Mechanical Operations 0070700222, 9780070700222

Citation preview

Anup Kumar Swain is presently Assistant Professor, Department of Chemical Engineering at Gandhi Institute of Engineering and Technology, Gunupur, Odisha. He obtained his BE degree from Utkal University, Odisha, in 1999 and ME from The M S University of Baroda, Gujarat, in 2003. He has one year of research experience at Bayer ABS Ltd., Gujarat and nine years of teaching experience at various levels in engineering colleges of Odisha. He has published six papers in national and international journals and is a life member of Indian Institute of Chemical Engineers and Indian Society for Technical Education. His research interests include adsorptive removal of organics from industrial waste water using low-cost adsorbents, and synthesis and characterisation of polymers. His subjects of interest include mechanical operations, polymer technology, mass transfer operations, fluid mechanics, and chemical process calculations.

Hemalata Patra is presently Assistant Professor, Department of Chemical Engineering at Gandhi Institute of Engineering and Technology, Gunupur, Odisha. She obtained her BE degree from Utkal University, Odisha, in 1999. She is currently pursuing PhD from the Ceramic Engineering Department of National Institute of Technology, Rourkela and has nine years of teaching experience at various levels in engineering colleges of Odisha. She has published five papers in national and international journals, has also attended five short-term courses and presented four papers in national-level conferences. Her subjects of interest include mechanical operations, mass transfer operations, fluid mechanics, and ceramic materials. Her research interests include solid oxide fuel cell (SOFC) materials.

Gopendra Kishore Roy is presently Professor, Department of Chemical Engineering at National Institute of Technology, Rourkela. He obtained his BSc (Chemical Engineering) degree from Banaras Hindu University, in 1966, MTech from IIT Kharagpur in 1971, and PhD from Sambalpur University in 1975. He was the Principal (of erstwhile Regional Engineering College, Rourkela) and thereafter the Director of the Institute from October 2001 to May 2003. He has over 43 years of teaching and research experience with authorship of more than 125 research publications and six books. He was post-doctoral fellow at the University of Karsruhe, Germany, during 1977–78 and represented developing countries in an international conference on Chemical Engineering Education in London in June 1978. He received Sir Gangaram Memorial Award (1974) and certificates of merit (1978, 1984, and 1998) of the Institution of Engineers (India) for his publications in the institutional journal, DAAD Award (1993), and the Indian Institute of Public Health Engineers Award (1994). He has been honoured as a renowned engineer of the state of Odisha by the Rourkela Local Centre (2002) and the Odisha State Centre (2007) of the Institution of Engineers (India). He is a recipient of the Samanta Chandra Sekhar Award (2005) of the Department of Science and Technology, Government of Odisha. He is a fellow of Indian Institute of Chemical Engineers, the Institution of Engineers (India), and the Institution of Public Health Engineers, India. He is a life member of the Indian Society for Technical Education, Indian Institute of Metals, Indian Computer Society, and Indian Ceramic Society, and also a Chartered Engineer (India). On invitation, he presented a paper in the 17th International Conference of Chemical and Process Engineering held in Prague, Czech Republic, during August 2006. In addition to Germany, UK, and the Czech Republic, he has visited France, Switzerland, Italy and Scotland.

Tata McGraw Hill Education Private Limited NEW DELHI McGraw-Hill Offices New Delhi New York St. Louis San Francisco Auckland Bogotá Caracas Kuala Lumpur Lisbon London Madrid Mexico City Milan Montreal San Juan Santiago Singapore Sydney Tokyo Toronto

Tata McGraw-Hill Published by the Tata McGraw Hill Education Private Limited, 7 West Patel Nagar, New Delhi 110 008. Mechanical Operations Copyright © 2011 by Tata McGraw Hill Education Private Limited. No part of this publication may be reproduced or distributed in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise or stored in a database or retrieval system without the prior written permission of the publishers and the authors. The program listings (if any) may be entered, stored and executed in a computer system, but they may not be reproduced for publication. This edition can be exported from India only by the publishers, Tata McGraw Hill Education Private Limited ISBN (13): 978-0-07-070022-2 ISBN (10): 0-07-070022-2 Vice President & Managing Director—MHE, Asia Pacific Region: Ajay Shukla Head—Higher Education Publishing and Marketing: Vibha Mahajan Manager—Sponsoring: SEM & Tech Ed: Shalini Jha Assoc. Sponsoring Editor: Suman Sen Development Editor: Devshree Lohchab Executive—Editorial Services: Sohini Mukherjee Sr Production Manager: P L Pandita Dy Marketing Manager—SEM & Tech Ed: Biju Ganesan General Manager—Production: Rajender P Ghansela Asst General Manager—Production: B L Dogra

Information contained in this work has been obtained by Tata McGraw-Hill, from sources believed to be reliable. However, neither Tata McGraw-Hill nor its authors guarantee the accuracy or completeness of any information published herein, and neither Tata McGraw-Hill nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information. This work is published with the understanding that Tata McGraw-Hill and its authors are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought. Typeset at Mukesh Technologies Pvt. Ltd., #10, 100 Feet Road, Ellapillaichavadi, Pondicherry 605 005 and printed at Sai Printo Pack, A–102/4, Phase II, Okhla Indl. Area, New Delhi 110 020 Cover: Sai Printo Pack RCLLCRQZRQRXX The McGraw-Hill Companies

Kamini Kumar Swain and Annapurna Swain Anup Kumar Swain

Gayadhar Patra and Sukantilata Patra Hemalata Patra

Late Aditya Prasanna Marhual and Late Shailalata Marhual Gopendra Kishore Roy

Foreword Preface Acknowledgements

xii xiii xv

1. Introduction

1

1.1 Unit Operations 2 1.2 Unit Systems 3 Nomenclature 9

2. Properties and Storage of Solids

11

2.1 Characterisation of Solid Particles 12 2.2 Solids in Bulk 22 Points to Remember 27 Short Questions with Answers 29 Review Questions 30 Exercise Problems 30 Objective Questions with Answers 31 Nomenclature 32

3. Size Reduction of Solids 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9

34

Objectives of Size Reduction 35 Size-Reduction Methods 35 Principles of Size Reduction 37 Size-Reduction Equipments 48 Coarse Crushers 50 Intermediate Crushers 64 Fine Crushers (Grinders) 71 Ultra-Fine Grinders 78 Effective Methods for Operating Size-Reduction Equipments Points to Remember 84 Short Questions with Answers 86 Review Questions 88 Exercise Problems 88 Objective Questions 89 Nomenclature 91

4. Separation of Solids: Introduction 4.1 Separation Processes 94 Points to Remember 96 Short Questions with Answers

97

81

93

Review Questions 97 Objective Questions 97

5. Solid–Solid Separation 5.1 5.2 5.3 5.4 5.5

6. Solid-Liquid Separation 6.1 6.2 6.3 6.4

99

Screening 100 Electrical Separation 138 Classification with Water 150 Gravity Concentration 159 Floatation 166 Points to Remember 171 Short Questions with Answers 173 Review Questions 175 Exercise Problems 175 Objective Questions with Answers 177 Nomenclature 178

179

Terminologies 180 Sedimentation (Thickening and Clarification) 180 Equipments (Thickeners and Clarifiers) 190 Filtration 197 Points to Remember 221 Short Questions with Answers 224 Review Questions 225 Exercise Problems 226 Objective Questions with Answers 227 Nomenclature 228

7. Gas-Solid Separation

231

7.1 Gas-Cleaning Equipments 232 Points to Remember 243 Short Questions with Answers 244 Review Questions 245 Exercise Problems 246 Objective Questions with Answers 246 Nomenclature 247

8. Transportation of Solids

248

8.1 Transportation Equipment 249 Points to Remember 260 Short Questions with Answers 261 Review Questions 262 Exercise Problems 262 Objective Questions with Answers 262 Nomenclature 263

9. Mixing of Solids 9.1 Liquid Mixing 266 9.2 Solid Mixing 270 9.3 Mixing Equipment 274

265

Points to Remember 281 Short Questions with Answers 282 Review Questions 283 Exercise Problems 284 Objective Questions with Answers 284 Nomenclature 285

10. Auxiliary Operations

287

10.1 Size Enlargement 288 10.2 Crystallisation 295 10.3 Feeding 299 10.4 Weighing 305 10.5 Coagulation and Flocculation 306 Points to Remember 307 Short Questions with Answers 308 Review Questions 309 Exercise Problems 310 Objective Questions with Answers 310 Nomenclature 311

Appendix–I Appendix–II Appendix–III References Web References Index

313 314 315 317 318 319

It gives me immense pleasure in introducing the first title of Tata McGraw Hill Education Private Limited on Mechanical Operations. I take this opportunity to congratulate the authors as well as the publisher for this. Whether the industry is related to Chemical, Ceramic, Metallurgical, Mining, Pharmacy, or Biotechnology, Mechanical Operations find its applications wherever solids are handled. Various mechanical operations are transportation, feeding, weighing, storage, size reduction, size separation, and mixing. The study of these operations is important since the handling of solids by any of these operations is more difficult compared to liquids and gases, because, gases and liquids do not have their own shape and size rather they take the shape of the container, whereas solids have a definite shape and size. Thus, the need for a good textbook is highly essential. In different unit operations and mineral processing books, only scattered information are available on this subject. This book is simple and syllabus compatible. The whole of the contents are written keeping in mind the present industrial practices. Figures of a large number of recent industrial equipments obtained from world-class manufacturers are included with their permission. A large number of numerical examples with solution have been incorporated in each of the chapters to explain the concept more clearly. In addition, each chapter contains review questions and short and multiple choice questions with answers which are unique to the present title. I am sure this book will be able to fill the void and will meet the needs of the students (Chemical, Ceramic, Metallurgical, Mining, Pharmacy, and Biotechnology), practising engineers as well as the subject teachers. I wish the authors all the best and the book all the success. V K Srivastava President Indian Institute of Chemical Engineers

Mechanical Operations are those unit operations of Chemical Engineering, which involve mechanical forces, either small or large. These mainly deal with the handling and processing of the solids and the solids present in other phases. Generally, solids are more difficult to handle and process than liquids and gases, because gases and liquids do not have their own shape and size; rather they take the shape of the container. In contrast, solids have a definite shape and size, due to which their handling becomes difficult. For example, liquids and gases can easily be transported through pipes from one place to another, but for solids we have to decide the means according to their shape and size. Mechanical Operations are broadly classified in the following ways: (i) Particulate Solids Characterisation of solids, Handling of solids (Transportation, Feeding, Weighing, and Storage), Size reduction, and Size separation (ii) Particle Dynamics Sedimentation, Filtration, Elutriation, Classification (iii) Mixing Mixing of solids with solids, Mixing of cohesive solids and Mixing of liquids Mechanical operations play an important role in every kind of chemical process industries. They also find major applications in mineral processing, ceramic, and metallurgical industries. In spite of a volume of scattered information available on this subject in different unit operations and mineral processing books, no single textbook comprising the various aspects is available. Keeping this in mind, the present title on Mechanical Operations is being brought out. The special feature of this book is that the whole of the content has been written keeping in view the present shop-floor practices. Also, the figures of a large number of recent industrial equipments obtained from world-class manufacturers over the globe are included with their permission. Photographs to depict the equipments used in real life in various separation processes are also given. Numerical examples with solutions, totalling to over 45, have been incorporated in each chapter to explain the concepts more clearly. In addition, the excellent pedagogy includes 135 Solved Conceptual Questions, 135 Review Questions, 40 Exercise Problems and over 100 Multiple Choice Questions with answers which are unique to the present title. In the forthcoming editions, we plan to include other related chapters. The text is being proposed keeping in view the syllabus followed by various Indian universities, which we hope will be of much help to the students (Chemical, Ceramic, Metallurgical, Mining, Pharmacy, and Biotechnology), practising engineers as well as to the subject teachers.

The book is organised in ten chapters. Chapter 1 is an introductory one and describes the brief history of chemical engineering, concept of unit operations, and the importance of mechanical operations. This also includes the unit system and the various dimensionless groups. In Chapter 2, the properties and storage of solids have been given. In this chapter, properties like shape, size, storage and flow of bulk-solids are discussed. Chapter 3 is about size reduction of solids and describes the importance of size reduction, actions involved, and parameters affecting size reduction; power and energy relation with crushing efficiencies; and the recent industrial size-reduction equipments. Chapter 4 is an introductory chapter on size separation of solids and summarizes various separation processes and the types of separation equipments available to separate solids from different phases. The separation of solids from solids both in dry state (screening and electrical separation) and wet state (classification, gravity concentration, and froth floatation) and also the recent industrial equipments have been discussed in Chapter 5. Chapter 6 deals with solid-liquid separation and describes the theory and equipments of sedimentation (thickening and clarification) and filtration. In Chapter 7, the principles of gas-solid separation have been discussed and the various gas-solid separators including air classifiers have been described. Chapter 8 deals with the transportation of solids and discusses the equipments like conveyors and elevators. The mixing of solids along with the theory of liquid and solid mixing has been given in Chapter 9. Various solid, liquid, and viscous mixers are also discussed. In Chapter 10, some auxiliary mechanical operations like size enlargement by agglomeration, crystallization, coagulation, feeding, and weighing have been briefly dealt with. The Web Supplements can be accessed at http://www.mhhe.com/swain/mo and contain the Solution Manual and PowerPoint lecture slides for Instructors and, Web Links for additional readings are given for Students. We have tried to contact most of the owners of copyrighted materials. However, we offer our apology to any copyright holder whose rights we may have unwittingly infringed. In spite of our best efforts, some errors might have crept in to the book. Report of any such errors and suggestions for improving the book are welcome and will be gratefully acknowledged. In case of any query, readers are requested to feel free to contact us at [email protected], [email protected] and [email protected]. Anup Kumar Swain Hemalata Patra Gopendra Kishore Roy Publisher's Note Tata McGraw-Hill invites comments, views and suggestions from readers, all of which can be sent to [email protected]. “Feel free to report any piracy spotted by you as well!!”

We are extremely grateful to the following companies and individuals for providing text, illustrations, images, data, and suggestions for this book and giving their permission to reproduce copyrighted materials. 1. Pennsylvania Crusher Corporation, USA 2. Outotec Oyj., Finland (Eila Paatela, Anna-Kaisa Varamaki, Misty Dobbins, Timo Nore) 3. Ronald Gill Associates, UK (Ron Gill) 4. M/S Hosokawa Micron India Pvt. Ltd., India (V Manjula) 5. JOEST Australia Pvt. Ltd., Australia (Steve Clifford) 6. Eriez Manufacturing Company, USA (Partha Venkatraman, Dave Heubel, Rob Yandrick) 7. Metso Minerals Inc. (Jarmo Eloranta, Tuulikki Oittinen, Eero Hamalainen, Kevin Moore, Janne Rannanpaa, Marja-Liisa Jarvinen) 8. Sandvik Mining and Construction, Sweden (Shib Bhowmik, Anil Martyris, Sandeep Bhattacharjee) 9. McGraw-Hill Companies, Inc., USA (Cynthia Aguilera) 10. Vedanta Aluminium Ltd., India (Mukesh Kumar) 11. John Thixton, Australia (Inventor of the Supaflo High Rate Thickener) 12. M/S Amar Equipments Pvt. Ltd., India (Avinash Mukundan) 13. Orissa Sponge Iron and Steel Limited, India (S C Khattoi, Asaman Prasad Patnaik) 14. FLSmidth A/S, Denmark (Sudhir Kamath, Shomeet Pattanayak) 15. Unique Mixers and Furnaces Pvt. Ltd., India (Jayesh Tekchandaney) 16. M/S IKA Werke GmbH & Co. KG., Germany (Daniel Loeffler, Frauke Muller) 17. Hosokawa Bepex GmbH, Germany (Werner Bakela)

18. Sturtevant, Inc., USA (Michelle Smith, Joseph Muscolino) 19. Pampa Enterprises, India (Sirur Pampapathi) 20. Haver & Boecker OHG, Germany (Walter Haver, Sabine Poepsel) 21. IKA India Private Limited, India (Usha Rani) 22. Elsevier (Sam Mahfoudh) We express our heartfelt thanks to the following reviewers for their valuable suggestions for the improvement of the book. 1. Timo Nore, Outotec Oyj., Finland, for Chapters 5 and 6 2. V Manjula, M/S Hosokawa Micron India Pvt. Ltd., India for Chapter 3 3. Jarmo Eloranta and Janne Rannanpaa, Metso Minerals Inc. for Chapters 2, 3, 5, 8, and 10 4. Sandeep Bhattacharjee, Sandvik Mining and Construction, Sweden for Chapters 3 and 5 5. Sudhir Kamath, FLSmidth A/S, Denmark for Chapters 2, 5, 6, and 8 6. Jayesh Tekchandaney, Unique Mixers & Furnaces Pvt. Ltd., India, for Chapter 9 7. Frauke Muller, M/S IKA Werke GmbH & Co. KG., Germany for Chapter 9 8. Werner Bakela, Hosokawa Bepex GmbH, Germany for Chapter 10 9. Michelle Smith and Joseph Muscolino, Sturtevant, Inc., USA for Chapter 7 10. Walter Haver, Haver & Boecker OHG, Germany for Chapter 5 11. Usha Rani, IKA India Private Limited, India for Chapter 9 Besides the above, we would also like to thank the reviewers commissioned by the publisher. Their names are given below. K K Pant Indian Institute of Technology (IIT), New Delhi Ashish M Gujrathi Birla Institute of Technology and Science (BITS), Pilani, Rajasthan Sunil Kumar Maity National Institute of Technology (NIT), Rourkela, Odisha Gopinath Halder Indian School of Mines (ISM), Dhanbad, Jharkhand Somak Jyoti Sahu Haldia Institute of Technology (HIT), Haldia, West Bengal Z V P Murthy Sardar Vallabhbhai National Institute of Technology (SVNIT), Surat, Gujarat V Sivasubramanian National Institute of Technology (NIT), Calicut, Kerala

Jayasankar E Variyar Vellore Institute of Technology (VIT), Vellore, Tamil Nadu K V Radha A C College of Technology, Chennai, Tamil Nadu Y Pydi Setty National Institute of Technology (NIT), Warangal, Andhra Pradesh We are obliged to Louis C Flanagan of Flanagan Advertising Inc., USA, for providing materials of Pennsylvania Crusher Corporation, USA, and to Deepak Mehta of Leevams Incorporated, India, for providing materials of Sturtevant Inc., USA. We express our sincere thanks to S P Panda (Chairman), C D Panda (Secretary), and N V J Rao (Dean—Administration) of Gandhi Group of Institutions, Gunupur, Odisha and to S K Sarangi (Director, NIT, Rourkela) for their moral support. A heartfelt note of thanks goes to the librarians of GIET, Gunupur, and NIT, Rourkela, for their timely help and literature support. We are also thankful to Asaman Prasad Patnaik of OSIL, India and to Pradeepta Kalia of TAL Manufacturing Solutions Ltd., India, for their valuable suggestions and timely help. We also express our gratitude to Vibha Mahajan, Shalini Jha, Devshree Lohchab, Surabhi Shukla, Sohini Mukherjee, Piyaray Lal Pandita, and to the entire team of Tata McGraw Hill Education Private Limited for their constant support in bringing out their first title on Mechanical Operations. We are indebted to V K Srivastava (retired professor of IIT Delhi, India) President of IIChE for graciously agreeing to write the Foreword for this book. And last but not the least, we acknowledge the contribution of all our loved ones—our parents, family members, and elders for their support, encouragement, and blessing without which this work would not have been successful. Anup Kumar Swain Hemalata Patra Gopendra Kishore Roy

i

ni

i i n Mixin F din .

i

ni i n

i d

in

n d

ni

i n

A

M

n in 1 00

d in in 1 2

in 1 15

F id n

M n

A

id i n i n i n

id

r /m

Oxid i n d i n d n i n n i n i i n .

Dr Arthur D Little first introduced the concept of unit operations in 1915. Broadly, the unit operations are Mechanical operations, Fluid-flow operations, Heat-transfer operations, and Mass-transfer operations. The present text covers mechanical operations — one of the unit operations of chemical engineering, as it is not practicable to cover the entire unit operations of chemical engineering under a single head due to its variety and complexity. Mechanical operations are the unit operations of chemical engineering in which mechanical forces, either small or large, are involved for the processing and handling of solids as such and the solids present in other phases. Generally, solids are more difficult to handle and process than liquids and gases. This is because gases and liquids do not have their own shape and size; rather they take the shape of the container; whereas solids have a definite shape and size, due to which their handling becomes difficult. For example, liquids and gases can be easily transported through pipes from one place to another, but for solids we have to decide

the means according to their shape and size. Also, of all the shapes and sizes that are found in solids, the most important one from the chemical-engineering viewpoint is the small-sized particles. Thus, for a better understanding of the subject of mechanical operations, it is broadly classified as the following: Characterisation of solids, handling of solids (transportation, feeding, weighing, and storage), size separation/screening, size reduction Sedimentation, filtration, fluidisation, elutriation Mixing of solids, cohesive solids, and liquids Mechanical operations play an important role in almost all chemical-process industries. These also find major applications in the mineral processing and the metallurgical industries.

Chemical engineers often find the various data expressed in four different units: cgs, mks, fps, and SI. But the official international system of units is the SI system (System International d Unites), which covers the entire field of science and engineering and is widely accepted worldwide. Thus, it becomes necessary to be thorough in the use of this system. The various systems of units and the basic quantities associated with them are given in Table 1.1.

Quantity

System cgs

SI

fps

Mass, M Length, L Time, q Force, F

gram centimetre second dyne

kilogram metre second newton

pound foot second poundal

Temperature,

degree centigrade

degree Kelvin

degree fahrenheit

MKS kilogram metre second kilogram force degree centigrade

Table 1.2 lists various basic SI units. Table 1.3 lists the various prefixes for the SI system. Table 1.4 lists some constants while Table 1.5 lists important conversion factors to SI units. Finally, to get the students acquainted with various dimensionless quantities, they are presented in Table 1.6 with their formulae and significance.

Mass Length Time Force Energy Temperature Mole

: : : : :

Kilogram, kg Metre, m Second, s Newton, N Joule, J = Newton.Metre, N.m : Kelvin, K : Kilogram mole, kmol

Factor 1012 109 106 103 102 101 10−1 10−2 10−3 10−6 10−9 10−12

Prefix tera giga mega kilo hecto deka deci centi milli micro nano pico

Symbol T G M k h da d c m m n p

Acceleration due to gravity, g

= 9.81 m/s2 = 981 cm/s2 = 32.2 ft/s2

Gravitational conversion factor, gc

= 1 kg.m/N.s2 = 1 g.cm/dyn.s2 = 981 g.cm/gmf.s2 = 32.2 lb.ft/lbf.s2

Molar volume of ideal gases at STP (0°C, 1 std atm)

= 22.4 m3/kmol = 22.4 l/gmol = 359 ft3/lbmol

Gas constant, R

= 8314 N.m/kmol.K = 1.987 cal/gmol.K = 0.7302 atm.ft3/lbmol.K = 0.08205 atm.m3/kmol.K

Conversion from

o

Multiply by

Length, L ft in cm

m m m

0.3048 0.0254 0.01

Area, L2 ft2 in2 cm2

m2 m2 m2

0.0929 6.452 × 10−4 10−4

Volume, L3 ft3 cm3 Volume, L3 l US gal UK gal

m3 m3

0.02832 10−6

m3 m3 m3

10−3 3.785 × 10−3 4.546 × 10−3

Specific area, L2/L3 ft2/ft3 cm2/cm3

m2/m3 m2/m3

3.2804 100

Velocity, L/q ft/s ft/h

m/s m/s

0.3048 8.467 × 10−5

Acceleration, L/q 2 ft/s2 cm/s2

m/s2 m/s2

0.3048 0.01

Volume flow rate, L3/q ft3/s cm3/s l/s

m3/s m3/s m3/s

0.02832 10−6 10−3

Mass, M lb Ton (short, 2000 lb) Ton (long, 2240 lb) metric ton

kg kg kg kg

0.4536 907.2 1016 1000

Density, M/L3 lb/ft3 g/cm3 lb/US gal

kg/m3 kg/m3 = g/l kg/m3

16.019 1000 119.8

Specific Volume, L3/M ft3/lb cm3/g

m3/kg m3/kg

0.0624 0.001

Mass flow rate, M/q lb/s lb/h

kg/s kg/s

0.4536 1.26 × 10− 4 (Continued )

Conversion from

o

Multiply by

Viscosity, M/Lq lb/ft.s Poise (P) cP

kg/m.s = N.s/m2 kg/m.s kg/m.s

1.488 0.1 0.001

Mass flux, M/L2q lb/ft2.h g/cm2.s

kg/m2.s kg/m2.s

1.356 × 10−3 10

Mass-transfer coefficient, mole/L2 q (F/L2) lb mol/ft2.h.atm lb mol/ft2.h.(lb mol/ft3) Force, F lbf kgf dyn

kmol/m2.s.(N/m2) kmol/m2.s.(kmol/m3)

1.338 × 10−8 8.465 × 10−5

N N N

4.448 9.807 10−5

Surface tension, F/L lbf /ft erg/cm2 dyn/cm

N/m = kg/s2 N/m N/m

14.59 10−3 10−3

Pressure, F/L2 lbf /ft2 atm in Hg in H2O dyn/cm2 mm Hg = torr bar kgf /cm2

N/m2 = Pa N/m2 N/m2 N/m2 N/m2 N/m2 N/m2 N/m2

47.88 1.0133 × 105 3386 249.1 10−1 133.3 105 9.807 × 104

Work, Energy, Heat, FL Btu erg cal kW.h

N.m = J N.m N.m N.m

1055 10−7 4.187 3.6 × 106

Enthalpy, FL/M Btu/lb cal/g

N.m/kg = J/kg N.m/kg

2326 4187

Heat capacity, Specific heat, FL/M Btu/lb.°F cal/g. °C

N.m/kg.K = J/kg.K N.m/kg.K

4187 4187

Energy flux, FL/L2q Btu/ft2.h cal/cm2.s

N.m/m2.s = W/m2 N.m/m2.s

3.155 4.187 × 104 (Continued )

Conversion from

To

Multiply by

Thermal conductivity, FL2/L2qT Btu.ft/ft2.h.°F cal.cm/cm2.s.°C kcal.m/m2.h.°C

N.m/m.s.K = W/m.K N.m/m.s.K N.m/m.s.K

1.7307 418.7 1.163

Heat transfer coefficient, FL/L2qT Btu/ft2.h.°F cal/cm2.s. °C

N.m/m2.s.K = W/m2.K N.m/m2.s.K

5.679 4.187 × 104

Power, FL/q ft.lbf /s hp Btu/h

N.m/s = W N.m/s N.m/s

1.356 745.7 0.2931

Name

Symbol

Formula

Significance

Archimedes number, Ar

g.r.L3 ( rp − r ) m2

(Inertial forces × Buoyancy forces)/(Viscous forces)2

Bingham number, Bm

t y .L

Yield stress/Viscous stress

m∞ .V Biot number, BI

h.Δ X k V .r m (1 − ε ) s

Thermal resistance/Surface film resistance

Bond number, BO

g .L2 ( rL − rG ) s

Gravitational force/Surface tension force

Brinkman number, Br

m v2 k ΔT

Heat production by viscous dissipation /Heat transport by conduction

Cauchy Number, C

r .V 2 b

Inertial force/Compressibility force

Cavitation Number, s

2( p − pv ) r .V 2

Excess pressure above vapour pressure/Velocity head

Colburn–Chilton j factor or heat-transfer factor, jH

h ⎛ C .m ⎞ . P CP . r.V ⎜⎝ k ⎟⎠

Blake number, B

Inertial force/Viscous force

2

3

—

(Continued )

Name & Symbol

Formula

Significance

Drag coefficient, CD

2FD A.r.V 2

Drag Force / (Projected area × Velocity head)

Eckert number, Ec (Br /Pr)

v2 Cp ΔT

Flow s kinetic energy/Flow s enthalpy

Elasticity number, EI

λ .m r.L2

Elastic force/Inertial force

Euler number, Eu

Δp r.V 2

Friction pressure loss/Velocity head

Fanning friction factor, f

D.Δp 2r.V 2 .L

Wall shear stress/Velocity head

Fourier number, FO

a.t L2

—

Froude number, Fr

V2 g .L

Inertial force/Gravitational force

Gratz number, Gz

m.CP k .L

Thermal capacity/Convective heat transfer

Grashof number, Gr

L3 .r 2 .g .β ′.ΔT m2

Buoyancy force/Viscous force

Knudsen number, Kn

λ′ L

Length of mean free path/ Characteristic dimension

Lewis Number, Le

k α = D ′.r.CP D ′

—

Mach Number, M

V c

Fluid velocity/Sonic velocity

Mass-transfer factor, jM

kC ⎛ μ ⎞ . V ⎜⎝ r.D ′ ⎟⎠

Nusselt number, Nu

hD k L.V D

Peclet number, Pe (Re × Pr or, Re × Sc)

2

3

—

Total heat transfer/Conductive heat transfer ⎛ L.V ⎞ ⎜⎝ or, α ⎟⎠

Convective transport/Diffusive transport

Power number, Po

P r.N 3 .L5

Drag force/Inertial force

Prandtl number, Pr

C P .μ ⎛ ν⎞ or, k ⎜⎝ α ⎟⎠

Momentum diffusivity/Thermal diffusivity (Continued )

Name & Symbol

Formula

Significance

Rayleigh number, Ra

L3 .r 2 .g .β ′.ΔT .CP μ .k

—

Reynolds number, Re

LVr L.G LV = = μ μ ν

Inertial force/Viscous force

Richardson number, Ri

g H′ u2 ν D

Potential energy/Kinetic energy

Sherwood number, Sh

kC .L D′

Mass diffusivity/Molecular diffusivity

Stanton number, St (Nu/Pe)

h CP .r.V

Heat transferred/Thermal capacity of fluid

Weber number, We

L.V 2 .r σ

Inertial force/Surface tension force

Schmidt number, Sc

kC

Momentum diffusivity/Mass diffusivity

q

Å

i i

a

Φ

6V D S

|| Solids are found in a great variety of forms: spherical, cubical, rectangular, cylindrical, powder, angular pieces, etc., which may be soft, hard, tough, rubbery, free-flowing, or sticky. Irrespective of their forms, the three most important characteristics of an individual particle such as composition, size, and shape need to be studied for various reasons. The composition will determine properties like density and conductivity. The particle size and shape affect properties such as the surface area per unit volume and the rate at which the particle will settle in a fluid. The shape and size are easily defined for regular particles like spheres and cylinders, but for irregular particles such as sand and crushed glass, the shape and size are not clearly defined. All these factors decide as to how solids will be stored, how they will be separated, how they will be mixed, how their size will be reduced, how they will behave in a fluid, how they will be transported, and many more.

Aside from physical form of the solids, the two important factors which must be defined for a solid material are shape and size. These are related since in order to define a size, one has to make some assumption about shape. For some regular shapes, there is a single measurement which completely defines the particle, e.g., if the diameter of the sphere or the side length of a cube is known, the volume and surface area may be easily calculated. For other regular shapes, more than one measurement is required. Cylinders require two: diameter and length; and cuboids require three: length, breadth, and depth. For irregular shapes, some typical dimensions must be defined. The simplest of the three-dimensional shapes is the sphere. The dimensionless term sphericity, Φ, is in common use to compare particles of irregular shapes with that of a spherical one. Hakon Wadell, in 1935, defined sphericity as the surface area of a sphere of the same volume as the particle divided by the actual surface area of the particle. In another way, sphericity can be defined as the ratio of the surface–volume ratio for a sphere of diameter Dp and the surface–volume ratio for the irregular particle whose nominal size is Dp . For a non-spherical particle, the sphericity is Φ=

Surface to volume ratio of sphere of diameter Dp Surface to volume ratio of particle whose nominal size is Dp

=

⎛ Sp ⎞ ⎜V ⎟ ⎝ p ⎠ sphere of particle volume ⎛ Sp ⎞ ⎜V ⎟ ⎝ p ⎠ particle

⇒Φ=

6 Dp

⎛ Vp ⎞ ⎜ ⎟ ⎝ Sp ⎠ particle

(2.1)

⎡ ⎤ π Dp 2 ⎢ ⎛ Sp ⎞ 6 ⎥ = = ⎢∵ ⎜ ⎟ ⎥ ⎢ ⎝ Vp ⎠ sphere of diameter D p 1 π Dp3 Dp ⎥ 6 ⎣ ⎦ = Nominal or equivalent diameter of sphere of equal volume of that of the particle, Sp = Surface area of one particle, and p = Volume of one particle. For a spherical particle of diameter p, from Eq. (2.1), the sphericity, Φ = 1.

where,

p

Sphericity values for solid particles of various shapes which we often encounter in process industries and for a few products are mentioned in Table 2.1 and Table 2.2 respectively.

Particle name

iagram

Sp ericity Φ

Particle name

iagram

Sp ericity Φ

Sphere

1.0

Cube

0.81

Sand

0.9

Crushed particles

0.6 to 0.8

Cylinder (length = diameter)

0.87

Flakes

0.2

Tetrahedron

0.671

Octahedron

0.846

Dodecahedron

0.91

Icosahedron

0.939

Ideal Cone

0.794

Hemisphere

0.84

Industrial products

Sp ericity Φ

(Size range = 55 – 440 μm) Silica sand Concentrates of rutile Ilmentite Titania slag

0.7 0.8 0.8 0.5

Food Materials Wheat Bean Intact red lentil Chickpea Coarse bulgur

Sp ericity Φ 0.01038 0.00743 0.00641 0.00240 0.01489

It is evident from the sphericity values given in Table 2.1 that as the shape of the particle deviates from that of a spherical shape, the sphericity goes on decreasing towards zero. For this, sphericity is sometimes defined as how close the irregular particle is to a spherical particle. It is to be noted that sphericity is independent of particle size because from the definition of sphericity it is clear that sphericity compares the surface area of the particle to that of the equivalent spherical particle and defines only the particle shape. For fine granular materials, it is difficult to determine the exact volume and surface area of a particle. For these materials Dp is usually taken to be the nominal size based on the screen analysis or microscopic examination. The surface area can be found from adsorption experiment or from pressure drop in a bed of particles. The volume can be calculated using a factor called volume shape factor. We know that the volume of a spherical particle is proportional to the cube of its diameter and if we assume the same is true for irregular particles, then Vp α Dp3 ⇒ Vp = aDp3

where, a = Volume shape factor. π For spherical particles, a = . 6 The reciprocal of sphericity is known as the surface shape factor. Thus, 1 Φs = Φ

(2.2)

(2.3)

From Eq. (2.1), we have the sphericity of a cube as 6 ⎛ Vp ⎞ Φ cube = . ⎜ ⎟ Dp ⎝ Sp ⎠ cube Here, for this cube, p = a3 and Sp = 6a2. To find p, we have to equate the sphere volume with the cube volume. π 3 6 Thus, D = a3 ⇒ Dp = a × 3 . 6 p π Thus,

Φ cube =

⎛ a3 ⎞ π 3 ⎜ 2 ⎟ = 6 = 0.81 a 6 ⎝ ⎠ 6 a× 3 π 6

(Ans)

Size is the linear dimension of the particle. Sphere is the ideal example again, whose size is defined by its diameter. For irregular particles, the size may be found as the average of the shortest and the longest dimension of the particle or, as the second-largest dimension. Sometimes, the size for irregular particles is defined in terms of the equivalent/ nominal diameter. Equivalent diameter is defined as the size of spherical particle having the same controlling characteristics as the particle under consideration. The controlling characteristics like volume, surface area, surface area per unit volume, settling velocity, etc., depend upon the system and the process in which the particle is involved. Different ways to express the particle size depending on the various controlling characteristics are surface diameter, mass diameter, volume diameter, and volume–surface (or Sauter) diameter. Particle sizes are expressed in different units depending on their size and are presented in Table 2.3.

Particle si e

nits

Coarse Fine Very fine Ultra fine

Inches or millimetres (in or mm) Screen size Micrometers or nanometres (μm or nm) Surface area per unit mass (m2/g)

The particle size can be measured using a wide range of measuring techniques, such as (i) (ii) (iii) (iv) (v) (vi) (vii)

Screening (for particles of size > 50 μm), Sedimentation (for particles of size range of 1–100 μm), Elutriation (for particles of size range of 5–100 μm), Electron microscopy (for particles of size range of 0.0005–5 μm), Light scattering (for particles of size range of 0.1–10 μm), Laser diffraction (for particles of size range of 0.1–600 μm), and Photon correlation spectroscopy (for sizes ranging from a few nanometres to a few μm).

Among all the methods mentioned above, one of the cheapest and easiest methods of particle size determination is the screening.

A sample of solid particles contains a wide range of particle sizes and densities for which their analysis becomes extremely difficult. For this reason, the whole sample is separated into a number of fractions, each of constant density and nearly constant size by some mechanical means and then each fraction is analysed separately, as discussed below. For a sample of uniform particles having diameter as p, total mass as m, and density of each particle as rp, the total volume of the particles is Vs =

m ρp

(2.4)

If the volume of one particle is vp then the number of particles in the sample is V m Ns = s = (2.5) vp ρ p × vp If the surface area of each particle is Sp then the total surface area of particles is m × Sp (2.6) As = N s × Sp = ρ p × vp Simplifying Eq. (2.1), we have Sp 6 = (2.7) vp Φ × Dp Replacing the value of

Sp

in Eq. (2.6), we have

vp As =

6m ΦDp ρp

(2.8)

And for a mixture of particles the analysis is done for each fraction of constant density and constant size. Equations (2.5) and (2.8) are applied to each fraction to estimate the number of particles and the total surface area and the results are added. In this text, we assume constant density for particles for ease of understanding. Using Eq. (2.8), we can calculate the surface area of the particles in each fraction provided the particle density and sphericity are known. The results for all the fractions are added to give what is called the specific surface of the mixture, Ass, or total surface area of a unit mass of particles. For particles having constant density and sphericity, the specific surface of the 6 x1 6 x2 6 xn sample is Ass = + + ...................... + Φρp Dp1 avg Φρp Dp2 avg Φρp Dpn avg ⇒ Ass =

6 Φρ p

i=n

∑D i =1

xi

(2.9)

pi avg

xi = Mass fraction in a given increment, n = Number of increments, and pi avg = Average particle diameter (average of smallest and largest particle diameter in the increment). The specific surface is an important property of solids and is dependent on the condition of the surface as well as the particle size. For regular particles, the estimation of specific surface is easy, but the task is difficult for irregular particles. In this connection, one parameter known as the specific surface ratio, NSSR, is popularly used to overcome the difficulty, which is defined as the ratio of the specific surface of the particle to the specific surface of a spherical particle of the same diameter. The specific surface ratio is a function of average particle diameter. If p avg is the average size of the particle then Assp N SSR = (2.10) ⎞ ⎛ 6 ⎜ρ ×D ⎟ ⎝ p p avg ⎠ where, Assp = Specific surface of the particle. where,

The specific surface for a mixture of particles containing many different sizes of particles of same density can now be expressed as A ss =

6 ρp

i= n

∑ i =1

N SSRi xi Dpi avg

(2.11)

For spherical particles, NSSR = 1. A plot of specific surface ratio versus average size of particles for a few common materials is given as Fig. 17, page 22 of Unit Operations by G G Brown, et. al., Wiley, New York, 1950.

To describe the particle size of a mixture, we use average size or mean diameters. It should be remembered that a mean size will describe only one particular characteristic of the sample and it is important to decide what that controlling characteristics is before the mean is calculated. The volume–surface mean diameter, Dvs, is the most widely used among all average sizes and is related to the specific surface area Ass. It is defined by 6 (2.12) Dvs = ΦAss ρp Substituting the value of Ass from Eq. (2.9) in Eq. (2.12), we have Dvs =

1 i= n

∑D i =1

(2.13)

xi

pi avg

This is also known as the Sauter mean diameter. It is defined by i= n

(

Dm = ∑ xi × Dpi avg i =1

)

(2.14)

This is also known as the mass mean diameter. This is the diameter of the average volume of particles found in the mixture and is found by dividing the total volume of the sample by the number of particles in the mixture. It is defined by 1/ 3

⎡ ⎤ ⎢ ⎥ ⎢ ⎥ 1 Dv = ⎢ ⎥ ⎢ i = n ⎛ xi ⎞ ⎥ ⎢∑⎜ 3⎟ ⎥ ⎢⎣ i =1 ⎝ Dpi avg ⎠ ⎥⎦

This is also known as the volume mean diameter.

(2.15)

It is defined by i= n ⎛

DA =

Ni ⎞ ⎟ pi avg ⎠

∑ ⎜⎝ D i =1

i= n

i= n ⎛

=

Ni ⎞ ⎟ pi avg ⎠

∑ ⎜⎝ D i =1

∑ Ni

(2.16)

NT

i =1

where, NT = Total number of particles. This is also known as the arithmetic mean diameter. All these mean diameters are based on different factors like volume–surface, mass, volume, number of particles, etc. The values of the mean diameter differ and are suitable for specific applications. For example, the mean diameter based on surface area is useful in the study of mass transfer, catalytic reactions, etc.; the mean diameter based on volume or mass is useful in the study of spray drying, in the gravitational free settling velocity of a particle in a liquid, etc.

The specific surface area and the Sauter mean diameters are given by the relations Ass =

6 Φρ p

i= n

∑D i =1

xi

and Dvs =

pi avg

1 i= n

∑D i =1

.

xi

pi avg

For finding these, we have to proceed as follows: Average diameter pi avg cm 0.0252 0.0178 0.0126 0.0089 0.0038

Mass fraction xi g g

xi D pi avg

0.088 0.178 0.293 0.194 0.247

∑ xi = 1.000

3.492 10.000 23.254 21.797 65.000

∑D

xi

pi avg

= 123.543

Thus, the specific surface area, Ass =

6 Φρ p

i= n

∑ i =1

xi Dpi avg

=

6 (123.543) 0.5 × 1.2

= 1235.43 cm 2/g

and the Sauter mean diameter, 1 1 Dvs = i = n = = 0.008094 cm = 8.094 × 10 −3 cm 123 543 . x ∑D i pi avg i =1

(Ans)

The volume–surface mean diameter is given by the relation 1 Dvs = i = n . For finding this, we have to proceed as follows: xi ∑D pi avg i =1 xi D pi avg –710 + 300 –300 + 180 –180 + 90 –90 + 38 Pan

505 240 135 64 38

30 35 65 70 55

0.117 0.137 0.255 0.275 0.215

0.00023 0.00057 0.00189 0.00429 0.00566

∑D

xi

= 0.01264

pi avg

1 (Ans) = 79.11 μm 0.01264 The negative (–) sign indicates that the material passes through the screen and the positive (+) sign indicates that the material is retained on the screen. The details about screening are discussed in Chapter 5 . Thus,

Dvs =

(Continued )

The average particle size (Eq. 2.13) is given by Dvs =

1 i= n

∑D i =1

.

xi

pi avg

Hence, by plotting a graph between 1/ pi avg and the cumulative mass fraction, , and then taking the inverse of the area under the curve, we can estimate the average particle size. Mes no

Mes opening mm

Avg particle si e pi avg mm

4 5 6 8 10 14 18 25 30 36 44 50 52 85 100 120 150 200 Pan

4.75 3.35 2.8 2 1.8 1.7 0.85 0.6 0.5 0.425 0.355 0.3 0.25 0.18 0.155 0.125 0.106 0.075 –

> 4.75 4.05 3.075 2.4 1.9 1.75 1.275 0.725 0.55 0.4625 0.39 0.3275 0.275 0.215 0.1675 0.14 0.1155 0.0905 0.0375

Mass retained g

Mass fraction overflo xi

Cumulative mass fraction

mm

33.5 324 315.5 120 182 78 79 39 29 26 27 28 40 26 27 28 29 69

0.022 0.216 0.210 0.080 0.121 0.052 0.053 0.026 0.019 0.017 0.018 0.019 0.027 0.017 0.018 0.019 0.019 0.046

0.022 0.238 0.448 0.528 0.650 0.702 0.754 0.780 0.800 0.817 0.835 0.854 0.880 0.898 0.916 0.934 0.954 1.000

0.247 0.325 0.417 0.526 0.571 0.784 1.379 1.818 2.162 2.564 3.053 3.636 4.651 5.970 7.143 8.658 11.050 26.667

pi avg

From the graph (Fig. 2.1) we have the area under the curve = 2.0995 mm−1. Area under t e curve as determined using rigin soft are Thus the average particle size = (area)–1 = (2.0995)−1 = 0.476 mm (Ans) 0

−1

25 20

1/

i

15 10 5 0 0

0.2

0.4

0.6

0. i n

iv

1

The Sauter mean diameter (Eq. 2.13) is given by Dvs =

1 i= n

∑D i =1

.

xi

pi avg

x = 0, pi avg = 1 μm and x = 1, pi avg = 101 μm The pi avg vs xi line (Fig. 2.2) is given by pi avg = mxi + c Given that at

(A)

100

n

0

i v

i

60 40 20 0 0

0.2

0.4

0.6 xi

0.

1

Here the slope, m =

101 − 1 100 = = 100. 1− 0 1

When pi avg = 1, xi = 0, then from Eq. (A), we have c = 1 micron. Thus, Eq. (A) becomes: (B) pi avg = 100 xi + 1 micron Now, for various values of xi, pi avg is calculated and xi / pi avg for each fraction was found out as follows: xi

pi avg

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

1 11 21 31 41 51 61 71 81 91 101

xi

pi avg

0.0000 0.0091 0.0095 0.0097 0.0098 0.0098 0.0098 0.0099 0.0099 0.0099 0.0099 Sum = 0.0972

Now, Sauter mean diameter, Dvs =

1 i= n

∑D i =1

xi

piavg

= 1/0.0972 = 10.29 microns

(Ans)

The properties of solids in bulk are dependent on the properties of the individual particles including their shape and size, and the way in which they interact with each other. When solid particles are dry and non-cohesive, they behave like a fluid, for example, they flow through orifice or openings and exert pressure on the side walls of the container. But they differ in many ways, like they pose greater problems in storage, do not come out from the container like fluids, interlock under pressure, and do not slide over one another unless the force applied reaches a certain magnitude. The pressure on them in one direction creates some pressure in another direction having lesser magnitude (than the applied pressure). For homogeneous solid particles, the ratio of the normal pressure, pN to the applied pressure, pA, is a constant. It is given by p (2.17) K= N pA which is the characteristic of the material and it is nearly independent of particle size. K is also known as the coefficient of flowability.

It (K ) depends on the three factors, such as shape and interlocking tendencies of the particles, degree of packing, and stickiness of the particles. The value of K is nearly equal to zero for cohesive solids and for free-flowing granular materials it varies between 0.3 and 0.6. The densities of the particles in bulk vary, depending on their physical properties and the way they are packed in the container. Regular particles like: spheres, cubes, etc., pack more densely than irregular ones. Both regular and irregular particles pack more densely if the bulk mass is subjected to vibrations. The frictional force within the particles is measured by using, the angle of internal friction, ai. The tangent of this angle is the coefficient of friction between two layers of particles. The angle of internal friction which determines the flowing characteristics of particles is important for the design of storage vessels like bins, silos, and hoppers. The angle of repose, ar is the angle at which the sides of the pile make with the horizontal when solids are piled up on a plane surface, as shown in Fig. 2.3. It is useful for a determining the capacity of a bin or a pile and is also useful during transportation. For homogeneous solid particles, these two angles are nearly the same, but in practice, the angle of repose is less than the angle of internal friction because the solid particles at the exposed surface are more loosely packed than the materials inside the pile and, are drier and less sticky. The values of ar are low for smooth and rounded particles, and it is high for sticky and angular particles. In general, the values of ai vary between 15° and 30° for granular solids and it is as high as 90° for cohesive solids. Table 2.4 presents the values of ai and ar for different materials. When solid particles are poured on to a plane surface, they will form an approximately conical heap and the angle formed by the sloping side with horizontal plane surface is called the dynamic angle of repose, a , or, the angle of repose of the material when forming a pile. And when the solid is poured on to a sheet which is then tilted slowly until the particles start sliding, the angle of slide is referred to as the static

Material Anthracite coal Fine sand Bituminous coal Wet clay Gravel

Angle of repose ar 27° 31° 35° 17° 39 to 48°

Material Granular solids Cohesive solids

Angle of internal friction a i 15 to 30° ≅ 90°

Material

Particle s ape

Si e mm

Natural sand Manufactured sand Crushed stone Crushed stone Crushed stone Crushed stone Pebbles Dry earth Iron ore Coal

Round Cubic Cubic Slabby Cubic Slabby Round – Slabby –

0–3 0–3 0 – 63 0 – 63 0 – 25 0 – 25 0 – 63 – 0 – 63 0 – 100

ga ton m

a deg

b deg

1.6 1.6 1.5 1.4 1.4 1.5 1.5 1.4 2.7 0.9

35 35 40 40 45 30 30 40 40 30

40 40 45 45 55 35 35 40 45 35

angle of repose, b, or, the angle of repose of the material when reclaiming under pile. Table 2.5 shows some of the material features as provided by Metso Minerals Inc. The relation between the material characteristic K and the angle of internal friction ai is given by 1 − sin α i (2.18) K= 1 + sin α i Generally, a bulk solid is defined as numerous dry or wet solid particles ranging from fine powder to coarse-sized particles that are being handled in bulk form. All these materials are stored either outside in bulk manner or, in vessels like bins, silos, elevators, or process vessels. Coarse solids like coal, gravel, sand, and water-insoluble materials are stored outside in open and large piles, usually unprotected from weather. At the same time,

outdoor storage leads to environmental pollution like dusting or leaching of a soluble matter from the solids. Solids like rock salt, gunpowder, ind in i solid chemicals which are either valuv able or hazardous to be stored outside in v bulk, are stored in bins or silos. These are usually of cylindrical or rectangular shape and made of metal, or reinforced concrete. Bins are used to store abrasive materials and are wider and short in height. Silos are tall and smaller in diameter, as shown in Fig. 2.4. The vertical portion of these vessels is the cylinder and the converging portion is the hopper, as shown in Fig. 2.5. All these containers are charged through the open top and are usually discharged through openings at the bottom. With every storage vessel like a bin or a silo, there usually is friction between the vessel wall and the solid particles. And due to interlocking of the particles, the effect of this friction is observed throughout the solid mass. This frictional force at the wall tends to reduce the weight of the solids and thus the pressure exerted by the solids on the vessel floor gets reduced. Apart from friction, the actual pressure depends on two other parameters, namely • the K (= pN /pA ) values of the solids, and • the manner in which solids are packed in the container. It is interesting to note that when the height of the solids in the container exceeds more than three times the diameter of the container, the additional solids have no effect on the pressure at the vessel floor, rather increase the load on the foundation [McCabe, 1993]. Another important point to be noted is the increased pressure often packs the granular solids more tightly and makes the flow more difficult, which is not the case for fluids. At a same cross-section inside a bin or a silo, the lateral pressure on the bin wall is less than the vertical pressure, as the ratio of normal pressure to the applied pressure K is less than unity. Therefore, the bottom discharge of solids is generally preferred over the side discharge.

