui et al., 2017). Conventional CFD techniques based on the principle of continuum mechanics and control volume methods have greatly evolved after decades of dedicated and continuous research (Gao and Herbst, 2009). In practice, CFD usage is not as easy as expected because of complex geometries, free-surface flows, and complex-phase interactions. Producing accurate volume mesh for such complex geometry is also a challenging task, even with the help of commercial programs like ANSYS ICEM. In the mineral-processing industries, the highly turbulent and typically complex multiphase nature of the systems makes numerical modeling a challenging task. The multifaceted particle
fluid and particle
particle interactions occurring in mineral-processing systems inspired researchers to study the internal flow behavior, thereby, making numerical modeling and optimizing a separate research area. The complete literate review on the turbulence and multiphase flow modeling in hydrocyclones is given below.

7.4.1.1 Turbulence modeling The operation of hydrocyclones at high velocities causes turbulence. The presence of a strong swirl and the flow reversal in the conical section introduce anisotropy and strain into the turbulence. Turbulence plays an important role in predicting the accurate flow field, air-core diameter, and thereby particle separation efficiency. Therefore the usage of an appropriate turbulence model is crucial in the modeling of hydrocyclones. In the earlier modeling work of Pericleous and Rhodes (1986), turbulence was modeled by the Prandtl-mixing length model. A fraction of cyclone diameter was used as constant-mixing length (λ) to model the turbulent viscosity. Hsieh and Rajamani (1991), Monredon et al. (1992), and Devulapalli (1997) have modeled hydrocyclones by a 2D axis-symmetric grid where the air core was not resolved; instead, the air/water interface was treated as a shear free boundary condition. Turbulence anisotropy was incorporated into the model by using a modified mixing length turbulence model similar to Pericleous and Rhodes (1986), but a different mixing length constant was used for each component of the momentum equation as the turbulent length scales were different in axial and tangential directions. Although the model required calibration, it could predict tangential and axial velocities very close to LDA measurements.

268

Mineral Processing

Radial velocity profiles were not compared due to the inefficiency of LDV radial measurements. According to turbulent mixing theory, the assumption of mixing length was the only parameter to describe turbulent transport. This length entirely depends on flow geometry and takes no account of turbulence intensity and eddy size and structure. This shortcoming has been addressed by the k-ε model, in which the eddy viscosity depends on the turbulent kinetic energy and dissipation energy. Dyakowski and Williams (1993) used k-ε turbulence model with appropriate equations for normal Reynolds stresses and modified empirical coefficients of Launder et al. (1975) to predict turbulence anisotropy. Reasonable tangential and axial velocity profiles were predicted in small diameter (10
44 mm) hydrocyclones. Malhotra et al. (1994) also used the k-ε to model the turbulence with an additional equation for turbulent dissipation in a 78-mm cyclone. Dabir and Petty (1986) used LDA measurements to validate the predicted mean tangential and axial velocities at different inlet fluid Reynolds numbers (14,300
26,600). But the usage of the k-ε model was also limited due to the assuption of isotropic turbulence, that is, equality of Reynolds stresses in all directions. Further, Boussinesq approximation intrinsically implied equilibrium between stress and strain. These assumptions were known to be unrealistic for swirling turbulent flows, and this would suggest that k-ε models were not suitable for modeling turbulence in hydrocyclones, (Ma et al., 2000; Sevilla and Branion, 1997; Narasimha et al., 2005; Delgadillo and Rajamani, 2005; Vakamalla and Mangadoddy, 2017). To address this, simulations were performed using Re-Normalization Group (RNG) k-ε model with swirl correction (He et al., 1999; Narasimha et al., 2005; Delgadillo and Rajamani, 2005; Vakamalla and Mangadoddy, 2017). RNG k-ε turbulence model is similar to k-ε model but includes additional terms for dissipation rate (ε). This improves accuracy for rapid strain flows. Most of the studies till the early 2000s were limited to two-dimensional geometries. The two-dimensional calculations assuming axisymmetry could predict reasonable fluid flow patterns in some (Dabir and Petty (1986) and Hsieh and Rajamani (1991)) hydrocyclones, but the results were not as accurate as those assuming the correct three-dimensional geometries (He et al., 1999; Narasimha et al., 2005). Three-dimensional calculations with k-ε turbulence model and Discrete Phase Model (DPM) model accurately predicted particle separation in 75 mm Hsieh and Rajamani (1991) hydrocyclone for 10.47% limestone slurry, whereas the predictions from two-dimensional models were far from accurate (He et al., 1999). It was also observed that the error in the two-dimensional results becomes larger when the particle density is close to the fluid density. Slack et al. (2000) modeled the turbulence in 205 mm gas cyclone using Reynolds Stress Model (RSM) and Large Eddy Simulation (LES). Axial and tangential velocity profiles were compared with experimental

Numerical methods in mineral processing: an overview Chapter | 7

269

LDA measurements (Boysan et al., 1983). He concluded that steady-state RSM simulation with coarse mesh predicted the flow field quite well with less computational cost. Cullivan et al. (2003) used the RSM model with quadratic pressure strain to accurately predict air core. Numerical predictions were compared against air core measured by nonintrusive electrical impedance tomography technique and were shown to be in good agreement. Even though the RSM model did not model the turbulence accurately, it could predict good velocity profiles with low computational power. The lack of accuracy was due to the assumption of equilibrium turbulence, particularly, in subgrid-scale modeling. Equilibrium turbulence assumes the rate of transfer of turbulence through length scales as constant. This is not true in the case of hydrocyclones, which have high swirling flows and short residence times. Delgadillo and Rajamani (2005) compared the predicted values of aircore diameter, mass split, and tangential and axial velocities of a 75-mm hydrocyclone with three different turbulence models, RNG k-ε, RSM, and LES. LES gave the best results even though it took higher computational time than the RSM model. This is because most of the energy and momentum transfer is associated with large eddies. Thus, by resolving large-scale eddies and modeling the smaller eddies, LES model could capture timedependent vortex oscillations and nonequilibrium turbulence quite well (Nowakowski et al., 2004). Therefore air core, velocity fields, and particle separation predicted by the LES model closely matched the experimental data. Brennan (2006) and Brennan et al. (2007) compared the tangential and axial velocity profiles predicted by three different turbulence models (1) RSM with linear pressure strain, (2) RSM with quadratic pressure strain, and (3) LES to LDA data in (Hsieh and Rajamani, 1991) 75 mm hydrocyclone. They observed that axial and tangential velocities with linear and quadratic pressure strains were nearly identical and were underpredicted in the apex region. Narasimha et al. (2006a) also predicted the diameter of the air core and its shape using LES and RSM turbulence models in combination with the VOF multiphase model. The effect of spigot and vortex finder variations on the air-core diameter was tested at different velocities. Slurry viscosity was varied at constant velocity. They found that the air-core diameter decreased at high viscosity. In all the cases, the predictions from the LES model were closer to experimental (Hsieh and Rajamani, 1991) measurements due to the improved turbulence field. Stephen used different turbulence models like k-ε, SST, and RSM to model a 75-mm (Monredon et al., 1992) hydrocyclone and compared the results to experiments. For the SST model, he used a modification in curvature to model the turbulence. Predictions of axial and tangential velocities were similar in both models. Murthy and Bhaskar (2012) used the RSM turbulence model with a continuous Eulerian phase for their parametric studies with different diameters of spigots and vortex finders. Water split and throughput measurements were validated with experiments. Mousavian and Najafi (2009)

270

Mineral Processing

compared the mean-flow field and separation performance predicted by RNG k-ε, RSM, and LES turbulence models in a (Hsieh and Rajamani, 1991) 75-mm hydrocyclone. They observed better predictions with the LES model. Further, they also studied the effect of underflow and overflow diameters and cone angle on the water split and pressure drop of hydrocyclone. DPM was used for predicting cut size and sharpness of separation. Ghadirian et al. (2013) used LES to model the turbulence accurately in a 75-mm (Hsieh and Rajamani, 1991) hydrocyclone and a 45-mm (Lim et al., 2010) hydrocyclone. Ghodrat et al. (2014) successfully used RSM to study the effect of different vortex finders and conical designs on the separation performance of hydrocyclone.

7.4.1.2 Multiphase modeling - homogeneous feed Along with turbulence, the flow in hydrocyclone also consists of multiple phases such as air/free surface, water, and a number of particle phases in varying degrees of density and size. Therefore there is a need to develop a multiphase model to predict the flow and particle separation accurately. 7.4.1.2.1

Fully solved Eulerian
Eulerian models

Full Eulerian
Eulerian models (EE) consider both the phases to be interpenetrating continua, whose dynamics are governed by the Navier
Stokes equation. Further, the closure of the model requires additional formulation of constitutive equations for each phase and interphase momentum transfer models. The full Eulerian multiphase flow approach has been used for systems with very high particle-phase concentrations, where particle/particle interactions carry a significant amount of stress. The usage of the full Eulerian multiphase modeling approach is limited in cyclones because of its high computational cost. They are generally used along with the k-ε, RSM models for turbulence. Very limited studies are available in the literature on the use of the full EE multiphase model for hydrocyclones. Swain and Mohanty (2013) studied the effect of turbulence model (k-ε and RSM) in a 50-mm hydrocyclone using EE model with two different average sizes of particles. Even though they worked with the EE model, the simulation predictions did not match those from experiments. Aurelien et al. (2012) studied the effect of feed solids concentration on the performance of 100 mm hydrocyclone. They numerically modeled the cyclone behavior using EE multiphase model with the RSM model for turbulence. Drag was modified with two correlations. They validated the numerically measured data with their own experimental results. Cut size and sharpness of separation were found to deviate when the solids percentage was above 30% by weight. They concluded that the cut diameter (d50) increased with an increase in concentration. Decreasing the spigot diameter increased the solids concentration and created roping conditions. The classification was very low at high

Numerical methods in mineral processing: an overview Chapter | 7

271

concentrations (50%) due to the absence of sufficient swirling flow for separation. This decreased the efficiency, and the cut diameter increased. They observed that the distribution of solids inside cyclone was uniform, except in the near wall regions, and in the conical section, where there was a dense concentration of solids. Raziyeh and Ataallah (2014) also used EE multiphase model coupled with the RNG k-ε turbulence model to predict performance in a 500-mm hydrocyclone. They varied the spigot diameters and solids concentration. The predicted results were close to the actual values upto 30% solids by weight in feed. 7.4.1.2.2 Simplified Eulerian
Eulerian models and discrete phase model model The Volume Of Fluid (VOF) and mixture models are simplified versions of Eulerian multiphase models that solve the equations of motion for the mixture and additional transport equations for volume fractions of additional phases, respectively. VOF and mixture models solve a lesser number of transport equations than the full EE models. Therefore they require less computational time and are numerically more efficient. The mixture model uses an additional slip velocity formulation to calculate the relative velocity between the phases. Although the full EE multiphase equations are theoretically more advanced, the simplified EE approach (the mixture model) is more reliable than the full EE model in terms of uncertainties in closure relations and computational time (Manninen et al., 1996). In the Lagrangian Particle Tracking (LPT)/DPM approach, the solid phases are tracked by performing a force balance around particles of different sizes and densities. The Lagrangian approach or the DPM is usually used when the solids percentage is limited to 10% by weight. Delgadillo and Rajamani (2005), Narasimha et al. (2005), Wang et al. (2009), Ghadirian et al. (2013), and Vakamalla and Mangadoddy (2017) in the past have utilized the DPM model to predict the performance at two different feed solids content (5% and 10% by weight) in a 75 mm hydrocyclone (Hsieh and Rajamani, 1991). In all the studies, the cut size predicted by the DPM model was close to the experimental data. However, slight deviations were observed at the tail ends of the partition curve for both fine and coarse particles. To overcome the drawback of DPM model, a Dense DPM (DDPM) model was developed by assuming a parcel concept to represent a definite number of particles (Popoff and Braun, 2007) instead of a single particle, thereby enhancing the computational efficiency. The interaction of the parcel particles was modeled using Kinetic Theory of Granular Flow (KTGF). Zhou et al. (2016) adopted DDPM coupled with the RSM turbulence model for predicting performance in a 660 mm cylindrical hydrocyclone. The effect of inlet flow rate, feed solids content, vortex finder, and spigot ratios on the particle separation efficiency was studied. They found that the particle

272

Mineral Processing

separation efficiency was sensitive to feed solids content. Razmi et al. (2019) used Multiphase Particle in Cell (MP
PIC) method in combination with the LES turbulence model and found that the density of particles had a significant effect on the cyclone efficiency. In both cases of DDPM, the effect air core on the separation efficiency of hydrocyclone was neglected, that is, air core was not modeled. Algebric Slip Mixture (ASM) model was successfully used to model multiphase flows in industrial cyclones and slurry flows of various systems. ASM model has its significance since the initial days of computational modeling (Pericleous and Rhodes, 1986) of hydrocyclones. Pericleous and Rhodes (1986) developed a 2D mathematical model with the help of PHEONICS code. The flow split, cut point, and efficiency results were validated with well-known Kelsall (1952) experiments and empirical model data from Plitt (1976). Hsieh and Rajamani (1991) solved single-phase flow (only water) in a 75 mm hydrocyclone by using the cylindrical coordinate system of the Navier
stokes equation. Further, Hsieh and Rajamani (1991) and Monredon et al. (1992) extended this model to two-phase flow by calculating the particle slip velocity using dynamic force balance. Numerically measured classification curves by LPT model matched well with those from experiments except for coarser particles. The conclusion was that (1) the velocities can be affected by variations in local densities and viscosities, which in turn were functions of particle size distribution and feed solids concentration and (2) these effects can be neglected in case of dilute slurries (i.e., ,5 wt.%). The numerical model was also extended to predict performance curves with five different conical geometries by changing the cone angles. Davidson (1994) modified the mixture model with Bagnold forces and turbulent diffusion forces to account for medium segregation inside the hydrocyclone. The flow field data was compared against the results from Kelsall’s cyclone. Although the tomographic measurements were not available at the time of Davidsons’ work, the drop in medium concentration at the wall was similar to the findings of Galvin and Smitham (1994) and Subramanian (2002). Kuang et al. (2012) studied the effect of variation in feed solids concentration (0
25 vol.%/0
31.3 wt.%) on 225 mm hydrocyclone performance. The mixture model was modified with a granular viscosity obtained from kinetic theory. Drag was also modified using equations by Ergun (1952); Wen and Yu (1966). Observations comprised an improvement in cut size with solids concentration. An interesting point was the movement of fine particles with water and its relation to water split, which was consistent with data from the literature (Sletcha, 1984). The major drawback of this work was the absence of experimental validation beyond 7 vol.%/10 wt.% solids, when the slurry rheology, particle
solid, and particle
particle interactions start to increase drastically. Narasimha et al. (2012) successfully predicted separation performance of particles along with their radial segregation using

Numerical methods in mineral processing: an overview Chapter | 7

273

the modified ASM model in a 150-mm hydrocyclone at 21.79 wt.% solids concentration and validated them against Rennar’s (1976) data. 7.4.1.3

Multiphase modeling - heterogeneous feed

In the past few decades, extensive experimental and numerical studies have been conducted to understand the particle dynamics in hydrocyclones, mainly with homogeneous feed. However, feed to the hydrocyclone is generally multicomponent in nature, that is, multi-size and multi-density. Generally, due to the interdependent operation, multicomponent studies become crucial for any ball mill—hydrocyclone close circuit. Huge amounts of fines are continuously generated in liberating the desired minerals from mined ores. The liberated ore, which consists of multiple minerals, is fed to the classification circuit for successive separation of the desired mineral. It is essential to ensure that fine particles report to the overflow and coarse particles to the underflow. In several instances, like lead/zinc regrind circuits, coal partitioning, or UG2 platinum ore (upper group two platinum ore from Merensky reef, South Africa), due to the occurrence of multi-density particles in the ores, the single average density model is generally unable to predict the hydrocyclone classification effectively. The presence of multicomponent particles in the separation process enhances the particle
particle interactions, increasing the misplacement of particles due to the difference in their relative settling velocities. Experimental studies that attempted to understand the multi-density and polydispersed particle size behavior during classification in a hydrocyclone are limited. Weller et al. (1988) developed a multi-component model for grinding and classification circuits using copper ore for their study. The copper ore contained copper, pyrite, and gangue minerals. Cho (1993) studied the effect of binary, ternary, and quaternary components with different proportions of coal, limestone, quartz, and magnetite. Mainza (2006) explored the challenges using conventional hydrocyclones for classifying the UG2 platinum ore that contained silica and chromite, the two major components of the ore that differed significantly in their densities. From their work, it was observed that chromite [Specific gravity (s.g.) 4.5] had a lower cut-size than silica [PGM (Platinum group metals) carrying component, (s.g-2.7)], which resulted in a large quantity of chromite reporting to underflow at small enough particular sizes, which otherwise would have escaped through the overflow. This resulted in a capacity loss for fresh feed and loss of energy by grinding the recirculating fine particles. The individual density components followed the standard shape for efficiency curves. The low-density components display a fish-hook behavior and a higher cut size compared to the heavier component. Kawatra and Eisele (2006) used a mixture of quartz and magnetite to explain the “coarse and fine inflection phenomenon” observed in hydrocyclone

274

Mineral Processing

efficiency curves. In recent studies, Collins (2016) attempted to study the combination of dual-component systems. It was observed that the different density components did not behave independently during classification, even when they were fully liberated, and the operating conditions of the hydrocyclone influenced the degree of interaction amongst components. Recently, Padhi et al. (2019) attempted to study the behavior of dual components (magnetite and silica) through numerical experiments in a 75 mm hydrocyclone. The variation in cut size of the components was explained with the help of the locus of zero vertical velocity and equilibrium orbit positions. The performance data predicted from CFD were validated with in-house experiments. It was observed that with an increase in the magnetite percentage in the mixture, the cut size of the component (both light and heavy) increased when compared to the separation behavior of the standalone pure component. Following this, an in-depth study on the effect of turbulence dispersion, drag, and centrifugal forces on the individual size and density of the particle was also attempted (Padhi et al., 2020).

7.4.2

Dense medium cyclones

Dense medium cyclones are gravity separators that work on a principle similar to hydrocyclones. They are generally used to clean ores with a high amount of near gravity material (NGM). The ore, once crushed to the required size is mixed with a heavy medium (e.g., coal with magnetite) and is fed to the cyclone under pressure. Due to the forces inside the cyclone, the heavier ore particles (say coal rich in ash) discharge through the underflow, while the lighter (clean coal) reports to the overflow. The flow in dense medium cyclones is too complex; along with the ore particles, there is also a heavy medium slurry that also undergoes segregation and separation inside the cyclone. The particle separation mechanism in the cyclone separators depends on the flow field (tangential, axial, and radial velocities). The precise measurement of flow field will help in understanding the separation mechanism inside the cyclone and in suggesting future modifications for an improved DMC design. Most of the experimental studies on the DMCs are restricted to the measurement of overall partitioning characteristics [cut density (ρ50), Ecart Probable (Ep)] with respect to operating and design parameters. Limited studies are available on the flow field (Fanglu and Wenzhen 1987) and medium segregation (Galvin and Smitham 1994; Subramanian, 2002) measurements inside the DMC. In predicting the performance characteristics of DMC, usage of empirical (Dungilson, 1998; Wood, 1990) and analytical modeling approaches (Bloor and Ingham, 1987; Boysan et al., 1983) are limited because of their inherent assumptions. The CFD technique based on fundamental flow physics equations has proven helpful in understanding the flow behavior across different laboratory/industrial-scale systems (Gao and Herbst, 2009). Zughbi et al. (1991)

Numerical methods in mineral processing: an overview Chapter | 7

275

started 2D numerical modeling using PHEONICS code in 400 mm DSM cyclone with an imposed air core of constant diameter. In the same study, a multiphase mixture model was adapted to study the wear effects inside the cyclone. They concluded that the presence of high-velocity particles near the vortex finder was the main reason for the wear near the vortex finder. Further, Suasnabar and Fletcher (1998) modeled continuous media as an Eulerian phase, and coal particles were tracked by DPM in a 200 mm DSM cyclone for dilute feed solids. They found a constant air core with 30 mm diameter and this was validated by Wood (1990) experiments. Particle segregations toward radial and axial positions were also included in their results. All these models were two dimensional and could not visualize the dynamic flow behavior inside cyclones. Brennan et al. (2002) started 3D multiphase simulations with a single average particle size in 350 mm DMC with the standard mixture model (Manninen et al., 1996) available in Fluent. The air core was developed by treating air as an additional dispersed phase. Numerically predicted data showed a ring-like structure with high density around the air core, and it overpredicted the experimental GRT data (Subramanian, 2002). High medium density was predicted toward the walls in the conical section. They summarized that overpredicting the levels of medium segregation in the cyclone body might be the reason for the underprediction of overflow densities by the standard mixture model; also, the medium consisted of only one average mono-size magnetite particle. Subsequently, Narasimha et al. (2007a,b) improved the CFD model proposed by Brennan et al. (2002) in which the flow medium was simulated with particle size distribution. Also, slip velocity in the mixture model was modified with shear lift forces, and the slurry rheology was modeled by Ishii and Mishima’s (1984) Newtonian viscosity relation. Density levels near the cyclone wall and medium segregation levels in the axial direction were closer to experiments. However, the segregation levels were still overpredicted near the walls compared to the experimental GRT data. They further studied the effect of magnetite particle size distribution on the flow behavior and observed that fine particles were distributed throughout the cyclone and coarse particles were very dense near the walls. Further, the model was tested for various feed densities, and they compared the overflow and underflow product densities with empirical Wood (1990), Dungilson (1998) models, and Subramanian’s (2002) GRT experimental data. Overflow densities were still underpredicted at higher feed densities. They concluded that excessive underflow volumetric flow rates might be the reason for the underprediction of overflow densities. Narasimha et al. (2007a,b) further extended the multiphase ASM model to track the coal particles through the Langrangian frame of reference by integrating a force balance around coal particles with sizes ranging from 0.5
8 mm and densities ranging from 1000
2000 kg/m3. Validation was

276

Mineral Processing

performed against the sink and float analysis data, and close agreements with Ecart Probable (Ep) predictions were found. However, there were slight deviations with cut-point data. Wang et al. (2009) studied the flow characteristics in 350 mm DMC using a multiphase mixture model modified with a viscosity correction factor while DPM was used for coal particle tracking. Along with short-circuiting phenomena, (Chu et al., 2009) extended the study to find the reasons for surging. They concluded that the instability of the flow field and low medium to coal ratios () were the reasons for surging. Though the DPM model could predict the dynamics of various particles with different sizes and densities, it is unsuitable for the dense slurry system since it neglects the particle
particle interactions and particle concentration effect on fluid flow. Advanced modeling methods include coupling of Discrete Element Modelling with SPH. The conventional CFD technique can only model the air core and predict the flow behavior of the magnetite medium. On the other hand, the DEM model can simulate the flow of coal particles in a DMC when its volume fraction exceeds 10% and can be coupled with a medium-based CFD model. Numerical implementation of a twoway coupled CFD
DEM can be implemented as follows. At each time step, DEM provides information about the velocity and position of each particle, which can be used to evaluate the volume fraction and particle
fluid interactions in a computational cell. CFD can then utilize data supplied by DEM to determine the flow field and update the forces of particle
fluid interaction on individual particles at each computational cell. This CFD
DEM coupling approach has an advantage over the regular DPM model. It can model the particle
particle interactions by applying Newton’s laws of motion to individual particles and can also model particle
fluid interactions by solving the locally averaged Navier
Stokes equation. It has been one of the most effective models currently used to account for particle
particle interactions in many particulate flows. Despite DEM’s ability to solve the particle
particle interactions effectively, there are some limitations too. Because of the wide range of coal particles (0.5
50 mm) presencent in the separation process, one needs to apply this model to billions/ trillions of particles in DEM, in addition to the magnetite particle phases via CFD. This process is computationally very expensive. Alternatively, a continuum approach based on fully EE and ASM models can still be used to simulate both magnetite and coal particles inside a DMC.

7.4.2.1 Rheological modeling Napier
Munn explained the effect of viscosity on the separation of DMCs and dense medium baths. He (1994) studied the rheology effects and medium stability on a six-inch DMC. There was a reduction in the efficiency and an increase in the cut diameter of the cyclone with increased viscosity. He also observed similar results as shown by Napier-Munn (1990). In both cases,

Numerical methods in mineral processing: an overview Chapter | 7

277

adding clay increased the stability of the medium and decreased the cutpoint shift. The important conclusion was that the finer particles had a higher effect on slurry rheology than coarser particles. Davidson (1994) used a viscosity model like Roco (1990) to model the viscosity at high percentage of solids of 28% by volume. Predictions by Hsieh and Rajamani (1991) model showed an increase in cut size from 15 μm to 78 μm when the viscosity increased from 1cp to 10 cp in a hydrocyclone. This was due to the strong enhancement of drag force because of increased slurry viscosity that altered the particle trajectories. Hence, cut size increased and the sharpness of separation decreased at high-feed solids content. As the concentration of feed solids increases beyond 5% by volume, the presence of particles produces extra inertial stresses, thus resulting in stresses due to viscosity. Therefore usage of viscosity models based on volume fraction become necessary (Davidson, 1988). Suasnabar and Fletcher (1998) used the Eulerian granular flow model and compared the velocity profiles of different viscosity models (power law, Herschel Bulkley) to a turbulence model and concluded that the effect of turbulence was significantly higher compared to viscosity. Narasimha et al. (2007, 2012), Narasimha et al. (2007), and Vakamalla and Mangadoddy (2015) used modified versions of Ishii and Mishima (1984) viscosity model corrected for volume fraction of solids and the fines fraction to account for viscosity effects. Wang et al. (2007,2009,2014) also used a variant of Ishii and Mishima (1984) viscosity model with a correction factor of 3.8. Vakamalla and Mangadoddy (2015) compared the density differentials with four different viscosity models, that is, Granular, Ishi
Mishima model with a correction factor similar to Wang et al. (2009), including a fines correction for particles below 38 microns and the non-Newtonian Herschel Bulkley model. Vakamalla and Mangadoddy (2021) made numerous improvements to the existing CFD models using user-defined functions and including additional forces to the Algebraic slip mixture and the Reynolds stress models. His models could predict the performance of dense medium cyclones quite effectively. The model will be dealt with in greater detail in the subsequent chapters.

7.5

Conclusions

As can be seen, numerical models like PBM, DEM, and CFD have come a long way from simple models to complex multiphase multicomponent models that can predict the performance of processing units with a considerable degree of accuracy. The development of high-performance computing has also played a significant role in reducing the times for simulation from months to days. The models have provided great insight into the working of unit operations and have helped in the optimization of process units. There is no doubt that such numerical models will turn out to be ideal optimization

278

Mineral Processing

tools in helping the process engineer to understand and improve plant performance.

References Asakura, K., Nagoa, M., Mizuno, M., Harada, S., 2007. “Numerical simulation of particle motion in a jig separator.” In: 5th Joint ASME/JSME Fluids Engineering Conference, San Diego, California, USA. Asomah, A.K., 1996. Improved Models of Hydrocyclones (Ph.D. thesis). JKMRC, The University of Queensland, Australia. Asomah, A.K., Napier-Munn, T.J., 1997. An empirical model of hydrocycolnes- incorporating angle of cyclone inclination. Miner. Eng. 10, 339
347. Austin, L.G., Bagga, P., 1981. An analysis of fine dry grinding in ball mills. Powder Technol. 28, 83
90. Austin, L.G., Shah, J., Wang, J., Gallagher, E., Luckie, P.T., 1981. An analysis of ball-and-race milling. Part I. The hardgrove mill. Powder Technol. 29, 263
275. Aurelien, D., Eric, C., Florent, B., Kumar, M.A., 2012. Analysis of swirling flow in hydrocyclones operating under dense regime. Miner. Eng. 31, 32
41. Austin, L.G., 1971. A review: introduction to the mathematical description of grinding as a rate process. Powder Technol. 5, 1
17. Basset, A.B., 1961. A Treatise on Hydrodynamics with Numerous Examples. Cambridge Deighton, Bell and Co. Beck, A.J.G., Holtham, P.N., 1993. Computer simulation of particle stratification in a twodimensional batch jig. Miner. Eng. 6 (5), 523
532. Bhaskar, K.U., Murthy, Y.R., Raju, M.R., Tiwari, S., Srivastava, J.K., Ramakrishnan, N., 2007. CFD simulation and experimental validation studies on hydrocyclone. Miner. Eng. 20, 60
71. Bilgili, E., Scarlett, B., 2005. Population balance modelling of non-linear effects in milling Processes. Powder Technol. 153, 59
71. Bloor, M.I.G., Ingham, D.B., 1987. The flow in industrial cyclones. J. Fluid Mech. 178, 507
519. Boysan, F., Ewan, B.C.R., Swithenbank, J., Ayers, W.H., 1983. Experimental and theoretical studies of cyclone separator aerodynamics. Inst. Chem. Eng. Symp. Ser. 69, 305
319. Bradley, D., 1965. The Hydrocyclone. Pergamon Press Ltd., London. Brennan, M.S., Holtham, P.N., Rong, R., and Lyman, G.J., 2002. Computational fluid dynamic simulation of dense medium cyclones. In: Proc. of the ninth Australian Coal Preparation Conference, Yeppoon, Australia, pp. 13
17. Brennan, M., 2006. CFD simulations of hydrocyclones with an air core: comparison between large eddy simulations and a second moment closure. Chem. Eng. Res. Des. 84 (6 A), 495
505. Brennan, M.S., Narasimha, M., Holtham, P.N., 2007. Multiphase modelling of hydrocyclones
prediction of cut-size. Miner. Eng. 20, 395
406. Broadbent, S.R., Callcott, T.G., 1957. Coal breakage processes III. The analysis of a coal transport system. J. Inst. Fuel 30, 13
17. Broadbent, S.R., Callcott, T.G., 1956a. A matrix analysis of processes involving particle assemblies. Phil. Trans. R. Soc. A249, 99
123. Broadbent, S.R., Callcott, T.G., 1956b. Coal breakage processes: II. A matrix representation of breakage. J. Inst. Fuel. 29 (1956), 528
539.

Numerical methods in mineral processing: an overview Chapter | 7

279

Broadbent, S.R., Callcott, T.G., 1956b. Coal breakage processes: I. A new analysis of coal breakage processes. J. Inst. Fuel. 29, 524
528. Bu¨rger, R., Bustamante, O., Fulla, M.R., Rivera, I.E., 2018. A population balance model of ball wear in grinding mills: an experimental case study. Miner. Eng. 128, 288
293. Castro, O., 1991. An Investigation of Pulp Rheology Effects and Their Application to the Dimensionless Type Hydrocyclone Models (M.Sc. thesis). JKMRC, University of Queensland, Australia. Celic, M.S., 1988. Acceleration of breakage rates of anthracite during grinding in a ball mill. Powder Technol. 54, 227
233. Chen, J., Chu, K.W., Zou, R.P., Yu, A.B., Vince, A., 2012. Prediction of the performance of dense medium cyclones in coal preparation. Miner. Eng. 31, 59
70. Chu, K.W., Wang, B., Yu, A.B., Vince, A., Barnett, G.D., Barnett, P.J., 2009a. CFD
DEM study of the effect of particle density distribution on the multiphase flow and performance of dense medium cyclone. Powder Technol. 193, 235
247. Chu, K.W., Wang, B., Yu, A.B., Vince, A., 2009b. CFD-DEM modelling of multiphase flow in dense medium cyclones. Powder Technol. 193, 235
247. Cleary, P.W., 2013. Particulate mixing in a plough share mixer using DEM with realistic shaped particles. Powder Technol. 248, 103
120. Cleary, P.W., 2001a. Charge behaviour and power consumption in ball mills: sensitivity to mill operating conditions, liner geometry and charge composition. Int. J. Miner. Process. 63, 79
114. Cleary, P.W., 2001b. Modelling comminution devices using DEM. Int. J. Numer. Anal. Methods Geomech. 25, 83
105. Cleary, P.W., 2009a. Industrial particle flow modelling using DEM. Eng. Comput. 26 (6), 698
743. Cleary, P.W., 2009b. Ball motion, axial segregation and power consumption in a full scale two chamber cement mill. Miner. Eng. 22, 809
820. Cleary, P.W., 2006. Axial transport in dry ball mills. Appl. Math. Model. 30, 1343
1355. Cleary, P.W., 2007. DEM modelling of particulate flow in a screw feeder. Prog. Comput. Fluid Dyn. 7, 128
138. Cleary, P.W., 2004. Large scale industrial DEM modelling. Eng. Comput. 21, 169
204. Cleary, P.W., Morrison, R., Morrell, S., 2003. Comparison of DEM and experiment for a scale model SAG mill. Int. J. Miner. Process. 68, 1
4. Cleary, P.W., Prakash, M., Ha, J., Stokes, N., Scott, C., 2007. Smooth particle hydrodynamics: status and future potential. Prog. Comput. Fluid Dyn. 7, 70
90. Cleary, P.W., Sawley, M.L., 2002. DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge. Appl. Math. Model. 26 (2), 89
111. Cleary, P.W., Sinnott, M.D., Morrison, R.D., 2006. Prediction of slurry transport in SAG mills using SPH fluid flow in a dynamic DEM based porous media. Miner. Eng. 19, 1517
1527. Collins, A.R., 2016. Classification of Multi-Component Feeds in a Hydrocyclone (Ph.D thesis). The University of Queensland, Australia. Cui, B., Zhang, C., Wei, D., Lu, S., Feng, Y., 2017. Effects of feed size distribution on separation performance of hydrocyclones with different vortex finder diameters. Powder Technol. 322, 114
123. Cullivan, J.C., Williams, R.A., Cross, C.R., 2003. Understanding the hydrocyclone separator through computational fluid dynamics. Chem. Eng. Res. Des. 81 (A), 455
465. Cundall, P.A., Strack, O.D.L., 1979. A discrete numerical model for granular assemblies. Geotechnique 29, 47
65.

280

Mineral Processing

Dabir, B., Petty, C.A., 1986. Measurements of mean velocity measurements in a hydrocyclone using laser doppler anemometry. Chem. Engg. Commun. 48 (4
6), 377
388. Dahner, J., Bosch, A.V., 2010. Total primary milling cost reduction by improved liner design. In: The 4th International Platinum Conference, Platinum in transition ‘Boom or Bust’, The Southern African Institute of Mining and Metallurgy, Sun City, Rustenburg, South Africa, 11
14 October, 2010. Davidson, M.R., 1988. Numerical calculations of flow in a hydrocyclone operating without an air core. Appl. Math. Model. 12, 119
128. Davidson. M.R., 1994. “A numerical model of liquid-solid flow in a hydrocyclone with high solids fraction.” International Conference on Numerical Methods for Multi-Material Fluid Flow, Nevada, 19
23 June, 1994. Delgadillo, J.A., Rajamani, R.K., 2005. A comparative study of three turbulence-closure models for the hydrocyclone problem. Int. J. Miner. Process. 77, 217
230. Devulapalli, B., 1997. “Hydrodynamic Modelling of Solid Liquid Flows in Large-Scale Hydrocyclones.” University of Utah. Djordjevic, N., 2005. Influence of charge distribution on net-power draw of tumbling mill based of DEM modelling. Miner. Eng. 18, 375
378. Djordjevic, N., Shi, F.N., Morrison, R.D., 2003. Applying discrete element modelling to vertical and horizontal shaft impact crushers. Miner. Eng. 16, 983
991. Dong, K.J., Kuang, S.B., Vince, A., Hughes, T., Yu, A.B., 2009. Numerical simulation of the inline pressure jig unit in coal preparation. Miner. Eng. 23 (4), 301
312. Dungilson, M.E. 1998. A model to predict the performance of the dense medium cyclone for low and high density applications. In: Seventh JKMRC Conference, Brisbane, Australia, pp. 67
84, 1998. Dyakowski, T., Williams, R.A., 1993. Modelling turbulent flow within a small-diameter hydrocyclone. Chem. Eng. Sci. 48, 1143
1152. Ergun, S., 1952. Fluid flow through packed columns. Chem. Eng. Prog. 48, 89
94. Fernandez, J.W., Cleary, P.W., McBride, W., 2011a. Effect of screw design on hopper drawdown of spherical particles in a horizontal screw feeder. Chem. Eng. Sci. 66, 5585
5601. Fernandez, J.W., Cleary, P.W., Sinnott, M.D., Morrison, R.D., 2011b. Using SPH one way coupled to DEM to model wet industrial banana screens. Miner. Eng. 24, 741
753. Flintoff, B.C., Plitt, L.R., Turak, A.A., 1987. Cyclone modelling: a review of present technology. CIM. Bull. 80 (905), 39
50. Fuerstenau, D.W., Abouzeid, A.Z.M., Phatak, P.B., 2010. Effect of particulate environment on the kinetics and energetics of dry ball milling. Int. J. Miner. Process. 97, 52
58. Fuerstenau, D.W., Abouzeid, A.M., Velamakanni, B.V., Deasen, D.M., 1986. Grinding of mixtures of minerals: kinetics and energy distribution. In: Proc. of First World Congress on Particle Technology, Part II, Comminution, Nuremberg, pp. 415
426. Fuerstenau, D.W., Phatak, P.B., Kapur, P.C., Abouzeid, M., 2011. Simulation of the grinding of coarse/fine (heterogeneous) systems in a ball mill. Int. J. Miner. Process. 99, 32
38. Galvin, K.P., Smitham, J.B., 1994. Use of X-rays to determine the distribution of particles in an operating cyclone. Miner. Eng. 7, 1269
1280. Gao, D., Herbst, J.A., 2009. Alternative ways of coupling particle behaviour with fluid dynamics in mineral processing. Int. J. Comput. Fluid D. 23, 109
118. Gaudin, A.M., Meloy, T.P., 1962. Model and a comminution distribution equation for single fracture. Trans. AIME. 223, 40
43. Ghadirian, M., Hayes, R.E., Mmbaga, J., Afacan, A., Xu, Z., 2013. On the simulation of hydrocyclones using CFD. Can. J. Chem. Eng. 91, 950
958.

Numerical methods in mineral processing: an overview Chapter | 7

281

Ghodrat, M., 2014. Computational Modelling and Analysis of the Flow and Performance in Hydrocyclones (Ph.D thesis). The University of New South Wales, New South Wales. Gupta, V.K., 1986. An appraisal of the linear first order kinetic model based ball mill design corrections. In: First World Particle Technology, Part II, Comminution, 6th European Symposium, Nuremberg, pp. 605
621. Heim, A., Leszczyniecki, R., 1985. Determination of parameters for wet-grinding model in perl mills. Powder Technol. 41, 173
179. Hennart, S.L.A., Wildeboer, W.J., van Hee, P., Meesters, G.M.H., 2009. Identification of the grinding mechanisms and their origin in a stirred ball mill using population balances. Chem. Engg. Science. 64 (19), 4123
4130. Herbst, J.A., Fuerstenau, D.W., 1968. The zero-order production of fine sizes in comminution and its implications in simulation. Trans. AIME 241, 538
548. Herbst, J.A., Grandy, G.A., Fuerstenau, D.W., 1973, “Population balance models for the design of continuous grinding mills,” In International Mineral Processing Congress, London, 261
274. Herbst, J.A., Nordell, L., 2001. Optimization of the design of sag mill internals using high fidelity simulation. In: Barratt, D.J., Allan, M.J., Mular, A.L. (Eds.), Proceedings of the SAG Conference, Vol. IV. Vancouver, BC, pp. 150
164. He, P., Salcudean, M., Gartshore, I.S., 1999. A numerical simulation of hydrocyclones. Chem. Eng. Res. Des. 77, 429
441. He, Y.B., 1994. The Effects of Rheology and Stability of Magnetite Dense Media on the Performance of Dense Medium Cyclones (Ph.D. thesis). University of British Columbia. Horsley, R.R., Tran, Q., Reizes, J., 1992. “The effect of rheology on performance of hydrocyclone.” In: 4th International Conference on Hydrocyclone, Cambridge, United Kingdom. Hsieh, K.T., Rajamani, R.K., 1991. Mathematical model of the hydrocyclone based on the physics of fluid flow. AIChE J. 37 (5), 735
746. Ishii, M., Mishima, K., 1984. Two-fluid model and hydrodynamic constitutive relations. Nucl. Eng. Des. 82, 107
126. Jayasundara, C.T., Yang, R.Y., Guo, B.Y., Yu, A.B., Govender, I., Mainza, A., et al., 2011. CFD
DEM modelling of particle flow in IsaMills -comparison between simulations and PEPT measurements. Miner. Eng. 24, 181
187. Jayasundara, C.T., Yang, R.Y., Guo, B.Y., Yu, A.B., Rubenstein, J., 2009. Effect of slurry properties on particle motion in IsaMills. Miner. Eng. 22, 886
892. Kalala, J.T., Breetzke, M., Moys, M.H., 2007. Study of the influence of liner wear on the load behaviour of an industrial dry tumbling mill using the Discrete Element Method (DEM). Int. J. Miner. Process. 86 (1/4), 33
39. Kanda, Y., Murata, H., Honma, T., 1989. Grinding of mixtures of coal and iron ore in order to prepare material for coal liquefaction. Powder Technol. 58, 175
180. Kawatra, S.K., Bakshi, A.K., Rusesky, M.T., 1996. The effect of slurry viscosity on hydrocyclone classification,”. Int. J. Miner. Process. 48, 39
50. Kawatra, S.K., Eisele, T.C., 2006. Causes and significance of inflections in hydrocyclone efficiency curves. In: Advances in Comminution, The Society for Mining, Metallurgy and Exploration, Littleton, CO, pp. 131
147. Kelsall, D.F., 1952. A study of the motion of solid particles in a hydraulic cyclone. Trans. Inst. Chem. Eng. 30, 87
108. Kojovic, T., 1988. The Development and Application Of Model
An Automated Model Builder for Mineral Processing (Ph.D. thesis). The University of Queensland, Australia.

282

Mineral Processing

Kuang, S.B., Chu, K.W., Yu, A.B., Vince, A., 2012. Numerical study of liquid
gas
solid flow in classifying hydrocyclones effect of feed solids concentration: effect of feed solids concentration. Miner. Eng. 31, 17
31. Launder, B.E., Reece, G.J., Rodi, W., 1975. Progress in the development of a Reynolds-stress turbulence closure,”. J. Fluid Mech. 68, 537
566. Lim, E.W.C., Chen, Y.-R., Wang, C.-H., Wu, R.-M., 2010. Experimental and computational studies of multiphase hydrodynamics in a hydrocyclone separator system. Chem. Eng. Sci. 65, 6415
6424. Mainza, A.N., 2006. Contributions to the Understanding of Three Product Cyclones in the Classification of Dual Density Platinum Ores (Ph.D thesis). The University of Cape Town. Makokha, A.B., Moys, M.H., 2006. Effect of cone-lifters on the discharge capacity of the mill product case study of a dry laboratory scale air-swept ball mill. Miner. Eng. 20, 124
131. Malhotra, A.R., Branion, M.R., Hauptmann, E.G., 1994. Modelling the flows in a hydrocyclone,”. Can. J. Chem. Eng. 72, 953
960. Mangadoddy, N., Vakamalla, T.R., Kumar, M., Mainza, A., 2020. Computational modelling of particle-fluid dynamics in comminution and classification: a review. Miner. Process. Extr. Met. 129, 145
156. Manninen, M., Taivassalo, V., Kallio, S., 1996. On the Mixture Model for Multiphase Flow. VTT Publications, Finland. Mayank, K., Malahe, M., Govender, I., Mangadoddy, N., 2015. Coupled DEM-CFD model to predict the tumbling mill dynamics. Procedia IUTAM 15, 139
149. Ma, L., Ingham, D.B., Wen, X., 2000. Numerical modelling of the fluid and particle penetration through small sampling cyclones. J. Aerosol Sci. 31, 23. Meloy, T.P., Williams, M.C., 1992. Problems in population balance modelling of wet grinding. Powder Technol. 71, 273
279. Mishra, B.K., Mehrotra, S.P., 1998a. Modelling of particle stratification in jigs by the discrete element method. Miner. Eng. 11 (6), 511
522. Mishra, B.K., Mehrotra, S.P., 1998b. Stratification in jigs by the discrete element method. Miner. Eng. 11 (6), 511
522. Mishra, B.K., Mehrotra, S.P., 2001. A jig model based on the discrete element method and its experimental validation. Int. J. Miner. Process. 63 (4), 177
189. Mishra, B.K., Rajamani, R.K., 1992. The discrete element method for the simulation of ball mills. Appl. Math. Model. 16, 598
604. Monredon, T.C., Hsieh, K.T., Rajamani, R.K., 1992. Fluid flow model of the hydrocyclones: an investigation of device dimensions. Int. J. Miner. Process. 35, 65
83. Morrison, R.D., Cleary, P.W., 2008. Towards a virtual comminution machine. Miner. Eng. 2008 (21), 770
781. Mousavian, S.M., Najafi, A.F., 2009. Numerical simulations of gas
liquid
solid flows in a hydrocyclone separator. Arch. Appl. Mech. 79, 395
409. Moysey, P.A., Baird, M.H.I., 2009. Size segregation of spherical nickel pellets in the surface flow of a packed bed: experiments and discrete element method simulations. Powder Technol. 196, 298
308. Moysey, P.A., Thompson, M.R., 2007. Determining the collision properties of semicrystalline and amorphous thermoplastics for DEM simulations of solids transport in an extruder. Chem. Eng. Sci. 62, 3699
3709. Moys, M., Bwalya, M., van Drunick, W., 2005. Mathematical modelling for optimization of mineral processing operations,”. J. South. Afr. Inst. Min. Metall. 105, 663
673.

Numerical methods in mineral processing: an overview Chapter | 7

283

Mukherjee, A.K., Mishra, B.K., 2006. An integral assessment of the role of critical process parameters on jigging. Int. J. Miner. Process. 81 (3), 187
200. Mukherjee, A.K., Mishra, B.K., 2007. Experimental and simulation studies on the role of fluid velocity during particle separation in a liquid-solid fluidized bed. Int. J. Miner. Process. 82 (4), 211
221. Murthy, Y.R., Bhaskar, K.U., 2012. Parametric CFD studies on hydrocyclone. Powder Technol. 230, 36
47. Nageswararao, K., 1978. Further Developments in the Modelling and Scale Up of Industrial Hydrocyclones (Ph. D. thesis). JKMRC, University of Queensland, Australia. Napier-Munn, T.J., 1990. The effect of dense medium viscosity on separation efficiency. Coal Prep. 8, 145
165. Napier-Munn, T.J., 1980. “Influence of medium viscosity on the density separation of minerals in cyclones.” In: 1st International Conference on Hydrocyclone, Cambridge, UK, pp. 63. Narasimha, M., Brennan, M., Holtham, P.N., 2006a. Large eddy simulation of hydrocyclone— prediction of air-core diameter and shape. Int. J. Miner. Process. 80, 1
15. Narasimha, M., Brennan, M.S., Holtham, P.N., 2006b. A review of flow modelling for dense medium cyclones. Coal Prep. 26, 55
89. Narasimha, M., Brennan, M.S., Holtham, P.N., 2012. CFD modelling of hydrocyclones: prediction of particle size segregation. Miner. Eng. 39, 173
183. Narasimha, M., Brennan, M.S., Holtham, P.N., Napier-Munn, T.J., 2007a. A comprehensive CFD model of dense medium cyclone performance. Miner. Eng. 20, 414
426. Narasimha, M., Brennan, M.S., Holtham, P.N., 2007b. Prediction of magnetite segregation in dense medium cyclone using computational fluid dynamics technique. Int. J. Miner. Process. 82, 41
56. Narasimha, M., Sripriya, R., Banerjee, P.K., 2005. CFD modelling of hydrocyclone—prediction of cut size. Int. J. Miner. Process. 75, 53
68. Nowakowski, A.V., Cullivan, J.C., Williams, R.A., Dyakowski, T., 2004. Application of CFD to modelling of the flow in hydrocyclones. Is this a realizable option or still a research challenge? Miner. Eng. 17, 661
669. Owen, P.J., Cleary, P.W., McBride, B., 2003. Simulated granular flow in screw feeders using 3D discrete element method (DEM). In: CHEMECA 2003, 31st Australian Chemical Engineering Conference, ISBN: 0
86396-829-5, paper no. 203. Padhi, M., Kumar, M., Mangadoddy, N., 2020. Understanding the bicomponent particle separation mechanism in a hydrocyclone using a computational fluid dynamics model. Ind. Eng. Chem. Res. 59, 11621
11644. Padhi, M., Mangadoddy, N., Sreenivas, T., Vakamalla, T.R., Mainza, A.N., 2019. Study on multi-component particle behaviour in a hydrocyclone classifier using experimental and computational fluid dynamics techniques. Sep. Purif. Technol. 229, 115698. Paul, W. Cleary, Rob, D. Morrison, 2012. Prediction of 3D slurry flow within the grinding chamber and discharge from a pilot scale SAG mill. Miner. Eng. 39, 184
195. Pericleous, K.A., Rhodes, N., 1986. The hydrocyclone classifier-a numerical approach. Int. J. Miner. Process. 17, 23
43. Plitt, L.R., 1976. A mathematical model of the hydrocyclone classifier. CIM. Bull. 69, 114
122. Popoff, B., Braun, M.A., 2007. ‘Lagrangian approach to dense particulate flows.’ In: 6th International Conference on Multiphase Flow, Leipzig, Germany. Powell, M.S., 1991. The design of rotary-mill liners, and their backing materials. South. Afr. Inst. Min. Metall. 91, 63
75.

284

Mineral Processing

Powell, M., Weerasekara, N.S., Cole, S., LaRoche, R.D., Favier, J., 2011. DEM modelling of liner evolution and its influence on grinding rate of ball mills. Miner. Eng. 24, 341
351. Prasher, C.L., 1987. Crushing and Grinding Process Handbook. Wiley, Chichester. Rajamani, R.K., Guo, D., 1992. Acceleration and deceleration of breakage rates in wet ball mills. Int. J. Miner. Process. 34, 103
118. Rao, T.C., 1966. The Characteristics of Hydrocyclones and Their Application As Control Units in Comminution Circuits (Ph. D thesis). University of Queensland (JKMRC), Brisbane, Australia. Raziyeh, S., Ataallah, G.S., 2014. CFD simulation of an industrial hydrocyclone with Eulerian
Eulerian approach A case study. Int. J. Min. Eng. 24, 643
648. Razmi, H., Goharrizi, S., Mohebbi, A., 2019. CFD simulation of an industrial hydrocyclone based on multiphase particle in cell (MPPIC) method. Sep. Purif. Technol. 209, 851
862. Renner, V.G., 1976. The Action of the Hydrocyclone (Ph.D thesis). The University of London, United Kingdom (unpublished). Rietema, K., 1962. Liquid solids separation in a cyclone the effect of turbulence on separation. Symposium on the Interaction Between Fluids and Particles. Institution of Chemical Engineers, London, pp. 275
281, V. Roco, M.C., 1990. In: Cheremisinoff, N.P. (Ed.), One Equation Turbulence Modelling of Incompressible Mixtures: Encyclopedia of Fluid Mechanics. Gulf Publishing Company, New Jersey. Rubinow, S.I., Keller, J.B., 1961. The transverse force on a spinning sphere moving in a viscous fluid. J. Fluid Mech. 11, 447
459. Saffman, P.G., 1965. Lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385
400. Saffman, P.G., 1968. Corrigendum to “The lift on a small sphere in a slow shear flow. J. Fluid Mech. 31, 624. Sedlatschek, K., Bass, L., 1953. Contribution to the theory of milling processes. Powder Metall. Bull. 6, 148
153. Sevilla, E.M., Branion, R., 1997. The fluid dynamics of hydrocyclones. J. Pulp Pap. Sci. 23, 85
93. Shi, F.N., Napier-Munn, T.J., 1996. A model for slurry rheology. Int. J. Miner. Process. 47, 103
123. Shimizu, Y., Cundall, P.A., 2001. Three-dimensional DEM simulation of bulk handling screw conveyors. J. Eng. Mech. 127 (9), 864
872. Sinnott, M.D., Cleary, P.W., Morrison, R.D., 2011. Slurry flow in a tower mil. Miner. Eng. 24, 152
159. Slack, M.D., Prasad, R.O., Bakker, A., Boysan, F., 2000. Advances in cyclone modelling using unstructured grids. Trans. IChem 78 (A), 1098
1104. Solnordal, C.B., Hughes, T., Gray, A.H., Schwarz, P.M., 2009. CFD modelling of a novel gravity separation device. Seventh International Conference on CFD in the Minerals and Process Industries. CSIRO, Melbourne, Australia. Srinivasan, R., Mishra, B.K., Mehrotra, S.P., 1999. Simulation of particle stratification in Jigs. Coal Prep. 20 (1
2), 55
70. Suasnabar, D.J., Fletcher, C.A.J., 1998. CFD simulation of dense medium cyclones. In: Proc. 13th Australasian Fluid Mech Conference, Melbourne, Australia, pp. 997
1000. Subramanian, V.J., 2002, Measurement of Medium Segregation in the Dense Medium Cyclone Using Gamma-Ray Tomography (Ph.D. thesis). JKMRC, University of Queensland, Australia. Svarovsky, L., 1984. Hydrocyclones. 1, Holt. Rinehart and Winson Ltd., London. Swain, S., Mohanty, S., 2013. A 3-dimensional Eulerian
Eulerian CFD simulation of a hydrocyclone. Appl. Math. Model. 37 (5), 2921
2932.

Numerical methods in mineral processing: an overview Chapter | 7

285

Tavares, L.M., Souza, L.L.G., Lima, J.R.B., Possa, M.V., 2002. Modelling classification in smalldiameter hydrocyclones under variable rheological conditions. Miner. Eng. 15, 613
622. Tsuji, Y., Kawaguchi, T., Tanaka, T., 1993. Discrete particle simulation of two-dimensional fluidized bed. Powder Technol. 77 (1), 79
87. Vakamalla, T.R., Mangadoddy, N., 2017. Numerical simulation of industrial hydrocyclones performance: role of turbulence modelling. Sep. Purif. Technol. 176, 23
39. Vakamalla, T.R., Mangadoddy, N., 2019. The dynamic behaviour of a large-scale 250-mm hydrocyclone: a CFD study. Asia-Pac. J. Chem. Eng. 14, e2287. Vakamalla, T.R., Mangadoddy, N., 2015. Rheology-based CFD modelling of magnetite medium segregation in a dense medium cyclone. Powder Technol. 277 (0), 275
286. Vakamalla, T.R., Mangadoddy, M., 2021. Comprehensive dense slurry CFD model for performance evaluation of industrial hydrocyclones. Ind. Eng. Chem. Res. 60 (33), 12403
12418. Venkataraman, K.S., Fuerstenau, D.F., 1981. “Kinetic and energy considerations in mixture grinding.” In: Proc. of the International Symposium on Powder Technology, pp. 380
387. Venkataraman, K.S., Fuerstenau, D.W., 1984. Application of the population balance model to the grinding of mixtures of minerals. Powder Technol. 39, 133
142. Viduka, S.M., Feng, Y.Q., Hapgood, K., Schwarz, M.P., 2011. Discrete particle simulation of solid separation in a jigging device. In: Luckos, A., Den Hoed, P. (Eds.), IFSA, (Industrial Fluidization South Africa). Southern African Institute of Mining and Metallurgy, Johannesburg, pp. 175
192. Wang, B., Chu, K.W., Yu, A.B., Vince, A., 2014. Computational investigation of the mechanisms of the “breakaway” effect in a dense medium cyclone. Miner. Eng. 62, 111
119. Wang, B., Chu, K.W., Yu, A.B., Vince, A., 2009. Modelling the multiphase flow in a dense medium cyclone. Ind. Eng. Chem. Res. 48, 3628
3639. Wang, B., Chu, K.W., Yu, A.B., 2007. Numerical study of particle-fluid flow in a hydrocyclone. Ind. Eng. Chem. Res. 46, 4695
4705. Weller, K.R., Sterns, U.J., Artone, E., Bruckard, W.J., 1988. Multicomponent models of grinding and classification for scale-up from continuous small or pilot scale circuits. Int. J. Miner. Process. 22, 119
147. Wen, C.Y., Yu, Y.H., 1966. Mechanics of fluidization. Chem. Eng. Prog. Symposium Ser. 62, 100
111. Wood, J.C. 1990. A Performance Model for Coal-Washing Dense Medium Cyclones (Ph.D. thesis). JKMRC, University of Queensland, Australia. Woodburn, E.T., Kalligeris-Skentzos, A., 1987. The investigation of the kinetics of breakage as a first step towards the assessment of the economics of ultra-fine grinding of a British lowrank coal. Powder Technol. 53, 137
143. Xia, Y.K., Peng, F.F., 2007. Numerical simulation of behaviour of fine coal in oscillating flows. Miner. Eng. 20 (2), 113
123. Zhong, Z., O’Callaghan, J.R., 1990. The effect of the shape of the feed opening on the performance of a horizontal screw conveyor. J. Agric. Eng. Res. 46 (1990), 125
128. Zhou, Q., Wang, C., Wang, H., Wang, J., 2016. Eulerian
Lagrangian study of dense liquid
solid flow in an industrial-scale cylindrical hydrocyclone. Int. J. Miner. Process. 151, 40
50. Zughbi, H.D., Schwarz, M.P., Turner, W.J., Hutton, W., 1991. Numerical and experimental investigations of wear in heavy medium cyclones. Miner. Eng. 4, 245
262.

