Flotation Plant Optimisation 9781921522215

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Flotation Plant Optimisation A Metallurgical Guide to Identifying and Solving Problems in Flotation Plants

Edited by C J Greet

Number 16

Flotation Plant Optimisation A Metallurgical Guide to Identifying and Solving Problems in Flotation Plants Edited by Christopher J Greet

The Australasian Institute of Mining and Metallurgy Spectrum Series 16 ISBN 978 1 921522 21 5

COPYRIGHT DISCLAIMER

© The Australasian Institute of Mining and Metallurgy 2010 No part of this publication may be may be reproduced, stored in a retrieval system or transmitted in any form by any means without the written consent of the publisher. The AusIMM is not responsible as a body for the facts and opinions advanced in any of its publications.

NUMBER 16

Published by: THE AUSTRALASIAN INSTITUTE OF MINING AND METALLURGY Ground Floor, 204 Lygon Street, Carlton Victoria 3053 Australia

HOW TO USE THIS BOOK It is intended that Chapter 1 (The Eureka Mine – An Example of How to Identify and Solve Problems in a Flotation Plant, by Christopher Greet) be used in parallel with subsequent chapters to gain a greater understanding of what is involved as one goes through the process of optimising the plant. The basic road map to follow on your quest to improve the metallurgical performance of your plant is given in the figure below. The first step in this process is the acquisition of quality data from the plant (or mine, in the case of a geometallurgical study (Chapter 12: Operational Geometallurgy by Dean David)). Chapter 2 (Existing Methods for Process Analysis by Bill Johnson), provides details of how to collect, mass balance, size and interpret metallurgical data collected from the plant. Mass Balancing Flotation Data by Rob Morrison (Chapter 3) describes in detail the considerations that must be taken into account when mass balancing survey data collected from a flotation plant. Having defined the recovery-by-size characteristics of the concentrator, the next step is to establish their mineralogical character; that is, their locking or liberation characteristics. Alan Butcher, in Chapter 4 (A Practical Guide to Some Aspects of Mineralogy that Affect Flotation), provides a summary of the mineralogical techniques available, their application and suitability to various situations. The combination of recovery-by-size and liberation-by-size and mineral class will define whether the losses occurring in the tailing stream are liberated or composite for each size fraction. The same can be determined for gangue minerals reporting to the concentrate. Geometallurgy (Dean David) Data acquisition (Bill Johnson)

Mass balancing (Rob Morrison)

Questions? (What and where?)

Mineralogy (Alan Butcher) Cell characterisation (Greg Harbort

Problem definition Machine Liberation Chemistry

Sarah Schwarz)

Electrochemistry (Ron Woods)

Pulp chemistry (Stephen Grano ) Surface chemistry

Laboratory testing

(Alan Buckley)

(Kym Runge)

Trials and stats (Tim Napier -Munn)

Communication (Joe Pease)

Schematic showing the broad road map of how to identify and quantify problems within base metal sulfide flotation plants.

Once the weaknesses within the concentrator have been identified it is possible to start looking for the root cause. For example, are the inefficiencies of the process related the equipment being used (Chapter 5: Characterisation Measurements in Industrial Flotation Cells by Greg Harbort and Sarah Schwarz)? If liberation is an issue then it may be a case of adding additional size reduction capacity at an appropriate position within the circuit. However, if fine liberated values are leaving the circuit via the tailing there may be a problem with the chemistry. Stephen Grano’s chapter (Chapter 6: Chemical Measurements During Plant Surveys and Their Interpretation) provides an explanation of the typical pulp chemical measurements that can be made in the plant to identify where the chemistry of the system is not optimal for separation. Ron Woods (Chapter 7: Electrochemical Aspects of Sulfide Mineral Flotation) discusses the significance of electrochemistry of the system and its impact on flotation. In some instances it is necessary to use more sophisticated surface analysis techniques to identify the species on the surfaces of minerals particles. Chapter 8: Surface Chemical Characterisation for Identifying and Solving Problems within Base Metal Sulfide Flotation Plants, by Alan Buckley presents the various techniques available (ie XPS, ToF-SIMS), discusses their merits and describes how the data can be interpreted. The above describes the steps, with increasing degrees of sophistication, one may take to identify the where, what and how in the focusing questions. The tremendous strength of these principles lies in the fact that they can be applied to almost any processing operation, not only the flotation of base metal sulfides, and at any scale (ie laboratory, pilot plant and industrial scale). Having identified where the weaknesses in your operation are, it is possible to devise laboratory experiments to test potential solutions. These programs may range from diagnostic test conducted on plant pulps to determine if changes made in the plant have resulted in a positive shift in metallurgy to simple laboratory flotation tests to screen reagents. The development of these ideas is discussed by Kym Runge in Chapter 9: Laboratory Flotation Testing – An Essential Tool for Ore Characterisation. Invariably encouraging laboratory solutions are applied to the operating plant with varying degrees of success. In Chapter 10 (Designing and Analysing Plant Trials), Tim Napier-Munn will discuss the steps required to conduct a successful plant trial and how the data generated may be analysed to give a statistically meaningful outcome. Finally, Joe Pease (Chapter 11: Economics and Communication) will supply a philosophical note on how best to communicate solutions developed by the technocrat to both operations personnel and management teams such that the economic benefits can be realised.

CONTENTS Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 The Eureka Mine – An Example of How to Identify and Solve Problems in a Flotation Plant C J Greet

Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Existing Methods for Process Analysis N W Johnson

Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Mass Balancing Flotation Data R Morrison

Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 A Practical Guide to Some Aspects of Mineralogy that Affect Flotation A R Butcher

Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Characterisation Measurements in Industrial Flotation Cells G J Harbort and S Schwarz

Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Chemical Measurements During Plant Surveys and Their Interpretation S R Grano

Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Electrochemical Aspects of Sulfide Mineral Flotation R Woods

Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Surface Chemical Characterisation for Identifying and Solving Problems Within Base Metal Sulfide Flotation Plants A N Buckley

Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Laboratory Flotation Testing – An Essential Tool for Ore Characterisation K C Runge

Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 Designing and Analysing Plant Trials T J Napier-Munn

Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 Economics and Communication J D Pease

Chapter 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 Operational Geometallurgy D David

HOME

CHAPTER 1

The Eureka Mine – An Example of How to Identify and Solve Problems in a Flotation Plant Christopher Greet MAusIMM, Manager Metallurgy – Minerals Processing Research, Magotteaux Australia Pty Ltd, 31 Cormack Road, Wingfield SA 5013. Email: [email protected] Chris commenced his working life as a Trainee Metallurgist at Bradken’s Adelaide steel foundry in 1978. He subsequently worked in a number of foundries, before becoming a shift foreman at Seltrust’s Teutonic Bore Mine in 1982. In 1985 he decided to formalise his knowledge by studying for a Bachelor of Engineering in Metallurgical Engineering at the South Australian Institute of Technology. Upon graduating, he worked as a Plant Metallurgist at Ok Tedi Mining Limited and Bradken Adelaide, before undertaking a PhD at the Ian Wark Research Institute in 1992. Since leaving the Wark, Chris has held applied research positions at Mount Isa Mines Limited, Pasminco, AMDEL, and now with Magotteaux Australia, where he leads the technical group identifying the impact of grinding chemistry on downstream processing.

Abstract Introduction The Eureka Mine Data Acquisition Problem Definition Solution Development and Testing The Cycle Begins Again Communication Conclusions References Appendix 1 – The Down-the-Bank Survey Appendix 2 – Estimated Mineral Assays from Elemental Data

ABSTRACT As the title implies, this chapter will provide, by way of example, a methodology for identifying and solving problems in a flotation plant. To do this a ‘mythical’ concentrator (The Eureka Mine) will be described and used to demonstrate to the reader how to go about the process of identifying where the losses of valuable mineral occur, and what gangue species are diluting the concentrate. It is intended that this chapter be used in parallel with subsequent chapters to guide the reader through the steps involved in the process of optimising the plant.

INTRODUCTION Many of us have, at one time or another, flicked through the newspaper or searched online for a job, and stumbled upon an ad not unlike the one that appears below. Whether we are jaded with our current role, looking for a step up to the next level, or wanting

Flotation Plant Optimisation

a new challenge, we prepare our resume and send it off in the vain hope that we may be the successful candidate. With the interview process out of the way, the waiting and self doubt start. And, after what seems an eternity you receive a phone call or letter telling you that you have got the job. Congratulations! Now what? You’re new, you have ambition, you have drive, and you want to make your mark! But, there’s a right way and a wrong way to do this. The first thing to remember is that this place has a history, and the people you are going to work with have been here much longer than you have. So, communication and respect are keys to your success. You need to discover the history of the concentrator, and discuss its operation with other members of staff (operators, metallurgical technicians, shift foremen, plant metallurgists, the chemist, mechanical and electrical maintenance, the mine (ie geologists and mining engineers) and supply). They will all give you their perspective,

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CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

SENIOR PROJECT METALLURGIST The key objectives of this position are to:

• identify opportunities for improvement within the process,

• develop, test, evaluate and implement process improvements,

• identify and evaluate new technologies that will improve

To assist you in this journey the performance of the Eureka Mine will be scrutinised and used as an example. The Eureka Mine treats a complex polymetallic sulfide ore supplied from an underground mine, producing three saleable concentrates. This chapter provides a description of the Eureka Concentrator, and its metallurgical performance since commissioning. Then provides, by example, the methodology used to collect plant data, analyse and interpret it to determine where the metallurgical problems lie.

our process, and

THE EUREKA MINE

• be actively involved in our future ores testing program. Operating in a climate of continuous improvement, you will be required to actively participate in the promotion of safe work practices, have good interpersonal skills and a professional work ethic.

Skills and experience The successful applicant candidate will have the following attributes:

• Bachelor of Engineering – Metallurgy or equivalent, • five years or more process experience, • a working knowledge of grinding and flotation processes,

• • • •

good communication skills,

Extensive geological surveying of the region north of Laylor River by Stockade Resources Limited resulted in the discovery of the Eureka deposit in 1990. Throughout 1991 and 1992, drilling continued to delineate the deposit. Preproduction geological studies indicated probable reserves of approximately 25 million tonnes of greater than 15 per cent zinc plus lead, with economically significant copper, silver and gold grades. A one million tonnes per annum processing plant was commissioned by Stockade in 1995 to treat ore with an average head grade of 0.4 per cent copper; three per cent lead; 12 per cent zinc; 130 g/t silver; and 2.0 g/t gold.

Geology

proven problem solving skills, good time management skills, and have sound leadership qualities and management skills.

Employment conditions Eureka Mining Limited is a wholly owned subsidiary of Stockade Resources Limited, an Australian based mining and exploration company with interests in Australia, New Guinea, Zambia and Peru. Reporting to the Metallurgy Manager, the successful candidate will work closely with production to maintain and improve plant performance. This is a residential position, with an attractive renumeration package commensurate with your qualifications and experience.

To apply Please submit your application including a cover letter and current copy of your resume via email to ...

and you need to respect their point of view. You will also work out who among these people hold the knowledge, the history; the real story of your concentrator. While you are establishing relationships you need to determine what (if any) data exists that will help you to develop a technical perspective of how your concentrator performs. The focusing questions in any process improvement strategy are:

• Where and how do the losses of valuable mineral occur? • What gangue minerals are diluting the concentrate and how did they get there? The intention of this book is to provide you with a sequence of logical steps to follow so that you can collect the necessary data to be able to define the problem(s) within your operation. Once the problems are defined, you can then prioritise them and develop experimental strategies that may lead to solutions that can be implemented in the plant.

2

Location and history

The Eureka volcanogenic massive sulfide deposit occurs within the Laylor-Eureka Volcanic sequence of the Mount Rush Volcanics. The deposit was formed when hot mineralised solutions were spewed out on to the ocean floor and were rapidly quenched by the surrounding seawater. Hence, the sulfide minerals that were precipitated from solution formed very fine crystals and intricate mineral textures. Subsequent geological changes to the orebody were few; therefore many of the original fine grain textures remained intact.

Deposit mineralogy To fully appreciate the complexity of flotation at Eureka it is necessary to have a rudimentary understanding of the mineralogy of the orebody. Eureka is unusually sulfide rich, and contains a relatively simple mineral suite: 58 per cent pyrite, 20 per cent sphalerite, four per cent galena, two per cent arsenopyrite, one per cent chalcopyrite, with minor amounts of tetrahedrite. The remaining 15 per cent of the ore consists of: quartz, barite, calcite, chlorite, sericite and siderite. Macroscopically the mineral textures are diverse, however, the orebody can be divided into two distinct metal zones. The demarcation between the two zones is set, arbitrarily, at 100 g/t of silver, and represents a continuous horizon across the deposit. Above this level is the hanging wall enrichment zone characterised by higher lead, zinc, silver, gold, and arsenic grades. Macroscopically the sulfides within the enrichment zone tend to be banded and very fine grained. The footwall-depleted zone occurs below the 100 g/t silver horizon. Pyrite and chalcopyrite are the dominant minerals within this part of the orebody, with reduced lead, zinc, silver, gold, and arsenic grades. The footwall-depleted zone is highly recrystallised, therefore the grain structure is comparatively coarse when compared with those observed in the hanging wall enrichment zone. It is important to note that the Eureka orebody is relatively free of non-sulfide gangue mineralisation. So, pyrite is the dominant gangue mineral, and is associated with all other minerals within the deposit. Therefore, the properties of pyrite will influence greatly the behaviour of all other minerals during processing.

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CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

The pyrite textures vary markedly across the deposit from coarse recrystallised grains in the footwall-depleted zone to compact microcrystalline masses, spongy and colliform clots, such as melnokovite (an amorphous pyrite of colloidal origin). Ultra-fine intergrowths of pyrite with other sulfides are common, particularly with galena and arsenopyrite (Figure 1). The association of auriferous arsenopyrite with pyrite is also of significance.

Process description Laboratory testing of the Eureka ore clearly demonstrated that it was possible to produce saleable copper, lead and zinc concentrates. The flow sheet developed in the laboratory was tested at pilot scale to prove that the process route selected was robust, and to produce sufficient quantities of concentrate for smelter testing. The final Eureka process flow sheet is presented in Figure 2. As the ore is mined the mine geologists classify it into three broad ore types based on texture (ie enrichment zone ore (banded), or footwall depleted zone ore (coarse grained)), and estimated pyrite content. Each ore type is crushed in batches to nominally 100 per cent passing 100 mm, in the underground jaw crusher before being trucked to the surface in 50 tonne dump trucks. Upon delivery to the run-of-mine (ROM) pad each ore type is stockpiled separately. The ore is fed onto a conveyor belt that leads to an open stockpile in specific ratios of each ore type. Apron feeders, underneath the open stockpile, feed the blended ore onto the primary mill feed conveyor at nominally 120 t/h. The primary mill is a low aspect ratio semi-autogenous grinding (SAG) mill in open circuit. The SAG mill product

discharges into a common sump shared with the ball mill. The pulp is pumped from the mill discharge sump to cyclones in closed circuit with a secondary ball mill. The cyclone underflow feeds the secondary ball mill, and the cyclone overflow reports to flotation feed. The cyclone configuration is designed to produce a P80 of 75 microns. The secondary cyclone overflow feeds a sequential copper/ lead/zinc flotation circuit. Each flotation section consists of a rougher/scavenger, with the rougher concentrate reporting to the cleaner circuit. The copper cleaning is achieved without regrinding, and with only one stage of cleaning. The lead rougher concentrate feeds the first of three stages of cleaning. The lead scavenger concentrate and lead first cleaner tailing are reground and recycled back to the head of the lead rougher. The lead scavenger tailing reports to the zinc circuit feed. The zinc rougher concentrate reports to two stages of cleaning. The zinc scavenger concentrate and the zinc first cleaner tailing are reground and recycle back to the zinc rougher feed. The concentrates produced from the copper, lead and zinc flotation circuits are pumped to thickeners. The thickened concentrate is filtered. The filter cake is stockpiled before loading into rail cars for shipment to the smelter. The flotation tailing is dewatered, and used as paste backfill in the underground workings.

Metallurgical performance The Eureka concentrator was commissioned in December 1995, reaching name plate throughput by July 1996. A further 18 months were required to achieve the design concentrate grades and recoveries. Typical metallurgical performance since 1998 is summarised in Table 1.

FIG 1 - Photomicrographs of various galena ore textures: (A) galena replacement in pyrite matrix, like melnokovite (magnification × 10); (B) galena blebs in pyrite matrix (magnification × 20); (C) galena in crystal voids around pyrite (magnification × 5); and (D) galena replacement in melnokovite colloform (magnification × 40). (Note: The blue/grey areas are galena and the golden areas are pyrite.)

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CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

Copper Circuit

Lead Circuit

Cu Ro

Zinc Circuit Pb Scav

Pb Ro

Zn Scav

Zn Ro

Feed

Zn Scavenger Tailing Grinding

st

Zn 1 Cl P80 = 75 microns

Copper Cleaner Concentrate Cu Cl Zn 2nd Cl

Pb 1st Cl

Zinc 2nd Cleaner Concentrate Zinc Regrinding P80 = 38 microns

Pb 2nd Cl Lead Regrinding P80 = 38 microns Pb 3rd Cl

Lead 3rd Cleaner Concentrate

FIG 2 - The Eureka Concentrator flow sheet.

TABLE 1 Typical metallurgical performance of the Eureka Concentrator since 1998. Stream

Wt %

Grade (%)

Recovery (%)

Ag (ppm)

Cu

Pb

Zn

Ag

Cu

Pb

Zn

Flotation feed

100.0

130

0.4

3.1

12.4

100.0

100.0

100.0

100.0

Cu concentrate

0.9

3190

25.4

5.2

6.2

21.9

53.2

1.5

0.4

Pb concentrate

3.6

1356

1.2

61.5

10.8

37.6

10.1

70.4

3.1

Zn concentrate

20.0

102

0.3

2.0

53.4

15.9

16.4

13.0

86.9

Final tailing

75.3

42

0.1

0.6

1.6

24.6

20.3

15.1

9.6

DATA ACQUISITION The first step towards a better understanding of how your plant is performing is being able to measure the plant’s performance. In today’s modern concentrator the process can be monitored using a multitude of sensors, however the data collected from inventory samples on a shift, daily, weekly and monthly basis, coupled with well executed metallurgical surveys can be invaluable in defining where valuable mineral losses occur and what gangue minerals are diluting the concentrate. In the first instance, as the new metallurgist you should acquaint yourself with the existing plant data. That is, review the shift mass balance data, interrogate the monthly composite data, and examine any plant surveys that have been conducted in the past. This analysis should provide some indication of where the metallurgical weaknesses lie in the concentrator. However, do not be surprised if the only data that is up-to-date and readily available are the shift mass balances. Therefore, it should be considered good practice to organise for a plant survey to be completed reasonably early in the piece so that you can quantify the metallurgical performance of each section of the plant. The shift data for the copper, lead and zinc circuits of the Eureka Concentrator appear in Figure 3 for the first half of 1998.

4

An examination of these data suggest that with the exception of the lead and zinc concentrate grades the plant performance is somewhat unstable. The copper concentrate grade and recovery tend to fluctuate wildly, lead recoveries are highly varied, with greater than ten per cent zinc grade in the lead concentrate, and zinc recoveries are more often than not in the low to middle 80s. Your gut feeling when you look more closely at the copper, lead and zinc recoveries should tell you that they appear lower than you would expect, therefore it should be possible to improve the plant performance. But you don’t know what the limiting factors are so completing a comprehensive plant survey is in order. The next item to decide is what level of detail does the survey have to go? This will obviously depend on what work has been completed previously. In this example it will be assumed that the available data is scattered and incomplete. Therefore, the objective of the survey will be to collect as much data as possible to provide you with sufficient information to describe the pulp chemistry and metallurgical performance of the plant. Ideally both sets of data can be collected in tandem, and complement each other. To add further value to your survey the collection of gas hold-up, superficial gas velocity and bubble size data will provide information about the hydrodynamics of the flotation cells.

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90.0

30.0

75.0

27.0

60.0

24.0

45.0

21.0

30.0

18.0

15.0

15.0

0.0

12.0

1/ 01 /9 8 15 /0 1/ 9 29 8 /0 1/ 9 12 8 /0 2/ 9 26 8 /0 2/ 9 12 8 /0 3/ 9 26 8 /0 3/ 98 9/ 04 /9 23 8 /0 4/ 98 7/ 05 /9 21 8 /0 5/ 98 4/ 06 /98 18 /0 6/ 98

Cu recovery, %

(a)

Cu grade, %

CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

Time, days Cu grade

90.0

90.0

75.0

75.0

60.0

60.0

45.0

45.0

30.0

30.0

15.0

15.0

0.0

0.0

Pb recovery

Sample type

Flotation feed (ball mill cyclone overflow)

Half moon cutter

Time, days

2

Copper rougher concentrate

Lip sample

Pb grade

3

Copper rougher tailing A

Dip sample

4

Copper rougher tailing B

Dip sample

5

Copper cleaner concentrate

Lip sample or OSA

6

Copper cleaner tailing A

Dip sample

7

Copper cleaner tailing B

Dip sample

8

Lead rougher concentrate

Lip sample

9

Lead rougher tailing A

Dip sample

10

Lead rougher tailing B

Dip sample

11

Lead scavenger concentrate

Lip sample Dip sample

Zn grade in Pb con

100.0

60.0

90.0

50.0

80.0

40.0

70.0

30.0

60.0

20.0

50.0

10.0

40.0

0.0

1/ 01 /9 8 15 /0 1/ 98 29 /0 1/ 98 12 /0 2/ 98 26 /0 2/ 98 12 /0 3/ 98 26 /0 3/ 98 9/ 04 /9 8 23 /0 4/ 98 7/ 05 /9 8 21 /0 5/ 98 4/ 06 /9 8 18 /0 6/ 98

Zn recovery, %

Process stream

1

Zn and Fe grade, %

(c)

TABLE 2 The sampling points and sample type for the metallurgical survey of the Eureka flotation circuit. Sample number

1/ 01 /9 8 15 /0 1/ 98 29 /0 1/ 98 12 /0 2/ 98 26 /0 2/ 98 12 /0 3/ 98 26 /0 3/ 98 9/ 04 /9 8 23 /0 4/ 98 7/ 05 /9 8 21 /0 5/ 98 4/ 06 /9 8 18 /0 6/ 98

Pb recovery, %

(b)

Pb and Zn grade, %

Cu recovery

product should be conducted. Ideally, a more detailed down-the-bank survey of the rougher/scavenger sections would also be included. An example of a down-the-bank survey is provided in Appendix 1. Further, to gain greater appreciation of how the circuit operates, more than one plant survey should be completed over a number of days. In fact, a good strategy to follow would be one detailed survey and several less detailed block surveys be completed to give a more balanced view of the metallurgical performance of the plant. Organisation and communication are the key to successfully completing surveys in a concentrator. In the first instance, decide on the sampling points and the type of sample to be taken. A list of samples for the Eureka concentrator is given in Table 2. It is important to note that all tailing samples are taken in duplicate to ensure sampling consistency, and are used as internal checks (note: the recovery calculation is dependent on the tailing assay).

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Lead scavenger tailing A

Time, days

13

Lead scavenger tailing B

Dip sample

Zn grade

14

Lead first cleaner concentrate

Lip sample

15

Lead first cleaner tailing A

Dip sample

16

Lead first cleaner tailing B

Dip sample

17

Lead second cleaner concentrate

Lip sample

18

Lead second cleaner tailing A

Dip sample

19

Lead second cleaner tailing B

Dip sample

20

Lead third cleaner concentrate

Lip sample or OSA

Why don’t metallurgists do surveys?

21

Lead third cleaner tailing A

Dip sample

The author has visited many plants around the world, and it is apparent that there is a wide spectrum of knowledge and experience. However, plants that conduct frequent, well focused surveys and have a clear understanding of their metallurgical performance, its strengths and weaknesses, are few and far between. The reasons for this are many and varied, but generally boil down to not knowing how to conduct a survey, and the fear of mass balancing!

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Lead third cleaner tailing B

Dip sample

23

Zinc rougher concentrate

Lip sample

24

Zinc rougher tailing A

Dip sample

25

Zinc rougher tailing B

Dip sample

26

Zinc scavenger concentrate

Lip sample

27

Zinc scavenger tailing A

Dip sample or OSA

28

Zinc scavenger tailing B

Dip sample or OSA

29

Zinc first cleaner concentrate

Lip sample

30

Zinc first cleaner tailing A

Dip sample

31

Zinc first cleaner tailing B

Dip sample

32

Zinc second cleaner concentrate

Lip sample or OSA

33

Zinc second cleaner tailing A

Dip sample

34

Zinc second cleaner tailing B

Dip sample

Zn recovery

Fe grade in Zn con

FIG 3 - Time series data for: (A) copper; (B) lead; and (C) zinc circuits.

The metallurgical survey (Chapter 2)

What do I have to do? The objectives of the survey(s) are to provide information about rougher/scavenger flotation performance in each of the flotation circuits, and to examine how the concentrates up grade during cleaning. In the first instance block surveys of each of the flotation sections (roughers, scavengers and cleaners) for each

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There are other process streams that you may consider collecting. For example, the copper rougher feed, lead rougher feed, and zinc rougher feed, just to name a few, that are redundant samples in the mass balance, but do provide valuable data for checking assays, and ensuring that the mass balanced data makes sense. With the sample list decided upon it is necessary to brief the team conducting the survey, prepare the equipment, and ensure that the plant is running in a fashion that will allow it to be surveyed. During this briefing, delegate tasks to each person taking part in the survey so that:

• sufficient sample buckets with lids are cleaned, weighed and labelled;

• the sampling equipment is checked, clean and ready for use; • each person taking part in the survey knows what is expected of them; and

• set the ground rules for the survey (ie number of rounds over what time interval).

elements like arsenic, antimony, bismuth, mercury and/or cadmium. Knowing how these penalty elements deport to the concentrate can lead to a way of minimising their recovery, which translates to a potential decrease in smelter penalties. Other data that can be useful when analysing the plant survey mass balance are:

• the throughput at the time of the survey, • reagent additions and other plant operating parameters (ie air flow rates and pulp levels),

• OSA readings, and • information about the ore being treated. In the context of a one off survey some of these pieces of information may not be of great value. However, when the analysis is extended to include other surveys on other ore blends, circuit configurations, reagent suites, these data provide a vital link in the comparison.

Further, it is wise at this point to inform operations of your intentions to conduct a plant survey(s). Give then the reasons for conducting the surveys and check that the plant will be available at the time you anticipate the survey(s) will be completed. You also need to inform the chemical laboratory that you intend to submit a large number of samples from a plant survey, and you would like to have them assayed for a range of elements. The day before conducting the survey it is wise to visit the plant and inspect the flotation circuit to make sure that all those participating in the survey know where the sampling points are that they are responsible for. It is also a time when flotation cell lips can be checked for build-up and cleaned in readiness for the survey. Of equal importance during the plant inspection is to ensure that the work area is free of hazards, and is safe to work in. On the day of the survey, attend the morning production meeting to establish how the plant has been operating overnight and inform operations of your intentions to survey the plant. Once you have the all clear commence setting up for the survey, set out the buckets in the correct positions, station the sampling equipment accordingly, check the flotation cell lips and clean them again. Check again that your team is familiar with the task ahead of them. Now that you are ready, go to the control room and check on the status of the concentrator. Ensure that the feed tonnage is steady, the feed grades are steady, and the circuit has not experienced a major disturbance in the last few hours. Once you are satisfied that the plant is running smoothly you can start the survey. It is suggested that a survey of this type be conducted over a number of hours, whereby multiple rounds of samples are collected to form a composite of the sampling period. In this particular case, the survey was conducted over a three hour period, during which time four ‘cuts’ from each sampling point were collected randomly. Once the metallurgical survey is completed, the samples are gathered together and taken to the laboratory.

How do I analyse the data collected (Chapter 3)?

What data do I need?

Step 2

In the laboratory the samples are weighed (to determine the wet weight), filtered, dried, weighed, prepped and submitted for assay. A summary of this data is given in Table 3. The wet and dry weights are used to determine the per cent solids of each sample, and calculate a water balance. In terms of assays, apart from those pertaining to the valuable minerals you are separating from the gangue (in Eureka’s case – copper, lead, zinc, silver and gold), it is also wise to assay for other elements. For example, iron and sulfur, to aid in performing mineral conversions so that information about the sulfide gangue can be extracted from the elemental assays, and deleterious trace

Balance the ‘outer’ circuit. That is, complete a mass balance of the feed, final concentrate and tailing for the copper, lead and zinc circuits (Figure 4). This balance will provide estimates of the tonnes of copper, lead and zinc concentrates produced. These values can be used in subsequent balances to estimate tonnages of the internal process streams within rougher, scavenger and cleaner circuits. Assign each process stream a number, and identify each of the nodes. So, the process streams are:

6

Once the assays have returned from the chemical laboratory the fun starts! You will be confronted with a list of numbers not unlike that presented in Table 4. Initially, this may be a little daunting, but once you have organised the data into a logical format, and brought order to the chaos you will be in a position to mass balance this survey. At the beginning of the mass balancing process it is necessary to make sure that you have received all the assays and that they are in good order. That is, do the tailing assays match? Do the concentrate assays follow a logical trend (for example, the rougher concentrate grade is higher than the scavenger concentrate, the cleaner concentrate grades increase as you pass from the first to the third cleaner)? Once you have satisfied yourself that the assays are good you can start the mass balancing process. Remember, if a water balance of the flotation circuit is required this can be achieved using the per cent solid values for each process stream. That is, you treat the per cent solids as an assay, and include it in your mass balance calculations. There are numerous mass balancing packages available, but the basic steps involved in completing the mass balance are the same for all. Unfortunately, it is not a case of plugging the numbers in and pressing ‘GO’, as invariably this leads to process streams having zero flow! The basic steps to following when mass balancing a survey are given below. A more detailed explanation is given in Chapter 3: Mass Balancing Flotation Data by Rob Morrison.

Step 1 Determine what the plant throughput was when the survey was completed. If the feed tonnage is not available, assign the fresh flotation feed a value of 100 per cent. It is further assumed that you have a high level of confidence in this value.

1.

Spectrum Series 16

flotation feed,

Flotation Plant Optimisation

CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

TABLE 3 Raw data from the metallurgical survey of the Eureka Concentrator. Sample number

Process stream

Sample weight (g) Gross wet

Bucket

% Solids

Cutter

Net wet

Dry

1880.9

909.8

48.4

347.8

1384.2

708.2

51.2 46.5

1

Flotation feed

2083.5

202.6

2

Copper rougher concentrate

1961.2

229.2

3

Copper rougher tailing A

2509.5

466.3

2043.2

949.7

4

Copper rougher tailing B

2480.9

466.0

2014.9

936.1

46.5

5

Copper cleaner concentrate

1386.7

225.0

836.9

536.3

64.1

6

Copper cleaner tailing A

1622.0

202.6

1419.4

144.8

10.2

7

Copper cleaner tailing B

1668.4

202.6

1465.8

141.8

9.7

8

Lead rougher concentrate

4842.2

225.3

4275.9

2695.1

63.0

9

Lead rougher tailing A

2395.6

464.3

1931.3

812.3

42.1

10

Lead rougher tailing B

2374.1

477.7

1896.4

772.0

40.7

11

Lead scavenger concentrate

1317.1

206.9

769.3

482.4

62.7

12

Lead scavenger tailing A

2416.1

465.0

1951.1

823.7

42.2

13

Lead scavenger tailing B

2357.1

446.3

1910.8

782.0

40.9

14

Lead first cleaner concentrate

10638.1

190.4

10106.6

6660.8

65.9

15

Lead first cleaner tailing A

2646.2

234.5

2411.7

1347.1

55.9

16

Lead first cleaner tailing B

2640.5

224.8

17

Lead second cleaner concentrate

5832.8

214.4

18

Lead second cleaner tailing A

2814.2

19

Lead second cleaner tailing B

2828.9

20

Lead third cleaner concentrate

2721.8

200.6

21

Lead third cleaner tailing A

2905.2

22

Lead third cleaner tailing B

2881.6

23

Zinc rougher concentrate

2779.3

226.4

24

Zinc rougher tailing A

2090.7

25

Zinc rougher tailing B

1992.0

26

Zinc scavenger concentrate

1565.6

200.4

27

Zinc scavenger tailing A

1983.0

28

Zinc scavenger tailing B

1753.0

29

Zinc first cleaner concentrate

3945.3

202.4

30

Zinc first cleaner tailing A

2316.8

31

Zinc first cleaner tailing B

2321.4

32

Zinc second cleaner concentrate

4209.1

211.9

33

Zinc second cleaner tailing A

2466.7

225.5

34

Zinc second cleaner tailing B

2474.3

234.0

324.8

341.0

340.9

341.1

2415.7

1343.7

55.6

5293.1

3547.9

67.0

233.6

2580.6

1608.0

62.3

228.2

2600.7

1424.7

54.8

2180.2

1395.7

64.0

238.1

2667.1

1635.1

61.3

225.8

2655.8

1650.7

62.2

2211.7

1287.8

58.2

224.9

1865.8

681.5

36.5

234.7

1757.3

638.8

36.4

1040.3

500.5

48.1

234.9

1748.1

629.1

36.0

225.5

1527.5

536.5

35.1

3401.7

1947.7

57.3

225.6

2091.2

1004.9

48.1

225.4

2096.0

1005.5

48.0

3656.0

2020.2

55.3

2241.2

1250.5

55.8

2240.3

1248.2

55.7

3. Cu scav tailing

325.3

341.0

341.2

324.9

341.2

341.2

5. Pb scav tailing

Cu Circuit (1)

Pb Circuit (2)

Zn Circuit (3)

2. Cu Clnr Con (Final Cu Con)

4. Pb 3rd Clnr Con (Final Lead Con)

6. Zn 2nd Clnr Con (Final Zn Con)

1. Flotation feed

7. Zn Scan Tail (Final Tail)

FIG 4 - The ‘outer’ circuit.

2.

copper cleaner concentrate,

5.

lead scavenger tailing,

3.

copper rougher tailing,

6.

zinc second cleaner concentrate, and

4.

lead third cleaner concentrate,

7.

zinc scavenger tailing.

Flotation Plant Optimisation

Spectrum Series 16

7

CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

The nodes are: 1.

flotation feed = Cu cleaner concentrate + Cu rougher tailing (or, 1 = 2 + 3);

2.

Cu rougher tailing = Pb third cleaner concentrate + Pb scavenger tailing (or, 3 = 4 + 5); and

3.

Pb scavenger tailing = Zn second cleaner concentrate + Zn scavenger tailing (or, 5 = 6 + 7).

this assay would be rejected from the data set. It is likely that having this sample reassayed would only confirm that the sample was contaminated during collection. However, care must be taken when rejecting assays because it may not always the case. This sample has a similar assay to that obtained for the copper rougher concentrate, so another possibility may be that samples have been wrongly labelled. Having sorted the data, identified the process streams, nodes and feed tonnage, the numbers can be plugged into your mass balancing program. In this case MATBAL, using a Monte Carlo simulation, was employed. The resultant mass balance is provided in Table 5, which includes a sigma value. If sigma is less than five per cent, then the data are considered to be good.

In this case, at the time of surveying the plant, throughput was 120 t/h. An examination of the tailing assays reveals that the assays are reasonably similar and in the expected range (indicating that the sampling was of a good standard). Therefore, taking an average of the two tailing sample assays is acceptable. However, if one assay was considerably higher than the other (for example, the copper cleaner tailing A, in Table 4), one suspects that this dip sample has been contaminated with froth during collection, and

Step 3 The next step in the mass balance is to balance the internal, or ‘inner’ circuits within the copper, lead and zinc flotation circuits.

