Solid/Liquid Separation: Equipment Selection and Process Design [1 ed.] 1856174212, 9781856174213

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Solid/Liquid Separation: Equipment Selection and Process Design

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Solid/Liquid Separation: Equipment Selection and Process Design E. S. Tarleton Senior Lecturer, Department of Chemical Engineering, Loughborough University, UK

R. J. Wakeman Professor, Department of Chemical Engineering, Loughborough University, UK Consultant Chemical Engineer

AMSTERDAM • BOSTON • HEIDELBERG • LONDON • NEW YORK • OXFORD PARIS • SAN DIEGO • SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO BUTTERWORTH-HEINEMANN IS AN IMPRINT OF ELSEVIER

Butterworth-Heinemann is an imprint of Elsevier Linacre House, Jordan hill, Oxford, OX2 8DP 30 Corporate Drive, Suite 400, Burlington, MA 01803 First edition 2007 Copyright © 2007 Elsevier Ltd. All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: [email protected]. Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material Notice No responsibility is assumed by the publisher 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. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN–13: 978-1-85-617421-3 ISBN–10: 1-85-617421-2

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07 08 09 10 11 10 9 8 7 6 5 4 3 2 1

Contents

Preface

xii

1

1 2 3 5 5 6 6 7 10 10 11 11 11 12 13 14 16 17 19 20 23 24 24 25 26 26 28

Solid/liquid separation equipment 1.1 Gravity thickeners and clarifiers 1.1.1 Circular basin thickener 1.1.2 High capacity thickeners 1.1.2.1 Circular 1.1.2.2 Deep cone 1.1.2.3 Lamella 1.1.3 Clarifiers 1.2 Hydrocyclones 1.2.1 Conical reverse flow 1.2.2 Circulating bed 1.3 Centrifuges 1.3.1 Sedimenting centrifuges 1.3.1.1 Tubular bowl 1.3.1.2 Basket 1.3.1.3 Disc stack 1.3.1.4 Scroll decanter 1.3.2 Filtering centrifuges 1.3.2.1 Basket 1.3.2.2 Cone screen 1.3.2.3 Pusher 1.3.2.4 Baffle 1.3.2.5 Inverting bag centrifuge 1.4 Filters 1.4.1 Vacuum filters 1.4.1.1 Single leaf 1.4.1.2 Multi-element leaf

vi Contents

1.5

1.6

1.7

1.8

1.9

1.4.1.3 Horizontal belt 1.4.1.4 Horizontal rotary 1.4.1.5 Rotary drum 1.4.1.6 Rotary disc 1.4.2 Pressure filters and presses 1.4.2.1 Single leaf 1.4.2.2 Multi-element leaf or candle 1.4.2.3 Filter presses 1.4.2.4 Sheet filter 1.4.2.5 Variable volume filters and presses 1.4.2.6 Continuous pressure filters 1.4.2.7 Cartridge filter 1.4.2.8 Bag filter 1.4.3 Precoat filters 1.4.3.1 Precoat rotary drum 1.4.3.2 Precoat pressure 1.4.4 Depth filters 1.4.4.1 Sand bed 1.4.4.2 Fibre bed Classifiers 1.5.1 Hydraulic 1.5.2 Mechanical 1.5.3 Screen Membrane filters 1.6.1 Dead-end 1.6.2 Low shear crossflow 1.6.2.1 Ultrafilters 1.6.2.2 Microfilters 1.6.3 High shear crossflow Other equipment 1.7.1 Flotation 1.7.2 Strainer 1.7.3 Gravity Nutsche filters 1.7.4 Gravity belt filter Force field assisted separations 1.8.1 Magnetic field 1.8.2 High voltage electric field 1.8.3 Low voltage electric field 1.8.4 Ultrasonic field Conclusions

29 31 33 35 37 37 38 40 43 43 49 51 53 54 54 55 55 56 56 58 58 59 60 61 61 63 64 66 67 69 69 70 71 72 73 73 74 75 77 77

Contents vii 2

Filter media 2.1 Properties of filter media 2.2 Textile media 2.2.1 Woven fabrics 2.2.1.1 Yarn types 2.2.1.2 Fabric constructions and properties 2.2.1.3 Fabric finishing processes 2.2.2 Composite media 2.2.2.1 Surface coated fabrics 2.2.2.2 Laminated fabrics 2.2.2.3 Double layer weaves 2.2.3 Needlefelts and other nonwoven media 2.2.4 Selection and applications of filter cloths 2.2.5 Damage to filter media 2.3 Filter papers and sheets 2.3.1 Filter papers 2.3.1.1 Industrial papers 2.3.1.2 Laboratory papers 2.3.2 Filter sheets 2.4 Membranes 2.5 Screens and meshes 2.5.1 Wire cloths 2.5.2 Perforated sheets 2.5.3 Wedge wire screens 2.6 Porous sheets and tubes 2.7 Cartridges 2.8 Precoats and body aids (filter aids) 2.9 Conclusions

78 80 84 84 85 86 94 95 95 96 97 98 101 102 109 109 110 110 110 111 112 113 114 115 117 118 120 125

3

Pretreatment of suspensions 3.1 Basic concepts 3.2 Coagulation principles and mechanisms 3.2.1 Mechanical agitation 3.2.2 Indifferent electrolytes 3.2.3 Multivalent metal ions (inorganic coagulants) 3.2.4 Lower molecular weight polymers (organic coagulants) 3.3 Flocculation principles and mechanisms 3.3.1 Forms of flocculation and polymer adsorption 3.3.2 Lower molecular weight polymers (charge neutralisation) 3.3.3 Higher molecular weight polymers (bridging flocculation)

126 126 130 130 130 132 134 134 135 137 139

viii Contents 3.4

3.5

3.6

3.7 4

Types of pretreatment chemicals 3.4.1 Coagulants 3.4.2 Flocculants Effectiveness and selection of chemical pretreatments 3.5.1 Jar settling test 3.5.2 Filter test 3.5.3 Capillary suction test 3.5.4 Coagulant and flocculant selection Other methods of pretreatment 3.6.1 Suspension heating 3.6.2 Suspension freezing 3.6.3 Particle/crystal formation 3.6.4 Elutriation and suspension thickening 3.6.5 Ultrasonics 3.6.6 Irradiation 3.6.7 Addition of solvents/surfactants 3.6.8 Addition of filter aid Conclusions

Data acquisition, analysis and scale-up 4.1 Filtration (cake formation) 4.1.1 Test procedures 4.1.2 General filtration equation 4.1.3 Evaluation of terms in the general filtration equation 4.1.4 Evaluation of filter cake properties 4.1.5 Example 4.1 4.2 Gas deliquoring 4.2.1 Test procedure 4.2.2 Data analysis procedure 4.2.3 Example 4.2 4.3 Cake washing 4.3.1 Test procedure 4.3.2 Data analysis procedure 4.3.3 Example 4.3 4.4 Jar sedimentation 4.4.1 Test procedure 4.4.2 Data analysis procedure 4.4.3 Example 4.4 4.5 Expression (cake formation/consolidation) 4.5.1 General test procedure 4.5.2 Data manipulation

141 141 142 144 144 145 145 146 147 147 148 148 148 149 150 150 151 151 152 152 152 155 157 158 161 164 164 165 166 168 169 170 172 174 175 176 177 178 178 180

Contents ix 4.5.3 4.5.4 4.5.5 4.5.6

4.6 4.7 4.8 5

6

Filtration phase analysis Consolidation phase analysis Example 4.5 Estimates of the transition point and consolidation index State-of-the-art apparatus Evaluation of scale-up coefficients 4.7.1 Example 4.6 Conclusions

Selection, data analysis and simulation by computer software 5.1 Equipment selection 5.1.1 Methods of equipment selection 5.1.2 Recommended selection procedure 5.1.2.1 Specification of duty 5.1.2.2 Specification of sedimentation performance 5.1.2.3 Specification of filtration performance 5.1.2.4 Tables of equipment and letter codings 5.2 Implementation of computer software 5.3 Descriptions of FDS 5.3.1 Equipment selection module 5.3.2 Data analysis module 5.3.3 Equipment simulation modules 5.4 Examples of FDS use 5.4.1 Example 5.1: Basic selection and data analysis procedures 5.4.2 Example 5.2: Advanced selection procedure 5.5 Shortlisting equipment for pilot scale testing and/or simulation 5.6 Conclusions Process design for batch separations 6.1 Batch filter cycle configurations 6.1.1 Nutsche filters 6.1.2 Multi-element vacuum filter 6.1.3 Multi-element leaf and candle pressure filters 6.1.4 Horizontal diaphragm, plate and frame, and recessed plate presses 6.1.5 Vertical diaphragm presses 6.1.6 Tube press

182 183 184 189 192 196 198 199

201 201 202 205 206 206 207 209 220 226 228 230 234 239 240 242 246 254 256 257 257 257 257 260 261 261

x Contents 6.2

6.3 6.4

6.5

6.6 7

Design equations for batch filter cycles 6.2.1 Filtration (cake formation) phase 6.2.1.1 Nutsche and multi-element vacuum filters 6.2.1.2 Filter and diaphragm presses and multi-element leaf pressure filters 6.2.1.3 Tube press 6.2.1.4 Multi-element candle filter 6.2.2 Compression deliquoring 6.2.3 Displacement washing 6.2.4 Gas deliquoring 6.2.5 Optimisation of filtration time for batch filters Design equations for centrifugal filter cycles Examples of batch filter cycle calculations 6.4.1 Example 6.1: Horizontal diaphragm filter press 6.4.1.1 Cake formation (filtration) phases 6.4.1.2 Consolidation (compression deliquoring) phase 6.4.1.3 Washing phase 6.4.1.4 Gas deliquoring phase 6.4.1.5 Summary of results and filter cycle illustrations 6.4.2 Example 6.2: Nutsche filter 6.4.2.1 Cake formation (filtration) phase 6.4.2.2 Washing phase 6.4.2.3 Gas deliquoring phase 6.4.2.4 Summary of results and process implications Example of computer simulation – diaphragm filter press 6.5.1 Fixed mass of solids 6.5.2 Fixed filter area Conclusions

Process design for continuous separations 7.1 Continuous filter cycle configurations 7.1.1 Horizontal belt filter 7.1.2 Rotary drum filter 7.1.3 Rotary table and tilting pan filters 7.1.4 Rotary disc filter 7.2 Design equations for continuous filter cycles 7.2.1 Filtration (cake formation) phase 7.2.2 Displacement washing 7.2.3 Gas deliquoring

264 265 266 268 271 272 273 276 280 285 286 288 288 289 295 298 302 306 306 309 312 315 318 320 320 325 328 329 330 330 331 332 333 334 336 339 341

Contents xi 7.3

7.4

7.5

Examples of continuous filter cycle calculations 7.3.1 Example 7.1: Horizontal belt filter 7.3.1.1 Cake formation (filtration) phase 7.3.1.2 Washing phase 7.3.1.3 Deliquoring phase 7.3.1.4 Summary of results and filter cycle illustrations 7.3.2 Example 7.2: Rotary drum filter 7.3.2.1 Cake formation (filtration) phase 7.3.2.2 Rise phase 7.3.2.3 Washing phase 7.3.2.4 Deliquoring phase 7.3.2.5 Summary of results and filter cycle illustrations Example of computer simulation – belt filter 7.4.1 Effects of belt speed 7.4.2 Effects of applied vacuum 7.4.3 Effects of plant altitude (barometric pressure) 7.4.4 Effects of temperature 7.4.5 Effects of particle size Conclusions

344 344 344 348 351 356 356 359 361 366 370 371 372 373 374 376 376 380 382

Nomenclature

383

Bibliography

391

Appendix A: Variable ranges for filter cycle calculations

410

Appendix B: Correlations for cake washing and gas deliquoring

420

Appendix C: Definitions and conversions for concentration

424

Appendix D: Troubleshooting filter operation

429

Appendix E: Comparisons between experimental data and design equation predictions

434

Index

441

Preface

The purpose of this book is to inform engineers and separations technologists about the available equipment options for solid/liquid separation, to put these into classifications so that informed equipment selections can be made for a particular separations problem, and to present applicable models so that meaningful design and simulation calculations can be carried out. Within this framework, the role of computer software is elucidated and through the use of numerous worked examples the nature and significance of calculations that can be undertaken are shown. Many previous texts have attempted to catalogue the range of equipment used in solid/liquid separation systems, and much of their content is devoted to descriptions of equipment types and their operational characteristics from a wholly empirical and pragmatic point of view. In general these texts do not take advantage of the models available to advance the design process and facilitate simulation, and therefore fail to offer the engineer the cost savings that can be made through simulation. Other texts have dealt with the theory and equations of filtration, sometimes with guiding examples. The link of theory to the design process is not developed in these texts, limiting their usefulness from a practical viewpoint. While a total theoretical description of filtration may not be possible currently, scientifically based data are available for many of the processes that can be modelled. When these models are used in conjunction with the heuristics that have evolved from practice, the results are a powerful set of modelling tools capable of predicting filter performance from a minimum of experimental data. Filtration and separation technology contains numerous heuristics that have evolved through experience. A majority of process engineers need to possess wide-ranging knowledge covering many unit operations, but they rarely have the opportunity to gain in-depth specialist knowledge of filtration and

Preface xiii separation technology. Consequently, the large number of heuristics that have evolved in the technology can lead to confusion for the non-expert. Greater confusion results when an engineer attempts to decide which type of filter or separator is most appropriate for his/her process. In attempting to select a separator a decision has to be made from a plethora of equipment types, with competing claims from manufacturers and suppliers about their equipment capabilities. The focus of this book is design and simulation, linking practical aspects of filter selection, data analysis and design to models that have been proven through industrial practice. The current state of knowledge is used to inter-relate the various stages of the filter cycle (i.e. cake formation, compression, deliquoring and washing) in order to provide the basis for an integrated design strategy. The approach enables an engineer to take into account the effects of upstream operations such as crystallisation or precipitation on the solid/liquid separation in question as well as the effects of the separation on downstream operations such as drying and briquetting. Tried and tested models for each stage of the filter cycle are described and related to the known operational and performance characteristics of equipment, to facilitate process calculations with a minimum of prior testing. The resulting simulations enable “what if?” questions to be answered quickly and at minimal cost, and provide detailed information about a process. The fundamentals that underpin the models are not included in this book, instead the interested reader is directed to the companion volume “Solid/Liquid Separation: Principles of Industrial Filtration, R.J. Wakeman and E.S. Tarleton, 2005 (ISBN 1-85617-419-0)”. For practical aspects of equipment scale-up, including comprehensive descriptions from major manufacturers, the reader is encouraged to consult “Solid/Liquid Separation: Scale-Up of Industrial Equipment, R.J. Wakeman and E.S. Tarleton (Eds.), 2005 (ISBN 1-85617-420-4)”. We are concerned primarily here with the process filter – its selection and design, and calculations for simulation and scale-up. During preparation of the current text a conscious decision was taken to largely limit the contents to cake filtration. However, although most chapters concentrate on cake filtration, it is not possible to give a balanced account of the practical aspects of filtration without some presentation of other separation techniques. To present information to a similar depth about all of these other processes would have made the book encyclopaedic. While there is certainly a technical need for such a book, or series of books, the authors did not set out to include all solid/liquid separation techniques in the current volume. This should not be seen as an attempt to diminish the importance of depth filtration, crossflow filtration or other solid/liquid separation techniques; it is

xiv Preface simply a reflection of a number of the aims behind writing the book. The overall aim is to bring closer together and rationalise both practical information and fundamental knowledge. In so doing, the importance of both must be recognised and the synergy that results from a good understanding used to improve design and simulation. With the practical problems related to equipment selection, scale-up and simulation in mind, the authors have developed and published a Windows® software package to accompany the current text. Filter Design Software® (2005) combines the calculation methods presented throughout the book and relates them to specific aspects of equipment design and performance using expert knowledge of solid/liquid separation systems and computer simulations. The process of obtaining appropriate and useful experimental data, analysing the data in a correct manner, and then using the analysed data for equipment selection, performance simulation and process modelling is brought together in the software. As well as enabling all these functions, the software is intended as a guide to the non-expert, giving information about solid/liquid separation equipment characteristics and features, together with illustrative diagrams and web access to equipment suppliers. Full details are available at www.filtrationsolutions.co.uk In Chapter 1 of the book a comprehensive description of the wide range of available solid/liquid separation equipment is provided. The text is accompanied by numerous schematics and photographs to aid reader understanding and interpretation. Chapters 2 and 3, respectively, present details of filter media and suspension pretreatment in recognition of the crucial role that both play in the successful operation of process scale filters. Chapter 4 describes the experiments and analysis techniques that can be performed in the laboratory to provide additional information for equipment selection as well as the prerequisite information required for simulation. In Chapter 5, an industrially proven equipment selection technique is presented in conjunction with descriptions of the Filter Design Software®. Chapters 6 and 7 form a substantial portion of the book and describe in detail the methodologies that can respectively be used for the process design and simulation of batch and continuous filters. Worked examples are shown throughout to guide the reader and provide more ready access to calculation procedures. The chosen structure makes the text useful as a handbook for both researchers and practitioners, and hopefully underlines the importance of the knowledge that both types of expert may possess. The thorough knowledge required for process design and simulation and further innovation in equipment design are likely to arise only when researchers have a good

Preface xv understanding of the practical problems and practitioners possess a more “in depth” theoretical background to their processes and equipment. Steve Tarleton and Richard Wakeman

Filter Design Software The software is written for use by engineers, consultants and others concerned with solid/liquid separation equipment specification, design and operation, as well as for educational and training purposes. Designed to run on a desktop personal computer, the software offers features including: • • • • • • • •

Analysis offilter leaf test results, jar sedimentation test data, and expression data Calculation of scale up parameters Direct comparison of data from different tests Selection of solid/liquid separation equipment Simulation of vacuum filter equipment (Nutsche, multi-element leaf filters, belt, drum, disc, table, and tilting pan filters) Simulation of pressure filter equipment (Nutsche, multi-element leaf filters, filter presses, diaphragm, and tube filters) Key features of over 70 types of solid/liquid separation equipment Web access to equipment suppliers

www.filtrationsolutions.co.uk

Published in the Butterworth-Heinemann/IChemE Series For further information about the series: books.elsevier.com/icheme IChemE is the hub for chemical, biochemical and process engineering professionals worldwide. With offices in the UK, Australia and Malaysia, the Institution works at the heart of the process community, promoting competence and a commitment to sustainable development, advancing the discipline for the benefit of society and supporting the professional development of members. For further information visit www.icheme.org.

1

Solid/liquid separation equipment

Over the years manufacturers have developed many generic forms of solid/liquid separator. The need to compete in the marketplace and gain a competitive edge, however, has led manufacturers to develop a plethora of variants. Rather than detailing all of these variants, this chapter attempts to give a descriptive overview of the generic equipment types and the main alternatives available to the design engineer (see Figure 1.1). The advantages and disadvantages of equipment are highlighted and an effort has been made to provide quantitative values whenever possible. More guidance values for the operational parameters of filters are shown in Appendix A, while greater details of recent developments in several equipment types are presented in Wakeman and Tarleton (2005b). In addition to the more specific references given throughout this chapter, the interested reader is also referred to the texts by Dickenson (1997), Kirk-Othmer (1980), Matteson and Orr (1987), Perry and Green (1984), Purchas (1981), Purchas and Wakeman (1986), Rushton et al (1996), Svarovsky (1990), Schweitzer (1997) and Wills (1992). General descriptions and typical equipment uses are shown under each main heading in addition to the solids concentration and particle size found in a typical feed. The process ratings used in the Filter Design Software® (FDS) package are described in Chapter 5. The ratings give relative values between 0 and 9 for cake dryness (and state), washing performance, liquid product clarity and crystal breakage, where 9 represents the best performance currently available; a ‘-’ indicates that either a rating is not applicable or the equipment is not capable of performing the operation. For instance, the ‘1 S, 2, 5, 9’ ratings shown for the circular basin thickener in Section 1.1.1 signify a wet solids discharge in the form of a slurry (‘C’ designates a cake and ‘N’ designates that solids are not recoverable), poor washing performance, near average liquid product clarity and minimal breakage of the solid product. Such representation allows potentially suitable equipment to be numerically

2 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 1.1 Broad classification chart showing the forms of solid/liquid separator described in this chapter. ranked. Simulation procedures for many of the filters described are presented in Chapters 6 and 7.

1.1 Gravity thickeners and clarifiers Gravity thickeners and clarifiers represent a class of solid-walled separator, where gravitational forces are used to raise the concentration of a suspension

1 · Solid/liquid separation equipment 3 through sedimentation to produce a thickened sludge with a clear liquid as overflow. The rate of sedimentation should be as high as reasonably possible to both increase throughput and reduce floor area. Sedimentation rates are often artificially increased by the addition of (relatively expensive) coagulants or flocculants. The cross-sectional area plan of a thickener controls the time available for sedimentation and is important in determining clarification capacity. The physical depth of a separator controls sludge thickening time and is an important parameter in determining thickening capacity. Thickeners and clarifiers can be designed to operate in either batch or continuous mode, although most commercial operations utilise the latter. More specific details of design are available in Akers (1974), Dixon (1979), Fitch (1966, 1975), Gough (2005), Hasset (1965), Kos (1974), Kynch (1952), Talmage and Fitch (1955), Wakeman and Tarleton (2005a) and Yoshioka et al (1957). 1.1.1 Circular basin thickener Typical uses: Larger scale thickening and deliquoring of solids from relatively dilute suspension. FDS process ratings: 1 S, -, 5, 9 (settling tank or lagoon); 1 S, 2, 5, 9 (thickener). Typical particle size and feed concentration range: 0.1–500
m and
20% w/w. A circular thickener comprises a relatively shallow, open-top cylindrical tank with either a flat bottom or a bottom shaped in the form of an inverted cone (see Figures 1.2 and 1.3). The feed mixture is gently and continuously introduced to the feedwell in which exists a pool of settling suspension along with any additional coagulant or flocculant. With settling and thickening proceeding, clear liquid (the overflow) is removed via an annular weir at the

Figure 1.2 Circular basin thickener showing rakes, drive head and walkway.

4 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 1.3 Photograph of a basin thickener installation (Dorr-Oliver Eimco). top of the unit and solids sludge (the underflow) is removed from a ‘well’ at the bottom. Slowly rotating arms (or rakes) mounted on a central drive head aid the thickening process by directing thickened solids towards the well for subsequent discharge, and by creating channels for release of further liquid from the sludge. The construction and form of the rake are important design parameters as is the rating of the motor in the central drive head which must be capable of moving the rake through the thickened solids both during normal operation and during start-up of the rake after a stoppage. Tanks with a diameter smaller than 25 m are usually formed from steel and have flat bottoms with rake arms at an angle less than 10º. Larger tanks between 25 and 200 m diameter are normally made from a combination of concrete and steel and employ rakes designed to match the angle of the conical bottom. Circular thickeners are frequently constructed to large scales and can be used to raise suspension concentration prior to another solid/liquid separation process. Continuous discharge of solids from a gravity settling tank can be achieved without mechanical aid if the tank is shaped so that the sludge flows naturally towards the discharge port. This requires relatively steep-sided conical vessels; the angle of the cone is generally between about 40º and 60º, and thus the diameter of a settling tank is invariably rather less than a thickener. A diaphragm baffle is located near the base to prevent arching of solids across the outlet port. Particularly large volumes of slowly settling slurries (which are also of low value) may be thickened in lagoons if land is not at a premium. Lagoons usually need to be lined to prevent seepage and are rarely an environmentally

1 · Solid/liquid separation equipment 5 friendly option. They are not usually a preferred technique for thickening suspensions. 1.1.2 High capacity thickeners Typical uses: Separation of rapid settling solids where available space is at a premium. High capacity thickeners work on a broadly similar principle to conventional thickeners. By the correct use of high molecular weight, fast-acting flocculants, however, large flocs that sediment very quickly can be generated to allow thickeners with high solids handling capacities and relatively small floor areas to be produced. Although high capacity thickeners have found many uses, particularly when significant amounts of fines are present, they do not represent a replacement for conventional thickeners as flocculant usage is notably higher and thus more costly. 1.1.2.1 Circular FDS process ratings: 1 S, -, 5, 9. Typical particle size and feed concentration range: 0.1–300
m and
15% w/w. The circular class of high capacity thickener is similar in general form to a conventional circular basin thickener, but cylinder diameters are limited to between 4 and 18 m (see Figure 1.4). Units are constructed from steel and include a cylindrical top portion, an inverted cone bottom section and an angled rake system mounted on a central drive head. Suspension throughputs are limited to about 4000 m3 h1.

Figure 1.4 Sectional view of the circular high rate thickener.

6 Solid/Liquid Separation: Equipment Selection and Process Design 1.1.2.2 Deep cone FDS process ratings: 1 S, -, 5, 9. Typical particle size and feed concentration range: 0.1–300
m and
15% w/w. The deep cone thickener shown in Figure 1.5 is again broadly similar in form to a conventional thickener, but the sides of the inverted cone have a much steeper angle, in the region of 37º. Units are available with diameters up to 15 m to process suspensions at throughputs as high as 70 m3 h1. A paddle/rake system rotating at speeds between 0.25 and 2 rpm is usually added to aid the thickening process and facilitate final sludge concentrations up to 70% w/w. Although deep cone thickeners are relatively cheap to install and occupy a small floor area, their operating costs can be higher. The flocculants required to promote efficient settling and operation are generally expensive, and high power inputs may be needed to maintain the stirring action of the paddle through pastes that are characteristic of the high viscosity underflows.

Figure 1.5 Schematic representation of a deep cone thickener and inset photograph (DorrOliver Eimco).

1.1.2.3 Lamella FDS process ratings: 1 S, -, 5, 8. Typical particle size and feed concentration range: 1–150
m and
15% w/w.

1 · Solid/liquid separation equipment 7 The lamella separator is characterised by an essentially rectangular tank containing a series of closely spaced rectangular plates inclined at an angle of about 50º to the horizontal (see Figure 1.6). The plates, which effectively increase the available settling area, allow the sedimenting solids from the feed to slide down their upper surfaces towards a sludge hopper. The clarified liquid overflow is removed from a suitable opening near to the top of the tank. Commercial designs exist for three basic flow arrangements, namely, crosscurrent, co-current and the most popular countercurrent, where the feed and clarified liquid flows can be most simply arranged. With plate spacings in the region of 50 mm, lamella separators offer a compact design, which may be up to 90% smaller than an equivalent conventional settling tank. However, maldistribution and solids re-entrainment problems can sometimes limit their effectiveness, a problem which also occurs in an alternative design incorporating inclined tubes rather than plates.

Figure 1.6 The operating principle of a Lamella separator. 1.1.3 Clarifiers Typical uses: Recovery of clear liquor from dilute suspension. FDS process ratings: 1 S, -, 6, 9.

8 Solid/Liquid Separation: Equipment Selection and Process Design Typical particle size and feed concentration range: 1–50
m and
15% w/w. The primary duty of a clarifier is to remove relatively small amounts of solid from more dilute suspension to yield a clarified liquid overflow and a generally unwanted solids sludge underflow. Although many variants exist, the basic single-pass unit shown schematically in Figure 1.7 is divided into a stirred flocculation/coagulation section and a rectangular settlement basin. During normal continuous operation the feed moves in a horizontal direction through the flocculator towards the settlement basin at throughputs of 1.5–3 m3 h1. While in the basin the solids undergo almost unhindered settling to the bottom of the basin and clarified liquid is discharged over a weir. Single-pass units can also be operated intermittently with little degradation in product quality.

Figure 1.7 Schematic of a single-pass rectangular basin clarifier. The size of the settlement basin is sometimes reduced by employing a series of internally mounted plates inclined at about 60º to the horizontal. In a similar manner to the lamella separator (see Section 1.1.2.3), the effective settling area is increased to allow sedimenting solids to slide down the plates and into the collecting well. Other variants include the vertical flow clarifier, the blanket clarifier and the circular clarifier; the latter is similar in form to a conventional circular thickener but of a much lighter construction. To accelerate flocculation and help the removal of excessive fines, recirculation of some sedimented solids to the incoming feed is sometimes used. The recirculation may be either internal or external to the clarifier and often results in higher throughputs, albeit at the expense of greater mechanical complexity. By way of example, internal recirculation is used in the Eimco E-Cat™ high-rate clarifier, which has a typical diameter between 4 and 12 m (see Figure 1.8). While the external form is similar to the deep cone

1 · Solid/liquid separation equipment 9

Figure 1.8 Schematic of an E-Cat high-rate clarifier (sometimes referred to as a thickener clarifier) showing the internal circulation of liquors. Inset photograph with permission from Dorr-Oliver Eimco.

thickener, the internals are modified by the addition of a centrally mounted sequence of dewatering cones as well as a series of relatively small diameter clarifier tubes mounted around the internal periphery of the upper portion of the clarifier. The rake system commonly found in other thickeners and clarifiers is unnecessary. During normal operation, feed is introduced into the feedwell at the top of the unit where it is automatically diluted to aid the initial solids settling rate. Fast-acting flocculant is dosed into the feedwell and into the rising dilution liquor as required. The diluted feed flows past the dewatering cones which act in a similar manner to the plates found in lamella separators (see Section 1.1.2.3). Some of the liquid is removed for the dilution of subsequent feed and solids settled onto the cone surfaces move downwards towards the bottom of the unit. Compaction of the sludge takes place here and the 60º cone angle facilitates removal of the underflow without the aid of rakes. All liquid that is not removed with the underflow leaves the unit as overflow through the clarifying cylinders which polish the effluent by promoting flocculation. The potential benefits of clarifiers that incorporate recirculation are offset by the short residence time of liquid and the strictly limited solids storage capacity. Both of these require a unit to be carefully controlled in order to prevent an overload due to an excess of incoming material.

10 Solid/Liquid Separation: Equipment Selection and Process Design

1.2 Hydrocyclones Typical uses: Suspension thickening, clarification and particle classification. Cyclones designed for use with liquids are referred to as hydrocyclones, hydraulic cyclones or hydroclones. The basic principle employed to effect either concentration or classification of the solids is centrifugal sedimentation, caused by introducing the feed suspension tangentially into the unit; they are particularly attractive for many applications because they have no moving parts. Specific aspects of design are provided by Svarovsky (1984). 1.2.1 Conical reverse flow FDS process ratings: 1 S, 2, 4, 7. Typical particle size and feed concentration range: 5–200
m and 2– 40% w/w. The reverse-flow hydrocyclone shown in Figure 1.9 is a relatively cheap, compact and versatile device. The basic unit has no moving parts and comprises an inverted conical bottom section attached to a cylinder containing a tangential inlet port. Feed is injected through the port at a mean velocity between 10 and 30 m s1 whence geometry-induced motion causes the (usually denser) suspended particles to experience centrifugal forces of between

Figure 1.9 Cross-section through a reverse-flow hydrocyclone showing the typical flow patterns. The inset photograph (Axsia-Mozley) shows a bank of six cyclones connected to a common feed manifold system.

1 · Solid/liquid separation equipment 11 70g and 18000g. The combination of these forces and a swirling motion causes the coarser particles to exit as a suspension in the underflow stream at the bottom of the hydrocyclone and the finer fractions to leave through the cylindrical vortex finder at the top. With short residence times the particles and liquid move at relatively high speeds and abrasion/particle breakage can sometimes be a problem, which necessitates the use of hard internal linings. Many standard sizes of hydrocyclone are available with cylinder diameters of 1–30 cm and cone angles of 25º–50º. The particle cut size, which is the size equally likely to find its way into the underflow or overflow, is limited to about 5
m and dependent on several factors including the size and geometry of the hydrocyclone, the inlet flow rate and the pressure drop across the unit. Separation is often more effective (in terms of a lower cut size) with a series of smaller diameter hydrocyclones as higher tangential velocities can be achieved. 1.2.2 Circulating bed FDS process ratings: 1 S, -, 4, 7. Typical particle size and feed concentration range: 2–500
m and 2–25% w/w. The circulating bed (or full length cylindrical) hydrocyclone is similar in general form to the more widely used conical reverse-flow hydrocyclone. However, a cone angle in the range 120 –180º is employed. The nearly flat bottom acts as a baffle ring to help keep the rotating bed of particles moving. Frictional forces induce a vertical convection stream to facilitate the separation of particulates. The circulating bed hydrocyclone is claimed to give a sharper cutoff as well as a reduced cut size when operated correctly.

1.3 Centrifuges Centrifuges are designed to either thicken or filter suspensions, which leads to two general classes of machine: sedimenting centrifuges and filtering centrifuges. Additional aspects of their operation (and modelling) are presented in Alt (1985), Ambler (1988), Burak and Storrow (1950), Chan et al (2003), Fan et al (1991, 1992), Grimwood (2005), Hallit (1975), Leung (1998, 2005), Records and Sutherland (2001), Rushton (1981), Smiles (1999), Stahl (2005), Valleroy and Maloney (1960), Wakeman (1994), Wakeman and Fan (1991) and Wakeman and Mulhaupt (1985). 1.3.1 Sedimenting centrifuges Sedimenting centrifuges employ centrifugal forces to accelerate the settling of particles (or liquid droplets) within rotating, solid-walled equipment.

12 Solid/Liquid Separation: Equipment Selection and Process Design With no filtration occurring, a density difference must exist between the phases present in the feed mixture, and the denser phase preferentially settles to the wall where it is removed in a concentrated form. The clarified phase is also discharged, often at the opposite end to the feed position. Both batch and continuous types are available and typical duties range from the clarification of dilute suspensions to the thickening of fast settling slurries. When fast-acting flocculants are used to aid separation, the shear resistance of flocs can be an important limiting factor as centrifugal forces can be high depending on the type of machine employed. Some basic characteristics of sedimenting centrifuges are shown in Table 1.1; the g-factor, defined by r
2/g, where r is the radius of the bowl rotating with an angular velocity
and g is the acceleration due to gravity, is often used as a measure of the separating power of a machine. It is simply the ratio of the maximum centrifugal force exerted on a particle in the suspension to the gravitational force exerted on a particle of the same mass. Table 1.1 Some basic characteristics of sedimenting centrifuges. Centrifuge type Tubular bowl Basket Disk stack Scroll decanter

Centrifugal force (g)

Rotational speed (rpm)

Throughput (m3 h1)

Cake condition

14000–65000 Up to 1600 Up to 14000

50000 (max) 450–3500 3000–10000

4 (max) 6–10 200 (max)

2000–6000

1600–6000


100

Pasty, firm Firm Pasty, flowable ; firm Pasty, granular

1.3.1.1 Tubular bowl Typical uses: Batch clarification and (occasionally) particle classification. FDS process ratings: 3 S, -, 6, 5. Typical particle size and feed concentration range: 0.1–100
m and
5% w/w. The tubular bowl centrifuge shown in Figure 1.10 is usually regarded as the most efficient of the industrial sedimenting centrifuges with separating forces in the range 14000g – 65000g. The long and narrow circular bowl, which typically has a diameter of between 5 and 15 cm and an aspect ratio between 4:1 and 8:1, is vertically mounted and rotates at up to 50000 rpm. The relatively dilute feed suspension is injected at the bottom of the bowl via a distributor and centrate overflows from the top. The normally denser solids accumulate at the wall of the bowl from where they are manually discharged at the end of a batch

1 · Solid/liquid separation equipment 13

Figure 1.10 Operating principle and general form of the tubular bowl centrifuge.

cycle; the discharge process is sometimes aided by the inclusion of paper liners. Due to the narrowness of the bowl the efficiency of separation is significantly influenced by solids accumulation at the wall and throughputs are restricted to ~6 m3 h1 with dry solid yields of up to 4 kg per batch. To achieve near-continuous operation two or more units are used in parallel. 1.3.1.2 Basket Typical uses: Recovery and concentration of solid sludges. FDS process ratings: 2 S, -, 5, 5. Typical particle size and feed concentration range: 0.1–100
m and
5% w/w. The basket bowl centrifuge shown in Figure 1.11 works on similar principles to the tubular bowl centrifuge (see Section 1.3.1.1). Semi-continuous operation is achieved, however, by using a bowl diameter between 25 and 150 cm and a much lower aspect ratio of about 0.6:1. The solids accumulate on the wall of the imperforate bowl and liquid overflows via a weir at the top. Cake discharge is performed manually on small machines with the bowl stationary. With larger machines, the supernatant liquid remaining in the bowl is siphoned off using a

14 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 1.11 Operating principle and general form of the basket sedimenting centrifuge.

skimmer pipe and the solids on the wall are removed automatically with a plough, sometimes at a reduced bowl speed. Basket bowl centrifuges operate at rotational speeds of 450 –3500 rpm to allow throughputs in the region 6 –10 m3 h1. The use of relatively low gforces (
1600g) has led to the development of multi-bowl basket centrifuges which comprise a series of concentric bowls mounted on a common vertical shaft. During rotation the feed moves progressively from the inner to the outer bowl with ever finer particles being removed each time. Multibowl basket centrifuges offer greater efficiency for a given speed of rotation with the disadvantages of increased capital and operating costs. 1.3.1.3 Disc stack Typical uses: Clarification and thickening to produce a solids sludge. FDS process ratings: 2 S, -, -, 6. Typical particle size and feed concentration range: 0.1–100
m and 0.05–2% w/w (self-cleaning and manual discharge), 0.5–10% w/w (nozzle discharge). The disc stack centrifuge is a versatile device, which may be used for separating solid/liquid mixtures in continuous, semi-continuous and batch configurations (see Figures 1.12 and 1.13). All except some batch-operated machines are able to handle toxic, flammable and volatile feeds at throughputs up to 200 m3 h1.

1 · Solid/liquid separation equipment 15

Figure 1.12 Schematic representation of a nozzle discharge disc stack sedimenting centrifuge.

Figure 1.13 Photograph (left) of an ejecting, self-cleaning, disc stack centrifuge showing an external view of the disc bowl and accompanying motor drive. Also shown (right) is a typical disc stack arrangement. Both photographs with permission from Alfa Laval.

Liquid–liquid mixtures can be separated and with more sophisticated units a three (two liquid and one solid) phase separation is achievable. In all cases, a sufficient density difference must exist between the phases present in the feed.

16 Solid/Liquid Separation: Equipment Selection and Process Design Although several variants exist, the generic type is characterised by an imperforate bowl surrounding an inverted stack of 30–200 thin conical discs separated by 0.3–3 mm spacers. The disc spacing is dependent on the viscosity and solids content in the feed and needs to be fixed accordingly, lower viscosities and solids concentrations favour spacings below 1 mm. As the discs are spun on a common vertical axis the process suspension, which is fed centrally from the top, travels through the annular spaces between the discs. Centrifugal forces up to 14000g cause particles to accumulate on the underside of the discs from where they slide down towards the outer periphery of the centrifuge bowl. In batch units the thickened solids remain in the bowl until the solids handling capacity of the centrifuge is reached. At this point rotation stops and the basket containing the trapped solids is manually replaced or a discharge valve on the periphery of the bowl is manually operated to facilitate removal of the sediment. In continuous units the solids sludge, which must be flowable, is automatically discharged, sometimes intermittently, through nozzles positioned on the outer periphery of the bowl; a typical centrifuge has between 12 and 24 nozzles. For cakes that exhibit poor flow characteristics, the ‘self-ejecting’ design variant allows the bottom part of the centrifuge to automatically separate at periodic intervals and discharge the accumulated solids. While disc stack centrifuges are able to accept a wide range of feeds they are both mechanically complex and expensive. Moreover, the close stacking of conical discs means that mechanical cleaning can be difficult, and resort is often made to chemical cleaning. 1.3.1.4 Scroll decanter Typical uses: Relatively coarse deliquoring and clarification of suspensions. FDS process ratings: 4 C, 3, 4, 3. Typical particle size and feed concentration range: 1–5000
m and 4–40% w/w. The scroll decanter centrifuge is a horizontally or vertically mounted machine which is best suited to the processing of free-draining solids from higher concentration feeds (see Figure 1.14). In extreme cases throughputs of solids can be as large as 90 te h1, while liquid throughputs are normally less than 60 m3 h1. In a typical unit a 10 to 200 cm diameter cylindrical bowl with a tapered, conical end is caused to rotate at speeds between 1600 and 6000 rpm. Inside the bowl a helical screw rotates at a differential speed of up to 100 rpm. The feed enters through the central axis of the centrifuge where inertial forces of less than 6000g cause the denser solids to move towards the imperforate wall of the bowl. The solids are conveyed co-currently

1 · Solid/liquid separation equipment 17

Figure 1.14 Schematic diagram of a horizontal axis scroll decanter centrifuge. The motor drive for the bowl and the gearbox required to produce the differential rotation speed between the bowl and screw conveyor are omitted for clarity.

along the walls of the bowl by the helical screw and moved through the narrower conical end of the centrifuge to discharge. The liquid phase, which may not always be clear due to the presence of fines, leaves the centrifuge via a weir or ports at the broader end of the bowl. In the alternative screen bowl design the conical section of the bowl is shortened and a supplementary cylindrical section is attached in an effort to promote more efficient separation. Other design variants rely on the addition of baffles, helical discs, vanes, conical disc stacks or fins, all of which alter the flow and/or residence time distributions within the centrifuge. Figure 1.15 shows an example of a decanter centrifuge fitted with a vane stack. When finer particles are being processed the flow properties of the thickened solids can be poor and this leads to high helical screw torques and associated mechanical difficulties. Wear problems on the screw can also be caused by more abrasive particles. Scroll decanters can be adapted for use with toxic, flammable and volatile substances and there is some scope to perform (relatively poor) washing. 1.3.2 Filtering centrifuges Filtering centrifuges use centrifugal forces to perform batch and continuous cake filtration on either cylindrical or conical semi-permeable surfaces. Displacement washing operations can be accommodated by most centrifuges in addition to efficient cake deliquoring. Several machines are capable of operating in both vertical and horizontal orientations, while some rely on the favourable sliding and conveying properties of the formed cake for successful operation. The basic characteristics of filtering centrifuges are shown in Table 1.2.

18 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 1.15 Photograph of a vane decanter centrifuge (Mitsubishi Kakoki Kaisha). The motor drive and gearbox are visible at the right hand end of the unit. Additional discs, the vane stack, are included in the cylindrical portion of the bowl to provide larger areas for separation and enhanced capacity.

Table 1.2 Some basic characteristics of filtering centrifuges. Centrifuge type

Centrifugal force (g)

Max. throughput (te h1)

Cake condition

Basket: Peeler Pendulum Pusher Baffle Inverting bag

800–2200 200–1200 800–1700 1200 max. Up to 1500

15 (of solids) 12 (of solids) 5–80 (of solids)

Dry ; pasty, granular Dry ; pasty, granular Dry, granular Dry, granular Dry, granular

Cone screen: Slip discharge Vibratory/oscillatory Tumbling Worm screen

Up to 2900* 30–150 50–300 500–2600


150 350 120
150

*At the lip (i.e. maximum diameter) of the cone.

Dry, granular Dry, granular Dry, granular Dry, granular

1 · Solid/liquid separation equipment 19 1.3.2.1 Basket Typical uses: Deliquoring of suspensions with reasonable drainage characteristics. FDS process ratings: 9 C, 6, 5, 6 (pendulum); 9 C, 6, 5, 5 (peeler). Typical particle size and feed concentration range: 10 –1000
m (pendulum), 2–1000
m (peeler) and 4 –30% w/w. These centrifuges are essentially batch operated and comprise a vertically or horizontally mounted basket with one closed end and one partially open end. The basket, which is perforated and covered by a combination of metal screen(s) and filter cloth, is rotated to give solids throughputs up to 15 te h1. The induced centrifugal forces allow centrate to pass through the cloth while particles accumulate in the form of a filter cake. The cake may subsequently be washed by sprays and/or allowed to deliquor prior to discharge. Variants of the basket centrifuge differ primarily in the process limitations imposed by the axis of rotation (see Figures 1.16 and 1.17).

Figure 1.16 The general form of a horizontal axis peeler centrifuge fitted with a screw conveyor discharge. An alternative design employs a simple chute for cake discharge.

Vertical axis: The vertical axis basket centrifuge, which is also known as the three-column or pendulum centrifuge, allows the feed suspension to be introduced when the basket is either stationary or rotating at a moderate speed. The rotational speed is often varied through a cycle with cake washing and deliquoring being performed at high speed (~1500 rpm) and cake discharge at a lower

20 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 1.17 Photographs of a siphon peeler centrifuge (left), with permission from Mitsubishi Kakoki Kaisha (under license from Krauss-Maffei), and a vertical basket centrifuge (right) with permission from Mitsubishi Kakoki Kaisha. speed (~60 rpm). On bottom driven machines the basket is usually lifted out manually to allow for cake discharge. The generally more expensive top driven machines are employed for heavier duties and faster filtering feeds. These units are discharged automatically by plough or with the assistance of a gas jet and/or compressed gas blowback when a residual heel of cake is unacceptable. For cakes that are inherently hard a partial length plough that moves up and down the axis of the basket can be used to advantage. Due to uneven cake formation, washing performance can be variable. Horizontal axis: The fully automated horizontal axis basket centrifuge, which is also known as the peeler centrifuge, operates for most of its cycle at constant rotational speed to give separation forces over 2000g in some instances. The operating cycle is generally shorter than for vertical axis machines and, with less time lost for acceleration and deceleration, higher throughputs can be achieved. Solids are discharged at moderate speed at the end of the cycle by a rigidly constructed peeler, sometimes with the aid of a compressed gas jet, or reciprocating knife. The relatively high speed discharge can induce glazing of the cake heel and hence low permeability (and reduced centrate flow rates) in subsequent cycles. Moreover, horizontal axis peeler centrifuges tend to be more expensive than equivalent capacity vertical axis machines. 1.3.2.2 Cone screen Typical uses: Continuous deliquoring of suspensions containing relatively free filtering solids.

1 · Solid/liquid separation equipment 21 FDS process ratings: 7 C, 5, 4, 4 (slip discharge); 8 C, 5, 4, 3 (vibratory, oscillatory or tumbling); 9 C, 5, 4, 4 (worm screen). Typical particle size and feed concentration range: 80 –10000
m (slip discharge), 100–10000
m (vibratory, oscillatory or tumbling), 60–5000
m (worm screen) and 10–40% w/w. The cone screen centrifuges shown schematically in Figure 1.18 all comprise a conical perforated metal screen across which wet solids slide after filtration from relatively high concentration suspension. During their passage, the solids, in the form of a cake, can be washed by sprays and/or deliquored prior to discharge at the wider end of the cone. The four variants of cone

Figure 1.18 Schematic representations of cone screen centrifuges. (a) slip discharge/wide angle cone; (b) vibratory/oscillatory; (c) tumbling; (d) single stage worm screen.

22 Solid/Liquid Separation: Equipment Selection and Process Design screen centrifuge differ primarily in the manner in which the solids are caused to translate along the screen: Slip discharge/Wide angle cone: In these vertical or horizontal axis machines the cake is caused to move by providing a cone with a half-vertex angle in excess of the angle of friction between the cake and the screen. The cone angle is critical for good operation and is typically in the range 25–35º, though the lubrication provided by the liquid in the cake can greatly assist the sliding operation particularly towards the start of the translation process. While good deliquoring is generally achieved with centrifugal forces up to 2900g, the rapid transit of solids through the centrifuge means there is a limited time available for washing on the angled surfaces of the cone. Slip discharge centrifuges are best suited to the processing of fairly coarse, fast filtering, granular solids. Vibratory/Oscillatory: These centrifuges work on a similar principle to the slip discharge centrifuge, however, the addition of an eccentric vibratory drive facilitates use of a cone angle lower than the angle of friction between the cake and the screen. Cone angles of 13–18º are common and vibrations in the region of 1700 min1 induce partial fluidisation of the cake which enhance its translation across the screen to give very high throughputs up to 350 te h1. As relatively low centrifugal forces are generated (typically below 120g), deliquoring and centrate clarity can sometimes be poor and this may in turn lead to lower quality solid and liquid products. Both horizontal and vertical axis machines are available and these are best suited to the processing of relatively coarse, fast filtering solids. Tumbling: A gyratory motion of the screen bowl about a vertical axis causes the inclination of the cone walls to alter about the angle of friction between the cake and the screen. The tumbling of the cone induces intermittent cake movements and throughputs up to 120 te h1. Despite relatively modest centrifugal forces, deliquoring can be very good. However, tumbling centrifuges are usually only employed when washing is not required and coarser, faster filtering solids are present in the feed. Variations of cone angle and the speeds of rotation and gyration dictate the compromise between throughput and the final moisture content of the cake. Worm screen: Also known as the conveyor discharge or screen scroll centrifuge, the worm screen centrifuge causes solids to move along the cone via an internal screw conveyor. The conveyor rotates at a differential speed to the cone screen and centrifugal forces below 2600g facilitate reasonable throughputs. The presence of the conveyor can sometimes lead to both

1 · Solid/liquid separation equipment 23 crystal breakage and abrasion problems as well as relatively poor washing. There is a compromise between throughput and final cake moisture and this is dictated by the conveyor speed, typical cake residence times on the screen lie in the range 4 –15 s. Worm screen centrifuges are available in either vertical or horizontal orientation and are most frequently used for the processing of fibrous solids. More sophisticated versions employ cones with up to four stages that allow cake formation, two periods of displacement washing (with the potential for segregation of the wash liquors) and final deliquoring to take place. 1.3.2.3 Pusher Typical uses: Deliquoring of relatively coarse particulate suspensions where good cake dryness at discharge is required. FDS process ratings: 9 C, 7, 4, 4 (single-stage); 9 C, 8, 4, 4 (multi-stage). Typical particle size and feed concentration range: 40–7000
m and 10– 40% w/w. The horizontal axis pusher centrifuge is probably the most commonly used design employing a continuous feed of suspension. The basic, single-stage, machine comprises a rotating cylindrical screen bowl into which suspension is introduced and filtered to form a cake. A plate positioned at the closed end of the bowl reciprocates with a 20–80 mm stroke at up to 100 strokes min1 to continuously push the forming cake towards the open end of the bowl and discharge. During transition across the screen, the cake may be washed by sprays on the horizontal bowl surfaces and efficiently deliquored as a result of the 500–1700g centrifugal forces generated and 6–20 s cake residence times. In order for the pusher centrifuge to work correctly the formed cake must have sufficient strength to withstand buckling and slide efficiently across the screen. For weaker, more friable cakes, or finer particulate cakes of greater frictional resistance, a single-stage machine may be unsuitable and a multistage unit may need to be substituted (see Figure 1.19). These more expensive machines include a sequence of up to four, relatively short, concentric cylindrical bowls with progressively increasing diameter. The solids are pushed more readily along the shorter bowls by the reciprocating piston and an ability to separate wash liquors allows for improved washing. The transfer between the bowls tends to lead to cake break-up, which can enhance the deliquoring process. As the open end of a rotating bowl does not have a retaining lip, there is a socalled ‘overflow limit’ which generally limits solids throughputs to 80 te h1

24 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 1.19 Schematic diagram of a three-stage pusher centrifuge.

for single-stage machines and ~45 te h1 for multi-stage machines; some manufacturers claim maximum throughputs of 100 te h1. The operation of both single and multi-stage centrifuges with solids below 100
m can be problematical due to blockage of the filtering screen. 1.3.2.4 Baffle Typical uses: Deliquoring coarse particulate (e.g. polymer pellet) suspensions where good cake dryness is required. FDS process ratings: 9 C, 5, 5, 4. Typical particle size and feed concentration range: 100 –7000
m and 10– 40% w/w. The family of baffle centrifuges are representative of specialist continuous filtering centrifuges. Both the baffle ring and screen baffle centrifuge can achieve very low residual moistures in granular type solids by causing particles to bounce against (baffle type) obstructions inside the filtering bowl. This action releases additional surface and occluded liquids from the solids. Although baffle centrifuges are relatively expensive and restricted to operations with certain types of solids such as polymers, their use can prove advantageous when other alternatives are unsuitable. 1.3.2.5 Inverting bag centrifuge Typical uses: Semi-continuous deliquoring of suspensions where complete cake discharge and high purity need to be maintained.

1 · Solid/liquid separation equipment 25 FDS process ratings: 9 C, 6, 5, 6. Typical particle size and feed concentration range: 2–1000
m and 5–30% w/w. The inverting centrifuge, shown schematically in Figure 1.20, operates semicontinuously via automatic control and features a horizontally mounted, cylindrical drum between 0.3 and 1.3 m diameter which restricts filtration area to ~2 m2. Suspension is introduced to the drum through gravity by means of a rigid filling pipe that projects through the solids discharge chute. The amount of material delivered is continuously monitored with a noncontact, load cell system resembling a beam type balance.

Figure 1.20 Schematic diagram of the inverting bag centrifuge. A typical cycle involves initial cake formation, intermediate deliquoring, rinsing/washing followed by final deliquoring. For discharge, a unique mechanism allows the end of the drum to open through a translational movement and the cake solids are removed completely under rotation as the filter bag inverts through the discharge chute. In this way cloth blinding is avoided and the entire cycle can be performed under high purity conditions. To improve deliquoring the pressure in the filling pipe and internal chamber of the drum can be raised, although any process advantages are offset by the increased mechanical complexity.

1.4 Filters Many types of filters are available, which are broadly classified here as vacuum, pressure, precoat and depth filters. Each classification contains a number of sub-classifications. More detailed aspects of their operation (and modelling)

26 Solid/Liquid Separation: Equipment Selection and Process Design are provided in, for instance, Brownell and Gudz (1949), Dahlstrom (1978b), Fitzgibbons (1976), Hermia (1981), Hermia and Brocheton (1993), Ives (1973; 1975), Kelsey (1965), Kobayashi et al (1993), Komline (1980), Kuo and Barrett (1970), Nyström (1993), Rushton (1969; 1978), Rushton and Wakeman (1978), Shirato et al (1986), Stahl and Nicolaou (1990), Tarleton (1998b), Tarleton and Wakeman (1994c), Wakeman (1984a, b), Wakeman et al (1994), Wakeman and Tarleton (1990, 1994a, 1999), Wakeman and Wei (1995) and Yelshin and Tiller (1989). 1.4.1 Vacuum filters A category of filter that uses vacuum induced driving forces and semipermeable media to facilitate the separation of solids from suspension. While pressure differences across the filter are limited to less than 85 kPa (usually
75 kPa), most units are capable of processing a wide range of feed materials in a continuous manner. Many types employ a rotary valve arrangement to set different vacuum levels over sequential phases in a filter cycle thus facilitating more control over cake formation, deliquoring and washing. Several vacuum filters have countercurrent washing capability. Although it is possible to enclose some types to conserve heat and/or vapours the processing of more volatile constituents at higher altitudes can cause significant problems. Woven filter cloths or specially developed coated media are used almost exclusively on continuous machines, despite the inherent difficulties of achieving clear filtrate. Tables 1.3 and 1.4 show some basic characteristics of continuous vacuum filters. 1.4.1.1 Single leaf Typical uses: Smaller scale batch processing where good solids washing is required. FDS process ratings: 6 C, 8, 7, 8 (Nutsche); 7 C, 9, 7, 8 (tipping pan). Typical particle size and feed concentration range: 1–500
m and 1–10% w/w (Nutsche); 20–80,000
m and 5–30% w/w (tipping pan). The Nutsche is a versatile batch filter comprising of a cylindrical vacuum vessel with a single planar leaf at the bottom (see Figure 1.21). The feed suspension, which may be toxic, is introduced to the fully enclosed vessel and a constant vacuum is applied beneath the filter cloth to initiate downward filtration. When cake formation is complete the other phases of the chosen filter cycle are performed. These may include cake deliquoring (by gas suction) and, when the distribution of wash liquors is good, high efficiency displacement washing. Some units allow for reslurry washing and although countercurrent washing is feasible, it can be difficult to separate the wash liquors reliably.

1 · Solid/liquid separation equipment 27 Table 1.3 Typical filter cycle data for continuous vacuum filters (adapted from Purchas and Wakeman, 1986).

Filter type

Effective Total under Max. max. active for washsubmergence vacuum ing (% (% of cycle)* (% of cycle)† of cycle)‡

Drum: Knife discharge Roller Belt Coil or string Precoat drum Horizontal belt Rotary table Rotary tilting pan Rotary disc

30 30 30 30 85 As required As required As required 28

80 80 75 75 93 As required 80 75 75

Max. for Required for deliquoring cake only (% discharge of cycle)$ (% of cycle)

29 50–60 29 50–60 29 45–50 29 45–50 30 10 As required As required As required As required As required As required None 45–50

10 20 25 25 5 0 20 25 25

* Consult manufacturers for availability of higher submergences (cake formation period). † Values for bottom fed filters assume no trunnion stuffing boxes, except for precoat. ‡ Washing on a drum filter starts at the horizontal centreline on the rising side and extends up to 15° past top dead centre. $ Deliquoring means drainage of liquor from cake formed during submergence.

Table 1.4 Minimum cake discharge thickness from continuous vacuum filters (Purchas and Wakeman, 1986).

Filter type Drum Knife discharge Roller Belt Coil String Precoat drum Horizontal belt Rotary table Rotary tilting pan Rotary disc

Minimum design thickness (mm) 6 1 3–5 3–5 6 0–3 max 3–5 20 20–25 10–13

28 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 1.21 Schematic diagram of an automated vacuum Nutsche filter.

Smaller Nutsche filters require a manual cake discharge while larger machines generally employ mechanical ploughs or rakes. Fully automated versions of the vacuum Nutsche filter are available and some include cake smoothing devices to minimise the problems of cake cracking. A range of filter media can be accommodated with filter areas up to a maximum of 10 m2. Another smaller scale, single leaf, batch filter which has the same general features as the vacuum Nutsche is the single pan tipping filter. Here, a manual or hydraulically operated pan that tips along its horizontal axis is used to aid cake discharge and the relative ease of wash liquor separation allows multistage washing to be performed. These filters have an open top and are most frequently used to establish basic filtration, washing and deliquoring characteristics at the laboratory scale. Typical filtration area is in the range 1–3 m2. 1.4.1.2 Multi-element leaf Typical uses: Larger scale, semi-continuous, processing where pressure filtration is unsuitable. FDS process ratings: 5 C, 5, 7, 8. Typical particle size and feed concentration range: 1–100
m and 5–30% w/w.

1 · Solid/liquid separation equipment 29 The multi-element vacuum filter is characterised by the Moore’s filter shown schematically in Figure 1.22. These semi-continuous filters comprise series of relatively large rectangular vertical leaves that are mechanically dipped into an open-top tank of suspension. Vacuum is applied to draw liquor into the filter leaves leaving cakes to form on each of the exposed cloth surfaces. Cake discharge is achieved by removing the filter leaves from the tank and applying a filtrate backflow. While Moore’s filters can be almost fully automated, washing is only fair (due to the vertical leaf orientation) and requires the filter leaves to be positioned within a second tank containing wash liquor. Moore’s filters are unsuited to operation with toxic feeds.

Figure 1.22 The typical operating cycle of a multi-element Moore’s vacuum filter. (a) filtration; (b) washing; (c) deliquoring prior to discharge. Vacuum needs to be maintained during transit of the leaves and cakes between tanks. 1.4.1.3 Horizontal belt Typical uses: Separation of relatively free filtering solids where good posttreatment is required. FDS process ratings: 7 C, 9, 7, 8. Typical particle size and feed concentration range: 20–80000
m and 5–30% w/w. The horizontal belt is a continuous filter with an endless cloth supported on a perforated belt (see Figure 1.23). The belt and cloth are driven around two rollers and across a sequence of evacuated suction boxes at linear speeds up to 0.5 m s1. The feed suspension is introduced at one end of the filter and deliquored to produce a cake. The length of the filter, which can be in excess of 60 m, is arranged to allow adequate cake formation as well as the

30 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 1.23 Photographs of a single horizontal belt vacuum filter with permission from Pannevis (top) and a large scale, multiple belt filter installation with permission from Delkor (bottom). A schematic of the belt filter cycle is shown in Figure 7.1.

requisite number of sequential deliquoring and washing operations. Due to the ease with which wash liquors can be segregated, it is relatively simple to perform countercurrent washing to exacting requirements provided wash liquor carry-over into the next suction box is avoided. The final cake is naturally discharged as it passes over the second roller and separation of the belt and cloth beneath the filter allows the exposed cloth to be cleaned by sprays as it returns. Horizontal belt filters are best suited to the larger scale filtration of medium and faster settling slurries. Although they occupy a large floor space and the cost of installation per unit filter area is relatively high, these disadvantages are generally offset by full automation, flexibility, high capacity and relatively

1 · Solid/liquid separation equipment 31 high speeds of operation. Filters may be sealed to prevent the escape of heat and/or vapours, however, should the belt or cloth be damaged then replacement of either component can be expensive. Some units are programmed to operate semi-continuously via intermittent motion of the belt. 1.4.1.4 Horizontal rotary Typical uses: Processing of fast settling slurries where good washing is required. FDS process ratings: 7 C, 8, 7, 8 (table); 7 C, 9, 7, 8 (tilting pan). Typical particle size and feed concentration range: 20–80000
m and 10–30% w/w (table), 5–30% w/w (tilting pan). The two forms of horizontal rotary filter differ primarily in the manner in which the filter cloth is arranged around the periphery of the circular separation surface. Table: The rotary table filter shown in Figure 1.24 comprises a rotating horizontal table with an annular filter cloth. Vacua are applied over individual

Figure 1.24 Photograph of a partially assembled horizontal rotary table filter (Dorr-Oliver Eimco). (1) Individual segments on which the cloth is mounted; (2) feed trough; (3) wash liquor delivery or additional feed points; (4) screw conveyor for cake discharge. A schematic of the table filter cycle is shown in Figure 7.4.

32 Solid/Liquid Separation: Equipment Selection and Process Design segments of the table to initiate filtration and the formed cake is subsequently deliquored and/or washed by sprays according to requirements. The final cake is continuously discharged via a screw conveyor to typically leave a residual cake heel of 3–4 mm. Dependent on the properties of the solids forming the cake, the presence of the heel can have undesirable consequences for future cycles and necessitates the use of more open filter media with the potential for cloudier filtrates. As the cloth surface is not physically divided into individual sectors some short-circuiting of the feed may occur as well as unwanted mixing of the wash and mother liquors. Cloth washing is difficult and must be performed off the filter. Although cloth area can be up to ~200 m2, alignment difficulties usually restrict machine size and the available filter area to less than 20 m2. Tilting pan: The rotary tilting pan filter is similar in general form to the table filter, except the cloth is replaced by a series of annular sectors or pans, each one of which is lined along its perforated bottom by an individual filter cloth (see Figure 1.25). After suspension is introduced to a pan, filtration, deliquoring and washing can take place under the required vacuum before cake discharge is achieved by a relatively complex tilting mechanism that inverts the pan. The discharge procedure, which may be assisted by air blowback, leaves no heel of cake and thus in situ filter medium cleaning is readily performed using sprays. As all liquors are kept separate, there is little unwanted mixing of mother and wash liquors and countercurrent washing can be very good. Tilting pan filters are available with total filter cloth areas up to 200 m2,

Figure 1.25 Schematic representation of the tilting pan filter cycle.

1 · Solid/liquid separation equipment 33 but many of their inherent advantages are offset by their mechanical complexity and high capital cost. 1.4.1.5 Rotary drum Typical uses: Separation of relatively easy to filter suspensions, efficiency of cake post-treatment depends on the type of drum. FDS process ratings: 6 C, 7, 7, 8 (bottom fed); 5 C, 2, 7, 8 (top fed); 5 C, - , 7, 8 (internal fed drum). Typical particle size range: 1–200
m (bottom fed, knife or belt discharge), 1–50
m (bottom fed, roller discharge), 1–70
m (bottom fed, string discharge), 1–600
m (top fed), 10–600
m (internal fed drum). Typical feed concentration range: 1–20% w/w (bottom fed, knife or belt discharge), 1–10% w/w (bottom fed, roller and string discharge), 10% w/w (top and internal fed). The versatile rotary drum filter (or rotary vacuum filter – RVF) is perhaps the most widely used of the continuous vacuum filters (see Figure 1.26). The generic type is characterised by a rotating, multi-compartment drum covered externally by a fixed filter cloth of total surface area between 0.05 and 180 m2 (most commercial units are in the range 1– 80 m2). The drum on bottom fed units rotates about a horizontal shaft at speeds up to 5 rpm and is partially submerged in a mechanically agitated tank of constantly replenished suspension. A constant vacuum of between 10 and 85 kPa is applied inside the drum via a control valve to initiate upward filtration over the submerged region. As the drum rotates so the filter cake formed on the cloth is exposed and a limited number of deliquoring and washing procedures can then be performed at the appropriate level of vacuum. Although washing efficiency is reasonable, the restricted horizontal filter area near the top of the drum prevents further efficiency gains. Cake discharge normally occurs at a point where the final cake is almost vertically oriented. Bottom fed units differ primarily in the manner in which cake is discharged: Knife/scraper discharge: The most widely used method when avoidance of cloth blinding can be more or less guaranteed. The knife is arranged to leave a heel of cake on the cloth and thus avoid potential damaging contact between the knife and drum. If the cake is thinner then air blow-back can be employed to break the vacuum and assist discharge, though with some filter designs this tends to cause filtrate to re-enter the cake. Roller discharge: Generally used for the complete removal of finer particulate, sticky cakes that do not crumble. The 0.5–3 mm cake must preferentially

34 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 1.26 Representations of rotary vacuum drum filters. (a) bottom fed, knife/scraper discharge (Filtration Services); (b) bottom fed, roller discharge; (c) bottom fed, string discharge; (d) bottom fed, belt discharge (Dorr-Oliver Eimco); (e) top fed (Filtration Services); (f) internal drum.

stick to the roller placed adjacent to the drum, a process that is aided by the shearing action of the faster rotating roller. A simple knife scraper continuously removes the cake from the roller. String discharge: Suited to the discharge of fairly thick, fibrous cakes that do not crumble. A number of endless strings pass over a series of external rollers

1 · Solid/liquid separation equipment 35 and the surface of the filter cloth. In the discharge zone the strings lift away from the cloth to remove the cake completely. The strings may be replaced by endless wires, coils or chains as appropriate. Belt discharge: Mostly used for the discharge of sticky, thin cakes (
3 mm) whose solids may tend to blind a filter cloth. In this case the endless cloth is not fixed to the drum, instead it passes around its outer periphery and a series of external rollers. At the discharge point the cloth lifts away from the drum and the movement over the rollers causes all the cake to be released. The exposed cloth is then cleaned by sprays before returning to the drum. Although relatively expensive to install, belt discharge systems can raise throughput by up to 30%. Drum filters can be enclosed to prevent the escape of heat and/or vapours and typically operate with a submergence equivalent to 30–40% of the available filter cloth area. Where cake formations are more difficult, this may be raised to 60 –75% to produce a ‘submerged axis’ filter. However, the option is rarely preferred as the trunnion mounts for the drum must be wholly or partly flooded with slurry which necessitates the use of stuffing boxes (i.e. sealing units) with their attendant capital and maintenance costs. For faster settling solids the mechanical agitation of suspension in the tank is more problematical and top fed or internally fed drums may be preferred. With the former the tank is removed and suspension is tipped directly onto the top of the rotating drum, sometimes into buckets or divided areas on the drum surface. Rapid filtration proceeds over a restricted area before cake deliquoring takes place followed by knife discharge in a region 90 –180º from the top of the drum. Although cake washing is almost impossible, a top fed drum employing a cake formation/deliquoring cycle can sometimes be a cheaper option than a filter/dryer combination. An internal drum has a filter cloth lining its internal periphery onto which the settling suspension is introduced. During correct operation a coherent and relatively sticky cake is formed over a limited area of the drum and discharged at a point diametrically opposite the feed point, often with the aid of a pulse of compressed air. Although internal drum filters are cheaper and able to accept a more variable feed composition, washing is not generally possible and their use has now been largely superseded by horizontal rotary filters (see Section 1.4.1.4). The precoat drum filter is described in Section 1.4.3.1. 1.4.1.6 Rotary disc Typical uses: Continuous larger scale separation of relatively free filtering suspensions where washing is not required.

36 Solid/Liquid Separation: Equipment Selection and Process Design FDS process ratings: 4 C, -, 6, 8 (cloth covered disc); 4 C, -, 9, 8 (ceramic disc). Typical particle size and feed concentration range: 1–700
m and 5–20% w/w. Units comprise up to 12 flat, circular discs mounted vertically on a central horizontal shaft (see Figure 1.27). The discs, which are themselves permeable, are usually covered externally by sectored filter cloths. Rotation causes them to pass through individual agitated tanks containing the feed suspension(s) and the vacua applied inside the discs promote cake filtration. After this is complete, deliquoring by air suction can be performed, however, cake washing is nearly impossible due to the vertical cake formation. The final cakes are discharged by blade or wire scrapers on either side of the discs. As an air blow-back system is often employed to aid cake removal, wetter cakes are discharged from disc filters in comparison to drum filters and the discharge of thin cakes can be particularly troublesome. The need to place the discharge scrapers close to the cloth surface frequently leads to cloth damage, though cloth sectoring means only portions need be replaced.

Figure 1.27 Schematic side view of a rotary disc vacuum filter (left) and photograph, with permission from Ceramec, of a multiple disc filter installation fitted with ceramic elements (right).

Rotary disc filters are available at a relatively low capital cost with total cloth areas between 0.05 and 300 m2. They have an inherently large filter area to floor space ratio and their flexibility is enhanced by an ability to process multiple feedstocks at the same time within a single unit. In the Ceramec variant, the filter cloths and supporting porous plates are replaced by sintered alumina membranes with near uniform micropores. Although a relatively small vacuum pump is needed to promote cake formation, cake deliquoring proceeds via capillary action with little or no air

1 · Solid/liquid separation equipment 37 consumption. While the use of a ceramic membrane material allows a clear filtrate to be readily obtained, disc replacement can be expensive. Moreover, backflushing with filtrate and periodic in situ ultrasonic cleaning must be performed in order to maintain the original permeability of the filtering discs. Ceramec disc filters are available with filter areas up to 45 m2 and have been used in both metal and mineral concentrate processing at throughputs up to 100 te h1. 1.4.2 Pressure filters and presses Pressure filters/presses generally operate in a batchwise manner and use positive pressure above the semi-permeable separating surface(s) to remove liquid and retain solids in the form of cakes. They are used in a wide range of chemical and process industries for the separation of suspensions which contain finer particles that settle slowly and exhibit poor filterability, and/or suspensions that contain higher solids contents. Filtration pressures are typically in the range from 0 to 800 kPa, and these are usually provided by centrifugal or positive displacement pumps. Smaller units employ compressed gas as the driving medium. Many types can be fully automated to sequence cake formation, washing and deliquoring operations. Some filter processes allow for cake consolidation through the inclusion of flexible diaphragms (see Section 1.4.2.5) and several pressure filters have been designed for semi-continuous and continuous operation (see Section 1.4.2.6). 1.4.2.1 Single leaf Typical uses: Fully enclosed batch processing of a wide range of feeds requiring good solids washing. FDS process ratings: 6 C, 8, 8, 8. Typical particle size and feed concentration range: 1–200
m and
1–20% w/w. The pressure Nutsche filter shown in Figure 1.28 is similar in many aspects to the vacuum Nutsche filter (see Section 1.4.1.1). A single leaf forms part of a fully enclosed cylindrical vessel capable of operation at internal pressures up to 800 kPa. The feed suspension, which may be toxic, volatile or flammable, is introduced to the vessel and pressure is applied above the cloth to initiate downward filtration. A typical filter cycle includes cake formation, cake deliquoring (by gas blowing) and cake washing (by displacement or reslurry). Many pressure Nutsche filters are fully automated including cake discharge by mechanical plough or reslurry. A range of filter media can be accommodated with filter areas up to a maximum of ~30 m2.

38 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 1.28 Photographs, with permission from Pope Scientific, of a 0.15 m3 capacity pressure Nutsche filter assembled (left) and disassembled showing the filter medium and sealing arrangements (right). A schematic of the typical pressure Nutsche filter cycle is shown in Figure 6.1. 1.4.2.2 Multi-element leaf or candle Typical uses: Batch operations with solids forming slightly compressible or incompressible cakes. FDS process ratings: 5 C, 8, 8, 8 (horizontal element); 5 C, 6, 8, 8 (vertical element); 5 C, 7, 8, 8 (tubular candle element). Typical particle size and feed concentration range: 1–100
m and
1–20% w/w (horizontal element), 0.5–100
m and
1–20% w/w (vertical element), 0.5–100
m and
1–20% w/w (tubular candle element). A multi-element pressure filter comprises a cylindrical vessel inside which a number of horizontal or vertical porous elements covered by filter cloths are placed (see Figures 1.29 and 1.30). The process suspension, which may be toxic, volatile or flammable, is pumped into the vessel at pressures up to 500 kPa. The positive pressure induces cakes to form on the outer surfaces of the cloths and filtrate is transported away through the elements and a suitable manifold system. Either flat elements, in the form of square, circular or rectangular leaves, or tubular candles are used. They are spaced sufficiently to avoid the possibility of cakes touching on adjacent elements. The pressure

1 · Solid/liquid separation equipment 39

Figure 1.29 Cross-sectional views of vertical vessel, multi-element pressure filters with horizontal (left) and vertical (right) leaves. A detailed schematic of the typical filter cycle is shown in Figure 6.2.

Figure 1.30 Cross-sectional view of a horizontal vessel, multi-element pressure filter with vertical leaves showing the in situ and extracted positions of the filter leaves.

vessel may be jacketed for operation at elevated temperatures and generally has only one opening through which cake discharge takes place. Filter leaves can be automatically extracted for cake discharge if adequate floor/height provisions are made. When more frequent cake discharge is required, solids

40 Solid/Liquid Separation: Equipment Selection and Process Design are generally removed with the filter leaves in situ either by vibration, rotating blades, centrifugal force (horizontal elements only) or liquid sluicing to give a wet discharge. Element precoating can be used (see Section 1.4.3.2) and for more extreme duties metallic or ceramic filter elements may be employed. Vertically mounted vessels: These filters contain either horizontal or vertical leaves with a maximum filter area of 65 m2 (see Figure 1.29). They utilise floor area economically but can require excessive height allowance, particularly when leaves need to be withdrawn vertically for cake discharge or cloth cleaning. Horizontal leaves are preferred when either washing is required, rapidly settling feeds are processed or intermittent operation is envisaged. However, the installation cost of filters with horizontal leaves can be high as filtration takes place only on the upper surfaces. Multi-element filters having vertical rectangular leaves are best suited to the processing of feeds with settling velocities less than 3 cm s1 but give relatively poor washing performance as cakes tend to prematurely fall off the filter leaves. Tubular candles can be used in place of horizontal or vertical leaves. Cakes form on the outer surfaces of the candle elements and this arrangement is most frequently used when washing is not required. Horizontally mounted vessels: These filters contain vertically mounted flat elements with filtration areas up to 300 m2 (see Figure 1.30). Whilst needing little height a large floor space can be required, particularly where filter elements are withdrawn for cake discharge or cloth cleaning. Washing, although possible, can be troublesome if cakes fall off the filter leaves prematurely. 1.4.2.3 Filter presses Typical uses: Batch processing of solids forming incompressible and moderately compressible filter cakes. FDS process ratings: 6 C, 8, 8, 8. Typical particle size and feed concentration range: 1–100
m and
1–30% w/w. Although variants exist, the basic unit shown in Figure 1.31 comprises sequences of narrow vertical chambers lined on both sides by filter cloths. The chambers, formed between hollow frames and flat filter plates or between adjacent recessed filter plates, allow for filter cake formations as well as washing and gas-blown deliquoring operations. Suspension is fed to the square, rectangular or circular chambers through a variety of plate porting

1 · Solid/liquid separation equipment 41

Figure 1.31 Schematic diagram of a typical overhead bar horizontal filter press showing aspects of filter cycle operations (top) and cloth washing (bottom). A detailed schematic of the typical filter cycle is shown in Figure 6.3.

arrangements and a suitable positive displacement or centrifugal pump. The cakes grow inside each chamber until they meet. Pressures, typically limited to a maximum of 800 kPa, are sufficient to allow centre ported plates to deliver higher solids content feeds while bottom and top fed plates generally facilitate more even cake formations and the processing of faster settling suspensions respectively. In some specially reinforced presses the filtration pressure can reach up to 7000 kPa. Although filter cakes can be removed by reslurrying, they are usually discharged by releasing the mechanical/hydraulic clamping pressure on the press and manually or automatically separating the plates and/or frames. Good cake/cloth release properties are thus preferable, particularly in an automated press. Cloth washing using sprays can also be performed when the

42 Solid/Liquid Separation: Equipment Selection and Process Design filter plates are separated. Modern filter plates are made from either polymers or steel with polymer coatings and formed to provide good drainage surfaces for the covering filter cloths. Plates with dimensions up to 2 m × 2 m are used to provide filter areas as large as 2000 m2, although cloth areas in the range 50–1000 m2 are more typical. Filter presses are available in two basic forms as shown schematically in Figure 1.32.

Figure 1.32 Examples of a top ported plate and frame (left) and a centrally ported recessed plate (right) from typical filter presses. Only part of each square/rectangular plate is shown. Plate and frame press: These units commonly facilitate cake formations up to a thickness of 50 mm, although 200 mm cakes can be generated in extreme cases. The basic arrangement comprises alternate sequences of flat filter plates and hollow chambers formed by the frames. The feed suspension and wash liquor enter through the same ports to facilitate cake formation and ‘simple’ washing respectively. A more sophisticated arrangement incorporates flat washing plates where suspension and wash liquor enter through separate ports to facilitate improved ‘through’ washing of filter cakes. In the context of filter presses, plate and frame units offer the advantages of longer cloth life, easily replaced cloths, more uniform cakes and an ability to accommodate alternative filter media such as paper. Their disadvantages include higher capital cost, inlet ports that are prone to blockage at higher feed concentrations and a tendency towards leakage. Recessed plate press: Here, the functions of the plate and frame are combined such that cake is formed within a recess on each plate. Unlike the plate and frame press, cake thickness is restricted to 32 mm unless additional

1 · Solid/liquid separation equipment 43 frames are used as spacers. Feed suspension usually enters through centrally ported plates. The inherent advantages of recessed plate presses include lower initial costs, less tendency towards leakage, an ability to process higher concentration feeds and ease of automation. Their disadvantages include shorter cloth life, longer cloth change times, a tendency to form uneven cakes and an inability to accommodate filter papers. 1.4.2.4 Sheet filter Typical uses: Beer filtration and clarification/sterilisation operations. FDS process ratings: N, -, 9, - . Typical particle size and feed concentration range: 0.1–80
m and

1–5% w/w. These filters are similar in appearance and function to plate and frame filter presses (see Section 1.4.2.3), but compound, relatively thick sheets formed from diatomite, glass fibre or combinations of polymeric fibres are used in place of filter cloths to promote depth filtration. As filtration pressures rarely exceed 300 kPa, units are of a lighter construction than filter presses and utilise narrower chambers to provide for the removal of small amounts of fine solids from dilute feeds. 1.4.2.5 Variable-volume filters and presses A family of filters devised to handle suspensions of finer solids which are difficult to pump and/or filter. Typical feeds include suspensions of gelatinous and fibrous materials and those particulates containing occluded liquid within an inherent porous structure. Horizontal diaphragm filter press Typical uses: Batch processing of suspensions forming compressible filter cakes where dry cakes and/or efficient post-treatment are required. FDS process ratings: 8 C, 8, 8, 7. Typical particle size and feed concentration range: 1–200
m and 0.3–30% w/w. These machines are similar in form and general operation to filter presses. However, the plate surfaces are modified by the addition of flexible diaphragms to form ‘membrane plates’ (see Figures 1.33 and 1.34). Although different processing conditions are employed, feed pumping is generally stopped after ~80% of the required volume of filtrate has been produced (see Figure 1.35). In this state the chambers in the press are partially filled with cake and residual unfiltered suspension. The diaphragms on each membrane

44 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 1.33 Photographs, with permission from Larox, of a diaphragm press installation (left) and the dry cake produced from a typical filter cycle (right). A detailed schematic of the diaphragm press filter cycle is shown in Figure 6.3.