This page intentionally left blank

Chapter 8

Computational fluid dynamic modeling of hydrocyclones Teja Reddy Vakamalla1, Sripriya Rajendran2, Mandakini Padhi3 and Narasimha Mangadoddy4 1

Department of Chemical Engineering, National Institute of Technology Calicut, Kozhikode, Kerala, India, 2Tata Steel Europe, Ijmuiden, Noord Holland, The Netherlands, 3 Pfizer Healthcare India Pvt Ltd, IIT Madras Research Park, Chennai, Tamil Nadu, India, 4 Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Sangareddy, Telangana, India

8.1

Introduction

The cyclones were introduced by the Dutch State mines (Driessen, 1945) for clean coal separation using fine sand medium. Since then, the cyclones have found use in various industries and even in agricultural applications, such as sand/manure separation. Its current industrial practice, it is used as a classifier in the mineral industry for recirculation of oversize particles in the grinding circuit, as a cleaner in the mining industry to separate clean coal, iron, diamonds, etc., in the paper industry to remove contaminants (sand, grit, stones, nuts, and bolts) from the pulp slurry, in the refineries to separate oil from water, and in the bio industries to recover starch from water (Bradley, 1965; Wills and Napier-Munn, 2006). Their wide usage in different industries is due to their structural simplicity, high throughput, compact size, low cost and maintenance. Conventional industrial hydrocyclone design, as shown in Fig. 8.1, consists of a cylindrical section followed by a conical section with a certain cone angle (responsible for flow reversal) attached to a single feed inlet and two product outlets, named the vortex finder and the spigot. Hydrocyclone utilizes the pressure energy of the fluid to create rotational motion thereby causing relative movement between the suspended particles in the fluid (Bradley, 1965). Tangential injection of the fluid generates outer rotational motion, called a free vortex. Concurrently, an inward rotational motion, called a forced vortex, is produced due to the conical

Mineral Processing. DOI: https://doi.org/10.1016/B978-0-12-823149-4.00001-6 © 2023 Elsevier Inc. All rights reserved.

287

288

Mineral Processing

FIGURE 8.1 Schematic of hydrocyclone.

geometry of the hydrocyclone. Any particle in the hydrocyclone subsequently faces two main opposing forces; centrifugal and drag forces. One is towards the outer direction due to the centrifugal acceleration, and the other is in the inward radial direction due to the inward moving fluid. The magnitude of these forces depends on the size, shape, and density of the particles dispersed in a fluid. Because of high centrifugal forces, the heavier density/larger size particles are transported towards the wall. Lower density/finer size particles remain in the liquid close to the center. As the fluid moves downwards, separation starts taking place, i.e, large/ heavy particles move towards the spigot region, which passes through the underflow. Smaller/lighter particles reverse their path, moving towards the vortex finder to escape through the overflow. Apart from this, a negative pressure region is also present in the centre of the cyclone due to high centrifugal forces. As both outlets are open to the atmosphere, air from the overflow and underflow gets sucked inside and forms an air core. Air core plays a vital role in separating the particles in hydrocyclone. Usually, the discharge through the spigot is a “spray”-like discharge with coarser and heavier particles and a small amount of liquid, whilst most of the liquid is carried upwards to the vortex finder by the lighter and finer particles. When the spigot capacity is exceeded, the air core is closed off, and all the particles tend to discharge through the spigot, thus changing the underflow

Computational fluid dynamic modeling of hydrocyclones Chapter | 8

289

FIGURE 8.2 Typical flow field distribution inside hydrocyclone.

discharge to a “rope” discharge, indicating a disturbance in the flow patterns inside the cyclone. The typical flow field (tangential and axial velocities) distribution in hydrocyclone is illustrated in Fig. 8.2. One can observe an increase in the tangential velocity from the wall towards the center, reaching a maximum, after that decreasing rapidly as the air
water interface is approached. Similarly, for axial velocities, downward velocities towards the wall and upward velocities towards the air core are observed. There are points at which the axial velocities are zero and loci of all the zero velocity points are termed as the locus of zero vertical velocities (LZVV). While the equipment is simple to operate and maintain, the flow inside is quite complex. Various models have been developed to predict the performance of hydrocyclones—from simple models based on correlations between static pressure drop and predicted cut size to complicated numerical models. Computational fluid dynamic (CFD) models are the most efficient models to predict accurate flow fields inside any operating system (Mangadoddy et al., 2020). The initial models were two-dimensional, i.e., axisymmetric and used isotropic turbulence models. The few multiphase models that were developed had unrealistic assumptions because of low computational power. Today, with vastly improved computational capabilities, these equations are solved with realistic assumptions in turbulence and are mostly threedimensional multiphase models. The details of turbulence and multiphase models used in the present study are provided below.

290

Mineral Processing

8.2

Computational methodology

The multiphase CFD approach used for the simulations in this chapter was developed by Narasimha (2010) using the commercial package Fluent with additional user-defined functions. This CFD model consists of simple submodels to simulate air/free surface, an algebraic slip mixture model (ASM) model modified with additional lift and drag forces to simulate size distribution of particles, and Reynolds stress model/large eddy simulation (RSM/ LES) models to model turbulence.

8.2.1

Turbulence modeling

Turbulence is a complex phenomenon, and it poses one of the main challenges in the CFD modeling of hydrocyclone. The flow in hydrocyclone is highly turbulent, having fluid Reynolds numbers in the range of 105 to 107. The large Reynolds number indicates high turbulence in the hydrocyclone. Turbulent flows are characterized by fluctuations of different length scales with high frequency. Complete resolution of these fluctuations is computationally expensive to simulate in practical engineering calculations. Instead, these can be expressed as a combination of time averaged and fluctuating fields, thereby, reducing the computational time. Mainly, three types of turbulence modeling techniques are available. The first is the direct numerical simulation (DNS) which solves the Navier
Stokes equation completely, without modeling (Orszag, 1970). This means resolving all the temporal and spatial scales of turbulence. The second is the large eddy scale (LES) turbulence model, which separates the flow structures into “resolved” and “subgrid-scale” components (Smagorinsky, 1963). In this, the large-scale eddies are resolved, and small-scale eddies are modeled based on a filtering function. Lastely there exists the Reynolds averaged Navier
Stokes (RANS)-based turbulence models. The motivation behind RANS-based turbulence models is to save computational resources by representing the flow field as a combination of time-averaged mean and fluctuating components. Though the average flow field may not describe the exact local physics (i.e., turbulence generation and dissipation), it is mostly sufficient to provide insight into the physics of the general flow.

8.2.1.1 Large eddy simulation model (LES) The velocity decomposition in the LES turbulence model is different compared to RANS-based turbulence models. LES model segregates the turbulence into small and large length scales using a filter function. Small-scale variables (that are universal in nature) are modeled. Large-scale variables that depend on the geometry and flow are resolved. Expressing the instantaneous velocity (ui ) into sum of resolved velocity 0 (ui ), and residual velocity (u i ) and time averaging the momentum equation

Computational fluid dynamic modeling of hydrocyclones Chapter | 8

291

gives the resolved velocity obtained by the volume-averaging procedure given in Eq. (8.1) ð
 uðxi ; tÞ 5 G xi ; xi 0i uðxi ; tÞdxi 0 ð8:1Þ vol 0

Here Gðxi ; x i Þ is the filter function. After the volume averaging, the filtered Navier
Stokes equation can be represented as Eq. (8.2)   2@ @ @
@ @u i ðρu i Þ 1 ρui uj 5 p1 μ ð8:2Þ @t @xj @xi @xj @xj Further, the nonlinear term (ρui uj ) of the filtered equation is expressed in terms of averaged and fluctuating terms as Eq. (8.3) @ρ @ui 1 50 @t @xi @ @
ðui Þ 1 ui @t @xj

ð8:3Þ

  21 @ @τ SGS @ @ui ij uj 5 p1 μ 1 gi 2 ρ @xi @xj @xj @xj

ð8:4Þ

In Eq. (8.4), τ SGS ij denotes the residual stress tensor and can be defined as τ SGS 5 ui uj 2 ui ij

uj

ð8:5Þ

Residual stress tensor is modeled by a simple eddy viscosity model (Smagorinsky 1963) as the product of eddy viscosity and strain rate  @ui @uj SGS 1 τ ij 5 2 μt ð8:6Þ @xj @xi LES is not well defined to solve the flow near the walls; therefore, Yakhot et al. (1989) introduced the renormalization group model, which effectively models the low Reynolds-number effect near the walls. Turbulent viscosity is defined as the difference between effective viscosity and molecular viscosity. μt 5 μeff 2 μ

ð8:7Þ

Effective viscosity is defined as   2  1=3 μ μ μeff 5 μ 11H s 3eff 2C μ Turbulent viscosity (μs ) in the subgrid scale is defined as  2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Sij Sij μs 5 CRNG V 1=3

ð8:8Þ

ð8:9Þ

292

Mineral Processing

V is the volume of the computational cell, Sij is strain rate, and H(x) is the Heaviside function  x; x $ 0 H ðxÞ 5 ð8:10Þ 0; x # 0 It has to be understood that no single turbulence model can be universally accepted as being suitable for all classes of turbulence problems. Each turbulence model solves the turbulent fluctuations to some extent and models the rest. The choice of turbulence model will depend on the problem under consideration, such as the physics encompassed in the flow, the established practice for a specific class of problem, the level of accuracy required, the available computational resources, and the amount of time available for the simulation. To make the most appropriate choice of model for the application, one has to understand the capabilities and limitations of various turbulence models.

8.2.2

Multiphase modeling

8.2.2.1 Volume of fluid (VOF) model VOF model is a multiphase CFD approach used for interface tracking between free surfaces (Hirt and Nichols, 1981) by solving the momentum Eq. (8.11). Continuity, Eq. (8.12) is solved for the volume fraction of the air (αq ) and this tracks the position of the air core in this problem. This work uses a geometric reconstruction scheme with a piecewise-linear approach to track the interface between air and water. In the piecewise-linear approach, the interface between air and water is assumed to have a linear slope within each cell and uses the linear shape to calculate the advection of fluids through the cell phases.   2 @p @
 @
@ @ui @uj ρuj 1 ρui uj 5 1 ρgi 1 μ 1 ð8:11Þ @t @xj @xj @xj @xj @xi @αq @αq 1 uj 50 @t @xi

ð8:12Þ

αq is the volume fraction of qth phase which varies between 0 and 1. uj is jth component of the velocity. The average density and viscosity are calculated in the following manner ρ 5 αρwater 1 ð1 2 αÞρair; μ 5 αμwater 1 ð1 2 αÞμair

ð8:13Þ

The surface tension model by Brackbill et al. (1992) is incorporated in Fluent as a source term in the momentum equation. A constant of 0.078 N/m is used for the surface tension between air and water.

Computational fluid dynamic modeling of hydrocyclones Chapter | 8

293

8.2.2.2 Discrete particle model (DPM) In this model, a Langrangian reference frame is used to solve the properties of discrete/dispersed phase particles, while the continuous phase is solved in an Eulerian reference frame using the Navier
Stokes equation, as described in the previous section. A large number of spherical particles is tracked under the influence of discrete-phase inertia, hydrodynamic drag, gravitational force, and shear lift forces for both steady and unsteady flows. The discrete random walk model is used to predict the dispersion effect on the particles due to turbulent eddies present in the continuous phase. The DPM model assumes that the volume fraction of the dispersed phase is very low, even though the mass loading is higher. Hence, particle
particle interactions and the effects of the particle volume fraction on the liquid phase are negligible. This model is unsuitable, if the volume fraction of the secondary phase is high. DPM involves the prediction of the trajectory of discrete-phase particles by computing the force balance in a Langrangian reference frame by equating particle acceleration to forces acting on the particle.   ρ 2 ρ
 p m d~ up g 5 FD ~ 1 FL ð8:14Þ u 2~ up 1 ~ ρp dt 18μ CD Rep ρp dp 2 24

ð8:15Þ

ρdp ~ u up 2 ~ Rep 5 μm

ð8:16Þ

 2Kν 1=4 ρdij
~ u 2~ up 1=4 ρp dp ðdlk dkl Þ

ð8:17Þ

FD 5

FL 5


 where FD ~ u 2~ u p is the drag force and FL is the lift force acting on the paru is continuous phase velocity, ~ u p is particle ticle, CD is drag coefficient, ~ velocity, ρp is particle density, ρ is fluid density, Dp is particle diameter, μm is fluid/mixture viscosity, Rep is the particulate Reynolds number, K 5 2.594, and dij is the deformation tensor.

8.2.2.3 Modified algebraic slip mixture (MASM) model As stated in the earlier section, the simplified mixture model is more reliable than the full Eulerian-Eulerian model in terms of lesser uncertainties in equation closure and computational time, as it solves lesser number of equations. Algebric slip mixture (ASM) model solves the equations of motion for slurry

294

Mineral Processing

mixture and additional transport equations for the volume fractions of particulate phases p, dispersed throughout a continuous water phase c:   @ @ 2 @p @ @umi @umj ρm umi 1 ρm umi umj 5 1 μm 1 1 ρgi @t @xj @xi @xj @xj @xi ð8:18Þ  @ Xn 1 α ρ u u p51 p p pmi pmj @xj   @ @
@
αp 1 α p ui 1 αp upm;i 5 0upm;i 5 upi 2 ui @t @xi @xi

ð8:19Þ

All the mixture properties are calculated similar to Eq. (8.13). Phase segregation in Eq. (8.19) is accounted for by the term upm,i, which is the drift velocity of the phase p relative to the mixture m. This is related to the slip velocity upc,i, which is the velocity of the phase p relative to the continuous water phase c by the formulation given in Eq. (8.20): upmi 5 upci 2

Xn αk ρ k ulci ; l51 ρ m

upci 5 upi 2 uci

ð8:20Þ

upc,i has calculated algebraically in Manninen et al. (1996) treatise by an equilibrium force balance and is implemented in Fluent in a simplified form as shown in Eq. (8.20). ASM works on the assumption that particles reach their equilibrium positions over short spatial length scales. This means that the particles accelerate rapidly to their terminal velocities relative to the mixture. In the basic formulation of the mixture model, the model by SchillerNaumann drag law (1935) is used.   dp 2 ρp 2 ρm  @ @ upci 5 gi 2 umi 2 umj umi ð8:21Þ @t @xj 18frep μc The term outside the brackets in Eq. (8.21) is called the particle relaxation time, and if the relaxation time is short compared to the time scale of the flow, then the assumption that the particles are always moving at their terminal relative velocity is considered to be valid. The terms inside the brackets are accelerations associated with the forces to which particles are subjected. This standard ASM model includes gravity, rate of change of time, and convective terms from the momentum equation. The convective term includes centripetal force on the particles in a flow and models the classification force arising from swirl in a hydrocyclone simulation. In principle, other forces such as lift, collisional, and turbulent dispersion can also be accounted for by including the acceleration associated with that force in Eq. (8.21). In this work, ASM model has been used with the granular options to account for the additional particle
fluid and particle
particle stresses

Computational fluid dynamic modeling of hydrocyclones Chapter | 8

295

generated at high feed solids content. Also, the slip velocity calculation has been modified to include a shear-dependent lift force based on Saffman’s (1965) expression and the corresponding equation is given below   " # dp 2 ρp 2 ρm @ @ ρc gi 2 umi 2 umj umi 1 0:75 Clp εijk ωmj upck upci 5 @t @xj 18frep μc ρp 2 ρm ð8:22Þ Eq. (8.22) has been implemented in Fluent as a custom slip velocity calculation using a user-defined function. frep has been modeled with the Schiller Naumann drag law (1935) but with an additional correction factor for hindered settling based on the Richardson and Zaki (1954) correlation.
 ð8:23Þ frep 5 1 1 0:15Rep 0:687 αp 24:65 The lift force is a mechanical force generated by solid particles as they move through a fluid, directed perpendicular to the flow direction. The inclusion of lift forces for slip calculation will account for the effect of shear forces exerted by particles at wall. The lift force expression derived by Saffman (1965) for the lift force on a single particle was used here: ρ ð8:24Þ Flpi 5 c πdp 3 Clp εijk ωmj upck 8 The lift coefficient has been calculated as " # ρf dp 2 jωj fc Clp 5 4:1126 μc

ð8:25Þ

fc corrects the lift coefficient using the correlation proposed by Mei (1992).

8.2.3

Rheology modeling

Slurry rheology plays a vital role in hydrocyclones wherein the particles settle in the gravity/centrifugal field at high solids concentration. Therefore, slurry rheology was modeled using the Newtonian viscosity model with solids and fines correction.

8.2.3.1 Newtonian model with total solids and fines correction The effect of fine particles on the rheology of the mixture is significant. The increase in fines fractions can lead to high viscosities in suspensions. Therefore, fines correction is needed for describing the slurry behavior through Newtonian formulations. The authors modified the Ishii and Mishima equation by including the fine fractions below 38 μm (Narasimha

296

Mineral Processing

et al., 2012a,b). Eq. (8.26) was obtained by calibrating against measured viscosity data of various mineral slurries (Narasimha et al., 2014). 0:39 μm h αp i21:55
5 12 F238μ ð8:26Þ μw 0:62

8.2.4

Details of simulation

The 75 mm conventional hydrocyclone (Hsieh, 1988) and a 75 mm laboratory hydrocyclone (Reddy, 2016) were modeled. The corresponding meshes are displayed in Fig. 8.3. Dimensional details of the hydrocyclones used in the simulation studies are provided in Table 8.1. The simulations used uniform velocity boundary condition for the feed inlet. Momentum equations were discretized using a bounded central differencing scheme. Pressure staggering option was selected to solve the pressure. Quadratic upstream interpolation convective kinetics was used to discretize volume fraction equations. Water with a density of 998.2 kg/m3 and viscosity of 0.001 kg/ms, air with a density of 1.225 kg/m3 and viscosity of 1.7894x10
5 kg/ms were used to run water
air two-phase simulations. In the simulations, the computational domain was initialized to the properties of the feed inlet. Turbulence was modeled using LES. At the feed inlet and pressure outlets, a turbulence intensity of 10% along with an equivalent hydraulic diameter was specified. The free surface between air and water (air core) was solved using the volume of fluid (VOF) model. An atmospheric pressure outlet with a back volume fraction of one for air was used at both outlets. This enabled the generation of air core by drawing air from both the outlets. The LES turbulence model used a fixed time step of 1.0 3 10
5s. Residuals were kept in the range of 1.0 3 10
5 for continuity, velocity and turbulence parameters. Each simulation was run for a time equivalent to the minimum equipment residence time, and the simulations were assumed to be converged when the residuals were less than 1.0 3 10
5. The model was changed from VOF to ASM in multiphase simulations before introducing solid particles with full-size distribution of particles as a dispersed phase. The slip velocity in the ASM model was disabled for the water
air interface. Therefore the ASM model behaved like the VOF model and could resolve the air core. For all other phases, the slip velocity calculations were enabled. All the results were ensemble-averaged over a few thousand iterations equivalent to approximately 2 s of physical time after the solution converged. The simulations were considered to be converged when the net mass flow rate between feed, overflow, and underflow were close to zero.

Computational fluid dynamic modeling of hydrocyclones Chapter | 8

297

FIGURE 8.3 (A) 75 mm hydrocyclone (Hsieh, 1988) and (B) 75 mm laboratory hydocyclones mesh used for the numerical studies.

298

Mineral Processing

TABLE 8.1 Details of hydrocyclone dimensions and solid properties used for the numerical studies. 75 mm hydrocyclone (Hsieh, 1988)

75 mm laboratory hydrocyclone (Kumar Reddy, 2016)

Inlet (mm)

25

45

Vortex finder (mm)

25

25

Spigot (mm)

12.5

10 2 17.5

Cylindrical length (mm)

75

70

Flow rate (kg/s)

1.12

0.5
2.5

0
10

0
50

Solid phase density (kg/m )

2700

2650

Solid phases (μm) used for multiphase computational fluid dynamic studies

3.5, 7.4, 15, 29.4, 43.5

3.35, 10.25, 19.37, 28.27, 48, 80

Solids % 3

8.3 8.3.1

Two-phase flow predictions 75 mm hydrocyclone

To test the accuracy of CFD model predictions, the results were compared with laser Doppler velocimetery (LDV) measurements in a 75 mm hydrocyclone (Hsieh, 1988). Two-phase (VOF coupled with LES turbulence model) simulations were initiated with a feed flow rate of 1.116 kg/s. Numerically predicted mean tangential and axial flow fields were compared against experimental data at two different axial positions as shown in Fig. 8.4. Tangential and axial velocities were found to be very close to the experimental data. The fluctuating velocities were normalized with respect to inlet velocity and were also compared against LDV measurements, as shown in Fig. 8.4. Here also, the predicted data from the LES model was in good agreement with experiments. After the validation of the mean and fluctuating flow field in 75 mm (Hsieh, 1988) hydrocyclone, the simulations were continued in a 75 mm laboratory hydrocyclone (Reddy, 2016) for various operating (inlet pressures) and design (spigot diameters) conditions. The predicted data was validated against experimental imaging and tomography (Rakesh et al., 2014) measurements. Further, the effect of these parameters on the flow variables such as the mean static pressure and tangential velocity was analyzed.

Computational fluid dynamic modeling of hydrocyclones Chapter | 8

299

FIGURE 8.4 Comparison of computational fluid dynamic predicted (A) mean, (B) fluctuating/ RMS tangential and axial velocities against experimental measurements (Hsieh, 1988) at an axial position of 60 and 120 mm from roof of the 75 mm (Hsieh, 1988) hydrocyclone.

8.3.2

75 mm laboratory hydrocyclone

Fig. 8.5 compares the throughputs predicted by CFD against experimental measurements (Reddy, 2016). The predicted volumetric flow rates matched closely with experimental measurements for various inlet pressures and spigot diameters. Water splits predicted by the CFD model for different spigot diameters were validated against experimental measurements in Fig. 8.6. Deviations were observed at low pressures (10 psig) and for the smallest spigot diameter (10 mm). An average deviation of 31.81% was observed for a 10 mm spigot diameter. The deviations decreased with an increase in spigot diameter; they were 2.97%, 3.88%, and 3.73% for 12.5, 15, and 20 mm spigot diameters, respectively. In addition, the two-phase CFD model was used to assess the effect of inlet pressure and spigot variations on the performance of hydrocyclone. In the numerical studies, the increase in inlet pressures from 5 to 15 to 25 psig caused an increase in inlet velocities from 0.539 to 0.965 to1.285 m/s, respectively. The variation of mean static pressure and tangential velocity profiles along the radius at 3 axial positions (100, 200, and 415 mm from the roof of the cyclone) for different inlet velocities are displayed in Fig. 8.7 for a spigot diameter of 15 mm.

300

Mineral Processing

2.5

Experimental throughput, kg/s

10 mm 12.5 mm 2.2

15 mm 20 mm

1.9

1.6

1.3

1 1.3

1

1.6

1.9

2.2

2.5

CFD predicted throughput, kg/s FIGURE 8.5 Pareto plot of computational fluid dynamic predicted throughput against experimental measurements at different pressure and spigots in a 75 mm hydrocyclone.

Experimental 10 mm 12.5 mm 15 mm 20 mm

0.5

Water Split

0.4

CFD 10 mm 12.5 mm 15 mm 20 mm

0.3

0.2

0.1

0 10

15

20

25

30

35

Feed inlet pressure, psig FIGURE 8.6 Comparison of computational fluid dynamic predicted water split with experimental measurements at different pressures and spigots in the 75 mm conventional hydrocyclone.

It can be observed that the positive values of static pressure increased and the negative values decreased, indicating an increase in pressure difference with an increase in velocity. This indicates that a larger pressure drop (also includes a larger low-pressure region) may increase the diameter of the air core.

Computational fluid dynamic modeling of hydrocyclones Chapter | 8 200,000

301

15

160,000

12

120,000

9 80,000

6 40,000

5 psig 15 psig 25 psig

3

5 psig 15 psig 25 psig

0 -40,000

0

200,000

15

160,000

12

120,000

9 800,00

6 400,00

3

0

0

-400,00

Mean Tangential velocity

Mean static pressure

15 200,000

12 160,000

9 120,000

6

80,000

3

40,000 0 -0.03

-0.02

-0.01

0 0

0.01

0.02

0.03

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

-40,000

FIGURE 8.7 Variation of computational fluid Dynamic predicted mean static pressure and mean tangential velocity at 5, 15, and 25 psig pressure with 15 mm spigot.

The increased air core diameter reduces the flow area, which results in a reduced water split to the underflow. Higher pressure drop directly affects the tangential velocity, as shown in Fig. 8.7. The mean tangential velocity and mean static pressure profiles predicted by CFD for different spigot diameters (10, 12.5, and 15 mm spigot) at 15 psig are displayed in Fig. 8.8. An increase in the mean static pressure and mean tangential velocity with an increase in the spigot diameter can be seen. A slight shift in tangential velocity towards the wall can be observed. This indicates an increase in air-core diameter. The size of air core measured using the high-speed video (HSV) and electrical resistance tomography (ERT) at different pressures and spigot diameters were used to validate the numerical air-core predictions by VOF model. The variation of air-core diameters at various pressures for a spigot diameter of 20 mm is displayed

302

Mineral Processing 12

120,000 90,000

9

60,000 6 30,000 3 0

10 mm 12.5 mm 15 mm

-30,000 120,000

10 mm 12.5 mm 15 mm

0 12

100 mm

90,000

9

60,000 6 30,000 3

0

200 mm 0

-30,000

Mean Tangential velocity, m/s

Mean static pressure, Pa

12

90,000

9

60,000

6

30,000

415 mm 3

0 -0.0375

-0.025

-0.0125

0

0.0125

0.025

0.0375 0

-30,000

Radial position, m

-0.0375

-0.025

-0.0125

0

0.0125

0.025

0.0375

Radial position, m

FIGURE 8.8 Variation of computational fluid dynamic predicted mean static pressure and mean tangential velocity at 15 psig pressure with 12.5, 15, and 17.5 mm spigot.

in Fig. 8.9. The mean error between CFD and HSV was estimated as 13.48% with a minimum error of 2.4% at 25 psig and a maximum error of 33.59% at 15 psig. The over prediction of air-core diameter may be the reason for the deviations in water split at intermediate pressures. Similarly, the average error between CFD and ERT was calculated as 5.8% with a minimum error of 1% at 30 psig and a maximum error of 11.3% at 5 psig. Fig. 8.10 shows the variation of air-core diameter with spigot diameters

Computational fluid dynamic modeling of hydrocyclones Chapter | 8

303

FIGURE 8.9 Cross validation of computational fluid dynamic predicted air core diameters against electrical resistance tomography and HSV measured air core diameters for different feed pressures with 25 mm vortex finder and 20 mm spigot of a 75 mm hydrocyclone.

FIGURE 8.10 Cross-validation of computational fluid dynamics-predicted air-core diameters against electrical resistance tomography and HSV measured air-core diameters for different spigots at 15 psig pressure with 25 mm vortex finder of a 75 mm hydrocyclone.

304

Mineral Processing

at 15 psig pressure and 25 mm vortex finder diameter. The predictions from the CFD model were similar to the earlier predictions, i.e., the diameter of the aircore increased with an increasing spigot diameter. CFD model slightly overpredicted the air-core diameter. The average percentage of error between HSV, ERT, and CFD was calculated as 7.82% and 8.57%, respectively.

8.3.2.1 Turbulence intensity (TI) Turbulent fluctuations inside hydrocyclones are expected to be significant due to the inherent turbulent flow of the fluid with Reynolds number varying between 105
107; Also, it is enhanced by the collision of the inlet stream with the rotating stream and flow reversal near the spigot zone. Turbulence is also directly related to large velocity gradients found inside cyclones (Brennan, 2006). Turbulence intensity (TI) is defined as the ratio of root mean square velocity of fluctuations (u’) to mean velocity (uavg) as shown in Eq. (8.27). TI 5

u0 uavg

ð8:27Þ

The predicted turbulence intensity profiles inside the 75 mm hydrocyclone using LES turbulence model is displayed in Fig. 8.11. High-turbulence intensities are observed inside the hydrocyclone especially near the air-core and towards the wall. High turbulence is visible near the flow reversal zone in the conical section at its bottom because of flow mixing. To quantify the effect of turbulence on the particle separation, an index called the dispersion index (Idis) was formulated.

(A) 2.00e-01 1.90e-01

(B) 0.4

1.80e-01 1.70e-01

150 mm

1.60e-01

1.20e-01 1.10e-01 1.00e-01 9.00e-02 8.00e-02 7.00e-02 6.00e-02 5.00e-02 4.00e-02 3.00e-02 2.00e-02 1.00e-02 0.00e+00

300 mm

0.3

Turbulence Intensity

1.50e-01 1.40e-01 1.30e-01

450 mm 0.2

0.1

0 0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Radial Position, mm

FIGURE 8.11 (A) Turbulence intensity contour and (B) radial variation of turbulence intensity at different axial positions in a 75 mm laboratory hydrocyclone.

Computational fluid dynamic modeling of hydrocyclones Chapter | 8

305

8.3.2.2 Turbulent dispersion of particles Dispersion index is the ratio of dispersion to agglomeration energy per unit of time that could be used as a measurement for particle dispersion (Roco, 1990). This technique quantifies the importance of turbulent dispersion force of particles to motion of particles by gravitational force. Classification energy (centrifugal force) is taken as the agglomeration energy in the case of hydrocyclones. This classification energy further can be articulated as particle diameter multiplied by classification force. Particle dispersion was predicted using this method (Roco, 1990; Vakamalla et al., 2014, Vakamalla and Mangadoddy, 2017) for the 75 mm laboratory hydrocyclone. Roco (1990) demonstrated the importance of turbulent dispersion force in classification of particles based on particle length scale and eddy size. The dispersion index is calculated as shown in Eq. (8.28). If the Idis value is less than 1, then the centrifugal forces dominate the particle behavior. If the Idis value is greater than 10, dispersion force drives the particle behavior. Using the above criterion, the dispersion levels were calculated which are analyzed in the following section.   2 u ri νi  Idis 5  ð8:28Þ dp ρ p 2 ρ m where vi is the tangential velocity at a radius ri, u is the root mean square (RMS) radial velocity, dp is the diameter of the particle, ρm and ρp are the mixture and particle density. The mean and turbulent flow field predicted by CFD (based on the LES model) was used to calculate the dispersion index for 1
100 μm silica particles with a density of 2650 kg/m3 in a 75 mm laboratory hydrocyclone. The calculated dispersion index profiles along the radius are shown in Fig. 8.12. The dispersion index for fine particles (1 μm) is above one. This states that fine particles are completely dominated by dispersion forces. As the particle size increases, the values of dispersion index fall below one (check 50 μm). This indicates that separation of bigger size particles is controlled by centrifugal forces. Industrially, hydrocyclones are operated at high-feed solids content. Therefore, a modified ASM multiphase model corrected for solids content was used to predict the effect of different solids content in feed for the 75 mm hydrocyclone. To show the importance of additional forces and rheology, especially at high solids concentration, multiphase simulations were also carried out with DPM and standard ASM models. Results were analyzed and validated. The cut size and diameter of the air core were measured using ERT and the radial volume fractions were compared. An attempt was also made to explain the reasons behind the increase in cut size through the LZVV analysis using the equilibrium orbit theory.

306

Mineral Processing

FIGURE 8.12 Dispersion index variation of different particles in a 75 mm conventional cyclone.

8.4

Multiphase flow predictions

In this section, the simulations were conducted with homogeneous feed in two different 75 mm hydrocyclone designs with different feed solids concentration, that was varied from 10 wt.% to 50 wt.%. For the homogeneous feed, the particles of different sizes with uniform density were considered. The complete feed details are provided in numerics section.

8.4.1

Conventional hydrocyclone: homogeneous feed

Initially, the DPM, the standard ASM model (Manninen et al., 1996) available in Fluent and the modified ASM model was used to model the classification efficiency curve of the 75 mm (Hsieh, 1988) hydrocyclone operating at low feed solids concentration (10.47 wt.%). The classification curves were compared against Hsieh’s (1988) experiment as displayed in Fig. 8.13. It can be seen that the predictions from the DPM model deviate from experimental measurements. The standard ASM model could predict fine particle recovery with good accuracy. However, the recovery of the coarse size (25 and 35 μm) fractions to underflow was underpredicted. The modified ASM model (explained later in the section) could predict the recoveries very close to the experimental data.

8.4.2

Laboratory hydrocyclone: homogeneous feed

Multiphase simulations are also performed in the 75 mm laboratory hydrocyclone using the DPM and standard ASM model coupled with the LES

Computational fluid dynamic modeling of hydrocyclones Chapter | 8

307

FIGURE 8.13 Comparison of discrete particle model, standard and modified algebraic slip mixture model predicted particle recovery with experimental measurements for 10.47 wt.% feed solids (Hsieh, 1988).

turbulence model for 10 wt.% feed solids at 15 psig pressure (Kumar Reddy, 2016). The CFD model predictions are compared against experimental data and are depicted in Fig. 8.14. A significant deviation is observed with the DPM model. The cause for this could be attributed to the DPM model neglecting the particle
particle interactions and the effect of particle volume fraction on the liquid phase. The predictions of the standard ASM model are in line with those observed earlier. At a feed solids content of 10%, the discrepancies in the predictions by the standard mixture model may be related to unaccounted slurry viscosity and particle
fluid interactions. As particle concentration increases, the slurry viscosity is also expected to increase. As slurry viscosity increases, the particles may accumulate near the apex region and the particles follow a “hindered settling” motion. In general, the standard mixture model assumes the particle velocity equals its terminal velocity which is true when the particles are “free settling.” Also, in the standard ASM model, the effect of particle concentration is accounted for by the granular viscosity model (Ding and Gidaspow, 1990) that holds reasonably well for Newtonian fluids. The discrepancies predicted by the standard ASM model may be believed due to the above mentioned model limitations in not correctly accounting for particle
fluid interactions.

8.4.2.1 Effect of feed solids concentration Further, simulations were done with the modified ASM model (modified with the aforementioned rheology and additional lift and drag forces) at 30

308

Mineral Processing

FIGURE 8.14 Discrete particle model, Standard and modified algebraic slip mixture model predicted efficiency curves compared against experimental classification curve for 10 wt.% solids with 12.5 mm spigot.

and 50 wt.% feed solids concentration in 75 mm cyclone with 12.5 mm spigot diameter. The modified ASM model-predicted performance curves were compared among and against experimental measurements at 10, 30, and 50 wt.% solids concentration. Corresponding results are shown in Fig. 8.15. As expected, an increase in cut size was observed with an increase in feed solids concentration. A slight reduction in the sharpness of separation was noted. The predicted particle classification curves for 10% and 30% solids by weight closely matched the experimental data for all the spigot diameters. Slight deviation in the cut size, an under prediction of fine particle recovery, and sharpness of separation was observed at high solids concentration (50 wt.% solids). This could be due to not accounting for the turbulent dispersion forces in the modified ASM model at high solids concentration. The tangential velocity, which is the fundamental reason for separation inside the hydrocyclone, is strongly affected by the feed solids concentration. Increasing feed solids concentration, affects the velocity distribution in the hydrocyclone adversely, thus reducing the differential motion of particles, and worsening particle separation. Fig. 8.16 displays the contours of steady-state volume fraction for different particle sizes for various feed solids content (10, 30, and 50 wt.%). In all these cases, 4.25 μm particles were dispersed throughout the cyclone. When the solids

Computational fluid dynamic modeling of hydrocyclones Chapter | 8

309

FIGURE 8.15 Modified Algebraic slip mixture model predicted d50 compared with experiments in a 75 mm laboratory hydrocyclone with 12.5 mm spigot at different solids concentration.

FIGURE 8.16 Modified algebraic slip mixture model predicted volume fraction contours of 3.35, 10.25, 19.37, 28.27, 48, and 80 μm particles for 10, 30, and 50 wt.% solid concentrations.

310

Mineral Processing

concentration in feed was 10%, the 10.25 μm particles were smaller than the cut size (B16 μm). Therefore, maximum portion of these particles reported to the overflow. The remaining particle sizes were larger than the cut size and escaped through the underflow. In 30% case, the cut size (B33 μm) was higher than 3.35, 10.25, 19.37, and 28.27 μm size. Hence, all these particles had a greater chance to escape through the overflow compared to the 10% case. Along with the 4.25 μm particles, the 10.25 μm particles were also completely dispersed in cyclone. The 19.37 μm particle, which were found closer to the wall in the 10% case, was also dispersed locally although more particles reported to the over flow. The 48 and 80 μm particles were carried away by centrifugal forces to the underflow. In the 50% case, the cut size (B46 μm) was much higher than the most of the particles. Hence, higher percentage of the 3.35, 10.25, 19.37, and 28.27 μm particles is moved towards the overflow. Another observation was that, the particle (let’s say 19.37 μm) which behaved as a coarse particle in 10 wt.%, behaved as a fine particle in the 50 wt.% solids case. From the studies, it could be concluded that with increase in solids concentration, the effect of tutrbulent dispersion on particle sizes also incraesed. Fig. 8.17 displays the viscosity contours of 10%, 30%, and 50% solids concentration. An increase in the viscosity is observed with an increase in solids content. High viscosities are observed in the conical section compared to the cylindrical section as the solids content is high in conical section. The feed

FIGURE 8.17 Steady state viscosity contours (in cP) for 10, 30, and 50 wt.% solid concentrations in 75 mm cyclone.

Computational fluid dynamic modeling of hydrocyclones Chapter | 8

311

solid concentration strongly influences the size of the air core; the size decreases as the percent of solids increase in the feed. This is due to the effect of viscosity on air core diameter (Castro and Concha, 1996). A reduction in the air core can be seen in Fig. 8.17. The reduction of air core size is basically attributed to the displacement of air volume due to an increased volume of granular solids. In other words, the increase of solids near the underflow zone represents higher slurry viscosity than in the water-only case. A rise in the viscosity of the medium reduces the tangential velocity at a smaller distance from the center, leading to a lower pressure drop over the cyclone, which in turn decreases the air-core diameter by allowing extra liquid/slurry into the center zone. This might be one of the reasons for the increase of water split with an increase in feed solids concentration.

8.4.2.2 Effect of solids concentration on equilibrium radii To assess the fundamental reasons behind the change in cut size with solids content, their effect on the equilibrium radii was studied. The equilibrium radii of different size particles in a 75 mm laboratory hydrocyclone for 10 wt.% and 30 wt.% feed solids content is plotted in Figs. 8.18 and 8.19. Equilibrium radius is defined as the radius of an orbit at which the particle tends to rotate after attaining terminal velocity inside the hydrocyclone. The loci of equilibrium

FIGURE 8.18 The particle equilibrium position of different size particles compared to LZVV in a 75 mm cyclone for 10 wt.% feed solids concentration (Vakamalla and Mangadoddy, 2021). From Vakamalla, T.R., Mangadoddy, N., 2021. Comprehensive dense slurry CFD model for performance evaluation of industrial hydrocyclones. Ind. Eng. Chem. Res. 2021, 60, 12403
12418. Available at: https://doi.org/10.1021/acs.iecr.1c01244.

312

Mineral Processing

FIGURE 8.19 The particle equilibrium position of different size particles compared to LZVV in a 75 mm cyclone for 30 wt.% feed solids concentration (Vakamalla and Mangadoddy, 2021). From Vakamalla, T.R., Mangadoddy, N., 2021. Comprehensive dense slurry CFD model for performance evaluation of industrial hydrocyclones. Ind. Eng. Chem. Res. 2021, 60, 12403
12418. Available at: https://doi.org/10.1021/acs.iecr.1c01244.

radius at different axial positions can be called as an equilibrium envelope. This equilibrium radius depends on the particle size and density. In a hydrocyclone, the LZVV is defined as the loci of all the zero axial velocity points. Generally, coarser particles have an equilibrium radius greater than the LZVV and pass through the underflow and finer particles have an equilibrium radius smaller than the LZVV and escapes through the overflow. Particles with sizes closer to the cut size usually have an equilibrium radius equal to LZVV and can report either to the overflow or the underflow. From Fig. 8.18, when the feed solids concentration is 10%, it can be observed that fine particles (3.35 μm) have an equilibrium radius less than LZVV, coarse particles (19 μm) have an equilibrium radius greater than LZVV, and near cut-size particles (10.25 μm) show an equilibrium radius equal to LZVV. When the solids concentration increased to 30 wt.%, the LZVV shifts toward the wall. Similar to the former case, fine particles (3.35 μm) have an equilibrium radius smaller than LZVV and report to overflow. The 10.25 and 19.37 μm particles also have a lower equilibrium radius than LZVV, which is different from the 10 wt.% case. The 19.37 μm particles which were behaving as coarse particles in 10 wt.% case behave as fine particles in 30 wt.% case. Near cut-size particles (28.27 μm) show an equilibrium radius similar to LZVV. The equilibrium envelop of 48 and 80 μm particles is away from the LZVV and is expected to report to the underflow.

Computational fluid dynamic modeling of hydrocyclones Chapter | 8

8.4.3

313

Laboratory hydrocyclone—heterogeneous feed

Natural ore in any mineral-processing classification circuit is a multicomponent feed (Kumar Reddy, 2016; Padhi et al., 2022). Unlike, single density particles, the fully liberated elements from the ore act as individual components. Hence, the particle dynamics during classification change based on the material properties. To study the multicomponent effect during hydrocyclone classification, a representative artificial mixture was utilized (i.e., silica and magnetite) at varying proportions. The silica: magnetite proportion was varied at five different levels, (100:0; 90:10; 80:20; 50:50; 0:100).

8.4.3.1 Effect of component proportions Based on the difference in the densities of component and the component proportions based on the liberation size, the efficiency of the hydrocyclone was observed to be deviating from the “overall efficiency.” “Overall efficiency” is the mixture/bulk separation performance of the equipment irrespective of the individual components. However, as the particle separation is a key function of particle properties, the evaluation of separation performance of individual components is essential. Fig. 8.20 represents the separation performance of silica in a mixture feed system, with an increasing

FIGURE 8.20 Illustration of separation performance curve for silica particles from mixture at various silica to magnetite proportion with pure components (100:0 and 0:100) in the feed system; for 75 mm hydrocyclone (Padhi et al., 2019). From Padhi, M., Mangadoddy, N., Sreenivas, T., Vakamalla, T.R., Mainza, A.N., 2019. Study on multicomponent particle behavior in a hydrocyclone classifier using experimental and computational fluid dynamics techniques. Sep. Purif. Technol. 229, 115698. Available at: https://doi.org/10.1016/j.seppur.2019.115698.

314

Mineral Processing

proportion of magnetite. Numerically predicted particle volume fraction contours using the bicomponent feed slurry are displayed in Fig. 8.21. It can be noted that the presence of the magnetite (i.e., heavy) particles towards the wall is more, displacing the coarse silica particles towards the center of the flow region (Padhi et al., 2019). Similarly, in a feed mixture where the heavy component composition increases, the particle misplacement becomes evident near the vortex finder through short-circuiting, with the coarse particles misplacing to overflow. The interaction of the particle in a mixture can be evaluated utilizing the interaction coefficient (IC) (see Fig. 8.22), defined as, IC 5

d50i 2 d50pc d50pc

ð8:29Þ

where, d50i and d50pc represent the corrected cut-size for component in mixture and pure component cut-size at same operating and design parameters.

FIGURE 8.21 Predicted volume fraction contours of different size particle (i) 2.75 μm, (ii) 11 μm, (iii) 22 μm and (iv) 44 μm when it was treated as (A) pure silica (B) mixture-based silica (C) pure magnetite (D) mixture-based magnetite, in a 75 mm hydrocyclone with 25 mm vortex finder and 12.5 mm spigot (Padhi et al., 2020). From Padhi, M., Kumar, M., Mangadoddy, N., 2020. Understanding the bicomponent particle separation mechanism in a hydrocyclone using a computational fluid dynamics model. Ind. Eng. Chem. Res. 59, 11621. Available at: https://doi.org/ 10.1021/acs.iecr.9b06747.26.

Computational fluid dynamic modeling of hydrocyclones Chapter | 8

315

FIGURE 8.22 Interaction coefficient variation for increasing magnetite proportion in the feed system; for 75 mm hydrocyclone (Padhi et al., 2019). From Padhi, M., Mangadoddy, N., Sreenivas, T., Vakamalla, T.R., Mainza, A.N., 2019. Study on multicomponent particle behaviour in a hydrocyclone classifier using experimental and computational fluid dynamics techniques. Sep. Purif. Technol. 229, 115698. Available at: https://doi.org/10.1016/j.seppur.2019.115698.

This parameter indicates the fractional change in cut-size for the component due to its presence in the mixture.

8.4.3.2 Effect of spigot diameter and solids concentration The spigot or apex in the hydrocyclone regulates the overall capacity. Fahlstrom (1963) analyzed the decrease in the capacity of hydrocyclone with increasing spigot diameter. He also studied the effect of solids concentration at apex and proposed the “crowding effect” concept. As the solids concentration increases, the hydrocyclone capacity reduces and the cut-size increases. Using statistical analysis, Lynch and Rao (1975) proposed log10 Q parameter relations, which increases linearly with spigot diameter to a certain value and then decreases linearly with increase in feed solids. The effect of spigot diameter in a system is usually considered along with the effect of vortex finder diameter, that is, apex to vortex ratio. Ghodrat et al. (2013), after conducting studies at different solids concentrations observed that the separation efficiency decreases inversely with feed solids concentration, only for coarse particles. An increase in the solids from 4.14% to 30% and a simultaneous decrease in apex to vortex ratio from 0.33 to 0.1,3 tend to increase shortcircuiting. Irrespective of the other operating and design variables, Perez et al. (2018), from his CFD studies, proposed to maintain an apex to vortex finder diameter ratio greater than 0.5 to avoid roping. Also, a volume ratio (Qu/Qo) . 0.5 would ensure that the underflow would always be in spray condition irrespective of the apex energy dissipation.

316

Mineral Processing

TABLE 8.2 Analysis of the effect of turbulence on particles. % Solids

Parameter Spigot diameter, mm

12.5

15

17.5

12.5

30

Cut size, μm,

25.5

19.6

15.6

16

Alpha Solids recovery, % Beta

10

Cut size, μm Alpha Solids recovery, % Beta

Silica

3.23 62.7 0.24

16.9 3.51 59.3 0.29

3.04 69.6 0.22

15.5 3.14 61.4 0.20

Magnetite

2.51 74.2 0.17

13.9 2.78 65.4 0.18

2.42 74.3

15 8.1 2.17 80.7

17.5 8.7 1.58 87.3

0.56

0.42

0.33

9.6

9.1

6.6

2.56

2.26

1.98

68.2 0.39

77.5 0.32

85.1 0.29

Source: From Padhi, M., Mangadoddy, N., Mainza, A.N., Anand, M., 2021. Study on the particle interaction in a hydrocyclone classifier with multicomponent feed blend at a high solids content. Powder Technol. 393, 380
396. Available at: https://doi.org/10.1016/j.powtec.2021.07.063

In a multicomponent feed system, the solids recovery to the underflow significantly changes each component. Due to high centrifugal forces, the heaviest/densest of all particles would occupy the outer most periphery in the segregated layers inside the flow regime. Hence, it would be present outside the locus of zero-vertical velocity, reporting to the underflow. At a smaller spigot diameter, a significant portion of the mixture slurry is expected to move towards the inner vortex resulting in coarse particles being swept into the stream, reporting to the overflow. As the spigot diameter increases, the probability of more particles reaching the loci of flow reversal diminishes. Hence, this phenomenon results in more solids reporting to the underflow. The influence of the spigot diameter on the cut size and solids recovery to the underflow of the silica and magnetite components at two different solids concentrations (10% and 30%) are shown in Table 8.2 (Padhi et al., 2021).

8.4.4

Analysis of the effect of turbulence on particles

8.4.4.1 Homogeneous feed Turbulent mixing number (Nt) which is the ratio of turbulent-mixing acceleration to the centrifugal acceleration is considered to analyze the effect of feed solids content on the turbulent dispersion behavior of different particles. It is hypothesized that turbulent mixing becomes significant when Nt 5 1

Computational fluid dynamic modeling of hydrocyclones Chapter | 8

317

and is unimportant when Nt ,, 1 (Padhi et al., 2020). The multiphase simulations were performed in a 75 mm laboratory hydrocyclone at 10 and 30 wt.% for calculating turbulent-mixing number. The turbulent-mixing number calculated for 3.35 and 10.25 μm particles at two different feed solids content at an axial position of 300 mm from the roof of hydrocyclone is compared with the water-only case (i.e., without solids) and shown in Fig. 8.23. As expected, the effect of turbulent dispersion force for the 10.25 μm particles is lower compared to 3.35 μm particles. A significant difference in the estimated Nt is observed at 30 wt.% feed solids content compared to the other two cases. The Nt calculated for both the particle sizes is lower than one at this solids content. This may indicate that the separation of these particles is strongly influenced by classification force in the 30 wt.% cases, in contrast to the others. When the feed solids content is 10%, the particles are mainly influenced by turbulent dispersion. To find out the reasons behind the particle behavior at different feed solids content, turbulent intensity and mean viscosity are plotted at two different axial positions and illustrated in Fig. 8.24. High-turbulent intensity is observed near the air core in all the cases. From Fig. 8.24, a slight rise

3.35 μm

100

10.25 μm

100 10

10 1

1

Nt 0.1

Nt 0.1 0.01

0.01

Two-Phase

Two-Phase 10 Wt%

0.001

10 Wt%

0.001

30 Wt%

30 Wt% 0.0001

0.0001 0

0.005

0.01

0.015 Radius, m

0.02

0.025

0

0.03

0.005

0.01

0.015 Radius, m

0.02

0.025

0.03

FIGURE 8.23 Comparison of Nt prediction for water, limestone slurry in 10% and 30% of solids (by wt.%) for 3.35 and 10.25 μm particles.

0.4

0.6

150 mm

300 mm Two-Phase

Two-Phase

10%

0.3

Turbulent Intensity

Turbulent Intensity

10% 30%

0.2

0.1

0.45

30%

0.3

0.15

0

0 0

0.005

0.01

0.015

0.02

0.025

Radial Position, m

0.03

0.035

0.04

0

0.005

0.01

0.015

0.02

0.025

0.03

Radial Position, m

FIGURE 8.24 Comparison of turbulent Intensity for only water, and slurry with 10% and 30% solids (wt.%) at two axial positions (i.e., 150 and 300 mm) from roof of 75 mm hydrocyclone.

318

Mineral Processing

6

6

150 mm

300 mm

5

5

Two-Phase 10%

Two-Phase 10%

4

30%

30%

Viscosity, cP

Viscosity, cP

4 3 2

3 2 1

1

0

0 0

0.005

0.01

0.015

0.02

0.025

Radial Position, m

0.03

0.035

0.04

0

0.005

0.01

0.015

0.02

0.025

0.03

Radial Position, m

FIGURE 8.25 Comparison of viscosity for only water, and slurry with 10% and 30% solids (wt%) at two axial positions (i.e., 150 and 300 mm) from roof of 75 mm hydrocyclone.

in turbulence intensity can be observed with an increase in solids content. A substantial difference in turbulent intensity is visible near the air core at high-feed solids content. This reconfirms that the air-core is more dynamic at higher feed solids content. The high-turbulence intensity and dilute flow stream in the forced vortex near the air core could be one of the causes for the high Nt near the air core. Although the turbulence levels are slightly higher at 30 wt.%, the 3.35 and 10.25 μm particles are unaffected by turbulent dispersion, unlike the other two cases. To investigate further, the predictions of mean viscosity are plotted at two different axial positions and depicted in Fig. 8.25. A significant rise in the mean viscosity at 30% feed solids by wt. can be seen from the same figure. The increased viscosities reduce the effect of turbulent dispersion on the smaller size particles at high feed solids content. This could be one of the reasons behind the reduction in the fish-hook phenomena at increased feed solids content.

8.4.4.2 Heterogeneous feed The particle dynamics during classification are determined by the force analysis acting on each particle to determine the locus of its position. Various forces acting on particles during the classification in a hydrocyclone include centrifugal force (Fc Þ, drag force (Fd Þ (Hsieh and Rajamani, 1991), pressure gradient force (Fp Þ, buoyant force (Fb Þ, Saffman-lift force (FSL Þ, additional mass force (FAM Þ, Magnus force(FM ), basset force (FBT ) (Kraipech et al., 2005), and turbulent dispersion force (FTD ). As per literature (Kraipech et al., 2005; Zhang et al., 2017), based on the force analysis, the dominating forces were found as the centrifugal, drag, and pressure forces. Based on the particle properties, and the significant forces acting on the particle, the particles report to either of the outflows. Similar to turbulent-mixing number, drag number (ND), another non-dimensional number which is, the ratio of acceleration due to turbulent dispersion to centrifugal acceleration can be

319

Computational fluid dynamic modeling of hydrocyclones Chapter | 8 2.75 μm 5.5 μm 11 μm 22 μm 44 μm

1000

NDpuresilica at 600 mm

1E-4

10 1 0.1 0.01 1E-3 1E-4 0.000

Aircore

NDpuresilica at 150 mm

100

0.005

0.010

0.015

0.020

0.025

0.030

0.035

1E-5

1E-6

1E-7

1E-8

Wall

LZVV

2.75 μm 5.5 μm 11 μm 22 μm 44 μm

1E-3

0.040

Aircore

10000

Radial Position (m)

Radial Position (m) (B)

(A) 2.75 μm 5.5 μm 11 μm 15.55 μm 22 μm 44 μm

100

1

1E-6

0.1 0.01 1E-3 1E-4 1E-5

1E-7 1E-8 0.000

1E-7 1E-8 1E-9 1E-10

0.005

LZVV 0.010

0.015

0.020

0.025

Radial Position (m) (C)

1E-111

Wall 0.030

0.035

0.040

Aircore

1E-6

Aircore

NDpuremag at 150 mm

10

2.75 μm 5.5 μm 11 μm 15.55 μm 22 μm 44 μm

1E-5

NDpuremag at 600 mm

1000

Wall

LZVV

0.0040 0.0045 0.0050 0.0055 0.0060 0.0065 0.0070 0.0075

0.0040

LZVV 0.0045

Wall 0.0050

0.0055

0.0060

0.0065 0.0070

0.0075

Radial Position (m) (D)

FIGURE 8.26 Nondimensional drag acceleration (ND) for silica and magnetite at 10 wt.% solids at axial position of 150 mm [(A) and (C)] and 600 mm [(B) and (D)].

computed. If ND . 1, particle drag force dominates, indicating a higher probability of particles migrating towards the forced vortex/overflow. The accelerations are determined by extracting the data from the converged, mean values of hydrocyclone simulation. Fig. 8.26 illustrates the ND values for magnetite and silica particles at 10 wt.% solids in a 3-inch hydrocyclone at two different axial locations. At an axial height of 150 mm, the ND for the silica having a density of 2650 kg/m3, attains a higher value in comparison to magnetite, that has approximately double the density (4500 kg/m3) of silica particles. Hence, the majority of the silica fines report to the overflow and vice-versa for the coarse particles and magnetite. All particles attained a scale of ND , 10
1 at 600 mm, which confirms the negligible influence of drag force after flow reversal in the apex zone of the cyclone. A similar analysis has been presented in Fig. 8.27, illustrating the effect of turbulent dispersion on fines for silica and magnetite separately. The radial comparisons of Nt confirm the dominance of turbulent dispersion over centrifugal forces mainly in the forced vortex region. Along the radius, turbulent dispersion is observed to be dominant only for finer size particles such as 2.75 and 5.5 μm for both the components. Magnetite attains high centrifugal force in the feed chamber and the probability of fines misplacement increases, due to short-circuiting near the vortex finder caused by a high-pressure drop.

320

Mineral Processing 2.75 μm 5.5 μm 11 μm 22 μm 44 μm

1000

0.01

10 1 0.1 0.01

Aircore

1E-3 1E-4 0.000

0.010

0.015

0.020

0.025

1E-3 1E-4 1E-5 1E-6 1E-7 1E-8 1E-9 1E-10

Wall

LZVV

0.005

2.75 μm 5.5 μm 11 μm 22 μm 44 μm

1 0.1

Ntpuresilica at 600 mm

Ntpuresilica at 150 mm

100

10

1E-11

0.030

Aircore

10000

Radial Position (m)

Radial Position (m)

(A)

(B)

1000000

100 10

1E-3

1 0.1 0.01 1E-3

1E-4

0.000

1E-4 1E-5 1E-6 1E-7 1E-8 1E-9

0.005 0.010

1E-10

LZVV 0.015

0.020

0.025

Radial Position (m) (C)

Wall 0.030

0.035

1E-11 0.040

Aircore

1E-7 1E-8

Aircore

Ntpuremag at 150 mm

1000

0.01

Ntpuremag at 600 mm

10000

2.75 μm 5.5 μm 11 μm 15.55 μm 22 μm 44 μm

0.1

2.75 μm 5.5 μm 11 μm 15.55 μm 22 μm 44 μm

100000

1E-5 1E-6

Wall

LZVV

0.0040 0.0045 0.0050 0.0055 0.0060 0.0065 0.0070 0.0075

0.035 0.040

Wall

LZVV

0.0040 0.0045 0.0050 0.0055 0.0060 0.0065 0.0070 0.0075

Radial Position (m) (D)

FIGURE 8.27 Nondimensional turbulence dispersion acceleration (Nt) for silica and magnetite at 10wt.% solids at axial position of 150 mm [(A) and (C)] and 600 mm [(B) and (D)].