TABLE 4 Raw assay data from the metallurgical survey of the Eureka Concentrator. Sample number

Process stream

% Solids

Raw assays Pb (%)

Zn (%)

1

Flotation Feed

48.4

135

0.43

4.02

15.80

14.30

2

Copper rougher concentrate

51.2

588

16.50

15.20

12.30

14.20

3

Copper rougher tailing A

46.5

92

0.19

4.04

15.40

13.40

4

Copper rougher tailing B

46.5

98

0.21

4.04

15.60

13.60

5

Copper cleaner concentrate

64.1

229

22.40

4.07

7.80

16.10

6

Copper cleaner tailing A

10.2

524

15.45

16.30

11.30

13.80

7

Copper cleaner tailing B

9.7

424

5.50

26.40

18.50

9.00

8

Lead rougher concentrate

63.0

184

0.32

21.42

29.97

8.97

9

Lead rougher tailing A

42.1

43

0.16

1.22

17.90

13.60

10

Lead rougher tailing B

40.7

34

0.16

1.25

16.60

13.50

11

Lead scavenger concentrate

62.7

179

0.36

8.16

39.84

11.57

12

Lead scavenger tailing A

42.2

38

0.14

0.67

15.20

13.90

13

Lead scavenger tailing B

40.9

18

0.15

0.50

14.60

13.70

14

Lead first cleaner concentrate

65.9

600

0.30

44.68

14.10

4.10

15

Lead first cleaner tailing A

55.9

184

0.28

18.50

30.65

8.80

16

Lead first cleaner tailing B

55.6

176

0.28

20.50

30.75

9.00

17

Lead second cleaner concentrate

67.0

960

0.51

50.90

10.10

2.50

18

Lead second cleaner tailing A

62.3

814

0.23

47.30

13.40

3.85

19

Lead second cleaner tailing B

54.8

800

0.27

47.40

13.60

3.95

20

Lead third cleaner concentrate

64.0

1060

1.08

60.00

9.40

1.70

21

Lead third cleaner tailing A

61.3

890

0.32

47.00

11.26

2.40

22

Lead third cleaner tailing B

62.2

900

0.40

49.00

11.34

2.80

23

Zinc rougher concentrate

58.2

53

0.33

1.63

45.10

8.40

24

Zinc rougher tailing A

36.5

16

0.13

0.45

1.72

15.35

25

Zinc rougher tailing B

36.4

15

0.13

0.55

1.74

15.65

26

Zinc scavenger concentrate

48.1

72

0.47

2.23

15.20

14.30

27

Zinc scavenger tailing A

36.0

12

0.09

0.32

0.85

15.32

28

Zinc scavenger tailing B

35.1

13

0.11

0.36

0.87

15.48

29

Zinc first cleaner concentrate

57.3

43

0.33

1.30

55.70

6.00

30

Zinc first cleaner tailing A

48.1

63

0.38

2.02

19.40

12.10

31

Zinc first cleaner tailing B

48.0

60

0.42

1.94

19.60

12.30

32

Zinc second cleaner concentrate

55.3

39

0.29

1.17

58.40

5.30

33

Zinc second cleaner tailing A

55.8

62

0.48

1.60

42.70

8.50

34

Zinc second cleaner tailing B

55.7

64

0.44

1.64

44.70

8.50

8

Ag (ppm)

Cu (%)

Spectrum Series 16

Fe (%)

Flotation Plant Optimisation

CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

TABLE 5 Adjusted assays for the ‘outer’ circuit mass balance. No

Stream

t/h

Adjusted assays (%) Ag (ppm)

Cu

Pb

Zn

Fe

120.00

0.09

135

0.43

3.99

15.04

13.17

1

Flotation feed

2

Cu cleaner concentrate

3

Cu rougher tailing

4

Pb 3rd cleaner concentrate

5

Pb scavenger tailing

6

Zn 2nd cleaner concentrate

27.70

2.14

39

7

Zn scavenger tailing

84.33

0.73

12

1.21

3.31

229

22.40

4.07

7.80

16.11

118.79

0.10

95

0.21

3.99

15.12

13.14

6.76

2.19

1060

1.07

61.01

9.42

1.70

112.03

0.16

28

0.15

0.55

15.46

13.83

0.29

1.18

59.92

5.35

0.11

0.34

0.86

16.62

1. Flotation feed

3. Cu rougher tailing

Cu rougher (1)

2. Cu rougher concentrate

5. Cu cleaner tailing

Cu cleaner (2)

4. Cu cleaner concentrate (Final Cu Con) FIG 5 - The copper circuit ‘inner’ mass balance.

These internal balances are broken down into ‘bite size’ pieces to simplify the balancing process, and generate estimates of tonnages that can be used in subsequent ‘inner’ circuit balances. The copper circuit (Figure 5) is comparatively easy to balance using the tonnage estimates for the flotation feed and copper cleaner concentrate generated in the ‘outer’ circuit mass balance. In this case the process streams are: 1.

flotation feed (120 00 t/h),

2.

copper rougher concentrate,

3.

copper rougher tailing,

4.

copper cleaner concentrate (1.21 t/h), and

5.

copper cleaner tailing. The nodes are:

1.

flotation feed + Cu cleaner tailing = Cu rougher concentrate + Cu rougher tailing (or, 1 + 5 = 2 + 3); and

In Balance 1 (the lead second and third cleaners), by using the third cleaner concentrate estimated tonnage generated in the ‘outer’ mass balance in Step 2 it is possible to estimate the tonnage for the lead first cleaner concentrate and the lead second cleaner tailing. Using these two values, it is then possible to mass balance the lead first cleaner. This will give tonnage estimates for the lead rougher concentrate and the lead first cleaner tailing. Balance 3 uses the tonnage estimate for the lead scavenger tailing determined in the ‘outer’ balance in Step 2. The mass balance of the lead scavengers yields an estimate of the tonnage for the lead scavenger concentrate. Once these three ‘inner’ mass balances are complete it is possible to fix certain tonnages (ie copper rougher tailing, lead scavenger tailing, lead first, second and third cleaner concentrates), and complete a mass balance of the lead circuit. The process streams used for this balance are: 1.

copper rougher tailing,

Cu rougher concentrate = Cu cleaner concentrate + Cu cleaner tailing (or, 2 = 4 + 5).

2.

lead rougher concentrate,

The resultant mass balance assays are provided in Table 6. A similar approach is adopted for the lead circuit (Figure 6) where the circuit is balanced in four parts:

3.

lead rougher tailing,

4.

lead scavenger concentrate,

2.

5.

lead scavenger tailing,

1.

the lead second and third cleaners,

6.

lead first cleaner concentrate,

2.

the lead first cleaner,

7.

lead first cleaner tailing,

3.

the lead scavenger, and

8.

lead second cleaner concentrate,

4.

the lead rougher/cleaner circuit.

9.

lead second cleaner tailing,

While this arrangement may appear to be counter intuitive, the reasons for moving backwards through the lead circuit are driven by the need to estimate tonnage figures for the recycle streams.

Flotation Plant Optimisation

10. lead third cleaner concentrate, and 11. lead third cleaner tailing.

Spectrum Series 16

9

CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

TABLE 6 Adjusted assays for the copper circuit ‘inner’ mass balance. No

Stream

Adjusted assays (%)

t/h Ag (ppm)

Cu

Pb

Zn

Fe

1

Flotation feed

120.00

0.10

135

0.44

3.99

15.04

13.17

2

Cu cleaner con

2.39

1.23

588

14.78

15.20

12.75

13.10

3

Cu rougher tailing

118.79

0.10

95

0.21

3.99

15.12

13.14

4

Cu cleaner con

1.21

0.09

229

23.63

4.14

7.71

16.83

5

Cu cleaner tailing

1.18

2.52

424

5.59

26.69

18.00

9.22

Balance 3

Pb rougher feed Pb rougher (1)

1. Cu rougher tailing

Pb scavenger (2)

3. Pb rougher tailing

5. Pb scavenger tailing

2. Pb rougher concentrate 4. Pb scavenger concentrate

Balance 2 Pb 1st cleaner feed

Pb 1st cleaner (3)

7. Pb 1st cleaner tailing

6. Pb 1st cleaner concentrate

Pb 2nd cleaner (4)

Pb 2nd cleaner feed

9. Pb 2nd cleaner tailing

8. Pb 2nd cleaner concentrate

Balance 1 Pb 3rd cleaner (5)

Pb 3rd cleaner feed

11. Pb 3rd cleaner tailing

10. Pb 3rd cleaner concentrate (Pb final con)

FIG 6 - The ‘inner’ mass balances for the lead circuit.

And, the nodes are: 1.

Cu rougher tailing + Pb scavenger concentrate + Pb first cleaner tailing = Pb rougher concentrate + Pb rougher tailing (or, 1 + 4 + 7 = 3 + 3);

2.

Pb rougher tailing = Pb scavenger concentrate + Pb scavenger tailing (or, 3 = 4 + 5);

3.

4.

Pb rougher concentrate + Pb second cleaner tailing = Pb first cleaner concentrate + Pb first cleaner tailing (or, 2 + 9 = 6 + 7); Pb first cleaner concentrate + Pb third cleaner tailing = Pb second cleaner concentrate + Pb second cleaner tailing (or, 6 + 11 = 8 + 9); and

balancing (Balance 2) step involves the zinc scavenger circuit. When these two internal mass balances are complete, it is possible to mass balance the zinc circuit while fixing certain flows. The process streams used for this balance are: 1.

lead scavenger tailing,

2.

zinc rougher concentrate,

3.

zinc rougher tailing,

4.

zinc scavenger concentrate,

5.

zinc scavenger tailing,

6.

zinc first cleaner concentrate,

7.

zinc first cleaner tailing,

Pb second cleaner concentrate = Pb third cleaner concentrate + Pb third cleaner tailing (or, 8 = 10 + 11).

8.

zinc second cleaner concentrate, and

The mass balanced assays for the lead circuit are given in Table 7. The same approach is employed when mass balancing the inner circuits for zinc flotation (Figure 7). The first balance (Balance 1) examines the zinc first and second cleaner, while the second mass

9.

zinc second cleaner tailing.

1.

5.

10

And, the nodes are:

Spectrum Series 16

Pb scavenger tailing + Zn scavenger concentrate + Zn first cleaner tailing = Zn rougher concentrate + Zn rougher tailing (or, 1 + 4 + 7 = 3 + 3);

Flotation Plant Optimisation

CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

TABLE 7 Adjusted assays for the ‘inner’ lead circuit mass balance. No

Stream

t/h

Adjusted assays (%) Pb

Zn

Fe

1

Cu rougher tailing

118.79

0.05

87

0.20

4.00

14.86

13.17

2

Pb rougher con

134.72

1.66

208

0.32

21.53

29.91

8.81

3

Pb rougher tailing

122.16

0.09

40

0.16

1.23

17.25

13.68

4

Pb scavenger con

10.14

1.34

179

0.36

8.20

39.79

11.55

5

Pb scavenger tailing

112.02

0.09

27

0.15

0.59

15.20

13.86

6

Pb 1st cleaner con

110.85

0.10

631

0.30

44.67

13.63

3.91

7

Pb 1st cleaner tailing

127.95

1.17

162

0.28

19.48

30.99

9.18 2.45

2nd

8

Pb

9

Pb 2nd cleaner tailing

10 11

cleaner con

Ag

Cu

31.98

0.09

940

0.51

50.72

10.54

104.08

0.11

602

0.25

43.65

13.91

4.06

Pb 3rd cleaner con

6.75

0.09

1077

1.08

60.39

9.35

1.71

Pb 3rd cleaner tailing

25.23

0.11

903

0.36

48.13

10.86

2.65

Balance 2

Zn rougher feed 1. Pb rougher tailing

Zn rougher (1)

3. Zn rougher tailing

Zn scavenger (2)

5. Zn scavenger tailing

2. Zn rougher concentrate 4. Zn scavenger concentrate Zn 1st cleaner feed

Zn 1st cleaner (3)

7. Zn 1st cleaner tailing

6. Zn 1st cleaner concentrate

Zn 2nd cleaner (4)

Zn 2nd cleaner feed

9. Zn 2nd cleaner tailing

Balance 1 8. Zn 2nd cleaner concentrate (Zn final con)

FIG 7 - The ‘inner’ mass balances for the zinc circuit.

2.

Zn rougher tailing = Zn scavenger concentrate + Zn scavenger tailing (or, 3 = 4 + 5);

3.

Zn rougher concentrate + Zn second cleaner tailing = Zn first cleaner concentrate + Zn first cleaner tailing (or, 2 + 9 = 6 + 7); and

4.

copper rougher is actually the fresh flotation feed plus the copper cleaner tailing. The sum of these recovery values should be the same as the copper rougher concentrate plus the tailing. That is, for copper: Rflotation feed + RCu cleaner tailing = RCu rougher con + RCu rougher tailing 100.00 + 12.54 = 66.15 + 46.39

Zn first cleaner concentrate = Zn second cleaner concentrate + Zn second cleaner tailing (or, 6 = 8 + 9). The adjusted assays for the zinc circuit are provided in Table 8.

Step 4 With the inner mass balances complete it is now possible to mass balance the whole circuit. The resultant mass balance is given in Table 9. When reviewing your mass balance it is always a good idea to check that the internal workings of the circuit are balanced. For example, in the copper circuit, the feed to the

Flotation Plant Optimisation

112.54 = 112.54 The balance holds, so we can have confidence that the mass balancing calculations have been completed correctly.

What does it mean? (Chapter 2) With the mass balance completed it is time to analyse the data and determine what it means. From this analysis it is possible to establish what and where the weaknesses are in the circuit, and

Spectrum Series 16

11

CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

TABLE 8 Adjusted assays for the ‘inner’ zinc circuit mass balance. No

Stream

t/h

Adjusted assays (%) Ag

Cu

Pb

Zn

Fe

1

Pb scavenger tailing

112.02

0.07

28

0.15

0.57

15.15

13.20

2

Zn rougher con

43.74

0.07

53

0.33

1.52

44.32

7.98

3

Zn rougher tailing

89.83

0.18

16

0.13

0.47

1.74

15.69

4

Zn scavenger con

5.51

2.56

72

0.47

2.26

15.17

14.29

5

Zn scavenger tailing

84.32

0.09

12

0.11

0.36

0.86

15.78

6

Zn 1st cleaner con

37.44

0.09

43

0.33

1.32

54.80

6.15

7

Zn 1st cleaner tailing

16.04

0.10

63

0.40

2.04

19.55

12.53

8

Zn 2nd cleaner con

27.70

0.09

39

0.29

1.22

58.66

5.34

9

Zn 2nd cleaner tailing

9.74

0.47

64

0.46

1.61

43.84

8.42

TABLE 9 Mass balance of copper, lead and zinc circuits of the Eureka Concentrator. No

Stream

t/h

Cu (%)

Pb (%)

Zn (%)

Fe (%)

Grade

Recovery

Grade

Recovery

Grade

Recovery

Grade

Recovery

120.00

0.05

0.43

100.00

4.00

100.00

14.92

100

13.06

100.00

2.39

0.41

14.29

66.15

15.10

7.50

12.76

1.70

13.10

1.99

118.79

0.05

0.20

46.39

4.00

98.97

14.99

99.48

13.02

98.69

1.21

0.11

22.74

53.61

4.07

1.03

7.71

0.52

16.84

1.31

1.18

0.84

5.52

12.54

26.54

6.47

17.99

1.18

9.22

0.69

134.72

3.12

0.32

85.07

21.44

611.75

29.86

228.56

8.84

77.31

0.23

0.17

39.52

1.24

31.39

17.40

119.05

13.52

105.65

3.00

0.36

7.25

8.17

17.72

39.71

23.11

11.58

7.70

0.14

32.27

0.58

13.67

15.33

95.94

13.70

97.95

64.56

44.68

1030.87

13.63

84.37

3.91

27.69

70.95

19.41

526.44

30.92

225.02

9.21

76.58

31.72

50.75

337.91

10.54

18.84

2.45

5.00

0.25

50.44

43.64

945.57

13.91

80.84

4.06

26.95

0.09

1.08

14.12

60.64

85.30

9.36

3.53

1.71

0.74

0.13

0.36

17.60

48.10

252.61

10.86

15.30

2.65

4.26

43.74

0.39

0.33

27.91

1.48

13.51

44.77

109.42

8.00

22.33

89.93

0.24

0.13

21.96

0.50

9.38

1.74

8.75

16.30

93.53

Zn scav con

5.51

3.59

0.47

5.12

2.23

2.58

15.14

4.71

14.26

5.07

Zn scav tailing

84.32

0.07

0.10

16.85

0.39

6.79

0.86

4.04

16.44

88.46

20

Zn 1st cleaner con

37.44

0.09

0.33

24.19

1.30

10.16

55.33

115.74

6.17

14.74

21

Zn 1st cleaner tailing

16.04

1.07

0.40

12.49

1.99

6.64

19.52

17.52

12.51

12.83

22

Zn 2nd cleaner con

27.70

0.09

0.29

15.42

1.19

6.88

59.41

91.91

5.38

9.50

23

Zn 2nd cleaner tailing

9.74

0.38

0.46

8.76

1.62

3.28

43.76

23.83

8.41

5.23

1

Flotation feed

2

Cu rougher con

3

Cu rougher tailing

4

Cu cleaner con

5

Cu cleaner tailing

6

Pb rougher con

7

Pb rougher tailing

122.16

8

Pb scav con

10.14

9

Pb scav tailing

112.02

0.10

10

Pb 1st cleaner con

110.85

0.10

0.30

11

Pb 1st cleaner tailing

127.95

2.27

0.28

12

Pb 2nd cleaner con

31.98

0.10

0.51

13

Pb 2nd cleaner tailing

104.08

0.11

14

Pb 3rd cleaner con

6.75

15

Pb 3rd cleaner tailing

25.23

16

Zn rougher con

17

Zn rougher tailing

18 19

determine what additional tests are required to give more definition to the data. As the mass balance was completed using elemental assays it is now possible to use this data to calculate what is happening on a mineral basis. That is, the mass balanced elemental assays can be converted to minerals by making certain assumptions about the elemental composition of the various minerals of interest within your system. Appendix 2 provides an example of these element to mineral calculations. The conversion to minerals allows you to examine the flotation behaviour of the iron sulfide and non-sulfide gangue species. Combining the calculated non-sulfide gangue mass balanced data with the water recovery data it is possible to gain an appreciation of how these minerals are being recovered (ie entrainment). Chapter 2: Existing

12

Methods for Process Analysis by Bill Johnson provides a detailed description of how to analyse and interpret your plant survey data. The copper grade/recovery curve for the copper circuit appears in Figure 8. This data, in conjunction with Table 9, indicates that there is a small circulating load (about 12 per cent) of copper returning to the rougher feed via the copper cleaner tailing. This is not a major concern. However, the poor selectivity for chalcopyrite against galena and sphalerite during copper roughing (ie the high lead and zinc grades) is an issue, and requires further investigation. Figure 9 contains the lead grade/recovery curve for the Eureka circuit. It is immediately obvious that there is a large circulating load of galena within the lead circuit centred around the lead first

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Flotation Plant Optimisation

CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

25.0 Cu cleaner concentrate

Cu grade, %

20.0

15.0 Cu rougher concentrate

10.0 Cu rougher feed

5.0 Flotation feed

0.0 0.0

20.0

40.0

60.0

80.0

100.0

120.0

Cu recovery, % FIG 8 - The copper grade/recovery curve for the copper circuit within the Eureka Concentrator. 70.0

Pb 3rd cleaner concentrate 60.0

Pb 2nd cleaner concentrate

Pb grade, %

50.0

Pb 2nd cleaner feed st

Pb 1 cleaner concentrate

40.0

Pb 1st cleaner feed

30.0

Pb rougher concentrate 20.0

Cu rougher tailing

10.0

Pb rougher feed

Flotation feed

0.0 0.0

200.0

400.0

600.0

800.0

1000.0

1200.0

1400.0

1600.0

1800.0

Pb recovery, % FIG 9 - The lead grade/recovery curve for the lead circuit within the Eureka Concentrator. 70.0 nd

60.0

st

Zn grade, %

50.0 Zn rougher concentrate

st

40.0 30.0 20.0 10.0

Zn rougher feed

Pb rougher tailing Cu rougher tailing

Flotation feed

0.0 40.0

60.0

80.0

100.0

120.0

140.0

160.0

Zn recovery, %

FIG 10 - The zinc grade/recovery curve for the zinc circuit within the Eureka Concentrator.

cleaner bank. A closer examination of the lead circuit mass balanced data in Table 9 reveals that accompanying the very large circulating loads of galena is a large circulating load of sphalerite. This would suggest that there may be liberation issues within this part of the circuit. Again, this warrants further investigation. The zinc grade/recovery curve (Figure 10) also reveals that there are circulating loads of zinc around the zinc first cleaner. While

Flotation Plant Optimisation

these loads are not as severe as those noted in the lead circuit, undoubtedly they are having an impact on the zinc metallurgy. Consulting Table 9, it was noted that there may be an issue with iron, particularly around the rougher/scavenger/first cleaner circuit. Further investigation is again needed to define the problem. It is apparent that there are opportunities for improvement in all three circuits. Equally, it is obvious that making improvements in

Spectrum Series 16

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CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

the copper circuit will have ramifications on both the lead and zinc circuits. And this makes for a good rule of thumb: start at the front of the circuit and work downstream. The test programs need to be prioritised so that resources can be focused on the project that has the greatest potential metallurgical (and financial) benefit to the plant. The survey data indicates that the lead circuit is very unstable with high circulating loads, and could be impeding both the lead and zinc circuit performance. It is recommended that further work be completed to determine the recovery-by-size and liberation characteristics through the lead circuit to see where improvements may be made.

Sample identification and storage At the risk of stating the obvious, having a workable sample identification and storage system will make life easier. A lack of attention to detail in this area will lead to mistakes in the assay laboratory with poor labelling, and can jeopardise the ability to locate samples for check assaying or for further testing (for example, sizing or mineralogical examination). Therefore, it is necessary to set up a system of identification that is both simple and effective. For example, all surveys are labelled with an ‘S’ and numbered consecutively, with each sample in that survey given a number. So, if the survey described in this chapter is the tenth survey completed in the Eureka Concentrator its identification code would be S10/1 to S10/34, where the sample numbers 1 to 34 correspond to the sample numbers listed in Table 2. The next survey would be S11, and so on. Flotation tests could be identified according to the operator’s initials, for example, CG351/1 to CG351/5, which would be read as flotation test 351 completed by CG with five test products. Once a numbering system has been put in place it makes it easy to develop a storage system. In developing your storage system you must set some rules regarding the length of time you are going to keep a sample, and then allow the laboratory technicians time, periodically, to maintain the storage facility. For example, it is wise to keep flotation test produces for nominally three months and plant surveys for up to 12 months. It is also wise have a clean up every three months to dispose of samples that have passed their storage date.

The pulp chemistry survey (Chapter 6) Concurrent to the metallurgical survey, pulp chemical data was collected from the plant to determine the pulp chemical conditions.

What do I have to do? The pulp chemical survey involves collecting Eh, pH, dissolved oxygen, and temperature data from the following process streams:

• • • • • • • •

SAG mill discharge,

• stir the pulp sample with a 25 ml syringe to produce homogeneous slurry;

• syringe a 25 ml aliquot of slurry from the sample bottle and weigh;

• inject the contents of the syringe into a 400 ml beaker containing 250 ml of three per cent (by weight) EDTA solution, pH modified to 7.5 with sodium hydroxide;

• thoroughly mix the slurry and EDTA solution using a magnetic stirrer, for five minutes;

• filter the slurry using a 0.2 micron millipore filter; and • submit the filtered EDTA solution for assay. The remainder of the pulp sample was pressure filtered, and the solids dried. The dry solids were weighed and submitted for assay.

What data do I need? The pulp chemical data (pH, Eh, dissolved oxygen and temperature) are stored on a data logger. These data now need to be downloaded into Excel, massaged and put into a logical format for analysis and interpretation. The samples for EDTA extraction (solids and liquids) are prepared and submitted for assay. Usually these samples are assayed for the base metals of interest; in the case of the Eureka Concentrator, the solids and liquids were assayed for copper, lead, zinc and iron. As with the metallurgical surveys, other data that can be useful when analysing the EDTA survey are:

• the throughput at the time of the survey, • reagent additions and other plant operating parameters (ie air

cyclone underflow, ball mill discharge,

flow rates and pulp levels),

cyclone overflow,

• OSA readings, and • information about the ore being treated.

copper circuit feed, lead circuit feed, zinc circuit feed, and final tailings.

To complete a pulp chemical survey, a sample of slurry is ‘cut’ from the process stream of interest, and poured into a small beaker. The sample is then stirred gently with the probes for nominally two minutes until equilibrium readings are obtained. The Eh, pH, dissolved oxygen, and temperature data are logged

14

on a data logger. The logged data can then be downloaded from the data logger to a laptop computer where it is able to be manipulated. All of the probes should be checked to ensure they are clean and in good working order, and it is imperative that they are calibrated before use. The pH probe should be calibrated using pH buffer solutions seven and ten, if this is the range expected in the plant. Alternative buffer solutions should be used if the pulp pH is outside this range. The Eh probe should be calibrated, for example, using Zobell solution (1:1 solution of Part A and B = 231 mV at 24°C), the dissolved oxygen probe calibrated in a 0.2 g/L solution of sodium sulfite for the zero calibration, and air. The temperature probe can be calibrated with the aid of a thermometer, using iced and heated water to give a two point calibration. To complete the data set, EDTA extractions should be completed on the same process streams as the pulp chemistry. For the Eureka survey, each stream was ‘cut’ and the sample poured into a small wide mouth, screw top sample bottle. The samples were taken back to the laboratory, and the wet weight recorded. The EDTA extraction procedure used was:

In the context of a one off survey some of these pieces of information may not be of great value. However, when the analysis is extended to include other surveys on other ore blends, circuit configurations and reagent suites, these data provide a vital link in the comparison. It can be beneficial to collect process water samples routinely to determine the free ions in solution (ie base metal ions (copper, lead, zinc, iron), calcium, magnesium, sulfate and chloride).

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CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

How do I analyse the data?

examining the pulp chemistry of a regrind/cleaner circuit, it is normal to collect a sample of the fresh concentrate that feeds the regrinding section. It is also good policy when completing surface analysis comparing pairs of streams (ie rougher concentrate and rougher tailing), to collect the pulp chemistry of the two process streams of interest.

With the exception of the Eh data the other pulp chemical measurements can be read directly from the measured data. The Eh should be adjusted so that it is referenced against the standard hydrogen electrode (SHE). Chapter 6: Chemical Measurements During Plant Surveys and Their Interpretation by Stephen Grano provides an explanation of how to manipulate and analyse the data you have collected. One method of analysing the EDTA data is given by Rumball and Richmond (1996), who developed a simple relationship for calculating the percentage of oxidised mineral present in a pulp from EDTA extraction data (Equation 1): % EDTA extractable M =

What does it mean? The pH, Eh, dissolved oxygen, and temperature data should be plotted in such a way to represent the pulp flow profile through the circuit to assist with the analysis and interpretation of the data. The profiles through the Eureka circuit are displayed in Figures 11 to 14, respectively. The pH profile (Figure 11) indicated that grinding occurs at natural pH (in the range 8.0 to 8.5). The slight reduction in pH in the ball mill discharge maybe attributed to pyrite oxidation. Sodium metabisulfite (SMBS) was added to the copper rougher feed, to depress galena during copper flotation. The addition of SMBS resulted in the pH being reduced to approximately 6.0. The pH was then increased to 8.0 for galena flotation and 11.5 sphalerite flotation thought the addition of lime. Figure 12 contains the Eh profile through the circuit. The Eh shifted to slightly less oxidising pulp potentials as the pulp flowed from the SAG mill through the ball mill, and became more oxidising during flotation where air is used as the flotation gas. The dissolved oxygen profile (Figure 6) through the circuit indicated that the oxygen content of the pulp was negligible during both grinding and flotation, registering zero on the meter. It was not until the zinc flotation stage that the dissolved oxygen content of the pulp was increased to 4.5 ppm in the final tailing. These data suggest that the ore is very reactive and continues to consume oxygen throughout the process. The pulp temperature ranged 33 to 35°C across most of the circuit (Figure 14). The spike in the pulp temperature in the ball mill discharge can be attributed to part of the addition grinding energy being dissipated as heat. The Eh-pH data for the grinding and flotation circuits of the Eureka Concentrator have been plotted in Figure 15 to determine where the reactions are occurring. From the Nernst Equation 2 there is a dependence of redox potential on pH:

Mass of M in EDTA solution × 100 (1) Mass of M in solids

where: M

is the metal ion under investigation

The data is generally presented graphically with the pulp chemical parameter on the y-axis and the circuit position on the x-axis. The process streams are set to mimic the normal flow of the slurry through the circuit. In this case: 1.

SAG mill discharge,

2.

cyclone underflow,

3.

ball mill discharge,

4.

cyclone overflow,

5.

copper rougher feed,

6.

lead rougher feed,

7.

zinc rougher feed, and

8.

final tailing.

When investigating the pulp chemistry within your circuit often the urge is to sample every stream in the concentrator. While this may be a good idea initially to get an idea of the variations between process streams, it soon becomes apparent that some of this data is redundant. For example, concentrate streams usually have high dissolved oxygen contents and very oxidising pulp potentials because the froth in the concentrate contains significant amounts of air. Therefore, when conducting a pulp chemistry survey of the primary grinding/rougher flotation circuit measuring the pulp chemistry of the rougher concentrate can produce numbers that skew the analysis. However, if you are

E = E °+

⎛ α Reactants ⎞ 0.059 log 10 ⎜ ⎟ n ⎝ α Products ⎠

(2)

12.0 10.0

pH

8.0 6.0 4.0 2.0

ee d ro ug he rf ee d Zn ro ug he rf ee Zn d ro ug he rt ai lin g Pb

ro ug he rf

ov er f lo w

Cu

Cy clo ne

di sc ha r

ge

flo w

m ill

un de r Ba ll

di s m ill SA G

Cy clo ne

ch ar ge

0.0

Circuit position FIG 11 - The pH profile through the grinding and flotation circuits of the Eureka Concentrator.

Flotation Plant Optimisation

Spectrum Series 16

15

CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

200.0

Eh, mV (SHE)

160.0

120.0

80.0

40.0

ee d ro ug he rf ee d Zn ro ug he rf ee Zn d ro ug he rt ai lin g Pb

Cu

ro ug he rf

ov er f lo w

Cy clo ne

di sc ha r

ge

flo w

m ill

un de r Ba ll

SA G

m ill

Cy clo ne

di s

ch ar ge

0.0

Circuit position FIG 12 - The Eh profile through the grinding and flotation circuits of the Eureka Concentrator. 6.0 5.0

DO, ppm

4.0 3.0 2.0 1.0

ee d ro ug he rf ee d Zn ro ug he rf ee Zn d ro ug he rt ai lin g Pb

ro ug he rf

ov er f lo w

Cu

m ill

Cy clo ne

di sc ha r

ge

flo w un de r Ba ll

SA G

m ill

Cy clo ne

di s

ch ar ge

0.0

Circuit position FIG 13 - Dissolved oxygen profile through the grinding and flotation circuits of the Eureka Concentrator. 45.0 40.0 o

Temperature, C

35.0 30.0 25.0 20.0 15.0 10.0 5.0

ee d ro ug he rf ee d Zn ro ug he rf ee Zn d ro ug he rt ai lin g Pb

ro ug he rf

ov er f lo w

Cu

m ill

Cy clo ne

di sc ha r

ge

flo w un de r Ba ll

Cy clo ne

SA G

m ill

di s

ch ar ge

0.0

Circuit position FIG 14 - Temperature profile through the grinding and flotation circuits of the Eureka Concentrator.

Applying the Nernst equation to water results in a Pourbaix diagram that describes three domains, separated by lines of equilibria. The upper most of these is the water-oxygen line (Equation 3), above which water decomposes and oxygen is evolved, and below which water is stable:

16

E 0 2 = +1.23 + 0.015 log 10 po2 − 0.059 pH

(3)

This can be simplified further (Johnson, 1988; Natarajan and Iwasaki, 1973) for an oxygenated aqueous solution with no well defined redox couples to (Equation 4):

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Flotation Plant Optimisation

CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

E 0 2 = +0.9 − 0.059 pH

remained negligible throughout the grinding circuit. The per cent EDTA extractable copper increased during the copper flotation step to approximately 2.5 per cent and this increases to 17 per cent in the zinc rougher feed, which can be attributed to the addition of copper sulfate for sphalerite activation. The first observation to be made is that the percentage of EDTA extractable lead is at least an order of magnitude greater than the values reported for zinc and iron. The percentage of EDTA extractable lead is higher as galena is a reactive mineral when in contact with other sulfide minerals, particularly pyrite. The EDTA extractable lead profile shows that the percentage of oxidised galena remained approximately constant through the grinding circuit, with values of around 1.0 per cent. The per cent EDTA extractable lead increased in the cyclone overflow, and remains reasonably constant through the copper circuit. After the lead flotation stage the lead scavenger tailing per cent EDTA extractable lead was 17 per cent, and then increased to almost 40 per cent after zinc flotation. These data suggest that the lead species that remain in the lead scavenger tailing are more heavily oxidised. The EDTA extractable zinc profile exhibits a very similar trend to that observed for lead. That is, through the grinding circuit the percentage EDTA extractable zinc remained approximately constant, with values of around 0.1 per cent. This indicated that sphalerite oxidation was largely unchanged through this circuit.

(4)

In broad terms, if the changes in Eh and pH result in a line parallel to the water-oxygen line this means that water equilibria is being maintained. That is, any change in Eh is directly proportional to a change in pH with a similar relationship to that expressed in Equation 4. If the changes in Eh and pH result in a line that is perpendicular to the water-oxygen line then the evidence suggests that oxidative reactions are occurring. Figure 15 shows that the Eh-pH lines between points 1 to 4 are perpendicular to the water-oxygen line. This indicates that oxidative reactions are occurring in the grinding circuit. It is likely that these oxidative reactions are corrosion of the grinding media and oxidation of the sulfide minerals. As the pH is decreased across the ball mill it is suggested that pyrite oxidation (an acidic reaction) may be one of the dominant reactions. The changes in the Eh-pH curve between Points 4 and 5, 5 and 6, and 6 and 7 can be attributed to the addition of reagents that alter the pH of the system. During copper flotation it is the addition of SMBS, while in the lead and zinc circuits it is the addition of lime. The EDTA extractable copper, lead, zinc and iron data are presented in Figure 16. The EDTA extractable copper profile (Figure 9) suggested that the percentage of oxidised chalcopyrite 250

Eh, mV (SHE)

200

6

150

8

4 5 1

100

1. 2. 3. 4. 5. 6. 7. 8.

50

0

SAG mill discharge; Cyclone underflow; Ball mill discharge; Cyclone overflow; Cu rougher feed; 3 Pb rougher feed; Zn rougher feed; and Final tailing

2 7

-50 4.0

5.0

6.0

7.0

8.0

9.0

10.0

11.0

12.0

pH

21.0

0.6

14.0

0.4

7.0

0.2

0.0

0.0

Pb

Zn

Fi

he r

ro ug

d ee

ro ug

er f

flo C u

ro ug h

ov er

ar ge

ne C yc lo

m il l

di

sc h

un de r Ba ll

ne C yc lo

ill m G SA

EDTA extractable Zn and Fe, %

0.8

na lt ai lin g

28.0

fe ed

1.0

he rf ee d

35.0

w

1.2

flo w

42.0

di sc ha rg e

EDTA extractable Cu and Pb, %

FIG 15 - The Eh-pH curve for the grinding and flotation circuits of the Eureka Concentrator.

Circuit position Cu

Pb

Zn

Fe

FIG 16 - The EDTA extractable copper, lead, zinc and iron profiles through the grinding and flotation circuits of the Eureka Concentrator.

Flotation Plant Optimisation

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CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

There was an increase in the per cent EDTA extractable zinc during the copper and lead flotation circuits (ie from 0.13 to 0.37 per cent) and then a significant increase after the zinc flotation circuit (to 1.0 per cent). This increase indicated that the zinc species that remained in the zinc scavenger tailing were more heavily oxidised. The EDTA extractable iron profile gives the best indication of the impact of grinding media corrosion on the system. The EDTA extractable iron through primary grinding ranged from 0.05 to 0.16 per cent, and then increased to 0.30 per cent in the cyclone overflow. That is, the pulp entering the flotation circuit contains elevated levels of EDTA extractable iron, presumably after contact with the forged grinding media. Interestingly, the levels of EDTA extractable iron decrease through the flotation circuit. This is probably due to the continuing oxidation of the iron species to higher level iron oxides, which are not soluble in EDTA.

You need to gather solid data that tells you which size fractions are being rejected from the circuit, and what their mineralogical characteristic is. Therefore, the first step in this analysis is to examine the recovery-by-size around the lead rougher feed.

What do I have to do? When you conducted the plant survey you may have had every intention to have the samples sized so that you can complete a recovery-by-size analysis. However, before having your metallurgical technicians launch into a large body of work sizing every sample collected during the survey it is best to mass balance the plant survey. Sizing samples prior to completing the mass balance may waste time, resources and money if the survey does not mass balance easily (ie poor sampling). Once you have established that the mass balance is good, you need to decide if completing a recovery-by-size analysis is warranted, and if it is, what samples you would like to have sized. It is not always necessary to size every sample in the survey. The sample selection will depend on what the survey reveals about plant performance. For example, sizing the concentrate and tailing from a section will show which size fractions of the valuable species are misbehaving (ie not being recovered efficiently), and which size fractions of the gangue species are being recovered. Sometimes completing recovery-by-size analysis on a downthe-bank survey can add value because it allows you to determine where size fractions are recovered in the circuit, and can be used to determine the kinetics of various species on a size basis. With these decisions made you need to retrieve the samples from storage, ensure that you have sufficient sample to complete a sizing (generally 200 grams is sufficient), and determine what sizes you require. If you need to obtain size fractions below 38 microns you will need to use a cyclosizer, which will give you six more size fractions. However, if cyclosizer is used in concert with a precyclone and a centrifuge the number of size fractions obtained can be extended to seven.

Summary of data acquisition The metallurgical survey suggests that there are a number of opportunities for improving the metallurgical performance of the Eureka Concentrator. It is suspected that these may be liberation related, and further data is required to identify exactly what the liberation characteristics are. The data strongly suggests that the first priority should be improving the lead flotation circuit. The pulp chemistry suggests that the ore is reasonably reactive, particularly during grinding, and consideration should be given to improve this aspect of plant performance. However, this should not be rectified until the liberation issues have been resolved.

PROBLEM DEFINITION From the metallurgical survey the circulating load observed in the lead rougher/lead first cleaner circuit were observed to be extremely high (Table 10), for both lead and zinc. In fact, the copper scavenger tailing contributed only 15.4 and 28.6 per cent of the lead and zinc units, respectively, to the lead rougher feed. The recycle from the lead first cleaner tailing contributed by far the most lead and zinc to the lead rougher feed (81.9 and 64.7 per cent, respectively).

What data do I need? With the sizing completed you will require the mass collected in each size fraction. If the sizing has been restricted to a simple sieve analysis, then you will need to determine how much mass you have in each size fraction to ensure that you have sufficient for assay (usually 5 grams is more than enough). If you do not have enough sample in each size fraction for an assay you need to either complete another sizing on this sample, or you combine size fractions to yield enough mass. However, if you do combine size fractions you must apply this across all of the samples within this data set. Not to do so will make it impossible to complete the analysis. That is, if you were required to combine the +300, +212 and +150 micron fractions in the feed sample, then you will need to do the same for all other samples in the suite of samples for this survey. When it comes to sizing the subsieve fractions using a precyclone/cyclosizer/centrifuge combination, you will need to know the water temperature, the elutriation time, the water flow

Recovery by size (Chapter 2) The mass balanced data gives you information about the grades and recoveries in the circuit. The data also provides information about the circulating loads. However, to gain a greater appreciation for where problems occur and their magnitude, it is advisable that samples from selected process streams be sized, and each size fraction assayed. By mass balancing the size fractions, the performance of each size fraction can be assessed. An examination of Table 9 and Figure 9 indicates that the lead rougher/first cleaner section of the plant has a large circulating load of galena and sphalerite. It is likely that this large circulating load produces instability within the circuit, and is probably due to composite particles. However, at this stage you are only guessing.

TABLE 10 Mass balanced data for the lead rougher feed, with respect to flotation feed. Note: Both the lead scavenger concentrate and the lead first cleaner tailing are recycled back to the head of the lead rougher. Stream

t/h

Grade (%)

Recovery (%)

Cu

Pb

Zn

Fe

Cu

Pb

Zn

Fe

Cu scav tailing

118.8

0.2

4.0

15.0

13.0

46.4

99.0

99.5

98.7

Pb 1st cleaner tailing

128.0

0.3

19.4

30.9

9.2

71.0

526.4

225

76.6

Pb scav concentrate

10.1

0.4

8.2

39.7

11.6

7.2

17.7

23.1

7.7

Pb rougher feed

256.9

0.3

11.8

23.9

11.1

124.6

643.1

347.6

183

18

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rate and the specific gravity of the mineral being separated. With these variables known using the cyclosizer manual (Warman International Limited, 1991) the ‘cut’ size for each cyclone can be calculated. That is, for quartz the cyclone ‘cut’ sizes for the cyclosizer are:

• • • • •

C1 = 44 microns, C2 = 33 microns,

If you are considering completing a mineralogical analysis it is at this point that you would ‘split’ out a small representative portion from the samples of interest prior to pulverising the samples for assay. Once you have reviewed the weights in each size fraction for each of the samples you have had sized, and decided which size fractions to combine, and ensured that there is enough sample for assay in each size fraction, the samples can be prepared and submitted of assay.

