Handbook on Material and Energy Balance Calculations in Material Processing, Third Edition

634 Pages·2011·18.03 MB·English

by  Arthur E. Morris

HANDBOOK ON
MATERIAL AND ENERGY
BALANCE CALCULATIONS IN
MATERIALS PROCESSING
HANDBOOK ON
MATERIAL AND ENERGY
BALANCE CALCULATIONS IN
MATERIALS PROCESSING
THIRD EDITION
Arthur E. Morris
Gordon Geiger
H. Alan Fine
TIMS
)WILEY
A JOHN WILEY & SONS, INC., PUBLICATION
Copyright © 2011 by The Minerals, Metals, & Materials Society. All rights reserved
Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada.
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Library of Congress Cataloging-in-Publication Data:
Morris, Arthur E., 1935-
Handbook on material and energy balance calculations in material processing / Arthur E. Morris, Gordon Geiger, H. Alan Fine. — 3rd ed.
p. cm.
Rev. ed. of: Handbook on material and energy balance calculations in metallurgical processes. 1979.
Includes bibliographical references and index.
ISBN 978-1-118-06565-5 (hardback)
1. Chemical processes—Mathematical models—Handbooks, manuals, etc. 2. Manufacturing processes—Mathematical models—Handbooks, manuals, etc.
3. Chemical processes—Mathematical models—Handbooks, manuals, etc. 4. Materials—Handbooks, manuals, etc. 5. Phase rule and equilibrium—
Handbooks, manuals, etc. 6. Heat balance (Engineering)—Mathematics—Handbooks, manuals, etc. 7. Conservation laws (Physics)—Mathematics—
Handbooks, manuals, etc. I. Fine, H. Alan. II. Geiger, Gordon Harold, 1937- III. Fine, H. Alan. Handbook on material and energy balance calculations in
metallurgical processes. IV. Title.
TP155.7.M66 2011
660'.28—dc22 2011010947
Printed in Singapore.
10 9 8 7 6 5 4 3 21
Contents
Preface to the First Edition xiv
Preface to the Third Edition xvii
Acknowledgements xix
Chapter 1. Dimensions, Units, and Conversion Factors 1
1.1 The SI System of Units 1
1.1.1 Derived Units 2
1.1.2 Units Outside the SI 3
1.1.3 Comments on Some Quantities and Their Units 4
1.2 The American Engineering System (AES) of Units 4
1.3 Conversion of Units 6
1.3.1 Conversion Factor Tables 6
1.3.2 The Dimension Table 7
1.3.3 Conversion Equations — Temperature and Pressure 8
1.4 Unit Conversions Using the U-Converter Program 11
1.5 Amount of Substance — the Mole Unit 11
1.6 Density and Concentration 13
1.6.1 Density 13
1.6.2 Composition and Concentration 16
1.6.3 Composition of Gases 18
1.7 Electrical Units 20
1.8 Calculation Guidelines 21
1.9 Summary 22
References and Further Reading 23
Exercises 23
Chapter 2. Thermophysical and Related Properties of Materials 26
2.1 State of a System and Properties of a Substance 26
2.2 The Gibbs Phase Rule 27
2.2.1 Consequences of the Phase Rule for Non-Reactive and Reactive Systems
2.2.2 Application of the Phase Rule to One-Phase Non-Reactive Systems 28
2.2.3 Application of the Phase Rule to Multi-Phase Non-Reactive Systems 28
2.2.4 Application of the Phase Rule to Reactive Systems 29
2.3 The Gas Phase 30
2.3.1 The Ideal Gas Law 30
2.3.2 Non-Ideal Gas Behavior 32
2.4 Condensed Phases 34
2.5 Vapor-Liquid Equilibrium (VLE) 35
2.5.1 Mixtures of Condensable and Non-Condensable Gases 3 8
2.5.2 Software for Making Dew Point and Humidity Calculations 39
2.6 Effect of Pressure on Phase Transformation Temperatures 42
2.7 Steam and Air Property Calculators 44
v
vi Contents
2.8 Properties of Solutions 44
2.8.1 Ideal Solutions — Raoult's Law 44
2.8.2 Non-Ideal Solutions — Activity Coefficients 46
2.8.3 Solutions of Gases in Condensed Phases 47
2.8.4 The Solubility Limit 48
2.8.5 The Solubility of Ionic Species in Water; the Solubility Product 49
2.9 Summary 50
References and Further Reading 51
Exercises 52
Chapter 3. Statistical Concepts Applied to Measurement and Sampling 54
3.1 Basic Statistical Concepts and Descriptive Tools 55
3.1.1 Histograms and Frequency Distributions 56
3.1.2 Mean, Standard Deviation, and Variance 59
3.1.3 Median, Percentile and Quantile 60
