An Insight into Chemical Engineering

An Insight intoChemical Engineering

Through Instant Notes, Objective Types and Problems

m subbu

An Insight intoChemical Engineering

Through Instant Notes, Objective Types and Problems

(Useful for GATE and other Aptitude Tests)

m subbu

<℘ Rishal Publications, Chennai-5

An Insight intoChemical Engineeringm subbuFirst Edition2003

All rights reserved. No part of this book may be reproduced in any form without the writtenpermission of the author.

Typeset in LATEX

Total number of pages: 400

Price: Rs. 270.00

Published by:Rishal Publications3/2, Dr.Nammalvar StreetVivekananda HouseChennai–600 005

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To Almighty

FOREWORD

Competitive examinations have become inevitable nowadays for admission to graduatecourses and placement in chemical and allied industries, for undergraduate students in chem-ical engineering. For such examinations, apart from a wide knowledge of all aspects of unitoperations of chemical engineering a quick wit to solve the questions/problems is absoluteleyessential. Exhaustic revision of all these operations studied in earlier semesters is a tediousprocedure. A quick insight into the same along with solutions to short answer objectivequestions or problems is necessiated. With this objective in view, the author has made anattempt to prepare this monograph after going through many question papers of this typefrom several universities along with an intensive study of the operations covered.

I had the oppurtunity of revising the text and providing academic advice wherever nec-essary. I am confident this effort of the author will be well received by the budding chemicalengineers taking their first degree from engineering colleges.

Dr. N. SUBRAMANIANFormer Professor & HeadDepartment of Chemical EngineeringIndian Institute of Technology Madras

ChennaiOctober 5, 2003

PREFACE

For competitive examinations to pursue higher studies or get jobs, depth of knowledge inproblem solving and answering objective type questions should be the essential qualities ofa successful Chemical Engineer.

A set of instant notes are given for various important topics in the core subjects ofChemical Engineering. I hope this set of topics detailed in this book will be of extreme useto the undergraduate students and practicing engineers for enhancing and checking theirknowledge in the core concepts of the subject. In any competitive examination due weightageis being given to objective type questions. In this book I have also given objective typequestions which will be useful for the chemical engineers and students for their preparation.

By lecturing for the past few years in core subjects of Chemical engineering like FluidMechanics, Thermodynamics and Process Control at Department of Chemical Engineering,Sri Venkateswara College of Engineering (SVCE), Sriperumbudur I have found that the stu-dents need additional input for applying theoretical knowledge for solving the problems. Inthis book a comprehensive set of problems in each of the nine subjects of Chemical Engi-neering are given with the steps in solving the same from the first principles which could beunderstood easily by a novice in the field also. Most of the problems are questions that wereasked in GATE (Graduate Aptitude Test in Engineering) and in University examinations.

I extend my heartful thanks to Dr.N.Subramanian (Visiting Professor, SVCE — For-mer Professor in Indian Institute of Technology Madras, Chennai) for sparing his valuabletime to review this book and provide technical guidance whenever needed.

I sincerely acknowledge the management of SVCE for their support.I am grateful to Dr.V.Ravichandran (Assistant Professor, Dept. of Computer Applica-

tions, SVCE) for introducing and enthusing me to learn LATEX software, with which thisbook is typeset. Also he helped me in solving the objective type questions of Mathematics.

Mr.B.Nedumaran (Assistant Professor, Dept. of Chemical Engineering, SVCE) was al-ways helpful in conducting GATE coaching to students of SVCE, that initiated me to preparethese materials.

Always my affection and thanks lie with my students who extended their interest tothe fullest. Also I thank the Chemical Engineering community allover the world for theirencouragement through my website http://www.svce.ac.in/∼msubbu for the study materialsprovided in the website.

My thanks are due to my wife Mrs.S.Panchi for her suggestions in publishing this bookand providing administrative assistance. I thank my dear parents and relatives for theiremotional support during these years.

I thank the publisher for bringing out this edition at the earliest.Awaiting for your valuable ideas, to be posted at http://www.msubbu.com

Chennai m subbuOctober 15, 2003 (M. SUBRAMANIAN)

Contents

1 Process Calculations 91.1 Instant Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.1.1 Units and Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.1.2 Material Balance Calculations . . . . . . . . . . . . . . . . . . . . . . . 101.1.3 Energy Balance Calculations . . . . . . . . . . . . . . . . . . . . . . . 111.1.4 Saturation & Humidity . . . . . . . . . . . . . . . . . . . . . . . . . . 121.1.5 Combustion Calculations . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.2 Objective Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.3 Problems with Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.3.1 Volume of Gas at STP . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.3.2 Orsat Analysis of Flue Gas . . . . . . . . . . . . . . . . . . . . . . . . 201.3.3 Concentration of SO2 in Flue Gas . . . . . . . . . . . . . . . . . . . . 201.3.4 Conversion of SO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211.3.5 Percentage Excess Air . . . . . . . . . . . . . . . . . . . . . . . . . . . 211.3.6 Calcination of Limestone . . . . . . . . . . . . . . . . . . . . . . . . . 221.3.7 Percentage of CH4 Burnt . . . . . . . . . . . . . . . . . . . . . . . . . 231.3.8 Percentage Conversion of C2H4 . . . . . . . . . . . . . . . . . . . . . . 241.3.9 Propane Dehydrogenation Plant . . . . . . . . . . . . . . . . . . . . . 251.3.10 Methanol Production in Recycle Reactor . . . . . . . . . . . . . . . . 261.3.11 Recycle Ratio in Reverse Osmosis Desalination . . . . . . . . . . . . . 271.3.12 Recycle to the Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . 281.3.13 Saturator Bypass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291.3.14 Drying of CaCO3 Slurry . . . . . . . . . . . . . . . . . . . . . . . . . 301.3.15 Crystallization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311.3.16 Heat Load on Heater . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321.3.17 Heat of Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331.3.18 Amount of Heat Required . . . . . . . . . . . . . . . . . . . . . . . . . 341.3.19 Flame Temperature and Excess Air . . . . . . . . . . . . . . . . . . . 351.3.20 Heat Released from Reaction . . . . . . . . . . . . . . . . . . . . . . . 351.3.21 Conversion in Exothermic Reaction . . . . . . . . . . . . . . . . . . . . 361.3.22 Maintaining Isothermal Operation of Reactor . . . . . . . . . . . . . . 37