C3 = 23 microns, C4 = 15 microns, and

How do I analyse the data collected?

C5 = 11 microns.

When the assays return it is important to check that the assays are in good order. This can be done by calculating the head assay from the size fraction assays and comparing it with the actual head assay. If they are in good agreement, then you can assume that both the sizing and the assays were completed properly. To construct a graph similar to that presented in Figure 17 the size and assay data for the copper rougher tailing, the lead first cleaner tailing, the lead scavenger concentrate and the lead rougher feed are required. To simplify the analysis only the lead assay data will be considered in this example. The starting point for determining the recovery-by-size behaviour in this part of the circuit is the mass balanced data from the plant survey given in Table 9, and for this section of the plant Table 10. Using the mass balanced tonnages for each of the process streams given in Table 10 the size distribution data determined from the sizing process (ie the weight per cent data) for each of these sample points were applied to yield the tonnes of ore in each size fraction (Table 12). The weight per cent and the assay for each size fraction are used to calculate the head grade:

The precyclone generally ‘cuts’ at about 7 microns. To convert these ‘cut’ sizes to values that are more representative of minerals such as chalcopyrite, galena, sphalerite and pyrite, then the ‘cut’ size for quartz must be multiplied by the overall correction factor: f = fT × fSG × fFM × fET

(5)

where: fT

is the temperature correction factor

fSG is the mineral specific gravity correction factor fFM is the flow meter reading correction factor fET is the elutriation time correction factor It is important to note that you should correct for each mineral in the system as each mineral has a different specific gravity. The cyclone ‘cut’ sizes for each of the cyclosizer cones are given in Table 11. Further, it must be realised that sizing the -38 micron material using the precyclone, cyclosizer and/or the centrifuge represents a change in the way the particles are sized. When using sieves the sizing is achieved by passing the particles over a nest of sieves. Particles that are larger than the screen aperture are retained on the screen and those that are smaller fall through. However, when sizing using the precyclone, cyclosizer and/or centrifuge sizing is completed hydraulically based on size and mineral specific gravity. When the two sizing methods are used together, the transition point from one technique to the other can lead to some unusual shaped curves which are purely due to the change in the sizing method. To overcome this it is usual to combine the -53 micron to +C2 size fractions. This smooths the curves and effectively removed the transition between sizing methods.

( mi × ai ) i=1 ∑ mi n

Head grade = ∑

(6)

where: m

is the weight per cent is size fraction i

a

is the assay for that size fraction

This calculated head grade is then compared with the assay of the head sample to determine how well the sizing and assay procedures have been completed. Unfortunately, in this instance the mass and assay of the -5.6 micron fraction was calculated by difference. That is:

TABLE 11 Cyclosizer cyclone ‘cut’ sizes for quartz, chalcopyrite, galena, sphalerite and pyrite. Correction factor

Mineral Chalcopyrite

Galena

Sphalerite

Pyrite

fT

Quartz

0.9815

0.9815

0.9815

0.9815

fSG

0.7181

0.5038

0.7416

0.6423

fFM

0.9519

0.9519

0.9519

0.9519

fET

1.0063

1.0063

1.0063

1.0063

f

0.6751

0.4737

0.6972

0.6038

Cyclone ‘cut’ size C1

44

30

21

31

27

C2

33

22

16

23

20

C3

23

16

11

16

14

C4

15

10

7

11

9

C5

11

7

5

8

7

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CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

100.0 90.0

Pb distribution, %

80.0 70.0 60.0 50.0 40.0 30.0 20.0

Pb rougher feed Pb 1st cleaner tail

10.0 0.0

Pb scav con Total -5.6

+5.6

+7.6

Particle size, microns

Cu scav tail +11.6

+16.7

+22.2

FIG 17 - Lead distribution by size in the process streams contributing to the lead rougher feed.

TABLE 12 The lead recovery-by-size data for the lead rougher feed calculated from the copper rougher tailing, lead first cleaner tailing and the lead scavenger concentrate. Stream/size

Wt %

Wt (t/h)

Pb parameter (%) Grade

Distribution

Recovery to Pb Ro feed

4.06

49.49

7.73

Cu scavenger tailing +22.2 μm

48.79

57.96

+16.7 μm

6.66

7.91

3.00

5.00

0.78

+11.6 μm

10.18

12.09

1.88

4.78

0.75

+7.6 μm

5.32

6.32

2.54

3.38

0.53

+5.6 μm

3.77

4.48

2.24

2.11

0.33

-5.6 μm

25.28

30.03

5.58

35.24

5.51

Head

100.00

118.79

4.00

100.00

15.62

+22.2 μm

82.44

105.48

22.12

93.96

76.72

+16.7 μm

6.13

7.84

8.84

2.79

2.28

+11.6 μm

3.19

4.08

8.64

1.42

1.16

+7.6 μm

1.17

1.50

5.10

0.31

0.25

+5.6 μm

0.81

1.04

4.10

0.17

0.14

-5.6 μm

6.26

8.01

4.18

1.35

1.10

100.00

127.95

19.41

100.00

81.65

+22.2 μm

70.32

7.13

9.66

83.14

2.26

+16.7 μm

10.48

1.06

8.20

10.52

0.29

+11.6 μm

6.69

0.68

2.62

2.15

0.06

+7.6 μm

2.15

0.22

3.20

0.84

0.02

+5.6 μm

1.37

0.14

3.68

0.62

0.02

-5.6 μm

8.99

0.91

2.49

2.74

0.07

100.00

10.14

8.17

100.00

2.72

+22.2 μm

66.40

170.57

15.46

86.72

86.72

+16.7 μm

6.55

16.82

6.05

2.25

2.25

+11.6 μm

6.56

16.85

3.55

1.97

1.97

+7.6 μm

3.13

8.03

3.03

0.80

0.80

+5.6 μm

2.20

5.65

2.62

0.49

0.49

Pb First cleaner tailing

Head Pb scavenger con

Head Pb rougher feed

-5.6 μm

15.16

38.95

5.22

6.68

6.68

Head

100.00

256.88

11.84

100.00

100.00

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n−1

m−5 .6 μm = mH − ∑ m1

(7)

i−1

What does it mean?

and

a−5 .6 μm

⎛ ⎛n−1 ⎞⎞ ⎜ mH × aH − ⎜ ∑ m1 × ai ⎟ ⎟ ⎠⎠ ⎝ i−1 ⎝ = m−5 .6 μm

(8)

where: mH and aH are the weight per cent and assay for the head By calculating the weight per cent and assay for the finest size fraction all the errors associated with the sizing, assaying and sampling are accumulated to this size fraction. In an ideal world as sample of this material would be collected. Having worked out the tonnes of ore and the assay for each size fraction the distribution-by-size within each process stream, and the recovery-by-size against a particular process stream can be calculated. The distribution within a process stream is given by: ⎛ ( m × ai ) ⎞ Distributiona = ⎜ i ⎟ × 100 ⎝ ( mH × aH )⎠

(9)

The distribution of lead within each process stream is provided in Table 12. In this case the recovery-by-size is calculated for the lead rougher feed because the copper scavenger tailing, the lead first cleaner tailing and the lead scavenger concentrate all combine to form the lead rougher feed. So, the recovery for each size fraction, i, is given by:

Recoveryi , a

⎛ n ⎞ ⎜ ∑ ( m p × a p )⎟ ⎟ × 100 = ⎜ P= 1 ⎜ ( mH × aH ) ⎟ ⎜ ⎟ ⎝ ⎠

(10)

Figure 17 contains the distribution by size, for galena, for the three process streams contributing to the lead rougher feed. The vast majority of the galena in the lead rougher feed is in the coarse (+20 micron) lead recycled back from the lead first cleaner tailing (80 per cent of the total lead in the lead rougher feed). Thus, the flotation characteristics of the lead rougher/scavenger unit are dominated by the behaviour of this material. The recoveries versus size data for the lead final concentrate are provided in Figure 18. These data show clearly that the lead final concentrate consists predominantly of fine (-20 micron) galena, with greater than 90 per cent lead recovery for the intermediate size fractions (+5/-20 microns). Either side of this size range the recoveries decrease. The recoveries of gangue minerals (sphalerite, iron sulfides and non-sulfide gangue) are low across all size fractions. The galena distribution, by size, of the lead scavenger tailing, with respect to flotation feed, is provided in Figure 19. Clearly the losses of galena from the lead circuit are bimodal, with significant losses in the fine (-5 microns) fraction (5.6 per cent) and coarse (+20 microns) fractions (19.9 per cent). Of greatest concern however are the losses in the coarse fractions. It is presumed that these coarse particles occur as galena deficient/sphalerite rich composites. Figure 20 shows the recovery by size data for the zinc final concentrate. These data show the peculiar behaviour of the coarse (+20 microns) galena, which exhibits recoveries as high as 60 per cent. It is presumed that this behaviour is related to the composition of these galena particles (ie galena deficient/ sphalerite rich composites).

Mineralogy (Chapter 4) Once the recovery-by-size data has been analysed and a theory formed, select streams should be examined mineralogically. As this is a relatively expensive process, it is wise to complete the work already discussed, prior to obtaining mineralogical analysis. The recovery-by-size analysis indicates that a significant amount

where: P

A similar approach is adopted for the more traditional recovery-by-size curves presented in Figure 18 and 20.

are the process streams of interest 90.0 80.0

Recovery, %

70.0 60.0 50.0 40.0 30.0 20.0 10.0 0.0 1.0

10.0

100.0

1000.0

Geometric mean particle size, microns Lead

Zinc

Copper

Iron

Silica

FIG 18 - Recovery-by-size data for the lead final concentrate, with respect to flotation feed for the Eureka Concentrator.

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CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

5.0 4.0 3.0 2.0 1.0

178.3

Geometric mean particle size, microns

126.1

89.2

63.0

48.8

41.0

28.0

17.6

11.7

7.9

6.0

0.0 2.3

Distribution (with respect to flotation feed), %

6.0

FIG 19 - The galena distribution by size, with respect to flotation feed, in the lead scavenger tailing for the Eureka Concentrator. 100.0 90.0

Recovery, %

80.0 70.0 60.0 50.0 40.0 30.0 20.0 10.0 0.0 1.0

10.0

100.0

1000.0

Geometric mean particle size, microns Lead

Zinc

Copper

Iron

Silica

FIG 20 - Recovery-by-size data for the zinc final concentrate, with respect to flotation feed for the Eureka Concentrator.

of material is recycled back to the lead rougher feed from the lead first cleaner tailing, and that the vast majority of this material occurs in the +20 micron size fraction. It is highly likely that these particles are galena/sphalerite composites. However, in order to prove this it is necessary to complete a mineralogical examination.

What do I have to do? To complete a mineralogical analysis of samples from you plant you need to provide the company completing the examination for you with a representative sample of the process stream that has not been pulverised. For liberation analysis, the sample provided will be of a number of closely sized size fractions. If you have completed a recovery-by-size analysis you should have prepared the samples for mineralogical examination at the same time. With the samples available for analysis it is then necessary to choose the method by which the mineralogical data will be collected. These methods range from optical microscopy through to automated methods such as QEMSCAN and MLA. Chapter 4: A Practical Guide to Some Aspects of Mineralogy that Effect Flotation, by Alan Butcher, describes the methods available.

22

What data do I need? When shipping samples off to a laboratory for mineralogical analysis it is wise to provide the mineralogist with a scope of work, and assays of the samples that will be examined. The scope of work will inform the mineralogist of the questions you would like answered. For example, at Eureka you are interested in the locking and liberation characteristics of galena and sphalerite around the lead rougher/first cleaner circuit. It is then clear to the mineralogist that the examination should provide information about the degree of liberation of these minerals, and how they are locked with other minerals. Supplying the assays for the samples you have supplied for examination allows the mineralogist to reconcile his calculated head grade based on the minerals present back to the assays. It is a check that the mineralogist uses to ensure the quality of the data that is provided.

How do I analyse the data collected? The mineralogical report provided will depend on the technique employed by the mineralogist to examine your samples. Essentially, the data provided should provide nominally the same information. That is, the percentage of liberated mineral within

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recovery-by-size and liberation analysis has clearly indicated that the recovery of +20 micron galena within the lead circuit is limited. The liberation analysis clearly shows that the galena in the +20 micron fraction is locked with sphalerite. Thus, the problem is: poor liberation of galena in the +20 micron size fractions.

the sample, the percentage of binary particles present and what the two minerals are, and the percentage of more complex composite particles measured. Table 13 provides a simplified list of the liberation data for galena in the lead rougher feed of the Eureka Concentrator. What this data means is that of the lead in the +28 micron size fraction 66 per cent occurs as liberated particles of galena and 28 per cent are present as binary composites with sphalerite. Minor amounts of galena are associated with pyrite and occur in ternary particles.

SOLUTION DEVELOPMENT AND TESTING It is apparent that to improve liberation one needs to grind finer. The first step in proving that improved regrinding is required in the lead circuit is to complete a series of laboratory tests examining the impact of regrinding the main feed source to the lead rougher, the lead first cleaner tailing.

What does it mean? Mineralogical examination of strategic process streams feeding into the lead rougher feed showed that about one third of the galena in the lead rougher feed occurs as coarse (+20 micron) galena/sphalerite composite particles (Figure 21), and the majority of this material emanates from the lead first cleaner tailing. Thus, two thirds of the galena in the lead rougher feed is liberated, which infers that the maximum lead recovery to the final lead concentrate, at grade, would be approximately 70 per cent. Therefore, galena liberation was considered to be the limiting factor impinging of improved metallurgical performance.

Laboratory investigation (Chapter 9)

What do I have to do? As the lead first cleaner tailing contributed the highest flow of material to the lead rougher feed, and this process stream contains a significant percentage of galena/sphalerite composite particles greater than 20 microns, it was decided that this process stream would be the best one to complete laboratory tests examining the impact of regrinding on lead rougher flotation. It is your job to design a series of laboratory flotation tests that would identify what changes would occur as the lead first cleaner tailing was reground to progressively finer sizes.

Problem definition summary The metallurgical survey suggested that the lead circuit was potentially unstable with large circulating loads of galena and sphalerite around the lead rougher/first cleaner circuit. The use of

TABLE 13 Galena liberation by size and mineral class for the lead rougher feed of the Eureka Concentrator. Size (μm)

Liberation class (%) Liberated

Total (%)

Binary with …

Ternary

Sphalerite

Pyrite

Gangue

+89

26

54

5

4

11

100

+28

66

28

3

0

2

100

+10

69

25

5

1

1

100

+6

93

6

0

0

0

100

-6

94

5

0

0

0

100

Head

66

28

3

0

2

100

100 90

Distribution

80 70 60 50 40 Liberated

30

Ga-Sp

20

Ga-Py

10

Ga-Gn

0 Head

2.3

Liberation class

Ternary 6.0

Size, microns

10.1

28.2

89.2

FIG 21 - Size by liberation class data for the lead rougher feed. Ga = galena; Sp = sphalerite; Py = pyrite; and Gn = gangue.

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CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

With the laboratory test program designed, sufficient pulp was collected from the lead first cleaner tailing. In addition to the lead first cleaner tailing pulp, a bulk sample of process water was also collected. The pulp was filtered and ‘cut’ into 1000 gram lots. The test program called for one test to be completed without regrinding, and then tests completed on ore ground for five, ten, 15 and 20 minutes. The tests were completed in a 2.5 litre flotation cell. Timed concentrates were collected after 0.5, 1.5, 2.0, 2.0, 2.0, 2.0 and 2.0 minutes for a total flotation time of 12 minutes. The seven concentrate and tailing samples generated for each test were prepped and submitted for assay.

What data do I need? The weights for each of the concentrates and the tailing samples as well as the assays are required to complete a mass balance for each of the tests. Additional information such as the pH, reagent additions and any observations made during the test are also helpful.

How do I analyse the data collected? The weights and assays are to be put into a spreadsheet that allows you to calculate the cumulative grades and recoveries for each of the tests. These data can then be used to construct lead grade/recovery curves (Figure 22). From the mass balanced data it is also possible to determine the kinetics (ie flotation rate constant and maximum recovery) using Equation 11, and the selectivity for galena against the gangue minerals.

R = Rmax × (1 − e − kt )

(11)

To assist with interpretation the kinetic data and the selectivity data can be tabulated. For example, Table 14 shows the lead concentrate grade, as well as the zinc and iron sulfide recoveries, at 80 per cent lead recovery. Selectivity curves can also be drawn.

What does it mean? Laboratory lead rougher flotation tests conducted on strategic process streams suggested that the introduction of regrinding significantly improved the position of the lead grade/recovery curve. Figure 22 shows that as the degree of regrinding increased the position of the lead grade/recovery curve improved. For example, at 80 per cent lead recovery the lead grade was increased from 30.8 per cent for the test conducted without regrinding, to 42.2 per cent after 20 minutes regrinding. The improvement in lead grade was due to better selectivity for galena against sphalerite and iron sulfides (Table 14). In the laboratory, regrinding improved lead metallurgy, and with the improved selectivity for galena against sphalerite it is expected that zinc metallurgy would also improve.

Plant trial (Chapter 10) As the existing lead regrind mill was inadequate for this duty, a larger mill would be required if improvements in metallurgical performance were to be realised. In light of the very first comment made at the beginning of this chapter about utilising the

60.0

Pb grade, %

55.0 50.0 45.0 40.0 35.0 30.0 25.0 10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

Pb recovery, % No regrinding 15 minutes regrinding

5 minutes regrinding 20 minutes regrinding

10 minutes regrinding

FIG 22 - Lead grade/recovery curves for lead rougher flotation tests conducted on lead first cleaner tailing, demonstrating the effect of regrinding.

TABLE 14 Lead grade and diluent recoveries, at 80 per cent lead recovery, for lead rougher flotation tests conducted on lead first cleaner tailing demonstrating the impact of regrinding. Test description

Pb grade (%)

Diluent recovery (%) Zn

IS

No regrinding

30.8

71.2

51.6

5 minutes regrinding

34.3

61.9

37.2

10 minutes regrinding

37.6

50.8

30.4

15 minutes regrinding

42.0

42.6

24.3

20 minutes regrinding

42.2

42.2

25.8

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• the zinc grade in the lead concentrate was reduced by 1.8 ±

resources around you, and especially people, this problem was discussed with the operations team and a solution was quickly found. As capital was not readily available an experienced flotation operator suggested swapping the lead and zinc regrinding mills, as the zinc regrinding mill was larger and more able to cope with the higher tonnages experienced in the lead circuit. Redirecting the lead scavenger concentrate and lead first cleaner tailing process streams to the zinc regrind mill was accomplished through a simple change in the pipe work. The existing pipe work to the old lead regrind mill was left intact so that a plant trial could be conducted. A randomised block on/off trial was designed, following the guidelines prescribed by Tim Napier-Munn in Chapter 10: Designing and Analysing Plant Trials, that would use the shift mass balanced data to statistically analyse the metallurgical performance of the Eureka Concentrator with and without effective lead regrinding. When the new lead regrind mill was turned on the impact on lead and zinc metallurgy was immediate and dramatic. Because of the magnitude of the improvements the on/off trial was abandoned. However changes of this magnitude are not always apparent, and strong statistical data analysis is often required as proof that there is a statistically confident change in the plant which was due to your implemented solution. In some cases, trials can run for a number of months but persistence pays off when you achieve the result you were aiming for. The lead recovery to final concentrate from June 1998 through to February 2000 is presented in Figure 23. It is apparent that the lead recovery has increased on average from 65 per cent up to 81.5 per cent. The most significant improvement to lead recovery was achieved through the application of an effective regrinding stage. Despite not undertaking the randomised block trial as first thought, it was possible to complete a statistical analysis using plant data from before and after the change. Using the Student t-test to analyse the data showed that installing effective lead regrinding produced the following results:

0.6 per cent, with greater than 99 per cent confidence. These changes to the lead circuit resulted in a decrease in the amount of sphalerite reporting to the lead concentrate, and shifted this material into the zinc circuit. Hence, zinc metallurgy was also improved, with:

• the zinc recovery increased by 1.5 ± 0.4 per cent, with greater than 99 per cent confidence; and

• the zinc concentrate grade increased by 2.1 ± 0.5 per cent, with greater than 99 per cent confidence. Other statistical methods (for example, comparison of regression lines) produced similar values.

THE CYCLE BEGINS AGAIN Despite the application of effective regrinding in the lead circuit, and the massive improvements in metallurgical performance, there is still room for improvement. There is not time to rest on your laurels, as the Senior Project Metallurgist it is your job to identify problems and develop cost-effective solutions to implement in the plant. You’ve only solved part of the problem, and opportunities for further improvement are available. So, sorry but the Senior Project Metallurgist’s work is never finished! The key areas where efforts can be made to improve metallurgy are:

• the optimisation of both the lead and zinc regrinding circuits, to improve liberation and subsequently concentrate grades and recoveries;

• the optimisation of chemistry for flotation to improve selectivity of valuable minerals against gangue minerals, and consequently increased concentrate grades; and

• to continue minimising variations in the process. More surveys To move forward it is necessary to continue monitoring the process through:

• the lead recovery was improved by 16.5 ± 2.5 per cent, with

• analysis of shift mass balances, • analysis of monthly composite samples (by size and

greater than 99 per cent confidence;

• the lead concentrate grade improved by 4.0 ± 0.8 per cent,

liberation class),

with greater than 99 per cent confidence; and 90.0

85.0

New Pb Feed distributor

Average % Rec.

80.0 MF4 used as lead regrind mill 75.0

Complete Pb froth level control + new 6" Pb regrind cyclones + Dedicated float operators

70.0

65.0

Initial Pb froth level control

60.0 Level on Pb conditioning tank dropped 55.0

2-Feb-00

12-Jan-00

1-Dec-99

22-Dec-99

20-Oct-99

10-Nov-99

8-Sep-99

29-Sep-99

18-Aug-99

7-Jul-99

28-Jul-99

16-Jun-99

5-May-99

26-May-99

14-Apr-99

3-Mar-99

24-Mar-99

20-Jan-99

10-Feb-99

9-Dec-98

30-Dec-98

28-Oct-98

18-Nov-98

7-Oct-98

16-Sep-98

5-Aug-98

26-Aug-98

15-Jul-98

3-Jun-98

24-Jun-98

13-May-98

1-Apr-98

22-Apr-98

18-Feb-98

11-Mar-98

7-Jan-98

28-Jan-98

50.0

W/E Average

Average CL

UCL

LCL

FIG 23 - Lead recovery versus time data from June 1998 to February 2000. Some milestones are highlighted.

Flotation Plant Optimisation

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CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

• routine metallurgical and pulp chemical surveys, • flotation cell characterisation (Chapter 5), and • the introduction of a future ores testing program (Geometallurgy, Chapter 12). After all, to measure is to know!

Chemistry With the improvements in the lead circuit through better regrinding perhaps it is time to study the chemistry of the system.

Pulp chemistry The pulp chemistry indicated that the lead rougher circuit operated in oxidising conditions, with Eh values between 150 and 200 mV (SHE). Figure 15 shows the Eh-pH curve for the circuit. The curve is essentially parallel to the water-oxygen line for the lead rougher circuit, and suggested that any changes in Eh or pH were due to the maintenance of water equilibria. These conditions points to a system operating in oxidising conditions.

Solution chemistry The EDTA extractable lead increased from approximately five per cent in the copper rougher tailing up to 17 per cent in the lead scavenger tailing. The EDTA extractable zinc and iron values were an order of magnitude lower than those reported for lead. These data suggest that the galena in the lead circuit feed is moderately oxidised, while the galena remaining in the lead scavenger tailing is heavily oxidised. The main point to come from this analysis is that there would appear to be a significant quantity of galena oxidation products present within the pulp, which under the right circumstances could lead to the inadvertent activation of sphalerite.

Surface chemistry

When collecting the samples for surface analysis it is important to use the right sample preparation protocols. The surface scientist will provide you with these. Generally, once the samples have been collected they need to be purged with nitrogen gas to remove oxygen from the pulp to prevent further oxidation. The sample is then sealed in the sample vial, and snap frozen in liquid nitrogen. The sample pairs are then shipped to the surface analysis facility frozen in a cryogenic container. Ideally, when you collect the samples for surface analysis you should complete a block survey of that part of the circuit of interest. At Eureka, a block survey of the lead rougher circuit would be the order of the day. Conducting a survey gives you a reference point in terms of metallurgical performance that can be used for comparison purposes. It is also wise to complete a pulp chemical and EDTA extractable metal ion analysis on the sample process streams that the surface analysis samples were collected from. This information should be transmitted to the surface scientist as it gives them some idea of the chemistry of the system and helps explain the observations they will make.

How do I analyse the data collected? The surface scientist will provide you with an analysis of the findings. You are not expected to know everything! However, it is wise to read the surface analysis report and ask questions. If you do not understand the analysis of the surface chemical data ask the surface scientist to explain. This will allow you to question the surface scientist to determine how they reached the conclusions and help you to understand these techniques, and the valuable information they can add to an investigation. It is very important to link the surface chemical observations to the pulp chemistry and metallurgical performance of the plant. After all the data generated will be used to confirm your theory as to why something is happening (at Eureka identification of the activating species on liberated sphalerite), and from this you will propose solutions for testing in the laboratory to solve the problem.

What does it mean?

To confirm your theory developed from the pulp chemistry observations it is wise to complete surface analysis on selected samples. Alan Buckely, in Chapter 8: Surface Chemical Characterisation for Identifying and Solving Problems Within Base Metal Sulfide Flotation Plants, provides details of the types of surface analysis and how they may be used in your quest for more information.

What do I have to do? With the decision made to complete surface analysis to validate your hypothesis you need to provide the institution conducting the surface analysis with a scope of work. It is imperative that you provide the surface scientist with a focused question that defines what you hope to get out of the surface analysis. In your case, at the Eureka Mine, you are very interested in knowing the surface chemistry of liberated sphalerite that reports to the lead rougher concentrate, and how this compares with free sphalerite in the lead rougher tailing. This essentially means that the surface scientist will examine liberated sphalerite in lead rougher concentrate and tailing process streams to identify differences that may explain why some of the liberated sphalerite is being recovered into the rougher concentrate. The surface scientist will suggest the surface analysis technique that they feel is best for your application. ToF-SIMS is frequently used because of its high surface sensitivity and its ability to analyse individual particles.

26

What data do I need?

Surface analysis was completed on samples of lead rougher concentrate and tailing samples using ToF-SIMS to determine the dominant species on the surfaces of the liberated sphalerite particles. The surface analysis investigation indicated that the liberated sphalerite particles contained within the lead rougher concentrate had statistically more collector, copper, silver and lead species on their surfaces than those reporting to the tailing (Figures 24 and 25). The conclusions reached from the chemical analysis were that:

• The flotation pulp in the lead rougher circuit operated in oxidising conditions.

• The level of EDTA extractable lead within the lead circuit was high, indicating the presence of a large quantity of galena oxidation species capable of activating sphalerite.

• The surface analysis confirmed the suspicion that the liberated sphalerite was activated by lead ions. Copper and silver were also observed on the surfaces of the sphalerite particles, but in lower concentrations. These data would suggest that some of the sphalerite is being recovered into the lead concentrate because it is activated by lead ions. You should propose that laboratory test work be completed examining the effect of various reagents to depress activated sphalerite. Should these tests prove positive, and the solution is economically sound, then it should be tested in the plant using statistically rigorous trial methodology.

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CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

0.3 0.25 0.2 0.15 0.1 0.05 0

Pb Pb O H

Zn Fe O H

C u

Fe

C a

Si

Ag

Pb cleaner con Pb cleaner tail

M g

Normalised Intensity

(+) SIMS sphalerite

(+) Fragment

Normalised Intensity

(-) SIMS sphalerite 0.5 0.4 0.3 0.2 0.1 0

Pb cleaner con Pb cleaner tail

C

CH

O

OH

S

SO3

SO4

IEX

(-) Fragment FIG 24 - Positive and negative mass spectra for sphalerite particles in the lead cleaner concentrate and tailing process streams – confidence intervals calculated for 95 per cent.

(A)

(B)

FIG 25 - ToF-SIMS images of sphalerite particles within the lead rougher concentrate: (A) the zinc ion image; and (B) the lead ion image.

COMMUNICATION The technical aspects of concentrator performance are very important in achieving optimum metallurgy. However, the best technical expertise is of little consequence if people and maintenance issues are not adequately addressed. Process variations are probably the hardest to monitor and control, and can result in operations personnel treating symptoms rather than causes (ie ‘fire fighting’). In most instances process variations, such as ore hardness, mineralogical changes with ore type, and head grade variation, are very difficult to measure online, but can be partially overcome with an effective ore characterisation program (geometallurgy) and good communication between the mine and the mill. Behavioural variations are often easily identified, but are difficult to correct because of the human factor. One way of improving the behavioural variations within a concentrator is to document and standardise each task. That is, if each operator

Flotation Plant Optimisation

performs the same task the same way, by following as standard work procedure, then behavioural variations can be minimised. Unfortunately, this is easier said than done. Another key element in altering behaviour to maximise metallurgical performance is the development of a proactive, interventionist metallurgical team, such that there are definite metallurgical targets and procedures prescribed to achieve these goals. A change in the perception of the metallurgist is required such that he should be viewed as a member of the team with specialist knowledge that is on-call when problems arise.

CONCLUSIONS At the Eureka Concentrator the use of classical metallurgical techniques (recovery- and liberation-by size analysis) has provided a high degree of certainty in determining the source of the metallurgical problem. Initially galena/sphalerite liberation was identified as a significant impediment to achieving better

Spectrum Series 16

27

CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

lead and zinc metallurgy. With the application of greater regrinding capacity the focus shifted from liberation to chemistry. The use of pulp and solution chemistry provided an indication that inadvertent activation of sphalerite by lead, copper and silver ions was probably the reason for the high recovery of liberated sphalerite into the final lead concentrate. The judicious application of appropriate surface chemical techniques provided confirming evidence. The Eureka metallurgists have now identified the reasons for the losses of sphalerite from the circuit, and can now develop solutions to this problem for testing in the laboratory, prior to trialling in the plant.

TABLE A1 The sample list for a down-the-bank survey conducted on the bank of 12 flotation cells pictured in Figure A1. Sample number

Sample name

Sample type

1

T bank feed

2

T bank combined concentrate

Lip or OSA sample

3

Con 1 – T bank cell 1

Timed lip sample

4

Con 2 – T bank cells 2 to 4

Timed lip sample

5

Con 3 – T bank cells 5 to 7

Timed lip sample

REFERENCES

6

Con 4 – T bank cells 8 to 10

Timed lip sample

Johnson, N W, 1988. Application of electrochemical concepts to four sulphide flotation separations, in Proceedings Electrochemistry in Mineral and Metal Processing II, pp 131-149. Natarajan, K A and Iwasaki, I, 1973. Practical implications of Eh measurements in sulphide flotation circuits, in AIME Transactions, 256:323-328. Rumball, J A and Richmond, G D, 1996. Measurement of oxidation in a base metal flotation circuit by selective leaching with EDTA, International Journal of Mineral Processing, 48:1-20. Warman International Limited, 1991. Cyclosizer Instruction Manual – Particle Size Analysis in the Sub-Sieve Range, Bulleting WCS/2 (Warman International Limited: Sydney).

7

Con 5 – T bank cells 11 and 12

Timed lip sample

8

T bank tailing A

Dip sample

9

T bank tailing B

Dip sample

APPENDIX 1 – THE DOWN-THE-BANK SURVEY Introduction Often it is of value to complete metallurgical surveys were samples are collected down a bank of flotation cells. This type of survey is referred to as a down-the-bank survey, and differs from a block survey, as it provides more detailed information about the flotation behaviour of the various species contained within that bank of flotation cells. In conducting a block survey you collect samples of the feed, concentrate and tailing from the section of the circuit you are interested in. This information provides you with data about the overall performance of that block of cells. The down-the-bank survey provides detail of the internal workings of that block of flotation cells.

How do I do a down-the-bank survey? Chapter 2: Existing Methods for Process Analysis, by Bill Johnson provides a detailed description of the two common methods employed. An example, using one of those methods is given below. The first step in completing a down-the-bank survey is to identify the samples that you wish to collect. Figure A1 is a schematic of the bank of 12 flotation cells you want to survey. You have decided to divide the flotation cells into groups such that you will collect five concentrate samples, in addition to the combined concentrate sample that the bank produces. The sample list is given in Table A1. 1. T bank feed

Cell 1

3. Con 1

Cell 2 to 4

4. Con 2

Dip sample

With the sampling points identified you need to communicate your intentions to various people involved and prepare your equipment. The same actions discussed above the Section: The Metallurgical Survey, What do I have to do? apply to conducting a down-the-bank survey. Communication and organisation are the key to success. In terms of sampling equipment you will need:

• • • •

dip and lip samplers that are clean and good working order; sufficient clean buckets, with lids, that have been tared; a stop watch for timing the lip sample collection; and a note book to record the times and any other observations that may be of use later.

Conducting a down-the-bank survey is usually a job for two people. One person collects the sample, and the other measures and records the time taken to collect each of the timed lip samples. Prior to conducting the survey it is wise to inspect the flotation bank to be samples, clean the cell lips to ensure that the froth flows freely, make the work area safe and free of tripping hazards, and establish how the lip sampling is going to occur, then perform a dry run to practice how the timed samples will be collected. One method of sampling that works effectively is for the sampler to yell ‘GO’ and ‘STOP’ as he starts and finishes the sample collection. On these commands the time keeper starts and stops the stop watch. It is imperative that the two people collecting the timed lip samples agree on the methodology, and work in concert. So, with all the preparations complete, the plant operating correctly it is time to conduct the survey. As with other surveys you would have decided before hand how many ‘cuts’ from each process stream will be taken over a specified sampling time. The two people detailed to conduct the down-the-bank survey will then collect the nine samples over the prescribed sampling period. Once the sampling is finished, the samples are gathered together and taken to the laboratory.

Cell 5 to 7

Cell 8 to 10

Cell 11 and 12

5. Con 3

6. Con 4

7. Con 5

8. T bank tailing

2. T bank combined concentrate

FIG A1 - A bank of 12 flotation cells, and the cell grouping for a down-the-bank survey.

28

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CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

TABLE A2 Summary of the down-the-bank survey data collected. No

Sample name

Weights (g) Gross Bucket

1

T bank feed

2 3

% solids

Tare

Wet

Dry

1235.3

471.9

38.2

Lip

1585.3

350.0

T bank combined con

1891.1

350.0

245.0

1296.1

331.8

25.6

Con 1 – Cell 1

1789.7

350.0

245.0

1194.7

630.8

52.8

4

Con 2 – Cells 2 to 4

2217.0

350.0

245.0

1622.0

361.7

22.3

5

Con 3 – Cells 5 to 7

2049.4

350.0

245.0

1454.4

315.6

21.7

6

Con 4 – Cells 8 to 10

2142.3

350.0

245.0

1547.3

379.1

24.5

7

Con 5 – Cells 11 and 12

1795.6

350.0

245.0

1200.6

187.3

15.6

8

T bank tailing A

1428.8

350.0

1078.8

372.2

34.5

9

T bank tailing B

1610.0

350.0

1260.0

459.9

36.5

What data do I need? In the laboratory the samples are weighed (to determine the wet weight), filtered, dried, weighed, prepped and submitted for assay. A summary of this data is given in Table A2. The wet and dry weights are used to determine the per cent solids of each sample, and calculate a water balance. In terms of assays, apart from those pertaining to the valuable minerals you are separating from the gangue. In example Eureka’s assayed for: silver, copper, lead, zinc, iron and silica. You will also need the times recorded for the timed lip samples, the lip lengths of the flotation cells, and the lip sample cutter length. With these data it will be possible to calculate the flow rate of concentrate from each of the groups of flotation cells. The data are supplied in Table A3.

Other data that can be useful when analysing the plant survey mass balance are:

• the throughput at the time of the survey, • reagent additions and other plant operating parameters (ie airflow rates and pulp levels),

• OSA readings, and • information about the ore being treated. In the context of a one off survey some of these pieces of information may not be of great value. However, when the analysis is extended to include other surveys on other ore blends, circuit configurations, reagent suites, these data provide a vital link in the comparison.

How do I analyse the data collected? TABLE A3 Lip sample details. No

Sample name

Sample time (s)

Cell lip

Length (mm) Cutter lip

3

Con 1 – Cell 1

31.6

1250 × 2

105

4

Con 2 – Cells 2 to 4

28.9

1250 × 6

105

5

Con 3 – Cells 5 to 7

28.4

1250 × 6

105

6

Con 4 – Cells 8 to 10

30.8

1250 × 6

105

7

Con 5 – Cells 11 and 12

39.7

1250 × 4

105

The assays will be returned to you in a form similar that shown in Table A4. Before proceeding with mass balancing the survey it is necessary to check these numbers are in good order. In this example, the tailing assays are in good agreement, and the silver, copper and lead assays all trend in the right way (ie from higher assays in Con 1 to progressively lower numbers by Con 5). Further, the combined concentrate assay falls within the extremes of Con 1 and Con 5 assays. Mass balancing this survey involves a number of steps. The first step is to calculated the mass flow rate from the timed lip samples. The mass flow rate is given by:

TABLE A4 Elemental assays for the down-the-bank survey. No

Sample name

Assay (%) Zn

Fe

SiO2

1

T bank feed

98

0.05

2.84

10.7

15.5

21.9

2

T bank combined con

444

0.24

14.20

11.1

23.0

9.2

3

Con 1 – Cell 1

644

0.47

21.40

10.7

21.2

7.6

4

Con 2 – Cells 2 to 4

490

0.28

15.70

11.3

22.9

8.5

5

Con 3 – Cells 5 to 7

406

0.21

12.60

11.3

23.8

9.1

6

Con 4 – Cells 8 to 10

346

0.18

10.60

11.6

24.2

10.0

7

Con 5 – Cells 11 and 12

306

0.18

9.15

11.7

24.3

10.9

8

T bank tailing A

70

0.02

2.04

10.5

14.8

22.6

9

T bank tailing B

72

0.02

2.13

10.6

14.9

22.6

Flotation Plant Optimisation

Ag (ppm)

Cu

Pb

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29

CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

Dry weight of sample, g 3600 × × Sample time, s 10 6 Cell lip length, mm number of cell lips × Cutter lip length, mm

concentrate produced is 6.96 tonnes per hour, compared to 11.76 determined from the timed lip tonnages. The difference is reconciled by applying the tonnage distribution from Table A5 to the mass balanced tonnage given in Table A6. Thus, using the ‘outer’ circuit mass balanced tonnage new values are calculated for each of the concentrates. These new values are presented in Table A7, and are used in the second mass balance incorporating the down-the-bank concentrates.

t/ h =

(A1)

Thus, by substituting the dry weights for each of the timed concentrate samples from Table A2, and the sample times, number of cell lips, cell lip length and cutter lip length from Table A3 in Equation (A1), you can calculate the tonnes per hour recovered into each concentrate. For example, for Con 1 – cell 1 Equation (A1) becomes: t/ hCon 1 =

TABLE A7 The ‘new’ tonnes per hour for the five concentrates collected in the down-the-bank survey calculated from the tonnage distribution and the ‘outer’ mass balanced tonnage recovered into the combined concentrate.