3.2 Distributions of Random Variables 62
3.2.1 The Uniform Distribution 62
3.2.2 The Normal Distribution 70
3.3 Basic Applications of Inferential Statistics to Measurement 75
3.3.1 Sampling Distributions of the Mean and the Central Limit Theorem 78
3.3.2 Confidence Intervals 82
3.3.3 Treatment of Errors 86
3.3.4 Error Propagation 92
3.4 Curve Fitting 95
3.4.1 Simple Linear Regression and Excel's Trendline Tool 96
3.4.2 Using Solver to Develop Single-Variable Regression Models 101
3.4.3 Multiple Linear and Non-linear Regression 102
3.4.4 Using Solver and Excel's SSD Tool to Find Equation Coefficients 105
3.4.5 Choosing Among Models 106
3.4.6 Polynomial vs. Rational Function Models 116
3.4.7 Outliers 117
3.4.8 Warnings 119
3.5 Experimental Design 119
3.5.1 Factorial Design 120
3.5.2 Fractional Factorial Design 130
3.6 Summary 137
References and Further Reading 137
Exercises 138
Chapter 4. Fundamentals of Material Balances with Applications to Non-Reacting Systems 144
4.1 System Characteristics 144
4.2 Process Classifications 145
4.3 Flowsheets 146
4.4 The General Balance Equation 150
4.5 Material Balances on Simple Non-Reactive Systems 151
4.6 Strategy for Making Material Balance Calculations 154
4.6.1 Guidelines for Setting up a Materials Balance 155
4.6.2 Guidelines for Resolving a Set of Equations 156
4.6.3 Objectives of a Material Balance 157
Contents vii
4.7 Degree-of-Freedom Analysis 158
4.7.1 DOF Concepts 159
4.7.2 DOF Calculation Strategy for a Single Non-Reactive Device 160
4.7.3 A Washing Process Having Zero Degrees of Freedom 162
4.7.4 A Washing Process Having a DOF = +1 168
4.7.5 A Leaching Process Having a DOF =-1 171
4.8 Using Excel-based Calculational Tools to Solve Equations 174
4.8.1 Goal Seek and Solver as Calculational Aids 174
4.8.2 Software for Conversion of Stream Units: MMV-C 178
4.9 Balances on Systems with Multiple Devices 179
4.10 Extension of Excel's Calculational Tools for Repetitive Solving 194
4.10.1 SuperGS 194
4.10.2 SuperSolver 196
4.11 Special Multiple-Device Configurations I — Recycle and Bypass 197
4.12 Special Multiple-Device Configurations II — Counter-Current Flow 205
4.13 Using FlowBal for Material Balance Calculations 216
4.13.1 FlowBal Example #1: Mixer/Splitter 217
4.13.2 FlowBal Example #2: Evaporation/Condensation Process 219
4.13.3 FlowBal Example #3: Systems with Multi-Phase Streams 221
4.14 Continuous-Mixing Devices 223
4.14.1 Steady-State Processes 223
4.14.2 Unsteady-State Systems 226
4.14.3 Inert Gas Flushing 229
4.15 Graphical Representation of Material Balances 232
4.16 Measures of Performance 232
4.17 Controllers 234
4.18 Summary 239
References and Further Reading 240
Exercises 241
Chapter 5. Stoichiometry and the Chemical Equation 248
5.1 Atomic and Molecular Mass 248
5.2 Composition of Compounds and the Gravimetric Factor 249
5.3 Writing and Balancing Chemical Equations 251
5.3.1 Chemical Reaction Concepts 252
5.3.2 Writing and Balancing Chemical Reactions for Simple Processes 253
5.4 Calculations Involving Excess and Limiting Reactants 256
5.5 Progress of a Reaction 258
5.5.1 Extent of Species Reaction and Rate of Reaction Terminology 258
5.5.2 Chemical Reaction Kinetics 259
5.5.3 Reaction Progress and Кщ 263
5.5.4 Кщ Values from FREED 264
5.5.5 Guidelines for Using Кщ to Determine Maximum Reaction Extent 265
5.5.6 Application of Equilibrium Limitations for Gas-Condensed Phase Reactions 266
5.5.7 Application of Equilibrium Limitations to Gas-Phase Reactions 268
5.6 Practical Indicators of the Progress of Reactions and Processes 269
5.7 Parallel, Sequential and Mixed Reactions 273
5.8 Independence of Chemical Reactions 274
viii Contents
5.9 Practical Examples of Reaction Writing and Stoichiometry 274
5.9.1 Calculations in Gas-Condensed Phase Processes 275
5.9.2 Calculations in Gas-Phase Processes 277
5.10 Use of Chemical Reactions in FlowBal 279
5.10.1 FlowBal's Extent of Reaction Tool 280