8.5

Conclusions

Numerical modeling of turbulent fluid flow and particle separation in hydrocyclones has been discussed using a multiphase CFD model. As discussed in the earlier chapters, the literature review on the CFD modeling of the cyclone clearly suggested that the computational focus should be to model the threedimensional flow in a hydrocyclone using the RSM/LES turbulence model. Since most of the multiphase models have limited capability in accounting for particle
particle interactions, a more comprehensive numerical method has been suggested, i.e., modifying the algebraic slip mixture model to simulate solids flow in hydrocyclones when the feed solids concentration varies from moderate (20 2 30 wt.%) to high (50
60 wt.%). Explicit models that account for hindered settling and turbulent dispersion in industrial cyclones, especially with high solids concentration has been investigated. Details of the LES turbulence model followed by VOF, DPM, and modified ASM multiphase models adapted for hydrocyclones, are presented. Further, this chapter validates the performance efficiency of hydrocyclones treating homogeneous and heterogeneous feed mixture from moderate to dense feed solids. The detailed force analysis of the cyclone both for single component and bicomponent feed systems is also presented. The mechanism of bicomponent particle classification in hydrocyclones is elucidated utilizing the CFD model.

Computational fluid dynamic modeling of hydrocyclones Chapter | 8

321

Acknowledgements The authors would like to express their sincere thanks to DST-SERB, India (EMR/2016/ 00378/046), IIT Hyderabad, NIT Calicut, and the Ministry of Education for the funding and resources support to undertake the numerical studies on hydrocyclones.

Abbreviations ASM CFD DPM ERT LES PRESTO RANS RSM VOF

algebraic slip mixture model computational fluid dynamics discrete particle model electrical resistance tomography large eddy simulation pressure staggering option Reynolds-averaged Navier
Stokes Reynolds stress model volume of fluid

References Bradley, D., 1965. The Hydrocyclone. Pergamon Press Ltd, London.. Brennan, M., 2006. CFD simulations of hydrocyclones with an air core: comparison between large eddy simulations and a second moment closure. Chem. Eng. Res. Des. 84, 495
505. Castro, O., Concha, F., 1996. Air core modeling for an industrial hydrocyclone. Hydrocyclones 96, 229
240. Ding, J., Gidaspow, D., 1990. A bubbling fluidization model using kinetic theory of granular flow. AlChE J. 36, 523
538. Driessen, M.G., 1945. The use of centrifugal force for cleaning fine coal in heavy liquids and suspensions with special reference to the cyclone washer. J. Inst. Fuel 18, 33
50. Fahlstrom, P.H., 1963. Studies of the hydrocyclone as a classifier, Proceedings, IV International Mineral Proccessing Congress Cannes. Pergamon, London, 87
112. Ghodrat, M., Kuang, S.B., Yu, A.B., Vince, A., Barnett, G.D., Barnett, P.J., 2013. Computational study of the multiphase flow and performance of hydrocyclones: effects of cyclone size and spigot diameter. Ind. Eng. Chem. Res. 52, 16019
16031. Hirt, C.W., Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201
225. Hsieh, K.T., 1988. Phenomenological model of the hydrocyclone: model development and verification for single-phase flow. Int. J. Miner. Process. 22, 223
237. Hsieh, K.T., Rajamani, R.K., 1991. Mathematical model of the hydrocyclone based on the physics of fluid flow. AlChE J. 37, 735
746. Kraipech, W., Nowakowski, A.V., Dyakowski, T., Suksangpanomrung, A., 2005. An investigation of the effect of the particle
fluid and particle
particle interactions on the flow within a hydrocyclone. Chem. Eng. J. 111, 189
197. Reddy, V.T.S.R.K., 2016. Developing a comprehensive CFD model for dense slurry flow in industrial cyclones, (PhD thesis), Indian Institute of Technology Hyderabad, India. Lynch, A.J., Rao, T.C., 1975. Modelling and Scale Up of Hydrocyclone Classifiers, XI IMPC, Cagliari, pp. 9
25.

322

Mineral Processing

Mangadoddy, N., Vakamalla, T.R., Kumar, M., Aubrey, M., 2020. Computational modelling of particle-fluid dynamics in comminution and classification: a review. Miner. Process. Extract. Metall. 129 (2), 145
156. Available from: https://doi.org/10.1080/25726641.2019.1708657. Manninen, M., Taivassalo, V., Kallio, S., 1996. On the Mixture Model for Multiphase Flow. VTT Publications, Finland. Mei, R., 1992. An approximate expression for the shear lift force on a spherical particle at finite reynolds number. Int. J. Multiph. Flow 18, 145
147. Narasimha, M., 2010. Improved computational and empirical models of hydrocyclones, (PhD thesis), JKMRC, University of Queensland, Australia. Narasimha, M., Brennan, M.S., Holtham, P.N., 2012a. CFD modeling of hydrocyclones: prediction of particle size segregation. Miner. Eng. 39, 173
183. Narasimha, M., Mainza, A.N., Holtham, P.N., Brennan, M.S., 2012b. Air-core modelling for hydrocyclones operating with solids. Int. J. Miner. Process. 102
103, 19
24. Narasimha, M., Mainza, A.N., Holtham, P.N., Powell, M.S., Brennan, M., 2014. A semimechanistic model of hydrocyclones
developed from industrial data and inputs from CFD. Int. J. Miner. Process. 133, 1
12. Orszag, S.A., 1970. Analytical theories of turbulence. J. Fluid Mechanics. J. Fluid Mech. 41, 363
386. Padhi, M., Kumar, M., Mangadoddy, N., 2020. Understanding the bicomponent particle separation mechanism in a hydrocyclone using a computational fluid dynamics model. Ind. Eng. Chem. Res. 59, 11621. Padhi, M., Mangadoddy, N., Mainza, A.N., Anand, M., 2021. Study on the particle interaction in a hydrocyclone classifier with multicomponent feed blend at a high solids content. Powder Technol. 393, 380
396. Padhi, M., Mangadoddy, N., Sreenivas, T., Vakamalla, T.R., Mainza, A.N., 2019. Study on multicomponent particle behaviour in a hydrocyclone classifier using experimental and computational fluid dynamics techniques. Sep. Purif. Technol. 229, 115698. Padhi, M., Vakamalla, T.R., Mangadoddy, N., 2022. Iron ore slimes beneficiation using optimised hydrocyclone operation. Chemosphere 301, 134513. Available from: http://doi.org/ 10.1016/j.chemosphere.2022.134513. 35421443. Pe´rez, D., Cornejo, P., Rodr´ıguez, C., Concha, F., 2018. Transition from spray to roping in hydrocyclones. Miner. Eng. 123, 71
84. Rakesh, A., Kumar Reddy, V.T.S.R., Narasimha, M., 2014. Air-core size measurement of operating hydrocyclone by electrical resistance tomography. Chem. Eng. Technol. 37, 795
805. Roco, M.C., 1990. One equation turbulence modelling of incompressible mixtures N.P. Cheremisinoff (Ed.). Encycl. Fluid Mech. 10, 1
68. Saffman, P.G., 1965. The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385
400. Schiller, L., Naumann, A., 1935. A drag coefficient correlation. Z. Ver. Dtsch. Ing. 77, 318. Smagorinsky, J., 1963. General circulation experiments with the primitive equations. I. The basic experiment. Monthly Weather. Rev. 91, 99
164. Vakamalla, T.R., Kumbhar, K.S., Gujjula, R., Mangadoddy, N., 2014. Computational and experimental study of the effect of inclination on hydrocyclone performance. Sep. Purif. Technol. 138, 104
117. Vakamalla, T.R., Mangadoddy, N., 2017. Numerical simulation of industrial hydrocyclones performance: role of turbulence modelling. Sep. Purif. Technol. 176, 23
39. Vakamalla, T.R., Mangadoddy, N., 2021. Comprehensive dense slurry CFD model for performance evaluation of industrial hydrocyclones. Ind. Eng. Chem. Res. 2021 (60), 12403
12418.

Computational fluid dynamic modeling of hydrocyclones Chapter | 8

323

Wills, B.A., Napier-Munn, T.J., 2006. Wills’ Mineral Processing Technology. ButterworthHeinemann, Oxford, UK. Yakhot, A., Orszag, S.A., Yakhot, V., Israeli, M., 1989. Renormalization group formulation of large-eddy simulations. J. Sci. Comput. 4, 139
158. Zhang, Y., Cai, P., Jiang, F., Dong, K., Jiang, Y., Wang, B., 2017. Understanding the separation of particles in a hydrocyclone by force analysis. Powder Technol. 322, 471.

This page intentionally left blank

Chapter 9

Numerical modeling of dense medium cyclones Teja Reddy Vakamalla1 and Narasimha Mangadoddy2 1

Department of Chemical Engineering, National Institute of Technology Calicut, Kozhikode, Kerala, India, 2Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Sangareddy, Telangana, India

9.1

Introduction

Dense medium cyclones (DMCs) are widely used devices in mineral processing industries to beneficiate coal, iron ore, tin, diamond, gold, lead-zinc, chromite ores, etc., where there is a significant density difference between the coarsely aggregated mineral and gangue particles. DMC uses centrifugal sedimentation to separate particles based on density difference. It provides very efficient separation than other gravity processing methods, especially when the near-gravity material (NGM) is above 10% (Burt and Mills, 1984; Wills and Finch, 2015). The DMC is popular due to its simple structure with high throughput, ability to treat fine particles, relatively small footprint, mechanical simplicity, low maintenance, and operating costs. The first DMC developed by Driessen (1945) and his co-workers at Dutch State Mines (DSM) is the most widely used design for separating clean coal from high ash particles in a size range of 10.5 to 250 mm. Coal particles mixed with magnetite slurry in a ratio (medium to coal) of 4:1 by volume is injected tangentially into the cyclone. Because of the centrifugal force, heavier/ high-density ash particles are transported toward the wall and are discharged through the underflow by a primary free vortex motion. Lighter/low-density coal particles remain in the liquid near the center and are discharged through overflow following a forced vortex. As both outlets are open to atmospheric launders/ducts, a low-pressure region is created at the center, generating the air-core. The presence of different sizes and densities of magnetite and coal particles along with water and the air-core in a highly turbulent Rankine vortex makes the DMC flow very complex. There have been many investigations to understand the physics of the swirling flow and particle dynamics - the assessment of particle separation Mineral Processing. DOI: https://doi.org/10.1016/B978-0-12-823149-4.00006-5 © 2023 Elsevier Inc. All rights reserved.

325

326

Mineral Processing

by experimental techniques, theoretical and semi-empirical approaches. In due course, regression models based on data collected from the pilot and plant-scale DMCs became more successful in predicting process performance for process design and optimization. Notable contributions on mathematical models are of Wood (1990) for coal partitioning and Dungilson (1998) for both coal and mineral separations. However, the models cannot be used to study changes in design parameters. Empirical models also do not indicate why and how changes in cyclone geometry influence separation behavior. Until the late 1990s, despite several attempts the particle separation mechanism in DMC was not fully understood, and research aimed at improving the knowledge on flow physics and particle dynamics continued. Although a number of experimental techniques such as gamma ray tomography (GRT), X-ray tomography and sampling probes were used for mapping the particle density/ concentration inside the DMC, precise experimental measurements of particle, fluid velocities and air-core were difficult. Because of these shortcomings, simulation and design of DMCs using Computational Fuid Dynamics (CFD) gained momentum. Computational modeling, which involves solving fundamental governing equations of fluid flow and particle dynamics is recognized as the best approach to understand the separation mechanism inside industrial DMCs. Of late, the authors, in collaboration with industries, JKMRC and the University of Queensland, have developed a comprehensive CFD model for DMC treating coal. CFD modeling of DMCs has now reached a stage where it is possible to provide plausible and valuable insights into the process (Narasimha et al., 2007a,b; Vakamalla and Mangadoddy, 2015). A detailed review on the CFD modeling of DMC’s can be found in Chapter 7. In this chapter, the authors briefly describe the development of CFD modeling of DMC treating coal as a multiscale modeling approach. They also attempt to show how the numerical approach can be further utilized for exploring alternative designs to improve efficiency.

9.2 Computational fluid dynamics approach for dense medium cyclone modeling The multiphase CFD approach used for the DMC simulations (Narasimha et al., 2007a,b) has been developed using the commercial package ANSYS’s FLUENT with additional user-defined functions (UDFs). This CFD model consists of simple sub-models for air/free surface, ASM model modified with additional shear, lift and hindered settling drag forces for particle size distribution (PSD) and RSM model for turbulence.

9.2.1

Governing equations

In the finite volume method, adopted in ANSYS’s FLUENT, the entire computational domain is divided into many control volumes, also known as

Numerical modeling of dense medium cyclones Chapter | 9

327

computational cells/grid. At each computational cell, the flow field equations are discretized and solved such that mass, momentum and energy are conserved. The DMC is operated at isothermal conditions, so the energy equation is not considered. Mass conservation and momentum conservation equations for an incompressible fluid in Cartesian coordinate are provided in Eqs. (9.1) and (9.2)

9.2.2

@ρ @ρui 1 50 @t @xi

ð9:1Þ

@ @ @p @u2 i ρui 1 ρui uj 5 2 1 μ 2 1 ρgi @t @xj @xi @x j

ð9:2Þ

Turbulence modeling

The flow in a DMC is turbulent, having a fluid Reynolds number in the range of 105. Turbulent flows are characterized by fluctuations of different length scales with high frequency which can be expressed as time-averaged mean and fluctuating fields, thereby reducing the computational time. This technique is widely known as Reynolds averaged Navier
Stokes (RANS) approach. Though the average flow field may not describe the exact local physics (i.e., turbulence generation and dissipation), it is mostly sufficient to provide insight into the physics of the general flow. Expressing the instantaneous velocity (ui ) into a sum of time-averaged velocity (u i ), fluctuating velocity (ui 0 ) and time-averaging the momentum equation after eliminating fluctuating terms gives @ @ @p @2 u i @ ρui 1 ρui uj 5 2 1 μ 2 1 ρgi 2 ρui 0 uj 0 @t @xj @xi @xj @x j

ð9:3Þ

The above Eq. (9.3) is the well-known RANS equation. The averaging process introduces additional fluctuating term ρui 0 uj 0 popularly known as the Reynolds (turbulent) stresses. The RANS equation is similar to the unaveraged Navier
Stokes equation except for the turbulent stress term. There are four known equations (3 momentum and 1 continuity) and a total of 10 unknown variables. To solve the additional 6 Reynolds stresses, turbulence models are used. A turbulence model is a procedure to close the system of mean flow equations.

9.2.2.1 Reynolds Stress model By modeling transport equations for the individual Reynolds Stresses, RSM does not make the assumption of local equilibrium for stress against strain. Further, they relax the assumption of turbulent isotropy because each Reynolds stress is modeled individually, although RSM still averages over all scales of turbulence. Wilcox (1998) notes that RSM provides physically

328

Mineral Processing

realistic predictions for flows with curved streamlines and system rotation without “ad hoc corrections.” In the RSM model, the unsteady transport equations below are solved for individual Reynolds stresses (Launder et al., 1975).  @
0 0 @
ρui uj 1 uk ρui 0 uj 0 5 φij 1 Pij 1 DT;ij 1 DL;ij 2 εij 1 Fij @t @xk

ð9:4Þ

Here φij is pressure strain, Pij is stress production, DT;ij is turbulent diffusion, DL;ij is molecular diffusion, εij is dissipation and Fij is production by system rotation. These are modeled as follows: The pressure strain can be modeled using either linear or quadratic methods. The linear pressure strain model proposed by Gibson and Launder (1978) and Fu et al. (1987) is used in ANSYS’s Fluent. It is modeled as shown next φij 5 φij;1 1 φij;2 1 φij;w Here φij;1 is the slow pressure strain term and modeled as   ε 2 ui 0 uj 0 2 δij k φij;1 5 2 C1 ρ k 3 φij;2 is the rapid pressure strain term and modeled as 
 2 φij;2 5 C2 Pij 1 Fij 1 Gij 2 Cij 2 δij ðP 1 G 1 C Þ 3

ð9:5Þ

ð9:6Þ

ð9:7Þ

Here C1 5 1:2; C2 5 0:6; P 5 12 Pkk ; G 5 12 Gkk and C 5 12 Ckk φij;w is the wall-reflection term. This is responsible for the redistribution of normal stresses near the wall. This term enhances the stress parallel to the wall, while dampening the normal stress perpendicular to the wall. This term is modeled as   3 0 0 3 0 0 Cl k2=3 0 ε 0 0 φij;w 5 C1 uk um nk nm δij 2 ui uk nj nk 2 ui uk ni nk k 2 2 εd ð9:8Þ   2=3 3 Cl k 0 1 C2 φkm;2 nk nm δij 2 φik;2 nj nk 2 φjk;2 ni nk 2 εd 0

0

Here C1 5 0:5, C2 5 0:3, nk is the xk component of the unit normal to the c

3=4

wall, d is the normal distance to the wall, C1 5 μk , Where Cμ 5 0:09 and k is the von Karman’s constant (50.4187)  
1   φij 5 2 C1 ρε 1 C1 P bij 1 C2 ρε bik bkj 2 bmn bmn δij 3  
2  pffiffiffiffiffiffiffiffiffiffi ð9:9Þ 1 C3 2 C3 bij bij ρkSij 1 C4 ρk bik Sjk 1 bjk Sik 2 bmn Smn δij 3
 1 C5 ρk bik Ωjk 1 bjk Ωik

Numerical modeling of dense medium cyclones Chapter | 9

Here bij is the Reynolds-stress anisotropy tensor and defined as   2 ρui 0 uj 0 1 23 ρkδij bij 5 2ρk Sij is the mean strain rate tensor and defined as   @ui @uj 1 Sij 5 @xj @xi The mean rate of rotation, Ωij tensor is defined as   @ui @uj 2 Ωij 5 @xj @xi     @uj @ui @ μt @ui 0 uj 0 1 uj 0 uk 0 Pij 5 2 ρ ui 0 uk 0 ; DT;ij 5 ; @xk @xk @xk σk @xk   @ @ui 0 uj 0 2 DL;ij 5 μ ; εij 5 δij ρε @xk 3 @xk

329

ð9:10Þ

ð9:11Þ

ð9:12Þ

ð9:13Þ

Here μt is turbulent viscosity. The turbulent viscosity is computed from the kinetic energy and dissipation rate transport equations as per the k-ε model, and constants used in the quadratic pressure strain are C1 5 3.4, C1 5 1.8, C2 5 4.2, C3 5 0.8, C3 5 1.3, C4 5 1.25, C5 5 0.4.

9.2.3

Multiphase modeling

9.2.3.1 Volume of fluid (VOF) model VOF model is a multiphase CFD approach used to track the free surfaces (Hirt and Nichols, 1981) by solving the momentum Eq. (9.14). Continuity Eq. (9.15) is solved for the volume fraction of the air (αq ). In this work, a geometric reconstruction scheme with a piecewise-linear approach is used to track the interface between air and water. In the piecewise-linear approach, the interface between air and water is assumed to have a linear slope within each cell and the linear shape is used for the calculation of advection of fluids through the cell phases.

   @ ρuj @ ρui uj @p @ @ui @uj 1 ρui uj 5 2 1 ρgj 1 μ 1 ð9:14Þ @xj @xj @t @xj @xj @xi @αq @αq 1 uj @t @xi

50

ð9:15Þ

αq is volume fraction of qth phase which varies between 1 and 0. uj is jth component of the velocity. The following Equations calculate the average density and viscosity ρ 5 αρwater 1 ð1 2 αÞρair

μ 5 αμwater 1 ð1 2 αÞμair

ð9:16Þ

330

Mineral Processing

The surface tension model by (Brackbill et al., 1992) is incorporated in Fluent as a source term in the momentum equation. A constant of 0.078 N/m is used for the surface tension between air and water.

9.2.3.2 Discrete Particle Model In this model, the Lagrangian reference frame is used to solve the properties of discrete/dispersed phase particles. The continuous phase is solved in the Eulerian reference frame using the Navier
Stokes equation described in the previous section. A specific number of particles are tracked under the influence of discrete phase inertia, hydrodynamic drag, gravitational force and shear lift forces for unsteady flow. The discrete random walk model (DRW) is used to predict the dispersion effect on the particles due to turbulent eddies present in the continuous phase. Basic assumptions behind the discrete particle model (DPM) is (1) the volume fraction of dispersed phase is very low, even though mass loading is higher, (2) particle
particle interactions and the effects of the particle volume fraction on the liquid phase are negligible. This model is not suitable if the volume fraction of the secondary phase is high (. 10% by weight). DPM predicts the particle trajectory by integrating force balance in the Lagrangian reference frame, equating the particle acceleration to forces acting on the particle. ðρp 2 ρm Þ d~ up 18μ CD Rep 5 FD ð~ Rep u 2~ upÞ 1 ~ g 1 FL FD 5 dt ρp ρp dp 2 24 ρdp ~ u up 2 ~ 2Kv1=4 ρdij 5 FL 5 ð~ u 2~ upÞ μm ρp dp ðdlk dkl Þ1=4

ð9:17Þ

where FD ð~ u 2~ u p Þ is the drag force, and FL is the lift force acting on the particle, CD is the drag coefficient, ~ u is continuous phase velocity, ρp is particle velocity, ρ is the fluid density, dp is particle diameter, μm is fluid/mixture viscosity, Rep is the particulate Reynolds number, K 5 2.594, dij is the deformation tensor.

9.2.3.3 Algebraic Slip Mixture (ASM) model As stated in the literature section, the simplified mixture model is more reliable than the full Eulerian Eulerian (EE) model in terms of uncertainties in closure and computational time as it solves a lesser number of equations. ASM solves the equations of motion for the slurry mixture and additional transport equations for the volume fractions of particulate phases ‘p’ dispersed throughout the continuous water phase c:   @ @ @ρ @ @umi @umj ρ umi 1 1 ρ umi umj 5 2 1 μ @t m @xj m @xi @xj m @xj @xi ! ð9:18Þ n @ X 1 ρgi 1 αp ρp upmi upmj @xj p51

Numerical modeling of dense medium cyclones Chapter | 9

  @ @
@
αp 1 αp u i 1 αp upm;i 5 0; @t @xi @xi

upm;i 5 upi 2 ui

331

ð9:19Þ

All the mixture properties are calculated using Eq. 9.18. Phase segregation in Eq. 9.19 is accounted for by upm,i, which is the drift velocity of the phase p relative to the mixture m. This is related to the slip velocity upc,i, which is the velocity of the phase p relative to the continuous water phase c by the formulation in Eq. 9.20: upmi 5 upci 2

n X αk ρ

k

l51

ρm

ulci ;

upci 5 upi 2 uci

ð9:20Þ

upc,i is calculated algebraically in Standard ASM (SASM) (Manninen et al., 1996) treatise by an equilibrium force balance. This is implemented in Fluent, as shown in Eq. 9.21. ASM works on the assumption of particles reaching equilibrium positions over short spatial length scales. This means that the particles accelerate rapidly to their terminal velocities relative to the mixture. In the basic formulation of the mixture model, the Schiller and Naumann (1935) drag law is used.   dp2 ρp 2 ρm  @ @ upci 5 T gi 2 umi 2 umj umi ð9:21Þ @t @xj 18frep μc The term outside the brackets in Eq. (9.21) is called the particle relaxation time. If the relaxation time is small compared to the time scale of flow, then the assumption that the particles associated with particles are always moving at their terminal relative velocity is considered to be valid. The terms inside the brackets are accelerations associated with the forces to which particles are subjected. This SASM model includes gravity, rate of change in time and convective terms from the momentum equation. The convective term includes centripetal force on the particles in a flow and models the classification force arising from swirl in a hydrocyclone simulation. In principle, other forces such as lift, collision, and turbulent dispersion can also be accounted for by including the acceleration associated with these forces in Eq. (9.21).

9.2.3.4 Modified Algebraic Slip Mixture (MASM) model The calculation of slip velocity in the SASM model in Fluent has been modified to include additional forces as shown next   " # dp2 ρp 2 ρm @ @ ρc upci 5 T gi 2 umi 2 umj umi 1 0:75 Clp εijk ωmj upck @t @xj 18frep μc ρp 2 ρm ð9:22Þ

332

Mineral Processing

Eq. 9.22 is implemented in Fluent as a custom slip velocity calculation using a UDF. frep has been modeled with the Schiller and Naumann (1935) drag law but with an additional correction factor for hindered settling based on the Richardson and Zaki (1954) correlation.   ð9:23Þ frep 5 1 1 0:15Re0:687 α24:65 p p The lift force is a mechanical force generated by solid particles moving through a fluid, directed perpendicular to the flow direction. The inclusion of lift forces for the slip calculation will account for the effect of shear forces at wall due to particles. The lift force expression derived by Saffman (1965) for the single particle is used here ρ Flpi 5 c πd3p Clp εijk ωmj upck ð9:24Þ 8 The lift coefficient has been calculated as

! ρf dp2 jωj fc Clp 5 4:1126 μc

ð9:25Þ

fc corrects the lift coefficient using the correlation proposed by Mei (1992).

9.3

Rheology modeling

Slurry rheology plays a vital role for particles settling in gravity/centrifugal field at high feed Relative Densities (RDs) in DMC. It is possible to model the slurry rheology using Granular Viscosity (GV), Newtonian viscosity model with solids correction (Nfs), Newtonian viscosity model with solids and fines correction (Nfsfc) and non-Newtonian Herschel
Bulkley model (HB) corrected with solids percent. The details of the viscosity models are given below.

9.3.1

Granular Viscosity (MASM 1 GV) model

The GV model by Ding and Gidaspow (1990) has been used in this work. Granular shear viscosity arises from particle momentum exchange due to translation and collision and is accounted for and calculated as shown in Eq. 9.26. μm 5 μp;col

1 μp;kin

ð9:26Þ

In the experimental work of flow through an annular shear shell, Bagnold (1954) observed that viscous forces dominate the flow in the low shear regions and the stresses are proportional to shear rate. On the other hand, in high shear regions, grain inertia dominates the flow behavior and stresses are proportional to the square of the shear rate and are independent of fluid

Numerical modeling of dense medium cyclones Chapter | 9

333

viscosity. Gidaspow (1994) modeled shear dependent granular viscosity expressions as shown in Eqs. 9.27
9.30. Collison or Bulk viscosity is modeled as 
 Θp 1=2 4 2 ð9:27Þ μp;col 5 αp ρp dp go;pp 1 1 epp 5 π Kinetic viscosity is modeled as 
 2 2μsdil 4  μp;kin 5
11 αp go;pp 11epp 5 96 1 1 epp go;pp

ð9:28Þ

Dilute viscosity of solids is μsdil 5

pffiffiffiffiffiffiffiffiffi 5 ρp dp Θp π 96

ð9:29Þ

Radial distribution function is   !21 3 αp 1=3 go;pp 5 1 1 λ 5 12 5 αp;max

ð9:30Þ

where particle concentration (λ) is defined as the ratio of particle diameter to distance between the particles, the radial distribution function is interpreted as the dimensionless distance between the particles.

9.3.2 Newtonian viscosity model with total feed solids correction (MASM 1 Nfs) Further, the modified viscosity model of Ishii and Mishima (1984), that is, with total solids correction, is used to measure the mixture viscosity (μm) (Eq. 9.31). This is similar to the model used by Wang et al. (2009). They had used a scale factor of 3.8 in the model to increase the viscosity levels in the cyclone as the Ishii and Mishima (1984) model-predicted low values of viscosity. h μm αp i21:55 5 3:8 12 ð9:31Þ μw 0:62

9.3.3 Newtonian model with total solids and fines correction (MASM 1 Nfsfc) The fine particles affect the rheology of the mixture substantially (He and Laskowski, 2000). The increase in fines fraction can increase the viscosity of suspensions. Therefore fines correction is needed for describing the slurry behavior through Newtonian formulations. In this work, Ishii and Mishima’s

334

Mineral Processing

Equation is modified by including the fine fractions below 38 μm (Narasimha et al., 2012). Eq. 9.32 is obtained by calibrating against the measured viscosity data of various mineral slurries (Narasimha et al., 2014). h 0:39 μm αp i21:55
5 12 F238μ ð9:32Þ μw 0:62

Non-Newtonian Herschel
Bulkley (MASM 1 HB) model _ within the cyclone, there is a need Due to the presence of high shear rates ðγÞ for shear dependent viscosity model. Therefore a shear dependent Herschel
Bulkley viscosity formulation is also used in the current study. The HB model parameters, that is, yield shear stress (τ 0 ), consistency (k), flow index (n) is fitted from the experimental data of He and Laskowski (2000). These parameters are dependent on the volume fraction of magnetite solids and correlated with the power-law functions. This data consists of magnetite solids concentrations varying from 5% to 30% with superfine PSD. 9.3.4

μm 5 τ 0 ϒ_ 1 κϒ_

9.4

n21

ð9:33Þ

Numerical modeling

A 350 mm conventional DMC used for the experimental GRT studies (Subramanian, 2002) was considered for multiphase simulations. Superfine quality magnetite with a density of 4950 kg/m3 and a feed size distribution of 2.4, 7.4, 15.4, 23.8, 32.2, 54.1, 82.2 μm was considered for simulating the medium segregation. The total feed medium concentration, volumetric flow rates, and the volume fraction of each particle size in the feed were selected similar to the experimental conditions (Subramanian, 2002). The free surface between air and water was initially resolved using the VOF model. After forming the air-core, the multiphase model was changed to ASM before introducing magnetite. RSM model was selected to solve the turbulent transport equations. A bounded central differencing scheme was chosen to discretize the momentum equations. Pressure was solved by using the PREssure STaggering Option (PRESTO). Quadratic Upstream Interpolation for Convective Kinematics (QUICK) is used to discretize dispersed phase transport equations. A fixed time step of 1.0x10
4 s was used in all the simulations. The inlet was set to velocity inlet, and outlets have been set to pressure boundary conditions. Once the multiphase simulations reached convergence, coal particles were introduced as a discrete phase through the DPM model (Vakamalla et al., 2017). A total of 2048 coal particles with a sphericity of 0.8 were chosen for injection. Five sizes of coal particles (0.5, 1, 2, 4, 8 mm) with a

Numerical modeling of dense medium cyclones Chapter | 9

335

density range from 1200
2000 kg/m3 were selected for the present study. A stochastic tracking model (random walk model) was opted to predict the effect of the turbulence in continuous phase on dispersed particles. The Discrete Random Walk (DRW) model includes the effect of instantaneous turbulent fluctuating velocity on particle tracking. Each particle was tracked at least thrice to get a statistical mean value. A maximum of 5 3 107 steps was used to terminate the solver. Particle dispersion was predicted by Lagrangian integral time (TL), defined as the time spent by a particle in turbulent motion in a specified path. TL was approximated as 0.30 (k/ε) for the RSM model. In the DRW model, each eddy was characterized by an eddy time scale. This was defined as a constant τe 5 2TL. Here particle interaction with fluid-phase eddy was assumed to be smaller than the eddy lifetime.

9.5 9.5.1

Results and discussion Mean flow field analysis and grid independence study

The experimental flow field measurements were not available for the 350 mm DMC. Therefore the experimental data in a 100-mm DMC (Fanglu and Wenzhen, 1987) was selected to validate the CFD model (VOF coupled with RSM) predicted two-phase flow field data. A grid size of 110 k was used for 100 mm DMC simulations. The predicted tangential and axial velocities were compared against experimental LDA data and shown in Fig. 9.1. It can be observed that the RSM model-predicted tangential and axial velocities were close to the experimental measurements. RSM coupled with the VOF model was used for predicting the air-core and flow field in 350 mm DMC. Grid independence study is crucial for selecting a suitable grid, thereby accurate predictions. For this purpose, grids of 100, 200 and 400 k nodes were selected. Corresponding flow field predictions in a 350 mm DMC cyclone are shown in Fig. 9.2. The mean flow field results were plotted across the XZ plane. These results were obtained by

FIGURE 9.1 Comparison of numerically predicted mean flow field against experimental data (Fanglu and Wenzhen, 1987) in a 100-mm DMC.

336

Mineral Processing

FIGURE 9.2 Comparison of numerically predicted mean flow field by 3 different grids at an axial position of 0.47 m from the roof of cyclone, for a feed volumetric flow rate of 0.0105 m3/s using VOF coupled with RSM turbulence model. From Vakamalla, T.R. Mangadoddy, N., 2015. “Rheology-based CFD modeling of magnetite medium segregation in a dense medium cyclone.” Powder Technol. 277, 275
286. Available at: https://doi.org/10.1016/j.powtec.2015.02.025.

averaging the data over a few thousand iterations equivalent to approximately 2 seconds of physical time after convergence. Tangential velcoity components predicted by simulating the 200 k and 400 k node geometries were almost identical, whereas the geometry with 100 k node predicted a lower magnitude of tangential velocity component. Similarly, the axial velocity component for 100 k mesh differed from the rest of the fine meshes. Hence, the grid with B200 k nodes was selected as the optimum mesh for running the multiphase simulations with the aforementioned feed size distribution in a 350 mm DMC. Complete details about the 350 mm DMC geometry and grid (B200 k) used for the simulations are given in Fig. 9.3.

9.5.2

Magnetite medium segregation prediction and validation

The multiphase simulations were conducted using (1) the SASM model (without additional forces and rheological corrections), (2) the SASM model with different rheological formulations and (3) the MASM model with different rheological formulations. The magnetite medium segregation predicted by the SASM model and MASM model with various rheological formulations is displayed in Fig. 9.4. The mean medium density contours shown in Fig. 9.4 are plotted across the XZ plane in the DMC. From the contours, it can be noticed that the MASM with GV and HB rheology models can predict magnetite medium segregation close to the experimental GRT data compared to the MASM with the Nfs and Nfsfc viscosity models. Table 9.1 shows the comparison of predicted overflow, underflow densities and underflow volume recoveries (Rm) by various models along with experimental GRT data (Subramanian, 2002) and the Wood (1990) model. This Wood (1990) model is widely used in coal preparation industries for predicting the performance of conventional DMCs. The medium slurry densities in Table 9.1 were calculated by computing the slurry volumetric flowrate to

Numerical modeling of dense medium cyclones Chapter | 9

337

FIGURE 9.3 (A) Detailed dimensional drawing of the 350 mm DMC and (B) numerical grid used for the simulations.

FIGURE 9.4 Comparison of numerically predicted mean density contours by (A) SASM model, (B) GV model, (C) Nfs model, (D) Nfsfc model, (E) HB model compared with (F) experimental GRT data for a feed RD of 1.465, feed volumetric flow rate of 0.0105 m3/s (Vakamalla and Mangadoddy, 2015). From Vakamalla, T.R. Mangadoddy, N., 2015. “Rheology-based CFD modeling of magnetite medium segregation in a dense medium cyclone.” Powder Technol. 277, 275
286. Available at: https://doi.org/10.1016/j.powtec.2015.02.025.

TABLE 9.1 Comparison of CFD predicted mean flow densities against experimentally measured GRT and Wood model data in a 350 mm DMC.

Feed density (kg/m3) 3

Underflow density (kg/m ) 3

Overflow density (kg/m ) Underflow volume fraction (Rm)

SASM

MASM 1 GV

MASM 1 Nfs

MASM 1 Nfsfc

MASM 1 HB

Experiment

Wood model

1467

1467

1467

1467

1467

1467

1467

1703

1737

1521

1549

1787

1965

1868

1295

1337

1428

1409

1314

1375

1366

0.404

0.262

0.348

0.445

0.297

0.17

0.142

Source: From Vakamalla, T.R. Mangadoddy, N., 2015. “Rheology-based CFD modeling of magnetite medium segregation in a dense medium cyclone.” Powder Technol. 277, 275
286. Available at: https://doi.org/10.1016/j.powtec.2015.02.025.

Numerical modeling of dense medium cyclones Chapter | 9

339

FIGURE 9.5 Axial variation of GRT measured 350 mm DMC air-core radius for feed relative density of 1.465, feed volumetric flow rate of 0.0105 m3/s (Vakamalla and Mangadoddy, 2015). From Vakamalla, T.R. Mangadoddy, N., 2015. “Rheology-based CFD modeling of magnetite medium segregation in a dense medium cyclone.” Powder Technol. 277, 275
286. Available at: https://doi.org/10.1016/j.powtec.2015.02.025.

water and magnetite (with all the phase volume fractions) flowrates. The predicted density data shown in Table 9.1 were collected by monitoring the mass flow rates over a few thousand iterations and then averaging them. It can be observed that the numerically predicted underflow volume recoveries (Rm) by all the models deviated from experimental measurements. The possible reason may be the underprediction of underflow densities. The closest Rm was associated with GV and HB models. The underflow and overflow densities predicted by the HB model were closest to the Wood model compared to other rheological model predictions. Fig. 9.5 compares the axial variation of air-core radius predicted by MASM modified with different rheological models against the GRT measurement. Similar to flow density and Rm predictions, the MASM with the adapted non-Newtonian HB rheological model predicted the air-core radius closest to the GRT data at the top portion of the cyclone, but it slightly underpredicted the values towards the cyclone bottom. The air-core radius predicted by MASM modified with GV, Nfs, Nfsfc models at all position sin the cylone differed from the GRT data. The air-core appears to be in a steady state in Figs. 9.4 and 9.5. It is believed that the statistically averaged air-core predictions depict the steadystate nature unless there is a variation in the feed flow characteristics. In reality, the shape of the air-core dynamically varies at any given time.

340

Mineral Processing

9.5.3 Medium segregation predictions by standard Algebraic Slip Mixture and modified Algebraic Slip Mixture models In this section, magnetite medium segregation predicted by SASM and MASM models is quantitatively analyzed and compared radially at different axial positions inside the DMC. Initially, the multiphase simulations were started with a SASM model (Manninen, Taivassalo, and Kallio, 1996) available in ANSYS’s Fluent. The SASM model with granular viscosity is a simplified version of the full Eulerian granular flow model (Ding and Gidaspow, 1990). This viscosity model is similar to the Nfs model. It limits the solids concentration to a realistic value by driving the mixture viscosity to finite when the total volume fraction of solids approach 0.62 (the packing limit). Fig. 9.6 compares the SASM model-predicted mean radial density profiles against the experimental GRT data at two different axial positions (i.e., 0.23 m and 0.65 m from the cyclone roof). Underprediction of mean density near the air-core and overprediction of mean density near the wall can be observed. Subsequently, the simulations were done using the SASM model with GV, Nfs, Nfsfc, and non-Newtonian HB rheology models to improve the density predictions. The predictions compared with the SASM model and experimental data at 0.23 m and 0.65 m axial locations are provided in Fig. 9.6. An improvement in the predictions near the air-core and the wall is visible at both locations. At 0.23 m, the SASM with different rheological models predict medium densities close to the experimental data. At 0.65 m, all the model predictions deviated from the experimental data. An increase in the medium density near the air-core and a reduction in the medium density near the wall at both the axial positions is visible with all the rheologically modified SASM models. The decrease in mean density near the wall is substantially higher in the conical section (0.65 m) than in the cylindrical section (0.23 m). Also, the medium density near the wall deviates substantially compared to experimental GRT data. In general, the presence of high solid

FIGURE 9.6 Mean radial density profiles plotted at 0.23 m, 0.65 m axial positions by SASM and MASM with GV model for a feed RD of 1.465, feed volumetric flow rate of 0.0105 m3/s.

Numerical modeling of dense medium cyclones Chapter | 9

341

concentration in the conical section alters the particle
fluid interactions. Lack of additional forces (Lift, drag, turbulent dispersion etc.) in the SASM to account for this (along with rheology) may be the plausible reason for deviations in model predictions. To enhance the wall density predictions, further simulations were done with the MASM model including the shear lift force, the hindered settling drag and rheology. The MASM model-predicted slurry density profiles were compared against the experimental GRT data at different elevations and are shown in Fig. 9.7
9.9. At the axial position of 0.23 m, the model predictions between the air-core and wall regions are close to the experimental data. GV, Nfs and Nfsfc rheology-based CFD models underpredict the densities near the air-core region. The mean densities predicted by the GV model deviate near the wall at both axial locations compared to GRT data. In contrast, MASM with the HB model-predict wall densities very close to the GRT values. The selected HB model behaves as a shear-thinning fluid, that is, the predicted viscosities will be low at high strain rates. In general, high

FIGURE 9.7 Mean radial density profiles plotted at 0.23 m, 0.65 m axial positions by SASM and MASM with Nfs model for a feed RD of 1.465, feed volumetric flow rate of 0.0105 m3/s.

FIGURE 9.8 Mean radial density profiles plotted at 0.23 m, 0.65 m axial positions by SASM and MASM with Nfsfc model for a feed RD of 1.465, feed volumetric flow rate of 0.0105 m3/s.

342

Mineral Processing

FIGURE 9.9 Mean radial density profiles plotted at 0.23 m, 0.65 m axial positions by SASM and MASM with HB non-Newtonian viscosity model and lift forces for a feed RD of 1.465, feed volumetric flow rate of 0.0105 m3/s.

FIGURE 9.10 MASM model with HB rheological model-predicted mean particle volume fraction contours in 350 mm DMC.

strain rates prevail at the walls of DMC. Hence, lower flow resistance can be expected for the particles at these zones in the simulations. This could be one of the reasons for the slight deviation in the predicted wall densities with the HB model. At 0.65 m elevation, where the high medium concentration prevails, the GV and HB based MASM model predictions were close to experimental values. The overprediction of medium densities near the walls with the GV model could be attributed to its lower viscosity predictions. This slurry viscosity (flow resistance) is enhanced partially by the Nfs and Nfsfc models by limiting the packing fraction. Although Nfs, Nfsfc formulation based MASM model predictions deviated substantially from the experimental values (Fig. 9.7 and Fig. 9.8), the overprediction of densities near the wall is minimized at both the elevations. The underflow stream densities predicted by Nfs and Nfsfc based CFD models were much lower compared to the GV model (Table 9.1). Due to the existence of high shear rates within the cyclone, the shear-thinning HB model predicted density levels closer to GRT data near the air-core and the wall. The same can be seen in Fig. 9.9. The predicted particle size segregation of magnetite inside the cyclone is presented in Fig. 9.10. Similar to particle classification in hydrocyclones, magnetite particles are also classified under centrifugal action in DMC.

Numerical modeling of dense medium cyclones Chapter | 9

343

It can be seen that very fine particles (i.e., 2.4 and 7.4 μm) are uniformly distributed inside the cyclone volume. The intermediate size particles (15.4, 23.8 μm) are around the air-core. They take the reverse path near the bottom portion of the conical section via the forced vortex. Coarse size particles (32.2
82.2 μm) segregate close to the wall because of centrifugal forces. These particles remain under the influence of the primary vortex.

9.5.4 Prediction of viscosity levels by different rheology based CFD models Fig. 9.11 presents the slurry viscosity contours predicted by the MASM model modified with various rheological formulations. The viscosities predicted by the GV model were close to the water and far from the expected viscosities inside DMC. Nfsfc model with total solids and fines fraction correction predicted higher viscosities compared to the GV model and the Nfs model with a correction factor of 3.8. The shear dependent non-Newtonian HB modelpredicted viscosity levels that were an order of magnitude higher than the other rheology model predictions. Figure 9.11 and 9.12 reaffirm that viscosities predicted by the shear-thinning HB model mainly depend on strain rate along with total solids fraction. Fig. 9.13 depicts the comparison of the viscosity data predicted by the MASM model with different rheological formulations against the offline viscometer data of He and Laskowski (2000) for different solids fractions. It can be noted that the GV model-predicted viscosities are

FIGURE 9.11 Viscosity contours predicted by (A) GV model, (B) Nfs model, (C) Nfsfc model, and (D) HB model (Vakamalla and Mangadoddy, 2015). From Vakamalla, T.R. Mangadoddy, N., 2015. “Rheology-based CFD modeling of magnetite medium segregation in a dense medium cyclone.” Powder Technol. 277, 275
286. Available at: https://doi.org/10.1016/j. powtec.2015.02.025.

344

Mineral Processing

FIGURE 9.12 Strain rate contours in the 350 mm dense medium cyclone (Vakamalla and Mangadoddy, 2015). From Vakamalla, T.R. Mangadoddy, N., 2015. “Rheology-based CFD modeling of magnetite medium segregation in a dense medium cyclone.” Powder Technol. 277, 275
286. Available at: https://doi.org/10.1016/j.powtec.2015.02.025.

close to 1 cP even at the high solid fraction. An increase in the viscosities is apparent with the Newtonian based CFD models, although the predicted viscosities are lower compared to the experimental measurements. Shear dependent HB model is able to predict high viscosities with solids fraction. The difference in predicted viscosities between Newtonian and non-Newtonian rheological models increased with solids fraction.

9.5.5 Simulating coal particle dynamics using discrete particle model The DPM model was superimposed on the HB modified MASM modelpredicted magnetite medium segregation to simulate the behavior of a coal particle in a 350 mm DMC. Coal particles of different sizes (8, 4, 2, 1, 0.5 mm) and various densities (1200 to 1800 kg/m3) were selected for particle tracking. About 1024 particles with a uniform diameter and sphericity of 0.8 were injected across the feed boundary. The partition curve as a function of particle size and density was constructed by noting the number of particles

Numerical modeling of dense medium cyclones Chapter | 9

345

FIGURE 9.13 Comparison of modified CFD model-predicted viscosities with offline viscometer-based experimental magnetite data of He and Laskowski (2000) for different solids volume fraction (Vakamalla and Mangadoddy, 2015). From Vakamalla, T.R. Mangadoddy, N., 2015. “Rheology-based CFD modeling of magnetite medium segregation in a dense medium cyclone.” Powder Technol. 277, 275
286. Available at: https://doi.org/10.1016/j.powtec.2015.02.025.

reporting to the underflow from the feed. The Lagrangian particle tracking was repeated 3 times and averaged to obtain the mean value. Ecart probable (Ep) was calculated, the inverse of which defines the sharpness of cut in a DMC. It is defined as follows ρ 2 ρ25 Ep 5 75 ð9:34Þ 2 where ρ75 and ρ25 are relative densities that correspond to 75% and 25% of feed material that is rejected to underflow. Due to the lack of experimental results on the coal partition in a 350 mm DMC, predicted coal partition data was validated against the empirical Wood (1990) model. The comparison between the GV and HB models along with the SASM model is shown in Table 9.2. From Table 9.2, one can notice that GV and HB models predicted cut densities and Ep closer to the Wood model. The non-Newtonian HB model not only predicted the medium overflow and underflow densities better, but also predicted the cut density and Ep closer to Wood (1990) model data. The EP and cut density predictions of the GV model were similar to HB model, although the predicted viscosities were very low. The computational time required for coal partitioning with the GV model was much lesser than the HB model. The partition curve predicted by the GV model is displayed

346

Mineral Processing

TABLE 9.2 Predicted cut densities, Ep for 350 mm DMC compared to Wood model. Model

Ep

Predicted cut density

Wood

0.037

1450

SASM

0.0405

1480

MASM 1 HB

0.043

1440

MASM 1 GV

0.0335

1460

CFD

FIGURE 9.14 Coal partition curves predicted by size and density in a 350 mm DMC for feed RD of 1.465, feed volumetric flow rate of 0.0105 m3/s (Aketi et al., 2018). From Aketi, et al., 2018. Numerical simulation of near-gravity coal particle behavior in a dense medium cyclone using a mixture model coupled with a discrete phase model. Int. J. Coal Prep. Util., 41 (8), 554
576. https://doi.org/10.1080/19392699.2018.14918.

in Fig. 9.14. Further, the same is utilized to predict other performance characteristics inside DMC. The performance curve shows that the efficiency is high for the particles whose densities are away from the cut density and lower for the particles whose densities are closer to the separation density, commonly termed as NGM. In all the cases, pivot phenomena in which all partition curves pass through a similar pivot point (Napier-Munn and Scott, 1990) is also observed. Generally, this pivot point corresponds to Rm values. The coal partitioning performance parameters (Ep, separation density, percent misplacement and imperfection) were calculated from the partition

Numerical modeling of dense medium cyclones Chapter | 9

347

TABLE 9.3 Coal partition data predicted by DPM model. Feed RD

size (mm)

Ep 5 (ρ75 2 ρ25)/2

Separation density (ρ50)

% misplacement

Imperfection (ρ75 1 ρ25)/2

1.465

0.5

0.13

1.47

26

0.28

1

0.06

1.468

12

0.129

2

0.05

1.46

10

0.108

4

0.03

1.457

6

0.065

8

0.03

1.452

6

0.065

Source: From Aketi, et al., 2018. Numerical simulation of near-gravity coal particle behavior in a dense medium cyclone using a mixture model coupled with a discrete phase model. Int. J. Coal Prep. Util., 41 (8), 554
576. https://doi.org/10.1080/19392699.2018.14918.

curves for different feed relative densities (RDs), coal particle sizes and are listed in Table 9.3. It can be seen that coarser (8 mm) size particles have lower Ep compared to smaller particles, owing to their esae of separation. This implies that it has least chances of misplacement to underflow/overflow depending on the particle density. Finer particles are relatively difficult to separate compared to larger ones. Decreasing the particle size reduces the sharpness of cut and increases the Ep value. This may be attributed to the low settling rates of fine coal particles for the operated slurry medium conditions. For a feed RD of 1.465, the misplacement increased from 6% to 26% when the particle size changed from 8 to 0.5 mm. The possible reasons could be (1) the increased interference due to surrounding particles, which is expected at high feed solids concentration and (2) the associated high drag resistance with finer size particles. Fig. 9.15 shows the predicted residence times of 5 different particle sizes plotted for different coal particle densities at a feed RD of 1.465 using DPM. It can be noted that finer-sized particles (0.5 mm) have the highest residence time and coarser-sized particles (8 mm) have the lowest. Due to their slow settling rates, the fine particles are more likely to flow with the medium. They would not get influenced by the centrifugal forces but rather by fluid turbulence. The particles that have a separation density away from separation cut density (the very low and very high density particles) exhibit less residence time inside the DMC, while particles with density close to separation cut density (generally referred as NGM) show longer residence times (Sripriya et al., 2007). Inside DMC, an asymmetrical zone exists where the ratio of drag to centrifugal force is very low. When a particle enters this zone, separation becomes difficult as the relative importance of centrifugal force and drag force on the particle may be continuously reversed (Qi et al., 2015). As a result, the residence time of particles entering this zone continuously increases. The same

348

Mineral Processing

FIGURE 9.15 RTD of various size and density particles at 1.465 feed RD.

FIGURE 9.16 Comparison of maximum residence times of different coal particle size of 3 different densities at a feed RD of 1.465.

is true for particles in the near-gravity zone. The particles close to separation density tend to recirculate inside the cyclone rather than getting separated, followed by reporting to the wrong products, thus reducing the separation efficiency of DMC. Fig. 9.16 depicts the averaged residence time versus particle size w.r.t to a specific particle density for a feed RD of 1.465. In Fig. 9.16 the top and bottom lines are for a particle density far from the NGM range. The center plot is for a particle density near to the separation density. From the figure,

Numerical modeling of dense medium cyclones Chapter | 9

349

it can be observed that the residence time is higher for small size particles, i.e. 0.5, 1, and 2 mm, compared to larger size particles. The particles far away from the NGM zone shows low and equal residence times. But the near-gravity particle shows high residence times with all size particles.

9.5.6 Simulating coal particle dynamics using Algebraic Slip Mixture model The flow of coal particles in DMC are commonly modeled using DPM (Mangadoddy et al., 2020; Narasimha, 2007a; Narasimha et al., 2007b; Wang et al., 2007). However, the DPM model is not suitable for dense solids flow as it only tracks individual particles. Further, the effect of particle
particle interactions and the effects of the particle volume fraction on the liquid phase cannot be comprehensively studied. Thus, the effect of the medium to coal (M:C) ratio, which is one of the important operational parameters for DMCs, cannot be investigated using the DPM method. Therefore MASM was utilized to simulate the coal particle dynamics. For this purpose, magnetite particles of different sizes (2.4, 7.4, 28.25, and 53.4 μm) and coal particles of different densities (1300, 1350, 1400, 1450, 1500, and 1763 kg/ m3) with a uniform size were selected along with water and air as the individual phases. The volume fractions of magnetite and coal particle phases were calculated to obtain an RD of 1.3 in feed (cyclone operating at 9D) with a medium to coal ratio of 4:1. The NGM fraction was about 35% at 1.35 separation density. All the components were mixed and fed through the inlet. The same numerical parameters as explained in the numerical modeling section were used for the simulations. Further, the ASM model was used to simulate coal partitioning. Fig. 9.17 displays the mixture density contours predicted by MASM with the GV model. A profound difference in the predicted medium density levels is visible with the addition of coal in the feed compared to medium densities without the coal in the feed (see Fig. 9.4). Additionally, a reduction in the

FIGURE 9.17 Predicted mixture density contour using ASM model for a feed RD of 1.3.

350

Mineral Processing

air-core diameter is also noticed. This might be due to the increase in solids concentration by the addition of fine coal fraction addition to the magnetite in the ASM model. The radial variation of magnetite medium segregation at three different axial locations is shown in Fig. 9.18. The mixture densities are plotted at 0.27 m, 0.47 m and 0.61 m axial locations from the roof of the cyclone. A sudden increase in wall densities is not seen here, unlike the case with only magnetite medium segregation (See Fig. 9.6). In the conical section (i.e., at 0.61 m), the mixture density is limited due to the presence of coal (low-density particle). Fig. 9.19 depicts the volume fraction of coal particles inside 350 mm DMC. Moving down the conical section, a steady rise in the volume fraction is visible even with coal particles.

FIGURE 9.18 Quantitative comparison of MASM predicted mixture density at 3 different axial locations for a feed RD of 1.3.

FIGURE 9.19 MASM predicted mean coal particle volume fraction distribution inside 350 mm DMC for a feed RD of 1.3.

Numerical modeling of dense medium cyclones Chapter | 9

351

FIGURE 9.20 CFD predicted volume fraction contours of different density coal particles ((A) 1.3, (B) 1.35, (C) 1.4, (D) 1.45, (E) 1.5, (F) 1.764) inside 350 mm DMC.

Fig. 9.20 represents the volume fraction contours for coal particles of varying density simulated by the ASM model along with the magnetite medium. The phenomenon can be explained as follows: As expected, the low-density coal particles, the 1.3 and 1.35 density particles, are distributed in the cylindrical and upper conical sections, and their maximum concentration is found around the air-core below the vortex finder region. The distribution of coal particles in Fig. 9.20B and C shows that the separation density of DMC operated at 1.3 RD lies between 1.35 and 1.4 specific gravity range. It means that the particles in the NGM range (having densities between 1.35 and 1.4) that are close to the separation density will be distributed uniformly in the cyclone. These NGM particles will recirculate in the cyclone resulting in longer residence times than other density particles. As the density of coal particle increases, away from the separation density, their volume concentration increases toward the wall (see Fig. 9.20D
F). With further increase in

352

Mineral Processing

density, the accumulation of these particles toward the conical section also increases, whereas the amount that reports to the overflow stream decreases. Despite the wall and the conical section showing the maximum concentration of coal particles with densities 1.45 and 1.5, a significant volume fraction of coal is still present within the vortex finder area, leading to a noticeable amount of misplacement to the overflow. The misplaced fraction decreases as the density of the coal particles move away from the NGM range. The far dense particles, that is, 1.5, and 1.764 are not affected and correctly report to underflow. The volume fraction profiles explain this phenomenon as can seen in Fig. 9.20D and E.

9.6 Using computational fluid dynamics to improve dense medium cyclone performance The design of dense medium cyclone has always been an adhoc process. In recent years, manufacturers and researchers have made changes to the standard design on a trial-and-error basis (Engelbrecht and Bosman, 1995; Rong and Napier-Munn, 2003). The work has mostly been driven by intuition and experience and, after numerous trials, has resulted in cyclones that appear to give more efficient separations. The way forward is to replace intuition with a real understanding of the operation of the cyclone and relate that understanding to develop a robust cyclone geometry. Design explorations for dense medium cyclones using CFD are advantageous because all the factors that influence the DMC performance are accounted for in CFD simulations. The operating pressure or the feed rate, and the overflow and underflow conditions are supplied as boundary inputs, while the cyclone geometry is implicitly accounted for. The flow features inside the DMC due to design changes can be studied, and the performance of each design can be quantified.