630.8, g 3600 1250, mm × ×2× 31.6, s 10 6 105, mm

No

t/ hCon 1 = 1.71 t/ h So, from the timed lip sample collected from Cell 1, the tonnes per hour recovered are 1.71. The same calculation was completed for each of the other concentrate. The values obtained are given in Table A5. The tonnage distribution over the five concentrate samples was calculated, and also appear in Table A5.

Sample name

New tonnes per hour

3

Con 1 – Cell 1

1.01

4

Con 2 – Cells 2 to 4

1.90

5

Con 3 – Cells 5 to 7

1.69

6

Con 4 – Cells 8 to 10

1.87

7

Con 5 – Cells 11 and 12

0.48

Total

6.96

TABLE A5 The down-the-bank mass balance has eight process streams:

The tonnes per hour and distribution of tonnes for the five concentrates collected in the down-the-bank survey. No

Sample name

Tonnage data Tonnes per hour

Distribution

1.

T bank feed,

2.

T bank combined concentrate,

3.

Con 1 – Cell 1,

4.

Con 2 – Cells 2 to 4,

3

Con 1 – Cell 1

1.71

14.55

4

Con 2 – Cells 2 to 4

3.22

27.36

5

Con 3 – Cells 5 to 7

2.86

24.30

5.

Con 3 – Cells 5 to 7,

6

Con 4 – Cells 8 to 10

3.17

26.91

6.

Con 4 – Cells 8 to 10,

7

Con 5 – Cells 11 and 12

0.81

6.88

7.

Con 5 – Cells 11 and 12, and

Total

11.76

100.00

8.

T bank tailing. There are two nodes:

The next step is to mass balance the ‘outer’ circuit. The process streams are:

1.

T bank feed = Con 1 + Con 2 + Con 3 + Con 4 + Con 5 + T bank tailing (ie 1 = 3 + 4 + 5 + 6 + 7 + 8); and

1.

T bank feed,

2.

2.

T bank combined concentrate, and

Con 1 + Con 2 + Con 3 + Con 4 + Con 5 = T bank combined concentrate (ie 3 + 4 + 5 + 6 + 7 = 2).

3.

T bank tailing.

The mass balance is accomplished by fixing the tonnage values for the T bank feed, and the five down-the-bank concentrates, then using a mass balancing software fitting the data. The down-the-bank mass balance is given in Table A8. The mass balanced down-the-bank data can now be used to construct a lead grade/recovery curve for this bank of flotation cells, as shown in Figure A2. This data can also be used to generate kinetic data examining the flotation rate constant and maximum recovery of the various species.

There is only one node in this mass balance: T bank feed = T bank combined concentrate + T bank tailing (1 = 2 + 8). In completing this mass balance it was assumed that the feed tonnage was 100 per cent. The mass balanced data are provided in Table A6. The mass balance has calculated that the tonnes of

TABLE A6 The mass balanced data for the ‘outer’ balance. No

Sample time

Wt (%)

Adjusted assay (%) Ag (ppm)

Cu

Pb

Zn

Fe

SiO2 21.78

1

T bank feed

100.00

98

0.04

2.91

10.67

15.48

2

T bank combined con

6.96

444

0.24

14.20

11.10

23.00

9.23

3

T bank tailing

93.04

72

0.03

2.07

10.63

14.92

22.72

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CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

TABLE A8 The down-the-bank mass balance. No

Sample name

Wt (%)

Ag

Cu

Weight (%) Pb

Zn

Fe

SiO2

Ag

Cu

Recovery (%) Pb

Zn

Fe

SiO2

100.00

98

0.04

2.9

10.6

15.5

21.8

100.0

100.0

100.0

100.0

100.0

100.0

T bank feed

2

T bank combined con

7.00

440

0.26

14.0

11.3

23.3

9.1

31.5

42.0

33.6

7.4

10.5

2.9

3

Con 1 – Cell 1

1.02

644

0.47

21.4

10.7

21.2

7.6

6.7

11.2

7.5

1.0

1.4

0.4

4

Con 2 – Cells 2 to 4

1.91

490

0.28

15.7

11.3

22.9

8.5

9.6

12.5

10.3

2.0

2.8

0.7

5

Con 3 – Cells 5 to 7

1.70

406

0.21

12.6

11.3

23.8

9.1

7.0

8.3

7.4

1.8

2.6

0.7

6

Con 4 – Cells 8 to 10

1.88

346

0.18

10.6

11.6

24.2

10.0

6.6

7.9

6.9

2.0

2.9

0.9

7

Con 5 – Cells 11 and 12

0.49

306

0.18

9.2

11.7

24.3

10.9

1.6

2.1

1.5

0.6

0.8

0.2

8

T bank tailing

93.00

72

0.03

2.1

10.6

14.9

22.7

68.5

58.0

66.4

92.6

89.5

97.1

Pb grade, %

1

25.0

Mineral conversions

20.0

Each conversion is based on the atomic mass of the elemental components of the mineral.

15.0

Galena Galena contains lead (207.2 amu) and sulfur (32.06 amu), therefore the atomic mass of galena (PbS) is:

10.0

5.0

0.0 0.0

PbS = Pb + S PbS = 207.2 + 32.06 amu 10.0

20.0

30.0

40.0

50.0

60.0

PbS = 239.26 amu

Pb recovery, % OUTER balance data

Down-the-bank balanced data

FIG A2 - The lead grade/recovery curve constructed from the mass balanced down-the-bank survey data.

Thus, ‘pure’ galena contains 86.6 per cent lead and 13.4 per cent sulfur. The conversion factor (fGa) to convert the lead assay to galena is given by: fGa =

fGa =

APPENDIX 2 – ESTIMATED MINERAL ASSAYS FROM ELEMENTAL DATA Introduction As iron occurs in a variety of minerals present in the Eureka orebodies’ interpretation of iron deportment from elemental assay data from flotation tests and plant surveys is a complex issue. Therefore, by making a few simple assumptions regarding the composition of the dominant sulfide minerals present in the orebody, it is possible to estimate mineral assays from the elemental assay data.

239.26 207.2

. fGa = 1155 So, an assay of ten per cent lead is equivalent to 11.6 per cent galena. The sulfur in galena conversion factor (fSGa) is given by: f SGa =

% sulfur in PbS % lead in PbS f SGa =

13.4 86.6

. f SGa = 0155

Assumptions The first set of assumptions relate to the minerals themselves. That is, the dominant sulfide minerals are: galena; sphalerite, chalcopyrite and pyrite. The lead occurs as galena; the zinc as sphalerite; the copper as chalcopyrite; and the iron occurs in sphalerite, chalcopyrite and pyrite. The mineral conversions are based on the assumption that each mineral is ‘pure’, for example galena is PbS, pyrite is FeS2, etc. Eureka sphalerites are known to contain, in solid solution, moderate iron levels. In this exercise 3.0 per cent was chosen. This value is an estimate of the average value. A calculated assay of the non-sulfide gangue (NSG) is made by assuming that everything that is not galena, sphalerite, chalcopyrite, or pyrite is non-sulfide gangue.

Flotation Plant Optimisation

PbS amu Pb amu

Sphalerite ‘Pure’ sphalerite (contains no iron) is made up of zinc (65.38 amu) and sulfur (32.06 amu), therefore the atomic mass of ‘pure’ sphalerite (ZnS) is: ZnS = Zn + S ZnS = 65.38 + 32.06 amu ZnS = 97.44 amu Thus, ‘pure’ sphalerite contains 67.1 per cent zinc and 32.9 per cent sulfur. Unfortunately, Eureka sphalerite contains an average of 3.0 per cent iron in solid solution. Further, it is assumed that

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CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

the iron replaced zinc in the sphalerite lattice. Thus, the composition of Eureka sphalerite is 64.1 per cent zinc, 3.0 per cent iron and 32.9 per cent sulfur. Hence, the conversion factor (fSp) to convert the zinc assay to sphalerite is given by: f Sp =

100.00 641 .

f Sp = 1.560

fCh = 2.888

fFeCh =

So, an assay of ten per cent zinc is equivalent to 15.6 per cent sphalerite. To determine the amount of iron present in sphalerite it is simply a matter of multiplying the zinc assay by the ratio of the per cent iron in the sphalerite and the per cent zinc in the sphalerite. So, the iron in the sphalerite conversion factor (fFeSp) is given by: fFeSp =

% iron in sphalerite % zinc in sphalerite fFeSp =

3.0 641 .

fFeSp = 0.047 Thus, for a sample containing ten per cent zinc, the per cent iron associated with the sphalerite is 0.47 per cent (ie 10 × 0.047). To check this, convert the zinc assay to per cent sphalerite (ie 10 × 1.560), and multiply by the amount of iron in solid solution in sphalerite (ie 3.0 per cent), and the per cent iron associated with sphalerite is 0.47 per cent. Similarly, the sulfur in the sphalerite conversion factor (fSSp) is given by: f SSp =

32.9 641 .

f SSp = 0.513 Thus, for a sample containing ten per cent zinc, the per cent sulfur associated with the sphalerite is 5.13 per cent (ie 10 × 0.513). To check this, convert the zinc assay to per cent sphalerite (ie 10 × 1.560), and multiply by the amount of sulfur in sphalerite (ie 32.9 per cent), and the per cent sulfur associated with sphalerite is 5.13 per cent.

fFeCh =

30.43 34.63

fFeCh = 0.879 Thus, for a sample containing ten per cent copper the per cent iron associated with the chalcopyrite is 8.8 per cent (ie 10 × 0.879). To check this, convert the copper assay to chalcopyrite (ie 10 × 2.888), and multiply this by the amount of iron in solid solution in chalcopyrite (ie 30.43 per cent), and the per cent iron associated with chalcopyrite is 8.8 per cent. Similarly, the sulfur in chalcopyrite conversion factor (fSCh) is given by: f SCh =

% sulfur in chalcopyrite % copper in chalcopyrite f SCh =

34.94 34.63

f SCh = 1.009

Pyrite Assuming that pyrite is the dominant iron sulfide mineral present (ie no pyrrhotite) it is relatively easy to calculate the per cent pyrite in a sample. Pyrite contains iron (55.85 amu) and sulfur (32.06 amu), therefore the atomic mass of pyrite (FeS2) is: FeS2 = Fe + S FeS2 = 55.85 + (2 x 32.06) amu

Chalcopyrite Chalcopyrite is made up of copper (63.55 amu), iron ( 55.85 amu) and sulfur (32.06 amu), therefore the atomic mass of chalcopyrite (CuFeS2) is: CuFeS2 = Cu + Fe + S CuFeS2 = 63.55 + 55.85 + (2 x 32.06) amu CuFeS2 = 183.52 amu Thus, stoichiometric chalcopyrite contains 34.63 per cent copper, 30.43 per cent iron and 34.94 per cent sulfur. Hence, the conversion factor (fCh) to convert the copper assay to chalcopyrite is given by: fCh =

32

% iron in chalcopyrite % copper in chalcopyrite

Thus, for a sample containing ten per cent copper the per cent sulfur associated with the chalcopyrite is 10.1 per cent (ie 10 × 1.009). To check this, convert the copper assay to chalcopyrite (ie 10 × 2.888), and multiply this by the amount of sulfur in solid solution in chalcopyrite (ie 34.94 per cent), and the per cent sulfur associated with chalcopyrite is 10.1 per cent.

% sulfur in sphalerite % zinc in sphalerite f SSp =

183.52 63.55

So, an assay of ten per cent copper is equivalent to 28.9 per cent chalcopyrite. To determine the amount of iron present in chalcopyrite it is simply a matter of multiplying the copper assay by the ratio of the per cent iron in the chalcopyrite and the per cent copper in the chalcopyrite. So, the iron in chalcopyrite conversion factor (fFeCh) is given by:

100.00 % Zn in sphalerite f Sp =

fCh =

FeS2 = 119.97 amu Thus, ‘pure’ pyrite contains 46.6 per cent iron and 53.4 per cent sulfur. Depending on the assay data the pyrite content of the ore can be calculated using either the iron or the sulfur assay. Generally speaking, the estimation of the pyrite concentration is more accurate using the sulfur assay because it is assumed that the vast majority of the sulfur in the ore is associated with the sulfide minerals. Iron, on the other hand, can be present in the sulfides as well as the non-sulfide gangue, for example as iron oxides such as haematite or magnetite, and feldspars to name but a few. Thus, the pyrite conversion factor (fFePy) based on the iron assay is given by:

CuFeS 2 amu Cu amu

fFePy =

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FeS 2 amu Fe amu

Flotation Plant Optimisation

CHAPTER 1 – THE EUREKA MINE – AN EXAMPLE OF HOW TO IDENTIFY AND SOLVE PROBLEMS IN A FLOTATION PLANT

fFePy =

119.97 5585 .

However, if the pyrite conversion factor (fSPy) based on the sulfur assay then: f SPy = 1871 . × (% S − (% sulfur in galena +

fFePy = 2148 . So, based on the conversion factor developed from the iron assay, an assay of ten per cent iron is equivalent to 21.5 per cent pyrite. Using sulfur, the pyrite conversion factor (fSPy) is given by: f SPy = f SPy

FeS 2 amu S 2 amu

From the discussion above the conversion factor for sulfur in galena from the lead assay is 0.155; sulfur in sphalerite from the zinc assay was determined to be 0.513, and a similar calculation revealed that the conversion factor for sulfur in chalcopyrite is 1.009. So, the per cent pyrite is given by: f SPy = 1871 . ×

119.97 = 6412 .

(% S − ( 0155 . × % Pb + 0.513 × % Zn + 1.009 × %Cu))

f SPy = 1871 . So, based on the conversion factor developed from the sulfur assay, an assay of ten per cent iron is equivalent to 18.7 per cent pyrite. Unfortunately, iron is also associated with sphalerite and chalcopyrite in the ore, so these contributions must be subtracted from the iron assay before determining the pyrite content. Thus, the pyrite conversion factor (fFePy) based on the iron assay becomes: . × fFePy = 2148

Thus, if an ore sample contained ten per cent sulfur, ten per cent lead, ten per cent zinc, and 0.1 per cent copper, the per cent pyrite is 6.0 per cent.

Non-sulfide gangue If it is assumed that galena, sphalerite, chalcopyrite, and pyrite are the only significant sulfide minerals present in the orebody it is possible to estimate the per centage of non-sulfide gangue present. This is achieved by subtracting the per cent galena, sphalerite, chalcopyrite, and pyrrhotite from 100 per cent. That is: % NSG = 100 – (%Ga + %Sp + %Ch + %IS)

(% Fe − (% iron in sphalerite + % iron in calcopyrite)) From the discussion above the conversion factor for iron in sphalerite from the zinc assay was determined to be 0.0.47, and a similar calculation revealed that the conversion factor for iron in chalcopyrite is 0.879. So, the per cent pyrite is given by: . × fFePy = 2148 (% Fe − ( 0.047 × % Zn + 0.879 × %Cu)) Thus, if an ore sample contained ten per cent iron, ten per cent zinc, and 0.1 per cent copper, the per cent pyrite is 20.28 per cent.

Flotation Plant Optimisation

% sulfur in sphalerite + % sulfur in chalcopyrite ))

Thus, if a sample assayed ten per cent lead, zinc and iron, and 0.1 per cent copper, the per cent non-sulfide gangue is 57.8 per cent.

Final comment These element to mineral conversions have been completed based on a lead/zinc ore, however a similar approach can be applied to other ore types provided the stoichiometry of the minerals in the system is known, and the assumptions made in the calculations are clearly explained.

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HOME

CHAPTER 2

Existing Methods for Process Analysis Bill Johnson FAusIMM(CP), Senior Principal Consulting Engineer, Mineralurgy, Suite 2, Level 1, 42 Morrow Street, Taringa Qld 4068. Email: [email protected] Bill Johnson obtained a PhD in mineral processing from the University of Queensland in 1972. After working for ASARCO in Arizona until 1976, he lectured at the University of Melbourne. He joined the CSIRO Division of Mineral Engineering (1978 - 1982) where research on the Lead-Zinc Concentrator at Mount Isa Mines Limited was his main project. In 1982, he moved to Mount Isa where he continued research on the Lead-Zinc Concentrator and other plants and ores. He was the Minerals Processing Research Manager (1989 - 1997). Development of a circuit for McArthur River ore recommenced in 1989 under his direction, one key outcome being the IsaMill technology. He was Professor of Minerals Engineering at the University of Queensland (1998 - 2005) and is presently Senior Principal Consulting Engineer at Mineralurgy.

Introduction Solid Balance and Water Balance Calculation by Surveying Calculation of Mineral Recoveries Calculation of Recovery-Size Data Interpretation of Recovery-Size Curves Addition of Liberation Data to Recovery-Size Data The Role of Surface and Solution Analyses for Organic and Inorganic Species Inclusion of Froth Recovery in Surveys Process Analysis with Down-the-Bank Flotation Data Use of Summary Graphs with Limits Imposed by Liberation General Outcomes of the Analysis – Magnitudes of Significant Process Weaknesses and Solutions to the Weaknesses References Appendix References

ABSTRACT

INTRODUCTION

This introductory chapter describes options for surveying flotation banks and calculation of their solid and water balances, including mineral recoveries. The calculation and interpretation of mineral recovery - size data and the more advanced mineral recovery - size - liberation data are then covered. The related role of surface analysis for elucidating unexplained process weaknesses in the mineral recovery - size liberation data is described. The chapter is aimed at recognition of the location and magnitude of process weaknesses in industrial plants and identification of the mechanism involved in each, allowing technical solutions for some or all weaknesses to be proposed and evaluated. Later chapters expand on topics in this chapter.

The first step in analysis of the flotation process is to obtain a mass or solid balance, which may be accompanied by a water balance, from surveying of the relevant portions of the plant. The key benefit of obtaining the corresponding water balance is that water flow rates, and hence pulp flow rates, can be calculated and hence residence times can be calculated, ie kinetic data can be obtained. Decisions have to be made in the design of an experiment or survey on the level of sampling detail which is appropriate for each portion of the plant. In general, the following options for sampling detail exist and different levels of detail may be selected for various parts of the plant:

Flotation Plant Optimisation

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CHAPTER 2 – EXISTING METHODS FOR PROCESS ANALYSIS

• block level, eg grouping of all cleaner banks or rougher banks;

• bank level, eg obtaining of information on feed, combined concentrate and tailing assays; or

• down-the-bank data (where data on each concentrate or grouping of concentrates are obtained). Of course, the whole plant may be treated as a block and this treatment is applied commonly for obtaining shift or daily composite samples from automatic inventory samplers from which shift or daily metallurgical performance is often calculated routinely. Such data can also be complementary to surveys on the banks or blocks in the circuit. In normal metallurgical accounting, daily samples from inventory samplers are often used to prepare monthly composite samples for the feed to and products from a concentrator. Samples from inventory samplers on all the inputs to and products from a plant can be processed at various levels of detail, to establish causes of misplaced valuable mineral and causes of dilution of concentrates by unwanted minerals. In broad terms, these are at the recovery-size level for each of the minerals, and at the next level which can be summarised as the recoverysize-liberation level. Analysis of such data allows definition of the weaknesses (and strengths) of the plant. While such data from inventory samples are valuable, the overall plant data do not provide clues to the location of the weaknesses in the plant, eg rougher section, cleaner section or retreatment section. Hence, surveys of the whole plant or of individual sections at appropriate times are needed to identify the origin of the weakness and to check progress during later corrective steps. Judgement is required in the frequency and design of such surveys. Surveys of the sections in a pilot plant circuit can be conducted by similar methods as for concentrators with some modification of the scale of sampling equipment. Such surveys can serve two purposes. One is to record the behaviour of an ore source or ore type in a new orebody for later comparison with the behaviour in a full-scale plant. The availability of detailed data within the pilot plant circuit and at a sized level for minerals (at least) will greatly improve the ability to perform troubleshooting in the later start-up of a new concentrator. A second purpose can be to perform a cycle of recognition of process weaknesses with later correction in a pilot plant scale development of a new flow sheet. As far as possible, such process development ought to be conducted at the laboratory scale where the development costs are much lower. Nevertheless, the methodology can be applied to pilot plants along the lines discussed earlier for full-scale plants. Samples which are produced from open circuit laboratory flow sheets or from closed circuit laboratory cycle tests can also be subjected to analysis at the mineral recovery-size-liberation level. The samples are easier to obtain in this laboratory situation but care is required to ensure enough sample exists for the envisaged procedure. For closed circuit cycle tests, the circuit must be at equilibrium for those cycles from which the samples are taken. Paired surveys are sometimes employed to provide insights. These surveys should be conducted with the same feed to plant or pilot plant scale processes. For plants in particular, the two surveys would normally be conducted within one day. For one of the surveys, a major change in conditions would be implemented and the effect of the change would be evaluated by comparison with the ‘reference’ data under normal conditions. Such paired tests can be valuable when surface analysis is included in the design for the experiment as convenient ‘reference’ surface analysis data are provided from the survey under normal conditions.

36

In past analysis of recovery-size data for minerals, there has been the convenient assumption that the solid in the pulp was fully dispersed. In other words, it has been assumed that any mineral reporting in a given size fraction in the recovery-size data existed in that fraction in the real pulp. While this is likely to be a sound assumption for most pulps, it is expected that there are pulps for which the lack of dispersion is sufficient to transfer minerals from one size fraction to another during the sizing procedure due to shearing apart of aggregated particles. In a plant pulp, a liberated valuable particle which adheres to other gangue minerals by some mechanism will usually be less recoverable. Further, if the liberated valuable particle is recovered, the grade of the concentrate will be detrimentally affected due to the adhering gangue mineral. For convenience, hand-held samplers will be considered in three categories: conventional hand-held or manual samplers for sampling streams at weirs or leaving launders or pipes, dip samplers for sampling the pulp in the pulp zone of a flotation cell, and lip sampling for providing a sample of the concentrate from one or more flotation machines where this usually also involves obtaining a value for the flow rate of solid by a timing procedure. Manual samplers may be used in conjunction with well formed sampling points in automatic inventory samplers in special circumstances. There have been major changes in the type and scale of cells employed in the last two decades of the 20th century. The introduction of flotation cells with washed froth technology has changed the nature of sampling problems. Further, the installation of very large unit cells has increased sampling difficulties in many new plants due to lack of access to the large machines and decisions during the plant layout phase of design which tend to increase sampling difficulties.

SOLID BALANCE AND WATER BALANCE CALCULATION BY SURVEYING Solid balance A solid balance is calculated after carefully planned data collection in a plant. A water balance can also be calculated from the same survey provided the relevant per cent solid data are collected. The complete procedure is relatively long and involves many steps, requiring careful planning, a plant at steady state during the survey, careful checking of the results and the execution of the necessary metallurgical calculations. The steps are summarised in Figure 1. In contrast, a solid balance is easily obtained from a laboratory batch testing procedure from the readily obtained weights of dry solid in the various concentrates and tailings, along with their assay values. There are a limited number of methods for collection of plant data from a bank that enables the calculation of a solid balance and related metallurgical information. To provide clarity on the key aspect of obtaining a solid balance, it is valuable to state what the generation of a solid balance does not involve. It does not involve obtaining estimates of the flow rates of solid in the relevant streams by independent and quite different means, and assembling these values from disparate sources. In contrast, it does involve using principally or solely the assay values for the relevant streams and a known reliable tonnage (eg from a weightometer) as the scaling factor. A survey of a total plant (many banks) or part of a plant (one bank or a limited number of banks) is obtained by matching the limited number of methods to the type of equipment in each part of the plant and the availability of sampling points, and from consideration of the purpose of the survey, ie the type of metallurgical data required from the survey. The limited number of

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CHAPTER 2 – EXISTING METHODS FOR PROCESS ANALYSIS

1. Establish objectives, ie type of survey, level of detail, etc

introduction, noting that knowledge of these designs can assist in determining the design of a survey for acquiring metallurgical data in more complicated situations. These designs can be summarised as listed:

2. Plan Survey • • • • •

Determine number of people/skill levels Prepare all sampling equipment that match tasks Review plans with sampling staff Check condition of sampling points Practise at sampling points

• two product (samples of feed, one concentrate and single tailing);

• three product (samples of feed, two concentrates and single tailing); or

• four product (samples of feed, three concentrates and single 3. Ensure circuit at steady state and fixed ore source to continue • • •

Steady inputs Steady circulating loads Steady assays from on-line systems

4. Execute survey (1 to 3 hours) •

Continue to monitor that circuit is at steady state (see 3)

tailing). Conceptually, the five product and ‘higher’ cases could be used but these cases are almost without exception impractical. In fact, the three and four product cases can only be utilised under appropriate circumstances which are now discussed. To apply the two product design in Figure 2, the following form of the two product equation is used to calculate the fractional recovery of solid (ie the solid split): α ( f − t) = F ( c − t)

5. Filter/dry products, perform sample preparation and extract samples for analysis

Solid recovery ( fractional ) =

6. Construct initial mass balance and review the quality of the survey data

The concentration of at least one mineral (eg chalcopyrite or the copper assay) in the feed needs to be significantly different from the value for the tailing, ie there must be a clear difference between feed and tailing assays in the numerator, otherwise f - t will be a very low value (and possibly negative), and very susceptible to considerable error from sampling and assaying. Therefore, the calculated fractional solid recovery will be prone to unacceptable errors. One contributor to the overall sampling error, the fundamental error, is very dependent on the sample mass and this issue is described in the appendix. This separation of the mineral in question would then normally result in a significant difference for the denominator (c - t). The assay values (feed, concentrate and tailing) for the key element (eg copper) can then be used as shown in Figure 2 to calculate the solid recovery (α/F) or the absolute value for α if F is known. In addition to a large separation occurring for the element used in the calculation, it is desirable that the selected element can be assayed accurately and that sampling errors are not unusually high. Low-grade samples containing some free gold can introduce large sampling errors. To apply the three product case, the concentration of at least one mineral in the feed would need to be significantly elevated in the first concentrate while the concentration of a second mineral would need to be significantly elevated in the second concentrate. A typical example is the separation of galena (PbS) and sphalerite (ZnS) into two separate concentrates and the two equations in the three product case in Figure 2 are solved by use of lead and zinc assays to obtain the solid balance. The four product case can be thought of as an extension of the three product case. However, three different minerals require concentrating into their respective concentrates. An example is the concentration of chalcopyrite, galena and sphalerite into their respective concentrates and the use of copper, lead and zinc assays to solve the three equations in the four product case, to obtain the solid balance. The three and four product cases can usually only be applied to the feed and products of a concentrator (ie inventory sampler products and shift or daily performance calculations) of a concentrator with multiple single mineral concentrates, as the special conditions for their successful application exist for the products from such concentrators and do not usually exist along individual banks. Therefore, the three and four product cases and ‘higher’ cases can usually be expected to play no role or only a supporting role in designing a survey for the banks in a

7. Move to next steps, if warranted, for more detailed data, eg sizing of samples and assaying of size fractions, obtaining liberation data on size fractions FIG 1 - Summary of steps in planning and execution of a survey.

methods will be described in following sections. The methods represent the building blocks from which surveys are designed and conducted.

Water balance The water flow rate in a stream can be calculated from the value for the solid flow rate which has been determined as part of the solid balance. The following relationship holds: Flow rate of water = Flow rate of solid (100 − per cent solids by weight) Per cent solids by weight

(1)

The per cent solid value (by weight) for flotation concentrates requires some discussion for the concentrate stream. The value of interest for analysis of flotation data is the per cent solid value for the concentrate as it traverses the cell lip. The value for the per cent solid in the concentrate should not reflect the water which has been added to the cell launder, the pump box or the gland seal water for the concentrate pump. Taking the concentrate sample at the cell lip provides the required per cent solid value. Similarly, in laboratory batch tests, the water in the concentrate (for process analysis purposes) should not include water which is added to wash the cell lip or the scraper during the collection of a given concentrate. This can be arranged by adding such additional water from a wash bottle for each concentrate and weighing the wash bottle before and after each concentrate is gathered.

Description of some basic designs for data acquisition Three traditional designs for acquisition of metallurgical data are depicted in Figure 2. These designs are presented as an

Flotation Plant Optimisation

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(2)

37

CHAPTER 2 – EXISTING METHODS FOR PROCESS ANALYSIS

Definitions Let f, c and t be the assays for a particular element in the feed, concentrate and tailings Let F = t/h of solid in feed (known) Let α, β and γ = t/h of solid in concentrate(s) Solid and Element Balances for Three Cases TWO PRODUCTS (one equation with one unknown α)

F–α

F

FOUR PRODUCTS (three equations with three unknowns α, β and γ)

THREE PRODUCTS (two equations with two unknowns α and β)

F – α– β

F

α Element 1 (Major separation occurring) fF = cα + t(F – α)

α

F – α– β – γ

F

α

β

fF = c1 α + c2 β + t(F – α – β)

β

γ

fF = c1 α + c2 β + c3 γ + t(F – α – β – γ)

Element 2 (Major separation occurring also for the second element) Not needed to solve for α.

1 1 l 1 f F = c1 α + c 2 β + t (F – α – β)

f1 F = c1 1 α + c21 β + c3 1 γ + t 1(F – α – β – γ)

Element 3 (Major separation occurring also for the third element) Not needed to solve for α. Solving for single unknown, α. fF = cα + tF – tα

α f -t = F c- t f -t or ∴α = F c- t

Not needed to solve for α and β.

Solve for α and β using two simultaneous equations.

f11 F = c1 11α + c2 11β + c311 γ + t 11(F – α – β – γ) Solve for α, β and γ using three simultaneous equations.

∴

FIG 2 - Three traditional designs for acquisition of metallurgical data, including the commonly used two product formula.

concentrator. In contrast, the two product case has often an important role in data acquisition from individual banks within a flotation plant.

Description of some designs for data acquisition from individual banks A traditional approach to data acquisition for a bank of small flotation machines is depicted in Figure 3. Provision is made in Figure 3 for intermixing or exchange of pulp between adjacent pulp zones. This situation existed in the layout of many commercial flotation machines which were bolted together to form banks and which were relatively small in volume, eg less than 10 to 20 m3 per impeller. Often, these banks contained ten to 20 flotation machines in series in order to provide the required residence time for relatively large tonnages of solid and pulp, given the relatively small flotation machines. For some banks in a plant, the objective of the survey may be to obtain the overall performance for the bank (and not down-thebank data). However, because no sampling point exists for the combined concentrate from the bank, a more detailed design for data collection (obtaining down-the-bank data) may be required,

38

making use of access to the concentrate discharge lips for example (to compensate for the absence of a sampling point for the combined bank concentrate). The approach depicted in Figure 3 represents repeated application of the two product equation to the data for each machine to obtain the solid balance. It must be recognised that the method is based on some simplifying assumptions:

• the pulp zone of each machine is perfectly mixed (to allow ready and reliable sampling via a dip sampler), and

• the effect of the intermixing flow rates (M) is disregarded in the mass balance for each machine (see Figure 3). There are some other properties of this type of sampling:

• A relatively large number of samples are required (compared to some other options) as a pulp sample from each cell is required.

• Experimental error in sampling, preparation and assaying of the series of pulp samples can result in irregularities in the data particularly towards the end of the bank where the additional recovery in each cell is low. For example, the recorded assay for the valuable element in the pulp region of

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CHAPTER 2 – EXISTING METHODS FOR PROCESS ANALYSIS

Individual concentrates from cells f c1, c2 … cn p1, p2 … p n t

X •

°

Feed sampling point Sampling points for concentrate from each cell Sampling points for pulp region in each cell Sampling point for bank tailing after last cell

Note: For the last cell in the bank, the tailing sample can be taken from the tailing stream ( ) or from the pulp in the last cell ( ) (if the mixing state is known for the last cell).

°

M = exchange of pulp due to intermixing between adjacent cells (zero if cells are isolated) in units of M t/h of solid Assays for calculating of solid balance for each cell using two product equation (ie ignoring the solid flows (M) from intermixing): Cell 1 Cell 2

Feed Assay f p1

Concentrate Assay c1 c2

Tailing Assay p1 p2

Cell n

pn-1

cn

pn

For the first cell in the bank: Let C = t/h of solid in concentrate and F = t/h of solid in feed and T = t/h of solid in tailing Stating the two product equation and inserting the symbols for cell 1: C f -t Solid Recovery * = = F c-t C f - p1 = F c1 - p 1 C =F×

f - p1 c1 - p1

T = F-C *expressed as a fraction This calculation is reapplied for cell 2, cell 3, etc. FIG 3 - Bank survey design involving repeated use of the two product equation.

cell n can exceed its assay in cell n-1. It should be noted that data smoothing techniques available since approximately 1970 may handle this issue but, for manual calculations, this property remains a difficulty. Use of the approach in Figure 3 declined during the period from 1970 to approximately 1990 because a more effective method emerged in terms of the quantity of samples required and its theoretical basis. This more effective method will be discussed shortly in conjunction with Figure 5. However, since approximately 1990, a change in the type and volume of flotation machines being installed (ie the use of large unit cells) has resulted in increased use of a closely related variant of the method in Figure 3. This variant is illustrated in Figure 4. The design of the unit cells precludes the possibility of any intermixing of pulp zones and removes any objections on this basis. However, for taking dip samples from the pulp zone of each cell, the degree of mixing in the pulp zone must be considered. However, it is also possible for valid sampling points to exist in the pipework between the cells, eliminating the use of

Flotation Plant Optimisation

dip samples which is time consuming and presents difficulties if the pulp zone is not perfectly mixed. Banks of unit cells contain typically six to ten cells and the moderate number of cells makes the work load of the method of sampling manageable. A competing method for sampling a bank emerged from approximately 1970 (Figure 5). It required samples of the feed, tailing and the various concentrates for which some grouping was possible. For each concentrate or concentrate grouping, the flow rate of solid discharging from the various cell lips had to be determined also (Restarick, 1976). From Figure 5, no assumptions on pulp intermixing between machines or the level of mixing within machines were required, the only possible exception being the collection of the tailing sample from the pulp zone (for which an alternative point, sampling the combined tailing stream after exiting the last cell, exists in some cases). The elimination of all or virtually all the pulp sampling reduced the quantity of work. However, a more advanced method of concentrate sampling, preferably requiring two people, was required to obtain values for the solid flow rate

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CHAPTER 2 – EXISTING METHODS FOR PROCESS ANALYSIS

Individual concentrates from cells F c1, c2 … cn t1, t2 …t n

X •

°

Feed sampling point Sampling points for concentrate from each cell Sampling points for tailing from each cell

Assays for calculating of solid balance for each cell using two product equation: Cell 1 Cell 2

Feed Assay f t1

Concentrate Assay c1 c2

Tailing Assay t1 t2

Cell n

tn-1

cn

tn

For the first cell in the bank: Let C = t/h of solid in concentrate and F = t/h of solid in feed and T = t/h of solid in tailing Stating the two product equation and inserting the symbols for cell 1: C f -t Solid Recovery * = = F c-t C f -t1 = F c1 - t 1

C =F×

f - t1 c1 - t 1

T = F-C *expressed as a fraction This calculation is reapplied for cell 2, cell 3, etc. FIG 4 - Bank survey design involving repeated use of the two product equation for a series of tank cells.

for each machine or grouping of machines. Details of this aspect of the sampling are provided in the appendix. In Figure 5, the two product equation is demonstrated to be a special case of a general equation for removal of many concentrates (designated as n). Figure 5 presents the general equation and the method for initial examination of the data from the survey. Concentrate assays and flow rates by lip sampling must be obtained for each concentrate and a feed and tailing assay for the bank must also be obtained. It is important to discuss the reliability which can be attributed to the measured values for the solid flow rate (C1, C2, C3, … Cn) in each concentrate (see Figure 5) and hence the appropriate means for processing the data from this type of sampling.

Reliability of measured concentrate flow rates A method of bank surveying has been described (Figure 5) requiring both the assay and concentrate solid flow rate for each flotation machine or grouping of machines along the bank. In using this method, it is important to appreciate the reliability of the method, in particular the required reliability for the measured flow rates of solid in each concentrate. As a minimum, the measured solid flow rate values for each of the concentrates along a bank must be correct on a relative basis. It is therefore advisable that the same lip sampling personnel (usually two people) conduct all the tonnage measurements along a given bank. It is also advisable that the personnel receive prior

40

training on the use of correct methods and that the training includes a convenient small sampling exercise where the correctness of the measured flow rates on an absolute basis could also be established for the personnel. By way of guidance, traditional sources of absolute solid tonnages, eg a weightometer on the grinding circuit feed should always be used as the ‘scaling tonnage’ in processing of plant surveys (Figure 5) and surveys should be designed to ensure that such sources of absolute solid tonnages are available. In some cases, extra metallurgical samples may have to be taken to link the plant section being surveyed in detail to the source of an absolute solid tonnage, eg weightometer, thereby removing reliance on the correctness of concentrate tonnages on an absolute basis. For various levels of reliability of the measured solid flow rates in the concentrate, the metallurgical performance information which can be reliably calculated is summarised in Figure 6. In summary, the measured solid flow rates in the concentrate from lip sampling should only be taken as correct on an absolute basis in unusual circumstances where a large amount of training and checking has been completed by the lip sampling personnel. Further, an unusual set of circumstances needs to exist where traditional scaling tonnages, eg weightometer tonnages do not exist. In other unusual circumstances, the combination of a magnetic flow meter and a density gauge (both of which are calibrated properly and checked regularly) may be used to provide a scaling factor for the tonnes per hour of solid for a key stream in a survey of some peripheral part of a circuit.