Figure 1.34 Typical membrane plates showing their general form during the filtration (left) and cake consolidation (right) phases of a diaphragm filter press cycle. Only one corner of each square/rectangular plate is shown. plate are then inflated from behind to induce pressures less than 1600 kPa, which filters the remaining suspension and squeezes the now joined cakes in each chamber. The combination of compression by the diaphragms and subsequent gas blowing reduces cake moisture content by up to ~25% more than that achieved in a conventional filter press. The compression process also tends to produce more uniform cake with improved washing characteristics and release properties; the latter also being aided by the correct choice of filter cloth. Although diaphragm presses are significantly more expensive than

1 · Solid/liquid separation equipment 45

Cumulative volume of filtrate

diaphragms inflated

filtration with diaphragm plates conventional plates

Identical filtration for diaphragm and conventional plates

Filtration time

Figure 1.35 Filtration performance with conventional and diaphragm filter plates.

conventional filter presses the additional capital and operating costs are often justified by shorter cycle times and the beneficial properties of the final cake. Vertical diaphragm filter press Typical uses: Semi-continuous processing of solids forming compressible filter cakes that require efficient post-treatment. FDS process ratings: 8 C, 8, 8, 7. Typical particle size and feed concentration range: 1–200
m and 0.2–30% w/w. The vertical diaphragm filter press, which is also known as the tower press, may be thought of as a conventional horizontal diaphragm press mounted on its end (see Figure 1.36). In place of the fixed filter cloths, a continuous cloth zigzags through the plate pack and is supported on grids within the horizontal chambers. After hydraulically closing and sealing the plate pack, pressure driven cake filtration takes place in the downward direction via a pump. Compression with elastomer diaphragms at up to 1600 kPa, cake washing, and gas-blown deliquoring at up to 1000 kPa are then simultaneously performed in sequence within each chamber. At the end of the cycle the plate pack opens and the cloth is driven forward to discharge the cakes without manual assistance. At the same time, the filter cloth leaving the plate pack is washed by high pressure water sprays to maintain permeability. The largest available units can produce in excess of 150 te h1 of dry solids. While vertical diaphragm presses are more expensive than basic, manually

46 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 1.36 Schematic and photograph (Larox), of the vertical diaphragm filter press. A more detailed schematic of the diaphragm press filter cycle is shown in Figure 6.4. operated machines they are comparable in cost and complexity to automated horizontal diaphragm and tube presses and can offer significantly better washing characteristics due to the preferable orientation of the cakes. Filtration areas up to 144 m2 can be routinely accommodated, while 168 m2 is technically feasible with special thin chambers; individual plate areas are in the range 0.4 –6 m2. Units generally operate at lower pressures than conventional filter presses. Although filtration usually takes place only on the upward facing part of the filter cloth, this disadvantage is reduced by complete automation and short downtimes. Some more complex machines have a filter cloth on both sides of each chamber. These ‘double sided presses’ allow simultaneous cake formations on both upward and downward facing filter surfaces, however, particle sizes in the feed must be towards the lower end of the allowable range to prevent excessive sedimentation. Outputs per unit filter area can be several times that of a conventional filter press and in many cases the relatively high initial capital cost is offset by reduced operational costs such as less labour and longer cloth life. Tube press Typical uses: Batch processing of compressible materials where drier cakes are required. FDS process ratings: 8 C, 4, 7, 7.

1 · Solid/liquid separation equipment 47 Typical particle size and feed concentration range: 1–200
m and 0.3–30% w/w. A tube press comprises two concentric cylinders where a permeable tube covered with a filter cloth is positioned centrally within a solid outer tube lined by an elastomer diaphragm (see Figure 1.37). The filter cycle is initiated by pumping the feed suspension into the annular space between the inner tube and the diaphragm. With sufficient suspension in the press, pressure is applied to induce radial filtration. This process is most often performed at constant pressure via the diaphragm in two stages where a lower pressure is used initially to promote more even cake formation. When filtration is complete the elastomer diaphragm is further inflated (hydraulically) to deliquor the cake via mechanical expression.

Figure 1.37 Representations of a single tube press and a multiple unit installation (Metso Minerals). A schematic of the tube press cycle is shown in Figure 6.5. Two versions of the tube press exist where the primary difference is the orientation of the filter element. The first, the Holliday VC filter is generally used as a single unit with a filtration area up to 6 m2. The cake is formed on the horizontal filter element and then squeezed at pressures up to 1500 kPa. Cake discharge is achieved when the central element is either mechanically or hydraulically withdrawn. The second, the vertical axis tube press originally developed by English Clays, is usually used in parallel groups to give the desired filter area as individual units are limited to an area of ~3.5 m2. Squeeze pressures here are up to 16000 kPa. Cake discharge is achieved by automatically opening the bottom end cover of the vessel, lowering the central element by ~0.3 m and applying a reverse back pulse of compressed air to dislodge the cake.

48 Solid/Liquid Separation: Equipment Selection and Process Design Very low moisture content cakes can be obtained with both versions of the tube press. Although capital and running costs can be high, tube presses offer the potential for short cycle times, near optimum cake thickness and, when applicable, reduced thermal drying requirements for the discharged cake. Expression press Typical uses: Deliquoring of finer particle suspensions forming compressible filter cakes. FDS process ratings: 6 C, -, 6, 5. Typical particle size and feed concentration range: 1–200
m and 10 –80% w/w. Both batch and continuous types of expression press are available. The batch units are characterised by series of cylindrical or square boxes containing semi-permeable cloths at their closed ends. The feed is introduced to the boxes and a moving piston expresses liquid through the cloth at pressures up to 40 MPa to leave the consolidated solids. Although many variants exist, the continuous expression press, which may also be classed as a continuous pressure filter (see Section 1.4.2.6), is typified by the most widely used screw press shown schematically in Figure 1.38. This comprises a variablepitch helical screw rotating at up to 2 rpm inside a perforated cylindrical or conical screen surround. As the (usually flocculated) feed moves through the unit, pressure is progressively increased to continuously express the liquid phase and discharge cake through a variable orifice nozzle. Although many continuous presses are relatively compact, larger units can have a length and

Figure 1.38 Schematic representation of a typical expression press.

1 · Solid/liquid separation equipment 49 screen diameter respectively in excess of 8 m and 1 m and are capable of dry solids throughputs greater than 1 te h1. 1.4.2.6 Continuous pressure filters Continuous pressure filters are inherently complex and expensive machines. Some are based on vacuum driven filters with the addition of an enclosing pressurised shell. Belt press Typical uses: Flocculated sludge deliquoring. FDS process ratings: 8 C, 7, 7, 7. Typical particle size and feed concentration range: 1–200
m and 0.2–30% w/w. The belt press shown in Figures 1.39 and 1.40 may be considered as something of a hybrid machine. It was originally conceived to deliquor highly flocculated materials but may be used to process a range of other materials. Although several variants exist, belt presses are characterised by two continuous, tensioned filter cloths. Flocculated sludge is introduced to the lower cloth (belt) and then progressively squeezed under pressure as the cloths move over a sequence of successively smaller diameter rollers. Liquor is removed through the cloths by mechanical expression to (ideally) produce a very dry, crumbly cake. Cake washing can be effective on many variants of the belt press and filter cloth washing to help recover initial permeability may be performed using water sprays at a convenient place after cake discharge. While power consumptions are relatively low, these truly continuous, complex and costly machines have several inherent disadvantages including high flocculant use (dependent on the nature of the feed), relatively low squeeze pressures and a need to use long, strong filter cloths which can be expensive to replace.

Figure 1.39 Schematic of the belt arrangement on a belt press filter.

50 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 1.40 Photograph of a belt filter press (Sernagiotto). Tower press Typical uses: Deliquoring of relatively free filtering solids. FDS process ratings: 6 C, -, 7, 7. Typical particle size and feed concentration range: 1–300
m and 0.1–25% w/w. A vertically oriented press where two endless, slightly off-vertical, filter cloths move continuously over a series of rollers. These moving belts are sealed at their edges by two other stationary belts in a manner that allows the feed suspension to be mechanically squeezed and cake filtration to occur. The maximum squeeze pressure is restricted to ~250 kPa and controlled as appropriate via the gap between the moving cloths at the base of the unit. Typical cake discharge thickness ranges between 6 and 8 mm. The tower press as described here, which should not be confused with the similarly named, but very different, unit described in Section 1.4.2.5, has now been largely superseded by the belt press (see earlier in this section). Rotary pressure drum Typical uses: Continuous separation of finer particle suspensions where cakes require post treatment. FDS process ratings: 6 C, 6, 7, 7.

1 · Solid/liquid separation equipment 51 Typical particle size and feed concentration range: 1–100
m and 5–30% w/w. The rotary pressure drum filter is similar in principle and basic form to the rotary vacuum drum filter (see Section 1.4.1.5). It comprises a rotating, bottomfed drum of area up to 120 m2 enclosed within a sealed housing. Rather than applying a vacuum inside the compartments of the drum, the pressure inside the housing is raised by compressed gas up to 800 kPa and this facilitates constant pressure filtration at the outer drum surfaces. Raised temperatures can be accommodated as can volatile and toxic feeds. Both cake deliquoring by gas blowing and displacement washing, can be performed reasonably effectively at different pressures through a multi-compartment arrangement within the housing. Cake discharge usually occurs at atmospheric pressure via a scraper blade. Rotary pressure disc Typical uses: Continuous, generally larger scale, separation of finer particle suspensions where cake washing is not required. FDS process ratings: 5 C, -, 6, 8 (cloth covered disc); 7 C, -, 9, 8 (ceramic disc). Typical particle size and feed concentration range: 1–100
m and 5–30% w/w. The rotary pressure disc filter is again similar in form and general operation to its vacuum driven counterpart (see Section 1.4.1.6) with the addition of an enclosing housing. Rotating cloth covered discs, having a total filtration area of between 2 and 120 m2, are pressurised externally up to 600 kPa to promote cake formations and generally higher throughputs than equivalent size vacuum units. Although able to handle volatile liquids more readily, the pressure disc filter’s inherent advantages are offset by increased costs and the difficulties which can be experienced in cake discharge; the latter is usually achieved by either reslurrying or the use of helical screw conveyors. A variant of the rotary pressure disc filter incorporating sintered alumina membranes rather than filter cloths is also available and offers significantly better cake deliquoring. 1.4.2.7 Cartridge filter Typical uses: Clarification and polishing operations. FDS process ratings: N, -, 9, -. Typical particle size and feed concentration range: 0.4–50
m and
0.1% w/w. These compact and relatively easy to operate devices are used to remove small amounts of finer solids from dilute suspensions. Although many variants exist,

52 Solid/Liquid Separation: Equipment Selection and Process Design perhaps the most common comprises a cylindrical, usually metallic or polymeric, support core onto which a string, paper or polymeric membrane filter medium is wound, pleated or bonded (see Figure 1.41). Usually several cartridges are placed within a sealed pressure vessel and the process suspension is pumped in at throughputs less than 1 m3 m2 h1 to promote radially inward filtration. The filter medium acts as a cake or depth filter depending on the nature of the feed and the unit is operated until the solids trapped by/near the outer surfaces of the cartridge lead to an unacceptable pressure drop. At this point the filtration is stopped and the cartridges are either replaced or, if sufficiently robust, cleaned of solids by, for instance, backflush or the addition of appropriate chemicals. It is important that both the filter cartridge and housing are inert to the process feed and for more extreme duties metal, woven wire and ceramic cartridges are available. Cartridge filters are sometimes used to remove trace solids from the filtrate of other solid/liquid separation devices and generally require low capital investment and little operator training. Cartridges which incorporate membranes may also be considered to be deadend membrane filters. Their general form is described in Section 1.6.2.

Figure 1.41 Schematic of a pleated filter cartridge with spigot mount (left) and photograph, with permission from domnick hunter, showing cartridges mounted in a typical housing (right). The Fibrotex filter may be considered to be a unique type of cartridge filter. It is formed from a central perforated core surrounded by loose nylon or polyester yarns. The yarns are attached to two circular end plates and prior to filtration one of the end plates is rotated until the yarns tighten

1 · Solid/liquid separation equipment 53 around the central core to produce a helically wound cartridge. After a period of filtration the pressure drop becomes excessive and the yarns are cleaned by unwinding and backflushing with filtrate. Although reusable and able to generate relatively high throughputs, the Fibrotex filter is initially more expensive than an equivalent conventional cartridge system and repeated cycling of the yarns may necessitate premature replacement of the filter element. 1.4.2.8 Bag filter Typical uses: Batch straining/classification of slurries to remove particulates down to a specific size. FDS process ratings: 6 C, -, 4, 7. Typical particle size and feed concentration range: 10–300
m and 0.2–10% w/w. Here, a highly porous (80%) polymer felt or woven textile in the form of a ‘bag’ is used to trap particles above a certain size while allowing finer particles to pass through largely unhindered (see Figure 1.42). The simplest arrangement comprises a single bag which is attached over the end of a pipe. The relatively dilute feed suspension is pumped through the pipe and into the bag until the pressures generated become excessively high and/or separation rates become unacceptably low. At this point the flow is interrupted and the bag manually changed (and then often discarded). In more

Figure 1.42 Photographs of typical bag filters and bag housings (Lenntech).

54 Solid/Liquid Separation: Equipment Selection and Process Design sophisticated versions, multiple bags are attached to a manifold system and the whole assembly is placed inside an enclosing vessel. Although suited to a wide range of slurries, unless special precautions are taken bag filters are not generally used with toxic or volatile feeds as some spillage occurs when the bag(s) are replaced. The fabric used to form the bag must be carefully chosen, in terms of pore size, to avoid undesirable blinding by particles. 1.4.3 Precoat filters Precoat, or filter aid, filtration is used to promote the formation of more porous filter cakes whose particles would otherwise cause severe filter medium blinding (see Chapter 2 for details). Standard filter aids include diatomaceous earth or diatomite, which is the most common, perlite and cellulose based products. These are used as filtration precoats and/or included as body-feed within otherwise standard filter arrangements. 1.4.3.1 Precoat rotary drum Typical uses: Clarification. FDS process ratings: 4 CN, 5, 8, 8. Typical particle size and feed concentration range: 0.5–100
m and
1% w/w. The precoat drum shown schematically in Figure 1.43 is similar in basic form and operation to the bottom fed rotary vacuum drum filter (see Section 1.4.1.5). Prior to filtration of the feed, a suspension of precoat is filtered under vacuum onto the drum surface to a depth between 4 and 15 cm. The feed is then introduced and filtration proceeds to produce thin, sometimes

Figure 1.43 Schematic representation of the precoat rotary drum filter.

1 · Solid/liquid separation equipment 55 gelatinous, cake which usually penetrates less than 0.5 mm into the surface of the precoat. The final cake, along with some precoat, is removed using a knife or blade which progressively advances at rates as low as 5
m per drum revolution. In this way the filtering surface is continually renewed to maintain good permeability, although the feed needs to be interrupted and the precoat replenished at intervals of less than 72 h in order to maintain overall filtration efficiency. Wherever possible the removed precoat is recycled to keep operational costs to a minimum. Due to the presence of a precoat, a more permeable filter medium can often be used without sacrificing filtrate clarity and some in situ cake washing is possible. 1.4.3.2 Precoat pressure Typical uses: Clarification. FDS process ratings: 5 CN, -, 9, -. Typical particle size and feed concentration range: 0.1–40
m and
1% w/w. Precoat filtration can be incorporated within a wide range of pressure filters including leaf, multi-element and plate and frame types (see Section 1.4.2). Up to 700 g m2 of precoat is typically filtered onto the filter medium prior to introduction of the feed suspension. The feed, which may also contain a significant addition of filter aid to improve cake permeability, is filtered until the filtrate flow rate is sufficiently low to warrant cake discharge in the normal way. It is not economical to recover the feed solids from the precoat, and it follows that washing of the solids is not practised. Moreover, the filter aid tends to abrade the pumps used to promote the filtration. Precoat pressure filtration is most often used for the removal of finer particles from dilute suspension where other potential processes would require too high an investment. 1.4.4 Depth filters Although some filters utilise depth filtration with thin filter media, most depth filters are characterised by a relatively thick bed of granules or fibres through which a dilute feed suspension is passed. As particles in the feed travel through the bed, they are moved towards the exposed surfaces of the granules/fibres by a combination of diffusional, gravitational and/or hydrodynamic forces. If particles get sufficiently close then attractive electrical forces or attractive van der Waals forces cause attachment to the media. As the filter becomes clogged the pressure drop becomes unacceptable and the filter media is backflushed using filtrate to remove trapped particulates, sometimes with the addition of a co-current compressed air scour. Typical filtration rates for a single unit range between 5 and 15 m3 m2 h1 and produce filtrates contaminated with 0.1–10 mg l1 of solid matter.

56 Solid/Liquid Separation: Equipment Selection and Process Design Several conventional units can be arranged in parallel to maintain a continuous flow of filtrate and facilitate installations with throughputs up to 500,000 te day1. 1.4.4.1 Sand bed Typical uses: Larger scale clarification. FDS process ratings: N, -, 8, -. Typical particle size and feed concentration range: 0.2–60
m (pressure fed), 0.2–50
m (gravity fed) and
0.1% w/w. The most common form of depth filter utilises 0.4–2.5 mm sand particles to provide either constant or declining rate filtration. The sand may be from a single sieve fraction or may possess a range of sizes; in the latter case the sand is typically graded with the largest media towards the top of the bed where the feed suspension is introduced. Filtrations are performed under pressure or gravity conditions until the pressure drop becomes too high (ca. 25 kPa for gravity filters and 70 kPa for pressure driven filters) or significant breakthrough of particulates occurs at the bottom of the bed. A typical unit operates for 24 h and then backflushes with up to 2% of the filtrate produced; cycles times up to 100 h can prevail under favourable processing conditions. The backflushing operation tends to unfavourably grade different size sands and it is common for mixed-media beds, such as anthracite and sand which exhibit different densities, to be used to reduce the problem. Although continuous operation can be achieved using conventional sand filters in parallel, truly continuous depth filters exist where filtration proceeds with virtually no head loss. These units, which are typified by the Tenten inclined bed and Dynasand devices, operate in the normal manner except a portion of the filter media is intermittently removed (see Figure 1.44). This portion is washed, and then automatically returned to the top of the filter bed in a cleaned condition. While being more expensive than conventional sand filters, continuous depth filters find use when frequent backwashing would otherwise be required. 1.4.4.2 Fibre bed Typical uses: Clarification and polishing. FDS process ratings: N, -, 8, -. Typical particle size and feed concentration range: 0.1–40
m and
1% w/w. In the Howden-Wakeman filter shown schematically in Figure 1.45, loosely packed 1–10
m diameter polymer or carbon fibres are compressed

1 · Solid/liquid separation equipment 57

Figure 1.44 Schematic representation of a continuous sand filter where wash liquid is used to progressively clean the sand bed (left) and photograph, with permission from Sernagiotto, of a sand filter with automated backflush facility (right).

Figure 1.45 Schematic representations of the typical cycle in a Howden-Wakeman fibre medium filter. (a) filtration; (b) cleaning; (c) sterilising.

by a hydraulically operated piston to produce a 5–10 cm bed having a porosity in excess of 80%. The dilute challenge stream is caused to flow under pressure through the bed until the trapped particles cause an excessive pressure drop. The fibres are cleaned by releasing the piston pressure and backwashing with filtrate to expand the bed; slow reciprocation of the piston and a co-current gas scour also aid the cleaning process. The high

58 Solid/Liquid Separation: Equipment Selection and Process Design porosity of the filter bed allows for a large dirt holding capacity and the fineness of the fibres helps the removal of smaller particles from the feed.

1.5 Classifiers Classifiers are grouped according to whether the solids are moved through the unit hydraulically or mechanically, and these machines are distinguished from screens. 1.5.1 Hydraulic Typical uses: Coarse classification of suspended solids into different size fractions. FDS process ratings: 3 C, 3, 3, 5. Typical particle size and feed concentration range: 50 –2000
m and 4–40% w/w. Hydraulic classifiers, which are also known as hydrosizers, generally comprise a series of connected vertical sorting columns through which a suspension is caused to flow sequentially (see Figure 1.46). Within each column, finer particles rise with the liquid moving into the overflow and larger particles settle downwards to be removed at the bottom of the column. During normal operation additional liquid is introduced to each column to help promote classification and successive columns have larger diameters. Thus, for

Figure 1.46 Basic operating principle of a hydraulic classifier.

1 · Solid/liquid separation equipment 59 a fixed throughput the fluid moves through the columns at progressively slower velocities such that coarser solids are removed in the first column and ever finer particles are removed in later columns. Hydraulic classifiers have the advantage of relatively simple construction, high capacity and can be operated in both the free and hindered settling modes. However, due to their mode of operation they are considered relatively inefficient at both sizing and sorting and are thus only used for relatively coarse separations. Some installations utilise single, rather than multiple, columns in which case a reduced number of size fractions are obtained. 1.5.2 Mechanical Typical uses: Coarse classification of suspended solids into different size fractions. FDS process ratings: 4 C, 2, 3, 4. Typical particle size and feed concentration range: 100 –3000
m and 4–40% w/w. The mechanical classifier is characterised by a trough inclined at about 20º, a settling pool and a mechanical device for removing larger settled particles (see Figure 1.47). The feed is introduced towards the bottom of the incline and just above the settling pool. The larger particles continuously settle under gravity towards the base of the pool from where they are transported upwards and away by a rotating helical screw or mechanical rakes. The liquid containing the finer particles overflows from a weir at the required rate. In general, helical screw classifiers can operate at greater trough inclines than rake classifiers to give drier solids concentrate streams and more fines in the liquid overflow. However, mechanical classifiers have an inherent disadvantage

Figure 1.47 The typical form of a mechanical classifier with rakes (in the rotating screw version a helical screw replaces the rake mechanism).

60 Solid/Liquid Separation: Equipment Selection and Process Design as feed dilution is often required for correct operation (i.e. to avoid zone settling of the solids) and this can lead to difficulties in producing liquid overflows with reasonable densities of finer particles. 1.5.3 Screen Typical uses: Classification and deliquoring of coarser particulate suspensions. FDS process ratings: 5 C, 4, 5, 4 (sieve-bend). Typical particle size and feed concentration range: 45–100000
m and 20–40% w/w. Screen separators are widely used in both the mining and minerals industries and are characterised by a surface having a multiplicity of regularly sized apertures. The relatively concentrated feed is caused to move across this screen by either gravity, gyration or vibration and, provided the screen does not blind, particles of given size or smaller pass through the screen apertures leaving the larger particles to move away. Depending on the type of separator, the screen is arranged to be either stationary or moving and is shaped into either a flat, circular or round form. For the removal of particles towards the finer end of the size range the sieve-bend screen shown in Figure 1.48 has

Figure 1.48 Schematic representation of a sieve-bend screen (left) and photograph (Sernagiotto) of a self-cleaning flat screen for wastewater treatment.

1 · Solid/liquid separation equipment 61 found wide acceptance. Here, the feed slurry passes tangentially over the upper surface of a curved and stationary screen at rates up to 180 m3 h1. Separation is achieved when the smaller particles pass preferentially through the upper part of the screen. With much coarser particle feeds the so-called ‘grizzly’ is often used where heavy, vibrated, equispaced parallel bars are used in place of a mesh type screen to separate up to 1000 te h1 of dry solids. For best results the mesh size of the screen must be carefully chosen in relation to the typical particle sizes present in the feed as blinding of the mesh can occur when they are too similar. The efficiency of separation is generally reduced as the particle size in the feed is decreased. Here, particles blind the relatively fragile, finer mesh screens more readily leading to poorer separations. Moreover, feeds should be either dry or in the form of a slurry as both blinding and poor solids translation across the screen can occur with damp and/or sticky feeds.

1.6 Membrane filters Membrane filters are classified according to whether they are operated in a dead-end or crossflow mode; crossflow filters are then differentiated according to the pore size in the membrane or according to size of contaminant they will remove from the process stream. In crossflow (or low shear) filters the filter surface is stationary, and these are distinguished from dynamic (or high shear) devices which usually contain a moving filter surface. Details of membrane material constructions are presented in Chapter 2, while more specific details of membranes and membrane processes are available in Baker and Dudley (1998), Bhave (1991), Cheryan (1998), Culkin et al (1998), Dubbin (2005), Field et al (1995), Ho and Sirkar (1992), Holeschovsky and Cooney (1991), Murkes and Carlsson (1988), Nachinkin (1991), Porter (1990), Purchas and Sutherland (2002), Scott (1997), Scott and Hughes (1996), Schaefer et al (2004), Sourirajan (1977), Tarleton et al (2005), Tarleton and Wakeman (1993, 1994a, 1994b), Wakeman (1996) and Zeman and Zydney (1996). 1.6.1 Dead-end Typical uses: Clarification and sterile filtration. FDS process ratings: N, -, 9, 8 (cylindrical cartridge and leaf elements). Typical particle size and feed concentration range: 0.1–10
m and
1% w/w. The simplest type of dead-end membrane filter shown in Figure 1.49, which is also known as a lenticular filter, resembles a small scale multi-element

62 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 1.49 Photographs of planar multi-element dead-end filters (Cuno).

pressure filter with horizontal elements (see Section 1.4.2.2). The more usual filter cloths, however, are substituted by planar, generally polymeric, microfiltration (MF) membranes with a pore rating between 0.02 and 10
m or microporous sintered discs. Membranes are normally of a symmetric construction and exhibit either a microporous form, where filtration takes place both on the surface and internally through the depth of the membrane, or a track-etched form, where filtration proceeds at the top of the membrane pores in a sieve-like manner. In some instances filter media of a microporous form that incorporate adsorptive components (e.g. activated carbon) can be utilised for the additional removal of dissolved solutes. Dead-end membrane filters remove fine particles from dilute suspension at permeation rates less than 1 m3 m2 h1 as the scale of separation is relatively small; filters are restricted to a diameter of 293 mm. Solids washing is not usually performed. Other versions of dead-end membrane filters comprise either single or multiple cylindrical cartridges enclosed within pressure vessels (see Figure 1.49 and also Section 1.4.2.7). Cylindrical cartridge forms are available in lengths between 250 and 1000 mm and arranged such that the membrane material within the cartridge is pleated to give a relatively large filtration area within a confined space. Permeation rates are again limited to less than 1 m3 m2 h1.

1 · Solid/liquid separation equipment 63 1.6.2 Low shear crossflow Low shear crossflow filters may be categorised as either microfilters or ultrafilters1 with the particle size separated being the dividing criterion. Typical units comprise either a single membrane module or several modules arranged in a series configuration. Referring to Figure 1.50, the feed suspension is pumped at a constant rate and pressure into the module(s) and caused to flow tangential to the stationary semi-permeable membrane surface(s). The generally turbulent crossflowing stream has a typical linear velocity of 1–2 m s1, but exceptionally up to 6 m s1, and the shearing action at the membrane surface(s) limits solids deposition to produce a relatively rapid flux decline towards the start of filtration followed by a near constant separation rate. The shear forces generated are dependent on and directly linked to the rate at which the feed is caused to flow over the membrane surface. In normal operation the permeate is collected and the retentate of thickened suspension is recirculated until the desired solids concentration is achieved, or pumping can no longer be performed satisfactorily.

Figure 1.50 Schematic representations of dead-end (left) and crossflow (right) filtration. Particulate deposition, fouling and adsorption of molecular species at the membrane surfaces often lead to lower than expected permeate fluxes. While chemical cleaning and periodic backflushing/backpulsing with permeate or compressed gas can temporarily increase fluxes, large installed membrane areas may be required to achieve the desired separation rates. This, in conjunction with relatively high pumping duties, means that both capital and 1

Reverse osmosis units are used for molecular separations such as the removal of salt from seawater. Nanofiltration is another variant of membrane filtration whose separation characteristics fall between reverse osmosis and ultrafiltration. Their description is beyond the scope of this text.

64 Solid/Liquid Separation: Equipment Selection and Process Design operating costs of membrane units can be higher. However, such costs are frequently offset by the ability to perform separations that are difficult, if not impossible, to achieve economically by other means and both ultra- and microfilters are becoming the technology of choice in several industrial sectors. 1.6.2.1 Ultrafilters Typical uses: Separation of macromolecules, viruses, bacteria, colloids and very fine suspended solids. FDS process ratings: 1 S, 2, 9, -. Typical particle size and feed concentration range: 0.001–0.05
m and
20% w/w. The membranes used in ultrafiltration (UF) are almost exclusively of an asymmetric, microporous construction and available with pore ratings in the range 0.001–0.02
m. They are manufactured as microporous structures from a range of polymers and ceramics and formed as either flat sheets or tubes for use in one of four basic arrangements (see Figure 1.51 and Table 1.5): Plate and frame: Flat porous plates covered with polymeric membrane material are assembled together with alternate hollow spacers to produce a crossflow system where feed moves through the annular spaces between adjacent membrane surfaces. Although now largely superseded by other designs, the plate and frame system is still available with membrane areas up to 80 m2. Tubular monolith: A thin membrane layer which facilitates the separation is formed on the inside of a more robust, and open, monolith support. In earlier examples of the technology the separating layer was formed to constant depth along the length of the monolith, however, newer designs employ a progressively reducing depth that promotes better overall flux performance. A typical monolith is made from alumina or zirconia ceramic and may contain more than 30 individual channels of 4 –7 mm diameter and length up to 1 m. The feed passes along the inside of each channel to allow a separation to proceed. Individual monoliths are normally assembled into a module similar in form to a single-pass shell-and-tube heat exchanger. Hollow fibre: Up to several thousand small diameter (ca. 40
m to 2 mm), hollow tubular membranes are externally sealed at both ends into a larger diameter, solid cylindrical housing. The pressurised feed stream usually flows into this polymeric lumen with the permeate moving radially outwards through the fibre walls (‘inside-out’ filtration). Hollow fibre systems can also be designed to have the feed flow on the outside of the fibres with the permeate collected from the inside of the fibres (‘outside-in’ filtration). Although hollow fibre ultrafilters offer the advantage of a large membrane

1 · Solid/liquid separation equipment 65

Figure 1.51 Examples of the membrane arrangements used in low shear crossflow membrane filters. (a) spiral wound; (b) hollow fibre; (c) plate and frame; (d) tubular monolith (atech innovations).

area in a small volume, they can be prone to blockage, greater membrane fouling and also cleaning problems. Spiral wound: Spiral modules are constructed using flat sheet polymeric membranes in the form of a pocket, consisting of two membrane sheets separated by a highly permeable mesh spacer. The mesh defines the region for permeate flow. The assembly is sealed using an appropriate epoxy or polyurethane adhesive along three edges. The open side of the pocket is glued to a central perforated tube that is used to collect the permeate flow.

66 Solid/Liquid Separation: Equipment Selection and Process Design Table 1.5 Relative comparisons between membrane arrangements. Parameter

Tubular

Plate and frame

Hollow fibre

Spiral wound

Availability Membrane surface per module volume (m2 m3) Investment cost Operating cost Flow control Ease of in situ cleaning

UF/MF 25–50

UF/MF 350–600

UF/MF 600–1200

UF 600

High High Good Good

High Low Fair Fair

Low Low Good Fair

Medium Low Fair Poor–fair

Several of these pockets are spirally wound around a single collecting tube using a feed-side mesh as a spacer between the pockets to establish the required feed channel thickness. Like the hollow fibre arrangement, the spiral wound module offers a large membrane area within a small volume but again suffers from potential blocking and cleaning problems. Typical ultrafilters operate with permeate fluxes in the region of 0.004–0.4 m3 m2 h1 and rejections in the range 90–99% depending on the nature of the feed. They are usually prevented from operating at higher separation rates by the formation of gel-like layers at the membrane surfaces. These layers, formed through a combination of particle transport with the filtering liquid and back-diffusion away from the membrane surface(s), are frequently of a compressible nature and generally require filtration pressures to be maintained below 1000 kPa. Ultrafilters are usually operated as multiplepass thickeners in either batch or continuous ‘feed and bleed’ modes. 1.6.2.2 Microfilters Typical uses: Separation of viruses, bacteria, colloids and fine suspended solids. FDS process ratings: 1 S, 2, 9, 6. Typical particle size and feed concentration range: 0.05–20
m and
20% w/w. Microfilters differ from ultrafilters primarily in the pore size range and construction of the membranes used to achieve a separation. The polymeric, flat sheet types are usually of a symmetric construction and exhibit either microporous or track-etched forms to facilitate either depth or surface filtration. These membranes are manufactured with pore ratings of 0.02–10
m.

1 · Solid/liquid separation equipment 67 Ceramic and metal microfilters are also available for more extreme duties as either flat sheet or tubular forms with pore ratings between 0.1 and 8
m or 0.2 and 20
m, respectively. Industrial microfilter modules containing tubes or tubular monoliths, similar to those used in UF, are capable of holding more than 100 tubes (see Figure 1.51 and Section 1.6.2.1). Alternative forms are plate and frame and hollow fibre. A microfilter typically operates with a flux of less than 1 m3 m2 h1 at a pressure below 500 kPa. Due to the processing of larger particles the gel formation observed in UF is not generally seen in MF and relatively high pressures can sometimes be beneficially employed. 1.6.3 High shear crossflow Typical uses: Suspension thickening and clarification. FDS process ratings: 2 S, 4, 6, 4. Typical particle size and feed concentration range: 0.1–20
m and
25% w/w. High shear crossflow filters offer many of the advantages of the low shear filters described in Section 1.6.2, but with the potential benefit of higher fluxes. Several variants exist. A typical unit comprises a cylindrical pressure vessel enclosing 12–15 filter leaves of ~0.5 m diameter (see Figure 1.52). The preferred type, which is typified by the Artisan filter, uses static circular filter elements with solid discs mounted between. The discs are attached to a central shaft rotating at constant speeds up to 2000 rpm. The rotation ensures the generation of relatively high shear forces and local suspension velocities in excess of 10 m s1. The feed suspension is pumped into the pressure vessel at a rate dependent on the inherent filtration properties and separation proceeds to produce a thickened suspension. As the feed thickens it invariably becomes more viscous with the result that significant rotational energy can be transferred to the feed in the form of heat and, perhaps more importantly, higher motor currents are required to turn the central shaft and discs. These disadvantages are offset by the inherent ability of the filter to decouple the shear generated at the separating surface from the overall suspension throughput, i.e. unlike a low shear crossflow filter the shear and feed flow rate are independent. A typical Artisan filter utilises flat sheet MF membranes or tightly woven, multi-filament filter cloths. In a variant the rotating discs are omitted and the circular filter elements themselves, which are double-sided and mounted on a hollow shaft, are caused to rotate. With some types a second, counter-rotating, set of filter elements overlaps the peripheries of the first set to further enhance shear at the

68 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 1.52 The general form of a high shear crossflow, Artisan type, filter (top) and photograph courtesy of Bokela (bottom).

separating surfaces. Motion of the filter elements tends to promote unwanted lateral flow of filtrate away from the central shaft which can limit the upper rotational speed, and hence ultimate throughput, of such units. Rather than using a continuous rotation of the filter elements or interstitial discs, another variant employs vibration of the elements to enhance filtration. In this case up to 100 double-sided, flat filter elements separated by thin spacers are clamped together within a cylindrical vessel and caused to vibrate by a motor drive assembly close to the resonant/natural frequency of the unit. The oscillatory motion in the plane of the horizontal elements produces a shear rate up to 150000 s1, which is many times greater than that observed in typical low shear crossflow filters. As the feed flow rate and

1 · Solid/liquid separation equipment 69 generated shear rate are again independent, higher solids content and rheologically sensitive feeds can be processed at a desired throughput. Provided that their mechanical integrity can be maintained, a wide range of membranes, including ultra- and nano-filtration membranes, can be accommodated to give filtration areas up to 200 m2 and permeates clear of particles and most macromolecules.

1.7 Other equipment This category contains a number of solid/liquid separation technologies that do not fit conveniently into the other broader classifications. 1.7.1 Flotation Typical uses: Selective removal of solids, generally from aqueous suspension. FDS process ratings: S, -, -, 8. Typical particle size and feed concentration range:
300 –2000
m and 1–20% w/w. Flotation is a continuous, generally large scale, separation process where solids in suspension are removed through their preferential attachment to air bubbles. During normal operation, the bubbles mix with the solid/liquid mixture at the base of a column (or cell) and rise through the liquid with solids attached to their surfaces. Towards the top of the column both the bubbles, which usually form a foam, and their solids load are mechanically removed (see Figure 1.53). The success of flotation is largely dependent on two factors, particle attachment and bubble generation. Bubble/particle attachment is frequently the controlling step in flotation and is influenced by bubble and particle size, the degree of turbulence within the liquid column and the hydrophobicity of the solids. As most solids are hydrophilic it is often necessary to continually add surface active agents (such as long chain hydrocarbons) to the feed to promote hydrophobicity and hence aid the attachment of particles to bubbles. To ensure a continuous supply of bubbles one of three methods is used, namely, mechanical agitation, which produces bubbles of ~1 mm diameter, electrolysis, which produces ~50
m bubbles with a minimum of turbulence, and the regeneration of dissolved air which produces bubbles in the range 50 –100
m. The latter two have become the favoured options with dissolved air often proving to be the most cost effective. Flotation has found widespread use in the selective recovery of minerals from complex mixtures.

70 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 1.53 Schematic diagram of a dissolved air flotation column/cell. Inset photograph shows a multiple flotation cell installation (Dorr-Oliver).

1.7.2 Strainer Typical uses: Coarse filtration of very dilute suspensions. FDS process ratings: N, -, 7, -. Typical particle size and feed concentration range: 5–200
m and
0.1% w/w. Strainers are used for the protection of pipelines and downstream equipment where generally coarser contaminants are to be removed from dilute flowing streams. A temporary strainer in the form of a mesh screen is often fitted between pipe flanges during the commissioning and early stages of plant operation. Permanent installations require their own housings and these types are characterised by the basket strainer. Here, a suitably strengthened wire mesh or perforated plate shaped into a basket is placed inside a sealed housing through which the feed stream flows under pressure. In simplex systems the flow continues until the strainer is clogged with the unwanted solids. At this point the flow is interrupted and the basket is manually changed. More complex, and expensive, duplex systems incorporate a diverting valve that switches flow between two adjacent series of baskets to facilitate continuous operation (Figure 1.54). Some duplex strainers also incorporate self-cleaning baskets that use filtrate backwash to remove solids from a mesh. Larger strainers, which can be attached to pipes greater than 1 m diameter, have the potential for throughputs substantially in excess of 10 m3 h1.

1 · Solid/liquid separation equipment 71

Figure 1.54 Schematic side and top views of a duplex strainer with two baskets (top) and photograph courtesy of Plenty Filtration (bottom).

1.7.3 Gravity Nutsche filters Typical uses: Separation of free filtering solids requiring gentle handling. FDS process ratings: 4 C, 7, 7, 9. Typical particle size and feed concentration range: 100 –10000
m and 1–10% w/w. Gravity Nutsche filters find limited use when larger particle sizes are present and gentle handling of a feed is required. General operation is similar to both vacuum and pressure Nutsche filters (see Sections 1.4.1.1 and 1.4.2.1) except the feed is introduced and processed within the filter chamber under the influence of gravitational forces alone. The most frequent application of gravity Nutsche filters is beer mash filtration.

72 Solid/Liquid Separation: Equipment Selection and Process Design 1.7.4 Gravity belt filter Typical uses: Separation of free-draining solids requiring gentle handling, e.g. municipal waste water. FDS process ratings: Not applicable. Typical particle size and feed concentration range: 100 –10000
m and
3% w/w. The gravity belt filter is a relatively simple device that is similar in general form to the horizontal belt filter (see Section 1.4.1.3) except separation is induced wholly by gravitational forces. Referring to Figure 1.55, the normally flocculated and dilute feed is introduced at one end of a continuously moving, semi-permeable, belt. During translation with the belt, the ‘free water’ in the feed drains to typically produce a 6 –10 fold increase in concentration at the point of discharge from the belt; the discharged solids usually exhibit the consistency of a pumpable slurry. In more sophisticated variants the thickening solids are gently agitated along the length of the belt to help promote liquid removal. The gravity belt filter is most often used to pre-concentrate a suspension in order to lessen the load, and thus size requirement, of a downstream separator. Flocculant use can be low, although dependent on the nature of the feed, and throughputs for single units are in the range 10 –200 m3 h1.

Figure 1.55 Photograph of a gravity belt filter (Sernagiotto). The unit can be covered to prevent the escape of vapours and/or odours as required.

1 · Solid/liquid separation equipment 73

1.8 Force field assisted separations In recent years there has been a growing recognition that imposed magnetic, electric, ultrasonic and vibration force fields can be used to improve separation processes. Although the mechanisms of operation are not always clear, their use has shown considerable promise in flux enhancement and process intensification (see, for instance, Bollinger and Adams, 1984; Birss and Parker, 1981; Gundogdu et al, 2003; Kyllönen et al, 2005; Lin and Benguigui, 1983; Murkes and Carlsson, 1988; Park, 2005; Saveyn et al, 2003; Tarleton, 1992; Wakeman, 1982b; Wakeman and Tarleton, 1991b; Watson, 1990). Vibration assisted filters are described in Section 1.6.3. 1.8.1 Magnetic field Typical uses: Separation of ferro- and paramagnetic materials such as minerals and ceramics. FDS process ratings: 3 C, 2, 4, 8 (LIMS or HIMS); 1 S, 2, 4, 8 (HGMS). Typical particle size and feed concentration range:
40 – 4000
m and 5–20% w/w (LIMS or HIMS),
400
m and
10% w/w (HGMS). Ferromagnetic solids of high magnetic permeability can be separated in a Low Intensity Magnetic Separator (LIMS) using permanent magnets of less than 2 T (see Figure 1.56). A typical unit operates continuously and comprises a rotating non-magnetic drum inside which four to six stationary magnets are placed. The wet or dry feed contacts the outer periphery of the drum and the magnetically susceptible particles are picked up and discharged leaving the weakly or non-magnetic material to pass by largely unaffected. Alternative designs include the disc separator and the cross-belt separator where dry solids are conveyed towards a cross-belt which moves across a series of permanent magnets. The efficiency of magnetic separation is generally improved by maximising both the intensity and the gradient of an applied non-uniform field. By doing so paramagnetic material of low magnetic permeability can be separated in a High Intensity Magnetic Separator (HIMS). Electromagnets, with intensities in excess of 2 T, are used in continuous equipment such as the Jones rotating disc separator to affect separations of dry feeds down to 75
m and wet feeds to finer sizes. Very weakly paramagnetic material cannot usually be separated satisfactorily with a HIMS, and a High Gradient Magnetic Separator (HGMS) must be used (Figure 1.56). In these units a matrix of fine stainless steel wool is placed between the poles of either electromagnetic or superconducting magnets, the latter generating magnetic intensities up to 15 T. Very high magnetic

74 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 1.56 Representations of magnetic field assisted separators. (a), (b) low intensity; (c) high intensity; (d) high gradient. Photographs with permission from Eriez.

gradients are produced adjacent to the wool fibres and this allows for the separation of very fine particulates. Although the capital cost of HGMS can be relatively high compared with more conventional equipment, commercial units are readily available. 1.8.2 High voltage electric field Typical uses: Clarification of non-aqueous, more dilute suspensions. FDS process ratings: 1 S, -, 7, 8. Typical particle size and feed concentration range:
20
m and
10% w/w. Dielectrophoretic separators utilise 10–25 kV non-uniform DC and AC electric fields to remove particles from dilute, generally non-aqueous suspensions. Particles moving through the electric field are polarised by redistribution of

1 · Solid/liquid separation equipment 75 their surface and/or internal charge and (usually) move towards the region of highest field intensity where they concentrate. Small scale dielectrophoretic separators employ relatively simple wire and plate or wire and cylinder electrode arrangements. Larger scale units employ a high porosity dielectric matrix between two, generally insulated, electrodes to form a High Gradient Dielectrophoretic Separator (HGDS, see Figure 1.57). The feed suspension flows through the matrix and field gradients up to ~10 kV cm1 induce sufficiently large dielectrophoretic forces to capture fine particles at the fibre surfaces. Cleaning of the clogged matrix is achieved by simply switching off the electric field. Although dielectrophoretic separators have found uses in the petroleum and biotechnology industries, operational problems can arise with suspension decomposition, current leakage and electric field generation.

Figure 1.57 The concept of a high gradient dielectrophoretic separator.

1.8.3 Low voltage electric field Typical uses: Enhancement of separation rates in otherwise more conventional equipment. FDS process ratings: Not applicable. Typical particle size:
10
m. Typical feed concentration range: Similar to range quoted for equipment to which the electric force field is applied. Uniform and non-uniform DC electric fields with field gradients less than 100 V cm1 can be combined with more conventional filtration and deliquoring apparatus to improve separation rates and reduce overall operating costs (see Figure 1.58). Electrokinetic phenomena such as electrophoresis (movement

76 Solid/Liquid Separation: Equipment Selection and Process Design

Filtrate flux (m3 m-2 h-1)

1.0

Applied vacuum = 35 kPa

no electric field E = 40 V cm-1 E = 80 V cm-1

0.8 0.6 0.4 0.2 0.0 0

500

1000

1500

2000

Filtration time (s)

Filtrate flux (m3 m-2 h-1)

4

Applied pressure = 140 kPa Crossflow velocity = 0.2 m s-1

no electric field E = 50 V cm-1

3

2

1

0 0

500

1000

1500 2000 2500 Filtration time (s)

3000

3500

Figure 1.58 Application of low voltage electric force fields to the dead-end vacuum filtration of 0.01% v/v aqueous bentonite suspensions (top) and the crossflow filtration of 1.4% v/v aqueous anatase suspensions (bottom).

of particles) and electroosmosis (movement of liquid) can be observed when electric fields are applied to filtering suspensions. It is a prerequisite that the majority of particles in the feed are less than 5
m in size and exhibit an average (absolute) zeta potential greater than 20 mV. Rates of separation can typically be improved by more than an order of magnitude with the application of a suitable electric field. This has facilitated the construction and commercial operation of modified leaf and belt filters and diaphragm filter presses for finer particle separations. Moreover, laboratory scale investigations with very low crossflow velocities (~0.1 m s1) and uniform DC fields have shown significantly reduced fouling in membrane systems. So-called ‘electrofilters’

1 · Solid/liquid separation equipment 77 show considerable promise in the processing of colloidal suspensions where the potential for enhancements in separation rates is greater. 1.8.4 Ultrasonic field Typical uses: Enhancement of separation rates in otherwise more conventional equipment. FDS process ratings: Not applicable. Typical particle size and feed concentration range:
10
m and
10% w/w. Ultrasound, with a sound wave frequency in excess of 16 kHz, is known to induce particle agglomeration, particulate dispersion, enhanced reaction rates and enhanced separation rates when conditions allow. The ultrasound is either applied prior to separation to condition the feed or during separation to reduce/prevent particle deposition at a filtering surface. However, as relatively little work has been done in applying ultrasound directly within solid/liquid separation processes, the enhancements of separations rates claimed to date have been relatively modest. It is realised that ultrasound and low voltage electric fields combine together in a synergistic manner and that the phenomenon could potentially offer significant processing advantages.

1.9 Conclusions The descriptions given in this chapter detail the generic equipment forms offered by manufacturers and indicate where some of the currently emerging technologies are likely to find future application. Although the range of equipment extends beyond just filters in order to give the reader a balanced perspective, in the context of this book the discussions of filter types are most pertinent as these relate directly to the theories and modelling procedures used in filter cycle calculations (see Chapters 4–7).

2

Filter media

The filter medium is that critical component which determines whether or not a filter will perform adequately. Within the context of solid/liquid separation the term filter medium can be defined as ‘any material that, under the operating conditions of the filter, is permeable to one or more components of a mixture, solution or suspension, and is impermeable to the remaining components’ (Purchas and Sutherland, 2002). The principal role of a filter medium is to cause a clear separation of particulates (which may be solid particles, liquid droplets, colloidal material, or molecular or ionic species) from the liquid with the minimum consumption of energy. In order to achieve this, careful selection of the medium must take into account many factors; criteria by which a medium is assessed include the permeability of the clean medium, its particle retention capability and the permeability of the used medium. Serious loss of permeability may follow plugging or blinding of pores in the filter medium, and can determine the lifetime of the medium if an uneconomic filtration rate results. Permeability and particle retention are dependent on the structure of the medium, but interaction of media structure with the shape and size distribution of the particles challenging the medium is also of crucial importance. A vast variety of materials in diverse forms are used as filter media for which Purchas (1981) produced a guideline classification, which is reproduced in Table 2.1. Alternative methods of classification are available, but there always exist media that cannot be fitted neatly into the classification scheme. For example, Flood et al (1966) classified filter media into surface and depth media types. Surface type media are distinguished by the fact that the particles in suspension are mostly retained on the surface of the medium, with little penetration into the pores. Examples are filter paper, filter cloths and wire mesh. Depth type media, used mainly for liquid clarification, are characterised by the fact that the particles penetrate into the pores, where they are retained. The pores of such media are considerably larger than the sizes of the particles in

2 · Filter media 79 Table 2.1 Generalised summary of filter media based on rigidity (Purchas, 1981). Main type

Subdivisions

Smallest particle retained (
m) (approximate)

Solid fabrications

Flat wedge-wire screens Wire-wound tubes Stacks of rings

100 100 5

Metal sheets

Perforated Woven wire

100 5

Rigid porous media

Ceramics and stoneware Carbon Sintered metals Plastics

1
1 3 10

Cartridges

Sheet fabrications Bonded beds Yarn wound

Plastic sheets

Woven monofilaments Fibrillated film Porous sheets

Membranes

Polymeric Ceramic Metal


0.1
0.1 0.2

Woven fabrics

Staple fibre yarns Monofilaments Multifilaments

5 10
10

Non-woven media

Filter sheets Felts and needlefelts Paper (cellulose and glass) Polymeric (melt blown, spun bonded, etc.)

Loose media

Fibres Powders

3 2 2

0.5 10 5 and 2 10 1
1

suspension, whose concentration is generally not high enough to promote particle bridging across the pores; the particles may be retained by adsorptive or mechanical mechanisms. However, some media function simultaneously as surface and depth types and do not fit readily into this mode of classification.

80 Solid/Liquid Separation: Equipment Selection and Process Design Textiles, as a woven cloth or a nonwoven fabric, are probably the most common industrial filter medium, and are made from natural (cotton, silk, wool) and synthetic fibres. Wire cloths and meshes are also widely used in industrial filtrations, produced by weaving monofilaments of ferrous or non-ferrous metals; the simpler plain weave is used for sieving and sizing operations, and the more complex weaves such as Dutch twills are used on pressure and vacuum filters. At the small scale, particularly for laboratory use, filter papers are common, made from fibrous cellulosic materials, glass fibre or synthetic polymers; these papers are made using developments from conventional paper manufacturing processes.

2.1 Properties of filter media Filter media are characterised by many different chemical and mechanical properties, and the right combination can usually be found for most applications. Purchas (1980) identified some 20 significant properties divided into three major categories: (1) machine-orientated properties (Table 2.2), (2) application-orientated properties (Table 2.3) and (3) filtration-specific properties (Table 2.4). These and the characteristics of the feed suspension interact to affect the lifetime of the filter medium, which has implications for the process productivity and economics – as illustrated in Figure 2.1. Although

Table 2.2 Machine-orientated properties of filter media (Purchas, 1980). Machine-orientated properties of filter media – which restrict the use of a medium to specific types of filter Rigidity Strength Resistance to creep/stretch Stability of edges Resistance to abrasion Stability to vibration Dimensions of available supplies Ability to be fabricated Sealing/gasketing function Note: Many of these mechanical properties are determined by the structure of the medium and its methods of manufacture; only limited use is made of much of this information, and some of it may not be readily available.

2 · Filter media 81 Table 2.3 Application-orientated properties of filter media (Purchas, 1980). Application-orientated properties of filter media – which control the compatibility of a medium with the process environment Chemical and thermal stability

The resistance of a medium to specified chemical and thermal environments is usually available in published technical data.

Biological stability

Natural fibres are more prone to biological degradation than synthetic, but both suffer from accumulation of biological growths over their surfaces. Some synthetic materials limit the extent of the accumulation.

Dynamic stability

Shedding of fibres and migration of the fragments into the filtrate can be critical in some applications. Some media may shed a limited amount when new; the impact of this must be assessed in relation to the filtration application.

Absorptive characteristics

The fibres may absorb the process liquid, and consequently swell. This can change filtration characteristics considerably, usually by making the medium less permeable.

Adsorptive characteristics

Adsorption of components from the feed stream at the surface of the filter medium may alter the performance of the medium; this is particularly pronounced with membranes. Adsorption results from intermolecular attractive forces and can promote media blinding.

Wettability

Wettability affects the pressure required to initiate flow through a medium; small amounts of impurity either in the medium or adsorbed onto its surface can significantly alter its wettability. This property is seldom used with other than membranes.

Health and safety aspects

Handling powdered media (e.g. filter aids) can pose health and safety problems, and disposal of contaminated media may require special considerations.

Static characteristics

Static generated during the filtration of solvents and hydrocarbons, particularly those with very low electrical conductivity, can be significant; if this is combined with a low flash point, an incendive discharge can result. Risks are reduced by the use of antistatic additives, or by providing a long residence time for fluid in a pipe immediately downstream of the filter before it is discharged into any receiving vessel.

Disposability

Used and discarded filter media must be treated as part of the effluent from a process; the method of disposal depends on the type of contaminant remaining on the used medium. continued

82 Solid/Liquid Separation: Equipment Selection and Process Design Table 2.3 continued Application-orientated properties of filter media – which control the compatibility of a medium with the process environment Suitability for reuse

Many media can be cleaned and reused; facilities to allow this are designed into the operating cycle of many filters. Some media are not suitable for reuse.

Cost

Media costs vary widely and often form a substantial part of the running costs of a filter; reuse of media is important to reduce replacement costs.

Table 2.4 Filtration-specific properties of filter media (Purchas, 1980; Hardman, 1994). Filtration-specific properties – which determine the ability of a medium to achieve a specified filtration task Smallest particle retained

This is important if 100% removal of particles is required; it should be borne in mind that the size of a particle depends on the measuring technique used to determine size. Although important, 'particle size' is often a difficult quantity to define.

Retention efficiency

For a particular medium, retention efficiency particle concentration downstream of the medium
⫽ ᎏᎏᎏᎏᎏᎏ particle concentration upstream of the medium

(2.1)

decreases as the size of the particles is reduced; the size corresponding to 100% retention is the cut-off point and is used to define the 'absolute' rating of the medium. The shape of the retention versus particle size curve is dependent on the structure of the medium, the shape and size distribution of the particles, their feed rate and concentration, and chemical environment of the solution contacting the particles and the media. Flow resistance

Flow resistance is dependent on structure of the medium. It is often reported as the permeability measured at specific flow conditions; this is often the permeability of the medium to flow of air, which can be misleading for media to be used in a liquid filter. It affects both capital and running costs, and large differences in flow resistance exist between the diverse media available. continued

2 · Filter media 83 Table 2.4 continued Filtration-specific properties – which determine the ability of a medium to achieve a specified filtration task Dirt holding capacity

Important for clarifying filters; this term is not used in relation to cake filters. This is usually the amount of solids (dirt) that can be held without exceeding a defined pressure drop across the filter. Higher capacity usually indicates a longer 'on stream' time before filter cleaning or replacement is needed.

Tendency to blind

Blinding is associated with solids that cannot be removed from the medium using the normal cleaning procedures; it causes an increase in the resistance to flow.

Cake discharge characteristics

The ease of removal of a cake from media used on either batch or continuous filters is crucial; the cake should not adhere to the medium (adhesion is a result of mechanical and electrical properties of the medium and the slurry).

FILTER ORIENTED FEED ORIENTED PROPERTIES PROPERTIES Ability to be fabricated Chemical/thermal stability Creep/stretch Biological stability Edge stability Dynamic stability Vibrational stability Ad/absorptive characteristics Rigidity Health and safety aspects Strength Disposability Sealing Re-use PRODUCTIVITY LIFETIME COST MEDIA STUCTURE Woven (mono-/multi-filament) Non-woven Cartridge Metal/solid fabrication Loose fibres/particles

FILTRATION PROPERTIES Particle retention Flow resistance Dirt holding capacity Tendency to blind Cake discharge characteristics Cleanability

Figure 2.1 The feed to the filter and the filter medium interact to an extent that depends in part on the operation of the filter, affecting process productivity and medium lifetime, and hence the process costs.

84 Solid/Liquid Separation: Equipment Selection and Process Design all are important in one way or other, the machine-orientated properties are often considered in discussion with the media supplier and the user may not have access to meaningful information on these properties. Nonetheless, the filtration engineer needs to be aware of generalities: for example, media flexibility is an important feature in certain applications such as caulking of woven cloths onto vacuum and pressure filter plates, and gasketing between plates and frames in pressure units. The ideal filter fabric should provide a long and trouble-free performance – to do this it must provide resistance to stretch, structural deformation and flex fatigue and it should not be affected by mechanical and abrasive forces. Many of the application-orientated and filtration-specific properties involve detailed knowledge about the process in which the filter medium is to be used, and the user should have most of this knowledge. Tables 2.3 and 2.4 therefore become more directly pertinent to the filter user as many affect health, safety, economic or operational aspects of the filtration. Notwithstanding the amount of background knowledge that may be available and should be collated in a convenient format by the filter user during the design stages of a project, in new applications repeated laboratory trials are needed to indicate the media changes that occur with use in filtration. Media suppliers tend to draw heavily on past experience when specifying a filter medium for a particular application. Even so, it is recognised that the filter fabric may not in isolation be the ideal medium for all process conditions; and in some cases filtration has to be assisted, for example, by the use of filter aids and/or body feeds, or by polyelectrolyte treatments or filter papers (Hardman, 1994).

2.2 Textile media The majority of filtration textiles are based on synthetic fibres, although some are made from natural fibres. Purchas (1996) noted the confusions that arise due to the multiplicity of synthetic fibres, which is further compounded by many different trade names. Out of this confusion he was able to define five convenient categories of filtration textiles: woven fabrics, needlefelts, bonded media, stretched film media and composites. 2.2.1 Woven fabrics Apart from the availability of a wide range of materials for manufacturing the fibres themselves, the construction and filtration characteristics of a filter cloth are determined by the type of yarn, the weave or fabric construction properties and the finish applied to the cloth.

2 · Filter media 85 2.2.1.1 Yarn types One of four basic yarn types, shown in Figure 2.2, is normally employed in the production of woven fabrics: monofilaments, multifilaments, staple spun yarns and fibrillated tape yarns (a helpful summary of trade names is given by Purchas and Sutherland, 2002).

Figure 2.2 Common yarn types used in the manufacture of filter media (Madison Filter). Monofilaments are single yarns made from molten polymer extruded through a die, then drawn through a series of rollers to orient the molecules in order to produce a filament with the desired stress/strain characteristics. Monofilaments usually have a circular cross-section (although other profiles are possible), with diameters in the range 0.1– 0.3 mm for filtration applications (larger are possible). Fabrics produced from monofilaments are characterised by their resistance to blinding, relatively high throughput and ability to discharge filter cakes cleanly and effectively at the end of a filter cycle. However, monofilaments do not always provide the necessary particle retention if the feed particle size is particularly small, so if excellent filtrate clarity is essential a monofilament cloth may not represent the best choice. Multifilaments are extruded and orientated in a similar way to monofilaments, but the die or ‘spinneret’ contains a large number of smaller apertures.

86 Solid/Liquid Separation: Equipment Selection and Process Design The diameter of individual filaments is usually about 0.03 mm, and the fineness of both the individual filaments and the assembly of filaments is expressed in terms of its linear density, typically in terms of denier (the weight in grams of 9000 m of filament), decitex (the weight in grams of 10000 m of filament) or tex (the weight in grams of 1000 m of filament). After extrusion the filaments are twisted; this binds the filaments together, helps protect the yarn against abrasion, strengthens the filament assembly and makes it more rigid. A high level of twist also reduces the blinding tendency of the cloth. Nonetheless, in spite of their better retention, higher strength and greater flexibility multifilament fabrics are more prone to blinding than monofilaments. Staple spun yarns are produced from short fibres using spinning techniques developed for natural fibres such as cotton or wool. As a general guide, yarns from wool spinning systems are bulkier than those from cotton systems. A consequence of this, combined with the relative ease with which the fibres can move within the yarn assembly, is that they are better for filtration than either multifilament yarns or staple yarns from cotton spinning systems in two respects – they provide a higher throughput and are less prone to blinding. After extrusion, the fibre length is cut to between about 40 and 100 mm, depending on the short staple spinning system employed. Fibrillated tape yarns are produced from narrow width polypropylene films that are converted into relatively coarse filaments using special cutters and pins. These yarns find only limited use in filtration, mainly as coarse, open weave structures to provide support or drainage fabrics behind finer grade filter cloths. 2.2.1.2 Fabric constructions and properties Three traditional weave patterns are used for filter cloths – plain, twill and satin weaves, together with a link construction. The plain weave, an example of which is shown in Figure 2.3, is the most basic of fabric constructions; it is also the tightest and most rigid of the elementary weave patterns and is particularly suited to multifilament or short staple yarns. In a plain weave, the warp (the yarn which runs along the length of the loom) passes over and under alternate weft yarns (the yarns which run across the loom). A twill weave involves the weft passing over or under two or more warp yarns, combined with a regular sideways displacement from one row to the next. There are numerous variations on the twill weave, although all of them feature the diagonal pattern running through the fabric: this is clearly seen in the 2/2 twill shown in Figure 2.4. (The notation 2/2 indicates that

2 · Filter media 87

Figure 2.3 A plain weave multifilament yarn fabric – the warp direction is vertical. Plain weaves produce tight, rigid structures and give high filtration efficiencies (Madison Filter).

Figure 2.4 A 2/2 twill weave fabric woven from woollen spun yarn – the warp direction is vertical. Twill weaves create bulky media with good mechanical properties and flexibility, but the ‘hairiness’ of staple fibres can cause cake release problems (Madison Filter).

88 Solid/Liquid Separation: Equipment Selection and Process Design any one warp of weft yarn is passed over or under by two weft or warp yarns). Twill weave fabrics are ideally suited to yarns produced on short staple fibre systems, and are more flexible than those produced using a plain weave. The concept of the twill weave is extended by the satin weave by using wider spacings between points of interlacing to produce a very smooth surface (and hence good cake discharge) without diagonal twill lines, as shown in Figure 2.5. The ability of threads being able to move relative to each other in satin weaves results in a more flexible fabric and one in which there is less likelihood of particles becoming entrapped. However, this characteristic is also associated with poorer collection efficiencies. Typical applications are in filter presses in effluent treatment processes, cement and coal dewatering, and rotary vacuum or disc filters operating in mining or hydrometallurgical refining processes. For filter presses, small horizontal belt, tipping pan, disc and rotary drum filters, monofilament cloths are usually in the weight range from 200 to 450 g m⫺2; for higher throughput, heavier duty applications (e.g. on horizontal belt or belt discharge rotary drum filters), the cloth weight range may extend to 1500 g m⫺2. Examples of filter cloths with warp and weft yarns of various fineness are listed in Table 2.5. The weight of multifilament cloths varies from about 100 g m⫺2 to as high as 1000 g m⫺2; the heavier constructions are used for more arduous duties such as vertical automatic filters. Some typical characteristics of multifilament cloths are shown in Table 2.6. Fabrics produced from staple spun fibres usually have a weight between about 400 and 700 g m⫺2 (see Table 2.7), and find applications in conventional filter presses, vacuum leaf, pressure leaf, disc and rotary drum filters. Instead of using identical yarns for both the warp (along the length of the loom) and the weft (across the loom), combinations of different yarns can be beneficial. For example, in a multifilament warp/staple weft cloth the multifilament component gives the cloth higher warp tensile properties and a reasonably smooth surface; whereas the bulk of the staple weft gives the cloth improved filtration effectiveness and durability. A monofilament warp/multifilament weft cloth (see for example Figure 2.6) has excellent discharge properties as typified by the monofilament warp, together with good retention characteristics given by the multifilament weft. The breadth of properties obtained with mixed yarn cloths is illustrated in Table 2.8, and their applications are mainly across the range of vacuum and pressure filters.

2 · Filter media 89

Figure 2.5 A satin weave fabric woven from monofilament yarns – the warp direction is vertical. Satin weaves create smooth release surfaces with flexibility and resistance to blinding (Madison Filter).

Figure 2.6 The face side (filtering surface) of a satin weave mono/multifilament cloth. The warp direction is vertical. The reverse side of the cloth has a rougher texture and both warp and weft yarns are clearly visible (Madison Filter).

Filterlink constructions for monofilament fabrics are produced by enmeshing preformed monofilament spirals, which are then linked together with a series of standard (straight) monofilaments (Figure 2.7). The spirals are pulled tightly into the straight filaments during a heating process that effectively

90 Solid/Liquid Separation: Equipment Selection and Process Design Table 2.5 Examples of monofilament cloth qualities for liquid filtration (Sefar). Fibre and weave

Air permeability (m3 m⫺2 h⫺1 at 20 mm w.g.)

Weight (g m⫺2)

Thickness (
m)

Polyamide 12 Satin

7200

335

635

Satin

9000

340

660

Twill Twill Twill

504 1080 3690

205 190 310

300 320 630

342

210

320

Twill Twill Twill Twill

360 684 1080 2250

136 235 255 260

200 380 480 525

Twill

6660

265

725

Twill Satin

12,060 11

420 285

1220 390

Satin

18

435

590

Satin

79

370

500

Satin

108

272

390

Satin

324

290

390

Satin

612

300

430

Satin Satin Satin

2988 6660 9900

260 310 300

450 610 750

Polypropylene Twill

Typical filter suitability

Belt filter, drum filter, leaf filter, filter press Belt, drum and rotary disc filters, filter press, centrifuge Centrifuge Leaf filter, filter press Belt and drum filters, filter press, centrifuge Leaf filter, filter press, centrifuge Filter press, centrifuge Leaf filter, filter press Filter press, centrifuge Drum filter, filter press, centrifuge Belt and drum filters, filter press Rotary table filter Leaf filter, filter press, centrifuge Leaf filter, filter press, centrifuge Leaf filter, filter press, centrifuge Leaf filter, filter press, centrifuge Drum filter, filter press Drum filter, filter press Filter press Belt and drum filters Belt and drum filters

2 · Filter media 91 Table 2.6 Examples of multifilament cloth qualities for liquid filtration (Sefar). Fibre and weave

Air permeability (m3 m⫺2 h⫺1 at 20 mm w.g.)

Weight (g m⫺2)

Thickness (
m)

Typical filter suitability

Polyamide 6.6 Plain Plain Twill Twill

72 252 900 3240

390 420 297 120

650 700 670 268

Filter press Leaf filter, filter press Rotary disc filter

Polypropylene Twill Twill Twill

14 65 144

660 540 505

1060 1100 990

Filter press Leaf filter, filter press Filter press

Table 2.7 Examples of woven staple yarn cloth qualities for liquid filtration (Madison Filter). Fibre and weave

Air permeability (m3 m⫺2 h⫺1 at 20 mm w.g.)

Weight (g m⫺2)

Tensile strength (kN m⫺1) Warp

Weft

Polyester Twill Twill Twill Plain

60 360 60 30

540 540 540 575

56 56 56 76

22 22 22 56

Polyamide Twill Twill Twill Twill Twill

570 600 600 240 78

460 560 570 710 710

36 40 40 70 70

24 28 28 26 26

Polypropylene Plain Twill Twill

420 600 210

240 375 410

28 44 44

20 28 28

Fibre Warp

Yarn types Weft

Weave

Weight (g m⫺2)

Air permeability (m3 m⫺2 h⫺1 at 20 mm w.g.)

Tensile strength (N m⫺1) Warp Weft

Polyester

Multi Multi

Staple Staple

Reversible satin Reversible satin

630 630

120 48

120 120

40 40

Polypropylene

Mono Mono Mono Mono Mono Mono Mono Mono Multi Multi Multi Multi Multi Multi Multi Multi Multi Multi Multi Multi Multi Multi Multi

Multi Multi Multi Multi Multi Multi Multi Multi Staple Staple Staple Staple Staple Staple Staple Staple Staple Staple Staple Tape Tape Tape Tape

Twill Twill Twill Satin Satin Satin Satin Satin Reversible satin Reversible satin Reversible satin Reversible satin Reversible satin Reversible satin Reversible satin Reversible satin Reversible satin Twill Twill Twill Twill Twill Twill

235 235 235 300 300 340 570 570 460 460 545 545 585 585 585 610 610 815 815 850 850 850 850

4800 1620 480 3000 144 144 1890 66 570 60 66 ⬍18 48 ⬍18 ⬍12 78 ⬍18 240 ⬍18 240 48 240 48

56 56 56 70 70 70 90 90 100 100 100 100 100 100 100 100 100 180 180 180 180 180 180

30 30 30 24 24 36 110 110 24 24 110 110 110 110 110 110 110 48 48 108 108 108 108

92 Solid/Liquid Separation: Equipment Selection and Process Design

Table 2.8 Mixed yarn cloth qualities for liquid filtration (Madison Filter).

2 · Filter media 93

Figure 2.7 Filter cloth with the filterlink construction together with a tape yarn filler. These fabrics have exceptionally smooth surfaces and offer extended life by reducing mechanical wear (Madison Filter).

imposes a heavy crimp and locks the structure. The tight packing of the spirals results in exceptional width stability and gives the fabric excellent resistance to distortion. The filtration effectiveness of this fabric construction is improved by filling the spirals with additional monofilaments having oval or rectangular profiles. A particular attribute of belts made from link fabrics is the absence of a mechanical seam, which is the weak link in conventional belts and is frequently the first point of failure. Because they are made from fairly coarse monofilaments, these materials can be quite heavy (frequently in excess of 1000 g m⫺2), and are particularly useful in multi-roll filters such as belt filters in the dewatering of polymer flocculated sludges such as sewage or coal. The filtration characteristics of woven fabrics are dependent on the weave, amongst other cloth properties; the dependence is summarised in Table 2.9. Table 2.9 Effect of weave pattern on the filtration performance of a cloth (Ehlers, 1961). Order of Maximum preference retention 1 2 3

Plain Twill Satin

Minimum resistance to flow

Minimum moisture in cake

Easiest cake discharge

Satin Twill Plain

Satin Twill Plain

Satin Twill Plain

Maximum Least cloth tendency life to blind Twill Plain Satin

Satin Twill Plain

94 Solid/Liquid Separation: Equipment Selection and Process Design Plain weave fabrics tend to be employed where maximum filtration efficiency is required; twill weave fabrics where greater bulk and mechanical durability are a primary concern; and satin weave fabrics (particularly with monofilaments) where good discharge and blinding resistance are the primary requirements. 2.2.1.3 Fabric finishing processes Fabric finishing processes, stabilisation and surface treatments, are carried out to ensure fabric stability and to modify its surface characteristics to regulate the fabric permeability. During the production process yarns are held under tension, so there is a tendency for them to relax once the tension is removed. This can cause major operational problems during filtration, such as cloth port holes moving out of alignment with the holes in the filter plate, thereby impeding flow of filtrate out of the press or feed slurry bypassing the filtration area. To avoid such problems, the fabric is subject to either hot aqueous or dry thermal treatment operations – stabilisation processes. This dry process involves breaking down the intermolecular bonds in the fibre, then allowing them to cool and reform in a new position. For belt filters and vertical automatic filter presses, it may be preferable to subject the fabric to a prestretching process which reduces the fabric tendency to stretch during filter operation and helps to ensure better tracking by equalising any tension variations that may exist across the width of the cloth. Surface treatments include singeing, calendering and other special treatments designed to give good filtrate clarity and cake discharge characteristics combined with a low cloth resistance and a reduced tendency to blind. Fabrics produced from short staple fibres have a natural fibrous surface (an example can be seen in Figure 2.4) that can impede cake discharge; this is overcome by singeing the fabric by passing it over a gas flame or a hot metal strip, which is usually followed by contact with a wet surface in order to stop any smouldering. Calendering is the most frequently used surface treatment process, and involves passing the fabric between heated, pressurised rollers. The temperature, pressure and speed through the rollers are selected to suit the polymer type from which the fabric is constructed, as well as to give the required permeability to the fabric. The process smoothens the surface of the fabric in order to give better cake discharge and to regulate its permeability. Figure 2.8 shows the effect of calendering a monofilament cloth, indicating the smoothing and pore size reduction effects that result from using the process.

2 · Filter media 95

Figure 2.8 Uncalendered and calendered monofilament weave fabrics – the warp direction is vertical (Madison Filter). 2.2.2 Composite media The properties of a filter medium can be changed by layering a second medium onto the surface of the first to make a composite medium. Examples of these media include surface coated fabrics, laminated media (where two or more woven or nonwoven materials are fixed together, either firmly or loosely) and multilayer weaves. 2.2.2.1 Surface coated fabrics Surface coatings applied to filter fabrics can enhance one or more of the filtration properties of the fabric. The coating may be sprayed on as a liquid or laid down as a sheet which is then bonded to the fabric. Microporous polymer coatings may be used to provide a smoother and fine aperture size to the fabric surface, which may enable easier detachment of the cake and prolong the lifetime of the medium. A polyurethane coating on woven polyester substrate is the basis for Madison’s Primapor fabric, for use on process filters such as rotary drums, filter presses and pressure vessel filters. A section through a Primapor cloth is shown in Figure 2.9. A development of this is the Azurtex coatings, again of polyurethane but coated onto a woven polyester or polypropylene substrate. Cross-sections through Azurtex cloths are shown in Figure 2.10; the coating lies predominantly on the surface of the fabric, which is consequently smoothed; the picture also shows that only limited polyurethane enters the spaces between the fibres.

96 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 2.9 Section through a Primapor fabric, showing the polymer coating lying on the feed surface of the woven fabric (Madison Filter).

Figure 2.10 Azurtex showing coating of the fabric by the polymeric film and the limited penetration of the polymer between individual yarns (Madison Filter).

2.2.2.2 Laminated fabrics Laminated media involve two or more layers of fabric being fixed together, such that the resulting laminate structure can give either depth or surface filtration characteristics to the medium. The layers usually have different properties, notably the size of the apertures (which is related to the size of the particle that can be captured). Where surface filtration is to be promoted, as in most cake filtrations, the finest layer is the first one met by the feed stream and acts as the filtering medium. The reverse is the case when depth filtration is to be encouraged as in, for example, cartridge filters where dirt holding capacity may be an important operational property of the filter.

2 · Filter media 97 2.2.2.3 Double layer weaves The double layer weave is an example of a multilayer weave that is becoming more common in liquid filtration applications. The weave effectively combines two fabrics in a single manufacturing step; in this way two different functional fabrics can be combined into a single multilayered fabric. Multilayer weaving has enabled manufacture of long belts with good stability characteristics for use as filter media on belt presses. For filtration applications, the fabric construction is usually a strong and relatively coarse support layer to give high transverse stability, to reduce the risks of distortion and wrinkling and remove the need for a separate support. The finer filter layer determines the filtration performance and effectiveness; Sefar TETEX double layer weave fabrics include a fine top layer that enables capture of particles with sizes as small as 8 ␮m. The interwoven support layer improves drainage and cake dryness, and provides mechanical strength for precise tracking and improved service life. The general structure of a double layer weave fabric is shown in Figure 2.11, and some typical cloth qualities are shown in Table 2.10.

Figure 2.11 Cross-section through a double layer weave, showing the finer weave at the upstream (filtering) surface and the coarser at the downstream surface (Madison Filter).

98 Solid/Liquid Separation: Equipment Selection and Process Design Table 2.10 Examples of double layer weave cloth qualities for liquid filtration (Sefar). Fibre and weave

Air Weight Thickness permeability (g m⫺2) (
m) (m3 m⫺2 h⫺1 at 20 mm w.g.)

PEEK (Polyether etherketone)

Typical filter suitability

4212 8496

515 505

925 1145

Belt and drum filters, centrifuge Belt and drum filters, centrifuge

108 180 360 720 1440 2160 6120

420 455 425 360 440 440 425

760 850 860 740 920 950 1280

Belt and drum filters, centrifuge Belt and drum filters, centrifuge Belt and drum filters, centrifuge Belt and drum filters, centrifuge Belt and drum filters, centrifuge Belt and drum filters Belt and drum filters

Polypropylene

2.2.3 Needlefelts and other nonwoven media Needlefelts (see Figures 2.12 and 2.13) are produced by stacking layers of carded fibre on top of one another to form a ‘batt’, the depth of carded fibre used depends on the desired thickness and density of the final needlefelt.

Figure 2.12 The top surface of a needlefelt cloth showing the random orientation of the fibres (Madison Filter).

2 · Filter media 99

Figure 2.13 Cross-section view of a calendered polypropylene needlefelt fabric. Points where the needles have penetrated are identified by the fibre direction orientated towards the scrim layer at the bottom (Madison Filter).

The batt is then transformed into a denser structure by needle-punching with special barbed needles. Usual practice is to needle the fibres into a woven scrim, which provides the structure with the necessary tensile properties. The finishing processes used on needlefelts are similar to those used for woven fabrics. Compared with woven fabrics, needlefelts provide many more readily accessible pores per unit area, and hence the potential for greater rates of filtration. It should be noted that needlefelts have only limited use in liquid filtration largely due to their instability and tendency to blind. Nonwoven media other than needlefelts are important in several areas of filtration, and hints to their diversity are given by Table 2.11. Three classes of media are identified; wet laid, dry laid and spun bonded. Spun bonded is further divided into three classes which possess progressively finer fibres: melt spun, melt blown and spun blown (omitted from Table 2.11). The basic methods of manufacture are derived from the textile or paper industries, and the fibres are made from polymers or cellulose. Wet laid media are derived from paper manufacturing processes and are composed of short staple fibres dispersed in water to form a slurry that is fed to a moving wire screen on which it is dewatered. The randomly orientated fibres form a web which is dried by a sequence of heated rollers. An adhesive or binding agent may be dispersed in the original slurry or sprayed onto the web during or after dewatering. Dry laid media manufacturing methods are based on traditional opening and carding processes used in the textile industry; the media are composed of short fibres. Multiple layers of the open fibres are laid mechanically to form

100 Solid/Liquid Separation: Equipment Selection and Process Design Table 2.11 Liquid filtration applications of non-woven media (adapted from Purchas, 1996 and Sanstedt, 1980).