1

2 AN INSIGHT INTO CHEMICAL ENGINEERING — m subbu

2 Fluid Mechanics 392.1 Instant Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.1.1 Fluid Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.1.2 Fluid Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.1.3 Flow Meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.1.4 Transportation of Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . 442.1.5 Flow Past Immersed Bodies . . . . . . . . . . . . . . . . . . . . . . . . 45


2.3.1 Two Layer Buoyancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552.3.2 Floating of Wood on Water . . . . . . . . . . . . . . . . . . . . . . . . 552.3.3 Force Required to Hold a Ball Immersed in Liquid . . . . . . . . . . . 562.3.4 Average velocity of Mixture . . . . . . . . . . . . . . . . . . . . . . . . 572.3.5 Flow Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572.3.6 Pressure Drop for Flow through Circular Pipe . . . . . . . . . . . . . 582.3.7 Velocity of Water in Circular Pipe . . . . . . . . . . . . . . . . . . . . 592.3.8 Flow Rate for a given Pressure Drop . . . . . . . . . . . . . . . . . . . 602.3.9 Pressure Drop per Unit Length for a given Flow . . . . . . . . . . . . 612.3.10 Pressure Drop for a given Flow . . . . . . . . . . . . . . . . . . . . . . 612.3.11 Pressure Drop due to Friction . . . . . . . . . . . . . . . . . . . . . . . 622.3.12 Velocity of Water in a Drain Pipe . . . . . . . . . . . . . . . . . . . . 632.3.13 Time Required to Empty a Conical Vessel . . . . . . . . . . . . . . . . 642.3.14 Energy Required for Pumping . . . . . . . . . . . . . . . . . . . . . . . 652.3.15 Power To Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 662.3.16 Friction Loss Factor of Bend-Reducer . . . . . . . . . . . . . . . . . . 672.3.17 Flow through Tank Bottom . . . . . . . . . . . . . . . . . . . . . . . . 682.3.18 Velocity Measurement by Orifice . . . . . . . . . . . . . . . . . . . . . 682.3.19 Orifice Size for a given Flow . . . . . . . . . . . . . . . . . . . . . . . . 702.3.20 Flow Measurement by Venturi Meter . . . . . . . . . . . . . . . . . . . 702.3.21 Flow Measurement by Pitot Tube . . . . . . . . . . . . . . . . . . . . 712.3.22 Minimum fluidization Velocity . . . . . . . . . . . . . . . . . . . . . . 722.3.23 Water Trickling by Gravity through a Packed Bed . . . . . . . . . . . 732.3.24 Particle Size of Powder . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3 Mechanical Operations 753.1 Instant Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

3.1.1 Size Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753.1.2 Size Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763.1.3 Size Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783.1.4 Filtration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803.1.5 Agitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82


3.3.1 Surface-Volume Mean Diameter of Particles . . . . . . . . . . . . . . . 883.3.2 Work Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893.3.3 Energy Consumption in Crushing . . . . . . . . . . . . . . . . . . . . . 90

CONTENTS 3

3.3.4 Specific Rate of Grinding . . . . . . . . . . . . . . . . . . . . . . . . . 913.3.5 Speed of Ball Mill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 923.3.6 Diameter of Roll Crusher . . . . . . . . . . . . . . . . . . . . . . . . . 923.3.7 Classification based on Terminal Settling Velocity-I . . . . . . . . . . . 933.3.8 Range of Velocities for Classification . . . . . . . . . . . . . . . . . . . 953.3.9 Classification based on Terminal Settling Velocity-II . . . . . . . . . . 953.3.10 Screening and Classification . . . . . . . . . . . . . . . . . . . . . . . . 973.3.11 Filtration Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 983.3.12 Constant Pressure Filtration-I . . . . . . . . . . . . . . . . . . . . . . 993.3.13 Constant Pressure Filtration-II . . . . . . . . . . . . . . . . . . . . . . 1003.3.14 Washing Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1023.3.15 Washing Time in Filter Press . . . . . . . . . . . . . . . . . . . . . . . 1033.3.16 Optimal Time in Filter Press . . . . . . . . . . . . . . . . . . . . . . . 1043.3.17 Compressibility of Filter Cake . . . . . . . . . . . . . . . . . . . . . . . 1053.3.18 Speed of Agitator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1063.3.19 Dimensional Analysis of Agitation . . . . . . . . . . . . . . . . . . . . 1083.3.20 Scale-up Criteria of Agitation . . . . . . . . . . . . . . . . . . . . . . . 109

4 Thermodynamics 1114.1 Instant Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

4.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1114.1.2 Energy and its Transformations . . . . . . . . . . . . . . . . . . . . . . 1124.1.3 Reversible and Irreversible Processes . . . . . . . . . . . . . . . . . . . 1124.1.4 First Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . 1134.1.5 PV T Realtionships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1144.1.6 Second Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . 1154.1.7 Refrigeration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1154.1.8 Thermodynamic Relations . . . . . . . . . . . . . . . . . . . . . . . . . 1164.1.9 Flow Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1184.1.10 Solution Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . 1184.1.11 Phase Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1194.1.12 Reaction Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . 119


4.3.1 Rise in Temperature of Air . . . . . . . . . . . . . . . . . . . . . . . . 1294.3.2 Work Required to Compress an Ideal Gas . . . . . . . . . . . . . . . . 1304.3.3 Triple Point Temperature and Pressure . . . . . . . . . . . . . . . . . 1314.3.4 Thermal Efficiency of Carnot Cycle . . . . . . . . . . . . . . . . . . . . 1314.3.5 Evaluating a Claim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1324.3.6 Entropy Change in Mixing of Two Gases . . . . . . . . . . . . . . . . 1324.3.7 Irreversibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1334.3.8 COP of Refrigeration Cycle . . . . . . . . . . . . . . . . . . . . . . . . 1344.3.9 Change in Entropy for Ice to Steam Transformation . . . . . . . . . . 1354.3.10 Change in Internal Energy of Non-ideal Gas . . . . . . . . . . . . . . . 1364.3.11 Thermodynamic Relations for a van der Waals gas . . . . . . . . . . . 1374.3.12 Joule-Thomson Expansion . . . . . . . . . . . . . . . . . . . . . . . . . 139