It is essential for the design engineer to have knowledge of the properties of the bulk material to be handled and the theory of flow of solids either in designing a new storage vessel or modifying an existing structure to improve their flow. Specific factors affecting the flowability of granular solids and powders are moisture content, humidity, temperature, pressure, and particle size. A few important flowability-related properties are angle of repose, bulk density, frictional forces, and compressibility. Stainless steel is used as the most common material of construction for storage vessels. Generally, people think that if one beats the structure or shakes it, a proper flow can be obtained, but in actual practice, these actions cause flow problem in a number of cases rather than solving it. The flow rate of the bulk solids can be increased by increasing the size of the outlet, by vibrating the vessels, and by an air injection system.

Generally, three types of flow patterns are observed funnel flow, mass flow, and expanded flow. All these have different characteristics that must be understood in order to address the flow problems of bulk solids. The funnel-flow pattern is best suited for free-flowing, non-segregating bulk solids and not recommended for cohesive solids. A cylindrical flow channel develops at the centre of the bin above the discharge outlet while the material against the bin walls remains stationary, as shown in Fig. 2.6. Once the central portion of materials is withdrawn, the material along the walls begins to flow laterally into the central column at an angle nearly equal to the angle of internal friction a i of the solids. In case of cohesive solids, a rat-hole may develop at the centre. This type of flow pattern can be referred to as first-in, last-out. If the hopper walls are not steep or if the inside wall of the vessel is rough, a funnel-flow pattern will develop and stagnant areas will appear along the hopper walls. This is the situation in many coal bunkers now-a-days, especially if the coal contains high amount of moisture or a lot of fines. Mass-flow pattern is ideal for cohesive solids and for those solids which degrade with time. In this type of flow, all of the bulk solids move whenever any of it is withdrawn, as shown in Fig. 2.7. As there is a flow along the walls, stagnant zones as well as rat-holes are also eliminated. Also, the solids velocity in the cylinder section is low. This type of flow can be referred to as first-in, first-out. Expanded flow type is a combination of both mass and funnel flow. In this case, funnel flow is observed in the upper portion while mass flow is observed in the lower section of the vessel. An expanded flow bin is shown in Fig. 2.8. Whatever the flow type may be, the flow of bulk solids includes the flow of air as all bulk solids have air between the particles and when the solid particles move, the air in the voids also moves along with them. Thus, the bulk density of solid mass gets affected by this air movement. During the flow of bulk solids, the pressure of solid particles increases from zero (i.e., atmospheric) at the top surface to a maximum at the transition region between the cylinder and the hopper sections. As the bulk solids flow down through the hopper, the solids pressure decreases and again becomes zero at the discharge end. In the cylinder section of the storage vessel, with the increase in solids pressure, the bulk density increases as the total volume of the voids decreases and at the same time, the air pressure in the voids increases. But in the hopper section as the solids pressure decreases, the volume of voids increases which reduces the bulk density and also the air pressure in the voids decreases, as shown in Fig. 2.9.

id ′

d n i

Ai

Certain problems associated with the flow of bulk solids are no flow, erratic flow, flushing, and segregation which are briefly discussed here. All these problems are common in every process industry and can result in quality problems, lost production, structural damages, personnel injuries, and loss of money and time. A high pressure often packs the solids more tightly rather increasing the flow. In some cases, a stable arch is formed over the hopper outlet and solids do not fall even when the material below them is removed. The arch is strong enough to support the weight of the material above it and it must be broken either by arch breakers or by air jets to induce flow again. It must be noted that vibrations tend to strengthen the arch as they cause more compaction of solid particles. Frequent formation and collapse of arches result in fluctuating discharge causing uneven vibrations which can lead to structural damage and personnel injuries. When an arch collapses, the solids fall uncontrollably into the open channel under pressure. This situation is referred to as flushing or flooding. During the filling of a storage vessel, the finer particles move towards the central portion while the larger particles move towards the wall which causes finer particles to discharge first and coarser particles last.

❑

Φ=

❑

Vpα Dp3 ⇒ Vp = aDp3 a=

6 ⎛ Vp ⎞ Dp ⎜⎝ S p ⎟⎠

π . 6 Φs =

❑ ❑ ❑ Ns =

V m = . v p ρp × v p

❑ As = Ns × S p =

m × Sp

ρp × v p

=

❑ Ass = ❑

6m . ΦDp ρp 6 i =n xi . ∑ Φρp i =1 Dpi avg

, NSSR =

Assp ⎛ ⎞ 6 ⎜ ⎟ ⎝ ρp × Dpavg ⎠

❑ Ass =

.

6 i =n NSSRi xi . ∑ ρp i =1 Dpi avg

❑ Dvs = i=n

(

Dm = ∑ xi × Dpi avg i =1

)

i=n

1 xi

∑D i =1

1/3

⎤ ⎡ ⎥ ⎢ ⎥ ⎢ 1 ⎥ Dv = ⎢ ⎢ i=n ⎛ x ⎞ ⎥ i ⎢ ∑⎜ ⎟⎥ ⎢ i =1 ⎜⎝ Dpi avg3 ⎟⎠ ⎥ ⎦ ⎣

pi avg

. particle

1 . Φ

i=n ⎛

DA =

Ni ⎞ ⎟ pi avg ⎠

∑ ⎜⎝ D i =1

i=n

∑ Ni

i=n ⎛

=

Ni ⎞ ⎟ pi avg ⎠ . NT

∑ ⎜⎝ D i =1

i =1

❑

K=

pN , pA

❑

❑ K=

1 − sinα i . 1 + sinα i

❑

1. What is the importance of internal friction It determines the flowing characteristics of the particulate solids and is important for the design of the storage vessels. 2. Which type of solids has a higher value of internal friction granular or cohesive Cohesive type of solids. 3. Why is it necessary to determine the angle of repose for solids It is useful to determine the storage capacity for solids. 4. Depending on the flowability, how are the particles classified Cohesive (reluctant to flow through the openings) and non-cohesive (readily flowable out of the storage).

5. What are the common types of flow encountered in bulk solids handling Funnel flow, mass flow, and expanded flow. 6. Which type of flow is seen in case of flow of wheat grain from a storage bin Funnel flow. 7. What type of flow pattern is observed in case of pulverized coal Mass flow. 8. What is the sphericity of a cuboid whose length, breadth, and depth are in the ratio of 3 : 2 : 1 The volume of the cuboid is = 3 × 2 × 1 = 6 cubic units and surface area of this cuboid = 2 (3 × 2) + (3 × 1) + (2 × 1) = 22 area units.

Let, p = diameter of the equivalent sphere. π 3 Then, D = 6 ⇒ Dp = 2.254 6 p Area of the sphere = p p2 = 15.96 Thus, sphericity = 15.96 / 22 = 0.726. 9. Name the important factors on which flowability of solids depend.

The factors are (i) moisture content, (ii) particle size, (iii) temperature, (iv) pressure, and (v) humidity. 10. Give a few flow-related properties for the granular solids. (i) angle of repose, (ii) bulk density, (iii) frictional forces, and (iv) compressibility.

1. Why is it necessary to characterise solid particles 2. Define shape and size for solid particles. 3. Mention sphericity values for particles of various shapes and give some practical examples. 4. Is sphericity independent of particle size 5. Name the methods available to measure the particle size along with their size range. 6. How are the total surface area and number of particles in a given sample of uniform size and density determined 7. How is the specific surface of a given sample having mixed particle sizes determined 8. What are the different ways to represent particle size of a mixture

9. Are all the mean diameters same 10. How do the solid particles behave in bulk 11. What are the angle of repose and angle of internal friction Write their importance. Also, mention their values for different materials. 12. How are bulk solids stored 13. Write briefly about the pressure developed by solid particles in bins or silos. 14. Write in detail about the flow of bulk solids from bins or silos. 15. Briefly explain the problems associated with bulk-solid flow. 16. Why is it generally preferred to take the discharge from the bottom of the container rather than from its side walls 17. How to increase the solid-flow rate out of bins

1. Find the shape factor of a cylindrical particle of 3-mm diameter and 3-mm length. 1.145

2. What is the sphericity of a cylindrical particle whose length is equal to its diameter 0.873

3. Calculate the Sauter mean diameter and mass-mean diameter for the following screen analysis. Si e mm

Mass retained g

– 1.70 0.85 – 0.85 0.60 –0.60 0.50 –0.50 0.425 Pan

25 30 40 35 20

[D vs = 0.585 mm and Dm] = 0.670 mm 4. Calculate the volume–mean and the volume–surface mean diameter for the following screen analysis. Mes No 4 5 6 8 10

Mes opening mm

Mass fraction

4.75 3.35 2.80 2.00 1.80

– 0.15 0.45 0.30 0.10

[D v = 2.644 mm and v D

s

= 2.77 mm]

5. Calculate the range of the values for internal friction for which a material is flowable. 14.48° to 32.58°

1. Arrange the following particle shapes in order of increasing sphericity: cube, sphere, cylinder, and hemisphere. (a) cylinder, cube, hemisphere, sphere (b) hemisphere, cube, cylinder, sphere (c) cube, cylinder, hemisphere, sphere (d) cube, hemisphere, cylinder, sphere

3. When compared to cohesive solids, the value of internal friction for granular solids is (a) higher (b) lower (c) nearly equal (d) none of the above

2. Which of the following shapes has the highest shape factor (a) Cylinder (b) Cube (c) Hemisphere (d) Sphere

4. The value of internal friction for granular solids varies from (a) 5°–10° (b) 10°–15° (c) 15°–30° (d) 40°–50°

5. Which of the following is a non-cohesive material (a) Plastic chips (b) Dehydrated peas (c) Dry sand (d) All of the above 6. For a cylindrical particle of height equal to twice the diameter, the sphericity value is (a) 0.655 (b) 0.728 (c) 0.832 (d) 0.915 7. The shape factor for a hemisphere is (a) equal to 1 (b) greater than 1 (c) less than 1 (d) none of the above 8. A bin is a rectangular or cylindrical storage vessel with

(a) (b) (c) (d)

1(d);

7(b);

DA Dm

Dv D vs

2(b); 3(b);

4(c);

5(d);

6(c);

height equal to width (diameter) height more than width height less than width nothing in particular

9. Which of the following particle has the lowest value of sphericity (a) Rounded sand (b) Pulverized coal (c) Tungsten powder (d) Mica flakes 10. For measurement of particle size in the range of 0.1–10 μm, the technique adopted is (a) sedimentation (b) screening (c) elutriation (d) light scattering

8(c);

9(d);

10(d)

id

i

d i

Fin

id

i n n

Size reduction of solids is carried out in almost all the process industries for a number of reasons. A few of them are (i) to increase the surface area, because in most chemical reactions and some unit operations (drying, adsorption, leaching, etc.) involving solid particles, the reaction/transfer rate is directly proportional to the area of contact between the solid and the second phase, (ii) to produce solid particles of desired shape, size or size ranges, and specific surface, (iii) to separate unwanted particles effectively, (iv) to dispose solid wastes easily, (v) to mix solid particles more intimately, and (vi) to improve the handling (storage and transportation) characteristics.

Various size-reduction equipments employ different actions to solid particles for size reduction, which is customer tailored. There are four basic ways to reduce the size of a material— impact, compression, attrition, and shear Pennsylvania, 2006 . Most of the size-reduction equipments employ a combination of all these size reduction methods. Apart from the above, another, but less popular, size-reduction method is cutting, which gives a particle of definite size and shape.

Here, the particle is subjected to a single violent force and in crushing terminology, it refers to the sharp, instantaneous collision of one moving object against another. Both objects may be moving, such as a cricket bat connecting with a fast moving ball, or one object may be motionless, such as a rock being struck by a hammer blow. There are two varieties of impact—gravity impact and dynamic impact. In gravity impact, the free-falling material is momentarily stopped by the stationary object. Coal dropped onto a hard steel surface is an example of gravity impact. It is most often used when it is necessary to separate two materials which have relatively different friability. The more friable material is broken first, while the less friable material remains

unbroken. Materials dropping in front of a moving hammer is an example of dynamic impact. When crushed by dynamic impact, the material is unsupported and the force of impact accelerates movement of the reduced particles towards the breaker plate and/or other hammers. The use of dynamic impact is advantageous for size reduction of many materials and it is specially needed when (i) a cubical particle is needed, (ii) finished product must be well graded and must meet intermediate sizing specifications, as well as top and bottom specifications, (iii) ores must be broken along natural cleavage lines in order to free and separate undesirable particles, such as mica in feldspars, and (iv) materials are too hard and abrasive [Pennsylvania, 2006].

Here, the particle is broken by two forces and the size reduction is done between two surfaces, with the work being done by one or both surfaces. aw crushers (discussed later in this chapter) using this method of size reduction are suitable for reducing extremely hard and abrasive rock. As a mechanical reduction method, compression is chosen (i) (ii) (iii) (iv) (v)

if the material is hard and tough, if the material is abrasive, if the material is not sticky, where the finished product is to be relatively coarser in size, and when the material will break cubically [Pennsylvania, 2006].

Attrition is a method of size reduction by rubbing or, scrubbing the materials between two hard surfaces. Hammer mills (discussed later in this chapter) operate with close clearances between the hammers and the screen bars, reduce the size of materials by attrition combined with shear and impact actions. Though attrition consumes more power, it is preferred for crushing the less abrasive materials such as pure limestone and coal. Attrition crushing is most useful when (i) the material is friable or not too abrasive, and (ii) a closed-circuit system is not desirable to control the oversize [Pennsylvania, 2006].

Shear consists of a trimming or cleaving action rather than the rubbing action associated with attrition. It is usually combined with other size-reduction actions, e.g., single-roll crushers (discussed later in this chapter) employ shear together with impact and compression. Shear method of size reduction is needed for (i) friable material, (ii) primary crushing with a reduction ratio (disscussed later in this chapter) of 6 to 1, and (iii) production of a relatively coarse product [Pennsylvania, 2006].

For a particular size-reduction operation, the choice of machine to be used mainly depends on (i) the size and the quantity of material to be handled, and (ii) the nature of the product required. But, the more important aspects about the feed material apart from its size and quantity are its properties such as hardness, toughness, stickiness, moisture content, friability, explosive nature, soapiness, crystallinity, and temperature sensitivity. The hardness of the material is its resistance to scratching and it affects the power consumption and the wear on the grinding machine. The Mohs Scale (Table 3.1) which was created in 1812 by the German mineralogist Friedrich Mohs, is commonly used to measure the hardness of minerals and many other solids. Toughness is the resistance of a material to impact. It is the reverse of friability or brittleness. Granular materials (such as coal or rock) can be easily crushed while fibrous materials need tearing action. The friability of the material is its tendency to fracture during normal handling. Generally, crystalline materials will break along well-defined planes. Materials do not flow well if the moisture content is higher (more than 3 to 4% by weight). They tend to cake and clog the machine which reduces the crushing effectiveness. Too dry a condition can result in excessive dust. Explosive materials must be ground under wet conditions or in the presence of an inert environment. Soapiness is the measure of the coefficient of friction, m, of the surface of the material. If m is low, the crushing will be more difficult.

Mo

ardness number

Materials

Category of materials

1 2 3

Talc, waxes, soapstone Rock salt, gypsum, soft coal Calcite, chalk, marble

Soft materials

4 5 6

Fluorspar, magnesite, limestone Apatite, chromite, bauxite Felspar, ilmenite

Intermediate hardness

Quartz, granite Topaz Corundum, sapphire, emery Diamond

Hard materials

7 8 9 10

Every solid material has a specific crystalline pattern. The atoms in the crystal are arranged in a definite, repeating geometric pattern and there are certain planes in the crystal, called cleavage planes, along which the breakage occurs when sufficient pressure is applied on the solid. The heat generated during size reduction can result in loss of heat-sensitive components from solids. Softening or melting may also be important-leading to clogging. In some cases, cryogenic crushing may be necessary using liquid nitrogen or, dry ice, e.g., in milling of spices or size reduction of meat.

Apart from the properties of solids, certain factors affecting the size-reduction process in terms of capacity and the performance are Metso, 2007 (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x) (xi)

presence of moisture and sticky materials in equipments feed, presence of fines in the feed, segregation of feed particles in the crushing chamber, lack of feed control, wrong motor size, insufficient crusher discharge area, insufficient capacity of the crushers discharge conveyor, materials being extremely hard to crush, surface energy of solids, power consumption, and selection of an appropriate crushing chamber.

When external stress/force is applied for size reduction, the solid particles at first are twisted and strained. The work required to strain them is stored temporarily in the solids as the mechanical energy of stress. When additional force is applied to these already stressed particles, they are distorted beyond their ultimate strength and are suddenly broken into smaller particles, which ultimately generate new surfaces. The unit area of solid has a definite amount of surface energy and when its size is reduced, the surface area per unit mass, specific surface, increases. This creation of a new surface requires work, which is supplied by the release of energy of stress at the time of rupture. But, it is important to note that only a small portion out of the total energy supplied to the equipment is utilised for the creation of a new surface and most of the energy is lost to overcome the friction (in the bearings and other moving parts of the machine); as heat (because by the principle of conservation of energy, all energy of stress in excess of new surface energy created are converted to heat); and as sound. Thus, the energy efficiency is less and when most of the energy is lost, the cost of power becomes a major constraint. A schematic diagram for the creation of a new surface is shown in Fig. 3.1. The crushing or grinding efficiency is one of the most important parameters in the subject of size reduction as the cost is represented in terms of energy, which draws much attention to the design engineers. But no such exact definition is available to define this entity.

nd id i

i

n in

i

d i

i n n d

M

ni

We know that energy is required to effect size reduction/comminution, or in other words, comminution may be a process of conversion of energy from one form to another. The energy is utilised in the form of kinetic energy and the energy recovered is in the form of potential (surface) energy, heat, and sound. But only the potential energy is needed for use. Hence, the crushing efficiency can be defined as the ratio of the surface energy created to the energy absorbed (kinetic energy) by the solid. In another way, this may be defined as the ratio of the energy absorbed by the solid to form heat and the energy input to the machine. The crushing or grinding efficiency ranges from a value as low as 10−3 per cent to a maximum of one per cent. The remainder of the total energy input is converted to heat, sound, and the rest is wasted. It is of much interest to note that when wheat flour comes out of a flour mill, the temperature of the mass rises by 10 to 20 C. The quantities needed to calculate the efficiency are total energy input, energy lost during size reduction, total new surface created , and specific surface energy. The total energy input can be measured either by mechanical means or by electrical instruments. The energy lost is difficult to measure but it may be measured in terms of energy consumption. Surface area may be determined from size distribution data or measured directly by flow through a powder bed or by the adsorption of gas molecules on the powder surface. Other methods such as gas diffusion, dye adsorption from solution, and heats of adsorption can also be used. The specific surface energy of liquids can be measured with precision as it is numerically the same as the surface tension. But for solids, indirect methods based on mathematical utilisation of physicochemical quantities only are available whose accuracy largely depends on the assumptions made in measuring it Gaudin, 1971 .

The determination of power consumption is important in the sense that the cost of power is a major expense in any size-reduction operation, and it is determined using crushing or grinding efficiency. As per definition, crushing efficiency is

ηc =

Surface energy created by crushing Total energy absorbed by the solid

(3.1)

Wa = Total energy absorbed by a unit mass of solid, J/kg Es = Surface energy per unit area, J/m2 and Assf, Assp = Areas per unit mass of feed and product respectively, (or, the specific surfaces), m2/kg, then, the surface energy created by crushing will be If,

Es (Assp − Assf)

(3.2)

Thus, using Eq. (3.1) and the above notations, the crushing efficiency, hc, becomes s ( Assp − Assf ) (3.3) ηc = a

But, we know that the energy absorbed by unit mass of the solid (Wa) is less than the energy fed (W ) for the purpose to the machine. A portion of the total energy input is used to overcome friction in the bearings and other moving parts, and the rest is available for size reduction, which leads to mechanical efficiency. Mechanical efficiency, hm, is defined as the ratio of energy absorbed and the energy fed to the machine. Thus, ηm = a (3.4) From Eq. (3.4), the total energy input is =

a

ηm Now, putting the expression for Wa from Eq. (3.3) in Eq. (3.5), we have s

(A

ssp

− Assf

(3.5)

)

(3.6) ηmηc If m is the flow rate of solids to the machine then the power required, P, by the machine is the product of the total energy input and the flow rate. Thus, =

=

×m

(3.7)

Using the expression for W from Eq. (3.6), we have =

s

(A

ssp

)

− Assf m

ηmηc

(3.8)

The expressions for the specific surfaces of feed and product materials (as per the Eq. 2.11) are 6 6 Assf = and Assp = (3.9) Φ f Dvsf ρpf Φ p Dvsp ρpp

where, Φf, Φp = Sphericity of the feed and the product materials, Dvsf , Dvsp = Sauter mean diameter for the feed and the product, m and rpf, rpp = Density of the feed and the product materials, kg/m3. For the homogeneous materials, rpf = rpp = rp (say) Using equations (3.9) and (3.10) in Eq. (3.8), we have 6 sm ⎛ 1 1 ⎞ = − ⎜ ⎟ ηm ηc ρp ⎝ Φ p Dvsp Φ f Dvsf ⎠

(3.10)

(3.11)

This relation tells us that the power requirement for crushing will be more for particles having higher surface energy and also for the higher flow rate. All the particles (each having certain surface area) in an unit mass of solid particles have a definite amount of surface energy and when their size is reduced, their surface area as well as the surface energy per unit mass increases. And when this occurs, the power requirement becomes more and more for reducing fine particles to still finer ones than for breaking down large pieces of rock.

It is almost impossible to find out the accurate amount of energy requirement in order to effect size reduction of a given material, mainly because (i) there is a wide variation in the size and shape of particles both in the feed and product, and (ii) some energy is wasted as heat and sound, which can t be determined exactly. But, a number of empirical laws have been proposed to relate the size reduction with the energy input to the machine. They are Rittinger s Law (1867), Kick s Law (1885), and Bond s Law (1952). According to this law, the wor re uired for size reduction is proportional to the new surface area created. Mathematically, this law can be written as R

=

m

=K

S

(A

ssp

− Assf

)

(3.12)

1 . ηc Using Eq. (3.9), Rittinger s law can be written as

where K = constant =

R

=

m

= 6K

S

⎞ ⎛ 1 1 − ⎜ ⎟ ⎝ Φ p Dvsp ρpp Φ f Dvsf ρpf ⎠

(3.12a)

For particles of constant sphericity and density, the work required will be R

where, K R =

=

⎛ 1 6K S ⎛ 1 1 ⎞ 1 ⎞ − − ⎜ ⎟ = KR ⎜ ⎟ Φρp ⎝ Dvsp Dvsf ⎠ ⎝ Dvsp Dvsf ⎠

6K S , is known as ittinger s constant. Φ ρp

(3.13)

Sometimes the expression KES is used as Rittinger s constant. But in the present 6K S text both the expressions and KES are used as Rittinger s constant. However, Φρ p 6K S the expression K R = is more valid as it involves both sphericity and density Φρ p terms. The inverse of Rittinger s constant is known as ittinger s number. Rittinger s law is applicable mainly to that part of the process, where new surface is being created and holds most accurately for fine grinding where the increase in surface per unit mass of material is predominant. Also, this law is applied in cases where the energy input per unit mass of material is not too high. This law is applicable for feed size of less than 0.05 mm. This law states that the wor re uired for crushing a given mass of material is constant for a given reduction ratio irrespective of the initial size. The reduction ratio is the ratio of initial particle size to final particle size. Mathematically, WK =

⎛ P = K K ln ⎜ m ⎝

⎞ ⎟ vsp ⎠ vsf

(3.14)

where, KK = ic s constant. For example, if a given quantity material is being crushed from 100 mm to 20 mm or, from 30 mm to 6 mm then in both the cases the energy requirement will be the same as the reduction ratio (100/20 = 30/6 = 5) is same for both the cases. Kick s law is based on stress analysis of plastic deformation within the elastic limit. This law is more accurate than Rittinger s law for coarse crushing where the surface area produced per unit mass is considerably less. This law is applicable for feed size of greater than 50 mm. Neither of the two laws mentioned above (Rittinger s or Kick s) give the accurate energy requirement and both the laws are applicable over a limited range of particle size, and hence, they have limited utility. But in the year 1952, F C Bond suggested an intermediate law, which states that the wor re uired to form particles of size Dpp from a very large particle size is proportional to the s uare root of the surface to volume ratio sp vp of the product. This law is applicable for feed size between 0.05 and 50 mm. Using Eq. (2.1), we have Sp 6 (2.1a) = Vp Φ Dp Mathematically, Bond s law can be written as

B

=

⎡⎛ S ⎞ ⎤ 6 6 1 p ⎥=K =K × = Kb = K ⎢⎜ ⎟ ⎢⎝ Vp ⎠ ⎥ ΦDpp Φ m Dpp p⎦ ⎣

where, K is some constant and K b = K

6 = ond s constant. Φ

1 Dpp

(3.15)

But more precisely, Bond s law can be written as ⎛ 1 1 ⎞ K = = − ⎜ ⎟ B b ⎜⎝ Dpp m Dpf ⎟⎠

(3.16)

1

When feed size is very large, the term

becomes negligible and the expresDpf sion for Bond s law remains same as shown in Eq. (3.15). The Bond s constant (Kb), is dependent on the type of machine used and on the material to be crushed. And it is found more accurately using wor index, i. It is defined as the gross energy re uirement in ilowatt hour per short-ton of feed h ton of feed to reduce a very large particle to such a size that % of the product will pass through a - m or . -mm screen. From the Eq. (3.15), we have 1 ⇒ K b = i Dpp (3.17) i = Kb Dpp Now, if P is in kW, m is in tons per hour, and (i) (ii)

is in μm then Kb = 10 Wi, and pp is in mm then K b = 0.1 i = 0 .3162 pp

i.

Thus, if 80% of feed particles pass through a pf mm screen and 80% of product particles pass through a pp mm screen then Eq. (3.16) can be written as B

=

m

= 0.3162

i

⎛ 1 1 − ⎜ ⎜⎝ Dpp Dpf

⎞ ⎟ ⎟⎠

(3.18)

The Bond work index provides a measure of how much energy is required to grind a sample of materials. Table 3.2 indicates some typical figures, a relative measure of what they mean. These values are for wet grinding and generally do not vary from one machine to another. For dry grinding the materials, these values are multiplied by 4/3.

Property

Soft

Medium

kWh ⎞ Bond WI, ⎛⎜ ⎝ tonne ⎟⎠

7–9

9–14

ard 14–20

ery ard >20

All the above three laws can be derived from a generalised differential equation relating to work required for crushing and the particle size. Mathematically, this can be written as

( ) ( )

Dvs ⎛ ⎞ ( ) = ⎜ ⎟ = −K n ⎝ m⎠ Dvs

(3.19)

Putting n =2, 1, and 1.5 in Eq. (3.19) and integrating between suitable limits, we will get Rittinger s, Kick s, and Bond s laws respectively.

Rittinger s law (Eq. 3.13) is

⎛ 1 1 ⎞ = KR ⎜ − ⎟. m ⎝ Dvsp Dvsf ⎠

Given in this problem are Dvsf = 50 × 10 −4 m, Dvsp = 10 × 10 −4 m, and m = 20 onne / h. As 5 kW of power is consumed for running the mill empty out of 40 kW of power fed to the mill, the actual power consumption is P = 40 – 5 = 35 kW. Putting all these values in the above equation, we have 35 1 1 ⎛ ⎞ = KR ⎜ − ⎝ 10 × 10 −4 50 × 10 −4 ⎟⎠ 20 ⇒ 1.75 = K R (1000 − 200) = 800 K R ⇒ K R = 2.1875 × 10 −3

kWh.m tonne

This value of KR is constant for the machine. Now, for Dvsf = 10 × 10 −4 m, Dvsp = 5 × 10 −4 m, and m = 12 tonne / h, we have 1 1 ⎛ ⎞ = 2.1875 × 10 −3 ⎜ − −4 −4 ⎟ ⎝ 12 5 × 10 10 × 10 ⎠ ⇒

= 2.1875 × 10 −3 × 12 ( 2000 − 1000)

⇒

= 26.25 kW

(Ans)

Rittinger s law (Eq. 3.12 and 3.13) is

m

(

)

= K R Assp − Assf =

(A

ssp

− Assf

)

.

Rittinger's number

Given in this problem are m = 5 tonne/h = 1.39 kg/s, Assf = 100 m2/kg, Assp = 200 m /kg, and Rittinger s number = 0.0765 m2/J. Thus, the power required for crushing is 2

1.39

=

200 − 100 = 1307.19 0.0765

⇒

= 1816.99 J/s = 1816.99 W 1816.99 ⇒ = hp = 2.43 hp 745.7 The efficiency of the machine is 2.43 × 100 = 60.75% 4

(Ans)

(Ans)

Given in this problem are Volume surface mean diameter of feed materials, Dvsf = 50 mm, Volume surface mean diameter of crushed materials, Dvsp = 10 mm, and Energy consumption,

m

= 13.0 kW /( kg/s) = 3.61

kWh . tonne

Case–I Rittinger s law (Eq. 3.13) is

⎛ 1 1 ⎞ = KR ⎜ − ⎟. m ⎝ Dvsp Dvsf ⎠

1⎞ ⎛ 1 3.61 = K R ⎜ − ⎟ = 0.08 K R ⎝ 10 50 ⎠

Thus,

K R = 45.125

kWh.mm . tonne

(

When the same machine is used to crush the same material from 75 mm = Dvsf to 25 mm = Dvsp size, then

(

)

)

1⎞ ⎛ 1 = 45.125 ⎜ − ⎟ = 45.125 × 0.027 ⎝ 25 75 ⎠ m ⇒ 1.218

kWh tonne

(Ans)

Case–II Kick s Law (Eq. 3.14) is

Thus,

⎛D ⎞ = K K × ln ⎜ vsf ⎟ . m ⎝ Dvsp ⎠

⎛ 50 ⎞ 3.61 = K K × ln ⎜ ⎟ = 1.609 K K ⎝ 10 ⎠ ⇒ K K = 2.24

kWh . tonne

(

Now the energy consumption for crushing the same material from 75 mm = Dvsf to 25 mm = Dvsp size, is

(

)

m

kWh ⎛ 75 ⎞ = 2.24 × ln ⎜ ⎟ = 2.46 ⎝ 25 ⎠ tonne

)

(Ans)

Rittinger s law (equations 3.12 and 3.13) is Assp − Assf = K R Assp − Assf = m Rittinger's number

(

)

(

)

Given in this problem are m = 2700 kg/h = 0.75 kg/s and Rittinger s number for limestone = 77.4 m2/kJ = 0.0774 m2/J. Assf = 2.9 m2/kg, Assp = 103 m2/kg

For Crusher Thus, power required,

(

= m × K R Assp − Assf

)

0.75 × (103 − 2.9) = 969.96J/s = 969.96 W 0.0774 As the efficiency of the crusher is 20 %, the actual power requirement is 969.96 = 4849.8W ≅ 4.85 kW. 0.20 For Grinder Assf = 103 m2/kg, Assp = 865 m2/kg. ⇒

Thus, power required,

=

(

= m × K R Assp − Assf

)

0.75 × (865 − 103) = 7383.72 J/s = 7383.72 W 0 0774 As the efficiency of the grinder is 25 %, the actual power requirement is 7383.72 = 29534.88 W ≅ 29.53 kW. 0.25 Hence, the total power requirement for the drive to run both the crusher and grinder is (Actual Power)Crusher + (Actual Power)Grinder = 4.85 + 29.53 = 34.38 kW (Ans) ⇒

=

Bond s law (Eq. 3.18) is

m

= 0.3162

⎛ 1 1 ⎞ − ⎜ ⎟. i ⎜⎝ Dpp Dpf ⎟⎠

(i) Given in this problem are m = 150 tonnes/h, P = 270 kW, pp = 3 mm. Thus, work index,

⇒

i

=

i

=

pf

= 50 mm, and

⎛ 1 1 ⎞ 0.3162 × m × ⎜ − ⎟ ⎜⎝ Dpp Dpf ⎟⎠

270 = 13.06 kWh/tonne ⎛ 1 1 ⎞ 0.3162 × 150 × ⎜ − ⎟ ⎝ 3 50 ⎠

(Ans)

(ii) For the same feed at same feed rate, if pp = 1.5 mm, the power required will be ⎛ 1 1 ⎞ = 0.3162 × m × i ⎜ − ⎟ ⎜⎝ Dpp Dpf ⎟⎠ 1 ⎞ ⎛ 1 = 0.3162 × 150 × 13.06 ⎜ − ⎟ = 418.16 kW ⎝ 1.5 50 ⎠

(Ans)

The amount of unground materials (220 microns), the cumulative amount of ground materials, and the amount of materials ground with time are given in the table below. Amount of unground materials (220 μm), g

60

20

15

10

8

4

Time, s

0

Cumulative amount of materials ground (W), g

0

60

90

120

150

240

40

45

50

52

56

Amount of materials ground (ΔW), g

0

40

5

5

2

4

Now, the percentage of materials ground can be calculated by the formula: ⎛ Weight in grams taken − Weight in grams remaining ⎞ ⎜⎝ ⎟⎠ × 100 = Weight in grams taken

(say)

Now, the incremental % material ground and incremental time are presented in the following table. Δt sec

M 60 − 20 × 100 = 66 % 60

60 – 0 = 60

20 − 15 × 100 = 25% 20

90 – 60 = 30

15 − 10 × 100 = 33.3% 15

120 – 90 = 30

10 − 8 × 100 = 20% 10

150 – 120 = 30

8− 4 × 100 = 50% 8

240 – 150 = 90

The specific rate of grinding can be found using the following formula:

∑( ⋅ Δ ) ∑ (Δ ) =

(66 × 40) + ( 25 × 5) + (33.3 × 5) + ( 20 × 2) + (50 × 4) 56

= 56.63 % per second

(Ans)

Size-reduction equipments are classified (Table 3.3) on the basis of: (i) the mode of operation, (ii) the method by which a force is applied, and (iii) the size of feed and product.

(i)

Mode of operation → Batch operated → Continuous operated

(ii)

Method by which a force is applied → Impact Impact at one surface Impact between particles (Continued )

→ Compression bet een t o solid surfaces Crushing Grinding → Rubbing t e materials bet een t o surfaces → S ear action of t e surrounding medium → Nonmec anical introduction of energy Thermal shock Explosive shattering Electrohydraulic crushing Cryogenic crushing Ultrasonic grinding (iii)

Size of feed and product → Coarse crus ers large feed si e to mm product si e Jaw crusher (Blake and Dodge) Gyratory crusher Cone crusher Crushing rolls (smooth and toothed rolls) Bradford breaker → Intermediate Crus ers mm to mm product si e Roller mill Cage mill Granulator Hammer mill Impactor Vertical shaft impactor → Fine crus ers Grinders mm to ≅ mes Ball mill Pebble mill Rod mill Tube mill Attrition mill/Pulveriser → ltrafine grinders mm to mm Fluid energy or jet mill Colloid mill Classifying hammer mill Fine impact mill → Cutting mac ines definite si e bet een to mm lengt Knife Cutter Scissors

While selecting a size-reduction equipment, the following criteria must be considered Pennsylvania, 2006 : (i) It should produce the materials of desired shape and size or the size distribution desired. (ii) It should accept the maximum input size expected.

(iii) (iv) (v) (vi) (vii) (viii) (ix) (x) (xi) (xii) (xiii)

It should have a large capacity. It should not choke or plug. It should pass unbreakable materials without causing damage to itself. It should operate economically with minimum supervision and maintenance. The power input per unit weight of product should be small. It should resist abrasive wear. It should be dependable and have prolonged service life. The replacement parts should be readily available at cheaper rate. The initial fixed cost and the operating cost should be minimum. It should be easy and safe to operate. It should have easy access to internal parts for maintenance and last but not the least. (xiv) It should be a versatile one.

The coarse crushers (jaw, gyratory, and crushing rolls) employ mainly the compression action to large lumps of solid materials and are slow-speed machines. In these machines, the size reduction results from stresses that are applied to the solid particles to be crushed by some moving part in the machine and against a stationary part or against some other moving part. This compression action builds up strain within the particles to be broken, which results in fracturing whenever they exceed the elastic limit of the materials. And the coarse crushing is always conducted on dry materials. Another coarse crusher, the Pennsylvania Bradford Breaker, also widely used, crushes by gravity impact only.

Jaw crushers consist of two crushing faces (jaws) — one of them is fixed vertically to the frame, while the other one is movable, which is either pivoted at the top or at the bottom. Depending on the type of arrangement of the movable jaw, the jaw crushers are classified into two types — bla e and dodge. In the blake type, the movable jaw is hinged at the top so that the greatest movement at the bottom is given to the smallest lumps. In the dodge type, the movable jaw is pivoted at the bottom giving minimum movement of jaw at the bottom by which more uniform products are obtained. But this type is less widely used because of its tendency to choke. In this text, the discussion about jaw crushers is kept limited to the Blake type only.

It works on the principle of compression and there are no rubbing or grinding actions, and it generally produces cubical products with minimum fines. Generally, the Blake type of jaw crushers has cast-steel lined supporting frames for a vertical fixed jaw and for a movable jaw pivoted at the top such that they form a V-opening at the top. The crushing faces of the jaws are made of manganese steel so as to make them abrasion resistant. The movable jaw moves in a horizontal plane usually making an angle of 20 to 30 with the fixed jaw. The jaw faces are of several patterns for gripping the material and for concentrating the pressure on smaller areas. Figure 3.2 shows some of the jaw-plate profiles. The

nd d

d

v d

by permission, Metso Minerals Inc. d

v d by permission, Sandvik Mining & Construction, Sweden

standard profile is suitable for both rock and gravel crushing, while heavy-duty profile is recommended for extremely hard materials. When a high production rate is needed, a corrugated profile is recommended. Sandvik s jaw plates have the additional advantage that they are reversible, i.e., they can be used on both the stationary and moving jaws. In addition to the jaw plates, jaw crushers consist of eccentric, pitman, toggles, flywheel, shaft, draw back rod (tie rod), and spring. The eccentric causes the pitman to oscillate vertically, and this vertical motion of the pitman is transmitted to the movable jaw to have a back-and-forth motion horizontally by the toggles. The movable jaw is held against the toggle by a tie rod and spring. Depending upon the number of toggles used, jaw crushers are further classified into single- and double-toggle aw crushers, as shown in Fig. 3.3 Metso, 2007 . In the single-toggle jaw crusher, an eccentric shaft is positioned on the top of the crusher. Shaft rotation causes, along with the toggle plate, a compressive action. While the double-toggle crusher has two shafts and two toggle plates. The first shaft

in

is pivoted at the top of the crusher, while the second shaft is an eccentric shaft that drives both toggle plates. The moving jaw has a pure reciprocating motion towards the fixed jaw. The single-toggle jaw crusher has better capacity compared to a doubletoggle crusher of similar size because the chewing movement in a single-toggle jaw crusher causes compression at both material intake and discharge regions. Because the crushing action is intermittent, the loading on the machine is uneven, and hence a heavy flywheel is incorporated. The material to be crushed is fed through a hopper between the two jaw plates from the top. The materials caught between the upper part of the jaws are crushed to smaller size during the forward motion of the movable jaw. The crushed materials then drop down to the narrower space during the backward motion of the movable jaw and are re-crushed during the next forward motion. The materials come out of the bottom of the machine after sufficient size reduction. It must be noted that the speed should not be so high that the materials get crushed several times and produce large quantity of fines. The Sandvik Jaw Crusher (Fig. 3.4) is a single toggle type of jaw crusher having the deep symmetrical crushing chamber designed for maximising feed size, capacity, and size reduction. The nip angle is so adjusted that the material progresses smoothly down through the crushing chamber to enable high reduction, productivity, and proper utilisation of jaw plates. The specialty in Sandvik jaw crushers is that the feed openings are effective and active, as shown in Fig. 3.5. Due to the symmetrical arrangement of the crushing chamber, the effective feed opening becomes equal to the nominal feed opening. A replaceable deflector plate is attached to the top of the moving jaw, which protects the top of the moving jaw from the impact of the feed materials. The use of a deflector plate is advantageous as large lumps fall straight into the active region of the crushing chamber, so there is 1.

1.

2.

2. in

i

nd i n

in

in

ix . i n 4.

id

i nd d

in i 5. 7.

n 6. n

nd di in

7. 6.

5.

4.

.

i

i n

no need for a stationary cross-wall in the feed hopper area. Here, all of the effective feed opening is active and material is crushed right at the top of the crushing chamber. Sandvik jaw crusher models accept feed sizes of 800 to 1500 mm and operate between 200 to 300 rpm. The Pennsylvania Jaw Crusher (Fig. 3.6) is a double-toggle type of jaw crusher accepting feed sizes up to 1200 mm and produces a nominal product size as small as 19 mm. The product size is determined by the distance between lower ends of the two jaws which is adjustable. The moving jaw moves at 250 to 400 strokes per minute.

in

iv nin

d

A iv

d

nin

The theoretical capacity of a jaw crusher is =

ρp A

jN j

60

(1 − ε )

kg/h

(3.20)

where, rp = density of materials, kg/m3 A = area of swing, m2 Wj = jaw width, m Nj = number of swings per minute, min–1, and e = porosity of particles The machine must be protected from damage if accidentally some unbreakable materials like nuts, bolts, or iron pieces enter into the crushing zone. This is usually done by making one of the toggles in the driving mechanism relatively weak, so that if any large stresses are build up, the toggles break first. Jaw crushers are widely applied to crush rocks of high or mild hardness to soft ones, and ores as well as to slag, construction materials, marbles, and many more. They can be used in mining and metallurgical industries, construction, road, and railways.

Gyratory crushers were developed more recently in order to have greater capacity over jaw crushers. The crushing process of gyratory crushers is similar to that of jaw crushers in that the maximum movement is at the bottom but the face is made to gyrate inside a stationary shell.

Gyratory crushers, like jaw crushers, employ compressive force for size reduction. The gyratory crusher (Fig. 3.7) consists of two vertical conical shells, the outer shell having its apex in downward direction while the inner cone is positioned with its apex upward. The inner shell acts as the crushing head, which is in the form of a truncated cone and is mounted on an oscillating shaft. The upper end of this cone is held in a flexible bearing while the lower end is connected to an eccentric. The eccentricity causes the conical crushing head to oscillate between open side setting (o s s) and closed side setting (c s s) discharge openings. Hence, the crushing action takes place around the whole of the cone and is continuous. The eccentricity also determines the capacity of gyratory crushers. The material to be crushed is fed from the top and is crushed between the stationary outer shell and the crushing head. They are crushed several times before being discharged from the bottom. An additional crushing effect occurs between the compressed particles, resulting in less wear of the crusher materials. This is known as interparticular crushing Metso, 2007 . As the crushing action is continuous, the fluctuations in stresses are smaller than that in the jaw crushers. Also, the load on the motor is uniform and the power consumption is less. These crushers have a large capacity per unit area of grinding surface if used to produce a small size reduction. Further, these crushers do not take large feed as the jaw crushers do and produce a more uniform product. Because of high initial investment, to optimise operating costs, and to improve the product shape, it is recommended to use gyratory crushers under choke-feed conditions. This can be done using a stockpile or a silo, which reduces the fluctuations of feed material flow. Primary gyratory crushers form a critical transition between the mine or quarry and the plant. They reduce a wide range of feed to a manageable size suitable for further processing. Primary gyratory crushers are taller, heavier, and require a massive foundation than primary jaw crushers. Secondary gyratory crushers are normally used in the second crushing stage. In traditional gyratory crushers, the hydraulic adjustment of the main shaft is used only to compensate for wear. But Sandvik applies modern crusher control systems, known as utomatic Setting egulation-intelligent S i1 , to fine tune throughput as well as the size distribution. Sandvik s CG Series of primary gyratory crushers are available in five sizes. Table 3.4 gives capacity data for the Sandvik s CG Series gyratory crushers. The CG650 particularly matches the need 1

Trademark of Sandvik Mining and Construction, Sweden.

Reference

46 – 71

54 – 75

61 – 96

61 – 106

65 – 119

Model

CG650

CG820

CG840

CG850

CG880

748

523

451

276

181

Approximate eig t tonnes

Maximum feed si e mm inc 800 × 1100 × 1600 (31 × 43 × 63) 950 × 1300 × 1900 (37 × 51 × 75) 1050 × 1500 × 2100 (41 × 59 × 83) 1050 × 1500 × 2100 (41 × 59 × 83) 1130 × 1600 × 2260 (44 × 63 × 89)

Feed opening mm inc

1150 × 3170 (45 × 125)

1350 × 3350 (53 × 132)

1550 × 4140 (61 × 163)

1550 × 4140 (61 × 163)

1650 × 4410 (65 × 174)

410

420

430

440

460

ori ontal s aft RPM

1100

800

600

450

375

Motor W

200 – 305 (7.9 × 12.0)

180 – 290 (7.1 × 11.4)

150 – 260 (5.9 × 10.2)

125 – 230 (4.9 × 9.1)

105 – 190 (4.1 × 7.5)

pen side setting mm inc

6160 – 10940

4170 – 7750

2750 – 5420

1730 – 3620

1140 – 2430

Capacity range tonnes our

of large-scale quarries. The CG800 family covers the broad range of capacities needed in mining. The Nordberg Superior MK-II Primary Gyratory Crushers (Fig. 3.8) are based on the Super Spider concept consisting of an additional top shell using the same base to obtain a large feed opening and higher capacity. These crushers are equipped with

id nd v d in

in in

in i M n n in

M in d

n nd n

x n ini n d n

n d

nd n

d i n M in ii n n n in ii n

n d n

a hydraulic method of vertical adjustment for the main shaft to compensate for wear and control the product size. The main shaft position system is also used to clear the crushing chamber. In case of a sudden power failure, the mantle can be lowered to release the load. These crushers are available in six sizes. Table 3.5 gives capacity data for the Superior MK-II Gyratory Crushers Metso, 2007 . Unbreakable materials must be prevented entry into the crushing zone so as to protect the machine from damage.

The history of roll crushers is more than 200 years old but in recent years they lost their popularity over jaw and gyratory crushers due to their poor wear characteristics with hard rocks. Depending on the number of rolls employed, roll crushers are of two types — single-roll crushers and double-roll crushers. The single-roll crusher is one of the oldest and the simplest crushers which are mainly used for primary crushing, whereas double-roll crushers are used for secondary crushing.