Market segment

Type of non-woven media Needlefelt

Bonded media Dry laid

Spun bonded†

Wet laid

Melt spun Tea bags Coffee bags Machine tool coolant Milk Edible oil Food & beverage Cartridges RO/UF

Melt blown

● ●

● ●

●

●

● ● ●

●

●

●

●

●

●

●

†

Purchas also lists spun blown media as a category of spun bonded, but they are omitted here due to their developmental status. Needlefelts are included to make the list of non-wovens comprehensive.

a web, with the orientation of the layers being selected to give the desired directional strengths to the finished fabric. Alternatively, the opened fibre is transported and dispersed pneumatically by ‘air layering’ to form a nondirectional web. Air layered webs are usually bulkier than carded webs. If the fibres are of an appropriate material, the web may be heat sealed by means of hot rollers. Alternatively, the web is treated with an aqueous binding resin by spraying or immersion before it is finally dried and cured. Spun bonded media production processes exploit the thermosetting properties of polymers, to form fibres that can be bonded by combinations of heat, pressure and chemical activation. Melt spinning, using conventional synthetic fibre technology, was the earliest method used for producing spun bonded filter media and continues to be of major importance, but finer fibres are produced by melt blowing and flash spinning processes. In melt spinning, the basic process is to extrude molten polymer through the orifices of a spinneret (which determine the fineness of the final fibres) to produce a large number of continuous filaments that are quenched with a crossflowing air stream. They are then drawn down by a concurrent air jet, and electrostatic charges separate the filaments which are laid down randomly on

2 · Filter media 101 to a moving screen belt beneath which is a suction box. Further processes, such as bonding or needle punching, are sometimes used. Melt blowing produces finer fibres by impinging a high velocity air jet on the filaments extruding from the spinneret, causing them to fibrillate and disintegrate into fine, short fibres with lengths 10 –20 cm (Meyer and Lim, 1989). A recent development is the production of nanofibres that are used in some cartridge constructions. The fibres are collected using techniques similar to those used in the melt spinning process. Flash spinning is used by DuPont (Meyer and Lim, 1989) to produce high density polyethylene sheet. Whereas pure molten polymer is extruded in the above melt blowing and spinning processes, in this process the extrudate is a partially separated two-phase mixture of pure solvent droplets and a highly saturated polymer/solvent mixture. Decompression across the spinneret capillaries induces flash evaporation and formation of fibrils. Expanding solvent vapour creates voids in the fibrils. The fibril webs are collected on a moving belt and are then subjected to a combination of heat and pressure to selfbond into sheets; the resulting high burst strength sheets comprise continuous strands of fine interconnected fibres with high surface area. 2.2.4 Selection and applications of filter cloths Table 2.12 classifies different types of cloths for liquid filtrations, and example applications are then given in Table 2.13. These tables collate some experiences of cloth applications into a preliminary selection guide for filter cloths, giving guidance as to what types of cloths have been found suitable Table 2.12 Cloth types for liquid filtration (Madison Filter, reported by Purchas, 1996). Filter cloth group

Cloth type

Weight (g m⫺2)

Air permeability (m3 m⫺2 min⫺1 at 12.7 mm w.g.)

Maximum continuous operating temperature (°C)

1

Woven monofilament polyester Woven multifilament polyester Woven staple polyester Needled polyester Woven monofilament polyamide

350–550

30–150

20

150–650

1–5

120

450–700 640 250–400

1–5 2 25–60

120 120 100–110

2 3 4 5

continued

102 Solid/Liquid Separation: Equipment Selection and Process Design Table 2.12 continued Filter cloth group

Cloth type

Weight (g m⫺2)

Air permeability (m3 m⫺2 min⫺1 at 12.7 mm w.g.)

Maximum continuous operating temperature (°C)

6

Woven multifilament polyamide Woven staple polyamide Needled polyamide Woven monofilament polypropylene Woven multifilament polypropylene Woven staple polypropylene Woven multifilament warp/staple weft polypropylene Needled polypropylene Woven monofilament polypropylene Woven monofilament polyvinylidene chloride (Saran) Woven staple modacrylic Woven cotton/nylon combination Woven cotton

100–250

1–5

110

400–800 600–1000 200–350

1–5 2–6 40–120

110 110 95

350–700

0.5–5

95

200–650

1–20

95

450–600

1–8

95

400–600 200–330

1–5 30–80

95 85

500–600

⬎200

85

430 800

negligible 0.5

85 100

500–650

0.5–2

100

7 8 9 10 11 12

13 14 15

16 17 18

for a range of applications. It can be observed that the cloth selection depends on the type of filter used as well as the feed, as noted in Figure 2.1. 2.2.5 Damage to filter media Fabric stretch arises in several types of filter, but the cause can depend on the design and operation of the filter. In filter presses and both vacuum and pressure leaf filters stretch may occur as a result of the vertical pull of heavy filter cakes on the cloth during cake discharge; in filter presses the stretch can result in portholes in the cloth being pulled out of alignment with the holes

Table 2.13 Liquid filter cloth applications (Madison Filter, reported by Purchas, 1996). Industry

Process

Filtration equipment

Sugar

1st and 2nd carbonisation Mud sweetening

Filter leaf Candle filter Rotary vacuum drum filter Filter press

pH

Process temperature (°C)

Particle type/size

7, 11 11 7, 11 6–10

95

Amorphous

Automatic pressure filter

Phosphoric acid

6, 7, 11 12

Juice filtration

Filter press

7, 11, 18

Cane sugar refining

Filter leaf

2, 7, 11

Removal of calcium sulphate

Horizontal pan filter

Up to 6

100

Crystalline/ coarse

Belt filter Alumina

Filter cloth group (see Table 2.12)

Filter leaf

Red mud underflow

Rotary vacuum drum filter

Hydrate product and seed

Rotary vacuum disc filter

1

13

Amorphous/fine

9, 10, 11

Amorphous/coarse

5, 9, 14

Crystalline/coarse

5, 9, 14

High throughput and resistance to blinding. Good mechanical resistance and cake discharge. Good mechanical resistance, dimensional stability and seal. Good dimensional stability, tracking and high strength. Good mechanical resistance, dimensional stability and seal. High throughput and resistance to blinding. Resists abrasion and blinding by crystal formation. Good dimensional stability. Dimensional stability to ensure good tracking. Resistance to red mud blinding. High throughput. Resistance to blinding and good cake discharge. Resists stretch and abrasion. High throughput and good cake discharge.

continued

2 · Filter media 103

Red mud overflow

1, 9

Filter media/filtration features

Industry

Process

Edible oils and fats

Expelled oil Bleaching Hardening

Filtration equipment

pH

Filter press

Process temperature (°C)

120

Particle type/size

Amorphous/ coarse

Winterising Ceramics and china clay

Slip dewatering

Filter press

7

40

Crystalline/ coarse

China clay Sewage and effluent

Municipal

Filter media/filtration features

3, 7

Good mechanical resistance and retention. Resistance to heat. Excellent retention of catalyst.

2, 3, 7 7, 17 7, 17

Resistance to blinding by fats. High throughput.

6, 7, 10, 12, 13

Good mechanical resistance and seal. Consistent cake density. Fine particle retention. Resistance to pin holing.

6, 10, 12 Filter press

Belt filter

Industrial

Filter cloth group (see Table 2.12)

Filter press

1, 5, 7, 11, 14, 15 5–10

30

Amorphous/ fibrous

1

Amorphous/ variable

1, 5, 7, 12

Good resistance to blinding and mechanical damage. Good cake discharge. High stability for good tracking. Strong belt joining, high mechanical resistance. Good cake discharge, fine particle retention and high throughput.

continued

104 Solid/Liquid Separation: Equipment Selection and Process Design

Table 2.13 continued

Table 2.13 continued Industry

Process

Dyestuffs, pigments and intermediates

Filtration equipment

pH

Process temperature (°C)

Particle type/size

Filter press Automatic pressure filter

1–13

90

Crystalline/ fine

Vacuum filter

Filter cloth group (see Table 2.12)

Filter media/filtration features

2, 10, 11, 12, 13

Fine particle retention and suitable for cake washing. Dimensional stability to ensure good tracking. Good resistance to chemical conditions and blinding.

10 2, 3, 9, 11, 12

Viscose

Gel filtration

Filter press

12

20

Amorphous or gelatinous

8

Optimum gel retention. High throughput. Ideal for offmachine and back washing.

Starch products

Starch, glucose and gluten dewatering

Filter press

5–8

30

Amorphous/ coarse

7

Good resistance to blinding, ease of washing. Good throughput.

Coal

Coal dewatering

Rotary vacuum belt filter

2, 6

Rotary vacuum disc Coal tailings

5–8

20

Filter press

Rotary vacuum disc

5–8

25

5–8

40

Crystalline/ coarse Amorphous/–

Variable/ coarse –/coarse

5, 9 1, 5, 14

7, 13 5, 14

Dimensional stability to ensure good tracking. Abrasion resistant and good cake discharge. Dimensional stability for large presses. Good cake discharge. Resists blinding. Good resistance to blinding, high throughput and low cake moisture content.

continued

2 · Filter media 105

Metal Non ferrous concentrates concentrates Iron ore

1

Industry

Process

Filtration equipment

Brewing

Mash Yeast

Sparging press Filter press

Roughing

Filter press

Non ferrous metal refining

Cement

5–8

Process temperature (°C)

Particle type/size

Filter cloth group (see Table 2.12)

Filter media/filtration features

80 20

Amorphous/coarse Amorphous/ fine

9 3, 12

Maintains high throughput. Fine particle retention at high throughput.

20

Amorphous/ fine

8

Maintains high throughput, regenerable.

3, 12, 13

Fine particle retention and resistance to blinding. Good blinding resistance, mechanical resistance and cake discharge. High throughput with good filtrate quality. Controlled permeability and low voltage drop.

Filter press Hydro metallurgy

Rotary vacuum drum filter

Filter leaf

Titanium dioxide

pH

Electrometallurgy

Diaphragm press

Clarification

Filter leaf

Removal of iron and treatment

Vacuum leaf filter

Washing and dewatering

Rotary vacuum drum filter

Raw feed dewatering prior to kiln

Filter press

1, 2, 5, 9, 13

1–14

100

Variable/ variable

2, 11 2, 10, 16

3–11 5

2, 9 25

Crystalline/fine

3, 11, 18

2, 3, 4, 11

5–8

25

Variable/coarse

1, 5

Good resistance to blinding. High throughput. Good cake pickup, resistance to blinding and retention efficiency. Low moisture content consistent with throughput. Good cake discharge. Good dimensional stability, mechanical resistance and discharge. High throughput.

106 Solid/Liquid Separation: Equipment Selection and Process Design

Table 2.13 continued

2 · Filter media 107 in the filter plate, thus impeding drainage of filtrate from the filter. In vertical automatic filter presses, stretch may be induced by filter belt tensioning forces, particularly on start-up; if the belt stretches to the limit of the filter’s tensioning stroke, then the filter has to be taken out of service while the belt is shortened and reseamed. In some types of disc and rotary drum filters fabric stretch may result from the repeated blowback of compressed air that is used at the end of the filter cycle to assist cake discharge; mechanical damage to the fabric can then occur if the stretched cloth is engaged by the filter’s scraper blade. Both structural deformation and flex fatigue may result not only from the filter operational aspects but also from high pressure water jets used for cleaning purposes, leading to particle retention deterioration through mechanical damage or distortion of the threads in the cloth construction. Hardman (1994) lists the following common causes of mechanical wear from abrasive forces: 1. on belt filters the moving edge of the belt may be subjected to abrasion through contact with stationary parts such as defective or poorly maintained cloth tracking mechanisms; 2. on belt, disc and rotary drum filters scraper blades may be too close to the face of the fabric, leading to abrasion or local damage if a large particle becomes trapped between the blade and the fabric; 3. scraper blades are often used by operators to assist cake discharge, and can inflict serious mechanical damage to the cloth (although this is reduced by the use of plastic scrapers); 4. under high pressure abrasive slurries can be very aggressive, causing and seeking out, and then enlarging, microscopic apertures or imperfections in the fabric; 5. rough surfaces on filter plates, on the drainage pips or occasionally on the sealing faces, cause mechanical damage of the fabric; this is exacerbated by the use of high filtration pressures. An example of the onset of abrasion damage is shown in Figure 2.14 where the exposed ends of fractured yarns are visible; failure to rectify the cause of the abrasion leads to serious wear of the cloth. Damage by particles becoming lodged in the weave structure, and subsequently creating a hole in the fabric, is illustrated in Figure 2.15. To avoid chemical or thermal damage to the yarns, the choice of material for construction of the filter medium for any particular filtration application is important. Historically, filter fabrics were produced by weaving yarns spun

108 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 2.14 The onset of abrasion damage to polyamide 66 yarns in a plain weave fabric (Madison Filter).

Figure 2.15 Damage created by sharp particles: near the centre of the photograph is a large particle endeavouring to pass through a hole in the fabric, and at the top right is a smaller hole that has become rounded from the force of abrasive particles (Madison Filter).

from natural fibres that, on wetting, would swell to produce very effective media. However, in chemically aggressive conditions their life expectancy is limited. Synthetic fibres are generally more durable, as indicated in Table 2.14, but it is still important to make the correct selection for the conditions that prevail in the filter.

2 · Filter media 109 Table 2.14 Thermal and chemical attributes of fibres (Hardman, 1994). Resistance to Fibre type

Polypropylene Polyethylene Polyester (PBT) Polyester (PET) Polyamide 6.6 Polyamide 11 Polyamide 12 PVDC PVDF PTFE PPS PVC PEEK

Density (kg m⫺3) 910 950 1280 1380 1140 1040 1020 1700 1780 2100 1370 1370 1300

Maximum operating temperature (°C) 95 85 100 100 110 100 100 85 100 150⫹ 150⫹ 80 150⫹

Acids

Alkalis

Oxidising agents

•••• •••• ••• ••• • • • •••• •••• •••• •••• •••• •••

•••• •••• •• • ••• ••• ••• ••• •••• •••• •••• •••• •••

• • •• •• • • • •••• ••• •••• •• •• ••

Hydrolysis

•• •• • • • • • ••• •••• •••• •••• •••• ••••

•••• very good; ••• good; •• fair; • poor.

Polyester fibres, for example, will degrade when exposed to strong bases and prolonged hydrolysing conditions, and polyamide fibres will not tolerate continuous exposure to strong acids. Polypropylene is widely used as a filter medium because it is relatively inert to both acids and bases, but is attacked in oxidising environments such as when chlorine or heavy metal salts are present. PTFE (polytetrafluoroethene) fibres are resistant to most chemicals, but their use is often prohibited by the high cost.

2.3 Filter papers and sheets Papermaking technology is used to make filter papers and sheets from cellulosic materials and glass fibres. Papers made from synthetic polymer, ceramic or metal fibres that are bonded and sintered are also available. 2.3.1 Filter papers Filter papers are manufactured in a wide range of specifications for laboratory, industrial and automotive filtration applications.

110 Solid/Liquid Separation: Equipment Selection and Process Design 2.3.1.1 Industrial papers Cellulose papers produced for general industrial purposes, often in filter presses, are available as smooth or crêpe papers. Crêping eases handling of the paper when it is wet, and the papers are given added wet strength by impregnation with a bonding agent such as melamine formaldehyde. Papers are used in the production of beverages, pharmaceuticals, light oils and syrups as well as in other polishing processes, and have typical mean pore sizes in the range from 5 to 20
m. Industrial glass microfibre papers are made from fibres that are longer and have a smaller diameter (from
0.5
m to 4
m) than cellulose fibres, and the paper mat requires strengthening by the inclusion of a binder. Typical binders are latex, acrylic polymers or polyvinyl alcohol. Typical mean pore sizes are between about 3
m and 30
m. 2.3.1.2 Laboratory papers Qualitative filter papers are available for qualitative analyses and general use; quantitative papers are for use in analytical work that is carried out to quantify the composition of materials, where the purity of composition of the filter paper can be crucial. Qualitative cellulose papers are available with or without binders with particle retention capabilities from
3
m to about 30
m. Quantitative papers are generally binder free and offer a similar range of particle retentions. Glass microfibre papers are made from 100% borosilicate glass or pure quartz. Their mechanical strength stems in part from very high surface areas of the sub-micron fibres, and from entanglement of very long fibres. They are particularly suitable for quantitative work, and may be used at temperatures as high as 500°C or at low temperatures without embrittlement. 2.3.2 Filter sheets Filter sheets have a similar fibrous structure to paper but tend to be much thicker (in the range from 2 to 6 mm), and often contain quantities of other fibrous or particulate materials that give the sheet a rougher texture together with greater hardness and rigidity. Their compositions are based on mixtures of kieselguhr, perlite, cellulose and resins. As their thickness implies, they tend to function as depth filters and are used in special forms of filter presses to clarify beverages such as beer or whiskey or to sterilise pharmaceutical solutions.

2 · Filter media 111

2.4 Membranes The industrial development of membrane filtration utilises thin sheets of permeable material, commonly made from polymers, ceramics and metals. It is common to classify membranes and membrane filtration processes according to the sizes of the pores or the sizes of substances that they will remove from the feed stream. To separate particles between 0.1 and 20
m microfiltration (MF) is used, between 0.001 and 0.1
m (molecular weights of approximately 500 to 500000) ultrafiltration (UF), between 200 and 1000 molecular weight nanofiltration (NF), and
200 molecular weight reverse osmosis (RO). RO is included in the list for comparison purposes but it is not strictly a filtration process; NF and UF, and UF and MF, differ only by degree and the boundaries noted here are therefore not absolute. Membrane filters use tubular and hollow fibre media as well as sheets (the latter may be configured into pleated or tubular structures). Many membranes are of an asymmetric structure, composed of a thin skin that acts as the surface filter that is supported by a thicker layer designed to give mechanical integrity to the whole structure. The thickness of the membrane varies with the type of material from which it is made, but may be from
1
m to several hundred microns. The aim of most membrane structures is to promote surface filtration whilst discouraging depth filtration; with this in mind, thinness is a desirable attribute that also leads to lower pressure losses. Polymeric membranes are probably the most widely used. These are made from a wide variety of polymers including nylon, polypropylene, polyethylene, polysulphone, PTFE, PVDF (polyvinylidenedifluoride), polycarbonates, acrylic copolymers and other materials such as cellulose. Several methods are used for production of membranes, including sintering of powders, stretching polymeric films, track-etching (exposing a polymer film to a beam of accelerated argon ions that pass through the film to ‘etch’ a more or less cylindrical pore) and solvent casting or phase inversion. Most commercially available membranes are obtained by phase inversion, which is a versatile technique allowing a range of different membrane morphologies to be produced. In summary, the technique is to transform a polymer in a controlled manner from a liquid to a solid state – the solidification process is often initiated by the transition of one liquid into two liquids (liquid–liquid demixing), and at some stage during the demixing a high polymer concentration phase solidifies to form a solid matrix. The process may use one of several methods – solvent evaporation, thermal precipitation and immersion precipitation (which is the most common). Depending largely on the manufacturing methods employed, alternative membrane structures can be formed (see Figure 2.16).

112 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 2.16 Microfiltration membrane filter media formed by different techniques.

Inorganic membranes are made of mainly ceramic and metallic materials. The ceramic ones are manufactured from a variety of materials including alumina, zirconia, titania and silica. The substrate (to give the thin membrane mechanical rigidity and strength) is either the same material as the membrane but with a larger pore structure, or a different material such as silicon carbide.

2.5 Screens and meshes A wide variety of screens and meshes are available, ranging from fine photoetched or electroformed perforated screens to the heavy duty wedge wire screens used in centrifuge and high pressure screw press construction. Simple sieves and coarse screens were used as early as the sixteenth century for processing metal ores. Modern woven wire screens are precision made cloths with aperture sizes as small as 20
m (smaller aperture sizes are supplied by some manufacturers) for industrial separations in filtration, clarification and extraction. Plastic meshes and plastic coated metal meshes are finding an increasing number of applications in separation processes.

2 · Filter media 113 2.5.1 Wire cloths For filtration purposes the most widely used forms of woven wire are constructed from the Dutch or Hollander weaves, wherein the warp and weft wires are of different diameters. If the warp wires (i.e. those along the length of the loom) are thicker a plain Dutch weave results, but when the weft wires (across the loom) are thicker a reverse Dutch weave is formed. The plain Dutch weave is easy to clean and has a low resistance to flow, but its strength is limited. The reverse plain Dutch weave is much stronger, has good flow characteristics and a high dirt holding capacity, making it widely used industrially. Some alternative weave patterns are shown in Figures 2.17 and 2.18 and Table 2.15.

Figure 2.17 Example of a precision plain weave wire cloth.

Two basic forms of twilled Dutch weave are produced by combinations of warp and weft wires of different diameters. The use of heavy warp wires (Dutch twill weave) permits production of fine grades of woven wire cloths which have very smooth surfaces on both sides, but these cloths have a relatively high flow resistance. With heavy weft wires (reverse Dutch twill weave) the flow resistance is less but there is a corresponding decrease in micron retention characteristics and both sides of the cloth have rougher surfaces. Numerous variants of these basic weaves exist, with many being specific to particular suppliers of wire cloths – Purchas and Sutherland (2002) summarise

114 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 2.18 Wire cloth weave patterns (Bruncher, 1984). The numbers refer to those used in Table 2.15 to identify the mesh and weave types.

the variants offered by different manufacturers. The main types of wire cloth used in filtration are shown in Table 2.15 and Figure 2.18. A wire cloth may be a preferred form of filter medium when the process temperature is high or when corrosive chemicals are to be filtered; for some applications, such as the filtration of radioactive products, the use of organic media is unacceptable and woven stainless steels are frequently recommended. If the shape of the filter is complex, as is the case with some types of in-line roughing filters for example, wire cloths are particularly suitable for forming the filter shape and providing the rugged constructions that are needed. An advantageous characteristic of wire cloths is their thinness that leads to a low resistance to flow, hence yielding the potential for high flow rate filtration. As with any other form of medium, the choice of wire cloth must ensure its suitability for the filtration problem in which it is to be used; some guidance is given in Table 2.16. 2.5.2 Perforated sheets Perforated sheets are made from solid sheets by punching holes, by slitting and stretching (expanding) metal sheets, by photoetching and electroforming and by laser cutting. The variety of fabrication techniques gives rise to a diverse range of perforated sheet configurations, made from stainless or mild

2 · Filter media 115 Table 2.15 Main types of wire cloths for filtration (Bruncher, 1984). Mesh

Weave

Texture

Plain

Rectangular

Plain Twill

Plain Triangular

Twill

Pattern (see Fig. 2.18)

Warp and weft wires of same section, spacing and material

1

Warp and weft wires of same section, spacing and material

2

High performance

Warp wires of thicker section than weft wires

3

Rectangular

Wires spaced differently in warp and weft

4 5

Dutch weave Reverse Dutch weave

Warp and weft wires of different sections, the finer wires being placed side by side

6 7

High porosity Dutch weave

The finest wires are of smaller section than diameter of wires laid in the other direction

8

Square Twill

Textural description

Dutch weave Reverse Dutch weave

The finest wires are overlapped

9 10

steels, brass, aluminium, nickel and various polymers. Typical smallest hole sizes in sheets manufactured by the different processes are shown in Table 2.17; it is evident that usefulness of the sheets is limited by the very low open areas when the hole sizes are smaller, and in order to obtain a reasonable open area the hole sizes tend to be larger. 2.5.3 Wedge wire screens Metal and plastic wedge wire screens are commonly used in the construction of filters and other separators, as either the support for finer filter media or as the filtering medium itself. The screens have typical aperture sizes of 50
m with an average tolerance of 10%. Metal, usually steel, screens are used in applications where separator robustness needs to be combined with slurry dewatering duties or when the solids are particularly coarse or abrasive.

116 Solid/Liquid Separation: Equipment Selection and Process Design Table 2.16 Factors to consider when choosing a wire cloth. Selection parameter

Factors to take into account

Material

The correct choice of metal must take account of the nature of the solids and liquids to be treated, their temperature and heat cycles and the presence of any other chemical contaminants. The metal must be capable of being drawn and woven.

Nominal aperture size

To filter particles larger than a given micron size, choose an aperture size that is about 80% of that size. To filter all particles, choose an aperture size smaller than the minimum size in the particle size distribution of the feed. If the feed size distribution is wide it may be necessary to consider multistage filtration (each filtration stage removing all particles larger than a specific size, with successive stages removing finer particles). The apertures of backing cloths in multistage filters are often square and should be 8–10 times greater than those in the cloth being backed.

Weave

Weave choice should take account of both filtration and medium cleaning (see Table 2.9). Mechanical stress during operation or cleaning may require use of higher strength wire cloth, such as the Dutch twill weave.

Table 2.17 Typical smallest hole sizes and open areas of perforated sheets. Sheet type

Typical finest hole size (mm)

Approximate open area (%)

Perforated metals with round holes Expanded metal mesh Photoetched sieve plates with round holes Photoetched sieve plates with slotted holes Laser cut screens

0.5–1 (dependent on metal)

27

1 (long) × 0.67 (wide) 0.02

32 1

0.04 (long) × 1.1 (wide)

6

0.04 (width)

7

2 · Filter media 117

2.6 Porous sheets and tubes A wide range of metal, plastic and ceramic porous sheets and tubes are available for use in filtration processes. Of particular interest are metal fibre webs such as the Bekipor range manufactured by Bekaert in Belgium which are available in 316L stainless steel, Inconel 601 or Hastelloy X, and metal media produced by sintering bronze, stainless steel, nickel, Monel, Hastelloy, Inconel, titanium, aluminium or tantalum. Sintered metal fibre media are made from long fibres of controlled diameters from 2
m upwards; such media retain the high porosity characteristic of beds of fibres, as illustrated in Table 2.18 where some example properties of Bekipor media are listed. The porosity of these fibre sinters is about twice that of powder sinters, giving a much lower resistance to flow; the method of manufacture usually also leads to a narrower pore size distribution. Table 2.18 Example characteristics of Bekipor ST sintered metal fibre media (Bekaert). Absolute filter rating (
m)

Permeability ×1012 (m2)

Thickness (mm)

Weight (g cm⫺2)

Typical porosity (%)

Dirt-holding capacity (mg cm⫺2)

3 5 7 10 59

0.48 1.76 2.35 4.88 107

0.35 0.34 0.27 0.32 0.70

975 600 600 600 750

65 78 72 77 87

6.40 5.47 6.47 7.56 33.97

5 10 59

1.17 2.59 24.3

0.17 0.17 0.15

300 300 300

78 78 74

4.00 4.63 21.50

6 11 15 22

4.38 10.7 22.9 36.7

0.82 0.74 0.75 0.74

975 900 900 900

85 85 85 85

11.67 17.13 18.95 29.10

The properties more typical for media prepared from sintered metal powders are shown in Table 2.19. These are made from powders of graded spherical particles, with sizes typically in the range 0.5–100
m, which are compressed and sintered in moulds. A range of shapes of media can be produced, which can be subsequently worked in similar way to other metal fabrications. Cylinders, tubes and sheets are commonly used in filtration

118 Solid/Liquid Separation: Equipment Selection and Process Design Table 2.19 Example characteristics of PSS sintered metal (316L stainless steel) powder media for liquid filtration (Pall).

Micron removal rating

Sinter thickness (mm)

Permeability to water (litres/dm2 min⫺1 at 10 mbar p)


⫽2 (50%)


⫽10 (90%)


⫽100 (99%)

Absolute (100%)

Sheets

0.5 2 5 8 15

2 4 7 12 22

3 7 9 15 25

5 9 13 20 35

1.3 1.3 1.6 or 3.1 1.6 or 3.1 1.6 or 3.1

0.07 0.22 0.26 1.13 3.7

Cylinders

0.5 4 7 13

2 7 10 17

3 8 14 24

5 10 20 35

1.6 or 3.1 1.6 or 3.1 1.6 or 3.1 1.6 or 3.1

0.11 0.28 1.48 5.90


is defined by equation (2.1) in Table 2.4.

applications. Sintered powder media have a fairly isotropic structure with the same pore size distribution through their depth, and tend to function by depth filtration. Whilst this gives the medium a high dirt holding capacity, it also makes them difficult to clean. Cleaning methods more stringent than simple backwashing are necessary, sometimes using ultrasonics or chemical cleaning, and cleaning can become a specialist job to be done off-site.

2.7 Cartridges Cartridges are special fabrications designed to house filter media in a convenient way to provide an economic means of filtration; they are useful when the concentration of the solid or liquid contaminant is low (usually less than about 0.1% by weight) and the contaminant particle size is predominantly smaller than 40
m. This makes them particularly suited for general clarification, polishing or sterilisation applications. A range of cartridges of differing constructions is shown in Figure 2.19. Yarn wound (or spool wound) cartridges are a widely used form of filter formed by winding yarn around a central former (which is typically a perforated tube that is open at each end). The yarns are mostly spun from short

2 · Filter media 119

Figure 2.19 Forms of cartridge filters vary widely; these examples show pleated metallic and polymeric cartridges towards the left hand side of the photograph, and wound cartridges towards the right (Amafilter).

staple fibres, the fibrillated surface of which is brushed or teased to produce a surface nap, which contributes to the filtration effectiveness. If monofilament yarns are used they are texturised or crimped before being formed into a cartridge. Yarn wound cartridges usually have a nominal micron rating (care needs to be exercised when applying these ratings) of between about 1 and 150
m, and the dirt holding capacity depends on both the nominal micron rating and the filter operating conditions. Cartridges manufactured from bonded materials, such as glass microfibres bonded together by a phenolic resin (for general purposes) or melamine (for food, beverage and pharmaceutical applications) are in common usage. The microfibres have a controlled size ranging from about 0.5
m to over 150
m; they are sprayed with resin and then formed into felt-like mats that are cut into predetermined lengths and rolled onto various sized mandrels. The mandrel then becomes the core of the cartridge, and is typically made of polypropylene, coated or stainless steels or resin impregnated materials. After curing, each tube is ground to the required diameter. Bonded cartridges are available of similar form but made from other fibres such as acrylic or cellulose. Nominal ratings of such cartridges are from about 2 to 125
m.

120 Solid/Liquid Separation: Equipment Selection and Process Design Also available are thermoplastic bonded cartridges made from polymers such as polypropylene that give efficiencies of up to 99.999% against 0.3
m bacterium. The elements in these cartridges often have a pleated construction to increase the surface area, and they may also be composed of more than one layer of filter medium. The multilayer assemblies may provide a graded structure (in similar manner to a laminated fabric), as well as incorporating layers to aid drainage, support more fragile media or act as a protective covering. Once a cartridge is fully loaded with collected contaminant the ease of cleaning it for reuse, either manually or automatically, depends on the nature of the filter medium used and the construction of the cartridge. In this respect Purchas (1996) identified four categories of cartridge: 1. the ‘throw away’ or ‘disposable’ cartridge, which cannot be cleaned and is therefore discarded and replaced once it has been fully loaded; 2. the ‘cleanable-in-place’ cartridge, which is readily cleaned (for example, by intermittent reverse flow as part of the operating cycle of the filter) and reused several times before it is replaced; 3. the ‘service-cleanable’ cartridge, which must be dismounted and subjected to specialised cleaning either on-site or by returning to the manufacturer or to a service company; 4. the ‘reclaimable’ cartridge, which must be returned to the manufacturer who strips down and rebuilds it after replacing the filter medium. As a general rule, cartridges that function as strainers or cake filters are easily cleaned. But those that operate as depth filters trap contaminant within the structure of the medium from where its removal is difficult or impossible; although the dirt holding capacity of such filters is often higher, they usually cannot be cleaned. Of the above, (1) and (2) are of the greatest practical importance in the chemical and processing industries, (3) are used in the manufacture and processing of polymers and (4) for filters used in high pressure hydraulic systems.

2.8 Precoats and body aids (filter aids) There are two principal ways of using powders and granules as filter media, and a third way involves mixing them into the feed suspension: 1. The powders or granules may be formed into a suspension and filtered as a precoat onto a more conventional rigid filter medium to protect the supporting medium from becoming fouled by the solid matter in the feed

2 · Filter media 121 suspension. This is also used to trap very fine particles which would otherwise pass through the medium. 2. The powders or granules may be formed into a deep bed to create a depth filter, or to cause the liquid to contact the solids for sufficient time to allow adsorptive processes to take place. 3. The powders or granules may be added to the feed suspension that is to be filtered. The purpose of this may be to either carry out an adsorption process, or to increase the porosity of the filter cake that is formed on the filter. Solids used as precoats or body aids are commonly known as filter aids. Use of the precoat technique is frequently combined with body aid, although different grades of material may be used for each purpose. The precoat will usually be selected to give good filtrate clarity and so will be fine solids, whilst the body aid is designed to increase the filtration rate and so is often a coarser grade of the same material. The dosage of body aid material is optimised – a dosage equivalent to 50–100% of the solid’s content of the feed suspension is often used, with experimentation providing the correct quantity to be used in any application. A useful summary of the typical properties of filter aids is given in Table 2.20. Diatomaceous earth or diatomite is the classic material to use for precoat or body aid purposes; these powders are the fossilised remains of microscopic algae or diatoms which once lived in the sea. The shells of diatoms are virtually pure silica and have a variety of curious shapes (some are shown on Figure 2.20). They are found as deposits that are worked using opencast methods, and the amorphous rock is refined by a sequence of crushing, grinding, screening, drying and calcining processes. The final calcining stage affects the surface of the diatoms by increasing the particle size and reducing the surface area, and thereby markedly increasing their filtration rates. Two common features about the diatom shapes are that they are all highly porous and chemically quite inert. They are typically about 90% SiO2, 4% Al2O3, 1% Fe2O3, 0.5% CaO and 0.5% MgO with lesser amounts of P2O5, TiO2, Na2O3 and K2O, with precise chemical compositions varying according to the source of the material. These properties make them very useful in filtration. Expanded perlite is established as a competitor to diatomite. Perlite is a rock with volcanic origins, being formed from molten lava that erupted from a volcano into water where it was quenched and rapidly cooled. It is a supercooled liquid or natural glass comprising a mass of small ‘pebbles’ that may be up to about 25 m in diameter, but are generally about 2
m or smaller. Occluded in the particles is a small amount of water, giving the mineral a water content of 3–4%. Perlite is prepared using a similar sequence of operations to those used for diatomite; the key operation is rapid heating of the

122 Solid/Liquid Separation: Equipment Selection and Process Design Table 2.20 Typical properties of major types of filter aids. Diatomite

Perlite

Wood products

Silica

Glassy silica

Cellulose

Number of grades

15

8

8

Range of relative flow rates†

1–23

1.7–9.3

5–23

Specific gravity

2.25–2.33

2.34

1.5

Wet cake density (kg m⫺3)

320–380

240–340

170–340

Good

Good

Excellent

Slight in dilute Slight in dilute

Slight in dilute Slight in dilute

None in dilute or strong None in dilute

General use for maximum clarity. Reduced dosage on pressure & vacuum filters.

Good on rotary filters

Excellent for precoating coarse screens. Highest purity for absorption of oil from condensate and removal of iron from caustic.

Composition

Retention on coarse screens Solubility (at room temperature) -In alkalis -In acids Prime advantages and applications

Water permeability ratio relative to a bed permeability of about 2 × 1010 m2.

†

perlite to its softening point to cause vapourisation of the occluded water, accompanied by swelling of the particle to about 20 times its original volume. The small hollow balls so formed are milled to give particles of irregular shape that are essential to a successful filter aid; balls that fail to fracture during milling appear as ‘floaters’ and may give rise to operational problems during filtration. Perlite is not quite so chemically inert as diatomite. It has a typical composition of about 75% SiO2, 13% Al2O3, 5% K2O, 4% Na2O3,
1% Fe2O3,
1% CaO and traces of MgO, P2O5 and TiO2 and is usable in the pH range 4–9. On the basis of permeability data the flow through perlite beds is similar to flow through diatomite beds, as indicated in Table 2.20. However, the equivalence of flow rate does not correspond to similar performance in respect of clarification achieved, where diatomite is likely to be superior if maximum clarity is required, as inferred in Table 2.21.

2 · Filter media 123

Figure 2.20 Some of the microscopic structures found in diatomite, showing their open porous structure.

Table 2.21 Summary guide comparing diatomite with perlite (Celite). Diatomite

Perlite

360

180

Particle size removal

Submicron and larger

Less effective for submicron particles

Particle quantity removal

Typically ⬍0.5% w/w

Typically ⬍2% w/w

600

400

Good resistance

Usually poor resistance

Very easy

‘Sticky’ cake

Admixture with perlite or cellulose recommended

Very good

Typical wet density (kg m⫺3)

Maximum operating pressure (kPa) Penetrability in rotary vacuum filter cakes Ease of filter cloth cleaning Precoating candle filters

Natural cellulose fibres (derived from wood chips processed to remove the lignins and other soluble impurities such as resins and sugars) offer some advantages for precoat filtration, the properties of which are compared with diatomite and perlite in Table 2.20. The fibre lengths vary from about 20
m to

124 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 2.21 Cellulosic filter aid; contrast the fibrous nature of these particles with the highly structured diatomaceous earth (see Figure 2.20) (SeitzSchenk).

Table 2.22 Some applications of DICAFLOCK cellulose filter aids (Grefco Inc.). Application

Grade

Alkaline chemicals, e.g. 50% sodium hydroxide, sodium silicate, preparations of alumina and plating solutions (where the soluble silica in diatomite and perlite makes them unsuitable)

DF5 DF10 DF40

Brine filtration – electrolytic cells in chlorine/caustic plants

DF40 DF200

Condensate – removes solid particles and traces of oil contained in boiler condensate water

DF40 DF100 DF200

Emulsions – breaks oil-in-water and water-in-oil, and where only traces of oil emulsified in water will absorb the oil

DF40

Catalysts and rare earth metals – filter aid is an almost ashless material, enabling recovery of catalysts and metals by incineration

DF40 DF200

Beer and beverages – avoids bleed through of diatomite or perlite

DF5 DF10 DF40

2 · Filter media 125 over 600
m, enabling them to rapidly form high permeability precoats on screens with little or no penetration through the screen – a photograph of a cellulose fibre filter aid is shown in Figure 2.21. Moreover, the precoat is stable to pressure fluctuations during the subsequent filtration cycle and releases cleanly from the screen when the filter is cleaned. Because of these characteristics, cellulose filter aids are frequently used in combination with other types of precoat, either as a preliminary layer or in the form of a mixture. Examples of the properties and use of cellulose filter aids are given in Table 2.22.

2.9 Conclusions A wide variety of filter media are available to suit most applications. Selection of a medium must take into account many factors and requires testwork to be undertaken to evaluate the suitability of a medium for any application. Bearing in mind the critical role played by the medium in a filtration process insofar as an incorrect selection may prevent correct functioning of the filter or lead to high running costs, or it may cause too frequent downtimes, or lead to a liquid product of low quality or to overly wet cakes; selection of an appropriate medium becomes self-evident. An investment in cloth selection can prevent avoidable costs after installation of the filtration system.

3

Pretreatment of suspensions

In this chapter the pretreatment of suspensions by chemical and physical means is described from a process engineering perspective. The majority of the text relates to the addition of chemicals that promote coagulation or flocculation, as these are the most widely used and important pretreatment processes. Towards the end of the chapter other methods are discussed; these include the physical pretreatments of heat, freezing and ultrasonics as well as suspension pre-thickening. For the interested reader, aspects of pretreatment processes are discussed in more detail by Akers (1972), Bratby (1980), Glover et al (2004), Gregory (1973), Hermia (1980), Hunter (1995), La Mer and Healy (1966), Kirk-Othmer (1980), Michaels and Bolger (1962), Michaels et al (1967), Moody (1995), Moody and Norman (2005), Purchas and Wakeman (1986), Shaw (1992) and Tchobanoglous and Burton (1991). Many practical aspects of chemical pretreatments, including extensive descriptions of test equipment and scale-up procedures, are given in Wakeman and Tarleton (2005b).

3.1 Basic concepts The throughput and efficiency of solid/liquid separation processes such as sedimentation, filtration and centrifugation are dependent on many interacting variables. They are all primarily affected, however, by the particle size and form of the solids to be separated from suspension. When particle size is small, both gravitational and centrifugal sedimentation rates can be low and filtration often results in the slow formation of high resistance cakes that are subsequently difficult to deliquor and wash. In order to improve the separation characteristics of finer and colloidal suspensions, the primary particle size can be increased by an aggregation process where the addition of a chemical agent

3 · Pretreatment of suspensions 127 alters either the surface properties of the particles, the properties of the suspending liquid or the manner in which the solids and liquid interact. Most particles acquire a surface charge when suspended in a polar medium such as water. Although the overall charging mechanism can be complex, it is usually due to either the ionisation of surface groups, the uneven distribution of ions, the substitution of ions or the specific adsorption of ions; in some cases a combination of charging mechanisms can occur. As a result of the surface charge, an electrical double layer (EDL) forms between the boundary of the solid and liquid phases such that the concentration of ions within the EDL is different from that of the bulk solution (see Figure 3.1). The EDL surrounding a particle can have a thickness up to several hundred nanometres depending on the composition of the liquid environment. The electrical voltage potential decays approximately exponentially with distance from the particle surface, and its magnitude is interpreted practically through measurement of

Figure 3.1 Schematic of the electrical double layer surrounding a particle suspended in a polar liquid. In the example, the counter-ions carry a
ve charge and the co-ions a ve charge.

128 Solid/Liquid Separation: Equipment Selection and Process Design the potential at the plane of slip between a particle and the surrounding liquid (i.e. the zeta(
)-potential). In a particle/liquid system there are also attractive van der Waals forces. These may have a reasonable magnitude but their range of influence is limited to ~10 nm from the particle surface.

repulsion

VR

VT

0 secondary minimum in VT

VA attraction

Potential energy of interaction

When particles approach each other, a result of the attractive van der Waals forces and the repulsive electrostatic forces is the generation of a potential energy barrier which tends to keep particles apart (see Figure 3.2). The Deryagin–Landau and Verwey–Overbeek theory describes the formation of the barrier such that for two spherical particles

primary minimum in VT

0 Distance between particles

Figure 3.2 Schematic of the potential energy barrier generated between two approaching particles.

 p a1a2 (12
22 )  212 VR   2
2 × a
a 1

2

1

2

(3.1)

  1
exp(H ) 
ln(1 exp(2H )) ln    1 exp(H )  

VA 

 x 2
xy
x   A y y (3.2)

2 ln  x 2
xy
x
y   12  x 2
xy
x x 2
xy
x
y

VT  VA
VR

(3.3)

3 · Pretreatment of suspensions 129 where a1 and a2 are particle radii, 1 and 2 are the potentials measured at the outer boundary of the Stern layer,  the reciprocal electrical double layer thickness, H the interparticle distance, A the Hamaker constant, x H/(a1
a2), ya1 /a2 and VT represents the total potential energy of interaction due to the sum of the attractive van der Waals and repulsive electrostatic interactions (VA and VR, respectively). If particles are brought sufficiently close to either the primary or secondary minima, the potential energy barrier is either partially or fully breached and the particles are considered to join together or aggregate. The chemical pretreatment of suspensions concerns the addition of substances that promote this attachment. In the current context, the most important methods of pretreating a suspension are coagulation and flocculation. Although a good deal of literature presents these terms interchangeably, the processes and the chemicals employed are quite different in each case. The International Union of Pure and Applied Chemistry (IUPAC) uses the terms coagulation and flocculation to refer to destabilisation of a suspension in the primary and the secondary minima of the total potential energy curve (see Figure 3.2). In water treatment various meanings are encountered, however, the most common are that coagulation refers to the chemical sensitisation of particles by the addition of reagents, and flocculation concerns the subsequent hydrodynamic processes which bring about the particle collisions necessary for aggregate formation. From the point of view of solid/liquid separation technology the following definitions are preferred by the authors (La Mer and Healy, 1966): Coagulation is the process whereby destabilisation (aggregation) of a suspension is effected by reducing the electrical double layer repulsion between particles through changes in the nature and concentration of the ions in the suspending electrolyte solution. Coagulant refers to the chemical or substance added to the suspension to effect the destabilisation. Flocculation is the process whereby a long chain polymer (or polyelectrolyte) causes particles to aggregate, often by forming ‘bridges’ between them. Flocculant refers to the chemical or substance added to a suspension to accelerate the rate of flocculation or to strengthen the flocs formed during flocculation. Sludge conditioners (sometimes called deliquoring aids) are those chemicals or substances added to a thickened suspension to promote deliquoring and/or to strengthen flocs prior to deliquoring. These definitions provide the basis for the descriptions in Sections 3.2 and 3.3.

130 Solid/Liquid Separation: Equipment Selection and Process Design

3.2 Coagulation principles and mechanisms Coagulation of a suspension can be brought about in a number of ways, which range from the input of energy through relatively vigorous mechanical agitation to gentle mixing with the addition of the correct amount and type of chemical. If the amount of energy transferred to a system by stirring is excessive, then the coagulation process will be hindered by the simultaneous break-up of aggregates. Coagulation is most widely used in water treatment. 3.2.1 Mechanical agitation Perhaps the simplest method of coagulation is mechanical agitation by paddles, mixers, pipe flows, etc. Here, shear forces impart energy to the suspended particles and in the appropriate solution environment primary sized particles as well as already formed aggregates are caused to join together to form larger aggregates. The energy provided to the system must be sufficient to overcome the potential energy barrier to coagulation and the process is frequently aided by the addition of chemicals to reduce the electrostatic repulsion between particles. If stirring is too vigorous, however, then aggregate breakage can occur. 3.2.2 Indifferent electrolytes The addition of an indifferent electrolyte to a suspension alters the composition and extent of the EDL surrounding the particles. This changes the range of both the interparticle electrostatic repulsion and the measured
-potential and can thus induce coagulation. As an indifferent electrolyte only affects the concentration of counter-ions without causing ion adsorption at the particle surfaces, the main effects of addition are to alter the ionic strength and pH of the solution environment. The chemicals used are typically mineral acids or alkalis such as sodium hydroxide or calcium oxide (lime). These substances reduce or increase pH by an amount dependent on their molarity and the quantities used, although the electrolyte concentration required to induce coagulation is (ideally) independent of the number of particles in suspension. The efficacy of the electrolyte is strongly dependent on the valency (z) of the counter-ions present and is predicted by the Schulze–Hardy rule, which states that the concentration of electrolyte required to induce coagulation is inversely proportional to z6. For example, with mono-, di- and tri-valent counter-ions the concentration of coagulant required would be in the ratio 800:12:1. Although the pH of a suspension may need to be altered for other practical reasons (e.g. to prevent corrosion of components or precipitation of soluble

3 · Pretreatment of suspensions 131 components such as transition metals), the best coagulation with indifferent electrolytes is generally achieved when the
-potential is low and effectively zero. Figure 3.3 illustrates how the average
-potential of a china clay suspension is altered by the addition of either HCl or NaOH; the isoelectric point occurs at a pH between 2 and 3. Some effects of modifying pH on the cake filtration of finer particulates are shown in Figure 3.4. At low pH, the feed suspension is close to its point of effective zero charge (isoelectric 0 -10 ζ-potential (mV)

-20 -30 -40 -50 -60 -70

xav = 3 µm

-80 2

4

6

8

10

12

pH (-)

Figure 3.3 A typical effect on
-potential of adding HCl or NaOH (i.e. indifferent electrolyte) to a china clay suspension.

pH = 2.9, ζ = 0 mV pH = 5.7, ζ = -28 mV pH = 8.0, ζ = -46 mV pH = 9.5, ζ = -60 mV pH = 11.6, ζ >-70 mV

3

Cumulative volume of filtrate (m )

14000 12000 10000 8000 6000 4000 2000 0 0

1000

2000

3000

4000

Filtration time (s)

Figure 3.4 The effect of pH on the dead-end cake filtration of china clay suspensions.

132 Solid/Liquid Separation: Equipment Selection and Process Design point, IEP), particle size is at its greatest due to coagulation and filtration is relatively easy. At higher pH there is a greater electrostatic repulsion, particles are more discrete in suspension and thus cakes of much higher resistance form during filtration. With suspensions that are in a state sufficiently well removed from the IEP, typically at pHs in excess of 11, the ionic strength in solution is high and the shape of the
-potential/pH curve indicates a reduced
-potential. Here, EDL compression occurs and filtration rates are seen to rise again due to the formation of less resistant filter cakes. Sedimentation rates are also usually greatest in the region of the isoelectric point of a suspension. While the above descriptions are valid in the general sense, they can present an oversimplification of real situations and consideration may need to be given to other factors. These include: 1. In some cases the transition to instability (coagulation) occurs over a relatively narrow and critical range of electrolyte concentration; 2. If the indifferent electrolyte concentration is increased to excess, there is frequently no effect on stability as a charge reversal can effectively occur at the particle surfaces; 3. Particle concentration can have an effect on the concentration of electrolyte required for coagulation and in some cases a stoichiometric relationship is evident; 4. The efficacy of multivalent ion species in promoting coagulation is often greater than that predicted by the Schulze–Hardy rule. 3.2.3 Multivalent metal ions (inorganic coagulants) With the addition of inorganic salts containing multivalent metal ions such as Ca2
, Fe3
and Al3
there is a possibility of specific ion adsorption at particle surfaces and considerations beyond that of double layer compression by increasing ionic strength become important. Adsorption of co-ion species may augment the original charge carried by particles or, in the case of adsorption of counter-ions, may negate or even cause charge reversal (see Figure 3.5). In general the greater the positive ion charge, the more effective is the suspension destabilisation by coagulation. The potential for ion adsorption allows for two further coagulation mechanisms. The first may be described as ‘adsorption destabilisation’ and ultimately has a similar effect to that described for indifferent electrolytes. Metal ions effectively act to neutralise particle charge, reduce the extent of double layer repulsive interactions and hence decrease the potential energy barrier to coagulation. The second, and perhaps more important, mechanism may be

3 · Pretreatment of suspensions 133

co-ion

Electrical potential

ψ0

typical counter-ion

0

polyvalent counter-ion Boundary of Stern layer

0 Increasing distance from particle surface

Figure 3.5 Examples of ion adsorption effects at a particle surface. thought of as a bridging process. Metal coagulants taking part in hydrolysis reactions have a pronounced tendency to undergo a form of polymerisation. In water, for example, metal (M) ions such as Al3
and Fe3
are strongly hydrated to form complexes of the type M(H2O)63+, which tend to dissociate and give rise to a series of hydroxylated species. Depending on solution pH a variety of species may exist in appropriate equilibrium concentrations, these include

In addition the sparingly soluble, neutral hydroxide M(H2O)3 (OH)3 will precipitate if the pH is suitable for its stable existence. For a hydrolysing salt to be an effective coagulant it must be used at a concentration in excess of the solubility of its hydroxide at the solution pH. Thus, with the adsorption of suitable species at particle surfaces a coagulant bridge spanning adjacent particles is formed, thereby promoting destabilisation. Moreover, with precipitating coagulants the presence of the precipitate can greatly enhance the kinetics of the coagulation reaction by physically entrapping material within the expanded aggregate structure; this effect is known as sweep coagulation. In some texts this process is, perhaps unfortunately, also referred to as sweep flocculation. While metal ion coagulants such as aluminium sulphate are widely used as reagents in potable water treatment (for instance), their tendency to form

134 Solid/Liquid Separation: Equipment Selection and Process Design precipitates can make up as much as 50 wt.% of the sludge recovered from a separation. Sludge disposal may then be a problem in a large scale process, however, disposal is made easier if the highly hydrated, gelatinous sludge can be effectively deliquored to reduce its bulk; the diaphragm filter press and belt filter press are useful here (see Sections 1.4.2.5 and 1.4.2.6). Polyelectrolyte flocculants, such as those described in Sections 3.3 and 3.4, can sometimes be incorporated in the main coagulation reaction as coagulant aids to help aggregate removal. Further considerations when using inorganic coagulants include their potential effects on suspension pH and the frequent need to use pH modifiers since optimum performance is generally achieved within a relatively narrow pH range. 3.2.4 Lower molecular weight polymers (organic coagulants) Within the context of this book, coagulation is considered to be caused by the addition of ionic substances such as indifferent electrolytes and inorganic salts while flocculation is induced by the addition of polymeric substances. In some texts, however, the effects due to lower molecular weight polymers are described as coagulation. When these polymers are used to promote particle aggregation the dominant mechanism is likely to be charge neutralisation rather than bridging by extended polymer chains (see Sections 3.3.2 and 3.3.3, respectively). With charge neutralisation the surface charge on the particles is effectively changed by the presence of the polymer and the distinction between coagulation and flocculation becomes less clear.

3.3 Flocculation principles and mechanisms In flocculation relatively long chain, synthetic polymers (polyelectrolytes) are used to overcome the potential energy barrier preventing the spontaneous aggregation of particles. While the presence of the correct dosage and type of polymer is important, the degree of flocculation is also dependent on a number of other factors including the amount of energy input during agitation. The polyelectrolytes used to promote flocculation contain functional groups that may or may not carry a charge. If the groups are charged they can give the chain an anionic (ve charge) character, a cationic (
ve charge) character or in some instances an amphoteric character exhibiting both anionic and cationic charges. The intensity of the charges is dependent on the degree of ionisation of the functional groups, the degree of co-polymerisation and/or the amount of substituted groups in the polymer structure. The extent of polymerisation of the polyelectrolyte is characterised by the molecular weight and high molecular weights are usually synonymous with long

3 · Pretreatment of suspensions 135 chains. Functional groups in the structure also constitute sites at which the polymer may adsorb onto a particle surface. 3.3.1 Forms of flocculation and polymer adsorption The term ‘perikinetic’ flocculation is used to describe a process where after addition of a polyelectrolyte the degree and the rate of flocculation are governed by Brownian motion alone. No shear forces are used to help promote flocculation. If it is assumed that every contact between particles leads to adhesion, then the rate of perikinetic flocculation is given by

dn kr n 2 dt

(3.4)

where n is the number of particles present and kr is a rate constant. While some fundamental studies of colloidal flocculation are performed in these unstirred conditions, in most industrial applications where appreciable floc formation is required some form of movement is artificially introduced to the suspension. This so-called ‘orthokinetic’ flocculation is promoted by polyelectrolyte addition coupled with either mechanical agitation or the induction of a tortuous flow pattern to the suspending medium. Examples of the latter include passage through granular filter media, flow around baffles in a flocculation tank such as may be found prior to a filter and a pipe flocculator which is frequently used to introduce the feed to a settling tank. If it is again assumed that each particle collision leads to aggregation, then the rate of orthokinetic flocculation is given by dn 0.66& x 3 n 2 dt

(3.5)

where x is particle diameter and · is the imposed shear rate. While orthokinetic flocculation generally occurs at a much higher rate than perikinetic flocculation, both rely on the distribution of polymer molecules to particle surfaces followed by an adsorption process. The combination gives the conditions necessary for particle aggregation to commence. Polyelectrolyte flocculants in solution generally exhibit low diffusion rates and raised viscosities, the latter increasing markedly with higher molecular weight polymers. As the adsorption of polymer is usually much faster than the diffusion process, it is necessary to mechanically disperse the polymer

136 Solid/Liquid Separation: Equipment Selection and Process Design into the suspension. In practice this is achieved by having a short, vigorous mixing stage to enable rapid dispersion, however, care must be taken that the mixing is not so vigorous as to degrade the polymer and also not overlong which can disrupt flocs as they form. When an adsorbable site on a polymer comes close enough to a particle, surface adsorption of one functional group may occur while the rest of the chain is momentarily free and extends into the surrounding solution. Depending on the composition of the solution, the chain may remain extended or become successively attached at more points along its length giving rise to so-called ‘trains’, ‘loops’ and ‘tails’ (Figure 3.6). The adsorption behaviour and configuration of the polymer chains are dependent on the properties of the polymer and particle surfaces, the concentration of ions in the liquid phase and for ionic polymers the pH. For example, high ionic strengths cause polymers to become compressed in solution, and if high enough may cause them to be precipitated, thus inhibiting their adsorption. A pH causing the polymer to become highly charged will force it into an extended configuration which is less readily adsorbed. The various theories for adsorption give rise to an adsorption isotherm similar in appearance to the Langmuir monolayer isotherm (although the reasons for the isotherm shape are quite different). The amount of material adsorbed is generally found to increase with increasing chain length and with the number of points attached to the surface until a form of equilibrium is achieved.

Figure 3.6 Schematic representation of the ‘trains’, ‘loops’ and ‘tails’ that may form during adsorption of a polymer chain to a particle surface.

The adsorption of polymers to the surface of particles leads to the two fundamental mechanisms of flocculation by polyelectrolytes. These are commonly referred to as the ‘electrostatic or charge patch mechanism’ and the ‘bridging mechanism’ and may act individually or, in some instances, simultaneously.

3 · Pretreatment of suspensions 137 3.3.2 Lower molecular weight polymers (charge neutralisation) In many applications, such as those found in water and effluent treatment, the most effective flocculants are those whose inherent charge is opposite in sign to that of the particles to be flocculated. Here, the flocculation process is generally brought about by the addition of lower molecular weight (less than 300000) cationic organic polymers and it is believed that their performance is governed by the charge patch mechanism proposed by Gregory (1973) (see Figure 3.7). As most naturally occurring particles are negatively charged in suspension, cationic polymers that carry an inherent positive charge are usually preferred. However, anionic polyelectrolytes are sometimes added to dispersions that have been destabilised by multivalent metalion coagulants. This method of flocculation is described in Section 3.3.3.

Figure 3.7 Schematic representation of the charge patch mechanism of flocculation (cationic polymer and negatively charged particles in the example shown). Taking the example of a negatively charged particle, the charge patch mechanism assumes that within a suspension a number of (for instance) cationic polymer molecules adsorb onto each negatively charged particle via electrostatic bonding to create local reversals of charge. Rather than each molecule attaching at only a few sites and the remainder of the chains extending into the solution, almost complete adsorption of the polyelectrolyte polymer molecules occurs. It is considered that the adsorbed polymer chains create a charge mosaic on each particle with alternating patches of positive and negative charge due to polymer and unaffected particle surfaces, respectively. The overall effect is a tendency towards charge neutralisation which is manifested as a change in the measured average
-potential of the suspension. Flocculation occurs when the charge mosaics of adjacent particles align to provide electrostatic attraction and thus breach the potential energy barrier. The concentration and hence number of polymer molecules present is an important factor. For flocculation by charge neutralisation, the optimum dosage of flocculant is usually stoichiometric with

138 Solid/Liquid Separation: Equipment Selection and Process Design respect to the particle surface area. If too much flocculant is added then surface coverage increases until effectively a reversal of charge takes place. At this point the suspension is likely to return to a dispersed state but with solids that are positively rather than negatively charged. Table 3.1 summarises some of the practical effects that are induced by a change in flocculation conditions. Table 3.1 Some parameters that influence the flocculation process and their induced effects. Parameter

Effects

Flocculant molecular weight increase

• • • • •

Flocculant dose increase

• • • • • • • • • • • • • • • • • • •

Increase in applied shear/stirring rate Particle surface area increase

Particle concentration increase

Suspension pH

Suspension ionic strength

Polymer charge density increase

Temperature change

Poorer solubility and more viscous solutions Polymer chains more shear sensitive Higher unit cost and optimum flocculant dose Bridging flocculation favoured Larger more fragile flocs which often settle faster but give higher sediment volume and water retention during deliquoring Better flocculation up to the optimum, then deterioration Breakdown of longer polymer chains Irreversible floc degradation Smaller equilibrium floc size Greater flocculant consumption Ultrafines are susceptible to overdosing and thus restabilisation Does not always affect optimum dose Smaller and perhaps stronger flocs Local overdosing possible Non-ionics are little affected Ionisation and chain extension of anionics at alkaline pH — converse is true for cationics Alters particle surface charge Combined effects on flocculation are complex (see Section 3.3.3) Similar comments to suspension pH Can promote or hinder flocculation Excess salts lower solubility and coil polymer chains in solution Extends polymer chains in solution under suitable conditions Decreases adsorption onto particles of the same charge sign Complex effects

3 · Pretreatment of suspensions 139 In the above considerations the action of low molecular weight polymers has been considered in isolation. However, as the molecular weight of polymer is increased there is less flocculation by charge neutralisation and a tendency to the mechanism of bridging flocculation, as described in Section 3.3.3. In reality, flocculation may occur by a combination of mechanisms and is sometimes deliberately engineered to do so. In general, low to medium molecular weight polymers form relatively small and strong flocs of fairly uniform size. 3.3.3 Higher molecular weight polymers (bridging flocculation) Higher molecular weight (30 × 104 to 30 × 106) synthetic polymers are generally used to promote bridging flocculation and these are broadly classified according to the degree of ionisation as non-ionic, anionic or cationic. In bridging flocculation, the long chain polymer molecules are adsorbed to the particle surfaces by electrostatic, hydrophobic, van der Waals, covalent or most likely hydrogen bonding. The polymers attach via relatively few sites to the particles leaving long loops and tails which stretch out into the surrounding liquid phase. For a bridging flocculant to function correctly it is necessary for these loops and tails to span at least the sum of the distance over which the electrostatic repulsion between two approaching particles acts (i.e. at least the extent of two electrical double layers). The spatial extension of polymer molecules generally increases with both molecular weight and charge density. This, coupled with a need to maintain good solubility in the suspending liquid, frequently dictates the use of a high molecular weight polyelectrolyte with a linear (i.e. noncyclic) molecular structure. For bridging flocculation to occur it is essential that the polymer loops and tails are sufficiently long. It is also a prerequisite that polymer molecules attached to one particle can subsequently attach to vacant sites on an approaching particle to complete the bridge (Figure 3.8a). This in turn implies that the optimum amount of flocculant is less than that required for complete coverage of all particle surfaces. Although the ideal polymer dosage may be thought to be sufficient to cover 50% of the available particle surface area, in practice the optimum can vary widely and is often observed to be at rather lower surface coverages (typically 30–35%). If high polymer concentrations are used then the particle surfaces can become completely coated such that there are no available sites across which bridges can form. Here, the polymer chains attach to individual particles in loops only (or remain in the suspending liquid) and particles stay discrete through steric stabilisation (Figure 3.8b). For the case of anionic polyelectrolytes added to a negatively charged suspension, destabilisation by a bridging mechanism can still take place, however, there is a need for free metal ions to be present

140 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 3.8 Schematic representation of (a) bridging flocculation, (b) steric stabilisation and (c) metal ion bridging between an anionic polymer chain and a negatively charged particle surface.

in the suspending liquid. Ions such as Ca2
or Cu2
act as electrolyte bridges between the negatively charged polymer and particle surfaces to provide a so-called combination treatment (Figure 3.8c). In general, high molecular weight polymers produce relatively large and more fragile flocs. The extent of bridging flocculation is dependent on many factors, including some of those summarised in Table 3.1. Highlighting pH/ionic strength as a somewhat complex example, it was shown in Section 3.2.2 that a raised ionic strength causes compression of the EDL. Hence it should be possible to use lower molecular weight polymers to induce flocculation, as the polymer chains are required to span shorter distances. However, at higher ionic strengths polymers tend to be more coiled than extended and thus their effectiveness as flocculants is not straightforward to predict. At lower values of pH, non-ionic polymers and polymers with few ionised groups are often found to give the best performance, but at very high pH values highly ionic polymers are usually the best. Moreover, the nature of the particle surface can also significantly influence the degree of aggregation achieved by a flocculant. With inorganic suspensions containing, for instance, minerals, non-ionic and anionic flocculants are generally found to give the best results. With organic suspensions such as sewage sludge, cationic polymers are frequently the most effective.

3 · Pretreatment of suspensions 141

3.4 Types of pretreatment chemicals A large number of commercial coagulants and synthetic flocculants are available with which to pretreat suspensions. While newer products have displaced the use of more traditional chemicals in recent years, few have been eliminated completely from the marketplace. The more important and widely used pretreatment chemicals are described here. 3.4.1 Coagulants Although some inorganic salts can act as indifferent (non-adsorbing) electrolytes, the more important types of coagulant from a process engineering viewpoint are the salts of multivalent metal ions such as Ca2
, Fe2
, Fe3
and Al3
. These ions hydrolyse or specifically adsorb to particle surfaces to induce coagulation. Of the aluminium derivatives, the sulphate and the chloride are the most common. Alum, which has the approximate formula Al2(SO4)3·(H2O)14, is probably the most widely used inorganic coagulant as it successfully aggregates a wide range of suspended particle types. Another advantage is that it can be stored almost indefinitely without loss of effectiveness. With organic sludges, however, the hydrated chloride (AlCl3·(H2O)6) can be more effective as less coagulant is needed to achieve the same degree of aggregation. In some instances polyaluminium chloride (PAC, Al(OH)1.5(SO4)0.25Cl1.25) is reported to give faster coagulation and stronger flocs than normal alum. As alternatives to aluminium, the salts of iron can make very effective coagulants. The most widely used is the trivalent ferric chloride (FeCl3). This is more effective than the equivalent hydrated sulphate compound Fe2(SO4)3 ·(H2O)8. Lime is often used in conjunction with multivalent metal ion coagulants. Although lime does not in itself produce polymeric species in the manner that aluminium and iron do, nor does it cause specific adsorption of ions, it can be used to control pH and/or precipitation behaviour. For instance, when combined with iron coagulants it ensures that the iron is precipitated as the hydroxide. Optimum coagulation performance is generally achieved within a relatively narrow pH range and thus pH modification, as achieved with lime, can play a critical role. Lime is a term covering a number of chemicals that are compounds of calcium, oxygen and in some instances magnesium. The principal types are quicklime (composed of CaO or mixed CaO and MgO) and slaked lime (composed of Ca(OH)2, mixed Ca(OH)2 and MgO, or mixed Ca(OH)2 and Mg(OH)2).

142 Solid/Liquid Separation: Equipment Selection and Process Design 3.4.2 Flocculants Most commercial flocculants are synthetic water soluble polymers with average molecular weights in the region 1000 to 30 × 106. They are generally supplied as powders that have a limited storage life, particularly when made up into solution. While there is an understandable reluctance for manufacturers to divulge their exact chemical nature, it is known that the majority of polymer flocculants are based on acrylamide chemistry. Those which carry charge sites are polyelectrolytes and are classed as either anionic (ve charge), cationic (
ve charge) or amphoteric (both
ve and ve charge sites); non-charged or polymers carrying less than 1% of charged monomer units are classed as non-ionic. The commercial success of synthetic polymer flocculants is a result of their versatility in copolymerisation and other techniques allow products to be ‘tailor made’ to a given set of process requirements. Although a description of all flocculants is beyond the scope of this text, a selection of synthetic polymers is shown in Figure 3.9. The variation and number of cationic flocculants are probably the greatest of those currently available. Many commercial cationic flocculants have quadrivalent nitrogen at charge sites along the polymer chain; the cationicity derives from either the protonation of amine groups or the generation of quaternary nitrogen groupings. While the latter is unaffected by pH (although other parts of the polymer chain may be), cationicity produced by protonation is sometimes severely affected by both pH and ionic strength to the extent that a flocculant may fail to function correctly unless the acid/base conditions in the surrounding solution are correct. It is thus often necessary to use cationic polymers in conjunction with some form of pH modifier. The lower molecular weight cationic polymers, such as polyethyleneamine, are usually used to bring about flocculation via the charge patch mechanism. With anionic flocculants there is a tendency to use high or very high molecular weight polymers as low molecular weight, highly anionic polymers can behave as dispersants. Unlike cationic flocculants, the charge carried by anionic flocculants can be due to a number of different element groupings, however the principal types in commercial use are the carboxyl ion and the sulphonic acid groups. Flocculants containing the carboxyl ion are usually pH sensitive and, particularly at lower anionicity, their effectiveness may be reduced in more acidic conditions. Flocculants that contain the sulphonic acid group are less sensitive to pH variations and maintain their anionic nature even at low pH. As non-ionic flocculants carry either no charge or a very low charge in aqueous media they need to function via the bridging mechanism in order to produce flocculation. Thus, for the polymer chains to stretch sufficiently far from the particle surfaces, the non-ionic flocculant must have a high or very high

3 · Pretreatment of suspensions 143

Figure 3.9 Chemical compositions and structures of some common flocculant types. molecular weight such that bridges can form. The most important non-ionic polymer flocculants are based on polyacrylamide and polyethyleneoxide. The inherently low surface charge carried on the polymer means that flocculation with non-ionics is generally less affected by pH and ionic strength. Of the other types, amphoteric, ‘structured’ and natural flocculants are perhaps the most important. In the former, the polymer molecules contain both cationic and anionic charge sites and/or functional groups. Although amphoteric polymers need to be manufactured under very carefully controlled conditions and little seems to be known about their modus operandi, there are claims for the improved flocculation of materials such

144 Solid/Liquid Separation: Equipment Selection and Process Design as sewage sludge. Structured flocculants are sometimes useful in applications where high flocculant dosage levels are necessary and higher floc strengths are required. Despite their lower solubility in aqueous media, structured polymers containing crosslinked molecules or some cyclic carbon chains can provide for improved flocculation, albeit at generally higher optimum doses. Natural flocculants have been utilised for many years, and even though most of their original applications are now performed using synthetic polymers, there are some specialist areas within mining and food processing where they are still employed. Natural flocculants are derived from plant and animal products with the principal types being polysaccharides (e.g. starches and guar gums), and to a lesser extent tannins and chitins.

3.5 Effectiveness and selection of chemical pretreatments The general effectiveness of coagulants and flocculants can be assessed in the laboratory using a range of relatively simple tests. While variants exist, of particular importance are the jar test, the filter test and/or the capillary suction test. More details on testing for coagulant/flocculant selection, including aspects of scale-up, are provided in Wakeman and Tarleton (2005b). 3.5.1 Jar settling test In the simplest and most widely used form of the jar test an array of identical variable speed stirrers and beakers are used to evaluate particle aggregation over a range of different conditions (see Figure 3.10). The coagulant and/or flocculants are prepared as stock solutions before the tests commence. The suspensions to be aggregated are placed into round 0.8–1 litre, clear glass beakers together with the coagulant/flocculant and the mixture is stirred at ~200 rpm for a short period to ensure thorough mixing. The stirring is subsequently slowed and continued for a time before being stopped to allow the formed aggregates to settle. A sequence of up to six beakers are normally used to assess comparative rather than quantitative performance. Typical tests with the apparatus would involve, for instance, otherwise identical conditions and ranges of coagulant/flocculant dosage or a fixed dosage and ranges of different stirrer speeds (i.e. shear rates). When the stirring is stopped approximate settling rates are visually determined from the declining height of the sediment/supernatant interface and when settling has finished the clarity of the supernatant and general aggregate

3 · Pretreatment of suspensions 145

Figure 3.10 Jar test apparatus for assessing the effectiveness of coagulants and flocculants.

appearance are recorded. The maximum settling rate is likely to occur for a given dosage and this may (or may not) coincide with the optimum supernatant clarity. It should be noted that the maximum settling rate does not necessarily correspond to a maximum aggregate size as structure and spatial arrangement of particles can also significantly influence settling characteristics. 3.5.2 Filter test While the jar test apparatus described in Section 3.5.1 should be regarded as an essential piece of equipment, further performance indicators can be gained from the filter test described in Section 4.1. Here, sequences of constant pressure or vacuum dead-end cake filtrations are performed using suspensions prepared under different coagulation/flocculation conditions. The resultant data allow determination of a number of parameters including the optimum filtration rate, deliquored cake moisture contents and filter cake resistances. In many cases the maximum filtration rate will coincide with the suspension condition giving the fastest settling rate. The number of filtration tests performed will depend on the nature of the results obtained and the envisaged processing route for the solid/liquid mixture under assessment. 3.5.3 Capillary suction test As an alternative to the filter test, the capillary suction test (CST) can give a more rapid, though potentially less accurate, assessment of filtration performance. Figure 3.11 shows a schematic of the apparatus required which essentially comprises a small reservoir and a relatively thick filter

146 Solid/Liquid Separation: Equipment Selection and Process Design paper upon which is placed a sequence of electrical probes. The suspension sample is introduced to the reservoir and capillary forces draw liquid from the suspension and into the filter paper. Subsequent movement of the wet/dry interface is determined from conductivity measurements. The rate of movement of the interface can be related to the resistance of the forming cake and favourable correlations between CST measurements and cake resistance have been reported (Chen et al, 2005). The CST apparatus is only suited to assessing the filterability of suspensions forming high specific resistance cakes and the results obtained can be very susceptible to variations in temperature and the surface tension of the liquid phase in the test suspension.

Figure 3.11 Schematic diagram of the capillary suction apparatus. 3.5.4 Coagulant and flocculant selection The test methods described in Sections 3.5.1–3.5.3 allow the general effectiveness of coagulants and flocculants to be assessed in terms of a range of both qualitative and quantitative parameters. It is only after evaluating a range of pretreatment chemicals that tests may reveal the best coagulant, flocculant or combination of chemical pretreatments to use in a given application. The extensive ranges of coagulants and flocculants available makes it very difficult for the non-expert to determine an optimum choice and it is probably wise to consult with manufacturers at a relatively early stage for advice. However, some general advice can be given to aid the nonexpert in the initial selection of pretreatment chemicals. Table 3.2 shows a comparison of some basic properties of dispersed, coagulated and flocculated suspensions in relation to their separation characteristics. These facts and other literature (e.g. Moody, 1995) also suggest that for flocculants:

• •

Lower molecular weight polymers are generally better suited to the flocculation of suspensions which subsequently undergo vacuum or pressure filtration; Higher molecular weight flocculants can provide cost effective performance in sedimentation, centrifugation and belt filtration applications;

3 · Pretreatment of suspensions 147 Table 3.2 Comparisons of the general properties of dispersed, coagulated and flocculated suspensions.

Property

Dispersed

Coagulated

Flocculated

Clarity Settling rate Sediment volume Reagent dose Unit reagent cost Filtration rate Cake moisture Media blinding Aggregate strength Suspension viscosity Pollution/pH change Flexibility of use

Very poor Very slow Low n/a n/a Very low Low High n/a Low n/a n/a

Good Fair Reasonably low High Low Fair Low Moderate Low Moderate Often Very little

Poor to good Fast Often high Low High Slow to fast High Low to high Low to high High Seldom High

• •

With inorganic suspensions non-ionic and anionic flocculants generally give the best performance; With organic suspensions cationic flocculants are generally most effective.

3.6 Other methods of pretreatment With some suspensions it is not possible to use chemical pretreatments, typical examples are in the processing of pharmaceutical and food products. Under such circumstances physical pretreatments may be employed to beneficially modify suspension properties, however, many of these methods are either relatively expensive to implement or only suitable for use in specialised situations and thus have limited application. A useful summary is provided by Hermia (1980). 3.6.1 Suspension heating When filtrate is relatively viscous, raising the temperature of the feed prior to separation can reduce the inherent viscosity of the suspending liquid and thus provide for faster filtration (and settling) as well as improved posttreatment processes. The need to provide heating energy is a disadvantage, as is the increased potential for flashing of volatile components and higher solubility of solids; the latter is a particular problem when the cake solids are the principal product. In specialist cases, such as the pretreatment and

148 Solid/Liquid Separation: Equipment Selection and Process Design conditioning of some sludges, a combination of raised pressures and temperatures can beneficially influence interactions at the particle/liquid interfaces and provide for better filtration and subsequent deliquoring. 3.6.2 Suspension freezing In a process which is now little used due to high energy consumption, a suspension is frozen until completely solid, maintained at the freezing temperature for a period and then thawed. The resultant mixture contains relatively weak aggregates of particles which generally show improved filterability despite being susceptible to breakage by shear. Although originally devised for use in the water and wastewater industries, success has been claimed for the treatment of some inorganic sludges. 3.6.3 Particle/crystal formation While the addition of chemical coagulants and flocculants can alter the particle size in an existing suspension, the primary size of particles can also be controlled during their initial formation. Solids to be filtered are often produced during a chemical reaction by either precipitation or crystallisation where shape, size etc. of particles are dependent on the complex interaction between many variables. The temperature gradient and rate of cooling in a reactor have a major effect on many particle/crystal formations. For example, if a given sample is cooled too quickly a solid ‘lump’ can be formed, whereas a more carefully controlled cooling leads to the formation of individual, ideally (from the filtration point of view) large, particles. The importance of regulating particle size in the feed to a filter is evidenced by considering its influence on cake formation. Cake resistance is inversely proportional to the square of particle size and thus for a fixed porosity a 50% reduction in size leads to a fourfold increase in specific resistance. The result is significantly slower cake formation, the potential for process ‘bottlenecks’ and increased cycle times. When there is a wider distribution of size present in a suspension and/or an excess of fines, specific cake resistance can increase still further as the smaller particles may fit between the larger particles in a cake to reduce the interstitial space for liquid flow. The issues arising from initial particle formation can account for many of the difficulties encountered during their subsequent separation from liquids. 3.6.4 Elutriation and suspension thickening Although many factors affect the specific resistance of filter cakes, and hence rates of filtration, both the presence of fines and low solids concentrations can

3 · Pretreatment of suspensions 149 have a pronounced influence. Each tends to raise cake resistance and pretreatment involving the removal of fines and/or the thickening of a suspension prior to filtration often has beneficial results. Fines can be removed from suspension by elutriation in, for example, a classifier. While a fuller description of classifiers is given in Section 1.5, the process requires additional volumes of initially clean liquid to move counter-current to the flow of suspension. The finer particles are carried away with the majority of the liquid, leaving the remaining suspension to be further processed. Fines can also be removed by passing a suspension through a hydrocyclone (see also Section 1.2). This compact and simple device relies on high centrifugal forces to split a feed into a coarse fraction and a finer fraction thereby simultaneously achieving both classification and thickening. The hydrocyclone is, however, generally ill-suited to the processing of more fragile particulates and relatively high amounts of energy are used to achieve a separation. Other methods of suspension concentration include gravity thickening, centrifugation and flotation (see Sections 1.1, 1.3 and 1.7, respectively, for more detailed descriptions of equipment). Unless the particles are relatively large and/or dense compared to the suspending liquid, gravity thickening usually requires the addition of pretreatment chemicals to induce coagulation or flocculation and as such cannot always be considered as a physical pretreatment process. Sedimentation in large tanks, pools or lagoons is a classical application for coagulants and flocculants, a classical method for raising suspension concentration and is widely used as a precursor to filtration. In some instances, the density and/or surface characteristics of particles mean that suspension concentration can be achieved more readily by flotation rather than gravity thickening. Although the addition of surfactants to alter particle surface charge and relatively high energy costs can present problems in some cases, flotation has found wide application in large scale minerals processing and waste water treatment. 3.6.5 Ultrasonics The influence of ultrasound on the separation of solids from liquids is often complex. If a high frequency (MHz) and high power ultrasonic standing wave is passed through a suspension, then aggregation of finer particles can occur. Ultrasound induces additional motions to the suspended matter which can be sufficiently large to overcome the potential energy barrier preventing natural aggregation. If a wave carrying too much energy or lower frequency (kHz) ultrasound is used, the opposite effect is observed and aggregates are dispersed. When ultrasound is employed to pretreat a suspension and make particle sizes larger, greater filtration and sedimentation rates are generally recorded. Should dispersion occur then filtration and sedimentation rates are

150 Solid/Liquid Separation: Equipment Selection and Process Design reduced. In addition to dispersion and aggregation, ultrasound can also change surface properties (e.g.
-potential), increase the solubility of solid species and cause local heating. As described in Section 1.8, the use of lower frequency ‘power’ ultrasound during filtration or deliquoring can improve separation rates, particularly when it is combined with imposed electric fields. Although the use of force fields in solid/liquid separation may still be in its infancy, it is clear that the extra energy required to generate the fields must be offset by sufficiently improved separation rates for the overall processes to be commercially viable. 3.6.6 Irradiation High energy radiation such as X-rays can be applied to suspensions as a pretreatment to kill pathogens, provide stabilisation and sometimes improve filtration rates, particularly for sewage sludges. The little work that has been done, however, suggests that the economics of irradiation are marginal and for many suspensions there are no measurable benefits of exposure to radiation. Radiation from ultraviolet (UV) light sources is commonly used to destroy microorganisms in both drinking and wastewater filtration and is a particularly attractive alternative to chlorination as there is no addition of chemicals. UV radiation with a wavelength of ca. 255 nm penetrates the cell wall of the microorganisms where it is absorbed by the DNA (and RNA) to either prevent replication of the cell or induce death of the cell. To be effective the water to be treated must exhibit relatively low turbidity (e.g. low solids concentration) as higher turbidities can prevent sufficient penetration of the UV into the depth of the process stream. 3.6.7 Addition of solvents/surfactants If the liquid phase of a suspension has a high viscosity and heating cannot be applied, the addition of a suitable solvent prior to processing can bring about a viscosity reduction and hence improved filterability, etc. However, the disadvantages of increased filtrate volume, solvent recovery and flammability issues often outweigh any benefits. The use of surfactants such as sulphosuccinates and aryl or alkyl ethoxylates can increase filtration rates and (particularly) reduce equilibrium cake moisture during gas deliquoring. These so-called ‘deliquoring aids’ or ‘sludge conditioners’ reduce the surface tension of the liquid phase in a filter cake and aid its removal albeit at the expense of contaminating the cake and liquors. While the addition of either a solvent or surfactant cannot strictly be considered to be a physical pretreatment, both are included here to distinguish them from coagulation and flocculation.

