Modeling-And-Simulation-Of-Mineral

Modeling and Simulation of Mineral Processing Systems This book is dedicated to my wife Helen Modeling and Simulation of Mineral Processing Systems R.P. King Department of Metallurgical Engineering University of Utah, USA Boston Oxford Auckland Johannesburg Melbourne New Delhi Butterworth-Heinemann Linacre House, Jordan Hill, Oxford OX2 8DP 225 Wildwood Avenue, Woburn, MA 01801-2041 A division of Reed Educational and Professional Publishing Ltd A member of the Reed Elsevier plc group First published 2001 © R.P. King 2001 All rights reserved. No part of this publication may be reproduced in any material form (including photocopying or storing in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication) without the written permission of the copyright holder except in accordance with the provisions of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London, England W1P 9HE. Applications for the copyright holder’s written permission to reproduce any part of this publication should be addressed to the publishers British Library Cataloguing in Publication Data King, R.P. Modeling and simulation of mineral processing systems 1. Ore-dressing – Mathematical models 2. Ore-dressing – Computer simulation I. Title 622.7 Library of Congress Cataloging in Publication Data King, R.P. (Ronald Peter), 1938– Modeling and simulation of mineral processing systems/R.P. King. p. cm. Includes bibliographical references and index ISBN 0 7506 4884 8 1. Ore-dressing–Mathematical models. 2. Ore-dressing–Computer simulation. I. Title. TN500.K498 2001 622’.7’015118–dc21 2001037423 ISBN 0 7506 4884 8 For information on all Butterworth-Heinemann publications visit our website at www.bh.com Typeset at Replika Press Pvt Ltd, Delhi 110 040, India Printed and bound in Great Britain. Preface Quantitative modeling techniques and methods are central to the study and development of process engineering, and mineral processing is no exception. Models in mineral processing have been difficult to develop because of the complexity of the unit operations that are used in virtually all mineral recovery systems. Chief among these difficulties is the fact that the feed material is invariably a particulate solid. Many of the conventional mathematical modeling techniques that are commonly used for process equipment have limited application to particulate systems and models for most unit operations in mineral processing have unique features. Common ground is quite difficult to find. The one obvious exception is the population balance technique and this forms a central thread that runs throughout the modeling techniques that are described in this book. The models that are described are certainly incomplete in many respects, and these will be developed and refined by many researchers during the years ahead. Nevertheless, the models are useful for practical quantitative work and many have been widely used to assist in the design of new equipment and processes. Some of the newer models have not yet been seriously tested in the industrial environment. The book is written at a reasonably elementary level and should be accessible to senior undergraduate and graduate students. A number of examples are included to describe the application of some of the less commonly used models, and almost all of the models described in the book are included in the MODSIM simulator that is available on the companion compact disk. The reader is encouraged to make use of the simulator to investigate the behavior of the unit operations by simulation. The main advantage of using quantitative models is that they permit the complex interactions between different unit operations in a circuit to be explored and evaluated. Almost all of the models described are strongly nonlinear and are not usually amenable to straightforward mathematical solutions, nor are they always very convenient for easy computation using calculators or spread sheets. In order to investigate interactions between models, the simulation method is strongly recommended, and the focus throughout this book has been on the development of models that can be used in combination to simulate the behavior of complex mineral dressing flowsheets. Simulation techniques are popular because they allow complex problems to be tackled without the expenditure of large resources. All the models described here can be used within the MODSIM simulator so they are readily accessible to the reader. The models are transparent to the user and the models can be tried in isolation or in combination with other unit operations. MODSIM has proved itself to be an excellent teaching tool both for conventional courses and, in recent years, to support an Internet course delivered from the University of Utah. I hope that distributing MODSIM widely, together with this book, will encourage vi Preface researchers and engineers to make use of this technique, which brings to every engineer the results of many man-years of research endeavor that have contributed to