9.6.1 Sources of inefficiencies in conventional dense medium cyclones In the past, many efforts have been made to develop efficient hydrocyclones and dense medium cyclones by changing their geometries to change the flow characteristics (Engelbrecht and Bosman, 1995; Rong and Napier-Munn, 2003). The primary sources of inefficiencies in conventional DMCs and efforts made by different researchers to address them are listed below: Entrainment of fine particles: Entrainment of fine or slower settling particles occurs in the void spaces between the coarser, or faster settling, particles discharged as the underflow. Large turbulence fluctuations: Turbulent fluctuations inside the cyclone are expected to be significant due to the collision of the inlet stream with the rotating stream. Turbulence is also directly related to large velocity gradients

Numerical modeling of dense medium cyclones Chapter | 9

353

found inside cyclones (Narasimha et al., 2007a,b). Different sources of turbulence are expected in a cyclone flow. Large short-circuit flow: CFD studies (Narasimha et al., 2007a,b) observed that about 20% of the feed slurry usually short-circuits to the overflow in a conventional dense medium cyclone without being subjected to centrifugal action. Chu and Luo (1994) and Rong and Napier-Munn (2003) modified the outer wall of the vortex finder to reduce the short-circuiting. Inadequate standard inlet and body section design: Mathewson et al. (1998) modified the DMC design with involute, cycloidal and helical feed entries, a longer body section and a smooth transition from the cylindrical body to the cone. They worked with four different design types: standard length involute feed, 1.25 D length involute feed, 1.5 D length involute feed and standard length cycloidal entry. Here, D represents the diameter of DMC. Their experimental trials showed that the cycloidal feed design gave the least Ep, followed by a longer body involute feed design. The standard length involute feed design reported the poorest performance. Approximately 4 times higher wear rate is found in all involute feed DM cyclones than the standard DM cyclone due to higher feed pressure. Short residence-time of the internal upward flow: The particles in the inner helical flow move directly upward without a good separation. To address this, Chu and Luo (1994) placed a solid central cone inside a hydrocyclone. Results indicated that the hydrocyclone with the cone and modified vortex finder had sharper separation efficiency than that of a conventional hydrocyclone.

9.6.2 Scope to improve the performance of different dense medium cyclone designs The following requirements are important while developing new dense medium cyclone designs for separation of fine coal: Longer residence time for fine coal particles Minimizing short-circuiting, both to overflow and underflow Minimizing the effect of turbulence on particles Reasonable capacity of cyclone Possibility to use superfine magnetite for separation Low specific gravity cut in the range of 1.3
1.45 RD. Better separation of fine coal particles can be ensured if sufficient residence time is provided for the materials to settle so that they can experience the tangential forces. A higher tangential flow field causes a better separation of fine coal particles. Apriori two-phase simulation can be used as an effective method for initial screening among the possible designs, as the simulations can give valuable information about the flow features such as the shape of the air-core,

354

Mineral Processing

velocity field and turbulence. This information can then be used to decide upon the designs that have the potential to provide better efficiency of separation. Multiphase simulations can then be carried out, taking into account magnetite medium and coal particles. The following section presents an example as to how the CFD model can be utilized to predict the flow physics and assess the performance of coal separation for the selected novel cyclone designs.

9.6.3 Prediction of the performance of novel dense medium cyclone designs using CFD The computational grids of standard design, Standard design with long cylinder (Standard_LC), standard design with modified cone angle (Standard_Cone), used for the simulation studies are displayed in Fig. 9.21. The corresponding design details are provided in Table 9.4. All the 3D unstructured hexahedral meshes were generated using the ANSYS ICEM meshing tool. The simulation and design assessment strategy is explained in Fig. 9.22.

9.6.3.1 Two-phase flow analysis Fig. 9.23 presents the comparison of G-force (ratio of centrifugal force to gravitational force) for selected designs against the standard design. From Fig. 9.21, it can be observed that the G-force for the majority of designs is similar to the standard design with reasonable water split (Table 9.5), except for the peak magnitude. The axial velocities of the designs are compared in Fig. 9.24. It can be observed that there is minimal change in the mean axial velocity component of the tested designs compared to the standard design. Figs. 9.25 and 9.26 show the quantitative comparison of predicted turbulence

FIGURE 9.21 Meshes used for the design exploration simulation studies.

Numerical modeling of dense medium cyclones Chapter | 9

355

TABLE 9.4 Details of designs obtained by modifying standard design cylindrical, vortex finder lengths and cone angles. S. no.

Design

Length of cylinder

Length of VF

Cone angle

1

Standard

0.6 x Dc

0.36 x Dc

20

2

Standard_LC

0.9 x Dc

0.36 x Dc

20

3

Standard_Cone

0.6 x Dc

0.36 x Dc

15

FIGURE 9.22 Simulation and assessment strategy adopted for finalizing the best design.

intensities against standard design at the cylindrical-conical mid-section. It can be observed that both the modified designs show lower turbulence intensities compared to the standard design. An improvement in the separation of fine particles can be expected with the modified designs. High turbulence intensities are generally associated with high dispersion of particles and hence a loss in efficiency.

9.6.3.2 Multiphase flow analysis in selective designs Further, multiphase simulations for the selected designs were carried out using the MASM model coupled with the RSM turbulence model. The magnetite medium segregation predicted by the MASM model is displayed in Fig. 9.27. In the three designs, the medium segregation looks similar except for a slight change in the diameters of the air-core. Higher densities can be found toward the wall in the conical section. A small change in the density

356

Mineral Processing

FIGURE 9.23 Comparison of CFD Predicted G-force among different DMC designs.

TABLE 9.5 CFD predicted two-phase flow parameters of different designs compared with standard design. Design

Head

Inlet velocity (m/s)

Flow rate (kg/ s)

Standard

9D

3.23

4.05

Standard_LC

10D

3.38

Standard_Cone

10D

3.38

Water Split (%)

Pressure drop (pa)

9.46

23366

4.24

9.01

23294

4.24

10.48

22900

levels near the inner vortex finder wall is also seen with different designs. The overflow and underflow densities predicted by the MASM model, along with density differential is provided in Table 9.6. The density differential is then selected as a criterion for screening the remaining designs. In general, a uniform density differential is required for accurate separation of particles of different densities. However, in DMC, because of its geometrical structure and its flow physics, it is impossible to obtain a uniform density differential. It is generally assumed that lower the density differential, the better will be the separation characteristics. From Table 9.6, one can observe that the density differential of Standard_Cone and Standard_LC designs is slightly lower

Numerical modeling of dense medium cyclones Chapter | 9

357

FIGURE 9.24 Comparison of CFD Predicted axial velocity among different DMC designs.

FIGURE 9.25 Turbulence intensity contours predicted for different cyclone designs.

358

Mineral Processing

FIGURE 9.26 Comparison of CFD predicted turbulence intensity among different designs.

FIGURE 9.27 CFD predicted mean density contours of modified designs compared with standard design.

Numerical modeling of dense medium cyclones Chapter | 9

359

TABLE 9.6 CFD predicted multiphase flow properties of different designs. Design

Volume split, %

Overflow density, kg/m3

Underflow density, kg/m3

Density difference, kg/m3

Standard

9.69

1261

1913

652

Standard_Cone

10.11

1266

1682

417

Standard_LC

10.84

1277

1639

363

FIGURE 9.28 CFD predicted partition curves of modified designs compared with standard design.

than the standard design. Hence the designs with lower density differential were selected to simulate coal partitioning performance.

9.6.3.3 Coal partitioning in selected designs DPM model was superimposed on the magnetite medium segregation predicted by ASM to track the coal particles. Then, the tracked coal particles were utilized to construct the partition curve. The partition curve was constructed by measuring the number of coal particles that report to the underflow from the feed. The predicted partition curves for various designs is shown in Fig. 9.28. From Fig. 9.28, it can be observed that Standard_LC

360

Mineral Processing

design has less Ep with higher efficiency compared to the remaining two designs. Therefore the Standard_LC design is recommended for further optimization.

9.7

Conclusions

The chapter describes in detail a comprehensive multiphase CFD model that can be used for predicting the performance of dense medium cyclone treating coal particles in the presence of magnetite as dense medium. SASM model, MASM model with shear, lift and drag along with Newtonian, nonNewtonian and granular viscosity corrections were used to simulate a 350mm DMC. RSM was used to model turbulence. Magnetite medium predictions by the Newtonian rheology models were close to the GRT data near the wall, but deviations were observed in the bottom section of the DMC. In spite of very good density predictions with GV model, the predicted viscosity levels were significantly lower. In the case of non-Newtonian Herschel
Bulkley based CFD model, the predicted viscosity levels were appropriate and the predicted values of medium densities were also close to the experimentally measured gamma ray tomography data. The predicted viscosity increased up to 18 cP with Herschel
Bulkley based CFD model. Prediction of overall volume split to underflow by all the rheology models deviated from the experiments. Two options were tested to understand the coal particle dynamics inside a 350 mm DMC. (1) the DPM superimposed on the converged medium segregation simulations from ASM. (2) running of multiphase simulations with both magnetite and coal as feed medium. Both GV and HB models coupled with DPM was able to predict cut point density and Ep closer to the Wood (1990) model. The increase in volume fraction of coal in the feed showed a significant decrease in the overall mixture density. Additionally, a reduction in the air-core diameter was also noted. The plausible reason could be the increase of slurry viscosity due to the addition of coal particles along with magnetite. Further, the MASM model coupled with DPM was utilized to explore different designs of DMC treating fine coal. Among the various designs, the long cylindrical design seemed to show minimum turbulence inside the cyclone and improved performance and hence was recommended for further optimization.

Acknowledgments The authors would like to acknowledge the management of R&D TATA Steel, India and JKMRC, University of Queensland, Australia for taking up the joint research on initial CFD studies on DMC, followed by R&D NMDC India, DST-CII and IITH for supporting further high NGM studies on DMCs by both GPU-CFD and experimentation.

Numerical modeling of dense medium cyclones Chapter | 9

361

Abbreviations 2D 3D SASM CFD DEM DMC DPM EE DSM GRT GV HB LC MASM Nfs Nfsfc PRESTO PSD QUICK RANS RD RSM SIMPLE TI UDF VOF

Two-dimensional Three-dimensional Standard algebraic slip mixture model Computational fluid dynamics Discrete element method Dense medium cyclone Discrete particle method Full Eulerian
Eulerian model Dutch state mines Gamma ray tomography Granular viscosity Herschel
Bulkley Long cylinder Modified algebraic slip mixture model Newtonian rheology with solids correction Newtonian rheology with solids and fines correction Pressure staggering option Particle size distribution Quadratic upstream interpolation convective kinetics Reynolds averaged Navier
Stokes Relative density Reynolds stress model Semiimplicit method for pressure linked equation Turbulence intensity User-defined function Volume of fluid

References Aketi, et al., 2018. Numerical simulation of near-gravity coal particle behavior in a dense medium cyclone using a mixture model coupled with a discrete phase model. Int. J. Coal Prep. Util. 41 (8), 554
576. Available from: https://doi.org/10.1080/19392699.2018. 1491844. Bagnold, R.A., 1954. “Experiments on a Gravity-Free Dispersion of Large Solid Spheres in a Newtonian Fluid under Shear,” Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences. The Royal Society, 225(1160), 49
63. Available from: ,http://www.jstor.org/stable/99440. (accessed 08.05.20.). Brackbill, J.U., Kothe, D.B., Zemach, C., 1992. A continuum method for modeling surface tension. J. Comput. Phys. 100 (2), 335
354. Available from: https://doi.org/10.1016/00219991(92)90240-Y. Burt, R.O., Mills, C., 1984. Gravity Concentration Technology, Developments in Mineral Processing. Elsevier, Amsterdam. Chu, L.-Y., Luo, Q., 1994. Hydrocyclone with high sharpness of separation. Filtration & Sep. 31 (7), 733
736. Available from: https://doi.org/10.1016/0015-1882(94)80156-8. Ding, J., Gidaspow, D., 1990. A bubbling fluidization model using kinetic theory of granular flow. AIChE J. 36 (4), 523
538. Available from: https://doi.org/10.1002/aic.690360404. John Wiley & Sons, Ltd.

362

Mineral Processing

Driessen, M., 1945. The use of centrifugal force for cleaning fine coal in heavy liquids and suspensions with special reference to the cyclone washer. J. Inst. Fuel 18, 33
50. Dungilson, M., 1998. A model to predict the performance of the dense medium cyclone for low and high density applications. Seventh JKMRC Conf. Brisbane, Australia. Engelbrecht, J., Bosman, J., 1995. Design criteria for an improved large diameter dense medium cyclone. Proc. Seventh Australian Coal Preparation Conf. Australian Coal Preparation Society. Fanglu, G., Wenzhen, L., 1987. Measurement and study of velocity field in various cyclones by use of laser Doppler anemometry. 3rd Int. Conf. Hydrocylones Oxford, England, 30 September 1987. Fu, S., Launder, B., Leschziner, M., 1987. Modelling strongly swirling recirculating jet flow with Reynolds-stress transport closures. 6th Symposium Turbul. Shear. Flows . Gibson, M.M., Launder, B.E., 1978. Ground effects on pressure fluctuations in the atmospheric boundary layer. J. Fluid Mech. 86 (3), 491
511. Available from: https://doi.org/10.1017/ S0022112078001251. 2006/04/12. Cambridge University Press. Gidaspow, D., 1994. Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions. Academic Press. He, Y., Laskowski, J., 2000. Rheological properties of magnetite suspensions. Miner. Procesing Extractive Metall. Rev. 20 (1), 167
182. Taylor & Francis. Hirt, C.W., Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. J. computational phys. Citeseer 39 (1), 201
225. Ishii, M., Mishima, K., 1984. Two-fluid model and hydrodynamic constitutive relations. Nucl. Eng. Des. 82 (2
3), 107
126. Elsevier. Launder, B.E., Reece, G.J., Rodi, W., 1975. Progress in the development of a Reynolds-stress turbulence closure. J. fluid Mech. 68 (3), 537
566. Cambridge University Press. Mangadoddy, N., Vakamalla, T.R., Kumar, M., Mainza, A., 2020. Computational modelling of particle-fluid dynamics in comminution and classification: a review. Min. Process. Extract. Metall. 129 (2), 145
156. Available from: https://doi.org/10.1080/25726641.2019.1708657. Manninen, M., Taivassalo, V., Kallio, S., 1996. On the mixture model for multiphase flow. Technical Res. Cent. Finl. Finland. Mathewson, D., Dark, C., Vince, A., 1998. Dense medium cyclone performance analysis and trials at Peak Downs mine. XIII Int. Coal Preparation Congr. Brisbane, Australia. Mei, R., 1992. An approximate expression for the shear lift force on a spherical particle at finite reynolds number. Int. J. Multiphase Flow 18 (1), 145
147. Available from: https:// doi.org/10.1016/0301-9322(92)90012-6. https://www.sciencedirect.com/science/article/abs/ pii/0301932292900126#!. Napier-Munn, T., Scott, I., 1990. The effect of demagnetisation and ore contamination on the viscosity of the medium in a dense medium cyclone plant”. Miner. Eng. 3 (6), 607
613. Elsevier. Narasimha, M., et al., 2007a. A comprehensive CFD model of dense medium cyclone performance. Minerals Engineering 20 (4), 414
426. Elsevier. Narasimha, M., et al., 2014. A semi-mechanistic model of hydrocyclones—Developed from industrial data and inputs from CFD. Int. J. Miner. Process. 133, 1
12. Elsevier. Narasimha, M., Brennan, M., Holtham, P., 2007b. Prediction of magnetite segregation in dense medium cyclone using computational fluid dynamics technique. Int. J. Miner. Process. 82 (1), 41
56. Elsevier. Narasimha, M., Brennan, M., Holtham, P., 2012. CFD modeling of hydrocyclones: prediction of particle size segregation. Miner. Eng. 39, 173
183. Elsevier.

Numerical modeling of dense medium cyclones Chapter | 9

363

Qi, Z., Kuang, S.B., Yu, A.B., 2015. Numerical investigation of the separation behaviours of fine particles in large dense medium cyclones. Int. J. Miner. Process 142, 35
45. Richardson, J., Zaki, W., 1954. Sedimentation and fluidisation: Part I. Trans. Inst. Chem. Eng. 32, 35
53. Elsevier. Rong, R., Napier-Munn, T., 2003. Development of a more efficient classifying cyclone. Coal Prep. 23 (4), 149
165. Taylor & Francis. Saffman, P., 1965. The lift on a small sphere in a slow shear flow. J. fluid Mech. 22 (2), 385
400. Cambridge University Press. Schiller, L., Naumann, A., 1935. A drag coefficient correlation. Zeit. Ver. Deutsch. Ing. 77, 318
320. Sripriya, R., Banerjee, P.K., Soni, Baijal, A.D., Dutta, A., Rao, M.V.S., Chatterjee, S., 2007. Dense-medium cyclone: plant experience with high near-gravity material Indian coals. Coal Prep. 27, 78
106. Subramanian, V.S., 2002. Measuring Medium Segregation in the Dense-Medium Cyclone Using Gamma-Ray Tomography (Ph.D. thesis). University of Queensland. Vakamalla, T.R., Mangadoddy, N., 2015. Rheology-based CFD modeling of magnetite medium segregation in a dense medium cyclone. Powder Technol. Elsevier 277, 275
286. Available from: https://doi.org/10.1016/j.powtec.2015.02.025. Vakamalla, T.R., Vadlakonda, B., Aketi, A.K., Mangadoddy, N., 2017. Multiphase CFD modelling of mineral separators performance: validation against tomography data. Trans. Indian Inst. Met. 70 (2), 323
340. Available from: https://doi.org/10.1007/s12666-016-0995-4. Wang, B., et al., 2009. Modeling the multiphase flow in a dense medium cyclone. Ind. & Eng. Chem. Res. 48 (7), 3628
3639. ACS Publications. Wang, B., Chu, K., Yu, A., 2007. Numerical study of particle 2 fluid flow in a hydrocyclone. Industrial & engineering chemistry research 46 (13), 4695
4705. ACS Publications. Wilcox, D.C., 1998. Turbulence Modeling for CFD. DCW industries, La Canada, CA. Wills, B.A., Finch, J., 2015. Wills’ Mineral Processing Technology: An Introduction to the Practical Aspects of Ore Treatment and Mineral Recovery. Butterworth-Heinemann. Wood, C.J., 1990. A Performance Model for Coal-Washing Dense Medium Cyclones (Ph.D. thesis). School of Engineering, The University of Queensland.

This page intentionally left blank

Chapter 10

Froth flotation and its modeling aspects B. Venkoba Rao DELKOR, Takraf India Private Limited, Bengaluru, Karnataka, India

10.1 Introduction Flotation is an important physicochemical process of particle separation, which is based on differences in the surface property of the minerals. It is a key unit operation for the beneficiation of minerals from the ore deposits that show fine liberation characteristics. Flotation has been in vogue for more than 100 years now. The technique has converted many of the old gravity concentrator tail dumps into useful resource material. The reasons are that the flotation technique can beneficiate much finer particles than the gravity concentrators. It can effectively separate minerals from lean-grade ores predominantly using surface properties rather than gravity differences. Operations like grinding, size classification, and conditioning of the feed ore particles along with suitable reagent additions are prior steps in flotation. Flotation follows a wet slurry process, wherein the required minerals from the input feed slurry are selectively floated to the top surface in an agitated holding tank by the use of fine disbursed air bubbles along with suitable reagents, which make the minerals of interest attach to air bubbles and bring them to the froth phase. The operation is carried out in several stages using flotation cells with varying capacities, arranged in series and/or parallel, as per the process requirements. Flotation upgrades ores from a given head grade to the final concentrate grade in several stages by cleaning and re-cleaning the rougher concentrates and scavenging the rougher tails to recover any left-out valuables in the reject streams. The number of stages provides the required residence time for the minerals to float and allows the minerals to refloat in subsequent stages before the slurry exits from the flotation circuit. The minerals are ground before flotation to liberate valuable minerals from their matrix associations with the gangue minerals. This also brings the particles to a consistent size range for flotation so that they can be Mineral Processing. DOI: https://doi.org/10.1016/B978-0-12-823149-4.00010-7 © 2023 Elsevier Inc. All rights reserved.

365

366

Mineral Processing

selectively uplifted by a swarm of air bubbles in the flotation cell. Grinding also creates a fresh surface for the minerals onto which the added reagents adhere and induce selectivity for floatation. If there is a lack of adequate liberation of valuable minerals, upgrading the feed to the specified grade becomes challenging using the flotation technique. Moreover, too fine particles (that are below 5
10 microns), as well as too large particles (that are above 500
800 microns), cannot be floated efficiently in industrial cells. Effective flotation of the particular size range of particles is quite dependent on the mechanism profile design, cell design, density of the ore particles and the reagent chemistry. Basically, flotation operation can be viewed as a one-input (i.e., feed stream), and two-output (i.e., concentrate and tail stream) system. Typically, for a mechanical flotation cell, the feed slurry enters the cell continuously at the bottom by a gravity flow from a feed column adjacent to the tank, which then gets churned by the rotor-stator mechanism in the holding tank, wherein the particles are made to collide with the swarm of air bubbles created by the stator-rotor mechanism. The pumping of the slurry by the rotor blades within the tank and the speed of rotation creates a suitable hydrodynamic flow pattern within the cell. Computational Fluid Dynamics (CFD) analysis and careful dye tests can reveal the flow patterns at various zones across the height of the flotation cell. The mechanism (i.e., the rotor-stator combination) is said to be the heart of the flotation cell. The mechanism shears the incoming air stream into small bubbles suitable for flotation operation. The bubbles thus generated show a typical Bubble Size Ddistribution (BSD), which in turn depends on the profile of the mechanism, rotor speed, and the air velocities. Usually, the bubbles generated by various mechanisms are well below 3 mm, and especially below 1 mm as stated in the literature. Their distribution and dispersion within the cell depend on the mechanism used and rotor tip speed. Due to intense agitation, the mechanism enables the incoming feed particles to collide with the generated air bubbles. There is a high probability that the hydrophobic particles within the slurry will get attached to these bubbles and rise to the top of the cell as froth, while the remaining slurry leaves the bottom of the cell as a tail stream. The exit location of the tail stream is usually placed at 180 degrees to the feed entry position to the cell, so that the short circuit of the feed to the exit stream is minimized. Thus, due to the flotation action the left-out slurry of the cell will be lean in the floatable mineral content. A large number of variables affect the flotation operation. Table 10.1 gives a list of measured, disturbance, manipulated, and controlled variables for a flotation operation (Klimpel, 1995; Bascur, 2019). Klimpel (1995) depicts a flotation system as a three-cornered interactive system as shown in Fig. 10.1, which includes equipment-related variables, operational variables and chemical reagents.

Froth flotation and its modeling aspects Chapter | 10

367

TABLE 10.1 Variables affecting flotation operation. Control related variables

Variables Operational related

Machine related

Reagent related

Disturbance

Mineralogical composition; Particle size distribution; Degree of oxidation; Throughput from the mill(s); Water characteristics; Pulp viscosity; Head grade;

Stator-rotor wear; Wear of dart valves; Shaft pulley belt issues; Maintenance issues;

Supplier variance; Reagent quality;

Manipulated

Feed percentage of solids; Water addition points; Water flow rate(s);

Airflow rate(s); Pulp level(s); Froth washing rate; Stream diversion;

Reagent addition points; Collector addition rate; Frother addition rate; Modifier addition rate;

Control

Product yield; Concentrate grade; Concentrate recovery; Circuit circulating loads;

Tip speed; Power Intensity;

Slurry pH

While the enrichment happens in stages, the process demands a high recovery of mineral from the feed into the final concentrate, so that the process can be sustained economically. It is essential not only to liberate the minerals in the feed ore stream to assist their recovery into the concentrate but also not to lose them as unrecovered minerals to the tails. Thus, a requirement for optimum grinding of a given ore can be established through laboratory studies and the results can be translated to the plant operations. A flow sheet for beneficiation of a given ore is derived from several laboratory tests under varied conditions. Sometimes, the tests are conducted in two or three reputed and established laboratories to determine an economically viable flow sheet for the beneficiation and to gain confidence in the results. This is because a large number of variables affect the flotation process. Grind size, reagent suite, the effect of pH, stages of treatment, circuit configuration, achievable final grade-recovery values, suitability of the site and/or recycled water for the process, etc., are decided based on these tests. A flow sheet also decides the requirements of capital and operating expenses (CAPEX and OPEX) requirements for a given flotation project. Sometimes, pilot-scale tests are also

368

Mineral Processing

FIGURE 10.1 Representation of flotation system as a three-cornered interactive system. Based on Klimpel, R.R., 1995. The influence of frother structure on industrial coal flotation. In: Kawatra, S.K. (Ed.), High-Efficiency Coal Preparation. Society of Mining, Metallurgy & Exploration (SME), Littleton, CO, pp. 141
151.

undertaken to confirm the lab results before establishing a large-scale plant. Mineralogy and microscopic studies conducted on the feed samples and products will provide an in-depth understanding of the floatability of the mineral and the achievable grades. Exercise on the mine plan and blending of ores have to be conducted before laboratory testing of the ores. A representative (blended) ore that is going to be fed to the plant has to be tested in the laboratory for its performance, as the circuit configuration and stages of separation required to produce the desired grade and recovery will depend on the head grade and mineral associations of the feed ore. In general, flotation is conducted for the beneficiation and recovery of: (i) precious minerals-containing gold, silver, platinum, etc., (ii) metallic sulfide minerals such as copper, lead, zinc, nickel, and molybdenum, etc., (iii) metallic oxides such as hematite and cassiterite, etc., (iv) industrial minerals such as phosphates, fluorite, potash, talc, barite, and lime, etc., and (v) fuel minerals such as coal, bitumen and oil sands. In addition, flotation is used for the separation of plastics as well as in deinking of recycled paper pulp. Flotation has garnered academic and industrial interests at micro and macro levels. This chapter mainly focuses on important subtopics of the macro level of industrial interest, as it is not possible to cover the entire gamut of the subject due to its vastness and its implied applications. The reader is requested to refer to the available literature for specific topics of interest and specific mineral applications.

Froth flotation and its modeling aspects Chapter | 10

369

10.2 A brief description of flotation reagents Many types of reagents are used in flotation to induce hydrophobicity to floatable particles and to modify their surfaces as desired for the separation. These reagents and their dosages influence the rate constant of flotation as well. A hydrophobic particle becomes water repellent and attaches to an air bubble and rises to the froth phase. The contact angle between the bubbleparticle aggregate is a measure of hydrophobicity and indicates the strength of the adhesive force between them. The higher the contact angle, the higher will be the hydrophobicity and the higher the strength of the system for a good separation of particles. Collectors are surface-active organic compounds (e.g., oils) that are used to make selective mineral surfaces hydrophobic, which are added to conditioner tanks before the flotation operation. These compounds when adsorbed onto the mineral surfaces, displace polar water molecules, and make them aerophilic. Collectors are classified as ionizing and nonionizing compounds. The ionizing compounds are further classified into anionic and cationic compounds. Based on their chemical properties, anionic compounds are divided into oxyhydryl and sulfhydryl compounds (Wills and Finch, 2016). Frothers are organic compounds that comprise a polar and nonpolar group that are water-soluble and adsorb at the gas/liquid interface. The polar group interacts with water molecules, whereas the nonpolar group orients towards the center of the air bubble. These reagents stabilize the bubble from bursting and reduce the surface tension of the slurry by reducing the interfacial energy between gas and water. Frother addition is usually 5
10 ppm in flotation. Any excess addition will create micelle formation. In some cases, some collectors also have frother properties and in such cases, no additional frother will be required for flotation. To enhance selectivity among the separating minerals, reagents called regulators are used. These are classified as pH modifiers, activators, and depressants. pH modifiers create favorable conditions for flotation, where the collectors are stable and specifically adsorb on some minerals. Generally, alkaline pH conditions are preferred as they reduce equipment corrosion. pH modifiers can help to discriminate between minerals having similar surface characteristics. pH modifiers are added at the earliest possible point in the flotation circuit, probably in the grinding section before flotation. For some of the mineral flotation, activators are used to activate the flotation of valuable minerals by modifying the mineral surface to facilitate collector adsorption in greater quantities. Depressants act on unwanted minerals and prevent their flotation. The reagent suite namely the collector(s), frother, and modifier(s) has to be optimized for any given ore operation. To adopt a new reagent suite, several bench-scale studies have to be performed and if the results are encouraging and convincing, then they can be adopted for the plant operation.

370

Mineral Processing

10.3 Concepts of grade and recovery The separation of particles in a flotation operation (or circuit) is always measured in terms of the grade and the recovery of valuable mineral(s) in the final concentrate stream(s) of the circuit. The grade represents the quality of the product produced in terms of the assay or the metal content of the valuable mineral in the product stream, whereas recovery represents the quantity of valuable mineral recovered into the product stream from the feed stream. Fig. 10.2 shows a schematic representation of flotation (with a tank and launder arrangement), where F, C, and T respectively represent the solid flow rates of the feed, the concentrate, and the tail streams, and f, c, and t respectively represent the assays of the valuable mineral in those streams. When the circuit is in the steady-state of operation, the percentage recovery of the element/mineral, R, can be represented as: R 5 100

Cc Ff

ð10:1Þ

In the above equation, the ratio, C=F; represents the yield (or the mass fraction recovery of valuable mineral) and the ratio, c=f ; represents the enrichment of the valuable mineral being separated. Fig. 10.3 provides a schematic representation of the grade-recovery curve as a function of the particle selection from the ground particle spectra. The particle spectra consist of liberated valuable minerals, the middlings, and the liberated gangue minerals. For example, the recovery of only liberated valuable minerals will produce a concentrate of high grade but with very low recovery. The additional recovery of middlings into the concentrate lowers the grade of the overall concentrate but increases the recovery of valuable mineral to the concentrate stream. Contrarily, the whole of the feed stream directly considered as the product (i.e., without any beneficiation) will produce 100% recovery but the grade will be the same as the feed itself, with no separation of the valuable mineral from the associated gangue minerals. The laboratory flotation test work with suitable reagents will produce the possible grade-recovery patterns for a given ore, which is a combination of recovery of these spectral fractions of the ground ore in various ways. Normally, the recovery of the liberated valuable mineral and the highgrade middlings into the product stream makes it an economically viable

FIGURE 10.2 Schematic representation of flotation separation.

Froth flotation and its modeling aspects Chapter | 10

371

FIGURE 10.3 Grade-recovery curve as a function of particle selection of various grade particles from the liberation spectra.

separation for many applications. The grade of the concentrate produced should satisfy the product specifications and/or the smelter norms for it to be sold in the market. Fig. 10.3 depicts an inverse relationship between grade and recovery for typical particle separation in a concentrator. The valuable mineral is distributed in the liberated valuable and middling particles, and the proportions of recovery of these fractions into the product stream depends on the grind size of the ore and the separation efficiency associated with the size fraction. Too fine grinding can liberate the valuable mineral(s) from the gangue minerals, but it is not encouraged in real operations due to the high grinding costs and associated decrease in recovery of very fine valuable mineral(s) by concentration processes such as flotation. Fig. 10.4 provides a schematic representation of three different types of grade-recovery curves, which arise due to the feed liberation characteristics. Curve (C) shows superior separation over the Curve (B), which shows better separation over the Curve (A) in terms of grade and recovery of the product. For a given operation, the grade-recovery curve can be optimized for a better separation. It is seen that the smooth curves represented in Fig. 10.4 are due to the kinetic study of semi-batch flotation tests conducted in a laboratory or due to the staged separations in industrial flotation cells. The cumulative grade and recovery curve obtained by summing the timed froth fractions shows that the separation values are dependent on the liberation characteristics as well as on the head grade of the ore sample and the reagent selectivity. When we look at the industrial circuits, the grade-recovery data for various shift

372

Mineral Processing

FIGURE 10.4 Schematic representation of grade-recovery inverse relationships.

operations generally shows a “scatter diagram” mainly due to variations in the flow rates of recycle stream and the associated variations in mass pulls at various subcircuits, arising from the imposed flotation operational conditions. In addition, notably the shift in the head grade (due to feed grade fluctuations) also shifts the grade-recovery values of the circuit. These aspects will be discussed in the next section. Given the factors that affect the graderecovery values (whether it is the grind size or the head grade or the operational set conditions), the flotation circuit operation has to be controlled online to optimize the circuit operational conditions to produce a targeted product of required grade at best possible yield from the incoming feed stream. In Fig. 10.5, circuit (A) shows a series of rougher cells with the incremental addition of floated valuables from each cell flowing to the concentrate stream. This configuration mainly increases the recovery of valuable mineral to the concentrate stream. Circuit (B) shows a series of cleaning stages with the incremental rejection of low-grade material as tails. This configuration mainly enhances the final concentrate grade. Both circuit (A) and circuit (B) with their incremental values at each stage, when cumulated, will produce a smooth grade-recovery curve like those shown in Fig. 10.4. This is mainly due to the absence of any recycle streams in these circuits. However, circuit (C) in Fig. 10.5 shows two streams being recycled back to the rougher feed, namely the scavenger concentrate and the cleaner tail streams. The variations in the mass pull in these two recycle streams (depending on the set operating conditions) affect the grade of the combined rougher feed stream, and thereby affect the grades and yield of all the circuit streams. These recycle streams thus shift the nature of the overall graderecovery value of the concentrate stream and hence depict scattered values on the grade-recovery plot for the various operational conditions. Figs. 10.6 and 10.7 show respectively the scatted grade-recovery plot of an industrial lead and zinc differential flotation circuit. The lead circuit has

Froth flotation and its modeling aspects Chapter | 10

373

FIGURE 10.5 Types of flotation circuits: (A) Staged roughing approach to enhance the product recovery; (B) Staged cleaning approach to enhance the product grade; (C) roughing-cleaning and scavenging approach with recycle streams to enhance product grade and recovery.

three cleaning stages, whereas the zinc circuit has four stages of cleaning, and the tails of each cleaning stage are recycled back to the previous separation stage. The scavenger concentrate is as well recycled to the rougher stage. The numbers on the plot indicate the campaign run numbers corresponding to various dates. Each run in these plots represents a steady-state condition of the circuit under a specified set of operating conditions. It is seen that some of the operational conditions show good grade-recovery values, while the other operational conditions show either poor grades and/or poor recoveries of lead and zinc minerals. Thus, the recycle streams of the flotation circuit contribute to the recovery of more valuable mineral to the concentrate stream but can also destabilize the target grade-recovery pattern of the circuit. So, to maintain product quality and quantity, it is essential to control the circuit operation by retuning the operating conditions dynamically at all time to get the best possible grade-recovery values. The last section of this chapter describes a process model approach that can help to achieve this control objective through constant optimization of the operating conditions of the flotation circuit for a given feed. In other words, the process model captures the entire gamut of grade-recovery scatter (shown in the above figures) in terms of their operational and process variables. Such process mathematical model(s) can become the backbone of the plant operations for its optimization and control.

10.3.1 Effect of head grade on mineral upgradation Head grade (also called the feed grade) affects the grade-recovery value of a flotation circuit and/or its subcircuits significantly. Usually, in an operating plant, the head grade fluctuates and this affects the performance of the

374

Mineral Processing

FIGURE 10.6 Variations in the product Grade-Recovery values for an industrial lead separation circuit, shown for various steady-state campaign runs. Based on Rao, B.V., Velan, H.K., Jamal, S.I., Mahadevan, R., 2014. Grade-recovery prediction of an operating plant using flotation model and operating conditions. Procedia Eng. 83, 148
158.

flotation circuit. With a fall in head grade, there will be a decrease in the achievable grade and recovery of the concentrate/product stream. Fig. 10.8 shows laboratory upgradation results of a Barite ore by reverse flotation, wherein the silica is floated out from the feed sample using an amine reagent in the basic pH range of B8.5. The Barite concentrate grade (remaining in the batch cell) is expressed in terms of particle density (g/cc) on the ordinate axis. The higher the particle density, the better is the grade of Barite concentrate. Several lab tests have been done for various reagent combinations for the three types of feed samples, having head grades corresponding to the densities of 3.7, 3.87, and 4.0 g/cc. For each feed sample type, the final grade and recovery of the lab flotation tests follow an inverse relationship individually. Each point on the plot corresponds to product produced from one flotation test under a given set of conditions for that head grade sample. The higher the head grade, the higher will be the position of

Froth flotation and its modeling aspects Chapter | 10

375

FIGURE 10.7 Variations in the product Grade-Recovery values for an industrial zinc separation circuit, shown for various steady-state campaign runs.

FIGURE 10.8 Effect of head grade (represented here by their feed density values) on GradeRecovery curves for Barite ore beneficiation. The grade here is expressed in terms of the density of the concentrate produced.

376

Mineral Processing

the grade-recovery curve as depicted on the plot. These lab tests are comparable to an industrial circuit represented in Fig. 10.5(A), with a series of rougher cells and thus the data produces a smooth inverse relationship. Suppose the objective of Barite flotation is to produce a concentrate bearing a product density of 4.2 g/cc, the plot shows that the yield will be 60% for a head grade of 3.7 g/cc, 70% for a head grade of 3.87 g/cc, and nearly 83% for a head grade of 4.0 g/cc. Circuit (B) in Fig. 10.5 also will produce smooth grade-recovery curves similar to those shown in Fig. 10.8 for the head grade variations. This type of circuit configuration is seen in Release Analysis, discussed later in this chapter. It should be noted that an increase in recovery also indicates a corresponding increase in the product yield value. For circuits with recycle streams as shown in Fig. 10.5(C), there will be a scattered grade-recovery plot with no smooth curves, and these plots will be similar to those indicated in Fig. 10.6 or Fig. 10.7, depending on the set operational conditions of the plant. However, such circuits with recycle streams also show an increase in product yield with an increase in head grade. Fig. 10.9 gives such a trend from the operational data of an overall lead beneficiation circuit represented by Fig. 10.10. Similar trends of an increase in the plant recovery with an increase in head grade (as shown in Fig. 10.9) have been presented by Napier-Munn

FIGURE 10.9 Plot showing an increase in product yield with increase in head grade, for a circuit shown in Fig. 10.10 having recycled streams.

Froth flotation and its modeling aspects Chapter | 10

377

FIGURE 10.10 Lead flotation circuit with roughing, scavenging, and three cleaning stages. Blue lines indicate sampled streams.

(1998) for Nickel, Zinc, Gold, and Copper-Gold plants. Bazin and Hodouin (1988) also showed that an increase in head grade increases the graderecovery of copper and zinc plants. Thus, it is clear that the achievable process guarantees for any flotation plant are also dependent on the head grade of the flotation feed stream and its ore compositional characteristics.

10.4 Smelter contract and economic sustenance To process an ore economically, the concentrate contained value (CCV, which is dependent on its metal content and the current market metal price) should be higher than the cost of mining and processing, and transportation. Loss of valuable mineral(s) to tailings has to be reduced to make the project viable. These losses to tails will depend on the mineralogy, texture associations of the ore, and the upgradation methods available for efficient concentration. If CCV is high, it allows plant owners to adopt expensive concentration processes such as grinding and flotation (that are dependent on reagents) as part of the beneficiation scheme. It should be noted that in mineral processing, milling and flotation are the two most expensive unit operations. As mineral processing operations aim to improve the economic value of the ore by concentration, it is always necessary to determine the best combination of grade-recovery for a given ore that produces the highest financial returns per ton of the ore treated. This greatly depends on the current price of the valuable product in the market, costs of mining and concentration, indirect costs incurred for the sustenance of the process plant, costs of transportation of concentrate to the smelter, and costs for smelter treatment. The costs of smelter treatment depend on the grade of the concentrate. A high-grade concentrate will have low smelter treatment costs and vice versa. However, the production of high-grade concentrate will have lower metal recovery during mineral upgradation. Therefore, an optimization of grade-recovery of valuable

378

Mineral Processing

mineral(s) that gives the highest returns from the smelter becomes essential with due considerations to smelter norms. If the costs of mining and concentration are kept minimum by following an adaptable and flexible approach for concentrate production in accordance with the market price, it will maximize the profit earned by the concentrator or the mill plant. A smelter contract is an agreement between the smelter and the concentrator on the pricing of the concentrate produced by the concentrator when the concentrate is delivered to the smelter. The quality of the concentrate in terms of its grade, moisture, presence of precious metals, and contaminants is quite important from the viewpoint of the operation of the smelter. Some impurities are difficult to remove in the smelter during metal production and these impurities will intervene in the subsequent processes when their concentration is more than the prescribed safe limits by the smelter norms. The smelter will penalize the concentrator for these elements, when present in more than the prescribed limits. For example, the smelter levies penalty for the excessive presence of arsenopyrite in tin concentrate and similarly for lead in copper concentrate. On the contrary, the presence of precious metals in the concentrate is a bonus. The presence of these precious metals make some of the low-grade copper ores economically viable for beneficiation. It is always essential to maintain the costs of mining, processing, and indirect costs at a minimum as much as possible, without compromising on the smooth operation of the plant. The indirect costs involve salaries, administration, laboratory, research and development, and medical and safety costs. The direct processing costs involve operation and maintenance, supplies, and energy, which mainly depend on the size and complexity of the operations. Large-scale operations have higher capital investment but lower operating costs than small-scale operations. The cost of underground mining is higher than the open-pit operations. Cheaper mining methods like alluvial mining, make even very low-grade or low-priced metal ore, such as 1% tin ore economically viable for beneficiation (Wills and Finch, 2016). Bulk rejection of tailings at coarse size, the choice of the beneficiation method and the separating equipment, mineralogical studies that decide grind size for fair liberation of valuable mineral to achieve targeted grade-recovery, minimization of over-grinding of minerals in the mill-classifier circuits, minimization of stages of beneficiation through proper selection of recycling streams, minimization of reagent consumption with efficient unit operations, building tolerance in the beneficiation circuit to the known feed fluctuations in terms of head grade and throughput, maintenance of the adequate quality of process water, choice of dewatering circuits to reduce the moisture content of product streams, adoption of environmentally safe waste disposal techniques, minimization of energy consumption, etc. have to be reviewed during the circuit development stage to reduce CAPEX and OPEX costs and to have a circuit that is flexible enough for reliable product production.

Froth flotation and its modeling aspects Chapter | 10

379

A smelter contract will guide the expected grade of the concentrate to be produced from the concentrator that is likely to earn maximum net smelter returns (NSR) based on the market price. Usually, the price at the London Metal Exchange (LME) is considered for the transactions. The grade choice will decide the possible recovery of the mineral, based on the grade-recovery curve that the concentrator can produce. In other words, a smelter contract will dictate the concentrator for a specific grade-recovery production that gives more returns. The NSR is given by: NSR 5 Smelter Payments 2 ðSmelter Charges 1 Transport CostsÞ

ð10:2Þ

Further, the profit or loss that the concentrator earns can be calculated by deducting mining costs and direct and indirect processing costs from NSR. Table 10.2 gives a typical tin smelter contract in a simplified form (Wills and Finch, 2016). Fig. 10.11(A) gives a typical tin grade-recovery curve from a plant whose feed has 1% Sn. It costs $26 per dry ton to transport the concentrate to a nearby smelter. Suppose the cost of mining is $52 per dry ton and the cost of processing is $10.4 per dry ton, Table 10.3 gives the calculation chart to find out the best grade-recovery combination to maximize the NSR and hence the profit, when the LME price of the tin market is at $ 11000/ton. Here it is assumed that the concentrate is free from arsenic

TABLE 10.2 Simplified tin smelter contract. Material

Tin concentrates, assaying no less than 15% Sn, to be free from deleterious impurities not stated and to contain sufficient moisture as to evolve no dust when unloaded at our works.

Quantity

Total production of concentrates.

Valuation

Tin, less 1 unit per dry ton of concentrates, at the lowest of the official LME prices.

Pricing

On the seventh market day after the completion of the arrival of each sampling lot into our works.

Treatment charge

US$501 per dry ton of concentrates.

Moisture

US$31 per ton of moisture.

Penalties

Arsenic US$52 per unit per ton.

Lot charge

US$228 per lot sampled ,17 t.

Delivery

Free to our works in regular quantities, loose on a tipping lorry (truck) or in any other manner acceptable to both the parties.

Source: Based on Wills, B.A., Finch, J.A., 2016. Wills’ Mineral Processing Technology, eighth ed. Butterworth-Heinemann, Oxford.

380

Mineral Processing

FIGURE 10.11 Net smelter returns (NSR) for the tin processing: (A) grade-recovery curve from the plant performance; (B) NSR for the current market price; (C) NSR when the tin price in the market increases. Data from Wills, B.A., Finch, J.A., 2016. Wills’ Mineral Processing Technology, eighth ed. Butterworth-Heinemann, Oxford.

TABLE 10.3 NSR calculation chart for the example discussed in the text. Grade, Sn %

Recovery, Sn %

Concentrate produced, kg

Smelter payment, $

Treatment charges, $

Transport charges, $

NSR, $

Profit, $

21.00

78.00

37.14

81.71

18.61

0.97

62.14

-0.26

25.00

77.19

30.88

81.51

15.47

0.80

65.24

2.84

30.00

75.95

25.32

80.76

12.68

0.66

67.42

5.02

42.00

72.00

17.14

77.31

8.59

0.45

68.28

5.88

50.00

68.75

13.75

74.11

6.89

0.36

66.87

4.47

63.00

62.00

9.84

67.12

4.93

0.26

61.93

-0.47

382

Mineral Processing

contaminants and hence there are no penalties. The calculations are made on the per ton basis of the throughput treated. This is depicted in Fig. 10.11(B) where the various cost curves are shown as a function of concentrate grade produced. Fig. 10.11(C) shows NSR and profit curves as a function of tin concentrate grade produced at the concentrator when the tin market price increases to US$16,000/ton. This increase in market price for tin lowers the NSR maxima from 42% Sn (as referred to in Fig. 10.11(B)) to a value of 30% Sn in the concentrate (as referred to in Fig. 10.11(C)), indicated by the red vertical lines on these plots. Thus, an increase in the market price not only shifts the expected grade from the concentrator plant to the lower values (making it easy to process) but also increases the profit margins, if the smelter accepts that grade concentrate.

10.5 Flotation kinetics From the process standpoint, it is important to know the kinetics of flotation, as these tests suggest how the grade and yield of the product change with progress in flotation time under given test condition(s). The mean residence time required for flotation to achieve the required grade and recovery in an industrial bank of cells is mainly derived from a knowledge of flotation kinetics.

10.5.1 First-order kinetics Taking chemical analogy into consideration, Beloglazov (1939) proposed that the rate of decrease of floatable material in a semi-batch flotation is proportional to the concentration of floatable mineral in the cell, which is given by: dM ðtÞ 5 2 k M ðtÞ dt

ð10:3Þ

where M ðtÞ is the amount of floatable material in the cell at a time, t, and k is the overall first-order rate constant for the separation. Integrating Eq. (10.3) with initial conditions gives: M ðtÞ 5 M ð0Þ expð 2 k tÞ

ð10:4Þ

where M ð0Þ represents the initial concentration of floatable material in the cell. The recovery of floatable mineral from the cell into the froth stream at the time, t, is given by: Rð t Þ 5 1 2

M ðtÞ M ð 0Þ

ð10:5Þ

Froth flotation and its modeling aspects Chapter | 10

383

Therefore, Eq. (10.4) can be written as: RðtÞ 5 1 2 expð 2 k tÞ

ð10:6Þ

10.5.2 Modified first-order kinetics Quite often Eq. (10.6) shows deviations in the fitment to first-order kinetics to an experimental flotation data due to the inability to float some of the floatable material from the cell. It has to be noted that even after an infinite time of allowance, 100% recovery of floatable material from the pulp is seldom attained from experiments, even under proper reagent dosing conditions. For a particle to report to the froth phase, the mineral should be exposed to the reagents at the particle surface. But, if the floatable species is present as microinclusions in the particles, levitation by bubbles may not take place, resulting in truncated recovery called “terminal-recovery” even after a long time of flotation. Therefore, the first-order rate equation can be modified to: dM ðtÞ 5 2 k ðM ðtÞ 2 M ðNÞÞ dt

ð10:7Þ

where M ðNÞ represents the irrecoverable float material in the feed. Integrating the above equation and rearrangement of terms results: RðtÞ 5 RN ð1 2 expð 2 k tÞÞ

ð10:8Þ

where RN represents the maximum percent of recoverable floatable material from the feed. Moreover, the time of flotation needs correction by a factor, φ (with either positive or negative value), which transforms Eq. (10.6) to the following form (Agar, 1987). RðtÞ 5 RN ð1 2 expð 2 kðt 1 φÞÞÞ

ð10:9Þ

The rate constant, k, in the above equation is called the apparent rate constant. It is because the flotation rate constant depends on operating conditions, such as pH of the slurry, pulp density, liberation characteristics of the ore, type, and dosage of the reagents and the machine characteristics, such as BSD, aeration rate, hydrodynamic mixing conditions, etc. Flotation rate constants of sulfide minerals are generally higher than those of oxide minerals. Usually, flotation rates increase with increasing particle size (up to a limit size) by having smaller bubble sizes and increasing collector dosage. Recently, it has been found that an increase in energy input (expressed in kW/m3) alters flotation rates. Typically, it has been found that an increase in energy input increases the rate of flotation of the fines (below 20 microns), retains optimum flotation rate for moderate particles (between 20 and 45 microns), and decreases the rate of flotation for coarse particles (above 45

384

Mineral Processing

microns) (Safari et al., 2016). At high energy inputs, the turbulence created will dislodge the coarse particles attached to the air bubbles and increase their drop back to the pulp phase and thus decrease their flotation rates. Usually, platinum flotation uses 3 kW/m3 of high-power density and copper flotation uses 0.7
1.2 kW/m3 (Nelson et al., 2009). Recently, Safari et al. (2017) reported that the optimum conditions for PGM flotation are achieved either using small bubbles at low energy inputs, or large bubbles at higher energy inputs. The higher the rate constant, the higher will be the rate of recovery of minerals into the froth phase and then into the launder and the lesser will be the residence time required to float the mineral. This in turn will require lesser cell volume for flotation operation. The rate constant is expressed in units of “per unit time.” It has been found that the rate constants of laboratory flotation tests will be higher than what is found in plant operation. The bypass of slurry at the tank bottom, recirculating flow patterns, the drop back of floated material from froth phase to the pulp phase in the industrial cells are some of the reasons for the decrease in the flotation rate constant for the industrial cells, which generally will be compensated by more residence time for industrial operation. Usually, the scale-up factor for residence time from bench scale to plant scale will be B1.8 to 2.5 times the lab value and this factor is dependent on the mineral type being floated (Noakes and Lanz, 1993; Metso Corporation, 2015). For example, in a semi-batch flotation cell, the kinetics of flotation of valuable and gangue minerals are represented by the following equations, where the flotation time is expressed in seconds: Rvaluable Rgangue

mineral mineral

5 0:95 ð1 2 expð 2 0:02 ðt 1 5ÞÞÞ & 5 0:25 ð1 2 expð 2 0:002 ðt 1 10ÞÞÞ

ð10:10Þ

The recoveries of valuable and gangue minerals can be visualized as shown in Fig. 10.12. The plot indicates that the valuable mineral floats at a faster rate, while the gangue mineral floats at a slower rate. It should be noted that any further removal of the floated gangue mineral from the froth requires a cleaner circuit to enhance the grade of the product. The initial fraction of the float will mainly consist of liberated valuable minerals and will be followed by recovery of middling particles as time progresses. In other words, the recovery rate, and the grade of the floated material, will fall as time progresses. For the above example, Fig. 10.13 shows the rate of fall in the recovery of the floatable species (both valuable and the gangue mineral) on a semi-log plot. It shows that the rate of recovery of gangue minerals exceeds that of the valuable mineral after a certain period of flotation. The time where the lines cross each other can be considered as the limiting period for the flotation (Agar, 1987).

Froth flotation and its modeling aspects Chapter | 10

385

FIGURE 10.12 Kinetics of flotation of valuable and gangue minerals defined by Eq. (10.10).

FIGURE 10.13 Fall in the rate of recovery of valuable and gangue minerals, as a function of float time for kinetics represented by Eq. (10.10).

386

Mineral Processing

10.5.2.1 Separation efficiency Schulz (1970) represented the separation efficiency, S. E., of floated minerals as: S:E: 5 Rvaluable

mineral

2

Rgangue

mineral

ð10:11Þ

The above equation represents the difference in recoveries of valuable mineral and gangue mineral for a concentrate. When the difference is maximum, it is considered that the separation is more efficient. The limiting time of flotation (for Fig. 10.13) can be obtained from Eq. (10.11) by setting: dðS:E:Þ 50 dt

ð10:12Þ

Solving the above equation with rearrangement of terms gives:   k R 2 kg φg 1 kv φv 1 ln kgv Rgv
 tlimit 5 kg 2 kv

ð10:13Þ

where suffix v stands for valuable mineral and g stands for gangue mineral. For the above example, tlimit is 198 seconds (as seen in Fig. 10.13). Wills and Finch (2016) analyzed the separation efficiency of the graderecovery separation scenario. The floated valuable mineral is said to have metal content, m. Its mineral assay is expressed as c=m. The remaining gangue mineral content of the concentrate is g 5 1 2 ðc=mÞ. The feed mineral content is f =m. The recovery of gangue mineral in the concentrate is thus expressed as:
 C 1 2 mc C ðm 2 cÞ Rg 5
ð10:14Þ 5 f F ðm 2 f Þ F 12 m Thus, Schulz mineral separation efficiency in Eq. (10.11) is calculated in terms of metallic contents as: S:E: 5

C F

ðc=mÞ ðf =mÞ

2

C F

ðm 2 cÞ C 5 ðm 2 f Þ F

m ðc 2 f Þ f ðm 2 f Þ

ð10:15Þ

Nonmetallic minerals like fluorite are directly expressed in mineral content (CaF2%) rather than metal content. Therefore, the maximum assay of separation of fluorite mineral can be considered as 100%, i.e., assay corresponding to the pure mineral. Table 10.4 gives yield % and grade of CaF2% achieved in roughing followed by staged repeated cleaning (similar to a case represented in Fig. 10.5(B)) for an ore containing 33.4% CaF2. The Schulz separation efficiency of this upgradation is shown in Fig. 10.14. Fig. 10.14 shows that the maximum Schulz separation efficiency of 87.26% occurs at 92.66% CaF2. However, acid-grade fluorite beneficiation

Froth flotation and its modeling aspects Chapter | 10

387

TABLE 10.4 The separation efficiency of fluorite mineral flotation for the given test condition response. Yield %

CaF2%

Recovery %

Gangue mineral %

Gangue recovery %

Separation efficiency (S.E., %)

28.40

95.10

80.86

4.90

2.09

78.77

29.86

94.97

84.91

5.03

2.25

82.66

31.09

94.37

87.83

5.63

2.63

85.21

32.75

92.66

90.87

7.34

3.61

87.26

36.73

84.80

93.26

15.20

8.39

84.87

48.33

66.03

95.54

33.97

24.65

70.89

71.12

45.65

97.21

54.35

58.04

39.18

100.00

33.40

100.00

66.60

100.00

0.00

FIGURE 10.14 Schulz separation efficiency as a function of yield for fluorite mineral for the given test condition.

always requires a minimum grade of 96.5% CaF2 to be achieved. Thus, Schulz separation efficiency should be considered as a guide for achieving the highest recovery possible at the best possible grade. However, for any

388

Mineral Processing

economically viable upgradation, a smelter contract and NSR always should be used as a guide to the process plant operation (Wills and Finch, 2016). A parametric approach to the bench-scale flotation kinetic studies also has been used to improve plant performances. A coal flotation bank performance containing four Outokumpu cells was optimized using the results obtained from the laboratory studies and analyzing the results using statistical techniques, resulting in more yield of coal with reduced ash (Sripriya et al., 2003).

10.5.3 Higher-order flotation kinetics As discussed earlier, the kinetic data from flotation tests may show a deviation from the first-order kinetics. In such cases, it can be thought that the second- or third-order kinetics may better explain the process. For the nth order kinetics ðn $ 2Þ; the fraction of mineral remaining in the cell is represented as: MðtÞ 5 Mð0Þ

Mð0Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 ðn 2 1Þ k t M ðn21Þ ð0Þ

ðn 2 1Þ

ð10:16Þ

Usually, the floatable species in the feed, M ð0Þ; is considered to be unity so that the fraction remaining in the cell at the time, t, can be expressed as M ðtÞ: Fig. 10.15 gives a pictorial view of the second-, third-, and fourthorder kinetics of a floatable material having a rate constant, k 5 0.02 sec21. It is seen that as the kinetic order goes up, the fraction remaining in the cell also goes up, and hence there is less recovery of mineral to the froth phase with an increased order of flotation kinetics. There is difficulty in explaining the physical relevance of these higher-order models and there is no compelling reason to abandon first-order kinetic behavior, just because of the poor fit to the experimental data. The feed can be thought as composed of material with distributed first-order rate constants, which will solve the issue of data fitment, while also retaining the first-order kinetics structure to the flotation phenomenon. Moreover, in reality, the fastfloating (liberated) species will float first, followed by the slow-floating (middling) species during the flotation operation. In a way, this behavior supports the existence of distributed rate constants for the floatable species.