5.10.2 FlowBal's Insert Equation Tool 282
5.11 Balancing Aqueous (Ionic) Reactions 283
5.12 Summary 286
References and Further Reading 288
Exercises 288
Chapter 6. Reactive Material Balances 294
6.1 The General Material Balance Procedure for a Reactive System 294
6.1.1 Independent Chemical Reactions, Independent Species, and Independent Elements 295
6.1.2 Molecular Species Material Balance Method 296
6.1.3 Atomic Species Method 300
6.1.4 Atomic and Molecular Species Balance Examples 302
6.2 The Use of Excel-based Computational Tools in Reactive System Balances 306
6.2.1 Application of SuperSolver 306
6.2.2 Reactive System Material Balances Using FlowBal 309
6.3 Combustion Material Balances 321
6.3.1 Material Balance for the Combustion of a Gaseous Fuel 322
6.3.2 Combustion of Liquid Fuels 327
6.3.3 Combustion of Solid Fuels 327
6.3.4 Use of Feed-Forward and Stack Gas Analysis for Combustion Control 329
6.3.5 Use of FlowBal for Combustion Calculations 333
6.3.6 Trace Combustion Products 335
6.4 The Production of a Reducing Gas 340
6.5 Gas-Solid Oxidation-Reduction Processes 345
6.5.1 Oxidation-Reduction During Calcination 345
6.5.2 The Reduction of Iron Ore Concentrate 348
6.5.3 The Chemistry of Fluidized Bed Reduction of Iron Ore by Hydrogen 349
6.5.4 Excel Simulation of the Fluidized Bed Reduction of Hematite 351
6.5.5 FlowBal Simulation of the Fluidized Bed Reduction of Hematite 355
6.5.6 Shaft Furnace Reduction of Iron Ore Concentrate 359
6.5.7 The Roasting of a Sulfide Concentrate 366
6.6 The Production of Gases with Controlled Oxygen and Carbon Potential 370
6.7 Processes Controlled by Chemical Reaction Kinetics 371
6.8 The Reconciliation of an Existing Materials Balance 372
6.9 The Use of Distribution Coefficients in Material Balance Calculations 377
6.9.1 Use of Tabulated Distribution Coefficients 377
6.9.2 Thermodynamic Databases as a Source of Distribution Coefficient Data 381
6.10 Time-Varying Processes 384
6.11 Systems Containing Aqueous Electrolytes 389
6.11.1 The Stability of Ions 390
6.11.2 Aqueous Processes 392
6.11.3 The Solubility of Ionizable Gases in Water 398
6.12 Summary 402
References and Further Reading 404
Exercises 405
Contents
Chapter 7. Energy and the First Law of Thermodynamics 410
7.1 Principles and Definitions 410
7.2 General Statement of the First Law of Thermodynamics 413
7.3 First Law for an Open System 415
7.4 Enthalpy, Heat Capacity, and Heat Content 416
7.5 Enthalpy Change of Phase Transformations 418
7.6 Enthalpy Change of Chemical Reactions 420
7.7 Thermodynamic Databases for Pure Substances 421
7.8 Effect of Temperature on Heat of Reaction 426
7.8.1 Application of Kirchhoff s Equation to Chemical Reactions 426
7.8.2 Heat of Transformation for Non-Standard and Non-Physical States 428
7.9 The Properties of Steam and Compressed Air 431
7.9.1 Properties of Steam 431
7.9.2 Properties of Compressed Air 432
7.9.3 Temperature Change for Free Expansion of a Gas 433
7.9.4 Cooling by Steam Venting 435
7.9.5 Enthalpy of Psychrometry 43 6
7.10 The Use of FREED in Making Heat Balances 437
7.11 Heat of Solution 441
7.11.1 Formation of Non-ideal Metallic Solutions 441
7.11.2 Polymeric Solutions 442
7.11.3 Aqueous Solutions 444
7.12 Summary 445
References and Further Reading 446
Exercises 447
Chapter 8. Enthalpy Balances in Non-Reactive Systems 450
8.1 Combined Material and Heat (System) Balances 450
8.2 Heat Balances for Adiabatic Processes 458
8.3 Psychrometric Calculations 462
8.4 Energy Efficiency 468
8.5 Recovery and Recycling of Heat 469
8.5.1 Heat Exchange Between Fluids 469
8.5.2 Heat Exchange between Solids and Fluids 474
8.5.3 Application of Heat Recovery Techniques to Aluminum Melting 474
8.5.4 Heat Exchange Accompanied by Material Transfer 478
8.6 Multiple-Device System Balances 483
8.7 Use ofFlowBal for System Balances 488
8.8 Heat Balances Involving Solution Phases 494
8.9 Enthalpy Change During Dissolution of an Electrolyte 496
