(Coulson richardsons chemical engineering) d g peacock, j f richardson chemical engineering volume 3, third edition chemical and biochemical reactors process control butterworth heinemann (1994

This page intentionally left blank Coulson & Richardson's CHEMICAL ENGINEERING VOLUME THIRD EDITION Chemical & Biochemical Reactors & Process Control EDITORS OF VOLUME THREE J F RICHARDSON Department of Chemical Engineering University of Wales Swansea and D G PEACOCK The School of Pharmacy, London I E I N E M A N N This page intentionally left blank Butterworth-Heinemann is an imprint of Elsevier Linacre House, Jordan Hill, Oxford OX2 8DP, UK 30 Corporate Drive, Suite 400, Burlington, M A 01803, USA First edition 197 Reprinted 1975 Second edition I979 Reprinted with corrections 1982, 1987, I99 I Third edition 1994 Reprinted 2001, 2003,2005, 2006, 2007 Copyright 1991, J M Coulson, J F Richardson, J R Backhurst and J H Harker Published by Elsevier Ltd All rights reserved The right of J M Coulson, J F Richardson, J R Backhurst and J H Harker to be identified as the author of this work has been asserted in accordance with the Copyright Designs and Patents Act 1988 No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elsevier's Science &Technology Rights Department in Oxford UK: phone: (+a) (0) I865 843830; fax: (+44) (0) 1865 853333: email: permissions@elsevier.com Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material Notice No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN: 978-0-08-04 1003-6 For information on all Butterworth-Heinemann publications visit our website at books.elsevier.com Transferred to digital printing 2009 Working together to grow libraries in developing countries www.elscvier.com I www.bookaid.org I www.sahre.org Contents PREFACE TO THIRD EDITION xiii PREFACE TO SECOND EDITION xv PREFACE TO FIRST EDITION xvi ACKNOWLEDGEMENTS xviii LISTOF CONTRIBUTORS xix Reactor Design-General 1.1 1.2 1.3 1.4 1.5 1.6 I Principles Basic objectives in design of a reactor 1.1.1 Byproducts and their economic importance 1.1.2 Preliminary appraisal of a reactor project Classification of reactors and choice of reactor type 1.2.1 Homogeneous and heterogeneous reactors I 2.2 Batch reactors and continuous reactors 1.2.3 Variations in contacting pattern-semi-batch operation 1.2.4 Influence of heat of reaction on reactor type Choice of process conditions 1.3.1 Chemical equilibria and chemical kinetics I 3.2 Calculation of equilibrium conversion 1.3.3 Ultimate choice of reactor conditions Chemical kinetics and rate equations 1.4.1 Definition of reaction rate, order of reaction and rate constant 1.4.2 Influence of temperature Activation energy I 4.3 Rate equations and reaction mechanism 1.4.4 Reversible reactions 1.4.5 Rate equations for constant-volume batch reactors 1.4.6 Experimental determination of kinetic constants General material and thermal balances Batch reactors 1.6.1 Calculation of reaction time; basic design equation 1.6.2 Reaction time-isothermal operation I 6.3 Maximum production rate 1.6.4 Reaction time-non-isothermal operation 1.6.5 Adiabatic operation Tubular-flow reactors 1.7.1 Basic design equations for a tubular reactor 1.7.2 Tubular reactors-non-isothermal operation 1.7.3 Pressure drop in tubular reactors 1.7.4 Kinetic data from tubular reactors V 1 2 3 10 10 11 14 15 16 17 18 20 21 24 24 27 27 28 30 31 32 34 36 40 41 42 vi CONTENTS 1.8 Continuous stirred-tank reactors 1.8.1 Assumption of ideal mixing Residence time 1.8.2 Design equations for continuous stirred-tank reactors 1.8.3 Graphical methods 1.8.4 Autothermal operation 1.8.5 Kinetic data from continuous stirred-tank reactors 1.9 Comparison of batch, tubular and stirred-tank reactors for a single reaction Reactor output 1.9.1 Batch reactor and tubular plug-flow reactor 1.9.2 Continuous stirred-tank reactor 1.9.3 Comparison of reactors 1.10 Comparison of batch, tubular and stirred-tank