10.5.4 Kinetic models with distributed rate constants To improve the fitment of kinetic data obtained from batch flotation, Kelsall (1961) proposed that the feed is comprised of two discrete fractions, a fastfloating species and a slow-floating species, which float at two different flotation rates. The mass fraction of the mineral remaining in the cell at the time, t, is represented by:
 M ðtÞ 5 φslow expð 2 kslow tÞ 1 1 2 φslow expð 2 kfast tÞ ð10:17Þ

Froth flotation and its modeling aspects Chapter | 10

389

FIGURE 10.15 Typical flotation behavior of material using higher-order kinetics.

where φslow represents the fraction of slow-floating species, and kslow and kfast represent the slow and fast-floating species rate constants respectively. The analogy can be extended to any number of discrete fractions, but it is necessary to satisfy: (i) the mass fractions should add up to unity, and (ii) each species should have a different first-order floatation rate constant. However, instead of having a predetermined number of discrete fractions representing the flotation kinetics, it can be thought that feed has a continuous distribution of particles with a varied first-order rate constant in the range 0 to N. Suppose M ðkÞ represents feed particle distribution (in density functional form) whose rate constant varies between k to k 1 dk; then the fraction of floatable species remaining in the cell at time t, i.e., M ðtÞ is represented by: ðN M ðt Þ 5 M ðkÞ expð 2 k tÞ dk ð10:18Þ 0

Also, the material balance constraints imply: ðN M ðkÞ dk 5 1

ð10:19Þ

0

Traditionally the above equation has been solved by assuming feed distribution represented by a few standard forms as shown in Table 10.5. These assumed standard forms may not truly represent the actual feed distributions in rate constants. Kapur and Mehrotra (1974) developed a

390

Mineral Processing

TABLE 10.5 Flotation kinetics with distributed rate constants for some of the standard functional feed forms. Feed distribution form Uniform/ rectangular distribution Exponential distribution Gamma distribution

Feed density distribution, M(k) 8 > < > :

1 for 0 # k # kmax kmax 0

Reference

ð1 2 expð 2 kmax t ÞÞ

Huber-Panu et al. (1976), Klimpel (1980)

ψ ψ1t

Imaizumi and Inoue (1963)

t kmax

for kmax # k # N

ψexpð 2 ψk Þ

1 km Γη

Mass fraction remaining in the cell, M(t)

 η21 k km

  exp 2 kkm



1 11km t

η

Imaizumi and Inoue (1963), Loveday (1966)

numerical method to carry out inversion of Eq. (10.18) to evaluate M ðkÞ from the experimental data by considering that M ðtÞ as Laplace transform of M ðkÞ. They used an 8-point Lobatto quadrature formula to solve the following equation wherein the feed M ðkÞ has been transformed into a cumulative form, RðkÞ to reduce solution sensitivity to experimental errors. ðN M ðtÞ 5 1 2 t RðkÞ expð 2 k tÞ dk ð10:20Þ 0

where RðkÞ is the cumulative form of the density function, M ðkÞ. The constraints imply that RðkÞ 5 1 when k 5 0 and RðkÞ 5 0 when k 5 N. Mehrotra and Padmanabhan (1990) developed an alternative numerical method to solve the feed distribution M ðkÞ when the maximum rate constant has a finite value much below infinity.

10.6 Some standard flotation testing procedures As flotation is a complex process of staged operations, it is essential to know the maximum recovery and maximum grade achievable for a given ore. To this end, some standard test procedures have been proposed in the literature, which are discussed briefly in this section.

10.6.1 Release analysis It is a procedure to characterize the ground feed ore, by separating it into several fractions of decreasing grade (or floatability). This fractioning is accomplished by repeated cleaning of the timed rougher flotation fractions

Froth flotation and its modeling aspects Chapter | 10

391

and combining all the tails from each stage of separation into a final tailings, in a manner described by Dell (1953) and Dell et al. (1972). Repeated cleaning stages reject the entrained gangue particles in the froth phase of the initial floats. The feed can be classified into different grades of particles based on their different surface flotation properties. This is a method similar to the concept of sink-float analysis of separating density fractions in gravity concentration and can help avoid liberation characterization under the microscope (Dell, 1953). Although the grind size, pH, and dosages of frother are similar to a normal plant test, plenty of collector dosage is usually desired to avoid stable froth (Dell, 1953). Two different test methods have been proposed (Dell et al., 1972), which are schematically represented in Figs. 10.16 and 10.17. The second method simplifies the original method and overcomes the difficulties of froth decantation every time before reintroducing the froth to the next cell operation, thus preventing overflow of pulp during the tests. However, it has been verified that both methods provide identical results (Sahu et al., 2019). In the second method, impeller speed and aeration rate are varied to collect the fractions, as these parameters influence the grade of the froth fraction. Table 10.6 gives an example of the release analysis data for metal recovery. The calculations of recovery and unit weights are made from the various

FIGURE 10.16 Diagrammatic representation of release analysis test: method A. Based on Dell, C.C., 1953. Release analysis
A new tool for ore dressing research. In: Recent Developments in Mineral Dressing. Institute of Mining and Metallurgy, London, pp. 75
84.

392

Mineral Processing

FIGURE 10.17 Diagrammatic representation of release analysis test: method B. Based on Sahu, L., Bhattacharya, S., Dey, S., 2019. Release analysis of coal fines: evolution of the methodology and critical issues involved. J. South. Afr. Inst. Min. Metall. 119, 595
606.

weight fractions and their assays. A plot of recovery vs unit weight is given in Fig. 10.18 for this data. Here, the unit weight refers to the weight/100 units of metal in the feed. On this plot, the slope of the curve between any two points represents the grade of that fraction. The unit weights can be converted to yield values by multiplying them with the feed grade. For example, Fig. 10.18 shows that it is possible to obtain the concentrate, the middling, and the tailing from the flotation of the given feed as indicated in Table 10.7. For a different grade concentrate, the slopes of the concentrate, middling, and tails can be rearranged in Fig. 10.18 and a decision can be made regarding regrinding and recycling of the middlings in the beneficiation circuit to enhance metal recovery at a higher grade.

10.6.2 Advanced flotation washability The traditional release analysis is conducted in a laboratory Denver flotation cell, which has turbulent mixing conditions within the cell and may hinder the process of finding out an optimum grade-recovery curve for a given ore. However, Mohanty et al. (1998) found that when the release analysis method (shown in Fig. 10.17) is followed on a coal sample with a packed flotation column (2 inches diameter and 5 feet tall) instead of the Denver flotation cell as shown in Fig. 10.19, a better optimum graderecovery curve was obtained. The enhanced selectivity is attributed to the plug-flow environment and the deep froth zone prevailing within the

TABLE 10.6 Release analysis of metal separation by flotation: an example. Fraction

Wt, g

Assay %

% Metal in the fraction, g

Cum Wt, g

Unit weight

Distribution %

Recovery %

Concentrate 1

24.5

55.60

13.62

24.50

69.48

38.63

38.63

Concentrate 2

27.5

43.00

11.83

52.00

147.47

33.53

72.17

Concentrate 3

18.5

31.90

5.90

70.50

199.93

16.74

88.90

Concentrate 4

21.4

10.90

2.33

91.90

260.62

6.62

95.52

Concentrate 5

14.3

4.41

0.63

106.20

301.17

1.79

97.30

Tails

132

0.72

0.95

238.20

675.51

2.70

100.00

Total

238.2

14.80

35.26

Source: Dell, C.C., Bunyard, M.J., Rickelton, W.A., Young, P.A., 1972. Release analysis: a comparison of techniques. Inst. Min. Metall. 81, C89
C96.

394

Mineral Processing

FIGURE 10.18 Release analysis curve for a metal separation. Based on Dell, C.C., Bunyard, M.J., Rickelton, W.A., Young, P.A., 1972. Release analysis: a comparison of techniques. Inst. Min. Metall. 81, C89
C96.

TABLE 10.7 Product fractions from release analysis. Fraction

Weight %

Assay %

Concentrate

26.65

46.06

Middlings

7.85

19.32

Tails

65.50

1.55

column. The dotted line shown in Fig. 10.19 separates the Phase I and Phase II activities of the test.

10.6.3 Flotation tree analysis Nicol et al. (1983) developed a “tree analysis” method to generate a graderecovery curve using repeated flotation of the products. Here separation is done using several cleaner and scavenger stages. Each flotation product is subjected to a repeated branch test, wherein the entrained particles are rejected to the tail stream to improve the grade of the concentrate stream. The collector is added as and when required. All mechanical parameters of the flotation test are kept constant throughout the experiment. Fig. 10.20 shows a four-level tree analysis test. Meloy et al. (1998) showed that the tree analysis can be represented as a triangular array of cells with the feed at its orthogonal corner. They showed

Froth flotation and its modeling aspects Chapter | 10

395

FIGURE 10.19 Schematic representation of advanced flotation washability (AFW) test procedure. Based on Mohanty, M.K., Honaker, B.Q., Patwardhan, A., Ho, K., 1998. Coal flotation washability: an evaluation of the traditional procedures. Coal Prep. 19(1
2), 33
49; Sahu, L., Bhattacharya, S., Dey, S., 2019. Release analysis of coal fines: evolution of the methodology and critical issues involved. J. South. Afr. Inst. Min. Metall. 119, 595
606.

FIGURE 10.20 A schematic representation of four-level tree analysis with the naming of the concentrates and tails obtained. Based on Meloy, T.P., Whaley, D.A., Williams, M.C., 1998. Flotation tree analysis
reexamined. Int. J. Miner. Process. 55, 21
39.

396

Mineral Processing

that the binomial expression ðC1T Þn represents the number of paths by which the particles reach the output stream in this test. For a three-level tree flotation, the binomial expression gives: ðC1T Þ3 5 CCC 1 3CCT 1 3CTT 1 TTT

ð10:21Þ

This indicates that there are mainly four product streams: one CCC stream; one TTT stream; three streams of CCT and three streams of CTT. For a four-level tree flotation, the binomial expression gives: ðC1T Þ4 5 CCCC 1 4CCCT 1 6CCTT 1 4CTTTT 1 TTTT

ð10:22Þ

In other words, in a four-level tree analysis, there is one product of type CCCC & TTTT; four products each of type CCCT and CTTT and six products of type CCTT: Fig. 10.21 gives a simplified version of Fig. 10.20 in triangular array form. Meloy et al. (1998) argued that there is no general grade-recovery boundary that is unique for a given ore and which can be determined from such flotation tests. They argued that the grade-recovery curve would always be dependent on operator skills, circuit design, froth/pulp level settings, and the type of equipment used for the separation. Through simulations, they showed that the sharpness of separation of the grade-recovery curve improves with more levels or stages of flotation.

FIGURE 10.21 Schematic representation of a four-level tree analysis (represented in Fig. 10.20) in a triangular array form. Based on Meloy, T.P., Whaley, D.A., Williams, M.C., 1998. Flotation tree analysis
reexamined. Int. J. Miner. Process., 55, 21
39.

Froth flotation and its modeling aspects Chapter | 10

397

However, an increase in the number of separation stages increases both CAPEX and OPEX of the plant. It is always recommended to minimize the number of stages of separation to get a better separation that meets the requirement of the final product, which thus lies at the skill set of the circuit designer.

10.6.4 Locked cycle test All the previous tests discussed above, do not have any recycle streams in the test work. In addition, a batch test will never reveal how a recycled material will report to either the concentrate or the tail, but the recycle streams (that usually merge with streams of equivalent composition in the circuit) are quite common in operating plants to reduce the number of separation stages, thus reducing the footprint of the plant and its CAPEX and OPEX. The recycle streams as well increase the yield and recovery of the valuable mineral in the final concentrate stream. It is common practice to develop a flow sheet for flotation with staged separations, based on responses from batch tests. The batch tests indicate the possibility of obtaining a desired grade product under a set of reagent suites. However, the recoveries achievable through recycling streams and their material split can only be studied through a locked cycle test (LCT), which mimics the industrial operation in a miniature version. Agar (1987) reports that there is always a good agreement between the two operations, that is, LCT and industrial circuit operation. Agar and Kipkie (1978) developed LCT to mimic operations of a continuous plant with recycle streams using batch tests. LCT involves cyclic batch tests to understand the grade-recovery and yield achievable for a given ore for a designed circuit configuration. The tests are tedious and involve many cycles of batch tests with additions of recycled material from the previous cycle at appropriate places in the next cycle. Usually, scavenger concentrate and cleaner tails are recycled within the circuit. These tests are continued under a specified reagent suite until a steady-state is reached, which represents the possible grade-recovery from the circuit. The fresh feed added to each cycle needs to be consistent in both composition and grind size. Owing to its miniature scale of operation, LCT saves cost, sample quantity, and labor essential to carry out a pilot-scale or continuous scale operations to verify the achievable grade-recovery for a given circuit configuration. Unlike the grindability tests for the ball mill, wherein the parameters for the next cycle are determined from the previous cycle, LCT results are analyzed only at the end of the entire test. Utilization of a cycle-by-cycle calculation procedure is recommended (Agar, 2000) to verify the achievement of steady-state conditions and to gain confidence in the tests.

398

Mineral Processing

The minimum number of cycles required to achieve a steady-state varies from three to fifteen cycles depending on the complexity of the ore and the circuit configuration. These tests can be used in general to test the effect of the following variables on the achievable grade and recovery (MacDonald et al., 1985; Thompson et al., 2019): G G G G

Circuit configuration. Reagent scheme and their dosages. Variability in the head grade and the ore composition. Effect of slime content and objectionable solids in the feed.

Since the pulp density needs to be continuously monitored and adjusted during the tests, several thickening, decanting, and filtration operations are involved, which may not exist in real plant operations. Therefore, these tests are used only for solid and component balance. Water balancing through LCT is not envisaged. Moreover, the aging of process water in tailing ponds and thickeners (that possess some reagent concentration) are not considered. If the water balance or effect of seawater is to be studied, pilot-scale tests are recommended (MacDonald et al.,1985; Thompson et al., 2019). Moreover, the tests have to be conducted continuously as far as possible without a time gap to avoid sample aging effects. Apart from this, these tests do not give any information on the kinetics of flotation. In LCT, the terminal products of each cycle, namely, the concentrate and the tail are dried, weighed, and subjected to chemical analysis. Similarly, the circulating streams from the final cycle are also analyzed after deciding to stop the LCT (Agar, 2000). One of the criteria for reliability of test results is to verify the attainment of steady-state in LCT. A steady-state would mean: (i) mass input equals mass output and (ii) no material accumulation internally. This can be viewed by plotting the amount of material flowing in circulating load, in the individual cycle product output flows and for the total circuit output flow as a function of cycle number, and also by verifying component balances (actual vs. calculated values) for the input-output and circulating streams, which should match in the last cycle, when the steady-state has been attained. Fig. 10.22 represents two different LCT plots. The sample weights flowing in output streams, total product stream, and circulating load are plotted as a function of cycle number. Fig. 10.22(A) represents results from Coleman’s data (Coleman, 1978) for a complex lead-zinc circuit with differential flotation of lead and zinc values, with a six cycle LCT. Fig. 10.22(B) represents results from Agar’s INCO bulk matte Cu-Ni separation with a nine cycle LCT. Fig. 10.22(A) indicates that steady-state is yet to be attained as revealed by the circulating load and weight of the product samples that are still increasing at the sixth cycle, whereas Fig. 10.22(B) indicates that the LCT has already attained a steady-state from the fourth cycle itself (Agar, 2000).

Froth flotation and its modeling aspects Chapter | 10

399

FIGURE 10.22 Verification for the attainment of steady-state in LCT: (A) Representation of Coleman’s data for Pb-Zn ore separation (Coleman, 1978); (B) Representation of Agar’s data for Cu-Ni bulk matte separation (Agar, 2000).

10.7 Data reconciliation Plant campaigns are usually conducted by setting up the desired operating conditions in the plant. The circuit is allowed to attain a fair degree of steady-state condition before undertaking a sampling campaign. During the campaign, samples of various streams across the flotation circuit are collected and sent to the laboratory for analyses. The samples are analyzed for assays, size distributions, size-wise assays, and pulp densities, as desired by the campaigner. The analyzed data is error-prone due to errors associated with sampling and chemical analysis, despite obseving utmost care. Sometimes human error also becomes unavoidable. Many streams in the circuit remain inaccessible during campaigns and hence, a local mass balance from the raw data becomes impossible. To use such data and to understand

400

Mineral Processing

the behavior of the circuit under the imposed operating conditions, a need for the mass balance of the complete circuit becomes essential. Smoothening of such error-prone measured data by minimal adjustment of the data, so as to maintain a mass balance of various components across the circuit can be accomplished by a data reconciliation exercise. Mathematically, data reconciliation is viewed as a constrained optimization problem. Even though data of some streams can be omitted during the campaign, a basic set of streams data is essential for data reconciliation for a given circuit configuration (Wills and Finch, 2016). Several techniques have been proposed in the literature for data reconciliation and the reader can refer to such techniques for a better understanding of the topic. Table 10.8 gives a typical mass balance of a campaign run obtained by data reconciliation of lead circuit samples, whose circuit configuration is represented in Fig. 10.10. The circuit has rougher, scavenger, and three cleaning stages for the beneficiation of lead mineral. The data comprises assays of lead, zinc, and iron for the ten streams, and these streams are represented as blue lines in Fig. 10.10. The reconciliation has been accomplished using PREDICT (a software developed by Tata Research Development and Design Center, Pune, India). Table 10.8 reveals that the measured assays are minimally adjusted to obtain reconciled values to maintain assay and solid flow balance across the circuit. All the missing stream solid flow rates have been evaluated from the data reconciliation technique.

10.8 Residence time distribution Residence Time Distribution (RTD) gives information regarding mixing patterns inside the agitated tank like the flotation cell and estimates the average time taken for the material to travel from the feed inlet to the tail outlet stream. Since it is a skewed distribution, it implies that a part of the particles and liquid entering the cell may exit after a very short period, while other particles may remain in the cell for a very long time. A mean of the distribution can be considered as the mean residence time of the operation. RTD can be measured from the concentrations of the tracer in inlet and outlet streams, as a function of time. So, RTD is a derived quantity. Usually, flotation cell manufacturers carry out such tests on their new machine designs to evaluate RTD (Nelson and Lelinski, 2019). However, RTD measurements for large industrial flotation cells are scarce (Yianatos et al., 2002). The operating conditions and slurry parameters, such as flow rate, size of the particle, pulp density, and stirring rate affect RTD (Mehrotra and Saxena, 1983). Also, the flotation cell needs to operate under a steady state for the determination of RTD (say, under a particular set of operating conditions). Sedimentation of solid particles as well as excessive manipulation of tail dart valves affects the determination of RTD of

TABLE 10.8 Data reconciliation of a lead flotation circuit (Campaign Run 10B dated 28/11/2000). Stream

Measured Flow, tph

Measured Pb%

Measured Zn%

Measured Fe%

Calculated Flow, tph

Calculated Pb%

Calculated Zn%

Calculated Fe%

Feed to N1

208.8

2.79

14.72

8.54

208.8

2.76

14.85

8.52

N1 output

—

—

—

—

210.89

3.14

14.76

8.6

N2 output

—

3.9

14.96

8.82

216.89

4.12

14.59

8.84

Rougher tail

—

2.3

14.49

8.82

208.74

2.34

14.89

8.68

Scavenger Tail

—

2.1

14.96

8.45

206.65

1.95

14.98

8.6

Rougher Concentrate

—

47.8

7.75

13.94

8.15

49.8

6.98

12.79

N3 output

—

—

—

—

11.52

56.19

6.34

9.75

Cleaner 1 Concentrate

—

75.3

3.85

1.76

5.52

75.33

3.85

1.76

N4 output

—

—

—

—

7.21

74.63

3.92

1.7

Cleaner 2 tail

—

—

—

—

3.37

71.6

4.8

2.42

Cleaner 2 concentrate

—

77.3

3.14

1.06

3.83

77.3

3.14

1.06

Cleaner 3 tail

—

—

—

—

1.68

72.31

4.13

1.47

Cleaner 3 concentrate

—

81

2.36

0.74

2.15

81.2

2.36

0.74

Cleaner 1 tail

—

40.7

8.06

16.26

6

38.56

8.63

17.11

scavenger Concentrate

—

43.6

6.22

16.6

2.09

40.94

6.34

16.69

402

Mineral Processing

industrial cells (Yianatos et al., 2002). The suitability of the salt, dye, or tracer types and a reliable detection method to determine its concentration need to be established before the start of such tests for conducting any RTD measurement exercise (Nesset, 1988). RTD gives distinctive clues on the existing type of mixing within the flotation cell. It can tell whether there is any bypass of the slurry or whether there are any dead zones in the flotation cell (Kelly and Spottiswood, 1982). For an operating flotation cell, RTD is measured experimentally by injecting a tracer into the feed stream at a time, t 5 0; and by measuring the concentration of the tracer, C ðtÞ; in the tails or the froth stream, as a function of time after that. Tracers used in these tests are inert or nonreactive material but have similar physical properties to the contents of the cell. They should not adsorb on the wall or other surfaces of the cell so that they reflect the flow characteristics within the cell. The tracers generally used in flotation RTD are Br-82 (liquid tracer) or irradiated floatable or nonfloatable solid tracers or inert gasses such as Krypton-85 or Freon 13B1. The salt solution (like LiCl) or dyes like Methylene blue can be used to understand liquid phase RTD (Bazin and Hodouin, 1988; Dowling et al., 1999; Goodall and O’Connor, 1989; Yianatos et al., 2002). Given the radioactive nature of the tracers, a pulse input form of measurement is preferred over the step input form. As low as 100 mL of liquid tracer is used to assess RTD of 130 m3 flotation cells (Yianatos and D´ıaz, 2011). However, a pneumatic system of high reliability is required to introduce a small amount of tracer quickly into the feed stream. This technique is a noninvasive technique, where the concentration at the cell discharge is measured online without the need for the process sampling of the discharge. The RTD, E(t), is calculated from the measured concentrations, C(t) of the input pulse tracer at the exit stream as given by: CðtÞ E ðt Þ 5 Ð N 0 CðtÞdt

ð10:23Þ

The area under the RTD curve satisfies the distribution property given by: ðN EðtÞ dt 5 1 ð10:24Þ 0

The mean residence time of the flotation cell can be calculated from the RTD measurement, EðtÞ; as its first moment, which is given by: τ RTD 5

ðN 0

t EðtÞ dt

ð10:25Þ

Froth flotation and its modeling aspects Chapter | 10

403

Under fully mixed conditions, the mean residence time of the flotation cell is the ratio of cell volume, Vcell to the volumetric flow rate of the pulp, Qpulp ; which is given by: τ5

Vcell Qpulp

ð10:26Þ

If there is any bypass or dead zone inside the cell, the mean residence time calculated by Eq. (10.26) differs from the value given by Eq. (10.25).

10.8.1 Dimensionless residence time distribution The time entity can be converted to a dimensionless entity, θ and RTD can be converted to dimensionless RTD form, E(θ). This conversion helps to compare flow patterns of different size particles inside the cell or RTDs of different cell sizes on one plot. EðθÞ 5 τ RTD EðtÞ & t θ5 τ RTD The dimensionless RTD also satisfies the distribution property given by: ðN EðθÞdθ 5 1 ð10:28Þ 0

When we characterize the flow, we find that there are two types of ideal flow scenarios, namely, the plug flow and the perfect mix (fully mixed) conditions. A real flow has components of both these types of ideal flows. Therefore, a single flotation cell may not be sufficient to recover all the floatable material, due to bypass of a portion of pulp from the cell, which exits the cell without participating in the flotation process. Therefore, it has become a practice to include four to eight cells in series to effectively recover floatable minerals in a rougher-scavenger bank. However, the number of cells to be selected for the bank is generally also based on technoeconomic considerations.

10.8.2 Plug flow If every species of the cell content (i.e., whether the solid particles or the liquid or the gas tracers) spend precisely the same amount of time within the flotation cell, then the flow will be a plug flow. The fluid stream entering the cell passes through it without mixing with the contents of the cell. Since flotation cells work on the principle of agitation to separate the minerals, ideal plug flow is seldom seen in flotation cells.

404

Mineral Processing

10.8.3 Perfect mixing Perfect mixing prevails in the cell when the concentration of any substance in the exit stream is the same as that in the tank. For pulse input study, a material balance of the tracer remaining in the cell of volume, Vcell ; at the time, t, can be written as: Vcell

dCðtÞ 5 2 Qpulp CðtÞ dt

ð10:29Þ

Where C ðtÞ is the concentration of the tracer in the cell at the time, t; and Qpulp is the volumetric flow rate of the pulp into the cell. Integrating Eq. (10.29) with initial conditions as Cð0Þ 5 C0 at time t 5 0 gives:
 ð10:30Þ C ðtÞ 5 C0 exp 2 t=τ where τ 5 τ RTD for perfect mixing. Following the definition of RTD in Eq. (10.23), it can be shown that for perfect mixing condition:  t 1 EðtÞ 5 exp 2 ð10:31Þ τ τ In terms of dimensionless form, the above equation can be expressed as: EðθÞ 5 expð 2 θÞ

ð10:32Þ

Fig. 10.23 gives a schematic diagram of RTD measurement by introducing a tracer in the inlet stream and measuring its concentration in the tails stream. Fig. 10.24 gives the concentration profile of tracer in the exit stream for a plug flow and perfect mixed (ideal) conditions. Generally, when there is a bypass of material in the cell, the effective flow rate to the cell will be reduced, as a portion of the feed stream flows from the inlet stream directly to the outlet stream without participating in the flotation process. This decreased flow to the cell results in an increased mean residence time, τ RTD than the value of τ (that is calculated from cell volume and volumetric flow rate considerations). Similarly, when there are

FIGURE 10.23 Schematic diagram for tail RTD measurement.

Froth flotation and its modeling aspects Chapter | 10

405

FIGURE 10.24 Exit concentration profile of a cell with plug flow and perfect mixing scenarios. Based on Kelly, E.G., Spottiswood, D.J., 1982. Introduction to Mineral Processing. A WileyInter Science Publication, Brisbane.

dead zones in the cell, say due to the sanding of particles in the bottom of the cell, the effective volume available for the pulp in the flotation cell decreases. Thus, the measured mean residence time of the flotation cell, τ RTD ; with dead zones will be less than the value of τ. Typically, a skewed peak in the initial period of the RTD curve characterizes bypass and a long tail end in the RTD curve characterizes the presence of dead zones.

10.8.4 Perfectly mixed flotation cells in series When N perfectly mixed flotation cells of the same volume are arranged in series, the concentration of the tracer in the exit stream is given by:
ðN21Þ
 t=τ exp 2 t=τ CN ðtÞ ð10:33Þ 5 ðN 2 1Þ! C0 where CN ðtÞ represents the concentration in the discharge stream of N th flotation cell at time t; C0 represents the concentration of the tracer introduced at time t 5 0; and τ represents mean residence time of each flotation cell. The RTD of such a system is given by:   t tðN21Þ exp 2 τ=N ð Þ E ðt Þ 5
ð10:34Þ N τ=N ðN 2 1Þ!

406

Mineral Processing

The above equation can be converted to a dimensionless RTD using definitions in Eq. (10.27). The following equation represents the dimensionless RTD for the perfectly mixed cells in series. It shows a single parameter, N; to represent the dimensionless RTD. EðθÞ 5

N N θN21 expð 2 NθÞ ðN 2 1Þ!

ð10:35Þ

Fig. 10.25 gives the dimensionless RTD, EðθÞ for a bank of N flotation cells in series with each cell having a perfect mixing flow pattern. The figure shows that as the number of cells increases, the system moves towards a plug-flow kind of flow pattern with the peak occurring at θ 5 1. Eqs. (10.34) or (10.35) may not be adequate to represent the RTD of real flotation cells in series. Van Orden (1986) used a three-parameter dimensionless RTD represented by Eq. (10.36) to depict measured RTD of N flotation cells in series for various makes. Fig. 10.26 shows RTD measurement data in a dimensionless form for the cell types: D-1, A, and C, which are shown with circular dots for Van Orden’s (1986) data. The best fits by Eq. (10.36) are represented by the solid lines. Type-C flotation cells in the series show a poor fit due to short-circuiting of slurry and a long tail representing dead volume. It should be noted that a good RTD of series cells is characterized by a peak near θ 5 1. EðθÞ 5 a θn expð 2 b θÞ

ð10:36Þ

FIGURE 10.25 Dimensionless RTD for N flotation cells in series with perfect mixing pattern prevailing in each cell. Based on Kelly, E.G., Spottiswood, D.J., 1982. Introduction to Mineral Processing. A Wiley-Inter Science Publication, Brisbane.

Froth flotation and its modeling aspects Chapter | 10

407

FIGURE 10.26 Dimensionless RTD fits for the flotation cells in series: (A) Type D-1; (B) Type A; and (C) Type C cells. Based on Van Orden, D.R., 1986. Chapter 43: Simulation of continuous flotation cells using observed residence time distributions. In: Somasundaran, P. (Ed.), Advances in Mineral Processing. SME-AIME, Littleton, CO, pp. 714
725.

408

Mineral Processing

where a, n, and b represent the parameters of the dimensionless RTD representation in the above equation.

10.8.5 Large and Small Tanks in Series (LSTS) model Diaz and Yianatos (2010) studied RTD distributions using liquid tracers in self-aerated 130 m3 Wemco cells in series at El Teniente, Codelco, Chile. The circuit consists of seven cells in series in one of the banks. Around 100 mL of liquid tracer (Br-82 in solution) was instantly introduced in the feed using a reliable pneumatic system and the exit concentrations were measured at the tail streams after the cell numbers #1, #3, #5, and #7. Although the RTD distributions for the cells in series could be fit by Eq. (10.34) for N . 2 (with refined N values), they found that the Eq. (10.34) is not adequate to represent RTD of a single large cell due to the presence of bypass. They showed that the RTD of the single large cell can be represented by a perfectly mixed large cell with a small cell in series and system having a time lag (LSTS model). The LSTS model is schematically represented in Fig. 10.27. The RTD of the LSTS model is given by:

 exp 2 ðt 2 LÞ=τ s 2 exp 2 ðt 2 LÞ=τ l EðtÞ 5 ð10:37Þ ðτ s 2 τ l Þ Where the overall mean residence time is given by: τ RTD 5 L 1 τ s 1 τ l

ð10:38Þ

In the above equation, L represents the dead or lag time; τ s represents the residence time of a small perfect mixer and τ l represents the residence time of a large perfect mixer.

10.8.5.1 Froth and tail residence time distribution of mechanical cells using LSTS model Fig. 10.28 gives the RTD distributions of the liquid tracer measured at the tail end of self-aerated 130 m3 flotation cells in series. The curves are drawn from the reported LSTS
RTD parameters from Diaz and Yianatos (2010).

FIGURE 10.27 Schematic representation of LSTS model with a time lag L. Based on Diaz, F., Yianatos, J., 2010. Residence time distribution in large industrial flotation cells. At. Peace Int. J. 3, 2
10.

Froth flotation and its modeling aspects Chapter | 10

409

FIGURE 10.28 RTD measurements were conducted on the froth stream of the first four selfaerated 130 m3 cells, using 245 micron particles. Based on Diaz, F., Yianatos, J., 2010. Residence time distribution in large industrial flotation cells. At. Peace Int. J. 3, 2
10.

FIGURE 10.29 Liquid RTD measurements on large 130 m3 self-aerated cells (N flotation cells in series) expressed in the dimensionless form. Based on data shown in Fig. 10.28.

It is noticed that the average mean residence time per flotation cell, for the cell combinations: #1, #1
3, #1
5, and #1
7 remain almost constant at B265 seconds for the data shown in Fig. 10.28. This data can be converted to dimensionless RTD as depicted in Fig. 10.29. As the number of cells increases, the dimensionless RTD for the flotation bank moves closure to a plug-flow pattern with the peak occurring near dimensionless time θ 5 1: Fig. 10.30 gives RTD of the froth phase for the first four cells of the bank of cells. RTD is calculated using concentrations of -45 micron particles,

410

Mineral Processing

FIGURE 10.30 Liquid RTD measurements on large 130 m3 self-aerated N flotation cells in series. Based on Diaz, F., Yianatos, J. 2010. Residence time distribution in large industrial flotation cells. At. Peace Int. J. 3, 2
10.

for the same bank of cells discussed above. The parameters given by Diaz and Yianatos (2010) have been used to draw the curves in Fig. 10.30. From the comparison of RTD measurements of the tail and the concentrate of the commonly assessed self-aerated cells (namely, for cell #1 and cell #3), it is found that the mean residence time estimated for the concentrate stream is less than that of the tail stream. The mean residence time of the froth phase to that of the tails shows a factor of 0.8 to 0.9. The decrease in the residence time for the froth phase is attributed to its instability that causes a drop back of a portion of floated particles (Diaz and Yianatos, 2010).

10.8.6 Hydrodynamics of scaled up cells Dimensionless RTD can be used to verify the correctness of scale-up in flotation cells. For properly scaled-up cells, the RTD in the dimensionless form should have a similar profile irrespective of the cell volume. The RTD of forced air mechanical cells in dimensionless form for OK-160 m3 cell and TC-300 m3 cell shows similar distributions, indicating that the hydrodynamic behavior within the cells is similar (Morales et al., 2009). Also, the RTD measurements expressed in dimensionless form for 130 m3 and 250 m3 selfaerated mechanical cells show quite similar distributions (Yianatos and D´ıaz, 2011).

10.8.7 Particle size effects on residence time distribution Solid particles segregate by gravity force within the cell despite the agitation, which can also be studied by RTD measurements. The RTD measurements

Froth flotation and its modeling aspects Chapter | 10

411

on various size fractions show that the ratio of the mean residence time of particles to that of liquid (i.e., τ particle =τ liquid ) within the cell gradually decreases from a value of 1 for very fine particles to a value of 0.8 for 200 micron particles in the mechanical flotation cells. However, this fall in the ratio is significant in the column flotation cells, indicating greater segregation of particles within the column cells. For example, in one such measurement in a column treating 100-micron particles, the ratio (i.e., τ particle =τ liquid ) was found to be 0.5 (Yianatos and D´ıaz, 2011). As there is no mechanical agitation of slurry within the column cells, the homogenization of slurry is insignificant, leading to insignificant recoveries of coarser particles to the froth phase. This is one of the reasons, why design engineers prefer mechanical rougher cells to column cells for roughing action in molybdenum flotation plants (Amelunxen et al., 2019). Given this, the RTD data of the column cell obtained from liquid tracers has to be used with caution. The columns show strong pulp short-circuiting, which decreases significant mineral recovery (Yianatos et al., 2002).

10.8.8 Reflection of process issues through residence time distribution measurements It is also possible to monitor the performance of a bank of cells operating in parallel under similar operating conditions through RTD. Table 10.9 shows RTD measurements using liquid and solid tracers from five banks of cells operating in parallel with a #3-#3-#3 cell subbank arrangement and each cell has a 42.5 m3 capacity. Both RTD measurements (on the solid particles and the liquid) show abnormal high mean residence times for the fourth bank indicating a process-related issue (Yianatos et al., 2002).

TABLE 10.9 Liquid and solid RTD of bank of cells in parallel. # Rougher bank

Liquid Br-82 residence time, min

Activated solid residence time, min

1

35.9

34.7

2

40.3

38.3

3

40.8

39.2

4

54.7

49.9

5

36.7

35.0

a

a

Abnormal behavior of the cells.

412

Mineral Processing

10.8.9 Residence time distribution of column flotation cell The RTD of column flotation cell can be represented as a resultant RTD obtained from two small perfect mixers in series having a residence time τ S with one large perfect mixer having residence time τ L (Yianatos and D´ıaz, 2011), which is represented as


 2 t=τ S 2 α exp 2 t=τ S 1 α exp 2 t=τ L E ðt Þ 5 & ðτ L 2 τ S Þ τL α5 ðτ L 2 τ S Þ The feed zone and bubble generation zones are considered to be the small perfect mixers and the zone from feed entry to bubble generation level is considered to be the large perfect mixer for a column. It should be noted that Eq. (10.39) is also used to represent the RTD of ball mills (Austin et al., 1984).

10.8.10 Kinetics of flotation in a continuously operated flotation cell The kinetics of bench-scale flotation discussed in the previous sections will not adequately represent the kinetics of a continuous flotation plant. In a continuous operation, both mineral contents and reagent concentrations vary with time, and thus the process is unsteady. The recovery of minerals not only depends on rate constants of flotation (as discussed previously) but also on RTD. The RTD depends on flow regimes within the cell. Some particles will participate in the process of separation, some will bypass and some will be locked in the dead zones (of sanding) if any. The batch flotation response can be combined with a continuous cell RTD to get the flotation kinetics for a continuous cell and this can be represented as: ðN M ðτ Þ 5 M ðtÞbatch operation EðtÞ dt ð10:40Þ 0

Substituting the batch kinetics from Eq. (10.4) and perfect mixing pattern given by Eq. (10.31) in the Eq. (10.40), followed by simplification yields: M ðτ Þ 5

1 1 1 kτ

ð10:41Þ

Thus the recovery of the mineral in a continuous cell with perfect mixing is given by: R 5 1 2 M ðτ Þ 5

kτ 1 1 kτ

ð10:42Þ

Froth flotation and its modeling aspects Chapter | 10

413

Instead of a single rate constant for flotation, suppose we consider that the feed is distributed in the rate constant (referring to Eq. (10.18)), the mineral recovery in a continuous flotation process can be derived from batch kinetics operation as: ðN ðN R5 ð1 2 expð 2 k tÞÞ M ðkÞ EðtÞ dk dt ð10:43Þ 0

0

10.9 Entrainment Entrainment is a physical activity and it is not related to chemical selectivity. In earlier days, it was thought that the recovery of gangue minerals to the concentrate stream was due to the flotation of gangue minerals with a lower rate constant (refer to Eq. (10.10)). But careful studies indicate that the recovery of fine gangue minerals to the froth phase is due to entrainment, which is proportional to the water recovery to the froth phase. When the swarm of air bubbles rises through the pulp phase into the froth phase, they carry a portion of pulp water along with fine gangue minerals into the froth. So, the composition of the pulp in the upper part of the flotation cell influences the entrainment. It is the entrainment that increases the number of cleaning stages in a flotation circuit to upgrade the mineral to higher assays. For example, six to ten stages of conventional cell cleaning are essential to reach the target grades for molybdenum flotation. The number of cleaning stages can be reduced with the use of column flotation, which uses froth wash water to reduce the gangue entrainment. Entrainment is a phenomenon dependent on particle size. Entrainment decreases as particle size increases and becomes almost zero at about 50 microns. This phenomenon can be better studied by taking a pulp sample that is beneath the froth phase and the froth phase sample and cyclosizing them. A size-wise mineral recovery can thus be calculated. Here, the collection of froth samples should be free from process spray water additions to the froth and the launder. Entrainment of gangue minerals into the froth can be decreased by: G

G G G

Having a rougher-scavenger-cleaning circuit, which improves the grade of valuables without significantly affecting their recovery. Having a deep froth phase and using fresh water to wash it. Having dilute pulps in the flotation cell. Decreasing the flow rate of air to the cell.

10.10 Industrial mechanical cells Mechanical cells are by far are the most preferred cells in the industry for the beneficiation of ores by flotation. From the standpoint of air supply to

414

Mineral Processing

the cell, they can be either self- aerated type (representing the cells that do not require an external air blower) or forced air type (representing the cells that require an external air blower). Commonly, the air is fed to mechanical cells through a hollow shaft. The incoming air is continuously sheared into small bubbles by the rotor (also called the impeller) and the stator. The rotor-stator combination is referred to as the “flotation cell mechanism.” The shearing of air is a two-step process. In the first step, the air forms an air pocket behind the impeller blades, which is the region of low pressure. In the second step, from the tail of this air pocket, the bubbles are formed by shredding of vortices (Gorain et al., 2000). Further reduction of bubbles size happens by the stationary stator blades. A mechanical cell with the bottom agitation has three zones, namely, a turbulent bottom zone, a less turbulent middle zone, and a relatively quiescent top froth zone. The bubble-particle aggregates rise to the top of the tank to a relatively less turbulent zone by dislodging much of the entrained gangue minerals. The froth phase with its depth also serves as another cleaning stage in the flotation operation. The turbulence within the cell is heterogeneous and anisotropic; the turbulent intensities near the impeller are orders of magnitude higher than anywhere found in the cell. The bubbles produced show a size distribution depending on the mechanism’s ability to shear the volume of the incoming air and typically the bubble sizes are well below the limit of 3 mm (with more emphasis to produce bubbles below 1 mm). The BSD is dependent on several factors, such as profiles of the impeller and the stator assembly, the tangential tip speed of the impeller, the ratio of the size of the impeller to the size of the flotation tank, the flow rate of air and the concentration of the frother in the slurry. The mean bubble size in the industrial mechanical cell varies typically from 0.5 to 2 mm depending on the above factors. An increase in air flow rate increases the mean bubble size, whereas the increase in impeller speed decreases the mean bubble size. A burst of big bubbles in the froth phase is likely to dislodge the floated particles causing a drop back or drainage of floated mineral back to the pulp phase and also causing a boiling froth, which in turn decreases the efficiency of separation. Typically, the rougher flotation feed slurry will be 30% solids (w/w), while the cleaner cells are operated at 10%
15% solids (w/w). Cleaner cells will be smaller in size compared to rougher or scavenger cells due to reduced flow rates. A more dilute feed helps to reduce the entrainment of gangue minerals to the froth phase.

10.10.1 Power input parameters Parameters such as tangential impeller tip speed, power number, absorbed power, and power intensity are referred to as power-related parameters of a mechanical cell.

Froth flotation and its modeling aspects Chapter | 10

415

10.10.1.1 Tangential impeller tip speed The tip speed influences the fluid velocity around the impeller and thus affects both gas dispersion and pulp circulation within the cell. Typically for industrial cells, the tip speed varies from 4.9 to 8.8 m/s, but the majority of the cells operate in the range of 5
7 m/s (Deglon et al., 2000). The tip speed, ω (in m/s) for a given impeller size is calculated by: ω 5 πDN

ð10:44Þ

Where D is rotor diameter (in m) and N is rotational speed (in s21).

10.10.1.2 Power number of the impeller The power number of the impeller, Np ; is an important dimensionless number used to scale up agitation tanks. It is given by: Np 5

P ρN 3 D5

ð10:45Þ

Where P is the power drawn by the mechanism (in W), ρ is slurry/pulp density (in kg/m3), N is rotor tip speed (in s21) and D is rotor diameter (in m). Power number also depends on aeration level and the frother dosage to the flotation cell operation. Typically, it has values varying from 3.4
6.6.

10.10.1.3 Absorbed power The power consumption of a cell in operation, P (in W) can be calculated as: pffiffiffi P 5 3 V I cosðφÞ ð10:46Þ Where V is the Voltage (in V), I is the current (in A) and φ is the power ratio (%).

10.10.1.4 Power intensity Power intensity is a measure of power input to the cell per unit cell volume,
 P=Vcell . It varies typically between 1 and 3 kW/m3. This factor influences the flotation rate constant and hydrodynamics of the cell. Sulfide minerals require less power intensity than oxide minerals (Safari et al., 2016).

10.10.2 Gas dispersion parameters The gas dispersion parameters include superficial gas velocity, Sauter mean bubble diameter, bubble surface area flux, and gas hold up. These parameters are indicators of flotation performance.

416

Mineral Processing

10.10.2.1 Superficial gas velocity Superficial gas velocity, Jg (in m/s), is defined as volumetric gas flow rate to the pulp (Qg in m3/s) to the cross-sectional area of the cell (Acell in m2). It varies in the range of 0.7 to 2.7 cm/s depending on the operational conditions of the cell. The typical accepted values are in the range of 1.3 to 1.8 cm/s. This factor influences flotation kinetics. High values of Jg produce a disruptive effect on the froth phase. Jg 5

Qg Acell

ð10:47Þ

10.10.2.2 Sauter mean bubble diameter Sauter mean bubble diameter, d32 (in m), is a form of representation of BSD. It is used to calculate the bubble surface area flux, Sb . P 3 di ð10:48Þ d32 5 P 2 i di i Since BSD is influenced by both the aeration rate and the frother concentration, the Sauter mean bubble diameter, d32 is also influenced by these factors. Sauter mean bubble diameter increases with Jg (for a given frother concentration) and is given by (Finch et al., 2008): d32 5 d0 1 c Jg n

ð10:49Þ

Where n has a value of 0.5 and d0 and c are constants. The decrease in Sauter mean bubble size with the frother addition (in ppm) is given by (Nesset et al., 2012): d32 5 dlimit 1 A expð 2 B ppmÞ

ð10:50Þ

Where A and B are parameters and dlimit is the limiting size reached when the frother concentration reaches Critical Coalescence Concentration (Laskowski, 2003).

10.10.2.3 Bubble surface area flux Bubble surface area flux, Sb (in s21) is calculated from Jg (in m/s) and d32 (in m) as: Sb 5

6Jg d32

ð10:51Þ

This factor combines both gas rate and BSD in the cell. Gorain et al. (1997) showed that the apparent flotation rate constant from the pulp phase is directly proportional to the Sb value. Typical values range from 30 to

Froth flotation and its modeling aspects Chapter | 10

417

150 s21 depending on airflow rate, which is an advantage in the forced air flotation cells, as it can be manipulated by varying the airflow rate. These values always lie in the specified range despite enormous variations in types and sizes of mechanical cells and their operating conditions. This is due to the intrinsic limitation in the production of high bubble surface area flux, due to the method of gas dispersion in mechanical cells (Deglon et al., 2000).

10.10.2.4 Gas holdup Gas holdup εg represents the volume fraction of air within the flotation cell. εg

5

Vgas Vcell

ð10:52Þ

It is also represented as: εg 5

αJg Sb

ð10:53Þ

Where α is the total bubble surface area per unit cell volume. The gas holdup of the flotation cell varies from 5% to 15%. An increase in gas hold up to a certain value increases flotation kinetics due to the generation of a greater number of bubbles. Gas hold up in the cell increases with an increase in tip speed with the generation of smaller bubbles.

10.10.3 Selection tips for mechanical flotation cells The following are the guidelines recommended by Outokumpu Technology for the selection of flotation cells: G

G

G

G

The rougher-scavenger bank should have five to eight cells, with a minimum of 5 cells to reduce short-circuiting of pulp to the tails stream. For large cells it is recommended to have single-cell stage control. In general, there should be a minimum number of cells in each stage of control. Froth lip loading should be below 1.5 tons per linear meter per hour. A froth carry rate of 0.8
1.5 tph/m2 for rougher cells, 0.3
0.8 tph/m2 for scavenger cells and 1
2 tph/m2 for cleaner cells is recommended. At least there should be four control stages in a circuit to aid operational flexibility for optimization of the circuit performance.

10.10.4 k
Sb relationship Gorain et al. (1997) showed a linear relationship between flotation rate constant, k and the bubble surface area flux, Sb for the performance of the

418

Mineral Processing

industrial cells. The measurements were made in a 2.8 m3 mechanical cell fitted with four different types of impellers. The tests were conducted on zinc cleaner streams under varied operating conditions at Hellyer concentrator in Tasmania, Australia. The rate constant was calculated using the following relationship (which is transformed form of Eq. (10.42)). Fig. 10.31 shows the results from their published data. It appears that the relationship is independent of the impeller type. Thus, bubble surface area flux, Sb ; is a good indicator of the hydrodynamics of the cell in terms of cell performance and gas dispersion properties. k5

R τð1 2 RÞ

ð10:54Þ

where τ represents the mean residence time of the cell and R represents the mineral recovery percent. From the liner relationship in Fig. 10.31, we can express flotation rate constant for pulp phase in terms of bubble surface area flux as: k p 5 P Sb

ð10:55Þ

where P is floatability proportionality constant.

FIGURE 10.31 k
Sb relationship for various impeller profiles. This plot is generated from Gorain et al. (1997) published data.

Froth flotation and its modeling aspects Chapter | 10

419

10.10.5 Pulp-froth multiphase model In this approach, the recovery of particles from the flotation operation is considered with two distinct zones, namely the pulp phase and the froth phase. In the pulp phase, the particle-bubble aggregates are formed and transported to the pulp-froth interface. From the froth phase, the particles in the concentrate overflow into the launder, while some of the particles along with the entrained particles drain back from the froth phase to the pulp phase. This is schematically shown in Fig. 10.32 with a steady-state mass balance, where Rp represents the recovery of particles from the pulp phase, while RF represents the recovery of particles from the froth phase (Finch and Dobby, 1990). The overall mass balance from Fig. 10.32 indicates:
 ð10:56Þ F 5 X Rp RF 1 X 1 2 Rp Therefore, the overall recovery of particles from the feed stream to the concentrate stream is given by Roverall 5


Rp

R p RF Rp RF
 5 1 2 Rp ð 1 2 RF Þ RF 1 1 2 Rp

ð10:57Þ

Using the first-order continuous recovery model represented by Eq. (10.42), it can be shown that koverall 5 kp

RF

ð10:58Þ

Substituting kp from Eq. (10.55) into Eq. (10.58) yields: koverall 5 P

Sb

RF

ð10:59Þ

FIGURE 10.32 Schematic representation of pulp-froth recovery model. Based on Wills, B.A., Finch, J.A., 2016. Wills’ Mineral Processing Technology, eighth ed. Butterworth-Heinemann, Oxford.

420

Mineral Processing

Using Eq. (10.42), the overall recovery is written as: Roverall 5

P Sb R F τ ð 1 1 P Sb RF τ Þ

ð10:60Þ

With due consideration to entrainment (particles entrained between bubbles), Schwarz et al. (2006) represented the overall recovery of ith class of particles, Ri as Ri 5

Pi Sb RF τ ð1 2 Rw Þ 1 ENT: Rw ð1 1 Pi Sb RF τ Þ ð1 2 Rw Þ 1 ENT: Rw

ð10:61Þ

where Rw represents the water recovery and ENT represents the degree of entrainment, which is defined as: ENT 5

Rentrainment Rw

ð10:62Þ

where Rentrainment represent the recovery of entrained material. The overall recovery for a feed with n classes is given by Roverall 5

n X

mi Ri

ð10:63Þ

i51

where mi represents the mass fraction of particles in the ith class. JKMRC flotation models are based on this approach of pulp-froth multiphase modeling.

10.10.6 Neethling and Cilliers model on grade-recovery curve Neethling and Cilliers (2012) presented a steady-state model to predict grade-recovery of cells in series. The main objective of a flotation operation is to enhance both grade and recovery with as little sacrifice of valuable mineral to the tails stream. The model is based on two key relationships about the evaluation of concentrate grade, c, and concentrate mass flow, C, from the tails grade, t. Expressions for these entities are represented as: c5 

Gmax 

Gmax b t 2 GNF

11

C 5 m ðt 2 ðGNF 2 b Gmax ÞÞ

ð10:64Þ ð10:65Þ

The parameters m, b, Gmax ; and GNF have to be estimated from the measured plant data. Gmax and GNF represent a mass fraction of valuable material in the floatable and the nonfloatable components respectively. As an example, using a bank of five copper rougher floatation cells in series, Neethling and Cilliers (2012) evaluated the effect of the feed rate and head grade on copper rougher flotation in terms of grade-recovery curves.

Froth flotation and its modeling aspects Chapter | 10

421

They showed that head grade has a much more pronounced effect on the grade-recovery curve than the feed rate effect. An increase in head grade (for a specified feed rate) increased both grade and recovery down the bank. This is similar to what has been described earlier in this chapter in Fig. 10.8. However, an increase in the feed rate (for a specified head grade material) increases slightly the grade and recovery of each cell.

10.11 Effect of mechanism profile on the mineral upgradation As discussed in the introduction section, the mechanism profile plays a vital role in the beneficiation of the ores, as it produces the necessary BSD for the flotation operation and creates the agitation intensity necessary for the bubble-particle collisions within the cell. The mechanism is at the heart of flotation cell performance. Each manufacturer will have a standard proprietary mechanism profile for the flotation cell. Fig. 10.33 gives a pictorial view of the lead enrichment ratios produced by three different mechanisms A, B, and C in the same operating plant and for the same lead beneficiation circuit configuration represented by Fig. 10.10. The lead enrichment ratio on the ordinate axis depicts the ability of the mechanism to upgrade any input grade fed to the cell, which are represented on the abscissa. The trends in the enrichment ratio as a function of head grade by these three mechanisms are represented by the regression lines on the plot. It clearly shows that Mechanism C with its higher enrichment ratios performs better than Mechanism B, which in turn performs better than Mechanism A. Also, Mechanism A can upgrade lead in the circuit to a maximum of B55% Pb, the Mechanism B can upgrade lead to 60% Pb, while the Mechanism C can upgrade lead to 70 1 % Pb for the same circuit. So, the use of the

FIGURE 10.33 Effect of the mechanism type on the lead enrichment ratios in an operating lead beneficiation plant.

422

Mineral Processing

Mechanism C in the circuit can drastically reduce the volume of cells required or the number of stages involved for the beneficiation for the lead ore to reach the target grade in the product stream. Moreover, Mechanism C can produce concentrate grades much higher than the other two mechanisms.

10.12 Brief description on flotation circuit process modeling Several methods of modeling have been proposed in the literature to mathematically model the flotation performance, which vary from semi-empirical models to data-driven models to guide the operations to get better grades and recoveries from the flotation plants for a given feed composition. These models can be broadly categorized as (a) steady-state models, (b) transientstate models, and (c) dynamic models. Good instrumentation, online assaying (with automatic samplers) and skilled operators can optimize a flotation circuit to get better quality of concentrate under any given circumstances of the operation. The main control variables of the mechanical cells for better plant performance include - the control of the particle grind size from the grinding-classification circuit, the control of pulp levels and the airflow rates of individual cells, the control of pH and reagent dosages at various locations of the circuit, the maintenance of pulp density of various streams and the froth washings. Regular maintenance of the cell condition and the health check-up of the mechanism is envisaged. In the following section, we discuss some of the process models that will help to improve the plant operations.

10.12.1 Steady-state process model A steady-state process model of the flotation circuit under varied operating conditions can be built from several meaningful steady-state campaign data. The model is built by expressing the component flow rates in various streams of the circuit (i.e., solid, water, and valuable mineral flow rates) in terms of multi-component split factors of locally staged separations and integrating these split factors for a given circuit configuration. A split factor explains how a given component (say solids, water, and valuable mineral) is split from the feed stream to the concentrate stream locally. Moreover, relations can be built among the split factors and the local operating conditions using multivariate regressions (or machine learning techniques). In the formal run of the model, the local operating conditions determine the split factors, and these split factors in turn help to establish the mass balance of the entire circuit. As this model holds good for various operating regimes reliably, it can be used to improve the grade and recovery of valuable mineral for the circuit by arriving at the optimum operating conditions for any given situation. The framework of building such a model is discussed below with an example of a lead circuit.

Froth flotation and its modeling aspects Chapter | 10

423

The lead circuit shown in Fig. 10.10 can be simplified to a form shown in Fig. 10.34 by lumping the cells or sub banks into rougher, scavenger, and cleaner sections with interconnected (recycle) streams. From the massbalance data of various campaign runs, it is possible to calculate the flow split factors for the total solids, lead species and water respectively represented as Fi ; Si ; and Wi , which are shown in flower brackets in Fig. 10.34 for each stage of operation (namely for rougher, scavenger and cleaner stages), where the subscript i stands for the stage involved. For example, i 5 1 represents the roughing stage; i 5 2 represents the scavenging stage and i 5 3 represents the cleaning stage. The square brackets comprise, the solids flow rate (in tph), Pb% assay, and water flow rate (in m3/h) of individual streams respectively, and are represented on each flow stream that connects the flotation stages. The fresh water additions (in m3/h) to the scavenger and the rougher concentrates are represented by E1 and E2 respectively and are needed for the water balance of the circuit. Using steady-state mass balance, the solid flow rate (in tph), % lead recovery (with reference to the fresh feed), % Pb (grade), and water flow rate (in m3/h) of various streams can be expressed in terms of flow split factors as shown in Table 10.10. As indicated earlier, the multivariate regression relationships that relate the local split factors (of the solid, the lead, and the water) with local operating variables are developed from the campaign data. The regression relations should have an R2 value of 0.8 and above (with an adjusted R2 value of at least 0.75) to capture the performance trends in a better way. Typically, 70% of the measured campaign data is used to develop the relations and the remaining 30% of data is used to verify the developed relations. The

FIGURE 10.34 Split factors and component flow rate representation for the lead circuit for a steady-state mass balance.

