Principles and Practice of Engineering PE Chemical Reference Handbook [2.0 ed.]

Table of contents :
COVER AND COPYRIGHT......Page 1
PREFACE: ABOUT THE HANDBOOK......Page 3
TABLE OF CONTENTS......Page 4
1.1 Terms, Symbols, and Definitions......Page 11
1.1.1 Constants......Page 13
1.1.2 Dimensional Analysis......Page 15
1.2.1 Metric Prefixes......Page 18
1.2.2 Base and Derived SI Units......Page 19
1.2.3 Unit Conversion Tables (U.S. and Metric)......Page 20
1.3.1 Algebra......Page 40
1.3.2 Geometry and Trigonometry......Page 44
1.3.3 Calculus......Page 56
1.3.4 Statistics and Probability......Page 67
1.4.1 Periodic Table of the Elements......Page 79
1.4.2 Industrial Chemicals......Page 84
2 MASS AND ENERGY BALANCES......Page 87
7.1 Symbols and Definitions......Page 0
2.2.1 Measures of Composition......Page 88
2.2.2 Density......Page 94
2.3.2 Mass Balances With Reaction......Page 95
2.4.1 Energy Balances without Reaction......Page 96
2.4.2 Energy Balances with Reaction......Page 97
3 THERMODYNAMICS......Page 102
3.2.1 State Functions......Page 105
3.2.2 First and Second Laws of Thermodynamics......Page 115
3.3.2 Compression and Expansion......Page 119
3.4.1 Efficiency of Power Cycles......Page 122
3.4.2 Gas Power Cycles......Page 123
3.4.3 Vapor Power Cycles......Page 132
3.4.4 Refrigeration Cycles......Page 134
3.5.3 Concentration Dependence......Page 139
3.6.1 Definitions......Page 140
3.6.2 Pure Substances......Page 141
3.6.4 Nonideal Systems......Page 144
3.6.5 Phase Behavior......Page 146
3.6.6 Phase Equilibrium Applications......Page 151
3.7 Tables......Page 153
4 HEAT TRANSFER......Page 154
4.2.1 Heat Transfer Without Phase Change......Page 157
4.2.2 Heat Transfer With Phase Change......Page 170
4.3.1 Heat-Exchange Equipment Design......Page 175
4.3.2 Heat-Exchange Equipment Analysis......Page 189
4.4.1 Tables of Heat-Transfer Data......Page 195
4.4.2 Charts with Heat-Transfer Data......Page 206
4.4.3 Heat-Exchanger Design Information......Page 207
4.4.4 F-Factor Charts......Page 208
5.1 Symbols and Definitions......Page 215
5.2.1 Reaction Rate......Page 216
5.2.2 Rate Equations in Differential Form for Irreversible Reactions......Page 217
5.2.3 Yield and Selectivity......Page 218
5.3.1 Types of Reactors......Page 219
5.3.2 Integrated Reactor Equations for Irreversible Reactions......Page 221
5.3.3 Complex Reactions......Page 223
5.4.3 Enzyme Kinetics: Michaelis-Menten......Page 224
5.5.3 Continuous Stirred Tank Reactor......Page 226
6 FLUID MECHANICS......Page 227
6.2.1 Mechanical Energy Balance......Page 230
6.2.2 Viscosity and Fluid Properties......Page 232
6.2.3 Velocity......Page 234
6.2.4 Reynolds Number......Page 235
6.2.5 Friction......Page 240
6.2.6 Pressure Drop for Laminar Flow......Page 241
6.2.7 Pressure Drop for Turbulent Flow......Page 242
6.2.8 Flow Through an Orifice......Page 247
6.2.9 Particle Flow......Page 248
6.2.10 Open-Channel Flow......Page 252
6.2.11 Two-Phase Flow......Page 255
6.2.12 Compressible Flow......Page 257
6.3.1 Pumps......Page 261
6.3.3 Control Valves......Page 268
6.3.4 Jet Propulsion......Page 269
6.3.5 Air Lift......Page 270
6.3.6 Solids Handling......Page 273
6.3.7 Mixing......Page 277
6.4.1 Manometers and Barometers......Page 280
6.4.2 Flow Measurement Devices (Summary)......Page 282
6.4.3 Orifice, Nozzle, and Venturi Meters......Page 291
6.5 Tables......Page 296
7 MASS TRANSFER......Page 304
7.2.1 Diffusion......Page 307
7.2.2 Mass-Transfer Coefficients......Page 310
7.2.3 Convective Mass Transfer......Page 311
7.2.4 Mass Transfer Between Phases for Dilute Systems ......Page 314
7.2.5 Mass Transfer Between Phases for Concentrated Systems......Page 315
7.2.6 Height of a Transfer Unit......Page 316
7.2.7 Mass Transfer with Reaction......Page 317
7.3.1 Batch Distillation......Page 320
7.3.2 Continuous Distillation......Page 321
7.3.3 Absorption and Stripping......Page 332
7.4.1 Trayed Columns......Page 334
7.4.2 Packed Columns......Page 346
7.5.1 Fundamentals of Liquid-Liquid Extraction......Page 364
7.5.2 Theoretical (Equilibrium) Stage Calculations......Page 366
7.5.3 Rate-Based Calculations With Mass-Transfer Units......Page 370
7.5.4 Liquid-Liquid Extraction Equipment......Page 373
7.6.2 Adsorption Operation......Page 383
7.6.3 Adsorption Regeneration......Page 385
7.7.1 Adiabatic Humidification and Cooling......Page 386
7.7.2 Drying of Solids......Page 390
7.8 Filtration......Page 396
7.9 Membrane Separation Processes......Page 397
7.10 Crystallization......Page 404
7.11 Leaching......Page 408
7.12.1 Particle Settling......Page 410
7.12.2 Cyclone Separators......Page 411
8.1 Terms and Definitions......Page 414
8.2.1 Hazard Identification......Page 419
8.2.2 Hazard Management......Page 437
8.2.3 Hazard Communication......Page 442
8.2.4 Personal Safety and Industrial Hygiene......Page 449
8.3.1 Overpressure Protection/Pressure Relief......Page 470
8.3.2 Other Protections......Page 481
8.4.1 Air Pollution......Page 482
8.4.2 Mitigation......Page 486
8.5.2 Process Diagrams......Page 487
8.5.3 Layout and Siting Considerations......Page 498
8.5.4 Economics......Page 516
8.6.1 Material Selection......Page 521
8.6.2 Corrosion......Page 525
8.7 Process Equipment Design......Page 546
8.8.1 Sensors......Page 548
8.8.2 Controller Actions......Page 549
8.8.3 Alarms......Page 552
8.8.4 Safety Instrumented Systems......Page 553
8.9.1 Operating Procedures......Page 557
8.9.2 Start-up and Shutdown......Page 559
8.10.1 Testing and Inspection......Page 560
8.10.2 Maintenance......Page 561
8.11 Process Improvement and Troubleshooting......Page 562
8.12 Flammability Data......Page 564
9.1 Symbols and Definitions......Page 567
9.2.1 U.S. Customary Units......Page 568
9.2.2 SI Units......Page 569
9.3.1 U.S. Customary Units......Page 570
9.3.2 SI Units......Page 571
9.3.3 Chemical Resistance of Plastics......Page 572
9.4.1 U.S. Customary Units......Page 573
9.4.2 SI Units......Page 575
9.5.1 U.S. Customary Units......Page 577
9.5.2 SI Units......Page 581
9.6.1 Dry Atmospheric Air Composition......Page 584
9.6.2 Dry Atmospheric Air Properties......Page 585
9.6.3 Temperature-Dependent Properties of Air (U.S. Customary Units)......Page 586
9.6.4 Temperature-Dependent Properties of Air (SI Units)......Page 587
9.6.5 Psychrometric Chart (U.S. Customary Units)......Page 588
9.6.6 Psychrometric Chart (SI Units)......Page 589
9.7.1 U.S. Customary Units......Page 590
9.7.2 SI Units......Page 592
9.7.3 Properties of Water......Page 594
9.8.1 Properties of Saturated Steam (U.S. Customary Units)......Page 595
9.8.2 Properties of Saturated Steam (SI Units)......Page 598
9.8.3 Superheated Steam (U.S. Customary Units)......Page 603
9.8.4 Superheated Steam (SI Units)......Page 608
9.9 Diagrams for Water and Steam......Page 612

Citation preview

PE Chemical Reference Handbook Version 2.0

This document may be printed from the NCEES Web site for your personal use, but it may not be copied, reproduced, distributed electronically or in print, or posted online without the express written permission of NCEES. Contact [email protected] for more information.

Copyright ©2020 by NCEES®. All rights reserved. All NCEES material is copyrighted under the laws of the United States. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means without the prior written permission of NCEES. Requests for permissions should be addressed in writing to [email protected]. First posting October 2019 Version 2.0

PREFACE About the Handbook The Principles and Practice of Engineering (PE) Chemical exam is computer-based, and the PE Chemical Reference Handbook is the only resource material you can use during the exam. Reviewing it before exam day will help you become familiar with the charts, formulas, tables, and other reference information provided. You will not be allowed to bring your personal copy of the PE Chemical Reference Handbook into the exam room. Instead, the computer-based exam will include a PDF version of the handbook for your use. No printed copies of the handbook will be allowed in the exam room. The PDF version of the PE Chemical Reference Handbook that you use on exam day will be very similar to this one. However, pages not needed to solve exam questions—such as the cover, introductory material, and exam specifications—will not be included in the exam version. In addition, NCEES will periodically revise and update the handbook, and each PE Chemical exam will be administered using the updated version. The PE Chemical Reference Handbook does not contain all the information required to answer every question on the exam. Theories, conversions, formulas, and definitions that examinees are expected to know have not been included. The handbook is intended solely for use on the NCEES PE Chemical exam.

Updates on Exam Content and Procedures NCEES.org is our home on the web. Visit us there for updates on everything exam-related, including specifications, exam-day policies, scoring, and practice tests.

Errata To report errata in this book, send your correction through your MyNCEES account. Examinees are not penalized for any errors in the Handbook that affect an exam question.

©2020 NCEES

CONTENTS 1 GENERAL INFORMATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Terms, Symbols, and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1. Constants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.2. Dimensional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Units of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.1. Metric Prefixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.2. Base and Derived SI Units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.3. Unit Conversion Tables (U.S. and Metric) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 1.3.1. Algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 1.3.2. Geometry and Trigonometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 1.3.3. Calculus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 1.3.4. Statistics and Probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 1.4 Chemistry and Physical Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 1.4.1. Periodic Table of the Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 1.4.2. Industrial Chemicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 2 MASS AND ENERGY BALANCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 2.1 Symbols and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 2.2 Composition and Density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 2.2.1. Measures of Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 2.2.2. Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 2.3 Mass Balance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 2.3.1. Mass Balances Without Reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 2.3.2. Mass Balances With Reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 2.4 Energy Balances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 2.4.1. Energy Balances without Reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 2.4.2. Energy Balances with Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3 THERMODYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.1 Symbols and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.2 Basic Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 ©2020 NCEES

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3.2.1. State Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3.2.2. First and Second Laws of Thermodynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3.3 Work, Heat, and Efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 3.3.1. Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 3.3.2. Compression and Expansion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 3.4 Power cycles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 3.4.1. Efficiency of Power Cycles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 3.4.2. Gas Power Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 3.4.3. Vapor Power Cycles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 3.4.4. Refrigeration Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 3.5 Chemical Reaction Equilibria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 3.5.1. Gibbs Free Energy and the Equilibrium Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 3.5.2. Temperature Dependence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 3.5.3. Concentration Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 3.5.4. Pressure Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 3.5.5. Le Chatelier's Principle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 3.6 Phase Equilibria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 3.6.1. Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 3.6.2. Pure Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 3.6.3. Ideal Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 3.6.4. Nonideal Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 3.6.5. Phase Behavior. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 3.6.6. Phase Equilibrium Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 3.7 Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 4 HEAT TRANSFER. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 4.1 Symbols and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 4.2 Fundamentals of Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 4.2.1. Heat Transfer Without Phase Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 4.2.2. Heat Transfer With Phase Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 4.3 Applications of Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 4.3.1. Heat-Exchange Equipment Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 4.3.2. Heat-Exchange Equipment Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 ©2020 NCEES

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4.4 Tables and Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 4.4.1. Tables of Heat-Transfer Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 4.4.2. Charts with Heat-Transfer Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 4.4.3. Heat-Exchanger Design Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 4.4.4. F-Factor Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 5 CHEMICAL REACTION ENGINEERING. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 5.1 Symbols and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 5.2 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 5.2.1. Reaction Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 5.2.2. Rate Equations in Differential Form for Irreversible Reactions . . . . . . . . . . . . . . . . 207 5.2.3. Yield and Selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 5.2.4. Pressure Dependence (Gas Phase Reactions). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 5.3 Reactor Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 5.3.1. Types of Reactors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 5.3.2. Integrated Reactor Equations for Irreversible Reactions . . . . . . . . . . . . . . . . . . . . . . 211 5.3.3. Complex Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 5.4 Catalytic Reactors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 5.4.1. Key Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 5.4.2. Surface Reaction Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 5.4.3. Enzyme Kinetics: Michaelis-Menten. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 5.5 Heat Effects in Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 5.5.1. Batch Reactor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 5.5.2. Plug-Flow Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 5.5.3. Continuous Stirred Tank Reactor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 6 FLUID MECHANICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 6.1 Symbols and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 6.2 Fundamentals of Fluid Mechanics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 6.2.1. Mechanical Energy Balance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 6.2.2. Viscosity and Fluid Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 6.2.3. Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 6.2.4. Reynolds Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 6.2.5. Friction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 ©2020 NCEES

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6.2.6. Pressure Drop for Laminar Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 6.2.7. Pressure Drop for Turbulent Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 6.2.8. Flow Through an Orifice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 6.2.9. Particle Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 6.2.10. Open-Channel Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 6.2.11. Two-Phase Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 6.2.12. Compressible Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 6.3 Applications of Fluid Mechanics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 6.3.1. Pumps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 6.3.2. Fans, Blowers, Compressors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 6.3.3. Control Valves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 6.3.4. Jet Propulsion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 6.3.5. Air Lift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 6.3.6. Solids Handling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 6.3.7. Mixing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 6.4 Flow and Pressure Measurement Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 6.4.1. Manometers and Barometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 6.4.2. Flow Measurement Devices (Summary) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 6.4.3. Orifice, Nozzle, and Venturi Meters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 6.5 Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 7 MASS TRANSFER. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 7.1 Symbols and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 7.2 Fundamentals of Mass Transfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 7.2.1. Diffusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 7.2.2. Mass-Transfer Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 7.2.3. Convective Mass Transfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 7.2.4. Mass Transfer Between Phases for Dilute Systems. . . . . . . . . . . . . . . . . . . . . . . . . . 304 7.2.5. Mass Transfer Between Phases for Concentrated Systems. . . . . . . . . . . . . . . . . . . . 305 7.2.6. Height of a Transfer Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 7.2.7. Mass Transfer with Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 7.3 Vapor-Liquid Separations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 7.3.1. Batch Distillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 ©2020 NCEES

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7.3.2. Continuous Distillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 7.3.3. Absorption and Stripping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 7.4 Design of Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 7.4.1. Trayed Columns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 7.4.2. Packed Columns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 7.5 Liquid-Liquid Extraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 7.5.1. Fundamentals of Liquid-Liquid Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 7.5.2. Theoretical (Equilibrium) Stage Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 7.5.3. Rate-Based Calculations With Mass-Transfer Units . . . . . . . . . . . . . . . . . . . . . . . . . 360 7.5.4. Liquid-Liquid Extraction Equipment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 7.6 Adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 7.6.1. Adsorption Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 7.6.2. Adsorption Operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 7.6.3. Adsorption Regeneration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 7.7 Humidification and Drying. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 7.7.1. Adiabatic Humidification and Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 7.7.2. Drying of Solids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 7.8 Filtration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386 7.9 Membrane Separation Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 7.10 Crystallization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 7.11 Leaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398 7.12 Particle Settling and Cyclonic Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 7.12.1. Particle Settling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 7.12.2. Cyclone Separators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 8 PLANT DESIGN AND OPERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 8.1 Terms and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 8.2 Safety, Health, and Environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 8.2.1. Hazard Identification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 8.2.2. Hazard Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 8.2.3. Hazard Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432 8.2.4. Personal Safety and Industrial Hygiene. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

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8.3 Protective Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460 8.3.1. Overpressure Protection/Pressure Relief . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460 8.3.2. Other Protections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471 8.4 Environmental Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472 8.4.1. Air Pollution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472 8.4.2. Mitigation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476 8.5 Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477 8.5.1. Process Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477 8.5.2. Process Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477 8.5.3. Layout and Siting Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488 8.5.4. Economics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506 8.6 Materials of Construction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 8.6.1. Material Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 8.6.2. Corrosion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515 8.7 Process Equipment Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536 8.8 Instrumentation and Process Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538 8.8.1. Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538 8.8.2. Controller Actions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539 8.8.3. Alarms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542 8.8.4. Safety Instrumented Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 8.9 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547 8.9.1. Operating Procedures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547 8.9.2. Start-up and Shutdown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549 8.10 Process Equipment and Reliability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550 8.10.1. Testing and Inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550 8.10.2. Maintenance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551 8.11 Process Improvement and Troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552 8.12 Flammability Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554 9 PHYSICAL PROPERTIES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557 9.1 Symbols and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557 9.2 Physical Properties of Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558 9.2.1. U.S. Customary Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558 ©2020 NCEES

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9.2.2. SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559 9.3 Physical Properties of Plastics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560 9.3.1. U.S. Customary Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560 9.3.2. SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561 9.3.3. Chemical Resistance of Plastics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562 9.4 Physical Properties of Liquids and Gases—Temperature-Independent Properties . . . . . . . 563 9.4.1. U.S. Customary Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 9.4.2. SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565 9.5 Physical Properties of Liquids and Gases—Temperature-Dependent Properties . . . . . . . . 567 9.5.1. U.S. Customary Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567 9.5.2. SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571 9.6 Physical Properties of Air. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574 9.6.1. Dry Atmospheric Air Composition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574 9.6.2. Dry Atmospheric Air Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575 9.6.3. Temperature-Dependent Properties of Air (U.S. Customary Units) . . . . . . . . . . . . . 576 9.6.4. Temperature-Dependent Properties of Air (SI Units) . . . . . . . . . . . . . . . . . . . . . . . . 577 9.6.5. Psychrometric Chart (U.S. Customary Units). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578 9.6.6. Psychrometric Chart (SI Units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579 9.7 Physical Properties of Water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580 9.7.1. U.S. Customary Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580 9.7.2. SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582 9.7.3. Properties of Water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584 9.8 Steam Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585 9.8.1. Properties of Saturated Steam (U.S. Customary Units). . . . . . . . . . . . . . . . . . . . . . . 585 9.8.2. Properties of Saturated Steam (SI Units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588 9.8.3. Superheated Steam (U.S. Customary Units). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593 9.8.4. Superheated Steam (SI Units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598 9.9 Diagrams for Water and Steam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602

©2020 NCEES

x

1 GENERAL INFORMATION 1.1 Terms, Symbols, and Definitions Symbols Symbol

A

Area or surface area

a

Acceleration

ci

Molar concentration

cp

Heat capacity

D

Diameter

DAB

Mass diffusivity

d

Distance or diameter or diagonal

f

Friction factor (Darcy-Weisbach)

f

Frequency

g

Gravitational acceleration

h

Height

h

Convection heat-transfer coefficient

hm

Mass-transfer coefficient

Dhfusion Dhvap ©2020 NCEES

Description

Units (U.S.)