reactors for multiple reactions Reactor yield 1.10.1 Types of multiple reactions 1.10.2 Yield and selectivity 1.10.3 Reactor type and backmixing 1.10.4 Reactions in parallel 1.10.5 Reactions in parallel-two reactants 1.10.6 Reactions in series 1.10.7 Reactions in series-two reactants 1.1 Further reading I 12 References 1.13 Nomenclature Flow Characteristics of Reactors-Flow 2.1 2.2 2.3 2.4 2.5 2.6 2.7 Modelling Non-ideal flow and mixing in chemical reactors 2.1.1 Types of non-ideal flow patterns 2.1.2 Experimental tracer methods 2.1.3 Age distribution of a stream leaving a vessel-E-curves 2.1.4 Application of tracer information to reactors Tanks-in-series model Dispersed plug-flow model 2.3.1 Axial dispersion and model development 2.3.2 Basic differential equation 2.3.3 Response to an ideal pulse input of tracer 2.3.4 Experimental determination of dispersion coefficient from a pulse input 2.3.5 Further development of tracer injection theory 2.3.6 Values of dispersion coefficients from theory and experiment 2.3.7 Dispersed plug-flow model with first-order chemical reaction 2.3.8 Applications and limitations of the dispersed plug-flow model Models involving combinations of the basic flow elements Further reading References Nomenclature Gas-Solid Reactions and Reactors 3.1 Introduction 3.2 Mass transfer within porous solids 3.2.1 The effective diffusivity 3.3 Chemical reaction in porous catalyst pellets 3.3.1 Isothermal reactions in porous catalyst pellets 3.3.2 Effect of intraparticle diffusion on experimental parameters 3.3.3 Non-isothermal reactions in Dorous catalvst < Dellets 3.3.4 Criteria for diffusion control' 43 43 44 47 49 50 51 52 52 54 55 56 57 57 58 61 63 67 68 68 68 71 71 71 71 73 75 78 80 80 83 84 88 93 96 98 102 104 105 105 106 108 108 111 112 115 116 122 124 I28 CONTENTS Selectivity in catalytic reactions influenced by mass and heat transfer effects 3.3.6 Catalyst de-activation and poisoning Mass transfer from a fluid stream to a solid surface Chemical kinetics of heterogeneous catalytic reactions 3.5.1 Adsorption of a reactant as the rate determining step 3.5.2 Surface reaction as the rate determining step 3.5.3 Desorption of a product as the rate determining step 3.5.4 Rate determining steps for other mechanisms 3.5.5 Examples of rate equations for industrially important reactions Design calculations 3.6.1 Packed tubular reactors 3.6.2 Thermal characteristics of packed reactors 3.6.3 Fluidised bed reactors Gas-solid non-catalytic reactors 3.7.1 Modelling and design of gas-solid reactors 3.7.2 Single particle unreacted core models 3.7.3 Types of equipment and contacting patterns Further reading References Nomenclature vii 3.3.5 3.4 3.5 3.6 3.7 3.8 3.9 3.10 Gas-Liquid and Gas-Liquid-Solid Reactors 4.1 Gas-liquid reactors 4.1.1 Gas-liquid reactions 4.1.2 Types of reactors 4.1.3 Equations for mass transfer with chemical reaction I Choice of a suitable reactor 4.1.5 Information required for gas-liquid reactor design 4.1.6 Examples of gas-liquid reactors 4.1.7 High aspect-ratio bubble columns and multiple-impeller agitated tanks 4.1.8 Axial dispersion in bubble columns 4.1.9 Laboratory reactors for investigating the kinetics of gas-liquid reactions 4.2 Gas-liquid-solid reactors Gas-liquid-solid reactions Mass transfer and reaction steps Gas-liquid-solid reactor types: choosing a reactor Combination of mass transfer and reaction steps Further reading References Nomenclature 4.2 I 4.2.2 4.2.3 4.2.4 4.3 4.4 4.5 Biochemical Reaction Engineering 5.1 5.2 Introduction I Cells as reactors 5.1.2 The biological world and ecology I Biological products and production systems 5.1.4 Scales of operation Cellular diversity and the classification of living systems 5.2.1 Classification 5.2.2 Prokaryotic organisms 5.2.3 Eukaryotic organisms 5.2.4 General physical properties of cells 5.2.5 Tolerance to environmental conditions 129 139 143 144 146 148 148 148 150 151 