Single-roll crushers employ three different methods of size reduction — impact, shear, and compression. Single-roll crushers are typically used as primary crushers. Pennsylvania single-roll crushers (Fig. 3.9) have a roll assembly consisting of a roll shaft and a fabricated roll shell with integral fixed teeth. Entering the crusher through the feed hopper, the feed material is struck by the teeth of the revolving roll. While some breakage occurs here by impact, the rotation of the roll carries the material into the crushing chamber formed between the breaker plate and the roll itself. As the turning roll compresses the material against the stationary breaker plate, the teeth on the roll shear the material. Sized materials fall directly out through the discharge end of the crusher which is completely open. As there are no screen bars, there is no re-crushing of the already sized materials, which helps to reduce the power demand while minimising the fines. The clearance between the breaker plate and the roll determines the product size and this clearance is adjustable from outside the machine by a shim arrangement. The Pennsylvania Crusher Corporation builds several types of single-roll crushers in a great number of sizes and capacities, with product sizes ranging from 75 to 300 mm depending on machine size. For protection against uncrushable materials, the breaker plate assembly of Pennsylvania single-roll crushers is attached to an automatic release device. As pressure from the uncrushable is exerted against the plate, the device allows the entire breaker plate assembly to move away from the roll instantly. The uncrushable drops out of the machine by gravity and the breaker plate assembly returns back to its normal position immediately. Pennsylvania single-roll crushers are used in crushing petroleum coke, coal, limestone, chemicals, phosphate rock, shale, and many other materials Pennsylvania, 2006 .

1065 (42)

1270 (50)

1370 (54)

1575 (62)

1525 (60)

1525 (60)

42–65

50–65

54–75

62–75

60–89

60–110

514

600

600

600

600

600

Pinion RPM

1000 (1400)

600 (800)

450 (600)

450 (600)

375 (500)

375 (500)

Max KW P

mm 1635 (1800)

mm

2575 (2840)

2555 (2820)

2245 (2475)

1880 (2075)

mm

4100 (4520)

3080 (3395)

2855 (3145)

2625 (2895)

2100 (2315)

mm

5575 (6150)

4360 (4805)

3280 (3615)

3025 (3335)

2760 (3040)

2320 (2557)

mm

5845 (6440)

4805 (5295)

3660 (4035)

3215 (3545)

mm

pen side settings of disc arge opening

6080 (6705)

5005 (5520)

3720 (4205)

3385 (3735)

mm

6550 (7520)

5280 (5820)

mm

millimeters inc es

6910 (7620)

5550 (6115)

mm

7235 (7975)

mm

7605 (8385)

mm

Note: The above capacities are based on an assumed feed where 100% of the feed passes 80% of the feed opening, 80% of the feed passes 50% of the feed opening and 30% of the feed passes a sieve size that is 10% of the top size. The capacities are for feed materials with a bulk density of 1,6 tonne/m3 (100 pounds per cubic foot). All capacities are calculated at maximum throw for each respective machine.

Feed opening mm in

Si e

Here, the crushing is primarily accomplished by compression. Pennsylvania double-roll crushers (Fig. 3.10) consist of two heavy metal rolls of equal diameter placed horizontally which are rotated towards each other at same or at different speeds. The rolls are mounted on heavy shafts. One of the rolls is motor driven while the other roll rotates due to friction. The gap between the two rolls is adjustable because of two reasons—the product size is determined by the size of the gap between the rolls and to compensate for wear. The rolls have narrow faces and are large in diameter so that they can squeeze sharply (nip) the large lumps. The roll surfaces may be smooth, corrugated, or, toothed. A number of roll tooth patterns are shown in Fig. 3.11. The materials to be crushed are fed from the top. As the rolls rotate they are nipped between them and get crushed by compression, and are discharged from the bottom. Compression crushing is extremely efficient, as energy is only used to crush those particles larger than the gap between the rolls. Fines are minimised because already crushed materials pass freely through the crusher with no further size reduction. Typical roll dimensions vary from 600 mm (24 in) in diameter with a 300-mm (12 in) width face to 2000 mm (78 in) in diameter with a 914-mm (36 in) width face. The speed of rolls varies from 50 to 300 rpm. These machines give a reduction ratio of 4 to 1 with few fines McCabe, 1993 . Pennsylvania double-roll crushers accept feed sizes up to 150 mm, though larger feed can be effectively handled in certain applications Pennsylvania, 2006 . The machine is protected against damage due to unbreakable materials like nut or bolts, by spring mounting at least one of the rolls. It retracts instantly when an unbreakable is encountered, then reverts to its original position once the unbreakable passes through the crushing chamber with no stoppage of the crusher.

id

id

Double-roll crushers are typically used in situations in which fines are to be minimised. They are employed for crushing of oil seeds, coal, phosphate rocks, abrasive materials, lime, limestone, petroleum coke, and explosive materials in gunpowder industries.

While selecting the rolls for a certain duty, it is necessary to know (i) the size of feed, (ii) the size of the product, and (iii) the amount of material to be handled.

The coefficient of friction between the roll surface and the material to be crushed, incorporated with a relation between the size of the feed and the size of the product fixes the diameter of rolls and also determines whether a particle will be drawn into the rolls and gets crushed or not Brown, 1995 . The assumptions followed for the calculations are (i) the particle to be crushed is spherical, (ii) the roll surfaces are smooth, and (iii) the gravity of the feed particle is negligible. Consider a spherical particle of diameter 2 that is to be crushed. It is positioned between a pair of crushing rolls of diameter 1 as shown in Fig. 3.12. Let 3 be the minimum spacing between the rolls which is also the maximum dimension of the crushed particles and AN be the angle between the two common tangents to the particle and each of the rolls. Let FT and FN be the tangential and normal forces acting on the particle respectively at a point of contact with the rolls, and let FR be the resultant force of these two forces. It may be noted that the particle will be nipped and gets crushed if the resultant force FR is directed downwards. Otherwise the particle will ride on the rolls or be thrown up and will not be crushed at all. In other words, if the vertical component ⎛ ⎛ A ⎞⎞ of the tangential force, FTV ⎜ = FT cos ⎜ N ⎟ ⎟ is greater than the vertical component ⎝ 2 ⎠⎠ ⎝ ⎛ ⎛ A ⎞⎞ of the normal force, FN ⎜ = FN sin ⎜ N ⎟ ⎟ then only the particle will be nipped and V ⎝ 2 ⎠⎠ ⎝ crushed between the rolls. Mathematically, this condition may be written as TV > N V ⇒

⎛A ⎞ cos ⎜ N ⎟ > ⎝ 2 ⎠

T

N

⎛A ⎞ sin ⎜ N ⎟ ⎝ 2 ⎠

D2 AN

id i

FT C E

R

2

FR FN

F

AN 2

A

D R1

D1

R

D

in B

AN (3.21) 2 N But, the ratio of the tangential force to the normal force is the coefficient of fricA (3.22) tion, m. Thus, from Eq. 3.21, we have μ > tan N 2 when, A (3.23) μ = tan N 2 ⇒

T

> tan

under this limiting condition of crushing, the angle AN is called the angle of nip. For all practical purposes, the value of the angle AN is usually taken as 32 . Now from the triangle AC , we have ⎛ A ⎞ AD cos ⎜ N ⎟ = ⎝ 2 ⎠ A ⇒ cos

AN = 2

+ + 1 1

3

(3.24)

2

D3 2 . Equation 3.24 gives the relationship between the size of feed, radius of rolls, and the gap between the rolls with the angle of nip. For AN = 32°, we have + 3 ⎛ 32° ⎞ (3.25) cos ⎜ = cos16° = 0.961 = 1 ⎝ 2 ⎟⎠ 1+ 2 where R3 = half the distance between two rolls =

Equation 3.24 can also be written in terms of diameters as A D + D3 cos N = 1 2 D1 + D2

(3.26)

AN at which the resultant force FR acts horizon2 tally is called the angle of bite and under this condition, there will be little or no crushing at all. The limiting value for the angle

The theoretical capacity of a crushing roll Q in kg/h is given by = 60 π D1 D3 Nρ

(3.27)

where, b = breadth of roll face, m N = number of revolutions per minute, rpm, and r = density of the material to be crushed, kg/m3. The volumetric capacity is affected by speed, nip, diameter, and breadth of roll face. And, the actual capacity is usually between 10 to 30 per cent of the theoretical one.

(i) From Eq. (3.26) we have cos Given in this problem are AN = 30°, cos

Thus,

1

AN D1 + D3 = . 2 D1 + D2

= 150 cm = 1.5 m, and

3

= 1 cm = 0.01 m.

30° 1.5 + 0.01 = 2 1.5 + D2

⇒ 0.965 =

1.51 1.5 + D2

⇒ D2 = 0.0647 m = 6.47 cm is the maximum feed size to the crusher.

(Ans)

(ii) The theoretical capacity of crushing rolls (Eq. 3.27) is = 60π D1D3 Nρ kg / h. Given in this problem are 1 = 1.5 m, 3 = 0.01 m, b = 50 cm = 0.5 m, N = 100 rpm, and specific gravity = 2.66. Thus, the density of limestone = 2.66 × 103 kg/m3. Now, the theoretical capacity, ⇒

= 60 × π × 1.5 × 0.01 × 0.5 × 100 × 2.66 × 103

= 376048.64 kg/h ≅ 376.049 tonne/h

(Ans)

Angle of nip (Eq. 3.23) is AN = 2 tan −1 μ and from Eq. (3.26) we have A D + D3 cos N = 1 . 2 D1 + D2 Given in this problem are m = 0.28, 1 = 140 cm = 1.4 m, and Now, AN = 2 tan−1 m = 2 tan−1 (0.28) = 31.28°. Thus,

cos

2

= 60 cm = 0.6 m.

31.28° 1.4 + D3 = 2 1.4 + 0.6

⇒ D3 = 0.526 m = 52.6 cm is the maximum size of product obtained from this crusher. (Ans) And when m = 0.32, the angle of nip, AN = 35.48°. Thus,

cos

35.48° 1.4 + D3 = 2 1.4 + 0.6

⇒ D3 = 0.228 m = 22.8 cm is the maximum size of product obtained from this crusher. (Ans) NOTE: It is evident from the above results that with the increase of coefficient of friction, smaller and smaller product size can be obtained using the same feed size and the same crusher.

2

Bradford breakers crush by gravity impact only. The Pennsylvania Bradford breaker consists of a large cylinder made of perforated screen plates, fitted with internal shelves. In many respects, this crusher resembles with a ball mill without balls. As the cylinder rotates, the shelves lift the feed and, in turn, the feed slides off the shelves and drops onto the screen plates below, where it shatters along natural cleavage lines. A roller-mounted Bradford breaker is shown in Fig. 3.13. Breaker cylinders rotate at slow speeds at 12 to 14 rpm depending upon cylinder diameter. Compared with most other crushers, a Bradford breaker is extremely long lived. The size of the screen-plate openings determines the product size.The sized product falls through these openings while the oversized pieces will again be lifted and dropped by the shelves until they too pass through the screen plates. Uncrushable debris like tramp iron or lumber that enters the breaker along with the feed is transported to the discharge end of the cylinder. There, these uncrushables are scooped out continuously by a refuse plow which channels this debris out of the cylinder and into a disposal bin. Bradford breakers are used for crushing of coal and other friable materials. They are used to produce a product that is relatively coarse, with minimum fines, and that is 100% to size [Pennsylvania, 2006].

In practice, the size-reduction machines used for intermediate crushing are charged with the product obtained from coarse crushers. The common intermediate crushers are roller mills, cage mills, granulators, hammer mills, and impactors.

Size reduction is effected purely by impact. The Pennsylvania Cage Mill (Fig. 3.14) consists of a casing inside which rows of sleeves are arranged in a circular manner which are attached to a number of rotating disks. Feed enters the innermost cage where it is initially struck by the first row of sleeves. They scatter the shattered materials toward the next row which rotates in the opposite direction. Further reduction occurs in the second row and each successive row until the material exits the final row, to be thrown against impact plates that line the crushing chamber. The sized material then discharges through the open bottom of the mill. Fine, medium, or coarse size products can be obtained by selecting the spacing between sleeves on each row. Product size is also dependent on the speed of the cages. Cage mills are employed for size reduction of friable, dry bulk substances such as chemicals, grain, fertilizer, coal, slag, glass, soap and many more, and for the beneficiation of materials that vary in hardness [Pennsylvania, 2006].

Granulators crush by a combination of impact and rolling compression. The Pennsylvania Granulator (Fig. 3.15) uses rows of ring hammers which crush with a slow, positive rolling action. This produces a granular product with minimum fines. Granulators produce high reduction ratios at high capacities. The product size is determined by the screen opening which forms the bottom of the casing. The product size can also be adjusted by changing the clearance between the cage and the path of the ring hammers. For protection against uncrushables, these granulators have a tramp iron pocket for continuous removal of uncrushables from the crushing zone. These are used for crushing coal, particularly for power plants. They are also used for gypsum, salt, chemicals, and for moderately hard materials.

i n

Coalpactors were originated by the Pennsylvania Crusher Corporation to crush coking coals and to produce an optimum percentage of product below 3 mm (1/8 in), but with a minimum amount of fines (100 mesh or smaller). Impact is the main method of size reduction in coalpactors. A Pennsylvania Coalpactor (Fig. 3.16) is similar to a simple impactor, but it has breaker plates that are fully adjustable from the outside of the frame to enable operators to vary the degree of pulverisation. This allows the maintenance of a uniform product size throughout the life of hammers and breaker plates. The Coalpactor rotor can rotate both clockwise and counterclockwise to provide for equal wear on both hammer faces. This helps to extend hammer life and to reduce maintenance problems. The Coalpactor is not affected by uncrushables. These are used to crush coking coals and petroleum coke for fluid bed boilers. These can be used even when the coal is wet.

Hammer mills are among the oldest, yet still the most widely used crushers. Pennsylvania Hammer mills crush the materials in two stages—first, the size reduction occurs by dynamic impact and then the sizing occurs in the second zone, where small clearances exist between hammers and screen bars, by attrition and shear. The advantages of Pennsylvania hammer mills are their ability to produce the specified top size without the need for a closed-circuit crushing system and to produce a cubical product with a minimum of flats. Large particles cannot escape the screen bars until sized, resulting in great product uniformity with a minimum of oversize. The product size can be controlled by a number of factors, such as (i) (ii) (iii) (iv) (v)

the feed rate, the speed of rotation of disk, the number and types of hammers used, the clearance between the hammers and breaker plates, and the size of screen opening.

Hammer mills have high reduction ratios and have high capacities whether used for primary, secondary, or tertiary crushing. Due to excessive wear, these are not recommended for the fine grinding of very hard and abrasive materials. In hammer mills, the hammer design plays a significant role as the hammers do most of the work. The factors taken into consideration while designing the hammers are mass, general shape, the air paths created by hammer sweep, and heat treatment Pennsylvania, 2006 . The centre of gravity determines the focus of impact and must be controlled to utilise the full mass of the hammer against the feed materials. The shape of the hammers is also important. The hammers may be of T-, bar-, or, of ring-shaped (plain and toothed) as shown in Fig. 3.17. The hammer heads must be extremely hard and resistant to wear—this can be done by heat treating the hammer materials. During rotation of hammers, a large current of air is produced which carries away a certain amount of fines. These must be directed away from the rotor disk and other vital parts to prevent premature wear. Hammer mills are classified into reversible and nonreversible types based on the rotation of rotor in clockwise or counter-clockwise direction, or in both directions. Though their construction differs in many respects, their working and crushing actions remain similar. In general, the hammer mills consist of a cylindrical casing inside which a high-speed rotating disk (rotor) is incorporated, to which a number of swing hammers are pinned / hinged. A cylindrical screen or grating is attached to the bottom of the casing, which encloses all or, part of the rotor. The material to be crushed is fed either at the top or at the centre through a hopper, and is thrown out centrifugally and crushed either by hammers or against breaker plates fixed around the periphery of the casing. The material is beaten several times until it passes through the screen opening. Due to excessive wear, hammer mills are not recommended for fine grinding of very hard materials. In reversible hammer mills, the rotor can run clockwise or counter-clockwise. Reversal of the rotor permits the operator to utilise the opposite face of the hammer

Basic hammer types

in

d

in

for maximum hammer sharpness. Reversal also brings the opposite set of breaker plates and screen bars into use. Pennsylvania reversible hammer mills are available in a great variety of sizes and are used for the size reduction of coal; fuels and sorbents in fluid-bed boiler applications; and rock, limestone, minerals, and chemicals. Reversible hammer mills for coal (Fig. 3.18) have more rows of hammers than found in the reversible hammer mills used for stone or rock. The reversible hammer mills for rock and minerals (Fig. 3.19) have massive breaker plates and screen bars than those used for crushing coal and have fewer rows of hammers than the coal version. The bottom of these mills is open and the sized material passes through almost instantaneously. Pennsylvania nonreversible hammer mills (Fig. 3.20) consist of a cylindrical grating below the rotor for product discharge. Size reduction starts by impact when

the hammer strikes the material as it enters the crushing zone. Shattered fragments are swept down into the final crushing zone for further reduction at the pinch points between the hammers and screen bars. The oversize material remains in the machine until it is reduced sufficiently to fit through the screen bar openings. These crushers accept feed sizes of up to 750 mm (30 in). The tighter the clearance between the screen bars and hammers, the smaller the particle size of the crushed product. The hammers are not fixed to the disk rather they are hinged, so that the presence of any hard material does not cause any damage to the machine and if the hammers are worn out, they can easily be replaced. In these mills tramp iron pockets are provided for continuous removal of uncrushables from the crushing zone. The large current of air produced during hammer sweep makes the environment dusty. Hence, a cyclone separator or a bag filter is used to separate dust from the product. Reversible hammer mills are employed for reduction of coals, limestone, rock, minerals, and chemicals; while nonreversible hammer mills are used for primary or secondary reduction of dry, friable, low abrasive rocks, ores, and chemicals Pennsylvania, 2006 .

The Vertical Shaft Impactors (VSI) are one type of impact crushers, which offer higher reduction ratios at a lower energy consumption. These impactors

can be considered as a stone pump operating like a centrifugal pump. The material is fed through the centre of the rotor, where it is accelerated to high speed before being discharged through openings in the rotor periphery. The material is crushed as it hits the liners of the outer body at high speed and also due to the roc -on-roc action, as shown in Fig. 3.21. These crushers are mainly used in the production of fine materials, including sand, with a good cubical shape. A number of VSIs are available in the market. The most popular VSIs are the Sandvik s CV Series by Sandvik Mining and Construction, Sweden, and the Barmac B and VI Series by Metso Minerals, Finland. These crushers use the impact and rock-on-rock crushing principle for size reduction, which minimise wear costs. Sandvik s CV range of VSI crushers are autogenous VSI crushers covering a capacity range extending to 600 tph nominally. The whole range has been designed to ensure maximum production and yield of product for the lowest possible power consumption. Sandvik s VSI crusher is primarily a third or fourth stage crusher. The rock-on-rock crushing principle offers two main advantages: (i) product gradation remains constant, even as rotor-wear parts wear, and (ii) contamination rates are extremely low, as no wear parts are used to directly crush the rock. Feed material enters the crusher via a rock-lined hexagonal feed hopper, as shown in Fig. 3.22. Rotor-material feed rate is controlled by the hydraulically operated rotor throttle gate. This material falls by gravity into the feed tube, which subsequently feeds the hurricane3 rotor. The crusher uses a rock-lined hurricane rotor to accelerate material. This material is accelerated by centrifugal force to typically 45 to 62 m/s. The crushing chamber is lined with a solid bed of material against which the energised rotor material impacts. It is this high-velocity autogenous impaction that causes impact, cleavage and attrition of the feed material. The computer-designed crushing chamber geometry of these crushers give improved crushing action within the chamber when combined with the i- low3 system. The path of the material from entry (feed hopper) to exit (discharge chute) is controlled via autogenous rock-lined pockets within the crusher. This improved design further reduces points of contact within the crusher, resulting in extremely low crusher component wear. Sandvik VSIs have the ability to handle hard, abrasive, fine, moist, or sticky feed materials, which makes them suitable for all of applications, such as quarries and gravel plants (production of premium-shaped aggregates for concrete and asphalt); recycling 3

Trademark of Sandvik Mining and Construction, Sweden.

x d

n

i

i

n

in din

nd

in i iv v

i

in nd d

v dd i n in id

i

i

d nd d

i

n

(processing glass bottles, etc., to sand specification and recycling of ceramics); mines (liberation of ores for heap leaching and differential liberation of hard particles, e.g., gemstones from softer matrix); cement works (crushing cement clinker to maximise fines prior to milling); and industrial minerals (crushing of highly abrasive minerals, e.g., fused alumina, silicon carbide, zirconia, mulochite, calcined bauxite, etc.). Sandvik s CV series of VSI crushers are available in six different sizes accepting maximum feed sizes from 40 to 55 mm. Their capacity ranges from 10 –50 tph for CV115 to 445–600 tph for CV129.

Grinders are a variety of size-reduction machines employed for fine grinding which reduces the intermediate product to a finer size. The common grinders are autogenous/semi-autogenous mills and tumbling mills (ball, rod, and pebble mills). These mills are different in their ratio of diameter-to-length of the cylinder and the type of grinding media used.

Autogenous (AG) and Semi-Autogenous (SAG) mills are currently the industry standard for primary milling. These are a type of tumbling mill having a large diameter relative to their length, generally in the ratio of 2:1 to 2.5:1. Figure 3.23 shows a 10.36 m × 5.18 m (34 ft. × 17 ft.) – 12,500 HP SAG Mill.

Autogenous grinding is the size reduction of material in a tumbling mill utilising the feed material itself as the grinding media. But the product obtained from AG mills is inconsistent. The problem is rectified in semi-autogenous grinding, which is the size reduction of material utilising the feed material plus the supplementary grinding media, usually steel balls in the range of 5 to 10 per cent of the volume of the tumbling mill. AG/SAG mills are normally used to grind run-off-mine ore or primary crusher product. Feed size to the mill is limited to that size which can be practically conveyed and introduced into the mill. The mill product can either be finished size ready for processing, or an intermediate size ready for final grinding in a rod, ball, or pebble mill. In recent years these mills are finding an increased use in mineral processing industries like gold, copper, alumina, lead, and zinc.

A cylindrical shell rotating with its axis either horizontal or at a small angle to the horizontal and charged with a grinding medium to about half its volume constitutes a tumbling / revolving mill. Tumbling mills are widely used as fine grinding machines. Generally, tumbling mills are categorised into four types—ball, rod, tube, and pebble mills, which are charged with specific grinding media like: steel balls, rods, small balls, and ceramic pebbles respectively. They may be operated batchwise or continuously. Different characteristics of these mills are presented in Table 3.6. In each of these mills, grinding is achieved due to one common action, i.e., the tumbling action of the grinding media over the feed particles. Among all these, the ball mill is easy to operate and is the most versatile one for fine grinding, which is discussed here in detail.

C aracteristics

Ball mill

Rod mill

Tube mill

Pebble mill

Principle of comminution

Impact

Rolling compression and attrition

Impact

Impact

Grinding media

Balls

Steel rods

Small balls and pebbles

Pebbles

Material of construction of grinding media

Steel

High carbon steel

Steel

Ceramic pebbles made of flint or porcelain

Diameter of grinding media

12–125 mm

50 mm

Feed size

Up to 50 mm

Up to 25 mm

Up to 25 mm

Up to 25 mm

Product sizes

Fine

Uniform fine

Fine

Fine

L/D ratio

1 to 1.5 : 1

1.5 to 3 : 1

3 to 4 : 1

1 to 2 : 1

Applications

Coal, pigment, feldspar for pottery

Particularly for sticky materials and not suitable for tough materials

Same as ball mill, but the residence time is more here

In paint and pigment industries, and in cosmetic industries where iron contamination is objectionable. And also for high specific gravity feed

–

–

Ball mills are popular due to their low operating and maintenance costs regardless of whether the material displays Mohs hardness values of over 4 or is soft — such as limestone or barite. The principle of size reduction in ball mills is impact of balls, which fall from the top of the shell on to the feed particles near the bottom of the shell. In general, ball mills consist of a hollow cylindrical or conical shell, made of steel or rubber-lined steel, with approximately half-full of steel balls, rotating about its axis, either horizontal or at a small angle to the horizontal. The grinding media is the balls, which may be made of steel or stainless steel. The material to be ground may be fed in through an opening at one end and the product leaves through a similar opening at the other end, which is covered with a coarse screen to prevent the escape of balls. Figure 3.24 shows a ball mill, as provided by Hosokawa Micron India, Pvt. Ltd., India. The inner surface of the mill is lined with an abrasion-resistant material such as manganese steel or rubber. For rubber-lined mills, less wear takes place than steellined mills. Another advantage in case of rubber-lined mills is that due to higher coefficient of friction between the balls and the cylinder, the balls are carried to a greater height in contact with the cylinder and thus drop on to the feed particles from a greater height causing the size reduction to be more effective.

The length of the ball mill is nearly equal to its diameter ( / D ratio varies from 1 to 1.5:1). The balls occupy about 30 to 50 %of the volume of the mill. The diameter of the balls used varies between 12 to 125 mm. The optimum ball diameter is nearly proportional to the square root of the size of the feed and the proportionality constant is a function of the nature of the material to be ground Coulson, 1991 . The mill is rotated at low speed between 60–100 rpm through a drive gear. During grinding, the balls themselves wear (wear rate varies from 450 to 1350 g per ton of product) Brown, 1995 and are constantly replaced by new ones. So, at any point of time, balls of different ages and various sizes are found inside the mill. This is advantageous because the larger balls crush the coarse feed and the smaller balls grind the material to a finer product. For finer grinding, a compound ball mill can be used which consists of two to four cylindrical compartments separated by grates. Each successive compartment is of small diameter and contains balls of smaller size Brown, 1995 . Super-Orion4 Ball Mills (Fig. 3.24) are designed to ensure low-wear and cost-effective processing. These mills have cast side plates bolted to a rolled-steel drum with an integrated manhole. Mills are driven by ring and pinion gear with automatically controlled tooth lubrication. The product is discharged through adjustable slots located around the periphery of the drum.

,

din

4

i n

F

i n

The speed of rotation is a crucial factor for ball mills. At low speeds of rotation, the balls are lifted and simply roll back over feed materials. Size reduction is caused by attrition and little crushing action takes place. Under this condition, the mill is said to be cascading. At slightly higher speeds, the balls are carried up further inside the mill and fall back due to gravity on to the feed particles at the bottom. Grinding takes place by impact and the mill is said to be cataracting. The ball mill operating at different speeds is shown in Fig. 3.25. If the speed of rotation is increased further and further, a stage is reached when the balls are carried along with the inside walls of the mill

Trademark of Hosokawa Alpine Aktiengesellschaft & Co. OGH, Germany.

due to higher centrifugal force and mv 2 do not fall at all, and the mill is said R−r to be centrifuging. The minimum r A speed at which centrifuging occurs B is called the critical speed of the q mill. mg At the critical speed, the balls mg will be at the uppermost position of the mill and there will be no resultant force acting on the ball as the centrifugal force will be balanced by the weight of the ball. This can be understood from the following mathematical expressions. Consider at any point of time the ball is at a point A inside the mill, as shown in Fig. 3.26. Let, R = Radius of the ball mill, m (= AC ), r = Radius of the ball, m (= AB), q = Angle between AC and C , v = Peripheral speed, m/s, and m = Mass of the ball, kg. At location A, the forces acting on the ball are

D

R q q C

i

(i) Force of gravity, mg and 2 (ii) Centrifugal force, m v . ( − )

The component of gravity force opposing the centrifugal force is mg cos q. As long as the centrifugal force is more than the component of gravity force, the ball will not loose its contact with the inside wall of the mill. Whenever and wherever these two opposing forces become equal, the ball will loose contact and will fall down onto the particles. At this condition, m v2 −

mg cos θ = ⇒ cosθ =

(

v2 − )g

(3.28)

But, the peripheral speed is related to the speed of rotation, N by v = 2π N ( − Thus,

cos θ =

)

4π 2 N 2 ( −

(3.29)

)

g

At critical speed , N = NC and q = 0 . Thus, cos q = cos 0 = 1.

(3.30)

Thus, from Eq. (3.30), we have cos θ = cos 0° = 1 = ⇒ NC =

4π 2 N C2 ( −

)

g 1 2π

(

g −

)

(3.31)

It is clearly evident from Eq. 3.31 that for increased size of ball, the critical speed increases for a given size of the mill. The ball mill finds its application in a great number of industries, including coal, pigments, feldspar for pottery, food, pharmaceuticals, and chemicals.

With high feed rates, less size reduction is achieved as the material remains inside the mill for a relatively shorter time. For hard materials, less size reduction is achieved under a given operating conditions. Heavyweight balls produce a fine product, which can be increased either by increasing the number of balls or by using materials of high densities. And as the optimum grinding condition is achieved when the volume of balls is half the volume of the mill, the weight of balls is being varied using materials of different densities. With small size balls the production of fine size materials is more and they are not effective for larger feed particles. For a given size of balls, the limiting size reduction achieved is known as the free grinding limit. With the increase in the slope of the mill, the capacity increases, at the same time a coarser product is obtained. As discussed earlier in this section, at low speed, the balls simply roll over one another and little crushing is achieved and at very high speed centrifuging occurs and little grinding takes place. For effective grinding, the ball mills are usually operated between 50 to 75% of the critical speed, i.e., in the fringe area between cascading and free-fall. This is often referred to as the angle of brea . With the increase in level of material inside the mill, the cushioning action increases causing wastage of power, which produces excessive quantity of undersize materials. The use of ball mills is advantageous due to the following reasons: (i) (ii) (iii) (iv)

The low cost of installation and of power requirements, The cheap grinding medium, The mill can be operated batchwise or continuously, and wet or dry, The mill is suitable for materials of all degrees of hardness,

(v) As grinding takes place inside the mill where an inert environment can be easily maintained and, therefore, a ball mill can be used for grinding of explosive materials, and (vi) The mill can be used for open and closed-circuit grinding.

The critical speed from Eq. (3.31) is N C =

1 2π

(

g −

)

.

Given in this problem are = 1000 mm and d = 70 mm. Thus, R = /2 = 500 mm = 0.5 m and r = d/2 = 35 mm = 0.035 m. Now, the critical speed, N C =

1 2π

9.81 = 0.730 rps = 43.85 rpm . (0.5 − 0.035)

But, the operating speed of the ball mill is 50 to 75% of the critical speed. Hence, the operating speed is 21.90 to 32.88 rpm. (Ans)

We know for a ball mill from Eq. (3.30) cos θ =

4π 2 N 2 ( −

)

. g Given in this problem are = 2000 mm, d = 100 mm, and N = 15 rpm. Thus, R = /2 = 1000 mm = 1 m, r = d/2 = 50 mm = 0.05 m, and N = 0.25 rps. 4 × π 2 × ( 0.25) × (1 − 0.05) = 0.238. 9.81 Now, the 100-mm steel balls are replaced with 50-mm balls. Hence, r = 50/2 = 25 mm = 0.025 m. g cos θ Thus, N= 4π 2 ( − ) 2

Now,

cos θ =

⇒N =

9.81 × 0.238 4π 2 (1 − 0.025

)

= 0.0606

⇒ N = 0.2461 rps = 14.77 rpm is the speed of the ball mill when the balls are replaced with 50-mm balls. (Ans)

Rod mills are almost similar to ball mills in appearance and working principle with the exceptions that the grinding medium here is the rods and the length of the mill is greater than its diameter. Rod mills can also be cylindro-conical with the cylindrical section being relatively long and smaller in diameter.

The grinding action in a rod mill is a little different in that the rods are kept apart by the coarsest particles. Further, the grinding action is exerted on the coarsest particles preferentially. Thus, the product from a rod mill contains less amount of fines compared to a ball mill. Consumption of rods is nearly the same as in case of a ball mill employed for a similar duty using steel balls Gaudin, 1971 .

A great variety of ultra-fine grinding machines are on the market to grind both dry as well as wet materials. These reduce the solids to an average particle size of 1 to 20 microns. Some of the popular ultra-fine grinding machines are: Fine Impact Mills, Spiral Jet Mills, Fluidized-Bed Opposed Jet Mills, Fluid-Energy Mills, Classifying Hammer Mills, etc. and a few are discussed here.

The Hosokawa Alpine Fine Impact Mills UPZ5 offer versatility and simplicity, because of the wide variety of materials to be ground, where every size-reduction task demands its own solution. UPZ is also called Universal Mill, since it can be used to grind all kinds of materials. UPZ grinding technology delivers excellent product quality on a constant basis over extensive production periods. A decisive factor for their efficiency and operating safety is not only the high mechanical robustness, but also the ease with which the wear parts can be exchanged and the possibility of thoroughly cleaning the machine during product change. The UPZ models range from the size of 100 to 1400 (model number refers to the approximate diameter of the grinding media in mm). Impact mills work on the principle by impact of fast revolving hammers with the particle and by collision of particles over the specially designed stationary grinding tracks on the walls of the grinding chamber. Hosokawa Alpine Fine Impact Mills UPZ are high-speed impact mills with one rotating and one stationary stud disk, as shown in Fig. 3.27. According to the system, the material is fed through the front door at the middle, directly into the grinding chamber of the UPZ. Due to impact and collision, the particle size-reduction occurs in the grinding chamber. The chamber has been designed to accommodate interchangeable size-reduction elements, such as beater and pin disks, swing and plate beaters, sieves, and grinding tracks according to the different kinds of material, capacity, and fineness required by the manufacturers. The mill also has inbuilt interchangeable sieving screens by which the particle size can be maintained with reference to the size of the mesh chosen. The end product has the fineness in the range of 50 μm to 5 mm. The Alpine Fine Impact Mills UPZ can be employed for different products and applications—even under extreme conditions. Typical application areas and some of the materials are chemical industries (fertiliser, pesticide, paints and pigments); pharmaceutical industries (antibiotics, herb teas, roots, rose 5

Trademark of Hosokawa Alpine Aktiengesellschaft & Co. OGH, Germany.

hips); herbs and spice industries (savoury, rosemary, onions, turmeric); food and confectionery industries (oat and potato flakes, casein, skimmed milk powder, sugar, starch, food colourings); animal feed industries (soya meal, freeze-dried meat, corn cobs); wood and chipboard industries; mineral powder industries; plastics industries (PVC, PTFE, PE); etc. UPZ can also be used with the system of cryogenic grinding with liquid nitrogen and it also comes with a special design of a 10-bar (over pressure) grinding system for grinding dust explosive materials, acrylic resin, cornstarch, sugar, insecticides, vitamins, etc.

The Alpine Spiral Jet Mill 50 AS is ideal for the ultrafine comminution of dry substances with a crystalline structure to a Mohs hardness of 3, whereby particle sizes in the range between 5 μm and 30 μm are achieved. Even extremely small amounts can be processed easily with maximum yield. Thus, it finds its use mainly in pharmaceutical industries. Impact and attrition are the main mode of size reduction. In the Alpine Spiral Jet Mill 50 AS, the grinding air flows through the socket into the air ring ducting, as shown in Fig. 3.28. As a result of the spiral arrangement of the nozzles, the grinding air enters the grinding bin at high velocity. The propellant air enters the injector via the socket. The feed material is suction-transferred out of the feed chute into the grinding chamber by the propellant air exiting the injector. The material is immediately caught up in the grinding air in the area where the air-flow spirals. The particles are comminuted as a result of their impacting against each other and against the nozzle ring. The fines are conveyed by the grinding air to the discharge port, whereas coarse material is catapulted to the periphery again where it is re-ground. These units are extremely compact and lightweight and are ideal for laboratory applications. These mills achieve particles with a fineness of nearly 5 μm at pressures as low as 4–5 bar. These mills are suitable for the processing of numerous pharmaceutical substances including parenterals, DPI (Dry Powder Inhalants), and other active substances.

The fluidised-bed opposed jet mills are better and more versatile solutions for ultrafine size reduction of materials up to a Mohs hardness of 10. These mills are used for manufacturing powders with a steep particle size distribution and sharp top size limitation in the range < 5 μm to 200 μm. These mills require less energy than any other conventional jet mills and the noise emission is less than 8 dB(A). Inter-particle attrition and impact are the main mode of size reduction in these mills. The material is fed either by gravity from the side or via a rotary valve, as shown in Fig. 3.29. First, a bed of material is prepared and the compressed air (called grinding gas) through the nozzle is switched on. The air is of 20 C and 6 bar over pressure and comes out of the nozzle with a tip speed of around 500 m/s. As a result of this, the fluidisation of bed material takes place which enables inter-particle collision, i.e., particles hit against each other and micronisation takes place. Due to the high-speed classifier which is rotating on the top, the classifying air flows through the classifying wheel in centripetal direction; the fines are sucked/ extracted and conveyed to the fines discharge. The coarse material is rejected back to the milling area for further milling. The fineness is controlled by the speed of the classifying wheel using a frequency converter, i.e., at different speeds, different micron sizes. The micronisation in AFG is exclusively the result of particles impacting against each other in the gas jets and is therefore contamination-free. This means, extraordinary purity can be achieved using these mills. That is also the reason why

many pharmaceutical companies in India as well as worldwide have this system for contamination-free grinding of pharmaceutical powders. Typical application areas of fluidised-bed opposed jet mills are grinding of highly pure substances such as fluorescent powders, silica gels, silicic acids for chromatographic applications, etc.; highly abrasive materials such as tungsten carbide, silicon carbide, boron carbide, corundum, etc.; temperature sensitive substances like plant protectives, wax, resins, fats, hydrogenated oils, etc.; minerals like talcum, mica, graphite, quartz; cryogenic grinding with liquid nitrogen; and toner grinding.

In almost all the size-reduction equipments, most of the input energy is lost and the crushing efficiencies are less, as discussed earlier in this chapter. Thus, the cost of sizereduction process is comparatively high. Hence, there is a need to operate the machines effectively and efficiently, so as to prevent further loss of power and money. A size-reduction equipment, whether crusher or grinder, cannot work effectively, unless (i) the method of feeding the solids is proper (the feed should be of suitable size to a particular equipment and the feed should enter at a uniform rate), (ii) the crushed products are removed as soon as they are produced ,

(iii) the heat generated is removed , and (iv) the unbreakable material is kept out of the crushing zone. The solids can be fed to a machine in two distinct ways: (i) The first case, where the material is fed at a low rate so that the product can come out easily, is known as free crushing or free feeding. Here, the retention time is short and hence, the product contains less quantity of undersize materials. (ii) The second case, where the machine is kept full of materials so that the materials remain in the machine for a long time, is known as cho e feeding. This method results in a high degree of crushing as the materials are crushed several times, resulting into production of large quantity of undersize materials. Hence, in this method the large reduction ratio is achieved. But at the same time, the capacity of the machine is reduced and the energy consumption is high because of the cushioning action produced by the fine materials accumulated. This method is, therefore, used in a limited number of cases, like when it is desired to complete the size-reduction process in one operation and when a small amount of materials is to be crushed. In many industrial practices, the feed material is reduced to the desired size by passing it once through the machine. And when no attempt is made to return the oversize material back to the machine, the process is known as open-circuit crushing grinding. On the other hand, if partially ground material from the machine is screened, from where the oversize material is fed back to the machine again for further reduction, the process is known as closed-circuit crushing grinding. This process requires less energy as compared to open-circuit grinding and is widely used in industries.

A

MA O

OF M

Ov

F

i

d

n nv Fini

d

d

i

i

d

d

0

i

5

nd i

d

100 n

200 nd

d

i

n

vi n

in

A typical set of size-reduction machines and separators operating in closed circuit is shown in Fig. 3.30 and a portable plant consisting of a vibrating feeder, grizzly, primary jaw crusher, secondary cone crusher, vibrating screen, and belt conveyors operating in a closed circuit is shown in Fig. 3.31. The crushing/grinding operation can be carried out either as wet or dry, but wet grinding is generally applicable only with low-speed mills. Wet grinding is preferred over dry grinding due to (i) (ii) (iii) (iv) (v) (vi) (vii)

low power consumption (nearly 20 to 30% less), increased capacity of the plant, easy removal of the product, amount of fines is reduced, ease in solids handling, reduction in dust formation, and low heat generation.

At the same time the disadvantages of wet grinding are (i) it may be necessary to dry the products after grinding, and (ii) high wear on grinding medium.

❑ ❑

❑

❑

ηc =

❑

ηm =

❑ ❑

Es ( Assp − Assf )

P=

Wa Wa W

6E s m ⎛ 1 1 ⎞ − ⎜ ⎟ ηmηc ρp ⎝ Φp Dvsp Φ f Dvsf ⎠

❑ ⎛ 1 1 ⎞ WR = K R ⎜ − ⎟. ⎝ Dvsp Dvsf ⎠ WK =

⎛D ⎞ P = K K ln ⎜ vsf ⎟ . m ⎝ Dvsp ⎠

WB =

⎛ 1 P 1 ⎞ = 0.3162 Wi ⎜ − ⎟ m Dpf ⎠ ⎝ Dpp

( ) ( )

d Dvs P d (W ) = d ⎛ ⎞ = − K n ⎝ m⎠ D vs

❑ ❑

Q=

❑

ρp AWj N j (1 − ε ) 60

kg/h.

❑

❑ Q = 60π D1D3 bN ρ

❑

❑

❑ ❑ ❑ ❑

❑

NC =

1 g 2π ( R − r )

1. Why is size reduction carried out Size reduction of solids is carried out for a number of reasons: (i) to increase the surface area, (ii) to produce solid particles of desired shape, size or size ranges, and specific surface, (iii) to separate unwanted particles effectively, (iv) to dispose solid wastes easily, (v) to mix solid particles more intimately, and (vi) to improve the handling characteristics. 2. Differentiate between gravity impact and dynamic impact. In gravity impact, the free-falling material is momentarily stopped by the stationary object. Coal dropped onto a hard steel surface is an example of gravity impact; while materials dropping in front of a moving hammer is an example of dynamic impact. When the materials are crushed by dynamic impact, the materials are unsupported and the force of impact accelerates the movement of the reduced particles towards the breaker plate and/or other hammers. 3. Name the properties of solids affecting the size-reduction operation. Properties of solids affecting the size-reduction operation are hardness, toughness, stickiness, moisture content, friability, explosive nature, soapiness, crystallinity, and temperature sensitivity. 4. Why are the crushing efficiencies low Out of the total energy supplied, only a small portion (maximum one per cent) is utilised for the creation of a new surface and rest of the energy is lost to overcome

the friction, as heat, and as sound. Thus, the energy efficiencies are less. 5. Discuss the range of applicability of crushing laws. Rittinger s law holds most accurately for fine grinding where the increase in surface per unit mass of material is predominant. This law is applicable for feed size of less than 0.05 mm. Kick s law is more accurate than Rittinger s law for coarse crushing where the surface area produced per unit mass is considerably less. This law is applicable for feed size of greater than 50 mm. Bond s law is applicable for feed size between 0.05 and 50 mm. 6. Give examples of a few cases of size reduction involving nonmechanical introduction of energy. Size-reduction methods involving nonmechanical introduction of energy are explosive shattering, cryogenic crushing, ultrasonic grinding, electrohydraulic crushing, and thermal shock. 7. How does a dodge-type of jaw crusher differ from that of a Blake type In Blake types of jaw crushers, the movable jaw is hinged at the top so that the greatest movement at the bottom is given to the smallest lumps; while in Dodgetypes, the movable jaw is pivoted at the bottom giving minimum movement of the jaw at the bottom by which more uniform products are obtained. But, this type is less widely used because of its tendency to choke. 8. Differentiate between single- and double-toggle jaw crushers. In the single-toggle jaw crusher, an eccentric shaft is positioned on the top of the crusher. Shaft rotation causes, along with the toggle plate, a compressive action. The double-toggle crusher

has two shafts and two toggle plates. The first shaft is pivoted at the top of the crusher, while the second shaft is an eccentric shaft that drives both toggle plates. The moving jaw has a pure reciprocating motion towards the fixed jaw. The single-toggle jaw crusher has better capacity compared to a double-toggle crusher of similar size because the chewing movement in a single-toggle jaw crusher causes compression at both material intake and discharge regions. 9. What is the difference between a crusher and a grinder The crushers employ mainly the compression action to large lumps of solid materials and are slow-speed machines. These reduce materials of large feed size to (50–5) mm product size, while grinders are employed for fine grinding of intermediate products of 5 to 2 mm size to finer ones of ≅ 200 mesh size. 10. Give four examples of intermediate crushers. Cage mill, roller mill, hammer mill, and impactor. 11. What are angle of nip and angle of bite A When coefficient of friction, μ = tan N , 2 under this limiting condition of crushing, the angle AN is called the angle of nip. For all practical purposes, the value of the angle AN is usually taken as 32°. And when the limiting value for the A angle N for which the resultant force 2 FR acts horizontally, it is called the angle of bite, and under this condition there will be little or no crushing at all. 12. Discuss the operating principle of vertical-shaft impactors. The vertical-shaft impactors are a type of impact crushers to which the material is fed through the centre of the rotor,

where it is accelerated to high speed before being discharged through openings in the rotor periphery. The material is crushed as it hits the liners of the outer body at high speed and also due to the rock-on-rock action. 13. Suggest size reduction equipments to reduce 2 mm size coal particles to 200 mesh. Ball mill, rod mill, pebble mill, pulveriser, and tube mill. 14. What do you understand by cascading, cataracting, and centrifuging For a ball mill operating at low speeds of rotation, the balls are lifted and simply roll back over feed materials. Size reduction is caused by attrition and little crushing action takes place. Under this condition, the mill is said to be cascading. At slightly higher speeds, the balls are carried up further inside the mill and fall back due to gravity on to the feed particles at the bottom. Grinding takes place by impact and the mill is said to be cataracting. If the speed of rotation is increased further and further, a stage is reached when the balls are carried along with the inside walls of the mill due to higher centrifugal force and do not fall at all, and the mill is said to be centrifuging. 15. Why is the closed circuit grinding generally chosen over open-circuit grinding method In open-circuit grinding no attempt is made to return the oversize material back to the machine. While in closedcircuit grinding, partially ground material from the machine is screened, from where the oversize material is fed back to the machine again for further reduction, and this process requires less energy as compared to opencircuit grinding and is widely used in industries.

1. What do you understand by the term size-reduction’? 2. What are the objectives behind size reduction? 3. What are the different actions commonly employed by the size reduction equipments? Classify them. 4. What should be the criteria for the selection of size-reduction equipments? 5. Discuss the properties of the material and the factors that affect the sizereduction process. 6. How do the solid particles break into smaller fragments? 7. How the energy and power consumption play an important role in size reduction? 8. What is crushing or grinding efficiency? How are the energy and power consumption are related to crushing or grinding efficiencies? 9. Why do we require more and more power to grind smaller and smaller particles? 10. Discuss the empirical laws for size reduction.

11. Explain in detail the construction and working of various coarse crushers with neat sketches. Mention their advantages, disadvantages, and industrial applications. 12. Explain in detail the construction and working of various intermediate crushers with neat sketches. Mention their advantages, disadvantages, and industrial applications. 13. Discuss the construction and operation of vertical-shaft impactors. 14. Explain in detail the construction and working of various grinders with neat sketches. Also, mention their advantages and disadvantages along with their industrial applications. 15. Distinguish between autogenous and semi-autogenous grinding mills. 16. Explain in detail the construction and working of various ultra-fine grinders with neat sketches. Also, mention their advantages and disadvantages along with their industrial applications. 17. How should the comminuting equipments be operated?