Units (SI)

ft2

m2

ft sec 2 lb mole ft 3

m s2 mol m3

Btu lbm-cF ft or in.

J = m2 kg : K s 2 : K m

ft 2 hr

m2 s m

ft or in. dimensionless

1 sec ft sec 2 ft or in.

1 s m s2

Btu hr-ft 2-cF ft hr

W = kg m 2 : K s3 : K m s

Latent heat of fusion

Btu lbm

J = m2 kg s 2

Latent heat of vaporization

Btu lbm

J = m2 kg s 2

1

m

Chapter 1: General Information Symbols (cont'd) Symbol

Description

Units (U.S.)

Units (SI)

W = kg : m m : K s3 : K m

k

Thermal conductivity

Btu hr-ft-cF

L

Length

ft or in.

MW

Molecular weight

lbm lb mole

N

Number of moles

lb mole

n

Impeller speed (revolutions per time)

1 sec

m

Mass

lbm

P

Power

Btu hr

P

Pressure

lbf in 2

P

Perimeter

ft or in.

P

Probability

r, R R

kg mol mol 1 s kg kg : m 2 s3 kg N = Pa = 2 m m : s2 m W=

dimensionless

Radius Universal gas constant

ft or in.

m

psi-ft 3 Btu lb mole -cR or lb mole -cR

J mol : K

RD

Relative density

dimensionless

SG

Specific gravity

dimensionless

T t

Temperature

°F or °R

Time

hr or sec

u

Velocity

usound

m s m s

ft sec ft sec ft3

Local speed of sound

m3

V

Volume

Wi

Mass ratio

dimensionless

wi

Mass fraction or weight fraction

dimensionless

Xi

Molar ratio

dimensionless

xi

Mole fraction

dimensionless

x a, b, q, f, j

©2020 NCEES

°C or K s

ft or in.

Distance

degree or radians

Angle

a

Thermal diffusivity

β

Coefficient of thermal expansion

gi

Mass concentration

m

2

ft 2 hr 1 cR

m2 s

lbm ft 3

kg m3

1 K

Chapter 1: General Information Symbols (cont'd) Symbol

1.1.1

Description

Units (U.S.)

Units (SI)

lbf in.

N kg m = s2 m

g

Surface tension

λ

Molecular mean free path

μ

Dynamic viscosity

n

Kinematic viscosity

ft 2 hr

m2 s

r

Density

lbm ft3

kg m3

t

Shear stress

lbf in 2

N = kg m2 m : s2

ji

Volume fraction

fi

Volume concentration

ft or in. cP or

lbf -sec ft 2

kg Pa : s = m : s

dimensionless

ft 3 ft 3

m3 m3

Constants Physical Constants Symbol

co

Value 6.706 • 108 2.998 • 108 3.44 • 10–8

G 6.674 •

g

10–11

32.174 9.8067 32.174

gc

k

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Units

miles hr m s ft 4 lbf -sec 4 N : m2 kg 2 ft sec 2 m s2 lbm-ft lbf -sec 2

1

kg : m =1 N : s2

5.66 • 10–24

ft-lbf cR

1.3806 • 10–23

2 J = kg : m K s2 : K

1.3806 • 10–16

erg K

3

Description Speed of light

Gravitational constant

Gravitational acceleration (Earth)

Gravitational conversion factor

Boltzmann constant

Chapter 1: General Information Physical Constants (cont'd) Symbol

NA

Value

Units

2.731 • 1026

1 lb mole

6.022 • 1023

1 mol

8.314

3 J = m : Pa mol : K mol : K

83.14

cm 3 : bar mol : K

8314

m 3 : Pa kmol : K

82.06

cm 3 : atm mol : K liter : atm mol : K liter : Torr mol : K

0.0821

R

62.36 62,360 10.73 1.987

Avogadro's Number

Universal gas constant

cm 3 : Torr mol : K psi-ft3 lb mole-cR Btu = cal lb mole-cR mol : K

1545

ft-lbf lb mole-cR

0.7302

atm-ft3 lb mole- cR

1.71 • 10–9

Btu ft - hr -cR 4

5.67 • 10–8

W = kg m2 : K4 s3 : K4

v

Description

2

Stefan-Boltzmann constant (radiation)

Mathematical Constants Symbol p

e g

©2020 NCEES

Value 3.14159 2.71828

Description Archimedes constant (Pi) Base of the natural log

0.57722

Euler's constant

4

Chapter 1: General Information Standard Values

Note: The definitions for STP (standard temperature and pressure) vary between industries. The table below contains several conditions as specified. Property Conditions U.S. Units SI Units

P = 1 atm = 14.696 psia T = 0°C = 32°F

Molar standard volume, ideal gas (STP)

m3 0.0224 mol liter 22.41 mol

3

ft 359 lb mole

m3 0.02365 mol liter 23.645 mol

Molar standard volume, ideal gas (ambient)

P = 1 atm = 14.696 psia T = 15°C = 59°F

Standard cubic foot (scf)

P = 1 atm = 14.696 psia T = 15.6°C = 60°F

Density of air (STP)

P = 1 atm = 14.696 psia T = 0°C = 32°F

0.0805

lbm ft3

1.29

Density of air (ambient)

P = 1 atm = 14.696 psia T = 15.6°C = 60°F

0.0764

lbm ft3

1.22

Density of air (ambient)

P = 1 atm = 14.696 psia T = 20°C = 68°F

0.0749

lbm ft3

Density of mercury

P = 1 atm = 14.696 psia T = 20°C = 68°F

848

lbm ft 3

Density of water

P = 1 atm= 14.696 psia T = 4°C = 39.2°F

62.4

lbm ft 3

Density of water

P = 1 atm= 14.696 psia T = 15.6°C = 60°F

62.37

lbm ft 3

kg m3 kg 999.0 3 m

Sea level

14.696

lbm in 2

1.013 : 105 Pa

Atmospheric pressure Triple point of water Speed of sound in air (STP) Speed of sound in air (ambient) Energy of visible light

P = 1 atm= 14.696 psia T = 0°C = 32°F P = 1 atm= 14.696 psia T = 20°C = 68°F

ft 3 379.49 lb mole

kg m3 kg 1.20 3 m

13, 579 1000

0.01109cC 0.6123 kPa

ft 1090 sec

m 330 s

ft 1130 sec

m 343 s −3

Btu * hr

1 cd : sr = 1.46 : 10

* cd • sr = candela steradian; see derived SI units for definition

1.1.2

Dimensional Analysis

A dimensionally homogeneous equation has the same dimensions on the left and the right sides of the equation. Dimensional analysis involves the development of equations that relate dimensionless groups of variables to describe physical phenomena.

©2020 NCEES

5

kg m3

32.02cF 0.0887 psia

1 cd : sr = 4.98 : 10

Wavelength: 555 nm

kg m3

−3

W

Chapter 1: General Information 1.1.2.1 Buckingham Pi Theorem The number of independent dimensionless groups that may be used to describe a phenomenon known to involve n variables is equal to the number (n-r ), where r is the number of basic dimensions (e.g., mass, length, time) needed to express the variables dimensionally.

1.1.2.2 Similitude To use a model to simulate the conditions of the prototype, the model must be geometrically, kinematically, and dynamically similar to the system that is modeled. Systems that have the same dimensionless numbers are similar.

Dimensionless Numbers1 Symbol

Definition

Ar

gD p3 ρf `ρp - ρf j µ2

Bi

hL hV k or k A

Bim

hm L DAB x y gc L nu

Name Archimedes Biot Biot (mass transfer)

Description Ratio of buoyancy forces to viscous forces for a particle (p) in a fluid (f) Ratio of internal thermal resistance of a solid body to its surface thermal resistance (used for heat transfer) Ratio of the internal species transfer resistance to the boundary layer species transfer resistance (used for mass transfer)

Bingham

Ratio of yield stress (τy) to viscous stress for Bingham fluids in laminar flow

Bond

Ratio of buoyancy force to surface tension (used for boiling and condensation)

Brinkman

Ratio of viscous dissipation to enthalpy change (for use in high-speed flow)

Drag or friction coefficient

Ratio of surface shear stress to free-stream kinetic energy; dimensionless surface shear stress

n u We c = Re

Capillary

Ratio of viscous forces to surface tension (for use in two-phase flow)

u2 = Ma 2

Cauchy

Ratio of inertia forces to compression forces (for use in compressible flow)

Ca

Pref - Pvap 1 2 2 tu

Cavitation

Ratio of pressure forces to inertia forces for pumps (special case of Euler number) with Pref local absolute reference pressure

Ec

u2 c p DT

Eckert

Kinetic energy of flow relative to boundary-layer enthalpy difference (for use in high-speed flow)

Eu

DP t u2

Euler

Ratio of upstream and downstream pressure difference to inertia force

Fo

at L2

Fourier

Dimensionless time; ratio of rate of heat conduction to rate of internal energy storage in a solid (for use in transient heat-transfer problems)

Fom

DAB t L2

Fourier (mass transfer)

Dimensionless time; ratio of the rate of species diffusion to the rate of species storage (for use in transient mass-transfer problems)

Fr

u2 gL

Froude

Ratio of flow inertia to gravitational forces (for flow over a free surface)

f

DP L 1 2 Dt2u

Friction factor

Ratio of shear force to inertia force; dimensionless pressure drop for internal flow

Bm Bo Br Cf Ca Ca

©2020 NCEES

(t1 - tv) g L2 c n u2 k DT x 1 2 2tu

2 usound

6

Chapter 1: General Information Dimensionless Numbers (cont'd) Symbol

Definition

Ga

g L3 v2

Gr Gz

g b DT L3 v2 Re Pr = u L x x aD D

Jal

cp.l DT Dhvap

Jav

cp.v DT Dhvap

jH

St Pr 3

jm

Stm Sc 3

Ka

g n4 t c3

2 2

Name Galilei

Ratio of gravitational forces to viscous forces

Grashoff

Ratio of buoyancy to viscous forces (for use in natural convection)

Graetz

Ratio of enthalpy flow rate to axial heat conduction

Jakob

Ratio of sensible heat to latent heat (for use in film condensation and boiling)

Colburn factor (heat) Colburn factor (mass)

Knudsen

Ratio of mean free path to a characteristic length (for use in non-continuum flow)

Lewis

Ratio of molecular thermal diffusivity to mass diffusivity

Ma

u usound

Nu

hL k

Np

P t n3 D5

Pe

u3 L a = Re Pr

Peclet

Pem

u3 L = DAB Re Sc

Peclet (mass transfer)

Pr

cp n k

Ra

g b DT L3 Pr v2

Sc Sh

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tu D n v DAB hm L DAB

Dimensionless mass-transfer coefficient Ratio of surface tension forces to viscous forces (used for waves on a liquid film)

Le

Re

Dimensionless heat-transfer coefficient

Kapitza

m L a DAB

Kn

Description

Mach Nusselt Power number

Prandtl

Rayleigh Reynolds Schmidt Sherwood

Dimensionless velocity; ratio of velocity to speed of sound (for use in compressible flow) Dimensionless heat-transfer coefficient; ratio of convection heat transfer to conduction in a fluid layer of thickness L (for use in convective heat transfer) Ratio of drag force to inertial force for power consumption calculation of a mixing impeller (where P is the impeller power) Ratio of enthalpy flow rate to heat conduction rate (for use in forced convection heat transfer) Ratio of mass convection rate to mass diffusion rate (for use in forced convection mass transfer) Relative effectiveness of molecular transport of momentum and energy within the boundary layer; ratio of molecular momentum diffusivity to thermal conductivity (for use in convective heat transfer) Product of Grashoff and Prandtl numbers (for use in natural convection) Ratio of inertia and viscous forces (for use in forced convection and fluid flow) Ratio of molecular momentum diffusivity to mass diffusivity (for use in convective mass transfer) Ratio of convection mass transfer to diffusion in a slab of thickness L (for use in convective mass transfer) 7

Chapter 1: General Information Dimensionless Numbers (cont'd) Symbol

Definition

Name

Description

Sk

DP L nu

St

Nu = h Re Pr t u c p

Stanton

Stm

Sh = hm Re Sc u

Stanton (mass)

Ste

c p DT Dhfusion

Stefan

Ratio of sensible heat to latent heat for the solid/liquid transition (for use in melting and solidification)

Sr

Lf u

Strouhal

Time characteristics of fluid flow (for use in oscillating flow)

We

t u2 L c

Weber

Ratio of inertial to surface tension forces (for use in liquid/vapor phase change)

Stokes

1Verify

Ratio of pressure force to viscous force Dimensionless heat-transfer coefficient, ratio of actual convection heat flux to enthalpy energy heat flux (for use in forced convection heat transfer) Dimensionless mass-transfer coefficient (for use in forced convection mass transfer)

whether gravitational conversion factor (gc) is required before using.

1.2 Units of Measurement 1.2.1

Metric Prefixes Metric Prefixes and Their Symbols

©2020 NCEES

Multiple 10–18 10–15 10–12

Prefix atto femto pico

Symbol a f p

10–9 10–6 10–3 10–2 10–1 101 102 103 106 109 1012 1015 1018

nano micro milli centi deci deka hecto kilo mega giga tera peta exa

n μ m c d da h k M G T P E

8

Chapter 1: General Information

1.2.2

Base and Derived SI Units Base SI Units Quantity

Name

Length Mass Time Electric current Temperature Amount of a substance Luminous intensity

Symbol

meter kilogram second ampere Kelvin mol candela

m kg s A K mol cd

Derived SI Units With Special Names Quantity Name

Unit Symbol

Name

Symbol

Definition

Electric capacitance

C

farad

F

C A : s2 A2 : s4 F= V = J = kg : m 2

Electric charge

Q

coulomb

C

C = A:s

Electric conductance

G

siemens

S

S=

Energy or work or heat

H

joule

J

J = N:m =

Force

F

newton

N

Frequency

f

hertz

Hz

Inductance

L

henry

H

2 V : s kg : m H = X:s = A = 2 2 A :s

Electric potential

E

volt

V

kg : m 2 J V = A:s = 2 3 A :s

Power or energy flux

P

watt

W

2 J N : m kg : m W= s = s = 3 s

Pressure or stress

P

pascal

Pa

Pa =

Electric resistance

R

ohm

Ω

2 V kg : m X= A = 2 3 A :s

lux

lx

lx =

Illuminance

2

1 = A = A 2 : s = A 2 : s3 J X V kg : m 2 kg : m 2 s2

kg : m s2 1 Hz = s N=

N = kg m2 m : s2

lm = cd : sr m2 m2

Luminous flux

UV

lumen

lm

lm = cd : sr

Magnetic flux

UE

weber

Wb

Wb = V : s =

tesla

T

Magnetic flux density

T=

kg : m 2 s2 : A

Wb = V : s = kg m2 m2 s2 : A

Note: Steradian or square radian (sr) is dimensionless and represents a solid angle in three-dimensional space (angle at the tip of a cone). ©2020 NCEES

9

Chapter 1: General Information

1.2.3

Unit Conversion Tables (U.S. and Metric)

1.2.3.1 Time Time Time 1 sec = 1 min = 1 hr = 1 day = 1 week = 1 year =

Second (sec) 1 60 3600 8.6400E+04 6.0480E+05 3.1536E+07

Minute (min) 0.01667 1 60 1440 1.0080E+04 5.2560E+05

Hour (hr) 2.7778E–04 0.01667 1 24 168 8760

Day 1.1574E–05 6.9444E–04 0.04167 1 7 365

Week 1.6534E–06 9.9206E–05 5.9524E–03 0.14286 1 52.143

Year 3.1710E–08 1.9026E–06 1.1416E–04 2.7397E–03 0.01918 1

Additional Unit Conversions for Time



1 fortnight = 3.4560 • 105 sec = 14 days 1 astronomical year = 365.2422 days

1.2.3.2 Angle Conversion Table for Common Units of an Angle Angle 1° = 1 rad = 1' = 1" = 1 rev =

©2020 NCEES

Degree (°) 1 57.296 0.01667 2.7778E–04 360

rad 0.01745 1 2.9089E–04 4.8481E–06 6.2832

Minute (') 60 3437.7 1 0.01667 2.1600E+04

10

Second (") 3600 2.0626E+05 60 1 1.2960E+06

Revolution 2.7778E–03 0.15915 4.6296E–05 7.7161E–07 1

Chapter 1: General Information 1.2.3.3 Length Conversion Table for Common Units of Length Length 1m= 1 in = 1 ft = 1 yd = 1 mile = 1 mil =

m 1 0.0254 0.3048 0.9144 1609.4 2.5400E–05

in. 39.370 1 12 36 6.3362E+04 0.001

ft 3.2808 0.0833 1 3 5280.2 8.3333E–05

yd 1.0936 0.02778 0.3333 1 1760.1 2.7778E–05

mile 6.2135E–04 1.5782E–05 1.8939E–04 5.6816E–04 1 1.5782E–08

Additional Unit Conversions for Length

©2020 NCEES

1 league 1 m (micron) 1 mile (nautical) 1 nautical league

= = = =

4828.2 m 1 • 10–6 m 1853.3 m 5559.9 m

= = = =

3 miles 3.937 • 10–5 in. 1.1515 miles 3 nautical miles

1 furlong

=

201.17 m

=

1 8 mile

1 perch = 1 rod = 1 pole

=

5.292 m

=

1 fathom 1 cable length (U.S. Survey) 1 chain (U.S. Survey) 1 link

= = = =

1.8288 m 219.456 m 20.117 m 0.2012 m

= = = =

5.5 yds = 4 chain 6 ft = 2 yds 120 fathoms = 240 yd 0.1 furlong 0.001 furlong

1 cubit

=

0.4572 m

=

1 bolt 1 skein 1 span 1 hand (horses)

= = = =

36.576 m 109.728 m 0.2286 m 0.1016 m

= = = =

1 caliber

=

2.54 • 10–4 m

=

1 Å (Angström) 1 fermi 1 astronomical unit 1 light year 1 mm 1 cm 1 km

= = = = = = =

1 • 10–10 m 1 • 10–15 m 1.496 •1011 m 9.4605 • 1015 m 0.001 m 0.01 m 1000 m

= = = = = = =

11

1

1 2 yard = 18 in. 40 yd 120 yd 9 in. 4 in. 1 100 in. 3.937 • 10–9 in. 3.937 • 10–14 in. 9.2954 • 107 miles 5.8783 • 1012 miles 0.03937 in. 0.3937 in. 0.62135 mile

mil 3.9370E+04 1000 1.2000E+04 3.6000E+04 6.3362E+07 1

Chapter 1: General Information 1.2.3.4 Area Conversion Table for Common Units of Area Area 1 m2 = 1 in2 = 1 ft2 = 1 yd2 = 1 acre = 1 sq mile =

m2 1 6.4516E–04 0.09290 0.83613 4046.9 2.5900E+06

in2 1550 1 144 1296 6.2727E+06 4.0145E+09

ft2 10.764 6.9444E–03 1 9 4.3560E+04 2.7879E+07

yd2 1.196 7.7160E–04 0.1111 1 4840 3.0976E+06

acre 2.4710E–04 1.5942E–07 2.2957E–05 2.0661E–04 1 640

Additional Unit Conversions for Area r –7 2 1 circ mil = 5.067 • 10–10 m2 = 4 sq.mil = 7.8539 • 10 in r 2 2 1 circ inch = 5.0671 • 10–4 m2 = 4 in = 0.78539 in 1 ha (hectare) 1 township 1 homestead 1 rood 1 sq rod 1 section 1 barn (bn) 1 are 1 centiare 1 mm2 1 cm2 1 km2

©2020 NCEES

= = = = = = = = = = = =

1 • 104 m2 9.324 • 107 m2 6.475 • 105 m2 1011.725 m2 25.2926 m2 2.59 • 108 m2 1 • 10–28 m2 100 m2 1 m2 1 • 10–6 m2 1 • 10–4 m2 1 • 106 m2

= = = = = = = = = = = =

12

2.471 acres 144 homesteads 160 acres 0.25 acre 30.25 sq. yd 1 sq. mile 100 fm2 (femtometer) 119.6 sq. yd 10.764 ft2 1.55 • 10–3 in2 0.155 in2 0.3861 sq. mile

sq mile 3.8610E–09 2.4910E–12 3.5870E–10 3.2283E–09 1.5625E–05 1

Chapter 1: General Information 1.2.3.5 Volume Conversion Table for Common Units of Volume Volume 1 m3 = 1 in3 = 1 ft3 = 1 gal = 1 barrel = 1 liter =

m3 1 1.6387E–05 0.02832 3.7850E–03 0.15898 0.001

in3 6.1024E+04 1 1728 231 9701.6 61.024

ft3 35.314 5.7870E–04 1 0.13367 5.6143 0.03531

gal 264.20 4.3295E–03 7.4814 1 42.0 0.2642

barrel (oil) 6.2901 1.0308E–04 0.17812 0.02381 1 6.2901E–03

Additional Unit Conversions for Volume

©2020 NCEES

1 yd3 1 register ton 1 dry gal (U.S.) 1 U.S. bushel

= = = =

0.7646 m3 2.8317 m3 4.405 • 10–3 m3 0.0353 m3

= = = =

27 ft3 100 ft3 1.164 gal (U.S.) 8 dry gal (U.S.) = 9.31 gal (U.S.)