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Individual concentrates from cells f c1, c2 … cn

x 

Feed sampling point Sampling points for concentrate from each cell allowing estimate of solid flow rate (C1, C2 … Cn) where the values are correct on a relative basis (as minimum standard) and provision of solid assay (c1, c2, … cn) t  Tailing sample point (after end of bank or possibly pulp region in last machine) General case: Let Ci = t/h of solid in the ith concentrate and F = t/h of solid in the feed to bank and T = t/h of solid in the bank tailing It can be shown that: n

¦ C (c i

F

i

- t)

i 1

n

and T F - ¦ Ci

f -t i 1 The calculated value for F is compared with its known value from the weightometer. The observed lip tonnages for each concentrate (C1, C2 … Cn) are then rescaled upwards or downwards to ensure the value for F based on the rescaled values for C1, C2, … Cn equals the true value from the weightometer.

For the general case above applied to a bank with seven concentrates:

Individual concentrates from cells For n=7 in the above equation: 7

¦ C (c i

i

- t)

7

and T F - ¦ Ci f -t i 1 Rewriting the two product equation where F is calculated from the concentrate flow rate C and the feed (f) and the product assays (c and t): C(c - t) F and T F - C f -t It can be observed that the two product equation for F is a special case of the above equations for F with 7 and n cells in the bank. F

i 1

FIG 5 - Bank survey requiring assays for the feed, tailing and concentrates and the relative flow rates for each concentrate (no knowledge of the degree of intermixing (M) is needed for legitimate use of this method – see also Figure 3).

CALCULATION OF MINERAL RECOVERIES The traditional technologies for obtaining the composition of ore samples have provided elemental assays. While assays for elements are very useful for providing information for downstream processes such as smelting, elemental assays would not normally be the first choice for a concentrator metallurgist in most circumstances in a perfect world. It is now possible to obtain the assays for minerals directly. However, there are various limitations to the currently available methods. The most basic information on the behaviour of a mineral is its recovery, ie its distribution between the concentrate and tailing streams for a separation. Hence, in this section, the objective is to discuss the calculation of recovery values for minerals from survey data. The necessary prerequisite is to obtain mineral assays by suitable means.

Obtaining mineral assays After laboratory preparation of dry solid from each sampling point in the survey, the next step is to submit representative

Flotation Plant Optimisation

portions of each sample for assaying. Metallurgists would prefer to receive assays of both minerals and elements, each for different purposes. Traditionally, the industrial assaying methods (atomic absorption spectroscopy (AA), X-ray fluorescence (XRF), inductively coupled plasma emission spectroscopy (ICP) and fire assaying) have provided the concentration of valuable metallic elements such as Cu, Ni and Au and the concentration of other metallic elements such as Fe, often contained in both gangue and valuable minerals. There has been an increase in the ability to provide assays for entities often associated with gangue minerals, such as silica (SiO2) and calcium oxide (CaO). Elements such as barium may be associated solely with the mineral barite (BaSO4) in some ores. These methods do not provide mineral assays but provide the total concentration of elements such as copper, iron and silica resulting from the various minerals in which they exist. The iron assay represents this element in gangue sulfide minerals such as pyrite and pyrrhotite, in non-sulfide gangue minerals such as dolomite and various silicate minerals and may include iron in a valuable copper-bearing mineral such as chalcopyrite (CuFeS2) or

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Case 1 Lip tonnages correct on absolute basis ie compatible with reference tonnage and correct relative to each other

Grade

Residence times measured correctly

Recovery

Case 2 Lip tonnages correct relative to each other but all 10% too high in comparison to reference tonnage (lip tonnages not rescaled as described in Figure 2.5)

Grade

Calculated residence times lower by 10% than correct value Position of grade-recovery curves for cases 1 and 2 is the same.

Recovery

Case 3 Lip tonnages correct relative to each other but all 15% too low in comparison to reference tonnage (lip tonnages not rescaled as described in Figure 2.5)

Grade

Calculated residence times higher by 15% than correct value Position of grade-recovery curves for cases 1, 2 and 3 is the same. Recovery

Case 4 Lip tonnages not correct relative to each other Position of grade recovery curve becomes subject to additional errors and is no longer the same as for cases 1, 2 and 3 FIG 6 - Illustration of the reliability of calculated metallurgical performance for a valuable mineral/element using the method with measured lip tonnages (see also Figure 5).

bornite (Cu5FeS4). Equally, a silica assay usually does not reflect the occurrence of one non-sulfide gangue mineral. In the supergene or oxidised portion of a copper orebody, a copper assay is likely to reflect the existence of various codominant copper-bearing minerals such as chalcocite (Cu2S), covellite (CuS), native copper (Cu), secondary chalcopyrite (CuFeS2), bornite (Cu5FeS4) and others. Clearly, in these examples, mineral assays cannot be calculated from the elemental assays alone. In the fortunate case where all the copper exists as chalcopyrite, which is often the case in the deeper primary zone in a copper orebody, the stoichiometry of the mineral can be used to convert the copper assay to a chalcopyrite assay. In the primary zones of orebodies, it is reasonably common for the valuable element to reside in just one mineral. However, for species such as iron or silica, this situation is almost non-existent. Mineral assays can be obtained by three methods: 1.

the use of a quantitative analysis method for minerals such as quantitative X-ray diffraction;

2.

the use of point counting or related methods involving an optical microscope, image analyser or automated electron microscope for mounted samples, often size fractions and

42

sometimes on the original sample containing all sizes; and 3.

the use of approximate methods for conversion of elemental assays to mineral assays where the approximations are specific to a given ore or site.

Methods 1 and 2 provide mineral assays but some understanding of their limitations is required. Quantitative X-ray diffraction is suitable for assaying total samples or individual size fractions from samples. Point counting methods as practised via an optical microscope are usually applied to size fractions and the finest size fraction from a given sample cannot be measured by this method. In this situation, assumptions have been needed to sum the data across the size fractions to obtain the mineral head grade. In general, these mineral assay methods are less accurate than traditional assaying methods for elements and they have increased technical difficulty and/or become much more costly if minerals are being assayed in the low concentration region of less than one per cent by weight. In practice, methods 1 and 2 need to be used in conjunction with elemental assays. Further, in many cases, the use of all the methods in combination is warranted, allowing a method which draws on the strengths of the data from various methods for obtaining mineral assays. Suitable programs are needed for execution of the necessary calculations to produce a combined set of mineral assays.

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Obtaining mineral recoveries with introduction of the recalculated feed

It has been observed that operating sites with both traditional assaying facilities for elements and recently acquired assaying facilities for minerals generally do not merge the two sources of assay data well to maximise the benefit to the site. Method 3 relies on the elemental assays which are very reliable but requires assumptions for conversion to mineral assays, which are of various levels of reliability. As an example, consider a simple ore containing lead (only as galena), pyrite, a small amount of copper (only as chalcopyrite) and various non-sulfide gangue minerals including talc. Clearly, the lead and copper assays can be converted to galena and chalcopyrite assays, preferably by using the measured stoichiometry for galena and chalcopyrite in that ore. If sulfur only existed in the galena, chalcopyrite and pyrite, the sulfur assay could be corrected for sulfur in the galena and chalcopyrite, and the corrected sulfur assay converted to a pyrite assay, preferably using the measured stoichiometry for pyrite in that ore. By subtracting the mineral assays for galena, pyrite and chalcopyrite from 100 per cent, a useful estimate of the non-sulfide gangue assay would be obtained. If a substantial and variable proportion of the magnesium in the ore existed in non-talc minerals, conversion of magnesium assays to talc assays may provide unreliable information on the talc. In such circumstances, a combination of elemental assays which are converted to mineral assays and directly measured mineral assays for the talc (eg by X-ray diffraction) could be devised for that particular ore.

After calculation of the solid balance, obtaining the recovery (the distribution of a mineral, or element, between the concentrate and tailing streams for a separator) becomes a simple calculation. It is recommended that the recovery is calculated with respect to the recalculated feed, which is illustrated in Figure 7 for a separator producing two products and for which the raw assays are used (ie no statistical adjustment of the assays to provide ‘smoothed’ or completely internally consistent assays has occurred). In Figure 7, the solid balance was calculated using the method shown for the feed, concentrate and tailing assays of mineral A, the only mineral for which there was a large difference between the feed and tailing assays. As a result, a mineral balance must also exist for mineral A (see the same flow rates for mineral A in the actual feed and recalculated feed (from summation of flows of mineral A in the products) in Figure 7). However, for minerals B and C, it is very unlikely that an exact mineral balance will exist using the observed assays for minerals B and C and the solid balance calculated from mineral A. In Figure 7, the different flow rates of minerals B and C are shown for the actual feed and for the recalculated feed (defined as the sum of the flow rates in the concentrate and tailing). The recovery values for minerals B and C can be expressed with respect to the recalculated or the actual feed. It is recommended that the recovery value is calculated with respect to the recalculated feed because:

The following raw mineral assays were obtained for a separator producing two products.

Mineral A Mineral B Mineral C Total

Feed 10.2 19.7 70.1 100

Concentrate 81.3 11.6 7.1 100

Tailing 1.2 21.6 77.2 100

Feed

Tailing

F t/h solid

F –D t/h solid Concentrate D t/h solid

The major separation is occurring for mineral A and its assays will be used to calculate the solid split. Using the two product equation and noting the feed flow rate is 1000 t/h of dry solid:

D F

?D

f t ct 10.2  1.2 81.3  1.2 0.112 0.112 u 1000 112 tph

Summary of Flow Rates and Recoveries

Mineral A Mineral B Mineral C Solid

Feed (t/h) 102 197 701 1000

Recalculated Feed # (t/h) 102 205 693 1000

Mineral A Mineral B Mineral C Solid

Recovery* 89.2% 6.6% 1.1% 11.2%

Recovery** 89.2% 6.3% 1.2% 11.2%

# * **

Concentrate (t/h) 91 13 8 112

Tailing (t/h) 11 192 685 888

sum of mineral flow rates in concentrate and tailing with respect to actual feed with respect to recalculated feed

FIG 7 - Illustration of calculation of mineral recoveries with respect to the recalculated feed. A similar method can be used for calculations based on element assays.

Flotation Plant Optimisation

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CHAPTER 2 – EXISTING METHODS FOR PROCESS ANALYSIS

• the resulting recovery value is less affected by sampling and assay errors existing in the data, particularly for minerals with higher flow rates in the concentrate than the tailing;

• the values are bounded between zero per cent and 100 per cent; and

• a consistent approach is provided. There are several practical advantages in obtaining the recovery of minerals, aside from the previously stated observation that, because minerals are being separated, logic dictates that mineral data are the most relevant. When metallurgical data are analysed on the basis of elements, some or all of the solid in the non-sulfide gangue category may be ignored. Further, knowledge of an ore’s behaviour via minerals allows ready calculation of the effects from changing ore head grade, assuming all other properties remain fixed. Because this approach requires a knowledge of the stoichiometry of each mineral and because the concentrations of minor and trace elements in the lattice of each mineral should also be found in detailed analyses, more complete information on the real limits to a separation can be obtained, based on the properties of the minerals. For example, most sphalerite contains some iron in solid solution and the mineral marmatite reflects naturally occurring zinc sulfide with very high levels of iron.

which may indicate experimental errors. Further, the position of the curve, ie its coarseness or fineness should be compared with the typical range of values for that stream. If the sizing is outside the expected range, further checking is needed. For the various assays, the first check is to calculate the head grade for the sample by using the size distribution and the assay for each size fraction. The consistency between this value and the head grade for the sample (assayed at the same time as the size fractions) needs to be checked. Further, these two values for the head grade of the sample should be compared with the value obtained for the sample when the survey was conducted and assayed initially. After checking the integrity of the data, a system is needed for processing the data to provide useful information on the recovery values for each mineral in each size fraction. The concept of the recalculated feed remains relevant for the sized data. Initially, consider sized data for the simplest situation, ie two output streams and one input. The following two options exist for processing the data when there is no size reduction inside the section considered: 1a.

CALCULATION OF RECOVERY-SIZE DATA The calculation of recovery values for each mineral for a bank in the previous section specifies the behaviour of each mineral but, if some values are abnormal or if there is an economic imperative to improve the recovery value in some size fractions, there is no direct clue to the mechanism by which the gangue mineral was recovered or the valuable mineral was not recovered. The first step towards determining the clues is to obtain recovery values for all the minerals in all size fractions and to summarise the information for all the minerals (and also water) in a graph of mineral recovery (y-axis) plotted with the mid-point of each size fraction using a logarithmic scale (x-axis). The key steps in generating this information are now listed: 1.

Deciding if there is sufficient quality in the mass balance calculated from the original survey to warrant generation of more detailed data.

2a.

Selection of the sizing method(s).

2b. The sizing of the samples. 3.

Specification of any grouping of size fractions before assaying to lower costs, ensuring consistent grouping of size fractions for each group of samples involved in a particular bank or plant section. (This extends to a consistent approach to the size fractions combined at or near the boundaries of sizing methods based on different principles, eg screening (sizing method based on physical dimensions) and cyclosizing (sizing method based on hydraulic size), for example.)

4.

Specification of the assays (elemental and/or mineral) to be obtained and submission of the size fractions to the assay laboratory after pulverising the relatively coarse fractions to provide a low fundamental error (see the appendix) in sampling a very small mass for chemical analysis. For each stream, a ‘head’ sample (unsized) should be submitted for checking consistency of the assays on the size fractions.

A number of checking steps are required during the procedure, particularly with the sizing step (2b) and the internal consistency of the assays. These are now discussed. After each sizing is completed, the size distribution should be graphed to detect any irregularities in the shape of the curve

44

use the solid balance established with the original survey data to calculate the flow rate for each mineral in each size fraction in the recalculated feed (by summing the flow rates of each mineral in the concentrate and tailing), and compare each value with the observed value for the feed stream;

1b. calculate the recovery value for each mineral in each size fraction with respect to its flow rate in the recalculated feed; 2a.

use a data smoothing program to adjust the assays statistically and provide balanced data for each mineral in each size fraction; and

2b. calculate the recovery value for each mineral in each size fraction, noting that the recovery values with respect to the actual feed and recalculated feed will be the same as the data were adjusted statistically to provide internally consistent assays in 2a. When there is size reduction inside the section considered, it is only possible to employ methods 1a and 1b for the recovery calculation for each mineral in each size fraction, there being no basis for data smoothing. It is also relatively common that no sized data exist for the feed stream. This can arise because a sampling point did not exist or the available sample was not selected for sizing. In this case, the recoveries can only be calculated by use of the recalculated feed. The next step which allows interpretation of the recovery-size information more readily is to summarise the information in a graph of mineral recovery (y-axis) and the mid-point of the size fraction (x-axis) using a logarithmic scale on the x-axis. All the minerals should be plotted on the one graph for a given processing stage and the values for the mid-points on the x-axis should reflect the specific gravity of the minerals when the sizing device operates on the basis of hydraulic equivalents such as for a cyclosizer, its predecessor (infrasizer) or for sizings by beaker decantation. When the sizing is obtained by sieving, the mid-points for all minerals will be the same. To appreciate fully recovery-size data for minerals, the flow rates of each mineral in each size fraction in the recalculated/ actual feed also need to be reviewed. The values for mineral recovery are key indicators of metallurgical performance but the practical and economic significance of the recovery values depends on the quantity of each mineral in each size fraction on which the recovery value acts. While it is less common to include this information in the recovery-size curves, this can be done by way of a histogram along the base of the recovery-size curve. Alternatively, tables or other means may be devised to allow convenient recognition of this important information.

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INTERPRETATION OF RECOVERY-SIZE CURVES The hydrophobic mineral The position and shape of the recovery-size (log scale) curves have metallurgical significance for liberated valuable and gangue minerals from the sequence of subprocesses in the pulp zone, which are particle/bubble collision and adhesion, followed by successful transportation through the pulp zone. Detachment of a particle from a bubble can be caused by turbulence during the transportation step. The next necessary step is successful transportation through the froth zone. Survey methods now exist for examination of the recovery of the hydrophobic and other minerals across the froth zone as discussed in a following section. Particle/bubble collision depends on physical properties of the particles (eg particle diameter and density) and the system (eg level of turbulence and bubble size). The chemical surface properties of the particles (particularly their hydrophobicity) and bubbles are dominant in the particle/bubble adhesion step and remain important for a successful transportation step, ie the avoidance of detachment. Appropriate settings for both the physical and chemical properties of the particles and the system are important to minimise detachment. Hence, the position and shape of the resulting recovery-size (log scale) curves are related to the physical and chemical properties of the system through their effect on the subprocesses in the pulp zone for liberated particles. For technical and economic reasons, complete liberation of all minerals cannot be achieved. Hence, preceding comments in this section which referred only to liberated particles have to be tempered with the superimposed effects from incomplete liberation which affect all size fractions, but which typically affect the less liberated coarse size fractions to the greatest extent for a given ore. It must be noted that, by obtaining liberation data as a next step, the effects of this complication can be understood for a given ore. This avoids having full reliance on deductions from recovery-size graphs, particularly for an ore whose liberation characteristics are not well known. It is also assumed that a particle which reports to a given size fraction in the recovery-size curves existed in that size fraction in the flotation process. The existence of a fully dispersed pulp is therefore assumed. It is useful to summarise the general form of some basic relationships (Pyke, Fornasiero and Ralston, 2003) between the efficiency of each subprocess in the pulp zone and particle diameter (Figure 8). Figure 8 arises from ongoing investigations at the Ian Wark Research Centre. The authors used the following equation to describe the collection or capture efficiency (Ecoll) for a particle and bubble in terms of the efficiencies of the subprocesses in the pulp zone: Ecoll = EcEaEs where: Ec

= collision efficiency

Ea

= adhesion efficiency

Es

= stability efficiency

For each of the efficiencies in the subprocesses (Ec, Ea and Es), Pyke, Fornasiero and Ralston (2003) provided equations relating them to properties of the flotation system. For the particle/bubble collision step, there is a direct relationship between collision efficiency and size (see Figure 8). This arises because small particles approaching a bubble tend to be swept along the stream-lines around bubbles while larger particles with higher momentum have an increased ability to cross the stream-lines and complete a collision. This inability to

Flotation Plant Optimisation

FIG 8 - Calculated relationships between collision efficiency Ec, adhesion or attachment efficiency Ea and stability efficiency Es and particle diameter dp, and the resulting calculated relationship between the first-order rate constant k and particle diameter dp for the pulp zone, where cases a, b and c are for advancing contact angles of 50°, 65° and 80° respectively (Pyke, Fornasiero and Ralston, 2003).

cross stream-lines means that the probability is low for small particles to approach a bubble sufficiently closely for a collision to have occurred, ie sufficiently closely for the adhesion process to commence. For a particle of a given diameter, its momentum and its ability to cross the stream-lines is increased if it has a higher density. The second subprocess (known as adhesion or attachment) commences after a particle and bubble approach each other very closely. Pyke, Fornasiero and Ralston (2003) described the approach of the particle and the bubble: Should they approach quite closely, within the range of attractive surface forces, the intervening liquid film between the bubble and particle will drain, leading to a critical thickness at which rupture occurs. Movement of the three-phase contact line (the boundary between the solid particle surface, receding liquid phase, and advancing gas phase) then occurs, until a stable wetting perimeter is established. There is an inverse relationship between the adhesion efficiency and particle diameter (Figure 8), noting that this subprocess is referred to as attachment in the reference (Pyke, Fornasiero and Ralston, 2003). Small particles slide more slowly over the surface of a bubble as they are ‘protected’ due to their low diameter by existing in the more slowly moving boundary region of the water phase near the surface of the bubble. The lower sliding velocity for smaller particles allows a greater time for the adhesion subprocess to be successful, ie for the actual contact time between the particle and the bubble to exceed the needed contact time for adhesion, known as the induction time. Similarly, for the transportation step in the pulp zone, there is also an inverse relationship between the stability efficiency and particle diameter (Figure 8). Small particles are subjected to lower forces of detachment and have a higher probability of successful transportation as a particle/bubble aggregate to the base of the froth phase.

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CHAPTER 2 – EXISTING METHODS FOR PROCESS ANALYSIS

In Figure 8, Pyke, Fornasiero and Ralston (2003) provided the summation of the relationships for the three described subprocesses by calculating the relationship between the firstorder rate constant (k) and particle diameter for the hydrophobic mineral for a set of conditions. This calculation involved the use of typical parameters for the induction time. The first-order rate constant (k) for a mineral is closely related to its recovery (see section – Process Analysis with Down-theBank Flotation Data) and summarises the propensity for the flotation process for a mineral to proceed in the pulp region for a set of conditions. The rate constant for the pulp region is linked to the efficiencies in the three subprocesses by the following equation (Pyke, Fornasiero and Ralston, 2003): k = z Nb Ec Ea Es where: z

= frequency of particle bubble collision

Nb

= number of bubbles per unit volume

It can be seen that the relationship between the rate constant and particle diameter in the example has a maximum as a result of the interaction of the direct relationship between efficiency and particle diameter for the collision subprocess and the two indirect relationships discussed for the adhesion and transportation subprocesses. In some cases, a small plateau region may result from the interactions of the three relationships. The importance of a high particle hydrophobicity in the adhesion subprocess and in avoiding detachment in the transportation subprocess is highlighted in Figure 8 where calculated outcomes are provided for contact angles of 50, 65 and 80 degrees. For convenience of presentation and interpretation, industrial recovery-size data are graphed with a logarithmic scale for the particle size on the x-axis. This step spreads the values for particle diameter conveniently, as for plotting sizing distribution data.

The hydrophilic minerals The entrainment mechanism is a non-selective physical mechanism for transfer of minerals from the pulp zone to the concentrate launder. The entrainment mechanism does act on all minerals – both hydrophilic and hydrophobic – because it is a non-selective physical mechanism. It will be discussed principally in terms of the hydrophilic minerals because the mechanism provides a much higher proportion of the total recovery of these minerals. For the finest size fractions, the entrainment mechanism can be the sole recovery mechanism for the non-sulfide gangue minerals in some ores. The pattern of behaviour of hydrophilic particles of various sizes in the froth phase is better described through knowledge of the entrainment mechanism. Throughout a perfectly mixed pulp zone, hydrophilic particles of all sizes exist at a uniform concentration in each unit of water in the pulp zone. These particles are subject to hydraulic classification in the froth region because the water in the froth region must contain a representative sample of the hydrophilic particles when the water enters the froth. It must be noted that water from the pulp zone is the only source of water essential for a stable froth zone in a conventional flotation machine.

Knowledge of the water recovery assists in interpretation of the relationship between the recovery of unwanted minerals (usually gangue sulfide minerals and non-sulfide gangue minerals) and particle diameter (log scale). With the value for water recovery for a bank, it can be seen if the entrainment mechanism explains all the recovery of the gangue minerals or only a portion. This is possible because it is observed that the recovery of liberated, hydrophilic gangue in the 0 - 10 μm region is 0.8 of the value for the water recovery. If the water recovery were ten per cent, a normal flotation system would exhibit a recovery of eight per cent in the 0 - 10 μm fraction for a hydrophilic gangue mineral (specific gravity of 2.7) from the entrainment mechanism. It can be visualised that, for a perfectly mixed pulp zone of a conventional flotation machine, the recovery of ten per cent of the water would result in recovery of ten per cent of the 0 - 10 μm liberated non-sulfide gangue by this non-selective physical mechanism if there was no drainage of this mineral in the froth region. In this situation, the entrainment efficiency value would be 1.0. In real flotation systems, the observed entrainment efficiency factor is 0.8 for the 0 - 10 μm fraction for siliceous non-sulfide gangue. The entrainment efficiency value for a size fraction can be defined formally: Entrainment Efficiency Value for size i (ENTi ) =

(Mass of free gangue per unit mass water)Con (Mass of free gangue per unit mass of water)Top of pulp

The entrainment efficiency value for size i has been called the classification function (Johnson, 1972) or the classification vector (Lynch et al, 1981). It is commonly described by the term ENTi in the present literature and the topic was reviewed recently (Johnson, 2005). Typical values for ENTi for a range of size fractions of siliceous non-sulfide gangue are provided in Table 1. On a sized basis, the simplest mathematical depiction of entrainment is a series of entrainment efficiency values approaching unity for the fine sizes and which approach zero for sizes exceeding 50 μm. If a gangue mineral has an elevated specific gravity, its value can be determined to establish if lower values for ENTi are required for that system. The following relationship can be demonstrated from the definition of the entrainment efficiency factor (Lynch et al, 1981) for the first-order rate constant (ki) of a mineral in size fraction i being recovered by entrainment: ki = ENTi kw where: kw = the first-order rate constant for water recovered in the concentrate Because the first-order rate constant is closely related to the recovery of a mineral or water (see section – Process Analysis with Down-the-Bank Flotation Data) from a cell or bank, the previously described comparisons of the water recovery value and the recovery of gangue minerals in the relatively fine size fractions are validated as part of interpretation of mineral recovery-size (log scale) data.

TABLE 1 Values for entrainment efficiency factors (ENTi) for siliceous non-sulfide gangue (Lynch et al, 1981). Size fraction (μm) Entrainment efficiency

46

-11

-16 +11

-23 +16

-33 +23

-44 +33

-75 +44

+75

0.83

0.44

0.24

0.11

0.04

0.03

0.0

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Review To understand the behaviour of a particular ore, there is often a benefit from observing its flotation behaviour in the absence of collector but in the presence of a normal frother addition (and possibly depressant addition). The benefit can be increased if the recovery-size behaviour is obtained for the recovered minerals. Minerals which display normal flotation through the particle/ bubble collision sequence in the absence of collector can be readily recognised (recovery values in some size fractions considerably larger than water recovery) and the size fractions in which this occurs can be readily identified (Johnson and Jowett, 1982). Minerals which display this behaviour can be valuable sulfides, non-valuable sulfides and non-sulfide gangue (eg talc). Hydrocarbons present during ore formation and which remain associated with a portion of one mineral (eg pyrite with a rimming of hydrocarbons) can cause this behaviour (Croxford et al, 1961). As a result of the various mechanisms for flotation and the steps involved in each mechanism, recovery-size curves for the valuable mineral being recovered by flotation adopt a general form with many variations, of which a few are demonstrated in Figure 9. It is given that the curves were observed after high residence times, ie their position and shape were changing only very slowly with additional residence time. For the valuable mineral in all graphs, two scenarios (Johnson, 2006) are shown for the fine fractions. In scenario 1, the diminished recoveries are typical of those arising from deficiencies in the collision subprocess. In scenario 2, the more greatly diminished recoveries result from an additional effect beyond the collision deficiency likely to result from an imbalance in the ratio of adsorbed hydrophobic/hydrophilic species. For the minerals for which recovery is not being sought, an extremely wide range of positions and shapes exist (Figure 9). For the hypothetical fully liberated feed, the following are demonstrated:

• entrained liberated non-sulfide gangue (cases A, C and E); • entrained and hydrophobic (collector), liberated sulfide gangue (case C); and

• entrained and naturally hydrophobic liberated sulfide gangue (case E). For the realistic cases (B, D and F) with an imperfectly liberated feed, cases are shown with increased recoveries of sulfide and non-sulfide gangue due to their recovery in composites, along with lower recovery of coarse valuable mineral due to the lower hydrophobicity of composite particles containing some valuable mineral.

ADDITION OF LIBERATION DATA TO RECOVERY-SIZE DATA The addition of liberation data to recovery-size data eliminates the need for deductions and inferences about the state of liberation of a mineral in given size fraction of a given product. For a new ore or for an ore which is unfamiliar to a metallurgist, the collection of liberation data in initial phases of the work can

increase confidence in the interpretation of recovery-size data for the ore in question such that less liberation data may be required in further stages of experimental work on the same ore. Liberation data have been collected traditionally on size fractions and there are lower and upper limits (mounting size limitations) to the size fractions which can be examined. The lower limits result from the physics of the method employed (Jones, 1987). For techniques based on optical microscopy or generation of X-rays by electron microscopy, different reasons exist for the lower limit but the value is typically in the region of 5 μm, sometimes slightly lower. The limit can be much lower if a different method with different limitations is useable for a given ore, eg one based on backscattered electrons. Size fractions submitted for liberation analysis must not have been pulverised. For a given size fraction in a separation with one concentrate and one tailing, the liberation data can be used in two complementary ways. For the concentrate, the liberation state of the unwanted minerals can be recognised, providing strong clues to their mechanism of recovery. Equally, the liberation state of the valuable mineral is determined. If significant losses of valuable minerals in composites are observed, corrective steps involving grinding or regrinding may be assessed. Liberation data allow the flow rate of each mineral in each size fraction of each product (obtained from the recovery-size (log scale) level of analysis) to be distributed between a number of categories (typically from five to ten). The performance of the various categories becomes the basis of the next level of analysis. Liberation data for a mineral are supplied in one of two basic forms. The traditional point counting method with use of an optical microscope provides liberation data in the general format as shown in Table 2 for a size fraction. Automated scanning electron microscopes can also provide the data in the point counting format illustrated in the preceding table. The data from these devices are also commonly supplied in another format based of the percentage of the mineral of interest in each category. An example is shown in Table 3. In the type of data indicated in the preceding table, some grouping of the original data has been performed. Typically, the data are provided with increments of ten per cent from category to category. The reader is reminded that several calculation steps, as described in preceding sections of this chapter, are the necessary precursors to incorporation of liberation data. These steps are listed: 1.

Calculation of the mass or solid balance for the circuit. The water balance should also be calculated.

2.

Use of size distributions and assays for the size fractions of the concentrate and tailing (as the minimum relevant streams), along with the solid flows from item 1, to calculate the flow rates of minerals in each size fraction of the concentrate and tailing.

3.

Calculation of the recovery of each mineral in each size fraction with respect to the recalculated feed.

TABLE 2 Example of some point count data for sphalerite in one size fraction. Liberation data (categories) % Liberated % in each category †

60

% in ternary composites†

% in binary composite with listed minerals Galena

Iron sulfide

Non-sulfide gangue

16

4

11

9

Includes quaternaries.

Flotation Plant Optimisation

Spectrum Series 16

47

CHAPTER 2 – EXISTING METHODS FOR PROCESS ANALYSIS

Fully Liberated Feed (All minerals 100% Liberated)

Typical Feed (Liberation of valuables >80%) (Liberation of other minerals 70 to 90%) Case B 100

90

90

80

80

70

70

Recovery (%)

Recovery (%)

Case A 100

60

50

40

30

60

50

40

30

20

20

Water Recovery (10%)

10

Water Recovery (10%)

10

0 1

10

0

100

1

10

log Size (um)

Case C

Case D

100

100

90

90

80

80

70

(%)

60

Recovery

Recovery (%)

70

50

40

30

60

50

40

30

20

Water Recovery (10%)

20

10

Water Recovery (10%)

10

0 1

10

0

100

1

10

log Size (um)

100

log Size (um)

Case E

Case F

100

100

90

90

80

80

70

70

60

Recovery (%)

Recovery (%)

100

log Size (um)

50

40

30

60

50

40

30

20

20

Water Recovery (10%)

Water Recovery (10%)

10

10

0

0

1

01

001

1

10

100

log Size (um)

log Size (um)

Valuable Mineral (Scenario 1) – ‘collision effect’ for fine valuables Valuable Mineral (Scenario 2) – additional deleterious effect beyond ‘collision effect’ for fine valuables Non-sulfide Gangue (Case 1) Non-sulfide Gangue (Case 2) – lowered contribution from recovery in composites with valuable mineral compared to case 1 Sulfide Gangue FIG 9 - Examples of some mineral recovery – particle diameter (log scale) curves for a feed with perfect liberation (cases A, C, E) and for a feed with acceptable liberation (cases B, D, F) for which recovery of unwanted minerals in composites becomes a possible mechanism.

Steps 2 and 3 represent the calculations required for graphing the mineral recovery – particle size (log scale) curves as discussed in earlier sections. The next level of analysis (liberation level) is now discussed. An example in the literature with the same methodology can also be reviewed (Johnson, 1987). To provide an example of the type of calculations required for the liberation level of analysis, some sphalerite liberation data for

48

a single selected size fraction are presented for a system with such data for the concentrate and tailing only. In Table 4, the calculations for one size fraction of one mineral are illustrated. The flow rate of sphalerite in the concentrate and tailing were 6188.2 and 1155.9 kg/h respectively. These flow rates (column A) were multiplied by each liberation value (each divided by 100) in the five columns labelled as B to distribute the mineral

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CHAPTER 2 – EXISTING METHODS FOR PROCESS ANALYSIS

TABLE 3 Example of second form of liberation data for sphalerite in a size fraction. Liberation data (per cent of mineral of interest defined in each category) Percentage in category

100

90 - 100

70 - 90

50 - 70

30 - 50

20 - 30

10 - 20

0.1 - 10

61.2

30.4

4.1

2.1

1.1

0.4

0.4

0.3

TABLE 4 Example of processing of point count form of some sphalerite liberation data for one size fraction. Product

Concentrate Tailing Recalculated feed

Mineral flow Liberated (kg/h) (A) category 6188.2 1155.9 7344.1

75.6 12.7 65.7

Liberation data (B)

Mineral flow in categories (kg/h) (C)

% in binaries with

Tern

Galena

Iron sulfide

Non-sulfide gangue

5.1

12.2

2.4

2.9 4.8

24.2 14.1

10.6 3.7

4.6 49.6 11.7

Liberated category

Binaries with Galena

Iron sulfide

Tern

Non-sulfide gangue

4678.3

315.6

755.0

148.5

284.7

(97.0)

(90.4)

(73.0)

(54.8)

(33.2)

146.8

33.5

279.7

122.5

573.3

(3.0)

(9.6)

(27.0)

(45.2)

(66.8)

4825.1

349.1

1034.7

271.0

858.0

(100.0)

(100.0)

(100.0)

(100.0)

(100.0)

Notes: Tern = category containing ternary and quaternary composites. Recalculated feed = recalculated feed from summation of flows in concentrate and tailing as shown in columns labelled as (A) and (C). Liberation values for each category in the row ‘Recalculated feed’ and in columns labelled as (B) calculated using the flow rates for the recalculated feed in columns labelled as (C) and the total flow rate of sphalerite (7344.1 kg/h) in column (A).

flow rates amongst the various liberation categories (columns labelled as C). The recalculated feed is obtained in the table by summation of the flow rates in each liberation category. In a further step, the distribution of sphalerite between the concentrate and tailing in each liberation category is calculated (see values in brackets). In other words, the recovery of mineral in each liberation category has been calculated with respect to the recalculated feed. Although the calculations are straightforward, the presentation of the calculated quantities is more difficult for the listed reasons:

• there is interest in information on the feed, concentrate and tailing streams;

• there are many size fractions and minerals; and • there are many liberation categories of relevance. For compactness in some examples of presentation methods, data are used for a bank where only four size fractions encompass all the solid in the concentrate and tailing. The first presentation uses tables only (see Table 5). This table provides the flow rates and recoveries for all the minerals in the various liberation categories and size fractions in the concentrate. This table is particularly valuable for recognition of the major sources of gangue dilution in the concentrate. Therefore, the dominant flow rates for the gangue minerals (>200 kg/h) in the concentrate have been highlighted. In reading the flow rates for minerals in a typical binary in Table 5, the reader is reminded of the following example for the sphalerite/ iron sulfide binary (+38 μm fraction): 281.8 kg/h of sphalerite and 117.8 kg/h of iron sulfide. The table also provides the recovery values for all the categories in the various size fractions. The recovery values are particularly valuable for examination of metallurgical behaviour of the various liberation categories of the valuable mineral in the concentrate. The recovery values represent the metallurgical performance for the valuable mineral in the category. However, it must be noted that the significance of a high or low recovery value for the valuable mineral in a category

Flotation Plant Optimisation

depends also on its flow rate in the feed. For example, a category with a high flow rate in the feed and a metallurgical recovery of 95 per cent may result in a much higher flow rate of valuable mineral to the tailing than another category with a low flow rate in the feed and a low metallurgical recovery of 20 per cent. Some recovery values have not been entered in Table 5. In collecting data from a standard number of particles, the number of observations in some liberation categories may be too small to provide reliable recovery values. For example, galena was present in the tailing in small amounts only and no observations existed for some liberation categories in the tailing, implicating a recovery of 100 per cent. A second phase of data collection recording only information on a selected mineral (in this case for galena) in some liberation categories is required in such circumstances. The graph of recovery-particle diameter (log scale) for the valuable mineral can be updated with the additional liberation categories for the valuable mineral as shown in Figure 10 where the curve for sphalerite contained six data points. With the grouping of size fractions, the curves for the various liberation categories contained four size fractions in this example. It can be noted that the curve for liberated sphalerite displayed higher recoveries than for the overall sphalerite curve. Further, the points available for sphalerite-galena binaries were in a similar region to the liberated sphalerite because both the galena and sphalerite were hydrophobic in these binary particles. For the other liberation categories containing sphalerite in composites with less hydrophobic unwanted minerals, lower recoveries were observed in general. Similar patterns of behaviour are often observed in data sets of this type. Graphical presentations can be extended to three-dimensional graphs (with axes of size fraction/liberation category/measure of quantity) of the types listed: 1.

distribution of a selected mineral in the feed, concentrate or tailing;

2.

flow rate of a selected mineral in the feed, concentrate or tailing; and

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CHAPTER 2 – EXISTING METHODS FOR PROCESS ANALYSIS

TABLE 5 Listing of flow rates (kg/h) and recoveries for sphalerite, galena, iron sulfide and non-sulfide gangue in the various liberation categories and size fractions for a zinc rougher. All gangue mineral flow rates >200 kg/h have been highlighted to indicate the dominant gangue mineral flow rates. Flow rate of mineral in all liberation categories in concentrate Flow in binary with Mineral

Liberated

Galena

Sphalerite

Iron sulfide

NSG

0.6

-

61.1

0.0

108.3

117.8

Sphalerite

1199.3

858.5

-

281.8

180.2

756.9

Iron sulfide

43.4

0.0

117.8

-

0.0

256.4

NSG

84.5

65.2

297.6

71.3

-

362.8

Galena

Ternary +38 μm

Flow in binary with Mineral

Liberated

Galena

Sphalerite

Iron sulfide

NSG

Ternary

3.9

-

61.8

10.8

25.5

127.8

Sphalerite

4678.3

315.6

-

755.0

148.5

284.7

Iron sulfide

266.5

13.1

339.1

-

13.9

139.1

NSG

214.3

0.0

267.2

80.7

-

641.6

Liberated

Galena

Sphalerite

Iron sulfide

NSG

Ternary

7.0

-

11.0

1.3

4.4

4.7

Sphalerite

1336.7

29.4

-

29.4

63.3

13.3

Iron sulfide

116.9

3.5

46.4

-

18.9

0.0

NSG

143.9

12.4

87.5

43.7

-

0.0 Ternary

Galena

-38 μm +11 μm

Flow in binary with Mineral Galena

-11 μm +8 μm

Flow in binary with Mineral

Liberated

Galena

Sphalerite

Iron sulfide

NSG

56.5

-

89.3

10.3

35.6

37.9

Sphalerite

5978.3

131.7

-

131.7

283.1

59.3

Iron sulfide

575.3

17.4

228.3

-

93.2

0.0

NSG

1206.4

103.8

733.5

366.7

-

0.0

Galena

-8 μm

Recovery of mineral in all liberation categories in concentrate Recovery in binary with Mineral

Liberated

Galena

Sphalerite

Iron sulfide

NSG

#

-

#

0.0

12.9

6.9

Sphalerite

80.5

92.3

-

39.1

9.9

19.9

Iron sulfide

1.6

0.0

13.5

-

0.0

5.0

NSG

0.2

2.8

12.7

0.3

-

2.6

Galena

Ternary +38 μm

Recovery in binary with Mineral Galena

Liberated

Galena

Sphalerite

Iron sulfide

NSG

Ternary

#

-

79.3

20.0

12.9

29.4

Sphalerite

97.0

90.4

-

73.0

54.8

33.2

Iron sulfide

3.3

10.5

31.0

-

1.0

11.1

NSG

0.9

0.0

33.1

1.9

-

29.6

NSG

Ternary

-38 μm +11 μm

Recovery in binary with Mineral Galena

Liberated

Galena

Sphalerite

Iron sulfide

#

-

#

#

9.1

24.2

Sphalerite

92.4

#

-

66.5

63.3

44.1

Iron sulfide

7.2

#

37.3

-

12.3

##

NSG

2.5

28.1

58.0

8.2

-

##

-11 μm +8 μm

Recovery in binary with Mineral

Liberated

Galena

Sphalerite

Iron sulfide

NSG

Ternary

#

-

#

#

5.3

15.1

Sphalerite

74.6

#

-

32.5

29.4

16.0

Iron sulfide

5.0

#

29.0

-

8.8

##

NSG

2.0

24.3

53.2

6.9

-

##

Galena

-8 μm

Notes: NSG = non-sulfide gangue; = gangue flow >200 kg/h; # = insufficient observations of this category in tailing for reliable value; ## = insufficient observations of this category in concentrate for reliable value.