3 · Pretreatment of suspensions 151 3.6.8 Addition of filter aid Filter aids can improve the permeability and sometimes porosity of a filter cake, improve filtrate clarity and help to prevent filter medium blinding. They comprise relatively porous particles such as diatomite, perlite and activated carbon and are either filtered as a precoat onto the medium or mixed as body feed with the suspension during a pretreatment stage; the latter beneficially improves the porosity of a subsequently formed filter cake. Both the cost of filter aid and the need to remove filter aid from the processed solids can present problems; however, the use of filter aids on rotary drum filters and in the filtration of dilute feeds (such as those found in the brewing industries) can bring undoubted benefits. More detail on filter aids is provided in Chapter 2.

3.7 Conclusions The discussion of chemical and physical pretreatments given in this chapter highlights the potential benefits (and pitfalls) of artificially changing the particle size present in a suspension. Chemical pretreatments in particular can enhance performance in all phases of a filter cycle and provide for improved filtration rates and reduced cake moistures. Some separation devices such as the deep cone thickener and belt filter press rely on the satisfactory performance of flocculants to function correctly and their use is a necessary prerequisite. The use of coagulants and flocculants with other separation devices must be assessed on an individual basis. Their introduction generally increases the operating cost of a separation which must be balanced by the potential improvements in separation characteristics.

4

Data acquisition, analysis and scale-up

In this chapter practical methods of obtaining information for filtration, consolidation, cake washing, gas deliquoring and sedimentation are described. The aim is to illustrate how important data for equipment selection (see Chapter 5), scale-up and process simulation (see Chapters 6 and 7) can be measured in the laboratory using either well established, manually operated apparatus or stateof-the-art, automated apparatus. In some cases details of step-by-step experimental procedures are presented to illustrate best practice. Methods of data analysis are also presented and their use is illustrated through worked examples. The fundamental concepts that underpin this chapter are not described in detail, as emphasis is placed on more practical issues. The interested reader is referred to Wakeman and Tarleton (2005a,b).

4.1 Filtration (cake formation) Filtration tests can be carried out with quite simple apparatus where the objectives are principally twofold. Firstly, cake formation rate is required for preliminary equipment selection, and secondly parameters such as cake specific resistance and solids concentration values are needed, ideally as functions of the applied pressure/vacuum, for filter sizing and filtration rate calculations (Tarleton, 1998a,b; Tarleton and Wakeman, 1994c, 1999; Wakeman and Tarleton, 1990, 1991a, 1994a). 4.1.1 Test procedures Figure 4.1 shows a test filter comprising a funnel, a graduated cylinder and a vacuum generation system that can be used to obtain basic data. The drainage characteristics of the normal ceramic perforate bottom Buchner funnel are

4 · Data acquisition, analysis and scale-up 153

Figure 4.1 Test apparatus for obtaining basic vacuum filtration data. A suitably modified apparatus can be used to provide data at elevated pressures.

poor and make it unsuitable for these tests; it is preferable to use a filter funnel with a porous sintered bottom, or ideally a top-fed leaf assembly equipped with a filter cloth. To simplify analysis of the data it is usual to operate at a constant pressure difference. In normal practice the same type of filter medium is used in laboratory tests as may be used at the full scale so that any medium effects are incorporated into the experimental results. The general procedure for obtaining filtration data is as follows: 1. Determine the solids concentration in the slurry sample before carrying out the filter test(s). 2. With needle valve A in the vacuum line closed, adjust the bleed needle valve B to give the required level of constant vacuum. This is likely to be in the region of 50 –70 kPa (380–530 mmHg). In the wastewater treatment industry the standard used is 49 kPa (386 mmHg). 3. Pour the well stirred slurry sample into the filter funnel containing the filter cloth and open needle valve A in the vacuum line so that a pre-set vacuum level is achieved as rapidly as possible in the graduated cylinder. It is better not to pour the sample directly onto the cloth, but to feed it onto a perforated plate located 2–3 cm above the cloth. The plate acts as a distributor to (i) prevent solids approaching the pores in the cloth at an unrealistically high velocity and thereby causing unexpected plugging of the pores, and (ii) spread the feed over the full area of the funnel, enabling formation of a cake of more uniform thickness.

154 Solid/Liquid Separation: Equipment Selection and Process Design 4. Monitor the filtration test by recording the filtration rate by measuring the volume of filtrate collected at various time intervals. The intervals between recording the measured volumes need not be constant but may be increased progressively to compensate for the gradual drop in filtrate flow rate. 5. If the cake form rate is too slow (e.g. of the order of cm h
1), it may be desirable to add flocculants or pretreatment chemicals to the slurry and repeat the filtration test(s) as appropriate. For slow filtering slurries it may be necessary to use smaller measuring cylinders. 6. When ten or more sets of volume–time readings have been obtained fully open both needle valves to break the vacuum. There should be some surplus unfiltered slurry visible on top of the cake at this stage. If there is no surplus slurry it is likely that the cake will have started to deliquor and subsequent cake moisture measurements will be erroneously low, while leaving the surplus on the cake will lead to incorrectly high moisture measurements. 7. Pipette the excess slurry from the surface of the filter cake. 8. If possible, measure the thickness of the filter cake. 9. Remove as much of the cake as possible from the filter, weigh it, dry it and reweigh it. From these measurements, calculate the ratio of the mass of wet/dry cake. For an initial determination of filtration performance the procedures described in Steps 2–9 are adequate. If data are required for filter sizing and simulation, then Steps 2–9 need to be repeated at a range of different constant pressures/vacua to establish any variation of cake resistance and solids concentration and thus cake compressibility (see also Section 4.7). It is likely that more sophisticated equipment, such as that described in Section 4.6, will give more reliable results. Although not normally performed in the laboratory due to operational difficulties at the small scale, filtration tests can also be undertaken at either constant rate or variable rate–variable pressure. In constant rate filtration the filtrate flow is maintained at a constant level by progressively raising the applied pressure gradient to compensate for the increasing resistance of the growing cake. This mode of operation mimics filtration at the full scale with a positive displacement pump. In variable rate–variable pressure filtration both the filtrate flow and pressure vary throughout cake formation to mimic filtration with a centrifugal pump. More details of variable pressure filtration, including the pertinent equations, are available in Tarleton (1998a) and Wakeman and Tarleton (2005a), and Section 4.6 details how it is technically possible to perform these filtrations with laboratory scale equipment.

4 · Data acquisition, analysis and scale-up 155 4.1.2 General filtration equation Considering pressure to represent either pressure or vacuum, the filtration process is most commonly analysed using the following general filtration equation R dt 1  l ( av cV  AR )  l  av c    2 V l 2 A
p A
p A
p dV q

(4.1)

where V is the cumulative volume of filtrate, t the filtration time, q the filtrate flow rate, A the filter medium area,
p the filtration pressure, l the viscosity of liquid, av the average specific cake resistance, R the medium resistance and c the effective feed concentration. The latter is ideally given by c

l s 1
mav s

(4.2)

where l is the density of liquid, mav the ratio of mass wet/dry cake and s the mass fraction of solids in the feed. Integrating equation (4.1) with
p  constant gives  c R K t
ti  av2 l (V  Vi )  l  1 V  K 2 2 A
p V
Vi 2 A
p

(4.3)

ti and Vi represent the time and corresponding volume of filtrate where the constant pressure filtration is considered to start. K1 and K2 are regarded as constants which implies that the individual parameters constituting K1 and K2 are also constant or can be adequately represented by an average value over the test duration. Most frequently ti  0 and Vi  0. Noting equation (4.3) and Figure 4.2, a ‘Characteristic Plot’ of (t
ti)兾(V
Vi) vs. (VVi) should exhibit a substantial linear region which allows av and R to be evaluated from gradient 

 av c l 2 A 2
p

y  axis intercept 

(4.4)

l R A
p

(4.5)

156 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 4.2 Typical forms of the t/V vs. V plot showing examples of where non-linearities can be observed and the reasons for their occurrence. Care must always be taken when carrying out an experiment to obtain the data, as experimental methodology can also be the cause of non-linearities. Sometimes these can make the linear part of the data so small as to be quite useless.

Alternatively, equation (4.1) can be used directly without integration by again assuming that
p  constant. In this case a Characteristic Plot of 1兾q vs. V should exhibit a linear region with

gradient 

 av c l A 2
p

(4.6)

The y-axis intercept is again given by equation (4.5). It is sometimes more convenient to use a plot of 1兾q vs. V if the filtration test recorded q vs. t rather than V vs. t. However, equation (4.3) describes a cumulative plot which has reduced sensitivity to fluctuations in the raw experimental data, while direct use of equation (4.1) is more sensitive and shows deviations from the intended straight line plot more clearly (albeit at the expense of more scatter in the plotted data).

4 · Data acquisition, analysis and scale-up 157 4.1.3 Evaluation of terms in the general filtration equation While most of the terms in equations (4.1)–(4.6) are known directly from the conditions used in a test, the effective feed concentration (c) needs to be calculated. Depending on the level of data recorded, three methods can be used. If a complete set of data are available, then c is best calculated using equation (4.2) where the mass of wet cake (⬅(Ms)e (Ml)e) needs to be measured at the end of an experiment. The wet cake sample is weighed and then subsequently dried to give the mass of dry cake (⬅(Ms)e) which in turn allows mav to be determined via a simple ratio. If only (Ms)e is known, then

c⬇

( M s )e Ve

(4.7)

where Ve is the total volume of liquid filtered during the test. If neither (Ms )e nor (Ml )e is known, then c must be approximated using the feed suspension concentration expressed in terms of mass of solid per volume of liquid (i.e. Cl ). While a complete listing of conversion factors for suspension concentration is given in Appendix C, by way of example, if the mass fraction (s) is known, then c ⬇ Cl 

l s 1
s

(4.8)

which is equivalent to ignoring the liquid present in the cake. It is generally accepted that the accuracy of the expressions for c decreases in the order of equation (4.2);(4.7);(4.8). The equations for c may need to be modified when considering a batch filtration. Unless care is taken the entire batch of suspension can be filtered and the experiment can be continued with the result that undesirable cake deliquoring, and sometimes cake compression, occur. As seen in Figure 4.2 these phenomena manifest themselves on a t兾V vs. V plot as a sharp deviation at longer filtration times, and hence larger volumes of filtrate. Should cake deliquoring occur then both mav and Ve need to be adjusted in order to calculate correct values for specific cake resistance and the volume fraction of cake solids (Cav) as the mass of wet cake recorded at the end of an experiment will be too low. When the volume of filtrate at the transition from cake formation to gas deliquoring is

158 Solid/Liquid Separation: Equipment Selection and Process Design denoted as Vtr , corrections to equations (4.2) and (4.7) to account for deliquoring are c

l s 1
(mav )tr s

c⬇

Ms Vtr

(4.9)

(4.10)

where (mav)tr , the ratio of mass wet/dry cake at the transition, is given by (mav )tr 

( M s )e  ( Ml )e  l (Ve
Vtr ) ( M s )e

(4.11)

It is noted that curvature of the t兾V vs. V plot can occur for a number of reasons and may appear over regions other than the end period of filtration. Curvature can be observed to differing extents at both short and intermediate filtration times, and choosing the limit of the linear portion on the Characteristic Plot in order to apply equations (4.9)–(4.11) must be done with care. If the technique is applied without some feeling for the consequences (and the reasons for plot curvature), then false answers may ensue. Also, where a filtration test is stopped before all the suspension is filtered then only values recorded at the end of the filtration test have physical meaning and equations (4.9) and (4.10) cannot be used. In this case suspension remains above the cake which must be siphoned away before the cake is sampled in order to achieve an accurate analysis. It is evident that close observations towards the end of an experiment can help to establish correct analysis procedures. 4.1.4 Evaluation of filter cake properties While specific cake resistance and filter medium resistances are determined as shown in Section 4.1.4, several other useful values can also be obtained from a filtration test provided sufficient data are recorded. Ratio of mass wet/dry cake As already noted, where values are correctly measured at the end of a filtration mav 

( M s )e  ( M l )e ( M s )e

(4.12)

and when cake compression or deliquoring occur then equation (4.11) should be used instead.

4 · Data acquisition, analysis and scale-up 159 Filter cake solids fraction The volume fraction of solids (solidosity) in a filter cake as defined by Cav  1
 av 

volume of solids in cake total volume of cake

(4.13)

can be determined in at least two ways. When the filter cake thickness (Le) is known Cav 

( M s )e Le A s

(4.14)

where s is the solids density. If the mass of wet filter cake is recorded, then Cav can also be calculated according to Cav  1


 s (mav
1)  s (mav
1)  l

(4.15)

Where cake compression or deliquoring occurs towards the end of a test equation (4.15) must be modified by substituting (mav)tr for mav. No similar correction can easily be applied to equation (4.14) to account for cake deliquoring as neither the cake thickness nor the mass of solids deposited is usually known as a function of the filtration time. Cake moisture content The cake moisture content (M) which is defined as

M  100

( M l )e mass of liquid in wet cake  100 total mass of wet cake ( M s )e  ( M l )e

(4.16)

can be expressed in several ways including

M  100

l (1
Cav ) l  Cav ( s
l )

(4.17)

M  100

mav
1 mav

(4.18)

160 Solid/Liquid Separation: Equipment Selection and Process Design which implies that M can be evaluated from either a known cake thickness or the ratio of mass wet/dry cake (see equations (4.14) and (4.15)). Mass dry cake produced per filter area The mass of dry cake produced per filter area is a measure of filter capacity and defined by w

( M s )e A

(4.19)

Average cake formation rate In its simplest form, the cake formation rate (Lgr) is given by Le te

Lgr 

(4.20)

although care needs to be exercised if the cake has undergone deliquoring as shrinkage can occur. When the cake thickness (Le) has not been measured at the end of a filtration it can be estimated in either of two ways dependent upon the values known Le ⬇

Ve l  1
s   (1
s)   A s 
(1
Cav )  s 1   l s   s

  sVe l  s (mav
1) 1  l  Le ⬇ A s (1
mav s)

(4.21)

(4.22)

With less accuracy the average cake growth rate can be estimated using Lgr ⬇

Ve c  s Ate

(4.23)

and where deliquoring has occurred at the end of a test Lgr ⬇

Vtr c  s Attr

(4.24)

The average cake growth rate is useful in filter selection (see Chapter 5) where it is used to shorten a list of equipment potentially suited to a given duty and separation.

4 · Data acquisition, analysis and scale-up 161 4.1.5 Example 4.1 For the constant pressure filtration data shown in Table 4.1 calculate the specific cake resistance, filter medium resistance, cake solids volume fraction and other characterising parameters. The test has been performed in accordance with the procedure described in Section 4.1.1. Table 4.1 Experimental data for the constant pressure filtration analysed in Example 4.1. t (s)

V (m3)

t/V (s m
3)

t (s)

V (m3)

0 9 19 31.5 49.5 70 93 120 152 187 227 270 319 371 425 485

0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 0.001 0.0011 0.0012 0.0013 0.0014 0.0015

90000 95000 105000 123750 140000 155000 171429 190000 207778 227000 245455 265833 285385 303571 323333

548 615 682 758 838 923 1013 1105 1202 1304 1550 1880 2000 2250 2700

0.0016 0.0017 0.0018 0.0019 0.002 0.0021 0.0022 0.0023 0.0024 0.0025 0.00273 0.003 0.00305 0.00308 0.0031

Filter diameter  7.2 cm Filtration pressure  100 kPa Solids density  2500 kg m
3 Liquid density  1000 kg m
3 Liquid viscosity  0.001 Pa s

t/V (s m
3) 342500 361765 378889 398947 419000 439524 460455 480435 500833 521600 567766 626667 655738 730519 870968

Feed slurry concentration  0.116 w/w Wet cake mass  200 g Dry cake mass  155 g Cake depth  4.7 cm

Solution The time (t) vs. cumulative volume (V) sequence recorded during the test is plotted in Figure 4.3 having been converted into the form of t兾V vs. V. These data show that the cake has been allowed to deliquor as indicated by the sharp upward trend at longer times. Some deviation from linearity is also present towards the start of the test. The two vertical lines represent the extent of the linear region where the right hand line indicates the transition to deliquoring such that Vtr  0.003 m3 and hence ttr  1880 s. Regression analysis over the linear region gives t兾V  1.92 × 108V  37790 as shown in Figure 4.3.

162 Solid/Liquid Separation: Equipment Selection and Process Design 1e+6

Time/volume (s m-3)

8e+5 regression line

6e+5

4e+5

2e+5

0 0.000

0.001

0.002

0.003

0.004

Cumulative volume of filtrate (m3)

Figure 4.3 Time/volume vs. volume data for Example 4.1. Using equations (4.11) and (4.9) to compensate for the volume of liquid removed from the cake during deliquoring gives (mav )tr  c

200 × 10
3 1000 (0.0031
0.003) = 1.94 155 × 10
3

l s 1000 × 0.116   150 kg m
3 1
(mav )tr s 1
1.94 × 0.116

(4.25)

(4.26)

Noting that A  (7.2 × 10
2兾2)2  4.1 × 10
3 m2 and using rearranged versions of equations (4.4) and (4.5) gives  av  

gradient × 2 A2
p c l 1.92 × 108 × 2 × (4.1 × 10
3 )2 × 100 × 103 150 × 0.001

 4.3 × 10 9 m kg
1 R 

intercept × A
p l 37790 × 4.1 × 10
3 × 100 × 103 0.001

 1.5 × 1010 m
1

4 · Data acquisition, analysis and scale-up 163 As both the cake thickness and the ratio of mass wet/dry cake are known, the cake solids volume fraction can be calculated using equation (4.14) and a rearranged version of equation (4.15) with (mav)tr substituted for mav Cav 

( M s )e 155 × 10
3   0.32 vv Le A s 4.7 × 10
2 × 4.1 × 10
3 × 2500

Cav  1
 1


 s 关(mav )tr
1兴  s 关(mav )tr
1兴  l 2500 (1.94
1) 2500 (1.94
1) 1000

(4.27)

 0.30 vv The cake moisture content is given by equation (4.17) and, for instance, with Cav  0.30 v/v then M  100  100

l (1
Cav ) l  Cav ( s
l ) 1000 (1
0.3) 1000  0.3 (2500
1000)

(4.28)

 48.3% As the cake thickness was recorded at the end of the test the cake growth rate is given by equation (4.20), however, deliquoring of the cake for the final 820 s means that a more representative time for cake formation is 1880 s. Assuming that negligible shrinkage of the cake occurs during deliquoring Lgr ⬇

Le 4.7 × 10
2   2.5 × 10
5 m s
1 1880 ttr

(4.29)

Alternatively, equation (4.24) can be used where Lgr ⬇

Vtr c 0.003 × 150   2.3 × 10
5 m s
1  s Attr 2500 × 4.1 × 10
3 × 1880

If the volume of liquid removed from the cake during deliquoring is not accounted for then several calculated values are revised. Assuming that the same linear region shown in Figure 4.3 still applies then mav  200 × 10
3兾155 × 10
3  1.29, c  137 kg m
3, av  4.7 × 109 m kg
1 and, from

164 Solid/Liquid Separation: Equipment Selection and Process Design equations (4.15) and (4.17), Cav  0.58 v/v and M  22.5%. Taking the entire dataset and applying linear regression give t兾V  2.12 × 108V  21422 s m
3 and thus mav  1.29, c  137 kg m
3, av  5.1 × 109 m kg
1, R  8.7 × 109 m
1, Cav  0.58 v/v, M  22.5% and, from equation (4.20), Lgr  4.7 × 10
2兾2700  1.74 × 10
5 m s
1. Comparing these results with the original calculations shows that when suitable corrections are not applied, av can be in error by up to ~19%, R by ~42%, Cav by 93%, M by ~53 % and Lgr by 30%. Such errors can have significant consequences in filter sizing and scale-up.

4.2 Gas deliquoring In order to predict gas deliquoring performance on a full scale filter it is a prerequisite to determine the threshold pressure ( pb), the minimum pressure difference that must be applied across a cake to effect any deliquoring whatsoever, and the irreducible saturation (S) which is the lowest saturation achievable by fluid displacement alone. While the former can be calculated with reasonable confidence, the latter is far more difficult to predict and is best measured in the laboratory test described below. Both quantities are obtainable from the same experiment although the threshold pressure can, on occasion, be a troublesome measurement. The irreducible saturation can sometimes be inferred from the moisture content of a cake discharged from a test filter. It is noted that Chapters 6 and 7 describe in detail how pb, S, and ua, the superficial gas velocity through the cake, can be predicted from a knowledge of cake, particle and liquid properties for both pressure and vacuum driven deliquoring. 4.2.1 Test procedure When historical data are unavailable it is recommended that a capillary pressure curve is measured. The experiment is readily performed in the laboratory and greatly improves the accuracy of later calculations. The necessary equipment is shown in Figure 4.4 and principally comprises a filter at the bottom of a cylindrical funnel (a useful size is about 45 cm long by 10 cm in diameter and the filter cloth should be the same as that intended for use on the actual filter). The funnel is filled with a known volume of suspension at a known solids concentration and is filtered to form a saturated cake. The cake depth and volume of drained filtrate are recorded. A complete capillary pressure curve is obtained by successively incrementing the pressure gradient across the cake and inferring corresponding decrements in the

4 · Data acquisition, analysis and scale-up 165

Figure 4.4 Apparatus for measuring threshold pressures and capillary pressure curves, vacuum driven (left) and pressure driven (right). The latter can utilise an electronic balance in place of the measuring cylinder if required. The flow meter is not necessary but does provide useful additional design information regarding gas flow rate.

liquid volume remaining in the cake. The latter are calculated from measurements of the liquid volume extracted after each increment in pressure gradient and knowledge of the final mass of liquid in the cake as determined by thermal drying at the end of the test. It is wise to measure the cake depth at each pressure gradient, as compressible cakes may remain almost saturated if their bulk volume is reduced but no flow of gas occurs into the pores of the cake (although their moisture content is decreased). 4.2.2 Data analysis procedure The Characteristic Plot for a gas deliquoring test is a graph of applied gas pressure gradient vs. cake saturation from which both S and pb can be estimated (see Figure 4.5). The final, or irreducible, saturation (S), which is achieved at the highest applied pressure or vacuum, is deduced directly from the experimental measurements. The minimum, or threshold pressure ( pb), which is required to give an initial reduction in saturation is given by point T in Figure 4.5. This point can be difficult to identify reliably and it is usually easier to obtain a modified threshold pressure by using linear regression over the main portion of the curve and then extrapolation to the point A which also lies on the line S  1. The threshold pressure value given by A is always greater than that given by T.

166 Solid/Liquid Separation: Equipment Selection and Process Design 1200

Applied pressure (kPa)

1000 800 600

regression line

400 S∞

200

A

pb 0 0.0

T 0.2

0.4

0 .6

0.8

1.0

Cake saturation

Figure 4.5 Typical capillary pressure curve (also a plot of the experimental data shown in Table 4.2).

By definition, the cake saturation (S) at any point on a capillary pressure curve is given by equation (4.30) S

Ml volume of liquid in cake   av AL l  av AL

(4.30)

where AL represents the bulk volume of cake and av is its average porosity which may be determined from  av  1
Cav  1


Ms  s AL

(4.31)

Alternatively, if a filtration test has been performed and analysed according to the procedures in Section 4.1, Cav, and hence av, can be derived from equation (4.15). 4.2.3 Example 4.2 An experiment has been performed to determine the deliquoring characteristics of a filter cake formed to a depth of 6 cm. The data obtained over the pressure range 0 –1140 kPa are shown in Columns (1) and (2) of Table 4.2. At the

4 · Data acquisition, analysis and scale-up 167 Table 4.2 Experimental data recorded for the capillary pressure experiment described in Example 4.2 and values of cake saturation calculated using equation (4.30).

Applied pressure
p (kPa) (1) 0 30 80 110 140 240 340 440 540 640 740 840 940 1040 1140

Mass of liquid extracted (g) (2)

Volume of liquid extracted (cm3) (3)

Volume of liquid in cake (cm3) (4)

Cake saturation, S (5)

0 0 5.69 14.07 25.35 53.59 84.63 124.1 155.1 183.3 203.1 214.4 222.9 225.6 225.6

0 0 5.7 14.1 25.4 53.7 84.8 124.3 155.4 183.7 203.5 214.8 223.3 226.1 226.1

282.6 282.6 276.9 268.5 257.2 228.9 197.8 158.3 127.2 98.9 79.1 67.8 59.3 56.5 56.5

1.00 1.00 0.98 0.95 0.91 0.81 0.70 0.56 0.45 0.35 0.28 0.24 0.21 0.20 0.20

end of the experiment all of the cake was removed from the test apparatus and weighed to give a wet cake mass of 810 g. Subsequent thermal drying removed all the remaining liquid to give a dry cake mass of 528 g. Noting that s  2800 kg m
3, l  998 kg m
3 and the filter diameter is 10 cm (to give A (10 × 10
2兾2)2  7.85 × 10
3 m2), plot the capillary pressure curve and determine the irreducible cake saturation and threshold pressure. Assume that the cake thickness remained constant throughout deliquoring. Solution As the data were taken with an electronic balance it is necessary to convert the recorded masses to equivalent volumes by dividing each value by l as shown in Column (3) of Table 4.2. Using equation (4.31) and converting to SI units as appropriate gives  av  1


(528 1000)  0.6 2800 × 7.85 × 10
3 (6 100)

(4.32)

168 Solid/Liquid Separation: Equipment Selection and Process Design At the start of the test when S  1, a rearranged version of equation (4.30) gives the initial volume of liquor in the cake

 Ml     l

 S av AL  1 × 0.6 × 7.85 × 10
3 (6 100) t0

 2.83 × 10
4 m 3 ⬅ 282.6 cm 3 The remaining values in Column (4) are obtained by subtracting values in Column (3) from the initial volume of liquor in the cake (i.e. 282.6 cm3). The cake saturations in Column (5) are calculated using equation (4.30) and the values of (Ml兾l)tt from Column (4).

S  (volume of liquid in the cake)

1  av AL

M  1  l   l  tt 0.6 × 7.85 × 10
3 (6 100)

(4.33)

The complete capillary pressure curve is plotted in Figure 4.5. It is evident that no more deliquoring occurs at pressures above ~1000 kPa and thus S  0.2. The cake begins to deliquor at a pressure between 30 and 80 kPa. While more experimental data could be obtained at intermediate pressures, a regression analysis over the central linear region of the curve gives
p 
866S  933 kPa and when S  1 the threshold pressure is
p  pb ⬇ 67 kPa. The value at the point A is usually sufficiently accurate for design and simulation purposes.

4.3 Cake washing While washing performance in process scale filters can be theoretically predicted a priori from a knowledge of cake and wash liquor properties (see Chapters 6 and 7), laboratory testing is usually concerned with the evaluation of two parameters:

•

How much of the soluble species will be removed by a given volume of wash liquid?

•

How long will the wash liquid take to effect such a removal?

4 · Data acquisition, analysis and scale-up 169 Both displacement and reslurry washing can be investigated on a small scale, although only the former is described in detail here. The conditions of test work should replicate as far as is practicable the actual conditions under which any larger scale filter will operate. In addition, the temperature, the pH value, and the composition of the wash liquid and slurry or cake being washed must correspond to the conditions likely to be met in practice, otherwise misleading results may be obtained. 4.3.1 Test procedure If the washing is to be done on a vacuum filter, then an apparatus similar to that shown in Figure 4.1 may be used. The main difference is that a means of feeding wash liquid to the surface of the cake needs to be added; this is often a spray or a weir over which the wash liquid flows. Whichever is used, feeding the wash liquid to the cake should not cause any disruption of the surface. After cake formation in the way described in Section 4.1.1, a steady flow rate of wash liquid is required to keep a thin (ca. 1 mm deep) pool of liquid covering the cake surface. The pool helps to prevent cake deliquoring at any stage during the test; deliquoring is usually recognised when the cake surface appearance changes from being shiny or reflective to being mat or dull. Displacement cake washing is normally performed at a constant pressure gradient which helps to ensure a constant flow rate of wash liquid through the cake. When a fixed volume of wash liquid has passed through the cake the experiment is stopped. Any excess wash liquid is removed from the cake surface using a pipette and the whole (saturated) cake is removed from the filter. The amount of remaining soluble species is determined by reslurrying the cake in a known volume of distilled water, mixing for a set period and refiltering the resultant suspension, a process that is repeated until all the solute is transferred to the filtrate. The concentration of solute in the cake at the end of displacement washing can be determined by a titration or conductivity measurement on all of the filtrate and by a knowledge of the total volume of distilled water used to reslurry the filter cakes. By repeating the experiment several times but using a different volume of wash liquid each time, the variation of the amount of soluble species in the cake can be plotted as a function of the amount of wash liquid permeated through the cake (i.e. a wash curve). The amount of wash liquid used is estimated from a knowledge of the amount of residual liquid in the cake just before washing is started which can, for instance, be determined by measurements in accordance with Step 9 in Section 4.1.1. The wash liquid amount should be varied from about 0.5 up to 3.5 times the residual amount (i.e. between 0.5 and 3.5 wash ratios).

170 Solid/Liquid Separation: Equipment Selection and Process Design Many determinations of washing only use measurements of residual solute in the cake as described above. However, there are additional methods for evaluating washing performance which are both simple and reliable. The instantaneous concentration of solute () emerging from the cake can be monitored by either taking measurements of conductivity directly as liquor emerges from a cake or collecting samples of these washings in individual jars for subsequent analysis by conductivity or titration. Either method requires changes to be made to the apparatus shown in Figure 4.1. Alternatively, the wash liquor effluent emerging from the cake can be continuously collected in a single vessel and its bulk concentration (av) can be determined. The use of individual, rather than cumulative, measurements usually leads to more accurate determinations of the washing curve as solute concentrations towards the end of washing can be very low. Whenever washing data are obtained it is important to always measure the solute concentration present in the cake at the end of an experiment, even though the solute concentration in the washings, i.e. the liquid emerging from the cake, may have been measured carefully. The reason for this is twofold. Firstly, porous particles or poor flow distributions in the cake can lead to holdup of solute during washing that is not always detectable from measurements of solute concentration in the washings. Secondly, a solute mass balance can be established over the washing operation which helps to ensure an accurate experiment and faith in both the apparatus and reliability of the data obtained. 4.3.2 Data analysis procedure The aim of experimental washing curve determinations is to gain a knowledge of the amount of wash liquor, number of wash ratios (W) and washing time (t) required to remove a given quantity of solute from a filter cake. It is usually necessary to calculate the amount of solute to be removed from a specification of the allowable solute concentration remaining in the cake at the end of the wash. When typical data are recorded, the results can be plotted in a number of ways as the: 1. dimensionless instantaneous concentration of solute in the wash effluent (*) vs. wash ratio (see Figure 4.6), 2. dimensionless concentration of solute in the wash effluent collected in a * ) vs. wash ratio, single washings receiver vessel (av 3. fraction of solute remaining in the cake (R) vs. wash ratio, and 4. fraction of solute removed from the cake (F) vs. wash ratio.

4 · Data acquisition, analysis and scale-up 171 1.0 0.9 Dimensionless concentration of solute in washings

A 0.8 B

0.7

1

2

0.6 0.5 0.4

C

0.3 3

0.2 0.1 0.0 0.0

0.5

1.0 Wash ratio

1.5

2.0

2.5

Figure 4.6 Plots of the dimensionless instantaneous concentration of solute in the wash effluent (*) from the cake vs. the wash ratio (or alternatively wash volume used or washing time) are referred to as washing curves; curve 1 shows a typical washing curve, curve 2 shows the ideal washing curve and curve 3 shows an extreme which is obtained by washing highly deliquored cakes, e.g. in a centrifuge. The initial part of curve 3 does not show any displacement washing as the pores of the cake are almost empty before washing starts. On curve 1, in region A retained liquor is displaced from the pores in the cake, region C is controlled by mixing and mass transfer processes, and B is an intermediate region.

where

W  

ⴱ 

volume of wash liquid used volume of liquor in cake at start of washinng Qt wash liquid volume   av ALS cake void volume × St0

(4.34)

number pore volumes wash liquid S


w

0
w

(4.35)

172 Solid/Liquid Separation: Equipment Selection and Process Design W


w dW

0
w 0

F=∫

(4.36)

W


w dW

0
w 0

R  1
F  1
∫

(4.37)

t

av 

1

dt t ∫0

ⴱ

av 

av
w 1
w F = ∫ dW 

0
w W 0 0
w W

(4.38)

W

(4.39)

and Q is the (constant) volume flow rate of wash liquid passing through the cake, A the filter area on which the cake is formed,  the instantaneous solute concentration in the wash liquid discharged from the cake, 0 the solute concentration in the liquor in the cake voids prior to washing, w the solute concentration in the feed wash liquid and av the solute concentration in a wash effluent that is collected over a period and mixed. The usefulness of the wash ratio terms in equations (4.34)–(4.39) for scaleup purposes is evidenced by the inclusion of the wash flow rate and the washing time. However, in all but the most carefully performed experiments it can be difficult to obtain the value of the wash ratio with a high degree of accuracy, and it is almost impossible to obtain an accurate value from a process scale filter. The porosity of the cake is important in this context as it not only affects the liquor volume in the cake at the start of washing, but also affects the volume flow rate of wash through the cake. When the porosity is very low, the washing rate is very low but the washing effectiveness is very high. 4.3.3 Example 4.3 Incremental volumes of clean wash water (w  0 ppm) were drawn through a cake preformed under vacuum to a depth of ~3 cm. Individual samples of the washings, i.e. the liquid exiting the cake, were subsequently analysed by titration to determine the concentration of the salt compounds removed. The data recorded are shown in Columns (1) and (2) of Table 4.3. The cake was formed from aqueous suspension with l  0.998 g cm
3.

4 · Data acquisition, analysis and scale-up 173 Table 4.3 Measured and calculated data for Example 4.3. Volume of wash liquid used (cm3) (1)

 (ppm) (2)

0 55 93 103 137 171 188 205 369

130 130 117 104 52 13 7.8 5.2 1.3

* 兾0

冕ww2  dW

F

R

(3)

(4)

(5)

(6)

(7)

0.00 0.40 0.68 0.75 1.00 1.25 1.38 1.50 2.70

1.00 1.00 0.90 0.80 0.40 0.10 0.06 0.04 0.01

0.000 0.400 0.266 0.060 0.150 0.063 0.010 0.006 0.030

0.000 0.400 0.666 0.726 0.875 0.939 0.949 0.955 0.985

1.000 0.600 0.334 0.274 0.125 0.061 0.051 0.045 0.015

W

1

0

At the end of the experiment the cake was removed from the apparatus and weighed, the mass was 412.7 g. To determine the residual quantity of salts, a 137 cm3 aliquot of distilled water was used to reslurry the cake. The resulting suspension was filtered and analysis of the filtrate showed a concentration of   0.9 ppm. The reslurrying/filtration process was performed a further three times with the filtrate being analysed each time to respectively give   0.5 ppm,   0.2 ppm and   0 ppm. Thermal drying of the final cake yielded a mass of 276.0 g. Plot the wash curve for the experiment. Solution To plot a wash curve it is necessary to manipulate the data recorded in the experiment. The mass of liquid in the cake Ml  412.7
276  136.7 g equates to a volume of 136.7兾0.998  137 cm3 and represents a wash ratio W  1. The complete list of wash ratios shown in Column (3) of Table 4.3 is obtained by dividing each value in Column (1) by 137. As indicated in Section 4.3.2 there are numerous ways to represent a wash curve and, by way of example, three are derived here. Values of * in Column (4) are obtained using equation (4.35) by noting that 0  130 ppm and w  0 ppm. The data in Column (5) are required to evaluate both F and R. The integral is approximated using the trapezium rule where, for example, the value corresponding to W  0.4 is 0.5(1  1)(0.4
0)  0.4 and at W  0.68 the value is 0.5(1  0.9)(0.68
0.4)  0.266. The fraction of solute removed from the cake, F, is given exactly by equation (4.36) or approximately by summing the values in Column (5) up to a given wash ratio. The fraction of solute remaining in the cake is given by equation (4.37).

174 Solid/Liquid Separation: Equipment Selection and Process Design Plots of the washing curve in the form of * vs. W, F vs. W and R vs. W are shown in Figure 4.7.

1.0

(a) (b)

Dimensionless parameter

0.8

0.6

0.4

0.2

0.0 0.0

(c)

0 .5

1.0

1 .5 Wash ratio

2.0

2 .5

3.0

Figure 4.7 Washing curve data derived for Example 4.3. (a) instantaneous solute concentration in the wash liquid discharged from the cake, φ /φ0; (b) fraction of solute removed from the cake, F; (c) fraction solute remaining in the cake, R.

The reslurrying/filtering process performed at the end of washing is used to check for a mass balance. Using the method outlined for the calculation of values in Column (5), for each 137 cm3 addition of water values of 冕ww2(/0)dW are 0.0085, 0.0055, 0.003 and 0.001 which gives a total frac1 tional recovery of 1.003. A solute mass balance in the range 1–1.05 is generally considered acceptable for a laboratory experiment.

4.4 Jar sedimentation In the current context the results of a sedimentation test are used in equipment selection to eliminate unsuitable equipment from a sometimes lengthy list. The objective is to determine the initial (constant) rate of settling, clarity of the supernatant liquid and the final proportion of sludge.

4 · Data acquisition, analysis and scale-up 175 4.4.1 Test procedure With reference to Figure 4.8, it is a normal practice to use a conventional measuring cylinder and a typical sedimentation test follows a sequence dependent on the nature of the slurry.

Figure 4.8 Photograph and schematic of the apparatus used for determining basic settling characteristics.

1. Determine the solids concentration in the slurry sample before commencing the jar sedimentation test(s). 2. For a preliminary test, to determine if flocculants or other pretreatment chemicals need to be used, fill completely a one litre graduated measuring cylinder with a sample of slurry. Shake to ensure uniform dispersion of the particles and then place the cylinder on a rigid, level surface and allow the slurry to settle. At suitable intervals record the suspension volume and/or suspension–supernatant interface height from the graduations on the cylinder and note the corresponding elapsed time. Allow settling to continue until at least 10 sets of time vs. height readings have been taken and/or settling is finished. If the supernatant liquid has poor clarity or the settling rate is excessively low (e.g. 0.1 cm s
1), consideration should be given to modifying the feed slurry by pretreatment as indicated in Step 3 below and repeating the sedimentation test. If the settling test appears to be satisfactory with a reasonable settling rate and good supernatant clarity, then proceed to Step 4. 3. Add flocculants or pretreatment chemicals as necessary (more information on the choice of pretreatment chemicals can be found in

176 Solid/Liquid Separation: Equipment Selection and Process Design Chapter 3). A preferred technique is to place the required amount of diluted flocculant into an empty beaker, pour the measured amount of feed slurry rapidly into the flocculant, and then promptly pour back and forth repeatedly. If the concentration does not need further adjustment, immediately introduce the sample into the graduated measuring cylinder. During settling record the time vs. suspension volume and/or suspension–supernatant interface height as indicated in Step 2. 4. Note the volume of sludge at the bottom of the measuring cylinder after the slurry has finished settling, and check the acceptability of the supernatant liquid. 5. Repeat Steps 1– 4 as necessary to ensure data accuracy and reproducibility. 4.4.2 Data analysis procedure The typical result of a sedimentation test is a Characteristic Plot as shown in Figure 4.9. From this settling curve the required initial constant rate of settling (ui), clarity of the supernatant liquid and final proportion of sludge (Sp) are determined. The linear, or sometimes near linear portion marked by the

35 (a)

Interface height, Hi (cm)

30

regression line

25 20

(b) 15 H∞

10 5 0 0

50

100

150

200

250

300

Time, t (s)

Figure 4.9 Plot of suspension–supernatant interface height vs. time data for a typical laboratory scale jar sedimentation experiment (also a plot of the data for Example 4.4).

4 · Data acquisition, analysis and scale-up 177 regression line is termed as the ‘free settling zone’ and the gradient of the line is equivalent to ui where ui 


Hi ,( a )
Hi ,( b ) (4.40)

t( a )
t( b )

The proportion of sludge, Sp, is defined as the ratio of the final sludge volume to the initial volume of suspension. For a measuring cylinder of constant cross-sectional area (A), Sp is equivalent to the ratio of final sludge height (H) to initial suspension height (H0) such that S p  100

AH  H ⬅ 100  AH 0 H0

(4.41)

When a test is not continued until equilibrium the final sludge height can be estimated by extrapolating the settling curve on the Hi vs. t plot. 4.4.3 Example 4.4 The time vs. suspension volume data shown in Table 4.4 were obtained using a one litre measuring cylinder with an inside diameter of 6.5 cm. Noting that Table 4.4 Time vs. suspension volume data for Example 4.4. Settling time (s) 0 10 20 30 40 50 65 90 130 180 220 250

Suspension volume (cm3)

Interface height (cm)

1000 910 830 750 660 580 500 410 370 340 332 332

30.1 27.4 25.0 22.6 20.0 17.5 15.1 12.4 11.2 10.3 10.0 10.0

178 Solid/Liquid Separation: Equipment Selection and Process Design the supernatant clarity was good, determine the initial settling rate and proportion of sludge. Solution The recorded suspension volumes are converted to give the equivalent suspension–supernatant interface heights (Hi) according to

Hi  (suspension volume)

4 6.52 

which allows Figure 4.9 to be plotted. From a linear regression analysis over the region shown, Hi 
0.252t  30.1 cm s
1 and thus u i 
0.252 cm s
1. As the test was allowed to continue until equilibrium, H  10 cm and using equation (4.41) gives Sp  100 × 10兾30.1  33.2% v兾v.

4.5 Expression (cake formation/consolidation) The principal objective of an expression test is to determine the compression deliquoring characteristics of a cake. However, the nature of the test allows both filtration and compression characteristics to be determined when the starting mixture is a suspension (i.e. where the solids are not networked or they are interacting to a significant extent). Cake formation rate, specific resistance and solids volume fraction data can be determined for the filtration phase while analysis of a subsequent consolidation phase allows the calculation of parameters such as consolidation coefficient, consolidation index and ultimate solids concentration in the cake. Repeated use of the expression test over a range of constant pressures allows the evaluation of scale-up coefficients for filter sizing and simulation as described in Section 4.7. 4.5.1 General test procedure The effects of compression on a filter cake or suspension can be measured using a piston press as illustrated in Figure 4.10. The press comprises an upright cylinder mounted on a base plate, where both the cylinder and plate are usually made from stainless steel. The base of the plate is recessed to accommodate a loosely fitting sinter drainage plate which is used to support the planar filter medium. The drainage plate must be sufficiently permeable to allow unrestricted passage of the filtrate. Liquid is forced from the cylinder by a piston which is actuated either hydraulically or pneumatically. In more sophisticated units a force transducer can be mounted in the piston shaft to measure

4 · Data acquisition, analysis and scale-up 179

Figure 4.10 Piston press apparatus for determining consolidation (and filtration) data. To aid correct force transmission to the solid/liquid mixture it is recommended to use a cylinder with a height/diameter aspect ratio of 4:1 or greater.

the force applied to the suspension. A good liquid seal between the piston and cylinder is provided by low friction seals which help to transmit the applied load to the mixture undergoing expression. At the start of a test the cylinder is completely filled by the solid/liquid mixture which can exhibit the characteristics of a slurry, where both filtration and consolidation processes take place, or by a networked semi-solid where consolidation commences from the start of the test. In general the mixture will be concentrated and/or composed of fine particulates that do not settle appreciably under gravity. The piston is introduced to the open end of the cylinder and the constant applied force causes pressure to be generated within the cylinder. Liquid is expelled through the filter medium and collected in either a measuring cylinder or, in more sophisticated units, a vessel mounted on a load cell or electronic balance. The volume or mass of liquid is measured at various time intervals from the start of expression. The thickness of suspension (or cake towards the end of the test) in the cylinder can be calculated from a knowledge of the volume of liquid removed from the cylinder, or from measurements of the piston displacement from the beginning of the test should an appropriate transducer be fitted.

180 Solid/Liquid Separation: Equipment Selection and Process Design 4.5.2 Data manipulation During the filtration process cake progressively grows upwards from the filter medium surface, liquid is expelled from the press and the piston moves downwards in the direction of the medium. When the particles become sufficiently networked (which can be from the very start of the test), or enough cake has formed for the piston to touch the top of the cake, further deliquoring is achieved by consolidation where liquid is expelled as the porosity of the cake decreases. Consolidation continues until an equilibrium state is reached such that the particle structure/cake is sufficiently strong to withstand any tendency to compress under the applied piston loading. Determination of the transition between filtration and consolidation is critical to the successful analysis of data and this is associated with a unique thickness of the solid/liquid mixture, Ltr, which can be calculated from  ( m )
1 1  Ltr =  av tr   s0 l s  

(4.42)

where (mav)tr is the ratio of the mass of wet to dry cake in the press at the end of the filtration process and 0 is the volume of solids in the press per unit area (which is constant during a test provided there is no bleeding of solids through the medium). The value of (mav)tr cannot be easily measured during a normal expression test so it is estimated from the known characteristics of constant pressure filtration. The transition from filtration to consolidation mechanisms occurs when the solid/liquid mixture has a thickness Ltr and the preferred method to estimate its position in a recorded dataset uses a plot of

L/
兹苶t vs. t. Here, constant pressure filtration data should be represented by a straight line parallel to the t-axis (Shirato et al, 1970, 1971, 1986, 1987). It is often preferable to use logarithmic scales so that data scatter does not obscure the transition point. When the concentration of solids in the mixture exceeds a limiting value, the mixture passes into a semi-solid state. From thereon it is consolidated and the value of

L/
兹苶t decreases; at the end of consolidation a value of zero is reached but this true equilibrium state can take a long time to achieve. The transition point for the mixture under test, Ltr, is determined from the graph as the point where

L/
兹苶t starts to decrease rapidly which corresponds to tttr. The typical form of a

L/
兹苶t vs. t plot where both filtration and consolidation processes occur is shown in Figure 4.11. If the solid/liquid mixture exhibits the characteristics of a networked structure from the start of a test, such as may be observed with a flocculated or high surface

4 · Data acquisition, analysis and scale-up 181

∆L /∆t0.5 (m s-0.5)

10-2

10-3 transition point

10-4

10-5 101

102

103

104

105

Time (s)

Figure 4.11 Typical form of the
L /
t 0.5 vs. time plot used to identify the transition from filtration to consolidation phases in an expression experiment (also a plot of data from Example 4.5).

charge/concentration system, then no filtration phase exists and consolidation takes place from t0 s. Alternative methods for identifying the transition from filtration to consolidation require the use of t兾V vs. V, dt兾dV vs. V or V vs. 兹苶t plots where V is the cumulative volume of filtrate. More details are provided in Section 4.5.6. The volume of the solid/liquid mixture in the press at the start of the test (V0) and 0 are given by V0  AL0

(4.43)

 0  (Vs )0 L0

(4.44)

where (Vs)0 is the solids volume fraction of the mixture in the press at t  0 and L0 is the initial mixture thickness which is normally equal to the height of the cylinder in the press. If the time vs. cumulative volume of filtrate data sequence is recorded, then the thickness of the mixture at any time can be determined from L

V0
V A

(4.45)

182 Solid/Liquid Separation: Equipment Selection and Process Design where A is the area of the filter medium. Alternatively, in a more sophisticated apparatus, the time vs. piston displacement (x) data sequence can be measured and in this case L  L0
x

(4.46)

V  V0
LA

(4.47)

Whichever data sequence is recorded, the average solids volume fraction, (Vs)t, ratio of mass of mixture to mass of dry solids, (mav)t, average porosity, (av)t and average moisture content, (Mav)t in the press at any time are given by (Vs )t  (Vs )0

L0 L

(4.48)

(mav )t  1

l 关1
(Vs )t 兴  s (Vs )t

(4.49)

( av )t  1
(Vs )t

( M av )t  100

(mav )t
1 (mav )t

(4.50)

(4.51)

The time variant sequences of (t
ti)兾(V
Vi), (VVi) and

L/
兹苶t can also be evaluated which allow the transition point ttr to be graphically identified (e.g. visually as in Figure 4.11 or more rigorously using the methods described in Section 4.5.6) and the filtration and consolidation phases to be analysed in detail as shown in Sections 4.5.3 and 4.5.4. It is noted that when t ttr the piston touches the top of the cake and values of (mav)t , (av)t and (Mav)t equate to conditions in the cake and (Cav)t, the solids volume fraction in the cake, equals (Vs)t. 4.5.3 Filtration phase analysis With ttr known, the extent of the filtration phase is defined and the corresponding value of Vtr is interpolated from the t vs. V dataset. Ltr is calculated from equation (4.45) which allows (Vs)ttr and (mav)ttr to be calculated from equations (4.48) and (4.49) respectively. Equations (4.2)–(4.5) can now be used in

4 · Data acquisition, analysis and scale-up 183 the manner described in Section 4.1 to determine the parameters that characterise the filtration phase including cake and filter medium resistances, cake solids volume fraction and average cake growth rate. 4.5.4 Consolidation phase analysis The consolidation phase is defined for t ttr and analysed through an empirical relationship relating the consolidation ratio Ltr
L Ltr
L

Uc =

(4.52)

to a dimensionless consolidation time as defined by Tc 

i 2 Ce t c  2o

(4.53)

where i is the number of drainage surfaces in the piston press (i  1 unless a special double sided press is used) and tc is the consolidation time; tc  0 and Uc  0 when t  ttr (Shirato et al, 1974, 1986). Ce is a modified consolidation coefficient that partially characterises the consolidation process. The relationship between Uc and Tc is normally stated as

Uc 

4Tc  1 2

  4T  2   c 1          

(4.54)

where is the consolidation behaviour index that is also characteristic of the test mixture. is determined either graphically (as shown in Example 4.5 below) or by a curvefit procedure as discussed in Section 4.5.6. tc or 兹T 苶c苶 is a straight According to equation (4.54), Uc plotted against either 兹苶 line during the early stages of consolidation. For small values of Tc, equation (4.54) reduces to Uc ⬇

4Tc 4i 2 C e   tc  (gradient) tc   20

(4.55)

184 Solid/Liquid Separation: Equipment Selection and Process Design such that Ce is obtained from the gradient of the line. Cake properties at the end of consolidation can be determined using equations (4.48), (4.50) and (4.51). 4.5.5 Example 4.5 The time vs. filtrate volume data collected from the expression of an aqueous suspension of china clay are shown in Columns (1) and (2) of Table 4.5. The expression was carried out at an applied pressure of 20 bar in a piston press with a height of 193 mm (⬅ 0.193 m) and an internal diameter of 43 mm (⬅ 0.043 m). The volume fraction of solids in the initial suspension was 0.1 Table 4.5 Measured time vs. volume of filtrate data and calculated data for Example 4.5.

(3)



L 冫
兹t苶 (m s
0.5) (4)

t/V (s m
3) (5)

0.1930 0.1820 0.1781 0.1705 0.1650 0.1597 0.1555 0.1445 0.1322 0.1169 0.1039 0.0925 0.0825 0.0725 0.0642 0.0604 0.0567 0.0532 0.0525 0.0518 0.0515 0.0512 0.0512

8.21 × 10
4 9.88 × 10
4 1.07 × 10
3 1.00 × 10
3 1.13 × 10
3 1.03 × 10
3 1.08 × 10
3 1.11 × 10
3 1.13 × 10
3 1.15 × 10
3 1.14 × 10
3 1.10 × 10
3 1.20 × 10
3 1.07 × 10
3 — 1.55 × 10
3 7.30 × 10
4 3.00 × 10
4 3.05 × 10
4 1.55 × 10
4 7.95 × 10
5 0

1.13 × 107 1.39 × 107 1.84 × 107 2.21 × 107 2.48 × 107 2.76 × 107 3.40 × 107 4.08 × 107 4.89 × 107 5.56 × 107 6.16 × 107 6.73 × 107 7.20 × 107 7.69 × 107

t (s)

V (cm3)

L (m)

(1)

(2)

0 180 300 600 900 1200 1500 2400 3600 5400 7200 9000 10800 12600 14400 15000 15600 16800 17400 18000 18600 19800 21000

0 16 21.6 32.7 40.7 48.3 54.4 70.5 88.3 110.5 129.4 146.0 160.5 175.0 187.0 — 198.0 203.0 204.0 205.0 205.5 206.0 206.0

兹苶 tc (s0.5)

Uc

兹苶 Tc

(6)

(7)

(8)

0 24.5 42.4 49.0 54.8 60.0 69.3 77.5

0 0.407 0.778 0.852 0.926 0.963 1.000 1.000

0 0.389 0.673 0.778 0.869 0.952 1.101 1.231

The value of t tr  15000 s is estimated from Figure 4.13 and L tr  0.0604 m is then determined by interpolation.

4 · Data acquisition, analysis and scale-up 185 (i.e. 10% v/v), the density of the solids was 2600 kg m
3 and the liquid density and viscosity were 998 kg m
3 and 0.001 Pa s respectively. Determine the point in the test where the transition from filtration to consolidation occurs and the parameters that characterise the two phases in the expression process. Solution The thickness of the solid/liquid mixture in the press at any instant is determined from the sequence of filtrate volume shown in Column (2) of Table 4.5. Noting that A (0.043兾2)2 1.45 × 10
3 m2, from equation (4.43) the initial volume of suspension in the press is V0  1.45 × 10
3 × 0.193  2.8 × 10
4 m 3 and the thickness is calculated according to equation (4.45) L

2.8 × 10
4
V m 1.45 × 10
3

as shown in Column (3). The values in Column (4) are calculated using the data in Columns (1) and (3) where, for instance,

L/
兹t苶 that corresponds to t  300 s is calculated by
(0.1781
0.1820)兾(兹苶3苶0苶0
兹苶1苶8苶0)  9.88 × 10
4 m s
0.5. The complete t vs.

L/
兹苶t dataset is plotted in Figure 4.11 where the transition from filtration to consolidation is estimated to occur at ttr ⬇ 15000 s and by interpolation of the data in Column (3), Ltr  0.0604 m. (i) Filtration phase To determine the characterising parameters for the filtration phase it is first necessary to determine the ratio of the mass wet/dry cake at t  ttr. From equations (4.48) and (4.49) (Vs )tttr  0.1

0.193  0.319 vv 0.0604

(mav )tttr  1

998 (1
0.319)  1.82 2600 × 0.319

(4.56)

Converting the volume fraction of solids in the initial suspension to an equivalent mass fraction using equation (C.9), see Appendix C, gives s

 sVs 2600 × 0.1   0.224 ww Vs ( s
l )  l 0.1 (2600
998)  998

186 Solid/Liquid Separation: Equipment Selection and Process Design which allows the effective feed concentration to be calculated from equation (4.2) where c

0.224 × 998 s   378.6 kg m
3 1
mav s 1
1.82 × 0.224

(4.57)

Assuming that ti  0 s and Vi  0 m3, the data in Columns (1) and (2) together with the appropriate conversion factor give the values of t兾V shown in Column (5). With reference to Figure 4.12, the Characteristic Plot of t兾V vs. V yields a straight regression line t兾V  3.8 × 1011V  6.3 × 106 s m
3 and from rearranged versions of equations (4.4) and (4.5) the specific cake resistance (av) and filter medium resistance (R) are calculated  av  

gradient × 2 A2
p c 3.8 × 1011 × 2 (1.45 × 10
3 )2 × 20 × 10 5 378.6 × 0.001

 8.5 × 10 R 

(4.58)


1

12

m kg

intercept × A
p  6.3 × 106 × 1.45 × 10
3 × 20 × 10 5 0.001 13

(4.59)


1

 1.8 × 10 m

Other parameters that characterise the filtration phase include the average cake porosity (av), solids volume fraction (Cav) and moisture content (Mav) at the end of filtration, mass of dry cake per unit filter area (w) and average cake formation rate (Lgr) as given respectively by equations (4.50), (4.13), (4.51), (4.19) and (4.20)  av  1
Cav  1
0.319  0.681 M av  100

w

1.82
1  45% 1.82

V0 (VS )0  s 2.8 × 10
4 × 0.1 × 2600  50.2 kg m
2 =
3 A 1.45 × 10

(4.60)

(4.61)

(4.62)

4 · Data acquisition, analysis and scale-up 187

Time/volume (s m-3)

8e+7

6e+7 regression line 4e+7

2e+7

0 0.00000

0.00005

0.00010

0.00015

Cumulative volume of filtrate

0.00020

(m3)

Figure 4.12 Plot of time/volume vs. volume for data representing the filtration phase in Example 4.5.

Lgr 

0.0604  4 × 10
6 m s
1 15 000

(4.63)

(ii) Consolidation phase The consolidation phase exists for t 15000 s such that values of the consolidation time are given by tc  t
15000 s (兹苶 tc is shown in Column (6) of Table 4.5)). Corresponding values of the consolidation ratio are shown in Column (7) as determined by equation (4.52) Uc 

0.0604
L 0.0604
0.0512

and the plot of Uc vs. 兹t苶c that characterises the consolidation phase is shown in Figure 4.13 together with the regression line Uc  0.0179兹t苶c. Noting that i  1 and from equation (4.44) 0  0.1 × 0.193  0.0193 m, equation (4.55) gives Ce 

0.01792 ×  × 0.01932  9.4 × 10
8 m 2 s
1 4 × 12

(4.64)

The consolidation index, v, can be obtained graphically which requires values of the dimensionless consolidation time (Tc) to be determined according to equation (4.53) where

188 Solid/Liquid Separation: Equipment Selection and Process Design 1.0

Consolidation ratio, Uc

0.8 regression line 0.6

0.4

0.2

0.0 0

20

40

(Consolidation

time)0.5,

60 0.5

tc

80

(s0.5)

Figure 4.13 Plot of Uc vs. 兹t苶c for data representing the consolidation phase in Example 4.5.

12 × 9.4 × 10
8 × tc Tc  0.01932 Figure 4.14 shows the experimental data from Columns (6) and (7) plotted together with the family of curves obtained from the theoretical equation (4.54) over a range of Tc and v values. A comparison shows that for Example 4.5, v ⬇ 5. Other cake properties that characterise the consolidation are determined using equations (4.48) – (4.51) and (4.13) such that

(Vs )tte  (Cav )tte  0.1

0.193  0.377 vv 0.0512

( av )tte  1
(Cav )tte  1
0.377  0.623 (mav )tte  1

(4.65)

(4.66)

998(1
0.377)  1.63 2600 × 0.377

( M av )tte  100

1.63
1  38.7% 1.63

(4.67)

4 · Data acquisition, analysis and scale-up 189 1.0

2.0 5.0

0.9

1.5

1.0

0.75

0.625 0.5

Consolidation ratio, Uc

0.8 0.7

0.375

0.6 0.5

ν = 0.25

0.4 0.3 0.2 0.1

data from Example 5.5

0.0 0

1

2

(Dimensionless consolidation

3 time)0.5,

4 0.5

Tc

Figure 4.14 A plot of equation (4.54) showing the variation of the consolidation ratio with (dimensionless consolidation time)0.5 and the behaviour index . Experimental data from Example 4.5 are superimposed onto this plot to estimate the value of  (which may alternatively be calculated using the curve fitting procedure described in Section 4.5.6).

4.5.6 Estimates of the transition point and consolidation index The choice of transition point between filtration and consolidation is crucial to the accurate determination of parameters that characterise expression as well as any subsequent determinations of scale-up parameters (Anderson et al, 2004; Christensen et al, 2006; Salmela and Oja, 2005; Wakeman et al, 1991). As illustrated in Sections 4.5.2– 4.5.5, a plot of

L/
兹t苶 vs. t can be successfully used to estimate the transition, however, alternative and more refined approaches are also available (Tarleton and Wakeman, 1999). In a typical expression test t vs. V data are recorded throughout and Figure 4.15 shows four ways in which the same dataset can be represented. In Figure 4.15(a) and (b) t兾V vs. V and dt/dV (or strictly
t/
V) vs. V plots well known in constant pressure filtration are presented. In accordance with equations (4.3) and (4.1), the initial linear portion on each plot represents the extent of the filtration phase. The ill-defined transition towards the end of the filtration in Figure 4.15(a) is typical of t/V vs. V data while the sharper, but more scattered data in the region of the transition in Figure 4.15(b) is frequently observed with dt/dV vs. V data. The representation of V vs. 兹苶t shown

(a)

(b) Reciprocal filtrate flow rate

Time/cumulative volume of filtrate

190 Solid/Liquid Separation: Equipment Selection and Process Design

Cumulative volume of filtrate

Cumulative volume of filtrate

(d)

−∆L/∆t0.5

Cumulative volume of filtrate

(c)

(Filtration time)0.5

Filtration time

Figure 4.15 Alternative representations of data from an expression test comprising filtration and consolidation phases; the correct transition between phases is represented by the dashed vertical line on each plot.

in Figure 4.15(c) also has a poorly defined transition from filtration to consolidation which renders the log-log plot of

L/
兹苶t vs. t in Figure 4.15(d) the preferred option. As tested with a wide range of experimental data (e.g. Wakeman et al, 1991), this generally represents a good balance between the often unavoidable problems of experimental data scatter and a well-defined transition. However, a more accurate determination of the transition can be obtained by using the

L/
兹苶t vs. t plot to give an initial estimate and then employing separate plots of t/V vs. V and Uc vs. tc to refine the estimate. Using the experimental data plotted in Figure 4.15(d) as an example, datapoints to the left of the dashed vertical line comprise the filtration phase while data to the right constitute the consolidation phase. These two data sequences can respectively be recast in the form t/V vs. V and Uc vs. tc as illustrated in Section 4.5.5 and Figure 4.16(a) and (b) show the results. A correct

4 · Data acquisition, analysis and scale-up 191 (b)

line gadient = G2

line gradient = G1

Consolidation ratio

Time/volume of filtrate (s m-3)

(a)

line gradient = G4 line gradient = G3

Cumulative volume of filtrate (m3)

(Consolidation time)0.5

Figure 4.16 Graphical representations used to check the correct transition from filtration to consolidation in an expression test.

choice of transition will yield data linearity for the majority of the filtration phase and a linear region towards the start of the consolidation phase. If the transition in Figure 4.15(d) is chosen too far to the left, the t/V vs. V data will still be linear however the Uc vs. tc data will exhibit a characteristic ‘S’ shape. A choice of transition too far to the right may still yield a linear region towards the start of consolidation, but the data for the filtration phase will show an upward deviation towards the end (i.e. similar in form to that shown in Figure 4.15(a)). While a visual check on the correct choice of transition can be made, a more formal method can also be established. Noting the indicated gradients (G1 to G4) on Figure 4.16, by performing repeated calculations where a fresh estimate of the transition is made each time, it is possible to form a sequence of values for the sum of the ratios (Gs ) such that  G G G  G  GS  Max ∑  Max  1 and 2   Max  3 and 4   G1  G3    G2  G4 

(4.68)

Provided that the scatter in the original t vs. V data is not excessive, the correct transition is chosen when Gs is maximised. In Example 4.5 the value of the consolidation index (v) was calculated by T苶c as calculated from equation visually comparing theoretical values of Uc vs. 兹苶 (4.54) with the experimental data. A more formal, and alternative, two-step approach involves minimising the differences between the experimental and theoretical modified consolidation curves as shown in Figure 4.17. In Step 1, for a range of v values between 0.5 and 5 (using intervals of 0.5), equation (4.54) is evaluated and the sum of the squares of the errors in the fit between

192 Solid/Liquid Separation: Equipment Selection and Process Design 1.2 experimental data theory Consolidation ratio, Uc (-)

1.0 0.8 0.6 0.4 sum of the differences in consolidation ratio is minimised

0.2 0.0 0.0

0.3

0.6

0.9

(Dimensionless consolidation

time)0.5,

1.2 Tc

0.5

1.5

(-)

Figure 4.17 Method for calculation of the consolidation index () by minimisation of the difference (error) between experimental data and theory as defined by equation (4.54).

each theoretical curve and the experimental data is recorded; the minimum error and associated v value are noted during the calculation. In Step 2, the procedure is repeated using a smaller (0.05) interval for v and involves taking values in the range 0.5 of the v which gave the best fit in Step 1. With the procedure complete the value of v giving the lowest error of fit between experiment and theory is known to an accuracy of 0.05. The methodologies presented in this section, as well as many of the procedures defined in Sections 4.1–4.5, are used for data analysis in the Filter Design Software described in Chapter 5 (see also Filter Design Software (2005)).

4.6 State-of-the-art apparatus When a relatively skilled operator performs experiments carefully, the methods described in Sections 4.1– 4.5 can give sufficiently reliable results for filter design work. In some cases it is possible to obtain data for sequential operations such as those performed in filter cycle operations, however, performing these tasks manually is difficult and can introduce significant errors unless care is taken. It is probably fair to say that a significant proportion of previous filtration research and data acquisition by

4 · Data acquisition, analysis and scale-up 193 commercial organisations has been blighted by experimental difficulties, the skill (or otherwise) with which experiments are performed, the lack of ‘standard’ test methods and to some extent a lack of consistent analysis procedures. Such problems have led to the widespread use of heuristics or ‘rules-of-thumb’ in filter design. The advent and now widespread availability of suitable transducers, computers and control software allow more accurate and reliable experimental filter cycle data to be obtained together with less reliance on heuristics. Experimental data can be analysed more rigorously and the results used in formalised filter cycle design procedures. Figure 4.18 shows state-of-the-art, laboratory scale experimental apparatus capable of automated data acquisition during sequential filtration, washing and deliquoring phases of a filter cycle; the level of hardware and software

Figure 4.18 Schematic of a state-of-the-art apparatus for investigating the filtration, displacement washing and gas deliquoring phases of the filter cycle. (1) suspension feed vessel; (2) wash liquor feed vessel; (3) filter cell; (4) rotary index table; (5) electronic balance; (6) pressure regulator. The inset photograph shows fully automated apparatus for obtaining filtration and deliquoring data including facility for transient measurements of cake growth and state.

194 Solid/Liquid Separation: Equipment Selection and Process Design sophistication can be varied according to requirements (Tarleton, 1996, 1998a,c; Tarleton and Hadley, 2003; Tarleton and Hancock, 1996, 1997; Tarleton and Willmer, 1997; Tarleton et al, 2001). The basic hardware comprises a stainless steel (s/s) dead-end Nutsche filter (area 80–500 cm2) and two s/s storage vessels connected by s/s piping and computer controlled electro-pneumatic valving; the storage vessels incorporate temperature sensors and stirrers. The storage vessels contain the feed suspension and wash water respectively. A heater/cooler system regulates the temperature of the filter cell and storage vessels by continuously passing a fluid through their surrounding jackets to facilitate operation over the range 0 –70ºC. Various transducers attached to the apparatus allow pressures and other measured parameters to be recorded and/or controlled by the interfaced computer and dedicated software. The pressures required to progress filtrations are provided by a compressor and an electronic pressure regulator over the range 10–1000 kPa. The regulator is adjusted by the computer and the filtrate flow rate is semi-continuously transmitted to the computer via successive timed readings of mass from the electronic balance. By monitoring the flow rate in such a manner, use of a suitable software control algorithm allows either constant pressure, stepped pressure, constant rate or variable pressure/variable rate filtration to be performed without changing the suspension properties through inappropriate pumping operations. The rate and magnitude of the pressure adjustments is dependent on the nature of the feed, the compressibility of the filter cake and the desired process conditions. The electronic pressure regulator is also used to provide the driving pressures for the deliquoring and washing phases of a given filter cycle. For deliquoring, compressed gas is automatically introduced to the filter cell at the desired pressure and its flow rate is monitored using an electronic rotameter interfaced to the computer. For displacement washing, the wash liquor is introduced to the filter cell and liquor samples are diverted to a rotary indexing table at the desired intervals. In order to monitor (in real time) the rate of cake growth, filter cake structure (during filtration), solute concentration profiles in the cake (during washing) and/or cake saturation profiles (during deliquoring) a series of small electrodes can be fitted internally within the filter cell. The electrodes which may protrude a short distance into the cell are arranged in single vertical planes or, if maximum data are required, in sequences of horizontal rings. Signals to electrode pairs are switched by the attached computer via electronic circuitry to facilitate measurements. Alternatively, micro-pressure transducers can be used in place of electrodes to determine cake structure

4 · Data acquisition, analysis and scale-up 195 and these are capable of delivering measurements of liquid pressure within 0.3 mm of the filter medium (Tarleton and Hadley, 2003). The use of computer control allows sequential filter cycle data to be acquired in a repeatable and reliable manner with a minimum of operator interference. By defining the desired cycle phases through a software algorithm, a cake formation phase can be directly followed by the chosen combination of washing and deliquoring. The real time measurement of experimental parameters also allows continuous display of results and the use of on-line analysis techniques as an experiment proceeds. Figure 4.19 shows a schematic representation of state-of-the-art expression apparatus. The more conventional piston press apparatus described in Section 4.5.1 is augmented with the addition of a computer driven pressure regulator which allows the pressure applied to the piston to be carefully controlled and varied according to a preset pattern (e.g. ramp, sinusoidal etc.). The interfaced rotary or linear encoder, force transducer and electronic balance allow semicontinuous measurements of piston displacement, transmitted pressure and

Figure 4.19 Schematic of a state-of-the-art apparatus for investigating the filtration and consolidation phases of a filter cycle.

196 Solid/Liquid Separation: Equipment Selection and Process Design expressed liquid mass respectively. Where maximum information is required, the piston can be rotated via computer control and a suitable gearbox to impart shear as well as compressive forces to the filtering and/or consolidating solid/liquid mixture; such measurements can be useful for determining performance on belt press filters (see Section 1.4.2.6). Although the state-of-the-art equipment shown in Figures 4.18 and 4.19 represents the limits of what can be achieved with readily available technology, such apparatus are yet to be used widely for the acquisition of filter cycle data; it is noted that sophisticated filtration apparatus is becoming more widespread in universities (Andersen et al, 2004; de Kretser et al, 2001; Johansson and Theliander, 2003; Teoh et al, 2001) and within some companies (Townsend, 2002). Such test equipment does offer the potential and basis to develop standard methods for filter cycle testing, however, their greater cost and potential accuracy must be justified in relation to the more conventional techniques described in Sections 4.1.1 and 4.5.1.

4.7 Evaluation of scale-up coefficients While valuable information on settling, filtration and cake post-treatments such as washing and gas deliquoring can be obtained from individual tests, in order to subsequently simulate filter performance it is usually necessary to evaluate so-called ‘scale-up coefficients’ from sequences of tests. These empirical coefficients principally relate to cake formation (compressibility) and compression deliquoring (consolidation), as it is currently impossible to predict either from a knowledge of fundamental solid and liquid properties. Many filter cakes are compressible to some extent, and increases in filtering pressure lead to less porous and more resistant cakes. For these systems data are needed which relate the specific resistance, av, a measure of cake structure such as solids volume fraction, Cav, and where appropriate the modified consolidation coefficient, Ce, to variations in the applied pressure difference
p. It is conventional practice to assume that av, Cav and Ce are solely functions of
p. Scale-up coefficients can be determined from sequences of tests with a leaf filter or piston press (see, for instance, Anderson, 2004; Ives, 1975; Lu, 1998b; Purchas and Wakeman, 1986; Rushton et al, 1996; Tarleton, 1998a,b; Tarleton and Wakeman, 1994c; Tarleton and Willmer, 1997; Tiller, 1953, 1955, 1975; Wakeman et al, 1991). Each experiment is performed under otherwise identical conditions at a different constant pressure such that the pressure range of interest is covered; the latter is most often the pressure range over which a process scale filter will operate. Using the analysis and calculation procedures outlined in Sections 4.1.2–4.1.5 and 4.5.2–4.5.5, individual values of av and

4 · Data acquisition, analysis and scale-up 197 (Cav)f can be determined for each experiment and thus functionality with the filtration pressure,
pf , can be established according to  av   0 (1
n)
p nf

(Cav ) f  (C0 ) f
p f f

(4.69) (4.70)

where 0, n, (C0)f and f are the required scale-up coefficients; for practical purposes
pf is assumed to approximate the solids compressive pressure, ps. In order to calculate values for the coefficients it is necessary to first linearise equations (4.69) and (4.70). For instance, av vs.
pf values can be plotted on logarithmic axes and a regression line fitted; n, the compressibility index, is determined directly from the gradient and 0 (1
n) represents the y-axis intercept from which α0 can be calculated. If n  0 a filter cake is said to be incompressible and av maintains the same value irrespective of the applied pressure. In this case, (Cav)f  constant and f  0. Most of the cakes exhibit some compressibility and n usually falls in the range 0–1 where the latter represents a very compressible cake. Although 0, n, (C0)f and f may all be functions of, for instance, pH particle size and concentration, provided these parameters are maintained constant then the scale-up coefficients will be representative of cake formation for a particular solid/liquid mixture. They relate changes of av and Cav with
p, which is particularly important when determining the performance of filters that use pumps to bring about filtration. If tests are performed with a piston press and compression deliquoring takes place after filtration has been completed then it is possible to determine further scale-up coefficients that are characteristic of cake consolidation. In a similar manner to that described above the modified consolidation coefficient, Ce, and the cake solids volume fraction at the end of consolidation, (Cav)c or (Cav), can be related to the consolidation pressure,
pc, according to Ce  Ce 0
pc

(4.71)

(Cav )c  (Cav )  (C0 )c
pc c

(4.72)

where Ce0, , (C0)c and c are the scale-up coefficients. Their knowledge allows the prediction of, for instance, compression deliquoring in process scale, variable volume filters and presses. It is noted that the scale-up parameter v, the consolidation index, is not normally a function of
pc and for the purposes of simulation and scale-up an average representative value is usually taken.

198 Solid/Liquid Separation: Equipment Selection and Process Design In equations (4.70) and (4.72) the average solids concentration in the cake expressed in terms of a volume fraction has been used to represent the cake structure. Several alternative expressions for cake structure are found in the literature, the two most common involve the cake porosity (av) and the voids ratio (e)  av  1
Cav   0
p
 e

1
Cav  e0
blog
p Cav

(4.73)

(4.74)

where 0, , e0 and b are scale-up coefficients. Although Cav is used throughout this book, in practice it does not matter which representation is used as conversions between the different variants are readily achieved. Further details of conversions are shown in Appendix C. The use of scale-up coefficients in filter simulations is demonstrated in Chapters 6 and 7 while Appendix E illustrates their use in predicting filter performance. 4.7.1 Example 4.6 A sequence of constant pressure piston press experiments have been performed over the pressure range
p  0.33 ; 20.56 MPa using samples of a mineral suspension. Each experiment comprised a filtration phase followed by a consolidation phase and the results of individual analyses are shown in Table 4.6. Determine the scale-up coefficients that characterise the suspension. Solution The av , (Cav)f , Ce and (Cav)c data in Table 4.6 are each plotted in Figure 4.20 against pressure on logarithmic axes. Noting that in each experiment
p
pf 
pc and (for this particular calculation) scale-up coefficients are to be evaluated with
p expressed in kPa, regression analyses give  av  1.16 × 1011 p 0.612  2.99 × 1011 (1
0.612) p 0.612 m kg
1 f f (Cav ) f  0.18∆p 0.112 v v f Ce  2.08 × 10
9
pc0.472 vv (Cav )c  0.22
pc0.099 m 2 s
1

4 · Data acquisition, analysis and scale-up 199 Table 4.6 Values of specific cake resistance, cake solids volume fraction, modified consolidation coefficient and consolidation index for the sequence of piston press experiments used in Example 4.6.


p

av

(MPa)

(kPa)

(m kg )

0.33 1.65 2.36 6.41 10.79 14.50 20.56

330 1650 2360 6410 10790 14500 20560

1e-7

1e-8


1

4.0 1.1 1.3 2.6 3.3 4.1 5.0

1e+14

1e+13

1e+12

× 1012 × 1013 × 1013 × 1013 × 1013 × 1013 × 1013

(Cav )f (v/v)

Ce (m s
1) 2

0.345 0.405 0.419 0.468 0.502 0.525 0.545

3.0 7.1 9.5 1.2 1.4 2.1 2.3

× 10
8 × 10
8 × 10
8 × 10
7 × 10
7 × 10
7 × 10
7

(Cav )c (v/v)

v

0.395 0.450 0.483 0.528 0.553 0.570 0.595

4.0 4.0 4.0 4.0 4.0 4.0 4.0

1 Cake solids volume fraction (v/v)

1e-6 Specific cake resistance (m kg-1)

Modified consolidation coefficient (m2 s-1)


p

0.1 102

volume fraction (filtration) volume fraction (consolidation) specific resistance modified consolidation coefficient 103

104

105

Applied pressure (kPa)

Figure 4.20 Example of the plots used to evaluate scale-up coefficients for filtration and cake consolidation (compression deliquoring).

which suggests that the cake formed is moderately compressible. From Table 4.6, v  4.0.

4.8 Conclusions The methodologies presented in this chapter illustrate how characterising parameters for cake formation, compression and gas deliquoring, washing and

200 Solid/Liquid Separation: Equipment Selection and Process Design jar sedimentation can be determined from laboratory scale experiments. While the procedures and apparatus are not intended to constitute internationally recognised ‘standards’ they do represent current best practice and their worth has been repeatedly proven in industrial applications. The integration of experiment and empiricism with analysis and modelling helps to bridge the gaps in fundamental knowledge of how solid/liquid mixtures behave in filtration and subsequent posttreatment processes. The philosophy is explored in more depth in Chapters 5–7 where details and examples of equipment selection, scale-up and simulation are shown together with descriptions of the Filter Design Software (2005) which unites these concepts.

5

Selection, data analysis and simulation by computer software

The purpose of this chapter is twofold, firstly to introduce a methodology for equipment selection and secondly to describe the principal features of Filter Design Software® (FDS). With respect to the former, a technique for preliminary equipment selection is presented and it is shown how an equipment list can be ranked to help refine further selection considerations. Descriptions of FDS illustrate how equipment selection, data analysis and equipment simulation procedures can be combined into computer software, a basic flowsheet is shown in Figure 5.1. Worked examples are given. Although comprehensive descriptions of equipment selection are given in this chapter the specifics of data analysis and equipment simulation are presented elsewhere. Chapter 4 provides practical methodologies, theories and principles that underpin the analysis of filtration, jar sedimentation and expression tests. Chapters 6 and 7 respectively present extensive descriptions of batch and continuous filter simulations, however, an introduction to simulation is described here.