1. A certain crusher accepts the feed rock having a volume–surface mean diameter of 20 mm and discharges a product having a volume–surface mean diameter of 5 mm. The power required to crush 1200 kg/h of material is 9.5 kW. What would be the power consumption if the capacity is reduced to 100 kg/h and the product size to 4 mm? Assume mechanical efficiency to be same in both the cases. 1.054 kW 2. A continuous grinder obeying the Bond crushing law grinds a solid at the rate of

800 kg/h from the initial diameter of 12 mm to the final diameter of 2 mm. If it is required to produce particles of 1-mm size, what would be the output rate of the grinder (in kg/h) for the same power input? 470.32 kg/h 3. What will be the power required to crush 150 ton/h of limestone (work index for limestone is 12.74) if 80% of the feed passes a 60-mm screen and 80% of the product passes a 6-mm screen? 168.68 kW

7. Power required to crush 100 tonnes/h of limestone is 123 kW. If 80% of the feed passes through a 50-mm screen and 80% the product passes through a 5 mm screen, find out the work index of limestone. 12.72 kWh/tonne 8. Particles of the average feed size of 3 mm are crushed to an average product size of 0.6 mm at the rate of 15 tonnes/h. At this rate, the crusher consumes 35 kW of power of which 5 kW are required for running the mill empty. If the same material is crushed further to 0.1-mm size at the same rate, what is the additional power requirement 187.5 kW 9. A feed of gypsum with 80 % of material passing through a 50-mm

screen is washed to a product with 80 % passing through a 5-mm screen. If power required for crushing is 80 kW, what is the capacity of the crushing unit Work index for gypsum is 6.73 kWh/tonne. 122.9 tonnes/h 10. A set of crushing rolls of 50-cm diameter takes a feed of a size equivalent to 5 cm sphere to crush to 12 mm. What is the value of coefficient of friction of the rolls = 0.392 11. 2 tonnes of galena is to be reduced to fine powder by passing through a crusher and a grinder in succession, drawing power from the same drive. Screen analysis of feed, product from the crusher, and product from the grinder indicated surface areas of 3, 114, and 900 m2/kg respectively. If the power required by the drive to run the crusher–grinder assembly is 18 kW and efficiency of the crusher is 25 %, find the efficiency of the grinder. Rittinger s number of galena = 95.7 m2/kJ. 29.6 % 12. A cement manufacturing unit uses a set of crushing rolls to crush dolomite (specific gravity = 2.85) from a maximum feed size of 6.5 cm to a product size of 1 cm. The rolls with a width of 50 cm run at 90 rpm and have a clearance of 1 cm between them. If the angle of nip is 30°, find the diameter of the rolls and the actual capacity, if the actual capacity is 15 % of the theoretical one. 1.552 m, 56.28 tonne/h

1. Rittinger s law is best applicable to feed materials of (a) fine size (b) coarse size (c) intermediate size (d) coarse and intermediate sizes

2. For feed size greater than 50 mm, the crushing law applicable is (a) Rittinger s law (b) Kick s law (c) Bond s law (d) all the above laws

4. What should be the diameter of a set of rolls to take feed of a size equivalent to 0.04 m sphere and crush to 0.01 m, if the coefficient of friction is 0.35 0.484 m 5. A double-roll crusher having a set of crushing rolls of 100-cm diameter and 35-cm width face are set so that the crushing surfaces are 1.4 cm apart at the narrowest point. Find out the maximum permissible feed size to the crusher if the angle of nip is 32 . 5.51 cm 6. Derive the three laws of size reduction from the generalised equation: Dvs ⎛ ⎞ . ⎜⎝ ⎟⎠ = − K n m Dvs

( ) ( )

3. The value of work index (kWh/tonne) for hard material is: (a) 7 – 9 (b) 9 – 14 (c) 14 – 20 (d) greater than 20 4. Jet mill comes under the category of (a) grinder (b) intermediate crusher (c) coarse crusher (d) ultra fine grinder 5. An example of an intermediate crusher is a (a) roll crusher (b) cage mill (c) rod mill (d) ball mill 6. Reduction ratio of a coarse crusher varies from (a) 1 – 2 (b) 3 – 7 (c) 8 – 12 (d) >12 7. The hardness of the following materials expressed in Mohs scale in the increasing order will be (a) diamond, bauxite, marble, talc (b) bauxite, diamond, talc, marble (c) talc, bauxite, diamond, marble (d) talc, marble, bauxite, diamond 8. An example of an ultrafine grinder is (a) semi-autogenous mill (b) ball mill (c) fluidised-bed opposed jet mill (d) pebble mill 9. Size-reduction equipment required to get a product of 0.2-mm size from a feed of 2-mm size is a (a) hammer mill (b) Bradford breaker (c) semi-autogenous mill (d) fluidised-bed opposed jet mill 10. Cone crusher is reduction equipment under the category of (a) intermediate crusher (b) coarse crusher

(c) fine crusher (d) ultrafine grinder 11. The method(s) by which size reduction of solids takes place in the equipments is/are (a) compression and impact (b) attrition (c) cutting (d) all of the above 12. Rittinger s number has the unit of (a) m2/J (b) kJ/cm2 (c) m.kgf /kgm (d) m.kgf /m2 13. (a) (b) (c)

Bond s law is applicable for feed sizes greater than 50 mm less than 50 microns greater than 50 micron and less than 50 mm (d) greater than 50 micron and less than 5 mm 14. An example of a crushing equipment in which size reduction as well as screening of the product can be achieved is a (a) Bradford breaker (b) cone crusher (c) cage mill (d) granulator 15. Soft material like ice can be crushed to smaller size by a (a) jaw crusher (b) Cage mill (c) crushing rolls (d) hammer mill 16. Reduction ratio is the ratio of (a) initial particle size to final particle size (b) final particle size to initial particle size (c) none of the above (d) all the above 17. An example of a size-reduction equipment in which feed materials itself is used as grinding media is (a) pebble mill (b) autogenous mill (c) semi-autogenous mill (d) vertical shaft impactor

18. For effective grinding, the ball mills are usually operated between to % of the critical speed. (a) 60 to 90 (b) 30 to 50 (c) 40 to 80 (d) 50 to 75 19. The grinding mill used for size reduction of materials up to a Mohs hardness of 10 is (a) ball mill (b) spiral jet mill

(c) fluidised bed opposed jet mill (d) rod mill 20. In a double-roll crusher, little or no crushing is observed when the resultant force (of tangential and normal forces acting on a particle at a point of contact with the rolls) acts (a) vertically upwards (b) vertically downwards (c) horizontally (d) none of the above

1(a); 2(b); 3(c); 4(d); 5(b); 6(b); 7(d); 8(c); 9(a); 10(b); 11(d); 12(a); 13(c); 14(a); 15(c); 16(a); 17(b); 18(d); 19(c); 20(c)

Dvs vsf

vsp

m

Mix i

i di

n n

i

I

Depending on the raw mixture, various separation processes are employed, which are broadly categorised into two groups—chemical diffusional and mechanical.

In chemical separations, the transfer of material takes place from one phase to another through various unit processes, for example, distillation, gas-absorption, adsorption, drying, and are based on the differences in physico-chemical properties like boiling point and solubility, which are beyond the scope of discussion of this text.

Mechanical separation techniques are based on the differences in phase density, and phase fluidity, and in such mechanical properties of particles as size, shape, colour, and density; and on such particle characteristics as wettability, surface charge, magnetic susceptibility, and electrical conductivity. Such techniques are applicable to the separation of phases in a heterogeneous mixture; however, they may be applied to all kinds of mixtures containing two or more phases: S–S, S–L, S–G, L–L, L–G, G–G, or S–L–G. Various types of chemical and mechanical separation processes are given in Table 4.1. The choice of separation depends on the pros and cons of these two methods. The mechanical separation methods are usually favoured, if possible, due to the lower cost of the operations as compared to the chemical methods. Mixtures that cannot be separated by purely mechanical means are treated by chemical methods. 1

S = Solid, L = Liquid, G = Gas phases

Sometimes, a combination of these two is employed for better efficiency and economic reasons.

C emical met ods Absorption Adsorption Crystallisation Distillation Drying Electro-phoresis Evaporation Extraction (L-L and S-L) Stripping/Desorption Sublimation Winnowing

Mec anical met ods Centrifugal separations Chromatography Classification Decantation Electrostatic separation Elutriation Filtration Floatation Flocculation Fractional freezing Jigging Magnetic separation Precipitation Scrubbing Sedimentation Sieving Sorting Tabling

The mechanical separation techniques are broadly classified as (i) (ii) (iii) (iv)

those employing a selective barrier such as a screen or a filter media, those depending on the difference in phase density alone, those depending on the fluid and particle mechanics, and those depending on the surface, electrical, or magnetic properties of particles.

Separation by a certain process depends on some physical properties of the solids. For example, if a material is to be separated into various size fractions on dry basis, a screening method is chosen as this method mainly depends on the size of solid particles. The separation based on the differences in the behaviour of solids in a static or moving fluid (on wet basis) depends mainly on the density. Generally, large particles are separated into size fractions by screening and small particles which may clog the fine screens are separated by using fluid or fluid motion. But, density separation becomes ineffective with decrease in particle size. For particles below 100 μm size, separation methods use magnetic, electrical, and surface properties. A great variety of mechanical separation devices are in current use and a few of them are listed in Table 4.2, grouped according to the phases involved.

P ases separated L from L G from L L from G S from L L from S S from G

S from S – by size – by density – by magnetic and electrical properties – by surface properties

❑ ❑

❑

❑

❑

E uipments Settling tanks/Coalescers/Liquid cyclones/Centrifugal decanters Foam breakers/Deaerators/Still tanks Settling chambers/Cyclones/Electrostatic precipitators (ESPs)/Impingement separators Filters/Clarifiers/Thickeners/Hydrocyclones/Wet screens/ Centrifuges Presses/Centrifugal extractors Settling chambers/Air filters/Bag filters/Cyclones/ ESPs/Scrubbers/Impingement separators/High-tension precipitators Screens/Air and wet classifiers/Centrifugal classifiers Jigs/Tables/Spiral concentrators Magnetic separators/Electrostatic separators Floatation cells

1. What are the benefits of a separation process (i) Produces valuable components (ii) Discards undesirable components of the mixture (iii) Reduces transportation and handling costs 2. Discuss the parameters which constitute the basis for mechanical separations. Any difference in physical properties like size, shape, density, colour, and surface, magnetic, and electrical properties can be the basis for mechanical separations. 3. Why are the mechanical separation methods favoured over the chemical ones

Due to the lower cost and ease of the operations, mechanical separation methods are preferred over the chemical ones.

1. What do you understand by separation process Discuss its importance. 2. Discuss in detail the various separation processes.

3. Discuss in detail about mechanical separation techniques and classify them.

1. The basis for mechanical separation is (a) size (b) density (c) electrical conductivity (d) all of the above 2. An example of a chemical separation process is (a) evaporation (b) filtration

(c) jigging (d) flocculation 3. A clarifier is used to separate (a) a liquid from a liquid–liquid mixture (b) a solid from a solid–liquid mixture (c) a solid from a solid–solid mixture (d) a solid from a gas–solid mixture

4. Name a few equipments used for the separation of solids from a solid–gas mixture. (i) Settling chamber (ii) Bag filter (iii) Electrostatic precipitator (iv) Cyclone (v) Scrubber 5. Name the properties upon which the separation of finer particles below 100-micron size depends. Finer particles below 100-micron size are separated using surface, electrical, and magnetic properties.

4. Write in brief about the separation of solids from different phases by mechanical means.

4. For solid particles below 100 μm size, the property used for separation is (a) density (b) size (c) magnetic property (d) shape

1(d);

2(a);

3(b);

4(c);

5 (d)

5. Separation of solid from a solid–liquid mixture is achieved by (a) foam breaker (b) settling chamber (c) cyclone (d) hydrocyclone

Mix i

F id in

d

n

v

nd i

n

di i

i

nd in i

Screening is the process of separating a mixture of particles of different sizes into two or more number of fractions, each of which is more uniform in particle size than the original mixture. In screening practice, a mixture of particles is taken and separated into multiple grades on the basis of particle size, as shown in Fig. 5.1. This practice is followed in a great variety of industries, such as mining and mineral processing, food, chemical, agriculture, plastics, recycling, and pharmaceuticals. Figure 5.2 illustrates the screening operation. The purpose of screening need not to be over emphasized, but to recall, a few important purposes of screening are

F

F

din :

d

(i) to remove the coarse particles for further size reduction, (ii) to remove the fine particles from crusher feeds to save power by preventing over-grinding, (iii) to grade the crushed products into commercial sizes, and (iv) to perform a step in a concentration process.

i d

nin

x

in

d

in d d

Screening is accomplished by passing the material in an open cylindrical container with uniformly spaced openings of the desired size at the base called the screen. The screen through

which the particles have passed is called the limiting screen and which has retained them is called the retaining screen. Material that remains on a given screening surface is the oversize (>) or plus (+) material and that passing is the undersize ( 1.5w) are less important for the screening result as these particles will not at all pass through. At the same time, their presence causes wear and increases power consumption. Particles having a dimension less than half the size of screen opening (dp < 0.5w) are also of lesser importance as they will pass through easily. But particles of 0.5w < dp < 1.5w are of much interest, known as critical class, which determine both efficiency and capacity. Particles of (i) 0.5w < dp < w, require several attempts before passing through and (ii) w < dp < 1.5w, clog many openings before leaving the screen as they are oversized material Metso, 2007 . The throughput along the length of a screen surface depends both on the stratification and the separation probability. When the material is fed to the screening surface using a feed plate, stratification occurs both on the feed plate and at the feed end of the screening surface, as shown in Fig. 5.4, and this section is between points A and B, with the maximum stratification occurring at B. Maximum particle removal occurs from B to C because of high percentage of fines and thus having a high separation probability. The next section C to represents the larger percentage of particles in the critical class and the probability of the particles passing through the screen is less Metso, 2007 . Perfect separation or 100 per cent screen efficiency is not practically possible because from point onwards, the probability of particles passing through the screen opening becomes extremely low and for this reason perfect screening is normally regarded as of around 90 to 95 per cent efficiency. For absolutely perfect separation, the screen would have to be infinitely long Metso, 2007 .

F

din

n d

A

B

C

D

Another easy-to-understand and self-explanatory plot on the throughput along the length of a screen as provided by Sandvik Mining and Construction, Sweden, is shown in Fig. 5.5. The speciality of this plot is the throughput along the length of the screen is given for different range of particle sizes which constitutes the whole sample. Once the particle has sifted through the bed of materials and reached the screen opening, the principle of probability becomes significant. As it is conveyed from feed end to the discharge end of the screen surface, the particle is subjected to the probability of either passing through the opening or striking the wires of the screening surface. ii n n

i n nin

i n nin

ii i n d

F

i

d

i

nin

= Fin

25 i n

=

nd

=

70 ii n 70−100

ii

n

i

i i n i

Fin

nd i

i

i

Material much smaller than the screen opening (fines < 25 per cent of holes and easy undersize < 70 per cent of holes) easily passes through the screen aperture. This is depicted by the first two regions of the plot. Maximum particle removal occurs in these sections. Due to the high percentage of fines, the probability is the highest. For critical nearsize particles (70 to 100 per cent of holes) the degree of probability of screening reduces as depicted by the last region of the plot. This is due to the fact that the relation of the particle size to the screen openings is closer. Hence, more near size particles means the chances of material passing through is less. The important factors affecting the passage of undersize particles are (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x) (xi)

the size of the screen openings, the size of particles with respect to the screen openings, the percentage of openings with respect to the total screening surface, the moisture content of the particles, the direction from which the particles come to the openings, the velocity with which the particles strike the surface, the motion given to the bed of materials — sinusoidal vibration or gyratory vibration, the density of the material — for heterogeneous materials density causes stratification on the screening surfaces, the gravity — pulls the particles through the screen, the electrostatic force — arises when particles are extremely dry, and the blinding, dampening, and screen tearing also affect the screening operation.

Screening surfaces — important for the study of industrial screening equipments — are generally of three types: parallel bars/rods, punched plates, and woven wires. Parallel bar/rod screens are usually made of steel bars, discarded rails, or cast-iron bars, fixed in parallel positions by cross-bars and spacers. These types of screens are used for coarsest work and not intended for close/fine size separations. Punched plate screens are made of metal/plastic sheets punched by dies of various patterns — circular, square, rectangular, hexagonal, and slotlike. They are arranged on the surface either in staggered manner or in straight rows. And the slotted openings have the additional arrangement in a diagonal manner. Figure 5.6 shows some punched plate screens. For coarse-size separations, circular opening punched-plate screens are chosen; while for fine-size separations, slotted openings are preferred over the circular openings due to lesser tendency to blind with slotted types. The advantages of punched screens include wear is evenly distributed and hence longer life; lesser tendency to blind; and the discharge of the oversize at a given rate requires lesser slope. But the major drawback with these screens is its low percentage of open area. Woven-wire screens are woven of gauged wires, generally made of steel to produce either square or rectangular openings and in different manners intended to

i

x d

n

n

n

n

n

i

i

i i

prolong their life or to prevent displacement of the wires. In all woven-wire screens, both the warp and shoot wires are crimped to prevent distortion under impact of load. Figure 5.7 shows some wire-cloth weaving patterns. Woven-wire screens can be made of any length and in width up to 5 feet. Greater widths can be made depending on the requirement. The percentage of openings with respect to the total screening surface is greater in rectangular types than in square types. But square openings make a more rigid cloth. For this reason, square opening wovenwire screens are preferable for very coarse screening while for intermediate and fine screening, rectangular opening screens are chosen. Figure 5.8 shows two types of rectangular opening screens — Trellex Rek-Tang and Sta-Clear. When greater production is desired along with accurate sizing, Trellex Re Tang is preferred. The rectangular opening forms a large open area allowing more material to pass through while maintaining accurate sizing of the desired product. When the screening material has a tendency to adhere to the wire (blinding), or become wedged ( pegging) in square opening or rectangular opening screens with a short slot length, Sta Clear screens are chosen. The Sta-Clear screens offer longer slotlike openings without the loss in strength by using three cross-wires. Materials for screening surfaces include cast iron, steel, manganese steel, chrome–nickel (stainless) steel,

A

i

v

v

i

v

brass, bronze, Monel metal, and some alloys. Currently, synthetic screens are available in rubber and poly-urethanes to optimise both wear resistance and performance. The screening surface must be strong enough to carry its load. x n A fine screen is often reinforced by laying it on the top of a coarser and stronger screen. The screen should resist abrasion and corrosion and at the same time it should be cheap. When corrosion is not a factor, highcarbon steel and alloy steel are used as screen material. Steel also resists x abrasion. When corrosion is a factor, iron, copper, bronze, and Monel metals are used, but these are not highly resistant to abrasion. When both corrosion and abrasion is to be resisted, stainless steel is chosen Taggart, 1945 . The minimum clear space between the edges of the opening in a screening surface is called the aperture, w. Generally, aperture is expressed in inches, centimetres, or millimetres. Aperture for parallel bar screens is expressed in inches as they are meant for coarsest work. The aperture of punched-plate screens has a dimension near that of some woven-wire screen of same designation. The aperture of woven-wire screens is expressed as mesh, meaning, the number of apertures per linear inch, counting from the centre of any wire to a point exactly 1 inch distant. For example, a 20-mesh screen will have 20 openings per inch. But this kind of designation is valid only when the wire size is defined. Mesh, therefore, gives a nominal figure of the screen opening. If d is the diameter of the wire, and m is the mesh then the aperture found by 1 = − m

can be (5.1)

This kind of screen designation is followed by American Standards (ASTM and W S Tyler Co.), British Standards (BS), and German Standards (DIN). Clearly, in all these standards, higher the mesh number, smaller will be the screen aperture. In some countries, especially in South Africa, mesh is defined as the number of openings per square inch and in continental Europe, it is defined by the number of openings per square centimetre Taggart, 1945 . ISO, DIN, BS, and AFNOR are based on aperture. ASTM and Tyler are based on the meshcount, using number of wires per linear inch Haver . However, the Indian Standards (IS) follow a different definition — the mesh is equal to its aperture size expressed to the nearest deca-micron. Thus, an IS screen of 100 mesh will have an aperture of approximately 1.00 mm. Clearly, in IS screen series, higher the mesh number higher is the screen aperture and vice-versa Narayanan, 2003 . Table 5.1

2

R 40/3

125

125

100

112

w

106

125

w

Square Holes �

Round Holes �

Woven Wire Cloth

2000

R 20

w

ISO 3310-2

ISO 3310-1

R 20/3

3

Supplementary sizes

ISO 565 . ISO 3310 Table 1, Millimetre sizes

Principal sizes

1

112 106 100

125

w

125–4

125–1

125–1

2001

DIN ISO 3310

DEU

4

112 106 100

125

w

125–4

125–1

125–1

2000

AFNOR NF ISO 3310

FRA

5

112 106 100

125

w

125–4

125–1

125–1

2000

BS 410 ISO 3310

GBR

6

112 106 100

125

w

125–4

125–1

125–1

1998

NEN 2560

NLD

7 USA

9

106 100(b)

125

w

125–3.35

125–1

125–1

4.24 in. 4 in.(b)

5 in.

No.

ASTM E 11 , 2004 ASTM E 323 , 1980 (2004)

8

TYLER

11

100

112

125

w

125–1

1988

Continued

Mesh

26,5–1

1910

CAN/CGSB- TYLER 8.2-M88 Screen scale metric

CAN

10

22,4

31,5

45

63

90

18

20

22,4

25

28

31,5

35,5

40

45

50

56

63

71

80

90

19

22,4

26,5

31,5

37,5

45

53

63

75

90

20 19 18

22,4

28 26,5 25

31,5

40 37,5 35,5

45

56 53 50

63

80 75 71

90

20 19 18

22,4

28 26,5 25

31,5

40 37,5 35,5

45

56 53 50

63

80 75 71

90

20 19 18

22,4

28 26,5 25

31,5

40 37,5 35,5

45

56 53 50

63

80 75 71

90

20 19 18

22,4

28 26,5 25

31,5

40 37,5 35,5

45

56 53 50

63

80 75 71

90

19.0

22.4

26.5 25.0(b)

31.5

37.5

45

53 50(b)

63

75

90

3/4 in.

7/8 in.

1.06 in. 1 in.(b)

1.1/4 in.

1.1/2 in.

1.3/4 in.

2.12 in. 2 in.(b)

2.1/2 in.

3 in.

3.1/2 in.

18.0

20.0

22.4

25.0

28.0

31.5

35.5

40.0

45.0

50.0

56.0

63.0

71.0

80.0

90.0

.742 in.

.883 in.

1.05 in.

4

5,6

8

11,2

16

3,15

3,55

4

4,5

5

5,6

6,3

7,1

8

9

10

11,2

12,5

14

16

3,35

4

4,75

5,6

6,7

8

9,5

11,2

13,2

16

3,55 3,35 3,15

4

5 4,75 4,5

5,6

7,1 6,7 6,3

8

10 9,5 9

11,2

14 13,2 12,5

16

3,55 3,35 3,15

4

5 4,75 4,5

5,6

7,1 6,7 6,3

8

10 9,5 9

11,2

14 13,2 12,5

16

3,55 3,35 3,15

4

5 4,75 4,5

5,6

7,1 6,7 6,3

8

10 9,5 9

11,2

14 13,2 12,5

16

3,55 3,35 3,15

4

5 4,75 4,5

5,6

7,1 6,7 6,3

8

10 9,5 9

11,2

14 13,2 12,5

16

3.35

4.00

4.75

5.6

6.7 6.3(b)

8.0

9.5

11.2

13.2 12.5(b)

16.0

6

5

4

3.1/2

0.265 in. 1/4 in.(b)

5/16 in.

3/8 in.

7/16 in.

0.530 in. 1/2 in.(b)

5/8 in.

3.15

3.55

4.00

4.50

5.00

5.60

6.30

7.10

8.0

9.0

10.0

11.2

12.5

14.0

16.0

Continued

6

5

4

3.1/2

3

2.1/2

.371 in.

.441 in.

.525 in.

.624 in.

Woven Wire Cloth

1

1,4

2

2,8

1

1,12

1,25

1,4

1,6

1,8

2

2,24

2,5

2,8

Round Holes �

1

1,18

1,4

1,7

2

2,36

2,8

1

1,25 1,18 1,12

1,4

1,8 1,7 1,6

2

2,5 2,36 2,24

2,8

Square Holes �

1

1,25 1,18 1,12

1,4

1,8 1,7 1,6

2

2,5 2,36 2,24

2,8

1

1,25 1,18 1,12

1,4

1,8 1,7 1,6

2

2,5 2,36 2,24

2,8

1.00

1.18

1.40

1.70

2.00

2.36

2.80

(b) ASTM Supplementary Values

1

1,25 1,18 1,12

1,4

1,8 1,7 1,6

2

2,5 2,36 2,24

2,8

18

16

14

12

10

8

7

1.00

1.12

1.25

1.40

1.60

1.80

2.00

2.24

2.50

2.80

16

14

12

10

9

8

7

2

500

710

w

400

450

500

560

630

800 710

900

w

425

500

600

710

850

w

450 425 400

500

630 600 560

900 850 800 710

w

500–5

Electroformed

ISO 3310-3

450 425 400

500

630 600 560

900 850 800 710

w

500–5

2000 900–20

2001

900–20

R 40/3

AFNOR NF ISO 3310

FRA

5

Woven Wire Cloth

R 20 2000

DIN ISO 3310

DEU

4

ISO 3310-1

R 20/3

3

Supplementary sizes

ISO 565 . ISO 3310 Table 2, Micrometre sizes

Principal sizes

1

450 425 400

500

630 600 560

900 850 800 710

w

900–20

2000

BS 410 ISO 3310

GBR

6

450 425 400

500

630 600 560

900 850 800 710

w

500–5

900–20

1998

NEN 2560

NLD

7 USA

9

425

500

600

710

850

w

500–5

850–20

40

35

30

25

20

No.

850–20

ASTM E 11 , 2004 ASTM E 161 , 2000 (2004)

8 TYLER

11

400

450

500

560

630

800 710

900

w

900–32

1988

Continued

35

32

28

24

20

Mesh

850–20

1910

CAN/CGSB- TYLER 8.2-M88 Screen scale metric

CAN

10

90

125

180

250

355

71

80

90

100

112

125

140

160

180

200

224

250

280

315

355

75

90

106

125

150

180

212

250

300

355

80 75 71

90

112 106 100

125

160 150 140

180

224 212 200

250

315 300 280

355

80 75 71

90

112 106 100

125

160 150 140

180

224 212 200

250

315 300 280

355

80 75 71

90

112 106 100

125

160 150 140

180

224 212 200

250

315 300 280

355

80 75 71

90

112 106 100

125

160 150 140

180

224 212 200

250

315 300 280

355

75

90

106

125

150

180

212

250

300 280

355

200

170

140

120

100

80

70

60

50

45

71

80

90

100

112

125

140

160

180

200

224

250

280

315

355

200

170

150

115

100

80

65

60

48

42

Woven Wire Cloth

16 10 5

32 25 20

R’10

45

63

36

40

45

50

56

63

38

45

53

63

32 25 20

40 38 36

45

56 53 50

63

16 10 5

Electroformed

16 10 5

32 25 20

40 38 36

45

56 53 50

63

32 25 20

40 38 36

45

56 53 50

63

16 10 5

32 25 20

40 38 36

45

56 53 50

63

15 10 5

32 25 20

38

45

53

63

450 500 635

400

325

270

230

32

36

40

45

50

56

63

450 500 635

400

325

270

250

shows the comparison table of different standard sieves. Tyler sieve series and its Indian equivalents and particle size conversion chart are given in appendix.

The evaluation of a screening operation is best determined by size analysis using testing screens, hereafter, sieves, in terms of given percentages of materials passing or retained on specified testing sieves. Testing sieves are used for control and analytical purpose, for example, determining the efficiency of screening devices and the work of crushing and grinding equipments. Testing sieves (Fig. 5.9) are constructed of woven-wire cloths as per some specified standard. These wire cloths form the bottom of circular metal pans about 8 inches in diameter and 2 inches high whose sides are so designed that the bottom of one sieve sits on the top of the next sieve. It is essential that standard sieves with standard size openings be used for sieve analysis, otherwise the analysis may be misleading as the opening of all the sieves are dependent on both the number and the diameter of the wires of which they are made. Sieve analysis is also dependent on the time of sieving and the method of agitating the materials on the sieve — both these should also be standard. For sieve analysis, a sieve scale is used which consists of a series of testing sieves having openings in a fixed succession. The first known standard sieve scale was introduced by W S Tyler Co. in the early 1900 s, having the widths of the successive openings with a constant ratio of 2 2 or 1.414, such that the areas of the successive openings have a constant ratio of 2. The Tyler Standard sieve scale series is based on a 200-mesh screen in which the opening is 0.075 mm (0.0029 inch) with a wire diameter of 0.053 mm (0.0021 inch). Years later, the Tyler scale has been enlarged to include intermediate openings so that the entire scale has successive openings with a constant ratio of 4 2or 1.189. Standards like National Bureau of Standards, American Standards for Testing Materials, American National Standards Institute, and many others are based on fourth-root-of-2 principle. In making a sieve analysis, the individual test sieves of one specified sieve scale series are stacked one above the other in the ascending order of their openings. A pan at the bottom and a cover at the top are put to make a complete set. A weighed amount of material is fed to the topmost sieve and the cover is replaced. The whole assembly can be shaken continuously, either manually by hand or by machines. Machine sieving is preferable over hand sieving because the hand method is open to error. One popular machine used for such analysis is the Ro Tap Sieve S a er (Fig. 5.10). The whole assembly of sieves is fastened into a vertical framework of the shaker which provides a circular motion in a horizontal plane and a blow at the top for each revolution. Shaking is continued for 5 to 10 minutes. Then the material retained on each sieve including the pan are weighed. The sieving procedure is illustrated in Fig. 5.11.

The material, for example, which has passed the 20-mesh sieve but is retained on the 24-mesh sieve, is designated as (20/24) or (−20 + 24) fraction.

in

i

in

i

in

i v

i

i v nd nd Fin

(i) by calculating the mass percentage of each size fraction, (ii) by calculating the cumulative percentage of size fractions retained on each sieve, and (iii) by calculating the cumulative percentage of size fractions passing through each sieve.

i

Fin

The sieving results obtained from sieve analysis can be compiled in three different ways:

Mix

A typical example is given in Table 5.2 and the graph for this compiled data is shown in Fig. 5.12, which represents the cumulative percentage of material passing each sieve. In order to visualise the size fractions, the compiled data can be presented graphically in different ways. The most common plots are differential and cumulative plots. Differential plots are the plots of the mass fraction (or the percentage of mass fraction) retained on each sieve versus average sieve size, while cumulative plots are the plots of the mass fraction (or the percentage of mass fraction) passing through or retained on each sieve versus particular sieve aperture.

Microns t roug

Si e mes t roug

Si e mes on

Wt on gr

– 26500 19000 13200 9500 6700 4750 3350 2360 1700 1180 850 600 425 300 212 150 106 75 53

– 1.050 0.742 0.525 0.371 3 4 6 8 10 14 20 28 35 48 65 100 150 200 270

1.050 0.742 0.525 0.371 3 4 6 8 10 14 20 28 35 48 65 100 150 200 270 PAN

– 0 0 0 2 7 13 36 71 160 254 319 352 381 407 429 444 461 463 471

Cum t ru – 100.0 100.0 100.0 100.0 99.6 98.5 97.2 92.4 84.9 66.0 46.1 32.3 25.3 19.1 13.6 8.9 5.7 2.1 1.7

Bet een sieves – 0.0 0.0 0.0 0.4 1.1 1.3 4.9 7.4 18.9 20.0 13.8 7.0 6.2 5.5 4.7 3.2 3.6 0.4 1.7

50.0

100.0

45.0

0.0

40.0

0.0

5.0

70.0

0.0

60.0

25.0

50.0

20.0

40.0

15.0

0.0

10.0

20.0

5.0

10.0

0.0 270

*

150

65

5

20 10 Mesh, Tyler

% Between sieves n i v

6 Cum % thru

0.0 0.525 1.050

Cum % thru

% Between sieves*

( Mat:Petroleum Coke, H2O:15.3 %, Rate:10 TPH, Equip:Coalpactor, Speed:1350 RPM)

Screen opening mm

Tyler screen scale

Average diameter of particles mm

Mass retained g

Mass % retained

− 26500 19000 13200 9500 6700 4750 3350 2360 1700 1180 850 600 425 300 212 150 106 75 53

+1.050 −1.050 + 0.742 −0.742 + 0.525 −0.525 + 0.371 −0.371 + 3 −3 + 4 −4 + 6 −6 + 8 −8 + 10 −10 + 14 −14 + 20 −20 + 28 −28 + 35 −35 + 48 −48 + 65 −65 + 100 −100 + 150 −150 + 200 −200 + 270 −270 + PAN

>26500 22750 16100 11350 8100 5725 4050 2855 2030 1440 1015 725 512.5 362.5 256 181 128 90.5 64 7) because most collectors are stable at higher pH values. The optimum pH value is generally prescribed by the reagent manufacturers. When the desired mineral particles to be separated are not naturally hydrophobic, collectors are added to the slurry, which are adsorbed selectively on the surface of the particles to make them hydrophobic. These are generally hetero-polar compounds of fatty acids, sulfates, sulphonates, xanthates, and dithiophosphates, consisting of a polar head with a long nonpolar tail. The collectors’ polar heads get attached to a polar mineral surface, leaving the nonpolar tails toward the surrounding water molecules,

rendering the mineral particle hydrophobic, as shown in Fig. 5.65. This causes the mineral particle to be repelled by water. Min When the mineral surfaces have i been rendered hydrophobic by the collector, the frothers are added to n produce stable air bubbles for particle– bubble attachment and their removal as froth. These are organic surfactants consisting of a polar head oriented outward toward water and a nonpolar tail oriented inward toward the air, as shown in Fig. 5.66. The frothers must provide adequate stability of the froth on the top of the slurry and prevent the release of the hydrophobic particles d back into the slurry. Too stable a froth Ai also results in too much frothing and n i hinders the subsequent processing of the froth laden with mineral particles. Example of frothers includes pine oil, cresylic acid, polypropylene glycol, and methyl isobutyl carbinol Perry, 1997 . The activators are generally soluble salts that ionize easily in water and are used to make selectively the mineral surfaces more favourable for the adsorption of a collector. For example, copper ion is used to activate sphalerite surfaces for the adsorption of xanthate collector, whereas the depressors are inorganic compounds and are used to make selectively the mineral surfaces hydrophilic. This decreases their activity towards collectors and thus, the flotation of undesired particles can be prevented. For example, sodium or calcium cyanide is used to depress pyrite (FeS2) while floating galena (PbS) or sphalerite (ZnS) Perry, 1997 .

The larger particles, being heavy, require much larger bubbles for flotation than the smaller particles. Too small a particle size, results in more amount of collector consumption and the movement of these particles in upward direction by the turbulence created by the upward movement of air bubbles. Also, the bubble diameter plays a vital role in flotation operation, since with the reduction of bubble diameter the total available surface increases for the particle–bubble attachment.

A great variety of flotation machines are available on the market which can be classified into different categories based on the methods of generation and introduction of

F

i

i

i n

i

n

i

v d i

n

i

d i

M

n

ni

i n

air bubbles into the machines, as shown in Fig. 5.67. One of the machines is the f lotation cell, a type of mechanical M flotation equipment in which air is dispersed by mechanical means. Ai The flotation cell consists of a cylinF drical tank, equipped with a turbine and baffles at the periphery, as shown in Fig. 5.68. The slurry is fed to the cell near the bottom end of the tank, so as nd not to disturb the froth at the top. Air F d n x enters the machine through a concentric pipe surrounding the turbine shaft, due to the vacuum created by the rotation of turbine or if required air is injected using a low-pressure blower. Due to the rotation of the turbine, the air is dispersed in the slurry as fine bubbles to which hydrophobic particles get attached and rise to the surface where they accumulate as froth. At the top of the tank, an overflow launder is attached along the periphery to collect this froth laden with hydrophobic particles with the help of a scrapper; whereas the hydrophilic particles will either sink or remain in suspension and are removed as underflow tailings. Figure 5.69 shows the Outotec TankCell flotation unit. The cylindrical TankCell operates as an ideal mixer and maximises the number of collisions between the mineral particles and air bubbles, as well as reduces short circuiting. TankCell units are available with cell sizes from 5 to 300 m3. They are easy to operate and consume low power and air. Figure 5.70 shows the operation of a WEMCO SmartCellTM Flotation machine which is provided with a semicircular feed box, hybrid draft tube, beveled cell bottom,

A F

i n

i

d M

i i

A i d

x

i

F di in nd

d i

ni d nd n n

Mixin

i n id d F

v

radial launders and mixing baffles. The cylindrical tank design improves efficiency and air dispersion. The hybrid draft tube and beveled tank improves hydrodynamic mixing, increases solid suspension, and improves coarse particle recovery. The radial launder and mixing baffles increase froth mobility, decrease froth residence time,

increase recovery, and enhance froth stability. The SmartCellTM units are available with cell sizes from 0.05 to 250 m3. The flotation technique is used for the recovery of fine coal and for the concentration of barite, iron oxide, mica, talc, pyrite, feldspar, calcite, and many more minerals. In addition to minerals, this technique finds application in wastewater treatment, separation of proteins from milk, recovery of bitumen from tar sands, de-inking of waste paper, recovery of petroleum hydrocarbons and polycyclic aromatic hydrocarbons, and clarification of fruit juices [Perry, 1997].

❑

❑

❑ ❑ ❑ ❑ w=

1 − d. m

❑

2

❑

❑

E = (Recovery ) × (Rejection).

❑ E=

E= ❑

❑

❑

❑ ❑

❑

❑

❑ ❑

xD (1 − xB )( xF − xB )( xD − xF ) xF (1 − xF )( xD − xB )2

or,

xD ( xF − xB ) ⎡ (1 − xD )( xF − xB ) ⎤ ⎥. ⎢1 − xF ( xD − xB ) ⎢⎣ (1 − xF )( xD − xB ) ⎥⎦

1. What is a limiting screen The screen through which the particles have passed is called a limiting screen. 2. What is a retaining screen The screen that has retained the particles over it is called a retaining screen. 3. Why is wet screening practiced It is carried out to remove undesirable materials, mostly clay and extremely fine particles. 4. Why is screening widely used in size analysis Screening is the easiest, cheapest, and a rapid method of size analysis. 5. What is the importance of stratification in screening It is essential for the transport of the oversize materials and for the prevention of blinding of the screen openings. 6. Name the factors which affect stratification in screening. The factors affecting the stratification process are (i) material travel flow, (ii) stroke characteristics, and (iii) surface particle moisture. 7. Why are, slotted openings preferred to circular openings for fine size separation Slotted-type openings have lesser tendency to blind the screen. 8. What are the advantages of punched screens The advantages are (i) wear is evenly distributed and they have hence longer life, (ii) lesser tendency to blind , and (iii) lesser slope for the discharge of oversize particles at a given rate. 9. Name the different weaving patterns of Metso Minerals Inc. for the woven-wire screens.

The weaving patterns are (i) Arch Crimp, (ii) Sta-Smooth, and (iii) Double Crimp. 10. Give the common standards followed for screen designation. The common standards are (i) American standards (ASTM and Tyler), (ii) British standards (BS), (iii) German standards (DIN), and (iv) Indian standards (IS). 11. How is the screen size specified under the Indian Standards The mesh size is expressed to the nearest decamicron. For example, an IS screen of 100 mesh will have an aperture of approximately 1.00 mm. 12. Define screen effectiveness. It is the product of the recovery and the rejection. Recovery refers to desired materials in product and rejection refers to the undesired materials in the reject. 13. Name a few common types of screening equipments. Common screening equipments are grizzly screens, trommels, vibrating, gyratory, shaking, and banana screens. 14. What are the advantages of vibrating screens The advantages of vibrating screens are (i) high capacity and efficiency, (ii) applicable to coarse, medium, and fine particles, (iii) lower operating and maintenance costs, (iv) less space requirement, and (v) lesser blinding of screen openings. 15. What are the advantages of electromagnets over permanent magnets The electromagnets are advantageous because by varying the intensity of the electrical current, the magnetic field intensity can be adjusted. Also, the

magnetic field produced by an electromagnet reaches a much higher intensity than the field intensity created by a permanent magnet. 16. What are the advantages of highgradient magnetic separators The advantages are (i) ease of operation and maintenance, (ii) greater efficiency with smaller-sized particles, (iii) high beneficiation ratio, (iv) high recovery, and (v) minimised matrix blocking. 17. Give the process application for superconducting high-gradient magnetic separators. These are used for processing of kaolin, calcium carbonate, and talc, and fine materials less than 100 microns. 18. What are the applications of triboelectrostatic separators Triboelectrostatic separators are used for the separation of plastics in the recycling industries, e.g., cable plastics, automobile, multilayered bottles, PET/PVC, ABS/ HIPS, PVC/PC, PVC/PE, Nylon, etc. 19. What is the unique feature of a Spitzkasten classifier The flow rate between each vessel is adjustable in order to provide the desired degree of separation. 20. Why are hydrocyclones widely used in chemical and mineral-processing industries Hydrocyclones have large capacity relative to their size and can make extremely fine separations. 21. What is the difference between a forward and a reverse hydrocyclone The forward hydrocyclones remove particles which are denser than the surrounding fluid, while the reverse type removes particles lighter than the surrounding fluid. 22. What are the factors on which the effectiveness of separation of hydrocyclones depends

The factors are (i) pulp density, (ii) feed f low and pressure, (iii) diameter of vortex finder and apex, and (iv) angle and length of conical section. 23. What are the advantages of hydrocyclones The advantages of hydrocyclones are (i) absence of mechanical or moving parts, (ii) no requirement for a separate power source, (iii) less maintenance, (iv) low equipment costs, and (v) ability to make extremely fine separations. 24. Name a few fields of applications for hydrocyclones. Fields of applications are desanding, desliming, sewage treatment, flue gas desulphurisation, degritting of red mud in alumina production, mining and mineral processing industries, and in pulp and paper industries to remove sand and other contaminants. 25. What is a Floatex density separator It is a hindered settling classifier for classifying particles based on size and/ or density. 26. What are the various zones of a mechanical classifier The zones are transport zone, classification zone, and settled solids zone. 27. What are the special features of a Wemco Remer jig The compact design of a Wemco Remer jig provides maximum capacity for minimum floor space. 28. What is the unique feature of spiral concentrators These units have no moving parts. As the slurry flows down the spiral, the separation is achieved by stratification of material caused by the complex combined effect of size, density, and to a lesser extent, shape; centrifugal force; differential settling; friction against the spiral surface; drag of the water; and the hindered

settling through the flowing particle bed. The low-density particles are carried away with the bulk of water towards the outer side of the spiral, while the heavier particles move toward the inner side. 29. Name the floatation reagents. Various flotation reagents used for the modification of the surface properties of the mineral particles are pH regulators, activators or depressors, collectors, and frothers. 30. What are the applications of the floatation technique

The floatation technique is used for the recovery of fine coal and for the concentration of barite, iron oxide, mica, talc, pyrite, feldspar, calcite, and many more minerals. In addition to minerals, this technique finds application in wastewater treatment, separation of proteins from milk, recovery of bitumen from tar sands, de-inking of waste paper, and recovery of petroleum hydrocarbons and polycyclic aromatic hydrocarbons.

1. What do you understand by screening Discuss the importance of separation based on particle size. 2. Why is screening practiced in industries 3. Discuss the mechanism of screening. 4. Mention the factors affecting the screening operation. 5. Discuss the types of screening surfaces and their material of construction. 6. How are screen sizes designated for different types of screens 7. Discuss the method of screen/size analysis. 8. Discuss the method of reporting sieve-analysis data. 9. What do you understand by screen efficiency and capacity 10. Give the factors affecting screen effectiveness. 11. Discuss ideal and actual screening.

12. Discuss the types of screening equipments. 13. Discuss in detail the electrical (magnetic and electrostatic) separation methods and equipments. 14. Discuss the difference between sizing and sorting as practiced in case of classification of solid particles. 15. Give the various parameters on which the terminal settling velocity depends. 16. Discuss various types of classifying equipments. 17. Discuss various types of gravity concentration equipments. 18. Discuss the role of various floatation reagents used to modify the surface properties of the solid particles. 19. Discuss the effect of particle and bubble sizes on separation by froth floatation method. 20. Give the various fields of application of floatation techniques in mineral and chemical industries.

1. A crushed ore was screened, using a 3.35-mm (340 mesh) screen to separate the oversize material to be recycled for further crushing. The screen analysis of

feed, overflow, and underflow are given below. Find the input to the crusher for 100 kg/h of product and the screen effectiveness.

ISS mes + 480 − 480 + 340 − 340 + 120 − 120 + 60 − 60 + 30 − 30

Feed

verflo

nderf lo

0.548 0.146 0.109 0.045 0.034 0.118

0.596 0.168 0.096 0.039 0.029 0.072

0.00 0.113 0.147 0.086 0.037 0.621

30.62 % 2. Dolomite is produced at a rate of 2 tonne/h by crushing and then screening through a 16-mesh screen. Calculate the Mes 4 8 16 32 60 100 100 through

Feed % 12 21 22 30 8 5 2

total load to the crusher and the effectiveness of the screen for the following screen analysis (weight percent). ndersi e % – – 0 42 28 18 12

versi e % 22 26 28 24 – – –

61.4% 3. A sample of pyrite powder has the screen analysis given below. Calculate the specific surface in cm2/g. Specific gravity of pyrite = 5.0. Mes no −4+6 −6+8 − 8 + 10 − 10 + 14 − 14 + 20 − 20 + 28 − 28 + 35 − 35 + 48 − 48 + 65 − 65 + 100 − 100 + 150 − 150 + 200

Percentage retained 5.0 6.2 13.0 16.6 15.0 12.4 9.0 8.2 5.0 4.8 3.3 1.5

⎡ cm2 ⎤ ⎢59.37 g ⎥ ⎣ ⎦

4. In a cement manufacturing unit, 36 tonne/h of calcite of 5-cm size is fed to a gyratory crusher. Screen analysis from the crusher shows a surface area of product of 61.7 m2/kg. The crushed material is then subjected to fine reduction in a hammer mill. Mill product analysis indicates a surface area of 740 m2/kg. Rittinger s number for calcite is 75.9 cm2/kg.cm. Efficiency of the grinder is 30%. The crusher and grinder are driven on the same shaft (by an electric motor) whose transmission efficiency is 90%. If 480 hp is fed at the other end of the shaft, compute the efficiency of the crusher. ata Density of calcite = 2.65 g/cc and Specific surface ratio for feed = 3.5. 25.3 %

1. If is the screen aperture and dp is particle dimension, the critical class of particles have dimension equal to (a) dp > 1.5 (b) < dp < 1.5 (c) 0.5 < dp < 1.5 (d) < dp < 2 2. The successive opening in the Tyler series of screen is with a constant ratio of (a) 2 (b) 2 2 (c) 3 2 (d) 4 2 3. The Tyler standard sieve scale series is based on a screen size of (a) 100 mesh (b) 200 mesh (c) 400 mesh (d) none of the above 4. Grizzly screens are recommended for separating particles in the size range of (a) 5 – 50 mm (b) 10 – 100 mm (c) 15 – 200 mm (d) 20 – 300 mm 5. Maximum screening efficiency can be achieved in a (a) gyratory screen (b) grizzly screen (c) trommel screen (d) vibratory screen 6. The operating speed of a trommel is (a) 5 – 10 rpm (b) 15 – 20 rpm (c) 25 – 40 rpm (d) 30 – 50 rpm 7. The charging mechanisms used for the electrical separation of minerals are (a) contact electrification (b) ion bombardment

(c) conductive induction (d) none of the above (e) all the above 8. For the separation of weakly magnetic materials, the equipment used is (a) magnetic drum separator (b) rare-earth magnetic rolls (c) high gradient magnetic separator (d) induced roll magnetic separator 9. The common way of cooling a superconducting magnet is to immerse it in a bath of (a) ice at 4 K (b) mercury at 4 K (c) liquid helium at 4 K (d) liquid nitrogen at 4 K 10. Gravity concentration equipments work on the principle of (a) density (b) film sizing (c) shaking (d) all the above 11. Spiral concentrators are used for the concentration of (a) high grade ore (b) low grade ore (c) all grades of ore (d) none of the above 12. Recovery of ilmenite from beach sands is achieved by (a) Wemco Remer jig (b) shaking table (c) spiral concentrator (d) rake classifier 13. Floatation is carried out generally at a pH value of (a) less than 7 (b) greater than 7 (c) 0 to 14 (d) nothing in particular

14. Methyl isobutyl carbinol is used in floatation as a (a) depressor (b) collector (c) frother (d) pH-regulator

15. A depressor which can depress pyrites from lead ore to float galena is (a) calcium cynamide (b) pine oil (c) polypropylene glycol (d) oleic acid

1(c); 2(b); 11(b); 12(c);

6(b);

Dm

3(b); 13(b);

4(d); 14(c);

5(a); 15(a)

7(e);

8(c);

9(c);

10(d);

F F

Ov nd

d

d

ii

i n

in

n

n Ov i n

n i n

n

Fi

Fi

di

i nd

v vin

i

di

Solid–liquid separation is often encountered in various stages of industrial processes ranging from raw material purification to waste management with an objective of separation and removal of the suspended solids from the liquid. The most common methods available for this job are sedimentation and filtration. The theory of separation by these methods is much more complicated because of the complex nature of solid-liquid systems. Also, the selection of proper equipment and optimum operating conditions are the biggest challenge for the design engineers.

Various terms related to this unit operation are dewatering, draining, sedimentation, thickening, clarification, filtration, and drying. The separation of a slurry into two parts, one of which is dense and relatively liquid-free and the other being dilute and relatively solid-free, is termed as dewatering. Removal of water from relatively coarse solids, for example, sands, is known draining. But if the solids are very fine such that any slight disturbance causes them to be suspended in water then the sedimentation method can be brought into action. In this case, separation is achieved by bringing the water substantially to rest and allowing the solid particles to settle down under the action of gravity. The sedimentation method is further divided into two operations — thic ening and clarification, which occur simultaneously. The purpose of thickening is to increase the concentration of solids, whereas in clarification, a relatively small quantity of suspended solids is removed to get a clear liquid. The separation of suspended solids from a liquid with the help of a porous medium or screen which retains the solids and allows the liquid to pass through is known as filtration. The near complete removal of relatively small amounts of water from the solid particles is known as drying (which is beyond the scope of this book).