1 quart (U.S.)

=

9.4625 • 10–4 m3

=

1 4 gal (U.S.)

1 pint (U.S.)

=

4.7313 • 10–4 m3

=

1 cup (U.S.)

=

2.3656 • 10–4 m3

=

1 gill (U.S.)

=

1.1828 • 10–4 m3

=

1 fl oz (U.S.)

=

2.9570 • 10–5 m3

=

1 fl dram (U.S.)

=

3.6963 • 10–6 m3

=

1 minim (U.S.)

=

6.1605 • 10–8 m3

=

1 cm3 = 1 mL 1 mm3 1 hectoliter 1 hogshead 1 UK bushel 1 Imperial gal (UK) 1 quarter (UK) 1 peck (UK)

= = = = = = = =

1 • 10–6 m3 1 • 10–9 m3 0.1 m3 0.2385 m3 0.0364 m3 0.0045 m3 0.291 m3 0.0091 m3

= = = = = = = =

1 1 8 gal (U.S.) = 2 quart (U.S.) 1 1 2 pint = 16 gal (U.S.) 1 1 4 pint = 32 gal (U.S.) 1 1 8 cup = 128 gal (U.S.) 1 1 8 fl oz = 1024 gal (U.S.) 1 1 60 dram = 480 fl oz 0.06102 in3 6.1024 • 10–5 in3 26.42 gal (U.S.) 63 gal (U.S.) 8 dry gal (UK) 1.201 gal (U.S.) 64 gal (UK) 2 gal (UK)

1 quart (UK)

=

0.0011 m3

=

1 4 gal (UK)

1 pint (UK)

=

5.6826 • 10–4 m3

=

1 barrel (UK) 1 barrel (U.S. liq) 1 barrel (U.S. dry) 1 cord (lumber) 1 stere (lumber)

= = = = =

0.1637 m3 0.1192 m3 0.1156 m3 3.625 m3 1 m3

= = = = =

1 8 gal (UK) 36 gal (UK) = 43 gal (U.S.) 31.503 gal (U.S.) = 26 gal (UK) 30.55 gal (U.S.) 128 ft3 1.308 yd3

1 boardfoot (lumber)

=

2.3597 • 10–6 m3

=

13

1 3 12 ft

liter 1000 0.01639 28.317 3.7850 158.98 1

Chapter 1: General Information U.S. Conversion for Liquid Volume 1 gal (U.S.) 1 quart 1 pint 1 cup

= = = =

4 quarts 2 pints 2 cups 8 fl oz

U.S. Conversion for Dry Volume 1 cup 1 Tbsp 1 tsp 1 pinch

= = = =

16 tablespoons (Tbsp) 3 teaspoons (tsp) 8 pinches 2 dashes

1.2.3.6 Mass Conversion Table for Common Units of Mass Mass 1 kg = 1 lbm = 1 oz = 1 ton (short) = 1 ton (long) =

kg 1 0.45359 0.02835 907.18 1016.1

lbm 2.2046 1 0.0625 2000 2240

oz 35.273 16 1 3.1999E+04 3.5840E+04

ton (short) 1.1023E–03 5.0000E–04 3.1251E–05 1 1.12

ton (long) 9.8420E–04 4.4642E–04 2.7902E–05 0.89285 1

slug 0.06852 0.03108 1.9426E–03 0.62162 69.622

1 slug =

14.594

32.174

514.78

0.01608

0.014363

1

Additional Unit Conversions for Mass 1 hundredweight (short) 1 hundredweight (long)

= =

45.3592 kg 50.8023 kg

= =

100 lbm 112 lbm

1 tonne (metric) 1 centner 1 dram 1 grain 1 carat 1 atomic mass unit

= = = = = =

1000 kg 100 kg 1.7719 • 10–3 kg 6.4799 • 10–5 kg 2.0000 • 10–4 kg 1.6605 • 10–27 kg

= = = = = =

2204.6 lbm 220.5 lbm 0.0625 oz 2.2857 • 10–3 oz 7.0547 • 10–3 oz 3.6608 • 10–27 lbm

=

21.62 lbm

=

14 lbm

1

©2020 NCEES

kgf : s 2 = 9.8067 kg m 1 stone = 6.3503 kg 1 firkin

=

40.8231 kg

=

90 lbm

1 lb (apothecary/troy)

=

0.3732 kg

=

13.166 oz = 12 oz (ap/troy) = 0.8229 lbm

1 oz (apothecary/troy)

=

3.1103 • 10–2 kg

=

1.0971 oz

1 dram (apothecary)

=

3.8879 • 10–3 kg

=

0.13714 oz

1 scruple (apothecary)

=

1.2960 • 10–3 kg

=

0.04571 oz

1 grain (apothecary/troy)

=

6.4799 • 10–5 kg

=

2.2857 • 10–3 oz = 1.4286 • 10–4 lbm

1 carat (troy)

=

2.0500 • 10–4 kg

=

7.231 • 10–3 oz

1 pennyweight (troy)

=

1.5552 • 10–3 kg

=

0.05486 oz

10–6

1 mite (troy)

=

3.2400 •

kg

=

1.1428 • 10–4 oz

1 doite (troy)

=

1.3500 • 10–7 kg

=

4.7618 • 10–6 oz

14

Chapter 1: General Information Apothecary Measures 1 lb 1 lb 1 oz 1 dram 1 scruple

= = = = =

373.242 grain 12 oz 8 drams 3 scruples 20 grains

Troy Measures 1 lb 1 lb 1 ozt

= = =

373.242 grain 12 oz (ozt) 20 pennyweight (dwt)

1 dwt 1 grain 1 mite

= = =

24 grains 20 mites 24 doites

1.2.3.7 Density Conversion Table for Common Units of Density Density

kg m3

lbm ft 3

lbm gal

kg liter

lbm in 3

ton yd 3

1

kg = m3

1

0.06243

8.3452E–03

0.001

3.6128E–05

7.5250E–04

1

lbm = ft 3

16.018

1

0.13367

0.01618

5.7870E–04

0.01205

lbm 1 gal =

119.83

7.481

1

0.11983

4.3292E–03

0.09017

kg 1 liter =

1000

62.43

8.3452

1

0.036128

0.7525

1

lbm = in 3

2.7679E+04

1728

231

27.679

1

20.829

1

ton = yd 3

1328.9

82.963

11.09

1.3289

0.048011

1

Additional Unit Conversions for Density slug kg lbm = 515.379 3 = 32.175 3 1 3 ft ft m g lbm 1 liter = 1 kg3 = 0.06243 3 ft m oz 1 gal

=

7.4906

kg m3

=

0.46764

grain ft3

=

0.0023

kg m3

=

1.4286 : 10

lbm 1 UK gal

=

99.978

kg m3

=

6.2416

1

©2020 NCEES

15

lbm ft 3 -4

lbm ft 3

lbm ft 3

Chapter 1: General Information Specific gravity (also called relative density): The ratio of the density of a substance to the density of water at 4°C (39°F):

= SG

t t = kg lbm 1000 3 62.4 3 ft m

API gravity:

141.5 − 141.5 API = SG 131.5 ; SG60cF = API + 131.5 60cF

1.2.3.8 Specific Volume Conversion Table for Common Units of Specific Volume Specific Volume

m3 kg

liter kg

ft 3 lbm

gal lbm

in 3 lbm

ft 3 kg

1

1000

16.018

119.76

2.7680E+04

35.314

0.001

1

0.01602

0.11976

27.68

0.03531

ft 3 1 lbm =

0.06243

62.428

1

7.4764

1728

2.2046

gal 1 lbm =

8.3500E–03

8.35

0.13375

1

231

0.29488

in 3 1 lbm =

3.6127E–05

0.03613

5.7870E–04

4.3266E–03

1

1.2758E–03

0.02832

28.317

0.45359

3.3913

783.81

1

m3 1 kg = liter 1 kg =

ft 3 1 kg =

1.2.3.9 Velocity Conversion Table for Common Units of Velocity m s

ft min

miles hr

km hr

knots

m 1 s =

ft sec

1

3.2808

196.85

2.2369

3.6

1.9423

ft 1 sec =

0.3048

1

60

0.68182

1.0973

0.592

ft 1 min =

5.0800E–03

0.01667

1

0.01136

0.018288

9.8667E–03

mile 1 hr = km 1 hr = 1 knot =

0.44704

1.4667

88

1

1.6093

0.86827

0.27778

0.91134

54.681

0.62137

1

0.53952

0.51486

1.6892

101.35

1.1517

1.8535

1

Velocity

©2020 NCEES

16

Chapter 1: General Information 1.2.3.10 Acceleration Conversion Table for Common Units of Acceleration m s2

ft sec 2

in. sec 2

cm s2

g

km hr : s

1

3.2808

39.37

0.01

0.10197

3.569

0.3048

1

12

3.0480E–03

0.03108

1.0878

0.0254

0.08333

1

2.5400E–04

2.5901E–03

0.09065

100

328.08

3937

1

10.197

356.9

1g=

9.8067

32.174

386.09

0.09807

1

35

km 1 hr : s =

0.28019

0.91926

11.031

2.8019E–03

0.02857

1

Acceleration 1

m= s2

1

ft = sec 2

in. = sec 2 cm 1 2 = s 1

1.2.3.11 Volumetric Flow Volumetric Flow

Conversion Table for Common Units of Volumetric Flow MMgal ** barrel * gal m3 ft 3 day day min s hr

ft 3 sec

m3 1 s =

1

1.5851E+04

1.2713E+05

5.4345E+05

22.8

35.314

gal 1 min =

6.3089E–05

1

8.0207

34.286

1.4384E–03

2.2280E–03

ft 3 1 hr =

7.8658E–06

0.12468

1

4.2747

1.7934E–04

2.7778E–04

barrel 1 day =

1.8401E–06

0.02917

0.23394

1

4.2000E–05

6.4982E–05

0.04386

695.2

5576

2.3835E+04

1

1.5489

0.02832

448.84

3600

1.5389E+04

0.64563

1

1

MMgal = day

ft 3 1 sec =

* 1 barrel of oil = 42 gallons

©2020 NCEES

17

** million gallons

Chapter 1: General Information

Additional Unit Conversions for Volumetric Flow ft3 1 min

=

4.7195 : 10

gal 1 hr

=

1.0515 : 10

UK gal 1 min

=

7.5766 : 10

UK gal hr

=

1.2628 : 10

MM gal (UK) day

=

m3 0.0526 s

m3 1 hr

=

2.778 : 10

liter 1 min

=

1.667 : 10

liter 1 s

=

m3 0.001 s

mliter s

=

10

-6

nliter s

=

10

-9

1 1

1

1

©2020 NCEES

U.S.gal min U.S.gal 0.01667 min

-4

m3 s

=

-6

m3 s

=

-5

m3 s

=

1.201

-6

m3 s

=

0.02

=

834.01

7.4807

U.S. gal min

U.S. gal min U.S. gal min

-4

m3 s

=

4.403

-5

m3 s

=

0.2642

U.S. gal min

=

15.852

U.S. gal min

m3 s

=

0.01585

m3 s

=

1.5851 : 10

18

U.S. gal min

U.S. gal min -5

U.S. gal min

Chapter 1: General Information 1.2.3.12 Mass Flow

Mass Flow

kg 1 s =

kg s

Conversion Table for Common Units of Mass Flow kg MMlbm * lbm lbm year hr hr min

ton (short) day

1

7936.5

132.28

3600

69.524

95.238

lbm 1 hr =

1.2600E–04

1

0.01667

0.4536

8.7600E–03

0.012

lbm 1 min =

7.5600E–03

60

1

27.216

0.5256

0.72

kg 1 hr =

2.7778E–04

2.2046

0.03674

1

0.01931

0.02646

1

MMlbm = year

0.01438

114.16

1.9026

51.781

1

1.3699

1

ton (short) = day

0.0105

83.33

1.3889

37.8

0.73

1

* million pounds

Additional Unit Conversions for Mass Flow

©2020 NCEES

1

ton (long) day

=

kg 0.0118 s

=

lbm 930, 333 hr

1

ton (short) hr

=

kg 0.2520 s

=

lbm 2000 hr

1

ton (long) hr

=

kg 0.2822 s

=

lbm 2240 hr

slug 1 hr

=

4.0539 : 10

=

lbm 32.174 hr

lbm 1 sec

=

kg 0.4536 s

=

lbm 3600 hr

19

-3

kg s

Chapter 1: General Information 1.2.3.13 Mass Flux Conversion Table for Common Units of Mass Flux Mass Flux

kg s : m2

kg hr : m 2

g s : cm 2

lbm hr -ft 2

lbm sec -ft 2

lbm sec - in 2

1

kg = s : m2

1

3600

0.1

737.35

0.20482

1.4223E–03

1

kg = hr : m 2

2.7778E–04

1

2.7778E–05

0.20482

5.6894E–05

3.9510E–07

1

g = s : cm 2

10

3.6000E+04

1

7373.5

2.0482

0.01422

1

lbm = hr -ft 2

1.3562E–03

4.8823

1.3562E–04

1

2.7777E–04

1.9290E–06

1

lbm = sec -ft 2

4.8824

1.7577E+04

0.48824

3600

1

6.9444E–03

1

lbm = sec - in 2

703.07

2.5310E+06

70.307

5.1841E+05

144

1

1.2.3.14 Force

Force

1N= 1 lbf = 1 pdl = 1 dyne = 1 kgf = 1 ozf =

kg : m s2 1 4.4482 0.13825 1.0000E–05 9.8067 0.27801 N=

Conversion Table for Common Units of Force g : cm lbm -ft dyne = pdl = lbf kgf = kilopond (kp) s2 sec 2 0.22481

7.233

1.0000E+05

0.10197

3.5969

1

32.174

4.4482E+05

0.45359

16

0.03108

1

1.3825E+04

0.01410

0.4973

2.2481E–06

7.2330E–05

1

1.0197E–06

3.5969E–05

2.2046

70.932

9.8067E+05

1

35.274

0.0625

2.0109

2.7801E+04

0.02835

1

Additional Unit Conversions for Force 1

kg : m = 1 dyne = 1 N s2 1 dyne = 1 : 10 5 N

=

0.22481 lbf

=

0.22481 : 10 5 lbf

-

1 tonf (long)

=

9964 N

=

2240 lbf

1 tonf (short)

=

8896.44 N

=

2000 lbf

=

1000 lbf

=

2.2046 • 10–3 lbf

1 kip = 1 kilo lbf = 4448.2 N 1 pond = 1 p = 0.0098 N

©2020 NCEES

ozf

20

Chapter 1: General Information 1.2.3.15 Pressure/Stress Conversion Table for Common Units of Pressure Pressure

Pa =

kg m : s2

psi =

lbf * in 2

Torr = mmHg

in w. c.**

bar

atm

1 Pa = 1 psi*= 1 Torr = 1 in w. c.** = 1 bar =

1 6894.8 133.32 249.08 1.0000E+05

1.4504E–04 1 0.01934 0.03613 14.504

7.5008E–03 51.716 1 1.8683 750.08

4.0148E–03 27.681 0.53525 1 401.48

1.0000E–05 0.06895 1.3332E–03 2.4908E–03 1

9.8717E–06 0.06806 1.3161E–03 2.4588E–03 0.98717

1 atm =

1.0130E+05

14.696

759.83

406.7

1.013

1

*0 psig (gauge) = 14.696 psia (absolute) = 1 atm = 1.013 • 105 Pa ** inches water column

Additional Unit Conversions for Pressure and Stress kg N = 1 2 m m : s2 1 in Hg lbf 1 2 ft kgf 1 at = 1 2 cm kgf 1 mm w. c. = 1 2 m 1 ft w. c. dyne 1 cm 2 pdl 1 2 ft pdl 1 2 m tonf (long) 1 in 2 1

1

tonf (short) in 2 N cm 2 lbm -g 1 ft 2 1

1 bar

©2020 NCEES

=

1 Pa

=

1.4504 • 10–4 psi

=

3386.6 Pa

=

0.49118 psi

=

47.8803 Pa

=

6.9444 • 10–3 psi

=

9.8067 • 104 Pa

=

14.223 psi

=

9.8067 Pa

=

1.4223 • 10–3 psi

=

2988.98 Pa

=

0.4335 psi

=

0.1 Pa

=

1.4504 • 10–5 psi

=

1.4882 Pa

=

2.1584 • 10–4 psi

=

0.1383 Pa

=

2.0052 • 10–5 psi

=

1.5444 • 107 Pa

=

2240 psi

=

1.3790 • 107 Pa

=

2000 psi

=

1 • 104 Pa

=

1.4504 psi

=

47.88 Pa

=

6.9444 • 10–3 psi

=

1 : 10 6

=

0.98692 atm

dyne cm 2

21

Chapter 1: General Information 1.2.3.16 Energy and Torque Conversion Table for Common Units of Energy (Work or Heat) Btu

kcal

kWh

ft-lbf

hp-hr

1J= 1 Btu = 1 kcal = 1 kWh =

kg : m 2 s2 1 1055.1 4186.8 3.6000E+06

9.4778E–04 1 3.9682 3412

2.3885E–04 0.25201 1 859.85

2.7778E–07 2.9308E–04 1.1630E–03 1

0.73757 778.21 3088.1 2.6553E+06

3.7251E–07 3.9303E–04 1.5596E–03 1.341

1 ft-lbf = 1 hp-hr =

1.3558 2.6845E+06

1.2850E–03 2544.3

3.2383E–04 641.19

3.7661E–07 0.7457

1 1.9800E+06

5.0504E–07 1

Energy

J=

Additional Unit Conversions for Energy (Work or Heat) and Torque

©2020 NCEES

kg : m 2 1 = 1= N : m 1W : s s2

=

1J

=

9.4778 • 10–4 Btu

1 therm 1 cal = 0.001 kcal 1 CHU 1 ton-hr (refrigeration) 1 PS • hr (metric) 1 kgf • m