5.1 Equipment selection There are many solid/liquid separation techniques which have established general application within the process industries, and there are a few that are currently in their early stages of commercial exploitation. The dividing line between the two categories is open to dispute and difficult to identify in a field which is noted for innovation and development. The selection of appropriate equipment is thus a challenge to the design engineer and it is often difficult to identify the most appropriate separator without extensive previous knowledge of a similar separation problem. The purpose of the following is

202 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 5.1 Simplified flowsheet showing the role of computer software and simulations in the selection, sizing and optimisation of solid/liquid separation equipment.

to provide guidance on what form of small scale tests and results analysis are appropriate for the selection of equipment. It is shown how a knowledge of experimental data (derived in accordance with the descriptions of Chapter 4), selection charts and an expert system approach can be used to select and rank potentially suitable equipment. 5.1.1 Methods of equipment selection Although there are a number of different approaches to equipment selection, the overall procedure can be summarised by the flowchart shown in Figure 5.2. The basic principle is to use a limited amount of data about the

5 · Selection, data analysis and simulation by computer software 203

Figure 5.2 Flowchart for the selection of solid/liquid separation equipment; the region highlighted in the top half of the flowchart is performed by the equipment selection module of FDS (Filter Design Software, 2005). purpose of the process and some preliminary knowledge of the process feed stream separability together with a form of inference mechanism such as a selection chart or table. This combination, which is shown within the highlighted region in Figure 5.2, allows the identification of a range of equipment that could be expected to carry out the required duty. If necessary, the equipment list can be shortened by performing further small scale test work more

204 Solid/Liquid Separation: Equipment Selection and Process Design germane to the identified equipment. The final shortlist of equipment contains those items of equipment which are worth further evaluation through pilot testing and/or computer simulation. To perform the tasks shown in Figure 5.2, a number of different equipment selection schemes have been proposed, both in the public domain and within the inaccessible private domain of commercial organisations. Although some literature appeared as early as the 1920s (e.g. Sperry, 1924), the few publications before the 1960s primarily concerned details of filters, their qualitative performance and/or general guidance towards their use (see, e.g. Grace, 1951; Smith, 1955). Since 1964, however, the scope and number of selection procedures in the public domain has widened and followed a number of diverse, and sometimes confusing, routes. The information available may be categorised into five groups: a. General information: Hicks and Hillgard (1970), Maloney (1972), Alt (1975). b. Non-ranked table: Equipment is placed in a list relative to some characterising parameter or performance indicator such as feed concentration, particle size in the feed or standard cake formation time (SCFT). Tables have been produced by Flood et al (1966), Davies (1970), Hawkes (1970), Purchas (1970, 1972a, 1978, 1981), Emmett and Silverblatt (1974, 1975), Day (1974), Dahlstrom (1978a), Gaudfrin and Sabatier (1978), Trawinski (1980) and Purchas and Wakeman (1986). c. Ranked table: Equipment performance is rated by one or more numerical indices to produce ranked lists. Indices are typically valued between two extremes (e.g. 0 and 9) and related to operational parameters such as solid product dryness, crystal breakage, cost etc. Contributions have been made by Davies (1965), Purchas (1972b), Fitch (1974, 1977), Moos and Dugger (1979), Komline (1980) and Ernst et al (1987, 1991). d. Logic diagram: A decision tree guides a user through a series of yes/no choices towards a potentially suitable generic class of separation equipment. Logic diagrams have been produced by Davies (1965), Tiller (1974) and Pierson (1990). e. Expert system: Rule-based computer programs select and rank potentially suitable separation equipment. Expert system approaches have been independently developed by Ernst et al (1987, 1991), Korhonen et al (1989), Garg et al (1991) and Tarleton and Wakeman (1991), but only the latter became commercially available (as pC-SELECT). The charts, tables and general information contained in categories (a)–(d) can be used as guides towards an initial selection of solid/liquid separation

5 · Selection, data analysis and simulation by computer software 205 equipment. The better contributions consider a wider variety of possible eventualities and indicate clearly where decisions must be made. The charts and tables have generally been devised by experts to be fairly comprehensive and are of greatest value to the solid/liquid separation expert. They, unfortunately, also illustrate the near-impossibility of combining comprehensive descriptions with usability. Without ‘expert’ guidance it is extremely difficult for an end user to correlate information and decide which equipment is more suitable for any particular application. Also, having identified potentially suitable equipment, it can be equally as difficult to check such basic requirements as separator area and likely throughput rate. It is clear that there has previously been no accepted standard approach to solid/liquid equipment selection. With the now widespread availability of personal computers, however, the development of computer software is an ideal way to solve the problem of equipment selection. While rule-based expert systems appeared to provide the optimum solution at first, it became apparent to some researchers that inherent restrictions would prevent their widespread application. Thus, interactive personal computer software, partly based on an expert system approach, was developed to commercial standards (i.e. pC-SELECT, Tarleton and Wakeman, 1991; see also Wakeman and Tarleton, 1991a) and further adapted for incorporation within FDS (Filter Design Software, 2005). The philosophies, charts, tables and knowledge used are described in the remainder of this section. 5.1.2 Recommended selection procedure The general procedure originally developed by Purchas (see Purchas and Wakeman, 1986) provides a valuable, non-specialist, guide through the complex and confusing area of equipment selection. The basis of that procedure has been adopted and extended to include a wider range of separation methods as well as a method for the ranking of potentially suitable equipment. An initial list of equipment can be drawn up by following the steps shown in Figure 5.2. The first step is a preliminary specification of the separator duty to define three characterising letter codes. The second and third steps involve fairly rudimentary bench scale sedimentation and filtration tests. Their analysis yields overall settling and cake formation rates as well as another four characterising letter codes. Although it is not necessary to collect additional information, it is recommended that as much data as possible is obtained from the tests as this can aid later refinement of an equipment list (see Sections 5.3.2 and 5.4.1). The characterising letter codes defined for required duty, settling and filtration are compared with selection tables to give a list of equipment that is potentially suited to the required separation objective(s).

206 Solid/Liquid Separation: Equipment Selection and Process Design 5.1.2.1 Specification of duty The first step in defining a selection problem is to specify the general requirements of the process environment. An initial specification can be quite limited and is essentially confined to the scale, mode of operation and overall objective of the separation. These objectives and unavoidable restrictions can be specified before any experiments are undertaken. Other specifications, such as the need for filter sterility or the possibility of toxic or flammable hazards, can be considered at a later stage in the selection process. The principles involved in duty specification are shown in Figure 5.3. Each specification is identified by a characteristic letter, so that a group of letters define the nature of a problem. For example, a large scale batch operated system for the recovery of untreated solids would be coded as adg.

Figure 5.3 Coding the duty specification (adapted from Purchas and Wakeman, 1986). 5.1.2.2 Specification of sedimentation performance The objective of the sedimentation test is to determine the initial (constant) rate of settling, clarity of the supernatant liquid and the final proportion of

5 · Selection, data analysis and simulation by computer software 207 sludge. The sedimentation test and analysis procedures follow a sequence dependent on the nature of the test slurry and are described in detail in Section 4.4. In brief, a jar settling test using about one litre of slurry is performed. The height of the interface between the slurry/sediment and clear supernatant liquid is measured as a function of time and plotted graphically. The settling rate is determined from the initial linear region of the graph and the proportion of sludge, or volume of sediment, is expressed as a percentage of the original slurry volume. If no clear interface forms, consider using coagulants or flocculants, and repeat the test. The results are coded using a second set of characteristic letters as shown in Figure 5.4. For example, a slurry which settles at 3 cm s
1 to yield a clear liquid and a 15% proportion of sludge would be coded BEG.

Figure 5.4 Coding the slurry settling characteristics (adapted from Purchas and Wakeman, 1986).

5.1.2.3 Specification of filtration performance The objective of the filtration test is to determine the average rate at which cake is formed. It is more useful to know the rate of cake formation over a reasonable period so that the likelihood of marked reductions in form rate with time can be assessed. A Buchner funnel arrangement can be used for the filtration test(s) provided the funnel drainage characteristics are good.

208 Solid/Liquid Separation: Equipment Selection and Process Design A funnel bottom with a sinter plate rather than a low permeability ceramic perforated plate is preferred, and such an arrangement is shown schematically in Section 4.1 where the filtration test procedure and analysis procedures are also described in detail. Data from the test(s) require the average cake growth rate to be determined, for instance, by dividing the final cake height by the filtration time. Although a knowledge of the cake growth rate is sufficient for initial selection purposes, it is preferable to fully analyse a filtration test using all the available data. As detailed in Section 4.1.2, a (linear) graph of time/cumulative filtrate volume (t/V) vs. V allows the average specific cake resistance to be calculated. Other parameters such as cake porosity and mass of dry solids per unit filter area can be determined from measurements taken on the final cake. The results from the test procedure are coded as shown in Figure 5.5, using a third set of characteristic letters. For example, a slurry which forms a cake at the rate 0.5 cm min
1 is coded K. Combining this with the settling characteristics gives a total preliminary description of the separation characteristics of the slurry (e.g. BEG, K). If the proposed duty is simply to thicken a slurry then it is not necessary to carry out a filtration test. However, for a total separation of the solid from the liquid (as obtained in a filter, for example) both settling and filtration tests need to be performed.

Figure 5.5 Coding the slurry filtration characteristics (adapted from Purchas and Wakeman, 1986).

5 · Selection, data analysis and simulation by computer software 209 5.1.2.4 Tables of equipment and letter codings The duty specification, jar sedimentation and filtration tests enable the slurry settling and filtering characteristics to be broadly classified, and a selection problem to be specified through a series of letter codings. In order to select and rank equipment from this information it is necessary to provide charts and/or tables which relate equipment performance to the letter codings. Comparisons between the user defined specifications and the tables/charts enable the selection process. Section 5.1.1 detailed the charts and data tables which exist in the public domain. While they provide an insight into the application and operation of particular classes of equipment, they rarely address the problem of how a class of equipment is correctly chosen in the first instance. Generic classes of equipment have been described in Chapter 1 and previously identified by Davies (1965), Moos and Dugger (1979), Purchas (1981), Purchas and Wakeman (1986), Tarleton and Wakeman (1991) and Wakeman and Tarleton (1991a). In Table 5.1 these generic classes are reiterated and associated with the letter codings for duty specification, jar sedimentation and Table 5.1 Classification of equipment according to suitability for duty and slurry separation characteristics.

Type of equipment

Duty specification

Separation characteristics Settling

Gravity thickeners and clarifiers • Circular basin thickener

• Settling tank or lagoon thickener • Circular high capacity thickener • Deep cone thickener

• Lamella separator

a, b or c d or e g or h a, b or c d or (e) f or g a or b e f a or b e f a, b or c e f

Filtering

B or C E F or G A, B or C (D) or E F, G or H B or C E F or G B or C E F or G (A), B or C (D) or E F or G continued

210 Solid/Liquid Separation: Equipment Selection and Process Design Table 5.1 continued Type of equipment

Duty specification

Separation characteristics Settling

• Clarifiers

Filtering

a, b or c d or e f or g

A, B or C E F

a or b e f, g or h

B or C D or E F or G

b or c d f or (g)

A or B D or E F

• Basket bowl

b or c d f or g

(A) or B D or E F, G or H

• Disc stack (self clean, manual or nozzle discharge)

a, b or c d or e f or g

A or B D or E F or G

• Scroll decanter

a, b or c e f, g, (h) or (i)

(A), B or C (D) or E F, G or H

b or c d g, h or i

A, B or C D or E G or H

J, K or L

• Basket (peeler)

a, b or c d g, h or i

A, B or C D or E G or H

K or L

• Cone screen (slip discharge)

a e g or i

C E G

L

• Cone screen (vibratory/ oscillatory or tumbling)

a e g or i

C E H

L

• Cone screen (worm screen)

a e g or i

C E H

K or L

Hydrocyclones • Conical reverse flow or circulating bed Sedimenting centrifuges • Tubular bowl

Filtering centrifuges • Basket (pendulum)

continued

5 · Selection, data analysis and simulation by computer software 211 Table 5.1 continued Type of equipment

Duty specification

Separation characteristics Settling

Filtering

b or c e g, h or i a or b e g, h or i b or c e g, h or i

A, B or C D or E G or H B or C E G or H B or C E G or H

J, K or L

c d g, h or i c d g, h or i

A, B or C D or E F or G A, B or C D or E F or G

J, K or L

• Multi-element leaf

a, b or c d or e g, h or i

A, B or C D or E F or G

J or K

• Horizontal belt, rotary table or rotary tilting pan

a, b or c e g, h or i

A, B or C D or E F, G or H

J, K or L

• Rotary (vacuum) drum (bottom fed)

a, b or c e f, g, h or i

A or B D or E F, G or H

I, J or K

• Rotary (vacuum) drum (top fed)

a, b or c e g, (h) or i

C E G or H

L

• Rotary (vacuum) drum (internal fed)

b or c e g or i a, b or c e g or i

B E G or H A or B D or E G or H

J or K

• Inverting bag

• Pusher

• Baffle

Vacuum filters • Single leaf (vacuum Nutsche)

• Single leaf (tipping pan)

• Rotary (vacuum) disc

K or L

K or L

J, K or L

J or K

continued

212 Solid/Liquid Separation: Equipment Selection and Process Design Table 5.1 continued Type of equipment

Duty specification

Separation characteristics Settling

Filtering

a, b or c d g, h or i

A or B D or E F, G or H

J, K or L

• Multi-element leaf (horizontal element)

b or c d g or h

A or B D or E F or G

J or K

• Multi-element leaf (vertical element)

a, b or c d f, g, h or i

A or B D or E F or G

I or J

• Multi-element (tubular candle)

a, b or c d f, g, h or i

A or B D F or G

I or J

• Filter press

a, b or c d f, g, h or i

A or (B) D or E F, G or H

I or J

• Sheet filter

a, b or c d f

A D F

I

A or B D or E G or H

J or K

Pressure filters and presses • Single leaf (pressure Nutsche)

Variable volume (pressure) filters and presses • Diaphragm filter press a, b or c d g, h or i • Tube press

a, b or c d g, (h) or (i)

A or (B) D or E G or H

J or K

• Expression press

a or b d or e g

A D or E H

I or J

a, b or c e g or i

B or C D or E G or H

J

Continuous (pressure) filters • Belt press

continued

5 · Selection, data analysis and simulation by computer software 213 Table 5.1 continued Type of equipment

Duty specification

Separation characteristics Settling

Filtering

• Vertical diaphragm filter press

a or b e g, h or i

A or B D or E G or H

J or K

• Tower press

a or b e g or i

A or B D or E G or H

J or K

• Rotary (pressure) drum

b e g, h or i

A or B D or E G or (H)

(J) or K

• Rotary (pressure) disc

a or b e g or i

A or B D or E G or H

(J) or K

b or c d f

A or B D or E F

I

a, b or c d or e f or g

C E F or G

I or J

a, b or c e f or (g)

A D or E F or (G)

I or (J)

b or c e f

A D F

I

a, b or c e f

A D F

I

a or b e f

A D F

I

Miscellaneous pressure filters • Cartridge filter

• Bag filter

Precoat filters • Precoat rotary (vacuum) drum

• Precoat (pressure) filter and filter press Depth filters • Deep bed (pressure fed) sand

• Deep bed (gravity fed) sand

continued

214 Solid/Liquid Separation: Equipment Selection and Process Design Table 5.1 continued Type of equipment

Duty specification

Separation characteristics Settling

Filtering

b or c d or e f

A D or E F

I

a, b or c e g or h

B or C E G or H

L

• Mechanical

a, b or c e (f), g or h

B or C E G or H

L

• Screen (sieve bend)

a, b or (c) d or e f, g or h

(B) or C E F or (G)

I, J, K, or L

b or c d or e f

A or B D or E F

I

• Low shear crossflow ultrafilter

b or c d or e f, g or (h)

A or B D or E F

I

• Low shear crossflow microfilter

(a), b or c d or e f, g or (h)

A or B D or E F or G

I or J

• High shear crossflow

b or c e g or (h)

A or (B) D or E F or G

J or K

a or b e f or g

A or B D or E F

• Strainer

a, b or (c) d or e f

A D or E F

I

• Single leaf (gravity Nutsche)

(b) or c d f, g, h or i

B or C D or E F, G or H

K or L

• Deep bed (fibre)

Classifiers • Hydraulic

Membrane filters • Dead-end

Miscellaneous separators • Flotation

continued

5 · Selection, data analysis and simulation by computer software 215 Table 5.1 continued Type of equipment

Duty specification

Separation characteristics Settling

Filtering

a, b or c d or e f, g or (h)

A, B or C D or E F or G

I or J

• High gradient magnetic

a, b or c d or e f, g or (h)

A, B or C D or E F or G

I or J

• High voltage electric

b or c e f

A D F

I

Force field-assisted separators • Low gradient or low intensity magnetic

‘()’ around a letter index indicates a marginal choice.

filtration performance. Within each generic class a wide range of different types of separator exists; for example, more than ten sub-classes of pressure filters are identified in Table 5.1. While each sub-class may contain a variety of types, they tend to differ in detail of design rather than possess major differences related to their fields of application. Naturally, designs from different manufacturers will differ, but almost all will fit into a sub-class. It, therefore, becomes important to identify the sub-class of equipment that will be suitable for any specific application. Inspection of Table 5.1 permits identification of those types of equipment which are potentially suitable for the specific duty, thereby indicating in which areas more detailed testing should be concentrated to generate further data for specification or design purposes. It is possible to specify two letter code combinations for which equipment types are not identifiable, these are (i) ‘--- C-- I’ and (ii) ‘--- --H I’. The series represented by (i) and (ii) indicate a high settling rate (C) or large sludge volume (H), both of which would be incompatible with negligible cake formation (I). If experimental results appear to lead to these combinations, the integrity of the experimental tests and subsequent calculations should be checked. While many classes of solid/liquid separation equipment will permit most functions to be performed (e.g. cake formation, cake washing etc.), not all will execute a function with the same degree of effectiveness. The basis of relative performance indices for equipment was set out by Davies (1965) and Moos and Dugger (1979); their methodologies have been adopted and extended in Table 5.2. Each class of equipment is allocated an index of

216 Solid/Liquid Separation: Equipment Selection and Process Design Table 5.2 Relative performance characteristics of solid/liquid separation equipment. Type of equipment

Performance indices Feed solid properties Solids Washing Liquid Crystal Particle % by product product breakage size mass dryness quality (
m) solid in & state† feed

Gravity thickeners and clarifiers • Circular basin thickener 1 S • Settling tank or lagoon thickener • Circular high capacity thickener • Deep cone thickener • Lamella separator • Clarifiers Hydrocyclones • Conical reverse flow • Circulating bed Sedimenting centrifuges • Tubular bowl • Basket bowl • Disc stack (self clean) • Disc stack (manual discharge) • Disc stack (nozzle discharge) • Scroll decanter Filtering centrifuges • Basket (pendulum) • Basket (peeler) • Cone screen (slip discharge) • Cone screen (vibratory, oscillatory or tumbling) • Cone screen (worm screen) • Inverting bag • Pusher (single stage) • Pusher (multi-stage) • Baffle

2

5

9

0.1–500

20

1S

-

5

9

0.1–500

20

1S

-

5

9

0.1–300

15

1S 1S 1S

-

5 5 6

9 8 9

0.1–300 1–150 1–50

15 15 15

1S 1S

2 -

4 4

7 7

5–200 2–500

2–40 2–25

3S 2S 2S

-

6 5 -

5 5 6

0.1–100 0.1–100 0.1–100

5 5 0.05–2

2S 2S

-

-

6 6

0.1–100 0.1–100

0.05–2 0.5–10

4C

3

4

3

1–5000

4–40

9C 9C 7C

6 6 5

5 5 4

6 5 4

10–1000 4–30 2–1000 4–30 80–10000 10–40

8C

5

4

3

100–10000 10–40

9C

5

4

4

60–5000

9C 9C 9C 9C

6 7 8 5

5 4 4 5

6 4 4 4

2–1000 5–30 40–7000 10–40 40–7000 10–40 100–7000 10–40

10–40

continued

5 · Selection, data analysis and simulation by computer software 217 Table 5.2 continued Type of equipment

Performance indices Feed solid properties Solids Washing Liquid Crystal Particle % by product product breakage size mass dryness quality (
m) solid in & state† feed

Vacuum filters • Single leaf (vacuum 6C Nutsche) • Single leaf (tipping pan) 7 C • Multi-element leaf 5C • Horizontal belt or rotary 7 C tilting pan • Rotary table 7C • Rotary (vacuum) drum (bottom fed) Belt discharge 6C Knife discharge 6C Roller discharge 6C String discharge 6C • Rotary (vacuum) drum 5C (top fed) • Rotary (vacuum) drum 5C (internal fed) • Rotary (vacuum) disc 4C (cloth covered) • Rotary (vacuum) disc 4C (ceramic) Pressure filters and presses • Single leaf (pressure 6C Nutsche) • Multi-element leaf 5C (horizontal element) • Multi-element leaf 5C (vertical element) • Multi-element 5C (tubular candle) • Filter press 6C • Sheet filter N

8

7

8

1–500

1–10

9 5 9

7 7 7

8 8 8

20–80000 5–30 1–100 5–30 20–80000 5–30

8

7

8

20–80000 10–30

7 7 7 7 2

7 7 7 7 7

8 8 8 8 8

1–200 1–200 1–50 1–70 1–600

-

7

8

10–600

10

-

6

8

1–700

5–20

-

9

8

1–700

5–20

8

8

8

1–200 1–20

8

8

8

1–100 1–20

6

8

8

0.5–100 1–20

7

8

8

0.5–100 1–20

8 -

8 9

8 -

1–100 1–30 0.1–80 1–5

1–20 1–20 1–10 1–10 10

continued

218 Solid/Liquid Separation: Equipment Selection and Process Design Table 5.2 continued Type of equipment

Variable volume (pressure) • Diaphragm filter press (horizontal) • Tube press • Expression press

Performance indices Feed solid properties Solids Washing Liquid Crystal Particle % by product product breakage size mass dryness quality (
m) solid in & state† feed filters and presses 8C 8

8

7

1–200 0.3–30

8C 6C

4 -

7 6

7 5

1–200 0.3–30 1–200 10–80

7 8

7 8

7 7

1–200 0.2–30 1–200 0.2–30

6 -

7 7 6

7 7 8

1–300 1–100 1–100

0.1–25 5–30 5–30

-

9

8

1–100

5–30

-

9 4

7

0.4–50 10–300

0.1 0.2–10

5

8

8

0.5–100

1

-

9

-

1–40

1

N

-

8

-

0.2–60

0.1

Continuous (pressure) filters • Belt press 8C • Vertical diaphragm 8C filter press • Tower press 6C • Rotary (pressure) drum 6 C • Rotary (pressure) disc 5C (cloth covered) • Rotary (pressure) disc 7C (ceramic) Miscellaneous pressure filters • Cartridge filter N • Bag filter 6C Precoat filters • Precoat rotary 4 CN (vacuum) drum • Precoat (pressure) filter 5 CN and filter press Depth filters • Deep bed (pressure fed) sand • Deep bed (gravity fed) sand • Deep bed (fibre)

N

-

8

-

0.2–50

0.1

N

-

8

-

0.1–40

1

Classifiers • Hydraulic • Mechanical • Screen (sieve bend)

3C 4C 5C

3 2 4

3 3 5

5 50–2000 4–40 4 100–3000 4–40 4 45–100000 20–40 continued

5 · Selection, data analysis and simulation by computer software 219 Table 5.2 continued Type of equipment

Membrane filters • Dead-end (leaf or tubular element) • Low shear crossflow ultrafilter • Low shear crossflow microfilter • High shear crossflow Miscellaneous separators • Flotation • Strainer • Single leaf (gravity Nutsche)

Performance indices Feed solid properties Solids Washing Liquid Crystal Particle % by product product breakage size mass dryness quality (
m) solid in & state† feed N

-

9

8

1S

2

9

- 0.001–0.05 20

1S

2

9

6

0.05–20

20

2S

4

6

4

0.1–20

25

S N 4C

7

7 7

8 300–2000 1–20 5–200 0.1 9 100–10000 1–10

2

4

8 40–4000 5–20

2 -

4 7

8 8

Force field assisted separators • Low gradient or low 3C intensity magnetic • High gradient magnetic 1 S • High voltage electric 1S

0.1–10

400 20

1

10 10

A ‘-‘ performance index may be taken to mean either zero (that the equipment is not effective) or that the equipment is not suitable for that particular duty. † State of solids product: S ⬅ slurry or free flowing, C ⬅ cake, N ⬅ solids not generally recoverable.

performance between 0 and 9, with larger numbers indicating better performance. Indices are given for dryness of the solids product, the effectiveness of solids washing, the quality of the liquid product and the tendency of the equipment to cause crystal breakage. Table 5.2 also shows whether the solids are usually discharged as a cake or as a slurry, and the basic feed properties which the equipment can generally handle. While this information provides useful guidance there may be some specific designs of separators which fall outside of the guidelines. Nonetheless, once an initial selection of equipment has been drawn up using Table 5.1, the list can be sensibly ranked using Table 5.2. Ranking the list or considering some of the other basic

220 Solid/Liquid Separation: Equipment Selection and Process Design equipment characteristics may point to some types being unsuitable for an application. Worked examples of equipment selection are shown in Section 5.4.

5.2 Implementation of computer software Industrial process engineers need to possess a wide ranging knowledge that covers many unit operations. They are often aided by standard design and specification procedures, and these are well developed for branches of engineering such as distillation, heat transfer and process simulation. However, for filtration and general solid/liquid separation, the available procedures are more limited. It would be rare practice to use fundamental theoretical relationships and/or simulations for either the selection, design or the optimisation of solid/liquid separation equipment with the result that filters are mistakenly assumed to represent a trivial part of an overall operation. The large number of rules-of-thumb that have evolved, together with a vast, rather fragmented literature, serves to confuse the non-expert in the technology and maybe presents an image of disarray. The computer technologist might thus target solid/liquid separation as a technology ripe for the application of socalled ‘expert systems’. Expertise comprises knowledge about a particular topic, understanding of the problems in the topic and skill at solving some of these problems. Knowledge in this sense is usually of two sorts, either public or private. Public knowledge includes published definitions, facts and theories of which textbooks are typically composed. However, expertise in a technical area usually involves rather more than just public knowledge; human experts generally possess private knowledge that has not found its way into the published literature. This private knowledge may consist of unpublished techniques or approaches, or it may take the form of rules-of-thumb that have become known as heuristics. Heuristics enable the human expert to make ‘educated guesses’ when formalised or algorithmic solutions are difficult, to recognise promising approaches to problems, and to deal in the best practicable way with errors or incomplete data. Elucidating and reproducing such knowledge is a central task in designing an expert system. An expert system, therefore, is simply a computer algorithm that achieves high levels of performance in tasks for which human beings would require years of special education, training or experience. The design of an expert system for use in solid/liquid separation involves considerations such as generality and completeness of both the available data and the ultimate software, programming language features and database structures and the control mechanisms that shape and restrict the

5 · Selection, data analysis and simulation by computer software 221 representation of procedural knowledge within the system. Probably the most important features of any expert system are its ultimate practical success (expressed through its ease of use or user friendliness) and the reliability and quality of the advice it dispenses. These considerations are infinitely more important than any technical evaluation perceived by the computer scientist, which would refer to optimisation of the hardware/software combination. The ability of the expert system software to give advice or educate the user in a congenial fashion and in the user’s own terms is paramount, so that any psychological barriers to computer use are avoided. Expert systems, in their originally conceived form, are not able to satisfy many of the prerequisites required to assist the understanding of solid/liquid separation technology. Given the present state of knowledge about suspensions and dispersions, and their behaviour in process separators, it is considered most appropriate to have interactive computer software which is designed to be run in an integrated fashion with an experimental program. The software can ensure the correctness of input data as far as possible, utilise interactive graphics facilities to show the effects of changes in variables and/or allow the engineer access to calculations and make value judgements where these are peripheral to the expert system. Thus, to be most effective the software must be a well chosen mix of algorithm, expert system and input information from the engineer. The potential roles that computer simulations and software have in the choice, sizing, simulation and optimisation of solid/liquid separation equipment are shown schematically in Figure 5.6. Despite the relative complexity of the flowsheet, it should be realised that Figure 5.6 represents only some of the potential scenarios that an end user may encounter. The paths indicated differ mainly in the degree of experimentation and use of computer software such as FDS; the latter is based upon the concepts proposed by Wakeman and Tarleton (1991a, 1993), Wakeman (1995) and Tarleton and Wakeman (2003, 2005a,b): a. Consult manufacturers directly without performing any experiments. Most manufacturers specialise in certain types of solid/liquid separator and an approach from a potential customer immediately narrows the choice of equipment, as a manufacturer is unlikely to recommend competing, maybe more appropriate, products. The chosen manufacturer is likely to perform some basic experiments and then make a recommendation from a combination of the results, in-house experience and a number of rules-of-thumb. b. Perform basic laboratory scale tests, analyse data and perform equipment selection. The initial tests required for equipment selection are filtration

222 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 5.6 The role of computer software in the selection, sizing, simulation and optimisation of solid/liquid separation equipment. FDS modules: (1) equipment selection; (2) and (4) data analysis; (3) scale-up data generation; (5) equipment simulation.

and settling test(s). Using the philosophy attributed to Purchas (see Purchas and Wakeman, 1986) and the FDS computer software for consistent data analysis and equipment selection, a ranked list of equipment can be produced according to established and fixed criteria; the basic process is shown in Area (1) on Figure 5.6. If no suitable equipment can be identified then consideration should be given to modifying the properties of the feed through, for instance, the use of flocculants. These selection procedures are detailed in Sections 5.1.2.1–5.1.2.3.

5 · Selection, data analysis and simulation by computer software 223 c. Further selection criteria. It may be important to include other selection criteria at this point, including special properties of the feed, economic and safety factors and/or any special process requirements (Area (2), see also Section 5.5). Such factors will tend to reduce the list of potentially suitable equipment and may even eliminate all of the initial choices. The phases proposed in a filter cycle may also eliminate certain types of equipment. If all equipment is rejected at this stage then it may again be necessary to modify the properties of the feed. No computer software currently exists for the evaluation of these additional selection criteria. d. Perform scale-up tests. Using the laboratory equipment and procedures described in Chapter 4, scale-up parameters are determined from sequences of tests and analysed by calculations, preferably carried out in a consistent manner via computer software such as FDS (Area (3)). These procedures establish basic performance parameters and values of the scale-up constants for each phase in a filter cycle. e. Filter cycle simulation or further experimentation? At this point some laboratory scale-up data are available as well as a relatively short list of potentially suitable equipment. It may be considered appropriate to perform pilot or semi-technical scale experiments provided the necessary equipment is available. Starting from the top of the equipment list, experiments should (ideally) be performed on each equipment type to determine whether the chosen cycle sequence is feasible and the desired results can be achieved in the most efficient manner. Sufficient experiments may be required to establish near optimum processing conditions and ensure successful operation over the range of potential process conditions encountered during variations in the feed properties. Equipment manufacturers can be consulted as appropriate. It is noted that performing pilot scale experiments is potentially very expensive. Alternatively, at much reduced cost computer simulations of a filter and its cycle can be used to advantage. Provided the necessary simulations are available, a range of scenarios can be examined relatively quickly and comparisons between equipment types can be made. ‘What if?’ questions can be readily answered and the consequences of, for instance, variations in feed properties or processing different feed types assessed. In principle, near optimum processing conditions can also be established. A further benefit of using a range of simulations is that an unbiased assessment of separator performance can be acquired prior to approaching a manufacturer, thus reducing the risk of incorrect or non-ideal equipment selection. Manufacturers are likely to verify for themselves and confirm a selection and sizing, but a purchaser should be aware of the likely outcome of their

224 Solid/Liquid Separation: Equipment Selection and Process Design selection and sizing procedures and be wary if a manufacturer supplies only one type of filter. f. Final choice and sizing of separation equipment. The alternative paths provided by (a)–(e) should highlight the separator that is most capable of satisfying the required duty and product specifications. The costs involved in arriving at the final choice and size of separator will vary according to the number and scale of the experiments performed, the reliance on computer software for data analysis and separator simulation and ultimately the time devoted to the overall process. Figure 5.6 and the descriptions given indicate the various roles of computer software in selection, analysis and simulation. The detailed calculations shown in Chapters 6 and 7 illustrate the benefits of using filter cycle equations and propose well defined modular procedures for filter design. The relative complexity of the design equations also suggests that computer simulations can be written to perform the calculations, provided the appropriate levels of user interaction and ease of information transfer can be maintained. The hierarchical steps involved in a filter cycle simulation are illustrated (in a simplified form) in Figure 5.7. Early efforts to model the filter cycle (e.g. Carman, 1938) were followed in the years up to 1990 by several attempts to produce charts for selecting solid/liquid separation equipment (see Section 5.1.1 for details). During the same period, attempts were also made to model aspects of the filter cycle on devices such as rotary vacuum filters and centrifuges (see, for example, Nelson and Dahlstrom, 1957; Kelsey, 1965; Rushton, 1978; Wakeman, 1979c, 1981c; Wakeman and Mulhaupt, 1985; Shirato et al, 1987; Yelshin et al, 1989). In more recent years, efforts have led to further simulations of rotary vacuum filters (Stahl and Nicolaou, 1990; Nicolaou, 2003) as well as investigations of the belt press filter cycle (Kobayashi et al, 1993) and the rotary disc filter (Nyström, 1993). Perhaps the greatest progress has been made by the authors who have produced commercial software for data analysis and equipment selection (pC-SELECT), a range of technical publications concerned with the simulation of filter cycles (Wakeman and Tarleton, 1990, 1994a,b, 1995, 1999; Tarleton and Wakeman, 1994c) and now FDS which integrates equipment selection, data analysis, scale-up and equipment simulation into a single computer software package (Tarleton and Wakeman, 2003, 2005a,b; Filtration Solutions, 2005). The design of computer software requires a number of considerations. Firstly, and perhaps most importantly, software must be based on sound calculation procedures that are proven for a wide range of scenarios. In the context of filter cycle simulations these include the methodologies defined previously by the authors for the modelling of cake formation, deliquoring, washing and expression (Wakeman and Tarleton, 2005a) and the design

5 · Selection, data analysis and simulation by computer software 225

Figure 5.7 Basic flowsheet for filter cycle simulations. equations given in Chapters 6 and 7. Given current level of knowledge, it is necessary for software to be interactive and designed in a way to be integrated with some form of basic experimental programme. Ideally measurable microscopic properties of suspensions and filter cakes could be related to the bulk behaviour of such systems. The need for empirical ‘correction’ factors would then be eliminated and all macroscopic properties could be predicted from the individual properties of the particles and fluid. Although engineers and scientists have pursued this goal for many years, the present reality necessitates some reliance on experimental data. For the above situation to be satisfactory it is necessary to have consistent analysis procedures which facilitate the calculation of parameters such as

226 Solid/Liquid Separation: Equipment Selection and Process Design cake resistance and scale-up constants from sequences of experimental data; the results from a data analysis are subsequently used in filter cycle simulations. Thus, to be most effective software must include well chosen calculation procedures and algorithms, ensure the correctness of data input as far as this is possible, utilise interactive graphics facilities and be sufficiently easy to use. Filter cycle simulations provide detailed data throughout each sequential phase, and given their modular nature the potential exists to model most filter and press types. The simulations facilitate preliminary sizing, scale-up and optimisation and require no ‘correction’ factors or additional rules-of-thumb to provide engineering solutions to practical problems.

5.3 Descriptions of FDS The following details FDS, Windows® software for the selection and simulation of solid/liquid separation equipment as well as the analysis of test data. FDS has been developed in collaboration with multi-national companies spanning a wide range of industrial sectors, the aim being to provide a comprehensive calculation, education and training tool that maintains a balance between ease of use, level of knowledge conveyed and comprehensibility. FDS is a sequence of interlinked modules that can be used independently from one another as necessary; Figure 5.8 shows the Start Menu display. The selection module compares seven user-defined selection criteria with equipment specific information contained in databases to produce a numerically ranked list of potentially suitable equipment. FDS allows access to text and pictorial descriptions of more than 70 equipment types and hyperlinks provide more specific equipment manufacturer details via the Internet. The data analysis module facilitates interactive analysis of leaf filtration, jar sedimentation and piston press test data. Calculations are performed in a hierarchical manner using the available information; if some data are not measured then FDS performs the best possible analysis using approximations. The results of an analysis can be used to refine (shorten) a list of selected equipment and/or provide scale-up information for equipment simulation. The two equipment simulation modules provide calculation sequences for more than 20 types of vacuum and pressure filters, potentially involving combinations of cake formation, compression, gas deliquoring and washing. Batch filters include single and multi-element leaf filters, filter presses and diaphragm and tube presses while continuous filters include the horizontal belt, drum, disc, table and tilting pan filters. The user is able to define filter

5 · Selection, data analysis and simulation by computer software 227

Figure 5.8 Initial display screen of FDS showing access to the Equipment Selection, Data Analysis and two Simulation modules for vacuum (partially hidden) and pressure filters. Images used with permission from Amafilter, Andritz, atech innovations, Axsia Mozley, Broadbent, Dorr-Oliver Eimco, Filtration Services, Larox, Leiblein, Lenntech, Mavag and Sernagiotto.

228 Solid/Liquid Separation: Equipment Selection and Process Design cycle data in their preferred units and guidance is given to suitable numeric ranges for the type of filter being simulated. Results are presented on-screen in graphical and tabular forms and a mass balance quantifies the amounts of solid, liquid and dissolved solute components present in the input and output streams. The results are also made available in data sheet form which can subsequently be imported into a spreadsheet. 5.3.1 Equipment selection module Figure 5.9 shows a typical screen display from the Equipment Selection module. When the module is invoked from the Start menu only the ‘Specifications’ box in the top left hand corner of the screen is displayed. The available entries allow the user to select up to seven items from dropdown lists. With reference to Sections 5.1.2.1–5.1.2.3, these define the Duty, which must be specified, and the Settling and Filtration characteristics which are optional entries. In the example shown, an item in each dropdown list has been chosen indicating that experimental data are available. If equipment selection is performed by specifying only the items for Duty, then a longer list of equipment (with accompanying warnings) is likely to result. Choosing the ‘Select’ command button displays the ‘Selected Equipment List’ box towards the top right of the screen where the user specifications have been compared against the FDS database of separation equipment; the database incorporates Table 5.1. Choosing an equipment item with the mouse subsequently displays the text and pictorial information towards the bottom of the display. With reference to Figure 5.9, features of the module functionality include:

•

Selected equipment list: Ranked listing of solid/liquid separation equipment that matches the specifications, this includes separators other than filters to give the broadest possible spectrum of choice. Five indices are shown for each equipment type; the indices range between 0 and 9 where higher values indicate better performance. The listing can be prioritised according to the index for solids dryness, liquid clarity, washing ability or crystal breakage as well as an overall index which is the sum of these four indices. This facility allows the user to choose the criterion that is most important for the problem of interest and reorder the list of equipment accordingly. The letter designations ‘C’ and ‘S’ indicate whether the solid is generally discharged in the form of a cake or a slurry. The suitability of the selected equipment is also related to typical particle size ranges and feed concentrations. Although the latter information may not have been used in the preliminary selection, values have been implied through other data such as initial settling rate. Some potentially suitable equipment is

5 · Selection, data analysis and simulation by computer software 229

Figure 5.9 Example screen display from the Equipment Selection module of FDS.

230 Solid/Liquid Separation: Equipment Selection and Process Design likely to be marginally acceptable for the user chosen criteria, these are noted below the ‘Warning’ command button which also displays their meaning in a pop-up menu. For instance, the warning ‘B’ against the filter press, screen classifier and tube press in Figure 5.9 indicates marginality for suspensions that settle with a rate of 0.1–5 cm s
1. It is advised that separators without warnings are examined in more detail before marginally suitable separators are considered.

•

Equipment descriptions: The descriptions give general and detailed technical and design information about the chosen equipment. All separators will fall into 1 of 11 classes namely gravity filters or sedimenters, batch or continuous vacuum filters, batch, semi-continuous, variable volume or continuous pressure filters, centrifugal filters or sedimenters and force field assisted separators. The general information reflects the principal characteristics of the separator class. Information more specific to a particular separator is presented adjacent to the general information (e.g. diaphragm filter press in Figure 5.9).

•

Equipment schematic etc.: Schematic diagrams and photographs of the highlighted equipment are provided to illustrate the principal aspects of operation and an overall appreciation of size and form. With reference to Figure 5.10, alternative views show additional information which can help to eliminate equipment from the ranked list. A customisable display of equipment suppliers can also be viewed by choosing the relevant command button. The ability to ‘cut and paste’ the web address of a potential supplier to an on-line browser is provided which enables the user to inspect ever more detailed information as well as contact details.

Results of an equipment selection can be saved to the hard drive of the host computer for later retrieval by FDS or a spreadsheet program. In addition to the selection procedure, the Equipment Selection module also provides an Equipment Catalogue. The display is broadly similar to that in Figure 5.9, but the FDS equipment database is categorised according to the 11 classes noted previously and arranged in the form of a reference manual. The intention of the Equipment Catalogue is to provide facility for education and training rather than equipment selections. 5.3.2 Data analysis module The Data Analysis module of FDS facilitates the interactive analysis of constant pressure and constant flow filtration, jar sedimentation and piston press (expression) tests; the procedures are computer software implementations of the analysis techniques described in Chapter 4. Data obtained at the laboratory, pilot and even full scale can be analysed in a consistent manner

suppliers' (right).

5 · Selection, data analysis and simulation by computer software 231

Figure 5.10 Alternative views on the Equipment Selection display showing 'Additional information' (left) and 'Equipment

232 Solid/Liquid Separation: Equipment Selection and Process Design to give either additional information for equipment selection or (by repeated use) scale-up correlations for equipment simulation. By way of example, screen displays for a piston press analysis are shown in Figures 5.11–5.13 while Figure 5.14 shows the screen display during the calculation of scaleup coefficients for cake formation and consolidation. Referring to Figure 5.11, the user is initially required to type or select choices in the ‘General Information’ box towards the top left hand corner of the display. Descriptions for the test to be analysed can be typed and the Data and Unit Files selected. The Data File is specific to the type of analysis,

• • • •

Constant pressure filtration: time (tf) vs. cumulative volume of filtrate (Vf) Constant pressure expression: time (t) vs. cumulative volume of filtrate (V) Constant flow filtration: time (tf) vs. pressure (
pf) Jar sedimentation: time (t) vs. suspension/supernatant interface height (Hi)

and can be either typed by the user or imported from a spreadsheet as required. The Unit File allows the user to enter information in their preferred units by selecting individual items from a sequence of drop-down lists; ranges of SI, CGS, American and Imperial units are available. The ‘Experimental Data’ box towards the top right of the display is used to enter the other relevant data from a test including properties of the feed and operational parameters for the test apparatus. Even with well conducted tests, some of the necessary input data can be missing yet the best possible analysis must still be done with the available information. FDS deals with this situation in two ways. Firstly, when the input data are entered they are checked as far as possible and if FDS suspects that the data may be incorrect it warns the user or does not accept the data. In many cases FDS displays a range of acceptable values for the data as a guide to the user. Secondly, the calculation sequences within FDS are hierarchical. Depending on which data are missing, a sequence of assumptions are made in order to carry out the calculations. After an assumption has been made, a warning may appear against item(s) of output data in the ‘Tabulated Results’ box towards the bottom of the display (e.g. [25] in Figure 5.11). Results of an analysis are shown in the lower half of the display in either tabulated form, as in Figure 5.11, or graphical forms. For each type of analysis, a ‘Characteristic Plot’ is produced towards the bottom right-hand corner of the display: Constant pressure filtration: tf /Vf vs. Vf

Constant flow filtration: tf vs.
pf

Constant pressure expression:

L/
兹苶t vs. t Jar sedimentation: Hi vs. t

same as those in the worked example shown in Section 4.5.5.

5 · Selection, data analysis and simulation by computer software 233

Figure 5.11 Example screen display of an expression analysis using the Data Analysis module of FDS. The data are the

234 Solid/Liquid Separation: Equipment Selection and Process Design Vertical line cursors are used to identify a linear or transition region on the Characteristic Plot and these are initially positioned by FDS. However, the user has facility to interact with the software and move the cursors as appropriate in order to overcome their potential misplacement due to data scatter. In this way the analysis can be amended as many times as required and optimised. During the analysis of a jar sedimentation test a third, horizontal line cursor is used to specify the final height of sediment, which is particularly useful when a test is not continued to equilibrium. In the case of a piston press analysis, and in accordance with the recommend procedure described in Section 5.5, additional representations of test data are shown for the filtration and consolidation phases to check the choice of transition between the two. For example, in Figure 5.12 the correct transition has been identified on the Characteristic Plot such that the resultant tf /Vf vs. Vf plot is linear throughout and the consolidation ratio (Uc ) vs. (consolidation time, tc)0.5 exhibits an initial linear portion. In Figure 5.13 the transition point has been deliberately chosen too far to the left on the Characteristic Plot such that the Uc vs. tc plot exhibits an incorrect ‘S’ shape. When the required region has been chosen on the Characteristic Plot, the numerical values appearing towards the lower right hand corner of the display represent the correct analysis of the test data. Depending on the type of analysis performed, these can include the parameters required to shorten a selected equipment list such as average cake formation rate (filtration test) and initial settling rate (sedimentation test). The results of an analysis can be saved to disk in spreadsheet readable format. If several filtration and/or expression tests are performed at different constant pressures but otherwise identical experimental conditions, then scale-up coefficients can be determined. By way of example, Figure 5.14 shows the screen display for a sequence of three constant pressure filtrations where the lower half of the display contains both graphical and tabular results. These coefficients are used in equipment simulations to characterise cake resistance, cake structure and, where applicable, cake consolidation. 5.3.3 Equipment simulation modules As previously noted, there are two available modules for equipment simulation, namely vacuum filters and pressure filters (which include variable volume filters). Within either module there are several options available from the Start Menu (see, e.g. Figure 5.8), each of which facilitates the simulation of a particular type of filter. All simulations are performed in the same general manner, the principal differences arise as a consequence of the operational limitation(s) of filter type. Figure 5.15 shows an example screen display for the simulation of a bottom fed rotary drum filter fitted with a knife discharge.

5 · Selection, data analysis and simulation by computer software 235

Figure 5.12 Interactive graphical display screen for the expression analyses shown in Figure 5.11 where the correct choice of transition from filtration to compression deliquoring has been made. The data are the same as those in the worked example shown in Section 4.5.5.

Figure 5.13 Interactive graphical display screen for the expression analyses shown in Figure 5.11 where the transition point has been (deliberately) chosen too early in the data sequence. The ‘General Information’ box towards the top left hand corner of the display is used to start a simulation procedure. The Cycle configuration, Unit File and, where appropriate, Pump and Wash curves are defined here; invoking any of these activates the ‘Cycle configuration…’ box towards the middle top of the display. For vacuum filters the cycle can comprise combinations of cake formation, washing and gas deliquoring, however, FDS prevents impractical phases on particular filters, for instance, cake washing on a rotary disc filter. For variable volume filters the cycle can additionally include cake consolidation (compression deliquoring). User choices are

236 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 5.14 Example screen display of scale-up correlations obtained from a sequence of constant pressure filtration experiments using the Data Analysis module of FDS.

5 · Selection, data analysis and simulation by computer software 237

Figure 5.15 Example screen display for a rotary vacuum drum filter simulation using FDS. The data are the same as those in the worked example shown in Section 7.3.2 (with no deliquoring during the rise phase).

238 Solid/Liquid Separation: Equipment Selection and Process Design made by selecting items from drop-down lists. Similar to the descriptions for the Data Analysis module, the Unit File allows the user to specify their preferred units for data entry. Several types of pressure filter use positive displacement or centrifugal pumps to bring about filtration and in these cases a pump curve must be defined (typed) by the user in an x, y format of flow rate vs. pressure. The default for washing calculations is the dispersion model, however, the user can choose to override this default and use an experimentally measured wash curve. The data need are defined in the x, y format of time vs. cake solute concentration (or fraction of solute retained). The remainder of the information required for simulation is typed by the user in the ‘Simulation Data’ box towards the top right hand corner of the display. Each ‘tab’ corresponds to a phase in the filter cycle or provides facility to enter data specific to the filter or the feed solids, liquid and solute.

•

Filter tab: Process parameters specific to the type of filter being simulated. Entries typically include filter area (or entries that allow its calculation), medium resistance and in the case of continuous filters, rotational or linear speed of the cloth.

•

Suspension tab: Parameters related to the feed suspension. Entries are ideally required for solids density, filtrate density, viscosity and surface tension, feed slurry and solute concentrations, solute diffusivity and mean particle size in the feed suspension.

•

Phase 1 tab (always filtration): Parameters specific to the filtration phase including two scale-up coefficients for specific cake resistance, two scale-up coefficients for cake solids concentration and, where appropriate, filtration pressure or vacuum.

•

Phase 2–4 tabs: The nature of the entries on these tabs is linked directly to the phases constituting the cycle configuration: – Compression deliquoring: Parameters specific to a consolidation phase including compression pressure, consolidation index, two scaleup coefficients for cake solids concentration and two scale-up coefficients for consolidation coefficient. – Washing: Parameters specific to a washing phase including washing pressure, wash liquid density, viscosity and surface tension, solute concentration in the wash liquid and the required washing model/curve. – Gas deliquoring: Parameters specific to a gas deliquoring phase including deliquoring pressure, breakthrough pressure or vacuum for the cake, barometric pressure, irreducible cake saturation and gas viscosity.

The results of a simulation are shown towards the bottom half of the display. In the ‘Schematic Mass Balance’ box, a graphical display of the mass

5 · Selection, data analysis and simulation by computer software 239 balance enables a rapid check of the amounts of solid, liquid and solutes involved in the simulation. In the ‘Graphical/Tabulated Results’ box the principal results of a simulation are initially presented to the user in graphical form through selectable items from two drop-down lists. The upper list specifies whether results pertaining to the whole cycle or an individual phase are displayed. The lower list, whose entries change to reflect the selected item in the upper list, shows the graph options available. A summary of the results can also be viewed in tabular form while saving the results to the hard drive of the host computer allows their later retrieval by FDS or spreadsheet. Other key features of the simulation modules include:

•

Checking of input data – for each required entry FDS displays a range of numerical values to guide the user as to what is realistic for a particular filter

•

Where possible the calculation sequences are hierarchical - depending on which data are missing, a sequence of assumptions are made in order to carry out a calculation

•

FDS takes account of practical constraints, for example, the minimum cake thickness that can be discharged from a particular filter.

Although a substantial amount of data are required to perform a simulation, the results give comprehensive descriptions of filter performance. For batch filters the time dependency of parameters such as mass of solids, liquids and solutes (both extracted and retained), cake thickness and moisture content and fractional solute recovery can be obtained for the whole cycle, or individual phases where appropriate. The production rates are also given for both products and potential waste streams. In the case of continuous filters throughputs rather than masses are calculated. As with most simulation packages, ‘what if?’ calculations can be undertaken to investigate filter performance for different operating conditions in order to determine an optimum.

5.4 Examples of FDS use Although it is difficult to convey the operation of computer software through written text, two examples of how FDS can be used in equipment selection and data analysis are shown below. The first illustrates the basic selection procedure from data analysis to initial equipment selection. The second example shows the results of a more sophisticated selection where a separator

240 Solid/Liquid Separation: Equipment Selection and Process Design is required to process batches of five different feeds having a range of properties. The capability and use of FDS in equipment simulation is more appropriately presented in Sections 6.5 and 7.4 for batch and continuous filters respectively, a worked example is shown in each case. 5.4.1 Example 5.1: Basic selection and data analysis procedures Problem The continuous recovery of dewatered (unwashed) solids from a slurry is required, the throughput of the latter is 10 m3 h
1. Basic properties, sedimentation and filtration test results are available for a sample of the slurry. Draw up a preliminary list of equipment which may be suitable for this separation. The density of the solid and the liquid are 2650 and 998 kg m
3 respectively while the liquid phase viscosity is 0.001 Pa s. The solids concentration in the slurry has been determined as 23% w/w. The time vs. suspension–supernatant interface height data shown in Table 5.3 were obtained from a jar sedimentation test using a one litre measuring cylinder with an inside diameter of 6.5 cm. The supernatant clarity was good. The time vs. cumulative filtrate volume data shown in Table 5.4 were obtained from a leaf filter (Buchner) test using a vacuum of 70 kPa. The filter leaf had an area of 38 cm2, and the final masses of wet and dry cake were 197 g and 128 g respectively. The final cake height was estimated to be 3.1 cm. Both tests were performed in accordance with the recommendations shown in Chapter 4. Table 5.3 Time vs. suspension–supernatant interface height for Example 5.1. Settling time (s) 0 10 20 30 40 50 65 90 130 180 220 250 †

Suspension volume (cm3)

Interface height (cm)†

1000 910 830 750 660 580 500 410 370 340 332 332

30.1 27.4 25.0 22.6 20.0 17.5 15.1 12.4 11.2 10.3 10.0 10.0

4 ×(suspension volume)/( 6.52).

5 · Selection, data analysis and simulation by computer software 241 Table 5.4 Time vs. cumulative filtrate volume for Example 5.1. Filtration time (s)

Filtrate volume (cm3)

Cake thickness (cm)†

0 13 40 58 80 102 120 141 162 180 200

0 30 80 110 140 165 190 210 230 250 270

0 0.26 0.69 0.95 1.20 1.42 1.63 1.81 1.98 2.15 2.32

†

Estimated using equation (4.22).

Solution The first step in the equipment selection process is to analyse the available experimental data. This is achieved using the Data Analysis module of FDS and the general procedure described in Section 5.3.2. In brief, and taking the filtration data first, the Data File comprises the data in Table 5.4 and the Unit File reflects the units specified in the problem. With the remaining experimental data specified, the Characteristic Plot shown in Figure 5.16 is produced. The interactive (vertical) cursor lines can be moved by the user to define a portion which is linear in accordance with equation (4.3); in the current example all the data points lie close to a straight line and the entire dataset is taken. With the correct portion assigned a linear regression and calculations are performed to produce both a graphical and a tabular display of results; the latter are summarised in the datasheet shown in Figure 5.17 and the equations that underpin the calculations are presented in Section 4.1. The datasheet contains all the information inputted (typed) during the analysis, a list of results including filter cake porosity, specific cake resistance and average cake growth rate (0.93 cm min
1) as well as data sequences derived from the Data File. The jar sedimentation experiment is analysed using a similar general procedure to the filtration experiment. In this case, however, the interactive Characteristic Plot shows suspension–supernatant interface height vs. time data. An additional horizontal cursor allows the final sediment height to be interactively defined by the user (see Figure 5.16). For the experimental data in Table 5.3, the results show a settling rate  0.25 cm s
1 and a proportion of sludge  33%.

242 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 5.16 Interactive graphical display screens from FDS for the constant pressure filtration (left) and jar sedimentation (right) tests described in Example 5.1.

With the experimental data analysed the equipment selection can be performed in accordance with the procedure detailed in Section 5.3.1. In brief, the process duty, settling and filtration characteristics are defined via the user selectable choices and these are compared with the FDS equipment database to produce a screen display similar in form to Figure 5.9 and the datasheet in Figure 5.18. The datasheet shows the basic inputs to FDS and a shortlist of solid/liquid separation equipment potentially suited to the application in rank order of overall performance. Against two pieces of equipment there are selection warnings which indicate that the equipment is a marginal choice against one or more of the duty, settling or filtration criteria. 5.4.2 Example 5.2: Advanced selection procedure For batch plants where several products are manufactured in small to medium quantities the same piece of equipment may be required to perform several different separations. In such circumstances a good deal of heuristic information and detailed knowledge of a wide variety of separators is needed in order to produce a shortlist of equipment. However, a sophisticated selection is readily performed using FDS without a need for user expert knowledge. Problem Consider a plant which is required to process five separate feeds in batches at rates equivalent to ~15 m3 h
1. At the current stage of process specification it is not clear whether the prime objective for the separation of two of the feeds is solids dewatering or washing. Sedimentation and filtration tests have been performed on small samples of the slurries and analysed using

5 · Selection, data analysis and simulation by computer software 243 Datasheet for experiment analysis General information Type: Experiment description: Solids description: Fluid description: Data file: Unit file: Result file:

Constant pressure/vacuum filtration Leaf filter test Process solids Process water Example data file Example unit file File 1

Experimental data Filter diameter: Pressure difference: Solids density: Liquid density: Liquid viscosity: Feed slurry concentration: Wet cake mass: Dry cake mass: Cake depth:

6.96 cm 70 kPa 2650 kg m
3 998 kg m
3 0.001 Pa s 23% w/w 197 g 128 g 3.1 cm

Analysis results Specific cake resistance: 7.48 × 109 m kg
1 Filter medium resistance: 1.04 × 1011 m
1 Effective feed concentration: 355.3 kg m
3 Mass dry cake/filter area: 33.68 kg m
2 Average cake formation rate: 0.93 cm min
1 (using masses at end of filtration/at cursor) Cake solids concentration: 0.411 v/v Cake moisture: 35.03% Cake wet/dry mass ratio: 1.539 (using cake depth at end of filtration) Cake solids concentration: 0.41 v/v Cake moisture: 35.15% Filtration time (s) 0 13 40 58 80 102 120 141 162 180 200

Cumulative filtrate volume (m3) 0 3.00 8.00 1.10 1.40 1.65 1.90 2.10 2.30 2.50 2.70

× 10
5 × 10
5 × 10
4 × 10
4 × 10
4 × 10
4 × 10
4 × 10
4 × 10
4 × 10
4

Filtrate flow rate (m3 s
1)

(t–ti)/(V–Vi) (s m
3)

No data 2.30 × 10
6 1.80 × 10
6 1.60 × 10
6 1.30 × 10
6 1.10 × 10
6 1.30 × 10
6 0.90 × 10
7 0.90 × 10
7 1.10 × 10
6 No data

No data (1) 4.33 × 105 5.00 × 105 5.27 × 105 5.71 × 105 6.18 × 105 6.32 × 105 6.71 × 105 7.04 × 105 7.20 × 105 7.41 × 105 (11)

Portion chosen for analysis between data groups 1 and 11, approximated filtrate flow rate(s).

Figure 5.17 Example of an FDS data analysis datasheet.

244 Solid/Liquid Separation: Equipment Selection and Process Design Datasheet for equipment selection Duty specifications Feed rate: Operation: Objective:

5–50 m3 h
1 continuous deliquored solids

Settling specifications Settling rate: Supernatant clarity: Sludge proportion:

0.1–5 cm s
1 good 20% v/v

Filtration specification Cake growth rate:

0.02–1 cm min
1

Selected equipment

Selection warnings (1)

Horizontal belt filter Rotary tilting pan filter Vertical diaphragm filter press Rotary table filter Bottom fed drum filter, belt discharge Bottom fed drum filter, knife discharge Bottom fed drum filter, roller discharge Bottom fed drum filter, string discharge Inverting bag centrifuge Rotary drum pressure filter Pusher (multi-stage) centrifuge Pusher (single-stage) centrifuge Baffle centrifuge Rotary disc vacuum filter, ceramic Internal fed drum filter Rotary disc pressure filter, cloth Rotary disc vacuum filter, cloth Scroll decanter centrifuge

(2)

Index (3) (4) (5)

Particle size (µm)

Feed conc. (% w/w)

None None None None None

7C 7C 8C 7C 6C

7 7 8 7 7

9 9 8 8 7

8 8 7 8 8

31 31 31 30 28

20–80000 20–80000 1–200 20–80000 1–200

5–30 5–30 0.2–30 10–30 1–20

None

6C

7

7

8

28

1–200

1–20

None

6C

7

7

8

28

1–50

1–10

None

6C

7

7

8

28

1–70

1–10

None 1H None None None None None None None 1i

9C 6C 9C 9C 9C 4C 5C 5C 4C 4C

5 7 4 4 5 9 7 6 6 4

6 6 8 7 5 0 0 0 0 3

6 7 4 4 4 8 8 8 8 3

26 26 25 24 23 21 20 19 18 14

2–1000 1–100 40–7000 40–7000 100–7000 1–700 10 –600 1–100 1–700 1–5000

5–30 5–30 10–40 10–40 10–40 5–20 10 5–30 5–20 4– 40

Indices: (1) solid product dryness, (2) liquid product clarity, (3) washing performance, (4) crystal breakage, (5) overall performance.

Figure 5.18 Example of an FDS equipment selection datasheet.

5 · Selection, data analysis and simulation by computer software 245 FDS to give the data summarised in Table 5.5. Determine if the separation of all five feeds can be achieved effectively using a single separator. Solution The data in Table 5.5 indicate that the separation characteristics of each feed are quite different. By repeated use of the automated selection procedures in FDS, the information shown in Table 5.6 can be produced. The numbers listed under the subheadings ‘D’ and ‘W’ indicate the relative performance index of the equipment as a solids dewatering or cake washing device respectively (better performance is associated with greater index values). A ‘-’ indicates that the equipment is not suitable for the particular separation. Inspection of Table 5.6 shows that none of the separators identified are capable of processing all five feeds in an effective manner, although the pressure Nutsche filter and basket pendulum centrifuge are suited to processing four of the five feeds. Should only the unflocculated feeds need to be processed, then the pressure Nutsche is a good choice for initial further investigations. While the diaphragm filter press has high ratings for feeds #2–#4, difficulties are identified with the processing of feeds #1 and #5 due respectively to a small proportion of sludge (which infers a low cake volume and long cycle times) and excessive particle settling in the chambers of the press. The basket pendulum centrifuge is also eliminated for feed #1 due to the inadequate proportion of sludge. The quality choice of separator(s) may ultimately depend upon

Table 5.5 Settling and filtration characteristics of five batch feeds. Selection parameter in FDS

Feed #1

#2

#3

#4

#5*

D

D

D

D or W

D or W

(Sedimentation test data) Settling rate (cm s
1) Clarity of supernatant Sludge proportion (%) FDS coding

0.1 Poor 2 ADF

0.1 Poor 20 ADH

0.1 Good 20 AEH

0.1–5 Good 2–20 BEG

5 Good 2–20 CEG

(Filtration test data) Cake growth rate (cm min
1) FDS coding

0.02 J

0.02 J

0.02–1 K

0.02–1 K

1 K

Primary separation objective

D ⬅ dewatered, W ⬅ washed (FDS codings ‘bdi’ and ‘bdg’ respectively). *#5 is flocculated from #4.

246 Solid/Liquid Separation: Equipment Selection and Process Design Table 5.6 Equipment potentially suited to the processing of the five batch feeds. Equipment identified by FDS

Filter press Single leaf (pressure Nutsche) filter Multi-element (tubular candle) pressure filter Multi-element leaf (vertical element) pressure filter Multi-element leaf (horizontal element) pressure filter Diaphragm filter press Multi-element leaf vacuum filter Tube press Basket (pendulum) centrifuge Basket (peeler) centrifuge Circular basin thickener Screen classifier Gravity Nutsche filter

Feed #1 D

#2 D

#3 D

D

#4 W

D

#5 W

6 6

6 6

6

6

8

-

-

5

-

-

-

-

-

-

5

-

-

-

-

-

-

5 -

8 8* 9 -

8 8* 9 9 -

8 5 8* 9 9 4*

8 8 5 4* 6 6 2 4* 7*

9 9 4*

6 6 2 4* 7*

D ⬅ dewatering index, W ⬅ washing index, * marginally acceptable on selection criteria. ‘-’ ⬅ unsuitable equipment.

either modification to the separation characteristics, for instance, of feeds #1 or #5 or consideration of additional factors such as those described in Section 5.5.

5.5 Shortlisting equipment for pilot scale testing and/or simulation Although FDS is able to produce a shortlist of equipment, it is possible to further refine the equipment choice. This requires consideration of additional selection parameters (indicated through Tables 5.7–5.11) and provides a basis for deciding which types of solid/liquid separation device merit the time and cost of executing detailed testing and/or simulation programmes. The selected shortlist of equipment may be further shortened if the applications problem is more precisely defined or if additional laboratory experiments are carried out. The additional tests, indicated on Table 5.7, are dependent on

5 · Selection, data analysis and simulation by computer software 247 Table 5.7 A summary of additional selection criteria. Parameter Potential further tests Process requirements Solid phase properties

Liquid phase properties

Additional criteria Settling, cake washing/deliquoring, magnetic, flotation, electrofiltration Integration into the flowsheet, use of additives, reliability, space, product value, cost Chemical composition, size distribution, particle shape/strength, solubility, toxicity, reactivity, sterility, abrasivity, surface properties, value Chemical composition, temperature, pH/ionic strength, viscosity, toxicity, volatility, flammability, sterility, surface tension, value

the type of separator in the selected list. For example, if the initial selection has not uncovered magnetic separations as potentially suitable, then there is no point in attempting to carry out the magnetic tests shown in Table 5.8. It is likely that some form of filter will be on the initial shortlist, and further filter leaf tests will be necessary. Whether these are pressure leaf or vacuum leaf tests depends on the filter type(s) on the selected list, but in either case it may be prudent to consider the need for flocculants at this stage. The effects of pressure will need to be evaluated for pressure filter applications. Carrying out the appropriate tests in Table 5.8 will provide more information about the slurry and/or eliminate some equipment from the initial shortlist. Many other facets of the process and the materials being separated may need to be taken into account during refinement of the selected equipment list. Table 5.9 is an aide-mémoire that details aspects of the process to be considered at this stage. Not all will be relevant during any one selection procedure, but against each aspect is a comment which may have relevance to the final choice of equipment. Also, it is essential to take more account of the properties of the solids and liquids to be handled during the separation; these are listed in Tables 5.10 and 5.11. The properties of the slurry are also important, but any particular property will normally be dominated by the corresponding property of one of the phases to be separated. Many properties of the slurry (e.g. solids concentration in the slurry, filtrate fluxes, settling and filtration rates, slurry flow characteristics, particle size distribution and their state of aggregation in the slurry and pH value) will have been ascertained in a well designed experimental programme. It is also important to perform some kind of sensitivity analysis to assess the likelihood and extent of variations in flow rate and solids content of the feed slurry, the particle size distribution in the feed and

248 Solid/Liquid Separation: Equipment Selection and Process Design Table 5.8 Further tests to be performed on a suspension. (Preliminary selection has identified a range of equipment types which are likely to be suitable. Further tests need to be performed only for those equipment types identified in the preliminary list.)

Process

Nature of test

Settling

Centrifugal: Using a laboratory centrifuge with an acceleration of about 1000 g, and various spinning times, determine the consistency of the settled solids (firm paste, flowable, etc.) and the time taken for the solids to settle and the supernatant liquid to clear. These tests are helpful, but not necessarily essential.

Filtration posttreatment

Cake washing: If washing is envisaged a preliminary indication of the likely ease of washing is required at this stage. Feed wash liquid to the cake, measure solute concentration in the washings as a function of the washing time. A total volume of wash equal to the volume of formed cake usually provides adequate data for this stage in the selection. Cake dewatering (dried in situ): Suck or blow air through the cake for various times, and measure the moisture content of the cake at these times.

Magnetic

Immerse a hand magnet (~ 0.2 T) protected by a plastic bag in a beaker of slurry and determine the mass of (ferromagnetic) solids that collects at the poles of the magnet. The amount of paramagnetic material in a slurry can be measured only with more specialised equipment generating ~1 T.

Flotation

Used to recover small amounts of suspended solids, and requires particles to be hydrophobic so that they attach to air bubbles. Hydrophobicity can be conferred by use of chemical additives in the suspension. ‘Natural’ hydrophobicity can be determined by bubbling fine air bubbles through about 1 litre of suspension; any hydrophobic particles should float.

Electrofiltration Requires the particles to be small and charged; a measure of the zeta potential is helpful. Assessing the potential of electrical assistance is relatively difficult and requires specialist apparatus.

temperature. These can have a marked effect on equipment performance, are greatly influenced by process operations upstream of the separator and may have a profound influence on the economics of both the separator choice and the overall process. Careful consideration of the above factors should lead to the elimination of further equipment from the initial shortlist and identify those separators

5 · Selection, data analysis and simulation by computer software 249 worthy of pilot scale testing and/or detailed computer simulation. However, there is a further category of information which may be useful at this point on the basis of the accumulated experience of equipment users and suppliers. Much of this type of information exists as proprietary knowledge owned by equipment suppliers and users, and clearly only that data in the public domain Table 5.9 Process requirements to be considered during equipment/process selection. Property

Comment

Scale of operation

Total slurry volume to be separated affects equipment choice. For large volumes, either large scale equipment or greater numbers of smaller units are needed. This is particularly true when the feed solids concentration is low, giving large liquid volumes to be handled. It may be necessary to consider a staged separation to concentrate the solids to an intermediate level before a complete separation is attempted (e.g. use a thickener to preconcentrate the feed to a vacuum filter).

Required phase

Reason for separation is to remove the solid from the liquid phase. Either or both phases may be the desired product (in the case of many waste treatment processes neither are necessarily ‘wanted’ products). Identification of uses for either ‘product’ of the separation can affect economics and the need for subsequent treatment.

Solid product

This may come from the separator as either a cake or as a slurry. Downstream processes or uses may decide the best solids product moisture content (e.g. only a narrow range may be permissible if the solids are to be briquetted). It is possible for solids product size distributions to differ from feed distributions.

Liquid product

The solids content and/or the degree of saturation by soluble impurities are important properties of the liquid product. It is preferable for liquids not to be close to saturation.

Washed solids

Cake washing may be needed to improve the purity of the solids product, or to increase the recovery of the liquid phase. Solids product purity may be improved by reslurry washing when the wash time is constrained unduly by the equipment design (e.g. this may occur with rotary drum filters). Reslurrying involves additional equipment for re-suspending the cake solids and re-filtering. Washing may have a great effect on process economics, such as when the wash liquor is a solvent that must be regenerated. continued

250 Solid/Liquid Separation: Equipment Selection and Process Design Table 5.9 continued Property

Comment

Dewatered solids

See solid product above.

Process integration

With downstream processes: Downstream processes often put a requirement on some of the solids properties (e.g. moisture content, continuity of solids production). Very dry cakes can lead to solids handling difficulties. With upstream processes: Upstream processes determine if the separator needs to be operated in a batch or continuous mode, or if it will have to handle a range of products. The type of process used to form the particles (e.g. reactor, crystalliser etc.) will often control the size distribution of the solids, which in turn has a marked effect on separation rates With ancillary equipment: Pumps, instruments, feed and effluent tanks need to be specified. Pump type has an effect on filtration rates and filter sizing; use of the incorrect type may cause solids product degradation.

Use of additives

pH reagents and coagulants: pH reagents used for acidity or alkalinity control. Both types of chemical additive may affect the state of dispersion (i.e. aggregation) of the particles. Flocculants: Generally polymers used to aggregate fine particles to improve their settling and/or filtration rates. Filter aids: Used as a precoat to prevent blinding of filter media, or as body aid to add bulk to a feed and to produce a more permeable filter cake. Only useful when the solid is not a desired product. In cases where the solid is the product, separation of the filter aid is usually required after filtration Surfactants: Have some use to assist dewatering of the filter cake by lowering the surface tension of the liquid and/or changing the contact angle (wettability) on the solid.

Equipment reliability

Experiences of operating equipment for the separation of similar slurries are helpful here. Users of a large range of equipment types should build up a reliability data bank.

Space availability

New equipment may need to fit into an existing plant. Need to consider headroom and floor area, together with feed and discharge port elevation/orientation.

Product value

See entries in Tables 5.10 and 5.11.

Special requirements

See toxicity, volatility and flammability in Tables 5.10 and 5.11.

5 · Selection, data analysis and simulation by computer software 251 Table 5.10 Properties of the solid phase to be considered during equipment/process selection. Property

Comment

Chemical composition

The chemistry of the system should be known so that possible reactions due to changes of pH, solvent, temperature or pressure may be anticipated. This requires identification of the solids present, which may not always be possible.

Solids concentration

Best operation of most separator types is obtained for a limited range of solids concentration in the feed slurry. If solids recovery is required from a low concentration feed, staged separation should be considered. This often involves pre-concentration before filtration and does not necessarily imply the use of similar types of separator at each stage.

Size distribution

Size and size distribution of the particles should be determined - these have a marked effect on sedimentation and filtration properties. Many separators operate most effectively over a limited size range.

Density

The density difference between the particles and the liquid controls sedimentation (or flotation) rates. Small differences may make some centrifugal techniques unsuccessful. Porous particles tend to have a lower density.

Particle shape

Shape affects particle packing density and specific surface, which has a marked effect on pressure rise in constant rate filtrations (or filtrate flux decline in constant pressure processes). Needle shaped particles lead to lower pressure losses than equiaxed particles. Platelet shaped particles can be difficult to wash and dewater.

Particle strength

Zones of high shear in equipment (e.g. centrifuges) will fracture brittle particles, leading to a broadening of the particle size distribution and (generally) a reduction in cake porosity.

Solubility

Filtration from saturated (or near saturated) solutions can cause nucleation and crystal formation in filter media, and hence blocking in the media or feed pipework. During washing, the solubility of the particles in the wash liquor must be taken into account to avoid excess losses.

Toxicity

Closed equipment is desirable for handling toxic systems to avoid creating a health hazard. Manual handling of separation products should be avoided wherever possible. continued

252 Solid/Liquid Separation: Equipment Selection and Process Design Table 5.10 continued Property

Comment

Chemical reactivity

Reactive substances may be explosive or flammable and require the selection of completely enclosed equipment. Special seals, flameproof motors and appropriate switchgear are needed. Cake dewatering may need to be done using gases other than air, and nitrogen purging of equipment may be needed prior to discharging products. (After nitrogen purging, care must be taken to avoid air (oxygen) condensation on equipment and products, together with sources of ignition).

Sterility

Ingress of contaminants should be avoided and may require fully enclosed separator designs. Contamination prevention of product(s) during and after discharge also requires special consideration.

Abrasivity

Abrasive solids cause rapid wear of equipment when its design causes high velocities and/or rapid changes of direction of the solids flow (e.g. as in the entry zones of scroll and decanter centrifuges). Materials selection then becomes of greater importance.

Magnetic properties

The response of the solids to magnetic fields may enable selection of magnetic separators. Ferromagnetic substances respond to fairly weak fields (~0.2 T) such as those generated from permanent magnets. Paramagnetic and diamagnetic substances respond only to high intensity fields (1 T).

Surface properties

Surface charge affects the state of dispersion of the particles and is pH dependent. Close to the iso-electric point, aggregation tends to occur. Surface charge determines adsorption of flocculants and dispersants. Surface hydrophobicity/philicity can be modified to make particles respond to flotation.

Value

The product value, combined with the scale of operation, has a bearing on equipment selection. If the solid is the desired product, addition of filter aids may not be allowable.

5 · Selection, data analysis and simulation by computer software 253 Table 5.11 Properties of the liquid phase to be considered during equipment/process selection. Property

Comment

Chemical composition

Chemical composition of the liquid phase affects separability of the particles. Electrical conductivity may determine suitability of electrically assisted separation processes. Paramagnetism may prevent use of high intensity magnetic separation methods.

Density

See Table 5.10.

Temperature

Temperature affects liquid viscosity, effectiveness of flocculants, dewaterability and may influence materials of construction.

pH/ionic strength

Affects extent of aggregation and choice of flocculants and dispersants by altering electrical charge on the particle surfaces. Plays an important role in determining corrosivity of liquid, which in turn affects choice of materials of construction.

Viscosity

Controls rate of sedimentation/filtration. Higher rates are obtained at lower viscosities, which may be achieved by elevating the temperature. See Table 5.10.

Toxicity Volatility

Containment of volatile liquids by fully enclosed equipment is essential, particularly if toxic or flammable dangers are associated with the vapours. Variation of the vapour pressure of the liquid with temperature and pressure is important, especially with vacuum filtration equipment. Vapour formation in or just downstream of the filter medium or in vacuum lines and pumps should be avoided.

Flammability

Containment of flammable vapours by enclosed equipment is essential. Hoods may be suitable under some circumstances.

Sterility

See Table 5.10.

Surface tension

Combined with the particle/liquid contact angle, controls the moisture content of dewatered filter cakes.

Value

See Table 5.10. The greater the value of the liquid, the more important it may be to prevent losses. If the liquid is the desired product, the addition of solute additives (e.g. flocculants) may not be permitted.

254 Solid/Liquid Separation: Equipment Selection and Process Design can be accessed. Purchas (1981) and Pierson (1990) provide coverage of a wide range of separations equipment, with particularly useful information provided by Purchas. Applications details of centrifuges (Moyers, 1966; Ambler, 1971, 1988; Day, 1974), hydrocyclones (Svarovsky, 1984), classifiers (Hawkes, 1970), gravity filters (Pierson, 1970), pressure filters (Emmett and Silverblatt, 1974), filters with compression (Blagden, 1975), vacuum filters (Blagden, 1975; Dahlstrom, 1978a,b; Moos and Dugger, 1979), crossflow filters (Porter, 1990) and magnetic separators (Birss and Parker, 1981; Watson, 1990) are also available in the public literature. Various other classifications of separation techniques exist and provide further worthwhile references, these include Tiller (1974), Alt (1975, 1985), Fitch (1977), KirkOthmer (1980), Komline (1980), Perry and Green (1984), Purchas and Wakeman (1986), Matteson and Orr (1987), Svarovsky (1990), Wills (1992), Rushton et al (1996), Schweitzer (1997) and Dickenson (1997).

5.6 Conclusions This chapter has outlined how the non-expert can make rational decisions about equipment selection without the need to consult an expert in the earlier stages of solving the problem. Such an ability is important in solid/liquid separation, not least because the expert is often a representative of an equipment manufacturing company whose job is to sell a particular type of separator! Taking filters as an example, many types are usually capable of carrying out a particular filtration, but probably only a few types will be most suited to the task. It is wise to have an insight into which these are before consulting an expert. The engineer is in a position to ask more penetrating questions of whichever expert may be consulted, and reduces expenditure on unwarranted pilot scale test work too early in the selection process. The principal features of the FDS have also been shown. The integrated modules comprising the software, which can also be used in isolation, enable:

•

An automated selection procedure that facilitates ranked listing and access to on-line equipment and process information from a knowledge of the required duty and basic experimental data

•

The consistent analysis of filtration, expression and jar sedimentation tests to allow the accurate determination of the parameters required for process simulation and the basic information needed for equipment selection

•

The detailed simulation of process scale batch and continuous filters involving combinations of filtration, consolidation, washing and deliquoring.

5 · Selection, data analysis and simulation by computer software 255 By use of computer software a number of benefits arise, including:

•

The ability to investigate new plant and ask ‘what-if’ questions about filter installations to facilitate optimum equipment selection(s), filter sizing, cycle configuration(s) and filter operation

•

The ability to troubleshoot existing filter installations and identify potential solutions

•

Consistent experiment analysis to give characterisation and scale-up parameters

•

Unbiased information on solid/liquid separation equipment so that appropriate manufacturers can be approached in the early stages of equipment selection

•

The ability to educate and train a user in solid/liquid separation technology.

6

Process design for batch separations

In this chapter the equations and models previously described in detail (Wakeman and Tarleton, 2005a) are summarised and brought together so that the various phases in a batch filter cycle can be related to one another and meaningful process engineering models obtained. These models facilitate sequential calculations to provide the basis for computer simulations. Whilst there is scope to predict the performance of most of the filter types described in Chapter 1, those shown in Table 6.1 are presented in sufficient detail to model their filter cycles. Section 6.1 describes the principal features of filter cycles in relation to common batch filters while Sections 6.2 and 6.3 present the equations required to

Table 6.1 Batch filters and presses and potential phases in their operational cycles. Filter/press type Single leaf (Nutsche) filter – pressure and vacuum Multi-element filter – horizontal and vertical leaf, candle Filter press – plate and frame, and recessed plate Horizontal diaphragm filter press Tube press Vertical diaphragm filter press – single and double-sided

Compression deliquoring

Y Y Y

All feature an initial cake formation (filtration) phase(s).