Sedimentation is a physical process used to separate the suspended solids from a liquid under the influence of gravity. It is one of the most widely used processes in the treatment of water and wastewater. In this process, the dilute slurry is separated into a clear liquid and a slurry of higher solid content. The simplest method of removing the suspended solids is by plain sedimentation, where the water is brought substantially to rest in which suspended solids are settled down under the influence of gravity. In industries, sedimentation is carried out on a continuous basis in sedimentation tanks of large diameter that receive the slurry generally at the centre, allowing the clear liquid to flow over the weirs at the sides, and produce a thick sludge at the bottom of the tank. In these tanks, the upward velocity of the liquid is kept less than the settling velocity of the particles. The sedimentation rate can be increased by adding an electrolyte, which causes precipitation

of colloidal particles. The degree of separation is greatly affected by particle size, retention period, liquid viscosity, solid and slurry densities, type and concentration of electrolyte, and the temperature of the liquid. The solid particles settle under two different conditions—free and hindered settling. When the particles fall in a gravitational field through a stationary fluid and their fall is not affected by the walls of the container and by other particles, the settling process is termed as free settling. This is observed if the concentration of the particles is less than 1% by weight of solids. In free settling, as the particle falls, its velocity increases and will continue to increase until the resisting and accelerating forces become equal. When this condition is reached, the particles settle at constant velocity during the remainder of its fall, known as terminal settling velocity. But when the fall of a particle through the stationary fluid is impeded by the presence of other particles, the process is called hindered settling. In this case, the settling velocity is considerably less than the terminal settling velocity under free settling conditions.

The mechanism of settling may be best described by the batc sedimentation test before the continuous operation is considered. The procedure of the batch sedimentation test is quite simple. A sample of the slurry containing finely divided solid in water is taken in a graduated glass cylinder and is allowed to stand undisturbed, as shown in Fig. 6.1 (a). This test is to be carried out at a uniform temperature to avoid free convection currents due to density differences resulting from the difference in temperature. As soon as the process starts, all the particles begin to settle and are believed to approach rapidly the terminal settling velocities under hindered settling condition. Various zones of different concentrations are developed with the progress of the settling process, as shown in Fig. 6.1. A zone of clear liquid (A) develops at the top and below this, the zone B exists, which is a zone of uniform concentration of approximately the same concentration as that of the original slurry. The interface between zones A and B is sharp for closely sized solid particles. But for a slurry containing particles of different sizes, the interface is not sharp and the liquid in the zone A may be hazy. In both the cases, the particles begin to pile up at the bottom of the test

D

D i d

cylinder, indicated by the zone . Above this zone exists another layer, called the zone C, a region of variable size distribution and non-uniform concentration. The interface between C and is usually not sharp since fluid rises from the zone as it compresses. The zone C is also known as the transition zone. As the sedimentation process proceeds, the heights of each zone vary, as shown in figures 6.1 (b) to (d). The heights of zones A and increases at the expense of the zone B, while the height of the zone C remains constant. But with the progress of sedimentation process, zones B and C disappear. All the solids present in the slurry appear in the zone , as shown in Fig. 6.1 (d). The height of the zone decreases further due to slow compaction of solids. During this compaction, the liquid associated with the solids in the zone is expelled to the zone A and an ultimate height of the zone is reached, as shown in Fig. 6.1 (e). The four different zones as discussed for batch sedimentation operation will also be present in continuous sedimentation operation, but in continuous process the heights of various zones will vary till the steady state is reached. Figure 6.2 shows the various zones in a continuous sedimentation equipment. The continuous sedimentation process is preferred over the batch process in industries to meet the process requirements.

The study of particle dynamics is important in many mechanical operations like sedimentation, classification, elutriation, filtration, etc., which involve relative movement between solid particles and a fluid. The study is initially focused on the movement of a single particle in a fluid and then the resulting equations with necessary modifications are applied to practical problems. The analysis can be simplified by making the following assumptions: (i) the particle is spherical, (ii) the particle is nonporous and incompressible and chemically inert with the fluid, (iii) the density and viscosity of the fluid are constant, F F

d

d

ii

i n

in

n

n Ov

Ov i n

nd n

i n

nd

v vin

n

(iv) the particle is settling freely under gravity, and (v) the fluid forms an infinite medium Narayanan, 2003 . When a particle settles in a fluid under gravity, the forces acting on it are Fig. 6.3

n

(i) the force of gravity, Fg acting downwards, (ii) the force of buoyancy, Fb acting upwards, which is equal to the weight of the displaced fluid, and (iii) the drag force, Fd offered by the fluid on the particle acting opposite to the particle motion.

d

vi

The force balance on the particle can be written as m ⇒m

v

=

g

−

b

−

d

⎛ m⎞ ⎛ ρ v2 ⎞ dv = mg − ⎜ ⎟ ρf g − ⎜ CD × Ap × f ⎟ 2 ⎠ dt ⎝ ⎝ ρp ⎠

(6.1)

where, m = mass of the particle, v = particle velocity, dv dt = particle acceleration, g = gravitational acceleration, rp = particle density, rf = fluid density, CD = drag coefficient, and Ap = projected area of the particle in a direction perpendicular to the flow. Equation 6.1 can be written as

⎛ CD Ap ρf v 2 ⎞ dv ⎛ ρp − ρf ⎞ =⎜ g − ⎜ ⎟ ⎟ dt ⎝ ρp ⎠ 2m ⎝ ⎠

(6.2)

At the initial stages of settling, the particle starts falling from zero velocity and goes on increasing rapidly because of negligible drag force. But as the velocity increases, the drag force also increases and the rate of change of velocity decreases. Ultimately, a stage is reached when the total downward force acting on the particle becomes just equal to the total upward force. This means there will be no net force acting on the particle and the particle settles down with a constant velocity or with zero acceleration. This constant velocity is known as the terminal settling velocity, vt. Thus, at the terminal settling velocity, Eq. 6.2 can be written as ⎛ CD Ap ρf vt 2 ⎞ ⎛ ρ p − ρf ⎞ dv =0=⎜ ⎟ ⎟ g −⎜ dt 2m ⎝ ρp ⎠ ⎝ ⎠ ⇒ vt = For a spherical particle, m =

(

2mg ρp − ρf Ap ρp ρf

π π 3 Dp ρp and Ap = Dp 2 . 4 6

)

(6.3)

(

4 Dp g ρp − ρf

vt =

Thus,

3

)

(6.4)

ρf

The drag coefficient, CD is a function of the Reynolds number, N Re =

Dp vρf

μf and their relation is given in graphical form by means of a log-log plot as shown in Fig. 6.4. The graph is divided into four different regions of settling according to the Reynolds number. This is known as the Sto es law region for which the relationship between the drag coefficient and Reynolds number is given by a straight line of slope 1. In other words, at low Reynolds numbers, the drag coefficient varies inversely with NRe. =

For this region,

Thus,

and

d

=

vt =

⇒ vt =

24 N Re

(6.5)

2 2 ρ v2 24 μf π Dp 24 Ap ρf v × = × × f = 3π Dp μf v N Re Dp vρf 2 4 2

(

4 Dp g ρp − ρf 3ρf

(

)× N

Re

24

=

(

4 Dp g ρp − ρf 3ρf

(6.6)

)× D v ρ

p t f

24 μf

)

Dp 2 ρp − ρf g

(6.7)

18μf i n

i n

i n

i n

4

10 10

i i n

102

10 100 10−1 10−2 10−

10−2

10−1

100

10 102 n d

10

104

105

106

107

In this region, as the Reynolds number increases, the slope of the curve changes gradually from 1 to 0. No accurate equation is available to describe the flow in this intermediate region. Several authors have suggested approximate equations for this region and one such equation is D

=

24 + 0.44 N Re

(6.8)

This region is known as the ewton’s law region and the value of the drag coefficient remains constant at 0.44, i.e., (6.9) CD = 0.44 2 π D 0.44 p × × ρf v 2 = 0.173 Dp 2 ρf v 2 Thus, (6.10) d = 2 4 and

vt =

(

)

3.03 Dp ρp − ρf g

(6.11)

ρf

When the Reynolds number exceeds 2 × 105, the flow in the boundary layer changes from streamline to turbulent type and the separation takes place at the rear end of the sphere by which the drag force is decreased considerably. The drag coefficient is seen to remain constant at 0.1, i.e., CD = 0.1 (6.12) 0.1 π Dp × × ρf v 2 = 0.04 Dp 2 ρf v 2 2 4 2

Thus,

d

=

vt =

and

(

)

13.33 D p ρp − ρf g

(6.13)

(6.14)

ρf

From equations 6.7, 6.11, and 6.14, it is seen that the terminal settling velocity of a particle in a given fluid increases with the increase in both particle size and particle density. When two solid particles having different densities but the same size are separated using a fluid, the method is known as elutriation. If there is a wide difference in densities of the two materials, the separation technique is known as floatation. Two particles, say A and , having the same terminal settling velocity in a fluid are called equal settling particles. And under the condition of equal terminal settling velocity, the ratio of their sizes is called the settling ratio. In the Stokes law region, the settling ratio can be obtained by equating the terminal settling velocities for both the particles. Thus, using Eq. 6.7, we have νtA = νtB ⇒

⇒

(

)

DpA 2 ρpA − ρf g 18μf Dp DpB

⎛ ρpB − ρf ⎞ =⎜ ⎟ ⎝ ρ p − ρf ⎠

= 1

(

)

DpB2 ρpB − ρf g 18μf

2

(6.15)

Similarly, in the Newton s law region, the settling ratio is ⎛ ρpB − ρf ⎞ Dp ⇒ =⎜ ⎟ DpB ⎝ ρp − ρf ⎠

(6.16)

In general, the equation for the settling ratio is ⇒

Dp DpB

⎛ ρpB − ρf ⎞ =⎜ ⎟ ⎝ ρ p − ρf ⎠

n

(6.17)

where, n = for the Stokes law region, < n < 1 for the intermediate region, and 1 for the Newton s law region. When there is a mixture of particles of various sizes and shapes, settling at different velocities, the separation technique is known as sedimentation. The individual particles collide with each other affecting their settling velocities and thus the rate of settling of each individual particle will be less than the settling velocity under free settling conditions. This is generally known as hindered settling. Here, each particle is settling through a suspension of other particles in the liquid than the plain liquid itself. Thus, the settling medium offers higher resistance to the motion of particles. The upward velocity of the displaced liquid in the suspension is thus large. The phenomenon of hindered settling is complex, hence difficult to analyse. Because of differences between the density and the viscosity of a suspension and that of a plain liquid, the analysis is made simpler by replacing density and viscosity with bul density, rb and bul viscosity, mb respectively in the equations derived earlier in this section on the assumption of free settling conditions of the solid particles. The bulk density of the suspension can be calculated by dividing the mass of fluid and suspended matter by the total volume occupied by the suspension. Thus,

ρb =

ass of fluid + ass of solids Total volume of the suspension ⇒ ρb = ρf ∈+ ρp (1− ∈)

(6.18)

where, ∈ = Porosity or volume fraction of liquid in the suspension Void volume (6.19) Total volume And the bulk viscosity of the suspension can be determined experimentally. Hindered settling velocity, vh for the Stokes law region can be obtained by substituting rb and mb in Eq. 6.7. Thus, =

vh =

Dp 2 ( ρp − ρb ) g 18μ b

(6.20)

The settling velocities under free settling at infinitely diluted and hindered settling conditions are related by vh (6.21) = ∈n vt∞ where, n = Richardson–Zaki index, and vt∞ = Settling velocity at infinitely diluted solid concentration.

From Eq. 6.21, it is clear that with the decrease in porosity of the suspension, the settling velocity of particles under hindered settling conditions decreases and vice versa. For particles other than spherical ones like cylindrical, cubical, etc., the equations for spherical particles can be used using the sphericity correction factor, which is beyond the scope of this book.

The terminal velocity of particles for free falling in the laminar zone is Dp 2 ( ρp − ρf ) g . given by (Eq. 6.7) vt = 18μf Here, density of particles = rp = 2.6 × 103 kg/m3, density of fluid (water) = rf = 103 kg/m3, diameter of particles = p = 40 micron = 40 × 10–6 m, and viscosity of fluid (water) = 1 cP = 10–3 kg/(m.s). Thus,

vt =

( 40 × 10 −6 ) 2 ( 2600 − 1000)9.8 18 × 10 −3

= 0.0014 m/s

(Ans)

The bauxite being lighter shall be mostly in the overflow. The biggest bauxite particles shall have a higher setting velocity and shall go down with silica. So the middling shall consist mostly of heavier silica particles having the same velocity as that of the biggest bauxite particle and the bauxite particles having the same velocity as the smallest silica particle. For laminar zone, we have (Eq. 6.15)

Dp DpB

=

ρpB − ρf ρ p − ρf

.

Let us denote A as silica and B as bauxite. Thus, ρp = 2.8 g/cm3 , ρpB = 2.2 g/cm3 , and ρf = 1 g/cm3 . Given that the particle range in the feed mixture is 10 to 500 microns. Considering the largest bauxite particle of size pB = 500 microns, the size of silica particle that shall settle at the same time can be found by Dp 500

=

2.2 − 1 = 0.81649 ⇒ Dp = 408.25 microns. 2.8 − 1

Hence, particles of silica bigger than 408.25 microns shall be in the underflow. Similarly, the size of bauxite particle which is equally settling as that of smallest silica particle of size 10 microns can be found by 10 = DpB

2.2 − 1 = 0.81649 ⇒ DpB = 12.25 microns. 2.8 − 1

Hence, particles of bauxite smaller than 12.25 microns shall be in the overflow. The middling shall consist of bauxite particles of size +12.25 to 500 microns and silica particles of 10 to 408.25 microns (Ans)

Particle si e mm +2−5 + 0.5 − 2 < 0.5

Dp DpB

=

Mass fraction 0.43 0.47 0.10

In the Stokes’ law region for equal settling velocities, we have (Eq. 6.15): ρpB − ρf

ρ p − ρf

where, pA = diameter of ore particles = 1mm, and pB = diameter of the smallest rock particle having same settling velocity. (The particles having more than pB particle size shall settle faster and are in the underflow.) Given that, density of ore = rA = 2.1 g/cm3 and density of rock = rB = 5.4 g/cm3. Thus we have

1 5.4 − 1 = = 2 ⇒ DpB = 0.5 mm. DpB 2.1 − 1

Hence particles of 0.5-mm size or less shall be settling along with the ore particles. Now for 100 kg of ore–rock mixture, rock present = 100 × 0.3 = 30 kg and ore present = 100 – 30 = 70 kg. The product shall contain rocks of size < 0.5 mm and it is given that the mass fraction for this size is 0.1. Thus, the amount of rock particles of size < 0.5 mm = 30 × 0.1 = 3 kg. Thus, the total amount of product = 70 + 3 = 73 kg. 70 Now the % purity of dressed ore = (Ans) × 100 = 95.89% 73

| First, we have to check the flow region (I, II, III, or IV) in which ⎛ D vρf D v ⎞ the bacteria is moving, by finding the Reynolds number ⎜ N Re = of = μf ν ⎟⎠ ⎝ bacteria. Here, P = 2 microns = 2 × 10- 6 m, v = 15 mm /s = 15 × 10-3 m/s, and ν = 10-6 m2/s. ⎛ 2 × 10 −6 × 15 × 10 −3 ⎞ N = So, ⎜ Re ⎟ = 0.03 . 10 −6 ⎝ ⎠ As NRe is between 10- 4 and 0.2, the flow region is I, i.e., the Stokes’ law region. 24 24 For this region, = = = 800 . N Re 0.03 Thus, the drag coefficient for bacteria is 800. (Ans)

Since the flow is laminar and assuming the particles to be spherical, Dp ρpB − ρf = from Eq. 6.15, we have DpB ρ p − ρf where A and B denote galena and quartz particles respectively. Here, rpA = 7500 kg/m3, rpB = 2650 kg/m3, and rf = 1000 kg/m3. Let us first find out the size of the quartz particles that are equally settling with the smallest galena particles. For the smallest galena particles, pA = 0.0004 cm. 0.0004 2650 − 1000 = = 0.504 Thus, DpB 7500 − 1000 ⇒

pB =

0.000794 cm.

This is the maximum size of quartz particles that settle with the same velocity as the smallest galena particles. Thus, the size range of only quartz particles is between 0.0004 and 0.000794 cm. Let us now find out the size of the galena particles that are equally settling with the largest quartz particles. For the largest quartz particles, pB = 0.001 cm. Thus,

Dp 0.001 ⇒

pA

=

2650 − 1000 = 0.504 7500 − 1000

= 0.000504 cm.

This is the minimum size of galena particles that settle with the same velocity as the largest quartz particles. Thus, the size range of only galena particles is between 0.000504 and 0.001 cm. While the mixed fraction contains the remaining quartz and galena particles. So, the fraction will have the following size ranges: (i) pure quartz: 0.0004 to 0.000794 cm (ii) mixed fraction: quartz: 0.000794 to 0.001 cm galena: 0.0004 to 0.000504 cm, and (iii) pure galena: 0.000504 to 0.001 cm

(Ans)

Generally, large upward flow of water is observed in the compression zone where the particle concentration is high and the particles settle under hindered settling conditions. Thus, from Eq. 6.21, we have νh = ∈n νt∞. Here, vt∞ is the settling velocity at infinitely diluted solid concentration, which is generally observed in the Stokes law region. v t∞ =

Thus,

(

)

Dp 2 ρp − ρf g 18μf

.

Here, p = 0.0002 m, rp = 7500 kg/m3, rf = 1000 kg/m3, g = 9.81 m/s2, mf = 0.001 kg/m.s, ∈ = 0.5, and n = 4.5. Thus,

v t∞ =

0.00022 (7500 − 1000)9.81 = 0.1417 m/s 18 × 0.0001

and νh = 0.54.5 × 0.1417 = 6.262 × 10–3 m/s. The upward water velocity = vh (1− ∈) 6.262 × 10 −3 (1 − 0.5) = = 6.262 × 10 −3 m/s ∈ 0.5

(Ans)

Thickeners and clarifiers are gravity sedimentation basins which are employed to separate suspended solids from a liquid by gravity settling, prior to filtration or centrifugation. Normally, a larger fraction of the total liquid is removed in this process than in subsequent operations. The functions of thickening and clarifying are similar and occur simultaneously. The primary function of a continuous thickener is to concentrate a large quantity of relatively concentrated slurry by

gravity settling and to produce a stream of thickened solids at the rate of feed as underflow. Continuous clarifiers are generally employed to remove a relatively small quantity of suspended particles, to produce a clear liquid as overflow to meet statutory requirements for effluent quality and to minimise the loss of product in the overflow stream. The basic design of thickeners and clarifiers is the same and they commonly contain a large tank to hold the slurry, a feed well to allow the slurry to enter into the tank, an overflow launder at the top to collect the clear liquid, an underflow pipe to discharge the thickened solids, and a raking mechanism for moving the thickened sludge towards the central discharge pipe. The selection of these equipments is important in plant design for several reasons: (i) they occupy large spaces, sizes of up to 200 m in diameter; (ii) for repairing they require days to empty the tank, clean the sludge, and refill them again; and (iii) their position determines the elevation of the entire plant because large volumes of liquid are fed by gravity to minimise pumping costs. A great variety of thickeners and clarifiers are on the market. Broadly these are grouped into conventional and high-rate types in which the rake driving mechanisms may be centrally or peripherally driven. And there are two ways of supporting the drive system with its shaft and the raking arms the bridge type and the column type. In the bridge type, the drive is supported by the bridge that spans across the tank and drives the rakes with a central shaft; while in the column type, the drive and the rake mechanisms are both supported by a stationary central column of steel or concrete. A few of these equipments are discussed here.

FLSmidth Dorr-Oliver EIMCO is the world leader in designing and supplying a wide range of thickeners and clarifiers a type of solid–liquid separation equipments for the mineral processing and chemical industries. FL Smidth Dorr-Oliver EIMCO Bridge-Supported Thickeners (Fig. 6.5) are beam or truss-supported units that can be used with light, medium, or heavy-duty applications with diameters of up to 54 m (178 ft). In this design, the drive is supported by the bridge and drives the rakes with a central shaft. Underflow is removed from a discharge cone at the bottom-centre of the thickener.

Tanks can be in-ground, on-ground, or elevated. Figure 6.6 shows the schematic diagram of a bridge-supported thickener. FLSmidth Dorr-Oliver EIMCO ColumnSupported Thickeners are supported by a stationary centre column of steel or concrete. The centre column supports the drive and rake mechanisms, while the truss extending from the center pier to the tank periphery supports the walkway, power lines, and feed launder. These units are suitable for basins and raking arms with diameters of up to 180 m (600 ft). Figure 6.7 shows the schematic diagram of a column-supported thickener. FLSmidth Dorr-Oliver EIMCO Traction Thickeners (Fig. 6.8) have a stationary centre pier, which partially supports the rake mechanism and serves as a pivot about which the rakes rotate. The rakes are powered by one or two drive units that run steel traction wheels round a steel rail at the periphery of the tank. These units are normally installed in concrete tanks and are available in diameters of up to 200 m (≈ 650 ft). Maintenance is generally less difficult in these thickeners, which is an advantage. FLSmidth Dorr-Oliver EIMCO Caisson Thickener (Fig. 6.9) designs are column-mounted thickeners with an enlarged centre pier which houses the drive control system and the underflow pumping station, as well as supports the rake assembly. This eliminates the need for an underflow tunnel because the pumps

are housed at the bottom of the caisson chamber and deliver the underflow upwards through the columns towards the periphery. FLSmidth Dorr-Oliver EIMCO CableTorq Thickeners and Clarifiers have streamlined rake arms, pulled by cables, connected to a torque (or drive) arm that travels above the sludge. The rake arms are attached to a special hinge. The arms thus are able to rise automatically when heavy sludge concentrations occur. But because of the unique hinge, the arms continue to operate in two planes keeping the rake blades in perfect position for most efficient raking and solids removal. Figure 6.10 shows the design of a CableTorq thickener.

The CableTorq equipments reduce two major thickening problems—downtime and maintenance costs.

Bridge-type thickeners are available in diameters from 12 to 30.5 m (40 to 100 ft) with an overhead feed. Torque arms are of single pipe construction. Rake blades are designed to provide double-sweep operation for continuously handling heavy sludge loadings. The drivehead and raking mechanism are supported by a wall-to-wall bridge across the diameter of the basin. The unit is ideal for thickening industrial wastes, ore concentrates and tailings, flue dust, fly ash, and utility stack gas scrubbings. Figure 6.11 shows the schematic diagram of a bridge-type CableTorq thickener. Column-type thickeners are available in diameters from 23 to 82.3 m (75 to 270 ft). The drivehead is supported on a centre pier. Two stub arms, in addition to the two rake arms, provide extra raking capacity at the tank discharge trench, the area where raking capacity is most critical. Feed is through a radial launder extending to the centre feed well. These thickeners are now in use on copper concentrates, middlings, alumina red mud, gold and diamond cyanide slimes, and in various tailings operations. Figure 6.12 shows the schematic diagram of a columntype CableTorq thickener.

Require lower torque capacity because of reduced drag Automatically protect against overload due to lifting action Blades maintain efficient raking angle even when the rake arms are in a lifted position Keep scraper blades in position in discharge cone or trench when arms are lifted As rakes clear overload, raking arms return smoothly to original position

n iv

d

v

M

ni

i i n

n

F

d

v

i

in F

i

v

d i

n i n xi iv in

i indi d

id i

n

n

n

F

d

F

i n

d i

i n

n

nd

v

i indi

n i n d iv

n

n

i

in n

n

Minimise island formation because of the smooth pipe design of the rake arms Allow temporary surges or shock loads in solids-handling capacity, Torque arms are out of the heavy mud zone and in some installations actually clear the liquid level, minimising the torque load Pipe design of rake arm minimises scale formation and reduces dead load on centre mechanism Each arm lifts independently for efficient continuous sludge discharge.

Alumina-red mud Alumina–hydrate Calcium carbonate Soda ash Pulp and paper waste Fly ash Sand slimes Gold – cyanide slimes Mineral concentrates Mineral tailings Limestone slurry.

FLSmidth Dorr-Oliver EIMCO Solids-Contact Reactor-ClarifierTM units combine chemical addition and mixing, solids-contact flocculation, clarification, and raked sludge removal in a single basin. They provide efficient removal of hard-to-settle suspended solids and are ideally suited for lime softening. A low-speed turbine maintains a large volume of flocculated solids re-circulating within the conical reaction well. Influent water and chemicals are introduced directly into the re-circulation stream, optimising chemical utilisation and floc growth. Heavy particles settle down and are collected by the rake arms, while clarified water passes to the clarification zone for collection in the launder system. Figure 6.13 shows the FLSmidth Dorr-Oliver EIMCO Solids-Contact ReactorClarifierTM unit.

Ann i n nd

i n di

nd

i

d i in iv

nd i id in

M O

O n

n i in

i d

2′′ n

n

i

in d

i nd n

i i n

i nd

Outotec is the global leader in the design, fabrication, and supply of thickening and clarifying solutions for the mineral industry. Outotec s SUPAFLO thickeners and clarifiers operate in mineral processing, chemical, water treatment, and industrial and effluent applications throughout the world. The SUPAFLO thickener was invented in March 1983 by John Thixton and the first commercial unit was commissioned in August 1984. The SUPAFLO units include a number of innovative features in their design over conventional thickeners. Special attention is given to engineering design of feedwells, rake profiles, drive systems, and control strategies to meet the challenge of dewatering materials that are often problematic for normal thickeners. In a conventional thickener, the slurry is introduced into a large tank at the liquid surface, while in SUPAFLO units the pre-flocculated pulp is introduced below the liquid surface into the settling pulp bed. This unit has an inbuilt open deaerator/feedwell flared at the bottom and an inverted cone deflector plate fixed to the thickener rakes to deflect the pulp downwards at an angle of 30 to 45 degrees from the horizontal Thixton, 2009 . Advantages of SUPAFLO units include low capital and operating costs, and high reliability. The major types of Outotec s SUPAFLO units are presented in Table 6.1.

Filtration may be defined as a solid–liquid separation process carried out either under pressure or in vacuum resulting in the separation of undissolved, particulate suspended solids from a solid–liquid mixture by passage of most of the fluid through a porous medium that retains the solid on it or within itself. In a broader sense of filtration, the fluid may be a liquid or gas or a mixture of the two. However, the discussion here is confined to liquid filtration only. As a separation process, filtration is used widely in chemical and other allied process industries to isolate finely suspended solid particles from its slurry with a liquid by passing the slurry through some form of porous medium called the filter medium or septum. The medium may be a screen, cloth, membrane, or a bed of solids. The isolation is accomplished by forcing the liquid through the medium while the solid particles are trapped within its pores to form a layer known as ca e. The liquid passing through the medium is called the filtrate. Filtration and filters can be classified in several ways: (i) by objective — the desired product being solid, clarified liquid, or both; (ii) by filtration mechanism — ca e filtration (when the proportion of solids in the suspension is large and most of the solids are collected above the filter medium as cake) and deep-bed filtration (when the proportion of solids in the suspension is very small and the particles are smaller than the pores of the filter medium, the particles will penetrate a considerable depth and are trapped within the pores of the filter medium). In this section, the discussion is confined to cake filtration only; (iii) by driving force — the driving forces in cake filtration are gravity, mechanical pressure, vacuum pressure, or centrifugal force; and (iv) by operating cycle — intermittent (batch) or continuous. Most of the pressure filters like the plate and frame filters and the leaf filters are operated in a

Type

High rate thickeners and clarifiers

High compression thickeners

Paste thickeners

Features

Suitability and applications

Floc-Miser feedwell De-aeration chamber Deflector plate Controlled bed level High throughput per unit area Free standing or in-ground tanks Short retention time Optional underflow recycle Clear overflow

These units are suitable for all applications where flocculants can be used in the process. Also ideally suited to clarifying, with overflow being filtered through a flocculated solids bed. External underflow recycling is sometimes used to improve floc formation and particle capture.

Floc-Miser feedwell De-aeration chamber Controlled bed level High throughput per unit area Free standing or in-ground tanks High rake torque capacity Extended high compression zone Supapickets (static and rotating) for improved water release Increased underflow density

These units provide consistently higher underflow density while maximising solution recovery. They are used for increasing tailings dam capacity, countercurrent decantation, increasing filter capacity, and increasing recovery of process water or chemicals.

Floc-Miser feedwell De-aeration chamber Controlled bed level High throughput per unit area Free standing tanks High rake torque capacity Extended high compression zone Supapickets (static and rotating) for improved water release Maximum underflow density Underflow slurry yield stress >200 Pa

This unit is designed to produce a consistent paste underflow with process control and mechanical reliability second to none. Primarily used for tailings disposal and pre-leach applications. Paste thickeners can be used for any application where underflow yield stress in excess of 200 Pa is required. (Continued )

Type

Features

Suitability and applications

• Small or shallow feedwell • Flocculants not essential • Insensitive to short-term process changes • Drive and rake torque to suit application

Conventional thickeners and clarifiers are available as traditional conventional units or fitted with flocculating feedwell. Hybrid versions are also available in which various design features of our high rate thickeners are used, for particular applications. These modifications can result in improved overflow clarity, lower flocculant usage, higher feed rates and improved control.

• Combines flash mixing, flocculation, clarifying, sludge collection and thickening in one operation • Minimises chemical requirements by using the solids contact or seeding principle • Variable speed impeller and separate rake drive mechanism • Deep clear water zone • Internal or external recirculation option • Dual chemical dosing option

A variable speed impeller can be used to internally recirculate and mix flocculated underflow, raw feed and chemicals to optimise flocculant usage and overflow clarity. Typically used for water or wastewater applications, where chemicals are added to enhance flocculation and sedimentation.

• Saturated lime solutions • Over 85% usage of available Ca(OH)2 • Variable speed impeller and separate rake drive mechanism • Controlled sludge level • High rate feedwell for improved solids dispersion • Internal or external recirculation option

Lime saturators are used to make clarified saturated lime solution for drinking water plants. Milk of lime solution is fed continuously into the reaction zone, where it is mixed with recycled sludge. The sludge is controlled at the required level by varying the sludge withdrawal rate.

Conventional thickeners and clarifiers

Solids contact and reactor clarifiers

Lime saturators

batch manner while most of the vacuum filters like rotary drum filters are operated continuously. On the other hand, centrifugal filters like centrifuges can be operated in batch as well as in continuous manner.

The cake filtration operation is shown in Fig. 6.14. During the initial period, filtration results in the formation of a layer of particulate solids on the surface of septum. The layer once formed, its surface acts as the filter medium with the solids deposited layer by layer adding to the thickness of the cake while the clear liquid flows in between Fi the capillaries of the deposited Fi di solid mass in streamlines. As the cake thickness increases, the i di resistance to flow increases, which decreases the rate of filFi tration for a given pressure drop across the septum.

Cake filtration can be operated at constant pressure and constant rate conditions. If the pressure drop across the filter is constant throughout the run, the filtration process is called constant pressure filtration. Here the rate of filtration is maximum at the beginning and decreases continuously towards the end of the run. One misconception here is that a higher initial pressure will result in a higher filtration rate, but actually the application of higher pressure results in a low rate of filtration as the particles will be compacted and will block the pores of the septum at a faster rate. The method in which the pressure drop is gradually increased so that the rate of filtration is constant throughout run is called constant rate filtration. The important variables which influence the rate of filtration are (i) (ii) (iii) (iv) (v)

pressure drop across the cake and the septum; resistance of the cake; resistance of the septum; area of the filtering surface; and viscosity of the filtrate.

Whether the filter is for cake filtration or for deep-bed filtration, all filters require a filter medium or septum to retain the solids. In case of cake filters, the selection of filter medium is the most important consideration in their satisfactory operation. The filter medium in any filter should have the following requirements: (i) it should retain the solids to be filtered; (ii) it should not plug or blind;

(iii) (iv) (v) (vi) (vii) (viii) (ix)

it should offer minimum resistance to filtrate flow; it should be mechanically strong to withstand the filtering pressure; it should be chemically resistant to corrosive fluids; it should be resistant to mechanical wear; it should have the ability to discharge the cake easily and cleanly; it should have long life; and it should be cheap.

Canvas cloth; woolen cloth; metal cloth of Monel, stainless steel, nickel, copper, bronze, or other alloys; paper; synthetic fiber cloth of nylon, polypropylene, etc., are used as filter medium depending upon the process conditions.

Filtration of slimy or very fine solids is very difficult due to the formation of a dense and impermeable cake which quickly plugs the filter medium. In such a case, the porosity of the cake needs to be increased so as to allow the filtrate to flow through at a reasonable rate. This is done by adding a filter aid such as diatomaceous silica or expanded perlite before filtration, which may later be separated from the cake or be discarded together with the cake. Filter aids are generally granular or fibrous solids which form a highly permeable cake. They should have low bulk density, should be porous, and should be chemically inert to the filtrate. The filter aids are used in two different ways: (i) as a precoat, and (ii) mixed directly with the slurry before filtration. In case of precoating, a thin layer is applied to the filter medium, which prevents gelatinous type of solids from plugging the filter medium and gives a clear filtrate. And when they are added to the slurry before filtration, their presence increases the porosity of the cake, decreases its compressibility, and reduces the resistance of the cake during filtration.

Though the cake filtration is operated either in a batch or a continuous manner, the theory for both the batch and the continuous filtration is similar. Initially, the theory for batch filtration is derived and then the resulting equations are modified for continuous filtration. The rate at which the filtrate is collected in a filtering operation is quite important and is necessary to calculate the area required for a given output. The rate of filtration is directly proportional to the filtering area and the pressure drop across the filter and inversely proportional to the filtrate viscosity and the combined resistances of the cake and the filter medium. The expression for differential rate can be written as V

=

μ(

AΔ C +

)

(6.22)

where, = volume of filtrate collected in time t, A = area of the filtering surface, ΔP = pressure drop across the filter, m = viscosity of the filtrate, RC = resistance of the filter cake, and RF = resistance of the filter medium.

The resistances vary directly with the cake thickness. The resistance of the filter medium can be expressed in terms of a theoretical cake thickness, F, which will have the same resistance as that of the filter medium. With C as proportionality constant, the resistances can be expressed as RC + RF = C( C + F) (6.23) where, C = thickness of the cake. The following terms are defined for further simplification of Eq. 6.22 and these are mass of dry cake solids W = , kg/m3 , volume of filtrate mass of dry cake solids , kg/m3 , and volume of et filter cake F = theoretical volume of filtrate collected per unit filtering surface to give a cake of thickness F, m3/m2. Making a material balance for the solids, we have

ρC = cake density =

( hC + h )ρC A = W (V + AV ) ⇒ ( hC + h ) =

W (V + AV ) AρC

(6.24)

Now, with the help of equations 6.23 and 6.24, the rate of filtration (Eq. 6.22) can be written as A2 ΔPρC dV = (6.25) dt CWμ (V + AV ) Putting α =

C , known as specific ca e resistance, in Eq. 6.25 we have ρC dV A2 Δ P = (6.26) dt αWμ (V + AV )

Equation 6.26 is the rate e uation for a batch filtration process. An alternate form of Eq. 6.26 can be obtained by putting α as a function of pressure drop and compressibility exponent of ca e, S expressed as

α = K ( ΔP ) S (6.27) where (i) K is a constant and its value depends essentially on the properties of the solid, and (ii) the exponent S depends on the cake characteristics and its values are as follows: S = 0 for totally noncompressible cake, = 1 for completely compressible cake, and = 0.1 to 0.8 for commercial slurries. Using Eq. 6.27, the rate equation (Eq. 6.26) can be expressed as dV A2 Δ P (1− S ) = (6.28) dt KWμ (V + AV ) The values for K, S, and F are determined experimentally in a laboratory test filter for their ultimate use in the design of process filter. Equation 6.28 can be applicable to both constant-rate and constant-pressure filtration conditions.

When a filtrate flows at a constant rate, Eq. 6.28 can be expressed as V

=

A2 Δ (1− S ) K μ (V + AV )

⇒ V 2 + AVV =

A2 Δ (1− S ) × K μ

(6.29)

Equation 6.29 being quadratic both in and A, can be used to calculate the output of a filter of given surface area for a given time interval. Conversely, if output and time interval is fixed, the required area for filtration can be calculated. Filtration with constant pressure drop is more commonly encountered in process industries. When the pressure drop across the filter is kept constant, Eq. 6.28 can be written as V A2 Δ (1− S ) ( V + AV ) V = ∫ ∫ K μ 0 0 ⇒ V 2 + 2 AVV =

2 A2 Δ (1− S ) × K μ

(6.30)

Equation 6.30 can be used either to calculate output or filtering area for a given output for a fixed time interval. Equations 6.28 to 6.30 are applicable to batch filters for operation as well as design. In case of design, laboratory test is to be carried out for the particular slurry to evaluate K, F, and S. These constants can be used with accuracy for varying filtration area, pressure drop across the filter, W, filtering time, and volume and viscosity of the filtrate. The constants evaluated for laboratory filter can be used safely for an actual filter with 100 times scale up for the area. The output is generally expressed in terms of the filtrate produced per batch of operation which is completed in a given specified time called cycle time, tcycle. The cycle time consists of (i) (ii) (iii) (iv) (v)

time for filtering, tF; time for washing (if washing is required), tW; time for dismantling, tD; time for reassembling, tR; and time for filling, tFL.

Thus the cycle time is

cycle

=

+

W

+

+

R

+

(6.31)

The time periods for dismantling, reassembling, and filling are almost constant for a particular unit. Since these operations do not pertain to active separation, these are collectively designated as idle time, tI. Thus Eq. 6.31 can be written as cycle

=

+

W

+

(6.32)

In continuous filters like rotary vacuum drum filters, due to the continuous removal of deposited cake, its thickness is restricted. Thus, the

filtration process can be conducted at a constant rate by applying a constant pressure drop across the filter medium. The operation of a rotary drum filter will be discussed later in this chapter. It can be seen that a single rotation of the drum involves batch cycles of cake formation, washing, drying, and cake discharging. Hence, equations developed for batch filtration with modifications can be used for continuous filtration. Let AD = total surface area of the drum and ∈D = fraction of the drum surface submerged in the slurry. (6.33) Thus, the effective filtering surface = AD ∈D Now, Eq. 6.22 can be written as A ∈D Δ V = (6.34) μ( C + ) = ( C + ). where, C+ The thickness of cake varies from zero (as the drum enters the slurry) to a value leaving (as the drum comes out of the slurry). The thickness of the cake leaving the slurry depends on slurry concentration, volume of filtrate collected per revolution, cake density, and surface area of the drum. The thickness of the cake leaving the filtering zone can be given as VR (6.35) leaving = ρC A where R = volume of filtrate collected per revolution of the drum. Since, entering = 0, an average value of the cake thickness is used in the rate equation. Thus, VR (6.36) avg = 2 ρC A Using Eq. 6.36, the total cake thickness to be used in the rate equation is ⎛ VR ⎞ = avg + = +A ∈ V ⎟ (6.37) C + ⎜ ⎠ ρC A ⎝ 2 Thus, the rate equation for continuous filtration becomes V

=

2A 2 ∈ Δ α μ (VR + 2 A ∈ V )

(6.38)

Integrating Eq. 6.38 between the limits = 0 to = R for t = 0 to t = 1/NR respectively, we have 2A 2 ∈ Δ 1 (6.39) VR 2 + 2 A ∈ V VR = x α μ NR where, NR = number of revolutions of the drum per minute. Putting for α from Eq. 6.27, we have 2 A 2 ∈ Δ 1− S VR 2 + 2 A ∈ V VR = (6.40) K μNR For further simplification of Eq. 6.40, the following assumptions may be made: (i) the cake is noncompressible (S = 0), and (ii) the resistance of the filter medium is negligible (VF = 0). Equation 6.40 now reduces to VR 2 =

2A 2 ∈ Δ K μNR

(6.41)

Hence, the filtrate output per revolution is VR = A The output of the filter (

O)

2∈ Δ K μNR

(6.42)

per unit time (minute) is

V = VR N R = A

2 ∈ Δ NR K μ

(6.43)

Amount of dry cake produced (WC) per minute is C

= VR N R

=A

2 ∈ Δ NR Kμ

The filtration equation is V 2 = K ⇒ Here, K =

A2 Δ

1− S

V

=

(6.44)

K . 2V

as the filter medium resistance = 0.

(a) When t = 10 hours,

= volume of filtrate produced = 30 m3.

30 × 30 = 90 m6 /h. 10 V K 90 m3 The final rate of filtration = = = 1.5 . 2V 2 × 30 h 1 The rate of washing for the fitter press = × final rate of filtration 4 1 m3 = × 1.5 = 0.375 . 4 h The volume of wash water used = 3 m3. volume of ash ater 3 = = 8 hours. Thus, the washing time = rate of ashing 0.375

So, K =

V2

=

(b) If the filtering surface is doubled, i.e., A′ = 2A, then K ′ = ⇒ K′ =

( 2 A) 2 Δ

1− S

=

4 A2 Δ

1− S

A′ 2 Δ

1− S

= 4K

⇒ K ′ = 4 × 90 = 360 m6/h. Thus, the time taken to produce a filtrate of 30 m3 is V 2 30 2 = = 2.5 hours K ′ 360

(Ans)

A2 Δ 1− S . K μ (V + AV ) Here, F = cloth resistance in terms of volume = 0. Assume noncompressible cake (S = 0). For constant pressure filtration, we have

Thus,

V

=

V

=

A2 Δ K′ = K μ V

A2 Δ . K μ Integrating the above equation, we have where, K ′ =

V V = K ′ ⇒ V 2 = 2K ′ . Now, when t = 1 hour and K′ =

= 2000 litres ( 2000) 2 = 2 × 106 litre 2 /h. 2 ×1

Final rate of filtration, K ′ 2 × 106 ⎛ V⎞ = = = 1000 litre/h. ⎜⎝ ⎟⎠ V 1 × 2000 1 × 1000 = 250 litre/h. 4 Volume of ash ater 500 Thus, the washing time = = = 2 hours. Washing rate 250 The time required for dismantling, dumping, and reassembling is given to be 3 hours. Thus, total cycle time, tcycle = 1 + 2 + 3 = 6 hours, i.e., in 6 hours the amount of filtrate collected = 2000 litres. In one operating day, i.e., 18 hours, the amount of filtrate collected = 2000 × 18 = 6000 litres. 6 The volume of filtrate produced in a day = 6000 litres (Ans) The washing rate =

V

= 45V + 75 s /m3

1 ⎛ dV ⎞ 3 (a) The final rate of filtration is given by ⎜ ⎟⎠ = 45V + 75 m /s ⎝ dt f f where f = final volume of filtrate collected. dt Again, = 45V + 75. dV Integrating the above equation, we have t

∫ dt = 0

⇒t =

Vf

∫ ( 45V + 75) dV 0

45Vf 2 + 75Vf 2

⇒ t = 22.5Vf 2 + 75Vf Putting t = 60 minutes = 3600 seconds, we have 22.5Vf2 + 75Vf = 3600 ⇒ Vf 2 + 3.33 Vf − 160 = 0 Solving the above equation, we have

f

= 11.09 m3.

1 ⎛ dV ⎞ The final rate of filtration ⎜ = = 0.00174 m3/s. ⎟ ⎝ dt ⎠ f ( 45 × 11.09) + 75 For the leaf filter, rate of washing = final rate of filtration = 0.00174 m3/s. 3 = 1722.58 s. 0.00174 = t + tW + t + tR

Thus, the washing time, t W = (b) The cycle time, tcycle

where, tF = time for filtration = 22.5Vf2 + 75Vf s and Volume of ash ater . Rate of ashing Here the rate of washing = rate of final filtration t = time of ashing =

1 ⎛ dV ⎞ . ⇒⎜ = ⎝ dt ⎟⎠ f 45Vf + 75 Now the volume of wash water is found out assuming the wash water used is in the same proportion to filtrate. 3 m3 = 0.2705. Ratio of volume of wash water to final filtrate = 11.09 Volume of wash water = 0.2705 f 0.2705Vf = 12.17Vf2 + 20.2875Vf second. ⇒ tW = ⎤ ⎡ 1 ⎥ ⎢ V ⎣ 45 f + 75 ⎦

And tD + tR = time for dumping and reassembling = 60 minutes = 3600 seconds. Thus, total cycle time, tcycle = ( 22.5 ⇒

2 f

cycle

+ 75

f

) + (12.17

cycle

=

2

34.67Vf + 95.2875Vf + 3600

34.67Vf + 95.2875Vf + 3600 =

+ 95.2875

f

24 × 3600

86400 Vf

(34.67 ⇒ 34.67

) + 3600

2

2

For optimum cycle time, Thus, 2

f

= (number of cycles /day) ×

Daily production of filtrate,

f

+ 20.2875

= 34.67Vf 2 + 95.2875Vf + 3600 seconds.

Number of cycles per day = 24 × 3600 =

86400 34.67

2 f

max

and for

2 f

+ 95.2875

f

+ 95.2875

f

.

to be maximum

+ 95.2875 − 86400

f

f

f

2 × 34.67

+ 3600)

+ 3600 − 69.34

2 f

.

V = 0. Vf f

+ 95.2895

f

=0

2

− 95.2875

=0

⇒ 3600 − 34.67Vf = 0 2

3600 = 10.19 m3 . 3467 Thus, the optimum f = 10.19 m3. The optimum cycle time, topt = 34.67 × (10.19)2 + 95.2875(10.19) + 3600 = 7771 seconds = 2.159 hours (Ans) ⇒ Vf =

For the plate-and-frame filter press Time for filtration, tF = 2 hours. Output/2 hours of filtration = 4500 kg. Time for washing and dumping = tW + tD = 3 hour/cycle. Hence, the cycle time, tcycle = 2 + 3 = 5 hours.

24 × 4500 = 21600 kg. 5 Assuming density of filtrate to be same as that of water, volume of filtrate/24 21600 hours = = 21.6 m3 . 1000 For the rotary vacuum drum filter Daily output of filtrate = 21.6 m3. Thus, hourly output of filtrate = 21.6 / 24 = 0.9 m3/h. Let, R1 = the volume of the filtrate collected at the present rpm, NR1 and R2 = the volume of the filtrate desired (i.e., 0.9 m3/h) at the new rpm, NR2. Here, R1 = 450/1000 = 0.45 m3/h, R2 = 0.9 m3/h, and NR1 = 0.6. Using Eq. 6.22, we have Maximum average output / 24 hours =

For case I VR1 = A For case II VR 2 = A

2∈ Δ K μ N R1

(I)

2∈ Δ K μNR2

(II)

Dividing equation (I) by (II) and simplifying, we have VR12 VR 2 So,

NR2 =

VR12 VR 2 2

2

=

NR2 N R1

(6.45) 2

⎛ 0.45 ⎞ × N R1 = ⎜ × 0.6 = 0.15. ⎝ 0.9 ⎟⎠

Thus, the required rpm = 0.15

(Ans)

Since the cake is incompressible, the compressibility exponent of cake is zero, i.e., S = 0. Thus, the specific cake resistance is independent of ΔP and can be taken as constant. 2∈ Δ . Filtration Eq. (6.42) is VR = A K μNR For the first filter, we have R = 300 L = 0.3 m3, AD = 0.75, ∈D = 0.20, NR = 2 rpm, and ΔP = 1.5 kg/cm2 = 1.5 × 104 kg/m2.

So, 0.3 = 0.75

2 × 0.2 × 1.5 × 10 4 1 = 41.08 K μ×2 K μ 1 = 7.3 × 10 −3. K μ

⇒ For the second filter we have kg/cm2 = 1.0 × 104 kg/m2. So, 2.75 = AD

R

= 2.75 m3, ∈D = 0.20, NR = 1.5 rpm, and ΔP = 1.0

2 × 0.2 × 1.0 × 10 4 1 = 51.64 AD KWμ × 1.5 KWμ ⇒ 2.75 = 51.64 AD × 7.3 × 10 −3 = 0.377 AD ⇒ A = 7.29 m 2 .

Thus, the total filtering area of the new unit = 7.29 m2

(Ans)

For any given filtration operation, the choice of a suitable filter largely depends on the minimum overall cost of the equipment which is related to the filtering area, pressure drop, mechanical design, operating cycle, cake resistance, ease of discharge of filter cake, and quality of filtrate. Other important factors to be considered for the selection of a filter are (i) the nature of solids present in the slurry — particle shape and size, size distribution, and their cake forming characteristics; (ii) the properties of the f luid — viscosity, density, and corrosiveness; (iii) the quantity of slurry to be filtered; (iv) the concentration of solids in the slurry; (v) the valuable product — solid , liquid , or both; and (vi) washing of the cake. Depending upon the driving force, cake filters are first divided into four types: gravity filters, pressure filters, vacuum filters, and centrifugal filters and then divided into batch and continuous types. The common industrial cake filters are usually classified as (i) Batch pressure filters — Filter presses (plate-and-frame filter press and recessed-plate filter press) and Pressure leaf filters; (ii) Continuous pressure filters — Rotary drum pressure filters; (iii) Batch vacuum filters — Nutsche filters, Vacuum leaf filters; (iv) Continuous vacuum filters — Rotary drum filters, Disk filters; and (v) Centrifugal filters (batch and continuous) — Filtering centrifuges. The important cake filters which will be discussed here are filter press, leaf filter, and rotary drum and disk filters.