4.3.13 Work of Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . 1394.3.14 Fugacity of van der Waals Gas . . . . . . . . . . . . . . . . . . . . . . 1404.3.15 Fugacity and Fugacity Coefficient . . . . . . . . . . . . . . . . . . . . . 1424.3.16 Partial Molal Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . 1424.3.17 Bubble Point Vapor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1434.3.18 VLE of Non-ideal Solution . . . . . . . . . . . . . . . . . . . . . . . . 1454.3.19 Activity Coefficient and Excess Gibbs Free Energy . . . . . . . . . . . 1464.3.20 Activity Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1474.3.21 Activity Coefficients as a Function of Compositions . . . . . . . . . . . 1474.3.22 Activity Coefficients and GE/RT . . . . . . . . . . . . . . . . . . . . . 1494.3.23 Dewpoint Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1504.3.24 Composition of Vapor . . . . . . . . . . . . . . . . . . . . . . . . . . . 1504.3.25 P − x− y Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1514.3.26 Variation of Equilibrium Constant with Temperature . . . . . . . . . . 1524.3.27 Partial Pressures at Reaction Equilibrium . . . . . . . . . . . . . . . . 1534.3.28 Dehydrogenation of Ethane . . . . . . . . . . . . . . . . . . . . . . . . 1544.3.29 Equilibrium Composition of Non-ideal Gas phase Reaction . . . . . . 155

5 Heat Transfer 1575.1 Instant Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

5.1.1 Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1575.1.2 Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1585.1.3 Boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1615.1.4 Condensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1615.1.5 Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1625.1.6 Evaporation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1655.1.7 Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166


5.3.1 Conduction through Thermopane . . . . . . . . . . . . . . . . . . . . . 1755.3.2 Conduction through Two Layers . . . . . . . . . . . . . . . . . . . . . 1765.3.3 Critical Thickness of Insulation . . . . . . . . . . . . . . . . . . . . . . 1775.3.4 Reduction in Heat Loss by Insulation . . . . . . . . . . . . . . . . . . 1795.3.5 Heat Conduction through Increasing Cross-Section . . . . . . . . . . . 1805.3.6 Expression for Steady State Temperature Profile . . . . . . . . . . . . 1815.3.7 Time Required for Cooling of Steel Ball . . . . . . . . . . . . . . . . . 1835.3.8 Unsteady Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . 1845.3.9 Expression for Unsteady Heat Transfer . . . . . . . . . . . . . . . . . . 1855.3.10 Time Required for Freezing the Tank Contents . . . . . . . . . . . . . 1875.3.11 Heat Transfer Area for Constant Heat Flux . . . . . . . . . . . . . . . 1885.3.12 Convective Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . 1895.3.13 Emissivity Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 1905.3.14 Momentum & Heat Transfer Analogy . . . . . . . . . . . . . . . . . . 1915.3.15 Expression for Optimum Length of Heat Exchanger . . . . . . . . . . 1925.3.16 Heat Transfer Area for Counterflow & Parallel flow . . . . . . . . . . . 1945.3.17 Heat Transfer Area of Jacketted Vessel . . . . . . . . . . . . . . . . . . 196

CONTENTS 5

5.3.18 Heat Transfer Area & Rate of Condensation of Steam . . . . . . . . . 1975.3.19 Condensation of Steam . . . . . . . . . . . . . . . . . . . . . . . . . . 1985.3.20 Time Required for Heating the Contents of Jacketted Vessel . . . . . . 1995.3.21 Estimation of Fouling Factor . . . . . . . . . . . . . . . . . . . . . . . 2005.3.22 Heat Transfer Area for 1-2 Exchanger . . . . . . . . . . . . . . . . . . 2015.3.23 Condenser Load in Evaporation . . . . . . . . . . . . . . . . . . . . . . 2025.3.24 Steam Economy & Heat Transfer Area . . . . . . . . . . . . . . . . . . 2035.3.25 Temperature of Radiation Shield . . . . . . . . . . . . . . . . . . . . . 204

6 Mass Transfer 2056.1 Instant Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

6.1.1 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2056.1.2 Convective Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . 2066.1.3 Gas-Liquid Contactors . . . . . . . . . . . . . . . . . . . . . . . . . . . 2086.1.4 Tray Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2096.1.5 Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2096.1.6 Distillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2116.1.7 Drying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215


6.3.1 Molecular Diffusivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2296.3.2 Diffusion of A through Non-diffusing B . . . . . . . . . . . . . . . . . 2306.3.3 Interfacial Gas Concentration . . . . . . . . . . . . . . . . . . . . . . . 2316.3.4 Heat and Mass Transfer Analogy . . . . . . . . . . . . . . . . . . . . . 2326.3.5 Sherwood Number for Equimolar Counter Diffusion . . . . . . . . . . 2346.3.6 Relative Humidity of Air . . . . . . . . . . . . . . . . . . . . . . . . . 2346.3.7 Dry-bulb Temperature of Air . . . . . . . . . . . . . . . . . . . . . . . 2356.3.8 Minimum Liquid Rate for Absorption . . . . . . . . . . . . . . . . . . 2366.3.9 Height of Absorption Column . . . . . . . . . . . . . . . . . . . . . . . 2386.3.10 Flash Vaporization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2416.3.11 Differential Distillation . . . . . . . . . . . . . . . . . . . . . . . . . . . 2426.3.12 Equation of q-Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2436.3.13 Reflux Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2456.3.14 Quality of Feed to Distillation Column . . . . . . . . . . . . . . . . . . 2466.3.15 Reflux Ratio and Composition of Vapor . . . . . . . . . . . . . . . . . 2486.3.16 Reflux Ratio and Vapor Rate . . . . . . . . . . . . . . . . . . . . . . . 2506.3.17 Distillation with Partial Condenser . . . . . . . . . . . . . . . . . . . . 2526.3.18 Adsorption of Moisture by Silica Gel . . . . . . . . . . . . . . . . . . . 2536.3.19 Leaching of Sulfur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2556.3.20 Time Required for Drying . . . . . . . . . . . . . . . . . . . . . . . . . 2566.3.21 Equilibrium Moisture Content . . . . . . . . . . . . . . . . . . . . . . 2586.3.22 Drying of Solid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2596.3.23 Drying of Slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2606.3.24 Extraction of Acetone . . . . . . . . . . . . . . . . . . . . . . . . . . . 261


7 Reaction Engineering 2637.1 Instant Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263

7.1.1 Reaction Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2637.1.2 Design of Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2637.1.3 Non-isothermal Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . 2647.1.4 Heterogeneous Reactions . . . . . . . . . . . . . . . . . . . . . . . . . 2657.1.5 Catalytic Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265