TABLE 10.10 Mass flow rates, the grade, and the recovery of the circuit streams (expressed in terms of flow split factors). Water flow rate, m3/h

Circuit stream

Solids flow rate, tph

Pb recovery %

Grade, Pb %

Rougher concentrate

C1 5

F F1 ð1 2 F1Þð1 2 F2Þ 1 F 1F3

RC 1 5

100 S1 ð1 2 S1Þð1 2 S2Þ 1 S1S3

c1 5

100 F f ðRC 1Þ C1

WC1 5

W 1ðE1 1 E2 1 WF 2 E2W 3Þ ð1 2 W 1Þð1 2 W 2Þ 1 W 1W 3

Cleaner concentrate

C2 5

F F1F 3 ð1 2 F1Þð1 2 F2Þ 1 F 1F3

RC 2 5

100S1S3 ð1 2 S1Þð1 2 S3Þ 1 S1S3

c2 5

100F f ðRC 2Þ C2

WC2 5

W 3ðE2 1 E1W 1 1 WF W 1 2 E2W 2 1 E2W 1W 2Þ ð1 2 W 1Þð1 2 W 2Þ 1 W 1W 3

Rougher tail

T15

F ð1 2 F1Þ ð1 2 F1Þð1 2 F2Þ 1 F1F3

RT 1 5

100ð1 2 S1Þ ð1 2 S1Þð1 2 S2Þ 1 S1S3

t1 5

100F f ðRT 1Þ T1

WT 1 5

ð1 2 W 1ÞðE1 1 E2 1 WF 2 E2W 3Þ ð1 2 W 1Þð1 2 W 2Þ 1 W 1W 3

Scavenger tail

T25

Fð1 2 F1Þð1 2 F 2Þ ð1 2 F1Þð1 2 F2Þ 1 F1F3

RT 2 5

100ð1 2 S1Þð1 2 S2Þ ð1 2 S1Þð1 2 S2Þ 1 S1S3

t2 5

100F f ðRT 2Þ T2

WT 2 5

ð1 2 W 1Þð1 2 W 2ÞðE1 1 E2 1 WF 2 E2W 3Þ ð1 2 W 1Þð1 2 W 2Þ 1 W 1W 3

Scavenger concentrate

R1 5

Fð1 2 F 1ÞF2 ð1 2 F1Þð1 2 F2Þ 1 F 1F3

RR1 5

100ð1 2 S1ÞS2 ð1 2 S1Þð1 2 S2Þ 1 S1S3

r1 5

100F f ðRR1Þ R1

WR1 5

ð1 2 W 1ÞW 2ðE1 1 E2 1 WF 2 E2W 3Þ ð1 2 W 1Þð1 2 W 2Þ 1 W 1W 3

Cleaner tail

R2 5

F F 1ð1 2 F 3Þ ð1 2 F1Þð1 2 F2Þ 1 F 1F3

RR2 5

100S1ð1 2 S3Þ ð1 2 S1Þð1 2 S2Þ 1 S1S3

r2 5

100F f ðRR2Þ R2

WR2 5

ð1 2 W 3ÞðE2 1 E1W 1 1 WF W 1 2 E2W 2 1 E2W 1W 2Þ ð1 2 W 1Þð1 2 W 2Þ 1 W 1W 3

Froth flotation and its modeling aspects Chapter | 10

425

relations once built can be further verified to be within the min-max limits (i.e., not to exceed the permitted limits) by perturbing all the influential variables of the multivariate regression equations randomly within their measured operating range, say, 10,000 times. The predicted split factors should fall within the min-max limits of the study, which will verify the robustness of the developed regression equations. The trends in the behavior of predicted split factors are more important than the accuracy of the prediction. Over-fit has to be avoided while developing these multivariate regressions. Fig. 10.35 shows a plot of predicted and actual flow split factors for the lead,

FIGURE 10.35 Actual and predicted flow split factors obtained from steady-state reconciled campaign data and the regression equations. Based on Rao, B.V., Velan, H.K., Jamal, S.I., Mahadevan, R., 2014. Grade-recovery prediction of an operating plant using flotation model and operating conditions. Procedia Eng., 83, 148
158.

426

Mineral Processing

the solids, and the water streams for roughing, scavenging, and cleaning stages using such relations built from the campaign data. The filled symbols indicate the predictions from trained data and open symbols indicate predictions for untrained data. The predicted values from the multivariate regressions fall on the 45-degree diagonal line when plotted against the actual values, indicating that the regression relations are quite satisfactory to capture the effect of influential variables on the various split factors (Rao et al., 2014). Now, using the set of influential operating conditions of the plant that are input into the multivariate regression relations, the nine local flow split factors are predicted (as shown in Fig. 10.35). In turn, using these nine predicted split factors (represented in Fig. 10.34), the solids flow rates, water flow rates, grade (Pb %), and Pb recovery %, across the lead circuit, can be predicted by using steady-state flow relations shown in Table 10.10. Figs. 10.36
10.39 depict a comparison of actual and predicted values of the campaign runs for the solids flow rate, the water flow rate for the staged concentrate streams, the grade (Pb%), and the Pb recovery % (w.r.t the fresh feed) respectively for the various streams across the circuit. These results are quite interesting as the predicted values match the actual campaign data pretty closely. The trends in the predictions of various local streams and separation stages are good enough to improve the performance of the plant, though they may not be highly accurate. For example, the final concentrate grade in some situations slightly exceeds 86.6% Pb, which is the limit of lead upgradation. However, the trends in data under various operating conditions are captured quite well to a fair degree of predictability, which can be used to improve flotation process performance for any unknown situation. So, the key lies in developing such relations for a given operating plant.

10.12.2 Transient-state process model A transient-state model captures the pattern of change of a process variable with time progress. It shows a path of transformation from the initial steadystate condition to a final steady-state condition when operating conditions are set afresh to a new set of values. Rao et al. (2014) built a transient-state model based on the concept that the material properties of the “before (or initial)” conditions fade away with the progressing time, while the material properties of the “after (or later)” conditions build up in the system with the progressing time. The initial or the later conditions correspond to a particular set of operating conditions representing the froth levels in subbanks, the airflow rates to various cells, the reagent dosages at various locations, pH, throughput, and head grade to the plant feed. The response properties of the material change with the operating conditions mainly due to changes in apparent flotation rate constants of the subbank cells (namely the rougher, the scavenger, and the cleaner cells).

Froth flotation and its modeling aspects Chapter | 10

427

FIGURE 10.36 Comparison of actual and predicted solid flow rates for the various streams of the lead circuit for steady-state operation under various operating conditions of the plant.

The change in apparent flotation rate constants will in turn change the mass balance of the circuit dynamically. The depletion of floatable solids for the before-condition is given by mF;b mh;b ðtÞ 5 expð 2 ðkb 1 λb ÞtÞ ð10:66Þ ðkb 1 λb Þ

428

Mineral Processing

FIGURE 10.37 Comparison of actual and predicted water flow rates for the concentrate streams of the lead circuit for steady-state operation under various operating conditions of the plant.

The build-up of floatable solids for the after-condition is given by mF;a mh;a ðtÞ 5 ð1 2 expð 2 ðka 1 λa ÞtÞÞ ð10:67Þ ðka 1 λa Þ

Froth flotation and its modeling aspects Chapter | 10

429

FIGURE 10.38 Comparison of actual and predicted Pb% for various streams of the lead circuit for steady-state operation under various operating conditions of the plant. Based on Rao, B.V., Velan, H.K., Jamal, S.I., Mahadevan, R., 2014. Grade-recovery prediction of an operating plant using flotation model and operating conditions. Procedia Eng., 83, 148
158.

where mF stands for the volumetric solids flow rate, k represents the apparent flotation rate constant for the solids, and λ represents the reciprocal of mean residence time. The suffixes b and a respectively

430

Mineral Processing

FIGURE 10.39 Comparison of actual and predicted Pb recovery % for various streams of the lead circuit for steady-state operation under various operating conditions of the plant. Based on Rao, B.V., Velan, H.K., Jamal, S.I., Mahadevan, R., 2014. Grade-recovery prediction of an operating plant using flotation model and operating conditions. Procedia Eng., 83, 148
158.

represent the before and the after conditions of the operational change. The term mh ðtÞ represents the volumetric solids hold up of the cell at the time, t.

Froth flotation and its modeling aspects Chapter | 10

431

FIGURE 10.40 Transition of steady-state #20 to steady-state #7 when the operating conditions of the plant change from run #20 to those of run #7.

432

Mineral Processing

The transient solids flow split factor, F ðtÞ can be calculated as: F ðt Þ 5

kb mh;b ðtÞ ka mh;a ðtÞ 1 mF;b mF;a

ð10:68Þ

Similarly, it is possible to calculate transient lead flow split factors for various local stages of separation, namely, rougher, scavenger, and cleaner stages. Using relations in Table 10.10 and considering split factors as transient split factors (similar to Eq. (10.68)), it is possible to calculate the transient paths of grade, recovery, and solid flow rates across the circuit streams when the operating conditions change. Fig. 10.40 shows the transition of these parameters when the conditions in run #20 change to conditions in run #7 for the campaign runs shown in Fig. 10.6. Fig. 10.40 shows that the stabilization happens to the new conditions approximately after half an hour, which is the residence time of the circuit.

10.12.3 Dynamic process model Mika and Fuerstenau (1968) proposed a detailed population balance model, which is the most detailed to date to describe a flotation process in terms of four subprocesses. These subprocesses consider the flotation process as an outcome of particles free in pulp, particles attached to the air bubbles in the pulp, particles free in the froth phase, and the particles attached to the bubbles in the froth phase. The attachment and detachment of the particles in these subprocesses are determined by rate constants, which are functions of operating conditions. The feed is discretized in “i” narrow size ranges and each size, in turn, is discretized in “j” narrow mineral composition classes. More details of this model are described by Herbst and Harris (2007).

10.13 Final remarks Flotation is a complex staged operation to upgrade the finely ground minerals. The ore grades of the world reserves are depleting day by day. They need to be ground to very fine sizes (maybe to the submicron range) in the years to come to liberate the valuables and thereby separate them. Methods need to be developed to recover valuable minerals from such complex ores economically. Each ore deposit is different as far as the separation of associated gangue minerals is concerned. The particle size, the reagent suite, and the circuit configuration that is suitable to achieve a target product grade have to be established through detailed laboratory tests. The head grade has a significant effect on the operation, which needs to be maintained consistently for the flotation operation by ensuring proper mining of the mine pockets and blending them thoroughly, and grinding those blended ores suitably. Fluctuating feed compositions to the flotation circuit poses challenges to the plant engineers as these abrupt fluctuations

Froth flotation and its modeling aspects Chapter | 10

433

result in inconsistent product quality. A mathematical model that captures such feed variations and the influence of the operating variables on the ore behavior, will help in the optimization of the circuit operation for a target grade-yield values that could be achieved. Each plant should invest in developing such models to facilitate a more efficient operation of the plant. The necessary instrumentation and control algorithms should be considered as part of plant operation for better performance of the plant. A better understanding of circuit behavior helps to design a good and stable operating plant and also this understanding aids better control of the flotation operations. More innovations in flotation equipment design should focus on improving the separation efficiency of particles with varying size distributions. The operations also should aim for the minimization of plant energy consumption. Process water quality plays a vital role in flotation. Salts dissolved in water will interfere in the separation of particles for the specific ores. Research should also aim at the use of hard / seawater for flotation with suitable reagents wherever possible. More research on reagents should bring selectivity among minerals being separated. Environmental safety and tailing disposal are to be given at most importance.

Acknowledgments Prof. Juan Yianatos, Universidad Te´cnica Federico Santa Mar´ıa Valpara´ıso, Chile; Emeritus Professor Tim Napier-Munn, Julius Kruttschnitt Mineral Research Centre, Australia; Prof. Claude Bazin, Universite´ Laval, Canda and Prof. Stephen Neethling, Imperial College London, U.K. are acknowledged for supporting to use some of their research topics and data as part of this chapter. BVR acknowledges Prof. P. C. Kapur, TRDDC Pune, India; Dr. N.P.H. Padmanabhan, BARC Hyderabad, India; Dr. Pradip, TRDDC Pune, India, Dr. Saptarshi Basu, IISc, Bangalore and Prof. S.J. Gopalkrishna, P.G. Centre, Sandur, India from whom the author learned flotation aspects in greater depth. The author acknowledges Mr. Ramesh Mahedvan and Mr. Indubhushan Jha, DELKOR, India, and Mr. Heiko Teuber, TAKRAF GmbH, Germany for their support and encouragement. BVR thanks all his friends at DELKOR who encouraged this contribution.

References Agar, G.E., 1987. Simulation in mineral processing. In: Yarar, B., Dogan, Z.M. (Eds.), Mineral Processing Design. Springer, Dordrecht. Available from: https://doi.org/10.1007/978-94-0093549-5_11. Agar, G.E., 2000. Calculation of locked cycle flotation test results. Miner. Eng. 13 (14
15), 1533
1542. Agar, G.E., Kipkie, W.B., 1978. Predicting locked cycle flotation test results from batch data. CIM. Bull. 71 (824), 140
147. Amelunxen, P., Schmitz, C., Hill, L., Goodweiler, N., Andres, J., 2019. Molybdenum. In: Dunne, R.C., Kawatra, S.K., Young, C.A. (Eds.), SME Mineral Processing and

434

Mineral Processing

Extractive Metallurgy Handbook. Society of Mining, Metallurgy & Exploration (SME), Colorado, USA, pp. 1891
1916. Austin, L.G., Klimpel, R.R., Luckie, P.T., 1984. Process Engineering of Size Reduction: Ball Milling. SME- AIME, New York. Bascur, O., 2019. Process control and operational intelligence. In: Dunne, R.C., Kawatra, S.K., Young, C.A. (Eds.), SME Mineral Processing and Extractive Metallurgy Handbook. Society of Mining, Metallurgy & Exploration (SME), Colorado, USA, pp. 277
316. Metso Corporation, 2015. Basics in Mineral Processing, tenth ed. Metso Corporation. Bazin, C., Hodouin, D., 1988. Residence time distributions modeling for mineral processes evaluation. CIM. Bull. 81 (911), 115
125. Beloglazov, K.F., 1939. The kinetics of the flotation process. Tsvetn. Metall. 9, 70
76. Coleman, R.L., 1978. Metallurgical testing procedures. In: Mular, A.L., Bhappu, R. (Eds.), Mineral Processing Plant Design. Society of Mining Engineers, New York. Deglon, D.A., Egya-mensah, D., Franzidis, J.P., 2000. Review of hydrodynamics and gas dispersion in flotation cells on South African platinum concentrators. Miner. Eng. 13 (3), 235
244. Dell, C.C., 1953. Release analysis
A new tool for ore dressing research. Recent Developments in Mineral Dressing. Institute of Mining and Metallurgy, London, pp. 75
84. Dell, C.C., Bunyard, M.J., Rickelton, W.A., Young, P.A., 1972. Release analysis: a comparison of techniques. Inst. Min. Metall. 81, C89
C96. Diaz, F., Yianatos, J., 2010. Residence time distribution in large industrial flotation cells. At. Peace Int. J. 3 (1), 2
10. Available from: https://doi.org/10.1504/AFP.2010.031015. Dowling Jr., E.C., Arnold, B.J., Klimpel, R.R., Aplan, F.F., 1999. Use of residence-time distribution techniques to analyze industrial scale froth-flotation circuits. Miner. Metall. Process. 16 (1), 18
26. Finch, J.A., Dobby, G.S., 1990. Column Flotation. Pergamon Press, Oxford, UK. Finch, J.A., Nesset, J.E., Acuna, C., 2008. Role of frother on bubble production and behavior in flotation. Miner. Eng. 21 (12/ 13/ 14), 949
957. Goodall, C.M., O’Connor, C.T., 1989. Residence time distribution studies of the solid and liquid phases in a laboratory column flotation cell. In: International Colloquium on Developments in Froth Flotation. The South African Institute of Mining and Metallurgy, Cape Town. Available at: http://www.saimm.co.za/Conferences/FrothFlotation/004-Goodall.pdf. Gorain, B.K., Franzidis, J.P., Manlapig, E.V., 1997. Studies on impeller type, impeller speed and air flow rate in an industrial scale flotation cell. Part 4: effect of bubble surface area flux on flotation performance. Miner. Eng. 10 (4), 367
379. Gorain, B.K., Franzidis, J.P., Manlapig, E.V., 2000. Flotation cell design: application of fundamental principles. In: Wilson, I.D., et al., (Eds.), Encyclopedia of Separation Science. Academic Press, pp. 1502
1512. Herbst, J.A., Harris, M.C., 2007. Modeling and simulation of industrial flotation processes. Froth Flotation: A Century of Innovation. SME- AIME, pp. 757
777. Huber-Panu, I., Ene-Danalache, E., Cojocariu, D.G., 1976. Mathematical models of batch and continuous flotation. In: Fuerstenau, M.C. (Ed.), Flotation: A.M. Gaudin Memorial Volume, Vol. 2. AIME, pp. 675
724. Imaizumi, T., Inoue, T., 1963. Kinetic considerations of froth flotation. In: Proceedings of the 6th International Mineral Processing Congress, Cannes, pp. 581
593. Kapur, P.C., Mehrotra, S.P., 1974. Estimation of flotation rate distribution by numerical inversion of Laplace transform. Chem. Eng. Sci. 29, 411
415. Kelly, E.G., Spottiswood, D.J., 1982. Introduction to Mineral Processing. A Wiley-Inter Science Publication, Brisbane.

Froth flotation and its modeling aspects Chapter | 10

435

Kelsall, D.F., 1961. Application of probability in the assessment of flotation systems. Trans. Inst. Min. Metall. 70, 191
204. Klimpel, R.R., 1980. Selection of chemical reagents for flotation. In: Mullar, A.I., Bhappu, R.B. (Eds.), Mineral Processing Plant Design, second ed AIME, New York, pp. 907
934. Klimpel, R.R., 1995. The influence of frother structure on industrial coal flotation. In: Kawatra, S.K. (Ed.), High-Efficiency Coal Preparation. Society of Mining, Metallurgy & Exploration (SME), Littleton, CO, pp. 141
151. Laskowski, J.S., 2003. Fundamental properties of flotation frothers. In: Proceedings of the 22nd International Mineral Processing Congress, Cape Town, RSA, pp. 788
797. Loveday, B.K., 1966. Analysis of froth flotation kinetics. Trans. Inst. Math. Mech. 75, C219
C225. MacDonald, R.D., Hellyer, W.C., Harper, R.W., 1985. Process development testing. In: Weiss, N. L. (Ed.), SME Mineral Processing Handbook. SME-AIME, New York, pp. 30/116
30/117. Mehrotra, S.P., Padmanabhan, N.P.H., 1990. Analysis of flotation kinetics of Malanjkhand copper ore, India, in terms of distributed flotation rate constant. Trans. Inst. Min. Metall. 99, C32
C42. Mehrotra, S.P., Saxena, S.K., 1983. Effects of process variables on the residence time distribution of a solid in a continuously operated flotation cell. Int. J. Miner. Process. 10, 255
277. Meloy, T.P., Whaley, D.A., Williams, M.C., 1998. Flotation tree analysis- reexamined. Int. J. Miner. Process. 55, 21
39. Mika, T.S., Fuerstenau, D.W., 1968. A microscopic model of the flotation process. In: Proceedings of the VIII International Mineral Processing Congress, Leningrad, pp. 246
269. Mohanty, M.K., Honaker, B.Q., Patwardhan, A., Ho, K., 1998. Coal flotation washability: an evaluation of the traditional procedures. Coal Prep. 19 (1
2), 33
49. Morales, P., Coddou, F., Yianatos, J., Contreras, F., Catal´an, M., D´ıaz, F., 2009. Hydrodynamic performance of the Division Codelco Norte Concentrator’s large flotation cells. In: Amenlunxen, P., Kracht, W., Kuyvenhoven, R. (Eds.), Proceedings of VI International Mineral Processing Seminar. Santiago, Chile, pp. 385
393. Napier-Munn, T.J., 1998. Analysing plant trials by comparing recovery-grade regression lines. Miner. Eng. 11 (10), 949
958. Neethling, S.J., Cilliers, J.J., 2012. Grade-recovery curves: a new approach for analysis of and predicting from plant data. Miner. Eng. 36
38, 105
110. Nelson, M.G., Lelinski, D., 2019. Mechanical flotation. In: Dunne, R.C., Kawatra, S.K., Young, C.A. (Eds.), SME Mineral Processing and Extractive Metallurgy Handbook. Society of Mining, Metallurgy & Exploration (SME), Colorado, USA, pp. 891
912. Nelson, M.G., Lelinski, D., Gronstrand, S., 2009. Design and operation of mechanical flotation machines. In: Malhotra, D., et al., (Eds.), Recent Advances in Mineral Processing Plant Design. Society of Mining, Metallurgy & Exploration (SME), Colorado, USA. Nesset, J.E., 1988. The application of residence time distributions to flotation and mixing circuits. CIM. Bull. 81, 75
83. Nesset, J.E., Zhang, W., Finch, J.A., 2012. A benchmark tool for assessing flotation cell performance. In: 44th Annual Canadian Mineral Processors Operators Conference, Ottawa, Ontario, pp. 183
209. Nicol, S.K., Bensley, C.N., Teh, K.C., Firth, B.A., 1983. The estimation of coal flotation response. In: Proceedings of the Congress for Improving Froth Flotation of Coal. Australian Coal Industry Research Laboratories, p. 116. Noakes, M., Lanz, T. (Eds.), 1993. Cost Estimation Handbook for Australian Mining Industry. The Australian Institute of Mining and Metallurgy, Victoria.

436

Mineral Processing

Safari, M., Harris, M., Deglon, D., Filho, L.L., Testa, F., 2016. The effect of energy input on flotation kinetics. Int. J. Miner. Process. 156, 108
115. Safari, M., Harris, M., Deglon, D., 2017. The effect of energy input on the flotation of a platinum ore in a pilot-scale oscillating grid flotation cell. Miner. Eng. 110, 69
74. Sahu, L., Bhattacharya, S., Dey, S., 2019. Release analysis of coal fines: evolution of the methodology and critical issues involved. J. South. Afr. Inst. Min. Metall. 119, 595
606. Schulz, N.F., 1970. Separation efficiency. Trans. SME/AIME 247, 81
87. Schwarz, S., Alexander, D., Whiten, W.J., Franzidis, J.P., Harris, M.C., 2006. JKSimFloat V6: improving flotation circuit performance and understanding. In: XXIII International Mineral Processing Congress, Istanbul, Turkey, pp. 1717
1722. Sripriya, R., Rao, P.V.T., Roy Choudhury, B., 2003. Optimisation of operating variables of fine coal flotation using a combination of modified flotation parameters and statistical techniques. Int. J. Miner. Process. 68 (1
4), 109
127. Thompson, P., Runge, K., Dunne, R.C., 2019. Sulfide flotation testing. In: Dunne, R.C., Kawatra, S.K., Young, C.A. (Eds.), SME Mineral Processing & Extractive Metallurgy Handbook. Society of Mining, Metallurgy & Exploration (SME), Colorado, USA, pp. 1029
1040. Van Orden, D.R., 1986. Chapter 43. Simulation of continuous flotation cells using observed residence time distributions. In: Somasundaran, P. (Ed.), Advances in Mineral Processing. SME-AIME, Littleton, CO, pp. 714
725. Rao, B.V., Velan, H.K., Jamal, S.I., Mahadevan, R., 2014. Grade-recovery prediction of an operating plant using flotation model and operating conditions. Procedia Eng. 83, 148
158. Available at. Available from: https://www.sciencedirect.com/science/article/pii/S1877705814011266. Wills, B.A., Finch, J.A., 2016. Wills’ Mineral Processing Technology, 8th (ed.) ButterworthHeinemann, Oxford. Yianatos, J., D´ıaz, F., 2011. Hydrodynamic characterization of industrial flotation machines using radioisotopes. In: Singh, N. (Ed.), Radioisotopes: Applications in Physical Sciences. IntechOpen. Yianatos, J., D´ıaz, F., Rodr´ıguez, J., 2002. Industrial flotation process modelling: RTD measurement by radioactive tracer technique. In: XV IFAC World Congress, Barcelona, Spain, 21
26 July, 2002. Available at: http://folk.ntnu.no/skoge/prost/proceedings/ifac2002/data/ content/02941/2941.pdf.

Chapter 11

Mathematical modeling of mineral jigs B. Venkoba Rao DELKOR, Takraf India Private Limited, Bengaluru, Karnataka, India

11.1 Introduction Jigs are the workhorse of the mineral industry for the last 100 years and will remain so for the next 100 years. Jigs separate minerals based on density differences present in the feed mineral particles along with the particle size effects. They use intermittent fluid pulsations that dilate and contract the bed of particles repeatedly to stratify the particles by their particle size and density. During the jigging action, the relatively fine light minerals move to the upper layers, while the heavy coarse particles move to the bottom layers. In a jig, the separation of particles is never perfect (unlike the sink and float analysis of the feed particles, which gives the feed washability curve). But a jig achieves a fair degree of rearrangement of particles near to perfection during jigging action. This segregation of particles helps to beneficiate the ores from a lower grade feed to a higher grade concentrate. Jigs are commonly used in the beneficiation of coal, iron ore, barite ore, manganese ore, etc. Metallic values associated with the ferroalloy slags and electronic circuit boards can be recovered by jigs. Recently, jigs have been used in the separation of plastics of different grades. Jigs are operated in both wet and dry forms depending on the availability of water and/or amenability of ores to dry beneficiation. Heavy media cyclones, sensor-based sorters, and other gravity-based centrifugal ore concentrators compete with jigs for particle separations in the mineral industry. Jigs seem to be cheaper both from the viewpoint of capital expenditures and operating expenses. Also, jigs can handle large tonnages in a single unit. The particles in the jig chamber have to be retained for a specified residence time, whereupon they are acted by the intermittent pulsations to stratify the particles. In other words, the particles in the bed have to be exposed to a certain number of fluid pulsations before the bed attains a good stratification. The bed dilates and contracts during each intermittent pulsation to Mineral Processing. DOI: https://doi.org/10.1016/B978-0-12-823149-4.00013-2 © 2023 Elsevier Inc. All rights reserved.

437

438

Mineral Processing

allow the heavy particles to move down. The kinetics of particle stratification is quite fast initially, but the pace recedes asymptotically to attain a state of equilibrium as time progresses. Finally, the segregated bed of particles needs to be sliced at the appropriate positions to get the desired concentrate, the middlings, and the tails. In an operating plant, the jig products, namely, the concentrate, the middling, and the tails are transported by conveyors and stored in different piles by their grades. The water from the wet jigged products has to be recovered and recycled back to the jig plant through a storage tank. In case of dry jigging, the dust coming from the top of the bed has to be collected and processed separately. Jigs operate on particles with a truncated size range, as the particle size has an important role to play in the segregation of particles along with the particle density. The amplitude and frequency of the pulsation in a jig operation are selected depending on the particle size-density consist. The coarser the particle size, the heavier the particle density, and the deeper the bed, the higher will be the amplitude required to pulse the particle bed. The jig feed is at first deslimed to remove the clayey material and the fines adhering to the coarse particles and the size range is truncated to a certain particle size ratio by the screens. These are done to improve the efficiency of particle separation in the jigs. It should be noted that the wave properties (the amplitude and the frequency) suitable for a coarse particle separation are not suitable for the fines separation in a jig operation, which otherwise misplace fine valuable minerals to the tails. Thus, the fine particles show lower efficiency of separation in a widely size distributed feed. Further, even though the feed size range is truncated to improve the jig particle separation efficiency, the fluctuations in the incoming feed concerning the size-density composition demand a more fine-tuning of the jig operation all the time to get a product with better grade and yield. Better control of jigs demands a better understanding of the particle separation in the jigs through mathematical models. This chapter focuses more on wet coarse particle jig operations, especially on the Batac type of jigs.

11.2 Test work and grade-yield-recovery curves Typically, the jig tests are conducted in bench-scale test equipment. Fig. 11.1 shows the M/s DELKOR laboratory jig facility for testing the ores in the size range of 1 mm (minimum) to 40 mm (maximum). The jig has a control facility to vary the jig wave pattern to adjust the wave specifications to suit the feed type. Generally, the maximum to minimum particle size ratio of feed is kept in the range of two to five to get better particle segregation. Excessive fines, if present in the feed distribute themselves across the bed to give a poor separation and thus dilute the grade of the concentrate.

Mathematical modeling of mineral jigs Chapter | 11

439

FIGURE 11.1 Photograph showing M/s DELKOR laboratory jig test facility.

Typically, the feed to the jig is scrubbed and screened before jigging to remove the adhering fines and also to break the loose clayey lumps in the feed. Each test in the M/s DELKOR lab jig requires around 3 kg of the representative feed sample. The test facility allows several bench-scale tests to be conducted to characterize the ore by varying the jig wave characteristics, mainly to understand the segregation patterns with the set waveform and jigging residence time. Elsewhere in other labs, test facilities require 50 to 100 kg of representative samples for each bench-scale test, which mainly depends on the capacity of the jig test facility. The M/s DELKOR jig chamber is made of attachable and detachable rings, which helps to slice the segregated bed into layered samples after the test. Each ring is about a centimeter high and 15 cm in diameter. These tests follow batch operations to understand the segregation patterns and density distribution across the bed height for the given feed sample. Typically, the tests are conducted for a period of 25 to 60 seconds for the M/s DELKOR jig. Within this period, the particles segregate and attain dynamic equilibrium. If the mineral particles are well liberated and easier to separate, then the feed sample requires less time to attain dynamic equilibrium. To conduct a bench-scale test, the representative feed sample is poured into the jig chamber filled partially with water when the first water pulse is triggered in the chamber. The particles are pulsated for a specified period, which allows them to segregate. The particles will soon come to a dynamic equilibrium by their size and density segregation, as the pulsations progress. When the test is over, the hutch water is drained into a bucket along with the hutch material which mainly consists of fine particles that pass through the jig screen deck during the pulsations. The bed of segregated particle is then

440

Mineral Processing

sliced into various layers from top to bottom to understand the stratification behavior. Typically the segregated bed shows a gradual increase in the density of particles from top to bottom of the bed. During jigging, the light minerals move to the upper layers while the heavy minerals move to the bottom layers. For heavy mineral separation (like the iron, manganese, and barite ores), the bottom layers are important as these layers get enriched with heavy minerals, while in the case of coal separation, the top layers are important where the coal particles get enriched. After the bed slicing, each layered sample is subjected to density analysis, drying and then weighed. The layers are then subjected to chemical analyses to know the assay composition of each layer. From such test data, grade-recovery and grade-yield curve(s) for various constituent elements of interest can be constructed. Table 11.1 gives typical segregation patterns for an iron ore jig test having feed particles in the size range of 4
20 mm. Fig. 11.2 gives a pictorial view of the jig layers along with the feed sample. Layer 1 is the topmost layer, and layer 8 is the bottom-most layer of the jig test. The hutch product (not shown in the figure) represents the material that has passed the jig screen deck during the pulsations. Here, the hutch product is a mediumgrade material and is not a part of the concentrate. Sometimes, hutch products will have high-grade fines that can be added to the concentrate to increase the product yield. As the layer numbers increase from top to bottom (refer to Table 11.1), the Fe assay of the layers increases, while silica and alumina content decrease gradually. This indicates that heavy and iron-rich particles have moved to the bottom layers by the jigging action. Depending on the Fe grade to be produced, one can decide on the slice position for the particle bed, which in turn decides the product yield and the concentrate grade achievable by jigging. For the batch jig separation data given in Table 11.1, Fig. 11.3A gives the component grades for Fe %, silica %, and alumina % as a function of the yield of the product. The head-grade assays 53.12% Fe, 17.38% silica, and 1.78% alumina. For the production of a 60% Fe concentrate, the test results indicate that a yield of 54% concentrate with around 9% silica and 1.5% alumina can be achieved. These are indicated by the marked dotted lines on the plot. Fig. 11.3B gives a pictorial view of the grade-recovery curve for Table 11.1 data, depicting an inverse relationship between the grade and recovery of Fe values.

11.3 Effect of head grade on the jig performance The head grade of the jig feed has a significant effect on the jig performance. The product yield achievable for a particular product grade is dependent on its head grade. If the head grade fluctuates a lot, the yield of the product will also fluctuate to produce a specified concentrate grade. The following example explains this.

TABLE 11.1 Typical layers of an iron ore sample separated in M/s DELKOR lab jig. Sl no.

Layer no.

Weight %

Layer assay, % Fe %

SiO2%

Al2O3%

Yield %

Cumulative layer grade, %

Cumulative layer recovery, %

Fe %

SiO2%

Al2O3%

Fe %

SiO2%

Al2O3%

1

Layer 1

4.51

37.45

38.65

2.33

91.18

53.48

16.95

1.74

91.80

88.93

89.02

2

Layer 2

8.47

37.34

32.9

2.14

86.67

54.32

15.82

1.71

88.61

78.90

83.12

3

Layer 3

8.69

42.62

31.66

2.16

78.20

56.15

13.97

1.66

82.66

62.87

72.96

4

Layer 4

10.75

49.62

21.95

2.09

69.50

57.85

11.76

1.60

75.69

47.04

62.43

5

Layer 5

9.28

52.97

21.85

1.6

58.75

59.35

9.90

1.51

65.64

33.46

49.83

6

Layer 6

8.83

59.36

8.96

1.87

49.47

60.55

7.66

1.50

56.39

21.79

41.50

7

Layer 7

13.42

60.05

7.54

1.79

40.64

60.81

7.37

1.41

46.52

17.24

32.24

8

Layer 8

27.23

61.18

7.29

1.23

27.23

61.18

7.29

1.23

31.36

11.42

18.78

9

Hutch product

8.82

49.4

21.8

2.22

442

Mineral Processing

FIGURE 11.2 Layered iron ore samples for data shown in Table 11.1.

Iron ore samples with varying head grades and having 1
6 mm size are batch jigged in M/s DELKOR jig for 30 seconds. These ore particles are sourced from the same ore by considering particles belonging to different densities, which thus influence their head grade. The jig layers obtained from the tests are dried, weighed, and chemically analyzed for Fe content. Fig. 11.4A depicts the segregation patterns of the particles in terms of product assay and the product yield, which are obtained by combining the layers cumulatively from the jig bottom layer (as discussed in Table 11.1). Each test curve independently shows that as the product grade increases, the yield value decreases. However, as the head grade increases, the curves shift to the right position on the graph. This indicates that there is possibility of obtaining a higher yield with better grade product by increasing the head grade (Rao et al., 2016a). This example also suggests that it is better to feed the jig with a consistent head-grade material to a continuous jig operation for its

Mathematical modeling of mineral jigs Chapter | 11

443

FIGURE 11.3 Iron ore (4
20 mm) separation in a jig (for the data shown in Table 11.1): (A) Product yield vs component grade curves; (B) Fe grade vs Fe recovery curve.

better-control to produce a consistent concentrate grade at the desired yield value. Fig. 11.4B shows a plot of product yield as a function of the head grade of the ore, for a specified concentrate grade production of 64% Fe and 64.5% Fe from the iron ore jig tests. The yield values in Fig. 11.4B are derived from Fig. 11.4A by slicing the bed at a particular concentrate grade (as indicated by the vertical lines shown in Fig. 11.4A). It shows that the yield of concentrate with 64% or 64.5% Fe is much higher when the ore head grade increases beyond 61.9% Fe. Therefore, to assess the expected yield from the plant operations, it is essential to test the same grade ore in the lab that would be treated in the plant. The higher the head grade, the higher will be the product yield.

444

Mineral Processing

FIGURE 11.4 Effect of head grade on the segregation patterns of particles: (A) product assay as a function of product yield for various head grade material; (B) head grade as a function of achievable product yield for a particular concentrate grade material (@ 64 and 64.5% Fe).

11.4 Timed batch jig tests and attainment of dynamic equilibrium of particles in the jig bed The time of batch jigging varies from one lab to the other lab. Some laboratories do jigging for 20 to 30 minutes, while others do the jigging for less than a minute. The time of batch jigging to segregate the particles properly depends on pulse characteristics as well as the capacity of the jig. The M/s DELKOR lab jig has a capacity of approximately 3 kg material and the testing time is less than 45 seconds typically. Timed batch jig tests can be conducted to understand the kinetics of particle segregation in a jig bed and to recognize the time required to attain

Mathematical modeling of mineral jigs Chapter | 11

445

FIGURE 11.5 Average particle bed density profiles of the batch jig operation for various timed jig tests.

dynamic equilibrium. The general thinking among the process engineers is that the more jigging time, the better will be the particle stratification. However, unnecessary jigging for long periods has to be avoided, as stratification is effective only before the attainment of dynamic equilibrium for the bed of particles. Tavares and King (1995) in their mathematical model assume that the jig bed will eventually attain dynamic equilibrium and it is believed that after the attainment of dynamic equilibrium of the particle bed, the segregation patterns of the bed almost remain unchanged. Therefore, there is no point in jigging for an extra duration after the attainment of dynamic equilibrium for a given feed ore. Fig. 11.5 shows the measured average bed density profiles for a lowgrade iron ore jigged for 3, 5, 10, 15, 20, 30, and 45 seconds independently, on the representative feed samples. The tests were conducted in the M/s DELKOR lab jig. After the completion of the test, the segregated jig bed was sliced into layers and analyzed to assess the layer mass fractions and the bed layer average densities. As shown in Fig. 11.5, the average bed density profile evolves with jig time and reaches a situation where the density profile does not significantly change further with progressing time. This indicates the attainment of dynamic equilibrium with progressing jig time, as perceived by Tavares and King (1995) to model the jig particle stratification.

11.5 Jig Stratification Index Buys and Jonkers (2012) have proposed the Jig Sratification Index (JSI) to assess the degree of stratification for a segregated jig bed. The index depends on two parameters of the particle jig bed, namely: (i) the mass fraction of the material in the layers, and (ii) the average particle density of the layers.

446

Mineral Processing

JSI indicates the completeness of the particle separation in a jig operation. It is the volume-weighted average of the absolute difference between the jig bed layer densities, ρi , and the entire bed average density, ρ. The entire bed average density represents the density of the feed particles for the jig operation. JSI shows a value of zero for a fully mixed bed (i.e., at the start of the jigging). JSI increases rapidly with progressing jig time and then it tapers off slowly, as it asymptotically approaches a maximum value. The maximum value of JSI depends on the ultimate degree of separation in the jig bed. If the sink-float washability data of the feed particles are made available, then the theoretical maximum possible value of JSI can be calculated for an ideal separation. The ratio of the maximum value of jig bed JSI from the actual test to the JSI value from ideal sink-float analysis suggests the fraction of completeness of particle separation. The jig operation will approach a value close to the ideal sink-float JSI value, but not equal to it, even after long periods of jigging. Jig test JSI is mathematically represented as: PN mi i51 ρi ρi 2 ρ JSI 5 ð11:1Þ PN m i

i51 ρi

where mi is the dry mass fraction of the ith layer material, ρi , is the average density of particles in the ith layer (in kg/m3), ρ is the average density of the entire jig bed (in kg/m3), and N is the number of layers sliced from the jig test. The average bed density can be calculated as: PN mi ρ 5 Pi51 ð11:2Þ N m i

i51 ρi

Since the bed particles rearrange with progressing jig time, the JSI value evolves with jigging time. The evolving JSI value with progressing time for the jig bed can be represented by: JSIðtÞ 5 β ð1 2 expð 2 δtÞÞ

ð11:3Þ

where β and δ are the model parameters and t is the jigging time at which JSI is calculated using Eq. (11.1). Fig. 11.6 shows typical JSI values from timed batch jig tests carried out on an iron ore sample in the M/s DELKOR jig. The dots in Fig. 11.6 show the test JSI values as a function of jig time and the continuous line shows a model fit using Eq. (11.3). The graph shows that there is no significant change in JSI values after 20 seconds of jigging, which is the time when a fair degree of dynamic equilibrium for the tested sample has reached in the equipment. The particles in the jig bed stratify due to their potential energy differences and the bed tries to reduce its potential energy during jigging with the

Mathematical modeling of mineral jigs Chapter | 11

447

FIGURE 11.6 Kinetics of JSI described for an iron ore sample using batch jig tests. The continuous line shows the model fit of evolving JSI using Eq. (11.3).

rearrangement of particles (Mayer, 1964). In essence, Fig. 11.6 shows that the jig bed initially stratifies at a faster rate because of the higher potential energy differences between the bed and the surrounding particles. As the bed layers stratify with progressing time, the potential energy of the segregated bed of particles to further stratify decreases, and the JSI value of the bed flattens gradually. Hence, with progressing time, the stratification rates drop and follow an asymptotic path to attain a dynamic equilibrium for the given feed particle consist.

11.6 Jig bed kinetics and bed assay evolution Fig. 11.7A
C gives a pictorial view of grade-recovery curves for timed batch jig tests for an iron ore. The tests were conducted on a (230 1 6) mm size fraction in M/s DELKOR jig. As jigging progresses, the heavy iron particles segregate to the bottom layers rejecting the lighter minerals to the top layers. The silica and alumina content of the bottom layers decreases and that of the top layers increases with the progressing jigging time. Moreover, Fig. 11.7 shows that the bed comes to an equilibrium position eventually, as there is no significant change in the grade-recovery curves for Fe %, SiO2%, and Al2O3% after 30 seconds of jigging.

11.6.1 Particle segregation in a continuous Baum jig operation Rong and Lyman (1992) tested a coal sample in a continuous Baum jig along with the tracer particles. They noticed that the tracer density particles in a Baum jig (that were in the range of 1300 , ρs , 2000 kg/m3) stratified rapidly till an operating time of 180 seconds. Beyond this point, the

448

Mineral Processing

FIGURE 11.7 (A
C) Grade-recovery curves for Fe %, SiO2%, and Al2O3% for an iron ore sample of (230 1 6) mm obtained from the timed batch jig tests.

Mathematical modeling of mineral jigs Chapter | 11

449

stratification rate decreased till the jigging time, t 5 300 seconds, when the bed equilibrium was reached. For particles below 8 mm, the equilibrium was reached at much longer periods, indicating that finer particles have slower segregation kinetics in the jig operation.

11.7 Kinetics of particle size segregation in a batch jig Although the jigs are known as gravity concentrators to separate particles of different densities, the particle size also plays an important role in their segregation. Fig. 11.8A
D shows the kinetics of particle size segregation patterns for various size fractions of a fluorite ore of (212.5 1 3) mm. The segregation is expressed in terms of yield percentage and the size fraction recovery percentage to the sink stream at the slice position. Tests were conducted in M/s DELKOR lab jig for various periods of jigging from 15 to 90 seconds on the fluorite ore. As time progresses, the bed evolves and the particle size fractions rearrange, indicating that the coarser size particles move more towards the bottom layers (the curves below the diagonal) and

FIGURE 11.8 (A
D) Kinetics of particle size fraction rearrangement for a batch jig operation using 212.5 1 3 mm fluorite ore.

450

Mineral Processing

finer size particles move toward the top layers (the curves above the diagonal). The change in patterns is quite fast in the initial period, which slows down with progressing time, as the bed starts reaching the state of dynamic equilibrium.

11.8 Jig types Based on the mechanism type used to generate the jig pulse wave, the jigs can be categorized into piston-type, diaphragm-type, air-pulsated, and mobile-sieve jigs. Fig. 11.9 shows a schematic diagram of types of jigs (Kelly and Spottiswood, 1982; Ambros, 2020). Harz jig is an old type of jig with a rectangular tank, which uses a plunger mechanism to create a sinusoidal pulse through the bed of particles. It contains three to four compartments juxtaposing each other, where the material flows from one compartment to the other. The first compartment

FIGURE 11.9 Schematic representation of jig types. After Kelly, E. G., Spottiswood, D. J., 1982. Introduction to Mineral Processing. A Wiley-Inter Science Publication, Brisbane; Ambros, W.M., 2020. Jigging: a review of fundamentals and future directions. Minerals 10(11), 998.

Mathematical modeling of mineral jigs Chapter | 11

451

produces high-grade product material, and the product material’s grade decreases in the subsequent compartments. The final reject leaves the last compartment. It is not easy to change and adjust the pulsating conditions (such as the wave height and the waveform) in these jigs. Denver jig, IHC radial jig, and Remer jig use a diaphragm to generate the jig pulse. The IHC radial jig is a circular jig, where the radial compartments are fed by a central pipe to segregate the particles. It uses a saw-tooth wave produced due to the asymmetric movement of the diaphragm that follows a rapid upward and a slow downward movement (Wills, 1997). Baum and Batac jigs are air-pulsated jigs. In these jigs, instead of mechanical movement of the plunger or the diaphragm, an intermittent entry and exit of pressurized air in a controlled manner into the air chambers by a set of special valves produce the pulsation required to fluidize the jig particle bed. The Baum jig uses compressed air instead of a plunger or diaphragm, to create a pulsating water flow. This is achieved by injecting and exhausting compressed air into the air chamber that displaces water, making it easy to adjust pulsating conditions to match the ore. The air chamber is positioned above the water level on one side of the jig and the other side has a jig chamber with a particle bed supported over a sieve deck. The hutch is a Ushaped tank. This jig is widely used in the field of coal beneficiation. As the device becomes larger, it becomes difficult to generate a uniform pulse across the jig width, which limits the jig size. The vari-wave jig is a type of Baum jig that uses a trapezoidal waveform to separate the particles, instead of the sinusoidal waveform. Batac jig is an under pulsated jig that can be used for coarse or fine particle separation (above 1 mm). The size range of the jig feed is truncated to remove finer particles from the feed to improve the efficiency of jig performance. Likewise, the upper particle size limit is also considered with a size ratio of 2
5 to its lowest particle size to improve jig performance. Batac jig shows an improved performance over that of the side pulsated Baum jig in terms of the spread of the pulse wave more uniformly over the entire deck area, even when the jig sizes are increased. The efficiency improvement is well recognized adjacent to the sidewalls of the jig, where the Baum jigs show poor performance. Batac jigs are constructed with multiple air chambers beneath the deck, where the pulsing characteristics of the waves can be tuned electronically for each chamber for a proper stratification of the particles. TACUB jigs and APIC jigs are forms of the Batac jig. Intermittent feeding of air into the air chambers using special valves and the air exhaust from the air chambers generates the water pulse(s). Mostly these units use a trapezoidal waveform, which gives better particle separation over the sinusoidal waveform. ROMJIG is a mobile-sieve jig, developed lately. When the particle size becomes too large [say, above 200 mm, like the run of mine (ROM) coal

452

Mineral Processing

particles], it becomes difficult to lift and fluidize them by plunger movement or diaphragm movement or with the use of intermittent compressed air in the air chambers like in the Baum and/or Batac jigs. However, with the recent development of hydraulic drives, it has become possible to develop a movable sieve jig to lift these coarse ROM particles and fluidize them. The feed side of the floor sieve is not fixed. The feed end is lifted by flood control and dropped by gravity. The jigging takes place in a water bath to separate the ROM coal particles into clean coal and refuse which are then transported over the chutes into the product streams. This jig can treat raw coal particles in the size range of 40
350 mm. Sometimes jigs use coarse ragging material placed over the deck of the jig to enhance the separation performance. Low-density fine particles smaller than the aperture size enter the hutch due to their low separation efficiencies during jigging. The use of ragging material avoids the entry of low-density fines into the hutch. For example, feldspar is used as ragging material in coal separation, whose density is intermediate to coal and ash particles. This allows only those particles greater than the density of the ragging material to enter the hutch stream. For a feed with a wide feed size distribution, the fine particles are difficult to separate along with the coarse particles, because the wave characteristics (namely, waveform, stroke length/amplitude, and frequency) used for coarse jigging are not suitable for the fine particle separation. This is the main cause for the truncation of the jig feed size range, to eliminate the fines and very big coarse particles in the feed. In the last three decades, tremendous progress has been made in developing jigs for treating the fine size range particles. Among these, the prominent ones are Kelsey Centrifugal Jig (KCJ), Altair centrifugal jig, and InLine Pressure Jig (IPJ). KCJ is a fine particle separator that can separate particles up to 10 microns using the conventional jigging phenomenon assisted by centrifugal forces. The spinning of the jig induces centrifugal forces that enhance the apparent gravity differences among the feed particles. Due to the use of centrifugal force (with a maximum of 60
100 times the gravitational force), the unit can separate minerals that have small specific gravity differences. A bed of ragging material retained over a wedge wire screen assists in the separation of fine heavy particles. Hutch water is elutriated at high-pressure across the ragging material with high frequency using a cam mechanism to generate the pulse. During the operation, a central pipe distributes the feed slurry (B25% solids and particles in the range of 5
500 microns) over the ragging material. The heavy minerals pass through the ragging material (i.e., into the hutch chamber), and constitute the concentrate, while the rest of the material overflows into the tailings stream. The variables used to control the operation are centrifugal force, the size and density of the ragging material, the water flow rate to the hutch elutriation, and the pulse frequency, which need to be optimized for a given operation. Advancements to KCJ operation include

Mathematical modeling of mineral jigs Chapter | 11

453

a programmable logic controller (PLC)-based control scheme, an automatic screen cleaning system, and an integrated lubrication arrangement. Although the KCJ is a very efficient separator, it faces problems like maintenance after 4000
8000 hours of operation; requirement of good quality clean water for pulsation; low feed throughputs to the amount of concentrate produced; and a challenge in the selection of specific ragging material for a given operation (Walklate and Fourie, 2006). Altair centrifugal Jig is another competing technology for KCJ. IPJ is a circular jig that is used for fine particle separation. It consists of an encapsulated and pressurized chamber filled with slurry. The feed is distributed over the bed through a central pipe. A vertically pulsated screen over which ragging material is placed acts as the separating media. The screen moves up and down with a hydraulically driven shaft. An asymmetric triangular waveform is generated for the separation of the particles. The upward movement is the suction stroke while the downward movement is the dilation (i.e., separation) stroke. The feed consists of particles from a few millimeters up to 25 mm. Particles with high specific gravity pass through the ragging layer and fall into the hutch chamber. The particles with low specific gravity move over the ragging layer and to the tailboard in the peripheral part. The screen aperture size, stroke length, and pulsation frequency can be adjusted to suit the application. IPJ is said to require less water for the jig operation. These units are used to recover valuables from circulating loads in the grinding circuit. Table 11.2 gives the classification of jigs using the proposal by Sampaio and Tavares (2005).

11.9 Jig wave forms The jig waveform characteristics, namely, its shape, amplitude, and frequency influence the particle separation in the jigs. Various types of jigs produce different waveform shapes as indicated in Fig. 11.10 (Ambros, 2020). In some of the recent equipment, the amplitude and the frequency of the pulse waves can be adjusted as per the feed characteristics through the PLC systems of the jigs. Fig. 11.11 gives a typical trapezoidal waveform generated by the M/s DELKOR laboratory jig. The data is gathered by pulsating the jig with water and monitoring the wavefront positions using a high-frequency water level sensor. Trapezoidal wave shows an upward lift of particles in the initial period (pulsion), a flat holding time, and then a downward compressing period (suction). The flat holding period allows differential settling of heavy and light particles much better than a sinusoidal wave. Hence, the trapezoidal wave is the preferred waveform over the sinusoidal waveform.

454

Mineral Processing

TABLE 11.2 Classification of jigs according to their types. Screen type

Heavy product discharge

Pulsation mechanism

Jig equipment

Common applications

Fixed screen

Over the screen

Piston

Harz

Coal

Diaphragm

Jeffrey

Coal

Bendelari

Ores

Air-pulsated

Baum/vari-wave

Coal and ores

Batac/TACUB/APIC

Coal and ores

Denver

Ores

Wemco/Remer

Ores

Yuba

Ores

Pan-American

Ores

Through the Screen

Mobile screen

Diaphragm

IHC Radial Jig

Ores

Air-pulsated

Baum/Vari-Wave/ Batac/TACUB/APIC

Coal and ores

Mechanic

Kelsey centrifugal jig/ Altair centrifugal jig

Ores

Over the screen

Mechanic

ROMJIG

Coal

Through the screen

Mechanic

Inline pressure jig

Ores

Source: Based on Sampaio, C.H., Tavares, L.M.M., 2005. Beneficiamento Gravime´trico: Uma Introduc¸a˜o aos Processos de Concentrac¸a˜o Mineral e Reciclagem de Materiais por Densidade. Editora da UFRGS, Porto Alegre, Brazil.

11.10 King’s stratification model King’s stratification model describes the segregation of particles of various densities in the jig bed mathematically. It uses Mayer’s potential theory (1964) that minimizes the potential energy of the bed (when pulsated), which is opposed by the dispersive forces that disperse the particles from an ideal stratification scenario. A balance between the stratification forces and the dispersive forces represents the actual particle stratification achieved in the jig bed (Tavares and King, 1995; King, 2001). Let us consider a bed of mono-sized spherical particles of uniform density, which are densely packed. Suppose we introduce an odd particle of the

Mathematical modeling of mineral jigs Chapter | 11

455

FIGURE 11.10 Jig wave patterns in different machines. After Ambros, W.M., 2020. Jigging: a review of fundamentals and future directions. Minerals 10(11): 998.

FIGURE 11.11 A typical trapezoidal waveform generated by M/s DELKOR laboratory jig.

456

Mineral Processing

same size but of different density into the bed, it will be held rigidly in the bed. If the bed is allowed to expand with random movement of particles, like the fluidization caused by the pulsation in a jig operation, then the odd particle will move, downward or upwards, depending on whether it is heavier or lighter than the surrounding particles. This eventually will lead to the reduced potential energy of the bed. This is depicted in Fig. 11.12. The variation in the potential energy of the system when two particles of different densities interchange their positions in a bed of particles can be analyzed as below. Suppose a particle of density ρ at height ðH 1 ΔH Þ interchanges with a particle of density ρ at height, H, then the change in potential energy due to the exchange of particle positions is given by: ΔE 5 Eðparticle at H 1 ΔH Þ 2 Eðparticle at H Þ 5 vp gðH 1 ΔH Þρ 1 vp gHρ 2 vp gðH 1 ΔH Þρ 2 vp gHρ 5 vp gðρ 2 ρÞΔH

ð11:4Þ

where E is the potential energy of the system, vp is the volume of a single mono-size particle, ρ is the density of the heavy particle and ρ is the density of surrounding particles. The potential energy gradient can be written as: dE 5 v p gð ρ 2 ρ Þ dH

ð11:5Þ

The above equation shows that the density difference among the particles is responsible for the movement of particles and thereby stratifying the bed. The rate at which the particles move relative to the bed is dependent on the potential energy gradient and the migration velocity, u; with which the particle penetrates the bed under unit potential energy gradient and is given by u dE=dH. The migration velocity is a strong function of the particle size and shape and is independent of the particle density (King, 2001).

FIGURE 11.12 Schematic diagram representing a change in potential energy when a heavy particle moves down by replacing the position with a light particle. After King, R.P., 2001. Modeling and Simulation of Mineral Processing Systems. Butterworth-Heinemann, Oxford.

Mathematical modeling of mineral jigs Chapter | 11

457

Suppose Cρ is the volumetric concentration of particles of density ρ in the bed, then the flux of particles of density ρ that move in the bed of particles of density ρ due to potential energy gradient is given by: ns 5 2 Cρ u

dE dH

ð11:6Þ

In the above equation, the negative sign indicates that the heavy particles move down during the expansion of the particle bed by the jig wave to minimize the potential energy gradient. The term, ns ; is called the stratification flux (expressed in m/s), which tries to sharpen the particle segregation in the bed. Substituting the potential gradient from Eq. (11.5) into Eq. (11.6) results: ns 5 2 Cρ uvp gðρ 2 ρÞ

ð11:7Þ

The particle
particle, the particle
wall, and the particle
fluid collisions within the bed cause diffusive flux, which opposes the stratification flux and tries to flatten the segregation pattern caused by the stratification flux. The diffusive flux is given by a Fickian equation, as given below: nD 5 2 D

dCρ dH

ð11:8Þ

The diffusion coefficient, D; depends on the particle size, shape, and bed expansion mechanism (King, 2001). A dynamic equilibrium exists in the bed when the stratification flux is balanced by the diffusion flux and is given by: nD 5 2 ns

ð11:9Þ

Substituting the flux values results: dCρ ugvp Cρ 52 ðρ 2 ρÞ dH D

ð11:10Þ

Expressing the relative bed height h as H/Hb, where Hb represents the total bed depth of particles in the jig chamber, and by further defining the specific stratification constant, α as: α5

ugvp Hb D

ð11:11Þ

It is now possible to express the dynamic equilibrium of the bed of particles as: dCρ 5 2 αCρ ðρ 2 ρ ðhÞÞ dh

ð11:12Þ

It has to be noted here that α is a strong function of the particle size and the bed expansion mechanism and is independent of the particle density (King, 2001).