Filter presses are the simplest of all pressure filters and the most widely used filtration equipment. These are available in two basic designs — plate-and-frame and

recessed-plate. Regardless of the design, filter presses separate solids and liquids by forcing the liquid fraction of a feed slurry through a permeable filter cloth. A standard plate-and-frame filter press (Fig. 6.15) consists of plates and skeleton frames arranged alternatively and supported either on a pair of side bars (Fig. 6.16) or on an overhead beam (Fig. 6.17). The plates are covered Ai in nn

i n

i d i d

i in

i

n

d

niv i i Standard ilters

ni

F

Fi

Fi

with a filter cloth on both of its sides, while the frames are hollow and provide space for cake accumulation. The sectional view of this type of filter press is shown in Fig. 6.18. The plates and frames are usually rectangular or square in shape and sometimes circular shapes are also used. They are made of metal (cast iron, stainless steel, aluminium), coated metals, or plastics. A typical plate and frame is shown in Fig. 6.19. Each frame has an inlet hole generally at the top corner for feed and wash purpose, while each plate has a port

at the bottom for filtrate discharge as shown in Fig. 6.20. When the plate and frames are closed, either manually or hydraulically, a chamber is formed between each pair of successive plates.

F d in

The slurry to be filtered is pumped into the chamber through the inlet hole in each frame. The filtrate passes through the filter cloth into the plates and leaves the filter through the discharge port, while the solids are trapped in the chamber. Filtration proceeds until the chamber is filled with the cake or a preset pressure is reached. Wash liquid may then be introduced to the chamber through the same inlet hole to remove soluble impurities from the cake. The press is then unclamped and the plates and frames are shifted. Compressed air is then delivered through each shifted plate into the space behind the filter cloth, which facilitates the release of cake from the cloth and from the chambers, as shown in Fig. 6.21. And the filter is ready to repeat the operation. Fi

Fi

nd

Ai

di i

id

A

d

In some presses, a heating arrangement is provided so as to reduce the viscosity of filtrate and to achieve a higher rate of filtration. EIMCO’s Shriver filter presses are available in plate sizes ranging from 470 by 470 mm to 1500 by 2000 mm. EIMCO’s Shriver filter presses have a wide range of applications: hazardous and metallic wastes; pharmaceuticals, chemical, and petrochemical products; pigments and dyes; precious metals; ore processing; coal dewatering; water treatment; biological sludges; clarification of liquid; oilfield muds; and food products and juices.

This type of filter press is similar to the plate-and-frame type but consists only of plates. Figure 6.22 shows a FLSmidth Dorr-Oliver EIMCO AFP IV recessed-plate filter press. Plates are hollowed on both of its sides by recessing the ribbed surface to form a chamber between the successive plates, when clamped together in a rugged steel frame. This makes the cake thickness twice the depth of the recess on each plate. Typical recessed plates are shown in Fig. 6.23. The molded plates have ports for slurry feed at the centre and for filtrate drainage at the bottom. Both sides of each plate are covered with a filter cloth which is sealed around the feed opening and the plates are clamped together using a hydraulic ram. The slurry is pumped in under high pressure, filling the chambers with solids and pushing the filtrate out through the filter cloth. When no more solids can be forced into the chambers, the feed pumps are turned off and compressed air is used to remove interstitial water from pores in the filter cake. When the desired residual moisture content has been achieved , the filter is opened , the cake is removed and the procedure is repeated. Figure 6.24 shows the operating principle of AFP IV recessed-plate filter press.

The AFP IV filter presses are simple, rugged, and reliable. These filters not only provide high throughput and efficient solids capture, but also operate continuously and automatically in harsh environments, and can handle abrasive or corrosive slurries. The AFP IV filter plates are available in 1200, 1500, and 2000 mm square sizes and are made of polypropylene or cast iron. They can be operated up to a pressure of 15 bar. Filter sizes and capacities are given in Table 6.2. In general, the advantages of the filter press are

Filtration

ischarge

S

x

(i) they are simple to construct and have low initial cost; (ii) they have low maintenance cost; (iii) most joints are external, hence leakage, if any, is easily detected; (iv) they provide large filtering area per unit floor space; (v) high operating pressures are easily obtained.

Model Number of chambers (increments of 2) Filtration Area (m2) Chamber Volume (m3)

10 – 40

24 –120

50 –120

23 – 91 0.5–2.0

95– 473 2.16–10.8

360 – 864 8.5–20.4

Leaf filters consist of flat filtering elements, known as leaves, which are supported either in a horizontal or vertical pressure vessel. The leaves are of circular or rectangular shape and have filtering faces on both of its sides. Figure 6.25 shows a vertical leaf filter. A leaf consists of a heavy coarse-mesh wire screen over which finer wire screen is fitted on both of its sides, as shown in Fig. 6.26. This assembly is held together by welding or riveting the upper edge with an inverted U-shaped light metal piece, which binds the edges and helps to suspend the leaf. Over the leaf, a sack of filter cloth is tightly sewn around the edge of the leaf. And all the leaves are mounted on

a common manifold. Figure 6.27 shows leaves in two different sizes for a vertical leaf filter. The vessel is locked and the slurry is pumped under pressure into the vessel. Filtration occurs on the leaf surfaces and the filtrate gets discharged from the bottom of each leaves into the manifold. Filtration is allowed to continue until a cake of desired thickness has formed. The cake can be dried by steam or hot air and then be discharged from the bottom with the help of a mechanical or pneumatic vibrator. The Amar Equipments’ vertical leaf filters are available with a filtration area of 1 to 60 m2, cake capacity of 1.5 m3, 5 to 19 number of leaves, and occupy a floor space of only 2.4 m × 2.4 m. They can be operated up to a pressure of 3 kg/cm2 (3 bar). The maximum working temperature of these filters is 120 C with neoprene gaskets and optionally 200 C with a viton/silicon gasket. The vessels are constructed of carbon steel while the leaves are of stainless steel of grades 316, 304, or 316. Vertical leaf filters are selected when (i) the liquids are volatile and may not be subjected to vacuum; (ii) the liquids are flammable, toxic, and corrosive; (iii) minimum floor space is available; and (iv) the cake is desired either in dry or thickened slurry form.

indin

Fi Fin

n n

M ni

d

The advantages of leaf filters over filter presses are (i) they are mechanically simple and flexible; (ii) there is automatic cake discharge in very short time without opening the filter, hence there is large saving in labour and time;

(iii) filtration rates are 2 to 3 times higher on same filtering area; (iv) they have a closed and pressurised operating system, hence no spillage and loss of liquid, which helps in handling volatile/inflammable liquids; and (v) they can be used for getting filtrate as well as cake. Amar Equipments leaf filters are used in edible/non-edible oil industry (bleached, winterised, deodorised, hydrogenated, fractionised oil, dewaxing, catalyst, mineral oil); beverage industry (glucose, fruit juice, cold drinks, sugar, vinegar); chemical industry (organic and inorganic salts, dyes, chemicals, plasticisers, sulphur, copper); pharmaceutical industry (syrup, bulk drugs, antibiotics, intravenous solution); and in petrochemical industries (crude oil, LPG, lubricating oil). A rotary drum filter is one of the oldest and the most widely used continuous vacuum filters applied to chemical process industries. This type of filter belongs to the bottom feed group. In addition to filtration, the process of cake washing, partial drying, and discharging is integrated to the filtration process. A rotary drum filter consists essentially of a cylindrical metal filter drum mounted horizontally on trunnions. The outer surface of the drum is formed of a perforated plate which is covered with a filter medium such as canvas cloth, synthetic materials like polypropylene or polyester with monofilament or multifilament yarns. At times, the drum is precoated with diatomaceous earth or perlite to aid to the filtration process. Figure 6.28(a) shows the different components of a FLSmidth Dorr-Oliver EIMCO drum filter while Fig. 6.28(b) shows its operating principle. Figure 6.29 shows a FLSmidth Dorr-Oliver EIMCO rotary drum filter. The slurry to be filtered is taken in a tank that houses the drum which is designed for a submergence of 33 to 35 % normally. The bottom of the tank contains an agitator to promote the suspension of solids and to prevent the settling of the solids. The drum filter has a drive for variable speed in the range of 1 to 10 rpm. Initially, vacuum is applied to that section of the drum which is submerged in the slurry through the rotary valve so as to suck the liquid from the slurry into the compartment and the solids are deposited on the filter medium in the form of cake. The thickness of cake can be regulated by adjusting the speed—with higher speeds, a thinner cake will be formed resulting into a higher filtration rate. The filtrate from the compartments then goes to the filtrate-collection tank through drain lines passing through the rotary valve.

Fi Fi

in

d

d

i n

i

i

Fi n n d iv in Fi v v

d in i

Fi d nd d

Fi

i n

i

A i nd

in n

iv

in n

i i n

i i d iv nd Fi

d iv nd Fi

n

d

v

d

in

d iv Fi

n

n

Fi 2 Fi

A i iv nd n d in

V

n

After emerging from the submergence, the cake is washed using a wash liquid, which is collected in a separate tank. The washed portion of the cake then enters into the drying zone where the cake is dried by sucking air through it. The vacuum is then cut off and the dried cake is discharged by scrapping it off with an adjustable blade. Air is blown in this portion in order to facilitate the cake discharge. Once the cake is discharged, the air blow is cut off, and the sector passes through a zone, known as dead zone, which is blocked with bridges so that no air is drawn through the exposed filter media which might cause the loss of vacuum on the entire drum surface. The drum then enters the slurry and the cycle is repeated. FLSmidth Dorr-Oliver EIMCO drum filters are available in sizes of 183 to 366 cm (6 to 12 ft) in diameter, 91.44 to 609.6 cm (3 to 20 ft) in filter face length, and 5.20 to 69.95 m2 (56 to 753 ft2) of filtration area. These are fabricated from metal parts for standard applications. When required, rubber coverings and linings are used. For handling acids and other corrosive materials, stainless steels of various grades and titanium can be used in fabrication. Drums are also fabricated from molded polypropylene components.

Advantages of drum filters are (i) continuous operation, hence cost of operation per unit volume of filtrate produced is less; (ii) large capacity; (iii) possible to build up the cakes of varying thickness; and (iv) slow rotation of the drum and reciprocation of agitator reduce the maintenance requirements. Applications of FLSmidth Dorr-Oliver EIMCO drum filters include clay, chemical processing, coal-preparation plants, automotive plating wastes, SO2 scrubber sludges, steel-mill wastes, food processing, water softening, tanning, foundry waste, red mud, leach residues, mineral concentrates, titanium dioxide, distillery wastes, organic sludges, dairies, pharmaceuticals and drugs, iron ore processing, wet-air oxidation, alumina, sodium bicarbonate, citric acid, solvent oil dewaxing, corn wetmilling, juice clarification, and winery operations. FLSmidth EIMCO AgiDiscTM filters are made of several parallel discs, each with a series of sectors radiating from a centrebarrel. Each sector is covered individually with a filter cloth (or metal screen) selected for specific applications. Connections between sectors and the centrebarrel are made by the use of a one-piece, rubber-covered steel ferrule with integral gasket. Figure 6.30 shows the cutaway view of an AgiDiscTM filter.

14

2

1 4 5

1 10

11

7 6 12

1 5

v Ai

12

2 Fi di 6 F in A i 10 Ov v d n 1 F

)

n

in d

4 id d x 7 id di x 11 A i d iv nd 14 n in

.

n

n in dd n

i d

di

Ov

in

dd

i

in

di

Slurry is fed into the tank through a feed manifold and kept in suspension by an efficient rotating paddle-shaft agitator which maintains a homogeneous slurry providing uniform cake thickness, resulting in lower moisture, and higher production. As the centrebarrel rotates, the filter discs travel through the slurry. Vacuum is applied to the sectors as they enter the slurry, and cake forms on the surface of the filter media. After the sector leaves the slurry, the continuous vacuum pulls air and filtrate through the inside of the sector, into and along the longitudinal port of the centrebarrel, and out through the valve to the vacuum receiver. Vacuum cut-off occurs just before the dewatered cake-laden sector approaches the discharge point. Pressurised air then loosens the cake from the filter media, and guided scrapper-blades direct the cake as it falls through the wide discharge chutes for removal. Figure 6.31 shows the operating principle of an AgiDiscTM filter and the discharge of cakes is shown in Fig. 6.32. AgiDiscTM filters consist of 1 to 15 discs. These are available in sizes of 122 to 198 cm (4 ft to 12 ft 6 inch) in diameter with 2 to 306.6 m2 (22 to 3300 ft2) of filtration area. Figure 6.33 shows disc sectors of different sizes.

Advantages of disc filters are (i) cost of operation per unit filtration area is low; (ii) large filtration areas can be accommodated in a small floor space; and (iii) the cake parts easily from the cloth with the help of a snap blow operation. AgiDiscTM filters are generally used in heavy-duty applications such as the dewatering of aluminum-trihydrate, barite, calcium carbonate, carbon, cement, coal, copper concentrate, flue dust, fluorspar, gilsonite, graphite, ilmenite, iron ores (hematite, magnetite, pyrite, taconite), lead concentrate, lithium ore, magnesium hydroxide, and zinc concentrate.

❑

❑

❑

❑

❑

❑ ❑

vt =

❑

4Dp g( rp − rf ) 3CD rf

❑

❑ CD =

24 NRe

vt =

Dp2 ( ρp − ρf ) g 18ρf

❑ CD = ❑ vt =

3.03Dp ( ρp − ρf ) g

ρf

❑

vt =

13.33 Dp ( ρp − ρf ) g

ρf

❑ ❑ ❑ ❑ ❑

DpA DpB

⎛ ρpB − ρf ⎞ =⎜ ⎟ ⎝ ρpA − ρf ⎠

n

24 + 0.44 NRe

❑ vh =

Dp2 ( rp − r b) g 18mb

.

❑

vh v t∞

= ∈n

❑

❑

❑

dV = dt

❑ A2 Δ P aW m(V + AVF ) a=

rC

a = K ( ΔP )S

❑

V 2 + AV VF =

❑

A2 Δ P (1− S ) × t. KW m

❑ V 2 + 2 AV VF =

2 A2 Δ P (1− S ) × t. KW m t cycle = t F + t W + t D + t R + t FL .

❑ ❑ 2 AD2 ∈D Δ P dV = . dt aW m VR + 2 AD ∈D VF

(

)

VR = AD

❑

2 ∈D Δ P KW mNR

❑ VO = VR NR = AD

2 ∈D Δ PNR KW m

.

❑ WC = VR NRW = AD

2 ∈D ΔPNRW . Km

1. What is the difference between thickening and clarification The purpose of thickening is to increase the concentration of solids, whereas in clarification a relatively small quantity of suspended solids is removed to get a clear liquid. 2. What is sedimentation It is a physical process practised to separate the suspended solids from a liquid under the influence of gravity. 3. What is the role of electrolyte in sedimentation The sedimentation rate can be increased by adding an electrolyte, which causes precipitation of colloidal particles. 4. Why is a constant temperature to be maintained in sedimentation test Constant temperature is maintained to avoid convection currents due to density differences which results from the difference in temperature. 5. What is elutriation

When two particles having different density values, but of the same size are separated using a fluid, the operation is called elutriation. 6. What are the advantages of CableTorq equipments Requires lower torque capacity because of reduced drag Automatically protects against overload due to lifting action Blades maintain efficient raking angle even when the rake arms are in a lifted position Keeps scraper blades in position in discharge cone or trench when arms are lifted As rakes clear overload, raking arms return smoothly to original position Minimises island formation because of the smooth pipe design of the rake arms Allows temporary surges or shock loads in solids handling capacity Torque arms are out of the heavy mud zone and in some installations actually

clear the liquid level, minimizing the torque load Pipe design of rake arm minimises scale formation and reduces dead load on center mechanism Each arm lifts independently for efficient continuous sludge discharge 7. Give a few industrial applications of bridge type CableTorq thickener. A few of the industrial applications include thickening industrial wastes, ore concentrates and tailings, flue dust, fly ash, and utility stack gas scrubbings. 8. What are the various types of filter medium used The filter medium may be a screen, cloth, membrane or a bed of solids. 9. How does a filter aid work when added to a slurry before filtration The filter aid increases the porosity of the cake, decreases its compressibility, and reduces resistance of the cake during filtration. 10. Name a few applications of the EIMCO s Shriver filter presses. Some of the applications include filtration of hazardous and metallic wastes; pharmaceuticals, chemical, and petrochemical products; pigments and dyes; ore processing; coal dewatering; water treatment; biological sludges; clarification of liquid; oilfield muds; and food products; etc. 11. What is the difference between plate-and-frame and recessed plate filter presses The recessed plate filter press contains only plates, while plate-and-frame filter press contains both plates and frames.

1. Define free and hindered settling conditions.

12. Give a few advantages of filter press. Some of the advantages of filter press are (i) low initial cost; (ii) low maintenance cost; (iii) large filtering area per unit floor space; (iv) high operating pressures can be easily obtained; (v) easy detection of leakage since most joints are external; and (vi) simple in construction. 13. Give a few advantages of drum filters. The advantages of drum filters are: (i) continuous operation, hence low operation costs; (ii) large capacity; (iii) possible to build up the cakes of varying thickness; and (iv) low maintenance requirements. 14. What is the difference between rotary drum and rotary disc filters Drum filters are horizontal and of bottom-feed type while disc filters are vertical and of side-feed type. 15. When the vertical leaf filters are recommended Vertical leaf filters are recommended when (i) the liquid is volatile and may not be subjected to vacuum; (ii) the liquid is flammable, toxic, and corrosive; (iii) minimum floor space is available; and (iv) the cake is desired either in dry or thickened slurry form.

2. Explain briefly the laboratory batch sedimentation test.

3. Define drag coefficient. Derive the Stokes law and Newton s law for calculating the terminal settling velocity of a particle settling through a fluid. 4. Derive the general equation for settling ratio. 5. Derive the equation for hindered settling velocity for the Stokes law region. 6. Discuss briefly about thickeners and clarifiers and their selection. 7. Explain briefly about bridge-supported and column-mounted thickeners. 8. What are the advantages of CableTorq thickeners and clarifiers Briefly explain different CableTorq models. 9. How does a SUPAFLO thickener differ from a conventional thickener

10. Define filtration and state the factors affecting the rate of filtration. 11. Write the principles of cake filtration and the types of cake filtration. 12. Discuss briefly about filter media and filter aids. 13. Derive the equations for the rate of filtration operated under batch and continuous conditions. 14. Classify filtration equipments. 15. Discuss in detail about various types of pressure filters. 16. Discuss in detail about various types of vacuum filters. 17. Give the working of a recessed plate filter press. 18. What are the advantages of leaf filter over filter press

1. Determine the settling velocity of spherical particles ( rp = 2700 kg/m3) settling under laminar conditions in water at 25 C. The average particle diameter is 1200 μm. Viscosity and density of water at 25 C are 1.004 cP and 998 kg/m3 respectively. 1.33 m/s

4. Find the terminal settling velocity of 25 % by volume of sand particles in a fluid having hindered settling velocity of 4.5 μm/s. The Richardson–Zaki index is 4.4. 15.96 mm/s

2. Quartz particles (specific gravity = 2.65) are settling in water at room temperature. What will be the maximum particle diameter so that Stokes law can be hold good in this case Viscosity of water at room temperature is 1.0 cP. 0.061 mm 3. Spherical particles of galena (Dp = 0.18 mm and rp = 7500 kg/m3) take 4 minutes to settle under gravity through a 10 m column of a fluid density 1300 kg/m3. Calculate the drag coefficient. 6.45

5. Two small spherical sand particles are settling at their respective terminal settling velocities through a highly viscous fluid filled in two identical glass columns. If one particle is twice as large as the other, how long will the larger particle take to reach the bottom of the column than the smaller particle Four times faster 6. A slurry is being filtered at constant pressure in a plate-and-frame filter press using 10 frames having a total filtration area of 10 m2. The filter delivers 250 litres of filtrate in 30 minutes. To increase filtration capacity 10 more frames are added to the filter. All other conditions

being the same as before, how long will it take to collect 500 litres of filtrate? Initial filter resistance is found to be negligible. 30 min 7. A plate-and-frame filter press is used to filter a known slurry mixture. At a constant pressure drop of 0.7 kg/cm2, 1400 litres of filtrate is delivered in 10 min starting with a clean filter. In a second run with the same slurry and filter press, 1140 litres of filtrate is obtained in 9 min when the pressure drop is 0.42 kg/cm2 starting with a clean filter. What is the compressibility exponent for the cake if the resistance of the filter medium is negligible? S = 0.4019

9. A vacuum leaf filter gives a total volume of 20 m3 of filtrate in 60 minutes. If the resistance of filter cloth is negligible, estimate the time taken for the collection of 25 m3 and 65 m3 of filtrate. 93.76 min and 633.81 min 10. A plate-and-frame filter press, having a filtering area of 1.5 m2 is used to filter a slurry of 10% by weight of calcite slurry (specific gravity = 2.3) in water. The volume of filtrate collected with time is as follows: Time (min) Volume of filtrate (m3)

10 75

30 115

60 150

100 200

The volume of filtrate collected is given by the relation:

8. A plate-and-frame filter press with negligible filter medium resistance is being used to filter a water slurry of fixed composition. Laboratory tests show that, during 3 hour of continuous operation at a constant pressure drop of 1.4 kg/cm2, 8500 litres of filtrate is delivered. The operation carried out at a pressure drop of 0.35 kg/cm2 for the above duration produced 4250 litres of filtrate. The unit is to be operated at a constant pressure drop of 1.05 kg/cm2 during filtration and washing. The cake is to be washed with 285 litres of wash water at the end of 2 hour a of continuous operation. If reverse thorough washing is used, estimate the time required for washing. 45.48 min

The cake is washed with water equal to 1/12 th of volume of filtrate delivered per cycle. The rate of washing is 1/4 th the final rate of filtration. Opening and dumping of cake and reassembling of the press takes 30 minutes. Determine (i) the washing time and volume of filtrate collected for a filtering time t of 45 minutes, and (ii) the optimum cycle time and the maximum output of filtrate per day. i 0.55 h and 137.65 m3 ii 0.842 h and 2160.6 m3

1. One of the most widely used processes in waste water treatment is (a) draining (b) thickening (c) sedimentation (d) filtration

2. When a particle settles in a fluid under gravity, the forces acting on it are (a) gravity and buoyant (b) gravity and drag (c) buoyant and drag (d) gravity, buoyant, and drag

V 2 = K1 + K 2 for t > 0, where, t = time of filtration in hours and K1 and K2 are constants.

3. The value of drag coefficient (CD) remains almost constant at a value of 0.1 for the Reynolds number (NRe) in the range of (a) NRe >2x105 (b) 500 < NRe < 2x105 (c) 0.2 < NRe < 500 (d) 10-4 < NRe < 0.2 4. The separation technique for a mixture of different sizes and shapes is called (a) classification (b) clarification (c) sedimentation (d) elutriation 5. For a wide difference in density between the materials, the separation technique adopted is (a) classification (b) floatation (c) sorting (d) elutriation

7. The AFP IV type recessed plate filter press can work up to a pressure of: (a) 5 bar (b) 15 bar (c) 25 bar (d) 35 bar

6. Properties of filtrate which is an important consideration in the selection of a filter include (a) viscosity (b) density (c) corrosiveness (d) all the above

10. For handling toxic and flammable liquid (filtrate), the recommended filter is: (a) leaf filter (b) disc filter (c) drum filter (d) filter press

1(c);

2(d);

3(a);

4(c);

5(b);

8. Rotary drum vacuum filters are designed for a slurry submerge of: (a) 10 – 15 % (b) 15 – 25 % (c) 33 – 35 % (d) 35 – 37 % 9. For a plate-and-frame filter press, the ratio of the rate of washing to the final rate of filtration is (a) 1.5 (b) 1.0 (c) 0.5 (d) 0.25

6(d); 7(b);

8(c);

9(d);

10(a)

in d

i

Gas-cleaning equipments, also known as gas collectors, vary widely in design, operation, effectiveness, space requirement, construction and capital, and operating and up-keep costs. The selection of a dust collector depends on the following factors: (i) (ii) (iii) (iv) (v)

dust concentration and particle size; air/gas stream characteristics; dust characteristics; degree of dust removal desired; and method of dust disposal.

A great variety of gas-cleaning equipment is available in the market, each type having its own advantages and disadvantages. A few of these are described in this section.

Gravity settling chambers are the earliest, simplest, and the most economical means of removing dust from gas. A settling chamber essentially consists of a large chamber of reasonable volume. The sudden increase in chamber size reduces the velocity of the dust-laden air-stream which enables the heavier and the coarser particles to settle out by the in action of gravity. Baffles are sometimes used to aid the separation as shown in Fig. 7.1. i Despite their simple design and economical mode of operation, these units are seldom used because of their large space requirements and low efficiency. Because of low gas velocities, the chamber is not subjected to abrasion and hence, is used as a pre-cleaner for the removal of coarse particles preferably in the range of 50 to 100 mm.

Inertial separators are based on the principle that the inertia (or momentum) of the dust particles is greater than that of the gas. So, when the direction of dustladen gas is suddenly changed around a body, the dust particles do not follow the same path by virtue of their greater inertia and move to the region of higher pressure drop. A great variety of inertial separator designs are available and one such design is the baffled separator as shown in Fig. 7.2. Here, the gas in direction is changed around the end of each of the baffles and the dusts are collected at the bottom of the separator. mpingement separators are a type of inertial separators in which the separation occurs by the inertial impingement of dust particles on the collecting bodies which are placed in their path. iscous air filters are a class of inertial impingement separators consisting of a series of square or rectangular plates covered with mats of asbestos, glass wool, or metal wires wet with a non-drying oil. The use of viscous oil improves efficiency because the oil acts as an effective filter and prevents the particles from re-entering the gas stream. The plates are replaced with new ones when the dust load on the mats becomes maximum and the plates are reused after washing the mats.

Fabric filters, commonly known as bag houses or bag filters, are one of the most efficient and cost-effective types of dust collectors available and are widely used for

the separation of dust from the gas stream by passing the dust-laden gas through a filter medium arranged in the shape of a bag. The bags are made of woven or felted cotton, wool, synthetic, or glass fibres. The bags are mounted on frames which are arranged in series. These are enclosed inside a large rectangular chamber with an inlet for dust-laden gas and an outlet for clean gas and having a number of conical discharge outlets for collecting dust, as shown in Fig. 7.3. The separation in fabric filters is achieved in a two-step process. Normally, the pores of the fabric filter are much larger than the size of the dust particles; hence, the collection efficiency is low during the initial period of separation. But with the passage of dust-laden gas through the pores of the fabric filter, the dust particles are deposited mainly due to inertial impingement, interception, gravity, and by Brownian movement, forming a dust layer. Once this layer has been formed, the separation is effected by filtration and the separation efficiency increases. Periodically these units are shaken, either mechanically or electrically, to discharge the accumulated dust. Bag filters, based on cleaning methods, are generally classified into three types: mechanical shaker, reverse air, and reverse jet.

In mechanical shaker bag filters, bags are attached to cell plates at the bottom of the bag filter and are suspended from horizontal bars located at the top. Dust-laden gas enters the bag filter through the bottom inlet and the dusts are collected inside the bags. Bags are shaken by vibrating mechanically the top horizontal bar from which the bags are suspended. In these filters the air-to-filter medium ratio is relatively low; hence these filters occupy large space. However, because of their simple design and operation, these are widely used in the minerals processing industries. The operation of reverse air bag filters is similar to the mechanical shaker types but they are different by their cleaning methods. Before the cleaning, the flow of dust-laden gas is stopped and the bags are cleaned by injecting clean air into the chamber in a reverse direction, which pressurises the bags from outside and the dusts fall down into the hopper below. At the end of the cleaning cycle, reverse airflow is stopped, and the filtration process is repeated. These filters need more maintenance than the mechanical shaker bag filters. In reverse jet bag filters, the bags are attached to cell plates at the top and the dust-laden gas enters from the bottom of the bag filter. The bags are supported by metal cages to prevent collapse, as the gas flows from outside to inside. The bags are cleaned by passing compressed air into the bags. These filters have higher filtration capacity due to their short cleaning time and are widely used in the minerals processing industries.

Wet scrubbers, commonly known as wet collectors, are a class of gas cleaning devices in which a scrubbing liquid (usually water) is used for the separation of dust particles from the gas stream. The separation efficiency largely depends on the degree of contact between the gas and the liquid d n streams. There are a large variety of wet scrubbers available and one such design is the venturi scrubber, which is also the most widely used type of wet scrubber. Venturi scrubbers are high-energy nv in type of wet scrubbers and work on the i n principle that the energy from the inlet i id gas stream is being utilised to atomise in the scrubbing liquid. A venturi scrubber essentially coniv in sists of a short converging section, a i n throat, and a long diverging section, as shown in Fig. 7.4. The dust-laden gas stream is introduced to the converging section and the liquid is injected at the throat. As the gas flows down the converging section, its velocity increases due to the decrease in flow area. The gas d n velocity in the throat section is generally i id d n between 60 to 120 m/s. These high-gas velocities break the liquid into enormous

number of fine droplets at the throat. Due to extreme turbulence at the throat section, the dust particles collide with liquid droplets and are encapsulated in them. Further collision among them occurs in the diverging section, mainly due to (i) their slowdown because of increase in flow area, and (ii) the differential rate of deceleration because of differences in their densities. This also causes the agglomeration among the dust-laden liquid droplets, which are then removed from the scrubber by inertial or cyclonic separators. These units are widely used to reduce particulate emissions in cement and steel industries.

Electrostatic precipitators (ESPs) are a type of gas-cleaning devices used for removing very fine particulate matter such as dust and smoke from a gas stream using the electrostatic forces. These units are very energy efficient, as in these units energy is applied only to the dust particles, in comparison to wet scrubbers in which energy is applied directly to the liquid medium. An ESP essentially consists of two electrodes: a high-voltage or discharge electrode and an earthed or collector electrode. The discharge electrode is generally smaller in cross-section. The dust-laden gas is passed between these two electrodes. A high potential difference, usually in the order of 50 to 100 kV, is applied with the negative charge on the discharge electrode. This produces a corona, around the discharge electrode, which releases electrons into the gas stream. These electrons attach themselves to the dust particles and ionise them by giving them a net negative charge. The ionisation process usually takes place in less than 0.1 second. These charged dust particles are then attracted towards the grounded collector electrode and get deposited there. The collected dust is periodically removed from the electrodes either by washing or vibration, which fall into the hoppers kept below. During this process, the gas velocity between the electrodes is kept low to allow the dust to fall into the hoppers and to prevent the dust from re-entering the gas stream. In industrial ESPs, the gas flows between the electrodes usually at 1 to 3 m/s with an average residence time of nearly 2 seconds. These units are capable of removing dust particles in the size range of 0.1 to 2 microns with a collection efficiency of >99%. The factors affecting the collection efficiency are (i) (ii) (iii) (iv) (v)

potential difference between electrodes; surface area of collector electrodes; gas flow rate; gas viscosity; and gas temperature.

Mainly there are two types of ESPs available: In these, both ionisation and collection are combined. These are commonly referred as ottrell precipitators and find applications in mineral industries. These are further classified into plate type and tubular type. In plate-type ESPs, the collector electrodes are flat parallel plates with a series of

discharge electrodes placed between two adjacent plates, as shown in Fig. 7.5, whereas in tubular-type ESPs, the collector electrodes are a nest of parallel pipes of cylindrical or hexagonal shape with discharge electrodes placed on the axis of the pipes, as shown in Fig. 7.6.

In these, ionisation and collection take place separately. These are mainly used in air-conditioning units. ESPs are good for some of the hot and corrosive applications with high gas flow but low dust load. These have been extensively used in coal burning units (thermal power plants), cement, sponge iron, and other metallurgical industries. However, their performance is poor on the highloading fine particulates.

i

v iv

n i d

n d n

d

nd d

i n

v iv

d

n

i d

nd d Cyclone separators, commonly known as cyclones, are the most d n widely used type of dust collection equipments and are normally used for the separation of the coarse dust particles or mist from gases. These are one of the cheapest type of dust-collection equipments as these do not have any moving parts. The separation is effected by the cyclonic action created by their design and the separation principle is similar to the hydrocyclones, as discussed in Chapter 5. Cyclones consist of a cylindrical section at the top and a conical section at the bottom, as shown in Fig. 7.7. The dust-laden gas enters the cylindrical section through the inlet pipe at the top, tangentially at a high velocity of about 30 m/s. The gas then moves downward in a helical motion, forming a peripheral vortex inside the cylindrical chamber. The dust particles gain centrifugal forces and are thrown towards the wall, which then move downwards and are discharged from the bottom outlet. While the dust-free gas, after reaching the bottom changes direction and follows a smallerdiameter rotating path back towards the top against gravity. The outlet section has a downward extending pipe, known as vortex finder, projected below the gas inlet pipe to cut the vortex and to prevent short-circuiting of the gas streams. Cyclones are operated at high temperatures of up to 1000°C and high pressures of up to 50 MPa and are very effective for treating dust particles in the range of 5 to 10 microns. While separation above 200 microns are possible in cyclones, these

n D d n in

Di

x ind

D

ind i i n ni i n

i

are generally not recommended due to abrasion problem. A gravity settling chamber is a better alternative for the purpose. For particles with high degree of agglomeration tendency, cyclones can be used to separate gas–solid systems with solid particles smaller than 5 microns. With predominating agglomeration, separation efficiency as high as 98% is achievable for separation of solid particles in the range of 0.1 to 2 microns from the dust-laden gas streams. Figure 7.7 shows various design parameters. The minimum particle diameter of density rp which can theoretically be separated from the gas stream is given by

1/ 2

( Dp ) min where, (

⎡ 3.6 A i 2 Do ρg μg ⎤ =⎢ ⎥ ⎢⎣ π Dc ρp g ⎥⎦

= minimum size of dust particles that can be separated, Ai = area of gas inlet, o = diameter of gas outlet, c = diameter of cyclone, = depth of the cyclone, rg = density of gas, rp = density of dust particles, mg = viscosity of gas, and Gg = mass velocity of dust-laden gas.

p)min

(7.1)

1/ 2

⎡ 3.6 A i 2 Do ρg μg ⎤ ⎥ . From Eq. 7.1, we have ( Dp ) min = ⎢ ⎢⎣ π Dc ρp g ⎥⎦ With Do = Dc /2 and = 4Dc, the above equation can be written in terms of Dc as 3.6 A i 2 ρg μg . Dc = 8πρp g ( Dp ) min 2 Given in this problem are Ai2 = 0.3 × 0.3 = 0.09 m2, rg = 0.001 g/cm3 = 1.0 kg/m3, rp = 1.24 g/cm3 = 1240 kg/m3, mg = 0.018 cP = 1.8 × 10−5 kg/m.s, Gg = 5400 kg/m2.h = 1.5 kg/m2.s, and (Dp)min = 5.0 microns = 5 × 10−6 m. Putting the values in the above equation we have Dc = 4.99 m ≈ 5 m. Thus, the dimensions of the desired cyclone are Diameter = 5 m, Depth = 20 m, and Diameter of gas outlet = 2.5 m. (Ans)

Sturtevant offers three high-performance air classifiers, namely: Whirlwind ; SuperFine ; and Side DraftTM which work efficiently and accurately all over the world in the food, chemical, and minerals industries. These are mainly used for particle classification through air separation. These three classifiers balance the physical principles of centrifugal, drag, and gravity forces to classify particles according to size or density. For dry materials of 100-mesh-size and smaller, air classification provides the most effective and efficient means for separating a product from a feed stream, for de-dusting, or, when used in conjunction with grinding equipment, for increasing productivity. The Whirlwind air classifier incorporates a selfcontained fan and rejecter blade classification system. Its internal fan design does not require cyclones, air locks, or bag-houses for product collection of particles in the range of 100 to 400 mesh. Figure 7.8 shows a Whirlwind air classifier. Material enters the classifier through the feed spout and is subjected to centrifugal force due to which the coarse particles are thrown away from the distributing plate and into the air flow. Due to gravity, large particles settle into the coarse cone. Finer particles are swept upward where selector blades generate further classification. During this secondary separation, oversized particles are spun out of the air flow and drop down into the coarse cone. The selected fines continue through the circulating fan and into the fines cone. Fines drop out of the recirculated air flow at the fixed return air vanes. These units are available with sizes of 20 inch to 26 ft in diameter having feed capacities of 1 to 800 tonne/h requiring air flow of 25–50 to 3000–6000 ft3/m.

F

d

i F n

Fin n n

in

in n

d n v

i

i

in n Ai n

Fin n n

i

Fin i

The advantages of Whirlwind air classifiers include (i) (ii) (iii) (iv) (v)

low capital cost, as no auxiliary equipments are needed; consistent, high-quality product; low energy consumption; less maintenance; and processes abrasive materials.

Whirlwind air classifiers have the following applications: (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix)

cement; ceramics; coal; diatomaceous earth; fly ash; gypsum; minerals; plastics; and soda ash, bicarbonate.

iv

F

Fin i

d

/Ai Ai n

F i

i

d i n Ai

i

in

n in n i

The SuperFine air classifiers achieve the high degree of accuracy demanded in the separation of particles of 44-micron size and smaller. Figure 7.9 shows a SuperFine air classifier. Material enters through the feed spout and is subjected to centrifugal force, which causes uniform distribution of the material into the upward moving air stream. The unique design of the SuperFine ’s variable speed, multi-blade rejecter cage allows only the selected particles to pass into the fines chamber and exhaust into the system collector. Oversized particles settle into the coarse discharge. The SuperFine system delivers maximum selection efficiency and productivity. These units are available with sizes of 3 ft to 6 ft in diameter having feed capacities of 0.5 to 15 tonne/h requiring air flow of 3000 to 9000 ft3/m. The advantages of Superfine air classifiers include (i) (ii) (iii) (iv) (v)

ultra-fine particle size separation of high-value materials, 44–5 microns; narrow particle-size distribution; easy access for cleaning and low maintenance; higher capacity and finer separations than screeners with no blinding; low energy consumption;

(vi) processes abrasive materials; (vii) effective product cooling; and (viii) fines collected in cyclone or process collector. SuperFine air classifiers have the following applications: (i) (ii) (iii) (iv) (v) (vi) (vii)

ceramics; chemicals; diatomaceous earth; food products; minerals; shredded fibers; and tobacco.

The Side DraftTM air classifiers represent a highly versatile, energy-efficient system for the consistent separation of particles in the 100 to 400 mesh range. Figure 7.10 shows a Side DraftTM air classifier. Material enters through the feed spout and is evenly conveyed across the top of the distribution plate and drops into iv F

Ai

i

d

F

d

i

in

i

v

Ai n

in Fin i

n

/Ai Ann

Fin

n

i

i n

the separating zone, creating a uniformly dispersed curtain of material. Forces generated by the rejector cage and process air subject the curtain of material to particle size classification. High separation efficiencies and precision of classification are obtained by controlling air flow and rejector cage speed. The multi-pin, variablespeed rejector cage allows only the selected fines to pass into the fines chamber and exhaust into the system collector. The coarse particles, after passing through the separating zone, fall into the coarse outlet. These units are available with Models of SD-20 to SD-180 having feed capacities of 4–12 to 360–1150 tonne/h requiring air flow of 3000 to 242000 ft3/m. The advantages of Side DraftTM air classifiers include (i) (ii) (iii) (iv) (v)

compact design; low energy consumption; durable, wear-resistant design minimizes maintenance; effective product cooling; consistent, high-quality product, regardless of variations in feed material and changes in air flow; (vi) processes abrasive materials; (vii) fines collected in cyclone or process collector; and (viii) high removal efficiency. Side DraftTM air classifiers have a wide range of applications, (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x) (xi) (xii) (xiii) (xiv)

❑

❑

ceramics; metal oxides; coal; chemicals; diatomaceous earth; flyash; gypsum; minerals; metals; iron ore; silica sand; feldspar; soda ash; and bicarborate.

❑ ❑

❑ ❑

❑

❑

1 /2

⎡ 3.6 Ai2 Do ρg μg ⎤ (Dp )min = ⎢ ⎥ ⎢⎣ π ZDc ρp Gg ⎥⎦

.

❑

1. Why is gas cleaning practised in the industry It is necessary to (a) control pollution, (b) prevent dust from entering a machine which reduce their maintenance, (c) prevent dust from spreading in the plant and in the neighbouring areas, and (d) prevent wastage of valuable materials. 2. Name the important factors affecting the gas–solid separation. The important factors affecting gas–solid separation are

(a) properties of dust (solid) particles, viz., size, density, and moisture content, etc., (b) quantity of dust to be handled, (c) moisture content of the gas stream, and (d) temperature of the gas–solid system. 3. What are the main separation mechanisms on which the gas–solid separators are classified (a) Gravity settling (b) Inertial separation (c) Liquid washing or scrubbing (d) Electrostatic deposition (e) Centrifugal separation

4. What are the materials used in the fabrication of bag filters The materials commonly in use are (a) woven or felted cloth, (b) wool, (c) synthetic fibre, and (d) glass fibre. 5. Name the various types of bag filters used in industries. The different types of bag filters used in industries are (a) mechanical shaker bag filters, (b) reverse air bag filters, and (c) reverse jet bag filters. 6. Why are the reverse jet bag filters more commonly used in mineral processing industries It is due to their (a) high filtration capacity, and (b) short cleaning time. 7. What is the working principle of a venturi scrubber The working principle is that, the energy from the inlet gas stream is utilised to atomise the scrubbing liquid. 8. Why are electrostatic precipitators considered to be energy efficient compared to wet scrubbers In electrostatic precipitators, energy is applied only to the dust particles while in a wet scrubber, it is applied directly to the liquid medium.

9. What are the factors affecting the collection efficiency of electrostatic precipitators The factors are (a) potential difference between the electrodes, (b) surface area of collector electrodes, (c) gas-flow rate and temperature, and (d) gas viscosity. 10. What are the field of applications of ESPs ESPs are effective for some hot and corrosive applications with high gas flow and low dust load. These perform poorly on the high loading fine particulates. 11. In which type of industries, the air classifiers are generally used The air classifiers are generally used in food, chemical, and mineral industries.

1. What are the factors affecting the gas–solid separation 2. What are the factors taken into consideration while selecting a gas–solid separation equipment 3. Discuss the principle of operation of gravity settling chambers. 4. Write the principle of operation of inertial separators. 5. Discuss the operating principle of different types of fabric filters. 6. Discuss the construction and working of venturi scrubbers.

7. How are dust particles removed in electrostatic precipitators 8. Discuss the construction and working of cyclones. 9. What is a Cottrell precipitator 10. What is the function of a vortex finder 11. Name a few advantages of Whirlwind air classifiers. 12. Give a few applications for SuperFine air classifiers.

12. Name a few applications of the Whirlwind air classifiers. The applications include: cement, ceramics, coal, flyash, gypsum, minerals, and plastic industries. 13. In what range of particles Side DraftTM air classifiers are efficient in separation Effective separation takes place in the particle size range of 100–400 mesh.

1. Dust-laden gas from a chimney enters a cyclone separator of dimensions given below at the rate of 9000 kg/m2.h. Find the minimum particle size of the dust that can be separated by the cyclone. Data Cyclone dimensions Diameter = 1200 cm

1. The selection of a dust collector depends on (a) dust concentration and particle size (b) air/gas stream characteristics (c) extent of dust removal (d) all of the above 2. The earliest and simplest form of gas-cleaning equipment is: (a) electrostatic precipitator (b) gravity settling chamber (c) hydrocyclone (d) bag filter 3. The particle size that can be effectively removed by a gravity settling chamber is (a) 0.1 to 1.0 mm (b) 0.05 to 0.1 mm (c) 0.001 to 0.01 mm (d) less than 0.001 mm 4. A viscous air filter belongs to which of the following category of gas-solid separators (a) Bag filter (b) Cyclone separator (c) Impingement separator (d) Wet scrubber 5. The normal velocity in the throat section of a venturi scrubber is (a) 60 to 100 cm/s (b) 1.0 to 10 m/s

Depth = 4800 cm Diameter of gas outlet = 50 cm Gas inlet = 40 × 40 cm2 Chimney gas properties Dust density = 1.2 g/cm3 Gas density = 0.0012 g/cm3 Gas viscosity = 0.018 cp 10.7 microns

(c) 10 to 60 m/s (d) 60 to 120 m/s 6. The velocity of gas between the electrodes of ESP is nearly equal to (a) 1 to 5 cm/s (b) 5 to 50 cm/s (c) 1 to 3 m/s (d) 3 to 10 m/s 7. Gas residence time between the electrodes of ESP is nearly equal to (a) 10 milliseconds (b) 100 milliseconds (c) 1 second (d) 2 seconds 8. The tangential velocity of gas in cyclones is nearly equal to (a) 1 m/s (b) 10 m/s (c) 30 m/s (d) 100 m/s 9. The cyclone separators can work at high pressure and temperature range of up to (a) 5 MPa and 500°C (b) 10 MPa and 1000°C (c) 15 MPa and 1000°C (d) 50 MPa and 1000°C

10. The size of dust particles that can be effectively handled in cyclones varies from (a) 5 to 10 microns (b) 10 to 50 microns (c) 50 to 100 microns (d) 100 to 200 microns 11. Whirlwind air classifiers are effective and efficient to separate particles in the size range: (a) 1 mm to 2 mm (b) 0.5 mm to 1 mm (c) 100 mesh and lower (d) 1000 mesh and lower

12. SuperFine air classifiers can achieve high degree of accuracy in separation in the particle size range of: (a) 1 mm to 2 mm (b) 0.1 mm to 1 mm (c) 100 micron and lower (d) 44 micron and lower 13. For the separation of abrasive materials, the air classifier used is: (a) Side DraftTM air classifier (b) SuperFine air classifier (c) Whirlwind air classifer (d) all the above

1(d); 2(b); 3(b); 12(d); 13(a)

7(d);

4(c);

5(d);

6(c);

8(c);

9(d);

10(a);

11(c);

|

For in-plant transport of solids, generally for short distances, hand or electric trucks, trolleys, or carts are used, while transport by rail, road, or ships are recommended for long-distance transport of bulk solids (mineral ores, coal, etc.). Transport by rail, road, or ships often becomes uneconomical and is disadvantageous because of increased fuel costs, environmental pollution, road and port traffic congestion, etc. and is not the subject of discussion of this text. The equipment discussed here are conveyors and elevators. onveyors either carry the solids on them or drag them through a channel or trough and are used both for short- and long-distance transport, operated either intermittently or continuously. Conveyors that lift the solids vertically are called elevators. There are a great variety of conveyor designs available and the popular ones discussed here are belt conveyors, screw conveyors, pipe conveyors, and bucket elevators. The selection of equipment depends upon (i) (ii) (iii) (iv) (v)

capacity requirements; distance of travel; shape and size of materials; material characteristics (both chemical and physical); and whether the solids are to be transported horizontally, vertically, or on an incline.

Since their invention in the year 1901 by Sandvik, belt conveyors have found application in a wide variety of industries and have become the most versatile among all the conveying equipments. They can be used both for short-as well as long-distance transport and can be operated horizontally or on an incline. A belt conveyor essentially consists of a continuous belt passing around two large pulleys at the two ends, one of which is a drive pulley and the other is a tail pulley, as shown in Fig. 8.1. Solids are loaded on the upper surface of the belt near the tail pulley through a feed hopper and are carried to the other end of the belt and are discharged

over the drive pulley. The loaded belt is supported during its carrying run by closely spaced rollers, known as idlers, while during the returning run the belt + + is supported by widely spaced idlers. i The idlers are so spaced to prevent the + iv sagging of the belt during its operation. d n i Figure 8.2 shows a conveyor belt supported by idlers, in operation at Orissa Sponge Iron and Steel Limited, India. The length of the belt may change due to the load of solids or seasonal changes in temperature and humidity. For this reason, a snub pulley is provided to the returning part of the belt. The conveyor belts can be operated under flat or troughed conditions, which are created by the arrangement of idlers. Figure 8.3 shows different belt profiles. Flat belts are generally used to transport boxes, solid units, and solid particles with a high angle of repose. The capacity of flat belts is low for solid particles with a low angle of repose. The capacity is higher for troughed belts. The angle of inclination of the belt is less than the angle of repose of solid particles to be transported and is usually between 10 and 20 . The belts are made up of canvas or rubber and are generally reinforced with steel wire to impart strength. But for rubber belts, age, light, heat, moisture, and chemical activity of solids to be transported are all destructive. Neoprene, vulcanised rubber, and other special types are available for handling hot and moist materials. id

F

d

An

An id

id

d d Flat elt

Troughed elt

The capacity of a belt conveyor depends upon (i) (ii) (iii) (iv) (v) (vi) (vii)

width and speed of the belt; friction between the surface of belt and the solids; angle of repose of solid particles; angle of inclination of the belt; stickiness of solid particles; degree of troughing; and shape, size, and specific gravity of the solids.