7.3.1 Activation Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2797.3.2 Expression for Rate for the given Mechanism . . . . . . . . . . . . . . 2797.3.3 Relation for Concentrations in Multiple Reactions . . . . . . . . . . . 2807.3.4 Material Balance Equations for Isothermal CSTR . . . . . . . . . . . . 2817.3.5 Conversion in CSTR for Zeroth Order Reaction . . . . . . . . . . . . . 2827.3.6 Conversion in Equal Volume CSTR & PFR . . . . . . . . . . . . . . . 2837.3.7 Conversion in Constant Pressure Batch-Reactor . . . . . . . . . . . . . 2847.3.8 Conversion in a Batch Reactor . . . . . . . . . . . . . . . . . . . . . . 2847.3.9 Order of Reaction from PFR Data . . . . . . . . . . . . . . . . . . . . 2857.3.10 Conversion of Second Order Reaction in CSTR . . . . . . . . . . . . . 2877.3.11 Size of PFR for Gas-phase Reaction-I . . . . . . . . . . . . . . . . . . 2877.3.12 Size of PFR for Gas-phase Reaction-II . . . . . . . . . . . . . . . . . . 2887.3.13 Reactors in Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2897.3.14 Reactors Arrangement . . . . . . . . . . . . . . . . . . . . . . . . . . . 2917.3.15 Increase in Production Rate by PFR . . . . . . . . . . . . . . . . . . . 2927.3.16 Actual Conversion in the Reactor . . . . . . . . . . . . . . . . . . . . . 2937.3.17 Expected Conversion in the Reactor System . . . . . . . . . . . . . . . 2957.3.18 Reactors Arrangement for Higher Conversion . . . . . . . . . . . . . . 2967.3.19 Rate Constants of Parallel Reactions . . . . . . . . . . . . . . . . . . . 2977.3.20 Catalyst Effectiveness Factor . . . . . . . . . . . . . . . . . . . . . . . 2987.3.21 Rate Controlling Step . . . . . . . . . . . . . . . . . . . . . . . . . . . 2997.3.22 Expression for Catalytic Reaction . . . . . . . . . . . . . . . . . . . . 3007.3.23 Expression for Rate of Catalytic Reaction . . . . . . . . . . . . . . . . 301

8 Process Control 3038.1 Instant Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303

8.1.1 Laplace Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3038.1.2 Qualitative Response of Systems . . . . . . . . . . . . . . . . . . . . . 3038.1.3 Open-loop Response of Dynamic Systems . . . . . . . . . . . . . . . . 3048.1.4 Dynamics of Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . 3058.1.5 Stability Analysis of Feedback Systems . . . . . . . . . . . . . . . . . . 307


8.3.1 Linearization of Single Variable . . . . . . . . . . . . . . . . . . . . . . 3168.3.2 Temperature of Solution Leaving a Stirred Tank . . . . . . . . . . . . 3178.3.3 Transfer Function for First Order Reaction . . . . . . . . . . . . . . . 3178.3.4 Dynamics of Thermometer . . . . . . . . . . . . . . . . . . . . . . . . 318

CONTENTS 7

8.3.5 Response of Thermometer to Step Input . . . . . . . . . . . . . . . . . 3198.3.6 Time Constant of Thermocouple . . . . . . . . . . . . . . . . . . . . . 3208.3.7 Dynamics of Temperature Alarm Unit . . . . . . . . . . . . . . . . . . 3208.3.8 Analytical Expression for Unit Impulse Response . . . . . . . . . . . . 3208.3.9 Step Input to Setpoint . . . . . . . . . . . . . . . . . . . . . . . . . . . 3218.3.10 Output from Control Valve . . . . . . . . . . . . . . . . . . . . . . . . 3238.3.11 Output of Proportional Controller . . . . . . . . . . . . . . . . . . . . 3238.3.12 Output from PID Controller . . . . . . . . . . . . . . . . . . . . . . . 3238.3.13 Block Diagram Reduction and Offset Calculation . . . . . . . . . . . . 3258.3.14 Servo and Regulator Transfer Functions . . . . . . . . . . . . . . . . . 3268.3.15 Steady State Error in a Closed Loop System . . . . . . . . . . . . . . 3278.3.16 Proportional Band of Pneumatic Controller . . . . . . . . . . . . . . . 3288.3.17 Offset in Feedback Control System . . . . . . . . . . . . . . . . . . . . 3288.3.18 Value of Kc from Routh Test . . . . . . . . . . . . . . . . . . . . . . . 3298.3.19 Maximum Gain for Stable Operation . . . . . . . . . . . . . . . . . . . 3308.3.20 Maximum Controller Gain for Stable Closed Loop System-I . . . . . . 3318.3.21 Maximum Controller Gain for Stable Closed Loop System-II . . . . . 3318.3.22 Limits on Controller Gain . . . . . . . . . . . . . . . . . . . . . . . . . 3328.3.23 Stability of Closed Loop System . . . . . . . . . . . . . . . . . . . . . 3338.3.24 Steady State Error in the Closed Loop System . . . . . . . . . . . . . 3348.3.25 Crossover Frequency & Ultimate Controller Gain - I . . . . . . . . . . 3358.3.26 Crossover frequency & Ultimate Controller Gain - II . . . . . . . . . . 336

9 Process Economics & Design 3379.1 Instant Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

9.1.1 Cost Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3379.1.2 Depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3389.1.3 Interest and Investment Costs . . . . . . . . . . . . . . . . . . . . . . . 3399.1.4 Mechanical Design of Process Equipments . . . . . . . . . . . . . . . . 341


9.3.1 Cost Index & Capacity Factor . . . . . . . . . . . . . . . . . . . . . . 3479.3.2 Capital Cost of Fluid-processing Plant . . . . . . . . . . . . . . . . . . 3489.3.3 Depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3489.3.4 Present Worth of a Future Amount . . . . . . . . . . . . . . . . . . . . 3499.3.5 Capitalized Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3509.3.6 Annuity & Periodic Payment . . . . . . . . . . . . . . . . . . . . . . . 3509.3.7 Net Profit & Payout Period . . . . . . . . . . . . . . . . . . . . . . . . 3519.3.8 Capitalized Cost - Useful Life for the Alternative . . . . . . . . . . . . 3529.3.9 Capitalized Cost as a Criteria . . . . . . . . . . . . . . . . . . . . . . . 3539.3.10 Discounted-Cash-Flow Rate of Return . . . . . . . . . . . . . . . . . . 3549.3.11 Alternative Investments . . . . . . . . . . . . . . . . . . . . . . . . . . 3549.3.12 Rate of Return as a Profitability Criteria . . . . . . . . . . . . . . . . 3559.3.13 Break-Even Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3559.3.14 Economic Pipe Diameter . . . . . . . . . . . . . . . . . . . . . . . . . 356