= = = = = =

1.0551 • 108 J 4.1868 J 1899.1 J 1.2661 • 107 J 2.6478 • 106 J 9.8067 J

= = = = = =

105 Btu 3.9682 • 10–3 Btu 1.8 Btu 1.2 • 104 Btu 2509.5 Btu 9.2946 • 10–3 Btu

1 dyne • cm = 1 erg 1 dyne • m 1 lbf -in 1 ft-pdl 1 ton (explosives)

= = = = =

1 • 10–7 J 1J 0.113 J 0.0421 J 4.1840 • 109 J

= = = = =

9.4778 • 10–11 Btu 9.4778 • 10–4 Btu 1.0708 • 10–4 Btu 3.9938 • 10–5 Btu 3.9655 • 106 Btu

1 eV 1 hp-hr (UK) 1 psi-ft3 1 atm • cm3

= = = =

1.6022 • 10–19 J 2.5645 • 106 J 195.2401 J 0.1013 J

= = = =

1.5185 • 10–22 Btu 2430.6 Btu 0.18504 Btu 9.601 • 10–5 Btu

22

Chapter 1: General Information 1.2.3.17 Specific Enthalpy Conversion Table for Common Units of Specific Enthalpy hp-hr J Btu kcal kWh kg lbm kg kg lbm

Specific Enthalpy

J 1 kg =

lbf -ft lbm

1

4.2992E–04

2.3885E–04

1.6897E–07

2.7778E–07

0.33456

Btu 1 lbm =

2326

1

0.55556

3.9301E–04

6.4611E–04

778.18

kcal 1 kg =

4186.8

1.8

1

7.0743E–04

1.1630E–03

1400.7

5.9184E+06

2544.4

1413.6

1

1.644

1.9800E+06

3.6000E+06

1547.7

859.85

0.60828

1

1.2044E+06

2.989

1.2851E–03

7.1392E–04

5.0505E–07

8.3029E–07

1

hp-hr 1 lbm = kWh 1 kg = lbf -ft 1 lbm =

Additional Unit Conversions for Specific Enthalpy Btu cal kcal = CHU = = 1.8 lbm 1 kg 1 lbm 1 g = 4186.8 J kg Btu kgf : m J = 9.8067 kg = 4.2161 • 10–3 lbm 1 kg psi -ft 3 = 1 lbm 1

atm : cm 3 = g

J 430.4329 kg

=

0.18505 lbm

Btu

J 101.3 kg

=

0.04355 lbm

Btu

1.2.3.18 Calorific Value Calorific Value

J = m3 Btu 1 3 = ft kcal 1 3 = m therm = 1 ft 3 therm 1 gal = 1

1

CHU = ft 3

©2020 NCEES

J m3

Conversion Table for Common Units of Calorific Value therm Btu kcal therm gal ft 3 m3 ft 3

CHU ft 3

1

2.6838E–05

2.3885E–04

2.6838E–10

3.5971E–11

1.4910E–05

3.7260E+04

1

8.8994

1.0000E–05

1.3403E–06

0.55556

4186.8

0.11237

1

1.1237E–06

1.5060E–07

0.06243

3.7260E+09

1.0000E+05

8.8994E+05

1

0.13403

5.5556E+04

2.7800E+10

7.4611E+05

6.6399E+06

7.4611

1

4.1451E+05

6.7067E+04

1.8

16.019

1.8000E–05

2.4125E–06

1

23

Chapter 1: General Information 1.2.3.19 Entropy

Entropy

Conversion Table for Common Units of Entropy kcal = Btu J CHU Clausius K cC cF cC

J 1K =

kcal cF

1

5.2654E–04

2.3885E–04

5.2654E–04

4.2992E–04

Btu 1 oF =

1899.2

1

0.45361

1

0.8165

kcal 1 oC =

4186.8

2.2045

1

2.2045

1.8

1

CHU = oC

1899.2

1

0.45361

1

0.8165

1

kcal = o F

2326.0

1.2247

0.5556

1.2247

1

1.2.3.20 Power

Power 1W=

Conversion Table for Common Units of Power Btu kcal W hp hr hr

therm hr

ton refrigeration

1

3.4120

0.85985

1.3404E–03

3.4120E–05

2.8434E–04

Btu 1 hr = kcal 1 hr =

0.29308

1

0.252

3.9285E–04

1.0000E–05

8.3335E–05

1.1630

3.9682

1

1.5589E–03

3.9682E–05

3.3069E–04

1 hp =

746.04

2545.5

641.48

1

0.02546

0.21213

2.9308E+04

1.0000E+05

2.5200E+04

39.285

1

8.3335

3516.9

1.2000E+04

3024.0

4.7141

0.12

1

1

therm = hr

1 ton refrigeration =

©2020 NCEES

24

Chapter 1: General Information Additional Unit Conversions for Power kg : m 2 J = 1 s V= :A s3 kgf : m 1 s

Btu

=

1W

=

3.412 hr

=

9.8067 W

=

33.461 hr

atm : m 3 hr

=

28.15 W

=

96.049 hr

1 PS (metric)

=

735.48 W

=

erg 1 s

2509.5 hr

=

1 • 10–7 W

=

3.412 • 10–7 hr

CHU 1 hr lbf -ft 1 min lbf -ft 1 sec

=

0.5275 W

=

1.8 hr

=

0.0226 W

=

0.0771 hr

=

1.3558 W

=

4.626 hr

pdl-ft 1 sec

=

0.0421 W

=

0.14378 hr

1 hp (British)

=

756.7 W

=

2581.9 hr

1 hp (Boiler)

=

9809.5 W

=

3.347 • 104 hr

1 hp

=

-ft 550 lbf sec

1

Btu Btu Btu Btu

Btu Btu

Btu Btu

Btu Btu

1.2.3.21 Heat Flux

Heat Flux

W = m2 Btu = 1 2 ft -hr kcal = 1 2 m : hr cal = 1 cm 2 : s kcal = 1 2 ft -hr CHU = 1 2 ft -hr 1

©2020 NCEES

W m2

Conversion Table for Common Units of Heat Flux Btu kcal cal kcal ft 2-hr m 2 : hr cm 2 : s ft 2-hr

CHU ft 2-hr

1

0.317

0.85985

2.3885E–05

0.07989

0.17611

3.1546

1

2.7125

7.5346E–05

0.25201

0.55554

1.163

0.36867

1

2.7778E–05

0.09291

0.20481

4.1868E+04

1.3272E+04

3.6000E+04

1

3344.6

7372.2

12.518

3.9682

10.764

2.9899E–04

1

2.2045

5.6784

1.8

4.8825

1.3563E–04

0.45362

1

25

Chapter 1: General Information 1.2.3.22 Dynamic Viscosity Viscosity (dynamic)

1 Pa • s = 1 cP = 1 Poise = lbf - sec = ft 2 lbf - sec = 1 in 2 1

lbm 1 ft -sec =

Conversion Table for Common Units of Dynamic Viscosity lbf -sec lbf -sec Pa • s cP Poise ft 2 in 2

lbm ft -sec

1

1000

10

0.02089

1.4504E–04

0.67195

0.001

1

0.01

2.0885E–05

1.4504E–07

6.7195E–04

0.1

100

1

2.0885E–03

1.4504E–05

0.06720

47.88

4.7880E+04

478.8

1

6.9444E–03

32.173

6894.8

6.8948E+06

6.8948E+04

144

1

4633

1.4882

1488.2

14.882

0.03108

2.1585E–04

1

Additional Unit Conversions for Dynamic Viscosity g dyne : s 1= Poise 1= cm : s 1 cm 2 lbf -sec = slug 1 1 ft -s ft 2 lbm pdl - s 1 ft - s = ft 2 lbm 1 ft - hr kgf : s 1 m2 kgf : hr 1 m2 kg 1 ft : hr

©2020 NCEES

lbf -sec ft 2

=

0.1 Pa • s

=

2.0885 • 10–3

=

47.8803 Pa • s

=

1

=

1.4882 Pa • s

=

0.03108

=

4.1338 • 10–4 Pa • s

=

8.6336 • 10–6

=

9.8067 Pa • s

=

=

3.5320 • 10–4 Pa • s

=

7.3767 • 10–6

lbf -sec ft 2

=

9.1134 • 10–4 Pa • s

=

1.9034 • 10–5

lbf -sec ft 2

26

lbf -sec ft 2 lbf -sec ft 2

lbf -sec ft 2 lbf -sec 0.20482 ft 2

Chapter 1: General Information 1.2.3.23 Diffusion Coefficient, Thermal Diffusivity, and Kinematic Viscosity Conversion Table for Common Units of the Diffusion Coefficient, T​ hermal Diffusivity, and Kinematic Viscosity 2 * 2 liter m ft 2 in 2 ft 2 cm Diffusivity = St in.-hr s sec sec hr s m2 1 s =

1

1.0000E+04

10.764

3.8751E+04

1550

9.1441E+04

1.0000E–04

1

1.0764E–03

3.8751

0.155

9.1441

ft 2 1 sec =

0.09290

929.03

1

3600

144

8495.2

ft 2 1 hr =

2.5806E–05

0.25806

2.7777E–04

1

0.04

2.3597

in 2 1 sec =

6.4516E–04

6.4516

6.9444E–03

25

1

58.994

liter 1 in.-hr =

1.0936E–05

0.10936

1.1771E–04

0.42378

0.01695

1

*

cm 2 = 1 St = s

* St = Stokes

1.2.3.24 Heat Capacity and Specific Entropy Conversion Table for Common Units of Heat Capacity and ​ Specific Entropy Btu W lbf -ft = Heat Capacity m:K lbm-cF lbm-cR W 1 2.3885E–04 0.18586 1m :k = Btu 4186.8 1 778.17 1 lbm-cF = lbf -ft 5.3803 1.2851E–03 1 1 lbm-cR = Btu kcal cal = CHU = 1= lbm- cF 1 kg : cC 1 g : cC 1 lbm-cC

©2020 NCEES

27

Chapter 1: General Information 1.2.3.25 Thermal Conductivity Thermal Conductivity

W 1m:K =

Conversion Table for Common Units of Thermal Conductivity Btu kcal W Btu- in m:K hr - ft -cF hr : m : cC hr - ft 2-cF

Btu 1 hr - ft -cF = Btu- in = hr - ft 2-cF kcal 1 hr : m : cC = cal 1 s : cm : cC = 1

cal s : cm : cC

1

0.57777

6.9334

0.85985

2.3885E–03

1.7308

1

12

1.4882

4.1339E–03

0.14423

0.08333

1

0.12402

3.4449E–04

1.163

0.67194

8.0635

1

2.7778E–03

418.68

241.9

2902.9

360

1

Btu CHU 1 hr - ft -cF = 1 hr - ft -cC

1.2.3.26 Heat-Transfer Coefficient Heat-Transfer Coefficient

W = m2 : K Btu = 1 hr - ft 2- cF Btu = 1 sec - ft 2-cF kcal = 1 hr : m 2 : cC cal = 1 s : m 2 : cC kcal = 1 hr - ft 2- cC

1

Conversion Table for Common Units of the Heat-Transfer Coefficient W Btu Btu kcal cal m2 : K hr - ft 2-cF sec - ft 2-cF hr : m 2 : cC s : cm 2 : cC 1

0.1761

4.8919E–05

0.85985

2.3885E–05

0.07989

5.6785

1

2.7779E–04

4.8826

1.3563E–04

0.45363

2.0442E+04

3599.8

1

1.7577E+04

0.48824

1633

1.1630

0.20481

5.6893E–05

1

2.7778E–05

0.09291

4.1868E+04

7373.1

2.0482

3.6000E+04

1

3344.6

12.518

2.2045

6.1237E–04

10.764

2.9899E–04

1

1

©2020 NCEES

kcal hr - ft 2- cC

Btu = 1 CHU hr - ft 2-cC hr - ft 2- cF

28

Chapter 1: General Information 1.2.3.27 Surface Tension Surface Tension

Conversion Table for Common Units of Surface Tension g N dyne lbf lbf cm m in. ft cm

pdl in.

N 1m =

1

5.7101E–03

4.7585E–04

1.0197

1000

0.18372

lbf 1 in. =

175.13

1

0.08333

178.58

1.7513E+05

32.174

2101.5

12

1

2143

2.1015E+06

386.09

0.98067

5.5997E–03

4.6665E–04

1

980.67

0.18017

dyne 1 cm =

0.001

5.7101E–06

4.7585E–07

1.0197E–03

1

1.8372E–04

pdl 1 in. =

5.4431

0.03108

2.5901E–03

5.5504

5443.1

1

lbf 1 ft = g 1 cm =

1.2.3.28 Cubic Expansion Coefficient Conversion Table for Common Units of Cubic Expansion g Cubic kg lbm 3 3 3 Expansion cm : cC m -cF m :K kg = m3 : K lbm = 1 3 m -cF g = 1 cm 3 : cC 1

1

0.03468

0.001

28.833

1

0.02883

1000

34.682

1

1.2.3.29 Temperature Conversion Table for Temperature Units

©2020 NCEES

Kelvin (K)

Celsius (°C)

Rankine (°R)

Fahrenheit (°F)

T(K) =

T(K)

T(°C) + 273.15

5 9 T(°R)

5 9 T(°F) + 255.37

T(°C) =

T(K) – 273.15

T(°C)

5 9 T(°R) – 273.15

5 9 T(°F) – 17.78

T(°R) =

9 5 T(K)

T(°R)

T(°F) + 459.67

T(°F) =

9 5 T(K) – 459.67

9 5 T(°C) + 491.67°R 9 5 T(°C) + 32

T(°R) – 459.67

T(°F)

29

Chapter 1: General Information

1.3 Mathematics 1.3.1

Algebra

1.3.1.1 Linear Algebra Straight Line General form:

Ax+By+C=0

Standard form:

y=mx+b

Point-slope form:

y - y1 = m (x - x1) y − y1 y 2 − y1 = x − x1 x 2 − x1

Two-point form: Intercept form:

x + y − = x0 y0 1 0 , where intercepts x0 ≠ 0, y0 ≠ 0 y −y

Slope: m = x 2 − x1 2 1 Angle between lines with slopes m1 and m2:

m − m1 o a = arctan e +2 1 m 2 m1

Distance between two points (two-dimensional space): Intersection of two straight lines:

d = ` y 2 − y1 j + _ x 2 − x1 i b −b m b −m b xi = m2 − m1 yi = 1m2 − m 2 1 1 2 1 2 2

1.3.1.2 Polynomials Quadratic Equation Standard form:

a x2 + b x + c = 0

x2 + p x + q = 0 −b ! b2 − 4 a c 4ac −b Roots: x 1, 2 = 2a d1 ! 1 − 2 n = 2a b Normal form:



p x 1, 2 = 2 !

Vieta's Rule:

p = – (x1 + x2)

p2 − 4 q q = x1 x2

If (b2 – 4 a c) > 0, the roots are real and unequal. If (b2 – 4 a c) = 0, the roots are real and equal. If (b2 – 4 a c) < 0, the roots are imaginary and unequal. If (b2 – 4 a c) = n2 (perfect square), the roots are rational and unequal.

©2020 NCEES

30

2

Chapter 1: General Information Expansion of General Algebraic Expressions (a ± b)2 = a2 ± 2 a b + b2 (a ± b)3 = a3 ± 3 a2 b + 3 a ∙ b2 ± b3 (a ± b)4 = a4 ± 4 a3 b + 6 a2 b2 ± 4 a b3 + b4

a2 – b2 = (a + b) (a – b) a3 + b3 = (a + b) (a2 – a b + b2) a3 – b3 = (a – b) (a2 + a b + b2) a4 + b4 = (a2 + a b 2 + b2) (a2 – a b

2 + b2)

a4 – b4 = (a2 + b2) (a2 – b2) Quadratic Surface (Sphere) Standard form:

(x – h)2 + (y – k)2 + (z – m)2 = r2

Distance between two points in three-dimensional space: d =

_ x 2 − x1 i + ` y 2 − y1 j + _ z 2 − z1 i 2

1.3.1.3 Logarithms, Exponents, and Roots Logarithms General definition:

logb(x) = c

where: x = bc

Natural logarithm:

ln(x) = c

where: x = ec (base: e = 2.71828)

Base 10 logarithm:

log(x) = c where: x = 10c (base: 10)

To change from one base to another:

log (x) logb (x) = loga (b) a log10 (x) = = 2.302585 log10 (x) ln (x) log 10 (e) ln (x) = = 0.4343 ln (x) log (x) ln (10) Identities: logb(1) = 0 logb(b) = 1 logb(bn) = n logb(xc) = c logb(x)

1 − log b c x c m = log b (x c) = − c log b (x) = c log b c 1x m 1 1 c c xi = = log log b_ b 8(x) B c log b (x)

©2020 NCEES

31

2

2

Chapter 1: General Information log b (x y) = log b (x) + log b (y) logb d xy n = logb (x) − logb (y)

b n log b (x) = x n b

log b (x) n

1

= xn

Rules for Exponents and Radicals a0 = 1 a1 = a Identities:

p an ± q an = (p ± q) an an am = an+m an = n − m a am (= a m) n (= a n) m a n m a

−n

n = 1n = c 1 m a a

an bn = (a b)n n an = c a m n b b 1

(a) n = n a n m n j = `= a (a) n a

m

m

nx

n am x = am

p ` n a j + q ` n a j = (p + q ) ` n a j

`m a j `n a j = n + m a n

ab = n a + n b

n a = n b

1

a c a mn = b b

n

1.3.1.4 Proportions c

Directly proportional (4th proportional):

x\c

a

a:b=c:x bc x= a b

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32

x

Chapter 1: General Information a c a+b c+x If b = x then: b = x

and

a−b = c−x x b

and

a−b = c−x a+b c+x

Square proportional (3rd proportional):

90°

x \ b2 a:b=b:x

b

2

b x= a

a

x

Mean proportional: 90°

x\ b

x

a:x=x:b x = ab a

Inversely proportional:

1 x\ b Inversely square proportional:

x\

1 b2

1.3.1.5 Complex Numbers Rectangular form: z = a + i b where

i = -1 a = real component b = imaginary component

Polar form: z = c+i = c _cos i + i sin i i = c e i i

c = a2 + b2 − i = tan 1 c ba m a = c cos i b = c sin i Addition and Subtraction (in rectangular form): z1 ! z 2 = (a1 ! a 2) + i _b1 ! b 2 i

©2020 NCEES

33

b

Chapter 1: General Information Multiplication and Division (in polar form):

z1 z 2 = _c1 c 2 i + _i1 + i 2 i z1 c1 − z 2 = d c 2 n + _i1 i 2 i

n z n = _ a + i b i = c n + ^n i h

Complex Conjugate:

z) = a − i b z z) = a 2 + b 2 Euler's Identity:

e i i = cos i + i sin i − e i i = cos i − i sin i 1 cos i = 2 _e i i + e −i i i 1 sin i = 2 i _e i i − e −i i i

1.3.2

Geometry and Trigonometry

1.3.2.1 Circular Transcendental Functions Trigonometric functions are defined using a right triangle:

y = sin i r= , cos i r = sec i x= , csc i y = tan i x= , cot i

x r r y x y

r

y

θ x

y = arcsin c r m i= , arccsc d ry n i = arccos b rx l i= , arcsec c rx m i y = arctan c x m i= , arccot d xy n i Law of Sines a b c = = sin A sin B sin C

c

B

Law of Cosines

a

a2 = b2 + c2 – 2bc cos A b2 = a2 + c2 – 2ac cos B c2 = a2 + b2 – 2ab cos C

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A b

34

C

Chapter 1: General Information Law of Tangents

1 a − b = tan 2 (A − B) a + b tan 1 (A + B) 2 1 b − c = tan 2 (B − C) b + c tan 1 (B + C) 2 1 a − c = tan 2 (A − C) a + c tan 1 (A + C) 2

sec

θ

Trigonometric Functions in a Unit Circle

(0, 1)

cot θ tan θ

csc

θ

cos θ

θ

sin θ

(1,0)

Trigonometric Identities

sin (–θ) = –sin θ cos (–θ) = cos θ tan (–θ) = –tan θ r r cos i = sin ci + 2 m =− sin ci − 2 m

r r sin i = cos ci − 2 m =− cos ci + 2 m 1 sin i 1 sec i = cos i sin i tan i = cos i 1 cot i = tan i csc i =

sin 2 i + cos 2 i = 1 tan 2 i + 1 = sec 2 i cot 2 i + 1 = csc 2 i

©2020 NCEES

35

Chapter 1: General Information Double-Angle Formulas sin 2a = 2 sin a cos a cos 2a = cos 2 a − sin 2 a = 1 − 2 sin 2 a = 2 cos 2 a − 1 tan 2a =

2 tan a 1 − tan 2 a

cot 2 a − 1 cot 2a = 2 cot a Two-Angle Formulas sin (a + b) = sin a cos b + cos a sin b cos (a + b) = cos a cos b − sin a sin b tan (a + b) =

(tan a + tan b) (1 − tan a tan b)

cot (a + b) =

(cot a cot b − 1) (cot a + cot b)

sin (a − b) = sin a cos b − cos a sin b cos (a − b) = cos a cos b + sin a sin b tan (a − b) =

(tan a − tan b) (1 + tan a tan b)

cot (a − b) =

(cot a cot b + 1) (cot b − cot a)

Half-Angle Formulas

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a sin c 2 m = !

(1 − cos a) 2

a cos c 2 m = !

(1 + cos a) 2

a tan c 2 m = !

(1 − cos a) (1 + cos a)

a cot c 2 m = !

(1 + cos a) (1 − cos a)

36

Chapter 1: General Information Combination of the Trigonometric Functions of Different Angles 1 sin a sin b = 2 8cos (a − b) − cos (a + b)B 1 cos a cos b = 2 8cos (a − b) + cos (a + b)B 1 sin a cos b = 2 8sin (a + b) + sin (a − b)B 1 1 sin a + sin b = 2 sin 1 − e 1 o P4

H

D

D

u

u

3"4

=0

114

P4 v3 = P3 v4

Dh3 " 4 = 0

v3 " 4 = v4 − v3

Ds4 " 1 = 0

DT4 " 1 = TH − TC

4"1

= cv `TH − TC j

Dh4 " 1 = cP `TH − TC j

q4 " 1 = 0

©2020 NCEES

P2/P1 = v1/v2

1"2

q2 " 3 = 0

k w4 " 1 =− k − 1 RTc Isentropic compression (compressor)

=0

D

k w2 " 3 =− k − 1 RTH

u

DT1 " 2 = 0

k

k P T k−1 v =d 4n e 1o=e C o v1 P4 TH

1

v4 Tc k − 1 = e o v1 TH

Chapter 3: Thermodynamics P

T qin H

TH

ON

ST .

TRO

N ISE

=C

NT ISE

PIC

2

qout

T

C

=C

TC

ON

PIC RO

4

3

ST.

qin

1

2 ISENTROPIC

T

ISENTROPIC

1

4

qout

3

s

v

where TC = temperature at which the working fluid is absorbing heat, which is the same as that of the fluid entering the turbine TH = temperature at which heat is emitted by the working fluid, which is the same as the exit temperature from the turbine The thermal efficiency of the Carnot Cycle is:

Q W T −T hth,Carnot = Qout = 1 − Qout = HT C H in in

The efficiency of the Carnot cycle represents an upper limit for the efficiency (maximum possible efficiency) of any power cycle operating between the two temperatures TH and TC.

3.4.2.2 The Stirling Cycle The Stirling cycle is similar to the Carnot cycle, but the isentropic compression and expansion are replaced by constant volume processes with regeneration. Step

Process

Work and Heat

1→2

Isothermal expansion (ΔT = 0)

P q1 " 2 = qin = RTH ln e P1 o =− w1 " 2

2→3

Isochoric regeneration (internal heat transfer from working fluid to regenerator)

q2 " 3 = qregen = cv `TC − TH j w2 " 3 = 0

3→4

Isothermal compression (ΔT = 0)

P q3 " 4 = qout = RTC ln e P3 o =− w3 " 4

4→1

Isochoric regeneration (internal heat transfer back from the regenerator to the working fluid)

q4 " 1 = qregen = cv `TH − TC j w4 " 1 = 0

©2020 NCEES

2

4

115

Chapter 3: Thermodynamics

P 1

T

GE

ST .

RA TIO

N

qout

T

C

=C

2 TC

ON

ST.

REGENERATION

V=

4

CO NS T.

NE

4

3

2

T.

RE

TH

ON

qin

1

CO

=C

H

V=

T

NS

qin

3

qout

v

s

The thermal efficiency of the Stirling cycle is:

Q W T −T hth,Stirling = Qout = 1 − Qout = HT C H in in

The thermal efficiency of the Stirling cycle is the same as the thermal efficiency of the Carnot cycle.

3.4.2.3 The Ericsson Cycle The Ericsson cycle is another variation of the Stirling cycle—the regeneration takes place at constant pressure rather than constant volume. Step

Process

Work and Heat

1→2

Isothermal expansion _DT = 0 i

P q1 " 2 = qin = RTH ln e P1 o =− w1 " 2

2→3

Isobaric regeneration (internal heat transfer from working fluid to regenerator)

q2 " 3 = qregen = cP `TC − TH j w2 " 3 = P2 _v3 − v2 j

3→4

Isothermal compression _DT = 0 i

P q3 " 4 = qout = RTC ln e P3 o =− w3 " 4

4→1

Isobaric regeneration (internal heat transfer back from the regenerator to the working fluid)

q4 " 1 = qregen = cP `TH − TC j w4 " 1 = P1 _v1 − v4 i

2

4

P

T

TIO RA

ST .

REGENERATION

P=

N

. NST

ON

2

NS

T. NS

NE

CO

=C

CO

GE

H

TH

qin

P=

RE

T L=

T

1

T.

qin

CO

1

4

qout

3

TC

2

qout

3 s

v

©2020 NCEES

4

116

Chapter 3: Thermodynamics The thermal efficiency of the Ericsson cycle is:

Q W T −T hth,Ericsson = Qout = 1 − Qout = HT C H in in

The thermal efficiency of the Ericsson cycle is the same as the thermal efficiency of the Carnot cycle.

3.4.2.4 Otto Cycle Idealized cycle to represent spark-ignition internal combustion engines Step

Process

Work and Heat ^k − 1h/k

1→2

k P w1 " 2 =− k − 1 RT1 : >1 − e 2 o P1

Isentropic compression

H

q1 " 2 = 0 q2 " 3 = qin = cv _T3 − T2 j w2 " 3 = 0

Isochoric heating (represents the internal combustion at TDC)

2→3

^k − 1h/k

k P w3 " 4 =− k − 1 RT3 : >1 − e 4 o P3

3→4

Isentropic expansion

4→1

Isochoric cooling (represents the two strokes that exhaust the combustion gases and draw fresh air and fuel in)

H

q2 " 3 = 0 v4 = v1 = vmax; v3 = v2 = vmin

P

q4 " 1 = qout = cv _T1 − T4 i w4 " 1 = 0 T

qin

3 ISENTROPIC

2

qin

qout

ISENTROPIC

3

T.

NS

4

2 1

1

v

O =C

4 NS

v

O =C

T.

qout

s

v The thermal efficiency of the Otto cycle is:

1 − rk 1 Typical compression ratios (r) are 7 – 10, higher ratios can lead to engine knock (premature auto-ignition of the fuel/air mixture) hth,Otto = 1 −

©2020 NCEES

117

Chapter 3: Thermodynamics 3.4.2.5 Diesel cycle Idealized cycle to represent compression-ignition internal combustion engines Step

Process

Work and Heat ^k − 1h/k

1→2

k P w1 " 2 =− k − 1 RT1 : >1 − e 2 o P1

Isentropic compression

H

q1 " 2 = 0 2→3

Isobaric heating (represents the internal combustion, which occurs during initial part of the power stroke)

^k − 1h/k

k P w3 " 4 =− k − 1 RT3 : >1 − e 4 o P3

3→4

Isentropic expansion

4→1

Isochoric cooling (represents the two strokes that exhaust the combustion gases and draw fresh air and fuel in)

P

w2 " 3 = P2 _v3 − v2 j q2 " 3 = qin = cP _T3 − T2 j

H

q3 " 4 = 0 v4 = v1 = vmax q4 " 1 = qout = cv _T1 − T4 i w4 " 1 = 0 T

qin

qin

2

3

3

NST.

P = CO

4

IC

OP

TR

EN

IS

2

IC

OP

1

ST.

ON

C V=

TR

EN

IS

4 qout

qout

1

v

s

Cut-off ratio rc Ratio of the cylinder volumes after and before the combustion process

V3 v3 = rc V= v2 2 Efficiency of the Diesel Engine

hth, diesel = 1 −

r

k−1 >

1

r ck − 1 H k _rc − 1 j

For the same compression ratio,ηth,diesel < ηth,Otto, but typical compression ratios for diesel engines are higher (about 12–24), since engine knock is not a concern for diesel engines.

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Chapter 3: Thermodynamics 3.4.2.6 Dual cycle Combination between Otto and diesel cycle to more closely resemble the internal combustion engine Step

Process

Work and Heat ^k − 1h/k

1→2

k P w1 " 2 =− k − 1 RT1 : >1 − e 2 o P1

Isentropic compression

H

q1 " 2 = 0 2→X

Isochoric heating (initial combustion)

q2 " X = qin, v = cv _TX − T2 i w2 " X = 0

X→3

Isobaric heating (continued combustion during power stroke)

wX " 3 = P3 _v3 − v2 j qX " 3 = qin, P = cP _T3 − TX j ^k − 1h/k

k P w3 " 4 =− k − 1 RT3 : >1 − e 4 o P3

3→4

Isentropic expansion

4→1

Isochoric cooling (represents the two strokes that exhaust the combustion gases and draw fresh air and fuel in)

P

q3 " 4 = 0 v4 = v1 = vmax

qin

ISE

P = CONST.

NT

2 ISE

NT

v = CONST.

RO

PIC

RO

PIC

2

4 qout

1

1

Efficiency of the Dual Cycle:

cv _T4 − T1 i cv _TX − T2 i + cp _T3 − TX j

The Otto and the diesel cycle are special cases of the dual cycle.

©2020 NCEES

X

qin v = CONST.

3

qin 4 qout s

v

hth,dual = 1 −

q4 " 1 = qout = cv _T1 − T4 i w4 " 1 = 0

T

3

X

H

119

Chapter 3: Thermodynamics 3.4.2.7 The Brayton Cycle The Brayton cycle represents compression and expansion in rotating machinery, such as gas turbines. Step

Process

Work and Heat ^k − 1h/k

k P w1 " 2 =− k − 1 RT1 : >1 − e 2 o P1 1→2

H

q1 " 2 = 0

Isentropic compression (in a compressor)

k−1 k

T2 P =e 2o T1 P1

2→3

w2 " 3 = P2 _v3 − v2 j q2 " 3 = qin = cP _T3 − T2 j T3 = Tmax P2 = P3

Isobaric heat addition (combustion chamber for open systems, heat exchanger for closed systems)

^k − 1h/k

k P w3 " 4 =− k − 1 RT3 : >1 − e 4 o P3 3→4

q3 " 4 = 0

Isentropic expansion (in a turbine)

k−1 k

T3 P =e 3o P4 T4

4→1

P

k−1 k

P =e 2o P1

=

T2 T1

w4 " 1 = P4 _v1 − v4 i q4 " 1 = qout = cP _T1 − T4 i T1 = Tmin P4 = P1

Isobaric heat rejection (exhaust and fresh air intake for open systems, heat exchanger for closed systems)

T

3

qin 3

2

S=

S

ST.

CON

ON

ST .

1

qout

. ST

N

CO

4

2 4

1

P=

qin

=C

H

P=

ST. CON

qout

s

v

Pressure ratio for the Brayton cycle

P2 P3 = rp P= P4 1 Typical pressure ratios for gas turbines range from 11 to 16 and are limited by the maximum temperature at the inlet of the turbine.

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Chapter 3: Thermodynamics Efficiency of the Brayton cycle

hth,Brayton = 1 −

1

r p^k

− 1 h/k

=

_T4 − T1 i _T3 − T2 j

For fixed values of Tmin and Tmax, the net work is at a maximum when: k

2^k − 1 h T rp = e Tmax o min

The conversion efficiency can be expressed as "heat rate" (typically in BTU⁄kWh, i.e., the energy required to generate 1 kWh of electricity:

BTU heat rate = hth,Ranking : 3412 kWh Back-work ratio is the ratio of the compressor work to the turbine work.

wcompressor Tmax − 1 1 = p rpw = − w − Tmin f r p^k 1h/k turbine The thermal efficiency of the Brayton cycle is reduced by the efficiency of the turbine and compressor. Including the isentropic turbine and compressor efficiencies can correct for the irreversibilities in the compressor and turbine. Regeneration In the Brayton cycle with regeneration, the exhaust from the turbine is used to pre-heat the outlet from the compressor, prior to heating it in the combustion chamber. It reduces the required heat input and thus improves efficiency.

3

T qin

qregen,max = h5l – h2 = h4 – h2

qregen 5

qregen,act = h5 – h2 = h4 – h6

5'

4

REGENERATION

6

Effectiveness of the Regenerator

T −T f , T5 − T2 4 2

2

Efficiency of ideal Brayton cycle with regeneration

qsaved = q regen

1

T − hth,Brayton = 1 − e Tmax o r p^k 1h/k min

qout s

Regeneration is most effective for low pressure ratios and low temperature ratios. Multistage compression with intercooling and multistage expansion with reheating can further increase the efficiency of the Brayton cycle.

3.4.2.8 The Jet Propulsion Cycle The jet propulsion cycle is similar to the Brayton cycle, but the gases are expanded in the turbine only until it produces enough work to drive the compressor and then exit at high velocity to provide thrust to an aircraft. Thus, the turbine in the Brayton cycle is replaced by a combination of turbine and nozzle. In the diffusor, the fluid changes velocity from that of the surrounding to that of the moving airplane. This is a deceleration when viewed from the airplane point of reference.

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T

qin

P=

4

T.

S ON

C

TURBINE 5 NOZZLE

3

6

COMPRESSOR 2 DIFFUSOR

1

P=

CO

. NST

qout

s

Chapter 3: Thermodynamics The net work for a turbojet is zero, efficiency is thus defined as propulsive efficiency based on the propulsive power _WoP i and energy input rate _Qo in i :

3.4.3

Wo hP = o P Qin o WP = mo `uexit − uinlet j uaircraft

Vapor Power Cycles

Vapor power cycles use a working fluid that evaporates and condenses in the course of a cycle. This allows the compression to occur in the liquid phase, where the smaller specific volume results in less work for the compression.

3.4.3.1 Rankine Cycle The Rankine cycle is the ideal cycle for vapor power plants. Step

Process

Work and Heat

1→2

Isentropic compression (of the liquid in a pump)

w1 " 2 = win = h1 − h2 = v _ P1 − P2 i q1 " 2 = 0 h1 = hliq@P1 v , v1 = vliq@P1

2→3

Isobaric heat addition (in a boiler, vaporizing and superheating the liquid)

w2 " 3 = 0 q2 " 3 = qin = h3 − h2

3→4

Isentropic expansion (of the gas in the turbine)

w3 " 4 = wout = h3 − h4 q3 " 4 = 0

4→1

Isobaric heat rejection (in a condenser, condensing the vapor exiting the turbine)

w4 " 1 = 0 q4 " 1 = qout = h1 − h4

T

Efficiency of the Rankine Cycle

q w w −w hth,Ranking = qnet = outq in = 1 − qout in in in

The conversion efficiency can be expressed as "heat rate" (typically in BTU⁄kWh, i.e., the energy required to generate 1 kWh of electricity:

BTU heat rate = hth,Ranking : 3412 kWh The backwork ratio for the Rankine cycle is much smaller than the backwork ratio for the Brayton cycle.

wpump win = rpw w= wturbine out

Efficiency calculations for an actual (not ideal) Rankine cycle include the isentropic efficiencies for the compressor and the pump.