the development of the models. Simulation does have its limitations and the reader is reminded that a simulator can not be relied upon to provide an exact replica of any specific real plant operation. The reliability of the simulator output is limited by the accumulated reliability of the component models. The work of many researchers in the field has been inspiration for the models that are described in this book. I have tried to extract from the research literature those modeling techniques that have proved to be useful and applicable to practical situations and I have tried to identify those modeling methods and process features that have been confirmed, at least partially, by careful experimental observation. In this I am indebted to many students and colleagues whose work has provided data, ideas and methods. The preparation of a book is always a time-consuming task and I wish to thank my wife, Ellen, for her patience and encouragement while it was being written and for typing much of the final version of the manuscript. The manuscript went through many revisions and the early versions were typed by Karen Haynes. Kay Argyle typed the illustrative examples. It is a pleasure to acknowledge their contributions for which I am very grateful. R.P. King Salt Lake City Contents Preface v 1. Introduction 1 Bibliography 4 References 4 2. Particle populations and distribution functions 5 2.1 Introduction 5 2.2 Distribution functions 6 2.3 The distribution density function 13 2.4 The distribution by number, the representative size and population averages 13 2.5 Distributions based on particle composition 16 2.6 Joint distribution functions 17 2.7 Conditional distribution functions 19 2.8 Independence 31 2.9 Distributions by number 32 2.10 Internal and external particle coordinates and distribution densities 34 2.11 Particle properties derived from internal coordinates 35 2.12 The population balance modeling method 35 2.13 The fundamental population balance equation 36 2.14 The general population balance equation for comminution machines 40 Bibliography 42 References 43 3. Mineral liberation 45 3.1 The beta distribution for mineral liberation 46 3.2 Graphical representation of the liberation distribution 49 3.3 Quantitative prediction of mineral liberation 51 3.4 Simulating mineral liberation during comminution 58 3.5 Non-random fracture 69 3.6 Discretized Andrews-Mika diagram 72 3.7 Symbols used in this chapter 79 Bibliography 79 References 80 viii Contents 4. Size classification 81 4.1 Classification based on sieving–vibrating screens 81 4.2 The classification function 86 4.3 A simple kinetic model for screening 91 4.4 Classification based on differential settling – the hydrocyclone 98 4.5 Terminal settling velocity 102 4.6 Capacity limitations of the hydrocyclone 124 4.7 Symbols used in this chapter 124 References 125 5. Comminution operations 127 5.1 Fracture of brittle materials 127 5.2 Patterns of fracture when a single particle breaks 129 5.3 Breakage probability and particle fracture energy 132 5.4 Progeny size distribution when a single particle breaks – the breakage function 136 5.5 Energy requirements for comminution 150 5.6 Crushing machines 152 5.7 Grinding 160 5.8 The continuous mill 174 5.9 Mixing characteristics of operating mills 179 5.10 Models for rod mills 180 5.11 The population balance model for autogenous mills 181 5.12 Models for the specific rate of breakage in ball mills 187 5.13 Models for the specific rate of breakage in autogenous and semi-autogenous mills 197 5.14 Models for the breakage function in autogenous and semi-autogenous mills 201 5.15 Mill power and mill selection 202 5.16 The batch mill 205 Bibliography 209 References 210 6. Solid–liquid separation 213 6.1 Thickening 213 6.2 Useful models for the sedimentation velocity 219 6.3 Simulation of continuous thickener operation 220 6.4 Mechanical dewatering of slurries 223 6.5 Filtration 227 Bibliography 230 References 231 7. Gravity separation 233 7.1 Manufactured-medium gravity separation 233 Contents ix 7.2 Quantitative models for dense-media separators 234 7.3 Autogenous media separators 243 7.4 Generalized partition function models for gravity separation units 263 Bibliography 266 References 266 8. Magnetic separation 269 8.1 Behavior of particles in magnetic fields 269 8.2 Forces experienced by a particle in a magnetic field 272 8.3 Magnetic properties of minerals 277 8.4 Magnetic separating machines 278 8.5 Dry magnetic separation 283 8.6 Wet high intensity magnetic separation 287 Bibliography 288 References 288 9. Flotation 289 9.1 A kinetic approach to flotation modeling 290 9.2 A kinetic model for flotation 293 9.3 Distributed rate constant kinetic model for flotation 307 9.4 Bubble loading during flotation 309 9.5 Rise times of loaded bubbles 312 9.6 Particle detachment 321 9.7 The froth phase 323 9.8 Simplified kinetic models for flotation 337 9.9 Symbols used in this chapter 346 Bibliography 347 References 348 10.

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