8.10 Graphical Representation of a Heat Balance 499
8.11 Summary 500
References and Further Reading 501
Exercises 502
X Contents
Chapter 9. System Balances on Reactive Processes 505
9.1 Thermal Constraints on a Material Balance 505
9.1.1 Uncoupled System Balances 506
9.1.2 Strategy for Coupled System Balance 508
9.2 Combustion of Fuels 511
9.2.1 Heat of Combustion Calculations 512
9.2.2 Use of Wobbe Index for Combustion Burner Control 514
9.2.3 Combustion of Fuels of Uncertain Molecular Composition 516
9.3 Adiabatic Processes 517
9.3.1 System Balances Involving Combustion Reactions 518
9.3.2 ART for Condensed-Phase Reaction Processes 531
9.4 System Balances Using FlowBal 533
9.5 Quality of Heat and Thermal Efficiency 542
9.6 System Balances with Heat Exchangers 548
9.7 Aqueous Processes 565
9.8 Electrolytic Processes 571
9.8.1 Energy Requirement for Electrorefming 571
9.8.2 Energy Requirement for Electrowinning 572
9.9 Summary 573
References and Further Reading 574
Exercises 574
Chapter 10. Case Studies 577
10.1 Material Balance for an H-Iron Reduction Process with Gas Tempering and Recycle 577
10.2 Mass and Heat Balance Simulation for the Use of DRI in EAF Steelmaking 581
10.3 Natural Gas Combustion Control and the Wobbe Index 588
10.3.1 The Stoichiometry of NG Combustion with Excess Air 588
10.3.2 The Wobbe Index as a Natural Gas Combustion Control Parameter 591
10.4 Reduction of Hematite to Magnetite 592
10.4.1 Preliminary Calculations — Single Reactor 593
10.4.2 Simulation of Hematite Reduction by a Multi-Stage Process 595
10.5 Conversion of Quartz to Cristobalite in a Fluidized Bed 598
10.5.1 Process Characteristics 598
10.5.2 Device Sizing and Heat Loss Calculation 598
10.5.3 Material and Heat Balance Calculations 599
Exercise 600
Appendix. Computational Tools for Making Material and Heat Balance Calculations 601
A.l U-Converter 601
A.2 Thermophysical Properties of Steam and Air 602
A.3 Stream Units Conversion Calculator (MMV-C) 602
A.4 Extension of Excel Tools for Repeat Calculation 603
A.5 Thermodynamic Database Programs 604
A.6 Flowsheet Simulation and System Balancing 604
General References 605
Index 606
Contents
List of Examples
Chapter 1. Dimensions, Units, and Conversion Factors
1.1 Mass and Weight of Aluminum 5
1.2 Kinetic Energy 6
1.3 Energy of Lifting 6
1.4 Units of Energy 7
1.5 Dimensions for Flowrate 8
1.6 Conversion of Temperature 9
1.7 Conversion Formula 9
1.8 Conversion of Pressure -1 10
1.9 Conversion of Pressure - II 10
1.10 Pressure in a Liquid 11
1.11 The SI and AES Mole 13
1.12 The Density of a Slurry 14
1.13 Bulk Density of a Solid-I 16
1.14 Bulk Density of a Solid - II 17
1.15 Concentration Conversion 17
1.16 Composition of a Gas on a Wet and Dry Basis 19
1.17 Electrical Flow in a Wire 20
1.18 Electrical Energy for Metal Deposition 20
1.19 Number of Significant Figures 22
Chapter 2. Thermophysical and Related Properties of Material
2.1 Removal of Air by a Vacuum Pump 31
2.2 Gas Volume and Flowrate 31
2.3 Compressibility of Steam 32
2.4 Thermal Expansion of Titanium 34
2.5 Evaporation of Water in a Closed Vessel 36
2.6 Humidity and Dew Point 38
2.7 Moisture Content of Clay Dryer Streams 40
2.8 Effect of Pressure on the Freezing Point of Water. 42
2.9 Effect of Pressure on the Vapor Pressure of Water 43
2.10 Vapor and Liquid Phase Composition for the Cu - Ni System 45
2.11 Evaporation from Liquid Cd - Mg Alloys at 700 °C 47
2.12 Volumetric Solubility of C0 in Water 48
2
2.13 The Solubility of CaF in Water 49
2
Chapter 3. Statistical Concepts Applied to Measurement and Sampling
3.1 A Histogram of Ceramic Strength Measurements 57
3.2 Percentiles of the %Cu Data using Excel 61
3.3 Uniformity of Vermiculite Particles 66
3.4 Evaluation of the Normal Distribution for Ceramic Strength Data 74
3.5 Finding a 90% Confidence Interval 84
3.6 Relationship Between Sample Size and Interval Width Using the SiON Example
2 2