10 Chemical Technology 35710.1 Instant Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357

10.1.1 Water Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35710.1.2 Fuel Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35710.1.3 Sulfuric Acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35910.1.4 Chlor-Alkali Industries . . . . . . . . . . . . . . . . . . . . . . . . . . . 36010.1.5 Nitrogen Industries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36110.1.6 Phosphorus Industries . . . . . . . . . . . . . . . . . . . . . . . . . . . 36210.1.7 Fertlizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36210.1.8 Cement Industries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36310.1.9 Sugar Industries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36310.1.10Alcohol Industries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36310.1.11Leather Industries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36410.1.12Oils and Fats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36410.1.13Pulp & Paper Industries . . . . . . . . . . . . . . . . . . . . . . . . . . 36510.1.14Petroleum Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . 36510.1.15Polymer Industries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36610.1.16Rubbers or Elastomers . . . . . . . . . . . . . . . . . . . . . . . . . . . 36710.1.17Common Names . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36810.1.18Safety Tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36810.1.19Materials of Construction for the Process Industries . . . . . . . . . . 368

10.2 Objective Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . 371

11 Mathematics 37711.1 Objective Type Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . 377

Recommended Books for Detailed Study 386

PROCESS CALCULATIONS 17

11. The flowsheet is given in figure.

-

Fresh Feed100 mol/hr

(Pure A)

'&

$%

REACTORA → B

-

'

&

$

%

SEPARATOR

-Product, P

(Pure B)

�

6

R (Pure A)

If the single-pass conversion (once-through conversion) of A to B is 20%, then the rateof recycle R (mol/hr) is (GATE-1997-2.05)

(a) 300 (b) 400 (c) 500 (d) 600

Answer: (b) A → B. By overall balance, product P = 100 mol/hr.Since conversion within the reactor is only 20%,

mixed feed to the reactor = 100/0.2 = 500 mol/hrrecycle rate R = 500− 100 = 400 mol/hr

PROCESS CALCULATIONS 27

1.3.12 Recycle Ratio in Reverse Osmosis Desalination

Sea water is desalinated by reverse osmosis as shown in figure.

-

Sea water1000 kg/hr

3% saltMixer -F (kg/hr)

4% saltReverse Osmosis

Cell-E (kg/hr) -

?

Recycle R (kg/hr)

All compositions are on mass basis. Calculate R/E. (GATE-1997-12)

Solution:

-

Sea water1000 kg/hr

3% saltMixer -F (kg/hr)2

4% saltReverse Osmosis

Cell-

?Desalinated water

0.05% salt

E (kg/hr) -

D (kg/hr)

i3

?

Recycle R (kg/hr)

Brine wasteB (kg/hr)5% salt

1

Mass balance around boundary 1:Overall:

1000 = B + D (1.1)

Balance on salt:1000× 0.03 =

0.05100

×D + 0.05×B (1.2)

Solving Eqns.(1.1) and (1.2), D = 404 kg/hr; B = 596 kg/hr.Mass balance around boundary 2:Overall:

F = 1000 + R (1.3)

Balance on salt:0.03× 1000 + 0.05×R = 0.04× F (1.4)

Solving Eqns.(1.3) and (1.4), R = 1000 kg/hr.From overall mass balance at junction 3,

E = B + R = 596 + 1000 = 1596 kg/hr

Therefore R/E = 1000/1596 = 0.627

FLUID MECHANICS 43

2.1.4 Flow Meters

• Venturi meter:

– The shape of the converging and diverging sections of venturi meter minimizeslosses by eddy formation. Experimental measurements show that for Re > 10000the frictional loss over the venturi meter is about 10 percent of ∆P . Where ∆P ispressure drop measured by the manometer connected between the upstream andthroat sections of venturi meter. (Re is calculated based on the pipe diameter)

– For Re > 10000, Cd of venturi meter is constant at about 0.98. For smallerReynolds numbers the coefficient decreases rapidly. This effect is partially causedby the non-uniform velocity distribution across the diameter in laminar flow (inthe length of venturi meter). (Re is calculated based on the pipe diameter)

• Orifice meter

– The orifice plate can easily be changed to accommodate widely different flowrates, where as the throat diameter of a venturi meter is fixed.

– The orifice meter has a large permanent loss of pressure because of the presenceof eddies on the downstream side of the orifice plate. The shape of the venturimeter prevents the formation of these eddies and greatly reduces the permanentloss.

– There are a number of customary positions of the pressure taps which lead to themanometer such as pipe taps, flange taps and vena contracta taps out of which,flange tapes are the most common.

– The coefficient of discharge of orifice Cd is dependent on the location of thepressure taps.

– For Re > 10000, Cd of orifice meter is constant at 0.61. At lower Reynoldsnumbers the orifice coefficient becomes a strong function of Re. (Re is calculatedbased on the diameter of orifice opening)

– The orifice discharge coefficient is significantly affected by flow disturbances whichoriginates in valves, bends, and other fittings located upstream from the orifice.It is less affected by downstream disturbances. As a general rule, the metershould be placed 50 pipe diameters downstream and 10 pipe diameters upstreamfrom any disturbances. The upstream distance can often be reduced by placingstraightening vanes in the pipe.

• Rotameter: In the case of venturi and orifice meters the area of constriction remainsconstant and the pressure drop varies with flow rate; in the rotameter, the pressuredrop remains nearly constant and the area of constriction varies.

FLUID MECHANICS 51

26. A rotameter, through which air at room temperature and atmospheric pressure isflowing, gives a certain reading for a flow rate of 100 cc/s. If helium (Molecular weight4) is used and the rotameter shows the same reading, the flow rate is (GATE-1996-2.02)

(a) 26 cc/s (b) 42 cc/s (c) 269 cc/s (d) 325 cc/s

Answer: (c) From Bernoulli’s equation, v ∝√

∆P/ρ. For variable area meters, ∆P

= const. Therefore v ∝√

1/ρ. For gases ρ ∝ M ; where M is the molecular weight.Therefore

v2

v1=

√ρ1

ρ2=

√294

i.e., v2 = v1

√29/4 = 100×

√29/4 = 269 cc/s.