Washing

Gas deliquoring

Y

Y

Y

Y

Y

Y

Y Y Y

Y Y

6 · Process design for batch separations 257 model each phase. An outline procedure for batch centrifuge cycles is also shown. Section 6.4 provides detailed example calculations for the diaphragm filter press and the Nutsche pressure filter as these are representative of typical batch cycles. Section 6.5 shows how computer simulations can be used to examine the effects of changed process variables on batch filter performance. Appendix A provides additional information on the acceptable ranges for operational parameters in batch filters while Appendix D outlines the process for troubleshooting their operation.

6.1 Batch filter cycle configurations Depending on the type and mode of operation of a batch filter, a cycle may comprise up to two filtration phases followed by a number of compression, gas deliquoring and washing phases, essentially in any order, as well as a cake discharge operation (see also Tarleton and Hancock, 1997;, Tarleton and Wakeman, 1994c, 2005b; Wakeman and Tarleton, 1994a,b, 1999). 6.1.1 Nutsche filters Vacuum and pressure Nutsche filters are similar in many aspects of the filter cycle and a typical example of the latter is shown schematically in Figure 6.1 (see also Sections 1.4.1.1 and 1.4.2.1). In both variants a single leaf forms part of a fully enclosed cylindrical vessel. An imposed constant pressure gradient across the leaf/medium induces combinations of cake formation, deliquoring and washing to meet process requirements. Cake discharge is by a mechanical plough, reslurrying or, in some smaller units, by separation of the filter base. 6.1.2 Multi-element vacuum filter The multi-element vacuum filter is characterised by the Moore’s filter (see Section 1.4.1.2 for a schematic of the filter cycle). These filters, which can also be considered semi-continuous, comprise series of double-sided vertical leaves that are mechanically dipped into an open-top tank of suspension. Vacuum is applied to draw liquor into the rectangular filter leaves leaving cakes forming on each of the exposed cloth surfaces. If necessary the leaves and cakes can be immersed into a second tank containing clean wash liquor. Discharge is achieved by positioning the filter leaves above a third tank and applying a filtrate backflow to dislodge the cakes. 6.1.3 Multi-element leaf and candle pressure filters Multi-element pressure filters usually comprise a cylindrical vessel inside which a number of horizontal or vertical porous elements covered by filter

258 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 6.1 Schematic diagram of a simple pressure Nutsche filter cycle. (a) Filtration; (b) displacement washing; (c) gas deliquoring; (d) cake discharge by plough. cloths are placed (see also Section 1.4.2.2). Either flat elements, in the form of square, circular or rectangular leaves, or tubular candles are used and these are spaced sufficiently far apart to avoid the possibility of cakes touching on adjacent elements. During a typical cycle the feed suspension is pumped into the vessel to induce variable pressure filtration and thus cake formation on the outer surfaces of the cloths (see Figure 6.2). In filters with horizontal elements, cake formation is restricted to the upper surfaces of leaves only. Washing and gas deliquoring phases at constant pressure often

6 · Process design for batch separations 259

Figure 6.2 Schematic diagram of a multielement, horizontal leaf filter cycle. (a) Filtration; (b) displacement washing; (c) gas deliquoring; (d) preparation for cake discharge by element removal.

occur in a cycle and these operations are readily arranged in all filter variants. Filter leaves can be automatically extracted for cake discharge if adequate floor/height provisions are made. When more frequent cake discharge is required, solids are generally removed with the filter leaves in situ either by vibration, rotating blades, centrifugal force (horizontal elements only) or liquid resluicing to give a wet discharge. It is noted that cake formation in a

260 Solid/Liquid Separation: Equipment Selection and Process Design filter fitted with candles can take place either at variable pressure, in a manner similar to the multi-element leaf filter, or at constant pressure. 6.1.4 Horizontal diaphragm, plate and frame, and recessed plate presses The typical sequence of operations in horizontal diaphragm and filter presses is shown schematically in Figure 6.3 (see also Sections 1.4.2.5 and 1.4.2.3). Suspension is fed into the chambers of the press, with either a positive displacement or centrifugal pump to initiate respectively constant rate/variable pressure or variable rate/variable pressure filtration. Cakes are usually formed simultaneously on the two opposing sides of each chamber. In plate

Figure 6.3 Schematic diagram of the horizontal diaphragm press cycle (side view of one chamber shown and cake discharge omitted). (a) Filtration via pump; (b) filtration via diaphragm; (c) compression deliquoring; (d) displacement washing; (e) gas deliquoring. Plate and frame and recessed plate press cycles are similar but the filtration phase using the diaphragm (b) and the compression deliquoring phase (c) are omitted.

6 · Process design for batch separations 261 and frame and recessed plate presses this filtration typically continues until the growing cakes meet near the middle of a chamber; if the maximum available pressure is reached before the cakes meet then filtration can be completed via the pumping action at constant pressure. With a horizontal diaphragm press the variable pressure filtration phase is sometimes stopped before the cakes meet, typically when 80% of the total volume of filtrate has been produced, and filtration then continues at constant pressure via flexible diaphragms to convert the remaining suspension to cakes. This secondary filtration proceeds through only one of the filter surfaces in each chamber. When sufficient diaphragm movement has occurred, constant pressure compression deliquoring (consolidation) begins to reduce the moisture content of the cakes. A typical filter cycle is completed by a combination of gas deliquoring and/or displacement washing operations prior to press opening and sequential cake discharge. 6.1.5 Vertical diaphragm presses In its most common form the vertical diaphragm press comprises a continuous cloth that zigzags through a hydraulically closed horizontal plate pack to form a sequence of chambers (see also Section 1.4.2.5). A typical cycle comprises variable pressure cake filtration via a pump followed by constant pressure cake compression with elastomeric diaphragms, displacement washing and gas-blown deliquoring (Figure 6.4). When pumping is stopped before each chamber is completely filled with cake, an additional constant pressure filtration using the diaphragms takes place to filter any remaining suspension. The cycle is completed when the plate pack opens and the cloth translates to discharge cake from each chamber. In some vertical diaphragm presses there are two filtering surfaces within each chamber on which cake formations take place; these are termed ‘double sided’ for the purpose of descriptions here. It is noted that in Chapter 1 the vertical diaphragm press is classified as a continuous filter for the purpose of equipment selection. Due to the nature of its operation, however, such a press could be considered to fall somewhere between the batch and continuous modes of operation. For the purposes of modelling and simulation the vertical diaphragm press is considered a batch filter as the equations and procedures for modelling are more appropriately formulated. 6.1.6 Tube press The typical cycle of operations available in a vertical tube press is illustrated in Figure 6.5 (see also Section 1.4.2.5). The press comprises an inner perforated

262 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 6.4 Schematic diagram of the single sided, vertical diaphragm press cycle (end view of one chamber shown and cake discharge omitted). (a) Filtration via pump and/or diaphragm; (b) compression deliquoring; (c) displacement washing; (d) gas deliquoring.

6 · Process design for batch separations 263

Figure 6.5 Schematic diagram of a tube press cycle. (a) Filling of press using pump; (b) filtration via diaphragm; (c) displacement washing; (d) cake discharge with element withdrawn.

tube on which the filter medium is fitted and a larger diameter solid tube that is lined with an inflatable and imperforate elastomeric diaphragm. The annular space in the press is initially filled with suspension and constant pressure filtration then proceeds on the tubular filter element via the hydraulically inflated diaphragm. When filtration is complete the diaphragm can be used to deliquor

264 Solid/Liquid Separation: Equipment Selection and Process Design the cake via mechanical compression. Following this consolidation the diaphragm is relaxed to allow for a displacement washing phase. Cake discharge occurs by opening the bottom of the press and applying a reverse pulse of compressed gas inside the cylindrical filter element to release the cake.

6.2 Design equations for batch filter cycles As described in Section 6.1, the cycle for a batch filter can comprise one or more cake formation phases followed by any sequential combination of consolidation, displacement washing and gas deliquoring phases. While a complex batch cycle may involve the list of operations shown in Table 6.2, a more typical cycle can be represented by  t t t t  tT
t f  tc  t w  t d  t dn
t f  1 c  w  d  dn  tf tf tf tf  

(6.1)

where the subscripts f, c, d and w are used to respectively indicate values during the filtration, consolidation, deliquoring and washing phases of a cycle of total duration tT; the term tdn denotes filter downtime, for cake discharge and Table 6.2 Potential operations in a relatively complex batch filter cycle with single washing and deliquoring phases (adapted from Purchas and Wakeman, 1986).

Stage 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Operation Fill vessel with precoat slurry Establish precoat on filtration surface(s) Recirculate precoat filtrate Drain precoat heel Fill with filter feed liquor Recirculate filtrate Filtration (cake formation) Drain any unfiltered heel Fill with wash liquor Wash filter cake Drain wash liquor Deliquor filter cake Discharge filter cake Rinse filter surface(s) and drain vessel

Approximate time 1 min 2–5 min As required 1 min 1 min As required Up to 10 h 1 min 1 min Up to 1 h 1 min 5–30 min 2–10 min 2 min

6 · Process design for batch separations 265 cloth cleaning, which is largely ignored for the purpose of calculations (although Section 6.2.5 shows how it can be incorporated in determinations of optimum filtration time). Each phase of the cycle can theoretically continue until the desired cake properties have been achieved or the economics of the operation dictate that a particular phase must end. More phases can be accommodated in a cycle by simple additions to equation (6.1). When terms on the right hand side of equation (6.1) are known, the equation can be used to indicate whether an existing filter has sufficient capacity for the given process requirements. In the descriptions that follow this scenario is assumed such that the physical dimensions of a separator are known a priori which allows the total filter medium area (AT) to be defined. Should filter sizing be required instead then the equations developed below for cake formation can be rearranged to allow the calculation of filter area for a given solids loading; in more complex cases a numerical/iterative solution is required. This procedure defines the filter dimensions and calculations for subsequent deliquoring or washing phases are identical to those shown. A particle size (x) representative of that in a feed can be calculated if necessary according to the Kozeny–Carman equation:

x
13.4

1
av  av  s
3av

(6.2)

where
av is the average cake porosity, av the average specific cake resistance and s the density of solids. It is noted that Cav
1
av where Cav is the average volume fraction of solids in the cake (sometimes termed solidosity). In the remaining part of Section 6.2 methodologies are detailed that allow data sequences, representative of all points through a filter cycle, to be produced. 6.2.1 Filtration (cake formation) phase Process design calculations for filtration are based on the general filtration equation which is usually stated as dV f dt f




A2f  p f  l ( av cV f  A f R )

(6.3)

where Vf is the cumulative volume of filtrate, Af the filter medium area devoted to filtration, pf the filtration pressure, l the viscosity of liquid,

266 Solid/Liquid Separation: Equipment Selection and Process Design c the effective feed concentration and R the medium resistance (Tarleton, 1998b; Tarleton and Wakeman, 1994c, 2005b; Wakeman and Tarleton, 1994a,b). The cake properties are related to the filtration pressure according to  av
 0 (1 n)  p fn

(6.4)

Cav
C0  p f

(6.5)

mav
1

c


l  1 Cav   s  Cav 

sl 1 mav s

(6.6)

(6.7)

where l is the density of liquid, mav the ratio of mass wet/dry cake, s the mass fraction of solids in the feed and 0, n, C0 and  are empirical scale-up constants derived from sequences of constant pressure or vacuum experiments (see Chapter 4). In equations (6.4) and (6.5) it is implicitly assumed that for practical purposes the pressure drop across the cake can be approximated by the filtration pressure. The scale-up constants are also assumed to be valid for variable rate filtrations. The cake thickness (Lf ) is related to the cumulative volume of filtrate and the cake properties through a mass balance:

Lf


V f s[ s (mav 1)  l ]  s (1 mav s) Af

(6.8)

6.2.1.1 Nutsche and multi-element vacuum filters In all variants of these filters, Af
AT, and the filtration pressure or vacuum is fixed such that av, Cav, mav and c remain constant throughout cake formation as given by equations (6.4)–(6.7). As cake growth is generally not restricted by space, a specified mass of cake solids (Ms ) up to the required amount (Ms )e is chosen to facilitate the calculation of all intermediate

6 · Process design for batch separations 267 values that are a function of filtration time. Integrating equation (6.3) with gives pf
constant gives t f  ti




V f  Vi

 av c l l R K (V f  Vi ) 
1 (V f  Vi )  K 2 2 2 Af  p f 2 Af  p f

(6.9)

where ti and Vi are respectively the time and volume at which filtration commences and K1 and K2 are regarded as constants. When ti
Vi
0, which is usually assumed to be the case in a process scale filter, the cake thickness (Lf), filtrate volume, cake formation time and filtrate flow rate (q) are given by

Lf


M s [ s (mav 1)  l ] l  s A f

Vf
L f

tf


q


A f  s (1 mav s) s[ s (mav 1)  l ]

 av c l R K V f
1 V f2  K 2V f V f2  l 2 2 A f p f 2 A f p f

dV f dt f

(6.10)

⬇

V f t f

(6.11)

(6.12)

(6.13)

For a given Ms, the mass of cake liquid (Ml), mass of cake solute (Msol) and cake moisture content (M) are respectively given by Ml
A f L f
av l

(6.14)

M sol
A f L f
av 0

(6.15)

Ml Ml  M s

(6.16)

M
100

where
0 is the solute concentration in the feed.

268 Solid/Liquid Separation: Equipment Selection and Process Design 6.2.1.2 Filter and diaphragm presses and multi-element leaf pressure filters Noting that Af
AT in all variants, pressure generally varies throughout cake formation according to a pump curve, i.e. pf vs. q relationship. Substituting q
dVf /dtf into equation (6.3) and rearranging gives an expression for the volume of filtrate

Vf


 p f  Af   l R   av  l c  q  Af

(6.17)

Using equation (6.17), cake formation starts when Vf
0 to give  p f  l R  q 
A f t
0

(6.18)

and ends when the required thickness of cake (Lf)e has formed on each filtration surface which corresponds to a point further along the pump curve, i.e. (pf /q)t
(tf )e , as shown in Figure 6.6. A choice of pf /q values between these two extremes is used to provide intermediate values for the other parameters that are a function of filtration time. Cake thickness is restricted on all presses by either the available chamber space or a fraction of this

Figure 6.6 Representation of a centrifugal pump curve. Point (1) corresponds to the start of filtration and denotes the point where the filter medium resistance is overcome such that equation (6.18) is satisfied. Point (2) represents a point close to the maximum pressure at which variable pressure filtration could occur; any further filtration with the pump would generally be performed at constant pressure.

6 · Process design for batch separations 269 space if cake does not entirely fill the chambers during filtration with the pump. In multi-element pressure filters, cake formation is limited by the inter-element spacing, although in most cases the required mass of solids will limit the extent of cake formation and prevent touching cakes. During cake formation with the pump all parameters are generally time variant such that av, Cav, mav and c change throughout filtration to an extent dictated by equations (6.4)–(6.7) where the pressure is specified by the chosen position on the pump curve. Combining equations (6.8) and (6.17) gives  p f  s[ s (mav 1)  l ] A f   l R q   Lf
 av  l c s (1 mav s)

(6.19)

which allows Lf to be evaluated at the known pf /q. The filtration time is Vf

obtained from tf
 (1/q)dVf which can be approximated using trapezium rule integration by Vf

tf ⬇ ∑ 0

0

(V f )i  (V f )i1  1 1     2  q i q i1 

(6.20)

The mass of solids on the filter medium is given by a mass balance where M s
A f L f Cav  s

(6.21)

The corresponding mass of cake liquid (Ml), mass of cake solute (Msol ) and cake moisture content (M) are given by equations (6.14)–(6.16). At the end of cake formation with the pump the two cakes in each individual half chamber of a recessed plate and a plate and frame filter press join to form a single cake. With the horizontal and vertical, double sided diaphragm presses single cakes also form when each chamber of the press is entirely filled with cake using the pump. In these diaphragm presses and the vertical, single sided press, however, constant pressure filtration may follow the variable pressure filtration period. When the chambers are not completely filled by cake and some unfiltered suspension remains, additional cake formation

270 Solid/Liquid Separation: Equipment Selection and Process Design takes place by either diaphragm inflation or pressure limited pumping. In either case the pressure is fixed and av, Cav, mav and c remain constant throughout the remainder of filtration. For the purpose of process calculations it can be assumed that: •

Existing cake instantaneously assumes the properties associated with the fixed filtration pressure (pf ) as given by equations (6.4)–(6.7), but the thickness of this cake remains unchanged. New cake forms at the pressure pf .

•

The additional cake formation in the horizontal press normally takes place through one side of each chamber only (i.e. Ac
Af /2). Within a chamber one cake grows in thickness while the other maintains its existing thickness. For the vertical, double sided press cake formation proceeds as previously on both sides of each chamber. With the vertical, single sided press cake formation continues as before on one side of each chamber only. In both cases, Ac
Af .

An additional cake thickness (L) up to the maximum formed by filtering all the remaining suspension, i.e. Le, is chosen in order to calculate a sequence of intermediate values. Denoting the cake height at the end of cake formation with the pump as Lpr gives L f
L pr  L

(6.22)

where for the horizontal diaphragm press Lpr represents the total cake thickness per chamber. Using equations (6.8) and (6.9) V f
Vpr 

 s (1 mav s) Ac  L s[ s (mav 1)  l ]

(6.23)

  c t f
t pr  (V f  Vpr )  av2 l (V f  Vpr )   2 Ac  p f   l   av cVpr  R   Ac  p f  Ac  

(6.24)

where the additional terms in equation (6.24) account for filtration through existing cake. The filtrate flow rate at all times is given by equation (6.13)

6 · Process design for batch separations 271 and the cake moisture by equation (6.16). For both variants of the vertical press the masses of cake solids, liquid and solute are given by equations (6.21), (6.14) and (6.15), respectively. For the horizontal diaphragm press

M s
Ac ( L pr   L ) Cav  s

(6.25)

Ml
Ac ( L pr   L )
av l

(6.26)

M sol
Ac ( L pr   L )
av 0

(6.27)

When any remaining suspension is filtered the two cakes in each chamber of the horizontal and vertical, double sided diaphragm presses join to form single cakes that dictate performance in subsequent phases. For the horizontal press the ultimate cake height becomes Lpr  Le while in the vertical, double sided press this height equals 2Lf . 6.2.1.3 Tube press Noting that Af
dh, where d is the filter element diameter and h the element length, the pressure imposed by the diaphragm is fixed and av, Cav, mav and c remain constant throughout filtration as given by equations (6.4)–(6.7). Cake formation is restricted by the extent of the annular space in the press and a specified volume of filtrate (Vf) up to a maximum (Vf)e is used to provide intermediate values for the parameters that are a function of time. From a modified version of equation (6.9) that accounts for the presence of the curved filter element   c l R t f
V f  av2 l V f  Af  p f  2 A f  p f 

 l R 4c   av c l 2 V  V f f  d c A f  3 A2f  p f 2 Af  p f  

K 4 c  K1 2 K 2  
Vf  1 Vf  K2   V f  V f   d c A f  3 2  2 

(6.28)

272 Solid/Liquid Separation: Equipment Selection and Process Design where c is the bulk density of the filter cake and K1 and K2 are regarded as constants. The cake thickness and the masses of solids, liquid and solute in the cake are respectively given by  4cV f d L f
 1 1 2 d c A f 

(6.29)

M s
0.25Cav  s h (d  2 L f )2  d 2 

(6.30)

Ml
0.25
av l h (d  2 L f )2  d 2 

(6.31)

M sol
0.25
av 0 h (d  2 L f )2  d 2 

(6.32)

The filtrate flow rate and cake moisture content are given by equations (6.13) and (6.16). 6.2.1.4 Multi-element candle filter If filtration takes place at constant pressure then the equations presented for the tube press in Section 6.2.1.3 are also valid for the multi-element candle filter noting that Af
ntdh where nt is the total number of candles in the filter. When filtration takes place at variable pressure then it is necessary to impose the pump curve characteristics to relate pf and q and a numerical solution to equation (6.17) is generally required. For the special case of variable pressure/constant rate filtration with a positive displacement pump

tf


 d c A f   4 A f p f  1 exp   4cq   d c q l  av  

(6.32a)

If the maximum pumping pressure is reached before cake formation is complete then constant pressure filtration occurs when tf  (tf)tr. Over this constant pressure period cake formation continues according to the general

6 · Process design for batch separations 273 form of equation (6.28), but due account is made for the existence of cake on the filtering element(s): K 
 1 V f  (V f )tr   K 2  V f  (V f )tr  2  t f  (t f )tr



4c d c ( A f )tr

 K1 2 2  V f  V f (V f )tr  (V f )tr  3  (6.33)

K   2 V f  (V f )tr   2 

where (tf)tr and (Vf)tr are respectively the time and volume at the transition from variable to constant pressure filtration, (Af)tr
nth(d  2(Lf)tr), avc(V f)tr avc1 1  R K1
 )tr . (Af Af2pf and K2
 Af pf

冢

冣

6.2.2 Compression deliquoring In the tube press and all variants of the diaphragm press, elastomeric diaphragms can be inflated at a constant pressure to facilitate compression deliquoring of the filter cake(s). This consolidation is most frequently performed immediately following cake formation to remove unwanted liquors and/or improve the distribution of cake solids to aid subsequent cake washing and/or gas deliquoring. In a typical press the duration of cake compression equals the total filtration time such that (tc)e
(tf)e. Noting that the mass of solids in the cake remains constant, i.e. Ms
(Ms)pr where the subscript ‘pr’ indicates the value at the end of the previous phase in the cycle, the cake properties during compression deliquoring are related to the compression pressure (pc) by Ce
Ce 0  pc

(6.34)

(Cav )
C0  pc

(6.35)

where Ce is the modified consolidation coefficient, (Cav) is the equilibrium cake solids volume fraction at infinite consolidation time and Ce0, , C0 and  are empirical scale-up constants derived from sequences of constant pressure

274 Solid/Liquid Separation: Equipment Selection and Process Design consolidation experiments (see Chapter 4). Process design calculations for compression deliquoring are based on the theories of Shirato et al (1970, 1971, 1986, 1987) where the cake thickness (Lc ) is related to a dimensionless consolidation time (Tc ) by

Lc
L pr  ( L pr  L )

Tc


4( jII )2 Tc  1 2

2   2   j T 4( ) c II 1         

i 2 Ce t c

20

L


Ms Ac  s (Cav )

(6.36)

(6.37)

(6.38)

where L  is the cake height at infinite consolidation time, jII the effective consolidation area factor that accounts for any filter element curvature, i the number of drainage surfaces per chamber, Ac the active filter area during consolidation and v is an empirical scale-up constant. The volume of solids per unit filter area, 0
Ms /(Acs). Values for i, Ac and jII vary according to the type of press: Horizontal press: i
1; Ac
Af /2; jII
1 Vertical, single-sided press: i
1; Ac
Af ; jII
1 Vertical, double-sided press: i
2; Ac
Af /2; jII
1 Tube press: i
1; Ac ⬇ h(d  Lpr); jII
0.703  0.297(d  2Lpr)/d where jII for the tube press is given by an empirical correlation. To use equations (6.36)–(6.38), a specified consolidation time (tc) up to the maximum (tc)e is chosen to provide intermediate values for parameters that are a function of time. tT
t pr  tc

(6.39)

6 · Process design for batch separations 275 Noting the value of Ac given above, in all variants of the diaphragm press the total volume of filtrate (VT) and mass of cake solute (Msol) are given by VT
Vpr  Vc
Vpr  Ac ( L pr  Lc )

M sol
Ac Lc c

M s M  s  l (100  M )

(6.40)

(6.41)

where c is the solute concentration in the cake liquors and M is the cake moisture content. Corresponding values for the tube press are VT
Vpr  Vc
Vpr  0.25h (d  2 L pr )2  (d  2 Lc )2 

M sol
0.25h c

M s (d  2 L f )2  d 2  M  s  l (100  M )

(6.42)

(6.43)

For all press variants the filtrate flow rate, mass of cake liquid and cake moisture content are represented by dVc Vc ⬇ dtc tc

(6.44)

Ml
( Ml ) pr  lVc

(6.45)

 M s (
av ) pr  100   Vc   (Cav ) pr  s  M
 100  M pr   M s (
av ) pr  M s (
av ) pr  M   (C )    (C )   Vc    av pr s  av pr s pr

(6.46)

Denoting Me as the cake moisture content at the end of compression deliquoring, the corresponding cake solids volume fraction and specific resistance are

276 Solid/Liquid Separation: Equipment Selection and Process Design obtained from application of the Kozeny–Carman equation which states that 3 avCav /
av

(Cav )e
1

Me s M e  s  (l ) pr (100  M e )

(6.47)

 (
av )3pr   (Cav )e  ( av )e
( av ) pr   3   (Cav ) pr   (
av )e 

(6.48)

6.2.3 Displacement washing Calculations for a washing phase are based on the dispersion model (Wakeman, 1986a; Wakeman and Attwood, 1988, 1990). The model requires the determination of a dispersion number (Dn) that characterises the washing process and use of a design chart (Figure 6.7), which allows the number of wash ratios (W) and fractional solute recovery (F) to be found. The pressure (pw) is fixed throughout washing and several properties of

Fraction of solute removed from the cake

1.0

1000

0.9

50

10 5

0.8

1

0.7

0.5

0.6 0.5 0.1

0.4 0.3 0.2

Dn=vL/DL=0.01

0.1 0.0 0.0

0.5

1.0

1.5

2.0 2.5 Wash ratio

3.0

3.5

4.0

Figure 6.7 The variation of the fraction of solute removed (F ) from a saturated filter cake with wash ratio (W) and dispersion number (Dn). For details see Wakeman and Tarleton (2005a).

6 · Process design for batch separations 277 the cake are assumed to remain constant and equal to the values at the end of the previous phase in the cycle, i.e. Lw
Lpr, av
(av)pr, Cav
(Cav)pr
1(
av)pr and Ms
(Ms)pr. In the dispersion model the superficial velocity (u) and pore velocity (v) of the wash liquor are related to the intrinsic properties of the cake by

u


 pw  w ( av  s LwCav  R )

(6.49)

v


u
av

(6.50)

where  w represents the viscosity of the wash liquor. For the solute, the ratio of the molecular diffusion coefficient (D) to the axial dispersion coefficient (DL ) is dependent on the product of the Reynolds (Re) and Schmidt (Sc) numbers as well as the cake thickness such that DL 1

0.707 D 2

ReSc 1

(6.51)

ReSc  1, Lw  10 cm

DL
0.707 1.75ReSc D

(6.52)

ReSc  1, Lw 10 cm

DL
0.707  55.5(ReSc)0.96 D

(6.53)

where ReSc
vx/D. Hence,

Dn
ReSc

Lw D x DL

(6.54)

In a batch filter the end of washing is normally specified in one of three ways, that is, the final fractional solute recovery (F e ), wash ratio (W e ) or washing time ((tw)e) and the sequence of calculations alters accordingly.

278 Solid/Liquid Separation: Equipment Selection and Process Design Known F e. Values of F up to the maximum F e are chosen to provide intermediate values in the calculated data sequence. The corresponding number of wash ratios (W) is determined from Figure 6.7 for a known F and Dn. The total cycle time (tT) in this case is given by

tT
t pr  t w
t pr 

WLw
av u

(6.55)

Known W e. Values of W up to the maximum W e are chosen to provide intermediate values for parameters that are a function of W and hence tw. The corresponding fractional recovery is determined from Figure 6.7 for a known and Dn. The total cycle time is again given by equation (6.55). Known (tw)e. Values of tw up to the maximum (tw)e are chosen to provide intermediate values in the cycle calculations such that tT
t pr  t w

W


ut w
av Lw

(6.56)

(6.57)

and fractional recovery is determined from Figure 6.7 for a known W and Dn. If the cake saturation (S) is less than 1 at the start of washing, for instance due to a previous gas deliquoring phase (see Section 6.2.4), then it is necessary to correct each chosen or calculated value of W according to Wcorr
WS
1 15.1(1 S )exp(1.56 * )  7.4(1 S 2 )exp(1.72 * )

(6.58)

where WS
1 represents the wash ratio for a saturated cake and * is the instantaneous concentration of solute at WS
1. For filter presses, the horizontal diaphragm press and the vertical, double-sided press the active filter area during washing Aw
Af /2. For the tube press it is assumed that Aw ⬇ h(dLpr) and similarly for the multi-element candle filter Aw ⬇ h(dLpr)nt. In all other batch filters and presses Aw
A f .

6 · Process design for batch separations 279 With tw, F and W known, the volume of washings (Vw), and hence the total volume filtrate/liquid volume, and wash liquor flow rate are given by VT
Vpr  Vw
Vpr  Aw ut w

(6.59)

dVw
uAw
constant dt w

(6.60)

and from a mass balance the amount of cake solute is

M sol


wVw 

V   ( M sol ) pr  w w  (1 F ) WS
1  WS
1 

(6.61)

where w is the solute concentration in the wash. The cake moisture (M) is calculated according to equation (6.16) where the mass of cake liquid (Ml) for the multi-element candle filter and tube press is given by

Ml
( Ml ) pr

w (l ) pr

(6.62)

and for all other batch filters Ml
Aw Lw  w
av

(6.63)

where w is the density of the wash liquid and (l )pr is the density of the liquid present in the cake at the start of washing (i.e. that present at the end of the previous phase in the cycle). For the purpose of calculations, the family of curves in Figure 6.7 can also be derived from sequences of coefficients that describe plots of dimensionless solute concentration ( *) vs. wash ratio for a range of dispersion number (see Appendix B and Wakeman and Tarleton (2005a)). Their numerical integration allows F to be evaluated as required. As an alternative to using the dispersion model a wash curve can be specified after experimental work, for instance in terms of F vs. W or F vs. tw. In this case a dispersion number does not need to be calculated and the fractional recovery is interpolated directly from the wash curve.

280 Solid/Liquid Separation: Equipment Selection and Process Design In some cases when the washing pressure is significantly higher than the pressure(s) previously used in a cycle and/or the cake is particularly compressible, then additional cake compression may occur at the start of (or throughout) a displacement washing process. While it is generally difficult to account for such instances, equations (6.4) and (6.5) can be used to recalculate av and Cav such that the resultant values are used in equation (6.49) and hence the subsequent washing calculations. For the majority of cases, however, such corrections are unnecessary and simply over-complicate calculation procedures. 6.2.4 Gas deliquoring Process design calculations for gas deliquoring require the specification of a threshold vacuum/pressure (pb), the pressure required to start deliquoring, and an irreducible saturation (S-) which is the cake saturation where deliquoring due to liquid displacement ceases (Wakeman, 1979c, 1982a, 1984b; Wakeman and Vince, 1986a,b). These can be either measured in a capillary pressure experiment or calculated using pb


4.6(1
av )
av x

N cap


(6.64)


3av x 2 (l gLd pd ) (1
av )2 Ld

S
0.155(1 0.031N

0.49 cap

(6.65) )

where is the cake liquid surface tension, g the acceleration due to gravity, Ncap the capillary number and pd the deliquoring pressure or vacuum. These parameters are used in conjunction with the intrinsic properties of the cake and two design charts (Figures 6.8 and 6.9) to evaluate the cake moisture content (M) or deliquoring time (td ) as well as the flux of gas (or gas/air rate) required to deliquor the cake. pd is fixed throughout gas deliquoring and several properties of the cake are assumed to remain constant and equal to the values at the end of the previous phase in the cycle, i.e. Ld
Lpr, av
(av)pr, Cav
(Cav)pr
1(
av)pr and Ms
(Ms)pr. The cake permeability (kav) is related to the cake porosity and specific resistance by kav


1  av  s (1
av )

(6.66)

6 · Process design for batch separations 281 1.0 0.9

Reduced saturation, SR

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.01

0.1

1

10

100

(Dimensionless deliquoring time)x(Dimensionless pressure),θp*

Figure 6.8 The reduced saturation of a filter cake (SR) as a function of a dimensionless deliquoring time ( ) during deliquoring using vacuum or pressure applied in a gas phase. For details see Wakeman and Tarleton (2005a).

In a batch filter the end of gas deliquoring is normally specified in one of two ways, either by the final cake moisture content (Me) or a maximum deliquoring time ((td)e) and the sequence of calculations alters accordingly. Known (td)e. Values of td up to the maximum (td)e are chosen to provide intermediate values in the calculation sequences. The total cycle time (tT) is given by tT
t pr  t d

(6.67)

and the actual deliquoring time (td) is related to a dimensionless deliquoring time ( ) by     pd  t d kav pb t d kav  pd

p *

2    
av  l ( Ld ) (1 S )   pb 
av  l ( Ld )2 (1 S )

(6.68)

282 Solid/Liquid Separation: Equipment Selection and Process Design

Averaged dimensionless air flow rate at p*a0

102

101

100

10-1 p*=0.5 1.0 2.0 5.0 10 15 20 30

10-2

10-3

10-4

10-5 10-4

p* = 0.5

10-3

10-2

10-1

100

101

102

103

104

Dimensionless deliquoring time, θ

Figure 6.9 The dimensionless air flow rate through a filter cake (u苶 a* ) during deliquoring using vacuum or pressure applied in a gas phase as a function of the dimensionless deliquoring time ( ) and pressure p*. For details see Wakeman and Tarleton (2005a).

where p*
pd /pb. A value for reduced saturation (SR) is determined from Figure 6.8 for the known p*, hence

S
S  SR (1 S )

M


100  s  Cav  1 Sl  1 Cav 

(6.69)

(6.70)

Known Me. Values of M down to the minimum (Me) are chosen to provide a range of other values at intermediate points in the cycle.

6 · Process design for batch separations 283 Cake saturation and reduced saturation are calculated using rearranged versions of equations (6.69) and (6.70) such that  M   sCav   100  M  S
l (1 Cav )

SR


S  S 1 S

(6.71)

(6.72)

and p* values are determined from Figure 6.8 for the known SR. The actual deliquoring time is obtained from a version of equation (6.68) where

td


( p* )
av  l ( Ld )2 (1 S ) kav  pd

(6.73)

and the total cycle time is given by equation (6.67). For filter presses, the horizontal diaphragm press and the vertical, double sided press the active filter area during deliquoring Ad
Af /2. For the tube press this area is approximated by Ad ⬇ h(d  Lpr) and for the multi-element candle filter Ad ⬇ h(d  Lpr)nt. In all other batch filters and presses Ad
Af . With td and M known, the other time dependent parameters are given by

VT
Vpr 

M s  M pr M    l  100  M pr 100  M 

(6.74)

dVd Vd ⬇ dt d t d

(6.75)

Ml
S ( Ml ) pr

(6.76)

M sol
S ( M sol ) pr

(6.77)

284 Solid/Liquid Separation: Equipment Selection and Process Design Calculations for gas deliquoring are completed by evaluating the design air rate (ua  des) which allows a vacuum pump or blower to be specified. In the vacuum Nutsche and multi-element vacuum filters the dimensionless pressure difference across the cake is given by * * pa*
paei  paeo


pB pB  pd  pd  ⬅ pb pb pb

(6.78)

and in batch operated pressure filters this is amended to * *  paeo
pa*
paei

pB   pd pB  pd  ⬅ pb pb pb

(6.79)

where pB is the barometric pressure. The averaged dimensionless air flow rate (u苶a*) is read directly from Figure 6.9 for the known p* and , hence the * superficial air velocity (ua) at pao is calculated according to * * *  ( paeo )2  ( paei )2  pao u
1.1u *  * 2  paeo  ( pao )  ( pai* )2  * ae

* a

ua
uae*

kav pb  a Ld

(6.80)

(6.81)

where a is the gas viscosity. By definition p*ai and p*ao
100p*a. For vacuum Nutsche and multi-element vacuum filters the design air rate is given by  pd pb ua des
ua  p  3300 *  d paei pb *  paei

(6.82)

whereas for all other (pressure driven) batch filters ua


ua des

* paeo  p  3300 *  d paeo pb

(6.83)

The empirical correction factors in equations (6.80), (6.82) and (6.83), namely 1.1 and 3300, are allowances to account for losses in the pipework

6 · Process design for batch separations 285 of the filter. For the purpose of calculations, the curve in Figure 6.8 and the family of curves in Figure 6.9 can also be represented through a sequence of coefficients (see Appendix B and Wakeman and Tarleton, 2005a); these also allow M, td and uades to be calculated in the manner as shown above. 6.2.5 Optimisation of filtration time for batch filters When constant pressure/vacuum filtrations are performed in batch filters the rate of filtration is generally a maximum at the start and then progressively decreases. A decision must be taken as to when the filter cycle should be ended. In Section 6.2.1.1, for example, the end of filtration was specified by the formation of a known mass of cake solids and the duration of subsequent phases was specified via a time or specific cake condition. An alternative way of making these decisions is to define an average filtration rate on the basis of the total cycle time. By incorporating equation (6.9) the overall production rate (Y) can be written as total filtrate collected total cycle time Vf Vf

n n t f  ∑ t n (0.5K1V f2  K 2V f )  ∑ t n

Y


2

(6.84)

2

n

where K1 and K2 are known constants and 2tn represents the total time occupied by all cycle phases other than cake formation, including any filter downtime. Differentiating equation (6.84) with respect to Vf , setting dY/dVf
0 and using equations (6.8) and (6.9) gives expressions for the optimum volume of filtrate, filtration time and cake thickness: n

2∑ t n

(6.85)

2

(V f )opt


K1 n

n

(t f )opt
∑ t n  K 2 2

( L f )opt


2∑ t n 2

(6.86)

K1

(V f )opt s关 s (mav 1)  l 兴 Af  s (1 mav s)

(6.87)

286 Solid/Liquid Separation: Equipment Selection and Process Design If the resistance of the filter medium is neglected (i.e. K2
0) then the ‘optimum’ cake form time is exactly equal to the total period for which the filter is carrying out non-cake forming duties. Similar calculation steps can be followed to find optimum conditions for variable pressure filtrations, although in some cases numerical techniques may need to be used.

6.3 Design equations for centrifugal filter cycles Although the main purpose of this chapter is to present design procedures for batch filter cycles, the methodologies described can be adapted to the operations performed in a batch centrifuge and by way of example Figure 6.10 illustrates a typical peeler centrifuge cycle. During the filtration of a suspension batch, the perforated basket covered by a filter cloth is rotated at a constant speed and the induced centrifugal forces cause the

Figure 6.10 Schematic diagram of a peeler centrifuge cycle. (a) Filtration; (b) displacement washing; (c) deliquoring; (d) cake discharge by plough.

6 · Process design for batch separations 287 centrate to pass leaving the filtered particles to form the cake. Following the completion of cake formation, the cake may subsequently be washed by sprays and/or allowed to deliquor prior to discharge by mechanical plough or peeler. With centrifugal filters the filtration area is a function of time and for a peeler centrifuge the equation relating filtrate flow rate (q) to cake growth is

l 2 2 (r0  rl2 ) 2 q
R ln(r0 rc )  av  l M s  l 2 2 2h h(r0  rc )  2r0 h

(6.88)

where is the angular velocity of the basket, r0 the inner radius of the basket, rl the radius of the liquid layer, rc the inner radius of the cake and h the basket depth. Noting that the average flow area (Af)av
h (r0  rc) and the logarithmic mean flow area (Af)lm
2h(r0  rc)兾ln (r0 rc), equation (6.88) may be rewritten as

q


p f 0.5l 2 (r02  rl2 )
 av  l M s R  av  l M s R  l  l ( A f )av ( A f )lm ( A f )0 ( A f )av ( A f )lm ( A f )0

(6.89)

An equation relating cake radius (rc) to the filtration time is rc
r02 

Vs qt f h(1
av )(1 Vs )

(6.90)

where Vs is the solids volume fraction in the feed. When the radius of the centrifuge is large in comparison to the cake thickness, an essentially planar cake surface can be assumed to exist. Modelling of a washing phase in this case is accomplished by noting that the driving pressure for the washing operation is pw
0.5l (r 20  rl2). With smaller centrifuges, however, the curvature of the filter cake must be considered and in a similar manner to the tube press (see Section 6.2.3) an active filter area during washing is defined. Detailed procedures for modelling cake deliquoring in centrifuges have been previously described in Wakeman and Tarleton (2005a).

288 Solid/Liquid Separation: Equipment Selection and Process Design

6.4 Examples of batch filter cycle calculations The calculations presented in this section illustrate the level of detail that can be achieved when appropriate design equations and procedures are used to predict the performance of batch filters. Although the examples of the diaphragm filter press and the pressure Nutsche filter have been chosen for illustrative purposes, the methodologies can be readily adapted with the aid of the equations shown in Section 6.2 to analyse the performance of most other filters. 6.4.1 Example 6.1: Horizontal diaphragm filter press Problem As part of a modification to a chemical plant it is proposed to install a filter to process an aqueous based slurry containing 8% w/w of clay-like solids (see Figure 6.11). A diaphragm filter press with a cloth area of 300 m2 is available on site and is currently not used. To meet process requirements a sequential cycle comprising filtration, compression deliquoring (consolidation), displacement washing and gas deliquoring phases is envisaged. Following filtration, cake homogeneity is to be improved through consolidation with the

Figure 6.11 Scanning electron micrograph of a clay.

6 · Process design for batch separations 289 diaphragms; the consolidation is to last for the same duration as cake formation. The resultant cakes need to be washed until 97% of the solute is recovered after which gas deliquoring reduces the moisture content to 25% for discharge. It is proposed to deliver the feed to the press via a centrifugal pump whose characteristics are shown in Table 6.3. Filtration with the pump is to be stopped when the cake thickness on each filtering surface reaches 20 mm (i.e. 40 mm total cake thickness per chamber ⬅ 50% of the 80 mm chamber thickness; see Table 6.4). The unfiltered suspension remaining between the two cakes in each chamber is filtered with the diaphragms at the specified constant pressure of 600 kPa. Table 6.3 Pump characteristics for the diaphragm filter press calculation (Example 6.1).

Flow rate (m3 s1) 0 0.022 0.03 0.035 0.037 0.0385 0.0395 0.04

Pressure (kPa) 360 300 250 200 150 100 50 0

The feed suspension characteristics have been measured experimentally and these are shown in Table 6.4 along with suggested operational parameters. Determine the solid, liquid and solute throughput rates, the filter cycle time and other performance indicators. Solution The calculations follow the procedures outlined in Section 6.2 and conveniently divide into five parts such that tT
(tf)1  (tf)2  tc  tw  td. 6.4.1.1 Cake formation (filtration) phases As cake formation with the centrifugal pump only fills half the available volume in each chamber, the filtration takes place in two stages denoted as primary and secondary. Primary filtration takes place in accordance with the pump curve while secondary filtration proceeds via the flexible diaphragm at a constant pressure of 600 kPa.

290 Solid/Liquid Separation: Equipment Selection and Process Design Table 6.4 Characteristic parameters for the diaphragm filter press calculation (Example 6.1). Parameter Filter and septum characteristics Filter chamber thickness (T ) Filter medium resistance (R) Filter area (A f ) Operating conditions Secondary filtration, consolidation and washing pressures (pf , pc and pw) Gas deliquoring pressure (pd)† Barometric pressure (pB) Solids mass fraction in the feed (s) Solute concentration in the feed ( 0) Solute concentration in the wash ( w)

Value 80 mm 3 × 1011 m1 300 m2 600 kPa 400 kPa 100 kPa 0.08 30 kg m3 0.5 kg m3

Cake properties Maximum thickness on each filter surface

20 mm

Constitutive equations for the filtration phase(s), pf in kPa‡

av
2.4 × 109 pf0.6 m kg1 Cav
0.25 pf 0.011 v/v

Constitutive equations for the consolidation phase, pc in kPa

Cc
1 × 108 pc0.01 m2 s1 Cav
0.36 pc0.012 v/v

Consolidation behaviour index ()

3

Particle and fluid properties Mean size of solids (xav ) Density of solids (s) Density of filtrate and wash (l ) Viscosity of filtrate and wash (l ) Surface tension of filtrate and wash ( ) Irreducible cake saturation (S- ) Viscosity of air (a ) Solute diffusivity (D)

10 m 2500 kg m3 998 kg m3 0.001 Pa s 0.07 N m1 0.22 1.8 × 105 Pa s 1 × 109 m2 s1

†

Restricted to prevent excessive, and process limiting, cake cracking. It is noted that av
0(1n)p n
6 × 10 9 (10.6)p 0.6
2.4 × 109p 0.6 m kg1.

‡

The primary filtration phase commences at a point on the pump curve where equation (6.18) is satisfied such that  p f   l R 0.001 × 3 × 1011


1 × 106 Pa s m3  q  300 Af t
0

(6.91)

6 · Process design for batch separations 291 Table 6.5 Data sequences for the primary filtration phase of a diaphragm press cycle. pf dVf /dtf Vf (m3) (kPa) (m3 s1) (1) (2) (3) 39.5 50.8 57.0 63.1 69.2 75.3 81.4 87.5 93.6 99.7 103.9

0.0396 0.0395 0.0394 0.0392 0.0391 0.0390 0.0389 0.0388 0.0386 0.0385 0.0384

0 10.6 15.4 19.7 23.6 27.1 30.5 33.5 36.4 39.2 41.1

Lf (m)† (4) 0 0.0052 0.0076 0.0097 0.0116 0.0133 0.0149 0.0164 0.0178 0.0191 0.0200

100(2Lf /T ) (%) (5)

tf (s)

Ms (kg)

Ml (kg)

Msol (kg) (9)

(6)

(7)

(8)

0 13.0 19.0 24.3 29.0 33.3 37.3 41.0 44.5 47.8 50.0

0 269 390 499 598 690 775 854 929 1000 1049

0 1023 1483 1895 2269 2611 2929 3225 3504 3768 3947

0 0 1156 34.7 1673 50.3 2135 64.2 2552 76.7 2934 88.2 3287 98.8 3615 108.7 3924 118.0 4215 126.7 4413 132.6

†

Cake thickness per filtration surface.

which by Lagrange interpolation of the data in Table 6.3 equates to a pressure and flow rate of 39.5 kPa and 0.0396 m3 s1. Noting that filtration occurs on both sides of each chamber in the press, the data sequences shown in Table 6.5 are evaluated to provide information at points throughout the primary filtration phase where: (1), (2) Filtration pressure (pf) and filtrate flow rate (q
dVf /dtf) are determined from the pump curve. In the current example, values of pf are chosen to allow values of q to be interpolated from Table 6.3. For each value of pf the corresponding values for av, Cav, mav and c are calculated: From equation (6.4): av
0(1n)(pf /1000 ) n
2.4 × 10 9 (pf / 1000) 0.6 m kg–1 From equation (6.5): Cav
C0(pf /1000 ) 
0.25(pf /1000 ) 0.011 v/v (where the correlations for av and Cav require pf to have the units of kPa) l 1Cav 998 1Cav 
1   From equation (6.6): mav
1  s Cav 2500 Cav

冢

冣

冢

sl 0.08 × 998 From equation (6.7): c

 kg m3 1mav s 1mav × 0.08

冣

292 Solid/Liquid Separation: Equipment Selection and Process Design (3) From equation (6.17), the cumulative volume of filtrate:

Vf


p f   300  0.001 × 3 × 1011  m 3 300  q  av × 0.001 × c  

(4) From equation (6.19), the cake thickness on each filtration surface:

p f   0.08[2500(mav 1)  998] 300  0.001 × 3 × 1011  q   Lf
m  av × 0.001 × c × 2500(1 mav × 0.08)

(6.92)

100 × 2Lf (5) Percentage of each chamber filled by cake
 T (6) From equation (6.20) and trapezium rule integration, the filtration time: Vf

tf ⬇ ∑ 0

(V f )i  (V f )i1  1 1     s 2  q i q i1 

(6.93)

(7), (8), (9) The total masses of solids, liquid and solute in the cakes are given respectively by equations (6.21), (6.14) and (6.15): M s
A f L f Cav  s
300 L f Cav × 2500 kg

(6.94)

Ml
A f L f
av l
300 L f (1 Cav ) × 998 kg

(6.95)

M sol
A f L f (1 Cav ) 0
300 L f (1 Cav ) × 30 kg

(6.96)

The moisture content is calculated by equation (6.16). The end of the primary filtration phase, represented by the final row of values in Table 6.5, is determined from the specification that cake formation with the pump stops when the cake thickness on each filtration surface reaches 20 mm. Although the value is calculated by equation (6.92), in reality, a point on the pump

6 · Process design for batch separations 293 Table 6.6 Data sequences for the secondary filtration phase of a diaphragm press cycle. Lf (m)† (1)

Vf (m3)‡ (2)

T (m) (3)

tT (s) (4)

tf (s) (5)

Ms (kg) (6)

Ml (kg) (7)

Msol (kg) (8)

0.0400 0.0405 0.0410 0.0415 0.0420 0.0425 0.0430 0.0435 0.0440 0.0445 0.0450

41.10 41.58 42.10 42.63 43.15 43.68 44.20 44.73 45.25 45.78 46.30

0 0.0032 0.0067 0.0102 0.0137 0.0172 0.0207 0.0242 0.0277 0.0312 0.0350

1049 1085 1121 1157 1194 1231 1268 1305 1343 1380 1418

0 36 72 108 145 182 219 256 294 331 369

3947 4074 4124 4174 4225 4275 4325 4376 4426 4476 4527

4413 4437 4491 4546 4601 4656 4711 4766 4820 4875 4930

132.6 133.4 135.0 136.7 138.3 140.0 141.6 143.3 144.9 146.5 148.2

†

Total cake thickness per chamber. Total volume filtered during filtration phases.

‡

curve dictates the end of filtration where the corresponding values of pf and q are used to calculate Lf. This point usually needs to be determined by trial and error, which may involve interpolation of the calculated dataset. In order to remove liquid from the unfiltered suspension remaining in the chambers and complete cake formation, the flexible diaphragms are inflated at 600 kPa and the secondary filtration phase proceeds until the two cakes meet within each chamber. To provide the cycle data sequences shown in Table 6.6 a range of additional cake thicknesses (L) are chosen, up to a maximum value that equates to the filtration of all the remaining suspension, and the remaining parameters are evaluated for each value of L. For the purpose of calculation it is assumed that the forming cake and the cake already present from the primary filtration phase now have the same average specific resistance at the diaphragm pressure of 600 kPa. Using equation (6.4):  av
2.4 × 10 9 (600)0.6
1.11 × 1011 m kg1 and from equations (6.5)–(6.7) at pf
600 kPa, Cav
0.268 v/v, mav
2.09 and c
95.9 kg m3. Noting that a secondary filtration phase with the diaphragms normally utilises only one filtration surface per chamber such that Ac
Af /2
150 m2 and the

294 Solid/Liquid Separation: Equipment Selection and Process Design subscript ‘pr’ denotes a value at the end of the previous primary filtration phase, the data in Table 6.6 are given by: (1) From equation (6.22), the total cake thickness per chamber: L f
L pr   L
2 × 0.02   L m

(6.97)

(2) From equation (6.23), the cumulative volume of filtrate: V f
Vpr 

 s (1 mav s) Ac  L s[ s (mav 1)  l ]


41.1

2500(1 2.09 × 0.08) × 150 L 3 m 0.08[2500(2.09 1)  998]

(6.98)

(3) Diaphragm displacement: T


V f  Vpr Ac




V f  41.1 150

m

(6.99)

(4) From equation (6.24), which accounts for the presence of cake formed during the primary filtration stage, the total cycle time is   c tT
t pr  (V f  Vpr )  av2 l (V f  Vpr )  2 Ac  p f 

  l   av cVpr  R   Ac  p f  Ac 


1049  (V f  41.1)  1.11 × 1011 × 95.9 × 0.001 (V f  41.1)  2 × 150 2 × 600 × 103

×



0.001 150 × 600 × 103

  1.11 × 1011 × 95.9 × 41.1  3 × 1011   s 150  

×

(6.100)

6 · Process design for batch separations 295 (5) Duration of secondary filtration phase: t f
tT  t pr
tT 1049 s

(6.101)

(6), (7), (8) The total masses of solids, liquid and solute in the cakes are given respectively by equations (6.25)–(6.27): M s
Ac ( L pr   L )Cav  s
150(2 × 0.02   L ) × 0.268 × 2500 kg Ml
Ac ( L pr   L )(1 Cav )l
150(2 × 0.02   L )(1 0.268) × 998 kg M sol
Ac ( L pr   L )(1 Cav ) 0
150(2 × 0.02   L )(1 0.268) × 30 kg

(6.102)

(6.103)

(6.104)

The filtrate flow rate is approximated by equation (6.13) and the cake moisture content is constant throughout the secondary filtration phase and given by equation (6.16) M cake
100

Ml 4930
100
52.1% Ml  M s 4930  4527

(6.105)

The end of the secondary filtration phase occurs when Lf  T
T
80 mm and the final row of data in Table 6.6 reflects this condition. The value of L that corresponds to the end of filtration is obtained by trial and error and interpolation as necessary. Knowing values throughout the period of cake formation allows other important values to be calculated, for instance

w


mass dry cake M s 4527


15.1 kg m2 filter area 300 Af

(6.106)

6.4.1.2 Consolidation (compression deliquoring) phase The cake consolidation period proceeds by using the flexible diaphragms at a pressure of 600 kPa and is specified to last for the same duration as the two cake formation stages (i.e. 1418 s). Noting that the consolidation pressure (pc ) in the scale-up equations for Ce and Cav has units of kPa and the active filter area

296 Solid/Liquid Separation: Equipment Selection and Process Design during consolidation Ac
Af /2
150 m2, the equilibrium cake solids volume fraction at infinite consolidation time is given by equation (6.35): (Cav )-
C0  pc
0.36(600)0.012
0.389 vv and the volume of solids per unit filter area and equilibrium cake height (per chamber) are respectively given by:

0


Ms 4527

1.21 × 102 m  s Ac 2500 × 150

(6.107)

L-


Ms 4527

0.031 m Ac  s (Cav )- 150 × 2500 × 0.389

(6.108)

Noting that the subscript ‘pr’ indicates a value from the end of the secondary filtration phase and the mass of solids in the cakes remains constant throughout consolidation and equal (Ms )pr
4527 kg, the data sequences shown in Table 6.7 provide information for the consolidation phase where: (1) Time throughout the consolidation phase is determined by choosing a value between tc
0 s and tc
1418 s. Table 6.7 Data sequences for the consolidation (compression deliquoring) phase of a diaphragm press cycle.

tc (s) (1) 0 142 284 426 568 710 851 993 1135 1277 1418

tT (s)

Lc (m)

V T (m3)

(2)

(3)

1418 1560 1702 1844 1986 2128 2269 2411 2553 2695 2836

0.0450 0.0429 0.0420 0.0413 0.0407 0.0402 0.0398 0.0393 0.0390 0.0386 0.0383

M (%)

(4)

dVc /dtc (m3 s1) (5)

(6)

Ml (kg) (7)

Msol (kg) (8)

46.30 46.62 46.76 46.86 46.95 47.02 47.09 47.15 47.21 47.26 47.32

– 0.0023 0.0010 0.0007 0.0006 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004

52.13 50.46 49.73 49.15 48.66 48.21 47.81 47.43 47.07 46.73 46.41

4930 4610 4477 4376 4290 4214 4146 4084 4026 3971 3920

148.2 138.6 134.6 131.5 129.0 126.7 124.6 122.8 121.0 119.4 117.8

6 · Process design for batch separations 297 (2) From equation (6.39), the total cycle time: tT
t pr  tc
1418  tc s

(6.109)

(3) From equation (6.36) and noting that for the horizontal diaphragm press jII
1, the cake thickness per chamber:

Lc
L pr  ( L pr  L )

4Tc  1 2 v

  4T  2 v  c 1          


0.045  (0.045  0.031)

1.273Tc

(1 ( 1.273Tc )2 × 3 )1 (2 × 3)

(6.110) m

where Tc is given by a combination of equations (6.34) and (6.37): Tc


i 2Ce 0  pc tc 12 × 1 × 108 × 600 0.1 tc


20 (1.21 × 102 )2

(6.111)

(4) From equation (6.40), the cumulative volume of filtrate: VT
Vpr  Ac ( L pr  Lc )
46.3 150(0.045  Lc ) m 3

(6.112)

(5) From equation (6.44), the liquid flow rate: dVc Vc 3 1 ⬇ m s tc dtc

(6.113)

(6) Noting that Mpr
52.1%, (Cav)pr
0.268 and (
av)pr
0.732, from equation (6.46) the cake moisture:  4527 × 0.732  100   Vc   0.268 × 2500  % M
 100  52.1  4527 × 0.732  4527 × 0.732  Vc   52.1   0.268 × 2500  0.268 × 2500

(6.114)

298 Solid/Liquid Separation: Equipment Selection and Process Design (7 ) From equation (6.45), the mass of liquid in the cakes: Ml
( Ml ) pr  lVc
4930  998Vc kg

(6.115)

(8) From equation (6.41), the mass of solute in the cakes:

M sol
150 Lc × 30

M × 2500 kg M × 2500  998(100  M )

(6.116)

Assuming that it is economical to continue cake consolidation until tc
1418 s, the end of phase values are given in the bottom line of Table 6.7 where the total cycle time is tT
2836 s and the final cake thickness (Lc)e
0.0383 m. In order to facilitate calculations for the remaining phases in the cycle the average solids volume fraction and specific resistance of the cake in each chamber needs to be determined. The former is given by equation (6.47)

(Cav )e
1

46.41 × 2500
0.316 vv 46.41 × 2500  998(100  46.41)

(6.117)

and, noting that (
av)e
1(Cav)e
0.684, the latter is given by equation (6.48)

( av )e
1.11 × 1011

0.7323 0.316
1.6 × 1011 m kg1 0.268 0.6843

(6.118)

6.4.1.3 Washing phase The displacement washing phase is performed at a constant pressure of 600 kPa and specifications require a fractional solute recovery (F) of 97%. Assume that the cake thickness, solids volume fraction (and hence porosity), specific resistance and wash flow rate are constant throughout washing and the active filter area is Aw
Af /2
150 m2. Using values from the end of the previous consolidation phase for (Cav)e
1(
av)e, (av)e and (Lc)e
Lw, the superficial wash velocity and mean

6 · Process design for batch separations 299 velocity of fluid through the cake pores are respectively given by equations (6.49) and (6.50):

u


600 × 103 0.001(1.6 × 1011 × 2500 × 0.0383 × 0.316  3 × 1011 )


1.17 × 104 m s1

v


u 1.17 × 104

1.71 × 104 m s1
av 1 0.316

and the wash flow rate is given by equation (6.60): dVw
uAw
1.17 × 10 4 × 150
0.018 m 3 s1 dt w and hence ReSc


vx 1.71 × 104 × 10 × 106

1.71 D 1 × 109

(6.119)

Since ReSc1 and Lw 10 cm then equation (6.53) applies: DL
0.707  55.5(ReSc)0.96
0.707  55.5(1.71)0.96
93.6 D

(6.120)

The dispersion number is calculated from equation (6.54): Dn
ReSc

Lw D 0.0383 1
1.71
70 x DL 10 × 106 93.6

(6.121)

The mass of solids in the cakes remains constant throughout washing and is equal to the value at the end of compression deliquoring (Ms
4527 kg). The mass of liquid in the cakes, as given by equation (6.63), also remains the same as the density of filtrate and wash are equal (Ml
3920 kg). The data sequences shown in Table 6.8 provide information for the washing phase where: (1) As the ultimate fractional solute recovery (F e) is known, intermediate values of F are determined by choosing a value between F
0 and F
0.97.

300 Solid/Liquid Separation: Equipment Selection and Process Design Table 6.8 Data sequences for the washing phase of a diaphragm press cycle. F (-) (1)

W (-) (2)

(-) (3)

tw (s) (4)

tT (s) (5)

VT (m3) (6)

Msol (kg) (7)

0 0.097 0.194 0.291 0.388 0.485 0.582 0.679 0.776 0.873 0.970

0 0.097 0.19 0.29 0.39 0.49 0.58 0.68 0.78 0.90 1.08

1.000 1.000 1.000 1.000 1.000 1.000 0.995 0.986 0.912 0.723 0.364

0 22 44 66 88 109 131 153 176 203 243

2836 2858 2880 2902 2924 2945 2967 2989 3012 3039 3079

47.32 47.70 48.08 48.46 48.84 49.22 49.60 49.99 50.39 50.85 51.56

117.8 106.4 95.0 83.5 72.1 60.7 49.3 37.8 26.4 15.0 3.53

(2) Wash ratio at the known F can be read directly from the design chart (Figure 6.7). Alternatively, as shown below, the curvefit coefficients for the plots of dimensionless solute concentration ( *) vs. W, from which Figure 6.7 is derived, can be used. Referring to Appendix B, values of * are evaluated at a chosen number of wash ratios for both Dn
50 and Dn
100 where

6 · Process design for batch separations 301 and each resultant pair of * values at the chosen W is interpolated to give the corresponding * value at Dn
70. Further interpolation of the entire * vs. W dataset is required to determine the value of W that satisfies the relation which defines the known F where W

W

 w dW dW ⬇

0  w 2 0

F
∫ dW
∫ ⴱ

0

W

∑ (

ⴱ i

 iⴱ1 )

0

(6.122)

and trapezium rule integration is used as an approximation. In the current example, the solute concentration in the wash w
0 kg m–3 and 0, the solute concentration in the cake at the start of washing, is 30 kg m–3. (3) Determined from the * vs. W dataset as calculated in (2). (4), (5) From equation (6.55), the washing time and total cycle time: tw


WLw
av W × 0.0383 × 0.684
s 1.17 × 104 u

tT
t pr  t w
2836  t w s

(6.123)

(6.124)

(6) From equation (6.59), the cumulative volume of liquid: VT
Vpr  Vw
Vpr  Aw ut w
47.32 150 × 1.17 × 104 t w m 3

(6.125)

(7) Note that w
0 kg m–3 and, as no gas deliquoring takes place prior to washing, the cake saturation S
1 and WS
1
W. From equation (6.61), the mass of solute in the cake: M sol
( M sol ) pr (1 F )
117.8(1 F ) kg

(6.126)

The cake moisture content at the end of washing is the same as at the end of consolidation (i.e. Me
46.41%). Although no corrections have been applied to the wash ratios to account for filling of the pipes in the press, in practice calculated values may be doubled to compensate for the additional volumes of wash liquor required. A simple multiplier applied to the values in column (2) of Table 6.8 accounts for any additional wash used.

302 Solid/Liquid Separation: Equipment Selection and Process Design 6.4.1.4 Gas deliquoring phase The gas deliquoring phase is performed at a constant pressure of 400 kPa and it is required to reduce the cake moisture content to 25%. Assume that the cake height, solids volume fraction (and thus porosity) and specific resistance are constant and the active filter area is Ad
Af /2
150 m2. The mass of solids in the cakes remains constant throughout gas deliquoring and equal to the value at the end of washing (Ms
4527 kg). Using relevant values from the end of the previous washing phase, i.e. Cav,
av, av and Lw
Ld, the threshold pressure and cake permeability are respectively given by equations (6.64) and (6.66): pb


4.6(1
av ) 4.6(1 0.684) × 0.07

av x 0.684 × 10 × 106

(6.127)

4


1.49 × 10 Pa

kav


1 1
11  av  s (1
av ) 1.6 × 10 × 2500(1 0.684)

(6.128)


7.9 × 1015 m 2 The irreducible saturation S-
0.22 is initially specified. The data sequences shown in Table 6.9 are evaluated to provide information for the gas deliquoring phase where: (1) As the moisture content at the end of deliquoring is specified, intermediate values of cake moisture are chosen between M
46.41% and M
25%. (2) From equation (6.71), the cake saturation:

 M   M   sCav  2500 × 0.316   100  M   100  M  S

998(1 0.316) l (1 Cav )

(6.129)

(S0.22) and from equation (6.72), the reduced saturation SR
 . (10.22) (3) The dimensionless deliquoring time ( ) at the known SR is read directly from the design chart (Figure 6.8). Alternatively, as shown below, the

6 · Process design for batch separations 303 Table 6.9 Data sequences for the gas deliquoring phase of a diaphragm press cycle. M (%) (1) 46.41 44.27 42.13 39.99 37.84 35.70 33.56 31.42 29.28 27.14 25.00

S (-)

td (s)

tT (s)

VT (m3)

(2)

(3)

(4)

(5)

1.000 0.917 0.841 0.769 0.703 0.641 0.583 0.529 0.478 0.430 0.385

0 20 48 84 130 188 264 365 486 896 1742

3079 3099 3127 3163 3209 3267 3343 3444 3565 3975 4821

51.56 51.89 52.19 52.47 52.73 52.97 53.20 53.41 53.61 53.80 53.98

dVd /dtd u苶a|des Ml (kg) (m3 s1) (m3 m2 s1) (6) (7) (8) – 0.0165 0.0107 0.0064 0.0057 0.0041 0.0030 0.0021 0.0017 0.0005 0.0002

– 9.18 × 106 3.50 × 105 7.88 × 105 1.43 × 104 2.30 × 104 3.43 × 104 4.78 × 104 6.29 × 104 9.98 × 104 1.42 × 103

3920 3595 3295 3016 2756 2514 2287 2074 1874 1686 1509

Msol (kg) (9) 3.53 3.24 2.97 2.72 2.49 2.27 2.06 1.87 1.69 1.52 1.36

curvefit coefficients for the plot of SR vs. can be used. Referring to Appendix B, equation (B.2) is rearranged to give 1  0.88  1  1    S 1  1.08  R   

p*
 1  0.48  1  1    1    1.46  SR 

SR 0.343 (6.130) SR 0.343

where SR is known from (2) and by definition p*


 pd 400 × 103

26.85 1.49 × 10 4 pb

(6.131)

Knowing the value of , equation (6.73) is used to give the actual deliquoring time (td): td


× 26.85 × 0.684 × 0.001 × 0.03832 (1 0.22) s 7.9 × 1015 × 400 × 103

(6.132)

304 Solid/Liquid Separation: Equipment Selection and Process Design (4) From equation (6.67), the total cycle time: tT
t pr  t d
3079  t d s

(6.133)

(5) From equation (6.74), the cumulative volume of liquid:

VT
51.56 

4527  46.41 M  3  m  998 100  46.1 100  M 

(6.134)

(6) From equation (6.75), the liquid flow rate: dVd Vd 3 1 ⬇ m s t d dt d

(6.135)

(7) The dimensionless air flow rate (u苶 a* ) is read directly from the design chart shown in Figure 6.9. Alternatively, as shown below, the curvefit coefficients for the plots of u苶 a* vs. can be used. Noting that p a*
p*, equation (6.79) gives * * pa*
paei  paeo




100 × 103  400 × 103 100 × 103  1.49 × 10 4 1.49 × 10 4


33.56  6.71
26.85 and values of u苶 a* are evaluated at the known for both p a*
20 and p a*
30 where (referring to Appendix B)

ua*
10 冢 0.79810.8823log 1.3651(log )2 0.3367(log )3 0.0314(log )4 冣 104  0.1  2 3 4 pa*
20 ua*
10 冢1.140.2554log 0.1888(log ) 0.0724(log ) 0.0108(log ) 冣 0.1   100  * 1.301

 100 ua
10

6 · Process design for batch separations 305

ua*
10 冢 0.95391.1129log 1.2848(log )2 0.2757(log )3 0.0225(log )4 冣 104  0.05  2 3 4 pa*
30 ua*
10 冢1.4050.142log 0.1481(log ) 0.0762(log ) 0.0143(log ) 冣 0.05   100  * 1.4771

 100 ua
10

The value of u苶 a* at p a*
26.85 is then determined by interpolation. Noting that by definition p a*i
100 and p a*o
100p a*, the averaged dimensionless air flow rate (u苶 a* e), superficial air velocity (ua) and design air rate (uades) are respectively given by equations (6.80), (6.81) and (6.83) such that * pao
100  pa*
100  26.85
73.15

uae*
1.1ua*
1.1ua*

ua
uae*

ua

* * *  ( paeo pao )2  ( paei )2  *  * 2 paeo )  ( pai* )2   ( pao

73.15  6.712  33.56 2  6.71  73.152 100 2 

kav pb 7.9 × 1015 × 1.49 × 10 4 3 2 1 m m s
uae*  a Ld 1.8 × 105 × 0.0383


ua des


ua

(6.136)

(6.137)

(6.138)

* paeo  p  3300 *  d paeo pb

6.71 m 3 m2 s1 3 400 × 10  3300 6.71 1.49 × 10 4

(6.139)

where ua and uades are measured at atmospheric pressure and an absolute * pb  pd  3300)
(6.71 × 1.49 × 104  400 × 103  pressure of (paeo 3300) ⬅ 503 kPa respectively. The empirical correction factors,

306 Solid/Liquid Separation: Equipment Selection and Process Design i.e. 1.1 and 3300, are allowances to account for losses in the pipework of the press. (8) From equation (6.76), the mass of liquid in the cakes: Ml
S ( Ml ) pr
S × 3920 kg

(6.140)

(9) From equation (6.77), the mass of solute in the cakes: M sol
S ( M sol ) pr
S × 3.53 kg

(6.141)

The relevant end of phase values are given in the bottom line of Table 6.9 where the total cycle time is tT
4821 s. 6.4.1.5 Summary of results and filter cycle illustrations From the calculations it is evident that the required separation and cake posttreatment can theoretically be achieved using a diaphragm press. The overall results are summarised in Table 6.10 and Figure 6.12 and graphs illustrating some of the cycle parameters are shown in Figures 6.13 and 6.14. Table 6.10 Summary of results for the diaphragm press cycle (Example 6.1). Parameter

Value

Filtration phase durations Compression deliquoring phase duration Washing phase duration Gas deliquoring phase duration

0 ; 1049 s and 1049 ; 1418 s 1418 ; 2836 s 2836 ; 3079 s 3079 ; 4821 s

Mass dry cake/filter area Volume solids/filter area Mass solids/cycle time†

4527/300
15.1 kg m2 4527/(300 × 2500)
6.04 × 103 m 4527/4821
0.94 kg s1

Total volume of liquids produced during cycle

⬇ 54.0 m3

†

Ignores cake discharge time, cloth cleaning time, etc.

6.4.2 Example 6.2: Nutsche filter Problem A pressure driven Nutsche filter is to be used to separate batches of a crystalline pharmaceutical product (see Figure 6.15) from a propanol based suspension.

6 · Process design for batch separations 307

Figure 6.12 Mass balance representation of the diaphragm filter press cycle (from FDS). The values shown for ‘filtrate’ include the masses of liquid and solute produced during the gas deliquoring phase.

0.05

0.00 0

1000

2000

3000

end of deliquoring

0.01

end of consolidation end of washing

0.02

end of secondary filtration

0.03

end of primary filtration

Cake thickness (m)

0.04

4000

5000

Cycle time (s)

Figure 6.13 Variation of total cake thickness per chamber during the diaphragm press cycle. Variations in upstream formulation mean that crystallisation of the -form, which is more difficult to filter, can occur in place of the -form. In each batch, 50 kg of solids are present at a concentration of 6% v/v and it is envisaged that cake formation will occur to a maximum depth of 50 mm. In order to meet product specifications this new filter installation requires a sequential cycle comprising filtration, displacement washing and gas deliquoring. Preliminary

308 Solid/Liquid Separation: Equipment Selection and Process Design

Mass of cake solute (kg) or cake moisture content (%)

160 140 120 100 80 60 40

moisture content

20 solute mass 0 0

1000

2000 3000 Cycle time (s)

4000

5000

Figure 6.14 Variation of cake moisture content and mass of solute in the cake during the diaphragm press cycle.

Figure 6.15 Scanning electron micrographs of two forms of crystalline pharmaceutical product; cubic, -form (left) and needle, -form (right). tests in the laboratory suggest that the cake formed in each cycle needs to be treated with 3.5 wash ratios of pure propanol to remove unwanted solute residues after which deliquoring (with pressurised nitrogen) proceeds for 25 min to dry the cake ready for discharge with the plough. The characteristics for both the  and  particle forms in suspension have been measured experimentally and these are shown in Table 6.11 along with other suggested operational parameters. For the -form, determine the required filter area, the solid, liquid and solute throughput rates, the filter cycle time and other performance indicators. Assess the impact on the filter cycle if -form crystallisation occurs. Solution For a filter cycle following the sequence filtration – washing – gas deliquoring, and with reference to the procedures outlined in Section 6.2, calculations

6 · Process design for batch separations 309 Table 6.11 Characteristic parameters for the Nutsche filter calculation (Example 6.2). Parameter Septum characteristics Filter medium resistance (R) Operating conditions Filtration, washing and deliquoring pressures (pf , pw and pd) Barometric pressure (p B) Solids volume fraction in the feed (Vs) Solute concentration in the feed ( 0) Solute concentration in the wash ( w)

Value 4 × 1010 m1 200 kPa 100 kPa 0.06 9 kg m3 0 kg m3

Cake properties Required cake thickness Mass of solids in a batch

50 mm 50 kg

Particle and fluid properties Density of filtrate and wash (l) Viscosity of filtrate and wash (l) Surface tension of filtrate and wash ( ) Viscosity of nitrogen (a) Solute diffusivity (D)

802 kg m3 0.0023 Pa s 0.025 N m1 1.8 × 105 Pa s 6 × 1010 m2 s1

Particle and cake properties specific to -form Density of solids (s) Constitutive equations for the filtration phase, pf in kPa†

1370 kg m3 av
5.6 × 109 p f0.2 m kg1 Cav
0.28 p f0.05 v/v

Particle and cake properties specific to -form Density of solids (s) Constitutive equations for the filtration phase, pf in kPa‡

1420 kg m3 av
4.5 × 109 p f0.5 m kg1 Cav
0.27 p f0.05 v/v

†

av
0 (1n) p n
7 × 109 (10.2) p 0.2
5.6 × 109p 0.2 m kg1 av
0 (1n) p n
9 × 109 (10.5) p 0.2
4.5 × 109p 0.5 m kg1

‡

divide into three parts such that tT
tf  tw  td. Several aspects are similar to those presented in Section 6.4.1 for the diaphragm filter press and repetitive detail has been omitted below where appropriate. 6.4.2.1 Cake formation (filtration) phase In the Nutsche filter cake formation takes place at constant pressure upon a single leaf. Considering the -form of particles, at the specified filtration

310 Solid/Liquid Separation: Equipment Selection and Process Design pressure of 200 kPa the cake properties are given by equations (6.4)–(6.6) where av
1.62 × 1010 m kg–1, Cav
0.365 v/v and mav
2.02. In order to calculate the effective feed concentration (c), the solids volume fraction in the feed (Vs) must be expressed on a mass fraction basis (s). Referring to Appendix C, equation (C.9) gives s


 sVs 1370 × 0.06
Vs ( s  l )  l 0.06 (1370  802)  802


0.098 ww

(6.142)

(⬅ 9.8% w/w). Hence, equation (6.7) gives c
98.4 kg m–3. Given that the mass of solids per batch is 50 kg and the maximum cake height is 50 mm, a modified version of equation (6.10) is used to determine the required filter medium area (Af): Af





( M s )e [ s (mav 1)  l ]  l  s ( L f )e 50[1370(2.02 1)  802]
2 m2 802 × 1370 × 50 × 103

(6.143)

The data sequences in Table 6.12 are calculated for the filtration phase where: (1) Mass of solids in the cake is determined by choosing a value between Ms
0 and 50 kg. (2) From equation (6.10), the cake thickness: Lf





M s [ s (mav 1)  l ] l  s A f M s [1370(2.02 1)  802] m 802 × 1370 × 2

(6.144)

(3) From equation (6.11), the cumulative volume of filtrate: Vf
L f

A f  s (1 mav s) s[ s (mav 1)  l ]

2 × 1370(1 2.02 × 0.098) m3
Lf 0.098[1370(2.02 1)  802]

(6.145)

6 · Process design for batch separations 311 Table 6.12 Data sequences for the filtration phase of a Nutsche filter cycle. Ms (kg)

Lf (m)

Vf (m3)

tf (s)

(2)

(3)

0 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050

0 0.051 0.102 0.152 0.203 0.254 0.305 0.356 0.407 0.457 0.508

(1) 0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0

Ml (kg)

Msol (kg)

(4)

dVf /dtf (m3 s1) (5)

(6)

(7)

0 18 47 88 141 206 283 371 471 583 707

– 0.0028 0.0018 0.0012 0.0010 0.0008 0.0007 0.0006 0.0005 0.0005 0.0004

0 5.1 10.2 15.3 20.4 25.5 30.6 35.7 40.7 45.8 50.9

0 0.06 0.11 0.17 0.23 0.29 0.34 0.40 0.46 0.51 0.572

(4) From equation (6.12), the filtration time: tf





 av c l l R V f2  Vf 2 Af  p f 2 Af  p f 1.62 × 1010 × 98.4 × 0.0023 2 0.0023 × 4 × 1010 s Vf  2 × 200 × 103 2 × 2 2 × 200 × 103

(6.146)

(5) From equation (6.13), the filtrate flow rate:

q


dV f dt f

⬇

V f t f

m 3 s1

(6.147)

(6) From equation (6.14), the mass of cake liquid: Ml
A f L f
av l
2 L f (1 0.365) × 802 kg

(6.148)

(7) From equation (6.15), the mass of cake solute: M sol
A f L f
av 0
2 L f (1 0.365) × 9 kg

(6.149)

312 Solid/Liquid Separation: Equipment Selection and Process Design As the pressure remains constant throughout filtration the cake moisture content is fixed and given by equation (6.16), where

M
100

Ml 50.9
100
50.46 % Ml  M s 50.9  50

(6.150)

6.4.2.2 Washing phase The dispersion model is again used to model the washing phase in the cycle. The initial step, i.e. the calculation of the dispersion number (Dn ), follows the procedure shown for the diaphragm filter press in Section 6.4.1. Noting values from the filtration phase where av
1.62 × 1010 m kg–1, Cav
0.365 v/v, (Lf)e
Lw
0.05 m and Aw
Af
2 m2 as well as relevant values from Table 6.11, the superficial wash velocity (u), mean pore velocity (v) and wash flow rate (dVw /dtw) are respectively given by equations (6.49), (6.50) and (6.60) where u
1.96 × 104 m s–1, v
3.08 × 104 m s–1 and dVw /dtw
3.92 × 104 m3 s–1. A particle size (x), representative of that in the feed is not specified, so equation (6.2) is used to give an estimate:

x
13.4

1
av 0.365
13.4  av  s
3av 1.62 × 104 × 1370(1 0.365)3

(6.151)


7.7 × 106 m As ReSc
vx/D
3.96 and Lw 10 cm, from equation (6.53) DL /D
208.6 and Dn is calculated from equation (6.54): Dn
ReSc

Lw D 0.05 1
3.96
123.2 6 x DL 7.7 × 10 208.6

(6.152)

The end of the washing phase is denoted (in this particular example) by a fixed number of wash ratios. The data sequences shown in Table 6.13 provide information for the washing phase such that: (1) Intermediate values of wash ratio are specified by choosing a value between W
0 and W
3.5.