458

Mineral Processing

The average bed layer density of the particles at relative bed height, h, is calculated as: ðN ρðhÞ 5 ρCρ ðhÞdρ ð11:13Þ 0

The solution to Eq. (11.12) gives the vertical concentration profiles of segregation for particles of density, ρ. As no concentration value for any of the particle species is known at the top or the bottom position or any intermediate bed positions, it is not possible to put any boundary conditions a priori for Eq. (11.12). To solve Eq. (11.12), it has to satisfy the following constraints: ð1 Cρ dh 5 Cρf for all ρ ð11:14Þ 0

where represents the volumetric concentration of particles of density ρ in the feed stream and ðN Cρ dρ 5 1 for 0 # h # 1 ð11:15Þ Cρf

0

For all practical purposes, the feed particle population can be discretized into n grade classes. The above equations can be expressed in discretized form as:

0 0


 dCi ðhÞ 5 2 αCi ðhÞ ρi 2 ρðhÞ for i 5 1; 2. . .n dh

ð11:16Þ

with constraints ρ ð hÞ 5

n X

Ci ðhÞρi

i51 n X

Ci ðhÞ 5 1 for all h

i51

Cif

5

ð1

Ci ðhÞ dh for all i

ð11:17Þ

0

The numerical solution to the set of differential equations in Eq. (11.16) subjected to the constraints in Eq. (11.17) gives the concentration profile of ith particle density across the bed height for a multicomponent particle density system for a batch jig operation. From the solution to the above equations, the mass yield of the solids to the floatstream, by slicing the segregated bed at relative slice height, h, is calculated as: Ð1 ρðhÞdh M ðhÞ 5 Ðh1 ð11:18Þ 0 ρðhÞdh

Mathematical modeling of mineral jigs Chapter | 11

459

The recovery of density component ρi to the float-stream by slicing the segregated bed at relative slice height, h; is given by: Ð1 Ri ð h Þ 5

h

Ci ðhÞdh Cif

ð11:19Þ

Eqs. (11.16
11.19) apply to a batch jig operation. A batch jig operation will not show the longitudinal transport of particles during jig pulsation action. But a continuous jig operation experiences the longitudinal transport of particles with varying particle flow velocities across the bed height. The particles in the bottom-most layer move very slowly when compared to the particles in the topmost layers. This phenomenon is incorporated in King’s continuous jig stratification model by using a monotonically increasing velocity profile given by: vðhÞ 5 κh 1 ð1 2 κÞh2

ð11:20Þ

where κ represents the shape factor of the velocity profile across the bed height. The set of differential equations to be solved for a continuous jig operation are Eq. (11.16) along with the constraints given by: ρ ð hÞ 5

n X

Ci ðhÞρi

i51 n X

Ci ðhÞ 5 1 for all h

i51

Ð1

Cif

Ci ðhÞvðhÞdh 5 Pn 0 Ð 1 for all i i51 0 Ci ðhÞvðhÞdh

ð11:21Þ

From the solution to the above set of differential equations, the mass yield of solid particles to the float-stream, by slicing the continuously operated jig bed at height, h; is given by: Ð1 ρðhÞvðhÞdh M ðhÞ 5 Ðh1 ð11:22Þ 0 ρðhÞvðhÞdh The recovery of density component ρi to the float-stream by slicing the continuously operated jig at relative bed height h is calculated as: Ð1 Ci ðhÞvðhÞdh Ri ðhÞ 5 Ðh1 ð11:23Þ 0 Ci ðhÞvðhÞdh

460

Mineral Processing

The float-stream particle distribution in terms of the particle density for both batch and continuous jig operations by slicing the bed at relative bed height, h; is given by: C f Ri ð h Þ CiP ðhÞ 5 Pn i f i51 Ci Ri ðhÞ

ð11:24Þ

11.11 Application of King’s stratification model to the continuous performance of an industrial jig Tavares and King (1995) verified the stratification model using the performance data of seven coal separating industrial continuous jigs that include both the Baum and Batac types. They showed that King’s stratification model describes the performances of the industrial jigs very well in terms of separation of particle densities. In the absence of precise velocity profile measurements, Tavares and King (1995) used a κ value of 0.3 to evaluate the specific stratification coefficient, α, by matching the partition coefficients of coal separation. The specific stratification coefficients for the industrial Baum and Batac jigs vary from 0.006 to 0.114 for coal separations. Tavares and King (1995) have felt that these stratification coefficient values are much lower when compared to the batch jig operation. They attributed this lowering to the inadequate residence time in industrial jigs to attain good particle dynamic equilibrium. However, the comparison is not based on the same material being tested in the lab and industrial jigs. Mostly, the data shows that the stratification coefficients from secondary chambers are better than those in the primary chambers. They have attributed this fact to the reduced bed heights and better mobility of particles in the secondary chambers. Tavares and King (1995) calculated the cut height of the bed and the particle densities at the cut height from the experimentally determined yield values to the refuse stream, using the stratification model.

11.12 Simulation studies of King’s stratification model for batch jig operation King’s stratification model for batch jig operation has a single model parameter, namely the stratification coefficient. For the continuous jig operation model, the velocity profile of the layers in the jig bed also needs to be considered along with the stratification coefficient. Fig. 11.13 depicts the batch jig simulation studies using King’s stratification model to attain a dynamic equilibrium of particles under various specific stratification coefficients for

Mathematical modeling of mineral jigs Chapter | 11

461

FIGURE 11.13 Simulation studies on species concentrations as a function of relative bed height for a feed with four equal volumetric concentrations using King’s stratification model for a batch jig operation using various specific stratification coefficient values: (A) α 5 0.01; (B) α 5 0.03; (C) α 5 0.05. Figure (C) also indicates a scenario of the ideal separation of feed particles represented by the vertical lines.

462

Mineral Processing

the same feed composition. The feed is composed of four density classes of particles of 1350, 1500, 1700, and 2100 kg/m3 with equal volumetric concentrations. The particle stratification profiles in the jig bed are shown in Fig. 11.13A
C for various stratification coefficients. It is seen that the spread of each particle density species is confined to a limited relative bed height range. Moreover, the plots show an overlap of various particle density classes across the relative bed height for the particle segregation by the jigging action. The plots indicate that as the values of specific stratification coefficient α increase from 0.01 to 0.05, the degree of segregation of particles improves in the bed. As the α value increases, each particle density class reduces its spread across the relative bed height but increases the peak concentrations at a certain zone of the bed, indicating better segregation of the feed particles. Fig. 11.13C also indicates an ideal separation of feed particles represented by the vertical lines of particle segregation across the bed height. An ideal separation of feed particles indicates a perfect separation of the feed particles according to their densities with no intermixing and overlap. This would mean that for an ideal separation, the particles with a density of 2100 kg/m3 should segregate at the bottom of the jig in the relative bed heights of 0 to 0.25, and the particles with a density of 1700 kg/m3 should segregate in the relative bed heights of 0.25 to 0.5, the particles with density 1500 kg/m3 should segregate in the relative bed heights of 0.5 to 0.75, and the particles with density 1350 kg/m3 should segregate in the relative bed heights of 0.75 to 1. However, since jig is not an ideal particle separator, the particles will be spread across a wider relative bed height and we see an overlap of different density particles at different layer portions of the relative bed height depending on the value of the specific stratification coefficient. For example, in the case of specific stratification coefficient α 5 0.05 and with the establishment of dynamic bed equilibrium (i.e., referring to Fig. 11.13C), the particles with the density 2100 kg/m3 segregate in the relative bed heights of 0 to 0.5, the particles with the density 1700 kg/m3 segregate in the relative bed heights of 0 to 0.9, the particles with the density 1500 kg/m3 segregate in the relative bed heights of 0.2 to 1, and finally, the particles with the density 1350 kg/m3 segregate in the relative bed heights of 0.3 to 1. Fig. 11.14 shows the average bed density profiles across the bed height for the simulation studies in Fig. 11.13. It shows that the average bed density profile improves with a better degree of segregation of particles as the specific stratification coefficient α increases from 0.01 to 0.05. The dotted line in red color indicates the average bed density profile for an ideal separation of feed particles. Since jigs are not ideal separators, the average bed density profile produced by the jig tests under various α values deviates from the ideal separation average bed density profile.

Mathematical modeling of mineral jigs Chapter | 11

463

FIGURE 11.14 Average density profiles for various specific stratification coefficients α along with the depiction of an ideal separation bed density profile for the four density component feed with equal volumetric concentrations.

11.13 Simulation studies of King’s stratification model for continuous jig operation The following example is an application of King’s stratification model to industrial continuous jig performance. Fig. 11.15A shows segregation patterns of various density particles in the primary separator of continuous Batac jig 3, which has been studied by Tavares and King (1995). The washability data of the coal feed particles are shown in Fig. 11.16. The red vertical line at a relative bed height of 0.42 in Fig. 11.15A has been optimized as the cut height by Tavares and King (1995) keeping in view that the partition coefficients at the cutter height from the model prediction match well with the experimentally measured values, as indicated in Fig. 11.15B. The shape factor of the velocity profile, κ, has been considered to have a value of 0.3. The optimum specific stratification coefficient, α, has been evaluated to be 0.068. Fig. 11.15C shows the average bed density profile as a function of relative bed height from the model simulation. The graph indicates the attainment of the highest bed density particles at the jig bottom (where h50) where the ash particles segregate and the lowest bed density particles at the jig top (where h51) where the coal particles segregate. The average bed density profile shows a monotonically non-decreasing function from top to bottom of the jig bed height. Fig. 11.17A
D shows segregation patterns of various density particles for the continuously operated Batac jig 3 primary separator using feed washability data shown in Fig. 11.16 using simulations for various specific stratification coefficients. The gate position for the refuse removal is kept constant at h50.42 for these simulations (as indicated before in Fig. 11.15A). The figure shows that the stratification of particles in the jig

464

Mineral Processing

FIGURE 11.15 (A
C) Simulation results of King’s model for continuous jig operation for Batac jig 3 primary separation: (A) Patterns of Particle Species Concentration as a function of relative bed height; (B) Model prediction of the experimental partition coefficients at the cutter position for various particle densities (for the case of feed particles split to the refuse stream); (C) Average bed density profile of the particle segregation as a function of relative bed height. Data after Tavares, L.M., King, R.P., 1995. A useful model for the calculation of the performance of batch and continuous jigs. Coal Prep. 15, 99
128.

Mathematical modeling of mineral jigs Chapter | 11

465

FIGURE 11.16 Coal feed washability data of Batac jig 3 primary separator. Data after Tavares, L.M., King, R.P., 1995. A useful model for the calculation of the performance of batch and continuous jigs. Coal Prep. 15, 99
128.

FIGURE 11.17 Species segregation patterns of the Batac jig 3 primary separator for various values of specific stratification coefficients: (A) α 5 0.035; (B) α 5 0.09; (C) α 5 0.15; and (D) α 5 0.3.

bed improves with an increase in the specific stratification coefficient, α. It shows that the spread of each density species across the relative bed height decreases to a narrow region with the sharpening of the species concentration

466

Mineral Processing

FIGURE 11.18 Simulation results of King’s stratification model for various specific stratification coefficients: (A) Average bed density profiles; and (B) particle density fraction recoveries to the refuse stream at the cut position.

peaks as the specific stratification coefficient value increases. This is similar to what has been found for the batch jig operation as depicted in Fig. 11.13. Fig. 11.18A shows the average bed density profiles for the above simulations depicted in Fig. 11.17 for various specific stratification coefficients. It shows improvements with the sharpening of the average bed density profiles, especially in the bottom layers with the increase in specific stratification coefficient value. Also, the recovery of the density particles to the refuse stream at the cut position (i.e., h 5 0.42) shows significant improvement in the particle density separation, with an increase in the specific stratification coefficient. This is depicted in Fig. 11.18B.

11.14 Partition surface Particles separate in gravity concentrators by their particle size and particle density using the prevalent segregating forces of the equipment. A partition surface represents a smooth three-dimensional view of the partition coefficients, indicating how the particles split to the product stream from the feed stream in terms of particle size and density attributes. It represents the recovery of particles of a given size and density from the feed stream to one of the product streams, generally to the sink stream. The separation of particles in all gravity concentrators (including jigs) can be assessed in terms of partition surface (Ferrara and Schena, 1987; Scott and Napier-Munn, 1992; Rao et al., 2003a,b). Fig. 11.19A shows a typical partition surface of particle separation. The partition surface in Fig. 11.19A can be sectioned by the planes normal to the density axis to produce a set of density-based partition curves shown in Fig. 11.19B. Similarly, the partition surface can be sectioned by the planes normal to the size axis to produce a set of size-based partition curves shown in Fig. 11.19C. All the size-based partition curves in Fig. 11.19C pivot at one point called pivot density, ρp .

FIGURE 11.19 Partition coefficients as a function of particle size and particle density: (A) partition surface that depicts a 3D view of size-density-based partition coefficients. (B) densitybased partition curves that depict partition coefficients as a function of particle size. (C) sizebased partition curves that depict partition coefficients as a function of particle density.

468

Mineral Processing

Fig. 11.19B and C show a 2D representation of the same partition surface in Fig. 11.19A but viewed from different directions. In Fig. 11.19B, the particles of density less than the separation density, ρp ; show a reverse classification of particles, indicating a decrease in particle recovery with an increase in particle size. In other words, as the particle size increases, those particles with less than pivot density report more to the float stream. The density-based curves in Fig. 11.19B converge to a single value of pivot density as the particle size, d-0, indicating that regardless of particle density, almost the zero-sized particles just separate as per the fluid recovery, where the partition coefficient of the separation is Yp , which is referred to as the bypass fraction of fine particles in hydrocyclone classification terminology. The size-based partition curves in Fig. 11.19C also pivot at pivot density, ρp . The partition surface shows that irrespective of the particle size, all the particles that have a density the same as the pivot density separate with a partition coefficient Yp , that is, equivalent to the fluid recovery to the sink stream. The partition surface profile is a function of operating conditions such as feed particle density distribution, feed flow rate, media viscosity, jig pulse waveform, and its characteristics, machine design factors, etc. The surface can become steeper or flatter depending on the influence of these operational variables, which is a crucial factor from an operational point of view to improve or deteriorate the separator performance. The partition surface profile also depends on the slice or cutter position of the segregated particle jig bed.

11.14.1 Mathematical representation of the partition surface Several mathematical models have been proposed in the literature to represent the size-density partition surface of gravity concentrators. Some of these models are empirically derived based on the sigmoidal nature of the sizebased partition curves and the imposition of the pivot phenomenon into the derivation. However, the stochastic model proposes a phenomenologicalbased approach to represent partition surfaces (Rao et al., 2003a,b). All the partition surface models use a four-parameter representation to visualize the partition surface at the slice position of the product split into float and sink streams. It should be noted that the pivot phenomenon parameters of the partition surface, namely, Yp and ρp have the same meaning for all the partition surface models discussed below.

11.14.1.1 Weibull model Rao (2004) proposed a Weibull model to represent the partition coefficients, Y, that indicate the recovery of particles of a given size and density to the

Mathematical modeling of mineral jigs Chapter | 11

469

sink stream from the feed stream for a gravity concentrator. Weibull model represents the size-density partition surface as: 0 0 !ðpdq Þ 11    1 ρ AA Y 5 100@1 2 exp@ 2 ln ð11:25Þ 1 2 Yp ρp where Yp ; ρp ; p, and q represent the Weibull model parameters, which need to be evaluated from the experimental data. The particle density is represented by ρ (in kg/m3), and the particle size is represented by d (in mm). The parameter ρp represents the pivot density (in kg/m 3), where all size-based partition curves meet. All particles having a density below that of pivot density ρp show reverse classification of particles in the separator. The parameter, Yp $ 0, is the pivot partition number representing the bypass fraction of the separation for the gravity concentrator at the product split position. The parameter p captures viscosity effects, whereas the parameter q captures the flow conditions of the separator (Rao, 2004).

11.14.1.2 Logistic model Scott and Napier-Munn (1992) proposed the logistic model, and this model was also independently proposed by Klima and Luckie (1989). According to this model, the recovery of particles of a given size and density to the sink stream is represented as: Y5

100       21 1 1 exp ln Yp 2 1 1 1:099 ρp 2 ρ =ðkd n Þ

ð11:26Þ

where Yp ; ρp ; k, and n represent the model parameters, which need to be evaluated from the experimental data. The parameter k incorporates the effect of viscosity and the strength of the forces acting within the separator, while the parameter n is related to the flow conditions prevailing within the separator (Scott and Napier-Munn, 1992).

11.14.1.3 Gamma model Rao (2005) proposed the partition surface representation in terms of a regularized incomplete gamma function as:    v ðud Þ γ a; ρρ p Y5 & a.0 ð11:27Þ Γð a Þ

470

Mineral Processing

where the model parameters a; ρp ; u, and v are estimated from the experimental partition coefficient data. The pivot partition coefficient, Yp , is calculated by imposing ρ 5 ρp in the above equation, which gives: Yp 5 100

γ ða; 1Þ Γð a Þ

ð11:28Þ

11.14.1.4 Stochastic model Rao et al. (2003a,b) proposed an elegant stochastic model to represent the size-density
dependent partitioning of particles in gravity concentrators. It considers a random walk on settling of particles that are resisted by the drifting fluid within the separator. The model derivation is in line with the suggestions by Kelly and Subasinghe (1991) for incorporating settling velocity to describe separation efficiency. According to the stochastic model, the recovery of particles of a given size and density to the sink stream under the steady-state operation of the gravity concentrator is given by:


  Y 5 50 1 2 erf Adc ρ 2 ρp 2 B ð11:29Þ where A; B; c, and ρp represent the model parameters. The parameter, A, incorporates the strength of the centrifugal and viscous forces, the parameter, B; reveals the strength of the drifting fluid, the parameter, c; indicates the degree of turbulence in the separator, and the parameter ρp ; represents the pivot density of the particle separation. The pivot partition coefficient representing the bypass fraction of the gravity separation is given by: Yp 5 50ð1 1 erf ðBÞÞ

ð11:30Þ

Fig. 11.19A shows the partition surface generated by the stochastic model using the parameters: A 5 2 0:025; B 5 2 0:4; c 5 1:5, and ρp 5 1550. For the jig operation, the partition surface profile depends on the slice position of the segregated particle bed (Rao et al., 2017b). Fig. 11.20 shows the partition surfaces at various slice positions for a batch jig segregated bed. The slice position is measured in terms of relative bed height, h: Fig. 11.21 shows all these partition surfaces superimposed in a single plot for those surfaces shown in Fig. 11.20 to visualize the importance of slice position in a segregated jig bed. In this plot, the partition surfaces generated at the top and bottom slice positions have been filled with color to comprehend the partition surface profile change across the relative bed height. The graph shows that the pivot partition number, Yp , also changes with slice position indicating different bypass fractions with the slice position.

Mathematical modeling of mineral jigs Chapter | 11

471

FIGURE 11.20 Slice position-dependent partition surfaces for a batch jig bed particle segregation. Data after Rao, B.V., Rishi, R., Kumar, N.M.H., Gopalkrishna, S.J., 2017b. Experimental validation of extended stratification model: part A—ore with tracer particle studies in a batch jig operation. Trans. Indian Inst. Met. 70(2), 359
373.

Recently, Rao (2021) improved the four-parameter stochastic model at each slice position to a six-parameter stochastic model to represent all the partition surfaces of the entire batch jig bed. The model represents the

472

Mineral Processing

FIGURE 11.21 Slice position-dependent partition surfaces for a batch jig bed particle segregation. Various partition surfaces shown in Fig. 11.20 are combined into a single plot. Data after Rao, B.V., Rishi, R., Kumar, N.M.H., Gopalkrishna, S.J., 2017b. Experimental validation of extended stratification model: part A—ore with tracer particle studies in a batch jig operation. Trans. Indian Inst. Met. 70(2), 359
373.

partition surface at any slice height of the jig bed (typically shown in Fig. 11.21). The six-parameter stochastic model is given by:      ðhl 2 hf Þ 2 Adc ρ 2 ρp 1 B Y ðhl ; tÞ 5 50 1 1 erf for 0 # hl # 1 & 0 # t # teq tD

ð11:31Þ where t is the batch jigging time of a given sample, hl represents the normalized slice height, hf represents the relative feed height position where the feed enters the jig bed for a given test, the parameter, D, accounts for the standard deviation of the particle separation and teq represents the dynamic equilibrium time for the test. The remaining parameters have the same meaning as discussed previously in Eq. (11.29).

11.14.2 Generation of partition coefficients for the partition surface representation The partition surface can be generated from the separator’s size-density partition coefficient data by fitting one of the models discussed above (Eqs. 11.25, 11.26, 11.27, or 11.29). These partition coefficients of the separator can be generated by one of the following methods: (a) Sieving followed by sink-float analyses on each size fraction of the feed and the product streams to generate bivariate distributions and then deriving the partition coefficients from these bivariate distributions,

Mathematical modeling of mineral jigs Chapter | 11

473

(b) Use of a small number of known tracers of various sizes and densities along with the feed particles to segregate in the jig bed and then count their split to various jig slice positions and thereby calculating the partition coefficients. In the first method, the three bivariate distributions of the feed, the sink, and the float streams have to be evaluated using representative samples to get the partition coefficients (Rao et al., 2017a). The samples can be sieved first followed by the sink and float analyses on each of the size fractions and combining the distributions to obtain the bivariate distributions of the streams or using a vice versa procedure wherein the sink-float analysis is done first followed by sieving of the sink-float fractions. In the former approach, the size distribution from sieve analysis is referred to as marginal distribution and the density distribution on each of the size fractions is referred to as conditional distribution. The bivariate distribution is a product of the marginal distribution and the conditional distribution for respective size fractions (King, 2001; Rao, 2007a). The mathematical treatment of this topic is detailed in the subsequent sections. Generally, the sink-float tests follow typical standard procedures. As per the safety norms, the tests have to be carried out under a hood with an exhaust fan, as many of the organic liquids used in these tests are volatile and toxic. The sink and float tests can be easily conducted for coal samples as the organic liquids required for these tests (below a density of 3000 kg/m3) are commercially available. Sink-float analysis of heavy minerals like barite ore, iron ore, manganese ore, etc. is still a challenge due to the non-availability of high-density organic liquids. In the latter approach, the use of tracers of known size and density helps to get the partition coefficients easily. The partition coefficients are evaluated from the counts of size-density tracers recovered in the product stream (i.e., below the slice position) to their total additions in the jig feed (Scott and Napier-Munn,1992). A small number of tracers of various sizes and densities can be added to the feed particles and collected in the product stream (de Korte, 2003). It is essential that the tracers added should not distort the feed bivariate distribution significantly and hence tracer addition should be in small quantities. This approach gives sparse partition coefficient data, which then can be fitted to one of the partition surface models discussed previously. Fig. 11.22 gives a pictorial view of the tracers used and their segregation in the batch jig bed (Rao, et al., 2017b).

11.14.3 Partition surface visualization using key parameter indices Some of the publications report the key parameter indices (KPI) such as Ecart Probable and cut density instead of partition coefficients for the separators. This section explains how to visualize partition surfaces from such data.

474

Mineral Processing

FIGURE 11.22 Pictorial view of (A) Tracers of various sizes and densities used for the batch jig test work; (B) A view of tracer segregation in the segregated batch jig bed. After Rao, B.V., Rishi, R., Kumar, N.M.H., Gopalkrishna, S.J., 2017b. Experimental validation of extended stratification model: part A—ore with tracer particle studies in a batch jig operation. Trans. Indian Inst. Met. 70(2), 359
373.

The KPI, that is, Ecart Probable, Ep ; and cut density, ρ50 , can be calculated from the Stochastic model represented by Eq. (11.29) (Rao et al., 2003a,b) as: Ep 5 2

0:476936 Ad c

ρ50 5 ρp 1

B Ad c

ð11:32Þ ð11:33Þ

Mathematical modeling of mineral jigs Chapter | 11

475

Eqs. (11.32 and 11.33) which are derived from the stochastic model indicate that the Ecart Probable is similar to an empirical power law in particle size as proposed by Scott and Napier-Munn (1992) and the cut density equation is similar to the empirical relation proposed by Collins et al. (1983). The above equations are a function of particle size, d, and contain all the four partition surface parameters, namely, A; B; c, and ρp . Hence, these equations can be used to find out the partition surface by estimating the parameters from the experimentally determined Ecart Probable and cut density values (Rao et al., 2016b). First, the parameters A and c can be calculated from Eq. (11.32), whose values can then be introduced into the Eq. (11.33) to find out B and ρp . Once all the four parameters are known, they can be readjusted by re-evaluating both Ep and ρ50 simultaneously through the estimated parameters using the optimization techniques to minimize the sum of squared errors between the measured and the calculated KPI values. Fig. 11.23 gives the fit to Baum jig KPI data. The evaluated partition surface parameters from the stochastic model are A 5 2 1:602 3 1023 ; B 5 2 0:734; c 5 0:433; ρp 5 1354: Rao et al. (2016b) have shown that the partition surface representation by this method is more sensitive to the estimation of parameters A and B than the parameters c and ρp .

11.15 Size-density bivariate distributions and their characteristics Fig. 11.24 represents a schematic diagram of a gravity concentrator with one input and two output streams. Here, the feed is an input to the separation equipment, while the sink stream that contains the heavy particles and the float stream that contains the light particles are the output product streams. The product streams are formed by the separation of particles in the jig equipment. Let the bivariate distributions of the feed, the float, and the sink streams be represented respectively as f ðdi ; ρj Þ; oðdi ; ρj Þ; and uðdi ; ρj Þ: The size distributions of the feed, the float, and the sink streams, namely, fdi ; odi , and udi are called the marginal distributions while density distributions that are determined for each of the size fractions, namely, fρj jdi ; oρj jdi , and uρj jdi , are called conditional distributions. Suppose we have n size classes and m density classes for the size-density analyses, then n X i51

fdi 5

n X i51

odi 5

n X i51

ud i 5 1

ð11:34Þ

476

Mineral Processing

FIGURE 11.23 Baum Jig KPI data is used to estimate partition surface parameters of the stochastic model: (A) Ecart probable as a function of particle size. (B) cut density as a function of particle size. Dots indicate the experimental data and lines indicate the fits from the estimated parameters. After Rao, B. V., Velan, H. K., Gopalkrishna, S. J., 2016b. Visualization of partition surface from performance indices of gravity separators. Trans. Indian. Inst. Met. 69, 33
38. https://doi.org/10.1007/s12666-015-0616-7.

FIGURE 11.24 Schematic diagram showing solid flow rates of the jig feed and product streams, with the associated marginal size distribution and conditional density distributions.

Mathematical modeling of mineral jigs Chapter | 11

477

For any given size class "i" represented by the size, di , the conditional distributions satisfy: m m m X X X fρj jdi 5 oρj jdi 5 uρj jdi 5 1 ð11:35Þ j51

j51

j51

Suppose the mass flow rates of the feed, the float, and the sink streams are represented respectively as F; O, and U, then the mass balance of the unit operating under steady state can be written as: F5O1U

ð11:36Þ

Ffdi 5 Oodi 1 Uudi

ð11:37Þ

Ffdi fρj jdi 5 Oodi oρj jdi 1 Uudi uρj jdi

ð11:38Þ

Eqs. (11.36
11.38), respectively, represent overall mass balance, size mass balance of the marginal distributions, and the size-density mass balance of bivariate distributions. The mass split of solid particles to the sink stream from the feed, that is, U=F should be the same irrespective of the method used for mass balance. Combining Eqs. (11.36) and (11.37), we get
 fdi 2 odi U  5
ð11:39Þ F ud i 2 od i Combining Eqs. (11.36) and (11.38), we get   f f 2 o o d ρ jd d ρ jd i i i i j j U  5 F ud uρ jd 2 od oρ jd i

j

i

i

j

Combining Eqs. (11.37) and (11.38), we get   f f 2 o di ρj jdi ρj jdi U  5  F ud uρ jd 2 oρ jd i

j

i

j

ð11:40Þ

i

ð11:41Þ

i

Eqs. (11.39
11.41) suggest that to know the mass split of solid particles, it is essential to know marginal distributions, without which the mass split of the solid particles to the sink stream in the separator cannot be calculated. The partition coefficients can be determined from conditional distributions as discussed below. Rearrangement of Eq. (11.41), gives the size partition coefficients in terms of conditional distributions as:   fρj jdi 2 oρj jdi U ud i  5  ð11:42Þ F fdi uρj jdi 2 oρj jdi

478

Mineral Processing

Similarly, the bivariate partition surface coefficients can be calculated using Eq. (11.42) as:   uρj jdi fρj jdi 2 oρj jdi Uudi uρj jdi   5 ð11:43Þ Ffdi fρj jdi fρj jdi uρj jdi 2 oρj jdi Eqs. (11.42) and (11.43) indicate that the size distribution information of the separator streams is not very much essential to calculate the size or the bivariate partition coefficients when the conditional distributions of the streams are known. The nonessentiality of marginal distribution data to evaluate partition coefficients helps when the size marginal distribution data is missed out (or corrupt) in the experiments under the study. Table 11.3 gives the values of marginal size distribution and conditional density distributions of a separating unit. The bivariate distributions in terms of the cumulative weight % of the material that pass through a given size and density, are calculated for the feed, the float, and the sink streams of the separator from the Table 11.3 data using Eq. (11.38) and are shown in Fig. 11.25. Suppose we represent the feed, the float, and the sink bivariate distributions as fρj ;di ; oρj ;di ; and uρj ;di , respectively, then, under the steady state of the jig operation, the mass balance across the separator unit is represented in terms of bivariate distributions as: Ffρj ;di 5 Ooρj ;di 1 Uuρj ;di

ð11:44Þ

Partition coefficients of ith size and jth density class, Yij , can be evaluated from the bivariate distributions as well as from the conditional distributions of the separator. Eqs. (11.45) and (11.46), respectively, represent these evaluations. Eq. (11.46) is the same as the Eq. (11.43) as discussed earlier.   uρj ;di fρj ;di 2 oρj ;di   Yij 5 ð11:45Þ fρj ;di uρj ;di 2 oρj ;di   uρj jdi fρj jdi 2 oρj jdi   Yij 5 fρj jdi uρj jdi 2 oρj jdi

ð11:46Þ

Table 11.4 gives the partition coefficients evaluated by both the Eqs. (11.45) and (11.46). Both the equations evaluate almost the same partition coefficients for any given size and density class. This verifies the fact that conditional distributions can also be used to evaluate partition coefficients, instead of the bivariate distributions.

TABLE 11.3 Marginal size distribution and conditional density distributions of a separating unit. Stream

Average particle size, microns

Marginal size distribution, weight %

Conditional distributions, weight % Average particle density, kg/m3

Feed

Float

1275

1425

1575

1725

2225

1340.0

26.41

14.58

54.07

13.37

5.87

12.12

925.0

9.16

13.97

54.91

12.55

6.55

12.01

675.0

18.34

9.49

55.07

15.27

7.09

13.09

427.5

16.35

9.17

49.36

17.31

8.26

15.90

283.5

14.81

5.4

47.94

19.58

6.82

20.26

106.0

14.93

0.94

29.14

32.15

7.03

30.74

1340.0

17.14

28.65

64.06

6.53

0.76

0.00

925.0

7.86

21.88

65.39

9.80

2.80

0.13

675.0

17.86

13.44

65.90

14.39

4.82

1.46

427.5

18.44

11.50

56.56

17.68

7.38

6.89

283.5

18.24

6.25

52.85

20.29

6.58

14.04

106.0

20.46

0.98

30.35

32.89

7.09

28.69 (Continued )

TABLE 11.3 (Continued) Stream

Average particle size, microns

Marginal size distribution, weight %

Conditional distributions, weight % Average particle density, kg/m3

Sink

1275

1425

1575

1725

2225

1340.0

38.79

6.29

48.16

17.40

8.89

19.26

925.0

10.89

6.43

44.81

15.24

10.19

23.32

675.0

18.99

4.53

41.44

16.38

9.95

27.70

427.5

13.56

5.01

36.28

16.59

9.88

32.23

283.5

10.23

3.32

36.36

17.89

7.43

35.00

106.0

7.54

0.80

24.80

29.44

6.90

38.06

Source: Based on Rao, B.V., Ganvir, V., Gopalakrishna, S.J., 2008. Reconciliation of size-density bivariate distributions over a separating node. Particuology 6, 167
175.

Mathematical modeling of mineral jigs Chapter | 11

481

FIGURE 11.25 Bivariate distributions expressed in cumulative weight percentage passing form, for the feed, the float, and the sink streams of the separator for the Table 11.3 data.

482

Mineral Processing

TABLE 11.4 Partition coefficients of the separator were calculated from the bivariate distributions as well as the conditional density distributions using data presented in Table 11.3. Method of evaluation of partition coefficients

From bivariate distributions

From conditional distributions

Partition coefficients for given size-density class Average particle density, kg/m3

1340.0

925.0

675.0

427.5

283.5

106.0

1275

27.20

23.59

21.18

19.52

18.06

18.37

1425

56.06

41.05

33.37

26.11

22.48

18.42

1575

81.85

61.63

47.31

33.85

27.00

19.79

1725

95.20

78.99

62.11

49.63

32.49

21.30

2225

100.00

99.48

93.80

72.11

51.48

26.68

1275

27.15

23.54

21.17

19.58

17.83

18.59

1425

55.95

41.56

33.32

26.11

22.59

18.65

1575

81.85

61.48

47.36

32.67

26.83

19.73

1725

95.19

78.95

62.13

42.09

30.85

27.90

2225

100.00

99.48

93.81

72.10

51.28

27.12

Average particle size, microns

11.15.1 Difference similarity among bivariate distributions The split of solid particles to the float and the sink streams from the feed stream can be represented, respectively, as:   f 2 u ρ ;d ρ ;d i i j j O  5 ð11:47Þ F oρ ;d 2 uρ ;d j



i

j

i

fρj ;di 2 oρj ;di



U  5 F uρj ;di 2 oρj ;di

ð11:48Þ

The split factors O=F and U=F are constants for a separation process under steady state. Therefore, from the Eqs. (11.47) and (11.48), we can write the proportionalities among the absolute differences of the bivariate distributions as:       Abs fρj ;di 2 uρj ;di ~ Abs oρj ;di 2 uρj ;di ~ Abs fρj ;di 2 oρj ;di ð11:49Þ

Mathematical modeling of mineral jigs Chapter | 11

483

Eq. (11.49) shows that the absolute differences in bivariate distributions of the feed, the float, and the sink streams of a separator are difference similar. These results are similar to the difference similarity of the marginal distributions of a separator expressed earlier by Rao (2006). We can express the difference similarity in terms of cumulative weight % passing distributions for the particle size, di ; and the particle density, ρj , as:       Abs Fρj ;di 2 Uρj ;di ~ Abs Oρj ;di 2 Uρj ;di ~ Abs Uρj ;di 2 Oρj ;di ð11:50Þ where Fρj ;di ; Oρj ;di , and Uρj ;di represent the cumulative passing bivariate distributions for the feed, the float, and the sink streams respectively. The normalized absolute difference similarity among the cumulative passing distributions is shown in Fig. 11.26. It has a dome-shaped surface. The normalization is with respect to the maximum value of the absolute differences for the distribution pairs considered. The shape of this surface is unique to each separation and hence can be considered as the characteristic feature of the separation.

FIGURE 11.26 The normalized absolute difference similarity among the cumulative passing bivariate distributions.

484

Mineral Processing

11.15.2 Sink and float distribution predictions from the feed distribution and partition surface concept The bivariate product distributions, namely, for the sink and the float streams, can be obtained by combining the bivariate feed distribution with the partition surface of the individual separator, and the procedure can be extended to simulate the circuit behavior (Rao, 2007a; Rao and Kapur, 2008). Here, the partition function acts like an operator in mapping the feed distribution to its product distributions. Further, from the bivariate distributions, it is possible to derive the marginal distributions for the size or the density alone separations. Under steady-state operation with solid mass flow rates of F; O, and U and the associated bivariate distributions in the frequency form as f ðd; ρÞ; oðd; ρÞ; and uðd; ρÞ for the feed, the float, and the sink streams, respectively, the mass balance around the separator is given by: Ff ðd; ρÞ 5 Ooðd; ρÞ 1 Uuðd; ρÞ

ð11:51Þ

Integrating out the attributes of size and density from Eq. (11.51) yields: F5O1U

ð11:52Þ

Eq. (11.52) is the same as Eq. (11.36). The mass flow rate of particles of size, d; and density, ρ; to the sink stream, is given by: U ðd; ρÞ 5 Ff ðd; ρÞY ðd; ρÞ

ð11:53Þ

where Y ðd; ρÞ represents the partition surface coefficients for the particle size, d, and the particle density, ρ. The total flow rate of particles to the sink stream is given by: ðð U 5 F f ðd; ρÞ Y ðd; ρÞ dd dρ ð11:54Þ Therefore, the normalized bivariate product distribution of the sink stream becomes: uðd; ρÞ 5 ÐÐ

f ðd; ρÞ Y ðd; ρÞ f ðd; ρÞ Y ðd; ρÞ dd dρ

ð11:55Þ

The discretized form of the above equation describing the sink stream is given by:       f di ; ρj Y di ; ρj    u di ; ρ j 5 P P  ð11:56Þ i j f di ; ρ j Y di ; ρ j

Mathematical modeling of mineral jigs Chapter | 11

Similarly, the discretized float-stream is given by:       f di ; ρj 1 2 Y di ; ρj    o di ; ρ j 5 P P  1 2 Y di ; ρ j i j f di ; ρ j

485

ð11:57Þ

The marginal size and density distributions of the sink stream are, respectively, given by:    P  j f di ; ρj Y di ; ρj    uð di Þ 5 P P  ð11:58Þ i j f di ; ρ j Y di ; ρ j    P    i f di ; ρ j Y di ; ρ j    u ρj 5 P P  i j f di ; ρj Y di ; ρj

ð11:59Þ

The marginal size and density distributions of the float-stream are, respectively, given by:    P  f ð di Þ 2 j f di ; ρ j Y di ; ρ j    ð11:60Þ oð di Þ 5 P P  1 2 i j f di ; ρj Y di ; ρj   P       f ρ j 2 i f di ; ρ j Y di ; ρ j    o ρj 5 P P  1 2 i j f di ; ρj Y di ; ρj

ð11:61Þ

Fig. 11.27 gives a schematic diagram used to predict the bivariate product distributions of a coal feed sample using air tables. An air table (also called the airflow cleaner) is a kind of dry jig separator. It stratifies the particles by pulsating air through a porous deck, which is mounted over an air chamber. The refuse formed in the bottom layers is withdrawn through the wells at the bottom of the deck, into which refuse particles move as they travel along the slope of the deck. Dust created by the pulsating air is sucked into the overhead hood and is recovered through a cyclone dust collector followed by a cloth filter. As shown in Fig. 11.27, the coal feed particles are initially split into clean coal and bulk refuse. The bulk refuse is again split into middlings and reject stream in a second-stage separation. The bivariate feed distribution and the partition surfaces of the first- and second-stage separations are shown in Fig. 11.28. The measured data are taken from the works of Llewellyn et al. (1979). Table 11.5 gives the partition surface parameters of the stochastic model for the two-stage separations considered. The bivariate product distributions are predicted by the previously discussed method using Eqs. (11.56 and 11.57) and are shown in

486

Mineral Processing

FIGURE 11.27 Schematic diagram of two-stage coal cleaning by using air tables. Based on Rao, B.V., Kapur, P.C., 2008. Simulation of multi-stage gravity separation circuits by size
density bivariate partition function. Int. J. Miner. Process. 89(1), 23
29.

Fig. 11.29. The dots represent the measured data, while the lines represent the model predictions. The predictions by this approach are quite close to the measured data (Rao and Kapur, 2008). Fig. 11.30A and B show the marginal distributions predicted by this approach using Eqs. (11.58
11.61) wherein the measured data are represented as dots. The model predictions are quite close to the measured marginal distributions.

11.15.3 Multistage separations Both the particle size and the particle density determine the separator efficiency of gravity concentrators along with the operating conditions and design variables of the equipment. Therefore, the bivariate partition function provides a more meaningful and quantitative assessment of the steady-state performance of the stand-alone and multistage separations than the more conventional partition curves in a single variable, namely, either the particle size or the particle density. The collective performance of multistage separators can be described and analyzed in terms of bivariate partition functions of the constituent equipment based on their circuit configurations (Rao and Kapur, 2008). This section focuses on two-stage separation circuits to derive generic expressions for the overall separation in terms of the bivariate partition functions. It also looks at the calculation of bypass fractions and the estimation of KPI parameters such as the Ecart Probable and the cut density for the circuit operation. A similar analysis can be extended to much more complex configurations of staged operations. Here, the partition function of the constituent equipment is described in terms of the stochastic model.

FIGURE 11.28 The feed bivariate distribution and the partition surfaces of the first- and second-stage separations. Data from Llewellyn, R.L., Humphryes, K.K., Leonard, J.W., Lawrence, W.F., 1979. Chapter 11: Dry concentration. In: Leonard, J.W. (Ed.), Coal Preparation, fourth ed. SME Inc., New York, pp. 1
32.

488

Mineral Processing

TABLE 11.5 Partition surface parameters of the stochastic model for the separation stages (Rao and Kapur, 2008). Stage no.

Partition surface parameters A

B

c

ρp

Stage 1

20.0008223

21.954

0.644

862

Stage 2

20.0001498

20.218

1.275

1509

FIGURE 11.29 The measured and predicted coal separation bivariate product distribution for the two-stage air table separations (data from Llewellyn et al., 1979). The measured data are represented as dots and the model estimation by lines (after Rao and Kapur, 2008).

The two-stage separations can be configured in four possible ways as shown in Fig. 11.31 (Heiskanen, 1993). Suppose the particle separation of the individual separators is described by partition functions Y1 ðd; ρÞ and Y2 ðd; ρÞ, then under the steady-state operation, the overall partition function Yo ðd; ρÞ of the circuits can be derived in terms of individual-separator

Mathematical modeling of mineral jigs Chapter | 11

489

FIGURE 11.30 The marginal size and density distribution predictions by the model equations (data from Llewellyn et al., 1979). The measured data are represented as dots and the model estimations by lines (after Rao and Kapur, 2008).

partition functions. These relationships are given in Table 11.6. The performance of the multistage circuits depends strongly on their configuration of stream connectivity (Rao, 2007a; Rao and Kapur, 2008). The overall bypass fraction of the circuits, Yp , also depends on circuit configuration as shown in Table 11.6. As the bypass fractions of the two separators (i.e., Yp1 and Yp2 ) are expressed as fractional values, it can be shown using the equations given in Table 11.6, that the circuits obey the following relationship (Rao and Kapur, 2008): Yp ðCircuit 1Þ , Yp ðCircuit 3Þ , Yp ðCircuit 4Þ , Yp ðCircuit 2Þ

ð11:62Þ

Considering the partition function parameters given in Table 11.6 for the individual separators 1 and 2, Fig. 11.32 represents the simulated overall

490

Mineral Processing

FIGURE 11.31 Four possible circuit configurations of two-stage separators. Adapted from Heiskanen, K., 1993. Particle Classification. Chapman and Hall, London.

TABLE 11.6 Expressions for the overall partition functions and bypass fractions for the four two-stage circuit configurations (shown in Fig. 11.31) are expressed in terms of partition functions and bypass fractions of the individual equipment (Rao, 2007a; Rao and Kapur, 2008). Circuit configuration

Overall partition function, Yo ðd; ρÞ

Overall bypass function, Yp

Circuit 1

Y1 ðd ; ρÞY2 ðd ; ρÞ

Yp1 Yp2

Circuit 2

Y1 ðd ; ρÞ 1 Y2 ðd ; ρÞ 2 Y1 ðd ; ρÞY2 ðd ; ρÞ

Yp1 1 Yp2 2 Yp1 Yp2

Circuit 3

Y1 ðd ;ρÞY2 ðd;ρÞ ð1 2 Y1 ðd;ρÞ 1 Y1 ðd;ρÞY2 ðd;ρÞÞ

ð1 2 Yp1 1 Yp1 Yp2 Þ

Circuit 4

Y1 ðd;ρÞ ð1 2 Y2 ðd;ρÞ 1 Y1 ðd;ρÞY2 ðd;ρÞÞ

ð1 2 Yp2 1 Yp1 Yp2 Þ

Yp1 Yp2

Yp1

Mathematical modeling of mineral jigs Chapter | 11

491

FIGURE 11.32 Partition surfaces of the individual separators and the four two-stage separation circuits that consider the stochastic surface parameters given in Table 11.7 for plotting. After Rao, B.V., Kapur, P.C., 2008. Simulation of multi-stage gravity separation circuits by size
density bivariate partition function. Int. J. Miner. Process. 89(1), 23
29.

partition surfaces for the four two-stage circuits. The figure also incorporates the individual-separator partition surfaces. The parameters given in Table 11.7 for the four circuits define the overall stochastic model parameters of the resultant partition functions. Circuits 1 and 3 show less quantity of fines as well as low-density particle recovery to the sink stream as

492

Mineral Processing

TABLE 11.7 Stochastic partition surface parameters of individual separators and the equivalent stochastic partition surface parameters of the two-stage circuits. Separator/circuit

Separator 1

Stochastic model partition surface parameters A

B

c

ρp ; kg=m3

20.00081600

21.067774

0.459675

1039.02

Separator 2

20.00088300

20.848340

0.368512

1000.96

Circuit 1

20.00108409

21.718520

0.411518

1014.17

Circuit 2

20.00103705

20.666103

0.421230

1033.64

Circuit 3

20.00116916

21.703160

0.435189

1030.94

Circuit 4

20.00106606

21.025900

0.490806

1066.50

compared to circuits 2 and 4. This is because, in circuits 1 and 3, the sink stream of the stage 1 separator is rewashed in stage 2, while the float stream of the stage 1 separator is rewashed in circuits 2 and 4. Therefore, the yield of circuits 1 and 3 is less than that of circuits 2 and 4. Using the overall partition function of the circuit, it is possible to derive the marginal distributions of the overall circuit as discussed in the previous sections. The bypass fraction of the individual separators and the two-stage circuits is depicted in Fig. 11.33 using the partition function data given in Table 11.7. The bypass fractions of the two-stage circuits follow the relationship given in Eq. (11.62). It turns out that the bypass fraction is a strong function of the circuit configuration. Fig. 11.34 shows the KPI parameters, namely, the Ecart Probable and the cut densities for the individual and the two-stage circuits as a function of particle size. The calculation is based on Eqs. (11.32) and (11.33) by using the overall circuit partition function parameters defined in Table 11.7. The calculated Ecart Probable values for the four circuits are less than the individual-separator values over the entire particle size range, indicating that all the two-stage circuits show sharper separation than the single-stage individual separators. The cut densities are higher than the individual-separator values for circuits 1 and 3, while the same values are less than the individual-separator values in case of the circuits 2 and 4. This is mainly attributed to a significant change in the fluid drift velocity parameter of the stochastic model, B, for the two-stage circuits as depicted in Table 11.7. This is also because the rewash streams are sent to the second-stage separation and there is an associated change in particle composition, which in turn changes the fluid drift velocities of

Mathematical modeling of mineral jigs Chapter | 11

493

FIGURE 11.33 Bypass fraction of the individual separators and the four two-stage separation circuits that consider stochastic surface parameters in Table 11.7 for the circuit evaluation. After Rao, B.V., Kapur, P.C., 2008. Simulation of multi-stage gravity separation circuits by size
density bivariate partition function. Int. J. Miner. Process. 89(1), 23
29.

the overall circuit to be high or low. The float stream has more fines, more light density particles, and more fluid associated with it.

11.15.4 Circuit sensitivity analyses of two-stage circuits for a fluctuating feed composition and varying operational variables In an operating plant, the separation efficiency of the individual separator changes due to fluctuations in the feed material composition as well as the operating variables. Therefore, relations have to be established between the feed characteristics, the operating variables, and the equipment design parameters with the partition surface coefficients to understand their influence on the circuit performance. However, not much work is done in this direction and such relations are not available readily. In the absence of such relations, by assuming that these fluctuations will affect the individual partition surface parameter values to fluctuate in some particular range of values, it is possible to simulate and evaluate the circuit robustness/sensitivity to these fluctuations, by perturbing the individual-separator parameters within a specified range (Rao and Gopalkrishna, 2010). Table 11.8 gives the range of stochastic model parameter variation considered for the individual separators in the current study. Based on the random variations in these parameters, the four twostage circuits are simulated to estimate the yield and particle recovery to the sink streams. The particle recovery in Fig. 11.35 is separately expressed for the recovery of particle size and the particle density for the

494

Mineral Processing

FIGURE 11.34 Ecart Probable and cut densities for the individual separator and the two-stage circuits are depicted as a function of particle size using the partition surface parameters in Table 11.7. After Rao, B.V., Kapur, P.C., 2008. Simulation of multi-stage gravity separation circuits by size
density bivariate partition function. Int. J. Miner. Process. 89(1), 23
29.

four circuit configurations, which are based on marginal distribution calculations. The feed bivariate distribution to the circuits is represented by values in Table 11.9 (Llewellyn et al., 1979). Here, for each random perturbation of the parameters, the marginal product distributions are calculated using the method described earlier. The same set of stochastic model random parameters are used to simulate each run for the four types of circuits.

Mathematical modeling of mineral jigs Chapter | 11

495

TABLE 11.8 Range of individual-separator partition-surface parameters used for the random perturbations to understand the circuit robustness/ sensitivity to simulate the random fluctuations in the operating variables. Stochastic model parameters

Range of perturbed values of the parameters

A

20.0010 to 20.0008

B

21.5 to 20.8

c

0.3 to 1.3

ρp ; kg=m

3

850 to 1200

The spread of partition coefficients (i.e., the recovery of the particles) is depicted along the ordinate axis and the size (or density) of the particles is depicted along the abscissa. Fig. 11.35 indicates that circuits 1 and 3 show sharp separation at any yield value and these circuits are more robust to circuit perturbations arising from fluctuations in feed characteristics and operating variables, than circuits 2 and 4. Circuits 1 and 3 show less spread of particles with reference to resultant partition coefficients. These circuits also show steeper separation lines, less yield, and less recovery of fine particles to the sink stream. It should be noted that the stability of the circuit configuration is of utmost importance in circuit designs for mineral processing plants as revealed in circuits 1 and 3. In general, the method of random perturbation of partition surface parameters can be applied to find out the robustness of any complex gravity particle separation circuit design, and thereby to understand circuit sensitivity to fluctuations in feed and operational parameters.

11.15.5 Data reconciliation of bivariate distributions of a separator using the concept of partition surface The bivariate distributions of the feed, the float, and the sink streams help to estimate the partition coefficients, which can then be fitted to a partition surface model. However, the experimentally estimated bivariate distribution fractions belonging to the individual size-density classes from the sink-float analyses of the three streams of the separator have errors associated with them, showing issues in the mass balance of the particles. These errors arise due to the improper sampling or due to the human errors associated with the analyses. Therefore, a data reconciliation of the size-density bivariate fractions of the input and the output streams is essential to restore the mass balance, by way of adjusting the measured values minimally.

496

Mineral Processing

FIGURE 11.35 Simulation of particle size and density recoveries as a function of sink stream yield, for the four two-stage circuits. These values are generated by the random parameters of the individual separators in a specified range and combining the resulting partition surfaces of the individual separators as per Table 11.6. After Rao, B.V., Gopalkrishna, S.J., 2010. Simulation studies on robustness of multi-stage gravity circuit performance by random perturbations. In: Singh, R., et al. (Eds.), XIth International Seminar on Mineral Processing Technology (MPT2010). Allied Publishers Pvt. Ltd., Mumbai, pp. 357
363.

TABLE 11.9 Bivariate feed distribution of the coal sample. f ðd; ρÞ

Particle size, di , mm

Particle density, ρj , kg/m

3

19 3 12.5

12.5 3 9.5

9.5 3 6.3

6.3 3 3.35

3.35 3 0.6

0.6 3 0

Float 1400

0.008791

0.010111

0.025161

0.116342

0.321257

0.178735

1400
1500

0.002783

0.002813

0.005342

0.014815

0.025604

0.019541

1500
1600

0.002383

0.001861

0.002587

0.007381

0.013719

0.011125

1600
1700

0.005028

0.003014

0.002425

0.005027

0.008882

0.006838

1700
1900

0.005847

0.003952

0.002884

0.005239

0.009424

0.007101

Sink 1900

0.021169

0.019250

0.017601

0.028196

0.038114

0.039660

Source: Based on Llewellyn, R.L., Humphryes, K.K., Leonard, J.W., Lawrence, W.F., 1979. Chapter 11: Dry concentration. In: Leonard, J.W. (Ed.), Coal Preparation, fourth ed. SME Inc., New York, pp. 1
32.

498

Mineral Processing

The Lagrange multiplier method with uniform weighting for all sizedensity classes produces sometimes negative reconciled values, especially for very small measured values (Heiskanen, 1993) and thus the reconciled values become unrealistic in such situations. Combining data by juxtaposing classes in such situations reduces the effect of getting negative values from the reconciliation procedure. However, this results in a significant loss of resolution in the data. Another way of overcoming inconsistent mass balance is by weighted adjustment. This would mean that the low precision measurements have to be adjusted more than the high precision measurements. This can be done by replicating the measurements and taking the standard deviation of the measurements. Sometimes repeated measurement to understand the precision of the measurement is not possible. In the absence of replicate measurements, Wills (1997) considered the square of the measured value/assays as the variance of an individual component. Sometimes an educated engineering guess is used for attributing the measurement precision. The main problem of weighted mass balance is its failure to preserve the unitary sum of mass fractions of the size and/or density classes. To overcome this issue, the last fraction is considered to be a difference between previous classes from the unity. Bazin and Hodouin (2001) showed that a unitary sum can be preserved for particle size distribution (PSD) data by considering the correlation between the measurement errors during data reconciliation. In essence, the approaches followed for data reconciliation are different and varied. Rao et al. (2008) developed a Lagrange multiplier method with uniform weights to reconcile the bivariate distributions of the feed, the float, and the sink streams to restore the mass balance of the individual size-density fractions with minimal adjustments. Although the residuals of the adjustments during data reconciliation followed a Gaussian distribution, the bivariate partition coefficients from the reconciled data from this approach showed some kinks that do not conform to the smooth partition surface. This necessitated a new method to be devised to obtain a smooth partition surface from data reconciliation, which is discussed below. The product distributions can be predicted by combining bivariate feed distribution with the partition surface coefficients as discussed previously in Eqs. (11.56) and (11.57). This concept can be used for the data reconciliation of bivariate distributions. Rao et al. (2008) proposed a reconciliation method that is based on combining the feed distribution with the partition surface through an optimization routine that optimizes the partition surface parameters to closely match the measured product distributions with the predicted ones from Eqs. (11.56) and (11.57). Here, it is assumed that the measured feed distribution has no errors, but the product distributions are prone to errors and hence can be reconciled with this approach. Table 11.10 gives the measured feed and product bivariate size-density distributions for a Harz jig separation on coal-ash separation. The data are generated by the sink-float analysis approach and thus need data reconciliation.

TABLE 11.10 Measured bivariate distribution data of Harz Jig Coal-Ash Separation. Streams

Average particle size, mm

Measured data of Harz jig separation for coal-ash separation Average particle density, kg/m3

Feed

Float

1250

1350

1450

1550

1650

1750

2225

3.35

2.656

29.627

6.730

1.322

0.144

0.093

0.469

2.53

0.880

14.687

2.690

0.421

0.099

0.039

0.098

2.18

0.305

5.171

1.682

0.245

0.067

0.037

0.069

1.85

1.069

16.015

3.694

0.580

0.034

0.099

0.225

1.55

0.046

0.274

0.104

0.020

0.000

0.004

0.010

1.20

0.629

7.305

1.852

0.269

0.034

0.032

0.176

3.35

3.407

34.176

5.167

0.309

0.000

0.000

0.000

2.53

1.073

16.464

2.133

0.135

0.026

0.000

0.000

2.18

0.360

5.185

1.284

0.073

0.013

0.000

0.000

1.85

1.280

16.146

3.161

0.250

0.011

0.000

0.000

1.55

0.058

0.359

0.099

0.009

0.000

0.000

0.000

1.20

0.673

6.549

1.466

0.113

0.022

0.000

0.000 (Continued )

TABLE 11.10 (Continued) Streams

Average particle size, mm

Measured data of Harz jig separation for coal-ash separation Average particle density, kg/m3

Sink

1250

1350

1450

1550

1650

1750

2225

3.35

0.633

17.384

10.935

4.049

0.530

1.733

1.733

2.53

0.362

9.904

4.188

1.193

0.296

0.362

0.362

2.18

0.157

5.133

2.753

0.707

0.212

0.254

0.254

1.85

0.500

15.663

5.129

1.467

0.096

0.829

0.829

1.55

0.014

0.043

0.116

0.051

0.000

0.035

0.035

1.20

0.512

9.340

2.892

0.687

0.068

0.649

0.649

Mathematical modeling of mineral jigs Chapter | 11

501

Combining the feed bivariate distribution in Table 11.10 with the size-density partition coefficients that can be generated from stochastic partition function using the four parameters (which is represented by Eq. 11.29), we can calculate the bivariate product distributions in Eqs. (11.56) and (11.57) namely, for the sink and the float streams. The stochastic model parameters are optimized to minimize the squared errors between measured and calculated bivariate mass fractions of the float and the sink streams. The optimized stochastic partition surface parameters for Table 11.10 Harz jig data using this reconciliation approach are A 5 2 1:78 3 1023 ; B 5 2 0:1235; c 5 1:0313; ρp 5 1451:06. Table 11.11 gives the reconciled product distributions for the measured data presented in Table 11.10. The reconciled values are reasonably close to the measured values.

11.16 Extended King’s stratification model Foregoing discussions on King’s stratification model shows its successful application to mimic industrial jig performance in terms of particle density. However, King’s stratification model considers all particles to be mono-size. But in reality, it is unlikely that a jig feed has all particles of mono-size. The jig feed will be somewhat distributed in particle sizes and will be truncated by removing the fine and very coarse fractions in it, to improve the separation efficiency of particles. Tavares and King (1995) indicated that the calculation of potential energy for a wide particle size range is a far more complicated task. Therefore, to bring the effect of particle size into the King’s formulation, Rao (2007b) proposed that the jig feed stream be composed of a bivariate size-density distribution and the specific stratification coefficient for particle segregation, αi be size dependent. Further, it was considered that the specific stratification coefficient follows a power law in particle size, as:   dCij ðhÞ 5 2 αi Cij ðhÞ ρj 2 ρðhÞ for i 5 1; 2; . . .; n & j 5 1; 2; . . .; m ð11:63Þ dh and αi 5 w diz

ð11:64Þ

where Cij ðhÞ represents the species concentration profile of ith size class and jth density class of particles. w and z are stratification coefficient parameters. It should be noted that the specific stratification constant αi is a strong function of particle size and independent of particle density (King, 2001).