151 172 180 181 182 183 186 190 190 192 196 196 196 196 197 202 204 205 216 218 223 229 229 230 23 235 248 248 249 252 252 254 255 256 257 259 260 262 265 269 270 viti CONTENTS Chemical composition of cells 5.3.1 Elemental composition 5.3.2 Proteins 5.3.3 Physical properties of proteins 5.3.4 Protein purification and separation 5.3.5 Stability of proteins 5.3.6 Nucleic acids 5.3.7 Lipids and membranes 5.3.8 Carbohydrates 5.3.9 Cell walls 5.4 Enzymes 5.4.1 Biological versus chemical reaction processes 5.4.2 Properties of enzymes 5.4.3 Enzyme kinetics 5.4.4 Derivation of the Michaelis-Menten equation 5.4.5 The significance of kinetic constants 5.4.6 The Haldane relationship 5.4.7 Transformations of the Michaelis-Menten equation 5.4.8 Enzyme inhibition 5.4.9 The kinetics of two-substrate reactions 5.4.10 The effects of temperature and pH on enzyme kinetics and enzyme de-activation 5.4.1 Enzyme de-activation 5.5 Metabolism 5.5.1 The roles of metabolism 5.5.2 Types of reactions in metabolism 5.5.3 Energetic aspects of biological processes 5.5.4 Energy generation 5.5.5 Substrate level phosphorylation 5.5.6 Aerobic respiration and oxidative phosphorylation 5.5.7 Photosynthesis 5.6 Strain improvement methods 5.6.1 Mutation and mutagenesis 5.6.2 Genetic recombination in bacteria 5.6.3 Genetic engineering 5.6.4 Recombinant DNA technology 5.6.5 Genetically engineered products 5.7 Cellular control mechanisms and their manipulation 5.7 I The control of enzyme activity 5.7.2 The control of metabolic pathways 5.7.3 The control of protein synthesis 5.8 Stoichiometric aspects of biological processes 5.8.1 Yield 5.9 Microbial growth 5.9.1 Phases of growth of a microbial culture 5.9.2 Microbial growth kinetics 5.9.3 Product formation 5.10 Immobilised biocatalysts 5.10.1 Effect of external diffusion limitation 5.10.2 Effect of internal diffusion limitation 5.1 Reactor configurations 5.1 I Enzyme reactors 5.11.2 Batch growth of micro-organisms 5.11.3 Continuous culture of micro-organisms 5.12 Estimation of kinetic parameters 5.12.1 Use of batch culture experiments 5.12.2 Use of continuous culture experiments 5.3 27 I 27 273 275 277 277 27 278 278 278 279 279 279 28 282 285 286 28 289 29 I 294 29 298 298 298 302 304 304 309 315 315 316 318 320 320 325 326 326 327 334 337 339 342 342 345 352 354 356 360 364 364 365 367 386 386 393 CONTENTS 5.13 Non-steady state microbial systems 5.13 I Predator-prey relationships 5.13.2 Structured models 5.14 Further design considerations 5.14.1 Aseptic operation 5.14.2 Aeration 5.14.3 Special aspects of biological reactors 5.15 Appendices Appendix 5.1 Proteins Appendix 5.2 Nucleic acids Appendix 5.3 Derivation of Michaelis-Menten equation using the rapid-equilibrium assumption Appendix 5.4 The Haldane relationship Appendix 5.5 Enzyme inhibition Appendix 5.6 Information storage and retrieval in the cell 5.16 Further reading 5.17 References 5.18 Nomenclature Sensors for Measurement and Control 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 Introduction The measurement of flow 6.2.1 Methods dependent on relationship between pressure drop and flowrate 6.2.2 Further methods of measuring volumetric flow 6.2.3 The measurement of mass flow 6.2.4 The measurement of low flowrates 6.2.5 Open channel flow 6.2.6 Flow profile distortion The measurement of pressure 6.3.1 Classification of pressure sensors 6.3.2 Elastic elements 6.3.3 Electric transducers for pressure measurement 6.3.4 Differential pressure cells 6.3.5 Vacuum sensing devices The measurement of temperature 6.4.1 Thermoelectric sensors 6.4.2 Thermal radiation detection The measurement of level 6.5.1 Simple float systems 6.5.2 Techniques using hydrostatic head 6.5.3 Capacitive sensing elements 6.5.4 Radioactive methods (nucleonic level sensing) 6.5.5 Other methods of level measurement The measurement of density (specific gravity) 6.6 I Liquids 6.6.2 Gases The measurement of viscosity 6.7 