2.3.9 Flow Rate for a given Pressure Drop

Nikuradse developed a semi theoretical correlation for f vs. Re for steady turbulent flow insmooth pipes (105 < Re < 107): 1/

√f = 1.75 ln(Re

√f)−0.4. Toluene (ρ = 866 kg/m3, µ =

0.0008 Ns/m2) is to be conveyed through a 100 m pipe -line of diameter 0.2 m. What is themaximum flow rate of toluene in kg/sec that can be maintained, if the frictional pressureloss is not to exceed 10 kN/m2? (GATE-1990-12i)

Solution:

∆P =2fLρv2

Drearranging,

v2 =∆PD

2fLLρ

Substituting the known values,

v2 =10000× 0.2

2× f × 100× 866=

0.01155f

That is, from the pressure drop relation,

v2 =0.01155

f(2.5)

Nikuradse relation for f (given):

1/√

f = 1.75 ln(Re√

f)− 0.4

Rearranging,

ln(Re√

f) =0.4 + 1/

√f

1.75

lnRe =0.4 + 1/

√f

1.75− ln

√f

ln(0.2× v × 866/0.0008) =0.4 + 1/

√f

1.75− ln

√f

ln v =0.4 + 1/

√f

1.75− ln

√f − 12.285 (2.6)

Equations (2.5) and (2.6) are solved by trial and error to get the value of v, and calculationsare given below:

SlNo Assumed value of f v from Eqn.(2.5) v from Eqn.(2.6)1 0.004 1.70 0.772 0.0035 1.817 1.5373 0.0034 1.843 1.7964 0.0033 1.871 2.1125 0.00338 1.848 1.854

FLUID MECHANICS 61

Since for the value of f = 0.00338, v from the two equations are approximately equal(differering only in the third decimal), v shall be taken as 1.85 m/sec.Volumetric flow rate(Q):

Q = (π/4) D2v = (π/4)× 0.22 × 1.85 = 58.1× 10−3 m/sec

Mass flow rate(m):m = Qρ = 58.1× 10−3 × 866 = 50.3 kg/sec

MECHANICAL OPERATIONS 87

19. A suspension of uniform particles in water at a concentration of 500 kg of solids percubic meter of slurry is settling in a tank. Density of the particles is 2500 kg/m3 andterminal velocity of a single particle is 20 cm/s. What will be the settling velocity ofsuspension? Richardson-Zaki index is 4.6 (GATE-1995-2.k)

(a) 20 cm/s (b) 14.3 cm/s (c) 7.16 cm/s (d) 3.58 cm/s

Answer: (c) Volume of solids = m/ρs = 500/2500 = 0.2 m3. Void fraction (ε) =(total volume − volume of solids)/(total volume) = (1 − 0.2)/1 = 0.8. u/ut = εn;Therefore, u = 20× 0.84.6 = 7.16 cm/s.

THERMODYNAMICS 121

4. Air enters an adiabatic compressor at 300 K. The exit temperature for a compressionratio of 3, assuming air to be an ideal gas (γ = CP /CV = 7/5) and the process to bereversible, is (GATE-2001-2.07)

(a) 300(32/7) (b) 300(33/5) (c) 300(33/7) (d) 300(35/7)

Answer: (a) For reversible adiabatic process PV γ = constant. From ideal gas law

PV = RT . Therefore, P 1−γT γ = constant. Given: P2/P1 = 3. T2/T1 = P(γ−1)/γ2

P(γ−1)/γ2

which gives T2 = 300(32/7)

THERMODYNAMICS 139

4.3.13 Joule-Thomson Expansion

A pure gas flows at a low rate through a well insulated horizontal pipe at high pressure andis throttled to a slightly lower pressure. The equation of state for the system is given asP (V − c) = RT , where c is a positive constant. Kinetic energy changes are negligible. Provewhether or not the gas temperature rises or falls due to throttling by using the followingequation for Joule-Thomson coefficient, µH , (GATE-1989-16i)

µH =(

∂T

∂P

)H

=T

(∂V

∂T

)P

− V

CP

Solution:For the equation of state P (V − c) = RT ,

V − c =RT

P

V =RT

P+ c(

∂V

∂T

)P

=R

P

Therefore

µH =T

(∂V

∂T

)P

− V

CP

=T (R/P )− V

CP=−c

P

Since c is positive, µH is negative.For the pressure difference ∆P at constant H,

∆T

∆P= µH

Therefore∆T = µH∆P

During throttling, pressure is reduced. i.e., ∆P (= P2 − P1) is negative. Therefore ∆T (=T2 − T1 is positive. In other words, (T1 − T2) is negative. Therefore temperature increasesduring expansion. (1 refers to inlet and 2 refers to outlet conditions)


8. At steady state, the temperature variation in a plane wall, made of two different solidsI and II is shown below:

I II

L L� -� -

Distance -

6

T

HHHHHHXXXXXXp p p p p p p pp p p p p p p p pp p p p p p p pp p p p p p p p pp p p p p p p pp p p p p p p p pp p p p p p p pp p p p p p p p pp p p p p p p pp p p p p p p p pp p p p p p p pp p p p p p p p pp p p p p p p pp p p p p p p p p

- - - - - - - -- - - - - - - -- - - - - - - -- - - - - - - -- - - - - - - -- - - - - - - -- - - - - - - -- - - - - - - -- - - - - - - -- - - - - - - -- - - - - - - -- - - - - - - -- - - - - - - -

Then, the thermal conductivity of material I (GATE-1997-2.09)

(a) is smaller than that of II(b) is greater than that of II(c) is equal to that of II(d) can be greater than or smaller than that of II

Answer: (a) q = kdT/dx = k × slope = const. Here slopeI > slopeII . ThereforekI < kII

MASS TRANSFER 211

6.1.7 Distillation

• Separation by distillation is accomplished by partial vaporization and partial conden-sation.

• Vapor-liquid equilibrium relationship

– y = Kx, where K is the equilibrium ratio.

– The equilibrium ratio for any component depends on temperature, on pressureand on compositions of the liquid and vapor. Because higher temperatures favorvaporization and higher pressure retard it, equilibrium ratios generally becomelarger as the temperature is raised or as pressure is reduced.

• First drop of liquid vaporizes at bubble point and last drop at dew point.