6 · Process design for batch separations 313 Table 6.13 Data sequences for the washing phase of a Nutsche filter cycle. W (-) (1)

tw (s) (2)

tT (s) (3)

* (-) (4)

F (-) (5)

VT (m3) (6)

Msol (kg) (7)

0 0.35 0.70 1.05 1.40 1.75 2.10 2.45 2.80 3.15 3.50

0 57 114 170 227 284 341 397 454 511 568

707 764 821 877 934 991 1048 1104 1161 1218 1275

1.000 1.000 0.992 0.407 0.037 0 0 0 0 0 0

0 0.350 0.700 0.969 1.000 1.000 1.000 1.000 1.000 1.000 1.000

0.508 0.530 0.553 0.575 0.597 0.619 0.642 0.664 0.686 0.708 0.731

0.572 0.372 0.172 0.018 0.000 0.000 0.000 0.000 0.000 0.000 0.000

(2) From equation (6.123), or a rearranged version of equation (6.57), the washing time:

tw


WLw
av W × 0.05(1 0.365) s
1.96 × 104 u

(6.153)

(3) From equation (6.56), the total cycle time: tT
t pr  t w
707  t w s

(6.154)

(4) The dimensionless solute concentration ( *) is derived from the correlations shown in Appendix B. For Dn
123.2, values of * are evaluated at the chosen wash ratio for both Dn
100 and Dn
500 where  *
1 0  W  0.6  * 2 
10.01 39.21W  46.46W 0.6 W 1.1 Dn
100  19.9W 3  2.122W 4  *
0.5789W 8.0948 1.1  W 2.2  * 
0 W 2.2

314 Solid/Liquid Separation: Equipment Selection and Process Design  *
1 0  W  0.8  * 0.8 W 1.1 
16.77  53.01W Dn
500   49.87W 2 14.23W 3  *
0.3095W 7.5097 1.1  W 2.1  * 
0 W 2.1 and the resultant pair of * values is interpolated to give the corresponding * value at Dn
123.2. (5) The fractional solute recovery (F) is determined from the * vs. W dataset calculated in (4). Using equation (6.122), F is calculated by trapezium rule integration where the upper limit is defined by the specified wash ratio: W

W

 w dW dW ⬇

0  w 2 0

F
∫ * dW
∫ 0

W

∑ (

* i

 i*1 )

(6.155)

0

Alternatively, the fractional solute recovery can be read directly from the design chart shown in Figure 6.7. (6) From equation (6.59), the cumulative volume of liquid: VT
Vpr  Vw
Vpr  Aw ut w
0.508  2 × 1.96 × 104 t w m 3

(6.156)

(7) As w
0 kg m–3 and the cake saturation S
1 and WS
1
W, from equation (6.61), the mass of solute in the cake: M sol
( M sol ) pr (1 F )
0.572(1 F ) kg

(6.157)

The mass of solid and liquid in the cake remains constant throughout washing and equal to the values present at the end of filtration (Ms
50 kg and Ml
50.9 kg) as does the cake moisture content (Me
50.46%). It is evident from the data in Table 6.13 that (theoretically) only 1.4 rather than the specified 3.5 wash ratios are required to purify the cake. However, as for the diaphragm press described in Section 6.4.1, losses in the pipes etc. of the filter will tend to raise the theoretical number of wash ratios as will any imperfections in the

6 · Process design for batch separations 315 cake structure (such as an uneven cake surface, leading to a non-uniform cake thickness). 6.4.2.3 Gas deliquoring phase The duration of the gas deliquoring phase is specified at 25 min and it is performed at a constant pressure of 200 kPa. For the purpose of calculations it is assumed that the cake height, solids volume fraction (and thus porosity) and specific resistance are constant and equal to the values at the end of washing. The masses of solids and solute in the cake also remain constant (i.e. Ms
50 kg and Msol
0 kg). Noting that Ad
Af
2 m2, the threshold pressure and cake permeability are respectively given by equations (6.64) and (6.66): pb


4.6 × 0.365 × 0.025
8582 Pa (1 0.365) × 7.7 × 106

kav


1  av  s (1
av )




1
1.24 × 1013 m 2 1.62 × 10 × 1370 × 0.365

(6.158)

(6.159)

10

As the irreducible saturation (S-) is not specified then it is necessary to approximate a value (with a degree of caution) using equation (6.65) N cap




3av x 2 (l gLd   pd ) (1
av )2 Ld (1 0.365)3 × (7.7 × 106 )2 (802 × 9.81 × 0.05  200 × 103 ) 0.3652 × 0.05 × 0.025


0.018 S
0.155(1 0.031 × 0.0180.49 )
0.189

(6.160)

The data sequences shown in Table 6.14 are evaluated to give information for a range of points throughout the gas deliquoring phase where: (1) Deliquoring time intervals are specified by choosing a value between td
0 and 1500 s (25 min).

316 Solid/Liquid Separation: Equipment Selection and Process Design Table 6.14 Data sequences for the gas deliquoring phase of a Nutsche filter cycle. td (s) (1) 0 150 300 450 600 750 900 1050 1200 1350 1500

tT (s)

S (-)

(2)

(3)

M (%) (4)

1275 1425 1575 1725 1875 2025 2175 2325 2475 2625 2775

1.000 0.539 0.437 0.405 0.384 0.368 0.356 0.347 0.339 0.332 0.326

50.46 35.44 30.81 29.20 28.11 27.29 26.64 26.11 25.66 25.28 24.94

VT (m3) (5)

dVd /dtd (m3 s1) (6)

 u a|des (m m2 s1) (7)

Ml (kg) (8)

0.731 0.7598 0.7663 0.7684 0.7697 0.7707 0.7714 0.7720 0.7725 0.7730 0.7734

– 1.95 × 104 4.31 × 105 1.36 × 105 8.96 × 106 6.52 × 106 5.05 × 106 4.07 × 106 3.38 × 106 2.87 × 106 2.48 × 106

– 2.58 × 103 4.91 × 103 6.51 × 103 7.69 × 103 8.59 × 103 9.32 × 103 9.92 × 103 1.04 × 102 1.08 × 102 1.12 × 102

50.90 27.45 22.27 20.63 19.55 18.76 18.16 17.67 17.26 16.92 16.62

3

(2) From equation (6.67), the total cycle time: tT
t pr  t d
1275  t d s

(6.161)

(3) To evaluate the cake saturation (S) it is necessary to determine the product of the dimensionless deliquoring time ( ) and the dimensionless pressure ( p*
pd /pb
200 ×103/8582
23.3) according to equation (6.68):

p *





t d kav  pd
av  l ( Ld )2 (1 S ) t d × 1.24 × 1013 × 200 × 103 (1 0.365) × 0.0023 × 0.052 (1 0.189)

(6.162)

The value of p* is used to determine the corresponding value of reduced saturation (SR), either directly from the design chart in Figure 6.8 or the equivalent curvefit coefficients shown in Appendix B. For the latter, equation (B.2) gives 1  11.08( p* )0.88  SR =  1  11.46( p* )0.48

0.096  ( p* )  1.915 1.915  ( p* )  204

(6.163)

6 · Process design for batch separations 317 and according to a rearranged version of equation (6.72) S
S  SR (1 S )
0.189  SR (1 0.189)

(6.164)

(4) From equation (6.70), the cake moisture content:

M


100 100
1370  0.365   s  Cav  1  1    S × 802  1 0.365  Sl  1 Cav 

(6.165)

(5) From equation (6.74), the cumulative volume of liquid:

VT
0.731

50  50.46 M  3   m 802 100  50.46 100  M 

(6.166)

(6) From equation (6.75), the liquid flow rate: dVd Vd 3 1 ⬇ m s t d dt d

(6.167)

(7) In a similar manner to that shown for the diaphragm press in Section 6.4.1, the dimensionless air flow rate (u苶 a* ) is calculated by means of the curvefit coefficients for the plots of u苶 a* vs. . Equation (6.79) gives * * pa*
paei  paeo

 100 × 103  200 × 103   100 × 103 
    8582  8582 

(6.168)


34.96 11.65
23.3 Values of u苶 a* are evaluated at the known where the latter is derived from equation (6.162). In this particular example, u苶 a* is calculated for both p*a
20 and 30 and the value of u苶 a* at p*a
26.85 is then determined by interpolation. The correlations for u苶 a* at both p*a
20 and 30 were previously stated in Section 6.4.1 and a list of all available correlations is shown in Appendix B.

318 Solid/Liquid Separation: Equipment Selection and Process Design Setting p*ai
100 and p*ao
100p*a allows the averaged dimensionless air flow rate (u苶 a*e), superficial air velocity (ua) and design air rate (uades) to be respectively calculated by equations (6.80), (6.81) and (6.83) where * pao
100  pa*
100  23.3
76.7

uae*
1.1ua*

(6.169)

* * *  ( paeo pao )2  ( paei )2  *  * 2 paeo )  ( pai* )2   ( pao

76.7  11.652  34.96 2 
1.1u 11.65  76.72 100 2 

(6.170)

* a

ua
uae*

ua

kpb 1.24 × 1013 × 8582 3 2 1 m m s
uae*  a Ld 1.8 × 105 × 0.05


ua des


ua

(6.171)

* paeo  p  3300 * paeo  d pb

11.65 m 3 m2 s1 200 × 103  3300 11.65  8582

(6.172)

As previous, ua and uades are measured at atmospheric pressure and an * pb  pd  3300)
(11.65 × 8582  200 × absolute pressure of (paeo 3 10  3300) ⬅ 303 kPa respectively. The empirical correction factors (1.1 and 3300) are allowances to account for losses in the pipework upstream of the Nutsche filter. Alternatively, but potentially with less accuracy, the values of u苶 a* can be read directly from the design chart in Figure 6.9 after which equations (6.169)–(6.172) are used in the same way shown above to evaluate uades. (8) From equation (6.76), the mass of liquid in the cakes: Ml
S ( Ml ) pr
S × 50.9 kg

(6.173)

6.4.2.4 Summary of results and process implications With the -form of particle, the required filter area is 2 m2 for the specified 50 kg of solids per batch and 50 mm cake thickness. Each cake discharged

6 · Process design for batch separations 319 from the Nutsche contains ⬃16.6 kg of propanol and (theoretically) no undesirable solutes. A total of 637 kg of propanol passes through the filter per batch, including 178 kg of wash liquid and 5.14 kg of solutes are removed with the filtrate (4.57 kg) and washings (0.57 kg). As shown in the bottom row of Table 6.14, the total cycle time is 2775 s. With reference to Figure 6.15 and Table 6.11, the -form of particle is more acicular (needlelike) and forms a cake of higher compressibility as evidenced by the constitutive equations for cake resistance and solids volume fraction. If a sequence of calculations are performed for the -form with the 2 m2 Nutsche derived for the -form then the results shown in Table 6.15 are obtained. Due to different intrinsic properties, a cake containing 50 kg of solids now exhibits a thickness of 47.4 mm rather than the 50 mm observed with the -form. The approximate fourfold increase in specific cake resistance with the -form more than doubles the total cycle time and leads to a significantly wetter cake at the end of deliquoring (i.e. 28.6% compared with 24.9% for the -form). To achieve a 24.9% moisture content would require either a deliquoring time of ⬃72 min at the original 200 kPa pressure or a raised deliquoring pressure of 480 kPa applied for the specified 25 min. Table 6.15 Comparison of filter cycle performance for two particle forms in a Nutsche filter. Parameter

-form

-form

707 1.62 × 1010 0.365 50 50.5

2363 6.36 × 1010 0.371 47.4 48.9

Washing phase Duration (s) Fractional solute recovery

568 1

1959 1

Deliquoring phase Duration (s) ⭤ (td)e Cake saturation at (td)e Cake moisture content at (td)e

1500 0.33 24.9

1500 0.42 28.6

2775 0.773

5822 0.736

Filtration phase Duration (s) Specific cake resistance (m kg1) Cake solids volume fraction (v/v) Cake thickness (mm) Cake moisture content (%)

Total cycle duration (s) Total volume of liquids produced during cycle (m3) pf
200 kPa; Af
2 m2.

320 Solid/Liquid Separation: Equipment Selection and Process Design The implications of processing the -form of particle are significant in terms of either longer cycle times and/or raised equipment specification. It is evident that a reduced maximum cake thickness would lead to reduced filtration and deliquoring times, albeit at the expense of a larger filter area and the potential limitation of increased channelling (during washing) and cake cracking (during deliquoring) with excessively thin cakes. Conversely, a thicker cake would lead to a smaller filter but longer processing times.

6.5 Example of computer simulation – diaphragm filter press The calculations presented in Sections 6.4.1 and 6.4.2 illustrate the degree to which the operation of a filter can be predicted from the knowledge of suspension and cake properties as well as basic operational parameters. Simulations develop these procedures to allow the performance of batch filters to be investigated over a wide range of process conditions without the need to perform costly sequences of experiments. While any of the filters shown in Table 6.1 can be simulated with the aid of the equations and procedures presented throughout this chapter, the diaphragm filter press cycle considered in Section 6.4.1 is chosen to illustrate the process. To aid the simulation process, the Filter Design Software® described in Chapter 5 has been used to investigate the effects of changing formed cake thickness on filter performance. There are several ways to consider this problem, two of which are highlighted below. In Section 6.5.1, the mass of solids in the feed that enters the press is maintained at a constant value (i.e. 4527 kg) and the cake thickness per filtering surface is varied over the range 10– 40 mm. The consequence is a changed filter area to compensate for the different cake thickness. In Section 6.5.2 a different approach is taken whereby the formed cake thickness is altered over the same range but this time the filter area is fixed (i.e. 300 m2) such that the mass of solids varies. 6.5.1 Fixed mass of solids It is known in practice that greater productivity is obtained from filters if thinner cakes are formed. Using the example from Section 6.4.1 as a ‘base case’ and maintaining the values of all other parameters (except filter area) constant, the effects of cake thickness can be examined by performing a number of simulations where the maximum cake thickness per filter surface at the end of filtration with the pump is specified. For the chosen set of simulation conditions, where this cake thickness remains below 40 mm, both

6 · Process design for batch separations 321 filtration with the pump (at variable pressure) and filtration with the flexible diaphragms (at constant pressure) take place. As the filter chamber thickness is 80 mm, when 40 mm cakes are formed the cakes meet in the middle of each chamber at the end of filtration with the pump after which consolidation, rather than filtration, via the diaphragms occurs. Examples of the many effects of formed cake thickness are shown in Figures 6.16–6.22.

Total cake thickness per chamber (m)

0.10

a - end of filtration; b - consolidation c - washing; d - deliquoring a

0.08

b c

d

a b c

0.06

d

a c

0.04

d

b

a b 0.02

c

10 mm 20 mm 30 mm 40 mm

d

0.00 0

3000

6000 Cycle time (s)

9000

12000

Figure 6.16 Variation of the total cake thickness during the operating cycle of a diaphragm filter press where the mass of solids per batch is a constant. The legends indicate the maximum thickness of cake on each cloth during filtration with the pump and the chamber thickness is 80 mm. Although it may be intuitive that thicker cakes will tend to form at even slower rates (Figure 6.16) dependent on the shape of the pump curve and when the pressure drop across thicker cakes is greater (Figure 6.18), the other effects of limiting or allowing further cake growth in the diaphragm press are not so obvious a priori because of the interactions between so many variables. A larger pressure drop across a compressible cake could cause more compaction, however, the time taken to compact a thicker cake is greater than that needed to compact a thinner one (Figure 6.19), and hence the filtrate flux from a thicker cake tends to be rather lower. An uneconomic flux is therefore reached when the cake is in a less consolidated state, leaving the ‘thicker’ cake with a more open structure; in the particular examples shown, during the consolidation phase the thickness of the 40 mm cake (per filter surface) is

322 Solid/Liquid Separation: Equipment Selection and Process Design

Cumulative volume of liquids removed (m3)

60 c 50

d d

b

a

c b

a 40

30 10 mm 40 mm

20

a - end of filtration b - consolidation c - washing d - deliquoring

10

0 0

3000

6000

9000

12000

Cycle time (s)

Figure 6.17 Effect of formed cake thickness on the volume of liquids extracted during a diaphragm press cycle where the mass of solids per batch is a constant.

700 10 mm 20 mm 30 mm 40 mm

Pressure in filter chamber (kPa)

600 500

remaining phases in cycle

400 300

a a

200 a

100

a - end of filtration with pump

a 0 0

500

1000

1500

2000

Cycle time (s)

Figure 6.18 Effects of formed cake thickness on the pressures generated in the filter chambers of a diaphragm filter press where the mass of solids per batch is a constant.

6 · Process design for batch separations 323

Average cake moisture content (%)

55

aa

10 mm 40 mm

b

50

c

a - end of filtration b - consolidation c - washing d - deliquoring

b

45

c

40 35 30 d

25

d

20 0

3000

6000

9000

12000

Cycle time (s)

Figure 6.19 Influence of formed cake thickness on cake moisture content during a diaphragm press cycle where the mass of solids per batch is a constant.

160

a a 10 mm 40 mm

Solute mass in cake liquor (kg)

b

a - end of filtration b - consolidation c - washing d - deliquoring

120 b

80

40

c

0 0

d 3000

c

d 6000

9000

12000

Cycle time (s)

Figure 6.20 Effects of cake thickness on the total mass of solute in the filter cakes formed during a diaphragm press cycle where the mass of solids per batch is a constant.

324 Solid/Liquid Separation: Equipment Selection and Process Design

Fraction of solute recovered (-)

1.0

0.8

0.6

0.4 10 mm 20 mm 30 mm 40 mm

0.2

0.0 0

100

200

300

400

500

Washing time (s)

Figure 6.21 Effects of formed cake thickness on the fractional recovery of solute during the washing phase of a diaphragm press cycle where the mass of solids per batch is a constant.

Design air rate (m3 m-2 s-1)

1e-2

1e-3

1e-4

1e-5 10 mm 40 mm 1e-6 0

1500

3000

4500

6000

7500

Deliquoring time (s)

Figure 6.22 Effects of formed cake thickness on the air rate required to deliquor the cakes formed in a diaphragm press cycle where the mass of solids per batch is a constant.

reduced by ⬃9% compared to ⬃22% for the 10 mm cake. When thicker cakes are formed under the chosen conditions the washing efficiency is marginally improved as the number of required wash ratios reduces from 1.18 (10 mm cake) to 1.05 (40 mm cake), however, the time required to perform a washing

6 · Process design for batch separations 325 operation is significantly increased (Figure 6.21). Thicker cakes also significantly affect gas deliquoring and for the given example this has perhaps the greatest impact on the filter cycle. Deliquoring times are 20 times greater with 40 mm cakes compared to 10 mm cakes. The simulations, Figures 6.16–6.22 and the summary data shown in Table 6.16, suggest that increasing the cake thickness causes a number of changes in the cycle which impact on the economics of the separation. The main factors are: a) The extension of the cycle time that, for the particular examples chosen, has greatest effect in lengthening of the deliquoring phase. b) Higher energy consumption per unit product mass is a result of longer cycle times. c) A reduction in the overall solids (and liquid filtrate) productivity rate. d) An increase in the total volume of wash liquor consumed, which is particularly important when the wash is regenerated thermally for reuse, as might be the case with a solvent wash. e) A reduction in the filtration area required for the separation. Of these factors (a)–(d) tend to increase separator operating costs (or decrease revenues in the case of (c)), while (e) reduces both capital and to some extent maintenance costs. 6.5.2 Fixed filter area Rather than specifying the mass of solids per batch as a fixed value, the effects of maximum cake thickness can be investigated for a constant cloth area and variant mass of solids entering the press. While the influences of cake thickness are similar in general trend to several of the results shown in Figures 6.16 –6.22, the variation of pressure in the filter during cake Table 6.16 Effects of formed cake thickness on filter size and productivity for a fixed mass of solids per batch. Cake thickness per chamber (mm)

Total filtration area (m2)

Total cycle time (h)†

Nominal solids production rate (te h1)†

20 (2 × 10)

491

0.76

6.0

40 (2 × 20)

300

1.3

3.5

60 (2 × 30)

216

2.3

2.0

80 (2 × 40)

170

2.9

1.6

†

Ignores cake discharge time, cloth cleaning time etc.

326 Solid/Liquid Separation: Equipment Selection and Process Design formation with the pump and the fractional solute recovery during displacement washing are markedly different (see Figures 6.23 and 6.24 and compare with Figures 6.18 and 6.21, respectively). 700 remaining phases in cycle Pressure in filter chamber (kPa)

600 500 400 300 200

10 mm 20 mm 30 mm 40 mm

a a

100

a

a - end of filtration with pump

a 0 0

500

1000

1500 2000 Cycle time (s)

2500

3000

3500

Figure 6.23 Effects of formed cake thickness on the pressures generated in the filter chambers of a diaphragm filter press where the filter area is a constant.

Fraction of solute recovered (-)

1.0

0.8

0.6

0.4 10 mm 20 mm 30 mm 40 mm

0.2

0.0 0

100

200 300 Washing time (s)

400

500

Figure 6.24 Effects of formed cake thickness on the fractional recovery of solute during the washing phase of a diaphragm press cycle where the filter area is a constant.

6 · Process design for batch separations 327 As the filter area is constant, specifying a thicker cake simply continues the filtration process for a longer time under the same conditions and the pressure profiles thus partially overlay each other as shown in Figure 6.23. Regarding the cake washing, Figure 6.24 shows that the fractional solute recovery vs. time profiles are out of sequence as the cakes initially formed at 40 mm are washed marginally more efficiently (i.e. in a shorter time) than the cakes formed at 30 mm. The situation is a consequence of the higher dispersion number (Dn
131) and lower specific cake resistance (av
7.7 × 1010 m kg1) exhibited by the cakes formed at 40 mm compared to corresponding values for the cakes formed at 30 mm (Dn
99 and av
1.5 × 1011 m kg1). The complexity of interacting variables is further emphasised by the summary data in Table 6.17. While both the mass of solids processed per batch and the cycle time increase sequentially with formed cake thickness, for the chosen simulation conditions the nominal solids production rate, which is the ratio of these two parameters, passes through a minimum for a filter cycle with cakes initially formed at 30 mm thickness. For cakes formed at the maximum 40 mm thickness the durations of the filtration, compression and gas deliquoring phases are longer, however, these adverse effects are positively counteracted by the greater amount of solids processed per batch which results in the observed improvement in solids production rate. However, higher production rates are obtained when thinner cakes are processed which reinforces the findings presented in Section 6.5.1. Table 6.17 Effects of formed cake thickness on filter size and productivity for a fixed filter area. Cake thickness per chamber (mm) 20 (2 × 10) 40 (2 × 20) 60 (2 × 30) 80 (2 × 40)

Mass of solids per batch (te)

Total cycle time (h)†

Nominal solids production rate (te h1)†

2.8 4.5 6.3 8.0

0.6 1.3 2.4 2.7

4.7 3.5 2.6 3.0

†

Ignores cake discharge time, cloth cleaning time, etc.

By repeated use of simulations for a given cycle configuration it is possible to identify the optimum cake thickness to be formed during the overall filtration process. The optimum is application specific and a compromise between the efficiency of cycle operations and the overall economics and time scale of the filter cycle operation. It is clear that the effects of other process parameters on filter performance can also be readily assessed using simulations.

328 Solid/Liquid Separation: Equipment Selection and Process Design

6.6 Conclusions The methods described in this chapter show how calculations can be performed for batch filters in a way that takes some account of physical properties and operating conditions. The models employed are based on fundamental theories and practical results of varying complexity, all of which are sufficiently well developed to facilitate filter design and optimisation. The simulations, which make use of the Filter Design Software® described in Chapter 5, show how detailed calculation procedures can be implemented to investigate ‘what if?’ questions as well as the general influence of process variables on filter cycle performance. It is envisaged that application of procedures will help prevent the use of equipment whose actual performance falls below anticipated operating demands. Moreover, it is hoped that the user engineer can perform independent checks on equipment manufacturers’ designs and performance claims. Although the examples of the diaphragm filter press and Nutsche filter have been detailed to highlight what can be achieved, it is intended that the equations and models presented are used to simulate other filter types, including those in Table 6.1. In many ways it is not the detailed results shown in this chapter that are of prime importance, but the underlying methodology.

7

Process design for continuous separations

In this chapter the equations and models previously described in detail (Wakeman and Tarleton, 2005a) are used to provide process engineering models for continuous filter cycles. The models facilitate detailed calculations and provide a platform for the development of computer simulations. While there is scope to predict the performance of many of the continuous filters described in Chapter 1, those shown in Table 7.1 are discussed in sufficient detail to model and simulate their filter cycles. Table 7.1 Continuous filters and potential phases in their operational cycles. Filter type Horizontal belt Rotary drum: Bottom fed, all variants Top fed Internal fed Rotary table Rotary tilting pan Rotary disc

Washing

Gas deliquoring

Y

Y

Y

Y Y Y Y Y Y

Y Y

All feature an initial cake formation (filtration) phase.

In Section 7.1 the principal features of common continuous filter cycles are described, while Section 7.2 presents the equations required to model these cycles. Section 7.3 provides detailed example calculations for the horizontal belt filter and the rotary drum filter as these are representative of typical continuous cycles. Section 7.4 shows how computer simulations can be used to examine in detail the effects of process variables on

330 Solid/Liquid Separation: Equipment Selection and Process Design continuous filter performance. Appendix A provides additional information on the acceptable ranges for operational parameters in continuous filters, while Appendix D outlines the principles involved in troubleshooting their operation.

7.1 Continuous filter cycle configurations Continuous filter cycles are differentiated from the batch variants described in Chapter 6 by the manner in which filter cake is continually formed, processed and subsequently discharged without interruption. While this mode of operation has many potential advantages, a limitation with several continuous filters is the time constraints imposed on each phase in a cycle by the basic filter geometry and configuration. Cycles most frequently comprise a cake formation phase followed by single washing and deliquoring phases and then a cake discharge phase. However, some continuous filters are not able to perform washing at all due to the orientation of the filter medium while others can readily accommodate multiple washing phases, sometimes with a countercurrent movement of wash liquors (see also Wakeman and Tarleton, 1990). 7.1.1 Horizontal belt filter With the horizontal belt filter cycle an endless cloth supported on a perforated belt is driven around two rollers and across a sequence of evacuated suction boxes (see Figure 7.1 and Section 1.4.1.3). The feed suspension is introduced toward one end of the filter and processed at constant vacuum to form cake which is subsequently washed and/or gas deliquored theoretically as many

Figure 7.1 Schematic representation of a horizontal belt filter cycle.

7 · Process design for continuous separations 331 times as required at appropriate levels of vacuum. In principle, the length of the filter can be as long as required to accommodate process requirements, however, economic factors or space constraints may necessitate compromises. The final cake is discharged as it passes over the second roller. 7.1.2 Rotary drum filter The bottom fed, rotary vacuum drum filter comprises a multi-compartment drum that rotates slowly through a mechanically agitated trough of constantly replenished suspension (see Figure 7.2 and Section 1.4.1.5). The cycle commences when the constant vacuum applied inside the drum initiates upward filtration over the submerged region. As the drum rotates, the filter cake emerges from the suspension in the trough, passes through a rise phase, then a limited number of deliquoring and washing procedures are used to post-treat the cake; these latter phases may be conducted at different levels of vacuum if necessary. Cake discharge occurs at a point somewhere after the top-dead-centre mark (the precise location depends on the method of discharge). In practice, cake formation on bottom fed drum filters may be affected by the rotary valve and by movement of the slurry close to the growing cake – several correction factors have been proposed (Gale, 1971; Rushton, 1969; Rushton and Griffiths, 1971). While factors such as changing pressure drop/variable submergence, cake cracking and/or cake drop-off can influence cake formation, many rotary drum filtrations are successfully predicted using the equations formulated in Section 7.2.

Figure 7.2 Schematic of a bottom fed rotary drum filter cycle with knife discharge. The cycles of the alternative roller, string and belt discharge variants are similar and differ only (from the viewpoint of calculation) in the fraction of the drum devoted to cake discharge.

332 Solid/Liquid Separation: Equipment Selection and Process Design The cycle for the top fed, rotary vacuum drum filter is largely restricted by its configuration (see Figure 7.3 and Section 1.4.1.5). Rather than using a trough, the suspension is fed directly to the top of the drum after which rapid cake formation, gas deliquoring and cake discharge toward the bottom of the drum subsequently follow. Washing is usually not possible.

Figure 7.3 Illustration of a top fed rotary drum filter cycle. Although not explicitly shown, the pressure variant of the drum filter described in Section 1.4.2.6 can be simulated using the equations formulated in Section 7.2 with appropriate modifications to allow for pressure driven gas deliquoring. Details of the latter are shown in Section 6.2.4. 7.1.3 Rotary table and tilting pan filters The table filter comprises a rotating horizontal table notionally divided into sectors (see Figure 7.4 and Section 1.4.1.4). At the start of the cycle the feed suspension is introduced onto the table where filtration takes place through application of a vacuum beneath the cloth. As the table rotates, the now formed cake may move through one or more zones of displacement washing before undergoing vacuum deliquoring and continuous discharge via a screw conveyor. The rotary tilting pan filter is similarly oriented to the horizontal table filter but the single cloth is replaced with a series of annular compartments, each one of which is discrete and lined along its perforated bottom by an individual filter cloth. In the cycle, constant vacua are applied over the cloth

7 · Process design for continuous separations 333

Figure 7.4 Schematic diagram of a rotary table filter cycle. segments to initiate filtration and the formed cake is subsequently deliquored and/or washed by sprays according to requirements. The cake is discharged via a repetitive mechanism which inverts each pan in turn. A schematic of the filter cycle and a more detailed description have previously been shown in Figure 1.25 and Section 1.4.1.4, respectively. 7.1.4 Rotary disc filter The rotary disc filter cycle as shown in Figure 7.5 is restricted to single cake formation and deliquoring phases (see also Section 1.4.1.6). Due to the vertical

Figure 7.5 Schematic diagram of a rotary disc filter cycle showing the end view of one disc only; typical installations comprise multiple discs mounted on a common central shaft. Suspension is fed into the trough at an appropriate position along its length.

334 Solid/Liquid Separation: Equipment Selection and Process Design orientation of the sectored discs, displacement washing, although technically feasible, is difficult to perform reliably. A typical cycle is initiated by causing the discs to rotate through the trough of suspension where the internally applied vacua induce cake formations on both sides of each disc. As the cakes move out of the trough, deliquoring commences and proceeds until the discs rotate sufficiently to reach the discharge point. Like the rotary drum filter, a pressure driven variant of the disc filter exists (see Section 1.4.2.6). Adjustments to the cycle calculations for these filters are made in similar manner to that outlined in Section 7.1.2.

7.2 Design equations for continuous filter cycles As previously described, the cycle for a continuous filter typically comprises a cake formation phase followed by a combination of sequential displacement washing and gas deliquoring phases, potentially in any order. If a cycle is assumed to comprise the sequence filtration–washing–deliquoring and the subscripts f, d and w, respectively denote values for these phases, then the total time (tT) devoted to a cycle is given by  t t t  tT
t f  t w  t d  t dn
t f  1 w  d  dn  tf tf tf  

(7.1)

The term tdn denotes a filter downtime for cake discharge and cloth cleaning, which is largely ignored for the purpose of calculations; Table 1.3 gives typical values tdn expressed in terms of percentage of total cycle time. For linear filters, such as the horizontal belt filter, the length of filter cloth devoted to each phase (zx) is derived from equation (7.1) by noting the duration of a phase, (tx)e:

(t x )e


zx vB

(7.2)

zT
z f  zw  zd
vB 关(t f )e  (t w )e  (t d )e 兴  (t ) (t ) 
v B ( t f ) e  1 w e  d e  (t f )e (t f )e  

(7.3)

7 · Process design for continuous separations 335 where vB is the linear velocity of the belt. The area of cloth devoted to a phase (Ax) and the linear displacement from the position on the filter where filtration starts (xB) are related to zx and tx by Ax
z x hB

(7.4)

x B
x pr  vB t x

(7.5)

where xpr denotes the displacement at the end of the previous phase in a cycle and hB is the width of the belt. With rotary type filters, such as the rotary drum and tilting pan, the duration of a phase is given by an alternative expression

(t x )e


2 x


(7.6)

where
is the angular velocity (measured in rad s1) and x is the fraction of the cycle devoted to a given phase. The combination of equations (7.1) and (7.6) gives


关(t f )e  (t w )e  (t d )e 兴 2  (t ) (t ) 

( t f ) e  1 w e  d e  2 (t f )e (t f )e  

T
f  w  d


(7.7)

The area of cloth devoted to each phase is defined according to the filter type:  x DhD  A  x T Ax
x AT
  x n p Ap 0.5 x nd  (do2  di2)

drums table tilting pan disc

(7.8)

where D is the drum diameter, hD drum width, AT total cloth area, np the number of pans, Ap the cloth area in a single pan, nd the number of discs and

336 Solid/Liquid Separation: Equipment Selection and Process Design di and do are, respectively, the inner and outer diameters of the cloth on a disc. With the table filter, x must represent a whole number of segments on the filter and with the disc filter the cake formation takes place on both sides of each disc. For all rotary filters, the angular displacement from the position on the filter where filtration starts is given by


pr 

180
t x 

(7.9)

where pr is the angular displacement at the end of the previous phase in a cycle. When terms on the right hand sides of equations (7.3) and (7.7) are known, they can be used to decide whether an existing filter is able to handle process requirements and/or indicate the filter dimensions required for a given solids throughput, washing efficiency, etc. More phases can be accommodated within a cycle by appropriate additions to equations (7.1), (7.3) and (7.7). In the following development of equations that describe the individual phases in a cycle it is assumed that the physical dimensions of a separator are known a priori. With a knowledge of the linear or rotational speed of a filter the duration and cloth area devoted to each phase can be fixed, which then allows the solid, liquid and solute throughputs to be calculated. Should filter sizing be required instead then the equations need to be rearranged to give the cloth area active during each phase for a specified cake thickness or solids throughput; to progress calculations it is also necessary to assume values for all but one filter dimension (or linear/rotational speed if all dimensions of the filter are specified). Subsequent calculations for deliquoring or washing phases are identical to those shown except that a phase duration is calculated from a specified cake moisture or fractional solute recovery, which in turn fixes the cloth area required for each cake post-treatment. If necessary a particle size (x) representative of that in the feed can be calculated according to the Kozeny– Carman equation as represented by equation (6.2) where the average cake porosity (av), average specific cake resistance (av) and density of solids (s) need to be known. It is noted that Cav
1av, where Cav is the average volume fraction of solids in the cake (or solidosity). 7.2.1 Filtration (cake formation) phase In all the filter variants shown in Table 7.1, the filtration vacuum (pf) is fixed throughout cake formation such that av, Cav, the ratio mass wet/dry

7 · Process design for continuous separations 337 cake (mav) and effective feed concentration (c) remain constant. These properties are related to pf by constitutive equations:  av ⫽  0 (1⫺ n)⌬p nf

(7.10)

Cav ⫽ C0 ⌬p f

(7.11)

mav ⫽ 1⫹

c⫽

l  1⫺ Cav   s  Cav 

sl 1⫺ mav s

(7.12)

(7.13)

where l is the density of liquid and s the mass fraction of solids in the feed. The empirical scale-up constants 0, n, C0 and  are derived from sequences of constant vacuum experiments (see Chapter 4). In equations (7.10) and (7.11) it is implicitly assumed that for practical purposes the pressure drop across the cake can be approximated by the applied filtration vacuum. On continuous filters cake formation is described by the general filtration equation (i.e. the integrated form of equation (6.3) with pf
constant) to an extent dictated by the time of filtration (tf) such that  av c l 2 R Vf ⫹ l Vf ⫺ t f ⫽ 0 2 2 A f ⌬p f A f ⌬p f

(7.14)

and a mass balance gives

Lf


Vf c A f  s (1  av )

(7.15)

where Vf is the cumulative filtrate volume, Lf the cake thickness, R the filter medium resistance and l the viscosity of liquid. The filtration time is directly linked to the constant rotational or linear velocity of the moving cloth and for the calculation of data sequences an incremental time up to the

338 Solid/Liquid Separation: Equipment Selection and Process Design maximum (tf)e is chosen to provide the intermediate values. Noting that Vf is related to Lf by equation (7.15), Af is given by equation (7.8) and equation (7.14) is quadratic in Vf , then expressions for Vf , Lf and the filtrate flow rate (q) can be related to cake and filter properties by 2 2ct f ⌬p f Af  R   R ⫺ ⫹ Vf ⫽ ⫹   c   av l  av   av  

   

2  2ct f ⌬p f  R 1  R ⫺ ⫹   ⫹ Lf ⫽  sCav   av l  av   av  

q⫽

dV f dt f

⬇

V f t f

(7.16)

   

(7.17)

(7.18)

At a given tf , for the horizontal belt filter the linear displacement (xB) from the start of filtration is given by equation (7.5), while equation (7.9) gives the corresponding angular displacement () for rotary filters. From mass balances, the throughputs of cake solids mass (Ms(t)), liquid mass (Ml(t)) and solute mass (Msol(t)) can be stated as M s (t )⫽ K l L f Cav  s

(7.19)

Ml (t ) ⫽ K l L f (1⫺ Cav )l

(7.20)

M sol (t ) ⫽ K l L f (1⫺ Cav ) 0

(7.21)

where K1⫽ vBhB for the horizontal belt filter and K1⫽
AT /2 for all the remaining rotary filters. 0 is the solute concentration in the feed. With a value of Lf that corresponds to t⫽(tf)e, equation (7.19) gives the solids production rate for a filter. The cake moisture content (M ) in all cases is given by M ⫽ 100

M l (t ) Ml (t )⫹ M s (t )

(7.22)

7 · Process design for continuous separations 339 7.2.2 Displacement washing To describe the washing phase on a continuous filter cycle the dispersion model is preferred (Wakeman, 1986a; Wakeman and Attwood, 1988, 1990). A dispersion number (Dn) that characterises the cake washing process is calculated and for a known number of wash ratios (W ) the fractional solute recovery (F ) can be found. The applied vacuum (pw) is fixed throughout washing and several properties of the cake are assumed to remain constant and equal to the values at the end of the previous phase in the cycle, i.e. Lw ⫽Lpr ⫽(Lf)e, av ⫽(av)pr, Cav ⫽(Cav)pr ⫽1⫺(av)pr and Ms(t)⫽(Ms(t))pr. Many of the calculation procedures for cake washing on continuous filters are similar to those previously described for batch filters in Section 6.2.3. Several aspects are different, however, and to help avoid confusion the principal equations are reiterated here. The superficial velocity (u) and pore velocity (v) of wash liquor are related to the intrinsic properties of the cake by

u⫽

⌬pw w ( av  s LwCav ⫹ R )

(7.23)

v⫽

u  av

(7.24)

The ratio of the solute molecular diffusion coefficient (D) to the axial dispersion coefficient (DL) depends on Lw as well as the product of the Reynolds (Re) and Schmidt (Sc) numbers, where ReSc⫽vx/D, such that 0.707 DL  ⫽ 0.707 ⫹1.75ReSc D  0.96 0.707 ⫹ 55.5(ReScc)

ReSc ⬍ 1 ReSc ⬎ 1, Lw ⬎ 10 cm ReSc ⬎ 1, Lw ⬍ 10 cm

(7.25)

Dn is given by Dn ⫽ ReSc

Lw D x DL

(7.26)

For a minority of filters a correction factor has been established that accounts for deviations between theory and the reduced washing efficiency on full-scale

340 Solid/Liquid Separation: Equipment Selection and Process Design installations. The correction is applied to the dispersion number and for bottom fed drum filters it may be expressed as ( Dn )corr ⫽ 3.22 log( Dn ) ⫹ 0.395

(7.26a)

Washing is dictated by the fixed time available on a filter (tw) and interpolation up to the maximum, (tw)e is used to provide intermediate values in data sequences where (tw)e is given by equation (7.2) or (7.6). Noting that the available area for washing (Aw) is given by equation (7.8) and the displacement along/around the filter is given by either equation (7.5) or (7.9) then tT ⫽ t pr ⫹ t w

(7.27)

VT ⫽ Vpr ⫹ Vw ⫽ Vpr ⫹ Aw ut w

(7.28)

dVw ⫽ uAw ⫽ constant dt w

(7.29)

W⫽

vt w Lw

(7.30)

With the number of wash ratios known from equation (7.30), the fractional solute recovery is calculated by interpolation of the family of F vs. W curves on the design chart (see Figure 6.7) at the known Dn (or (Dn)corr if available). Alternatively, the curvefit correlations of dimensionless instantaneous solute concentration ( *) vs. W (see Appendix B and Wakeman and Tarleton, 2005a) can be numerically integrated to give F. If a gas deliquoring phase precedes washing then the cake saturation (S) will be less than unity at the start of washing and it is necessary to correct each value of W (YWS⫽1) calculated by equation (7.30) according to Wcorr ⫽ WS⫽1 ⫹15.1(1⫺ S )exp(⫺1.56 ⴱ ) ⫺7.4(1⫺ S 2 )exp(⫺1.72 ⴱ )

(7.31)

In all cases the mass throughput of cake solute is (for tw ⬎ 0) M sol (t ) ⫽ (1⫺ F ) [(M sol (t )) pr ⫺ w uAw ]⫹ w uAw

(7.32)

7 · Process design for continuous separations 341 where w is the solute concentration in the wash liquid, and the cake liquid throughput and moisture content are respectively given by equations (7.20) and (7.22). As an alternative to the dispersion model a wash curve can be directly specified, for instance in terms of F vs. W or F vs. tw. In this case the fractional recovery is interpolated directly from the wash curve for the known W or tw and there is no need to calculate a value for Dn according to equations (7.23)–(7.26a). 7.2.3 Gas deliquoring Although the general methodology and several of the equations for vacuum driven deliquoring are stated in Section 6.2.4 for batch leaf filters, they are repeated here for completeness to clearly elucidate the calculation procedures for continuous filters. The calculations for gas deliquoring require a priori knowledge of the threshold vacuum (pb) needed to initiate deliquoring and the irreducible cake saturation (S-) which is the minimum saturation that can be achieved by displacement of the interstitial liquid by the applied vacuum. Although both pb and S- can be measured experimentally in a capillary pressure test, the former can be reliably calculated with knowledge of the average cake porosity (av), liquid surface tension ( ) and representative particle size in the cake (x). The irreducible saturation is more difficult to calculate accurately from cake and particle properties but can be estimated with caution using equation (6.65). With a knowledge of pb and S-, the moisture content (M) as well as the air rate required to deliquor the moving cake can be calculated. The applied vacuum (pd) is fixed throughout gas deliquoring and several properties of the cake are assumed to remain constant and equal to the values at the end of the previous phase in the cycle, i.e. Ld ⫽Lpr ⫽(Lf)e, av ⫽(av)pr, Cav ⫽(Cav)pr ⫽1⫺(av)pr and Ms(t)⫽(Ms(t))pr . The cake permeability (kav) is related to the cake porosity and specific resistance by kav ⫽

1  av  sCav

(7.33)

and the cloth area available for gas deliquoring (Ad) is given by equation (7.8). As noted previously, the displacement along/around the filter is given by either equation (7.5) or (7.9) depending in the type of filter being considered. The extent of gas deliquoring is directly linked to the phase duration on a continuous filter and values of time up to the maximum, (td)e, are chosen to

342 Solid/Liquid Separation: Equipment Selection and Process Design provide intermediate values in data sequences where the latter is fixed by equation (7.2) or (7.6). Thus tT ⫽ t pr ⫹ t d

(7.34)

where the actual deliquoring time (td) is related to a dimensionless deliquoring time () by pⴱ ⫽

t d kav ⌬pd  av l ( Ld )2 (1⫺ S⬁ )

(7.35)

and p*⫽pd /pb. The product p*, which equation (7.35) shows is related to known cake and process parameters, allows a reduced saturation (SR) to be read directly from a design chart (see Figure 6.8), or calculated from a corresponding curvefit correlation of SR vs. p* (see Appendix B and Wakeman and Tarleton, 2005a). The cake moisture content and other time dependent variables are then given by S ⫽ S⬁ ⫹ SR (1⫺ S⬁ )

M⫽

100  s  Cav  ⫹1 Sl  1⫺ Cav 

VT ⫽ Vpr ⫹

(t d )e M s (t )  M pr M  ⫺   l  100 ⫺ M pr 100 ⫺ M 

(7.36)

(7.37)

(7.38)

dVd Vd ⬇ t d dt d

(7.39)

Ml (t ) ⫽ S ( Ml (t ))pr

(7.40)

M sol (t ) ⫽ S( M sol (t )) pr

(7.41)

7 · Process design for continuous separations 343 The design air rate (ua des), which determines the rating of the vacuum pump needed to progress the cycle, requires the calculation of a dimensionless pressure difference across the cake such that ⴱ ⴱ paⴱ ⫽ paei ⫺ paeo ⫽

pB pB ⫺ pd ⫺ pb pb

(7.42)

For the purpose of calculation p*ai⫽100 and p*ao⫽100 – p*a, and the averaged dimensionless air flow rate at p*ao (i.e. u苶a* ) is determined either directly from a design chart (see Figure 6.9) or by interpolation of the corresponding curvefit correlations for the family of curves for u苶a* vs.  (see Appendix B and Wakeman and Tarleton, 2005a). Hence uaeⴱ ⫽ 1.1uaⴱ

ua ⫽ uaeⴱ

ⴱ pao ⴱ paeo

ⴱ ⴱ ( paeo )2 ⫺ ( paei )2   ⴱ 2 ⴱ 2   ( pao ) ⫺ ( pai ) 

kav pb a Ld

(7.43)

(7.44)

where a is the gas viscosity and ua the superficial gas velocity. It is conventional practice to specify the air rate for a continuous filter on a ‘total cycle basis’ and thus ua is corrected to give ua 冷tot ⫽ ua

td ( tT ) e

(7.45)

and the design air rate is given by ⌬pd pb ⌬p ⫹ 3300 ⴱ paei ⫺ d pb ⴱ paei ⫺

ua 冷des ⫽ ua 冷tot

(7.46)

For belt filters, (tT)e in equation (7.45) is assumed to equal 2zT vB based on equation (7.2) and for all other rotary filters (tT)e⫽2
as given by equation (7.6).

344 Solid/Liquid Separation: Equipment Selection and Process Design

7.3 Examples of continuous filter cycle calculations In this section the horizontal belt filter and the rotary drum filter are chosen to illustrate the level of detail that can be achieved when the design equations and procedures outlined in Section 7.2 are used to size and predict the performance of continuous filters. 7.3.1 Example 7.1: Horizontal belt filter Problem It is proposed to use an existing horizontal belt filter to separate phosphoric acid from a slurry containing gypsum at 30% w/w. Cake formation at 50 kPa is to be followed by displacement washing and deliquoring phases at the same level of vacuum. The three phases respectively occupy 1.5 m, 4.5 m and 3 m of the 9 m total belt length. The feed suspension and belt filter characteristics are shown in Table 7.2 in addition to other operational parameters. Determine performance indicators for the filter cycle and identify the parameters which characterise cake composition at points along the moving belt. Solution The calculations follow the procedures outlined in Section 7.2 and divide into three phases where tT ⫽ tf ⫹ tw ⫹ td; in accordance with Table 1.3, tdn ⫽ 0. 7.3.1.1 Cake formation (filtration) phase Noting that the filtration vacuum in the scale-up equations for av and Cav has units of kPa, at 50 kPa, equations (7.10)–(7.13) give  av ⫽  0 (1⫺ n)⌬p nf ⫽ 7.1 × 108 (50)0.46 ⫽ 4.29 × 10 9 m kg⫺1

Cav ⫽ C0 ⌬p f ⫽ 0.23(50)0.085 ⫽ 0.321 v/v

mav ⫽ 1⫹

c⫽

l  1⫺ Cav  1390  1⫺ 0.321 ⫽ 1⫹  ⫽ 2.25     s  Cav  2350  0.321 

sl (30 Ⲑ100) × 1390 ⫽ ⫽ 1283 kg m⫺3 1⫺ mav s 1⫺ 2.25 × (30 Ⲑ100)

7 · Process design for continuous separations 345 Table 7.2 Characteristic parameters for the horizontal belt filter calculation (Example 7.1). Parameter

Value

Filter and septum characteristics Filter belt width (hB ) Filter belt length (zT ) Linear velocity of belt (vB ) Filter medium resistance (R)

2m 9m 0.1 m s⫺1 2 × 109 m⫺1

Operating conditions Belt length devoted to filtration (zf ) Belt length devoted to washing (zw ) Belt length devoted to deliquoring (zd ) Applied vacuum (pf , pw and pd ) Barometric pressure (pB ) Solids mass fraction in the feed (S) Solute concentration in the feed ( o ) Solute concentration in the wash ( w )

1.5 m 4.5 m 3m 50 kPa 101 kPa 30% w/w 40 kg m⫺3 0.4 kg m⫺3

Cake properties Constitutive equations for filtration, p in kPa* Particle and fluid properties Mean size of solids (xav ) Density of solids (s ) Density of filtrate and wash (l ) Viscosity of filtrate and wash ( l ) Surface tension of filtrate and wash ( ) Irreducible cake saturation (S-) Viscosity of air ( a) Solute diffusivity (D)

av ⫽ 7.1 × 108p 0.46 m kg⫺1 Cav ⫽ 0.23p 0.085 v/v 20 µm 2350 kg m⫺3 1390 kg m⫺3 0.001 Pa s 0.07 N m⫺1 0.3 1.8 × 10⫺5 Pa s 1 × 10⫺9 m2 s⫺1

*It is noted that av⫽0(1-n) pn⫽1.31 × 109(1⫺0.46)p0.6 ⫽ 7.1 × 108 p0.46 m kg⫺1.

From equations (7.2) and (7.4)

(t f )e ⫽

zf vB

⫽

1.5 ⫽ 15 s 0.1

A f ⫽ z f hB ⫽ 1.5 × 2 ⫽ 3 m 2

346 Solid/Liquid Separation: Equipment Selection and Process Design Table 7.3 Data sequences for the filtration phase of a horizontal belt filter cycle. xB (m)

Vf (m3)

Lf (m)

(1)

(2)

(3)

0 1.5 3.0 4.5 6.0 7.5 9.0 10.5 12.0 13.5 15.0

0 0.15 0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50

0 0.015 0.021 0.026 0.030 0.034 0.037 0.040 0.043 0.046 0.048

tf (s)

(4)

dVf /dtf (m3 s⫺1) (5)

Ms (t) (kg s⫺1) (6)

0 0.0083 0.0119 0.0148 0.0171 0.0192 0.0211 0.0229 0.0245 0.0260 0.0275

– 0.0097 0.0043 0.0033 0.0028 0.0025 0.0022 0.0020 0.0019 0.0018 0.0017

0 1.25 1.80 2.23 2.59 2.90 3.19 3.45 3.70 3.93 4.14

Ml (t) (kg s⫺1) (7)

Msol (t) (kg s⫺1) (8)

0 1.56 2.26 2.79 3.24 3.63 3.99 4.32 4.62 4.91 5.18

0 0.045 0.065 0.080 0.093 0.104 0.115 0.124 0.133 0.141 0.149

and the data sequences shown in Table 7.3 are calculated to provide information for the cake formation phase where: (1) Filtration time is determined by choosing a value between tf ⫽0 s and tf ⫽ 15 s, where tf corresponds to a distance xB along the belt. (2) Noting that xpr ⫽0 m and from equation (7.5), the distance along belt: x B ⫽ vB t f ⫽ 0.1t f m

(7.47)

(3) From equation (7.16), the cumulative volume of filtrate:

(7.48)

7 · Process design for continuous separations 347 (4) From equation (7.17), the cake thickness:

(7.49)

(5) From equation (7.18), the filtrate flow rate:

q⫽

dV f dt f

⬇

V f t f

m 3 s⫺1

(7.50)

(6) From equation (7.19), the throughput of cake solids at xB: M s (t ) ⫽ vB hB L f Cav  s ⫽ 0.1 × 2 × L f × 0.321 × 2350 kg s⫺1

(7.51)

(7) From equation (7.20), the throughput of cake liquid at xB : Ml (t ) ⫽ vB hB L f (1⫺ Cav )l ⫽ 0.1 × 2 × L f × (1⫺ 0.321) × 1390 kg s⫺1

(7.52)

(8) From equation (7.21), the throughput of cake solute at xB: M sol (t ) ⫽ vB hB L f (1⫺ Cav ) 0 ⫽ 0.1 × 2 × L f (1⫺ 0.321) × 40 kg s⫺1

(7.53)

The end of phase values are given in the bottom line of Table 7.3 including the solids production rate WR ⫽ Ms(t) ⫽ 4.14 kg s⫺1. The cake moisture content (M) is constant throughout cake formation and given by equation (7.22) where M ⫽ 100

M l (t ) 5.18 ⫽ 100 ⫽ 55.56 % M l (t ) ⫹ M s (t ) 5.18 ⫹ 4.14

(7.54)

348 Solid/Liquid Separation: Equipment Selection and Process Design 7.3.1.2 Washing phase The displacement washing phase is performed at the same level of vacuum as the filtration phase. From equations (7.2) and (7.4) (t w )e ⫽

zw 4.5 ⫽ ⫽ 45 s vB 0.1

Aw ⫽ zw hB ⫽ 4.5 × 2 ⫽ 9 m 2

Using values of Cav and av from the end of the filtration phase, and noting that Lw⫽ (Lf)e ⫽ 0.0275 m and the wash flow rate is a constant, the superficial wash velocity, mean velocity of fluid through the cake pores and wash flow rate are, respectively, given by equations (7.23), (7.24) and (7.29): u⫽

50 × 103 0.001(4.29 × 10 9 × 2350 × 0.0275 × 0.321⫹ 2 × 10 9 )

⫽ 5.5 × 10⫺4 m s⫺1

v⫽

u 5.5 × 10⫺4 ⫽ ⫽ 8.1 × 10⫺4 m s⫺1  av (1⫺ 0.321)

dVw ⫽ uAw ⫽ 5.5 × 10⫺4 × 9 ⫽ 0.005 m 3 s⫺1 dt w

and hence

ReSc ⫽

vx 8.1 × 10⫺4 × 20 × 10⫺6 ⫽ ⫽ 16.2 D 1 × 10⫺9

(7.55)

Since ReSc⬎1 and Lw⬍10 cm, then from equation (7.25) DL ⫽ 0.707 ⫹ 55.5(ReSc)0.96 D ⫽ 0.707 ⫹ 55.5(16.2)0.96 ⫽ 805

(7.56)

7 · Process design for continuous separations 349 Table 7.4 Data sequences for the washing phase of a horizontal belt filter cycle. tw (s) (1) 0 4.5 9.0 13.5 18.0 22.5 27.0 31.5 36.0 40.4 45.0

tT (s)

xB (m)

W

F (-)

* (-)

VT (m3)

(2)

(3)

(4)

(5)

(6)

(7)

Msol (t) (kg s⫺1) (8)

15.0 19.5 24.0 28.5 33.0 37.5 42.0 46.5 51.0 55.5 60.0

1.50 1.95 2.40 2.85 3.30 3.75 4.20 4.65 5.10 5.55 6.00

0 0.13 0.27 0.40 0.53 0.66 0.80 0.93 1.06 1.20 1.33

0 0.119 0.252 0.385 0.514 0.635 0.745 0.833 0.897 0.942 0.961

1.000 1.000 1.000 0.994 0.951 0.881 0.755 0.577 0.401 0.254 0.157

0.048 0.071 0.093 0.115 0.138 0.160 0.182 0.204 0.227 0.249 0.271

0.149 0.130 0.110 0.091 0.072 0.054 0.037 0.025 0.015 0.009 0.0057

and the dispersion number is calculated from equation (7.26):

Dn ⫽ ReSc

Lw D 0.0275 1 ⫽ 16.2 ⫽ 27.6 20 × 10⫺6 805 x DL

(7.57)

The data sequences shown in Table 7.4 are now evaluated to provide information for the washing phase at positions along the belt between xB⫽1.5 m and xB ⫽6 m where: (1) Washing time is determined by choosing a value between tw ⫽ 0 s and tw ⫽ 45 s, where tw corresponds to a distance xB along the belt. (2) From equation (7.27), the total cycle time: tT ⫽ t pr ⫹ t w ⫽ 15 ⫹ t w s

(7.58)

(3) From equation (7.5), the distance along the belt:

x B ⫽ x pr ⫹ vB t w ⫽ 1.5 ⫹ 0.1t w m

(7.59)

350 Solid/Liquid Separation: Equipment Selection and Process Design (4) From equation (7.30), the wash ratio:

W⫽

vt w 8.1 × 10⫺4 t w ⫽ Lw 0.0275

(7.60)

(5) Noting from equation (7.60) that the maximum number of wash ratios applied in 45 s is 0.0295 × 45 ⫽ 1.33, the fractional recovery at the known W is read directly from a design chart (see Section 6.2.2 and Figure 6.7). Alternatively, as shown below, the curvefit coefficients for the plots of dimensionless solute concentration ( *) vs. W, from which Figure 6.7 is derived, can be used. Referring to Appendix B, values of * are evaluated for both Dn⫽10 and 50, where  ⴱ ⫽ 1 0 ⱕ W ⱕ 0.2  ⴱ 2  ⫽ 0.663 ⫹ 2.3569W ⫺ 4.9493W 0.2 ⬍ W ⬍ 1.7 Dn ⫽ 10  ⫹ 2.9684W 3 ⫺ 0.5826W 4  ⴱ ⫽ 11.5698exp(⫺2.9575W ) 1.7 ⱕ W ⬍ 3.3  ⴱ W ⱖ 3.3  ⫽ 0

 ⴱ ⫽ 1 0 ⱕ W ⱕ 0.5  ⴱ 2  ⫽⫺5.3263 ⫹ 26.272W ⫺ 37.56W 0.5 ⬍ W ⬍ 1.4 4 3 Dn ⫽ 50  ⫹ 21.47W ⫺ 4.3437W  ⴱ ⫽ 44.08exp(⫺4.667W ) 1.4 ⱕ W ⬍ 2.4  ⴱ W ⱖ 2.4  ⫽ 0 and each pair of * values at the wash ratio given by equation (7.60) is interpolated to give the corresponding * value at Dn ⫽27.6. Further interpolation of the * vs. W dataset facilitates determination of the value of W that satisfies the relation defining F, where W

F ⫽ ∫ ⴱdW ⬇ 0

dW 2

W

∑(

ⴱ i

⫹ iⴱ⫺1 )

0

and trapezium rule integration is used as an approximation.

(7.61)

7 · Process design for continuous separations 351 (6) Determined from * vs. W dataset described in (5). Interpolation is used as appropriate. (7) From equation (7.28), the cumulative volume of liquid extracted from filter:

VT ⫽ V pr ⫹Vw ⫽ V pr ⫹ Awutw ⫽ 0.048 ⫹ 9 × 5.5 × 10⫺4 tw m 3

(7.62)

(8) Noting that w ⫽ 0.4 kg m⫺3, then from equation (7.32) the throughput of cake solute: M sol (t ) ⫽ (1⫺ F )(0.149 ⫺ 0.4 × 5.5 × 10⫺4 × 9) ⫹0.4 × 5.5 × 10⫺4 × 9 kg s⫺1

(7.63)

The throughput of cake solids remains constant throughout washing and is equal to the value at the end of filtration (Ms(t) ⫽ 4.14 kg s⫺1). The throughput of cake liquid, as given by equation (7.20), also remains the same as the density of filtrate and wash are equal (i.e. Ms(t) ⫽ 5.18 kg s⫺1). Hence, noting equation (7.54), the cake moisture content also remains constant during washing (M ⫽ 55.56 %). Values at the end of the washing phase are given in the bottom row of Table 7.4. Although no corrections have been applied to the wash ratio to account for splashing and other losses, in practice the wash ratio is likely to be greater than the values shown. If the losses can be quantified (no theory currently exists) then a correction factor ⬎1 is applied to column (4) to account for the additional wash volumes required. 7.3.1.3 Deliquoring phase The deliquoring phase is again performed at the same level of vacuum as the filtration phase, and equations (7.2) and (7.4) give (t d )e ⫽

zd 3 ⫽ ⫽ 30 s vB 0.1

Ad ⫽ zd hB ⫽ 3 × 2 ⫽ 6 m 2

Assuming that the cake height (Ld), cake solids concentration, specific cake resistance and mass of cake solids are constant and equal to the values at the

352 Solid/Liquid Separation: Equipment Selection and Process Design end of washing, then deliquoring calculations commence with calculation of the breakthrough vacuum (pb) and cake permeability (kav) which are respectively given by equations (6.64) and (7.33): pb ⫽

4.6Cav

4.6 × 0.321 × 0.07 ⫽ ⫽ 7616 Pa (1⫺ 0.321) × 20 × 10⫺6  av x

kav ⫽

1 1 ⫽ 9  av  sCav 4.29 × 10 × 2350 × 0.321

(7.64)

(7.65)

⫽ 3.1 × 10⫺13 m 2

The data sequences shown in Table 7.5 are now evaluated to provide information for the gas deliquoring phase at positions along the belt between xB ⫽ 6 m and 9 m where: (1) Time intervals for the gas deliquoring phase are determined by choosing a value between td ⫽ 0 s and td ⫽ 30 s; td corresponds to a distance xB along the belt. (2) From equation (7.34), the total cycle time: tT ⫽ t pr ⫹ t d ⫽ 60 ⫹ t d s

(7.66)

Table 7.5 Data sequences for the gas deliquoring phase of a horizontal belt filter cycle. td (s) tT (s)

xB (m)

S (-)

M (%)

(1)

(2)

(3)

(4)

(5)

u苶a des (m3 m⫺2 s⫺1) (6)

0 3 6 9 12 15 18 21 24 27 30

60 63 66 69 72 75 78 81 84 87 90

6.0 6.3 6.6 6.9 7.2 7.5 7.8 8.1 8.4 8.7 9.0

1.000 0.894 0.827 0.776 0.736 0.703 0.676 0.652 0.631 0.613 0.597

55.56 52.78 50.83 49.26 47.93 46.79 45.79 44.90 44.11 43.40 42.75

⫺ 5.93 × 10⫺6 3.73 × 10⫺5 1.03 × 10⫺4 2.04 × 10⫺4 3.40 × 10⫺4 5.08 × 10⫺4 7.05 × 10⫺4 9.28 × 10⫺4 1.17 × 10⫺3 1.44 × 10⫺3

VT (m3) (7)

Ml (t) (kg s⫺1) (8)

Msol (t) (kg s⫺1) (9)

0.271 0.283 0.291 0.296 0.301 0.304 0.307 0.310 0.312 0.314 0.316

5.18 4.63 4.28 4.02 3.81 3.64 3.50 3.38 3.27 3.18 3.10

0.0057 0.0051 0.0047 0.0044 0.0042 0.0040 0.0039 0.0037 0.0036 0.0035 0.0034

7 · Process design for continuous separations 353 (3) From equation (7.5), the distance along belt: x B ⫽ x pr ⫹ vB t w ⫽ 6 ⫹ 0.1t d m

(7.67)

(4) Cake saturation (S) is evaluated using a design chart (see Section 6.2.3 and Figure 6.8) or the equivalent curvefit coefficients for the plot of reduced saturation (SR) vs. the product of dimensionless deliquoring time () and dimensionless pressure ( p* ⫽
pd /pb ⫽50 × 103/7616 ⫽ 6.57). Using the latter, equation (7.35) gives

t d kav ⌬pd  av l ( Ld )2 (1⫺ S⬁ ) t d × 3.1 × 10⫺13 × 50 × 103 ⫽ (1⫺ 0.321) × 0.001 × 0.02752 (1⫺ 0.3)

p ⴱ ⫽

(7.68)

Referring to Appendix B, equation (B.2) allows SR to be calculated: 1  1⫹1.08(pⴱ )0.88  SR ⫽  1   1+1.46(pⴱ )0.48

0.096 ⱕ (pⴱ ) ⱕ 1.915 1.915 ⱕ (pⴱ ) ⱕ 204

(7.69)

and thus according to equation (7.36) S ⫽ S⬁ ⫹ SR (1⫺ S⬁ ) ⫽ 0.3 ⫹ SR (1⫺ 0.3)

(7.70)

(5) From equation (7.37), the cake moisture content:

M⫽

100 100 ⫽ % 2350  0.321   s  Cav  +1  ⫹1  S × 1390  1⫺ 0.321 Sl  1⫺ Cav 

(7.71)

or alternatively equation (7.54) and corresponding pairs of values for Ms(t) and Ml (t) from Table 7.5 can be used.

354 Solid/Liquid Separation: Equipment Selection and Process Design * (6) The dimensionless air rate (u 苶a ) is read directly from a design chart (see Figure 6.9 and Section 6.2.3) or interpolated from the equivalent curvefit correlations shown in Appendix B. Noting that pa* ⫽ p*, equation (7.42) gives

ⴱ ⴱ paⴱ ⫽ paei ⫺ paeo ⫽

⫽

pB pB ⫺⌬pd ⫺ pb pb

101 × 103 101 × 103 ⫺ 50 × 103 ⫽ 13.26 ⫺ 6.69 ⫽ 6.57 − 7616 7616

(7.72)

and from the curvefit correlation, values of 苶ua* are evaluated at  calculated using equation (7.68) for both pa*⫽ 5 and pa*⫽ 10, where

uaⴱ ⫽ 10 冢 0.331⫹0.4431log ⫺0.4369(log  )2 ⫺0.0126(log  )3 ⫺0.0058(log  )4 冣 10⫺4 ⱕ  ⬍ 0.8  4 3 2 paⴱ ⫽ 5 uaⴱ ⫽ 10 冢 0.2765⫹0.4395log ⫺0.2264(log  ) ⫹0.0606(log  ) − 0.0062(log  ) 冣 0.8 ⱕ  ⱕ 10 4  ⴱ 0.7202  ⬎ 10 4 ua ⫽ 10

uaⴱ ⫽ 10 冢 0.4085⫺0.6765log ⫺1.3865(log  )2 ⫺0.3329(log  )3 ⫺0.0304(log  )4 冣 10⫺4 ⱕ  ⬍ 0.3  4 3 2 paⴱ ⫽ 10 uaⴱ ⫽ 10 冢 0.7071⫹0.4015log ⫺0.2104(log  ) ⫹0.0503(log  ) − 0.0046(log  ) 冣 0.3 ⱕ  ⱕ 103  ⴱ 1.0039  ⬎ 103 ua ⫽ 10

The two resultant values are interpolated to give 苶u a* at p*a ⫽ 6.57. Noting that pai* ⫽ 100, ua tot ⫽ ua, and assuming that the total cycle time for a horizontal belt filter (tT)e ⫽ 2 × 90 ⫽ 180 s, the design air rate (ua des) is calculated according to equations (7.43)–(7.46): ⴱ pao ⫽ 100 ⫺ paⴱ ⫽ 100 ⫺ 6.57 ⫽ 93.43

(7.73)

7 · Process design for continuous separations 355 ⴱ ⴱ ⴱ 2  ( paeo pao )2 ⫺ ( paei )  u ⫽ 1.1u ⴱ  ⴱ 2 ⴱ 2  paeo  ( pao ) ⫺ ( pai )  ⴱ ae

ⴱ a

93.43  6.692 ⫺13.26 2  6.69  93.432 ⫺100 2 

⫽ 1.1uaⴱ

ua ⫽ uaeⴱ

ua

tot

kav pb 3.1 × 10⫺13 × 7616 3 ⫺2 ⫺1 m m s ⫽ uaeⴱ a Ld 1.8 × 10⫺5 × 0.0275

⫽ ua

td t ⫽ ua d m 3 m⫺2 s⫺1 ( tT ) e 180

(7.74)

(7.75)

(7.76)

⌬pd pb ⌬pd ⫹ 3300 − pb

ⴱ paei ⫺

ua

des

⫽ ua

tot ⴱ paei

50 × 103 7616 m 3 m⫺2 s⫺1 ⫽ ua tot 50 × 103 + 3300 13.26 ⫺ 7616 13.26 ⫺

(7.77)

where ua and ua des are measured at the deliquoring vacuum and a vacuum of pd ⫹ 3300 Pa respectively. The correction factors (i.e. 1.1 and 3300) are allowances to account for losses in the pipework of the filter. (7) From equation (7.38), the cumulative volume of liquid extracted from the filter:

VT ⫽ Vpr ⫹

(t d )e M s (t )  M pr M  ⫺  100 ⫺ M l 100 ⫺ M   pr

⫽ 0.271⫹

M  3 30 × 4.14  55.56 ⫺ m  100 ⫺ 55.56 100 ⫺ M  1390

(7.78)

356 Solid/Liquid Separation: Equipment Selection and Process Design (8) From equation (7.40), the throughput of cake liquid: Ml (t ) ⫽ S(Ml (t )) pr ⫽ S × 5.18 kg s⫺1

(7.79)

(9) From equation (7.41), the throughput of cake solute: M sol (t ) ⫽ S( M sol (t )) pr ⫽ S × 0.0057 kg s⫺1

(7.80)

The relevant end of phase (and cycle) values are given in the bottom row of Table 7.5. 7.3.1.4 Summary of results and filter cycle illustrations From the calculations it is evident that separation of the feed suspension and cake post treatment can theoretically be achieved using the horizontal belt filter. While the cake formation and washing phases show reasonable results, calculations for the deliquoring phase suggest a relatively high moisture content for the discharged cake. Depending on process requirements, further consideration may need to be given to reduce this to a more acceptable level. For instance, the total length of the belt could be increased to devote more time to deliquoring; further calculations show that when zd ⫽ 6 m, Me ⫽ 39.1% and when zd ⫽ 24 m, Me ⫽ 34.7 %. A summary of the overall mass balances for the solid, liquid and solute components in Example 7.1 is shown schematically in Figure 7.6, and Figures 7.7 and 7.8 illustrate graphically how some of the calculated parameters vary with distance along the belt. 7.3.2 Example 7.2: Rotary drum filter Problem A high value catalyst is to be separated from aqueous suspension at a temperature of 50ºC using a bottom fed, knife discharge, rotary drum filter. The drum is 2.5 m in diameter, 1.4 m in width and rotates at 0.2 rpm. The filter cycle follows the conventional sequence of cake formation, displacement washing (also at 50ºC) and gas deliquoring, and all phases take place at an applied vacuum of 70 kPa. The characteristics of the catalyst and suspension are shown in Table 7.6 along with other operational parameters of the filter. Determine the throughputs of solids, liquid and solutes and other pertinent values at all points in the filter cycle and comment on the feasibility of operation.

7 · Process design for continuous separations 357

Figure 7.6 Mass balance schematic for solids, liquid and solute (from FDS). The values shown for ‘filtrate’ include the throughputs of liquid and solute from both the cake formation and gas deliquoring phases.

end of deliquoring

0.30 end of washing

0.25 0.20 end of filtration

Volume of liquids extracted (m3)

0.35

0.15 0.10 0.05 0.00 0

2

4 6 Distance along belt (m)

8

10

Figure 7.7 Variation in the volume of liquid extracted through the moving cloth during the horizontal belt filter cycle.

Solution With reference to the outline calculation sequence in Section 7.2, the cycle is divided into consecutive phases such that tT ⫽ tf ⫹ tr ⫹ tw ⫹ td ⫹ tdn, where tr represents the rise phase between where the formed cake exits the trough of suspension and the start of cake washing (see Figure 7.2). Several aspects of the calculations for the rotary drum filter are similar to those presented for the horizontal belt filter in Section 7.3.1 and thus excessive repetitive detail has been omitted wherever appropriate.

358 Solid/Liquid Separation: Equipment Selection and Process Design

solids liquids

5 4

end of washing

2 1 0 0

end of deliquoring

3 end of filtration

Throughputs of solids and -1 liquid in cake (kg s )

6

2

4 6 Distance along belt (m)

8

10

Figure 7.8 Variation of the solid and liquid throughputs in the cake during the horizontal belt filter cycle.

7.3.2.1 Cake formation (filtration) phase At a filtration vacuum of 70 kPa, the intrinsic properties of the filter cake are respectively determined using equations (7.10)– (7.12) where av ⫽ 5.25 × 1010 m kg⫺1, Cav ⫽ 0.413 v/v and mav ⫽ 1.46. To calculate a value for the effective feed concentration (c), the mass fraction of solids in the feed (s) needs to be evaluated. Referring to Appendix C, which details conversion factors for alternative expressions of suspension concentration, equation (C.9) gives

 10  3070   100   sVs ⫽ s⫽ ⫽ 0.257 wⲐw Vs ( s ⫺ l ) ⫹ l  10   (3070 ⫺ 988) ⫹ 988  100 

(7.81)

(Y25.7% w/w) where Vs is the solids volume fraction in the feed. Thus, equation (7.13) gives c ⫽ 405 kg m⫺3. Noting that rotational speed of the drum (0.2 rpm) is equivalent to 0.2 × 2/60 ⫽ 0.021 rad s⫺1, equations (7.6) and (7.8) give

7 · Process design for continuous separations 359

(t f )e ⫽

2 f


⫽

2 × 0.34 ⫽ 102 s 0.021

A f ⫽ f DhD ⫽ 0.34 × 2.5 × 1.4 ⫽ 3.74 m 2

Table 7.6 Characteristic parameters for the rotary drum filter calculation (Example 7.2). Parameter

Value

Filter and septum characteristics Drum diameter (D) Drum width (hD ) Rotational speed of drum Filter medium resistance (R)*

2.5 m 1.4 m 0.2 rpm 1 × 1010 m⫺1

Operating conditions Drum submergence ( f ) Fraction of drum devoted to washing ( w ) Fraction of drum devoted to deliquoring ( d ) Applied vacuum (pf , pr , pw and pd ) Barometric pressure (pB ) Solids concentration in the feed Solute concentration in the feed ( 0) Solute concentration in the wash

0.34 0.15 0.2 70 kPa 100 kPa 10% v/v 15 kg m⫺3 0 kg m⫺3

Cake properties Constitutive equations for filtration, p in kPa** Particle and fluid properties Mean size of catalyst particles (xav ) Density of catalyst (s ) Density of filtrate and wash (l ) Viscosity of filtrate and wash ( l ) Surface tension of filtrate and wash ( ) Viscosity of air ( a) Solute diffusivity (D)

av ⫽ 5.76 × 109 p 0.52 m kg⫺1 Cav ⫽ 0.27 p 0.1 v/v 15 µm 3070 kg m⫺3 988 kg m⫺3 5.5 × 10⫺4 Pa s 0.068 N m⫺1 1.8 × 10⫺5 Pa s 1.5 × 10⫺9 m2 s⫺1

*Includes an allowance for the resistance due to the residual heel of cake present after knife discharge. **It is noted that av ⫽ 0(1-n)pn ⫽ 1.2 × 1010 (1⫺0.52)p0.52 ⫽ 5.76 × 109 p0.52 m kg⫺1.