50

Spectrum Series 16

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CHAPTER 2 – EXISTING METHODS FOR PROCESS ANALYSIS

100

90

80

70

Recovery (%)

60 Total Sphalerite Liberated Sphalerite Binary with Galena Binary with Iron Sulfide Binary with NSG Ternaries

50

40

30

20

10

0 1

10

100

Particle Diameter (μm - log scale)

FIG 10 - Relationship between total sphalerite recovery and particle diameter (μm – log scale) for data from the recovery-size level of analysis and from the recovery-size-liberation level of analysis illustrating the recovery of the following sphalerite liberation categories in a sphalerite rougher – liberated, binaries with galena, binaries with iron sulfide, binaries with non-sulfide gangue (NSG) and ternaries.

3.

recovery values for a selected mineral (often the valuable mineral) in the concentrate or tailing.

The types of graphs in item 1 are demonstrated in Figure 11 because their structure is difficult to explain without an actual demonstration. However, the graph types in items 2 and 3 are not demonstrated because their structure is straightforward. The graph type in item 2 is suitable for demonstrating how each gangue mineral is diluting a concentrate and also for demonstrating the flow rate of the valuable mineral in each category and size fraction in the tailing. It can be noted that items 2 and 3 effectively represent a means of graphical presentation of the type of data presented in tabular form in Table 5. Liberation data can also be used to identify the extent of liberation achieved at each grinding or regrinding stage at the commencement or within a processing circuit. This information can be obtained by including samples of the combined feed and product for a grinding or regrinding circuit. For each size fraction, measurement of the liberation values for the minerals in the feed and product allows the liberation value for minerals in each stream to be calculated. For each mineral, the increase in liberation across the grinding circuit is calculated by difference. The method for calculating the liberation value within a given stream is illustrated in Table 6. The taking of a few extra samples in a plant survey may allow more reliable quantification of the changes in liberation at size reduction steps. For example, to improve the quality of the data, it is preferable that a single combined feed sample and a single product sample be taken for an overall regrinding system, which often will contain a mill for size reduction and a classification device. It is advisable that a survey plan is reviewed for the directness by which liberation data may ultimately be obtained. In other words, the technical viability of a ‘liberation survey’ within the larger plant or circuit survey needs to be addressed separately in the planning steps. Equivalent samples can be taken in pilot plant work and in laboratory batch or cycle tests involving regrinding.

Flotation Plant Optimisation

TABLE 6 Calculation method for the total liberation of a mineral in a given stream. Input information: Column 1 Flow of mineral in each size fraction (from size distribution and assays) Column 2 Liberation value for mineral in size fraction

Size

Column 1

Column 2

Column 3

Mineral flow

Liberation value

Flow of liberated mineral

-105 μm +53 μm

5

20

1

-53 μm +CS2

8

25

2

-CS2 +CS3

10

40

4

-CS3 +CS4

10

60

6

-CS4 +CS5

10

75

7.5

-CS5 +CS6

20

80

16

-CS6 +CS7

37

80*

29.6

Total

100 → A

66.1 → B

The liberation value is calculated as: B × 100 A ie

66.1 × 100 = 66.1%. 100

This is simply the weighted average of the liberation values in Column 2. Note: in this example, observations could not be made on the CS7 fraction. The liberation value for this size fraction (denoted by *) was assumed to equal the value for the C6 fraction because the liberation values had essentially reached a plateau region.

Spectrum Series 16

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CHAPTER 2 – EXISTING METHODS FOR PROCESS ANALYSIS

Recalculated Feed

90 80 70 60 50 40

0 Total

-8um

+8um

Liberated Sphalerite +11um

ata g

10

ti o nC

Total Ternaries Sphalerite in Binaries with NSG Sphalerite in Binaries with Iron Sulfide Sphalerite in Binaries with Galena

20

ory

30

Lib era

Distribution of Sphalerite in Recalculated Zinc Rougher Feed

100

+38um

Size Fraction

Concentrate

90 80 70 60 50 40

0 Total

-8um

+8um

Liberated Sphalerite +11um

Size Fraction

+38um

nC ata g

10

rat io

Total Ternaries Sphalerite in Binaries with NSG Sphalerite in Binaries with Iron Sulfide Sphalerite in Binaries with Galena

20

ory

30

Lib e

Distribution of Sphalerite in Zinc Rougher Concentrate (with respect to Recalculated Zinc Rougher Feed)

100

Tailing

90 80 70 60 50 40

0 Total

-8um

+8um

Liberated Sphalerite +11um

Size Fraction

+38um

go

10

nC ata

Total Ternaries Sphalerite in Binaries with NSG Sphalerite in Binaries with Iron Sulfide Sphalerite in Binaries with Galena

20

ry

30

Lib era t io

Distribution of Sphalerite in Zinc Rougher Tailing (with respect to Recalculated Zinc Rougher Feed)

100

FIG 11 - Examples of usage of three-dimensional graphs with axes of size fraction/liberation category/percentage of sphalerite (with respect to the recalculated feed). The diagram displays data for the zinc rougher concentrate, the zinc rougher tailing and also the recalculated feed to the zinc rougher.

52

Spectrum Series 16

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CHAPTER 2 – EXISTING METHODS FOR PROCESS ANALYSIS

Historically, metallurgists have often sought to determine the benefits of regrinding by examination of the separation results (often using the flotation process) with various levels of regrinding. Particularly for regrinding to fine sizings, it is much safer to establish initially if the regrinding step is causing a significant increase in the liberation level of the valuable mineral and the gangue minerals. If a significant increase in liberation is measured, the necessary conviction is provided to seek conversion of the increase in liberation into an increase in performance of the following separation. Such increases in performance may not emerge after initial cursory separation tests, even if a significant improvement in liberation is resulting from the regrinding. Optimisation of the chemical conditions during regrinding and the following flotation separation may require many months of tests for some systems. Liberation data can now be provided to customers with stereological corrections included. Such corrections allow for the well-known observation (Jones, 1987) that data from twodimensional mounts may overestimate the levels of liberation of each mineral because a two-dimensional intersection of a particle may, by chance, occur in one mineral only, even if there is more than one mineral in the particle. This is a phenomenon which is often quoted in texts. The existence of this technical issue along with the cost of obtaining liberation data may be two reasons for the limited use generally made by industrial metallurgists of the type of data in the past. It can be argued that the two-dimensional data, ie uncorrected data remain useful for process analysis. In terms of technical purity, it is preferable to employ corrected liberation data. However, uncorrected two-dimensional data may be used with caution and with other checks to improve understanding of the process for the listed reasons. Firstly, in calculation of the recovery values for liberation based species in Table 5, there may be correction factors (a and b) needed to the flow rates in the numerator and denominator of the following equation: % Recovery = (a × flow rate in conc × 100) / (a × flow rate in conc + b × flow rate in tailing) In percentage terms, the magnitude of the correction factor (slightly less than or equal to 1) for the tailing flow rate (b) may differ from the correction factor for the concentrate flow rate (a), ie b does not equal a. However, because the direction of the correction must be the same for both the numerator and denominator, there is at least partial cancellation of the stereological effect. When the flow rate for the concentrate in the equation is very large compared to the flow rate for the tailing, the cancellation of the stereological effect is more complete. Secondly, if a metallurgist is suspicious of the flow rates in Table 5 provided by uncorrected liberation data, it is possible with care and patience to section a given set of particles in a briquette at various levels to obtain, for practical purposes, three-dimensional liberation data. Note that this step is a possibility for particularly unusual circumstances or when very high confidence is required in the liberation data. Thirdly, the liberation level (two-dimensional basis) for the valuable mineral(s) in a process feed is used to judge if the sizing of the feed is at a value where an acceptable separation could be expected. On a two-dimensional basis, the guidelines shown in Table 7 can be used in process engineering where the majority of the liberation is occurring in a grinding circuit at the start of the circuit, ie very little or no regrinding exists inside the circuit. Of course, obtaining a high level of liberation does not guarantee an efficient separation as the appropriate settings for the process variables must also be obtained. For an efficient froth flotation separation, both a high level of liberation and suitable settings for the physical and chemical variables in the process are needed.

Flotation Plant Optimisation

In porphyry copper circuits, liberation levels for the copper minerals may sometimes be less than 50 per cent in the rougher feed. However, the regrinding steps in the circuit must raise the liberation level of the copper minerals such that the guidelines in Table 7 are achieved for the recalculated feed (summation of the final concentrate(s) and tailing(s)). This applies to other circuits with major regrinding and liberation steps in the flotation circuit. TABLE 7 The maximum potential quality of separation possible at various liberation levels (two-dimensional data) for the feed or recalculated feed. Liberation level (%) (2D data) >80% 70 to 80% 4

0.25

2 to 4

0.50

Narrow

>d1) which is being sampled. Consider a chalcopyrite ore which has the following properties (fully liberated (l = 1) with a top size of 200 μm and containing two per cent chalcopyrite (a = 0.02)). The following calculations can be performed using the previously described method (Gy, 1982), where the density of the chalcopyrite is 4.2 g/ml and the density of the combined gangue is 2.6 g/ml, and assuming the fundamental error for chalcopyrite does not exceed 0.06 per cent chalcopyrite (sFSE = 0.0006).

Flotation Plant Optimisation

In collection of samples from a flotation circuit with several rounds of sampling and using conventional types of samplers, the resulting sample mass is usually unavoidably in the region of 500 g (or larger). Hence, as dictated by the use of conventional sampling devices in a flotation circuit, the sample mass tends to be in a region where the value for the fundamental error is at acceptable low values. To obtain an assay for a sample or a size fraction, a very small mass (typically 0.25 g to 1 g) has to be sampled from a much larger mass of dry solid in the laboratory. The fundamental error for this step can also be calculated using the equation from Gy (1982) as described earlier. If the fundamental error is unacceptably high, the sample or size fraction can be pulverised to lower the top size, and greatly lower the mass of sample providing an acceptable fundamental error. Of course, if a property is to be measured which is affected by size reduction (eg liberation state), this approach cannot be taken. For a particular operation, it is clearly more effective to obtain a plant feed sample from the flotation circuit feed, rather than the coarser grinding circuit feed or the even coarser crushing circuit feed. For a given sampling error, the minimum mass of the

Spectrum Series 16

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CHAPTER 2 – EXISTING METHODS FOR PROCESS ANALYSIS

required sample is much smaller for the flotation circuit feed and cost savings result from handling of the smaller sample, aside from the convenience. In collecting a sample, a large number of frequent correctly executed sampling events with collection of the same small sample weight in each sampling event is superior to a small number of infrequent correctly executed sampling events which produces the same final sample weight. Some additional sources of information on sampling principles can be accessed (Weiss, 1985; Birnbaum, 1992).

• The time taken for the sampler to intercept the concentrate

Lip sampling

For obtaining the solid flow rate, the details of the correct lip sampling procedure for a single cell are illustrated in Figure A1 and the equation for conversion of the measurements of the total mass of collected solid and the total sampling time (for all traverses on the various rounds of sampling) is provided. The total mass of collected solid divided by the total sampling time is effectively the observed flow rate of solid per unit width of the sampler. Movement of the sampler across the cell width at fixed velocity allows this value to be averaged across the entire concentrate flow. In the equation, the ratio lip width/cutter width then allows scaling up of the observed flow rate of solid per unit width of the sampler to the full width of the cell lip. To this point, all the discussion of lip sampling to obtain the solid flow rate has been based on movement of the lip sampler across the cell lip at right-angles at fixed speed as indicated in Figure A1. This movement of the sampler addresses any variations in concentrate assay and flow rate across the full width of the lip. For a cell in good mechanical condition, such variations are usually minimal. However, given the large size and shape of some cells, the existence of floor grating over the top of the cells, the design and maintenance of the cell lips or the existence of water pipes/sprays or other obstacles in the launder, it is not possible to move the lip sampler across the entire lip width or a portion of the lip. In this situation, an estimate of the observed flow rate of solid per unit width of the sampler can be obtained by placing the sampler in one or more fixed positions where a portion of the cell lip is accessible. The observed value can then be scaled up to the full length of the cell lip. Large tank cells can be one example of the described situation for several reasons:

There are various types of data which can be collected in the lip sampling procedure: 1.

a reliable sizing and assay of the solid being recovered at the lip,

2.

a reliable value for the per cent solid of the pulp being recovered at the lip, and

3.

an estimate of the solid flow rate passing over the lip.

To satisfy requirements 1 and 2, the sampler should be moved at right angles to the lip across the full width of the cell lip at constant speed to intercept the discharging froth. The speed should be selected to ensure that overflowing of the sampler is not possible and to ensure that uninhibited entry of the discharging froth into the sampler is possible during the sampling. Such lip samplers have typically the following dimensions: width 9 cm, height 30 cm and length 20 cm. The method was described by Restarick (1976). To satisfy requirement 3, the time for which the sampler was intercepting the stream has to be recorded. Therefore, the lip sampling procedure is performed using a crew of two people with one recording the sampling times. The following points can be noted:

• The requirements for the starting and finishing points in the movement of the lip sampler are illustrated in Figure A1. These starting and finishing points arise because of the requirement for determination of the solid flow rate per unit width of the sampler as expressed in Equation A1, ie the full width of the sampler must be collecting sample during all the timing period. (This requirement differs subtly from the correct sampling motion of starting and finishing the sampler’s motion outside the flowing concentrate.)

stream has to be approximately the same for each traverse to obtain reliable estimates of the solid flow rate.

• For a group of cells being sampled together, the time taken for the sampler to intercept the concentrate stream for each cell also has to be approximately the same for each traverse of each cell. Initially, all the cells in the grouping have to be considered in selection of the required time for the group of cells.

• the existence of relatively inaccessible external and internal launders and sometimes cross launders, and

• the existence of floor grating over the top of cells with

Lip Width

possibly some small trapdoors for access.

Cell

Cell Discharge Lip

Starting Position

Finishing Position

Cutter Width TPH Solid =

Total weight ( g ) 3600 Lip width (mm) × × Total time (sec) 10 6 Cutter width (mm)

(A1)

For sampling a single cell, the discharge of concentrate into the various types of launders may have to be treated as separate but parallel sampling steps for that cell. It is also worth noting that, depending on the overall sampling scheme, the objective from sampling a single unit cell may be a sample of the combined concentrate for analysis without the need for an estimate of the solid flow rate. While such an objective appears less onerous, timing of the concentrate collection with the sampler in various fixed positions may still be required. For example, taking a cell with one internal launder and one external launder, if the concentrate discharging to the internal launder happened to be at a higher flow rate per unit length of the lip than for the external launder, its assay may differ from the concentrate at an external launder for the same cell. To obtain the assay of the combined concentrate for the entire cell, two approaches could be taken: 1.

FIG A1 - Illustration of the lip sampling technique as described in the appendix for one cell. The lip sampler is positioned under the lip from which concentrate is discharging in this plan view.

62

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The same lip sampling time for the concentrate discharging into the internal and external launders could be used as the basis for a concentrate sample representing the entire concentrate.

Flotation Plant Optimisation

CHAPTER 2 – EXISTING METHODS FOR PROCESS ANALYSIS

2.

The assays for the solid at the internal and external launders along with the flow rate estimate of each could be used to calculate the assay for the combined concentrate. (Clearly, it is preferable that the plant designer provides a sampling point to enable sampling of the entire concentrate from all launders at a single point, to obtain the overall assay of the stream.)

It can be noted that timing and recording of the lip sampling times would assist in correct execution of approach 1 even though obtaining a value for the lip tonnage is not the objective. Further, timing and recording of the lip sampling times at the internal and external launders is an integral part of execution of approach 2.

REFERENCES Birnbaum, P M, 1992. An evaluation of sampling errors in a mineral concentrator, in Proceedings Sampling Practices in the Mineral Industry, pp 49-58 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Flotation Plant Optimisation

François-Bongarçon, D and Gy, P, 2002a. Critical aspects of sampling in mills and plants: A guide to understanding sampling audits, J S Afr Inst Min Metal, Nov/Dec, pp 481-484. François-Bongarçon, D and Gy, P, 2002b. The most common error in applying ‘Gy’s Formula’ in the theory of mineral sampling, and the history of the liberation factor, J S Afr Inst Min Metal, Nov/Dec, pp 475-479. Gy, P M, 1982. Sampling of Particulate Materials – Theory and Practice, second edition (Elsevier: Amsterdam). Holmes, R J, 1992. Sampling of mineral process streams, in Proceedings Sampling Practices in the Mineral Industry, pp 33-37 (The Australasian Institute of Mining and Metallurgy: Melbourne). Restarick, C J, 1976. Pulp sampling techniques for steady state assessment of mineral concentrators, in Proceedings Sampling Symposium, pp 161-168 (The Australasian Institute of Mining and Metallurgy: Melbourne). Weiss, N L, 1985. SME Mineral Processing Handbook, (Society of Mining Engineers, AIME: New York).

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CHAPTER 3

Mass Balancing Flotation Data Rob Morrison MAusIMM, Chief Technologist, Julius Kruttschnitt Mineral Research Centre, 40 Isles Road, Indooroopilly Qld 4068. Email: [email protected] Rob is currently Chief Technologist at the JKMRC with responsiblity for technical oversight of the research activities of the centre and for promoting the transfer of technology from research to commercial application. His experience includes operations and process development during four years at Bougainville Copper and plant design, construction and commissioning during six years with Fluor Daniel Australia. Rob managed JKTech for nine years. He led Program 2 of the Centre for Sustainable Resource Processing for its first two years. Rob was also the leader of the AMIRA Metal Accounting project P754, which developed a Code of Practice and a text book. Technical interests include energy efficient mineral processing, simulation, mass balancing and measurement techniques. Rob has published more than 80 technical papers, contributed to several text books and holds several patents.

Abstract Introduction Accuracy Considerations The Simplest Case The Method of ‘Mass Flow Errors’ An Analytical Solution Estimating the Accuracy of the Flow Split The Monte Carlo Approach Generating Numerically ‘Exact’ Data for Further Analysis A First Pass at a More General Solution Elements Versus Minerals Practical Application – Single Level Balancing Selection of Measurement Points Analysis of More Complex Circuits Multi-Dimensional Balances (Size by Assay) Size by Assay Example Recap Conclusions Acknowledgements References Further Reading Useful Websites

ABSTRACT A flotation circuit survey will typically produce a substantial volume of data – usually as metal assays and flow rates.

Flotation Plant Optimisation

In general, these measured data will not be consistent around any separation unit or junction within the circuit. A fair assessment of circuit performance requires a set of numerically consistent data. Otherwise key performance indicators (KPIs), such as recovery in each section, will

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CHAPTER 3 – MASS BALANCING FLOTATION DATA

depend of which measured values are chosen as the basis of the calculation. Generating a set of self consistent data provides a basis for a single set of KPIs. The set of self consistent data should in some way be a ‘best estimate’ of the state of the circuit during the survey. This chapter discusses strategies for selection of flow measurement and sampling points. Various ways of estimating measurement accuracy are considered. Lastly, some calculation methods are described. These are supported by some simple examples.

adjustments. However, this strategy does not take any account of how well (or badly) a measurement may be defined. The estimated or measured standard deviation σi provides us with an estimate of how well each piece of data is defined. Hence, a better criterion for minimisation is a sum of squares where each adjustment is divided (or weighted) by our estimate of the standard deviation of its associated measurement. SSQ = ∑ (Δ i )2 i

INTRODUCTION The basis of mass balancing is that all measurements are subject to statistical variation. If we could make each measurement (sample, assay or flow rate) many times, the results would have a spread of values. In practice, we can typically only afford to take a few replicate samples at each measurement point. If we have some knowledge of the degree of variation expected in each measurement, we can analyse all of the data together to try to find a best estimate of the mass balance. Data which is self consistent with this mass balance can be used to assess and compare performance and as the basis of mathematical models of the process. The mass balancing process can also incorporate redundant data to produce not only mass split factors but a further estimate of how well that mass split is defined. The ‘traditional’ approach, using a two product formula based on a single assay, will also produce an estimate of the mass split. However, it provides no estimate of the accuracy of that mass split and therefore provides at best a poor basis for decision-making. Note that these techniques are not at all new. The first general purpose system is due to Weigel (1972) who developed the original MATBAL code. This chapter focuses on how to attack the simpler cases using spreadsheet technology. The other key factor is that the flow sheet being balanced must be operating in reasonable ‘balance’ during the measurement period. That is, operating at as close as possible to steady state for both flow rates and separation processes. Otherwise the fundamental assumption that ‘what goes in is equal to what goes out’ is not justified.

Objectives • We wish to produce sets of self consistent data to suit a range of measurement strategies to characterise the performance of flotation circuit or a part of it, and

• we wish to generate estimates of the self consistency of the data and of the accuracy of the flow rate measurements. For the general case we can express these objectives in mathematical terms as three types of data:

• x i is a measurement of some sort – assay, flow rate, size fraction, liberated mineral fraction, whatever. These values are generally not self consistent.

• x ∗ is the true value of the measured quantity. We can i

•

estimate this value at various levels of accuracy but can never know it exactly. These values are self consistent. x$ i is an adjusted value of xi which satisfies all of the constraints – that is – is self consistent and is in some way a best estimate of the true value. Hence we can define an adjustment Δ i of each measurement as: Δ i = ( x i − x$ i )

The simplest way to find a ‘best’ set of adjusted data is to find strategy which minimises the sum of squares (SSQ) of the

66

The weighted sum of squares (WSSQ) is the sum of squares of the adjustments where ‘weighted’ means that the adjustment is scaled in terms of the expected variation of that data. ⎛Δ ⎞ WSSQ = ∑ ⎜ i ⎟ ⎝ σi⎠ i

2

It is also necessary that the adjusted values satisfy all flow sheet and summation constraints. That is, what goes in is equal to what comes out and the various kinds of assays and subassays add up to one or to the assay in the next level of measurements.

ACCURACY CONSIDERATIONS We can estimate the standard deviation (‘sd’ or error for short) σi from experience or from repeated sampling and assaying or repeated measurements against a known standard. In practise this means taking five to ten replicate samples at several key points within a circuit and subjecting all of them to the same sample preparation and assaying process which you intend to use in the actual test work. The formula for sampling variance or standard error then provides an estimate of standard deviation at each measurement point: σ 2x = ∑ (x i - x)2 / ( n − 1) i

x = ∑ x i / n – the mean of the n measurements. i

Strictly speaking, the standard deviation refers to the complete distribution (which we can never measure completely) while the standard error is the same property (the square root of the variance) of the sampling distribution – which we can measure. However, the two terms are often used interchangeably. There are some suggestions in the examples for sd estimation based on experience, but it is usually worth doing some repeatability testing to obtain actual estimates. In general this does not mean doing a full sampling tree (AS 28841 precision and bias of mineral sands measurement) to split the errors into their components. If you cannot reduce process and assaying variability to less than a few per cent (relative), there is very little point in carrying out detailed test work as the results will mean very little. If in general the measurement variations are small, then the required adjustments will also be small and be drawn from the same population of differences. Therefore, we expect the average value of ( x i − x i ) / σi to be about equal to one and, as a consequence, the WSSQ to be roughly similar to the number of measurements. However, each time we apply a flow sheet or a summation constraint we lose one degree of freedom. This reduces the expected value of the WSSQ by one. Hence we now have a quite general way of looking at data quality. If the WSSQ is of the same order as the number of measurements, our data is likely to be suitable for further analysis. A note of caution: if you have taken multiple data sets, a few of these may balance well by pure chance and still be nonsense.

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CHAPTER 3 – MASS BALANCING FLOTATION DATA

Balances which are self consistent by chance are rarely sensible in terms of other criteria such as the size by recovery response. The WSSQ can also be used to provide an estimate of the standard deviation of each calculated result x$ i. If a small change in x i (or of a flow rate estimate) causes a large change in the sum of squares, then x$ i is well defined. If it causes no change, then it is not defined at all. This property is particularly useful for checking whether calculated flow rates are well defined. The formal name for this rule is the ‘propagation of variance’. An alternative approach is to apply some artificial (random) variation to each measured value and solve the problem many times. This is called a Monte Carlo method. The variation in results provides an estimate of the variation which might be expected from a single experiment and analysis if repeated many times. This overall approach is usually called the ‘minimisation of weighted squared errors’ or simply ‘least squares’. If for some reason the measured values are drawn from a highly asymmetric probability distribution, outlying values may cause biases in the calculations. An alternative approach to finding x$ i is to use what are called ‘maximum likelihood methods’. For measurement and analysis of flotation data, the probability distributions are sufficiently symmetrical for least squares methods to be quite adequate.

THE SIMPLEST CASE The simplest case is also the most common and warrants quite extensive consideration. Consider a single separator (or node) which has a feed stream of flow rate A, a product stream of flow rate B and a reject stream of flow rate C.

A

For the simplest possible solution we would like to solve for a single variable and the best way to do this is to consider the flow split as the ratio of B/A flowing into product stream B – which we will call ‘beta’ or β. B* = β * A * and C * = (1 − β *) A ∗ 0 = ai∗ − β * bi∗ − (1 − β ∗ )ci∗ β* = ( ai∗ − ci∗ ) / ( bi∗ − ci∗ ) This equation for β* offers the useful insight that – even with perfect data – this method is not going to work for splitters where we can expect: ai = bi = ci to within measurement variation. For this case β* is undefined as zero/zero, which is not zero but undefined. Beware of flow split estimates which are only based on experimental noise. If the flow split is defined to any reasonable degree, then the splitter is functioning as some kind of separator – which is not usually desirable. This general approach also works for measured data and provides a useful way to do an initial evaluation of a set of data. We can set up the preliminary balance around our separator in MS Excel following the general structure shown in Table 1. A spreadsheet containing some real data from a section of a flotation circuit is shown in Table 2. TABLE 1 Example of a preliminary balance set up around the separator in MS Excel.

B

Feed assay

Product assay

Reject assay

A

B

C

(bi - ci)

Beta (ai - ci)/ (bi -ci )

Flows

C

Assayi

FIG 1 - The simplest case is a single node which represents any process with one input and two outputs.

Assay 1

'

'

'

Assay 2

'

'

'

This single node case might represent a complete flotation circuit or a single flotation cell. Each stream is sampled and measured for i assays. For stream A we have assays a1, a2 .. …an. For stream B we have assays b1, b2.. …bn and so on. Note that these assays may be any self consistent, additive property – size or specific gravity fractions can also be used. Per cent solids is not suitable as an assay but can be used if converted to per cent water. This is because per cent solids is based on the total stream flow of ore and water while the other assays are percentages of the solid phase only. We also have some knowledge of (by repeated measurements or experience) the standard deviations for flow rates (σA, σB, σC) and assays σa1, σb1, σc1 and so on. We could tackle the problem directly but there are advantages in considering flow splits first and then looking at assay data adjustment. For the ‘true’ data (designated by a *):

Assay 3

'

'

'

A ∗ = B ∗ + C ∗ and A ∗ ai∗ = B ∗ bi∗ + C ∗ ci∗ for all of i. where: A, B and C are the total solids flow rate in each stream ai, bi and ci refer to a series of assays in each of those streams

Flotation Plant Optimisation

(ai - ci)

… Assay n

From the measured flow rate of copper cleaner concentrate, the mass split to concentrate (beta) should be about one per cent. Note that 890 kg/h is not too difficult to measure as the flow is only about 15 kg/min. The estimates of mass split due to the change in each assay vary from 30 per cent to -66.7 per cent, but perfect data should generate identical values which would be the same as the perfect mass split. The calculated mass split based on the copper assays is almost exactly one per cent. The split based on the silver assay is 1.5 per cent. In each of these cases, the process strongly concentrates the mineral containing that element. Our estimate of beta is the ratio of two differences. If these differences are small compared with the accuracy of measurement, then the ratio will be poorly defined – as it is here. If the differences are large compared with the accuracy of sampling and assay, then the ratio should be well defined. This is almost certainly not the case for the lead assays, where both concentrate and tailing assays exceed the feed value.

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67

CHAPTER 3 – MASS BALANCING FLOTATION DATA

TABLE 2 Spreadsheet containing some real data from a section of a flotation circuit. Stream Measured

Float feed (A) t/h

Relative flow

Cu clnr conc (B) Cu rghr tail (C)

87.90

0.89

1

Beta

(1-Beta)

ai

bi

ci

(ai - ci)

Beta for each assay (bi - ci)

(ai - ci)/(bi - ci)

Measured

Pb (%)

4.02

4.07

4.04

-0.02

0.03

-0.667

Measured

Zn (%)

15.80

7.80

15.50

0.30

-7.70

-0.039

Measured

Cu (%)

0.43

22.40

0.20

0.23

22.20

0.010

Measured

Fe (%)

14.30

16.10

13.50

0.80

2.60

0.308

Measured

Au (g/t)

1.05

47.50

0.94

0.11

46.56

0.002

Measured

Ag (g/t)

142

3023

97

45.00

2926.00

0.015

It is also clear that zinc is being rejected from the concentrate and that the zinc grade of the tailings is apparently reduced as a result. A more reasonable possibility is that the zinc assay of the tails is higher than that in the feed, but our measurement accuracy is insufficient to demonstrate this effect. The absolute value of an assay is also important. One gram per tonne is 0.0001 per cent or one per cent is 10 000 ppm. Hence the silver assays are really 0.0142 per cent, 0.3032 per cent and 0.0097 per cent. The gold assays are two orders of magnitude smaller again and the mass split of 0.2 per cent is a reflection of good sampling and assaying at those concentrations.

Error models There are some useful generic ways to ‘estimate’ likely measurement errors based on assay magnitude. The most popular method is to assume a constant relative (or per cent) error. This approach implies that the best defined values would be the tailings assays for gold and silver and is plainly nonsense. The next commonly used approach is to assume that the expected error is constant or (usually) one. This simplifies the arithmetic and is a more sensible estimate. The larger assays are now assumed to have the smallest relative error. The JKMRC approach is to measure the error distribution through repeated sampling or to use a well-proven heuristic – that is – a rule which should behave in a sensible manner. This rule is often attributed to Bill Whiten – who disclaims ownership. We assume that for assays (or size fractions) in the per cent range that the minimum sd is 0.1 per cent (absolute) and that for assays greater than nine per cent the absolute sd is one per cent. In between those two limits, the sd is 0.1 plus 0.1 times the assay value. Hence, the relative error at a measured value of 0.1 per cent is 200 per cent. The relative error at an assay value of ten per cent is also ten per cent. At a measured value of 0.5 per cent, the absolute error is 0.1 plus 0.05 per cent or 30 per cent relative. Some people refer to this as a ‘two term’ error model where 0.1 is the fixed error and 0.1 is the fractional error between zero and nine per cent. Another term is a ‘one over x’ model because the relative error curve has much the same shape as that function. If the analysis method used is very different, we can expect the error models to change. For example, the fire assays typically used for precious metals should be intrinsically more accurate at ppm values than standard techniques such as XRF and AAs for

68

base metals in the per cent ranges would be at ppm values. The reason for this is that the assaying technique itself uses some preconcentration before measurement.

THE METHOD OF ‘MASS FLOW ERRORS’ If we switch to measured values in the component balance equation, we can expect a measured ‘mass flow error’ for each assay (or size fraction) measured: Δ i = ai − βbi − (1 − β )ci Note that only one β value is required for all of the n assays and that Δ i should be zero for perfect data. Hence, a process which makes a large difference to the stream assays will have a better defined flow split than one which only makes a small difference, such as a final cleaner or scavenger bank. Similarly if a splitter is working well, it is essential to measure or estimate its flow split as mass balancing will not be helpful. Transposing and simplifying we get for each component: Δ i = ( ai − ci ) − β ( bi − ci ) If we square both sides and sum up all of the components: SSQ = ∑ Δ2i = [( ai − ci ) − β ( bi − ci )]

2

i

We might reasonably expect the value of β, which minimises SSQ, to be a reasonable estimate of β* which we can call β. As for the first case, this can use a quite generic spreadsheet format as shown in Table 3. Set up this spreadsheet as shown in Table 4. Then work through it with estimates of β of 0, 0.005, 0.01, 0.02, 0.1, 1.0, as we know from the measured flow rate that the mass split is about one per cent. The gold assays have been divided by 100 and the silver assays by 1000 to bring them closer to per cent values. (As an exercise, check out the minima with the unadjusted values.) If your set-up is correct, the SSQ should go from 0.783 at 0.0 to 550 at 1.0 with a minimum value of 0.742 at 0.01. It is also a useful exercise to tabulate β and plot it against SSQ as shown in Figure 2. This graph shows a well-defined minima at β is approximately 0.01. It is well defined because making a small change (±0.005) in β makes a ±10 per cent change in the SSQ. However, it is necessary to plot the log of the SSQ to be able to see the minima. Go through the β sequence again and watch how the SSQ or (Δ i )2 for each assay varies. They do not all have a minima at the same value of β.

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CHAPTER 3 – MASS BALANCING FLOTATION DATA

TABLE 3 Generic structure of a spreadsheet balance around a single node using the method of mass flow errors. Estimated beta

Initial estimate Feed assay

Product assay

Reject assay

A

B

C

'

'

'

Measured

(ai - ci)

*(bi - ci)

i

i

2

Flows Assayi Assay 1 Assay 2

'

'

'

Assay 3

'

'

'

Assay 4 … Assay n Total

value of the flow split. In this case, there is little room for debate about the value of the flow split. In general, it will be more useful to derive an estimate of the standard deviation of the flow split error based on our measured standard deviations. This estimate can be used to ‘weight’ the contribution of each flow split error to the sum of squares which is to be minimised.

Log of SSQ

100

10 SSQ

Δi

1 0

0.05

0.1

0.15

0.2

0.25

0.3

Estimated Beta FIG 2 - Log of the sum of squared errors at a range of estimates of the mass split – beta.

2

0.0036

Measured

t/h

Relative flow

2

2

⎡ ∂Δ ⎤ ⎡ ∂Δ ⎤ ⎡ ∂Δ ⎤ σ 2Δ= ⎢ ⎥ ( σ 2a ) + ⎢ ⎥ ( σ 2b ) + ⎢ ⎥ ( σ 2c ) ⎣ ∂a ⎦ ⎣ ∂b ⎦ ⎣ ∂c ⎦ = σ 2a + β 2 σ b2 + (1 − β )2 σ c2

TABLE 4 An example of the method of mass flow errors.

Stream

σΔi = [ a i − βbi − (1 − β )ci ] σΔi

The rule for ‘propagation of variance’ is that the variance of a function is the sum of the product of the variance of each input parameter and the square of its partial derivative – see Deming (1938) or almost any statistics reference. Dropping the i for the moment:

0.1

Est beta =

SSQ =

If we add some additional columns to our spreadsheet, we can derive a weighted sum of squares WTDSSQ of the mass flow errors.

A

B

C

Float feed

Cu clnr conc

Cu rghr tail

87.90

0.89

TABLE 5

1.000

0.004

0.996

Delta

Additional columns required for Table 3 to include a weighted sum of squares.

ai

Bi

ci

ai - B* bi-(1-B) *ci

Delta squared a

Measured

Pb (%)

4.02

4.07

4.04

-0.020

0.000

Measured

Zn (%)

15.80

7.80

15.50

0.328

0.108

Measured

Cu (%)

0.43

22.40

0.20

0.149

0.022

Measured

Fe (%)

14.30

16.10

13.50

0.790

0.625

Measured

Au (g/t) 0.0105

0.475

0.0094

-0.012

0.000

Measured

Ag (g/t)

3.023

0.097

0.020

0.000

SSQ =

0.759

0.142

How should we decide which value of β to use? Obviously, the value which has the most accurately measured data should dominate. Let us first consider the case where each of the minima is quite similar. Clearly the weighting will have very little effect on the

Flotation Plant Optimisation

b

c

(1 - )2

Δ2i

WSSQ = Note: WSSQ = weighted sum of squares.