TABLE 11.11 Reconciled bivariate product distributions for the measured data given in Table 11.10. Streams

Average particle size, mm

Reconciled product distributions for the measured data given in Table 11.10, using partition surface parameters. Average particle density, kg/m3

Float

Sink

1250

1350

1450

1550

1650

1750

2225

3.35

3.460

34.161

5.251

0.440

0.014

0.002

0.000

2.53

1.099

15.886

2.095

0.181

0.018

0.003

0.000

2.18

0.370

5.410

1.309

0.116

0.016

0.004

0.000

1.85

1.253

16.180

2.874

0.301

0.010

0.016

0.001

1.55

0.052

0.267

0.081

0.011

0.000

0.001

0.000

1.20

0.669

6.813

1.439

0.164

0.015

0.010

0.007

3.35

0.413

16.980

10.855

3.782

0.505

0.346

1.779

2.53

0.270

11.342

4.348

1.092

0.323

0.141

0.371

2.18

0.123

4.503

2.721

0.604

0.208

0.130

0.260

1.85

0.556

15.554

5.982

1.357

0.100

0.330

0.848

1.55

0.030

0.292

0.168

0.045

0.000

0.014

0.036

1.20

0.519

8.676

3.005

0.561

0.087

0092

0.648

Mathematical modeling of mineral jigs Chapter | 11

503

Combining Eqs. (11.63) and (11.64) yields:   dCij ðhÞ 5 2 w diz Cij ðhÞ ρj 2 ρðhÞ for i 5 1; 2; . . .; n & j 5 1; 2; . . .; m: dh ð11:65Þ For a batch jig separation, Eq. (11.65) has to be solved by a similar procedure described by King (2001), subject to the following constraints: Xn Xm ρ ðhÞ 5 C ðhÞρj ð11:66Þ i51 j51 ij Xn Xm i51

Cijf

5

ð1

j51

Cij ðhÞ 5 1 for all h

Cij ðhÞdh for all ijth bivariate species

ð11:67Þ ð11:68Þ

0

The solution to Eq. (11.65) gives concentration profiles for the ijth species across the relative bed height, for a given bivariate feed distribution. The mass yield of solid particles as well as the recovery of the ijth particle species to the float-stream by slicing the bed at relative bed height, h, are, respectively, given by: Ð1 ρðhÞdh M ðhÞ 5 Ðh1 ð11:69Þ 0 ρðhÞdh Ð1 Cij ðhÞdh ð11:70Þ Rij ðhÞ 5 h Cijf Eqs. (11.65
11.70) hold good for a batch jig separation. For a continuous jig operation with a dimensionless longitudinal velocity profile described by Eq. (11.20), the species concentration profiles of the segregated bed, Cij ðhÞ are given by solving Eq. (11.65) subjected to the constraints represented by Eqs. (11.66) and (11.67) and: Ð1

Cijf

0 Cij ðhÞvðhÞdh 5 Pn P for all ijth bivariate species m Ð1 i51 j51 0 Cij ðhÞvðhÞdh

ð11:71Þ

The mass yield and the recovery of the ijth species to the float-stream by slicing the bed at relative bed height, h, for the continuous jig operation are, respectively, given by: Ð1 ρðhÞvðhÞdh M ðhÞ 5 Ðh1 ð11:72Þ 0 ρðhÞvðhÞdh

504

Mineral Processing

Ð1 Rij ðhÞ 5 Ðh1 0

Cij ðhÞvðhÞdh Cij ðhÞvðhÞdh

ð11:73Þ

The float bivariate volumetric distribution for both batch and continuous unit operation, by slicing the segregated particles at relative bed height, h, is given by: Cijf Rij ðhÞ CijP ðhÞ 5 P n P m Cijf Rij ðhÞ

ð11:74Þ

i51 j51

Using the extended King’s stratification model, the simulations showed that it is possible to generate partition surfaces at various slice heights of the segregated bed, which are similar to those generated by the stochastic model (Rao, 2007b). The validation of the extended stratification model has been carried out for the segregation of coal-ash particles in a Harz jig, whose feed is represented by the bivariate feed distribution specified in Table 11.10. The feed particles were jigged for 20 minutes in a Harz jig and then sliced at relative bed heights of 0.25, 0.50, and 0.75 (Rao et al., 2017a). After drying the sliced samples, the particles in each slice were subjected to sieve analysis followed by sink-float analysis on each of the size fractions to understand the layer particle bivariate distributions. From these layer bivariate distributions, the partition coefficients corresponding to the particle split to the sink stream at each slice position have been calculated by combining the layers that are beneath the slice position. For the test data, the extended stratification model has been applied to solve Eqs. (11.65
11.68) to calculate the segregation patterns of the bed, to match the partition coefficients at various slice positions, by considering the bivariate feed distribution in Table 11.10 and thereby optimizing the average density profile of the bed and simultaneously evaluating the size-dependent specific stratification coefficient parameters of the model. For the test data, the optimum size-dependent specific stratification parameters were found to be: w 5 0:8913 and z 5 0:5681. Fig. 11.36 shows the measured partition coefficients as dots and the model predicted partition surfaces with the red lines for the various slice positions. The slice position height values are indicated on the plots. A good match between the partition coefficients of the measured data with those from model predictions indicates that the proposed extended stratification model can track the particle segregation in a batch jig bed aptly. Fig. 11.37 shows the average bed density profile from the optimized extended stratification model for the test data. It shows a monotonically non-increasing function for the average bed density as the bed height increases from the jig deck position.

FIGURE 11.36 Partition surface predictions from the extended King’s stratification model for the test data at various slice positions of the Harz jig separator. Dots indicate experimentally derived partition coefficients and the lines indicate the model predictions. After Rao, B.V., Jeelan, G., Satish, S., Gopalkrishna, S.J., 2017a. Experimental validation of extended stratification model part b: coal-ash segregation studies in a batch jig operation. Trans. Indian. Inst. Met., 70(2), 375
394.

506

Mineral Processing

FIGURE 11.37 Average bed density profile of coal-ash particle segregation in the Harz jig separator.

FIGURE 11.38 Concentration profiles of various ith size and jth density species (Cij ðhÞ) predicted by the model, across the relative bed height in the Harz jig separator. After Rao, B.V., Jeelan, G., Satish, S., Gopalkrishna, S.J., 2017a. Experimental validation of extended stratification model part b: coal-ash segregation studies in a batch jig operation. Trans. Indian. Inst. Met., 70(2), 375
394.

Mathematical modeling of mineral jigs Chapter | 11

507

Fig. 11.38A
D shows the concentration profiles for the various sizedensity particle species from the model fit. Here, instead of plotting all the curves in a single plot, they have been split into four plots (A
D) with different ordinate scales to visualize all the curve profiles in a better way. Fig. 11.39A
F shows the yield vs the particle density recovery to the sink stream for the various size fractions for the Harz jig test. These patterns indicate that as the particle size decreases from 3.35 to 1.20 mm, their separation efficiency within the jig bed also decreases marginally. The curves that are positioned below the diagonal correspond to the low-density particles of

FIGURE 11.39 (A
F) Yield vs particle density recovery for various size fractions in the Harz jig, as predicted by the extended stratification model. After Rao, B.V., Jeelan, G., Satish, S., Gopalkrishna, S.J., 2017a. Experimental validation of extended stratification model part b: coalash segregation studies in a batch jig operation. Trans. Indian. Inst. Met., 70(2), 375
394.

508

Mineral Processing

coal, depicting their efficiency of separation. For the present test data, the yield-particle recovery for all the size fractions is almost similar, with a minor change in their diagonal spread. This is mainly attributed to the narrow-truncated size distribution of the particles (namely, from 3.35 to 1.20 mm) for which the test has been conducted. However, if the PSD of the feed stream varies over a wide size range, then the plots show a much more pronounced effect on their separation efficiencies due to the power-law effect of particle size as discussed earlier (Rao, 2007b). That is one of the reasons for the truncation of PSD to a narrow size range in the jig feed, to improve the particle separation efficiencies of all the feed particles.

11.16.1 Comparison of the two jig models that define partition surfaces at various slice positions Partition surface representation is essentially a mathematical function to understand the segregation patterns of the jig bed. When it is combined with the size-density feed bivariate distribution, the bivariate product distributions from the separator can be predicted as discussed previously. In this chapter, two mathematical models, namely, King’s extended stratification model and the stochastic model, have been discussed which are capable of representing the partition surfaces at various slice positions of the jig bed. The mathematical approaches that these models adopt to represent partition surfaces across the bed height are not the same. While King’s extended stratification model brings the knowhow of the partition surface from the segregation patterns of the bed that follows a flux balance between stratification flux and diffusion flux, the stochastic model considers the partition surface based on the resultant particle velocities due to their settling in the jig chamber. The settling of the particles in the jig bed is opposed by the intermittently rising fluid and the random forces arising from particle
particle collisions and particle
fluid interactions within the bed. To apply King’s extended stratification model, it is mandatory to know the bivariate feed distribution, when we solve the set of differential equations in Eq. (11.65), which acts as a constraint to balance each size-density fraction that arranges in the entire segregated bed. The bivariate distribution measurement needs sieve analysis followed by sink-float analysis on each size fraction. As we know, sink-float analysis for particles above 3000 kg/m3 is quite difficult due to the non-availability of organic density liquids, applying an extended stratification model to heavy mineral separation (like iron ore, manganese ore, barite, etc.) is quite difficult in the current scenario. On the other hand, such a need does not arise for the stochastic model, where the model can be directly applied to measured sparse partition coefficients using tracer studies (Rao et al., 2017b). Moreover, the application of the stochastic model does not require the feed bivariate distribution to be known a priori.

Mathematical modeling of mineral jigs Chapter | 11

509

FIGURE 11.40 Comparison of the partition surfaces generated from the Stochastic Model (green lines) and the King’s Extended Stratification Model (red lines with gray shade) for the test data discussed in Fig. 11.36. Data after Rao, B.V., Jeelan, G., Satish, S., Gopalkrishna, S.J., 2017a. Experimental validation of extended stratification model part b: coal-ash segregation studies in a batch jig operation. Trans. Indian. Inst. Met., 70(2), 375
394.

Fig. 11.40 gives a pictorial view of the partition surfaces generated from the extended stratification model (shown with the red lines and gray color filling) and the stochastic model (shown with the green lines) for the same test partition coefficients data represented as black dots. These are the same data represented earlier in Fig. 11.36. It is seen that both the stratification models generate the partition surfaces that are quite close to the measured data. While King’s extended stratification model is just confined to the range of particle size and density under the study, the stochastic model extends it beyond the particle size-density range studied, especially to the finer size range, where the particle separation efficiencies fall drastically. The stochastic model indicates the combinations of size and density range where the jig performance can improve or deteriorate and thus the model guides the proper size range selection to truncate the size range for a better jig separation

510

Mineral Processing

performance. Fine particles below a certain size value deteriorate the jig performance irrespective of their particle density as shown by the stochastic model partition surface, which is indicated as below B0.7 mm for coal-ash separation in Fig. 11.40.

11.17 Control of industrial Batac jig performance Mineral jigs have been operated in batch mode since ancient times with the manual clearing of the segregated layers, but of late, jigs have been designed for industrial continuous operation. Batac jigs are gaining importance for relatively coarser particle separation (i.e., for particles in the size range of 1
70 mm with proper selection of the size ratio for each jig) due to their good separation performance and their ability to handle large throughputs in a single unit. The modern Batac jigs are fully PLC controlled with human
machine interface screen for the operator interface. Fig. 11.41 shows a schematic diagram of a typical Batac jig with multiple air chambers (Myburgh, 2010). The instruments include a float system at the product discharge end with its adjustable weights, pressure sensors in the upper and lower parts of the jig air chamber, and the air
water interface level sensors in the air chamber. PID control loops for gate operation and working-air-vessel pressure maintenance are an essential part of the design. Dual poppet valve with an opening and closing operation sequence by time settings to produce the desired wave

FIGURE 11.41 Batac jig schematic diagram. After Myburgh, H.A., 2010. The influence of control and mechanical condition of certain parameters on jigging. J. South. Afr. Inst. Min. Metall. 110, 655
661.

Mathematical modeling of mineral jigs Chapter | 11

511

for each chamber controls the operation. A belt scale control on the conveyor belt controls the throughput to the jig. It is essential that all the instruments/sensors need to be calibrated correctly and the plant engineers have to monitor them from time to time to assure a good jig performance. The sensors should have a good response time (say, in milliseconds for the air control valves) for the good control and operation of the jig. For a given jig design and operation, it is essential to control the feed characteristics, pulse characteristics, and product gate operation for continued good performance.

11.17.1 Feed composition control The mine pockets vary a lot in mineralogy, which causes fluctuations in the jig feed material. A consistent feed in terms of particle size, chemical assay, and Near Gravity Material (NGM) along with coarse liberated particles is essential for a good separation in a jig operation. However, in reality, the feed composition fluctuates a lot when the ROM is just crushed and screened, and supplied to the plant. A fluctuating feed changes the segregation patterns of the jig bed quite often and demands the pulse control be adjusted to suit the incoming feed. Some useful material may be lost to the tails to maintain a targeted chemical product assay. Moreover, these variations in various aspects (like chemical assay, NGM content, particle size range, etc.) need to be restricted to a narrow band for better performance of the jig. Therefore, size truncation and blending of ores to homogenize the PSD and the chemical assay before feeding the material to the jig plant is very much recommended.

11.17.2 Additional operational control aspects related to the feed material At the entry point, the feed material to the jig needs to be spread evenly across the jig width for better separation. There should not be any size segregation on the jig width, which, if present will cause an imbalance in the bed stratification. The pulse should be uniform across the jig width. It is important to monitor that the whole bed lifts simultaneously during pulsation. Any dead zones present on the screen deck (where pulsation is not felt due to screen deck blockages) causes a poor particle stratification and hence reduction in the achievable yield (Myburgh and Nortje, 2014). If NGM increases above 15%, either the feed flowrate to the jig has to be reduced to give more residence time to get optimum separation of particles or the weight on the float can be increased, which increases the cut density and reduces the amount of NGM material to segregate beneath the float,

512

Mineral Processing

which otherwise reports to the product. In a way, the increase in float weight allows more NGM material to be removed to the reject stream. However, if the float density is decreased, more NGM will report to the product stream diluting the product quality (Myburgh, 2010).

11.17.3 Pulse control The performance of a jig operation is greatly affected by the waveform type and its amplitude and frequency. Optimum performance of the jig requires the control of these conditions for a given feed consist. The trapezoidal waveform gives better separation than the sinusoidal waveform. Coarse and heavy particles require more amplitude than fine and low-density particles for a good separation. This will avoid remixing the segregated material in the jig layers. Finer particle separations require more pulse frequency. The pulse frequency usually varies from 40 to 90 cycles/minutes for Batac jigs, which can be electronically adjusted. The entry and exit of the air in the air chambers located beneath the screen deck generate the jig pulse. The entry of air expels the water from the air chamber, and thus creates a pulse in the jig bed. The exit of the air sets back the original condition. The air pressure and air volume required for the jig operation are generated by an air blower. The working air is stored in a header vessel. Poppet valves control the air entry and exit in the air chambers. Level probes in the air chamber measure the height of the air
water interface and guide the poppet valve operation to keep the stroke in the airchamber constant (Myburgh, 2010). The poppet valves use clean air at 6 bar pressure to operate correctly, and these valves are responsible for the generation of the water pulse and the proper fluidization of the particle bed. Two poppet valves per air-chamber control the inlet and outlet air flows. The timings of opening and closing of the poppets are controlled by a PLC program. For the pulse generation, the working poppet valve must open and close before the exhaust poppet opens and closes. The waveform generated depends on the timings of opening and closing of these valves, which happens in a few hundred milliseconds. The fine jigs will have the shorter cycle period. To generate a good pulse, all the mechanical parts should function properly (Myburgh, 2010).

11.17.4 Gate operation control Gate design and its control is the step for controlling the split of segregated particles from the stratified bed. An understanding of the forces acting in the jig bed to segregate the incoming feed particles is an important step for devising better control strategies to get good products continuously from the jig operation. To this end, the mathematical models help a lot to visualize the bed segregation patterns that change with any changes in feed

Mathematical modeling of mineral jigs Chapter | 11

513

characteristics, operating conditions such as throughput, the pulse characteristics, etc. This helps to achieve sophistication in jig control and product control than the operator-oriented skill-based conventional and rudimentary methods. The float system before the discharge gate measures both the stroke length as well as the product bed height. It guides the opening and closing of the product gate in small increments by maintaining the product bed height around the set value through the PLC program. The bed level present in front of the gate channel should decrease slowly during jig operation. If it falls drastically, there will be a mixing of low-grade material with the product stream material. The rejects overflow the weir at the other end of the jig (Myburgh, 2010). If the punch plates that are part of the gate system do not close properly, then there will be a direct bypass of feed to the product stream and the required segregated bed height underneath the float doesn’t form properly.

11.17.5 JigScan JigScan is an automatic controller for jig operation, developed at Julius Kruttschnitt Mineral Research Center, Australia to identify the changes in the feed characteristics and its segregation patterns & to act on the jig pulse characteristics to improve particle segregation and product removal. With the implementation of the JigScan controller, it has been reported that there is an increase in product yield to the extent of 2% for coal separation and greater than 8% for iron ore separation. It measures bed density and pulse velocity several times within a pulse cycle. It uses pressure sensors, level sensors for the air chamber (to measure water
air interface height), and nucleonic/float technology (to measure particle bed density distribution across the bed height or simply the product bed height). APIC jigs are integrated with JigScan software to control the jig operation (Loveday and Jonkers, 2002). Finally, a good operation of the jig requires a collaborative team effort between metallurgy, maintenance, operation departments, and the spare suppliers (Myburgh and Nortje, 2014).

11.17.6 Factors affecting jig operation Several factors affect the jig operation. These include feed particle characteristics like distribution of particle size, shape, and density; operating parameters like feed rate, bed depth, water flowrate, etc. for a given jig operation.

11.17.6.1 Particle size It is always good to treat mono-size particles as jig the feed. However, due to wide size distributions produced during the size reduction operation, it is

514

Mineral Processing

advised to truncate the feed with maximum to minimum particle size in the ratios of two to five for the feed stream for their better separation in the jig. The size ranges can be typically 1
5, 5
20, 20
60 mm, etc. The jig pulse characteristics suited for coarse particle separation (mainly the values of amplitude and the frequency) are not suited for fine particle separation. Kumba Iron ore’s Sishen Iron Ore Mine in South Africa treats 1
25 mm size fraction in three jigs. The fine jig receives 1
3 mm, the medium jig receives 3
8 mm, and the coarse jig receives 8
25 mm. Instead of jigging 1
8 mm in one jig, the splitting of two fractions 1
3 and 3
8 mm resulted in a 12% improvement in the product yield. Also, the pulse frequency varies with the particle size of the sample. The coarse jig has 60 pulses per minute, the medium jig has 70 pulses per minute, and the fine jig has 90 pulses per minute (Myburgh, 2010). The effect of particle size on separation efficiency is well depicted by a partition surface (Rao et al., 2003a,b). Myburgh and Nortje (2014) suggest for an iron ore operation that the particle lift height should be at least 3 times the coarse particle size (i.e., .75 mm lift for 225 1 8 mm ore) and up to six times the top size for the fine particles (i.e., .18 mm lift for 23 1 1 mm ore).

11.17.6.2 Particle density The density difference between the light and heavy minerals is quite important for their segregation under pulsation. If the difference becomes small, the operation is significantly affected. Particle segregation is not pronounced and hence the achievement of a product-grade material becomes difficult and the layers show the mixing patterns when density differences among the minerals to be separated are quite small. NGM represents the fraction of material present in the feed with 1 / 2 0.1 g/cc around the separation density. The allowed NGM in a jig operation is 7%
15% for good separation of particles (Ambros, 2020). 11.17.6.3 Particle shape Flaky and flat particle separation in jigs show poor segregation patterns, mainly because of the reduction in terminal settling velocities due to increased drag forces on them (in comparison with the spherical particles), and also their mobility in the jig bed gets restricted due to flakiness of the particles. 11.17.6.4 Bed height Usually, Batac jigs are operated with particle bed heights of 250 to 500 mm (Myburgh and Nortje, 2014). Thicker particle beds require more water force to fluidize the bed and hence under such situation can displace heavy particles more to the upper regions of the bed, which leads to loss of the heavies

Mathematical modeling of mineral jigs Chapter | 11

515

to the float-stream. In other words, thicker bed operations can contaminate the float-stream with heavy particles (Ambros, 2020).

11.17.6.5 Specific throughput The specific throughput depends on the type of jig operated. Typically, pneumatic jigs can treat 2
3 tph/m2, plunger jigs can have the capacity to treat 4 tph/m2, diaphragm jigs can treat 7 tph/m2, IHC radial jigs can treat 10 tph/m2, Baum jigs can treat 20 tph/m2, and Batac jigs can treat 24 tph/m2 (Kelly and Spottiswood,1982; Ambros, 2020). If the feed average particle size decrease, then the specific throughput of the jigs significantly decreases. This is because fines require more residence time in the jig for proper segregation. In other words, excessive feed rates than the specified values impede the stratification process and reduce the attainment of good heavy products at the bottom of the jig. 11.17.6.6 Water flow rates The jigs are operated at approximately 25%
35% solids (Bose, 1997). For continuous operation, excessive dilution (below 30% solids) results in more pronounced horizontal shear forces in the jig chamber and hence affects the segregation patterns (Ambros, 2020). The majority of the process water has to be recovered from the wet jig operations, through dewatering screens and thickeners from various product streams and has to be recycled into a process water tank for its reutilization.

11.18 Challenges ahead A proper understanding of lab test segregation with the plant jig bed segregation has to be developed in terms of scale-up requirements. The lab tests do not have longitudinal transport of particles, while a plant scale operation has this force. It is essential to understand the role of the longitudinal shear forces in the improvement of the segregation patterns. It is necessary to verify whether the same lab-specific stratification coefficient in King’s stratification model holds good for a continuous jig operation, assuming that the lab test feed composition remains the same for plant operation. Simulation studies of King’s stratification model indicate that particle separation efficiency improves by increasing the specific stratification coefficient. But means of improving this parameter have to be established with more careful studies. Better control algorithms are necessary to control jig operations with fluctuating feed composition and for difficult-to-separate ores. The application of King’s stratification model needs feed distribution to be known a priori. While it is possible to do a sink-float analysis for coal samples with the available organic liquids, methods have to be developed to

516

Mineral Processing

identify feed distribution for heavy minerals without conducting toxic sinkfloat tests. Online detection of variation in feed composition helps to control jig operations in a better way using suitable pulse forms. Such identification methods need to be developed. Equipment design enhancements are necessary to improve the segregation of particles in the jig bed to give better yield and grade of the concentrate for a given feed composition. More research should be directed towards dry beneficiation techniques, improving the separation enhancement ratios, and better control techniques to reduce water requirements. In addition, more research has to be carried out to improve the separation of flaky and flat particles and to evaluate the effect of particle shape on the segregation patterns.

Acknowledgments BVR acknowledges the late Prof. R.P. King, University of Utah, Salt Lake City, Utah for his guidance to understand the stratification model and for sharing the feed washability data of the industrial coal jigs. The interactions with Dr. Andrew Jonkers, Australia, and Mr. Anup Datta, India are highly acknowledged. The author acknowledges Mr. Ramesh Mahedvan and Mr. Indubhushan Jha, Takraf India Pvt. Ltd., India, and Mr. Heiko Teuber, TAKRAF GmbH, Germany for their support and encouragement. BVR thanks all his friends at Takraf India Pvt. Ltd. who encouraged this contribution, with special thanks to Mr. Kumar Velan and Mr. Rajiv Krishnamurthy. Mr. Mohan Kumar and Mr. Shivakumar K, C. are acknowledged for their dedicated support in the planned jig tests.

References Ambros, W.M., 2020. Jigging: a review of fundamentals and future directions. Minerals 10 (11), 998. Available from: https://doi.org/10.3390/min10110998. Bazin, C., Hodouin, D., 2001. Importance of covariance in mass balancing of particle size distribution data. Miner. Eng. 14, 851
860. Bose, A.N. (Ed.), 1997. Monograph on Iron Ore. Indian Bureau of Mines, Nagpur, India. Buys, A., Jonkers, A., 2012. J-Tube batch jig test work for FACOR for metal from slag. In: Bateman Report, pp. 1
19. Collins, D.N., Turnbull, T., Wright, R., Ngan, W., 1983. Separation efficiency in dense medium cyclones. Trans. Inst. Min. Metall. C. Miner. Process. Extr. Metall. 92, C38
C51. de Korte, G.J., 2003. Comments on the use of tracers to test dense medium plant efficiency. Coal Prep. 23, 251
266. Ferrara, G., Schena, G.D., 1987. Cycloning in dense media separation. In: Wood, P. (Ed.), Proceedings of the 3rd International Conference on Hydrocyclones. BHRA, Oxford, pp. 101
110. Heiskanen, K., 1993. Particle Classification. Chapman and Hall, London. Kelly, E.G., Spottiswood, D.J., 1982. Introduction to Mineral Processing. A Wiley-Inter Science Publication, Brisbane. Kelly, E.G., Subasinghe, G.K.N.S., 1991. Gravity performance curves: a re-examination. Miner. Eng. 4, 1207
1218.

Mathematical modeling of mineral jigs Chapter | 11

517

King, R.P., 2001. Modeling and Simulation of Mineral Processing Systems. ButterworthHeinemann, Oxford. Klima, M.S., Luckie, P.T., 1989. Application of an unsteady-state pulp-partition model to densemedium separations. Coal Prep. 6, 227
240. Llewellyn, R.L., Humphryes, K.K., Leonard, J.W., Lawrence, W.F., 1979. Chapter 11: dry concentration. In: Leonard, J.W. (Ed.), Coal Preparation, fourth ed. SME Inc, New York, pp. 1
32. Loveday, G., Jonkers, A., 2002. The APIC jig and the JIGSCAN controller take the guesswork out of jigging. In: Proceedings of the 14th International Coal Preparation Congress and Exhibition, Johannesburg, South Africa, pp. 247
251. Mayer, F.W., 1964. Fundamentals of a potential theory of the jigging process. In: Arbiter, N. (Ed.), Proceedings 7th International Mineral Processing Congress. Gordon and Breach, New York, pp. 75
86. Myburgh, H.A., 2010. The influence of control and mechanical condition of certain parameters on jigging. J. South. Afr. Inst. Min. Metall. 110, 655
661. Myburgh, H.A., Nortje, A., 2014. Operation and performance of the Sishen Jig Plant. J. South. Afr. Inst. Min. Metall. 114, 569
574. Rong, R.X., Lyman, G.J., 1992. The effect of jigging time and air cycle on bed stratification in a pilot scale Baum jig. Fuel 71, 115
123. Rao, B.V., 2004. Weibull partition surface representation for gravity concentrators. Miner. Eng. 17 (7
8), 953
956. Rao, B.V., 2005. General gamma representation for product particle split in gravity concentrators. Eur. J. Miner. Process. Environ. Prot. 5 (1), 84
93. Rao, B.V., 2006. The pivot phenomenon and difference-similarity of classifier particle distributions. Powder Technol. 168, 152
155. Rao, B.V., 2007a. Estimation of marginal and bivariate product distributions of gravity concentrators using partition surface coefficients. In: Singh, R., Das, A., Goswami, N.G. (Eds.), Proceedings of the Advanced Gravity Concentration, Jamshedpur, pp. 96
107. Rao, B.V., 2007b. Extension of particle stratification model to incorporate particle size effects. Int. J. Miner. Process. 85, 50
58. Rao, B.V., 2021. An improved stochastic model to describe partition surfaces of entire segregated batch jig bed. Miner. Eng. 170, 107064. Rao, B.V., Ganvir, V., Gopalakrishna, S.J., 2008. Reconciliation of size-density bivariate distributions over a separating node. Particuology 6, 167
175. Rao, B.V., Gopalkrishna, S.J., 2010. Simulation studies on robustness of multi-stage gravity circuit performance by random perturbations. In: Singh, R., et al., (Eds.), XIth International Seminar on Mineral Processing Technology (MPT-2010). Allied Publishers Pvt. Ltd., Mumbai, pp. 357
363. Rao, B.V., Kapur, P.C., 2008. Simulation of multi-stage gravity separation circuits by size
density bivariate partition function. Int. J. Miner. Process. 89 (1), 23
29. Rao, B.V., Kapur, P.C., Konnur, R., 2003a. A general model of particle size-density partitioning in gravity separators. International Conference on Mineral Processing Technology. Allied Publishers Private Limited, Mumbai, pp. 117
126. Rao, B.V., Kapur, P.C., Rahul, K., 2003b. Modeling the size-density partition surface of densemedium separators. Int. J. Miner. Process. 72, 443
453. Rao, B.V., Velan, H.K., Kumar, K.S.M., Ravindra, M., Anup, D., 2016. Slicing the Evolving Batch Jig Bed. MIST 2016, pp. 1
8. ,http://www.meconlimited.co.in/writereaddata/ MIST_2016/sesn/tech_1/2.pdf. (accessed 06.11.20).

518

Mineral Processing

Rao, B.V., Velan, H.K., Gopalkrishna, S.J., 2016b. Visualization of partition surface from performance indices of gravity separators. Trans. Indian Inst. Met. 69, 33
38. Available from: https://doi.org/10.1007/s12666-015-0616-7. Rao, B.V., Jeelan, G., Satish, S., Gopalkrishna, S.J., 2017a. Experimental validation of extended stratification model part b: coal-ash segregation studies in a batch jig operation. Trans. Indian. Inst. Met. 70 (2), 375
394. Rao, B.V., Rishi, R., Kumar, N.M.H., Gopalkrishna, S.J., 2017b. Experimental validation of extended stratification model: part A—ore with tracer particle studies in a batch jig operation. Trans. Indian. Inst. Met. 70 (2), 359
373. Sampaio, C.H., Tavares, L.M.M., 2005. Beneficiamento Gravime´trico: Uma Introduc¸a˜o aos Processos de Concentrac¸a˜o Mineral e Reciclagem de Materiais por Densidade. Editora da UFRGS, Porto Alegre, Brazil. Scott, I.A., Napier-Munn, T.J., 1992. Dense-medium cyclone model based on the pivot phenomenon. Trans. Inst. Min. Metall. C: Miner. Process. Extr. Metall. 101, C61
C76. Tavares, L.M., King, R.P., 1995. A useful model for the calculation of the performance of batch and continuous jigs. Coal Prep. 15, 99
128. Walklate, J.R., Fourie, P.J., 2006. A history of gravity separation at Richards bay mineral. J. South. Afr. Inst. Min. Metall. 106, 741
748. Wills, B.A., 1997. Mineral Processing Technology. Butterworth-Heinemann, Oxford.

Index Note: Page numbers followed by “f” and “t” refer to figures and tables, respectively.

A Advanced flotation washability, 392
394 Algebraic Slip Mixture (ASM) model, 290, 330
331, 340
343 simulating coal particle dynamics using, 349
352 Alumina companies and technology in India, 155t in the world, 155t Alumina production, refining of bauxite ore for, 119
120 Alumina refinery plants in India and abroad, 154
156 Aluminous laterite sample, 132
134, 146
147 reduction roasting followed by magnetic separation, 146
147 wet high intensity magnetic separation studies, 146 Anthracite coal, 3 Apatite, 172 Attrition, 61
62 Auger mining, 8

B Barite concentrate grade, 374
376 Batac jig performance, control of, 451, 510
515 factors affecting jig operation, 513
515 bed height, 514
515 particle density, 514 particle shape, 514 particle size, 513
514 specific throughput, 515 water flow rates, 515 feed composition control, 511 gate operation control, 512
513 JigScan, 513

operational control aspects related to feed material, 511
512 pulse control, 512 Baum jig, 451 Bauxite mining practices, 122
124 manually operated mines, 122
123 mechanized mines, 123
124 semimechanized mines, 123 Bauxite ores alumina refinery plants in India and abroad, 154
156 Bayer process, impact of different bauxites on, 153 Bayer process technology, 156
159 beneficiation of, 136
150 gibbsite
boehmite mix type ore, 136
146 low-grade bauxite ores, 146
150 characterization of, 125
135 gibbsite-boehmite mix ore, 126
131 low-grade bauxite ores, 132
135 geology of bauxite deposits, 124
125 green-field refinery, 159
160 pilot trials for developing beneficiation flowsheet, 150
152 refining of, for alumina production, 119
120 resources, 120
122 sustainability challenges, 160
164 acid neutralization, 163 alternative technologies, 164 bauxite residue management, 160
161 effluent management, 162
164 principles of effluent treatment, 162
163 seawater neutralization, 163
164 Bauxite residue disposal area (BRDA) design, 162
163 Bayer process, impact of different bauxites on, 153 Bayer process technology, 156
159

519

520

Index

Beach sand minerals, 183t Beneficiation, 60
69 Bioremediation, 104 Bituminous, 3 Brown coal. See Lignite Bubble size distribution (BSD), 366

C Calcination, 159 Capital investments (CAPEX), 159
160 Chromite ore beneficiation, 88
93 chrome ore beneficiation plant, Sukinda, India, 92 chrome ore gravity concentrator, challenges in, 92
93 Kemi chromium concentrator (Finland) flowsheet, 90 Turkish chromite concentrator flowsheet, 90
92 characterization, 87
88 physical properties, 88 effluent treatment processes, 96
108 bioremediation, 104 chromium existence, 97 Cr(VI) remediation, 105
108 effluent treatment methods, 99
100 electrolytic treatments, 102
103 electro methods, 101 hexavalent chromium, formation of, 98
99 ion exchange, 103 membrane separation, 103
104 phytoremediation, 104
105 water treatment and distribution, chromium chemistry in, 98 mining, 84
86 caving methods, 86 supported methods, 84
86 unsupported methods, 84 ore genesis, 80
83 chromite deposits, reserves of, 83 occurrence, 81
82 research & development, 94
96 low and subgrade chromite ore, beneficiation of, 94
95 stockpiled tailings, reprocessing of, 95 tailing losses, reduction of, 94 ultrafine size particles, processing/ recovery of, 95
96 Chromite ore beneficiation plant, 108
111

capital cost, 108 mineral value per ton, 110
111 operating cost, 108
110 processing cost, 108 Chromium, 79 Classifier size distributions, inverse problem of classifier analytical expressions for logistic efficiency curve, 227
229, 231t for Plitt’s efficiency curve, 226
227, 230t classifier inverse problem, 239
244 parameter sensitivity analysis, 244
249 logistic efficiency curve approach (case), 247
249 Plitt efficiency curve approach (case), 246
247 pivot phenomenon and difference similarity of, 234
238 proposed analytical expressions, validation of, 229
234 estimation of solid flow split to coarse product, 233
234 size classifier performance, evaluation of, 223
225 Coal blending of, 20 coking and noncoking coal, 4
5, 12t environment management, 36
37 dust pollution, 36 noise pollution, 37 rain water treatment, 36 slurry/effluent water treatment, 36
37 formation of, 1
2 depositional environments, 2 temperature, 2 time, 2 geology and occurrence of, 1 high/medium coking coal washery, 32
36 post washing section, 35
36 raw coal section, 32
33 utilities, 36 washing section, 34
35 instrumentation and control systems, 38
40 for dense medium cyclones (DMCs), 39 in fine coal flotation circuit, 39
40 metallurgical coal blends, 5
6 quality monitoring and control, 37
38 testing procedure for coal pertaining to beneficiation, 9
14

Index laboratory testing of different coals, 10
14 Coal beds, 3
4 Coal beneficiation plant guideline to plant availability, material and power consumption in, 40
41 Coal mining, 6
8 auger mining, 8 contour mining, 8 drift mine, 7 highwall mining, 8 long wall mining, 7 mountaintop mining, 8 open cast mine, 6 open-pit mining, 8 room and pillar mining, 7
8 shaft mine, 6
7 short wall mining, 7 slope mine, 7 Coal particle dynamics, simulating using Algebraic Slip Mixture model, 349
352 using discrete particle model, 344
349 Coal preparation, 20
30 coal cleaning, 22 coal dewatering, 28
30 coal sizing and classification, 21
22 coarse coal, 22
25 dry coal beneficiation, 30 fine coal, 25
28 raw coal pretreatment, 20
21 small coal, 25 Coal preparation plant, 30
32 Coal rank, 2
3 anthracite, 3 bituminous, 3 lignite, 3 subbituminous, 3 Coal sizing, 19 Coal transport, modes of, 8
9 bulk carrier, 9 storage, 9 trains, 9 trucks, 8 Coal washery, 32 loading section of clean coal, middling’s and rejects, 32 raw coal section, 32 washing section, 32 Coal washing plant, 41
52 dense medium cyclone separation, 42
43 froth flotation, 44
45

521

horizontal belt filters, 49 spirals, 45
46 thickeners, 46
47 troubleshooting, 51
52 trouble shooting guide, 48 wet drum magnetic separator, 49
51 dense media recovery, 51 distribution of feed slurry to magnetic separator, 50
51 feed slurry density, 50 magnetics content of feed particles, 50 Coarse coal, 22
25 Coarser fraction, 64 Coking coal, 4
5, 12t Collectors, 369 Column flotation cell, residence time distribution of, 412 Computational fluid dynamic (CFD) models, 263
277, 289, 354
360 Concentrate contained value (CCV), 377 Continuously operated flotation cell, kinetics of flotation in, 412
413 Contour mining, 8

D Data reconciliation, 399
400 dc electrode voltage, 192
193 Dense media recovery, 51 Dense-media separation (DMS) process, 64 Dense medium cyclones (DMCs), 39 computational fluid dynamics approach, 326
332 Algebraic Slip Mixture (ASM) model, 330
331 discrete particle model, 330 governing equations, 326
327 modified algebraic slip mixture model, 331
332 multiphase modeling, 329
332 Reynolds Stress model, 327
329 turbulence modeling, 327
329 volume of fluid model, 329
330 conventional dense medium cyclones, sources of inefficiencies in, 352
353 dense medium cyclone designs performance of different, scope to improve, 353
354 magnetite medium segregation prediction and validation, 336
339 mean flow field analysis and grid independence study, 335
336

522

Index

Dense medium cyclones (DMCs) (Continued) medium segregation predictions, 340
343 performance of novel dense medium cyclone designusing prediction, 354
360 coal partitioning in selected designs, 359
360 multiphase flow analysis in selective designs, 355
359 two-phase flow analysis, 354
355 numerical modeling, 334
335 rheology based CFD models, 343
344 rheology modeling, 332
334 granular viscosity (MASM 1 GV) model, 332
333 Newtonian model with total solids and fines correction, 333
334 Newtonian viscosity model withtotal feed solids correction, 333 non-Newtonian Herschel
Bulkley model, 334 simulating coal particle dynamics using Algebraic Slip Mixture model, 349
352 using discrete particle model, 344
349 Dense medium cyclone separation, 42
43 Dense medium separation (DMS), 197 Density separator principle, 187f Denver jig, 451 Derrick screen, 197f Diaspore, 119
120 Dimensionless residence time distribution, 403 Direct numerical simulation (DNS), 290 Disc magnetic separator/cross belt magnetic separator, 188
189 Discrete Element Methods (DEM), 252
260, 266
267 Discrete particle model (DPM), 293, 330 simulating coal particle dynamics using, 344
349 Discrete phase model, 271
273 Discrete Random Walk (DRW) model, 330 Dispersion index, 304 Dredging, 174
179 maneuvering, 175 operating cost drivers, 177
179 operation, 175
177 pond bottom losses, 177 Drift mine, 7 Dry coal beneficiation, 30 Drying, 205
206

fluidized bed dryer, 206 rotary drier, 205 Dynamic process model, 432

E Electrocoagulation (EC), 102
103 Electrode position, 192 Electrolytic treatments, 102
103 Electro methods, 101 Electrostatic plate separation (EPS), 194
195, 196f operating parameters, 195
196 electrode voltage, 195 feed rate, 195 feed temperature, 196 product splitters, 196 operating parameters, 195
196 electrode voltage, 195 feed rate, 195 feed temperature, 196 product splitters, 196 Electrostatic separation, 192
196 dc electrode voltage, 192
193 electrode position, 192 feed rate control, 192 feed temperature, 193
194 high tension roll separators, 192
194 operating parameters, 192 product splitters, 193 roll speed, 194 Entrainment, 413 Eulerian
Eulerian models, 271
273 fully solved, 270
271 Euler
Lagrange (CFD
DEM) model, 258

F Feed grade. See Head grade Feed rate control, 192 Feed temperature, 193
194 Fine coal, 25
28 Finer fraction, beneficiation of, 66
67 Flotation cell mechanism, 414 Flotation circuit process modeling, brief description on, 422
432 dynamic process model, 432 steady-state process model, 422
426 transient-state process model, 426
432 Flotation kinetics, 382
390 first-order kinetics, 382
383 higher-order flotation kinetics, 388

Index kinetic models with distributed rate constants, 388
390 modified first-order kinetics, 383
388 separation efficiency, 386
388 Flotation operation, variables affecting, 367t Flotation separation, 370f Flotation testing procedures, 390
398 advanced flotation washability, 392
394 flotation tree analysis, 394
397 locked cycle test (LCT), 397
398 release analysis, 390
392 Flotation tree analysis, 394
397 Fluidized bed dryer (FBD), 206 Free digging, 176
177 Frothers, 369 Froth flotation, 44
45, 197
199 data reconciliation, 399
400 entrainment, 413 flotation circuit process modeling, brief description on, 422
432 dynamic process model, 432 steady-state process model, 422
426 transient-state process model, 426
432 flotation kinetics, 382
390 first-order kinetics, 382
383 higher-order flotation kinetics, 388 kinetic models with distributed rate constants, 388
390 modified first-order kinetics, 383
388 flotation reagents, brief description of, 369 flotation testing procedures, 390
398 advanced flotation washability, 392
394 flotation tree analysis, 394
397 locked cycle test (LCT), 397
398 release analysis, 390
392 grade and recovery, concepts of, 370
377 mineral upgradation, effect of head grade on, 373
377 industrial mechanical cells, 413
421 gas dispersion parameters, 415
417 k
Sb relationship, 417
418 Neethling and Cilliers model on graderecovery curve, 420
421 power input parameters, 414
415 pulp-froth multiphase model, 419
420 selection tips for mechanical flotation cells, 417 mineral upgradation, effect of mechanism profile on, 421
422 residence time distribution (RTD), 400
413 of column flotation cell, 412

523

dimensionless, 403 hydrodynamics of scaled upcells, 410 kinetics of flotation in a continuously operated flotation cell, 412
413 large and small tanks in series model, 408
410 particle size effects on, 410
411 perfectly mixed flotation cells in series, 405
408 perfect mixing, 404
405 plug flow, 403 reflection of process issues through measurements of, 411 smelter contract and economic sustenance, 377
382

G Gamma model, 469
470 Garnet, 171
172, 214 Gibbsite-boehmite mix ore, 126
131 petrographic characterization, 127
131 megascopic studies, 127
128 mineralogy, 129 optical microscopy, 129
130 stereomicroscopic studies, 130
131 X-ray fluorescence study, 128 sample collection and chemical analysis, 126
127 Gibbsite
boehmite mix type ore, 136
146 flotation studies, 144
146 magnetic separation of bauxite ore, 142
143 size classification and scrubbing studies, 136
142 dry and wet sieving of the samples crushed to 25 and 100 mm top sizes, 136
137 scrubbing followed by hydrocyclone of 20.5 mm fraction, 137
142 Granular viscosity (MASM 1 GV) model, 332
333 Gravity concentrators, 182
199 dense medium separation (DMS), 197 electrostatic separation, 192
196 froth flotation, 197
199 hydrosizers, 186
187 magnetic separators, 187
192 disc magnetic separator/cross belt magnetic separator, 188
189 rare earth drum magnetic separator, 189
190

524

Index

Gravity concentrators (Continued) Wet high intensity magnetic separator, 189 screens, 196
197 shaking table, 184
186 spiral concentrator, 183
184 Green-field refinery, 159
160

H Hard coking coal (HCC), 4
5 Harz jig, 450
451 Head grade, 373
374 Heavy liquid separations (HLS) test, 65 Heavy-media separation, 65 Hematite, 57, 61 Hexavalent chromium, formation of, 98
99 High-gradient magnetic separators (HGMS), 66
67 High/medium coking coal washery, 32
36 post washing section, 35
36 raw coal section, 32
33 crushed coal storage, 33 crusher house, 33 primary screening and manual picking arrangement, 33 raw coal receipt section, 32 raw coal storage, 32 secondary screening, 33 utilities, 36 washing section, 34
35 desliming operation, 34 fine coal circuit, 35 heavy media beneficiation circuit and media recovery circuit, 34
35 High tension roll separators, 192
194 Highwall mining, 8 Hindalco, 156f, 160
161 Horizontal belt filters, 49, 204 Hydraulic mining, 179 Hydrocyclones, 264
274, 288f computational methodology, 290
297 multiphase modeling, 292
295 details of simulation, 296
297 rheology modeling, 295
296 turbulence modeling, 290
292 multiphase flow predictions, 306
319 conventional hydrocyclone, 306 laboratory hydrocyclone
heterogeneous feed, 313
316 laboratory hydrocyclone
homogeneous feed, 306
312

analysis of the effect of turbulence on particles, 316
319 two-phase flow predictions, 298
305 75 mm hydrocyclone, 297f, 298 75 mm laboratory hydrocyclone, 297f, 299
305 Hydrosizer separators in the plant, 187f Hydrotalcite formation, 163
164

I IHC radial jig, 451 Ilmenite, 173, 213 Indian iron ore resources, 56 Induced roll magnetic separator, 191, 191f feed rate, 191 field intensity, 191 roll speed, 192 splitter position, 191 Industrial mechanical cells, 413
421 gas dispersion parameters, 415
417 bubble surface area flux, 416
417 gas holdup, 417 Sauter mean bubble diameter, 416 superficial gas velocity, 416 k
Sb relationship, 417
418 Neethling and Cilliers model on graderecovery curve, 420
421 power input parameters, 414
415 absorbed power, 415 power intensity, 415 power number of the impeller, 415 tangential impeller tip speed, 415 pulp-froth multiphase model, 419
420 selection tips for mechanical flotation cells, 417 Industrial sedimentation, 46 InLine pressure jig (IPJ), 453 Ion exchange, 103 Iron ore beneficiation methods, 60
69 comminution and physical competency tests, 62
63 crushing and grinding, 63
64 finer fraction, beneficiation of, 66
67 heavy-media separation, 65 jigging, 64
65 liberation study, 61
62 multigravity separator (MGS), 68 reverse flotation, 69 spirals, 67 teeter-bed separator, 68

Index wet high-intensity magnetic separators, 68 beneficiation study, 63 beneficiation test, 64 of coarse 232 1 8 mm material, 65
66 of intermidate size 28 1 1 mm material, 66 of 21 mm fraction, 69 coarser fraction, beneficiation of, 64 geology and occurrence, 56
57 general geology, 56
57 Indian iron ore resources, 56 mining methods, 58
60 operating practices, 70
75 high-grade ore, processing of, 70
72 low-grade ore, processing of, 73 processing route, 75 Tata Steel Long Products Ltd, 74
75, 74f Tata Steel Minerals Canada (TSMC), 73
74, 73f

J Jig bed kinetics and bed assay evolution, 447
449 continuous Baum jig operation, particle segregation in, 447
449 Jigging, 64
65 Jigs, 257
260 JigScan, 513 Jig stratification index (JSI), 445
447 Jig types, 450
453, 450f, 454t Jig washers, 23 Jig wave forms, 453 Julius Kruttschnitt Mineral Research Centre, 23

K Kelsey centrifugal jig (KCJ), 452
453 Kemi chromium concentrator (Finland) flowsheet, 90 Key parameter indices (KPI), 473
475 Kinetic Theory of Granular Flow (KTGF), 271
272 King’s stratification model, 454
460 application of, to continuous performance of industrial jig, 460 simulation studies of for batch jig operation, 460
462 for continuous jig operation, 463
466 Kyanite, 172

525

L Lagrange multiplier method, 498 Large eddy simulation model (LES), 290
292 Lignite, 3 Locked cycle test (LCT), 397
398 Locus of zero vertical velocity (LZVV), 265, 288
289 Logistic efficiency curve, 231t case, 247
249 classifier analytical expressions for, 227
229 Logistic model, 469 London Metal Exchange (LME), 379 Long wall mining, 7 Low-grade bauxite ores, 132
135, 146
150 aluminous laterite sample, 132
134 aluminous laterite sample, 146
147 reduction roasting followed by magnetic separation, 146
147 wet high intensity magnetic separation studies, 146 partially kaolinized khondalite (PKK) sample, 134
135, 147
150 scrubbing and hydrocyclone studies, 149
150 wet high intensity magnetic separation studies, 147
149

M Magnetic separators, 187
192 disc magnetic separator/cross belt magnetic separator, 188
189 rare earth drum magnetic separator, 189
190 induced roll magnetic separator, 191 rare earth roll magnet separator, 190
191 wet high intensity magnetic separator, 189 Magnetite, 173 Manually operated mines, 122
123 MASM model, 340f, 341
342, 341f, 342f Mathematical modeling of mineral jigs challenges ahead, 515
516 effect of head grade on jig performance, 440
443 extended King’s stratification model, 501
510 comparison of two jig models, 508
510 industrial Batac jig performance, control of, 510
515

526

Index

Mathematical modeling of mineral jigs (Continued) additional operational control aspects related to the feed material, 511
512 factors affecting jig operation, 513
515 feed composition control, 511 gate operation control, 512
513 JigScan, 513 pulse control, 512 jig bed kinetics and bed assay evolution, 447
449 continuous Baum jig operation, 447
449 jig stratification index, 445
447 jig types, 450
453, 450f, 454t jig wave forms, 453 kinetics of particle size segregation in a batch jig, 449
450 King’s stratification model, 454
460 application of, to continuous performance industrial jig, 460 simulation studies of, for batch jig operation, 460
462 simulation studies of, for continuous jig operation, 463
466 partition surface, 466
475 generation of partition coefficients for partition surface representation, 472
473 mathematical representation of partition surface, 468
472 partition surface visualization using key parameter indices, 473
475 size-density bivariate distributions and their characteristics, 475
501 circuit sensitivity analyses of two-stage circuits, 493
495 data reconciliation of bivariate distributions of a separator, 495
501 difference similarity among bivariate distributions, 482
483 multistage separations, 486
493 sink and float distribution predictions from the feed distribution and partition surface concept, 484
486 test work and grade-yield-recovery curves, 438
440 timed batch jig tests and attainment of dynamic equilibrium of particles in jig bed, 444
445 Mechanized mines, 123
124 Membrane separation, 103
104 Metallurgical accounting system, 209 Metallurgical coal blends, 5
6

Mineral, 4 Mineral density separator (MDS), 64
65 Mineral processing, numerical methods in dense medium cyclones, 274
277 discrete element modeling, 252
260 Eulerian
Eulerian models and discrete phase model, 271
273 jigs, 257
260 milling/grinding, 253
255 milling/grinding, 261
263 computational fluid dynamics, 263
277 hydrocyclones, 264
274 multiphase modeling-heterogeneous feed, 273
274 multiphase modeling-homogeneous feed, 270
274 turbulence modeling, 267
270 population balance modeling, 260
263 rheological modeling, 276
277 screw conveyor/mixer, 255
257 Mineral sands, 169 availability and cost of utilities, 217 fuel, 217 location, 217 power tariff, 217 water, 217 concentration, 182 economic uses, 213
215 cost considerations, 214
215 garnet, 214 ilmenite and rutile, 213 monazite, 214 sillimanite, 213 zircon, 213 factors influencing minerals and processing, 207 formation of, 169
170 geology, 169
173 composition of mineral sands, 170 formation of mineral sands, 169
170 texture and transport of mineral sand, 170
173 heavy mineral ore, processing of, 199
206 pre concentration plant, 200
203 mineral separation plant, 204
206 metal accounting system, 210
211 metallurgical accounting system, 209 mine planning, 180
181 mineral sands project, methodology to develop, 212
213 mining technologies, 173
179 dredging, 174
179 dry mining, 179

Index hydraulic mining, 179 mining activities, 181 processing, 182
199 mineral sands concentration, 182 mineral separation equipment used in heavy mineral sands industry, 182
199 reconciliation, balancing and reporting, 210 record keeping, 212 resource characteristics, 216
217 grade, 216 mineral assemblage, 216
217 overburden, 216 proportion of slimes, 216 tailing’s disposal, 207
208 Mineral separation equipment used in heavy mineral sands industry, 182
199 gravity concentrators, 182
199 Mineral separation plant, 204
206 dewatering, 204 drying, 205
206 horizontal belt filters, 204 dewatering, 204 Mineral upgradation, effect of head grade on, 373
377 Miner’s Plow, 123 Modified algebraic slip mixture (MASM) model, 293
295, 331
332, 340
343 Monazite, 172, 214 Mountaintop mining, 8 Multigravity separator (MGS), 68 Multiphase flow predictions, 306
319 hydrocyclone, 306 laboratory hydrocyclone, 306
316 effect of component proportions, 313
315 effect of feed solids concentration, 307
311 effect of solids concentration on equilibrium radii, 311
312 effect of spigot diameter and solids concentration, 315
316 analysis of the effect of turbulence on particles, 316
319 heterogeneous feed, 318
319 homogeneous feed, 316
318 Multiphase modeling-homogeneous feed, 270
274

N Navier
Stokes equation, 258 Near gravity material (NGM), 274

527

Neethling and Cilliers model on graderecovery curve, 420
421 Net smelter returns (NSR), 379 Newtonian model with total solids and fines correction, 295
296, 333
334 Newtonian viscosity model with total feed solids correction (MASM 1 Nfs), 333 Noncoking coal, 4
5, 12t Non-Newtonian Herschel
Bulkley (MASM 1 HB) model, 334

O Oleic acid, 144
145 Open cut mining, 6 Open-pit mining, 8 Operating cost (OPEX), 159
160 Operating parameters, 192 Overall efficiency, 313
314

P Partially kaolinized khondalite (PKK) sample, 134
135, 147
150 scrubbing and hydrocyclone studies, 149
150 wet high intensity magnetic separation studies, 147
149 Particle size distribution (PSD), 498 Phytoremediation, 104
105 Pivot density, 458 Plitt’s efficiency curve, 230t case, 246
247 classifier analytical expressions for, 226
227 Plug flow, 403 Pond bottom losses, 177 Population balance modeling (PBM), 260
263 Power Station Fuel (PSF), 14 Product splitters, 193 Pulp-froth multiphase model, 419
420

Q Quartz, 171

R Rare earth drum magnetic separator, 189
190, 190f induced roll magnetic separator, 191 feed rate, 191

528

Index

Rare earth drum magnetic separator (Continued) field intensity, 191 roll speed, 192 splitter position, 191 rare earth roll magnet separator, 190
191 Rare earth elements (REE), 161 Rare earth roll magnet separator, 190
191, 190f Raw coal pretreatment, 20
21 Remer jig, 451 Residence time distribution (RTD), 400
413 of column flotation cell, 412 dimensionless, 403 kinetics of flotation in continuously operated flotation cell, 412
413 large and small tanks in series model, 408
410 of mechanical cells using LSTS model, 408
410 particle size effects on, 410
411 perfectly mixed flotation cells in series, 405
408 perfect mixing, 404
405 plug flow, 403 reflection of process issues through measurements of, 411 scaled upcells, hydrodynamics of, 410 Reverse flotation, 69 Reynolds Averaged Navier
Stokes (RANS) approach, 290, 327 Reynolds Stress model, 327
329 Rheology based CFD models, prediction of viscosity levels by, 343
344 Roll speed, 194 ROMJIG, 451
452 Room and pillar mining, 7
8 Run-off-mine ore (ROM), 92 Run-Of-Mine (ROM) coal samples, 10
14 Rutile, 172
173, 213

S Sand, 169 composition of mineral sands, 170 texture and transport of mineral, 170
173 Sauter mean bubble diameter, 416 Scatter diagram, 371
372 Schulz separation efficiency, 386
388, 387f Screw conveyor/mixer, 255
257 Scrubbing, 61
62 Semimechanized mines, 123

Shaft mine, 6
7 Short wall mining, 7 Sillimanite, 172, 213 Slope mine, 7 Small coal, 25 Smelter contract, 378 Smoothed Particle Hydrodynamics (SPH) modeling, 254, 266
267 Sodium hexametaphosphate (SHMP), 144
145 Spiral concentrator, 183
184 operating parameters, 184 operating parameters, 186 Spirals, 45
46, 67, 201 Steady-state process model, 422
426 Stochastic model, 470
472 Stockpiled tailings, reprocessing of, 95 Subbituminous, 3

T Tata Steel Long Products Ltd, 74
75, 74f Tata Steel Minerals Canada (TSMC), 73
74, 73f Teeter-bed separators, 27, 68 Terminal-recovery, 383 Thickeners, 46
47 Titanium, 167 Total available alumina (TAA), 125
126 Transient-state process model, 426
432 “Tree analysis” method, 394 Trouble shooting guide, 48 Turbulence intensity (TI), 304 Turbulence modeling, 267
270 Turkish chromite concentrator flowsheet, 90
92 Two-phase flow predictions, 298
305 75 mm hydrocyclone, 297f, 298 75 mm laboratory hydrocyclone, 297f, 299
305 turbulence intensity (TI), 304 turbulent dispersion of particles, 305

U Ultrafine size particles, processing/recovery of, 95
96

V Vitrinite, 3
4 Volume of fluid (VOF) model, 292

Index

W Weibull model, 468
469 Wet drum magnetic separator, 49
51 dense media recovery, 51 distribution of feed slurry to magnetic separator, 50
51 feed slurry density, 50 magnetics content of feed particles, 50

Wet high intensity magnetic separator (WHIMS), 66
68, 146, 189, 189f Wet shaking table principle, 186f Wet shaking table with feed, 186f

Z Zircon, 172, 213

529