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3

qin

wturb, out

2 1 wpump, in

qout

4

s

Chapter 3: Thermodynamics 3.4.3.2 Ideal Rankine Cycle with Reheat To improve efficiency of the Rankine cycle, the steam is expanded in the turbine in 2 phase, with a reheat in between. 3

BOILER

T LOW-P TURBINE

HIGH-P TURBINE

REHEATER 4

6 2

CONDENSER

1

PUMP

2

REHEATING 5 LOW-PRESSURE TURBINE

4

P4 = P5 = Preheat

5

HIGH-PRESSURE 3 TURBINE

6 s

1

With the reheat, the heat input and work output are calculated as follows:

qin = qprimary + qreheat = _h3 − h2 j + _h5 − h4 j wout = wturb,HP + qturb, LP = _h4 − h3 j + _h6 − h5 j

3.4.3.3 Ideal Rankine Cycle with Regeneration

For regeneration, part of the steam is extracted from the turbine and used to pre-heat the feedwater. Open feedwater heaters mix the steam directly with the water; closed feedwater heater use a heat exchanger. Regenerating increases the inlet temperature to the boiler and thus reduces the heat required in the boiler. 5

T

BOILER

5

TURBINE y OPEN FWH

4

1-y 7

6

4

3 PUMP II

2 2

CONDENSER PUMP I

1

6 3

1

7 s

With the regeneration, the heat input and work output are calculated as follows (where y is the fraction of steam that is extracted from the turbine):

mo y = mo 6 5 qin = h5 − h4 qout = `1 − y j_h7 − h1 j

wout = _h5 − h6 j + `1 − y j_h6 − h7 j win = `1 − y j wPump I,in + wPump II, in = `1 − y j v1 _ P2 − P1 i + v3 _ P4 − P3 j

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Chapter 3: Thermodynamics 3.4.3.4 Cogeneration Cycle A cogeneration cycle is based on the Rankine cycle, but instead of condensing the vapor leaving the turbine, it is used for process heating. The steam is thus extracted from the turbine at higher pressures, depending on the process heating needs. T 1

EXPANSION VALVE 4

5

TURBINE

PUMP II

7

10

4

10

6

PROCESS HEATER

11 MIXING CHAMBER

3

2

BOILER

1,2,3

11 9

7

5

CONDENSER

9

8

8

6 s

PUMP I

The use of the higher pressure steam reduces the net work delivered by the turbine but adds the process heat to the benefit. In actual cogeneration cycles, some losses occur due to inefficiencies of the turbine or combustion process or heat losses from the steam piping. The utilization factor (or "fuel chargeable to power", FCP) is:

FCP =

wo net + qo process qo = 1 − qoout qo in in

In an ideal cogeneration cycle, the efficiency is 100%, since no heat is wasted `qo out = 0 j . Typical cogeneration cycles include a condenser in parallel to the process heater and an expansion valve in parallel to the turbine for adjustable loads. When demand for steam is low, more power is generated by extracting less steam from the turbine. When demand for steam is high, the turbine is bypassed.

Qo in = mo 3 _h4 − h3 j Qo out = mo 7 _h7 − h1 j Qo process = mo 5h5 + mo 6h6 − mo 8h8

Woturbine = _mo 4 − mo 5 j_h4 − h6 j + mo 7 _h6 − h7 j

3.4.4

Refrigeration Cycles

Refrigeration cycles are the reverse of power cycles. Power cycles transfer heat from a hot reservoir to a cold reservoir and extract work. Refrigeration cycles use work to transfer heat from a cold reservoir to a hot reservoir. For a refrigerator (R), the objective is to remove heat from the low temperature reservoir. For a heat pump (HP), the objective is to add heat to the high- temperature reservoir.

3.4.4.1 Coefficient of Performance The coefficient of performance is defined similar to the thermal efficiency, but the purpose of refrigeration cycles differs from power cycles and thus the benefit and cost are defined differently:

Cooling effect QC = Wnet,in Work input Heating effect QH = COPHP = Wnet,in Work input

= COPR

Both COPR and COPHP can be > 1. When COPHP < 1, a simple resistance heater (which turns work into heat) would be more efficient. ©2020 NCEES

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Chapter 3: Thermodynamics For fixed values of QC and QH: COPHP = COPR + 1

3.4.4.2 Reverse Carnot Cycle and Reverse Stirling Cycle The reverse Carnot cycle is the most efficient refrigeration cycle operating between two temperatures, but it is not a realistic model for actual refrigeration cycles. It does provide a maximum achievable coefficient of performance against which other cycles can be compared. Carnot Refrigeration cycle

COPR,Carnot =

1 _TH /TC i − 1

Carnot Heat Pump cycle

1 1 − _TC/TH i The reverse Stirling cycle has the same coefficients of performance and is easier to implement in practice (example: Stirling refrigerators). COPHP,Carnot =

3.4.4.3 The Ideal Vapor-Compression Refrigeration Cycle The vapor-compression refrigeration cycle is the most widely used cycle for refrigerators and air conditioners. It is similar to a reverse Rankine cycle, but uses isenthalpic throttling instead of isentropic expansion. Step

Process

Work and Heat ^k − 1h/k

k P w1 " 2 = win =− k − 1 RT1 : >1 − e 2 o P1 1→2

Isentropic compression (of the vapor in a compressor)

q1 " 2 = 0

2→3

Isobaric heat rejection (in a condenser, exit condition saturated liquid)

w2 " 3 = 0 q2 " 3 = qH = qout = h3 − h2

3→4

Isenthalpic throttling (of the liquid in an expansion valve or capillary tube, exit conditions: 2-phase)

h= h= hliq _ P3 i 4 3 = w3 " 4 0 q3 " 4 = 0

4→1

Isobaric heat adsorption (in an evaporator,exit condition: saturated vapor)

©2020 NCEES

k−1

T2 P k =e 2o T1 P1 h1 = hvap _ P1 i

w4 " 1 = 0 q4 " 1 = qC = qin = h1 − h4

125

H

Chapter 3: Thermodynamics

T

P

2

SATURATED LIQUID QH

QH

3

3

2

Win

QC

4 4

Win

1

1

QC

SATURATED VAPOR s

h

Coefficient of Performance for the ideal Vapor-Compression Refrigeration Cycle

q h −h COPR, VCC = w c = h1 − h4 net,in 2 1

Coefficient of Performance for the ideal Vapor-Compression Heat Pump Cycle

q h −h COPHP, VCC = w H = h2 − h3 net,in 2 1

3.4.4.4 Cascade Refrigeration Systems Cascade refrigeration system with heat exchange between the stages allows the use of different working fluids for each cycle. WARM ENVIRONMENT QH 7 EXPANSION VALVE

CONDENSER

DECREASE IN COMPRESSOR WORK

T

6

A 8

HEAT EXCHANGER EVAPORATOR

5

QH

COMPRESSOR 7

HEAT

3 EXPANSION VALVE

CONDENSER

2

4

QC

A

5 B

COMPRESSOR 1

4

1 QC

INCREASE IN REFRIGERATION CAPACITY

COLD REFRIGERATED SPACE

The ratio of mass flow rates in each cycle is

mo A h2 − h3 mo B = h5 − h8

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2 8

3

B

EVAPORATOR

6

126

s

Chapter 3: Thermodynamics The coefficient of performance is

mo B _h1 − h4 i Qo   COPR, Cascade = o C = Wnet,in mo A _h6 − h5 j + mo B _h2 − h1 i

3.4.4.5 Multistage Compression Refrigeration Systems Multistage compression refrigeration systems are similar to cascade system, but use the same working fluid. A mixing chamber is used in place of the heat exchanger: WARM ENVIRONMENT QH 5

CONDENSER

4

T

HIGH-PRESSURE COMPRESSOR

EXPANSION VALVE 6

7

6

3 8

2

7 LOW-PRESSURE COMPRESSOR

EXPANSION VALVE 8

2

5 9

FLASH CHAMBER

EVAPORATOR

3

9 1

s 1

QC

COLD REFRIGERATED SPACE

The coefficient of performance is:

_1 − x i_h1 − h8 j qo qo c = COPR, GasRef = wo c = wo net,in comp, LP + wo comp, HP _1 − x i_h2 − h1 i + _h4 − h9 j

where x is the vapor fraction after the first expansion valve (Point 6).

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127

Chapter 3: Thermodynamics 3.4.4.6 Gas Refrigeration Systems The gas refrigeration cycle is the reverse Brayton cycle. WARM ENVIRONMENT QH

T

HEAT EXCHANGER

3

QH 2

TURBINE

Wnet, in

2

3

COMPRESSOR

1 1

4

4

HEAT EXCHANGER

QL

QL

s

COLD REFRIGERATED SPACE

The coefficient of performance is:

_h1 − h4 i qo qo c = COPR, GasRef = wo c = wo − w o net,in comp,in turb,out _h2 − h1 i + _h3 − h4 j

Coefficients of performance are lower than for the Carnot cycle and the vapor-compression refrigeration cycle. They are used in airplanes for cooling and in liquefaction of gases. Regeneration can be included if the turbine exit temperature is above the compressor inlet temperature. The heat transfer from the turbine inlet stream to the compressor inlet stream reduces the amount of heat absorbed in the cold exchanger and thus lowers the coefficient of performance. However, it also reduces the inlet temperature to the turbine and allows to achieve lower temperatures for the cold exchanger.

COLD REFRIGERATED SPACE QC REGENERATOR 6 HEAT

EXCHANGER

Q

T

QH

HEAT

3

3 EXCHANGER 5

4

WARM ENVIRONMENT QH

2

Qregen

1 4 5

TURBINE COMPRESSOR

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Wnet, in

2 1

6 QC s

Chapter 3: Thermodynamics

3.5 Chemical Reaction Equilibria 3.5.1

Gibbs Free Energy and the Equilibrium Constant DV g DV g r = − RT ln K or ln K = − RTr

where K is defined in terms of concentration or pressure in the Vapor Power Cycles and Refrigeration Cycles sections in this chapter.

3.5.2

Temperature Dependence

The change of the equilibrium constant with temperature is a function of the heat of reaction: d ^ln K h DV hr

=

dT

RT 2 The integrated equation is K 1 ln K2 = R 1

#T

T2

1

V e D h2 r o d T T

Over a range where DV h r is nearly constant, this simplifies to:

K DV hr 1 1 ln K2 = − R d T − T n 2 1 1

Gibbs-Helmholtz equation:

J N t K 2 d Dgt n O D h − = RT R T 2 KK 2T OO L PP At equilibrium: dP = 0 t0

Dh =− R T2

3.5.3

dd

Dgt 0 n RT d ^ln K h = dT dT

Concentration Dependence

General reaction: aA + bB * cC + dD At equilibrium:

rFWD = rREV

where

− rFWD = k1 C A a C B b − rREV = k 2 CC c C D d The equilibrium constant is defined as

= Kc

©2020 NCEES

CC c C D d k1 = CA a CB b k2

129

Chapter 3: Thermodynamics

3.5.4

Pressure Dependence

For general reactions: aA + bB * cC + dD At equilibrium:

rFWD = rREV

where

− rFWD = k1 PA a PB b − rREV = k 2 PC c PD d The equilibrium constant is defined as

= KP

PC c PD d k1 = PA a PB b k 2

When a + b = c + d, KP = Kc , and both are dimensionless. When they are not equal:

KP has units of pressure to the power (c + d – a – b). Kc has units of concentration to the power (c + d – a – b). Thus:

KP = Kc (R T)(c+d-a-b)

3.5.5

Le Chatelier's Principle

Le Chatelier's Principle describes the qualitative effect of pressure on equilibrium: For a gaseous reaction, increasing pressure will shift the equilibrium to the side of the reaction in the reaction equation with fewer moles. Changes in pressure have negligible effect on liquid- or solid-phase reactions.

3.6 Phase Equilibria 3.6.1

Definitions

3.6.1.1 Phase A phase is a homogeneous region of matter. Examples of phases include a gas, a mixture of gases, a liquid, a solution of liquids, and a solid.

3.6.1.2 Saturation Temperature The saturation temperature is the temperature at which both liquid and vapor exist in equilibrium at a given pressure.

3.6.1.3 Triple Point For a pure substance, the triple point is the point at which the solid, liquid, and vapor phases exist in equilibrium.

3.6.1.4 Critical Point For a pure substance, the critical point is the temperature and pressure at which the liquid and vapor phases exhibit identical properties and are indistinguishable from each other.

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Chapter 3: Thermodynamics 3.6.1.5 Phase Rule For nonreacting systems, the number of degrees of freedom F is the number of intensive variables (for example, temperature, pressure, and composition) that must be specified in order to fix the intensive state of a system at equilibrium.

F=2–p+N where p = number of phases

N = number of chemical species For reacting systems, the number of degrees of freedom F is:

F = 2−r+N−r where r = number of independent chemical reactions at equilibrium within the system

3.6.2

Pure Substances

3.6.2.1 Phase Transitions for Pure Substances DH DS = T at constant pressure, and DU DS = T at constant volume

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Chapter 3: Thermodynamics 3.6.2.2 Phase Diagrams for Pure Substances The pressure-temperature relationship for a pure fluid is often shown in a pressure-temperature plot. The intersection of the solidliquid-vapor lines is the triple point where the three phases coexist. The critical point is where vapor and liquid properties become identical. Four kinds of diagrams are often used for calculations involving a pure fluid. Figures below show the qualitative behavior of fluid properties.

Thermodynamic Diagrams for a Pure Fluid CRITICAL POINT

TRIPLE POINT

ST. Q CON

PRESSURE

PRESSURE

.V CONST

CONST. T

VAPOR

S T.

S ON

C

SUBLIMATION CURVE

TEMPERATURE

ENTHALPY

PRESSURE-TEMPERATURE DIAGRAM FOR PURE FLUID

PRESSURE-ENTHALPY DIAGRAM FOR PURE FLUID

ST. P

CONST. T

NS

ENTHALPY

CO

T. H

CRITICAL POINT

T. P

CON

CONS

QU SA T. L I

IQ U SA T. L

CONST. H

SA T. V AP

OR

CONST. T

CRITICAL POINT

ID

CONST. QUALITY

ID

TEMPERATURE

CONST. T

SOLID

VAPOR PRESSURE CURVE

SAT. VAPOR

LIQUID

FUSION CURVE

SA T. L IQU ID UAL ITY

CRITICAL POINT

CO

NS

SA T. VA PO UA R LIT Y

T. Q

ENTROPY

ENTHALPY-ENTROPY

TEMPERATURE-ENTROPY DIAGRAM FOR PURE FLUID

ENTHALPY-ENTROPY (MOLLIER) DIAGRAM FOR PURE FLUID

3.6.2.3 Vapor Pressure Vapor pressure is the pressure in a closed system containing a pure fluid with both liquid and vapor in equilibrium at a given temperature. The equilibrium phases are saturated. The Antoine equation can be used to estimate the temperature dependence of vapor pressure:

B log P sat = A − T + C ©2020 NCEES

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Chapter 3: Thermodynamics where

Psat = saturation pressure or vapor pressure A, B, and C = constants for a given species T = temperature

3.6.2.4 Clausius-Clapeyron Equation The Clapeyron equation relates enthalpy change to temperature, vapor pressure, and volume in the phase change of a two-phase, single-species system. sat D Dh d P= s = dT Dv T D v

where

Dh = specific latent heat for the phase change Ds = specific entropy for the phase change Dv = specific volume change for the phase change For the phase transition from liquid to vapor as an ideal gas, the Clapeyron equation becomes the Clausius-Clapeyron equation:

Dht vap d (ln P sat) =− R 1 dc T m Assuming a constant, or average, heat of vaporization between T1 and T2, the integrated form is − Dhtvap 1 1 P sat ln f 2sat p = R d T − T n 2 1 P1

3.6.2.5 Bubbles, Cavities, and Droplets Due to surface tension, the pressure on the inside of a curved surface is higher than on the outside (Laplace Equation): Pin = Pout + 2γr where r

= radius of the curved surface

γ = surface tension Droplets are spheres of the liquid phase in the vapor phase. A mist made from droplets has a higher vapor pressure than the bulk fluid (Kelvin Equation): sat sat = P bulk P mist exp d

2cvt n rRT

Cavities are holes in a liquid filled with vapor. Cavities have a lower vapor pressure than the bulk fluid: sat sat = P bulk Pcavity exp d −

2cvt n rRT

where v = molar volume of the liquid Bubbles are regions of vapor or gas trapped by a thin film. Due to the double surface area, the pressure increase in bubbles is twice that of cavities.

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Chapter 3: Thermodynamics

3.6.3

Ideal Systems

HA

3.6.3.1 Raoult's Law (for ideal solutions) Assuming a vapor phase that is an ideal gas and a liquid phase that is an ideal solution:

= pi y= iP

)

PA N

xi P isat

E

(H

DEVIATION FROM HENRY

= mole fraction of component i in liquid phase

TE

LU DI

LS EA

ID

DEVIATION FROM RAOULT

P isat = vapor pressure of pure component i

3.6.3.2 Henry's Law (for dilute ideal solutions)

IDEAL

The partial pressure of a component in the gas phase is proportional to the concentration of the component in the liquid phase:

pi = yi P = xi Hi

0 "A" AS SOLUTE

where Hi = Henry's law constant for component i

3.6.3.3 Distribution of Components Between Phases in Vapor/Liquid Equilibrium Assume Dalton's Law and Raoult's Law apply. The distribution coefficient (K-value) is defined as:

yi P isat K=i x= P i

where Ki = distribution coefficient for component i

Pisat = saturation pressure of pure component i



The relative volatility is defined as:

Ki = = a ij Kj

yi x j y j xi

where aij = relative volatility for components i and j For a binary system:

x a K x y1 = 1 + x 1(a 12 − 1) = K + x (1K1 − K ) 1 12 2 1 1 2 y K y x1 = a + y (11 − a ) = K + y (2K 1 − K ) 12 1 12 1 1 2 1

3.6.4

Nonideal Systems

3.6.4.1 Fugacity The criterion for the vapor-liquid equilibrium of non-ideal systems is

ftiV = ftiL where ∧ = indicates properties of the component in the mixture

ftiV = fugacity of component i in the vapor phase ftiL = fugacity of component i in the liquid phase ©2020 NCEES

W LA

OL

where

xi

IO UT

Y’S NR

134

TION

SOLU

XA

sat PA

W) T’S LA AOUL

(R

1 "A" AS SOLVENT

Chapter 3: Thermodynamics 3.6.4.2 Fugacity of Pure Component Vapor Fugacity of a Pure Component f V = zP where

z = fugacity coefficient of pure component in vapor phase

The fugacity coefficient of a pure component is a function of temperature and pressure and may be determined from any of: The residual Gibbs free energy (GR)

GR ln z = RT

An equation of state

ln z =

#0

dP ( Z − 1) P

P

A generalized correlation, e.g.,

ln z = (ln z) 0 + ~ (ln z)1

where w = the acentric factor

Liquid Fugacity of a Pure Component /i = exp =

f L = z sat P sat /

vt L (P − P sat) G RT

where

z sat = fugacity coefficient of pure component at saturation pressure /

= Poynting correction factor

vt L = molar volume of pure component in the liquid phase

3.6.4.3 Fugacity of Mixtures Vapor Fugacity of a Mixture = ft V zt= P zt y P i

i

i

i

i

t = fugacity coefficient of component i in the vapor phase where z i The fugacity coefficient of a component in a mixture may be determined from an equation of state and a mixing rule.