As before, run through in increments of 0.001 for β from 0.00 to 0.02 and watch how the minima change. For the first case, assume the sd of each assay is one. For the second case assume they are each five per cent of the assay value. For the third case, assume ten per cent. If your spreadsheet is right, the unit weighting case will look quite like the original but be driven by the larger assay values. For the second and third cases, the smallest assays will dominate. Neither seems very sensible and we will consider a better balanced approach in the section on error models.

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Arriving at a single numerical solution For the examples in MS Excel, the built-in minimiser called Solver provides a very simple solution. Designate SSQ (or WTDSSQ) as the target for minimisation and beta as the variable which can be adjusted. Run Solver. The result should be instantaneous.

The accuracy with which the flow split is defined depends on how rapidly the SSQ increases as we move away (in either direction) from the best fit value of beta. Once again from high school calculus, we recall that the curvature of a function is its second derivative: ∂SSQ = ∑ (( ai − ci )( b − ci )) − ∑ β ( bi − ci )2 ∂β i i

AN ANALYTICAL SOLUTION

∂ 2 SSQ = − ∑( bi − ci )2 ∂β 2 i

In the prehistoric days before PCs and Solver, a simple analytical solution was very useful. Recalling some high school calculus, if we wish to find the minimum (or maximum) of a function, we take the first derivative with respect to the variable of interest and set the result to zero. SSQ = ∑ [( ai − ci ) − β ( bi − ci )]

2

dSSQ = 2 ∑ i [( ai − ci ) − β ( bi − ci )]( bi − ci ) dβ 0=∑ i

[( a

i

β=

− ci )( bi − ci ) − β ( bi − ci ) i

i

]

i

2

i

i

THE MONTE CARLO APPROACH

∑ ( a − c )( b − c ) ∑ (b − c ) i

σ 2β = σ 2Δ ∑( bi − ci )2 In the Excel case, Solver does not provide this value for parameters but we can easily change beta by ±1 per cent and note the change on the sum of squares to test for a well-defined value.

i

2

Hence:

i

This is an interesting result. When ai = bi = ci, it is also undefined. The assays with the largest difference will dominate each sum. Hence the target of the separation process (for example, copper in a copper circuit) provides the best defined balance. As for the earlier cases, this approach is easy to set up in a spreadsheet. We already have columns of (ai - bi) and (bi - ci) in the first example. Hence we only need to add a column each for their product and the second term squared. Divide the sums of these columns for an analytical estimate of beta as shown in Table 6.

ESTIMATING THE ACCURACY OF THE FLOW SPLIT We can also estimate the variance of the residual errors at the best fit value of beta. σ 2Δ = ∑ Δ2i / ( n − 1) i

An alternative approach is to add some random variation to the input data, run Solver (or better our analytical formula) many times and consider the results as a mean and standard deviation for beta. There are some specialist add-ons for MS Excel for this purpose. However, for a simple case like this, a Monte Carlo investigation is not too difficult. You can set up the process as a ‘Macro’ (or a Visual Basic Application program) or set the spreadsheet to manual calculation and do a little manual accumulation. The latter is probably more useful for understanding the process. You can automate it with a macro as an exercise. We will use the same original data block and try the formula solution method. The Excel function RAND() draws a value from a calculated random distribution between zero and one. We can scale the range of values between ‘min’ and ‘max’ by multiplying by ((max-min) + min). This generates a uniform distribution of random values between min and max. However, what we actually need is a random set of variations drawn from a probability distribution similar to the distribution we were sampling by making measurements or taking samples. This is a little trickier than it sounds at first. If we consider the cumulative (or integral) form of any probability distribution, by definition, it will start at zero and end

TABLE 6 Spreadsheet balance including the analytical solution for the ‘best fit’ mass split. Data t/h

A

B

C

Flotation feed

Cu cleaner conc

Cu rougher tail

87.90

0.89

1

0.010

0.990

ai

bi

ci

(ai - ci)

Analytical

Estimate

(bi - ci)

(ai - ci)*(bi - ci)

(bi - ci)2

Pb (%)

4.02

4.07

4.04

-0.02

0.03

-0.001

0.001

Zn (%)

15.80

7.80

15.50

0.30

-7.70

-2.310

59.290

Cu (%)

0.43

22.40

0.20

0.23

22.20

5.106

492.840

Fe (%)

14.30

16.10

13.50

0.80

2.60

2.080

6.760

Au (g/t)/100

0.001

0.475

0.009

-0.01

0.47

-0.004

0.217

Ag (g/t)/1000

0.142

3.023

0.097

0.05

2.93

0.132

8.561

Sum

5.003

567.669

Beta

70

Spectrum Series 16

0.008813553

Flotation Plant Optimisation

CHAPTER 3 – MASS BALANCING FLOTATION DATA

at one. Hence we need the value of our cumulative distribution which corresponds to each random value between zero and one. This is the inverse of the probability distribution. This will work well most of the time but it is worth remembering that the normal distribution extends from negative to positive infinity. Most chemists will not accept this range of variation and will simply not report numbers which are statistically possible but not plausible. If we reduce the range of possible random values to say 0.025 to 0.975, then the inverse values will lie between plus and minus two standard deviations of the mean value. To test out this process, set up four blocks of similar structure as shown in Table 7. The first one is the measured data block. The second one is the block of estimated standard deviations. The third one is our scaled random number. The last one is the block of perturbed data which we can use to rerun our balance (and other calculations) to generate an estimated range of variation. Each time the sheet is executed (press F9 to force a recalculation), this process will generate an equally likely ‘plausible’ set of synthetic data, which our formula will then solve for beta.

After each run, jot down resulting beta. If you edit the spreadsheet, it will generate another value unless you switch to manual recalculation (Tools/Options/Manual Recalculation). In addition to the scaled RAND() function, you will need to use the INVNORMAL (inverse x, mean of x and sd) function to generate a deviation to add to the measured value. An example is shown in Table 7. Do as many runs as you like – but no less than ten. Now use the mean and sd functions (MEAN(Range) and STDEV(Range)) with your row of β values as the argument. If the mean is very $ there is a problem in the different from your original β, spreadsheet. The sd of the synthetic betas provides an estimate of the sd of the calculated beta. Some mass balance programs only provide this way of estimating how well the balance is defined for the balanced flow rates.

GENERATING NUMERICALLY ‘EXACT’ DATA FOR FURTHER ANALYSIS Given that we now have estimates of the flow split and its accuracy, we can consider various ways to generate an ‘exact’ data set.

TABLE 7 Spreadsheet example of a Monte Carlo analysis. Measured

Data

Stream Measured

t/h

Relative flow

A

B

C

Flotation feed

Cu cleaner conc

Cu rougher tail

87.90

0.89

1

0.010

ai

bi

ci

0.990

Measured

Pb (%)

4.02

4.07

4.04

Measured

Zn (%)

15.80

7.80

15.50

Measured

Cu (%)

0.43

22.40

0.20

Measured

Fe (%)

14.30

16.10

13.50

Measured

Au (g/t)/100

0.001

0.475

0.009

Measured

Ag (g/t)/1000

0.142

3.023

0.097

Standard deviation

Model

Stream Standard deviations

t/h

A

B

C

Flotation feed

Cu cleaner conc

Cu rougher tail

4.40

0.04

ai

bi

ci

5%

Standard deviations

Pb (%)

0.50

0.51

0.50

0.1 +10%

Or 1 if > 9

Standard deviations

Zn (%)

1.00

0.88

1.00

0.1 +10%

Or 1 if > 9

Standard deviations

Cu (%)

0.14

1.00

0.12

0.1 +10%

Or 1 if > 9 Or 1 if > 9

Standard deviations

Fe (%)

1.00

1.00

1.00

0.1 +10%

Standard deviations

Au (g/t)/100

0.050

0.050

0.050

0.05

Random values

RAND – min

0.025

RAND – max

0.975

0.008713

A

B

C

Flotation feed

Cu cleaner conc

Cu rougher tail

0.25

0.28

Est beta = Stream Measured Synthetic

t/h Pb (%)

ai

bi

Ci

0.47

0.30

0.84

Synthetic

Zn (%)

0.44

0.94

0.82

Synthetic

Cu (%)

0.79

0.84

0.97

Synthetic

Fe (%)

0.07

0.54

0.53

Synthetic

Au (g/t)/100

0.70

0.12

0.80

Synthetic

Ag (g/t)/1000

0.95

0.06

0.41

Flotation Plant Optimisation

Spectrum Series 16

71

CHAPTER 3 – MASS BALANCING FLOTATION DATA

TABLE 7 cont … Synthetic

Data

Stream

A

B

C

Flotation feed Cu cleaner conc Cu rougher tail

Measured

t/h

80.67

0.90

ai

bi

Analytical

Estimate (bi - ci)2

ci

(ai - ci)

(bi - ci)

(ai - ci)*(bi - ci)

Synthetic

Pb (%)

3.51

3.54

3.61

-0.10

-0.07

0.008

0.006

Synthetic

Zn (%)

15.13

9.12

16.04

-0.91

-6.92

6.277

47.819

Synthetic

Cu (%)

0.37

22.19

0.17

0.20

22.02

4.403

484.766

Synthetic

Fe (%)

13.13

16.24

12.57

0.56

3.67

2.060

13.460

Synthetic

Au (g/t)/100

0.02

0.52

0.00

0.02

0.52

0.010

0.267

Synthetic

Ag (g/t)/1000

0.18

2.98

0.11

0.07

2.87

0.207

8.243

Sum

12.964

554.560

Beta

Reconstitution If the flow split is well defined, adding the reject and concentrate together in the flow split ratio has much to recommend it. If the weighted sum estimate of the feed assays is within ±1 standard deviations of the feed measurement, this realisation will be quite adequate for further analysis. In practice, we can insert a single column to the right of the feed column and add β times the concentrate plus (1 - β) times the tailing assay. Note that the summation constraints are satisfied. TABLE 8 A self consistent data set generated by reconstituting products at the best fit mass split. Data

A Flotation feed

t/h Beta

Reconstituted feed

B

C

Cu cleaner conc

Cu rougher tail

87.90

0.89

1

0.0088

0.991

ai

bi

ci

4.07

4.04

Pb (%)

4.02

4.040

Zn (%)

15.80

15.432

7.80

15.50

Cu (%)

0.43

0.396

22.40

0.20

Fe (%)

14.30

13.523

16.10

13.50

Au (g/t)/100

0.001

0.014

0.475

0.009

Ag (g/t)/1000

0.142

0.123

3.023

0.097

0.023377

The mathematically preferred approach is to minimise the required adjustment in some way – and the sum of squares is a good general approach. Let Δa, Δb and Δc be the minimum adjustments and omit the i – as we can consider each assay as a separate case. Our adjusted data must balance if: 0 = ( a i − Δ a ) − β ( b − Δ b ) − (1 − β)( c − Δ c ) And be subject to the constraint that: Δ = Δ a − βΔ b − (1 − β )Δ c SSQ = (Δ a )2 + (Δ b )2 + (Δ c )2 We can use a Lagrange multiplier λ to impose the constraint by setting the constraint equation to zero and adding it to the SSQ. This is called a ‘modified’ sum of squares. We then minimise each adjustment and λ as well. SSQ = (Δ a )2 + (Δ b )2 + (Δ c )2 − 2λ ( −Δ + Δ a − βΔb − (1 − β) Δ c ) Then: ∂SSQ = 2Δa − 2 λ = 0 ∂Δ a ∂SSQ = 2βΔb + 2 λβ = 0 ∂Δ b ∂SSQ = 2Δc + 2 λ(1 − β) = 0 ∂Δ c ∂SSQ = 2( −Δ + Δa − βΔb - (1 - β) Δc) = 0 ∂λ We can drop all of the ‘2’s:

This strategy has the advantage that two thirds of our numbers are exactly the ones that we measured.

Δa = λ Δb = −βλ

Data adjustment Persons of a statistical bent will favour least squares adjustment of all of the assays. This does lead us back towards the general case, so it is useful as an exercise. We can start with the unit weighted case. Recall that:

and substitute into the last equation: β = λ + β 2 λ + (1 − β)2 λ Or:

Δ i = ai − βbi − (1 − β )ci If we want an exact solution, we need some strategy to apportion Δi across the measured assays. Strictly speaking, we $ However, as we are going should use the best fit value of beta – β. to do a combined minimisation a little later using β$ it is probably confusing. Some possible simple solutions are to divide delta by three or to proportion delta according to the flow in each stream.

72

Δc = −(1 − β )λ

λ = Δ / (1 + β 2 + (1 + β)2 ) As we already know the value of β and Δ for each assay, we can easily calculate a set of adjustments. For this case, the adjustment is proportional to the flow of that component (assay) in each stream. Table 9 shows the adjusted data and a check that it actually does add up.

Spectrum Series 16

Flotation Plant Optimisation

CHAPTER 3 – MASS BALANCING FLOTATION DATA

TABLE 9 A self consistent set of adjusted data generated by minimising the sum of squares of the required adjustments. Beta

0.008813553

A

Stream

B

C

1.982528

Flotation feed Cu cleaner conc Cu rougher tail

Measured

t/h

Relative flow

87.90

0.89

1

0.010

0.990

aI

bi

ci

Delta

Lambda

Check

Beta

Delta

Check

Adjusted

Pb (%)

4.03

4.07

4.03

-0.0203

-0.01

0

0.008814

Adjusted

Zn (%)

15.61

7.80

15.68

0.3679

0.19

0

0.008814

Adjusted

Cu (%)

0.41

22.40

0.22

0.0343

0.02

0

0.008814

Adjusted

Fe (%)

13.91

16.10

13.89

0.7771

0.39

0

0.008814

Adjusted

Au (g/t)/100

0.01

0.47

0.003

-0.0125

-0.01

0

0.008814

Adjusted

Ag (g/t)/1000

0.13

3.02

0.11

0.0192

0.01

0

0.008814

As before, we know β and the sd for each assay. Each set of assays has its own Lagrange multiplier – as shown in Table 10. The adjustments which are shown are based on the sd estimates provided in the Monte Carlo example. Assuming there is a reasonable quantity of gangue, the total assay summation constraint can be satisfied by difference for each stream. That is, work out the assays of interest and calculate the gangue by subtraction from 100 per cent. It is interesting to note that even though the Lagrange multipliers have changed considerably; the adjusted data is essentially identical with the unweighted case. If there were real differences in the estimated flow splits (not simply measurement noise), the assay with the smallest relative sds would dominate the flow split. A note on Lagrange multipliers: these are named after their inventor. Possibly a more instructive name would be ‘unknown’ multipliers. We are seeking a solution where each of the first derivatives is equal to zero and the required constraints are also satisfied. Hence the multiplier is always one result from a set of simultaneous equations. The technique is very unusual in that it is easier to use than to understand intuitively. See Boas (1966) for a clear and detailed explanation.

Examining the adjusted values for lead and zinc shows that in this case it would be very difficult to distinguish the likely change in the tailings assays as a result of the concentrate assays – that is – the difference imposed by the process. By way of contrast, copper, iron and silver are all changed significantly. If we wish to scale each adjustment by its own standard deviation, the solution is quite similar (subject to the same constraints as before): WSSQ = (Δa / σa )2 + (Δb / σb )2 + (Δc / σc )2 ∂WSSQ = 2Δa / σa − 2 λ = 0 or Δa + λσa ∂Δ a ∂WSSQ 2Δb = + 2 λβ = 0 or Δb + λβσb ∂Δ b σb ∂WSSQ 2Δc = + 2(1 − β )λ = 0 ∂Δ c σc ∂WSSQ = 2( −Δ − Δa − βΔb − (1 − β )Δc ) ∂λ Δa = λσa Δb = −βλσb Δc = (1 − β )λσc

A FIRST PASS AT A MORE GENERAL SOLUTION

Δ = λσ a + β λσ b + (1 − β) λσ 2 2

2

We can also see from the above analysis that a single flow split generates a full set of weighted assay adjustments.

λ = Δ /( σ a + β 2 σ b + (1 − β)2 σ c )

TABLE 10 A self consistent set of adjusted data generated by minimising the sum of squares of the adjustments weighted by the SD estimates from the Monte Carlo example. Beta

0.010778355

Stream Measured

t/h

A

B

C

Flotation feed

Cu cleaner conc

Cu rougher tail

87.90

0.89

1

0.010

0.990

Check

Beta

ai

bi

ci

Delta

Lambda

Delta

Check

Pb (%)

4.03

4.07

4.03

-0.0203

-0.02

0

0.010778

Weighted adj

Zn (%)

15.61

7.80

15.69

0.3830

0.19

0

0.010778

Weighted adj

Cu (%)

0.44

22.40

0.20

-0.0093

-0.04

0

0.010778

Weighted adj

Fe (%)

13.91

16.10

13.89

0.7720

0.39

0

0.010778

Relative flow Weighted adjustment

Weighted adj

Au (g/t)/100

0.01

0.47

0.003

-0.0134

-0.14

0

0.010778

Weighted adj

Ag (g/t)/1000

0.14

3.02

0.10

0.0135

0.14

0

0.010778

Flotation Plant Optimisation

Spectrum Series 16

73

CHAPTER 3 – MASS BALANCING FLOTATION DATA

In this case, we might consider converting the copper to chalcopyrite and the remaining iron to pyrite or phyrrhotite. However, this task is left as an exercise. In some cases, such as several species of copper minerals or a variable Zn:Fe ratio in sphalerite, quantitative mineralogy will become essential – each elemental assay will generate a flow split estimate but they will not define mineral behaviour.

The analytical solution is more complex and requires two steps to get to an answer. However, if we make the weighted sum of squares for all assays the minimisation objective for Solver and let Solver adjust the value of the flow split, we can achieve a simple version of the general solution. If you also have measured flow rates and estimates of their sds, they can easily be added to this solution. The weighted sum of squares of assay adjustments plus flow rate adjustments now becomes the objective to minimise. For this data set, the results are shown below. The flow split estimate changes from 0.0088 to 0.0108 and the weighted SSQ changes from 0.5138 to 0.5124. Whether either change represents a ‘genuine’ improvement is not a very useful debate. For reasonably self consistent data, the results of each of these methods will be very similar. For less well-defined data, the results will be dominated by the assays with the largest differences (usually what the circuit is trying to separate) and the smallest standard deviations.

PRACTICAL APPLICATION – SINGLE LEVEL BALANCING Now that the various approaches to balances have been covered, we can consider some common cases before starting on multilevel balances. Typical strategies for data collection are:

ELEMENTS VERSUS MINERALS

1.

the complete circuit;

2.

block level, eg cleaners or scavengers;

3.

bank level – combined feed, concentrate(s) and reject; and

4.

down-the-bank data.

Case 1 – The complete circuit can usually be considered as a single two product separator. There will often be metal accounting samplers available. Flow rates will often be known – at least for the circuit feed rate – from a (hopefully) wellcalibrated weightometer. Because the complete circuit maximises the differences in assays, the balance should be well defined. If it is not, it will be essential to refine your sampling and assaying techniques before attempting more detailed test work. Case 2 – Block level will often be covered by the two product case. However, it is worth reviewing the feed, rougher, scavenger case as it is also very common.

The flotation process will usually be dependent on mineral composition not assay composition. If an element appears only in one mineral, it will not matter if you use elements or minerals. For example, lead is often only present in galena. Many other cases are not so clear cut. For example, iron can be present in chalcopyrite, pyrite, phyrrhotite and iron silicates – or in varying proportions in sphalerite. If we have consistent assay ratios, we can convert our assays into equivalent minerals and use the mineral assays for balancing. This will often give results which are better defined and easier to understand – and are more suitable for modelling.

TABLE 11 A mass balance that combines the search for the best fit mass split with the minimised weighted assay adjustments. Adjusted

Beta

Weighted

Stream

Data

Measured

0.0107783

A

B

C

Flotation feed Cu cleaner conc Cu rougher tail t/h

87.90

0.89

ai

Bi

ci

Delta

Lambda

Delta

Pb (%)

4.03

4.07

4.03

-0.0203

-0.02

0

Pb (%)

Wtd adj

Zn (%)

Wtd adj

Zn (%)

15.61

7.80

15.69

0.3830

0.19

0

Cu (%)

Wtd adj

Cu (%)

0.44

22.40

0.20

-0.0093

-0.04

0

Fe (%)

Wtd adj

Fe (%)

13.91

16.10

13.89

0.7720

0.39

0

Au (g/t)

Wtd adj

Au (g/t)/100

0.01

0.47

0.003

-0.0134

-0.14

0

Ag (g/t)

Wtd adj

Ag (g/t)/1000

0.14

3.02

0.10

0.0135

0.14

0

A

B

C

Adjustments Stream Measured

Flotation feed Cu cleaner conc Cu rougher tail t/h

87.90

0.89

ai

bi

Weighted ci

SSQ 0.0008

Pb (%)

Wtd adj

Pb (%)

-0.02

0.000

0.02

Zn (%)

Wtd adj

Zn (%)

0.19

-0.002

-0.19

0.0741

Cu (%)

Wtd adj

Cu (%)

-0.04

0.000

0.04

0.0025

Fe (%)

Wtd adj

Fe (%)

0.39

-0.004

-0.39

0.3012

Au (g/t)

Wtd adj

Au (g/t)/100

-0.14

0.001

0.13

0.0361

Ag (g/t)

Wtd adj

Ag (g/t)/1000

0.14

-0.001

74

Spectrum Series 16

-0.13

0.0366

WTDSSQ

0.4514

Flotation Plant Optimisation

CHAPTER 3 – MASS BALANCING FLOTATION DATA

This case comes in two versions – one with four samples and one with five. Each case does have an analytical solution but they can also be set up as mass flow errors in each component for a straightforward solution in MS Excel. For the first case we only have one node. We retain the idea that beta is the flow split into stream B and add gamma for the flow split into stream C, as shown in Figure 3:

That is, minimise the modified sum of squares: SSQ + 2 λ 1 (Δ1 − Δa − βΔb − (1 − β )Δe) 2 λ 2 (Δ 2 − (1 − β ) Δe − (1 − β − γ )Δd − γΔc ) ∂SSQ / ∂Δa = 2Δa − 2λ 1 = 0 / ∂Δb = 2Δb − 2λ 1β = 0 / ∂Δc = 2Δc + λ 2 2 γ = 0

Δ i = ai − βbi − γci − (1 − β − γ)di

/ ∂Δd = 2Δd − 2λ 1 (1 − β − γ) = 0

SSQ = ∑ Δ i

/ ∂Δe = 2Δe − 2λ 2 (1 − β) = 0

2

i

A

E

We can express λ 2 in terms of λ 1 :

D

λ 2 = (Δe − λ 1 (1 − β )) / (1 − β ) λ 2 = Δe / (1 − β ) − λ 1

C

B

FIG 3 - A two node, rougher scavenger circuit.

As stream E is not measured for this case, we can use Solver to find ‘best fit’ values of β and γ. Similarly, we can use Solver to find the minimum squared data adjustments subject to the condition that the adjusted data add up to zero at the specified values of β and γ. As before, the adjustments can be weighted by their estimated standard deviations. However, tackling the complete problem in Solver will rapidly exceed the maximum number of constraints available with the add-in version. Various expanded versions are available for purchase. Note: 1. 2.

and calculate both Lagrange multipliers. This gives a direct solution for each adjustment. As before we can extend this to a direct solution of the minimum sum of squared adjustments or of weighted squared adjustments. The following set of data in Table 12 can be used as an exercise. TABLE 12 Measured assay data for the circuit shown in Figure 3. Stream

ID

Pb (%)

Zn (%)

Cu (%)

Fe (%)

Meas assay

Meas assay

Meas assay

Meas assay

Pb rougher feed

A

11.89

24.02

0.25

11.14

Pb rougher conc

B

20.20

30.10

0.31

9.10 13.50

You will need at least two independent assays to solve this balance at all as there are two unknowns.

Pb rougher tail

E

1.25

16.60

0.16

Pb scavenger conc

C

8.20

39.80

0.37

11.70

If stream C is a middlings stream with similar composition to the feed stream, the flow rate in stream C is not defined. Almost any flow measurement estimate (including a ‘calibrated eyeball’) will be more useful than the result of the balance.

Pb scavenger tail

D

0.51

14.60

0.14

13.70

For the second configuration (in which E is measured) there are two separations or nodes. Hence we need two error equations: Δ1i = ai − βbi − (1 − β)ei Δ2 i = (1 − β)ei − γci − (1 − β − γ)di

[

SSQ = ∑ (Δ1i )2 + (Δ2 i )2 i

]

This case is also quite straightforward to set up for Solver – with or without weighting the errors. As before, if your data is accurate and self consistent, there is much to recommend simple reconstitution to generate a self consistent set of data for further analysis. However, it is also fairly straightforward to do a least squares adjustment one assay at a time. We will work through the second case as it has two constraints. For each value of i, we wish to minimise:

Case 3 – The ‘simplest case’ considered earlier is applicable to bank level sampling and analysis for combined feed, concentrate and reject. A more detailed case is considered in the next case. Case 4 – Down-the-bank data – For a more detailed analysis, we may wish to sample the froth from each cell. We can either take samples of the product of each cell and a pulp sample between each cell or take timed lip samples of each concentrate and a feed and a tailings sample. Hopefully a combined concentrate will also be available. This problem provides a different kind of constraint. We have an estimate of the ratios of the flow rate from each cell but we do not know the total flow rate. We may or may not know the total assay of the concentrate. An analytical solution for this multiconcentrate plus each cell tail was developed by the author and published in Chapter 7 of Lynch (1977). It is outlined in Figure 4. The data from that example are shown in Table 13.

A1

SSQ = Δa 2 + Δb 2 + Δc 2 + Δd 2 + Δe 2

A2

B1

A3

B2

A4

B3

A5

B4

subject to: Δ1 = Δa − βΔb − (1 − β) Δe

B5

and: Δ 2 = (1 − β) Δe − γΔc − (1 − β − γ) Δd

Flotation Plant Optimisation

FIG 4 - A typical ‘Down-the-bank’ equivalent circuit for detailed sampling (after Lynch, 1977, Figure 7.8).

Spectrum Series 16

75

CHAPTER 3 – MASS BALANCING FLOTATION DATA

TABLE 13 Measured assay data for the circuit shown in Figure 4 (after Lynch, 1977, Table 7-IV) . A1

A2

A3

A4

A5

B1

B2

B3

B4

B5

Copper

3.03

1.0

1.15

0.75

0.52

21.2

22.5

17.1

9.7

15.5

Iron

8.2

7.1

6.4

6.0

5.7

23.8

25.9

23.4

20.2

21.4

Sulfur

6.5

5.3

4.4

3.8

3.3

26.5

29.2

25.9

20.8

23.0

Insoluble

46.6

49.0

51.0

51.8

52.8

14.4

11.4

18.4

27.6

21.6

The flow ratios to A2, A3 can be designated as alpha 2, alpha 3 and so on. The solution is a somewhat complicated matrix inversion: 0 ⎤ ⎡α 2 ⎤ ⎡x 1 ⎤ ⎡m11 m12 0 ⎢m21 m22 m23 0 ⎥ ⎢α 3 ⎥ ⎢ 0 ⎥ ⎢ ⎥⋅ ⎢ ⎥ = ⎢ ⎥ ⎢ 0 m 32 m 33 m 34 ⎥ ⎢α 4 ⎥ ⎢ 0 ⎥ ⎢⎣ 0 0 m43 m44 ⎥⎦ ⎢⎣α 5 ⎥⎦ ⎢⎣x 4 ⎥⎦ Each of the ‘m’ and ‘x’ terms is a sum of differences of assays. When a circuit reaches this level of complexity, it is recommended that the user switch to a more general approach or to a commercial package. The flow ratio case is better suited to a numerical approach. If we have measured flow rates, fi, f2 →fm we can assume that they will be related to the total functional flow rate by some ratio ρ. Hence our node equation becomes: Δ1 = a − βb − (1 − β )c Δ2 = βb − ρ( f1 conc1 + f2 conc2 + f3 conc3 KK ) or if we cannot measure b, we simply substitute: ⎛ ⎞ ρ ⎜ ∑ f j conc j ⎟ * for βb ⎝ j ⎠ In either case, we are solving the original problem for the flow weighted average of the concentrate assays and this will usually be a good first step to see if the lip sample data are reasonably self-consistent. If they are, weighted addition and reconciliation should be adequate for further analysis. Alternatively, a similar constrained least squares adjustment can be used – either weighted or unweighted.

TABLE 14 Connection matrix for the circuit shown in Figure 4. Note that ‘B’ streams are numbered 6 to 10 and zeros are omitted for clarity. Nodes 1 2

Now that we have considered a range of flow sheets, we can deduce some useful rules. If we wish to use assays to define flow splits, we need to use either very accurate sampling and assaying or survey around a separation process (or a series of separations), which will make a large difference to the assays. Hence the flow split around a rougher section or a complete circuit will usually be well defined by feed, product and tailing assays. Conversely, the flow split across cleaner and scavenger sections (and splitters!) will often be poorly defined by those assays. For all of these cases, flow measurements are essential. There is usually a good case for sampling and flow measurement across a complete circuit – even though the study objective may only be measurement of a single section.

ANALYSIS OF MORE COMPLEX CIRCUITS The methods which have been described so far can also be applied to more complex circuits.

Streams 1

2

1

-1 1

3

SELECTION OF MEASUREMENT POINTS

76

At this point, it is also worth commenting that several flow sheet mass balancers (using these principles) are available commercially (JKSimMet, JKMBal, JKSimFloat, MATBAL, BilMat). Some web sites which provide more detail are referenced at the end of this chapter. For more complex flow sheets, an ‘off the shelf’ solution has much to recommend it – lest all the time available for data analysis be spent trying to manufacture a balance. A useful compromise is a spreadsheet offered by Luttrell (2004). It is also possible to use a general purpose, constrained minimisation routine to solve the general problem, but the sheer numbers of adjustments and constraints make this an ineffective approach. Dividing the problem into flow rates estimation followed by assay adjustment makes it much more tractable. However, we do need samples and assays from all streams to be able to use this approach. The most important step towards a general solution is to convert the measurement flow sheet into a connection matrix. A connection matrix usually counts streams in columns and nodes in rows. Where a stream flows into a node, the matrix value is set to +1. Where a stream flows out of a node, the value is -1. All other values are set to zero. Table 14 is for the multi-concentrate example shown in Figure 4. ‘B’ streams are set in order at six to ten and the zeros are omitted for clarity.

3

6

-1

7

8

9

10

-1 -1 1

5

5

-1 1

4

4

-1 -1

-1 1

1

1

1

-1

The advantage of this approach is that we can use matrix arithmetic to express flow component errors and constraints in quite general (and very compact) fashion. If we have a vector of calculated flow rates where f1 is the flow in stream 1 and so on, then any self consistent set of flow rates must satisfy: [C ].[ f ] = [ 0 ] where: C

is the connection matrix for the flow sheet

Similarly, each assay times its stream flow rate times the relevant stream/node entry in the connection matrix will generate a vector of mass flow errors. Hence we can call [C i ] a connection matrix where each row is multiplied by assay type i, then:

Spectrum Series 16

[C i ]. f = Δ i for each assay i

Flotation Plant Optimisation

CHAPTER 3 – MASS BALANCING FLOTATION DATA

TABLE 15 Product of the Connection Matrix (Table 14) and the copper assay matrix. Nodes

Streams 1

2

3

4

1

3.03

-1

0

0

2

0

1

-1.15

0

3

0

0

1.15

4

0

0

5

0

0

5

6

7

8

9

10

-21.2

0

0

0

0

0

0

-22.5

0

0

0

-0.75

0

0

0

-17.1

0

0

0

0.75

-0.52

0

0

0

-9.7

0

0

0

0

21.2

22.5

17.1

9.7

-15.5

0

As MS Excel has a built-in function for matrix multiplication, it is straightforward to set up a spreadsheet to define constraints and the SSQ of mass flow errors for each assay type. The product of the Connection Matrix (Table 14) and the copper assay matrix is shown in Table 15. The best fit solution for all flows (based on f1 = 100) is shown with the copper SSQ.

TABLE 18 Best fit flow rate and constraint residuals around each node of the balance. The residuals are effectively zero. Flows

Estimates

Matrix product

1

100

-3.7E-14

2

93.13985

6.35E-14

3

90.13671

-1.5E-14

TABLE 16

4

88.13768

-2.1E-14

Best fit flow rate solution for all flows (based on f1 =100) is shown with the copper SSQ.

5

84.63477

1.78E-15

6

6.860148

Estimates

Matrix product

SQD

7

3.003143

1

100

64.4250163

4150.58

8

1.999028

2

93.13985

-78.0880874

6097.74

9

3.502911

10

15.36523

Flows

3

90.13671

3.37058247

11.3608

4

88.13768

-11.8850601

141.254

5

84.63477

43.0064029

1849.5

6

6.860148

7

3.003143

SSQ

8

1.999028

12250.5

9

3.502911

10

15.36523

MULTI-DIMENSIONAL BALANCES (SIZE BY ASSAY)

The best fit flow rates can be based on any one or any combination of assays by including its SSQ in the target for Solver to minimise. Weighting and sensitivity estimates can be added in much the same way as for the single node case. Once the best fit flow rates have been established, we can use a similar strategy to find each set of data adjustments. In this case, the adjustments become the parameters for Solver, the SSQ of the adjustments is the target for minimisation and our connection matrix multiplied by the flow rate of the selected component must be constrained to zero. The results for copper are shown in Table 17 – followed by the constraints in Table 18 – which are near enough to zero.

For detailed performance analysis, size by assay (or size by mineral) measurements will often be of interest as particle composition (and degree of liberation) and size underlie flotation performance. A major problem is that the coarse end of the size distribution is often in short supply. This makes accurate assaying or mineralogical measurement difficult. To overcome this problem, you can take multiple composite assays or simply wet screen some additional sample cuts to obtain a substantial mass of ‘coarse end’ sample. The definition of ‘coarse’ will vary with different circuits. Larger than the 90 per cent passing size is usually a reasonable definition. The first test for size by assay data is to see if it is self consistent within the sample itself. To do this, simply add the assays for each size fraction weighted by the mass fraction for each size fraction and see if the total assay resembles the measured total assay for that stream. If it does not, your sampling and analysis methods need to be examined in detail.

TABLE 17 Comparison of adjusted and measured copper assay data. Stream

1

2

3

4

5

6

7

8

9

10

Adjusted

-0.091

0.664

-0.166

-0.125

-0.250

-0.949

-0.437

-0.287

-0.498

2.139

Adjusted squared

0.008

0.440

0.028

0.016

0.062

0.900

0.191

0.082

0.248

4.576

Adjusted Cu

2.939

1.664

0.984

0.625

0.270

20.251

22.063

16.813

9.202

17.639

Measured

3.030

1.000

1.150

0.750

0.520

21.200

22.500

17.100

9.700

15.500

Total

SSQ

6.552

Flotation Plant Optimisation

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77

CHAPTER 3 – MASS BALANCING FLOTATION DATA

Assuming that the weighted sum of the fractional assays does agree reasonably with the measured total assays, we can now do a beta estimate for each total assay and each size fraction using the formula developed in the section ‘Accuracy Considerations’ or by using Solver as in the section ‘The Simplest Case’. As detailed in the section ‘Estimating the Accuracy of the Flow Split’, we can reconstitute product and reject in the mass split ratio to generate a feed stream which is exactly self consistent with the products. This strategy may require a little more explanation. After the best fit mass split (beta) has been estimated, convert the product into component flow rates by multiplying the concentrate size fraction by each assay (and the gangue fraction as 100 – sum of all assays). Do the same for the reject using (1 – the flow split) and add each component to generate each size fraction of the reconstituted feed. Next divide the assay component flows in each size fraction by the fraction total to convert them back to assays. As in our earlier example, if the reconstituted results are reasonably similar to the measured, the reconstituted results will usually be suitable for recovery calculations and modelling. A more quantitative way to check is too see if the reconstituted size fractions and assays are within the expected variation of the measured feed data. As in the simpler one-dimensional case, two thirds of the measured numbers are included in the data set for analysis. For this many data points, a plot of measured (x) against reconstituted (y) is a quick visual check for agreement. The data is from the example shown in Table 19. There are many more sophisticated approaches but they will not help very much with poor data – other than to spread the problems across the data set and make them more difficult to identify. Note that for diagnostic purposes, you can do a balance for each within each size fraction to see if the mass split within each size fraction is self consistent. The mass split calculated this way

100.00 Pb Zn Cu Fe

10.00

0.10

1.00 1.00

10.00

100.00

0.10

FIG 5 - Parity graph comparing measured total assays for each metal in each stream with those based on reconstitution of the assays for each size fraction of each stream.

should be close to the mass split in the size fraction, which is the concentrate size fraction multiplied by the overall mass split divided by the feed size fraction. There are a range of mathematically complex ways to approach the general case (Hodouin and Everel, 1980; Gay, 1999).

