Divided Solids Transport There are no such things as applied sciences, only applications of science. Louis Pasteur (11 September 1871) Dedicated to my wife, Anne, without whose unwavering support, none of this would have been possible. Inndustrial EEquipmentt for Chemmical Engineering SSet cooordinated by Jean-Paul Durooudier Divvidedd Solidds Trranspport Jeaan-Pauul Durouudier First published 2016 in Great Britain and the United States by ISTE Press Ltd and Elsevier Ltd Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. 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To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. For information on all our publications visit our website at http://store.elsevier.com/ © ISTE Press Ltd 2016 The rights of Jean-Paul Duroudier to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library Library of Congress Cataloging in Publication Data A catalog record for this book is available from the Library of Congress ISBN 978-1-78548-183-3 Printed and bound in the UK and US Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Chapter 1. Re-entrainment of Solid Particle Beds Swept by a Fluid Current . . . . . . . . . . . . . . . . . . . . 1 1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1. Significance of the problem . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.2. Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2. Shear velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1. Piping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.2. Flat plate (edge perpendicular to fluid flow) . . . . . . . . . . . . . . 4 1.3. Strength and lift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3.1. Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3.2. Mean thrust velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3.3. Drag force and lift force . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4. Entrainment criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4.1. Attachment forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.5. Quantity entrained . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5.1. Probability and frequency . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5.2. Results of Wu et al. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.6. Entrainment limit velocity (simplified method) . . . . . . . . . . . . . . 11 1.6.1. Mean geometry of spherical particles on the surface of the bed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.6.2. Velocity of sweeping for entrainment . . . . . . . . . . . . . . . . . . 12 1.6.3. Angular particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.6.4. Cleaning speed and non-entrainment velocity . . . . . . . . . . . . . 17 1.7. Entrained flowrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.7.1. Probability of entrainment and entrained flow . . . . . . . . . . . . . 18 vi Divided Solids Transport Chapter 2. Mechanical Conveying of Divided Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.1.1. Separation due to fall and pouring: dust formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.1.2. Flowrate and storage capacity combinations (notions) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.1.3. Organization of divided solid circulation . . . . . . . . . . . . . . . . 23 2.1.4. Extractors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2. Chutes and airslides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.2.1. Chutes inclined horizontally . . . . . . . . . . . . . . . . . . . . . . . 26 2.2.2. Vertical chute . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.2.3. Interruption or modulation of chute flow . . . . . . . . . . . . . . . . 29 2.2.4. Airslides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.3. Conveyor belts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.3.1. Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.3.2. Use criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3.3. Flow regulation by belt scale . . . . . . . . . . . . . . . . . . . . . . . 33 2.3.4. Safeguards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.3.5. Choice of belt width . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.3.6. Flowrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.3.7. Power consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.3.8. Effort incurred by the belt . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.3.9. Loading systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.3.10. Discharge systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.3.11. Metal conveyor belt . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.4. Chain conveyor(s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.4.1. Crossbar conveyor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.4.2. Scraper conveyors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.4.3. Metal pallet conveyors . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.5. Vibrating conveyor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.5.1. Operational principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.5.2. Types of conveyors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.5.3. Progression rate of the product in the trough . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.5.4. Flowrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.5.5. Power consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.5.6. Advantages and drawbacks of vibrating conveyors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Contents vii 2.6. Elevators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.6.1. Bucket elevator principle . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.6.2. Types of elevators and discharge . . . . . . . . . . . . . . . . . . . . . 59 2.6.3. Methods of filling buckets . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.6.4. Should a belt or chain be used? . . . . . . . . . . . . . . . . . . . . . . 61 2.6.5. Flowrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 2.6.6. Power consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.6.7. Vibrating elevator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.6.8. Screw lifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.7. Screw conveyor for divided solids . . . . . . . . . . . . . . . . . . . . . . 64 2.7.1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.7.2. Choice of screw characteristics . . . . . . . . . . . . . . . . . . . . . . 