I Off-line measurement of viscosity 6.7.2 Continuous on-line measurement of viscosity The measurement of composition 6.8.1 Photometric analysers 6.8.2 Electrometric analysers 6.8.3 The chromatograph as an on-line process analyser 6.8.4 The mass spectrometer 6.8.5 Thermal conductivity sensors for gases ix 396 396 398 402 405 405 409 410 410 416 418 419 42 42 43 43 43 437 437 438 438 439 445 448 448 449 452 452 454 454 463 465 466 468 473 478 479 480 48 482 484 484 484 488 489 489 493 495 497 503 51 515 516 Index Terms Links Stefan–Boltzmann law I Stefan's law of diffusion I radiation 475 I Step forcing function 594 response of first order system 597 second order system 598 input to reactor STEPHANOPOULOS, G 72 574 579 651 686 STEVENS, W.F 583 Stirred cell laboratory reactors 227 tank, model of real systems 104 models of reactors 78 reactors 43 residence time tracer flow STOCKWELL, P Stoichiometric coefficients 43 78 522 16 Stoichiometry of microbial growth 337 STOKES, D 464 Stokes' law II Stokes' law for bubbles II STOOR, P G J Storage Strain gauge transducer improvement methods Streamline boundary layer flow Streamlines 527 491 450 VI 458 315 I I I This page has been reformatted by Knovel to provide easier navigation 652 Index Terms Streamtubes Stroke (lift) of control valve Links I 455 724 STROUHAL, F 439 Strouhal number 439 Structural genes 326 Structured models of microbial growth 397 Styrene process 11 Substitution rule 602 Substrate inhibition 291 level phosphorylation 346 304 Suction potential II Supersonic flow I Supervisory control 335 692 and data acquisition (SCADA) 708 Surface area of catalyst, effect of 123 diffusion 112 reaction as rate limiting step in catalytic reactors 148 tension of mixtures VI Suspended bed reactors 232 Swirl 449 235 Symbols see Nomenclature Synthesis gas, catalysed reactions 111 System compensation 638 failure interrupt 696 security 708 stability and the characteristic equation 612 Systems in series, Bode diagram 622 SZEKELY, J 184 This page has been reformatted by Knovel to provide easier navigation Index Terms Links T TACUCHI, H 402 TAIRD, C K 518 TAKAHASHI, T 618 TAMARU, K 147 Tank reactors 43 Tanks in series model 103 TATTERSON, G B 205 524 208 Taylor–Aris dispersion 82 TAYLOR, G 82 95 Taylor's series 582 561 TCHOBANOGLOUS, G 351 Temperature distribution in reactors effect on reaction rate reactor yield measurement 17 60 36 rise in batch reactors 32 Tensile strength Terminal falling velocity, particle 467 VI II TETER, P O 723 THALLER, L 144 Thermal boundary layer 65 466 profile in reactors scale 238 724 I characteristics, packed catalytic reactors 172 conductivities, common gases 518 conductivity detector, process chromatograph 513 gas composition analyser 516 hot wire pressure sensor 465 This page has been reformatted by Knovel to provide easier navigation Index Terms Links Thermal boundary layer (Cont.) prediction of diffusion VI I flowmeter 440 Thermal–radiation detector (TRD) measurement 473 475 sensitivity, countercurrent cooled tubular catalytic reactors 172 volumetric flowmeter 449 Thermistor 473 Thermocouple 468 automatic reference junction compensation 470 contact potential 468 different types and characteristics 471 Thermocouple Instruments Ltd 471 Thermocouple, law of intermediate metals 469 temperatures 469 Thermodynamic equilibrium 10 selectivity factor 129 temperature scale 468 Thermodynamics of gas compression I Thermoelectric sensors 468 Thermojunction 470 Thermophiles 351 Thermopile 472 Thermowell 470 Thévenin circuit, equivalent 545 Thévenin’s theorem 544 472 Thickeners II VI Thickening II VI This page has been reformatted by Knovel to provide easier navigation Index Terms Links THIELE, E W 116 Thiele modulus II generalised 118 121 361 122 modified for non-isothermal catalytic reaction 127 relationship to effectiveness factor 121 Thiophene, hydro-desulphurisation in trickle bed reactors 246 THODOS, G 144 THOMAS, W J 137 138 139 149 THORNTON, J M 125 126 127 180 Three phase fluidised bed reactors 239 example beds reactors 240 232 229 Threshold, instrument 535 Time constant 581 apparent 636 of reaction for batch reactors 27 isothermal operation 28 non-isothermal operation 31 Time-dependent behaviour 232 31 I TINKLER, J D 124 Toluene chlorination, example 213 TOPIWALA, H H 351 TOPS∅E, H 230 TOPS∅E, N.