SIZE BY ASSAY EXAMPLE As noted in the previous section, a good place to start is to check the reconstituted size fraction assays against the measured total assay for each stream. Table 19 shows measured sizes, total assays and assays reconstituted from size fraction assays based on samples taken from a zinc circuit. Table 19 also shows mass split calculations for each total component and for each group of totals based on the formula developed earlier. The total assays and the reconstituted assays

TABLE 19 Measured sizes, total assays and assays reconstituted from size fraction assays based on samples taken from zinc circuit. Measured data Sizing

A

B

C

Wt %

Wt %

Wt % ai - ci

bi - ci

Beta

(ai - ci) * (bi - ci)

(bi - c-)2

+75

20.85

11.87

18.48

2.36

-6.61

-0.3571

-15.623

43.746

+53

12.46

15.73

8.58

3.88

7.16

0.5424

27.770

51.197

+38

11.53

14.22

7.07

4.46

7.15

0.6242

31.910

51.124

-38

55.17

58.18

65.87

-10.71

-7.69

1.3920

Totals

82.343

59.155

126.400

205.222

Pb

0.59

1.19

0.39

0.20

0.80

0.2438

0.156

0.640

Zn

15.34

59.41

0.86

14.48

58.55

0.2472

847.511

3428.103

Cu

0.15

0.29

0.10

0.05

0.19

0.2368

0.009

0.036

Fe

13.70

5.38

16.44

-2.74

-11.06

0.2477

30.304

122.324

Rem

70.24

33.73

82.21

-11.98

-48.48

0.2470

580.548

2350.310

1458.528

5901.413

Pb

0.71

1.49

0.41

0.30

1.08

0.2801

0.326

1.163

Zn

15.43

57.50

1.10

14.32

56.40

0.2540

807.833

3180.405

Recon totals

Cu Fe Remainder

0.14

0.34

0.12

0.02

0.22

0.0861

0.004

0.047

13.97

5.14

15.81

-1.84

-10.67

0.1729

19.668

113.755

69.75

35.53

82.55

-12.80

-47.02

0.2722 Overall

78

Spectrum Series 16

Beta bar

0.616

0.247

601.971

2211.343

1429.802

5506.712

0.260

3014.731

11613.34

0.260

Flotation Plant Optimisation

CHAPTER 3 – MASS BALANCING FLOTATION DATA

space but it is very important to ensure that the calculated data are complete and self consistent with respect to size and assays. Note that the ‘remainder’ assays are calculated by subtracting the measured assays from 100 per cent. This removes a substantial number of constraints from the solution. The weighting factor is (1 + β 2 + (1 − β )2 ) as derived earlier. The fully weighted case can be used in exactly the same way at the expense of more complexity. For example, a beta value of 0.15963 gives a weighting factor of 1.73169. The corresponding table of adjustments is shown in Table 23. We can now generate a complete set of data adjustments within each size fraction (weighted or not). To link the size fractions together and tie back to the total assays it is important to realise that the mass split within each size fraction has to be identical for the size fraction based calculation and the assay based calculations. Hence, we can multiply each feed size fraction by that mass to generate a set of concentrate flows and by one minus that split to generate a set of tailings size fraction flows and then convert the flow back to size distributions. This strategy makes another set of constraints implicit. The last constraint can be imposed by calculating one of the feed size fractions (usually the fines) by difference. We can use the other feed size fractions and each of the size fraction split factors as a set of parameters to minimise the total SSQ for all of the sets of data. One way to set this up is shown in Table 24. The parameters to minimise are identified in bold font as are the adjusted total assays. This approach is somewhat tedious to set up but does provide a very detailed view of the data. For example, the problem with the tailings size distribution identified earlier is now very clear. That set of sizing data contributes more than half the SSQ. We can

are quite consistent and indicate a mass split to concentrate of about 25 per cent. However, the splits based on size fractions are not consistent with each other or the assay estimates. It would be useful to investigate whether all of the size fractions are likely in error or a particular one is at fault. We can investigate by applying the 25 per cent split to the concentrate size distribution and the 75 per cent split to the tails. This generates mass flows of 2.97 and 13.86 respectively. The mass split within each size fraction can be estimated from the assays within that size fraction. Table 20 estimates the +75 micron mass split as 0.144, which gives flow rates of 3.00 and 17.85 respectively. This simple analysis suggests that the feed and concentrate are consistent with the assay split but the tailings are not. Hence investigating the collection and sample preparation for the tailings stream would be a good idea before doing more test work.

Size by assay balance Each size fraction can be thought of as a separate process (provided we use the same set of sieves) and we can apply the strategies developed earlier to investigate self consistency and to find a minimum SSQ of assay adjustments. Table 21 shows an example for the +75 micron samples. There is quite a bit of scatter but the split for zinc is very well defined – as might be expected. The next size fraction (Table 21) contains a little more mass, a lot more particles and is much more self consistent. The minimum data adjustment strategy is equally applicable. Tables 20 and 21 show how to set this up for one size fraction. Note the check sums in both directions. They do take up some

TABLE 20 Assay mass balance within the +75 micron size fraction. Mass splits in size fractions Measured data Sizing

A

B

C

Wt %

Wt %

Wt%

+75

Component ai - ci

bi - ci

Beta

ai - ci * bi - ci

(bi - c-)2

Pb

0.60

1.30

0.40

0.20

0.90

0.222

0.180

0.810

Zn

8.90

55.20

1.50

7.40

53.70

0.138

397.380

2883.690

Cu

0.17

0.30

0.18

-0.02

0.12

-0.125

-0.002

0.014

Fe

7.90

5.00

7.60

0.30

-2.60

-0.115

-0.780

6.760

Rem

82.44

38.20

90.32

-7.88

-52.12

0.151

410.966

2716.494

Fraction total

807.7444

5607.768

Beta bar

0.144040

ai - ci * bi - ci

(bi - c-)2

TABLE 21 Assay mass balance within the +53 micron size fraction. Measured data Sizing

A

B

C

Wt %

Wt %

Wt%

+53

Component ai - ci

bi - ci

Beta

Pb

0.65

1.00

0.50

0.15

0.50

0.300

0.075

0.250

Zn

18.3

59.00

1.30

17.00

57.70

0.295

980.900

3329.290

Cu

0.23

0.35

0.20

0.03

0.15

0.200

0.005

0.023

Fe

17.8

4.80

25.40

-7.60

-20.60

0.369

156.560

424.360

Rem

63.02

34.85

72.60

-9.58

-37.75

0.254

361.645

1425.063

100

100

100

Fraction total

Flotation Plant Optimisation

Spectrum Series 16

1499.184

5178.985

Beta bar

0.289474

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CHAPTER 3 – MASS BALANCING FLOTATION DATA

TABLE 22 Adjusted assays for the +75 micron size fraction. Adjusted

A

B

C

Sizing

Wt %

Wt %

Wt%

Exp

+75

Check

Delta

Lambda

Sum 0.000

Pb

0.57

1.31

0.43

0.06

0.03

Zn

9.58

55.09

0.93

-1.17

-0.68

0.000

Cu

0.18

0.30

0.16

-0.03

-0.02

0.000

Fe

7.49

5.07

7.95

0.72

0.41

0.000

Remainder

82.18

38.24

90.53

0.44

0.25

0.000

Fraction total

100.00

100.00

100.00

TABLE 23 Assay adjustments for the +75 micron size fraction. SSQ

A

B

C

Wt %

Wt %

Wt %

Pb

0.03

-0.01

-0.03

0.00

Zn

-0.68

0.11

0.57

0.79

Cu

-0.02

0.00

0.02

0.00

Fe

0.41

-0.07

-0.35

0.30

Remainder

0.25

-0.04

-0.21

0.11

SSQ

1.20

Sizing

Delta

+75

SSQ

Fraction total

TABLE 24 A simple spreadsheet strategy for a complete size by assay balance. Calc size Flows

A

B

C

Wt %

Flow

Flow

B

Adj A

C

Wt %

Wt %

Adj B

Adj C

+75 fit

18.89

3.02

15.87

11.81

21.31

+53 fit

13.05

3.74

9.31

14.63

12.50

+38 fit

12.08

3.76

8.31

14.74

11.16

-38

55.99

15.01

40.98

58.82

55.02

Totals

100.00

25.53

74.47

100.00

100.00

Adjusted

Assays

Size

Splits

Beta 75

0.15963

Beta 53

0.28631

Beta 38

0.31148

Beta-38

0.26814

Recon

Flows

A

Pb

69.76

38.14

B

C

31.62

0.698

1.494

0.425

Zn

1553.57

Cu

16.84

1468.72

84.85

15.536

57.540

1.139

8.54

8.30

0.168

0.334

0.111

Fe

1379.62

133.11

1246.51

13.796

5.215

16.737

Rem

6980.21

904.03

6076.18

69.802

35.417

81.587

Totals

10000.0

2552.54

7447.46

100.00

100.00

100.00

omit that contribution and reminimise to see how much the results change. As might be expected, the changes are mostly in the tailings size distribution but they are not very large. Hence either set of data would be similarly useful.

80

However, it does suggest that taking samples optimised for equi-probable selection is essential for this kind of work. That means cutting through the stream to be sampled – and avoiding any kind of dip sampling.

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Flotation Plant Optimisation

CHAPTER 3 – MASS BALANCING FLOTATION DATA

RECAP The suggested analysis sequence follows the order of the chapter. Run a check around each node using the method of mass flow errors detailed in earlier sections ‘The Simplest Case’ and ‘The Method of Mass Flow Errors’. The formulae derived in the sections ‘An Analytical Solution’ and ‘Estimating the Accuracy of the Flow Split’ are useful for a quick check on the flow split and how well it is defined. Where the data are very different in magnitude (ppm and per cent assays), it is usually worth using weighted least squares for both the flow split and the data adjustments. If the required data adjustments are large (more than ten per cent of the measurement) for more than a few of the measurements, redo the experiment. The total weighted sum of squares should always be of the same order as the number of measurements, node by node or across a complete circuit. Hence it is worth examining each total by node and for each set of assays. If the adjustments are small, there is a lot to be said for reconstituting concentrate and tailings to generate a set of self consistent data – at least two thirds of your numbers will be the ones you measured. Once you have checked each node for self consistency, you can continue on to the multinode balancing strategies outlined in the section on ‘Practical Application – Single Level Balancing’. However, as the circuit becomes more complex, it is well worth considering a commercial product. The single node checks will often pinpoint measurement problems which may be concealed by doing the complete balance first. Some commercial systems (such as JKSimMet) will let you select each node – or a broader subset of the flow sheet – for a check balance. Plotting measured data against adjusted data is a way of compressing a lot of data into a single graph. It is also an excellent way of detecting bias. If all of the small assays are adjusted upwards, there is likely a problem with low assay analyses. For more complex data, such as size by assay or size by mineral, the same guidelines apply. Consider the balance around each node with each size fraction before progressing on to total assay balances across the circuit and then total size by assay balances across the circuit. It is usually a poor strategy to attack the complete problem from the start as least squares balancing can spread a single wrongly measured (or transcribed) piece of data across the complete set. Such errors are much easier to identify and weed out in single node slices. Keeping backup splits of samples allows for reassaying of dubious values when the rest of the set are self consistent. For mineral based analysis (MLA or Q*S) be aware of the number of particles or sections which contribute to your measurement. Low number errors follow the Poisson distribution and even 100 sections will have a relative sd of ten per cent. Overall, try to use a systematic approach, starting at the node level and working across the circuit as you test each data point for its actual contribution to the balance. While we may never be able to know the ‘true’ value, careful measurement and analysis will produce data which can provide a sound basis for flotation modelling and for decision-making.

CONCLUSIONS The techniques outlined in this chapter provide a reasonably simple yet quite powerful approach to analysis of flotation data. Using a spreadsheet for the process avoids capital outlay but like all spreadsheet activity requires extreme care in checking and including checks on constraints. While setting up these

Flotation Plant Optimisation

spreadsheets is a good way to learn about the analysis process, they will not generally transfer between users. Hence, for shared use – or anything at all complex – investing in one of the commercial, flow sheet based products has much to recommend it. Their web sites are listed at the end of this chapter. Compared with even a very optimistic estimate of the true cost of professional labour, the cost of commercially available mass balancing systems is really very reasonable. A few days of time saved would pay for most of them. Unless you are quite an expert user, building your own spreadsheets for more than the single node cases is a high-risk endeavour. Using someone else’s spreadsheet is an excellent way to generate a misleading analysis as the subsequent users do not know what modifications have been made by others. If you are obliged to use a spreadsheet, the author strongly recommends that you also use it to generate checks for self consistency of your calculated or adjusted data and graphs of all measured and adjusted data. The well documented and secured spreadsheet offered by Luttrell (2004) may be a workable compromise in some cases as it should not be subject to unauthorised and undocumented ‘improvements’.

ACKNOWLEDGEMENTS Except as otherwise noted the data used for the examples in this chapter were provided by Dr Chris Greet. The author gratefully acknowledges permission granted by the Elsevier Scientific Publishing Company to reproduce Figure 7.7 and Table 7-IV from Lynch (1977).

REFERENCES Boas, M L, 1966. Mathematical Methods in the Physical Sciences (Wiley). Deming, W E, 1938. Statistical Adjustment of Data (Dover). Gay, S L, 1999. Avoiding the zero-flow solution in mass-balance equations, Transactions of the Institutions of Mining and Metallurgy, Mineral Processing and Extractive Metallurgy, 108:C121-126. Hodouin, D and Everel, M D, 1980. A hierarchical procedure for adjustment and material balancing of mineral processing data, International Journal of Mineral Processing, 7:91-116. Luttrell, G H, 2004. Reconciliation of excess circuit data using spreadsheet tools, Coal Preparation, 24:35-52. Lynch, A J, 1977. Mineral Crushing and Grinding Circuits, 340 p (Elsevier: Amsterdam). Wiegel, R L, 1972. Advances in mineral processing material balances, Canadian Metallurgical Quarterly, 11:413-419.

FURTHER READING Montgery, D C, Runger, G C and Hubele, N F, 2000. Engineering Statistics, second edition (Wiley). Morrison, R D, 1991. Material balance techniques, Evaluation and Opitmization of Metallurgical Performance, pp 209-218 (AIME: Denver). Morrison, R D (Ed), 2008. An Introduction to Metal Balancing and Reconciliation (Julius Kruttschnitt Mineral Research Centre: Brisbane). Morrison, R D and Richardson, J M, 1991. JKMBal – The mass balancing system, in Proceedings Second Canadian Conference on Computer Applications for the Mineral Industry (CAMI ‘91), vol 1, pp 275-286, Vancouver, September. Wills, B A and Napier-Munn, T J, 2006. Mineral Processing Technology, chapter 3 and associated spreadsheet examples (Elsevier).

USEFUL WEB SITES For JKSimMet, JKMBal, JKSimFloat: . For BilMat and MATBAL: . Email: [email protected] to request a copy of the spreadsheet mass balancer.

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CHAPTER 4

A Practical Guide to Some Aspects of Mineralogy that Affect Flotation Alan Butcher Strategic Marketing Manager, FEI Company, PO Box 2269, Milton Qld 4064. Email: [email protected] Alan R Butcher has over 29 years international experience as a field geologist, igneous petrologist, isotope geochemist and applied mineralogist. His professional career has spanned the entire spectrum from undergraduate and postgraduate teaching, to pure and applied research and consulting, and now commercialisation of technology. He is best known for his enthusiastic evangelism and visionary development of new and emerging capabilities in the field of Automated Mineralogy. Alan is a Fellow of the Geological Society of London.

Abstract Introduction Background to Ore Deposits Basic Ore Textures The Concept of Liberation A Review of Mineralogical Methods Available Application of Mineralogy to Flotation Example Case Studies Concluding Remarks References

ABSTRACT This chapter is designed to introduce some of the basic aspects of mineralogy that can influence flotation behaviour, with particular emphasis on sulfide flotation. The minerals industry has recently celebrated 100 years since the introduction of flotation, and we have had cause to reflect on the many and varied developments in chemical reagents and flotation cell technologies during this period, yet it is only more recently that the role of mineralogy has been realised as another important component in the better understanding of the flotation separation process. Most of the information required by mineral processing engineers involved in flotation can now be provided by geologists and mineralogists using well-established optical, X-ray, laser and electron-microbeam technologies. Metallurgically-relevant observations for flotation processing applications can be made at any time during the life of a mine, from first exploration drill core, which can flag-up problematic minerals and textures, through start-up phases to full production, which can allow fine tuning of a concentrator to produce acceptable grades and recovery. Finally, mineralogy can be used to optimise recycling and/or disposal of tailings during the mine closure phase.

Flotation Plant Optimisation

An understanding of the geological context, mineral assemblage, and textures of an ore is absolutely key to understanding its potential amenability to the flotation process. Equally important is the measurement of sizes, composition, locking and liberation, and flotation behaviour of particles as they pass through a circuit from blasting, crushing, grinding, flotation to final concentration, using the appropriate mineralogical techniques. This chapter will review the many and varied mineralogical techniques currently available, and will guide the reader through when and where to use them. Examples will be drawn from case studies which illustrate how mineralogy has allowed better understanding and improvement in the flotation process on a range of ore types.

INTRODUCTION An understanding of the geological context, mineral assemblage, and texture of an ore is absolutely key to efficient and effective unlocking and concentration of ore minerals during blasting, crushing, grinding and flotation. Whilst this opening statement might appear somewhat obvious to an experienced process

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mineralogist, it is seldom appreciated by geologists, let alone by mining and minerals engineers. Let us explore why this is so. The reasons for this are not always clear, or even logical, but experience has shown that it is due in part to one or more of the following factors:

• Historical: in the past, only mining of high-grade ores or

easy-to-process ores was practised and, generally speaking, these did not require strong geological input. In fact, in some of the early mines, a geologist, let alone a mineralogist, may not even have been on staff.

• Managerial: mineralogy is typically only considered and

commissioned during the exploration, feasibility and start-up stages, as part of due diligence exercises. It is not that common for a mine manager to agree to regular mineralogical audits once an operation is up and running, except of course when grade and recovery drop below unacceptable limits. Also, mining geologists rarely make it to mine manager level where they can influence behaviour patterns in such matters.

quick inspection of the ore by a mineralogist can immediately establish if the copper is deporting to the usual phases (say sulfides), at the same grain size (which affects grind size), and in the same host gangue (which affects flotation conditions) as the production ore. If conditions are the same, fine. If they have changed, you could have saved yourself a lot of expensive experimentation, not to mention embarrassment. Mineral processing plants process minerals, and for mostly practical reasons, it is accepted that conditions are often based on chemical assays rather than on mineralogical information. Hopefully, your opinion on the use of mineralogy will change after reading through this chapter.

BACKGROUND TO ORE DEPOSITS It is necessary at this point to introduce a number of technical terms commonly used to describe ore deposits, the minerals which make them up, and the textures which affect processing, all with special reference to flotation behaviour.

• Financial: there is real perception (which is also sometimes

Basic classification of deposit types

Of course, the modern mining industry is quite different to that in the past. Gone are the days where one could choose to mine only the near surface, high-grade, easy-to-process ores. With volatile metal prices, heightened expectations from shareholders, and unprecedented industrial growth from China and India, the race is on to extract as much from the Earth to keep up with demand. This must of course take place in a world where the awareness of human safety and the environmental footprint of mining are coming under ever-increasing scrutiny. All of these factors are challenging the viability of companies and mining operations every day as we move to a world where mining lower-grade, more-difficult-to-process resources will be the norm. Given that our mantra as professionals involved in the Earth Resources industry could be to ‘Take apart what Mother Nature has put together. Safely … with due regard for the Environment … and Economically’, we really need to make effective use of all the armoury available to us to succeed in this combat exercise. The science of mineralogy, and in particular that area of mineralogy which is dedicated to the application of mineralogical information to mineral processing and smelting in order to improve understanding, solve problems and improve efficiency of extraction, commonly referred to as Process Mineralogy, is one such effective weapon in our mining armoury which we can draw on. There is no doubt that process mineralogy, when used judiciously, can make a major difference to a mining operation. In the author’s opinion, this was first brought to the world’s attention in a seminal paper by Henley (1983), although many others followed shortly after that (Hiemestra, 1984; Petruk, 1984; Baum et al, 1989). A text book has recently appeared by Petruk which attempts to pull together his life’s experiences as a process mineralogist and is a good source of case studies (Petruk, 2000). Before we move on, let us consider a hypothetical, but typical situation, which hopefully will keep the sceptics interested and the novices alert. The situation involves an ore type from the Eureka Concentrator. It needs investigating because it is new. Routine assaying by the geologists in the mine suggests this ore type contains a three weight per cent copper head grade, similar to all existing production ores. The temptation is to go ahead, mine and crush the ore, and hope for the best. You might be lucky. But a

Believe it or not, it is helpful to know the geological context of a mine, especially where mineralogical work is required to be carried out. This is undoubtedly satisfying from an intellectual viewpoint. But more importantly, geologists need to do this all the time so that they can conjure up a mental 3D image of the deposit on which they are working. It helps us see things to scale, in some cases, put things back in order of formation and ultimately allows us to rationalise and categorise the apparent anarchy we find in nature. Ores are no different to any other rocks – they simply have an economic value and are defined as a mineral or aggregate of minerals that form a rock which can be mined at a profit. They can therefore be classified, like everything else in Earth Sciences, into conveniently simplified categories. There are classifications that are based on simple criteria, such as the minerals or metals contained (Pb-Zn; Cu-Au; PGM, etc). Better still, we can describe the structure of the deposit in terms of its shape or size (basin, pluton, diatreme, vein, fault, etc), its relationship to the host rocks, and the rocks which enclose or contain the deposit (eg stratabound, stratiform, volcanic-hosted, sedimentary-hosted, etc). Of less use, is to classify a deposit according to the geological processes which combined to form the deposit (or genesis). Why? Because most deposits are old, some very old, and whose formation has not been witnessed by geologists today. We therefore have to rely on interpretation alone, and given that there is considerable debate among geologists as to the exact mode of formation of most mineral deposits, this is not a good classification in isolation. So, in summary, it is best to stick to features which can be agreed on, such as the physical description of the deposit. And even though no two mineral deposits are exactly alike, most of them fall into a clear category. Each category often conveniently coincides with a generally accepted hypothesis as to how the mineral deposit formed. So we typically end up with a physically descriptive classification that includes a descriptor of how the deposit formed. Once one understands that certain ore types produce distinctive mineral assemblages and textures (and geologists are trained to know this), then it is easier to focus on issues that are of specific interest. Figures 1 and 2 summarise some of the basic ore deposit types and structures likely to be encountered by the professional minerals engineer. For a more thorough review, the interested reader is referred to Guilbert et al 1986; Evans, 1993; Roberts and Shehan, 1988; Eckstrand, 1984; Peters, 1978 and McKinstry, 1948.

based on truth) that mineralogy is costly, requires expensive equipment, and involves highly qualified personnel who write not particularly timely and relevant reports, which are all too often full of jargon, and serve only to alienate the very audience for which they were intended.

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Equigranular

following texts for further details: Petruk, 2000; Craig and Vaughan, 1994, and an excellent web-based atlas (Ixer and Duller, 1998). Of particular interest to flotation are the following basic types of textures. Starting at the most basic level (Figure 3), an ore texture can be evaluated as to whether it is equigranular or inequigranular. Milling strategies for the two extreme ores will be quite different.

Inequigranular

FIG 1 - Summary diagram illustrating the main types of ore deposit, classified according to mode of origin, host-rock and commodity, with real examples.

Mineralisation

Stratiform Stratabound

Ore mineral Vein-hosted Fault-hosted

• Exploration methods • Mining method • Sampling Strategies

Disseminated Replacement

FIG 2 - Cartoons to illustrate how the geological structure of an orebody controls how you explore for it, how you mine it and how you sample it. Here six typical types are presented. Black is mineral or ore of interest. No scale (after Butcher and Trudu, 1999).

Take, for example, the deposit on which Eureka Mine is positioned. We know at the most basic level that it is a polymetallic sulfide ore, and is mined underground. Armed with just this information, an experienced geologist and process mineralogist can mentally map this to be most likely a sediment-hosted, volcanogenic massive sulfide deposit, with an economic mineral assemblage of sphalerite (Zn), galena (Pb), chalcopyrite (Cu). With more information (such as age, geographic locality, geological model, tectonic history, historical company reports), a mental checklist can be immediately created, and forms the basis on which the mineralogist starts his or her campaign. It may include the following: look for oxidation effects of sulfides; watch for grain size reduction if metamorphosed; look for talc if sheared; check for more than one type of sphalerite; etc. More on this later on in the chapter.

BASIC ORE TEXTURES Once the macro-features (km-m) of an ore deposit have been established, it is then necessary to concentrate on the meso(m-cm) and micro-features (cm-mm-μm). It is at these scales we start to gain valuable insights into which minerals make up the ore and how they all fit together to form what is known as the texture. This is the area of study known as petrography. A comprehensive study of ore deposit textures is beyond the scope of this chapter but the interested reader is referred to the

Flotation Plant Optimisation

FIG 3 - Cartoons to illustrate the basics of ore textures, with special reference to flotation. At the simplest level, ores can be considered either equigranular (all grains same size) or inequigranular (not all same size). The mineral of interest is shown in black. Grain boundaries are straight or gently curved. No scale.

On a more complex level (Figure 4), it is crucial to ascertain how the economic minerals occur: if they are present as rims, disseminated inclusions (or exsolutions), or as interstitial phases – as this will control breakage mechanisms during blasting, crushing and grinding (intragranular versus intergranular), and will make it either relatively easy, or difficult (or impossible) to liberate and float effectively. It is not uncommon for an ore to have multiple textural deportments for the element of particular interest (see Figure 5). Finally, and for completeness, a further concept is now introduced. It was mentioned above that orebodies are generally contained within old rocks. Practically, this means that they have been around long enough to experience post-formation modification, which can take one of many forms (metamorphism, deformation, oxidation and weathering, to name a few). Sometimes these so-called secondary processes can overprint or obliterate those that developed at the time the deposit formed (so-called primary features). Metamorphism, for example, is generally bad news for the metallurgist as it often involves growth of new (and unwanted) minerals (such as mica, talc, graphite, serpentine, etc), which have an annoying habit of floating along with the ore minerals to contaminate the concentrate. Deformation can lead to fracturing of the ore, recrystallisation and grain-size reduction, which can change the comminution behaviour of an ore in a negative way (production of slimes). Oxidation and weathering, however, can be both good and bad for a minerals engineer – it can either upgrade (laterites, gossans) or downgrade (silcretes, calcretes and regoliths) the ore depending on which process is dominant. Figure 6 attempts to simplify what is obviously a very complex concept. The main point being made here is that it is the job of the process mineralogist to: firstly, identify the presence of these

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processes; then unravel them; and finally, understand how each one may impact on the physical and chemical processing of the ore under investigation, and report these results in a clear, easy to understand and practical way to the metallurgist.

THE CONCEPT OF LIBERATION Rims

Interstitial

Exsolved

Now that we have revealed that ore deposits form in different ways, and that resulting mineral assemblages and ore textures, to a large extent, reflect that heritage, we need to briefly review what we mean by liberation from a mineralogical perspective.

Inclusions

Disseminated

Laminated

FIG 4 - Further cartoons illustrating complex ore textures, with special reference to those which affect liberation and flotation performance. Mineral of economic interest shown in black. No scale.

FIG 5 - One major outcome of a textural analysis of an ore is to ascertain the deportment of elements of economic interest. In this case, the element of interest, shown in black (say copper) occurs as: chalcopyrite intergrown with pyrite (upper left); chalcopyrite blebs included within sphalerite (upper right); discrete native copper (centre); chalcocite rimming pyrite (bottom left); bornite inclusions within silicate (bottom right); and native copper within a cross-cutting vein (bottom left to top right). Scale: width 10 100 microns (after Butcher and Trudu, 1999).

FIG 6 - Cartoon illustrating some of the processes which are known to affect ores after initial formation. The fate of three pristine ore textures is considered (one equigranular and two inequigranular), which undergo progressively more aggressive modification from left to right (oxidation, hydrothermal alteration to metamorphism). The job of the process mineralogist is to identify the presence of these processes, unravel them and understand how each one may impact on the physical and chemical processing of the ore under investigation.

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This is quite important as mineralogists often get asked to provide an estimate of liberation or to estimate optimal grind sizes in their reports. Liberation is best studied, estimated and quantified in mineral agglomerates (rock particles). Particles are typically examined in 2D sections, and this is best achieved by setting them in epoxy resin blocks and exposing their cross-sectional geometry by combinations of cutting, grinding and polishing. Examination of images of particles allows for the classification of each particle in terms of whether it is ‘pure’, ‘barren’ or ‘locked’. This classification of particles is based on the volume of the mineral of interest in each particle. The concept can be illustrated with a cartoon in the same idealised format as we have seen previously. Figure 7 shows how a complexly-textured ore (as viewed, for example, in thinsection), and one that is essentially equigranular, starts to liberate the mineral of interest at particle diameters of around 70 microns. We will now see below that the degree of liberation can be quantified using a variety of optical and SEM-based image analysis techniques.

FIG 7 - Cartoon illustrating the effect of particle size reduction and increasing liberation from a complex, equigranular, ore texture, where the mineral of economic interest is shown in black. Note that even the finest particle sizes still contain locked particles.

For a complete background to the theory of liberation, please refer to Barbery (1991), and for further background on how automated SEM-images can be used to derive knowledge of particle behaviour in processing, see Sutherland et al, 1988; Sutherland, Wilkie and Johnson, 1989; Spencer and Sutherland, 2000.

A REVIEW OF MINERALOGICAL METHODS AVAILABLE There are a bewildering number of techniques available to determine the mineralogical and metallurgical behaviour of particles (of differing sizes) as they pass through a mineral processing circuit from blasting, crushing, grinding and flotation through to final concentration and disposal, in terms of their particle size and shape, composition, locking and liberation characteristics and flotation behaviour. The following is an essential guide to the main techniques, which briefly covers each technique and provides when-andwhere-to-use-it advice.

Hand-specimen analysis Every self-respecting geologist and mineralogist should be able to gain information from examination of materials in handspecimen, using the naked eye or aided only by a hand lens, a

Flotation Plant Optimisation

scratch plate and a bottle of acid. However, once materials become reduced in size to the point where they are barely visible to the naked eye, other techniques clearly need to be used.

Optical techniques This probably still remains the most widely used technique worldwide, and not surprisingly, it has been around almost as long as the science of geology. It turns out that cleverly designed combinations of reflected and transmitted light sources, in both polarised and unpolarised states, allows minerals to be identified by their characteristic optical behaviour, especially when viewed under magnification on a petrographic polarising microscope. Ore minerals (such as sulfides, precious metals and oxides) are best viewed in reflected light as they tend to be opaque, whereas gangue phases (such as silicates, carbonates, phosphates) are best examined in transmitted light as they are often translucent. Sample presentation normally takes the form of polished sections or petrographic thin-sections, although loose grains can also be usefully observed with a basic stereo microscope. Apart from the identification of minerals, the modal mineralogy of a sample can be determined by point counting. Textures can be observed and recorded photographically (photomicrographs) and typically are used to augment reports and illustrate features of the sample. A useful text on this topic is by Gribble and Hall (1992). In each case, optical techniques obviously require a competent person to operate the microscope and make meaningful observations, typically a graduate in geological sciences with a few years relevant experience. Great microscopists, however, are a greying workforce and are in serious decline. Good microscopists are getting harder to find. And it is becoming more and more difficult to encourage young graduates to move into optical mineralogy. Automation of phase identification, modal point counting and texture analysis goes someway to redress this situation (Clemex Technologies Inc, 2009). A clear advantage of this method is that, in the right hands, a quick (and often cheap) prognosis can be obtained for both unbroken ore as well as particulates. And that might be good enough. But like all techniques, it must be used judiciously, and in combination with other methodologies.

X-ray beam techniques A commonly used technique to assess a sample for the relative abundance of minerals present is by a method that utilises the unique diffraction properties of minerals when subjected to a primary X-ray beam, the so called X-ray diffraction method or XRD for short. XRD is particularly useful when trying to establish the nature of an unknown material, or tracking the presence of an undesirable phase in a sample. It can be used to gain both semi-quantitative and quantitative phase data. XRD is a very powerful analysis technique for distinguishing certain mineral groups such as the Clay Group (montmorillonite, illite, kaolinite), the Serpentine Group (lizardite, talc), and certain polymorphs (minerals with exactly the same composition but differing only in their crystal structure, such as rutile-anatase, quartz-coesite), or distinguishing minerals with similar, but not exactly the same compositions (haematite-geothite-magnetite) or optical behaviour. As it is a bulk method of analysis, it cannot provide information on particle shape, size, or internal texture. In certain situations, it can be a relatively quick and inexpensive method to solve a problem. It is best used, however, in combination with other mineral techniques. XRD, of course, is not to be confused with X-ray fluorescence spectrometry (XRFS), which is another established X-ray beam technique, but unlike XRD, provides whole-rock chemical data.

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It is most commonly used for grade determination (say, Fe-, Pband Zn-content of ores, Ti-contents of mineral sands, P-content of iron ores, etc).

Electron beam techniques The technology which has most revolutionised mineralogical investigation over the past 40 years or so has been that based on the utilisation of signals generated as a result of interaction between a highly focused electron beam and earth materials. As soon as scanning electron microscopes (SEM) and later electron probe micro-analysers (EPMA) were introduced, they found immediate appeal among geologists, mineralogists and materials scientists. Effectively non-destructive, and with the ability to image, analyse and quantify a range of earth materials (both unbroken rocks and particulates), they remain at the forefront of mineral analysis for the earth resources industry today. The underlying principles are common to all systems. electroninduced, secondary X-ray, energy dispersive spectrometry (EDS) can be used to qualitatively and quantitatively determine the composition of a phase under the electron beam. Secondary electrons (SEI), along with backscattered electrons (BSE) and cathodoluminescence, all of which are simultaneously generated along with the secondary X-rays, can be used to gain insights into other aspects such as sample topography, composition and crystal defects. EPMA systems (and some SEM systems) have both EDS and wavelength dispersive spectrometers fitted (WDS – for increased sensitivity using a particular crystal to tune into a suite of elements). The electron beam can be used in both a scanning or point-and-shoot mode. A number of research groups around the world have attempted to automate SEMs and EPMAs (King and Schneider, 1993; Schneider and Neumann, 2004; Jones, 1984 and 1987), but only the Australian systems have succeeded in being widely adopted by the global minerals industry (Gottlieb et al, 2000; Baum, Lotter and Whittaker, 2004; Gu, 2003). A particular strength of an automated SEM system is that it removes some operator strain, tedium and repeatability issues arising from manual SEM work. CSIRO developed a system known as quantitative evaluation of minerals by scanning electron microscopy (QEM*SEM) in the early 1980s (Grant et al, 1977; Miller, Reid and Zuiderwyk, 1982), which was used extensively by industry through ownership of their own systems as well as through a bureau service offered by CSIRO. The latest product of QEM*SEM technology is known as QEMSCAN®, and is a complete automated solution from sample preparation through analysis to data reporting (Pirrie et al, 2004). The University of Queensland, through the JKMRC research centre, developed an alternative technology with similar objectives in terms of automation. Known as the Mineral Liberation Analyser (MLA), it began in 1997 (Keith, 1998; Dou, 1998), and was offered as a bureau service from 1999 (Gu, 2003). Both QEMSCAN® and MLA are now owned by FEI Company, who continue to develop, market and sell the two technologies.

Other techniques Other technologies used by mineralogists include those which utilise proton beams, ion beams, laser beams and near infrared beams. A proton microprobe is ideal for mapping ultra-trace elements within minerals. An example application at Eureka Mine would be to examine the galena by PIXE to ascertain if silver was present in solid solution (Goodall and Scales, 2006; Goodall, Scales and Butcher, 2005). A secondary ion mass spectrometer (SIMS) can be used for accurately measuring invisible gold in sulfides – gold that is not possible to see with

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SEM or EPMA microbeams as it is in solid solution (Vaughan and Corrans, 1977). Fine grinding is not an option for this texture, but leaching could be. Logging of cores, chips and powders for mineralogical composition can now be undertaken using scanners which utilise near infrared radiation which is phase specific. This is ideal for on-site situations where rapid (near real-time) bulk mineralogical information is required to troubleshoot processing problems, or predict required conditions of operation as ores and products pass along conveyors (Huntington, 2006).

APPLICATION OF MINERALOGY TO FLOTATION Introduction Flotation isn’t about flotation cells. It is about minerals. Liberating the right minerals in the right place, with the minimum of grinding power. Preparing the surfaces for maximum selectivity for valuable minerals against gangue. Minimising entrainment. Responding to the needs of different size fractions. Doing all this at minimum cost, using the least new equipment possible. Understanding the economics of the operation. And making the whole circuit work together, simple, responsive and operable (Xstrata Technology, 2005). This quote appeared recently within the conference proceedings of the Centenary of Flotation Symposium held in Australia, which celebrated, as the name suggests, 100 years since the introduction of flotation. It encapsulates many of the concepts introduced so far, which is why it is reproduced here in full. Flotation, in fact, was started because in Australia at Broken Hill the ores were too fine to be separated efficiently by gravity (Figure 8). We now move on to consider the practical application of all this know-how, particularly the role of mineralogy, in the better understanding of the flotation separation process, with respect to the Eureka Mine. Let us imagine therefore, that we have been set a mineralogical task to try and understand why the metal recoveries at the Eureka concentrator are low despite the grades being acceptable.

Methodology First up, we need decent primary samples to examine. These must be representative of the problem we are trying to fix. A good starting point is to always organise for the collection of a feed, concentrate and tail for each of the main saleable products. Experience has shown that you need to involve all relevant personnel in all key areas of the mines’ activity in the sampling, and to make them aware of the common pitfalls and problems in sampling mineral processing plants (many of these issues are covered in this book in other chapters, and by other publications, eg Annels (1991). Sampling a dynamic system such as a mineral processing plant, where crushing throughputs can be in the region of 100 kt/d, is certainly a challenging exercise. Results of any kind always need to be viewed with this in mind. Next, we need to create secondary samples from the primary samples, using appropriate methods, which normally take the form of one or more of the following, all of which are familiar to the metallurgist: cone and quartering, splitting, riffling, sieving, cyclosizing and de-sliming. From these secondary samples, we are then able to produce genuine replicate aliquots which can be used for all mineralogy and allied testing and

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10 μm

10 μm

10 μm

10 μm

FIG 8 - Optical photomicrographs, taken using a digital camera attached to a reflected polarising petrographic microscope, of processed particles from an Australian lead–zinc operation (McArthur River), which contain textures that historically would have been too fine for conventional flotation, and now require combinations of staged and fine-grinding methods to separate the galena and sphalerite.

analysis (assaying, etc). Typically, these aliquots then get made into a number of products depending on what happens next. Polished thin-sections and polished blocks are best as these can be used for optical work, SEM and EPMA work, as well as automated SEM techniques. Then, we need to generate quality petrographic information from the prepared products. A typical checklist that most mineralogists might run through when examining samples could look something like:

• grain size estimates (used to determine optimum

• Complete inventory of all known mineral phases present

boundaries will affect behaviour during crushing and grinding as this imparts preferential breakage mechanisms – eg along or across boundaries);

liberation grain sizes and predict or prevent problems such as poor liberation, over-grinding of the valuables, production of slimes);

• mineral associations (important for optimising the separation process, say galena chalcopyrite from sphalerite);

• Detailed modal analysis for major minerals (>5 per cent),

• elemental

deportment information (important for tracking how metals behave during processing, covered by Figure 5); and

minor phases (>1 per cent -