• Relative Volatility (α)

– This is the ratio of A and B in one phase to that in the other and is a measureof the separability.

α =y∗/(1− y∗)x/(1− x)

=PsatA

PsatB

– If α = 1, no separation is possible.

– The relative volatility and hence the separability usually becomes less at highpressures.

– Volatility of different materials generally approach each other as temperature israised. Because increasing the pressure on any system raises its boiling temper-ature, relative volatilities become smaller as pressures are raised.

– Equilibrium relationy∗ =

αx

1 + x(α− 1)

– Relative volatility varies with the temperature.

– As the pressure is increased, the relative volatility decreases.

• Ideality of solutions

– A liquid or vapor mixture constitutes an ideal solution if there are no interactionswhen its components are mixed, no heat is evolved and volumes are additive. Bythis definition, vapor mixtures that obey perfect gas law must constitute idealsolutions.

– In ideal solutions, volatilities are independent of composition.

• Because distillation conditions are usually close to isobaric, equilibrium diagrams aredrawn for constant-pressure conditions.

• Positive deviations from ideality


– A mixture whose total pressure is greater than that computed for ideality is saidto show positive deviations from Raoult’s law. Most mixtures fall in this category.In these cases, the partial pressures of each component are larger than the ideal.

– Since the activity coefficient γ is greater than unity in these cases log γ is positive,and hence the name positive deviations from ideality.

• Minimum boiling azeotropes

– When positive deviations from ideality are sufficiently large and the vapor pres-sures of the components are not too apart, then minimum boiling azeotropes willform.

– Azeotropic mixtures of this sort are very common. One of the most important isethanol-water azeotrope which at 1 atm occurs at 89.4 mole percent of ethanoland 78.2◦C. Azeotropism disappears in this system at pressures below 70 mmHg.

• Partial liquid miscibility: Heteroazeotropes

– Example: Isobutanol-water system. In this azeotropic composition lies inside thelimits of solubility at the bubble point.

– In relatively few instances the azeotropic composition lies outside the limits ofsolubility, as in the systems of methyl ethyl ketone-water and phenol-water.

– Heterogeneous azeotropes are always minimum boiling mixtures because activitycoefficients must be significantly greater than 1 to cause splitting into two phases.

• When the components have a very large difference in their boiling points, no azeotropecan form, as for ammonia-toluene, and carbondioxide-water.

• Insoluble liquids: Steam distillation

– Mutual solubility of liquids is so small.

– If the liquids are completely insoluble, the vapor pressure of either componentcannot be influenced by the presence of the other and exerts its true vapor pressureat the prevailing temperature. When the sum of the seperate vapor pressureequals the total pressure, the mixture boils, and the vapor composition is readilycomputed, assuming the applicability of ideal gas law.

PA + PB = Pt

y∗ =PA

Pt

– By this method of distillation with steam, so long as liquid water is present, thehigh boiling organic liquid can be made to vaporize at a temperature much lowerthan its normal boiling point without the necessity of a vacuum pump.

– For the greatest economy in steam distillation, the still should be heated froman external source of energy to the highest allowable temperature, and should beoperated under as high a vacuum as the cooling water will permit.

MASS TRANSFER 213

• Negative deviations from ideality

– When the total pressure of a system at equilibrium is less than the ideal value,the system is said to deviate negatively from Raoult’s law.

• Maximum boiling azeotropes

– Maximum boiling azeotropes are less common than the minimum type.

– Examples: acetone-chloroform, HCl-water systems.

• x− y diagrams:

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32

4

51y

x0 10

1

1. Stereoisomers, α = 12. Ideal solutions3. Minimum boiling azeotropes4. Maximum boiling azeotropes5. Heteroazeotropes

– With systems of type 1, (y = x) no seperation is possible by distillation. Exam-ples: stereoisomers, H2O-D2O system.

– Those systems having curves of type 3, which crosses the diagonal, possess mini-mum boiling points at the intersection, while the systems of type 4 (curves withsteeper slopes than the disgonal at the point of intersection) are mixtures thatpossess maximum boiling points at the point where y = x.

• Differential or simple distillation

– Rayleigh’s Equation:

lnF

W=

∫ xF

xW

dx

y∗ − x

– For constant α:

lnFxF

WxW= α ln

F (1− xF )W (1− xW )

• Reflux ratio R

– R =L

D– At the minimum reflux ratio, column requires an infinite number of trays, and

consequently the fixed cost is infinite; but the operating costs (heat for reboiler,condenser cooling water, power for reflux pump) are least.


– Optimum reflux ratio is about 1.2Rm to 1.5Rm, where Rm is the minimum refluxratio.

• q-lines

– q = heat required to convert 1 mole of feed from its condition hf to a saturatedvapor hg divided by molar latent heat.

q =hg − hf

hg − hl

– Slope of q-line =q

q − 1

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CA

B

D

Ey

x

A - saturated liquidB - saturated vaporC - liquid + vaporD - liquid below bubble pointE - superheated vapor

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

• Fenske’s equation

– To find minimum number of trays Nm at total reflux, for systems of constantrelative volatility.

Nm + 1 =log

[xD

1−xD· 1−xW

xW

]log α

• The optimal reflux ratio to minimum reflux ratio is usually in the range of 1.1 to 1.5.

• Use of open steam

– When a water solution in which the nonaqueous component is the more volatile,is fractionated, so that the water is removed as the residue product, the heatrequired can be provided by admission of steam directly to the bottom of thetower. The reboiler is dispensed with.

– For a given reflux ratio and distillate composition, more trays will usually berequired in the tower.

– In trays calculation, the enriching section of the tower is unaffected by the use ofopen steam.

MASS TRANSFER 215

• It is the condensing temperature in a condenser which determines the operating pres-sure of the distillation column, since the saturation temperature of a vapor varies withits pressure. If the condensing temperature is very close to cooling water range atatmospheric pressure, the distillation pressure must be elevated to permit a larger∆T .

• Reboilers

– Kettle type reboiler — a theoretical stage.

– Thermosyphon reboilers: It is safest not to assume that theoretical stage’s worthof fractionation will occur with thermosyphon reboilers but instead to providethe necessary stages in the tower itself.

• Heat losses in the tower

– Heat losses increases the internal reflux ratio Ln/Gn+1, and for a given condenserheat load, fewer trays for a given sepration are required.

– For a given reboiler heat load, fewer trays are required for a given separation isthe heat losses are eliminated.