-Y 230 Torr 465 TORRANCE, K 504 505 II 112 Tortuosity calculation of 510 113 This page has been reformatted by Knovel to provide easier navigation Index Terms Links Total internal reflection 501 radiation pyrometers 475 Tower packings II Tracer flow in stirred tanks 78 ideal pulse input 84 injection theory, further development 93 measurements with two sampling points 95 methods in reactors 71 response curves, types of Trajectories of particles VI 75 103 II Transcription of DNA 425 Transcriptional control 336 Transducer, force balance 551 Transduction 319 Transfer coefficients, absorption II distillation II liquid–liquid extraction II functions 575 capacity systems 579 closed loop, fixed parameter feedback control 608 dead time 593 distillation process 585 first order system 580 systems in series, interacting 587 non-interacting 584 581 fixed parameter feedback controller 593 industrial PID controller 594 interacting tanks in series 587 liquid flowing through a tank 581 583 non-interacting tanks in series 584 586 583 This page has been reformatted by Knovel to provide easier navigation Index Terms Links Transduction (Cont.) open loop 609 poles 579 proportional controller 593 plus derivative (PD) controller 594 integral (PI) controller 594 plus derivative (PID) controller 594 pulse 675 second order system 589 stripping column 586 thermocouple junction with sheath U-tube manometer zeros line reactors units relation to HETP Transformation Transforms, Laplace Transient operation of chemical reactors 580 581 588 589 579 187 I II VI 576 726 II 319 I 26 Transition flow rcgion 114 Translation 425 theorem 593 Transmittance 591 498 502 Transport of gases I VI liquids I VI solids II VI 196 197 I 448 Tray reactors Triangular notch Tricarboxylic acid (TCA) cycle 311 This page has been reformatted by Knovel to provide easier navigation Index Terms Trickle bed reactors Links 233 combination of steps 242 example 246 steady state treatment 245 Triple point 468 TRUXAL, J G 664 TSUCHIYA, H M 397 399 400 Tubular flow reactors see also Packed tubular catalytic packed catalytic reactors, design calculations reactors 61 151 configurations 35 consecutive reactions 64 design 36 heat transfer 35 kinetic data 42 material balances 36 non-isothermal operation 40 output 52 pressure drop 35 TUFFS, P S 692 Tuning discrete time controllers 686 Turbidimeter, nephelometric (nephelometer) 502 Turbidity 502 Turbidostat 368 Turbine flowmeter 440 Turbines I Turbulent boundary layer I eddies I flow I 34 162 163 37 41 445 449 This page has been reformatted by Knovel to provide easier navigation 164 Index Terms Links Turbulent boundary layer (Cont.) axial dispersion 82 values of dispersion coefficients 97 Turndown 724 instrument 529 JRNER, J C R 36 Turnover number 279 Twisted pairs 703 Two position control 564 reactants, reactions in series substrate enzyme kinetics 67 291 Alberty equation 293 double displacement reactions 293 kinetic constant determination 293 single displacement reactions 292 Two-film theory absorption with chemical reaction of diffusion, Whitman Two-phase flow, pressure drop, frictional heat transfer coefficient I II I II I II I II I II VI U Ultimate periodic response 601 Ultra high vacuum 465 Ultra-low flow measurement 448 Ultrasonic agglomeration 449 II flowmeter 442 gas analyser 524 time-of-flight flowmeter 440 450 443 This page has been reformatted by Knovel to provide easier navigation Index Terms Links Uncertainty, instrument reading 532 Underdamped response 599 Under-specified