Metso Minerals Belt Conveyors are available with a belt width of 350 to 1600 mm and have a conveying capacity of 40 to 1000 tonne/h. The details are given in Table 8.1. The maximum capacity of belt conveyors is given by b

= Ab Vr b

(8.1)

where, Qb = maximum capacity of the belt conveyor, kg/s Ab = cross-sectional area of load on the conveyor belt, m2 = linear speed of the belt, m/s rb = bulk density of the solid materials, kg/m3 Ab = Ka Ci bl2

Here, where,

Ka = a constant whose value depends on the flowability of the material and the angle of inclination of side rollers Table 10.3 - Narayanan, 2003

Belt idt mm 350 500 650 800 1000 1200 1400 1600

(8.2)

Maximum capacity tonne 40 100 200 320 500 700 750 1000

Maximum slope

∞ 20 19 18 17 16.5 16 15.5 15

Belt speed ms

1.6

Ci = correction factor for inclination (function of inclination and flowability, i.e., high, medium, and low) Table 10.2 - Narayanan, 2003 bl = width of the belt carrying the load, m = 0.9 b − 0.05 where,

(8.3)

b = width of the belt, m

1600 x 1000 = 444.4 kg/s . 3600 = 1.6 m/s, r b = 2600 kg/m3, Ka = 0.067, and Ci = 0.95.

Capacity of the belt conveyor is Given that,

Using Eq. 8.1, we have Ab =

b

V rb

=

b

=

444.4 = 0.1068 m 2 . 1.6 x 2600

And using Eq. 8.2, we have bl2 = 1.678 ⇒ bl = 1.295 m. Thus, using Eq. 8.3, we have b = 1.494 m, say 1.5 m, is the required width of the belt (Ans)

Screw conveyors are one of the oldest type of conveying equipments, operated horizontally or at a slight incline (up to 20 ) and are extensively used for transporting finely divided solids; sticky materials; and semisolid materials including food waste, municipal solid wastes, and boiler ash. These are generally used for transporting over short distances, which may be about 40 m in the horizontal and 30 m in the vertical direction. A screw conveyor essentially consists of a U-shaped trough inside which a screw or spiral flight mounted on a shaft is placed parallel to the trough bottom, as shown in Fig.8.4. The shaft is supported on a bearing at each end and is generally driven at feed/one end. The solid particles to be conveyed are fed to the trough through a feed hopper and as the shaft along with the screw rotates, the solid particles are pushed forward towards the discharge end F d along the front face of the spiral. Inside the trough, the materials travel at such a level that the upward lifting force is just balanced by the downward M gravity force. This is due to the friction between the particles i and the spiral surface.

The spiral surfaces are available in continuous, bladed, or cut forms. Continuous spirals are used for transporting dry, grannd d i ular, and free-flowing materials, while discontinuous spirals are used for wet, muddy, and thick materials. The bladed or cut types of spirals are chosen when n i mixing during transportation is desired. The screw conveyors with various pitch designs are also available with a pitch equal to its diameter (standard pitch), long pitch, short pitch, and double pitch, a few of which are shown in Fig. 8.5. The clearance between the screw flight and the inside surface of the trough is nearly equal to the average size of particles in the feed. The maximum particle size in the feed that can be transported depends upon the diameter of the flight. Standard screw conveyors are 3 to 20 inches in diameter and 8 to 12 ft long. The advantages of screw conveyors are (i) (ii) (iii) (iv)

simple design and ease of maintenance; little headroom is required; slurry or sticky materials can be transported; with the increase of pitch spacing, the capacity can be increased without increasing the rotational speed of the screw; and (v) apart from conveying and mixing, these can be used for heating, cooling, or drying of solids.

While the disadvantages are (i) (ii) (iii) (iv) (v)

high wear of screw and trough materials; size reduction of feed materials; higher power consumption; capacity decrease with the increase of angle of inclination; and due to the stresses developed in the shaft, the conveyor length is restricted. The capacity of screw conveyors depends on

(i) screw diameter; (ii) screw pitch; and (iii) speed of rotation. The capacity is given by

s

=

⎛ p 2⎞ D ⎝ 4 s ⎟⎠

i⎜

⎛N⎞ ⎜⎝ 60 ⎟⎠ rs

f

(8.4)

where, Qs = capacity of screw conveyor, kg/s Ci = correction factor for inclination which varies from 1.0 for horizontal conveyor to 0.6 for inclination of 20 . Other values are 0.9, 0.8, and 0.7 for inclinations of 5, 10, and 15 degrees respectively [Narayanan, 2003]

s = screw diameter excluding shaft diameter, m P = screw pitch, m N = speed of the shaft, rpm ρs = density of solid materials, kg/m3 Cf = filling coefficient values depending primarily on the type of materials (values range from 0.125 to 0.4 depending on heavy/light, abrasive/ non-abrasive Table 10.1 - Narayanan, 2003

From Eq. 8.4, we have

s

=

⎛ p 2⎞ D ⎝ 4 s ⎟⎠

i⎜

⎛N⎞ ⎜⎝ 60 ⎟⎠ rs

f

.

Here, Ci = 1.0, since it is to be transported horizontally. Given that, rs = 1400 kg/m3, P s = 0.8, Cf = 0.125, and Qs = 15 tonne/h = (15 × 1000)/3600 = 4.167 kg/s. Thus using Eq. 8.4, we have 4.167 = 54.98 s3 ⇒ s = 0.423 m. Thus, the screw pitch = 0.8 s = 0.3384 m (Ans) FLSmidth Screw Conveyors (Fig. 8.6) are designed for inclined transport (up to 8°) of material with temperatures below 300 C. They have a conveying capacity up to 550 m3/h and are manufactured up to 60 m length. An 0.30–0.35 degree of filling is recommended, depending on the material (e.g., filter dust and coal meal = 0.32, cement and raw meal = 0.35). The FLSmidth Screw Conveyors designed in modules of 500 mm are supplied with steel plate trough (standard) or for use in a concrete trough. The screw pitch is individual for each of the ten conveyor sizes to attain lowest power consumption and smooth transport. The screw is completely enclosed, so the conveyance is weatherproof and dust-free. The maintenance requirements of the FLSmidth Screw Conveyors are negligible. End bearings take up axial as well as radial stresses. They are of the heavy roller type and are grease packed. Intermediate block bearings support the screw at 4–6 m intervals. Intermediate bearings can withstand the high temperatures and consist of Cr-alloyed bearing shells and Cr–Mo-alloyed special hardened journals. Intermediate bearings are suspended in open adjustable bearing bridges.

The major disadvantages of the conventional troughed belt conveyors are generation of dust and the spillage of solids during transportation. This leads to the development of enclosed material transport such as the pipe conveyors. The pipe conveyors were

developed towards the end of the seventies of the last century by Japan Pipe Conveyor mainly to reduce dust and spillage and for economical reasons. Figure 8.7 shows the operating principle of Metso Minerals Trellex FLEXOPIPE conveyor belts.

nv n i n di n n d n in din

di

din d nin nd

n

di din

i n

in.

M

nv n i n din

i n n i n

i n nv i

n nd

in n n v .

d

In the loading area, the FLEXOPIPE belt is troughed like conventional belts. After loading, special idlers form the belt into a pipe shape with overlapped belt edges. The material being conveyed is completely enclosed by the belt. Hexagonally arranged idler rolls keep the belt closed over the track. Close to the conveyor head the belt opens out into a normal troughed belt supported by three roll idlers and runs flat over the discharge pulley to unload the materials. In the return strand, the belt closes again into a pipe where its overlapped edges, in general, are on the bottom. Hexagon rolls provide the pipe shape also in the return run. At the end of the return strand the belt opens and runs flat over the tail pulley to be loaded again. Figure 8.8 shows a FLEXOPIPE conveyor belt. A special type of cross rigid rubber belts are used in the pipe conveyors which maintains the constant contact of the belt with the idlers and to keep the round form of the belt during transportation. The range of FLEXOPIPE belts comprises reinforcements with different elastic moduli. A more elastic belt allows narrower curves and shorter transition lengths (distance between pulley and first regular hexagon panel), but requires more take-up length. Enclosed transport of hot materials does not allow heat exchange to the atmosphere, therefore material temperatures must be lower than that in conventional installations.

nline arrangement

set arrangement

The arrangement of idlers plays an important role in the operation and performance of pipe conveyors. Figure 8.9 shows inline and offset arrangement of idler rolls. In the inline arrangement, all the six idler rolls are mounted on the same side of the frame with small gaps to avoid the belt edge to be trapped between two rolls. While in the offset arrangement, three idler rolls are placed on either side of the supporting frame which allows larger rolls and brackets. The nominal pipe diameters, belt width, capacity, and maximum lump size for FLEXOPIPE conveyor belts are given in Table 8.2. The advantages of Metso Minerals Trellex FLEXOPIPE conveyor belts compared to conventional troughed belt conveyors are (i) horizontal and vertical curves enable the routing over difficult terrain conditions;

Nominal pipe diameter mm

Belt idt mm

150 200 250 300 350 400 500

600 780 1000 1100 1300 1600 1900

( Filling rate 75 %, speed 1 m/s,

Capacity m 45 80 140 160 220 350 460

Maximum lump si e mm 50 70 90 100 120 140 180

Filling rate 75 %, reduced filling rate allows larger lumps)

(ii) fewer transfer points lead to smooth treatment of the material to be conveyed and reduces installation as well as operating costs; (iii) the narrow width of the installations needs less space requirements on the track; (iv) larger contact between material and belt allows increased angles of inclination (depending on the kind of material being conveyed); (v) material is completely enclosed, external environmental conditions such as rain, wind, temperature, and dust have no negative influences; and (vi) clean and spillage free material transport protects the environment and keeps maintenance costs on a low level. Pipe conveyors are used to transport cement, humidified ash, fly ash, minerals, pulp and paper, wood chips, coal, coke, fertiliser, and food grains.

The conveyors discussed earlier in this section, viz., belt conveyors, screw conveyors, and pipe conveyors, can lift solid materials at some angle of inclination, but none of them can lift solid materials vertically. Bucket elevators are used only for vertical transport of bulk solids. A bucket elevator essentially consists of a number of buckets attached to a continuous double-strand chain or belt which passes over two sprockets or pulleys located at different elevations inside a casing, as shown in Fig. 8.10. Solid materials are directly fed into the buckets partly and are scooped up from the boot partly, which are carried up vertically and are discharged into a hopper as the buckets turn over the upper sprocket. The emptied buckets faced downward travel vertically downward and again scoop up materials i as they pass the lower sprocket. Fi d Bucket elevators are mainly of three types:

F

d

(i) centrifugal-discharge type – buckets are spaced; (ii) continuous type – buckets are very closely spaced; and (iii) positive-discharge type – buckets are spaced and the return belts or chains are snubbed back beneath the upper sprocket to invert them for positive discharge. Centrifugal-discharge bucket elevators are mainly used to handle free-flowing materials or small-lump materials while continuous bucket

elevators are used for large-lump materials. But the positive-discharge bucket elevators are used to lift sticky materials or cohesive solids and are slow speed equipments. The FLSmidth fast-running bucket elevators (Fig. 8.11) are designed for centrifugal discharge of materials and can handle lumps up to 50 mm in size and can withstand temperatures up to 350°C. The chain speed is 1.0–1.9 m/s. The chains are made of special hardened steel. For handling abrasive materials, the digging edge of the buckets are reinforced.

The capacity of a bucket elevator depends on the lifting height, the bulk density of the materials, the volume per unit time, and the chain speed. FLSmidth bucket elevators are available with a belt width of 160 to 400 mm for single casing and 500 to 1600 mm for double casing. The maintenance requirements of the FLSmidth bucket elevators are negligible. Chain wheels have replaceable segment rims.

❑ ❑ ❑

=A Vr .

❑ ❑

❑

s

⎛p ⎞ ⎛N⎞ = Ci ⎜ Ds 2 ⎟ P ⎜ ⎟ rs Cf . ⎝4 ⎠ ⎝ 60 ⎠

❑

❑

1. What are elevators The conveyors which lift the solids vertically are called elevators. 2. What are idlers Closely spaced rollers to support the loaded belt are called idlers. 3. When are the flat belts used Flat belts are used for transporting boxes, solid units, and solid particles with a high angle of repose. 4. What are the common materials of construction for the belts The common materials for the construction for the belts include canvass or rubber reinforced with steel wire, neoprene, and vulcanised rubber. 5. What materials are used for belts to handle hot and moist materials Noeprene and vulcanised rubber can be used as belt material. 6. For which type of materials are screw conveyors used Screw conveyors are used for transporting finely divided solids; sticky materials; and semisolid materials including food waste, municipal solid wastes, and boiler ash.

7. For which type of materials are continuous spirals used in screw conveyors Continuous spirals are used for the transportation of dry, granular, and free flowing materials. 8. What is the normal size for screw conveyors The normal size varies from 3–20 inches in diameter and 8–12 feet in length. 9. How does the capacity of a screw conveyor alter with inclination The capacity is maximum for horizontal and decreases with inclination. 10. How does a pipe conveyor differ from other type of conveyors This is a closed type of transport system. 11. What specific advantages are obtained in a pipe conveyor The specific advantages of pipe conveyors are (i) reduces dust and spillage, (ii) clean transportation, and (iii) economical. 12. Name a few materials for which pipe transport is used. Cement, humidified ash, fly ash, coke, coal, fertilisers, and food grains.

13. What is the essential difference between bucket elevator and the other transport systems used in industry Bucket elevator is a vertical transport system.

14. What are the factors on which the capacity of bucket elevators depend The capacity depends on (i) the lifting height, (ii) bulk density of the materials, (iii) volume per unit time, and (iv) chain speed.

1. How do the conveyors carry solids on them? 2. What are the considerations for the selection of conveying equipment? 3. What is the function of idlers in belt conveyors? 4. Give the important factors on which the capacity of a belt conveyor depends. 5. What type of materials are transported by screw conveyors? 6. What are the different forms of spiral surfaces used in screw conveyors? 7. Give the various advantages of screw conveyors.

8. Give the important factors on which the capacity of screw conveyors depends. 9. What is the advantage of a pipe conveyor over troughed belt conveyor? 10. What are the factors on which the capacity of a pipe conveyor depends? 11. What is the mechanism of transport in the bucket elevators? 12. What are the different types of bucket elevators commonly used? 13. Differentiate between centrifugal discharge type and continuous-type bucket elevator. 14. Give specific features of FLSmidth fast-running bucket elevators.

1. Limestone from a quarry is to be transported at the rate of 900 tonne/h by a belt conveyor at an incline of 16 to the stockyard. The particles of limestone are fairly dry and are of size 15–30 mm. A belt conveyor of 1200 mm width is

available. Check whether the available conveyor is suitable for the service. Data: Density of limestone = 2500 kg/ m3, Ci = 0.9, Ka = 0.067, and belt speed = 1.6 m/s Ans. Suitable

1. The angle of inclination of the belt is (a) equal to the angle of repose of the material

(b) less than the angle of repose (c) greater than the angle of repose (d) not related to the angle of repose

2. What is the normal inclination of the belt in case of belt conveyors (a) 2–5 degrees (b) 5–10 degrees (c) 10–20 degrees (d) 15–25 degrees 3. Up to what horizontal length can a screw conveyor be used (a) 40 m (b) 60 m (c) 80 m (d) 100 m 4. The capacity of a screw conveyor depends on (a) material size (b) conveyor diameter (c) conveyor length (d) screw diameter 5. Which of the following conveyors can be used for the transportation of boiler ash

1(b);

2(c);

3(a);

4(d);

(a) Belt conveyor (b) Screw conveyor (c) Bucket elevator (d) Apron conveyor 6. What type of bucket elevator is used to lift sticky materials (a) Centrifugal discharge type (b) Continuous type (c) Positive discharge type (d) All the above types 7. Centrifugal discharge bucket elevators are mainly used for: (a) free flowing materials (b) large lumpy materials (c) sticky materials (d) cohesive solids 8. Humidified ash can be transported by (a) belt conveyor (b) screw conveyor (c) bucket elevator (d) pipe conveyor

5(b); 6(c); 7(a); 8(d)

|

Mixin i n

.

The objective of liquid mixing is to obtain a relatively uniform mixture from two or more components, both miscible and immiscible. The degree of uniformity obtained depends on the liquid characteristics. While it is possible to obtain an almost complete homogeneity in case of the miscible liquids, in case of the immiscible ones, the minor component is generally (but not necessarily) present as the dispersed phase (drops or filaments) in a continuous phase of the major component. In industry, the liquid mixing is generally achieved in vertical cylindrical vessels with some form of paddle or propeller stirrer to bring uniformity in the final mixture. These stirrers impart agitation to the system through radial, axial, or circumferential flow patterns. The vessel is rounded and not flat so that sharp corners which are the likely dead zones for mixing can be avoided. For the success of the mixing process, it is necessary to have an effective agitation of the components in the containing vessel. Agitation refers to the induced motion of a material in a specified manner, usually in the circulatory pattern inside some form of container. Agitation is generally accomplished by using mechanical impellers. The impeller creates a flow pattern in the system, causing the liquid to circulate through the vessel and return eventually to the impeller. The mechanical impellers broadly belong to two categories, namely, radial flow and axial flow types. The blades of an axial flow impeller make an angle equal to or less than 90° to the driving shaft to produce currents in the liquid primarily parallel to the impeller shaft. Propellers and fan turbines belong to this class. Propellers are widely used for agitating liquids of low viscosity with speeds varying from 400 to 1750 rpm. Radial flow impellers with blades parallel to the axis of the drive shaft produce currents in radial or tangential direction in the liquid. Paddles and turbines belong to this type of impeller. Normally, turbines have a number of short blades and operate at high speed while paddles are large slower-speed impellers with two or four blades.

The necessary flow patterns to facilitate mixing action in the vessel is the axial or longitudinal flow which is parallel to the impeller shaft caused by the rotation of

the impeller. In addition to the above flow patterns, however, some tangential flow following a circular path around the shaft takes place. This is undesirable as it creates a vortex at the liquid surface. To avoid this, baffles, which are vertical strips are fixed perpendicular to the tank wall. For normal sized tanks, four baffles are adequate for the purpose.

The most important parameter in the design of a stirred vessel for mixing is the power consumption. Flow patterns and mixing mechanisms vary widely for low and high viscosity systems. Here, the power consumption for low-viscosity Newtonian systems is considered.

Let, m = viscosity of the liquid, N⋅s/m2 r = density of the liquid, kg/m3 I = diameter of the impeller, m N = rotational speed of the impeller, rpm t = diameter of the tank/vessel, m, and P = power input to the impeller, N⋅m/s. From dimensional analysis, the following relationship is obtained for the calculation of power consumption in terms of dimensionless groups. P

ρN where,

3

5 I

ρN 3 D 5

⎛ ρN = f⎜ ⎝ μ

2 I

,

N2 g

= o er number,

I

,

t I

,

⎞ W M , ,......⎟ ⎠ I I

(9.1)

o,

ρ ND 2 = Reynolds number, R e , and μ N 2D = roude number, g

r.

The other dimensionless length ratios in the left-hand side bracket of Eq. (9.1) relate to specific impeller–vessel arrangement. So, in general terms (neglecting the length ratios which pertain to specific vessel–impeller combination) the above equation can be written as Po = f (Re, Fr)

(9.2)

As a power law function, the equation is Po = K Rem Frn

(9.3)

The values of K, m, and n are to be obtained from experimental measurements which depend on impeller–vessel configuration and the nature of flow (laminar/ turbulent/transition) prevailing in the mixer. In Eq. (9.3), the Froude number becomes significant only when there is gross vortexing and the propeller disturbs the liquid surface. It has been observed that below a Reynolds number of 300, the Froude number has little or no effect. The Froude

number affects power consumption only if vortex is present. Generally, vortex is avoided by putting baffles and hence in a baffled tank, the Froude number is not used in the power calculation. So, Eq. (9.3) becomes Po = K Rem

(9.4)

From Fig. 9.12 and 9.13 of McCabe, 1993, it is seen that for Re < 10, m = 1. So, the above equation reduces to Po = K (Re)−1 (9.5) Putting the expressions for Power number and Reynolds number, power input to the impeller is P = K m N 2 I3 (9.6) For the flow conditions with higher Reynolds number (>10), the value of the Power number can be obtained from the Fig. 9.12 and 9.13 of McCabe, 1993 and the power consumption can be calculated thereafter. At low values of the Reynolds number below about 300, the Power number vs. Reynolds number curve for both the baffled and the unbaffled tanks are identical. At a higher Reynolds number, vortex formation being prevalent, the power is influenced by the Froude number also and the equation is modified as Po

= K ′ ( Re ) F n The exponent n is related to the Reynolds number as n=

− log10 Re

(9.7)

(9.8)

where, a and b are constants and their values depend on the type of the impeller. The value of the Power number obtained from Po vs. Re plot for the unbaffled tank is multiplied with (Fr)n to get the correct value of Po, from which power consumption can be calculated.

Here,

I

= diameter of impeller = 0.6 m,

N = 90 rpm = 90/60 = 1.5 rps, m = 10 cP = 0.1 g/cm.s = 0.1 × 10−1 kg/m.s, and r = 1450 kg/m3. Thus,

e

=

ρ ND 2 (0.6) 2 × 1.5 × 1450 = = 78300. μ 0.1 × 10 −1

From the table, the value of Po may be taken as 6. gC = 6. Thus, ρN 3 D 5 So,

=

6 N 3 D 5 ρ 6(1.5)3 (0.6)5 × 1450 m.kg 232.7 = = 232.7 = = 3.005 hp is the gC 9.81 76.2 s

power consumption for the baffled mixer

Here, Re = 78300 The value of n (Eq. 9.8) =

and

(Ans)

Po = 6.0.

a − log10

e

=

1 − log10 78300 = − 0.097. 40

Since, Re > 300, the Froude number will effect the power consumption. Froude number,

r

=

N 2D (1.5) 2 × 0.6 = = 0.138. g 9.81

Thus, ( r ) n = (0.138) −0.097 = 1.212. Hence, the corrected power number = power number for baffled tank × (Fr)n = 6 × 1.212 = 7.272. Thus,

=

m.kg 282.1 7.272 × (1.5)3 × (0.6)5 × 1450 = 282.1 = = 3.7 hp. s 9.81 76.2

omment The power required for the same service is more in case of an unbaffled tank as compared to the baffled one: 3.7 − 3.05 × 100 = 21.3%. 3.05 Thus, the power consumption is reduced by 21.3% by making the vessel baffled (Ans)

Let us use the subscripts S for the small unit and L for the larger one. To preserve geometrical similarity, the dimensional ratios should be the same in the large tank as in the small. Given that the full scale tank is three times the model one. Thus, ( DT ) = 3( DT )S. Depth of large tank L = 3 S = 3 × 0.7 = 2.1 m. Propeller diameter in large tank = 3 ( I)S = 3 × 0.3 = 0.9 m. For dynamic similarly, (Re)L = (Re)S ⎛ D 2 Nρ ⎞ ⎛ D 2 Nρ ⎞ ⇒⎜ = ⎟ ⎜ μ ⎟ ⎝ μ ⎠ ⎝ ⎠S ⇒ ( D 2 N ) = ( D 2 N )S . So, N = large tank.

( D 2 )S N S (D 2 )

2

⎛ 1⎞ = ⎜ ⎟ × 450 = 50 rpm is the speed of the impeller in the ⎝ 3⎠

For the large tank, Re = (

2 I

) L N L ρ /μ = (0.9) 2 ×

50 1500 × = 155.8. 60 6.5

Since, Re < 300, the Froude number has no effect. With Eq. (9.4) and using K = 41 and m = −1. o

⇒

= 41(155.8) −1 3

⎛ 50 ⎞ − = 41(155.8) −1 × ( ρ N 3 D 5 ) = 41 (155.8) 1 × 1500 × ⎜ ⎟ × (0.9)5 = 134.8 J/s. ⎝ 60 ⎠ 1 hp = 746 watt (J/s). Thus, the power required to drive the motor =

134.8 = 0.18 hp. 746

(Ans)

Mixing of dry powders and granular solids, blending of pastes and plastic masses come under this category.

A mixing process begins with the components put together in some container with a suitable mixing device. With the progress of the mixing process, if samples are taken at different time intervals and analysed then the proportions of the components are found to approximate to the overall proportions of the components in the container. Complete mixing can be achieved when all samples tested are found to contain the components in the same proportions as in the entire mixture. Thus, the extent of mixing at a particular instant can be expressed in terms of the deviation of the sample compositions from the mean composition of the overall mixture. Mathematically, it can be expresses as 1 2 2 2 S 2 = ⎡( x 1 − x ) + ( x2 − x ) + ............. + ( xn − x ) ⎤ (9.9) ⎣ ⎦ n where, S = standard deviation; n = number of samples; x1, x2, . . . . . = fractional compositions of the component x in 1, 2, .., n samples respectively; x = mean fractional composition of the component x in the whole mixture; and S 2 = variance of the fractional sample compositions from the mean composition. Equation (9.9) can be simplified to 1 2 S 2 = ⎡⎣ ∑ ( xi ) 2 ⎤⎦ − ( x ) (9.10) n where, i refers to samples from 1, 2, .., n. If, So and Sr denote the initial and random values of S, there is a decrease in the value of S 2 with the progress of the mixing process. The course of mixing can be quantified through intermediate values between So2 and Sr2 and a term mixing index can be defined as under: =

So2 − S 2

(9.11)

So2 − Sr2

where, M = mixing index. If, 5% W is the desired mixture composition, then So2 = 0.05(1 − 0.05)

(9.12)

So2 (9.13) N where, N = number of particles in the sample analysed. Note For very small-sized particles, the value of N is very high and then N → •. And, Sr2 =

The rate of mixing is expressed by = K (1 − where, M = mixing index and K = constant.

)

(9.14)

On integration from t = 0 to t = t and M = 0 to M = M, we have (1 − M ) = e−K t ⇒ M = 1 − e−K t

(9.15)

The constant K depends on the type of the mixing equipment and the operating conditions. With the value of K known, Eq. (9.15) can be used to predict the degree of mixing after a given time interval and vice versa.

Although there is no necessary connection between energy consumption and the progress of mixing in well-designed mixers, energy input can be related to mixing process based on experimental investigations. In the mixing of pastes (e.g., plastics; flour dough in the food industry) using high-speed mixers, the energy consumed or the power input at any particular instant can be used to determine the necessary mixing time.

After 5 minutes, the compositions of NaHSO3 in the samples can be expressed in mass fractions as xi = 0, 0.165, 0.032, 0.022, 0.126, 0.096, 0.002, 0.046, 0.005, and 0.085. Here, n = 10 and x = 0.05 1 ⎡ ∑ ( xi ) 2 ⎤ − ( x ) 2 ⎦ n⎣ 1 ⇒ ⎡⎣ ∑ ( xi ) 2 ⎤⎦ − (0.05) 2 = 3.8 × 10 −3. 10

Using Eq. (9.10), we have S 2 =

Value of So2 = (0.05) (1 − 0.05) = 0.0475. So2 . N In the present case, since the number of particles are large (fine particles) N → •. Thus, Sr2 ≈ 0. Mixing index after 5 minutes: From Eq. (9.13), we have Sr2 =

5

=

So2 − S52 So2 − Sr2

=

0.0475 − 3.8 × 10 −3 = 0.92 0.0475 − 0

(Ans)

After 10 minutes, the compositions of NaHSO3 in the samples, expressed in mass fractions are xi = 0.034, 0.083, 0.072, 0.06, 0.043, 0.052, 0.067, 0.026, 0.043, and 0.02. 2 = S 2 (after 10 min) = 3.8 × 10−4. Using Eq. (9.10), S10 And mixing index after 10 minutes:

10

=

2 So2 − S10

So2

− Sr2

=

0.0475 − 3.8 × 10 −4 = 0.992 0.0475 − 0

(Ans)

Fractional content of dried vegetables = 0.35. Thus, (1 − P) = 0.65. S 2 0.2275 Now, So2 = 0.35 × 0.65 = 0.2275 and Sr2 = o = = 0.0091 as number of 25 N particles = 25. Mixing index after 4 minutes: S2 = 0.07 (given).

=

So2 − S 2 So2

− Sr2

=

0.2275 − 0.07 = 0.721, as 0.2275 − 0.0091

With Eq. (9.15), we have M = 1 − e−K t. Time, t = 4 min = 240 s. Thus, solving the above, K = 0.005317. Let, t = time in seconds, to get a variance (i.e., S 2) of 0.02 for the above condition. Let, M ′ = new value of mixing index. Thus,

′=

So2 − S 2 So2

− Sr2

=

0.2275 − 0.02 = 0.95. 0.2275 − 0.0091

With Eq. (9.15) we have 0.95 = 1 − e−0.005317 t. Solving, t = 563 seconds. Thus, additional mixing time required to reach the desired composition = 563 − 240 = 323 seconds (Ans)

3

Average current drawn in the first 10 seconds = Energy consumed in first 10 seconds,

= power × time

75 + 375 = 225 amp. 2

= 3 V I (cos j) h q watt hour (where, h = mechanical efficiency and q in hours) ⇒

= 3 × 440 × 225 × 0.9 × 0.7 ×

10 300 = 300 watt hour = = 0.2 watt.h/kg. 3600 1500

Total energy consumed = 7.5 watt.h/kg. Further, energy consumed per kg = 7.5 − 0.2 = 7.3 watt.h. After 10 seconds, a steady current of 375 amp is drawn. Additional time required will be 7.3 × 1500 × 3600 3 V (cos ϕ )η 7.3 × 1500 × 3600 = = 218.94 s ≅ 219 seconds. 3 × 440 × 375 × 0.9 × 0.7 Thus, total mixing time = 10

219 = 229 seconds = 3.82 minutes

(Ans)

Mixtures of solids and liquids are blended in different types of equipment depending on the physical characteristics of the mixture. The mixing equipment, hereafter mixers, are generally of three types: liquid mixers, solid (dry powder) mixers, and paste or viscous mixers. Pumpable suspensions with thin consistency are normally handled in tanks agitated with an impeller or fluid jet while non-flowing pastes are handled in slow speed non-circulating mixers.

Mixing of miscible liquids, dispersing immiscible liquids, heat transfer in agitated liquid, suspension of solids in liquids, etc. are generally carried out in agitated vessels (Fig. 9.1) by using mechanical impellers, which are broadly classified into two types: axial and radial. In axial flow impellers, the impeller blade makes an angle equal to or less than 90° with the plane of impeller rotation. As a result, the locus of flow occurs along the axis of the impeller (parallel to the impeller shaft), e.g., marine propellers and pitched blade turbine. While in radial flow impellers, the impeller blade is parallel to the axis of the impeller, and as a result, the radial-flow impeller discharges flow along the impeller radius in distinct patterns, e.g., flat blade turbine, paddle, and anchor. A few of the impeller designs are shown in Fig. 9.2.

in

i

d di

The mechanism of solid mixing, known as blending, is generally based on diffusion and convection. Diffusion blending is characterised by small-scale random motion of solid particles, whereas, convection blending is characterised by large-scale random motion of solid particles. Diffusion blending occurs where the particles are distributed over a freshly developed interface. Tumbler blenders like the V-blenders and double cone blenders function by diffusion mixing. In convection blending, groups of particles are rapidly moved from one position to another due to the action of a rotating agitator or cascading of material within a tumbler blender. The blending of solids in ribbon blenders

and vertical-cone screw blenders is mainly due to convection mechanism. A few equipments are discussed here. The V-blender is one of the most commonly used tumbling blenders, which is based upon the action of gravity to cause the powder materials to cascade within a rotating vessel. A V-blender essentially consists of two hollow cylindrical shells joined together at an angle of 70° to 90°, as shown in Fig. 9.3. The blender shell is mounted on trunnions to allow it to tumble on a horizontal axis. The material to be mixed is charged into the blender through either of the two upper ends. As the blender tumbles, the dry powder material continuously splits and recombines, with the mixing occurring as the material free-falls randomly inside the vessel. And the homogeneous material is discharged generally from the apex port. The blending efficiency is largely affected by the volume of the material taken inside the blender vessel. The recommended fill-up volume for the V-blender is generally 50 to 60% of the total blender volume. The blending efficiency is also affected by the blender speed and size. At lower blender speeds, the shear forces are low while at higher blending speeds, due to more shear, greater dusting is observed. There is a critical speed above which the blending efficiency decreases considerably. The V-blenders are generally operated at 50 to 80% of the critical speed. Also, with the increase in blender size, the rotational speed decreases.

Unique Mixers and Furnaces V-blenders are available in all grades of carbon and stainless steel materials with working capacities of 5 to 5000 litres. V-blenders have the following advantages: (i) (ii) (iii) (iv)

due to the absence of any moving blades fragile materials can be handled; they offer both short blending times and efficient blending; charging and discharging of material is easy; and they are easy to clean and maintain.

V-blenders are most often used for the dry mixing of free-flowing powders and are generally used for food products, milk powder, coffee, ceramic powders, pigments, pesticides and herbicides, plastic powders, fertilisers, baby foods, and cosmetics. A vertical cone screw blender essentially consists of a conical vessel to which a screw agitator is attached that rotates about its own axis while orbiting around the vessel s periphery, as shown in Fig. 9.4. The drive system of this type of blender consists of two motors–one for the rotation of the main drive, while the second one for the rotation of the screw. The screw is supported from the top drive assembly. The material to be mixed is charged from the top of the vessel. During its operation, as the screw shaft rotates around the periphery of the cone, the material is lifted from the bottom section of the vessel to the top section. And the mixing is effected by the differential travel speeds of product particles in the conical section of the vessel. The mixed material is generally discharged through a valve located at the bottom of the cone. Since the effective blending volume at any given time is a lot lesser than the horizontal blenders, it results in a lower power requirement. The screw rotates at low speeds, generally between 35 to 100 m/min. Thus, the blending action in the vertical-cone screw blender is much gentler than that taking place within the horizontal blenders. Advantages of the vertical-cone screw blender include (i) gentle blending action is ideal for friable or shear sensitive materials and also for heat sensitive products; (ii) wear is lower because of lower operating speed; (iii) flexibility of batch size; (iv) near 100% of the mixed materials are discharged;

(v) lower risk of contamination; (vi) easy cleaning; (vii) homogenous mixing; (viii) lower power requirements; and (ix) occupies less floor space. These blenders require a high head room for operation. Unique Mixers and Furnaces vertical cone screw blenders are available in all grades of carbon and stainless steel materials with working capacities of 5000 to 50000 litres. These blenders are best suited for dry mixing of free-flowing powders, granules requiring low shearing force and are excellent for bulk drugs and chemicals.

Mixing of heavy pastes, dough, plastic masses, and rubbery products require heavyduty machines, which involve stretching, folding, and compression of the masses many times before the final mixing is effected. The popular viscous mixers are the kneading machines, known as kneaders, which are slow-speed machines requiring high energy. IKA kneading machines are of three different types: (i) the horizontal kneading machines: IKA -DUPLEX and ZETA; (ii) the vertical kneading machines: PLANETRON ; and (iii) the continuous kneading and extrusion machine: CONTERNA. IKA horizontal kneading machines of HKD and HKS types are twin-bowl kneading machines with horizontally arranged kneading shafts which differ in their kneading tools. The HKD type is equipped with DUPLEX kneading blades, deeply intermeshing and stripping each other. The different speeds of the kneading blades (speed ratio 2:1) cause the kneading blade surfaces to alternately move towards and away from each other. This results in high pressure-, tensile-, and shear forces and thus in high friction within the kneading product which cares for excellent dispersing and homogeneity. The HKD kneading machine is shown in Fig. 9.5. The HKS type is equipped with two ZETA kneading blades, which distinguish by left-hand and right-hand twisting. This twisting of the Z-blades causes continuous movement of the material from the kneading bowl walls to its centre or vice versa, depending on the direction of rotation. The different speed of the counter rotating kneading shafts (speed ratio 5:3) creates high pressure and shear forces resulting in an intensive mixing. The use of these kneading blades patented by IKA results in a substantially improved product homogeneity and a saving of up to 30 % of kneading time compared to the classical Z-kneaders. Vaccum-tight and double-jacketed kneading bowls, high-quality stainless steel for all parts in contact with the product and high-quality shaft seals with easy access for service and maintenance are part of the IKA basic equipment. The applications of IKA horizontal kneading machines include glues (e.g., hotmelts); rubber masses; plastic mixtures; ceramic masses, porcelain; colour mixtures (e.g., printing inks); carbon pastes; and graphite mixtures.

IKA vertical kneading machines of PLANETRON type are equipped with two DUPLEX-like kneading blades, as shown in Fig. 9.6. The design of the PLANETRON allows for a bearing of the kneading shafts as well as their sealing outside the product area. Thus, absolutely clean masses can be produced. The excellent kneading and dispersing effect is based on the principle of intermeshing kneading blades, where one kneading blade is planetarily rotating around the central kneading blade and both blades are stripping each other. Thus created increasing and decreasing pressure and shear forces result within shortest time in an intensive kneading and finest dispersing of the product to be kneaded. Compared to the classical planetary mixer with only one drive motor, the IKA PLANETRON vertical kneading machine in the execution with three drive motors enables–additionally to the speed adjustment–a variable adjustment of the speed relation of the two kneading blades. Due to this fact, also very sticky masses like hot melts can now be processed in a vertical kneading machine. In standard planetary mixers, these masses climbed up at the kneading blades and were thus no more affected by the shear forces. PLANETRON heavy-duty kneading machines work with kneading blades that are only one-sided, running on bearings. Thus, the product to be kneaded neither comes into contact with seals nor with bearings, resulting in highest product purity. The applications of IKA vertical kneading machines include dental masses; ceramic masses; pharmaceutical and cosmetic products; plastics; and food. IKA continuous kneading machines of CONTERNA type (HKC type) are a continuously working multi-chamber kneading and extrusion machines having a modular design, i.e., according to application and the requested results the number of kneading chambers as well as the execution

of the kneading tools and the discharge modules can be varied. This flexibility of the CONTERNA adapted to the product requirements enables an adjustment of the product residence time in the machine individually adjusted to each application. Figure 9.7 shows a continuous kneading machine. While due to its design, the residence time in a classical extruder is relatively short and thus an energy input is limited to a certain time, the continuous multi-chamber kneading system allows for an infinitely adjustable residence time of the product. The CONTERNA design enables several process steps in one machine like mixing, kneading, rolling, and extruding of medium to high viscous media. IKA continuous kneading machines have the following advantages compared to batch processes: (i) less machine and personnel requirements, and (ii) constant quality over time.

The applications of I A continuous kneading machines include rubber masterbatches; plastics masterbatches; glues; sealing masses; food, animal food; and silicone rubber.

❑ ❑ ❑ ❑ ❑ ❑ ❑

❑

=

ρNDI2 , μ

=

N 2 DI . g

=

P , ρN 3DI5

❑

❑ ❑

❑ n=

a − log10 Re . b

Po = K ′ ( Re )

m

( Fr )n ,

❑ ❑ ❑ ❑ ❑ ❑ ❑ ❑ ❑ ❑

1. Why are mixing vessels rounded and not flat bottomed Mixing vessels are rounded and not flat bottomed so that sharp corners which are the likely dead zones for mixing can be avoided.

2. What are the different types of mechanical impellers The mechanical impellers are of two types: radial flow type and axial flow type.

3. What types of liquids can be handled by propeller mixers Liquids of low viscosity can be handled by propeller mixers. 4. What is the difference between a propeller and a paddle mixer The propeller mixer is of axial-flow type while a paddle mixer is of radial-flow type. 5. What is the value of the Reynolds number for which its exponent is minus units -1 in the Power number Eq. 9.4 The value of the Reynolds number is less than 10. 6. Under identical operating conditions and vessel dimensions, what is the effect of baffles on power consumption Power consumption in an unbaffled tank will be more compared to that in a tank with baffles. 7. What are the different types of mixers used in process industries The different types of mixers used are liquid mixers, dry powder mixers, and paste or viscous mixers.

1. What is mixing 2. How are non-flowing pastes handled in a mixer 3. How does the mixing of miscible liquids differ from that of the immiscible ones 4. How does a turbine-type impeller differ from a paddle type 5. Why are baffles used in liquid mixers 6. What is the value of the exponent for Reynolds number in the Power number Eq. (9.4) when Reynolds number is less than 10

8. What are kneaders Kneaders are slow-speed high-energy consuming machines used for mixing of heavy pastes, rubbery products, plastic masses, etc. 9. Name the various functions of a kneader while mixing heavy pastes. The various functions are stretching, folding, and compression of mass. 10. What are the different types of kneading machines The different types are horizontal kneaders, vertical kneaders, and continuous and extrusion kneaders. 11. What is the mechanism of mixing in V-blenders The mechanism of mixing is diffusion mixing. 12. What is the design speed of V-blenders The design speed is 50–80% of the critical speed. 13. What is the rotational speed of the screw in the vertical-cone screw blenders The rotational speed is 35–100 m/minute.

7. How is mixing index related to mixing time 8. Give the special features of the CONTERNA-type (HKC type) continuous kneading machine. 9. Name the blenders which function on the mechanism of convection mixing. 10. Give a few advantages of V-blenders. 11. Name a few process applications for V-blenders. 12. Give the advantages of vertical-cone screw blenders.

1. A solution of sodium sulphate with a density of 1700 kg/m3 and a viscosity of 40 mNs/m2 is to be agitated by a propeller mixer of 0.6-m diameter in a baffled tank of 2.4-m diameter where the liquid depth is 2.4 m. The propeller is situated 0.6 m above the bottom of the tank. For a rotational speed of 2 revolutions per second, what will be the power consumption by the motor to drive the propeller Note Power number remains almost constant at a value of 6.0 for Reynolds number above 10,000. 8.49 hp 2. An unbaffled tank uses a flat-blade turbine-type impeller installed centrally positioned 0.7 m from the bottom of the tank. The tank is 2.1 m in diameter and the turbine is 0.7 m in diameter. The tank is filled to a depth of 2.1 m with a solution of 50% caustic soda. The turbine is operated at 120 rpm. Estimate the power consumption for the operation of the mixer.

1. The speed of propellers in mixing vessels for liquids vary from (a) 100–1000 rpm (b) 200–1200 rpm (c) 400–1750 rpm (d) 500–2250 rpm 2. For a normal-sized liquid mixing vessels, the number of baffles used is (a) 4 (b) 6

ata Density of 50% caustic soda solution = 1490 kg/m3, Viscosity of this solution = 11.5 cP, and value of constants: a = 1.0 and b = 40.0. 18.3 hp 3. Analysis of the sodium bicarbonate content of samples from a mixture of NaHCO3 and Na2CO3 in which the overall NaHCO3 was 15%, gave the following results expressed as percentages: 23.4, 10.4, 16.4, 19.4, 30.4, and 7.6. For this mixture, estimate the values of S 2, So2, and Sr2 if the samples are 5 g and the NaHCO3 and Na2CO3 are in 0.05 g particles in the mixture. S2 = 0.64 ¥ 10-2, So2 = 0.1275, and Sr2 = 1.275 ¥ 10-3 4. If the sample in example 9.4 was taken 8 minutes after the initial separate ingredients i.e. NaHCO3 and NaCO3 were mixed, find the value of the mixing index after a further mixing for 6 minutes. 0.996

(c) 8 (d) 10 3. The Froude number has negligible effect in power calculation, when the Reynolds number value is (a) less than 100 (b) less than 300 (c) less than 1000 (d) less than 3000

4. For colour mixtures (e.g., printing inks) the mixing machine used is (a) horizontal kneader (b) vertical kneader (c) continuous kneader (d) turbine mixer 5. IKA continuous kneading machineHKC type can be used for the mixing of (a) glue (b) animal food (c) silicone rubber (d) all of the above

1(c);

2(a);

3(b); 4(a); 5(d);

6. The angle between the two hollow cylindrical shells of the V-blender is (a) 30°–45° (b) 45°–60° (c) 60°–75° (d) 70°–90° 7. Recommended fill-up volume for the V-blender is (a) 30–40% (b) 40–50% (c) 50–60% (d) 60–70%

6(d); 7(c)

x

+ A

+ F

d

In a size-enlargement operation, small particles are brought together purposely to form larger ones, generally by some mechanical means. The size-enlargement operations are many, namely, agglomeration, granulation, compaction, encapsulation, pelletising, sintering, etc., and the agglomeration method is discussed here in brief. Size-enlargement operations are followed in the process industries with a wide variety of objectives, such as (i) (ii) (iii) (iv) (v) (vi) (vii) (viii)

to improve storage and handling characteristics of materials; to improve flowability and dosability; to minimise dusting or material losses; to create a safe working environment; to increase or control bulk density; to control solubility and dispersibility; to produce a product of definite shape and size; and to enhance appearance.

A few applications of size-enlargement operations are associated with the following: (i) (ii) (iii) (iv) (v)

fertilisers (urea, ammonium nitrate); pharmaceuticals (tablets); chemicals (organic, inorganic, agricultural, ceramic); coal fines; minerals;

(vi) instant foods (milk powder, coffee powder, dry soups, flours); (vii) detergents; and (viii) animal feeds.

Agglomeration is a process, where fine particles are brought together in a loose state of binding to form larger particles and is a value-added step in a solids-processing plant. While some materials possess the inherent quality to agglomerate in their tiny form, others require the addition of binders or the application of heat or pressure for the purpose. Binders condition the surface of the particles to develop adhesive properties. Moistening with small amount of water, solvent, or oils, increases the surface adhesion and causes the particles to gather into larger ones.

The type of end product is the key factor in selecting a proper equipment for agglomeration. The selection of equipment mainly depends on (i) (ii) (iii) (iv) (v)

particle size distribution; shape; hardness; solubility and dispersibility; and binder addition.

The equipment are based on the type of agglomeration process adopted, which can be categorised into (i) (ii) (iii) (iv)

press agglomeration; composite agglomeration; extrusion agglomeration; and thermal agglomeration.

This is a dry method of agglomeration requiring little or no binder addition. Material masses are subjected to a pressure in excess of 2000 kg/cm2 which results in partial crushing and realignment of the individual particles. Further close proximity of the particles leads to binding as a result of inter-particle forces. This method is applied to cases where (i) large particles (> 25 mm) or particles of controlled size are desired; (ii) high density or resistance to attrition is required; and (iii) binder addition is not permissible. The equipment under this category are roll compactors, tablet presses, and piston presses. In a Kompaktor , a type of double-roll compactor, the finely dispersed bulk material is fed by means of a pre-densifier screw to the nip area of two compacting rolls working in opposite direction. On the one hand, the pre-densifier screw is responsible for the preliminary aeration of the material and on the other hand for the pressure build-up in the roll gap. The nip area of the rolls and, therefore, the proper compacting area, begins when the relative speed between the product and the roll

surface goes towards zero. To receive a final product with a granule bulk weight > 1.000 g/l later, a flake density of 2.1 g/cm3 minimum must be achieved. This density is achieved without any problems when using a ompaktor type MS 300 (Fig. 10.1) with a roll diameter of 712 mm, roll width of 310 mm, roll drive of 315 kW, roll speed of 28 rpm, and an effective specific press force of 100 kN/cm2 working width. Size enlargement of powders by roll compactors is of two types: compaction and bri uetting. Fine powders are compacted and pressed into a solid form called fla es by using either smooth or profiled rolls. The flakes are gently milled to the required particle-size distribution as required by the process. The compaction benefits are insuring good flow properties; increasing bulk density; particle-size control; low energy consumption; minimal product heating; dust-free processing; and good dosing properties. Figure 10.2 shows the compaction operation while flakes produced are shown in Fig. 10.3.

+

+

+

+

Figure 10.4 shows the briquetting operation. Briquetting processes utilise specially made compaction rolls enabling production of a variety of sizes and shapes. Typical shapes include pillow, almond, and stick, as shown in Fig. 10.5. Figure 10.6 shows two of the roll patterns: integral roll (options for alloy overlay against corrosion or welded-on hardfacing) and roll tires (made of stainless steel). This is a wet method of agglomeration handling fine powders as feed material. The material masses are combined with a binder and subjected to rolling or tumbling process resulting in loose agglomerates. Agitation can be high or low and binding is generally achieved through liquid bridges or chemical reaction. The units used for tumbling agglomeration include drum or cone mixers, pan or disc agglomerators, and pin or paddle mixers. A few products made by tumbling agglomeration include detergents, instant drink mixes, and agricultural chemicals. Good flowability, low density, rounded shape, and easy dispersion are common characteristics of the above materials. This method is practised when (i) the feed is a wet cake or paste; (ii) spherical shape or pellets are desired; and (iii) small and uniform-sized particles are desired.

n

i

In extrusion agglomeration, feed materials are subjected to forces pressing them through a die plate to form pellets. The feed must be a wet cake, paste, or dough. In addition, it must either have a melting component or a binder, or moisture must be added to it, so that it is formable by the die.