• Use of HETP data for packed-bed distillation

– Distillation design methods normally involve dtermination of the number of the-oretical equilibirum stages or plates N . Thus when packed columns are employedin distillation applications, it is common practice to rate the efficiency of towerpackings in terms of the height of packing equivalent to one theoretical stage(HETP).

MASS TRANSFER 231

6.3.4 Interfacial Gas Concentration

Consider a system in which component A is being transferred from a gas phase to a liquidphase. The equilibrium relation is given by yA = 0.75xA where yA and xA are mole fractionsof A in gas and liquid phase respectively. At one point in the equipment, the gas contains10 mole % A and liquid 2 mole % A. Gas film mass transfer coefficient ky at this point is10 kmol/(hr.m2.∆yA) and 60% of the resistance is in the gas film. Calculate:

(a) the overall mass transfer coefficient in kmol/(hr.m2.∆yA).

(b) mass flux of A in kmol/(hr.m2).

(c) the interfacial gas concentration of A in mole fraction. (GATE-1990-15iii)

Solution:Equilibrium composition of gas y∗A corresponding to xA = 0.02 (i.e., 2 mole %):

y∗A = 0.75xA = 0.75× 0.02 = 0.015

Since individual gas film resistance 1/ky is 60% of overall resistance 1/Ky,

0.61

Ky=

1ky

Ky = 0.6× 10 = 6 kmol/(hr.m2.∆yA)

Mass flux in terms of overall mass transfer coefficient:

Mass flux = Ky(yA − y∗A) (6.7)= 6(0.1− 0.015) = 0.51 kmol/(hr.m2)

Mass flux in terms of individual mass transfer coefficient:

Mass flux = ky(yA − yAi) (6.8)

where yAi = interfacial gas concentration.Substituting for mass flux, ky and yA in Eqn.(6.8),

10(0.1− yAi) = 0.51yAi = 0.049


20. A gaseous reaction A → 2B+C takes place isothermally in a constant pressure reactor.Starting with a gaseous mixture containing 50% A (rest inerts), the ratio of final toinitial volume is found to be 1.6. The percentage conversion of A is (GATE-1992-2.c)

(a) 30 (b) 50 (c) 60 (d) 74

Answer: (c) εA =VXA=1 − VXA=0

VXA=0=

3− 11

= 2

V

V0= 1.6 =

volume of inert + volume of A

volume at initial=

0.5V0 + 0.5V0(1 + εAXA)V0

Solving XA = 0.6.


8.3.18 Offset in Feedback Control System

A control system is shown below.

-+iSet-point

- 2(s + 1) - i?Load++ - 1

s+4-C

−6

(a) Determine the variation of C with time for a unit step change in the set-point.

(b) What is the offset? (GATE-1997-8)

Solution:

C(s) =2(1 + s) 1

s+4

1 + 2(1 + s) 1s+4

ysp(s)

=2(1 + s)

(s + 4) + 2(1 + s)ysp(s)

=2(1 + s)3(s + 2)

ysp(s)

For unit step change in setpoint, ysp(s) = 1/s. Therefore

C(s) =23

1 + s

s + 21s

=23

[1

s(s + 2)+

1s + 2

]=

23

[1/2s− 1/2

s + 2+

1s + 2

]=

13

[1s

+1

s + 2

]Using inverse Laplace transform,

C(t) = (1/3)[1 + e−2t

]This expression gives the variation of C with time for unit step change in setpoint.

Offset = 1− limt→∞

C(t)

= 1− 1/3 = 2/3

PROCESS ECONOMICS & DESIGN 337

9.1.2 Cost Estimation

• Total capital investement = Fixed capital investement + working capital

• Most chemical plants use an working capital accounting to 10 to 20% of the totalcapital investment.

• Cost indexes: for updating cost data from cost data for a particular year.

Present cost = original cost ×(index value at present time

index value at time original cost was obtained

)

• Cost scaling: cost data for a particular size. Normally six-tenths factor rule is used.According to this rule, if the cost of a given unit at one capacity is known, the costof a similar unit with X times the capcity of the first is approximately X0.6 times thecost of the initial unit.

Cost of equipment of a = cost of equipment b×(capacity of equipment a

capacity of equipment b

)0.6

However, the application of the 0.6 rule of thumb for most purchased equipment isan oversimplification of a valuable cost concept, since the actual values of the cost-capacity factor vary from less than 0.2 to greater than 1.0. Because of this, 0.6 factorshould only be used in the absence of other information. In general, the cost-capacityconcept should not be used beyond a tenfold range of capacity.

• Lang1 multiplication factors for estimation of fixed-capital investment ortotal capital investmentFactor × delivered equipment cost = fixed-capital investment or total capital invest-ment.

Factor forType of plant Fixed-capital Total capital

investment investmentSolid-processing plant 3.9 4.6Solid-fluid-processing plant 4.1 4.9Fluid-processing plant 4.8 5.7

1Ref: Plant Design and Economics for Chemical Engineers - Peters & Timmerhaus, McGraw-Hill


• Break-even point

6Rs.

Rate of production-�

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Fixed costloss�

profit-Total income

Total product cost@@I

-

xBreak even point

The fixed cost remains constant, and the total production cost increases as the rate ofproduction increases. The point where the total product cost equals the total incomeis known as break-even point.

• Turnover ratio =gross annual sales

fixed capital investmentThe reciprocal of turnover ratio is sometimes defined as the capital ratio or investmentratio. For the chemical industry, as a very rough rule of thumb, the turnover ratio canbe approximated as 1.


31. Dilute sulfuric acid is handled in vessels made of: (GATE-1989-9.i.a)

(a) Stainless steel (b) Brass (c) Lead (d) Cast iron

Answer: (c) Lead-chamber process produces < 70% H2O4, as lead is not suitable forhigh-concentrated sulfuric acid. But at concentrations less than 70% carbon steel isnot suitable. In other words lead is suitable for dilute sulfuric acid and carbon steelfor concentrated acid and vice versa.


12. limx→∞

x3 + 12x2 + 80x + 1

is (GATE-1997-1.02)

(a) 0 (b)12

(c) 1 (d) infinity

Answer: (d) Divide numerator and denominator by x3 to get

limx→∞

1 + 1/x3

(2/x) + (80/x2) + (1/x3)=

1 + 1/∞0 + 0 + 0

= 1/0 = ∞

An Insight into Chemical Engineering

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