360 Solid/Liquid Separation: Equipment Selection and Process Design Table 7.7 Data sequences for the filtration phase of a rotary drum filter cycle. tf (s) (1) 0 10 20 31 41 51 61 71 81 92 102

(°)

Vf (m3)

Lf (m)

(2)

(3) 0 0.040 0.057 0.070 0.081 0.091 0.099 0.108 0.115 0.122 0.1289

0 2.2 24.5 36.7 49.0 61.2 73.4 85.7 97.9 110 122

(4)

Ms (t) (kg s⫺1) (5)

Ml (t) (kg s⫺1) (6)

Msol (t) (kg s⫺1) (7)

0 0.0034 0.0048 0.0060 0.0069 0.0077 0.0085 0.0092 0.0098 0.0104 0.0110

0 0.157 0.225 0.277 0.321 0.360 0.395 0.427 0.457 0.485 0.512

0 0.072 0.103 0.127 0.147 0.165 0.181 0.195 0.209 0.222 0.234

0 1.09 × 10⫺3 1.56 × 10⫺3 1.93 × 10⫺3 2.23 × 10⫺3 2.50 × 10⫺3 2.74 × 10⫺3 2.97 × 10⫺3 3.18 × 10⫺3 3.37 × 10⫺3 3.56 × 10⫺3

and the data sequences shown in Table 7.7 are calculated for the cake formation phase where: (1) Time throughout the filtration phase is determined by choosing a value between tf ⫽ 0 s and tf ⫽ 102 s; tf corresponds to an angular displacement  around the drum from where filtration commences. (2) Noting that pr ⫽ 0º and from equation (7.9), the angular displacement around the drum:

⫽

180
t f 

⫽

180 × 0.021 × t f 

degrees

(7.82)

(3) From equation (7.16), the cumulative volume of filtrate:

(7.83)

7 · Process design for continuous separations 361 (4) From equation (7.17), the cake thickness at :

(7.84)

(5)–(7) From equations (7.19)–(7.21), and noting equation (7.8), the throughputs of cake solid, liquid and solute at  are respectively given by
DhD L f Cav  s 2 0.021 × 2.5 × 1.4 ⫽ L f × 0.413 × 3070 kg s⫺1 2

M s (t ) ⫽


DhD L f (1⫺ Cav )l 2 0.021 × 2.5 × 1.4 L f (1⫺ 0.413) × 988 kg s⫺1 ⫽ 2

(7.85)

M l (t ) ⫽


DhD L f (1⫺ Cav ) 0 2 0.021 × 2.5 × 1.4 ⫽ L f (1⫺ 0.413) × 15 kg s⫺1 2

(7.86)

M sol (t ) ⫽

(7.87)

From the bottom row of Table 7.7, the solids production rate WR ⫽ Ms(t) ⬇ 0.51 kg s⫺1 and the cake moisture content (M) is given by equation (7.22) where

M ⫽ 100

M l (t ) 0.234 ⫽ 100 ⫽ 31.39 % M l (t ) ⫹ M s (t ) 0.512 ⫹ 0.234

(7.88)

7.3.2.2 Rise phase The rise phase is the portion of the drum filter cycle between where the formed cake moves out of the suspension trough and the start of the next

362 Solid/Liquid Separation: Equipment Selection and Process Design phase in the cycle (for the given example this is cake washing). Assuming that the fraction of the drum devoted to cake discharge dis⫽ 0.1 (see Table 1.3 and thus from equation (7.6), tdn ⬇ 79 s), the fraction of the drum devoted to the rise phase is

r ⫽ 1⫺ dis ⫺ f ⫺ w ⫺ d ⫽ 1⫺ 0.1⫺ 0.34 ⫺ 0.15 ⫺ 0.2 ⫽ 0.21 Noting equations (7.6) and (7.9), at the end of the rise phase tT ⫽ t pr ⫹

2 × 0.21 ⫽ 102 ⫹ 63 ⫽ 165 s 0.021

e ⫽ 122 ⫹

180 × 0.021 × 63 ⫽ 198⬚ 

where (tr)e ⫽ 63 s and from equation (7.8) the area of the drum corresponding to the rise phase Ar ⫽ rDhD ⫽ 0.21 × 2.5 × 1.4 ⫽ 2.31m2. During the rise phase there are two potential scenarios which represent the extremes of operation. In the simplest case the cake is assumed to remain saturated and the values shown in the bottom row of Table 7.7 are valid throughout the whole phase with the exception of the displacement around the filter which ultimately becomes  ⫽ 198º. In practice this assumption is not unreasonable given that some wash liquor is likely to run down the rise side of the drum and (at least partially) cover the cake surface rather than permeate the cake. Alternatively the cake can be assumed to undergo deliquoring at the applied 70 kPa vacuum with the result that while cake height, resistance and solids concentration remain constant, the saturation and moisture content of the cake are progressively reduced over the interval  ⫽ 122;198º. For this scenario to occur no wash liquor must run down the rise side of the drum and all the wash liquor applied in the next phase permeates the cake. Following the procedure outlined in Section 7.2.3 and detailed in Section 7.3.1, the breakthrough vacuum and cake permeability are respectively given by equations (7.64) and (7.65) such that pb ⫽

4.6 × 0.413 × 0.068 ⫽ 14668 Pa (1⫺ 0.413) × 15 × 10⫺6

(7.89)

kav ⫽

1 ⫽ 1.5 × 10⫺14 m 2 5.25 × 10 × 3070 × 0.413

(7.90)

10

7 · Process design for continuous separations 363 As the irreducible cake saturation has not been measured it is necessary to calculate a value (with caution) using equation (7.65), N cap ⫽ ⫽

3av x 2 (l gLd ⫹⌬pd ) (1⫺  av )2 Ld

(1⫺ 0.413)3 × (15 × 10⫺6 )2 (988 × 9.81 × 0.011⫹ 70 × 103 ) 0.4132 × 0.011 × 0.068

(7.91)

⫽ 0.025 S⬁ ⫽ 0.155(1⫹ 0.031 × 0.025⫺0.49 ) ⫽ 0.184

The data sequences in Table 7.8 are calculated to give values at a range of points during the rise phase: (1) Time intervals are determined by choosing a value between tr ⫽ 0 s and tr ⫽ 63 s. (2) From equation (7.34), the total cycle time: tT ⫽ t pr ⫹ tr ⫽ 102 ⫹ tr s

(7.92)

Table 7.8 Data sequences for the rise phase of a rotary drum filter cycle where it is assumed that gas deliquoring at 70 kPa occurs throughout. tr (s) tT (s)

(º)

S (-)

M (%)

(1)

(2)

(3)

(4)

(5)

0 6 13 19 25 31 38 44 50 56 63

102 108 115 121 127 133 140 146 152 158 165

122 130 138 145 153 160 168 175 183 190 198

1.000 0.826 0.729 0.661 0.610 0.570 0.538 0.511 0.488 0.469 0.450

31.39 27.44 25.01 23.22 21.82 20.69 19.74 18.94 18.25 17.65 17.07

u苶a des (m3 m⫺2 s⫺1) (6) – 5.26 × 10⫺6 2.79 × 10⫺5 6.92 × 10⫺5 1.28 × 10⫺4 2.01 × 10⫺4 2.88 × 10⫺4 3.87 × 10⫺4 4.97 × 10⫺4 6.16 × 10⫺4 7.43 × 10⫺4

VT (m3) (7)

Ml (t) (kg s⫺1) (8)

0.1289 0.1315 0.1330 0.1340 0.1347 0.1353 0.1358 0.1362 0.1366 0.1369 0.1371

0.234 0.194 0.171 0.155 0.143 0.134 0.126 0.120 0.114 0.110 0.105

Msol (t) (kg s⫺1) (9) 3.56 × 10⫺3 2.94 × 10⫺3 2.59 × 10⫺3 2.35 × 10⫺3 2.17 × 10⫺3 2.03 × 10⫺3 1.91 × 10⫺3 1.82 × 10⫺3 1.74 × 10⫺3 1.67 × 10⫺3 1.60 × 10⫺3

364 Solid/Liquid Separation: Equipment Selection and Process Design (3) From equation (7.9), the angular displacement around the drum:

 ⫽ pr ⫹

180
tr 180 × 0.021 × tr ⫽ 122 ⫹ degrees  

(7.93)

(4) Cake saturation (S) is calculated using the correlation of reduced saturation (SR) vs. the product of dimensionless deliquoring time () and dimensionless pressure (p*⫽pr /pb⫽70 × 103/14668 ⫽ 4.77). Using a modified version of equation (7.35), where tr, pr and Lr replace td, pd and Ld, gives

pⴱ ⫽

tr × 1.5 × 10⫺14 × 70 × 103 (1⫺ 0.413) × 5.5 × 10⫺4 × 0.0112 (1⫺ 0.184)

Equation (7.69) provides a value for SR at the given p* and equation (7.36) allows S to be calculated where S ⫽ S⬁ ⫹ SR (1⫺ S⬁ ) ⫽ 0.184 ⫹ SR (1⫺ 0.184)

(7.94)

(5) From equation (7.37), (7.71) or (7.54) and corresponding values of Ms(t) and Ml(t) from Table 7.8, the cake moisture content:

M⫽

100 % 3070  0.413   ⫹1  S × 988  1⫺ 0.413 

(7.95)

(6) In order to calculate the design air rate (ua|des), the dimensionless air rate * (u 苶a ) is interpolated from the curvefit correlations as shown Section 7.3.1 and Appendix B. Noting that p*a ⫽p*, equation (7.42) gives

ⴱ ⴱ paⴱ ⫽ paei ⫺ paeo ⫽

100 × 103 100 × 103 ⫺ 70 × 103 ⫺ 14668 14668

⫽ 6.82 ⫺ 2.05 ⫽ 4.77

(7.96)

7 · Process design for continuous separations 365 From the curvefit correlation, values of u苶a* are evaluated at the known  for both pa* ⫽ 2 and pa* ⫽ 5 where the former is given by uaⴱ ⫽ 10 冢⫺0.3275⫹0.5687log⫺1.1410(log )2 ⫺0.3354(log )3 ⫺0.0359(log )4 冣 10⫺4 ⱕ  ⬍ 2  2 3 4 paⴱ ⫽ 2 uaⴱ ⫽ 10 冢⫺0.257⫹0.5046log⫺0.1602(log ) ⫹0.0253(log ) ⫺0.0016(log ) 冣 2 ⱕ  ⱕ 106  ⴱ 0.4456  ⬎ 106 ua ⫽ 10 and the corresponding correlations for the latter are shown in Section 7.3.1. The resultant pair of 苶ua* values is interpolated to give 苶ua* at pa* ⫽ 4.77. Noting that pai* ⫽ 100, ua|tot ⫽ ua and from equation (7.6) the total cycle time (tT)e ⫽ 2Ⲑ0.021 ⫽ 300 s, the design air rate (ua|des) is calculated according to equations (7.43)–(7.46): ⴱ pao ⫽ 100 ⫺ paⴱ ⫽ 100 ⫺ 4.77 ⫽ 95.23

uaeⴱ ⫽ 1.1uaⴱ

ua ⫽ uaeⴱ

ua 冷tot ⫽ ua

95.23  2.052 ⫺ 6.82 2  2.05  95.232 ⫺100 2 

1.5 × 10⫺14 × 14668 3 ⫺2 ⫺1 m m s 1.8 × 10⫺5 × 0.011

t tr ⫽ ua r m 3 m⫺2 s⫺1 ( tT ) e 300

70 × 103 14668 m 3 m⫺2 s⫺1 70 × 103 ⫹ 3300 6.82 ⫺ 14668

(7.97)

(7.98)

(7.99)

(7.100)

6.82 ⫺

ua 冷des ⫽ ua 冷tot

(7.101)

where ua and ua|des are measured at the deliquoring vacuum and a vacuum of
pr⫹3300 Pa respectively. The correction factors (i.e. 1.1 and 3300) are allowances to account for losses in the pipework of the filter.

366 Solid/Liquid Separation: Equipment Selection and Process Design (7) Substituting (tr)e for (td)e in equation (7.38), the cumulative volume of liquid extracted from the filter can be obtained: VT ⫽ 0.1289 ⫹

63 × 0.512  31.39 M  3 ⫺ m  988 100 ⫺ 31.39 100 ⫺ M 

(7.102)

(8) From equation (7.40), the throughput of cake liquid: Ml (t ) ⫽ S( Ml (t )) pr ⫽ S × 0.234 kg s⫺1

(7.103)

(9) From equation (7.41), the throughput of cake solute: M sol (t ) ⫽ S( M sol (t )) pr ⫽ S × 3.56 × 10⫺3 kg s⫺1

(7.104)

Comparing the data in Table 7.8 with the cake condition that exists when the cake does not undergo any change during the rise phase shows that with the former 6.4% more filtrate is produced, 55% of the solute is removed by the deliquoring process and the cake enters the washing phase with a saturation of 0.45 rather than 1. In the following, it is assumed that no cake cracking has occurred during the rise phase. 7.3.2.3 Washing phase From equations (7.6) and (7.8) (t w )e ⫽

2 w 2 × 0.15 ⫽ ⫽ 45 s 0.021


Aw ⫽ w DhD ⫽ 0.15 × 2.5 × 1.4 ⫽ 1.65 m 2

Irrespective of the initial saturation of the cake, the calculation of the dispersion number (Dn ) that characterises the washing process is procedurally identical to that shown in Section 7.3.1. Using values of Cav ⫽ 0.413 and av ⫽ 5.25 × 1010 m kg⫺1 from the end of the rise phase, and noting that Lw ⫽ (Lf)e ⫽ 0.011 m, the superficial wash velocity, mean velocity of fluid through the cake pores and wash flow rate are respectively given by equations (7.23), (7.24) and (7.29) such that u ⫽ 1.7 × 10⫺4 m s⫺1, v ⫽ 2.9 × 10⫺4 m s⫺1 and dVw Ⲑdtw ⫽ 2.8 × 10⫺4 m3 s⫺1. Since ReSc ⫽ vx/D ⫽ 2.92 and Lw⬍10 cm, then from equation (7.56) DL/D ⫽ 156 and Dn is calculated from equation (7.26): Dn ⫽ ReSc

Lw D 0.011 1 ⫽ 2.92 ⫽ 13.8 x DL 15 × 10⫺6 156

(7.105)

7 · Process design for continuous separations 367 For the drum filter a correction to Dn is applied that accounts for reduced efficiency at the full scale and according to equation (7.26a) ( Dn )corr ⫽ 3.22log( Dn ) ⫹ 0.395

(7.106)

⫽ 3.22log(13.8) ⫹ 0.395 ⫽ 4.1

Several of the data sequences that characterise the washing phase are dependent on the assumption made during the rise phase of the cycle. If the cake is assumed to remain saturated throughout the rise phase, then the values shown in Table 7.9 provide information for the washing phase at various positions around the drum where: (1) The washing time is determined by choosing a value between tw ⫽ 0 s and tw ⫽ 45 s where tw corresponds to a displacement  around the drum. (2) From equation (7.27), the total cycle time:

tT ⫽ t pr ⫹ t w ⫽ 165 ⫹ t w s

(7.107)

Table 7.9 Data sequences for the washing phase of a rotary drum filter cycle where it is assumed that no cake deliquoring occurs before washing commences. tw (s) (1) 0 4 9 13 18 23 27 32 36 41 45

tT (s)

 (º)

W

F (-)

* (-)

VT (m3)

(2)

(3)

(4)

(5)

(6)

(7)

Msol (t) (kg s⫺1) (8)

165 169 174 178 183 188 192 197 201 206 210

198 203 209 214 220 225 230 236 241 247 252

0 0.12 0.24 0.36 0.48 0.60 0.71 0.83 0.95 1.07 1.19

0 0.119 0.233 0.340 0.436 0.520 0.593 0.655 0.706 0.750 0.785

1.000 0.992 0.933 0.851 0.756 0.659 0.564 0.476 0.396 0.326 0.267

0.1289 0.1302 0.1315 0.1327 0.1340 0.1353 0.1365 0.1378 0.1391 0.1404 0.1416

3.56 × 10⫺3 3.13 × 10⫺3 2.73 × 10⫺3 2.35 × 10⫺3 2.01 × 10⫺3 1.71 × 10⫺3 1.45 × 10⫺3 1.23 × 10⫺3 1.04 × 10⫺3 8.91 × 10⫺4 7.64 × 10⫺4

368 Solid/Liquid Separation: Equipment Selection and Process Design (3) From equation (7.9), the angular displacement around the drum:  ⫽ pr ⫹

180
t w 180 × 0.021 × t w ⫽ 198 ⫹ degrees  

(7.108)

(4) From equation (7.30), the wash ratio:

W⫽

vt w 2.9 × 10⫺4 t w ⫽ Lw 0.011

(7.109)

(5) From equation (7.109), the number of wash ratios applied in a total of 45 s is 0.0264 × 45⫽1.19. At the known W, the fractional recovery (F) is determined as described in Section 7.3.1 and Appendix B. Using the available curvefit correlations, values of * are evaluated for both Dn⫽1 and Dn⫽5, where  ⴱ ⫽ 1  ⴱ  ⫽ 1.1433 ⫺1.9882W ⫹1.8761W 2 Dn ⫽ 1  ⫺0.9206W 3 ⫹ 0.1798W 4   ⴱ ⫽ 0.3515W ⫺1.4654

0 ⱕ W ⬍ 0.1 0.1 ⱕ W ⬍ 1.7 W ⱖ 1.7

 ⴱ ⫽ 1 0 ⱕ W ⱕ 0.1  ⴱ 2  ⫽ 1.0583 ⫹ 0.0795W ⫺1.7285W 0.1 ⬍ W ⬍ 2  ⫹1.241W 3 ⫺ 0.2603W 4 Dn ⫽ 5   ⴱ ⫽ 2.1739exp(⫺1.7383W ) 2 ⱕ W ⬍ 4.2   ⴱ ⫽ 0 W ⱖ 4.2 and each pair of * values at the known wash ratio (between W ⫽ 0 and) W ⫽ 1.19) is interpolated to give the corresponding * value at (Dn )corr⫽ 4.1. Further interpolation of the complete * vs. W dataset determines the value of W that satisfies the relation defining F in accordance with equation (7.61). (6) Determined from the * vs. W dataset described in (5). Interpolation is used where necessary.

7 · Process design for continuous separations 369 (7) From equation (7.28), the cumulative volume of liquid extracted from the filter: VT ⫽ Vpr ⫹ Vw ⫽ Vpr ⫹ Aw ut w ⫽ 0.1289 ⫹1.65 × 1.7 × 10⫺4 t w m 3

(7.110)

(8) Noting that w ⫽ 0 kg m⫺3, then from a simplified version of equation (7.32) the throughput of cake solute: M sol (t ) ⫽ ( M sol (t )) pr (1⫺ F ) ⫽ 3.56 × 10⫺3 (1⫺ F ) kg s⫺1

(7.111)

Noting that the filtrate and wash densities are identical, the throughput of cake solids, cake liquid and cake moisture content are equal to the values at the end of filtration where Ms(t) ⫽ 0.512 kg s⫺1, Ml(t) ⫽ 0.234 kg s⫺1 and from equation (7.22) M ⫽ 31.39 %. Alternatively, cake deliquoring can be assumed to occur during the rise phase at pr ⫽ 70 kPa such that cake entering the wash phase of the cycle has the unsaturated condition stated in the bottom row of Table 7.8. While several data sequences are identical to those obtained for a saturated cake, notably tw, tT, , F and *, Table 7.10 displays the sequences that are variant where: Column (4): The values of W (YWS⫽1) calculated using equation (7.109) are corrected for S ⫽ 0.45 according to equation (7.31): Wcorr ⫽ WS⫽1 ⫹15.1(1⫺ 0.45)exp(⫺1.56 ⴱ ) ⫺7.4(1⫺ 0.452 )exp(⫺1.72 ⴱ )

(7.112)

Columns (7) and (8): The cumulative volume of filtrate and mass of cake solute are amended to account for the revised values at the end of the rise phase/start of the washing phase: VT ⫽ Vpr ⫹ Vw ⫽ Vpr ⫹ Aw ut w ⫽ 0.1371⫹1.65 × 1.7 × 10⫺4 t w m 3 M sol (t ) ⫽ ( M sol (t )) pr (1⫺ F ) ⫽ 1.6 × 10⫺3 (1⫺ F ) kg s⫺1

(7.113)

(7.114)

370 Solid/Liquid Separation: Equipment Selection and Process Design Table 7.10 Data sequences for the washing phase of a rotary drum filter cycle where cake deliquoring has occurred prior to the commencement of washing. Values for tw , tT, , F and * are the same as those shown in Table 7.9.

tw (s)

W

VT (m3)

(1)

(4)

(7)

Msol (t) (kg s⫺1) (8)

0 4 9 13 18 23 27 32 36 41 45

0 0.82 0.99 1.19 1.42 1.67 1.92 2.18 2.44 2.70 2.94

0.1371 0.1384 0.1397 0.1410 0.1422 0.1435 0.1448 0.1460 0.1473 0.1486 0.1499

1.60 × 10⫺3 1.41 × 10⫺3 1.23 × 10⫺3 1.06 × 10⫺3 9.03 × 10⫺4 7.67 × 10⫺4 6.51 × 10⫺4 5.53 × 10⫺4 4.70 × 10⫺4 4.01 × 10⫺4 3.44 × 10⫺4

The cake is assumed to be fully resaturated as it exits the wash phase of the cycle such that Ml (t) ⫽ 0.234 kg s⫺1. 7.3.2.4 Deliquoring phase The calculation procedure for the gas deliquoring phase is identical to that shown for the rise phase where cake deliquoring is assumed to occur (i.e. equations (7.89)–(7.104)). Noting that the fraction of the drum devoted to deliquoring d ⫽ 0.2, equations (7.6) and (7.9) give values at the end of the deliquoring phase: tT ⫽ t pr ⫹

2 × 0.2 ⫽ 210 ⫹ 60 ⫽ 270 s 0.021

e ⫽ 252 ⫹

180 × 0.021 × 60 ⫽ 324⬚ 

where (td)e ⫽ 60 s. From equation (7.8) the area of the drum devoted to the deliquoring phase Ad ⫽ dDhD ⫽ 0.2 × 2.5 × 1.4 ⫽ 2.20 m2. Assuming that the cake does not change structure following washing, the cake height, resistance (and hence permeability) and solids concentration remain equal to

7 · Process design for continuous separations 371 the values used in calculations for the washing phase. With these assumptions equations (7.89)–(7.104) are used to evaluate the data sequences shown in Table 7.11 with appropriate values of deliquoring time between td ⫽ 0 s and 60 s. Table 7.11 Data sequences for the deliquoring phase of a rotary drum filter cycle where it is assumed that no gas deliquoring occurs during the rise phase. td (s)

VT (m3)

(5)

u苶a des 3 (m m⫺2 s⫺1) (6)

31.39 27.58 25.21 23.45 22.06 20.94 20.00 19.20 18.50 17.90 17.20

– 4.65 × 10⫺6 2.49 × 10⫺5 6.22 × 10⫺5 1.15 × 10⫺4 1.82 × 10⫺4 2.62 × 10⫺4 3.53 × 10⫺4 4.54 × 10⫺4 5.64 × 10⫺4 6.81 × 10⫺4

tT (s)

 (º)

S (-)

M (%)

(1)

(2)

(3)

(4)

0 6 12 18 24 30 36 42 48 54 60

210 216 222 228 234 240 246 252 258 264 270

252 259 266 274 281 288 295 302 310 317 324

1.000 0.832 0.737 0.669 0.619 0.579 0.546 0.519 0.496 0.477 0.454

(7)

Ml (t) (kg s⫺1) (8)

Msol (t) (kg s⫺1) (9)

0.1416 0.1440 0.1454 0.1463 0.1471 0.1476 0.1481 0.1485 0.1488 0.1491 0.1494

0.234 0.195 0.173 0.157 0.145 0.136 0.128 0.122 0.116 0.112 0.106

7.64 × 10⫺4 6.36 × 10⫺4 5.63 × 10⫺4 5.12 × 10—4 4.73 × 10⫺4 4.42 × 10⫺4 4.17 × 10⫺4 3.97 × 10⫺4 3.79 × 10⫺4 3.64 × 10⫺4 3.47 × 10⫺4

If the cake is assumed to undergo deliquoring during the rise phase, then the sequences for VT and Msol(t) are respectively amended to account for the different values of (VT)pr and 冇Msol(t)冈pr. In this case, at the end of the cycle (VT)e ⫽ 0.158 m3 and 冇Msol(t)冈pr ⫽ 1.56 × 10⫺4 kg s⫺1. 7.3.2.5 Summary of results and filter cycle illustrations The above calculations illustrate how the throughputs of solid, liquids and solute can be determined at all points in the drum filter cycle prior to discharge of cake with the scraper. A schematic of the cycle, as shown in Figure 7.9, serves to emphasise some of the restrictions imposed by the cylindrical geometry of the drum. Washing is largely restricted to the upper portions where the cake surface is near horizontal in orientation. For the particular example conditions chosen, should the washing phase be continued much further around the drum such that (w)e

252º, then wash liquors would tend to move over the surface of the cake undergoing final deliquoring to render this process less efficient. If the washing were to commence

372 Solid/Liquid Separation: Equipment Selection and Process Design

Figure 7.9 Schematic representation of the example rotary drum filter cycle. Cake formation phase 0 ; 122°, rise phase 122 ; 198°, washing phase 198 ; 252°, deliquoring phase 252 ; 324° and cake discharge 324 ; 360°.

earlier in the cycle such that (r)e198º, then wash liquors would, depending on the cake permeability, preferentially run down the surface of the rising cake and deposit in the feed trough rather than pass through the cake to facilitate washing. Such a process is sometimes deliberately introduced in the drum filter cycle to help prevent cake cracking during the rise phase; an alternative is to use a system of spray nozzles near the periphery of the drum to keep the cake moist. Unlike the example presented in Section 7.3.1 for the horizontal belt filter, it is more difficult to significantly alter the duration of a phase on a rotary drum cycle in isolation without impinging upon the operation of the overall cycle.

7.4 Example of computer simulation – belt filter Simulations provide the potential to investigate the performance of a filter over a range of process conditions, an ability to ask ‘what if?’ questions and ideally negate the need to perform costly sequences of experiments. To illustrate what can be achieved for continuous filters the horizontal belt filter cycle has been chosen. It is noted that any of the filters shown in Table 7.1 can be simulated using the equations and procedures presented throughout the earlier parts of this chapter. To aid the simulation process, the Filter

7 · Process design for continuous separations 373 Design Software® (FDS) described in Chapter 5 was used to investigate the effects of process parameters on filter performance where the example calculation shown in Section 7.3.1 provided the ‘base case’ data. In Sections 7.4.1–7.4.5, one operational parameter has been altered over a range each time while maintaining all the other process parameters, including the belt dimensions, at the values stated for the base case. 7.4.1 Effects of belt speed Changing the speed of the belt over the range 0.1–0.4 m s⫺1 alters the time available to accomplish each operation in the chosen cycle from a total of 90 s to 22.5 s (see Figures 7.10–7.12). A lower belt speed allows formation of a thicker cake with, for the example data chosen, slightly improved washing characteristics. The increased overall resistance to gas flow, however, reduces the air flux during the deliquoring phase and marginally raises the moisture content of the discharged cake from ⬃42.5% to ⬃42.8% . Higher belt speeds enable greater solids production rates by the formation of thinner cakes; final cake thickness varies between 27.5 mm and 13.4 mm. This may not be wholly desirable as washing efficiency is likely to be compromised due to an increased risk of channelling. Moreover, an increased belt speed requires more electrical power and can have detrimental effects for the life expectancy of filter belts and media. 9 0.2 m s-1 0.3 m s-1 0.4 m s-1

7 6 5 4 3

end of filtration

Throughput of solids in cake (kg s-1)

constant

0.1 m s-1

8

2 1 0 0.0

0 .5

1.0

1 .5

2.0

Distance along belt (m)

Figure 7.10 Effects of belt velocity on solids throughput during a horizontal belt filter cycle.

374 Solid/Liquid Separation: Equipment Selection and Process Design 0.35 0.1 m s-1 0.2 m s-1 0.3 m s-1 0.4 m s-1

Volume of liquids extracted (m3)

0.30 0.25

a end of filtration b washing c deliquoring

0.20 0.15

c b

0.10 0.05 a

0.00 0

2

4 6 Distance along belt (m)

8

10

Figure 7.11 Effects of belt velocity on the volume of liquids extracted through the moving cloth during a horizontal belt filter cycle.

0.1 m s-1 0.2 m s-1 0.3 m s-1 0.4 m s-1

0.003

0.002 end of deliquoring

Design air rate (m3 m3 s-1)

0.004

0.001

0.000 6

7

8

9

10

Distance along belt (m)

Figure 7.12 Effects of belt velocity on total cycle air rate during a horizontal belt filter cycle. 7.4.2 Effects of applied vacuum Figures 7.13–7.15 illustrate some of the effects of changing the constant vacuum along the belt between 25 and 75 kPa. In the chosen example the cake properties indicate moderate compressibility and an increased (constant) vacuum level changes the solids production rate from 3.6 to 4.5 kg s⫺1 with

7 · Process design for continuous separations 375 6 Throughput of liquid in cake (kg s-1)

a

b

5

4 c 3

2

1

a end of filtration b washing c deliquoring

25 kPa 75 kPa

0 0

2

4 6 Distance along belt (m)

8

10

Figure 7.13 Effects of applied vacuum on the liquid throughput in the cake during a horizontal belt filter cycle. 0.0030

48

cake moisture

0.0025

46 0.0020 44 0.0015 42

Design air rate (m3 m-2 s-1)

Cake moisture at discharge (%)

air rate

0.0010

40

0.0005 20

30

40

50

60

70

80

Applied vacuum (kPa)

Figure 7.14 Effects of applied vacuum on the deliquoring phase of a horizontal belt filter cycle. corresponding changes in liquid and solute throughputs. The relative differences in throughputs are maintained throughout the washing phase. As a result of the formation of thicker cake at higher levels of vacuum (28.9 mm at 75 kPa compared to 25.2 mm at 25 kPa) deliquoring is tempered to some extent although a raised vacuum still results in more gas flow and lower cake

376 Solid/Liquid Separation: Equipment Selection and Process Design

25 kPa 50 kPa 75 kPa

0.8

end of washing

Fractional recovery of solute (-)

1.0

0.6

0.4

0.2

0.0 1

2

3

4

5

6

7

Distance along belt (m)

Figure 7.15 Effect of applied vacuum on washing performance during a horizontal belt filter cycle.

moisture; the latter is primarily a consequence of the raised solids content due to additional cake compression rather than a significant difference in the throughput of cake liquid at the discharge point. In the case of washing, the formation of thicker cakes during filtration and higher vacua leads to greater removal of solute and the use of ⬃51% more wash liquor over the range investigated. With an incompressible filter cake whose structure does not change along the length of the belt, the effects of vacuum level on washing are almost solely to alter wash liquid flow rate according to Darcy’s Law. 7.4.3 Effects of plant altitude (barometric pressure) Barometric pressure affects the required capacity of the vacuum pump as shown in Figure 7.16. In the calculations the variation of barometric pressure with altitude was that recommended by DIN4705 (1979), and the applied vacuum was assumed to be constant at 50 kPa. No other effects on the filter cycle were observed. 7.4.4 Effects of temperature The effects of temperature on filter performance are complex in so far as physical properties which influence all parts of the cycle are affected. Temperature affects the rates of liquid flow through fluid viscosities and moisture contents during deliquoring through surface tensions (the effects of fluid densities being relatively insignificant). The important fluid property

7 · Process design for continuous separations 377 0.003

0.002

end of deliquoring

Design air rate (m3 m-2 s-1)

101 kPa 70 kPa

0.001

0.000 6

7

8

9

10

Distance along belt (m)

Figure 7.16 Effect of barometric pressure on the total cycle air rate for a horizontal belt filter cycle.

values over the temperature range from 5ºC to 35ºC are shown in Table 7.12. In the simulations for the effects of temperature it is assumed that: 1. The relations for specific cake resistance and cake solids concentration variation with applied vacuum are unaffected by temperature. 2. Washing occurs at the temperature of the feed and there is no change in solute diffusivity with temperature. 3. Deliquoring occurs at the temperature of the wash liquor. 4. When the wash and feed temperatures are independently varied either the wash or feed is assumed to be introduced to the filter at 25ºC. Table 7.12 Variations with temperature of wash and feed fluid properties. Temperature (°C) 5 15 25 35

(Pa s)

 (kg m⫺3)

(N m⫺1)

0.00171 0.00128 0.00100 0.00080

1395 1393 1390 1387

0.0728 0.0714 0.0700 0.0680

In Figure 7.17 the cake thickness (and hence solids throughput) increases as the feed temperature is increased due to the filtrate viscosity reduction, and most effects on the cycle are as a consequence of this. Over the feed

378 Solid/Liquid Separation: Equipment Selection and Process Design 0.04 5 °C 15 °C

0.02

end of filtration

Cake thickness (m)

constant

25 °C 35 °C

0.03

0.01

0.00 0.0

0.5

1.0

1.5

2.0

Distance along belt (m)

Figure 7.17 Effect of feed temperature on filtration performance for a horizontal belt filter cycle.

temperature range 5–35ºC the wash efficiency is marginally improved, the cake moisture content at discharge increases from 39.5% to 44.1% and the total cycle air rate reduces from 2.9 × 10⫺3 to 1.04 × 10⫺3 m3 m⫺2 s⫺1. Increasing the wash liquor temperature rather than the feed only causes changes to the deliquoring phase. Figure 7.18 shows that as the wash temperature increases so the cake moisture content at discharge decreases and 48

0.0018

0.0016 46 0.0014 44 0.0012 42

Design air rate (m3 m-2 s-1)

Cake moisture at discharge (%)

air rate

0.0010 cake moisture 0.0008

40 0

5

10

15

20

25

30

35

40

Wash liquor temperature (°C)

Figure 7.18 Effects of wash liquor temperature on the deliquoring phase of a horizontal belt filter cycle.

7 · Process design for continuous separations 379 the total cycle air rate increases correspondingly. The effects of wash temperature on cake moisture and air rate are a reversal of those seen on the same parameters for an increased feed temperature. Figures 7.19–7.21 show that preheating both the feed slurry and the wash liquor does not necessarily lead to better washing or reduced cake moisture contents. Raising 8 solids @ 5 °C liquids @ 5 °C

7

liquids @ 35 °C

5 4

end of washing

2 1

end of deliquoring

3 end of filtration

Throughputs of solids and liquid in cake (kg s-1)

solids @ 35 °C 6

0 0

2

4

6

8

10

12

Distance along belt (m)

Figure 7.19 Influences of changing both feed and wash liquor temperatures on the throughputs of solids and liquids in the cake during a horizontal belt filter cycle.

Volume of liquids extracted (m3)

0.4 5 °C 15 °C 25 °C 35 °C

0.3

a end of filtration b washing c deliqouring

0.2

c b

0.1

a

0.0 0

2

4

6

8

10

Distance along belt (m)

Figure 7.20 Influences of changing both feed and wash liquor temperatures on the volume of liquids extracted through the moving cloth during a horizontal belt filter cycle.

380 Solid/Liquid Separation: Equipment Selection and Process Design 48

0.0020

46

0.0018

44

0.0016 cake moisture

42

0.0014

40

Design air rate (m3 m-2 s-1)

Cake moisture at discharge (%)

air rate

0.0012 0

5

10

15

20

25

30

35

40

Temperature of feed and wash liquor (°C)

Figure 7.21 Influences of changing both feed and wash liquor temperatures on the deliquoring phase of a horizontal belt filter cycle. the feed temperature increases the throughput of solids and liquid in the cake (and cake thickness according to Figure 7.17) and raises wash liquor usage (shown by Figure 7.20). There is only a marginal change in both the washing efficiency and the cake moisture content at discharge. Although the assumptions made for the effects of temperature simplify the simulation process, the results shown are likely to provide reasonable approximations that are sufficiently accurate for initial design purposes. For better simulations more material specific experimental data are likely to be needed to assess the effects of temperature on the pertinent solid, liquid and solute properties. 7.4.5 Effects of particle size In many processing sequences a filter is preceded by a particle formation unit such as a crystalliser or precipitator, the product from which can have a profound effect on filter cycle performance. While the effects of particle size on washing and deliquoring are explicit in the equations, correlations and design charts relating to those processes, the effects on cake formation need to approximated for the purpose of simulation. Although ideally the variation of specific resistance and porosity with particle size would be assessed experimentally, for the current purpose approximations

7 · Process design for continuous separations 381 are made by assuming that cake solids concentration remains unchanged such that in accordance with permeability models:  av

1 ( xav )2

0.15 10 20 40 80

Cake thickness (m)

0.12

µm µm µm µm

constant a

0.09

a end of filtration

0.06

a

0.03

a a

0.00 0.0

0.5

1.0

1.5

2.0

Distance along belt (m)

Figure 7.22 Effect of feed particle size on formed cake thickness during a horizontal belt filter cycle.

10 20 40 80

0.006

µm µm µm µm

end of deliquoring

Design air rate (m3 m-2 s-1)

0.008

0.004

0.002

0.000 6

7

8

9

10

Distance along belt (m)

Figure 7.23 Effect of feed particle size on total cycle air rate during a horizontal belt filter cycle.

382 Solid/Liquid Separation: Equipment Selection and Process Design Figures 7.22 and 7.23 show that over the mean size range 10 – 80 m, larger particles can be expected to significantly increase the thickness and bulk volume of the cake and thus the solids throughput. With a thicker cake more effective washing is achieved at higher wash liquor flows (fractional recovery increases from 0.956 to 1), larger air volumes are consumed due to reduced resistance and a marginally lower cake moisture at discharge is observed (42.9% compared to 41.9%).

7.5 Conclusions The approach outlined in this chapter points a way to the design of continuous filters, which takes some account of the effects of physical properties and operating conditions. The models used for the calculations and simulations are based on fundamental theories and practical results of varying complexity, all of which are sufficiently well developed to facilitate filter sizing and other process calculations. The simulations, which make use of the Filter Design Software® described in Chapter 5, show how the detailed calculation procedures described can be implemented to investigate the influence of process variables on filter cycle performance. It is intended that application of the methodologies can help prevent the implementation of equipment whose actual performance falls below anticipated operating demands, and certainly enables the user engineer to perform independent checks on equipment manufacturers design and performance claims. Although the examples of the horizontal belt filter and rotary drum filters have been highlighted, the equations and models presented can be used by the reader to simulate other filter types. As such it is not the detailed results shown in this chapter that are important (although they may be of considerable interest to some), but it is the underlying methodology used to obtain the results which has widespread implications.

Nomenclature

Unless otherwise defined in the text, the symbols used have the following meanings: a 0, a 3, a 4

Constants

al~ a 2

Particle radius, m, or constants

A

Filtration area or settling area,

Aav

Arithmetic average surface area of cake in centrifuge in direction of filtration, m 2

A¢

Area of cloth used in a constant pressure filtration that follows cake formation with a pump or area of cloth used in a consolidation phase, m 2

Alm

Log mean surface area of cake in centrifuge in direction of filtration,

m 2, o r

Hamaker constant, J

m 2

Area of cylindrical filter element (candle) or filtering centrifuge bowl, m 2

Ao

Area of cloth in a single tilting pan, plate or chamber, Total area of cloth on filter,

Ar b, b o . . .

b 2

m 2

m 2

Constants Effective concentration of solids in the feed or suspension, kg m -3

C

Volume fraction of solids in a cake

Ce

Modified consolidation coefficient,

m 2 s-1

384 Solid/Liquid Separation: Equipment Selection and Process Design Ce0

Modified consolidation coefficient at unit applied pressure, m 2 s- 1 kPa-~

Cl Co

Mass of solid per volume of liquid in a suspension, kg m -3

Cs

Volume fraction of solids in a cake at unit applied pressure, kPa-~, or at zero applied pressure Suspension concentration expressed as mass of solid per volume of suspension, kg m -3 Diameter of a filter candle, m Inner diameter of filtering surface on a disc, m

do

Outer diameter of filtering surface on a disc or diameter of outer solid tube in a tube press, m

D

Diameter of tube, pipe, vessel or drum filter, m, or molecular diffusivity of solute, m 2 s - 1

OL

Axial dispersion coefficient, m 2 s -1

On

Dispersion number (=vL/DL)

(Dn )corr

Dispersion number corrected for full scale installation

e

Voids ratio, volume of liquid per volume of solid

eo

Voids ratio at unit applied pressure

E

Washing efficiency (defined as fraction of solute removed by one wash ratio), or electric field strength, V m -1

F

Fraction of solute removed from a filter cake by washing

g

Acceleration due to gravity, m s -2

G1-G 4

Gradients on Characteristic Plots for cake filtration, s m - 6 , and cake compression deliquoring, s -°5

GS

Sum of ratio of gradients

h

Candle length, or depth of centrifuge basket, m

hB

Filter belt width, m

hD

Filter drum width, m

H

Interparticle distance, m

He

Element, or closest element, spacing in a multi-element filter, m

Nomenclature 385 Height of suspension-supernatant interface as measured from the base of a containing vessel, m

11o

Initial height of suspension, m

H~

Final height of sludge in a jar sedimentation test, rn

i

Number of drainage surfaces

J.

Consolidation area factor applied to a 2-dimensional expression

k

Cake permeability, m 2

kr

Rate constant, s-1

K1, K2

Constants

L

Length of tube or pipe or thickness of a solid/liquid mixture, filter cake or bed, m

L gr

Average cake growth rate, m s-1

Ltr

Thickness of filter cake at the transition between filtration and consolidation stages of expression, m

m

Ratio of mass of wet cake to mass of dry cake

M

Moisture content of a filter cake, expressed as the ratio of mass of liquid in the cake to total mass of wet cake

Ml

Mass of liquids (in a filter cake if not otherwise stated), kg

Ml(t)

Throughput of liquids in a filter cake at a point on a continuous filter, kg s-1 Mass ratio, mass of solids per mass of liquid in a suspension

Ms

Mass of solids (in a filter cake if not otherwise stated), kg

Mso,

Mass of solute in a filter cake, kg

Ms(t)

Throughput of solids in a filter cake at a point on a continuous filter, kg s-1

Msol(O

Throughput of solute in a filter cake at a point on a continuous filter, kg s-1 Compressibility index, or number of particles in a suspension, or number of phases in a filter cycle

?/d

Number of discs

386

Solid/Liquid Separation" Equipment Selection and Process Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

np

Number of tilting pans, plates, flames or chambers

?lt

Number of candles or leaves in a multi-element filter Capillary number

p

Dimensionless pressure

Pa

Pressure in air phase, Pa

Paei

Pressure in air phase at air entry surface of cake on actual filter installation, Pa

Paeo

Pressure in air phase at air exit surface of cake on actual filter installation, Pa

Pal

Pressure in air phase at air entry surface of cake, Pa

Pao

Pressure in air phase at air exit surface of cake, Pa

Pb

Threshold pressure or vacuum, Pa

P8

Barometric pressure, Pa

PS

Compressive drag pressure acting on the solids in a filter cake, Pa

Ap

Pressure difference, Pa

q

=dV/dt, volume flow rate of filtrate, m 3 S - 1

Q

Volumetric flow rate, m 3 s -1 Radial co-ordinate, or half length/radius of a filter plate, or radius of rotation, m

re

Radius of cake layer in a centrifuge, m Inner radius of cake in a centrifuge or pan on a tilting pan filter, m Radius of liquid layer inside a centrifuge, m

r0

Inner radius of centrifuge drum or radius of a filter candle, m

R

Resistance to fluid flow through a filter cloth, m -~, or fraction of solute originally in a filter cake that is retained after washing

Re

Reynolds number Mass fraction of solids in a feed suspension Saturation, volume of liquid in a cake per unit volume of the voids

Nomenclature 387 Proportion of final sediment height to initial height of suspension in a jar sedimentation test Reduced saturation So

Specific surface of particles, m e m -3

S~

Irreducible saturation

Sc

Schmidt number

t

Time, s

td

Deliquoring time, s

ti

Time at which filtration is considered to commence, s

T

Thickness of a filter press frame or chamber, m, or temperature, K or °C

L

Dimensionless consolidation time

L

Depth of recess in a plate from a filter press, m

AT

Distance moved by a diaphragm, m Superficial velocity, m 3 m -e s-1

m,

bl

Dimensionless flux during deliquoring averaged over the deliquoring time

bla Ides

Design air rate, m 3 m -e s-1

bl altot

Design air rate on a total cycle basis, m 3 m -e s -1

bl i

Initial settling rate in a jar sedimentation test, m s -1

Uc

Consolidation ratio Pore (or interstitial) velocity of a fluid, m s -~

VB

Linear velocity of a filter belt, m s-

Vl

Volume of liquid, m 3

VS

Volume of solid, m 3

v,v

Filtrate volume, m 3

VA

Potential energy of interaction due to van der Waals attraction, J

cake

Vi

Volume of cake at start of compression deliquoring, m 3 Volume of filtrate at start of filtration, m 3

388 Solid/Liquid Separation" Equipment Selection and Process Design •

_

_

~

VR

Potential energy of interaction due to electrostatic repulsion, J

Vv

Total potential energy of interaction, J

V0

Volume of suspension in a piston press at the start of a test, m 3

VR

Volume ratio, volume of solids per volume of liquid

Vs

Solids volume fraction in a suspension or solid/liquid mixture

Vw

Wash liquor volume, m 3

w

Mass of dry cake per unit filter area, kg

W

Wash ratio (amount of wash liquid passed through a cake per unit amount of liquid in the cake at start of washing)

Wcorr

Corrected wash ratio that accounts for an initially unsaturated cake

x

Particle diameter or piston displacement in a piston press, m

x8

Distance along a belt filter, m

Y

Overall production rate from a filter, kg s-1 or m 3 s-

z

Co-ordinate direction, or valency, or length of filter devoted to a filter cycle phase, m

m -2

Greek letters Specific resistance of a filter cake, m kg -~

~0

Specific resistance at unit applied pressure or at zero applied pressure, m kg -1 kPa -n

O~av

Specific resistance of a filter cake averaged over the compressive drag stress, m kg-1 Compressibility index

6c

= 2/(r0 Pc), m2 kg-1 Porosity, volume of voids per unit volume of filter cake (or porous medium)

%

Effective porosity at unit applied pressure, kPa -~, or at zero applied pressure

ep

Permittivity of a suspending fluid, C 2 J-~ m -1

Nomenclature 389 Solute concentration in the liquid being discharged from a cake, kg m -3, or fraction of filter surface devoted to a filter cycle phase Solute concentration in the liquid in cake voids prior to washing, kg m -3

~C

Solute concentration in cake liquor, kg m -3

~a~

Solute concentration in a wash effluent that is collected over a period and mixed, kg m -3

~W

Solute concentration in feed wash liquor, kg m -3 Included angle of a tilting pan or angular displacement around a rotary filter, rad Index in scale-up equation for consolidation Shear rate, sReciprocal electrical double layer thickness, m Compressibility index Viscosity of filtrate or liquid in a feed, Pa s Dimensionless time Density of filtrate or liquid in a feed, kg m -3

PC

Bulk density of a filter cake, kg m -3

PS

Density of solids or particles, kg m -3 Surface tension, N m -~ Consolidation index

09

Angular velocity, rad s -~

(J)O

Volume of solids per unit filter area, m 3 m -2 Voltage potential at a particle surface, V

02

Voltage potential at boundary of Stern layer, V Zeta-potential, defined as the voltage potential at the plane of slip for a particle moving relative to a suspending fluid, V

Subscripts a

Referring to air

av

Average value

390 Solid/Liquid Separation: Equipment Selection and Process Design c

Referring to consolidation phase in a filter cycle

cake

Value for a filter cake

cycle

Referring to whole filter cycle

d

Referring to deliquoring phase in a filter cycle

dis

Referring to cake discharge

dn

Referring to filter downtime (e.g. for cake discharge and cloth cleaning)

e

Denotes end of a phase in a filter cycle or filter test

f

Referring to filtration phase in a filter cycle

g

Referring to the gas phase (subscripts a and g are used interchangeably)

i

Denotes position in a table or sequence of calculations

1

Referring to liquid

min

Minimum allowable value

opt

Optimum value

pr

Value at the end of the previous phase in a filter cycle

r

Referring to rise phase on a drum or disc filter

s

Referring to solids

susp

Value for a suspension

t

Value that is a function of time

T

Referring to a sum of values over several phases in a filter cycle or the whole cycle

tr

Referring to the transition point between phases in a filter cycle or filter test

w

Referring to wash liquor or the washing phase in a filter cycle

x

Referring to a phase in a filter cycle

0

Initial value, unless otherwise stated Equilibrium value

Superscripts Dimensionless value (unless otherwise stated)

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394 Solid/Liquid Separation" Equipment Selection and Process Design Hicks C.E and Hillgard A., 1970. Pressure filtration or centrifugal separation - complementary or competitive, Filtr. Sep., 7, 456-460. Ho W.S. and Sirkar K.K. (Eds.), 1992. Membrane Handbook, Van Nostrand Reinhold, New York. Holeschovsky U.B. and Cooney C.L., 1991. Quantitative description of ultrafiltration in a rotating filtration device, AIChEJ, 37, 1219. Hunter R.J., 1995. Foundations of Colloid Science, Clarendon Press, Oxford. Ives K.J., 1973. Mathematical models of deep bed filtration, in "The Scientific Basis of Filtration", Ed. K.J. Ives, pp. 203-224, NATO Advanced Study Institute Series E2, Noordhoff International Publishing, Leyden. Ives K.J. (Ed.), 1975. The Scientific Basis of Filtration, Noordhoff, Leyden. Johansson C. and Theliander H., 2003. Measuring concentration and pressure profiles in deadend filtration, Filtration, 3(2), 114-120. Kelsey G.D., 1965. Some practical aspects of continuous rotary vacuum filters, Trans IChemE, 43, T248-T255.

Kirk-Othmer Encyclopaedia of Chemical Technology, 1980, 3rd Edition, Wiley, New York. Kobayashi Y., Ohba S. and Shimuzu K., 1993. Analysis of dewatering performance of belt press filter, Proc. 6th World Filtration Congress, pp. 778-781, Japanese Filtration Society, Nagoya. Komline T.R., 1980. Sludge dewatering equipment and performance, AIChE Symp. Ser., 76(197), 321-332. Korhonen E., Lahdenper~i E. and Nystr6m L., 1989. Selection of equipment for solid-liquid separation by expert systems, Proc. Filtech Conference, pp. 436-443, The Filtration Society, Karlsruhe. Kos E, 1974. Gravity thickening of water-treatment plant sludges, 94th Annual Conference of AWWA, Boston. Kuo M.T. and Barrett E.C., 1970. Continuous filter cake washing performance, AIChEJ, 16, 633-638. Kynch G.J., 1952. A theory of sedimentation, Trans Faraday Soc., 48, 166-176. Kyll6nen H.M., Pirkonen E and Nystr6m M., 2005. Membrane filtration enhanced by ultrasound: a review, Desalination, 181, 319-335. La Mer V.K. and Healy T.W., 1966. The nature of the flocculation reaction in solid-liquid separation, in "Solid/Liquid Separation", Eds. J.B. Poole and D. Doyle, pp. 44-59, HMSO, London. Leung W.W.E, 1998. Industrial Centrifugation Technology, McGraw-Hill, New York. Leung W.W.E, 2005. Sedimenting centrifuges, in "Solid/Liquid Separation: Scale-up of Industrial Equipment", Eds. R.J. Wakeman and E.S. Tarleton, pp. 375-441, Elsevier, Oxford. Lin I.J. and Benguigui L., 1983. High-intensity, high-gradient dieIectrophoretic filtration and separation processes, in "Progress in Filtration and Separation 3", Ed. R.J. Wakeman, pp. 149-204, Elsevier, Amsterdam. Lu W.M., Huang Y.E and Hwang K.J., 1998b. Methods to determine the relationship between cake properties and solid compressive pressure, Separ. Purif Technol., 13, 9-23. Maloney G.E, 1972. Selecting and using pressure leaf filters, Chem. Eng., 79(11), 88-94. Matteson M.J. and Orr C. (Eds.), 1987. Filtration, Marcel Dekker, New York.

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396 Solid/Liquid Separation" Equipment Selection and Process Design Records A. and Sutherland K., 2001. Decanter Centrifuge Handbook, Elsevier Advanced Technology, Oxford. Rushton A., 1969. The effect of concentration in rotary vacuum filtration, Filtr. Sep., 6, 136-139. Rushton A., 1978. Pressure variation effects in rotary drum filtration with incompressible cakes, Powder Technol., 20, 39-46. Rushton A., 1981. Centrifugal filtration, dewatering and washing, Filtr. Sep., 18, 410-415. Rushton A. and Griffiths EV.R., 1971. Fluid flow in monofilament filter media, Trans IChemE, 49, 49-59. Rushton A. and Wakeman R.J., 1978. Theory vs. practice in vacuum, pressure and centrifugal filtration, J. Powder Bulk Solids Tech., 1, 58-65. Rushton A., Ward A.S. and Holdich R.G., 1996. Solid-Liquid Filtration and Separation Technology, VCH Verlagsgesellschaft, Weinheim. Salmela N. and Oja M., 2005. Analysis and modelling of starch dewatering, Filtration, 5(2), 134-145. Sambuichi M., Nakakura H., Nishigaki E and Osasa K., 1994. Dewatering of gels by constant pressure expression, J. Chem. Eng. Jpn., 27, 616-620. Sanstedt H.N., 1980. Non-wovens in filtration applications, Filtr. Sep., 17, 358-361. Saveyn H., Weber K., Van der Meeren E and Stahl W., 2003. Two-sided electrofiltration of yeast suspensions: Filtration kinetics and physiological impact, Filtration, 3(4), 224-230. Schaefer A., Fane A.G. and Waite T.D., 2004. Nanofiltration: Principles and Applications, Elsevier Advanced Technology, Oxford. Schweitzer EA. (Ed.), 1997. Handbook of Separation Techniques for Chemical Engineers, 3rd Edition, McGraw-Hill, New York. Scott K. and Hughes R. (Eds.), 1996. Industrial Membrane Separation Technology, Blackie, Glasgow. Scott K., 1997. Handbook of Industrial Membranes, Elsevier, Oxford. Shaw D.J., 1992. Introduction to Colloid and Surface Chemistry, 4th Edition, Butterworths, London. Shirato M., Murase T., Kato H. and Fukaya S., 1970. Fundamental analysis for expression under constant pressure, Filtr. Sep., 7, 277-282. Shirato M., Murase T., Negawa M. and Moridera H., 1971. Analysis of expression operations, J. Chem. Eng. Jpn., 4, 263-268. Shirato M., Murase T., Tokunaga A. and Yamada O., 1974. Calculations of consolidation period in expression operations, J. Chem. Eng. Jpn., 7, 229-231. Shirato M., Murase T. and Iwata M., 1986. Deliquoring by expression - theory and practice, in "Progress in Filtration and Separation 4", Ed. R.J. Wakeman, Elsevier, Amsterdam. Shirato M., Murase T., Iritani E., Tiller F.M. and Alciatore A.F., 1987. Filtration in the chemical process industry, in "Filtration", Eds. M.J. Matteson and C. Orr, Marcel Dekker, New York. Smiles D.E., 1999. Centrifugal filtration of particulate systems, Chem. Eng. Sci., 54, 215-224. Smith J.C., 1955. How to approach your separation problem, Chem. Eng., 62(6), 177-184. Sourirajan S. (Ed.), 1977. Reverse Osmosis and Synthetic Membranes. Theory, Technology, Engineering, National Research Council, Ottawa, Canada.

Bibliography 397 Sperry D.R., 1924. What is the most suitable filter, Chem. Metall. Eng., 31,422-428. Stahl W., 2005. Industrie-Zentrifugen, DrM Press, M~nnedorf. Stahl W. and Nicolaou I., 1990. Calculation of rotary vacuum plant, Proc. 5th World Filtration Congress, pp. 37-44, Soci6t6 Fran~aise de Filtration, Nice. Svarovsky L., 1984. Hydrocyclones, Holt, Rinehart & Winston, Eastbourne. Svarovsky L. (Ed.), 1990. Solid-Liquid Separation, 3rd Edition, Butterworths, London. Talmage W.L. and Fitch E.B., 1955. Determining thickener unit areas, Ind. Eng. Chem., 47, 38-41. Tarleton E.S., 1992. The role of field assisted techniques in solid/liquid separation, Filtr. Sep., 29, 246-252. Tarleton E.S., 1996. A mechatronics approach to solid/liquid separation, Proc. 7th Worm Filtration Congress, pp. 311-315, Hungarian Chemical Society, Budapest. Tarleton, E.S. 1998a. A new approach to variable pressure cake filtration, Minerals Eng., 11, 53-69. Tarleton E.S., 1998b. Predicting the performance of pressure filters, Filtr. Sep., 35, 293-298. Tarleton E.S., 1998c. The control of pressure in constant rate cake filtration, Proc. International Symposium Filtration and Separation, pp. 87-94, Ib6rica de Filtraci6n y Separaci6n, Las Palmas. Tarleton E.S. and Wakeman R.J., 1991. Solid~Liquid Separation Equipment Simulation & Design: pC-SELECT- Personal computer software for the analysis of filtration and sedimentation test data and the selection of solid~liquid separation equipment, Separations Technology Associates, Loughborough. Tarleton E.S. and Wakeman R.J., 1993. Understanding flux decline in crossflow microfiltration: Part I - Effects of particle and pore size, Trans IChemE, Part A, 71,399-410. Tarleton E.S. and Wakeman R.J., 1994a. Understanding flux decline in crossflow microfiltration: Part II - Effects of process parameters, Trans IChemE, Part A, 72, 431-440. Tarleton E.S. and Wakeman R.J., 1994b. Understanding flux decline in crossflow microfiltration: Part III - Effects of membrane morphology, Trans IChemE, Part A, 72, 431-440. Tarleton E.S. and Wakeman R.J., 1994c. The simulation, modelling and sizing of pressure filters, Filtr. Sep., 31, 393-397. Tarleton E.S. and Hancock D.L., 1996. The imaging of filter cakes through electrical impedance tomography, Filtr. Sep., 33, 491-494. Tarleton E.S. and Hancock D.L., 1997. Using mechatronics for the interpretation and modelling of the pressure filter cycle, Trans IChemE, 75, Part A, 298-308. Tarleton E.S. and Willmer S.A., 1997. The effects of scale and process parameters in cake filtration, Trans IChemE, Part A, 75, 497-507. Tarleton E.S. and Wakeman R.J., 1999. Software applications in filter control, data acquisition and data analysis, Filtr. Sep., 36(8), 57-64. Tarleton E.S., Foley M.D. and Ceruelo N., 2001. The use of mechatronics in cake filtration studies, Proc. 14th AFS Annual Meeting, pp. 1-15, Tampa, USA. Tarleton E.S. and Hadley R.C., 2003. The application of mechatronic principles in pressure filtration and its impact on filter simulation, Filtration, 3(1), 40-47. Tarleton E.S. and Wakeman R.J., 2003. New computer software for the selection of solid/liquid separation equipment, Proc. Filtech Conference, pp. 200-207, Dfisseldorf, Germany.

398 Solid/Liquid Separation" Equipment Selection and Process Design Tarleton E.S., Robinson J.E, Millington C.R. and Nijmeijer A., 2005. Non-aqueous nanofiltration: Solute rejection in low-polarity binary systems, J. Mem. Sci., 252, 123-131. Tarleton E.S. and Wakeman R.J., 2005a. Computer software for the specification of solid/liquid separation equipment, Proc. Filtech Conference, pp. 14-21, Weisbaden, Germany. Tarleton E.S. and Wakeman R.J., 2005b. Filter Design Software (FDS) for Filter Process Simulation, Paper presented at conference "Improving process efficiency through filter scale-up and evaluation", 8 pp., The Filtration Society, Runcorn. Teoh S.K., Tan R.B.H., He D. and Tien C., 2001. A multifunctional test cell for cake filtration studies, Filtration, 1, 81-90. Tiller EM., 1953. The role of porosity in filtration, Chem. Eng. Prog., 49, 467-479. Tiller EM., 1955. The role of porosity in filtration 2: Analytical formulas for constant rate filtration, Chem. Eng. Prog., 51,282-290. Tiller EM., 1974. Bench scale design of SLS systems, Chem. Eng., 81, 117-119. Tiller EM., 1975. Solid-Liquid Separation, 2nd Edition, University of Houston, Houston. Tchobanoglous G. and Burton EL., 1991. Wastewater Engineering: Treatment, Disposal and Reuse, 3rd Edition, McGraw-Hill, New York. Townsend I., 2002. Pressure Filtration, Paper presented at conference "Solid/liquid separation plant design", 13 pp., The Filtration Society, Birmingham. Trawinski H.E, 1980. Current solid/liquid separation technology, Filtr. Sep., 17, 326-335. Valleroy V.V. and Maloney J.O., 1960. Comparison of the specific resistances of cakes formed in filters and centrifuges, AIChEJ, 6, 382-390. Wakeman R.J., 1972. Prediction of the washing performance of drained filter cakes, Filtr. Sep., 9, 409-415. Wakeman R.J., 1973. Theoretical analyses of filter cake washing, The Chem. Engr. (London), 280, 596-602. Wakeman R.J., 1976a. Diffusional extraction from hydrodynamically stagnant regions in porous media, Chem. Eng. J., 11, 39-56. Wakeman R.J., 1976b. Vacuum dewatering and residual saturation of incompressible filter cakes, Int. J. Miner. Process., 5, 193-206. Wakeman R.J., 1976c. The influence of entrapped gas and resaturation on diffusional extraction in porous media, Chem. Eng. J., 16, 73-78. Wakeman R.J., 1979a. Low pressure dewatering kinetics of incompressible filter cakes: I Variable total pressure loss or low capacity systems, Int. J. Miner Process., 5, 379-393. Wakeman R.J., 1979b. Low pressure dewatering kinetics of incompressible filter cakes: II Constant total pressure loss or high capacity systems, Int. J. Miner. Process., 5, 395-405. Wakeman R.J., 1979c. The performance of filtration post-treatment processes: 1. The prediction and calculation of cake dewatering characteristics, Filtr. Sep., 16, 655-660. Wakeman R.J., 1980. The estimation of cake washing characteristics, Filtr. Sep., 17, 67-73. Wakeman R.J., 1981a. Cake washing, in "Solid-Liquid Separation", 2nd Edition, Ed. L. Svarovsky, pp. 408-451, Butterworths, London. Wakeman R.J., 1981b. Material balance calculations for multiple washing filter installations, Proc. Symposium on "Economic Optimisation Strategy in Solid~Liquid Separation Processes" pp. 159-176, Soci6t6 Belge de Filtration, Louvain-la-Neuve.

Bibliography Wakeman R.J., 1981 c. The analysis of continuous countercurrent washing systems, Filtr. Sep., 18, 35-41. Wakeman R.J., 1982a. An improved analysis for the forced gas deliquoring of filter cakes and porous media, J. Separ. Proc. Technol., 3, 32-38. Wakeman R.J., 1982b. Effects of solids concentration and pH on electrofiltration, Filtr. Sep., 19, 316-319. Wakeman R.J., 1984a. Filtration and washing on vacuum filters - process optimisation for economy, Filtr. Sep., 21, 201-205. Wakeman R.J., 1984b. Residual saturation and dewatering of fine coals and filter cakes, Powder Technol., 40, 53-63. Wakeman R.J., 1986a. Transport equations for filter cake washing, Trans IChemE, 64, 308-319. Wakeman R.J., 1986b. Theoretical approaches to thickening and filtration, in "Encyclopaedia of Fluid Mechanics", Vol. 5, Ed. N.E Cheremisinoff, Gulf Publishing, Houston. Wakeman R.J., 1994. Modelling slurry dewatering and cake growth in filtering centrifuges, Filtr. Sep., 31, 75-81. Wakeman R.J., 1995. Selection of equipment for solid/liquid separation processes, Filtr. Sep., 32, 337-341. Wakeman R.J., 1996. Fouling in crossflow ultra- and micro-filtration, Membrane Technol., 70, 5. Wakeman R.J. and Mulhaupt B., 1985. Process design and scale-up of multi-stage washing pusher centrifuges, Filtr Sep., 22, 231-234. Wakeman R.J. and Vince A., 1986a. Kinetics of gravity drainage from porous media, Trans IChemE, 64, 94-103. Wakeman R.J. and Vince A., 1986b. An engineering model for the kinetics of drainage from centrifuge cakes, Trans IChemE, 64, 104-108. Wakeman R.J. and Attwood G.J., 1988. Developments in the applications of cake washing theory, Filtr. Sep., 25, 272-275. Wakeman R.J. and Attwood G.J., 1990. Simulations of dispersion phenomena in filter cake washing, Trans IChemE, 68, 161-171. Wakeman R.J. and Tarleton E.S., 1990. Modelling, simulation and process design of the filter cycle, Filtr. Sep., 27, 412-419. Wakeman R.J. and Fan D., 1991. The control ring centrifuge - a new type of conical basket centrifuge, Trans IChemE, Part A, 69, 403-408. Wakeman R.J., Sabri M.N. and Tarleton E.S., 1991. Factors affecting the formation and properties of wet compacts, Powder Technol., 65, 283-292. Wakeman R.J. and Tarleton E.S., 1991 a. Solid/liquid separation equipment simulation and des i g n - an expert systems approach, Filtr. Sep., 28, 268-274. Wakeman R.J. and Tarleton E.S., 199 lb. An experimental study of electroacoustic crossflow microfiltration, Trans IChemE, Part A, 69, 386-397. Wakeman R.J. and Tarleton E.S., 1993. Sensitivity analysis for solid/liquid separation equipment selection using an expert system, Proc. Filtech Conference, pp. 43-57, The Filtration Society, Karlsruhe.

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Wakeman R.J., Burgess D.R. and Stark R.J., 1994. The Howden-Wakeman filter in wastewater treatment, Filtr. Sep., 31, 183-187. Wakeman R.J. and Tarleton E.S., 1994a. A framework methodology for the simulation and sizing of diaphragm filter presses, Minerals Eng., 7, 1411-1425. Wakeman R.J. and Tarleton E.S., 1994b. Scale-up procedures and test methods in solid-liquid separation: Methodology for the simulation and sizing of pressure filters, Proc. 15th Annual IFPRI meeting, Goslar. Wakeman R.J. and Wei X., 1995. Simulating the performance of tilting pan filters, Filtr. Sep., 32, 979-984. Wakeman R.J. and Tarleton E.S., 1999. Filtration: Equipment Selection, Scale-up and Process Design, Elsevier Advanced Technology, Oxford. Wakeman R.J. and Tarleton E.S., 2005a. Solid/liquid Separation- Principles of Industrial Filtration, Elsevier Advanced Technology, Oxford. Wakeman R.J. and Tarleton E.S. (Eds.), 2005b. Solid~Liquid Separation- Scale-up of Industrial Equipment, Elsevier Advanced Technology, Oxford. Watson J.H.P., 1990. High gradient magnetic separation, in "Solid-Liquid Separation", 3rd Edition, Ed. L. Svarovsky, pp. 661-684, Butterworths, London. Wills B.A., 1992. Mineral Processing Technology, 5th Edition, Pergamon, Oxford. Yelshin A. and Tiller EM., 1989. Optimising candle filters for incompressible cakes, Filtr. Sep., 26, 436-437. Yoshioka N., Hotta Y., Tanaka S., Naito S. and Tongami S., 1957. Continuous thickening of homogeneous slurries, J. Chem. Eng. Jpn., 21, 66-74. Zeman L.J. and Zydney A.L., 1996. Microfiltration and Ultrafiltration, Marcel Dekker, New York.

Additional bibliography The following are useful additional sources of reference information that have been helpful during the writing of this book. Akay G. and Wakeman R.J., 1994. Mechanisms of permeate flux decay, solute rejection and concentration polarisation in crossflow filtration of a double chain ionic surfactant dispersion, J. Mem. Sci., 88, 177-195. Alles C.M. and Anlauf H., 2003. Efficient process strategies for compressible cake filtration, Chem. Ing. Tech., 75, 1221-1230. Andersen N.P.R., Agerbaek M.L. and Keiding K., 2003. Measurement of electrokinetics in cake filtration, Coll. Surf. A - Physicochem. Eng. Aspects, 213, 27-36. Antelmi D., Cabane B., Meireles M. and Aimar P., 2001. Cake collapse in pressure filtration, Langmuir, 17, 7137-7144. Arnot T.C., Field R.W. and Koltuniewicz A., 2000. Crossflow and deadend MF of oily water emulsions: Pt II Mechanism and modelling of flux decline, J. Mem. Sci., 169, 1-15. Atsumi K. and Akiyama T., 1975. A study of cake filtration - formulation as a Stefan problem, J. Chem. Eng. Jpn., 8, 487-492. Baluais G., Dodds J. and Tondeur D., 1983. The kinetics of displacement dewatering in filter cakes" an analytical approach, IChemE Symposium Series No. 69, 107-122.

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404 Solid/Liquid Separation- Equipment Selection and Process Design Iritani E., Mukai Y. and Hagihara E., 2002. Measurements and evaluation of concentration distributions in filter cake formed in dead-end ultrafiltration of protein solutions, Chem. Eng. Sci., 57, 53-62. Iwasaki, T., 1937. Some notes on sand filtration, J. Am. Water Works Assoc., 29, 1591. J~irvinen K., Oja M. and Rantala E, 2005. Development of high pressure filtration cloths, Filtration, 5(4), 295-304. Jemaa E., Krempff R. and Depyre D., 1974. Mod61isation math6matique de la filtration et du lavage dans la fabrication de 1'acide phosphorique, Chem. Eng. J., 8, 103-111. Kapur EC., Laha S., Usher S., deKretser R.G. and Scales E, 2002. Modeling of the consolidation stage in pressure filtration of compressible cakes, J. Colloid Interface Sci., 256, 216-222. Kelly S.T. and Zydney A.L., 1997. Protein fouling during microfiltration: Comparative behaviour of different model proteins, Biotech. Bioeng., 55, 91. Kilchherr R., Koenders M.A., Wakeman R.J. and Tarleton E.S., 2004. Transport processes during electrowashing of filter cakes, Chem. Eng. Sci., 59, 1103-1114. Koenders M.A. and Wakeman R.J., 1996. The initial stages of compact formation from suspensions by filtration, Chem. Eng. Sci., 51, 3897-3908. Koenders M.A. and Wakeman R.J., 1997a. Filter cake formation from structured suspensions, Trans IChemE, Part A, 75, 309-320. Koenders M.A. and Wakeman R.J., 1997b. Initial deposition of interacting particles by filtration of dilute suspensions, AIChEJ, 43, 946-958. Koenders M.A., Reymann S. and Wakeman R.J., 2000. The intermediate stages of the deadend filtration process, Chem. Eng. Sci., 55, 3715-3728. Koenders M.A., Liebhart E. and Wakeman R.J., 2001. Dead-end filtration with torsional shear: Experimental findings and theoretical analysis, Trans IChemE, Part A, 79, 249-259. Kohaupt U., 2005. Filtration of fine particles by high gradient magnetic filtration, Filtration, 5(1), 48-50. Koltuniewicz A.B., Field R.W. and Arnot T.C., 1995. Crossflow and deadend MF of oily water emulsions: Pt II Experimental study and analysis of flux decline, J. Mem. Sci., 102, 193. Koo E.C., 1942. Expression of vegetable oils, Ind. Eng. Chem., 34, 342-345. Kos E, 1975. Transport phenomena applied to sludge dewatering, J. Environ. Eng. Div., ASCE, 101, 947-965. Kosvintsev S., Holdich R.G., Cumming I.W. and Starov V.M., 2002. Modelling of dead-end microfiltration with pore blocking and cake formation, J. Mem. Sci., 208, 181-192. Kozicki W., 1990. Factors affecting cake resistance in non-Newtonian filtration, Can. J. Chem. Eng., 68, 69-80. Kozinski A.A. and Lightfoot E.N., 1972. Protein ultrafiltration: a general example of boundary layer filtration, AIChEJ, 18, 1030. Kuo K.T., 1960. Filter cake washing performance, AIChEJ, 6, 566-568. Kukreja V.K., Ray A.K. and Singh V.E, 1998. Mathematical models for washing and dewatering zones of a rotary vacuum filter, Indian J. Chem. Technol., 5, 276-280. Landman K.A., Sirakoff C. and White L.R., 1991. Dewatering of flocculated suspensions by pressure filtration, Phys. Fluids A, 3(6), 1495-1509.

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408

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Bibliography 409 Wakeman R.J., Mehrotra V.R and Sastry K.V.S., 1981. Mechanical dewatering of fine coal and refuse slurries, Bulk Solids Handling, 1, 281-293. Wakeman R.J. and Jimenez-Novoa C.E., 1985. Lavado de tortas de filtrado, Ingeneria Quimica, 17, 147-156. Wakeman R.J., Davies T.E and Manning C.J., 1988. The HW filter- a new concept for clarification filtration, Filtr. Sep., 25, 407-410. Wakeman R.J., Thuraisingham S.T. and Tarleton E.S., 1989. Colloid science in solid/liquid separation technology - Is it important? Filtr. Sep., 26, 277-283. Wakeman R.J. and Akay G., 1997. Membrane-solute and liquid-particle interaction effects in filtration, Filtr. Sep., 34, 511-519. Wakeman R.J. and Bailey A.J.L., 2000. Sonothickening: continuous in-line concentration/clarification of fine particle suspensions by power ultrasound, Trans IChemE, Part A, 78, 651-661. Wakeman R.J. and Kotzian R., 2000. Cu 2+ and Cd 2+ removal from aqueous solutions using lecithin enhanced ultrafiltration, Trans Filt. Soc., 1(1), 8-13. Wakeman R.J. and Smythe M.C., 2000. Clarifying filtration of fine particle suspensions aided by electrical and acoustic fields, Trans IChemE, Part A, 78, 125-135. Wakeman R.J. and Williams C.J., 2002. Additional techniques to improve microfiltration, Separ. Purif Technol., 26, 3-18. Wakeman R.J. and Butt G., 2003. An investigation of high gradient dielectrophoretic filtration, Trans IChemE, Part A, 81, 924-935. Wakeman R.J. and Wu E, 2003. Neural network modelling of vibration filtration, Filtration, 3(4), 237-244. Walas S.M., 1946. Resistance to filtration, Trans Amer. Inst. Chem. Eng., 42, 783-793. Walker A., 2005. Applying filter aids to rotary drum vacuum filter installations, Filtration, 5(4), 258-263. Willis M.S., 1983. A multiphase theory of filtration, in "Progress in Filtration and Separation 3", Ed. R.J. Wakeman, Elsevier, Amsterdam. Wu D., Howell J.A. and Field R.W., 1999. Critical flux measurement for model colloids, J. Mem. Sci., 152, 89-98. Wu Y.X. and Wang B.Y., 2004. Analysis of the medium resistance for constant pressure filtration, Chinese J. Chem. Eng., 12, 33-36. Yim S.S., 1999. A theoretical and experimental study on cake filtration with sedimentation, Korean J. Chem. Eng., 16, 308-315. Yim S.S. and Kim J.H., 2000. An experimental and theoretical study on the initial period of cake filtration, Korean J. Chem. Eng., 17, 393-400. Yim S.S. and Kwon Y.D., 1997. A unified theory on solid-liquid separation: Filtration, expression, sedimentation, filtration by centrifugal force, and cross flow filtration, Korean J. Chem. Eng., 14, 354-358.

Appendix A: Variable ranges for filter cycle calculations The information in this appendix is given as guidance to typical ranges of values for the variables required in filter cycle calculations and simulations. These are suitable for most calculation purposes but some values may represent the extremes of what is reasonable in practice. The reader should also be aware that some combinations of variables will yield unrealistic results. For example, on a belt filter cycle comprising filtration and single washing and deliquoring phases, a total belt length of more than 190 m will occur if the extremes of all phase lengths are taken. Such a scenario is clearly unrealistic and 'additional constraints' are imposed in these cases. Variables below are arranged according to basic properties, parameters specific to potential phases in a cycle and parameters specific to individual types of filters and presses.

Basic properties of solids, solutes and fluids Filtrate and wash liquid density: Pl and Pw = 700--> ] 800 kg m -3 Filtrate and wash liquid viscosity: #~ and #w = 0.0001--, 100 Pa s Filtrate and wash liquid surface tension: ~r = 0 . 0 0 8 ~ 0 . ] N m -1

Gas viscosity: #a = 1 × 10 -5 ~ 3 x 10 -5 Pa s Solute concentration in feed/filtrate: 4>0 -> 0 kg m -3 Solids density: Ps = 700 ~ 5000 kg m -3 Solute concentration in wash liquid: ~bw _> 0 kg m -3 Solute diffusivity: D = 1 x

10-15-.

1x

Additional limitations: Ps > Pt (usually)

10 -7 m 2 S -1

Appendix A . Variable ranges for filter cycle calculations 411 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Miscellaneous .......

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Barometric pressure: PB -- 70 ~ 110 kPa Filter medium resistance (including any heel of cake): R - 1

× 105~

1 × 1013 m -1

Filtration phase .....W . L . . ~ . ~ . ? L _ . ? . ? _ . 7 . 7 . 7 . . . . . 7 _ _ _ . ~ L _ . . 7 . 7 . 7 . . L . ~ . ~ . L . . . . _ . ~ _ . . . ~ : L _ . ~ . ~ ........................................................................................................................................................................................................................... -LLWL?ZSLLTLW?.LL\L~L~TL\~???55?LLWLL~

Specific cake resistance at unit pressure: c~0 - 1 × 107--* 1 × 1016m kg -~ kPa -n Compressibility index: n - 0.05 ~ 1 (diaphragm and tube presses) and 0 ~ 1 (all other filters and presses). Physically n can be > 1 but this would represent an exceptional case. Solids concentration at unit pressure: C O - 0.02 ~ 0.9 v/v kPa -b Compressibility index" b > 0 (diaphragm and tube presses) and b->0 (all other filters and presses) Filtration pressure: Pump pressure - Apf A p f

Washing phase Washing pressure: A p w - 50--+2000 kPa (diaphragm filter presses), 50 ~ 1 4 0 0 0 kPa (tube press) and 50--+1000 kPa (Nutsche filter, multielement leaf filters and filter presses)

412 Solid/Liquid Separation" Equipment Selection and Process Design .........

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Washing vacuum: Apw = 10 --, 85 kPa Fractional solute recovery" F N u m b e r of w a s h ratios: W -

0.05--,0.995 0.5 --,6

Gas deliquoring phase _

~

~

~

Deliquoring pressure or vacuum: APd -- 10 ~ 1000 or 10-~ 85 kPa Breakthrough pressure or vacuum: Pb

0 . 1 - + 2 0 0 or 0.1--~70 kPa

=

Irreducible cake saturation: So~ - 0.07 ~ 0.98 Cake moisture (at end of phase)" M -

3--,60%

Filter specific parameters Single leaf (Nutsche) pressure filter (Sections 1.4.2.1 and 6.1.1) Feed slurry concentration: s - < 1--, 20 + % w / w M e a n particle size" Xav = 1 ~ 200 g m Mass of solids processed: M~ = 0.5--,22500 kg M i n i m u m cake thickness" Lmi n Filter area: A f -

5 mm

-

0.1 --, 30 m 2

Single leaf (Nutsche) vacuum filter (Sections 1.4.1.1 and 6.1.1) Feed slurry concentration" s - 1 ~ 10 % w / w M e a n particle size: Xav - 1 ~ 500 lam Mass of solids processed: M~ = 0.5 ~ 7500 kg M i n i m u m cake thickness: Lmi n Filter area: Af = 0.1 ~ 10

m

-

5 mm

2

Multi (tubular) element leaf pressure filter (Sections 1.4.2.2 and 6.1.3) Feed slurry concentration: s - < 1 ~ 20 % w / w M e a n particle size: Xav -- 0.5 ~ 100 g m Mass of solids processed: M~ - 0.5 ~ 15500 kg M i n i m u m cake thickness" Lmi n

-

1 mm

-

.--

Appendix A- Variable ranges for filter cycle calculations 413 N u m b e r o f filter candle elements: n t = 1 ~ 400 Closest e l e m e n t spacing: H e = 0.02 ~ 0.1 m Filter e l e m e n t diameter: d = 0 . 0 2 5 - - , 0 . 0 7 5 m Filter e l e m e n t length: h = 0.3 ~ 2 m

Multi (vertical) element leaf pressure filter, horizontal vessel (Sections 1.4.2.2 and 6.1.3) F e e d slurry concentration: s = < 1 ~ 2 0 % w / w M e a n particle size: x ~ = 0 . 5 ~ 1 0 0

~m

Mass o f solids processed: M s = 3 0 - - , 7 5 0 0 0 kg M i n i m u m cake thickness: Lmi n Filter area: A f -

10~300

=

5 mm

m 2

N u m b e r o f filter elements: n t = 5 ~ 7 0 Filer e l e m e n t spacing: H e = 0 . 0 3 ~ 0 . 2 m

Multi (horizontal) element leaf pressure filter, vertical vessel (Sections 1.4.2.2 and 6.1.3) F e e d slurry concentration: s = < 1 ~ 2 0 % w / w M e a n particle size: Xav = 1 ~ 100 ~tm Mass o f solids processed: Ms = 20 ~ 16000 kg M i n i m u m cake thickness: Lmi,, = 5 m m Filter area: A f -

5--,65

m 2

N u m b e r o f filter elements: n t = 5 - , 8 0 Filter e l e m e n t spacing: H e = 0.02 ~ 0 . 1 m

Multi (vertical) element leaf pressure filter, vertical vessel (Sections 1.4.2.2 and 6.1.3) F e e d slurry concentration: s = < 1--,20 % w / w M e a n particle size: Xav - 0.5 ~ 100 g m Mass o f solids processed: M s = 15 ~ 2 0 0 0 0 kg M i n i m u m cake thickness: t m i n Filter area: A f -

5 ~80 m 2

~-

5 mm

414 Solid/Liquid Separation" Equipment Selection and Process Design N u m b e r of filter elements: n t - 3--,20 Filter element spacing" H e - 0.03--,0.2 m M u l t i - e l e m e n t v a c u u m filter (Moore's filter, Sections 1.4.1.2 and 6.1.2) Feed slurry concentration: s - 5 - - , 3 0 + % w / w M e a n particle size" Xav = 1 ~ 100 ~tm Mass of solids processed: M s - 45 ~ 86000 kg M i n i m u m cake thickness" Lmi n Filter area: A f -

=

5 mm

10~230 m 2

N u m b e r of filter elements: n t - 5 ~ 3 6 Filter element spacing: H e - 0.05--,0.3 m

Plate and frame filter press (Sections 1.4.2.3 and 6.1.4) Feed slurry concentration" s - < 1 ~ 30 + % w / w M e a n particle size: Xav = 1 ~ 100 ~tm Filter area: Ay = 5 ~ 2 0 0 0 N u m b e r of frames: n p F r a m e thickness" T -

m 2

5 ~ 300 0.015--,0.2 rn

Recessed plate filter press (Sections 1.4.2.3 and 6.1.4) Feed slurry concentration: s - < 1 - - , 3 0 + % w / w M e a n particle size: Xav = 1 ~ 100 ~m Filter area: A f -

5 ~2000

N u m b e r of plates" n p -

m 2

5 ~ 300

Depth of recess in plate: T r - 0.01--,0.04 m

Horizontal belt filter (Sections 1.4.1.3 and 7.1.1) Feed slurry concentration: s - 5 ~ 3 0 + % w / w M e a n particle size: Xav = 20--*80000 ~tm M i n i m u m cake thickness: Lmi n

-

5 mm

Linear belt velocity" v 8 - 0.04 ~ 1 m s - 1 Length of belt devoted to filtration phase: z f - 1 - , 6 5 m

Appendix A. Variable ranges for filter cycle calculations 415 L e n g t h of belt devoted to a w a s h i n g phase: Zw = 1 ~ 6 4 m L e n g t h o f belt devoted to a gas deliquoring phase: Zd = 1---64 m Belt width: h 8 = 0.3 ~ 4 . 2 m A d d i t i o n a l limitations" Z T - zf + ~ z w -Jr- ~ Zd ~ 65 m; 4 --< ZT/h8 d i

Rotary drum filter, bottom fed, knife discharge (Sections 1.4.1.5 and 7.1.2) F e e d slurry concentration: s = 1 ~ 2 0 %

w/w

M e a n particle size: Xa~ = 1--+200 ~tm M i n i m u m cake thickness: Lmi n

--

6 mm

Rotational speed: o9 = 0.01 ~ 1.1 rad s - 1 ( = 0.1 ~ 10 rpm) Drum submergence: ~bf- 0.15~0.75 Fraction o f filter area d e v o t e d to a w a s h i n g phase: q5w = 0.05 ~ 0 . 2 9 Fraction o f filter area d e v o t e d to a gas deliquoring: q5d = 0.1 ~ 0 . 6 D r u m diameter: D = 0.5 ~ 7 m D r u m width: h D = 0.5 ~ 15 m A d d i t i o n a l limitations: 0.25

--