65 2.7.3. Darnell and Mol’s theoretical calculations for screw flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 2.7.4. Screw power consumption . . . . . . . . . . . . . . . . . . . . . . . . 69 2.8. Transport by loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 2.8.1. Containers and skips . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 2.8.2. Roller conveyor for boxes . . . . . . . . . . . . . . . . . . . . . . . . . 72 2.8.3. Material lifters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 2.9. Several properties of divided solids . . . . . . . . . . . . . . . . . . . . . 73 2.9.1. Abrasiveness – classes of abrasiveness . . . . . . . . . . . . . . . . . 73 2.9.2. Apparent density – friction with wall . . . . . . . . . . . . . . . . . . 74 2.9.3. Relationship between equipment and product flowability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 2.9.4. Release of dust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 2.10. Storage and transport logistics . . . . . . . . . . . . . . . . . . . . . . . . 75 Chapter 3. Pneumatic Conveying of Divided Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.1. Pneumatic conveying: introduction . . . . . . . . . . . . . . . . . . . . . . 77 3.1.1. Description of flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.1.2. Compacting of a sediment (or de-aeration of a fluidized bed) . . . . . . . . . . . . . . . . . . . . . . . . 78 3.1.3. Measurement of stiffness, k . . . . . . . . . . . . . . . . . . . . . . . . 81 3.1.4. Various regimes of horizontal pneumatic conveying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.2. Properties of divided solids . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.2.1. Density and porosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.2.2. Geldart classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.2.3. Precautions and choice according to products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 viii Divided Solids Transport 3.3. Operational curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.3.1. Types of operational curves . . . . . . . . . . . . . . . . . . . . . . . . 90 3.3.2. Power expression according to Hilgraf in dense state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 3.4. Velocity and pressure drops . . . . . . . . . . . . . . . . . . . . . . . . . . 96 3.4.1. Conveying velocity and loading rate – dense and diluted phases . . . . . . . . . . . . . . . . . . . . . . . . . . 96 3.4.2. Velocity of air for diluted state . . . . . . . . . . . . . . . . . . . . . . 98 3.4.3. Velocity for horizontal conveyance in dense phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 3.4.4. Yang blockage criteria for a vertical tube in dense phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 3.4.5. Power consumption in a tube . . . . . . . . . . . . . . . . . . . . . . . 103 3.5. Special study of vertical tubes . . . . . . . . . . . . . . . . . . . . . . . . . 110 3.5.1. Preliminary study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 3.5.2. Numerical simulation of Desgupta et al. . . . . . . . . . . . . . . . . 110 3.5.3. Minimal length of solid plugs (simplified estimate) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 3.5.4. Crossing solid plugs with gas . . . . . . . . . . . . . . . . . . . . . . . 113 3.5.5. Friction of solid plugs on a pipe . . . . . . . . . . . . . . . . . . . . . 113 3.5.6. Practical proceedings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 3.6. Ancillary equipment for pneumatic conveying . . . . . . . . . . . . . . . 120 3.6.1. Feeding systems for continuous installations . . . . . . . . . . . . . . 120 3.6.2. Expedition by discontinuous loads (dense phase) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 3.6.3. Criteria for the correct design of load conveying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 3.6.4. Separation of the product and carrier gas . . . . . . . . . . . . . . . . 126 3.6.5. Conclusion for these systems . . . . . . . . . . . . . . . . . . . . . . . 127 3.6.6. Block valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 3.6.7. Tubes for pneumatic conveyance . . . . . . . . . . . . . . . . . . . . 128 3.6.8. Receptors (gas–solid receptors) . . . . . . . . . . . . . . . . . . . . . 129 3.6.9. Control of solid flow: starting and stopping . . . . . . . . . . . . . . 129 3.6.10. Choice of driving machine for the gas . . . . . . . . . . . . . . . . . 130 Chapter 4. Hydraulic Conveying of Divided Solids: Standpipe and L-valve . . . . . . . . . . . . . . . . . . . . 133 4.1. Power dissipated in slurry . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 4.1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 4.1.2. Agitation of slurry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 4.1.3. Pumping power of slurry . . . . . . . . . . . . . . . . . . . . . . . . . 135 4.1.4. Pressure drop in conveying slurry . . . . . . . . . . . . . . . . . . . . 137 Contents ix 4.2. Descent tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 4.2.1. Standpipe characteristics: use . . . . . . . . . . . . . . . . . . . . . . . 137 4.2.2. Description of the divided solid in the tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 4.2.3. Operative mechanism of descenders . . . . . . . . . . . . . . . . . . . 139 4.2.4. Slip velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 4.2.5. Flow-pressure cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 4.2.6. Principle of performance curve calculation . . . . . . . . . . . . . . . 144 4.2.7. Standpipe simulation by calculation . . . . . . . . . . . . . . . . . . . 146 4.2.8. Aeration studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 4.2.9. Placing gas injection at the top of the tube . . . . . . . . . . . . . . . 147 4.2.10. Injection study: theory and experience . . . . . . . . . . . . . . . . 148 4.2.11. Conclusion: standpipes in industrial processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 4.3. L-valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 4.3.1. Description and operation . . . . . . . . . . . . . . . . . . . . . . . . . 150 4.3.2. Uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Appendix 1. Mohs Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Appendix 2. Apparent Density of Loose Divided Solids (kg.m−3) . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169