BP

For a pure component, using the virial equation: ln z = RT For a mixture, using the virial equation:

ln zt i = d

/ y j Bij − Bm n j

P RT

where

Bm =

/ / yi y j Bij i

j

Bm = second virial coefficient of the mixture Bij = virial coefficient that characterizes a bimolecular interaction between i and j For i = j, Bij = Bji = Bii

= j , Bij must be obtained from measured values or mixing rules. For i Y

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Chapter 3: Thermodynamics Liquid Fugacity of a Mixture = ft L c= x f L c x z sat P sat / i

i

i

i

i

i

i

i

i

where gi = activity coefficient of component i Activity coefficients are normally based on experimental measurements and fitted to an activity coefficient model, for example the Van Laar model: −2

A x ln c1 = A12 e1 + A 12 x1 o 21 2

and

−2

A x ln c 2 = A 21 e1 + A21 x 2 o 12 1

where A12 and A21 = Van Laar constants, typically fitted from experimental data

3.6.4.4 Vapor-Liquid Equilibrium (Gamma/Phi Approach) sat zt i yi P = c i xi z sat i Pi /i The distribution coefficient for component i in a non-ideal mixture is

yi ci zisat Pisat K=i x= t P i z i Special cases:

Ideal vapor phase, ideal liquid solution, and low pressure: Assume= zt i 1= , c i 1, and / i = 1, (Raoult's Law)

Pisat P Ideal vapor phase, nonideal liquid solution, and low pressure: sat = then yi P x= i Pi and Ki

= Assume zt i 1= and / i 1, (Henry's Law with Henry's Law Constant Hi = ci3 Pisat )

cPisat P Nonideal vapor phase, nonideal liquid solution, and low to moderate pressure: sat = then yi P c= i xi Pi and Ki

Assume / i = 1,

ci zisat Pisat sat sat t y P c= = then z x z P and K i i i i i i i tP z i

3.6.5

Phase Behavior

3.6.5.1 Lever Rule Binary Systems For a vapor-liquid mixture of A and B, the relative amounts of the liquid and vapor phases in a mixture with an overall composition of xF are given by the following equations:

P V

mL b = yA − xF = _1 − | i = + m L + mV a b yA − xA mV x −x = = a = F A m L + mV | a + b y A − x A

a

where χ is the vapor quality (i.e., the mass fraction of the vapor in the 2-phase mixture)

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136

0

xA

b xF

yA

CONCENTRATION OF COMPONENT A

1

Chapter 3: Thermodynamics Ternary, Two-Phase System In the following ternary phase diagram, two phases contain partially miscible components A, B, and C. One phase is rich in component B and one is lean in component B. The fraction of the B-lean phase is a , where a and b represent the length of the a+b tie line on each side of the overall composition, denoted by the heavy black dot.

Ternary Phase Diagram mβ b = mα + mβ a + b mα = a mα + mβ a + b



100% C

100% B

α PHASE

b

a

100% A

β PHASE

3.6.5.2 Vapor-Liquid Equilibrium in Binary, Fully Miscible System Typical Vapor-Liquid Equilibrium Diagrams for Binary, Fully Miscible Systems V

L

P = CONSTANT

V–L

P

y

T V–L

L

V x-y

x-y

x

3.6.5.3 Fully Miscible, Binary System with Azeotropes An azeotrope is a mixture that produces a liquid and vapor of equal composition when boiled. For a positive azeotrope (minimum-boiling azeotrope): • A positive deviation from Raoult's Law is exhibited on a P-xy diagram, with the P-x curve lying above that for ideal behavior. This behavior results when liquid-phase intermolecular forces between like molecules are stronger than between unlike molecules. • The P-x curve and the P-y curve exhibit maxima at a point for which x = y. • A T-xy diagram exhibits a minima at the point for which x = y, which represents a boiling point lower than that of any other composition.

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Chapter 3: Thermodynamics Positive Azeotrope Diagrams P = CONSTANT

L P

V–L

V V–L

T

V–L

V–L

V x-y

y

L x

x-y

For a negative azeotrope (maximum-boiling azeotrope): • A negative deviation from Raoult's Law is exhibited on a P-xy diagram, with the P-x curve lying below that for ideal behavior. This behavior results when liquid-phase intermolecular forces between unlike molecules are stronger than between like molecules. • The P-x curve and the P-y curve exhibit minima at a point for which x = y. • The T-xy diagram exhibits a maxima at the point for which x = y, which represents a boiling point higher than that of any other composition.

Negative Azeotrope Diagrams

P = CONSTANT V

L P

V–L V

V–L

T

V –L V –L

x-y

y

L x-y

x

3.6.5.4 Partially Miscible Systems Liquid-Liquid Equilibrium Many mixtures of chemical species, when mixed in certain ranges of composition, form two liquid phases of different compositions at thermodynamic equilibrium. The criterion for the liquid-liquid equilibrium of mixtures is

ftia = ftib where

ftia = fugacity of component i in the liquid phase designated a ftib = fugacity of component i in the liquid phase designated b

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Chapter 3: Thermodynamics If each species exists as a liquid at the system temperature, then:

x ia c ia = x ib c bi A solubility diagram is a T-x diagram at a constant pressure for a binary system. It depicts curves that indicate the compositions of coexisting liquid phases. Such diagrams may show: • A lower critical solution temperature, above which two liquid phases are possible and below which a single liquid phase exists for all compositions. • An upper critical solution temperature, below which two liquid phases are possible and above which a single liquid phase exists for all compositions.

Upper and Lower Critical Solution Temperatures UPPER CRITICAL SOLUTION TEMPERATURE

2 PHASES (PARTIALLY MISCIBLE)

T

T TWO PHASES (PARTIALLY MISCIBLE)

SINGLE PHASE (MISCIBLE)

LOWER CRITICAL SOLUTION TEMPERATURE x

SINGLE PHASE (MISCIBLE)

x

Partially Miscible Ternary Systems Most of the ternary or pseudoternary systems used in extraction are of two types: Type I System: One binary pair has limited miscibility. Type II System: Two binary pairs have limited miscibility. The compositions of the two phases are equal at the plait point. Examples of Type I and II systems are shown below.



Type I System

Type II System ONE LIQUID PHASE

PLAIT POINT

ONE LIQUID PHASE

f z a

c

e

b MOL FRACTION

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TWO LIQUID PHASES

TWO LIQUID PHASES

TIE LINES

MOL FRACTION

139

Chapter 3: Thermodynamics Vapor-Liquid-Liquid Equilibrium The gamma-phi approach to vapor-liquid equilibrium applies to each liquid phase. Assuming= that z 1= and / 1: a a sat = y i* P c= and y i* P c bi x ib P isat i xi Pi

For a binary system,

P = y1* P + y 2* P = c1b x1b P1sat + c a2 x 2a P 2sat

y i* =

and

c bi x ib P isat P

where

P = total pressure y i* = three-phase equilibrium concentration of component *i in the vapor phase x1b = concentration of Component 1 in the liquid β-phase x 2a = concentration of Component 2 in the liquid α-phase c1b = activity coefficient of Component 1 in the liquid β-phase c a2 = activity coefficient of Component 2 in the liquid α-phase a = liquid phase rich in Component 2 b = liquid phase rich in Component 1

Vapor-Liquid-Liquid Equilibrium Diagrams V V –Lβ Lβ – L α P

Lβ

V–Lα

T

Lα

Lβ

x-y

2 (α-PHASE)

Lα

y

V –Lα Lβ – L α

V–Lβ V 1 (β-PHASE)

P = C ON S TAN T

1 (β-PHASE)

x-y

2 (α-PHASE)

3.6.5.5 Immiscible Phases In an immiscible system, x1b, c1b, x 2a, and c a2 all are equal to 1. As a result:

P = P1sat + P 2sat

and

y1* =

P1sat + P 2sat

P1sat

For the range in which the vapor is in equilibrium with pure-liquid Component 1:

P sat y1 = P1

And similarly, for the range in which the vapor is in equilibrium with pure-liquid Component 2:

P sat y 2 = P2

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x

Chapter 3: Thermodynamics

3.6.6

Phase Equilibrium Applications

3.6.6.1 Bubble Point The bubble point is defined as the temperature/pressure combination in which the first bubble of vapor is formed in a liquid. It may be determined by iterative calculations from one of the following three relationships, given the liquid composition and either pressure or temperature: n

/

= yi

n

= / Ki xi

1

=i 1=i 1

n

n x P i i, sat / = 1 or P 1=i 1

n

For ideal mixtures: / yi = =i

P = / xi Pi, sat i=1

n

If

/ Ki xi > 1, decrease temperature or increase total pressure.

i=1 n

If

/ Ki xi < 1, increase temperature or decrease total pressure.

i=1

3.6.6.2 Dew Point The dew point is defined as the point where the vapor reaches saturation and the liquid phase begins to form. It may be determined by iterative calculations from one of the following relationships, given the vapor composition and either pressure or temperature: n

/

= xi

n

yi = / Ki

=i 1=i 1

n

1

n y P i / = 1 or sat P = 1 i 1 i

/ xi = For ideal mixtures: =i

P=

1

/ n= f i 1

yi p Pisat

n

If

/ Kyii > 1, increase temperature or decrease total pressure.

i=1 n

If

/ Kyii < 1, decrease temperature or increase total pressure.

i=1

3.6.6.3 Flash A single-stage flash determines the distribution of components between the liquid and vapor phase. It may be determined by iterative calculations from one of the following relationships, given the feed composition, the relative proportions of vapor and liquid resulting from the flash, and either pressure or temperature: n

n

i=1

i=1

/ xi = / 1 + f (zKi i − 1) = 1

where

or

n

n

i=1

i=1

/ yi = / 1 + fz(i KKii− 1) = 1

zi = mole fraction of component in the feed f = ratio of vapor-phase flow to the feed flow q = ratio of liquid-phase flow to the feed flow

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Chapter 3: Thermodynamics The lever rule may be applied to binary single-stage flash calculations as follows:

V = = − = zi − xi F f 1 q yi − xi L = − = = yi − zi F 1 f q yi − xi

F, zi

V, yi

f

T, Ptot L, xi

(1–f)

Equations for the operating line are:

z q 1−f 1 n L F o xi + i =−e − o xi + d − yi =− c V m xi + c V m zi =− e 1 q zi f 1 q f where F = total feed flow rate V = vapor flow rate L = liquid flow rate

3.6.6.4 Solubility of Solids The heat of solution for a solid in water can be calculated from the following equation: % = DHf% _aq i − DH %f ^ s h DHsolution

given that DHf% _aq i is known at the stated concentration. For salt compounds, the solubility product constant describes the extent to which the salt will dissolve. For the following general chemical reaction: y − AxBy ^ s h ? xA _aq i + yB x _aq i +

The solubility product (Ksp) at equilibrium is:

Ksp = 7A y+A 7B x−A x

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142

Chapter 3: Thermodynamics

3.7 Tables

Standard Gibbs Energies of Formation at 298.15 K (25˚C) State (Note 2)

Chemical species Paraffins: Methane Ethane Propane n-Butane n-Pentane n-Hexane n-Heptane n-Octane 1-Alkenes: Ethylene Propylene 1-Butene 1-Pentene 1-Hexene Miscellaneous organics: Acetaldehyde Acetic acid Acetylene Benzene Benzene 1,3-Butadiene Cyclohexane Cyclohexane 1,2-Ethanediol Ethanol Ethanol Ethylbenzene Ethylene oxide Formaldehyde Methanol Methanol Methylcyclohexane Methylcyclohexane Styrene Toluene Toluene

∆G °f 298 J/gmol

CH4 C2H6 C3H8 C4H10 C5H12 C6H14 C7H16 C8H18

g g g g g g g g

–50,460 –31,855 –24,290 –16,570 –8,650 150 8,260 16,260

C2H4 C3H 6 C4 H 8 C5H10 C6H12

g g g g g

68,460 62,205 70,340 78,410 86,830

C2H 4O C2H 4O 2 C2H2 C 6 H6 C 6 H6 C 4 H6 C6H12 C6H12 C 2 H6 O2 C 2 H6 O C 2 H6 O C8H10 C 2 H4 O CH2O CH4O CH4O C7H14 C7H14 C8H 8 C7H 8 C7H 8

g l g g l g g l

–128,860 –389,900 209,970 129,665 124,520 149,795 31,920 26,850 –323,080 –168,490 –174,780 130,890 –13,010 –102,530 –161,960 –166,270 27,480 20,560 213,900 122,050 113,630

g l g g g g l g L g g l

Notes: 1. The standard Gibbs energy of formation is the change in the Gibbs energy when 1 mol of the listed compound is formed from its elements with each substance in its standard state at 298.15 K (25°C). 2. Standard states: (a) Gases (g): the pure ideal gas at 1 bar and 25°C. (c) Solutes in aqueous solution (aq): The hypothetical ideal 1 molal solution of the solute in water at 1 bar and 25°C. 3. Joules per mole of the substance formed

Source: TRC Thermodynamic Tables, Hydrocarbons, Thermodynamics Research Center, Texas Engineering Experiment Station, Texas A & M University System, 1985; and Gaur and Wunderlich, Tables A1-A6, "Heat Capacity and Other Thermodynamic Properties of Linear Macromolecules V. Polystyrene," Journal of Physical and Chemical Reference Data, vol. 11, no. 2: 1982 (all volumes available online at https://aip.scitation.org/journal/jpr).

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4 HEAT TRANSFER 4.1 Symbols and Definitions Symbols Symbol

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Description

Units (U.S.)

Units (SI)

ft2

m2

Btu hr -cF

2 W = kg : m K s3 : K

A

Area

C

Heat-capacity rate

cp

Heat capacity at constant pressure

Btu lbm -cF

J = m2 kg : K s 2 : K

D

Diameter

ft or in.

m

d

Wall thickness, width

ft or in.

m

F

Correction factor for heat-exchanger configuration

dimensionless

Fij

Shape factor (radiation)

dimensionless

f

Friction factor (Darcy-Weisbach)

dimensionless

g

Acceleration of gravity

h

Convection heat-transfer coefficient

ft sec 2

m s2

Btu hr -ft 2-cF

W = kg m 2 : K s3 : K

Dhfusion

Latent heat of fusion

Btu lbm

J = m2 kg s 2

Dhsubl

Latent heat of sublimation

Btu lbm

J = m2 kg s 2

Dhvap

Latent heat of vaporization

Btu lbm

J = m2 kg s 2

144

Chapter 4: Heat Transfer Symbols (cont'd) Symbol

DH

Units (U.S.)

Change in enthalpy

Btu

Units (SI)

J=

kg : m 2 s2

jH

Colburn factor for heat transfer

k

Thermal conductivity

Btu hr -ft -cF

W = kg : m m : K s3 : K

L

Length

ft or in.

m

m

Mass

lbm

kg

mo

Mass flow rate

lbm hr

kg s

NTU

dimensionless

Number of thermal transfer units

dimensionless

n

Number of tubes (in shell-and-tube heat exchangers)

dimensionless

P

Pressure

psi =

lbf in 2

= Pa

kg N = m2 m : s2

Pc

Critical Pressure

psi =

lbf in 2

= Pa

kg N = 2 m m : s2

P

Thermal efficiency

Q

Heat

Btu

J=

kg : m 2 s2

Qo

Rate of heat transfer

Btu hr

W=

kg : m 2 s3

qo

Heat flux (rate of heat transfer per area)

Btu hr -ft 2

qo l

Rate of heat transfer per unit length

Btu hr -ft

W = kg m 2 s3 W = kg : m m s3

qo gen

Rate of heat generation per volume

Btu hr - ft3

W = kg m3 m : s3

Heat-transfer resistance

hr -cF Btu

K = s3 : K W kg : m 2

R RNTU

dimensionless

C

C

Heat-capacity rate ratio e C tube o or e C min o shell

dimensionless

max

Rf

Fouling factor

hr -ft 2-cF Btu

m 2 : K = s3 : K W kg

r

Radius

ft or in.

m

T

Temperature

cF or cR

cC or K

Log-mean temperature difference

cF or cR

K

DTlm

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145

Chapter 4: Heat Transfer Symbols (cont'd) Symbol Tr

Reduced temperature

Tn

Normal boiling point

t

Units (U.S.)

Units (SI)

dimensionless °F or °R

°C or K

hr

s

Btu hr -ft 2-cF

Time

u

Velocity

ft sec

W = kg m 2 : K s3 : K m s

V

Volume

ft3

m3

x

Distance

ft or in.

m

a

Adsorptivity (radiation)

a

Thermal diffusivity

ft 2 hr

m2 s

b

Coefficient of thermal expansion

1 cR

1 K

g

Surface tension

lbf in.

N kg m = s2

d

Thickness

ft or in.

m

e

Emissivity of a body (radiation)

dimensionless

e

Heat exchanger effectiveness

dimensionless

e

Void fraction (packed bed)

dimensionless

Uov

q, f

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Description

Overall heat-transfer coefficient

dimensionless

radians or degrees

Angle

m

Dynamic viscosity

cP or ft-sec

kg Pa : s = m : s

n

Kinematic viscosity

ft 2 hr

m2 s

r

Density

lbm ft3

kg m3

r

Reflectivity (radiation)

v

Stefan-Boltzmann Constant

t

Time constant

t

Transmissivity (radiation)

lbm

dimensionless

Btu ft - hr -cR 4

W m : K4

hr

s

2

dimensionless

146

2

Chapter 4: Heat Transfer

4.2 Fundamentals of Heat Transfer 4.2.1

Heat Transfer Without Phase Change

4.2.1.1 Definition of Heat dT Qo = m c p dt cp =

DH m DT

Heat transferred in or out of a flowing material:

Qo = mo c p DT

4.2.1.2 Physical Properties for Heat Transfer Thermal conductivity is a measure of the rate at which a substance transfers thermal energy:

k=

qo DT d

Thermal diffusivity is a measure of the rate at which a thermal disturbance is transmitted through a substance:

k a = tc p Kinematic viscosity (also called momentum diffusivity) is the ratio of the dynamic viscosity m to the density of the fluid r:

n v=t

4.2.1.3 Conduction The following equations assume that the thermal conductivity is constant.

Fourier's Law of Conduction

dT Total heat flux (rate of heat transfer): Qo = − k A dx Qo dT Heat flux per area (rate of heat transfer per area): qo = A = − k dx Qo

Heat flux per unit length (rate of heat transfer per unit length): qo l = L

Conduction Through a Plane Wall T1

kA Qo = (T − T ) d 1 2

k T2

where T1 = temperature of one surface of wall

δ

T2 = temperature of the other surface of wall

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Q

Chapter 4: Heat Transfer Conduction Through a Composite Wall A (T1 − T2) Qo = di i ki

/

Conduction Through a Cylindrical Wall

Q

T1

2r k L Qo = (T1 − T2) r2 ln d r n 1

T2 r1

k

where L = cylinder length

r2 Cylinder (Length = L)

Conduction Through a Spherical Wall 4r k r r Qo = r − r1 2 (T1 − T2) 2 1 Conduction Through a Cube With Thick Walls (Approximation) -T T Qo . 0.725 Aouter Ainner e inner outer o d where

Aouter Ainner $ 2

Steady Conduction With Internal Energy Generation For a plane wall: T(x)

d 2 T + qo gen = 0 k dx 2 qo gen d 2 T −T x T +T x2 T ^ x h = 2 k e1 − 2 o + d 2 1 nc m + d 1 2 n d 2 2 d

T1 qgen q1

For a long circular cylinder:

where

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+δ

0

T0

1 d c dT m + qo gen = 0 r dr r dr k

qo l0 =

q2 −δ

qo 1 + qo 2 = 2 qo gen d dT dT qo 1 = k c dx m and qo 2 = k c dx m −d +d

T (r ) =

T2

k

qgen

qo gen r 02 r2 f1 − 2 p + T0 4k r0

r0

r r 02 qo gen

W Btu qo l0 = heat transfer rate per unit length in hr -ft or m

148

k

qʹ 0

Chapter 4: Heat Transfer Transient Conduction Using the Lumped Capacitance Model The lumped capacitance model is valid if Body

hV Bi = k A 200,000

0.021

0.84

0

Staggered

>200,000 Pr > 1

0.022

0.84

0

Staggered

>200,000 Pr = 0.7

---

---

---

ST SL $ 0.7 1000–200,000 ST S 0.7 Uniform surface temperature or uniform heat flux: Re > 10,000; Pr > 0.7 Uniform heat flux: 0.003 < Pr < 0.05 Constant surface temperature: 0.003 < Pr < 0.05

t um D hD = and Nu D n k

where um = mean velocity of the fluid n3 = viscosity of the fluid at bulk fluid temperature ms = viscosity of the fluid at tube inside surface temperature

4 # cross-sectional area wetted perimeter For a circular annulus, use the equivalent hydraulic diameter: DH = Douter − Dinner For noncircular ducts, use the equivalent hydraulic diameter: DH =

Use the friction factor f from the Moody diagram to predict heat-transfer coefficients for turbulent flow: 2 f c Nu m Pr 3 = Re Pr 8

For flow in coiled tubes with Re > 104, the forced-convection heat-transfer coefficient for the inside of the coiled pipe is:

D hcoil = hstraight e1 + 3.5 Dtube o coil

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Tube-Side Heat-Transfer Curve (Adapted from Sieder and Tate)

1000 800

10

20

600 500 400

4

5 6 7 8 1000

153

2

3

4

5 6 7 8 10,000

2

3

4

5 6 7 8 100,000

2

3

100 80 60 50 40

2

3

4

5 6 7 8 10,000

2

3

4

5 6 7 8 100,000

2

3

Chapter 4: Heat Transfer

−1/3 µ − 0.14 µ µw

3

HEATING AND COOLING

200

cp k

200

u = VELOCITY ρ = DENSITY jH = COLBURN FACTOR c p = HEAT CAPACITY OF THE FLUID d = INSIDE DIAMETER OF TUBES h i = FILM COEFFICIENT k = THERMAL CONDUCTIVITY L = LENGTH OF PATH µ = VISCOSITY AT THE BULK TEMPERATURE µw = VISCOSITY AT THE TUBE WALL TEMPERATURE

300

hi d j H= k

30 40 50 60 80 100

30 20

10 8 6 5 4

24 L/D = 36 48 72 120 180 220 360 600

3 2 1

10

20

30 40 50 60 80 100

200

3

4

5 6 7 8 1000 Re =

d.u.ρ

µ

Source: Kern, Donald Q., Process Heat Transfer, 1990, p. 834.