Equipment for this type of agglomeration process include single screw extruder, gear pelletiser, basket-type extruder, and pellet mill. Figure 10.7 shows a gear pelletiser and its material flow diagram. Dry, moist, or pliable materials are formed into pellets using a pelletiser.

+

+

A few products made by extrusion agglomeration include animal feeds, wood products, and polymers. Products from the process are cylindrical in shape with diameter between 1 to 10 mm and of fairly uniform length. Extrusion agglomerates will have a density between those of the tumbling and pressure agglomerates. Heat-transfer processes are used to effect agglomeration in this case. The processes include sintering through heat application, solidification through cooling, or coagulation through melting. Drum flakers, rotary kiln modulisers, and prilling towers are the equipment used in this process. A common example of thermal agglomeration is a prilling tower using hot melt as feed material falling in the form of droplets through the tower against a counter-current flow of air. The product comes out as hard and nearly spherical with a typical size of 300 microns. With greater falling distance, large-sized products can be obtained. A prilling tower is generally followed by a fluid-bed dryer to get dry agglomerates. Products from thermal agglomeration include stearic acid prills, urea prills, fatty acids, and gelatin.

The phenomenon of the formation of solid particles within a homogeneous phase like solution, melt, or vapour is called crystallisation. However, the discussion here will be limited to that of solutions only. Crystallisation from solution is an important industrial operation since a large number of marketed products are crystalline. Further the crystals, product of any crystallisation process, usually separate out as a substance of definite composition from a solution of varying compositions. Thus, the process of crystallisation can be practised for the two basic purposes, namely, crystal production and product purification. For crystallisation to occur from a solution, it must be supersaturated. That is to say, the solution has to contain more solute dissolved than it would contain under equilibrium conditions, i.e., in its saturated state. To achieve this, one of the following methods is followed: (i) cooling of the solution; (ii) addition of a second solvent for the reduction of solubility of the solute—a technique called anti-solvent; (iii) chemical reaction; (iv) change in pH; and (v) solvent evaporation. While the feed solution giving rise to the formation of crystals is called the mother liquor, the two-phase mixture of the mother liquor and crystals withdrawn as product from the crystallisation process is called the magma. The crystallisation process consists of two major steps, namely, (i) nucleation, and (ii) crystal growth. ucleation is the step when the dispersed solute molecules in the solvent begin to flock into clusters on the nanometer scale. A stable cluster conforming to some

defined atomic arrangement results in a desired crystal structure to form an ultimate stable nucleus of critical size. Such critical size is dictated by the operating conditions, i.e., temperature and supersaturation. The crystal growth is the subsequent enlargement of the nuclei which succeed in achieving the critical cluster size. Nucleation and crystal growth continue to occur simultaneously while the supersaturation exists. Supersaturation being the prime driving force, the local operating conditions will decide whether nucleation or growth is predominant over the other and as a result, crystals of various sizes and shapes are obtained. With the supersaturation condition exhausted, the solid–liquid system reaches equilibrium and the crystallisation process comes to an end unless the operating conditions are modified to alter the equilibrium. The problems generally confronted by the engineers relating to crystallization are (i) (ii) (iii) (iv) (v)

yield and purity of a given product; size and shape of the individual crystals; energy requirement for the process steps like cooling, evaporation, etc.; uniformity or size distribution of the crystals; and rate of production of the desired crystals.

The average size to which crystals are grown may be decided by the use to which they are put such as granulation of sugar or the preparation of salts for various use. Normally, fine crystals have chance for agglomeration, occlude less mother liquor, but with the relatively greater surface area they create greater difficulty for the complete removal of the mother liquor.

A well-formed crystal is generally pure, but it retains mother liquor when removed from the magma. Filtration or centrifuging removes most of the mother liquor while the balance is removed by washing with fresh solvent. Effectiveness of purification primarily depends on the size and the uniformity of crystals. Many of the important inorganic substances crystallise with water of crystallisation to maintain the crystalline structure. A salt with water of crystallisation is called a hydrate. Removal of this water makes the crystalline substance amorphous. A few inorganic hydrates are given in Table 10.1.

C emical formula CuSO4.5H2O ZnSO4.7H2O MgSO4.7H2O Na2SO4.10H2O CaSO4.2H2O (CaSO4)2.H2O CaCl2.6H2O FeSO4.7H2O K2SO4.Al2(SO4)3.2H2O

C emical name

Common name

Copper sulphate pentahydrate Zinc sulphate septahydrate Magnesium sulphate septahydrate Sodium sulphate decahydrate Calcium sulphate dihydrate Calcium sulphate hemihydrate Calcium chloride hexahydrate Ferrous sulphate heptahydrate Potassium Aluminum sulphate dihydrate

Blue vitriol White vitriol Epsom salt Glauber s salt Gypsum salt Plaster of paris Dow flake Green vitriol Potash alum

Some crystalline solids do not contain water of crystallisation. A few examples are potassium chloride (KCl), sodium chloride (NaCl), potassium nitrate (KNO3), sodium nitrate (NaNO3), ammonium sulphate (NH4)2SO4, and silver iodide (AgI). If the crystals are anhydrous, the solid phase contains no solvent and the calculation is straightforward from the material balance. For crystals with water of crystallisation, the accompanying water must be considered in the material balance and accordingly, the crystal yield is calculated. Say, F = amount of feed solution, kg; M = amount of mother liquor left after crystallisation, kg; C = amount of crystals formed, kg; E = amount of evaporation during crystallisation, kg; xF = solid fraction in feed solution, kg solid per kg total solution; xM = solid fraction in mother liquor, kg solid per kg of mother liquor; and xC = solid fraction in crystals, kg solid (free of water of crystallisation) per kg of crystal formed. Thus, the overall material balance is F = M C E (10.1) and the solid balance is FxF = MxM CxC (10.2) And, xC = 1 for crystals formed without water of crystallisation.

Molecular weight of FeSO4 = 152 and of FeSO4.7H2O = 278. Solubility at 50°C is 140 parts of FeSO4.7H2O per 100 parts of excess 152 water = × 140 = 76.55 parts FeSO4 per 100 parts of water. 278 76.55 So, x = = 0.434. 100 + 76.55 Solubility at 18°C is 75 parts of FeSO4.7H2O per 100 parts of excess 152 water = × 75 = 41 parts of FeSO4 per 100 parts of water. 278 41 So, x = = 0.291. 100 + 41 152 = 0.547. And, xC = 278 From Eq. 10.1, we have F = M C E Since, E = 0, we have M = F − C. And from Eq. 10.2, we have FxF = MxM CxC ⇒ F × 0.434 = (F 1000) × 0.291 (100 × 0.542) ⇒ F = 1790.2 kg is the feed to crystalliser

(Ans)

Amount of KCl present = 2500 kg. Solubility of KCl at 90°C is 54 parts per 100 parts of water. 54 = 0.3506. 154 At 20°C, solubility of KCl is 35 parts per 100 parts of water.

So, x =

So, x =

35 = 0.259. 35 + 100

Amount of solution cooled at 90°C = 2500 ×

154 = 7129.6 kg. 54

7129.6 = 5.94 m3 . 1200 Thus, the required capacity of the tank = 5.95 m3 Now, from Eq. (10.2), we have FxF = MxM CxC ⇒ 7129.6 × 0.3506 = (7129.6 – C) 0.259 C (as xC = 1 and M = F ⇒ C = 881.3 kg is the weight of crystals obtained Volume of the solution =

(Ans) C) (Ans)

The crystallisation equipment, hereafter crystallisers, are of two main types: cool ing crystallisers and evaporative crystallisers. Tank and scraped surface types are two cooling crystallisers while forced circulating–liquid evaporator and circulating– magma vacuum types are two evaporative crystallisers. A few are discussed here. It is the simplest and the oldest type of equipment for crystallisation still used in some specialised cases. A saturated solution is allowed to cool by natural process and some evaporation may also occur to the atmosphere. Advantages of this type of crystalliser include (i) simple construction and low first cost; (ii) favours formation of large size crystals; and (iii) economical process for crystallisation of small quantity of materials. However, these types of equipment have a number of disadvantages like (i) batch process; (ii) no control over crystal size; and (iii) inefficient with regard to yield per unit floor space or unit time due to slow rate of cooling.

It is a continuous crystalliser which can be either of (i) single scraped surface or (ii) double–pipe scraped surface. The Swenson–Walker crystalliser is of single scraped surface type crystalliser and is a more commonly used scraped surface crystalliser. It consists of an open trough of about 60 cm wide with a semicircular bottom cross-section to provide the heat exchange surface between the annular cooling water jacket and the crystallising solution which is in the trough. Cooling can also be effected by circulating through a hollow screw conveyor or some hollow discs attached a rotating longitudinal axis which plunges in the solution of the trough. Crystals precipitate on the cold surface of the screw and the discs from which they are removed by scrapers. The crystalliser is normally built in 3-m long sections of which up to 4 sections can be operated with a single drive. For the removal of crystals from the end of the crystalliser, an inclined spiral flight conveyor is used which lifts the crystals either to a drain board or to a conveyer for transporting to centrifuge. Double-pipe scraped surface crystallisers also called votator crystallisers and they can be of two types: (i) double-pipe heat exchanger type construction fitted with internal helical ribbons with cooling water in the annular space and the crystallising solution in the tube, and (ii) a double-drum apparatus with the inner drum rotating rapidly and the crystallising solution entering to the annular space between the two drums. The cooling is effected by a cooling jacket surrounding the outer drum. A double-pipe scraped surface crystalliser is used in crystallising ice cream and plasticising margarine. Both crystallisation and evaporation are combined here which become the driving force for the supersaturation.

Feeding is one type of conveying operation, generally used to transport materials over a short distance. Feeding is necessary to deliver solid materials (dry or moist fractions of rock or minerals) at a uniform rate into solids-handling processes like crushing, grinding, screening, classification, transportation, mixing, weighing, etc., because these processes show better results at a uniform feed rate. A feeding equipment, hereafter feeder, essentially consists of a bin and a conveyor. A great variety of feeders are available and a few popular ones discussed here are apron feeders, vibrating feeders, and POSIMETRIC feeders.

Figure 10.8 shows an apron feeder. Metso Minerals apron feeders are available in a wide variety of sizes and meet the material handling needs in feeding and controlledquantity applications in mining, quarrying, and basic industrial operations. They can be used with dry, wet, or sticky materials and operate in polluted or corrosive environment. The feed capacity depends on the feeder width, material layer height, conveyor speed, material type and size, and fill factor [Metso, 2007].

C ain speed m min

C ain idt mm tonne

3 5 7 9 11

64 107 150 192 235

mm

m 40 67 93 120 147

tonne 107 178 248 320 390

m

mm tonne

67 111 155 200 244

150 248 350 448 550

m 93 155 218 280 343

mm tonne 240 400 560 720 880

m 150 250 350 450 550

* Always considering materials with bulk density of 1.6 tonne/m3. (for STPH multiply by 1.1)

Table 10.2 shows feed capacity details of apron feeders. The feed capacity of apron feeders is given by QA = 60 × B ×

× rb ×

A

×j

(10.3)

where, QA = feed capacity the apron feeder, tonne/h; B = hopper width, m; = height of the layer of material to be conveyed, m; rb = material bulk density, tonne/m3; A = conveyor speed, m/min; and j = fill factor.

Vibrating feeders are generally designed to handle large-size materials and are mainly used to feed primary crushers. Figure 10.9 shows a vibrating feeder. Sometimes these

are compared with grizzly screens as they remove the fines to bypass the primary crusher. These have a low purchase cost when compared to apron feeders. Metso Minerals vibrating feeders are available in different sizes, with a capacity range of 25 to 1500 tonne/h (15 to 1000 m3/h). The capacity of vibrating feeders is calculated using the following formula: QV = 3600 × j1 × j2 ×

× L × , m3/h

(10.4)

where, j1 = size factor, (1 for sand, 0.8 to 0.9 for crushed stone up to 6″, and 0.6 for sizes over 6″) j2 = moisture factor, (1 for dry material, 0.8 for wet material, and 0.6 for clayish material) = speed of the flow of material on the vibrating plate according to the graph shown in Fig. 10.10, as a function of rotation (rpm) and amplitude (mm), L = table width, and = height of the material layer on the table, which depends on the load type and the size of the material and which may not exceed the following: ≤ 0.5 × L for large stones, ≤ 0.3 × L for crushed stone up to 6″, ≤ 0.2 × L for sand and small stones. In Metso vibrating feeders, amplitude a can be adjusted from 3 mm to 7 mm by changing the eccentric weights. General characteristics of apron and vibrating feeders are briefed in Table 10.3.

V /

7 6

0

5

4

02

01

500

600 /

700 .2 25.4

00

00

Mac ine

Apron feeder

ibrating feeder

Capacity range

Up to 10,000 tonne/h

Up to 2,000 tonne/h

Max. size of material

Up to 50 % of chain width

Up to 80 % of table width

Main applications

– Heavy-duty use – Primary feed – Reclaiming of large volumes

– Heavy-duty use – Feeding of primary crushers – Reclaiming where large sizes are involved

Advantages

– High impact strength – High load per unit area – High availability – Good flow control – Ability to lift the material – Length according to needs – Reduction of plant height – Good handing of clayey materials with high moisture content

– High operating safety – Pre-separation of fines – Easy and reduced maintenance – Good feed control – Low purchase cost

Disadvantages

– High purchase cost – Bad sealing (accumulates fines requiring a belt or a chain conveyor for maintaining cleanness) – Does not classify or scalp fines

– Inability to be used to lift material – Limited length – High installed power – Lower capacity with material that is clayey or has higher moisture content; may become inoperative under certain conditions

(for STPH multiply by 1.1)

From Eq. (10.4), the capacity of the feeder is QV = 3600 × j1 × j2 × × L × . Here, j1 = 0.8 for stone size of 6″ (conservative value is taken instead of 0.9) and j2 = 0.8. = 0.3 L = 0.3 × 1.0 = 0.3 m.

From Fig. 10.10, for 800 rpm and 4 mm amplitude, Thus, QV = 3600 × 0.8 × 0.8 × 0.2 × 1.0 × 0.3

= 0.2 m/s.

2650 = 366.34 tonne/h. 1000 Hence, the available feed is not suitable. Modification in design Let, L = new table width. Thus, = 0.3 L. So, 400 = 3600 × 0.8 × 0.8 × 0.2 × 0.3 L × L × (2650/1000) Solving, L = 1.045 m. Hence, a vibrating feeder with a width of 1.045 metres will be required for this purpose (Ans) = 138.24 m3 /h = 138.24 ×

For 700 rpm and 3-mm amplitude, = 0.1 m/s (Fig. 10.10). Here, j1 = 0.8 and j2 = 1.0. = 0.28 L. Thus, QV = 3600 × 0.8 × 1.0 × 0.1 × 1.5 × 0.28 × 1.5 = 181.44 m3/h. Thus, for dry dolomite the capacity of the feeder = 181.44 × 2.8 = 508 tonne/h. Keeping all other operating conditions same and considering limestone to be dry, the capacity of the feeder = 181.44 × 2.65 = 480.8 tonne/h (Ans)

Pennsylvania POSIMETRIC feeders are designed to handle wet, dry, lumpy, sticky, abrasive, or granular materials. These feeders are virtually immune to jams and can accept dry, light particles at 544.32 kg/h (1,200 pounds per hour), or heavy sticky materials at 3398.4 m3/h (120,000 cubic feet per hour). Figure 10.11 shows a POSIMETRIC feeder. This feeder delivers materials with high accuracy of up to 99.5 per cent, unless the material changes. Regardless of moisture content, this delivers materials at a constant rate with each rotation delivering a fixed volume. This feeder essentially consists of a single moving part—the rotating duct. Because the feed material helps to turn this duct, only a small motor, usually less than 10 hp is required to drive it. This results in very low stresses. In addition, wear is negligible because there is almost no abrasive action of material against the working parts. The maintenance is also low for these feeders. Pennsylvania, 2006 .

With capacity enhanced and to save on labour, automatic weighing of solids has been largely adopted in chemical process plants in place of manual weighing. Further, automatic weighing is more dependable from the point of view accuracy. The weighing of bulk solids can be either batch or continuous.

In case of batch weighing, a given unit of batch is measured and then the desired total weight is to be obtained through multiples of the given unit. To carry out small weighings either singly or a few in sequence, batching scales are used. In most of the batch scales, a vessel is mounted on a beam which is counterbalanced by a set of weights nearly equal to the desired weighing. A signal generated by the motion of the scale beam activates or stops a feed source mounted over the feed vessel. The activation is by electrical controls. The principle of operation of batch type scales is based on the concept that a flowing stream has constant density.

In continuous weighing, the material stream in course of its transport is subjected to weighing and is widely used in mineral processing industries. In general, the continuous weighing machines consist of a belt conveyor, a section of which is suspended with the help of rods from weighing levers. The weight is counterbalanced on the

balance beam by means of an iron float in a mercury bath. With the change in weight on the belt, a change in the position of the beam takes place actuating a mechanical integrator. Speed of the belt can also actuate the integrator. By blank setting, the weight of the empty belt can be considered. For this method of measurement, calibration of the meter has to be done from time to time.

The coagulation and flocculation processes facilitate the removal of suspended solids and colloidal particles. It is used in the first stage of solid-liquid separation like settling, floatation, and filtration. In solid-liquid separation operations like sedimentation and filtration, an important physical property of solid which finds application is the tendency of the particulate phase of colloidal dispersions to aggregate. The aggregation of the colloids is termed as coagulation or flocculation. van der Waals forces and electrostatic forces are the generally occurring forces between the colloidal particles. While aggregation or coagulation is primarily due to van der Waals attractive forces, stability is due to repulsive interaction between identically charged double-layers. The rate of coagulation of particles in a liquid depends on the frequency of collisions between particles due to their relative motion. eri inetic coagulation is the result of particle motion due to Brownian movement while ortho inetic coagulation takes place when relative particle motion is a consequence of velocity gradients. Coagulation-flocculation influences the sedimentation process. In a coagulated suspension, the aggregates of fine particles or flocs are the fundamental structural units. In gravity sedimentation which is a low shear rate process, the settling rates and sediment volumes of flocs largely depend on volumetric concentration of flocs and inter-particle forces. Flocculated suspensions exhibit settling behavior which depends primarily on the initial solids concentration and chemical environment. Coagulation is the destabilization of colloidal particles brought about by the addition of a chemical reagent called a coagulant. Flocculation is the agglomeration of destabilized particles into microfloc and after into bulky floccules which can be settled called floc. The addition of another reagent called flocculant or a flocculant aid may promote the formation of the floc. The factors, which can promote the coagulation-flocculation, are the velocity gradient, the time, and the pH. The time and the velocity gradient are important to increase the probability of the particles to come together. Moreover the pH is a prominent factor in the removal of colloids. Coagulation and flocculation occur in successive steps intended to overcome the forces stabilizing the suspended particles, allowing particle collision and growth of the floc. If step one is incomplete, the following step will be unsuccessful. The first step destabilizes the charges of the particle. Coagulants with charges opposite those of the suspended solids are added to neutralize the negative charges on dispersed non-settlable solids and colour producing organic substances if present. Once the charge is neutralized, the small suspended particles are capable of sticking together. The slightly larger particles formed through this process and called microflocs, are not visible to the naked eye.

A high energy, rapid-mix to properly disperse the coagulant and promote particle collisions is needed to achieve good coagulation. Over mixing does not affect coagulation, but insufficient mixing will leave this step incomplete. The mixture is slowly stirred to induce particles to clump together into flocs. Coagulation and flocculation process are essential pretreatments for many water purification systems. All waters, especially surface waters, contain both dissolved and suspended particles. Coagulation and flocculation processes are used to separate the suspended solids and turbidity from water to prepare it for use or for further treatment. This step typically uses the difference in density between the water and the suspended material for separation. The process of coagulation along with flocculation is used whenever the natural settling rate of suspended material is too slow to provide effective clarification. Coagulants are used to neutralize the charge of the suspended solids, bringing the particles together to create a small pinfloc. To generate larger particles or flocs for faster settling, a high molecular weight, organic flocculant is generally used in combination with a coagulant.

❑ ❑

❑ ❑ ❑ ❑ ❑ ❑ ❑ ❑ ❑ ❑ ❑

❑ ❑ ❑ ❑ ❑ ❑ ❑

1. What is the function of a binder A binder conditions the surface of the particles to develop adhesive properties. 2. When is pressure agglomeration recommended Pressure agglomeration is applied to the cases where (i) large particles or particles of controlled size, (ii) high density particles, and (iii) resistance to attrition are desired. 3. What are the common characteristics of tumbling agglomerates These agglomerates have good flowability, low density, rounded shape, and easy dispersion. 4. Give the names of a few equipment for extrusion agglomeration. The equipment include single screw extruder, gear pelletiser, basket-type extruder, and pellet mill. 5. Name a few products of thermal agglomeration. The products include prills of urea and stearic acid, fatty acid, and gelatin. 6. What is an anti-solvent Addition of a second solvent for the

reduction of solubility of a solute in a solvent is called an anti-solvent. 7. What is mother liquor The feed solution giving rise to the formation of crystals is called mother liquor. 8. How are crystals purified from mother liquor Filtration or centrifuging removes most of the mother liquor while the balance is removed by washing with fresh solvent. 9. What happens to a hydrate when the water of crystallisation is removed The crystalline structure is lost and is converted to amorphous powder. 10. What is a votator crystalliser Double-pipe scraped surface-type crystalliser is called a votator crystalliser. It is a cooling crystalliser. 11. Name the factors on which the capacity of an apron feeder depends. The factors include (i) hopper width, (ii) height of the material layer, (iii) bulk density of the material, (iv) conveyor speed, and (v) fill factor.

12. What type of feeder is recommended for wet or sticky materials Apron feeder. 13. What is the advantage of a vibrating feeder over an apron feeder Low purchase cost. 14. What are the main field of applications of a vibrating feeder The applications are (i) heavy duty use, and (ii) feeding to primary crushers. 15. Why the POSIMETRIC feeders require a small motor These feeders have a single rotating duct (the only moving part). Because the feed materials help to turn this duct, only a small motor, usually less than 10 hp is required to drive it. 16. Name the forces responsible for coagulation. van der Waals forces and electrostatic forces.

1. Name a few industries where size enlargement is practised at the finalproduct manufacturing stage. 2. What are the different factors which decide upon the selection of agglomerators 3. Name the primary types of agglomerators. 4. What are the different equipment used for tumbling agglomeration 5. Name a few products made by extrusion agglomeration. 6. Give some examples of the thermal agglomeration process. 7. What are the main objectives of crystallisation 8. Name the various methods by which a solution attains supersaturation.

17. Differentiate between perikinetic and orthokinetic coagulation. Perikinetic coagulation is the result of particle motion due to Brownian movement while orthokinetic coagulation takes place when relative particle motion is a consequenc of velocity gradients. 18. Name the factors, which promote the coagulation-flocculation operation. Velocity gradient, time, and pH. 19. What are coagulant and flocculants Coagulant is a chemical reagent added for the destabilization of colloidal particles. The addition of another reagent called flocculant or a flocculant aid may promote the formation of the floc. 20. What are microflocs and flocs Flocculation is the agglomeration of destabilized particles into microfloc and after into bulky floccules which can be settled called floc.

9. What is the difference between mother liquor and magma 10. How does nucleation takes place in a crystallising solution 11. What are the common problems encountered in industrial crystallisation 12. What is the criterion for deciding the crystal size 13. Name a few hydrates of industrial importance. 14. What are the different types of crystallisers used in industrial practise 15. Give the working principle of a Swenson–Walker crystalliser. 16. What are the advantages of apron feeders 17. Give a few advantages of vibrating feeders.

18. What are the factors on which the capacity of the vibrating feeder depends 19. Give the capacity range for the POSIMETRIC feeders.

20. Discuss the weighing principle of batch and continuous weighing machines. 21. Discuss the coagulation-flocculation process.

1. 3000 kg/h of an aqueous solution of NaNO3 is cooled from 90°C to 40°C in a continuous crystalliser. The solution contains 16 moles of NaNO3 per 1000 g of water at 90°C. When the solution is cooled, water simultaneously evaporates to an amount equal to 3% of the initial amount of solution. If the solubility of NaNO3 is 12 moles per 1000 g of water at 40°C, find the crystal yield per hour. 522 kg

2. A jaw crusher crushing wet dolomite of 10-cm size and density 2800 kg/m3 at the rate of 360 tonne/h needs a vibrating feeder. If the feeder has to operate at 800 rpm with an amplitude of 4 mm, find the width of the feeder. Height of the feed material above the table feeder may be taken as equal to 30 % of the width. 0.96 m

1. Pressure agglomeration can produce particle size larger than (a) 5 mm (b) 10 mm (c) 15 mm (d) 25 mm

(c) gear pellitiser (d) prilling tower

2. A tablet press is a/an: (a) tumbling agglomerator (b) pressure agglomerator (c) extrusion agglomerator (d) thermal agglomerator 3. In a pressure agglomerator, material masses are subjected to pressure in excess of (a) 500 kg/cm2 (b) 1000 kg/cm2 2 (c) 2000 kg/cm (d) 5000 kg/cm2 4. An example of an extrusion agglomerator is a (a) roll compactor (b) paddle mixer

5. Supersaturation in a solution can be achieved by (a) cooling the solution (b) addition of anti-solvent (c) change in pH (d) all of the above 6. Nucleation in crystallisation starts when the solute molecules in the solvent begin to flock in clusters which is in the (a) nanometer scale (b) picometer scale (c) micrometer scale (d) nothing in particular 7. The hydrate which is known as green vitriol has the composition of (a) CuSO4.5 H2O (b) FeSO4.7 H2O

(c) ZnSO4.7 H2O (d) MgSO4.7 H2O 8. A sodium chloride crystal will have (a) two molecules of water of crystallisation (b) one molecule of water of crystallisation (c) no molecules of water of crystallisation (d) nothing in particular 9. An example of an evaporative crystalliser is (a) tank crystalliser (b) double-pipe scraped surface crystalliser (c) circulating magma vacuum crystalliser (d) Swenson–Walker crystalliser 10. Size-enlargement operation practised to produce a product of (a) definite shape and size (b) increased bulk density (c) enhanced appearance (d) all of the above

is

11. The capacity range of apron feeders can be up to (a) 1,000 tonne/h (b) 5,000 tonne/h

(c) 10,000 tonne/h (d) 50,000 tonne/h 12. The maximum size of the material that can be fed to a vibrating feeder in terms of the table width is (a) up to 90% (b) up to 80% (c) up to 60% (d) up to 50% 13. The capacity of a vibrating feeder depends on (a) feed size (b) moisture content of the feed (c) table width (d) all of the above 14. For crystallising ice cream, the equipment needed is (a) tank crystalliser (b) double-pipe scraped surface crystalliser (c) Swenson–Walker crystalliser (d) vacuum crystalliser 15. The factors upon which the coagulation-flocculation operation depends on are: (a) pH, solid concentration, and density (b) velocity gradient, time, and pH (c) viscosity, density, and pH (d) density, velocity gradient, pH

1(d); 2(b); 3(c); 4(c); 5(d); 6(a); 7(b); 12(b); 13(d); 14(b); 15(b)

8(c);

9(c);

10(d);

11(c);

yler (mesh) 4 5 6 7 8 9 10 12 14 16 20 24 28 32 35 42 48 60 65 80 100 115 150 170 200 250 270 325

uivalent Indian standards (No.) 480 400 340 280 240 200 160 140 120 100 85 70 60 50 40 35 30 25 20 18 15 12 10 9 8 6 5 4

Sieve opening (mm)

4.750 4.000 3.350 2.800 2.360 2.000 1.700 1.400 1.180 1.000 0.850 0.710 0.600 0.500 0.425 0.355 0.300 0.250 0.212 0.180 0.150 0.125 0.106 0.090 0.075 0.063 0.053 0.045

ire diameter (mm) 1.540 1.370 1.230 1.100 1.000 0.900 0.810 0.725 0.650 0.580 0.510 0.450 0.390 0.340 0.290 0.247 0.215 0.180 0.152 0.131 0.110 0.091 0.076 0.064 0.053 0.044 0.037 0.030

S mes 3 3-1/2 4 5 6 7 8 10 12 14 16 18 20 25 30 35 40 45 50 60 70 80 100 120 140 170 200 230 270 325 400

Inc es

Microns

Millimeters

0.265 0.223 0.187 0.157 0.132 0.111 0.0937 0.0787 0.0661 0.0555 0.0469 0.0394 0.0331 0.0280 0.0232 0.0197 0.0165 0.0138 0.0117 0.0098 0.0083 0.0070 0.0059 0.0049 0.0041 0.0035 0.0029 0.0024 0.0021 0.0017 0.0015

6730 5660 4760 4000 3360 2830 2380 2000 1680 1410 1190 1000 841 707 595 500 420 354 297 250 210 177 149 125 105 88 74 63 53 44 37

6.73 5.66 4.76 4.00 3.36 2.83 2.38 2.00 1.68 1.41 1.19 1.00 0.84 0.71 0.59 0.50 0.42 0.35 0.297 0.250 0.210 0.177 0.149 0.125 0.105 0.088 0.074 0.063 0.053 0.044 0.037

IS

IN

S Std ASTM E

Tyler

BS BS mes

microns

microns

S mes

Mes

26,5 25 22,4 19 16 13,2 12,5 11,2 9,5 8 6,7 6,3 5,6 4,75 4 3,35 2,8 2,36 2 1,7 1,4 1,18 1 Microns mm 850 – 710 600 500

25 22,4 20 18 16 14 12,5 11,2 10 8 7,1 6,3 5,6 5 4 3,55 2,8 2,5 2 1,8 1,4 1,25 1,0 Microns mm 900 800 710 – 500

1.06 1 7/8 3/4 5/8 0.530 1/2 7/16 3/8 5/16 0.265 1/4 3 4 5 6 7 8 10 12 14 16 18

1.05 – 0.883 0.742 0.624 – – 0.441 0.371 2.5 3 – 3.5 – 5 – – 8 – 10 12 14 16

– – – – – – – – – – – – 3 3 4 5 6 7 8 10 12 14 16

– 20 24 28 32

18 – 22 25 30

– 20 25 30 35

(Continued )

IS

IN

S Std ASTM E

Tyler

BS

microns

microns

S mes

Mes

BS mes

– 425 355 300 250 212 180 150 125 106 90 75 63 53 45 38 32 25 20 16 10

450 430 355 – 250 224 180 – 125 112 90 – 63 56 45 40 32 25 20 16 10

– 40 45 50 60 70 80 100 120 140 170 200 230 270 325 400 450 500 635 – –

– 35 42 48 60 65 80 – 115 150 170 200 250 270 325 400 450 500 635 – –

– 36 44 52 60 72 85 100 120 150 170 200 240 300 350 400 440 – – – –

Badger, W. L. and Banchero, J. T., Introduction to C emical Engineering, McGrawHill, Singapore, 1995. Brown, G. G., et. al., nit perations, John Wiley & Sons, Inc., New York, 1950. Chattopadhyay, P., nit perations of C emical Engineering olume , 2nd ed., Khanna Publishers, Delhi, 1996. Coulson, J. M., Richardson, J. F., Backhurst, J. R., and Harker, J. H., Coulson & Ric ardson s C emical Engineering olume Fluid Flo eat Transfer and Mass Transfer, 6th ed., Elsevier, India, 1999. Foust, A. S., et. al., Principles of nit perations, 2nd ed., John Wiley & Sons, Singapore, 1980. Gaudin, A. M., Principles of Mineral ressing, Tata McGraw-Hill Publishing Co. Ltd., New Delhi, 1971. Haver, W., Personal Communication ([email protected]). McCabe, W. L., Smith, J. C., and Harriot, P., nit perations of C emical Engineering, 5th ed., McGraw-Hill, Singapore, 1993. Metso Minerals Inc., Crus ing and Screening andboo , Finland, 2007. Narayanan, C. M. and Bhattacharyya, B. C., Mec anical perations for C emical Engineers, 3rd ed., Khanna Publishers, Delhi, 2003. Pennsylvania Crusher Corp., andboo of Crus ing, USA, 2006. Perry, R. H. and Green, D. W., Editors, Perry s C emical Engineers andboo , 7th ed., McGraw-Hill, New York, 1997. Peters, M. S., Timmerhaus, K. D., and West, R. E., Plant esign and Economics for C emical Engineers, 5th ed., McGraw-Hill, New York, 2003. Richards, R. H. and Locke, C. E., Text Boo of re ressing, 3rd ed., McGraw-Hill, New York, 1940. Richardson, J. F., Harker, J. H., and Backhurst, J. R., Coulson & Ric ardson s C emical Engineering olume Particle Tec nology & Separation Processes, 5th ed., Elsevier, India, 2002. Roy, G. K., Solved Examples in C emical Engineering, 9th ed., Khanna Publishers, Delhi, 2010. Subrahmanyam, N., Sixty ears of t e Indian Institute of C emical Engineers IIC E and C emical Engineering in India, Indian Chemical Engineer, Vol. 49, No. 4, 2007, pp. 458–468. Taggart, A. F., andboo of Mineral ressing res and Industrial Minerals, John Wiley & Sons, New York, 1945. Thixton, J., The inventor of Supaflo high rate thickener, Personal Communication ([email protected]). llmann s Encyclopedia of Industrial C emistry ol Si e Enlargement to Starc , 6th ed., Wiley-VCH, Germany, 2003. llmann s Processes and Process Engineering ol Separation and Classification Mixing Particle Tec nology eat Generation, Wiley-VCH, Germany, 2004.

1. Pennsylvania Crusher Corporation, USA www.penncrusher.com 2. Outotec Oyj., Finland www.outotec.com 3. Ronald Gill Associates, UK www.trommel.co.uk 4. M/S. Hosokawa Micron India Pvt. Ltd., India www.hosokawa.com 5. JOEST Australia Pty. Ltd., Australia www.joest.com.au 6. Eriez Manufacturing Company, USA www.eriez.com 7. Metso Minerals Inc. www.metso.com 8. Sandvik Mining and Construction, Sweden www.sandvik.com 9. Vedanta Aluminium Ltd., India www.vedantaresources.com 10. Supaflo High Rate Thickener www.supaflo.com 11. M/S. Amar Equipments Pvt. Ltd., India www.amarequip.com 12. Orissa Sponge Iron & Steel Limited, India www.orissasponge.com 13. FLSmidth A/S, Denmark www.flsmidth.com 14. Unique Mixers & Furnaces Pvt. Ltd., India www.uniquemixer.com 15. M/S. IKA Werke GmbH & Co. KG., Germany www.ika.net 16. IKA India Private Limited, India www.ika.net.in 17. Hosokawa Bepex GmbH, Germany www.bepexhosokawa.com 18. Sturtevant Inc., USA / Leevams Inc., India www.sturtevantinc.com / www.leevams.in 19. Pampa Enterprises, India www.pampa.co.in 20. Haver & Boecker OHG, Germany www.haverboecker.com / www.diedrahtweber.com/en/

Agglomeration 289 Classification 289 Composite Agglomeration 292 Extrusion Agglomeration 292 Gear Pelletizer 294 Press Agglomeration 289 Inter-particle Forces 289 Roll Compactors 289–290 Briquetting 290 Compaction 290 Flakes 290 Roll Patterns 292–293 Integral Roll 293 Roll Tires 293 Thermal Agglomeration 295 Selection of Agglomeration Process 289 Angle of Bite 62 Angle of Break 76 Angle of Internal Friction 23 Angle of Nip 62 Angle of Repose 23 Dynamic Angle of Repose 23 Static Angle of Repose 23–24 Automatic Setting Regulation-intelligent 54 Average Particle Sizes 17

Bi-Flow System 70 Blending 275 Convection 275 Diffusion 275 Bulk Solids 22 Flow of Bulk Solids 25 Expanded Flow 26 Funnel Flow 26 Mass Flow 26 Pressure and Density during Flow of Bulk Solids 27

Problems with Flow of Bulk Solids 27 Erratic Flow 27 Flushing 27 No Flow 27 Segregation 27 Storage of Bulk Solids 24

Cascading 74, 76 Cataracting 74 Centrifuging 75–76 Characterization of Solid Particles 12 Classification with Water 150 Dewatering 151, 155 Laws of Classification 151 Sizing 150 Sorting 150 Classifying Equipments (Classifiers) 151 Mechanical Classifiers 151, 157 Rake Classifier 158 Settling Zones 158 Classification Zone 158 Settled Solids Zone 158 Transport Zone 158 Spiral Classifier 158 Non-mechanical Classifiers 151–152 Density Separators 155–157 Gravity Settling Classifiers 152 Hydrocyclone Classifiers 153 Forces Acting on Particles 154 Forward 153 Reverse 153 Vortex 154 Primary 154 Secondary 154 Vortex Finder 154 Spitzkastan Classifiers 152 Coagulation 306 Coagulant 306 Floc 306

Flocculant / Flocculant Aid 306 Microfloc 306 Orthokinetic 306 Perikinetic 306 Coefficient of Flowability 22 Coefficient of Friction 37, 61, 62, 73 Comminution 35, 39 Constants 4 Conversion Factors to SI Units 5 Critical Class 102, 104 Critical pH 167 Critical Speed 75–76 Crystallization 295 Anti Solvent 295 Average Size of Crystals 296 Equipments (Crystallizers) 298 Forced Circulating Liquid Evaporator Crystallizers 299 Scraped Surface Crystallizers 299 Tank Crystallizers 298 Hydrate 296 Inorganic Hydrates 296 Magma 295 Mother Liquor 295 Nucleation 295 Supersaturation 296 Yield 297

Dewatering 180, 197, 213 Dimensionless Groups 7 Discharge Openings 54 Open Side Setting 54 Closed Side Setting 54 Draining 180 Drying 180, 204, 217

Electrical Separation 138 Electrostatic Separation 138, 145 Charging Mechanisms 145–146 Conductive Induction 145–146 Contact Electrification / Triboelectrification 145–147 Ion Bombardment 145–148 Equipments 146 Ion-Bombardment Separators 148 Triboelectrostatic Separators 147 Magnetic Separation 138

Materials 138 Diamagnetic 138 Ferromagnetic 138 Paramagnetic 138 Magnetic Field 138–145 Magnetic Susceptibility 138–142 Magnets 138 Electromagnet 138–139, 142 Permanent 138–139, 142 Equipments 139 High Gradient Magnetic Separators 142 Induced Roll Magnetic Separators 142 Magnetic Drum Separators 139 Dry 139–140 Wet 139–140 Rare Earth Magnetic Rolls 140 Superconducting High Gradient Magnetic Separators 143

Feed Openings 52 Active 52 Effective 52 Feeding 81, 299 Choke 82 Equipments (Feeders) 299 Apron Feeders 299 Capacity 299–301 General Characteristics of Apron and Vibrating Feeders 303 Posimetric Feeders 304 Vibrating Feeders 301 Capacity 302 Free 82 Filtration 180, 197 Cake 197 Equipments 210 Classification of Cake Filters 210 Filter Press 210 Plates and Frames 212–213 Plate and Frame Filter Press 211 Side Bar 211 Overhead Beam 211–212 Recessed-Plate Filter Press 214 Operating Principle 214–215 Leaf Filters 215 Leaves 215 Vertical Leaf Filters 215–216 Rotary Disc Filters 219–221

Rotary Drum Filters 217–219 Filtration ones 218 Operating Principle 217–218 Selection of Equipments 210 Filter Aids 201 Filter Medium 197, 200 Filtrate 197 Filtration Mechanism 197 Cake Filtration 197 Constant Pressure Filtration 200 Constant Rate Filtration 200 Factors Affecting the Rate of Filtration 200 Principles 200 Deep-Bed Filtration 197 Filtration Theory 201 Batch Filtration 201 Batch Filters 203 Compressibility Exponent of Cake 202 Cycle Time 203 Idle Time 203 Output of a Batch Filter 203 Rate Equation 202 Speci c Cake Resistance 202 Continuous Filtration 203 Septum 197 Floatation 166 Concentrate 166 Equipments 168 Classi cation of Floatation Cell 169 Floatation Cell 169 Floatation Reagents 167 Activators 167–168 Collectors 167–168 Depressors 167–168 Frothers 167–168 pH Regulators 167 Froth 166 Froth Floatation 166 Operating Principle 167 Conditioning Step 167 Process of Liberation 167 Surface Wetting Properties 166 Hydrophilic 166–169 Hydrophobic 166–169 Tailings 166 Flocculation 306 Free Crushing 82 Free Grinding Limit 76

Gas-Solid Separation 232 Equipments 232 Air Classi ers 239 Side Draft 242 SuperFine 241 Whirlwind 239 Cyclone Separators 237 Vortex Finder 237 Electrostatic Precipitators 236 Collection Ef ciency 236 Cottrell Precipitators 236 Factors Affecting Collection Ef ciency 236 Fabric Filters (Bag Houses / Bag Filters) 233 Mechanical Shaker 235 Reverse Air 235 Reverse et 235 Gravity Settling Chambers 233 Inertial Separators 233 Impingement Separators 233 Viscous Air Filters 233 Wet Scrubbers 235 Venturi Scrubbers 235 Wet Collectors 235 Factors Affecting Gas-Solid Separation 232 Gas Cleaning 232 Mechanism of Gas Cleaning 232 Gravity Concentration 159 Principles of Gravity Concentration 159 Density 159 Film Sizing 159 Shaking 160 Equipments 160 Heavy Medium Separators 160 Sink-and-Float Separation 160 igs 160 Differential Acceleration igging Action 161 Ragging 161 Shaking Tables 164 Left and Right Hand Shaking Tables 165 Rif es 164–165 Spiral Concentrators 161 Flow Patterns 163–164 Grinding Gas 80

Hammer Types 68 Hurricane Rotor 70

Nip 52, 59

Properties of Solids 22, 37–38 Interparticular Crushing 54

Jaw Plate Profiles 50–51

Reduction Ratio 36, 42, 59, 82 Rittinger s Number 42 Rock-on-Rock Action 70 Roll Tooth Patterns 59–60

Kneaders 278

Mechanical Separators 96 Mixing of Solids 265 Equipments (Mixers) 274 Liquid Mixers 274 Agitated Vessels 274–275 Impellers 274 Axial Flow 274 Radial Flow 274 Impeller Types 274–275 Solid Mixers 275 V-Blenders 276 Vertical Cone Screw Blender 277 Viscous Mixers (Kneaders) 278 Continuous Kneading Machines 279 Horizontal Kneading Machines 278 Vertical Kneading Machines 279 Liquid Mixing 266 Baf es 266–268 Froude Number 267–268 Power Consumption 267 Baf ed Tank 267 Unbaf ed Tank 268 Power Number 267–268 Objectives 266 Solid Mixing (Blending) 270 Energy Consumption 272 Measurement of the Extent of Mixing 271 Mechanism of Solid Mixing 275 Mixing Index 271 Rate of Mixing 271 Standard Deviation 271 Mohs Scale of Hardness 37

Screen 100 Deck 103, 129, 133, 137 Efficiency (Effectiveness) and Capacity 117 Effect of Feed Rate on Effectiveness 119 Factors Affecting Effectiveness and Capacity 120 Limiting Screen 101 Recovery 118 Rejection 118 Retaining Screen 101 Screen Sizes 106 Aperture 106 Mesh 106–115 Screen Analysis 114, 117 Cumulative 115–118 Differential 115–118 Screening 100 Actual Screening 127–128 Overlap Zone 128 Blinding 101, 105, 128 Ideal Screening 127 Cut Diameter 127 Mechanism 101 Separation Probability 101–103 Stratification 101–104 Factors Affecting Stratification 102 Pegging 105 Screening Operation 100 Dry 101 Wet 101 Factors Affecting Screening Operation 104 Surfaces 104 Material of Construction 105

Parallel Bars / Rods 104 Punched Plates 104 Staggered 104–105 Straight Row 104–105 Woven Wires 104 Rectangular Screens 104–106 Square Screens 104–105 Weaving Patterns 105 Throughput 102–103 Screening Equipments 128 Banana Screens 137 Grizzly Screens 128 Gyratory Screens 136 Moving (Revolving, Shaking, or Vibrating) Screens 128 Stationary Screens 128–129 Trommels 129 Compound Trommels 130 Factors Affecting the Operation of Trommels 130 Single Trommel 130 Trommel Arrangements 130, 132 Vibrating Screens 133 Electrical 133 Mechanical 133 Particle Motion 134 Projection and Free-passing Area 135 Theory of Vibrational Separation 134 Sedimentation (Thickening and Clarification) 180 Equipments (Thickeners and Clarifiers) 190 Bridge-Supported Thickeners 191 CableTorq Thickeners and Clarifiers 193 Caisson Thickeners 192 Column-Supported Thickeners 192 Solids-Contact Reactor Clarifiers 196 Supa o Thickeners 197–199 Traction Thickeners 192 Free Settling 181 Hindered Settling 181 Sedimentation Test 181 Sedimentation Theory 182 Bulk Density 186 Bulk Viscosity 186 Buoyancy Force 183 Drag Coefficient 183 Drag Force 183 Elutriation 185 Equal Settling Particles 185

Floatation 185 Hindered Settling Velocity 186 Newton s Law Region 185 Porosity or Volume Fraction 186 Reynolds Number 184 Richardson-Zaki Index 186 Settling Ratio 185 Stokes Law Region 184 Settling Zones 182 Separation of Solids 93 Separation Processes 94 Chemical / Diffusional 94 Mechanical 94 Settling 151 Free Settling 151 Hindered Settling 151 Shape 12 SI Prefixes 4 SI Units 4 Sieve 114 Sieve Shaker (Ro-Tap) 114–115 Sieving Procedure 114–115 Standard Sieves 106–114 Standard Sieve Scales 106–114 Testing Sieves 114 Sink-and-Float Separation 160 Size 12, 15 Average Particle Sizes 17 Arithmetic Mean Diameter 18 Mass Mean Diameter 17 Sauter Mean Diameter 17 Volume Mean Diameter 17 Measuring Techniques 101 Mixed Particle Sizes 15 Size Enlargement 288 Objectives 288 Size Reduction 34–35 Effective Methods for Operating Size Reduction Equipments 81–82 Open / Closed-Circuit Grinding 67, 77, 82–84 Energy and Power Consumption 38 Crushing Efficiency 39–40 Mechanical Efficiency 40 Surface Energy 38–41 Equipments 48 Classification of Size Reduction Equipments 48 Selection Criteria 49 Autogenous / Semi-Autogenous Mills 71–72

F

Fin

d

Fin

nd/ ii vi in

nd/ ii

vi in

i n ind d

n

i

F Fin

d / / i

i vi

nd/ ii in

in

1

i n/ nd

i 1 2

i n

i n d n i xi v i i n n n ii n n i n d n i n n nn i n

n

4 5 6

i

i

n

2

i

4

i

ii

vi

ii

vi

5

6

Bradford Breakers 64 Cage Mill 65 Coalpactors 66 Fine Impact Mills 78, 79 Fluidized Bed Opposed Jet Mills 80–81 Granulators 65 Gyratory Crushers 53–54, 56 Hammer Mills 36, 64, 67 Nonreversible 67–69 Reversible 67–69 for Coal 68 for Rock and Minerals 68–69 Jaw Crusher 50 Blake Jaw Crusher 50 Double Toggle Jaw Crusher 51–52 Single Toggle Jaw Crusher 51–52 Capacity 53 Dodge Jaw Crusher 50 Roll Crushers 57 Capacity 62 Double Roll 59 Single Roll 57 Spiral Jet Mills 79 Tumbling Mills 72 Characteristics of Tumbling Mills 73 Ball Mill 73 Factors Affecting Size of Product 76 Pebble Mill 71–73 Rod Mill 77 Tube Mill 72–73 Vertical Shaft Impactors 69 Factors Affecting Size Reduction 38 Laws of Comminution 41 Bond s Law 42 Generalized Law 43 Kick s Law 42 Rittinger s Law 41 Methods 35 Attrition 36 Compression 36 Cutting 35 Impact 35 Dynamic Impact 35 Gravity Impact 35

Shear 36 Objectives of Size Reduction 35 Principles of Size Reduction 37 Specific Surface 16–18, 38 Specific Surface Ratio 16 Sphericity 12 of different shapes 13 of some materials 14 Storage Vessels 23, 25 Bins 23–25 Silos 23–25 Surface Shape Factor 14

Terminal Settling Velocity 151, 181, 183, 185 Thickeners and Clarifiers 190 Transportation of Solids 249 Equipments (Conveyors and Elevators) 249 Belt Conveyors 249 Belt Conveyor Profiles 251 Flat Belts 250 Troughed Belts 250 Capacity 251 Idlers 250 Bucket Elevators 258 Pipe Conveyors 254 Idler Arrangements 257 Screw Conveyors 252 Capacity 253 Screw Conveyor Pitch Designs 253 Selection of Equipments 249

Unit Operations 2 Unit Processes 2 Unit Systems 3

Volume Shape Factor 14

Weighing 305 Batch 305 Continuous 305 Work Index 43