system 575 Unit display 707 output of reactors Units 51 I and dimensions Universal velocity profile I I Unreacted core models of reactors 183 Unstable (unbounded) system 614 V V-notch Vacuum, levels and measurement measurement pumps I 465 465 I relief VI vessels VI Valve body 719 control 719 flow coefficient 723 positioner 719 electropneumatic 551 trays, design trim types 448 VI 722 722 VI 719 723 I VI VAN DER BENT, H 448 VAN HEERDEN, C 165 VAN KREVELEN, D W 200 VAN SWAAIJ, W, P M 50 198 224 This page has been reformatted by Knovel to provide easier navigation Index Terms Links VAN, RIET, K 208 Vapour–liquid equilibrium Vapour-liquid equilibrium data Vapour pressure at convex surface prediction of Variable area flowmeters II VI II VI I 440 controlled 560 manipulated 560 563 VEERMAN, T 400 401 VEGA CONTROLS LTD 485 Velocities, settling II Velocity defect law I profile I propagation of a pressure wave I settling sonic terminal falling Vena contracta II I II I Vent piping design VI VENTRAS, J S 225 Venturi flowmeter flume I 198 Very high vacuum 465 Vibrating element pressure transducer Viscoelastic fluids Viscometer, Cannon–Fenske capillary 440 448 VERSTEEG, G F Vessel supports 402 VI 462 I 490 cone and plate 491 Couette type 491 falling sphere 490 This page has been reformatted by Knovel to provide easier navigation Index Terms Links Viscometer, Cannon (Cont.) in-line vibrating element 495 on-line capillary 493 Couette 494 Ostwald U-tube capillary 489 vibrating element 492 Viscometers, ranges of operation Viscosity 492 I apparent I measurement 489 on-line 493 prediction of VI shear-dependent I Viscous drag I Visual display unit (VDU) loading of screen (display density) 567 698 Volume of batch reactors 27 von Karman vortex street 439 Vortex flowmeter 439 forced I free I Votator I 440 II W WALSH, T M 495 WALTER, G 507 WALTERS, K 491 492 WARDLE, A P 651 712 WARNOCK, I G 710 Washout of biomass in CSTFs 370 in series 493 373 381 This page has been reformatted by Knovel to provide easier navigation Index Terms Links Washout of biomass in CSTFs (Cont.) with recycle WASSON, R 376 446 Waste incinerators VI water treatment 351 VI WASUNGU, K M 349 350 Water cooling towers construction for height detection WATSON, K M Waves, shock I I I 519 149 I WEHNER, J F 92 Weight of vessels VI Weir I WEISS, M.D 497 Weissenberg rheogoniometer 492 WEISZ, P B 125 Welded joint design VI WEN, C Y 95 WENNER, R.R 150 WEST, D M 531 WESTERTERP, K R Wet bulb temperature humidity determination Wetted sphere cantactor wall contactor Wetted-wall columns in absorption distillation 150 167 448 126 128 184 50 224 I II I 519 226 226 II II Wetting of solid 235 rates, packing II VI This page has been reformatted by Knovel to provide easier navigation 129 Index Terms Links WHEELER, A 130 134 WHERRY, T C 723 724 Whirling of shafts VI WHITAKER, A 269 WHITE, B A 725 WHITEHEAD, D G 547 WHORLOW, R W 492 WILHELM, R H 271 92 167 WILKE, C R 223 345 WILLARD, H H 515 WILLIAMS, F M 399 WILLIAMS, T J 585 WILSON, J 549 WILSON, J H 272 Wind loads VI WINDOW, A L 458 WITTENMARK, B 689 WOOD, R M 138 WOOD, W B 272 WORSHAM, R E 723 WRIGHT, C 552 WYLIE, C R 600 651 724 602 628 681 X Xylene, oxidation of o-, example 209 Y Yeasts 265 elemental composition 271 nucleic acid cantent 273 This page has been reformatted by Knovel to provide easier navigation 664 Index Terms Links Yeasts (Cont.) protein content Yield and output of reactors selectivity coefficient 273 60 57 339 for biomass formation 340 product fonnation 340 overall 341 high 60 overall 59 reactor comparisons 65 stress I true growth 341 YOUNG, R E 686 YOUNG, R M 723 Young's modulus 455 724 Z z-transform 673 Zero order hold element 679 shift, instrument 726 535 Zeros of transfer function 579 Zeroth law of thermodynamics 466 ZIEGLER, J G 634 Zirconia cell 510 ØSTERGAARD, K 134 ǺSTRÖM, K J 689 This page has been reformatted by Knovel to provide easier navigation