Chapter 4: Heat Transfer 4.2.1.6 Heat Transfer Coefficients/Correlations for Free Convection Natural (Free) Convection

Natural (Free) Convection Geometry

Sketch

Nu L = 1.36 _Gr L Pr i5

GrL Pr < 10 4

Nu L = 0.59 _Gr L Pr i4 1

10 4 < Gr L Pr < 10 9

Nu L = 0.10 _Gr L Pr i3

10 9 < Gr L Pr < 1013

1

∞ g

Vertical plate

Conditions

Correlation

1

L

Long, tilted plate with heated surface facing downward Long, horizontal plate with heated surface facing downward Long, horizontal plate with heated surface facing upward Horizontal circular plate with heated surface facing downward

∞ θ

g

g

L

Nu L = 0.56 _Gr L Pr cos i i4

10 5 < Gr L Pr cos i < 1011 0 # i # 89c

Nu L = 0.58 _Gr L Pr i5

10 6 < Gr L Pr < 1011

Nu L = 0.16 _Gr L Pr i3

7 # 10 6 < Gr L Pr < 2 # 10 8

Nu L = 0.13 _Gr L Pr i3

5 # 108 < GrL Pr

1

∞

1

L

1

g L

1

g

Nu D = 0.82 _Gr D Pr i5 Pr 0.034 1

D

Pr > 0.5 Single, long horizontal cylinder

Nu D = C _Gr D Pr i

n

D g

GrD • Pr 10–3 – 102 102 – 104 104 – 107 107 – 1012

∞

1

Nu D = 0.53 `Gr D Pr 2 j4 Thin horizontal wire

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D g

∞

Nu D = C _Gr D Pr i

n

154

C 1.02 0.850 0.480 0.125

n 0.149 0.188 0.250 0.333

Liquid metals, laminar flow

GrD • Pr < 10–5 10–5 – 10–3 10–3 – 1 1 – 104

C 0.49 0.71 1.09 1.09

n 0 0.04 0.10 0.20

Chapter 4: Heat Transfer Natural (Free) Convection (cont'd) Geometry

Sketch

Correlation

∞

Vertical cylinder

D

g

Conditions

Nu D = 0.59 _Gr D Pr i4 1

10 4 < Gr D Pr < 10 9

Nu D = 0.10 _Gr D Pr i3

109 < GrD Pr < 1013

1

Diameter D g

Sphere

Vertical cone

Nu D = 2 + 0.392 _Gr D i4 1

Nu L = 0.63 (1 + 0.73 e) _Gr L i4 2 e= 1 z Gr L4 tan 2 1

φ

g

1 < GrD < 105

L

3c < z < 12c 7.5 < log GrL < 8.7 0.2 < e < 0.8

Vertical enclosed space heated from the side

g

0.28 L Pr Nu d = 0.22 c m c 0.2 + Pr Ra d m d

L

L d Rad n − 1H 5830

g

δ

1708 Nu d = 1 + 1.44 d1 − Ra n + d 1 3

>d Ra d n − 1H + 2.0 f 5830

For plates and other linear geometry: Ra L = Gr L Pr = For cylinders and spheres:

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L < 10 d Pr < 10 Rad < 1010

2
Tsat:

qo = h `Ts − Tsat j = h DTe

where Ts

= temperature of solid

Tsat = saturation temperature of liquid at system pressure DTe = excess temperature Pool boiling: Liquid is quiescent; motion near the solid surface is caused by free convection and mixing induced by bubble growth and detachment. Forced convection boiling: Fluid motion is induced by external means in addition to free convection and bubble-induced mixing. Sub-cooled boiling: Liquid temperature is below the saturation temperature; bubbles forming at the heating surface may condense in the liquid. Saturated boiling: Liquid temperature slightly exceeds the saturation temperature; bubbles forming at the heated surface are propelled through the liquid by buoyant forces.

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Chapter 4: Heat Transfer Typical Pool Boiling Curve for Water at One Atmosphere Surface Heat Flux as a Function of the Excess Temperature

BOILING REGIMES

FREE CONVECTION

NUCLEATE

ISOLATED BUBBLES

107

C - CRITICAL HEAT FLUX, q"MAX

q"s (W/m2)

P B

105 q"MIN

104

103

FILM

JETS AND COLUMNS

q"MAX

106

TRANSITION

D A ∆Te,A

1

-LEIDENFROST POINT, q"MIN

ONB

5

∆Te,B 10

∆Te,C

∆Te,D

30 120 ∆Te =Ts –Tsat (°C)

1,000

Free convection boiling: There is insufficient vapor in contact with the liquid phase to cause boiling at the saturation temperature. Nucleate boiling: Isolated bubbles form at nucleation sites and separate from the surface; vapor escapes as jets or columns. Rohsenow equation for nucleate-boiling heat flux:

g `t liq − t vap jH > c p, liq (Ts − Tsat) H qo nucleate = n liq Dh vap > n Csf Dh vap Pr liq c

3

1/2

where g

= surface tension of vapor-liquid interface

Ts = surface temperature of heater Tsat = saturation temperature of fluid Csf = experimental constant that depends on surface-fluid combination n

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Chapter 4: Heat Transfer Values of the Coefficient Csf for Various Liquid-Surface Combinations

Fluid Water Water Water Water Water Water Water Water Water Water Ethyl alcohol Isopropyl alcohol n-Butyl alcohol n-Pentane n-Pentane n-Pentane n-Pentane n-Pentane Benzene Carbon tetrachloride Carbon tetrachloride 35% K2CO3 50% K2CO3

Heating Surface

Csf

Brass Copper Copper (emory-polished) Copper (emory-polished, paraffin-treated) Copper (scored) Platinum Stainless steel (ground and polished) Stainless steel (Teflon pitted) Stainless steel (chemically etched) Stainless steel (mechanically polished) Chromium Copper Copper Chromium Copper (emory-polished) Nickel (emory-polished) Copper (lapped) Copper (emory-rubbed) Chromium Copper Copper (emory-polished) Copper Copper

0.0060 0.013 0.0128 0.0147 0.0068 0.013 0.0080 0.0058 0.0133 0.0132 0.0027 0.00225 0.00305 0.015 0.0154 0.0127 0.0049 0.0074 0.0100 0.013 0.0070 0.0054 0.00275

The critical (also called "maximum" or "peak") heat flux (CHF) in nucleate pool boiling: 2 `t liq − t vap jC qo max = Ccr Dh vap 9c g t vap

1/4

where Ccr = constant whose value depends on the heater geometry, but generally about 0.15 The critical heat flux is independent of the fluid-heating surface combination, as well as the viscosity, thermal conductivity, and heat capacity of the liquid. It increases with pressure up to about one-third of the critical pressure, and then starts to decrease and becomes zero at the critical pressure. The critical heat flux is proportional to the latent heat of vaporization; large maximum heat fluxes can be obtained using fluids with a large enthalpy of vaporization, such as water. Values of the coefficient Ccr for maximum heat flux:

g `t liq − t vap j c c K1 = g `t liq − t vap j A heater L* = L

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Chapter 4: Heat Transfer Critical Heat Flux vs. Heater Geometry Characteristic Dimension (L) Width or diameter Width or diameter Radius Radius Radius Radius

Ccr

Heater Geometry Large horizontal flat heater Small horizontal flat heater Large horizontal cylinder Small horizontal cylinder Large sphere Small sphere

0.149 18.9 K1 0.12 0.12 L*-0.25 0.11 0.227 L*-0.5

Range of L* L* > 27 9 < L* < 20 L* > 1.2 0.15 < L* 4.26 0.15 < L* < 4.26

Minimum heat flux: This occurs at the Leidenfrost point and is of practical interest because it represents the lower limit for the heat flux in the film boiling regime. Minimum heat flux for a large horizontal plate:

RS V1 SS c g `t liq − t vap jWWW 4 W qo min = 0.09 t vap Dh vap SS SS `t liq + t vap j2 WWW T X Transition boiling: Rapid bubble formation results in vapor film on surface and oscillation between film and nucleate boiling. Film boiling: Surface is completely covered by a vapor blanket; includes significant radiation through the vapor film. Heat flux for film boiling on a horizontal cylinder or sphere of diameter D:

qo film = Cfilm *

g

3 k vap t vap (t liq

For horizontal cylinders:

Cfilm = 0.62

For spheres:

Cfilm = 0.67

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1

− t vap) 8Dh vap + 0.4 c p, vap (Ts − Tsat)B 4 4 (Ts − Tsat) n vap D (Ts − Tsat)

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Chapter 4: Heat Transfer 4.2.2.3 Evaporation Estimate Heat of Vaporization at the Normal Boiling Point DHvap, n Tn 1.092 _ln Pc − 1.013 j = R 0.930 − Trn

where Tn = normal boiling point ∆Hvap,n = latent heat of vaporization at Tn Pc = critical pressure, bar Tr

n

= reduced temperature at Tn

Estimate heat vaporization at any temperature from a known value 0.38

DHvap, 2 1 − Tr, 2 =f p DHvap, 1 1 − Tr, 1 where

∆Hvap = latent heat of vaporization Tr = reduced temperature Source: Republished with permission of McGraw-Hill, Inc., from Introduction to Chemical Engineering, J.M. Smith and H.C. Van Ness, 4th ed., New York: 1987; permission conveyed through Copyright Clearance Center, Inc.

4.2.2.4 Condensation Heat-Transfer Coefficient for the Condensation of a Pure Vapor Evaluate all liquid properties at the average temperature between the saturated temperature and the surface temperature, where rl = density of the liquid phase of the fluid ml = viscosity of the liquid phase of the fluid kl = thermal conductivity of the liquid phase of the fluid

Nu = average Nusselt number h = average heat-transfer coefficient Tsat = saturation temperature of the fluid Ts = temperature of the vertical surface P = wetted perimeter (width of a vertical plate, or pd, for a vertical tube)

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Chapter 4: Heat Transfer Condensation Film Coefficients Geometry

Correlation

Conditions 0.25

Condensation on a vertical or angled surface, laminar flow

t 2 g Dh vap L3 hL H Nu L = k = 0.943 > l n l kl (Tsat − Ts)

Vertical surface 0.25

t 2 g Dh vap L3 cos i hL H Nu L = k = 0.943 > l n l kl (Tsat − Ts)

0.25

Condensation on the outside of a horizontal tube, laminar flow

Condensation on a tall vertical surface or on the outside of a tall vertical tube, turbulent flow

t 2 g Dh vap D 3 hD H Nu D = k = 0.729 > l n l kl (Tsat − Ts)

Inclined surface, angle q measured from the vertical Single tube or horizontal layer of tubes

0.25

t 2 g Dh vap D 3 hD H Nu D = k = 0.729 > l N n l kl (Tsat − Ts)

Tube bank with N layers of horizontal tubes, arranged vertically over one another Condensation Reynolds number:

1

h= D = Nu D k

2 0.0076 Re h5

t 2 g Dh vap D 3 3 > l H n l2

4 mo Re h = P n > 1800 l oQ h A `Tsat − Ts j = mo = Dh vap Dh vap

0.25

Condensation on a sphere

t 2 g Dh vap D 3 hD H Nu D = k = 0.815 > l n l kl (Tsat − Ts)

4.2.2.5 Sublimation As shown on the thermodynamic diagram of pressure-temperature for a pure fluid, sublimation occurs when the pressure and temperature are below the triple point. As an estimate, at a constant temperature,

DHsubl = DHfus + DHvap Source: Republished with permission of McGraw-Hill, Inc., from Lange's Handbook of Chemistry, John A. Dean and N.A. Lange, 13th ed., 1985; permission conveyed through Copyright Clearance Center, Inc.

4.3 Applications of Heat Transfer 4.3.1

Heat-Exchange Equipment Design

4.3.1.1 Overall Heat-Transfer Coefficients Energy balance around a heat exchanger:

Qo = mo cold c p,cold (Tcold,out − Tcold,in) = mo hot c p,hot (Thot,in − Thot,out) Rate of heat transfer in a heat exchanger:

Qo = U ov A F DTlm where F = LMTD correction factor based on exchanger configuration (see F-factor charts in this chapter) Heat-transfer area in a shell-and-tube heat exchanger:

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Chapter 4: Heat Transfer where n = total number of tubes Mass flow rate in a shell-and-tube heat exchanger

D2 mo = npass r 4i t u

where npass = number of tubes in each pass Overall heat-transfer coefficient for concentric tube and shell-and-tube heat exchangers:

D ln e Do o R Rfi i 1 1 = + + + fo + 1 Ao ho Ao Uov A ref hi Ai Ai 2 r k L 1 = 1 e Do o + e Do o + Do e Do o + 1 Rfi D Rfo + h Uov hi D i 2 k ln Di i o where Ai = inside area of the tubes Ao = outside area of the tubes Aref = reference areas for the overall heat-transfer coefficient Uov (usually the outside area) Di = inside diameter of the tubes Do = outside diameter of the tubes hi = convection heat-transfer coefficient for inside the tubes ho = convection heat-transfer coefficient for outside the tubes Rfi = fouling factor for inside the tubes Rfo = fouling factor for outside the tubes

4.3.1.2 Fouling Factors Fouling factors are defined as:

1 − 1 Rf = h hclean fouled A table of fouling factors is shown in this chapter. Fouling factors increase with time. Some common approximations for time dependence are as follows: Linear:

Rf (t) = Rf, initial + a t

Falling-rate:

[Rf (t)] 2 = (Rf, initial) 2 + b t

Asymptotic:

Rf (t) = Rf, 3 a1 − e − x k t

where a, b, and t = empirical constants

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Chapter 4: Heat Transfer 4.3.1.3 Log-Mean Temperature Difference Temperature Profiles for Countercurrent and Cocurrent Heat Exchangers Without Phase Change For countercurrent flow in heat exchangers: T ∆Q = U OV ∆ A (THOT – TCOLD)

THOT, IN

HOT

FLUI

D

THO

T

TCOLD, OUT

CO

LD

FLU

ID

TC

OL

D

THOT, OUT

∆Q

∆A

TCOLD, IN A

DTlm =

`Thot, out − Tcold, in j − `Thot, in − Tcold, out j ln f

Thot, out − Tcold, in p Thot, in − Tcold, out

For cocurrent (parallel) flow in heat exchangers: T ∆Q = UOV ∆ A (THOT – TCOLD)

THOT, IN

HOT

FLUI

D

THO

T

THOT, OUT ∆Q

TCOLD, IN

COLD

D

FLUI

T

TCOLD, OUT

COLD

∆A

A

DTlm =

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`Thot, out − Tcold, out j − `Thot, in − Tcold, in j ln f

Thot, out − Tcold, out p Thot, in − Tcold, in

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Chapter 4: Heat Transfer Temperature Profiles for Evaporation and Condensation: During the phase change of a pure substance, the temperature remains constant. Evaporation: TCOLD, IN = TCOLD, OUT = TEVAP

T THOT, IN

HOT

∆Q = UOV ∆ A (THOT − TEVAP) FLU

ID

T

HOT

THOT, OUT TEVAP

∆Q

COLD FLUID

∆A A

DTlm =

`Thot, in − Thot, out j

ln f

Thot, in − Tevap p Thot, out − Tevap

Condensation:

THOT, IN = THOT, OUT = TCOND T ∆Q = UOV ∆ A (TCOND – TCOLD)

TCOND

HOT FLUID ∆Q

TCOLD, IN

LD D T CO

LUI LD F

CO

TCOLD, OUT

∆A

A DTlm =

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`Tcold, out − Tcold, in j

ln f

Tcond − Tcold, in p Tcond − Tcold, out

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Chapter 4: Heat Transfer Temperature Approach Minimum temperature difference between a hot and a cold fluid: Tapproach = (Thot - Tcold)min Cocurrent:

Tapproach = Thot, out - Tcold, out

Countercurrent, with Cmin = Chot

Tapproach = Thot, out - Tcold, in

Countercurrent, with Cmin = Ccold

Tapproach = Thot, in - Tcold, out

Evaporation

Tapproach = Thot, out - Tevap

Condensation

Tapproach = Tcond - Tcold, out

where = C m= o c p heat-capacity rate. For

Tapproach " 0 Constant heat-transfer coefficient Uov

A"3

Constant heat-transfer rate Qo

mo " mo min

Constant flow rate mo

Qo " Qo max

4.3.1.4 F-Factor DTmean = F DTlog mean Temperature efficiency:

Ttube, out − Ttube, in P= T shell, in − Ttube, in Ratio of heat-capacity rates:

Tshell, in − Tshell, out Ctube = RTS = T Cshell tube, out − Ttube, in

where = C m= o c p heat-capacity rate Charts of the F-factors for various configurations are shown in this chapter.

4.3.1.5 Equipment Selection Types of Heat Exchangers Flow Types Cocurrent or parallel flow: both fluids flow in same direction Countercurrent flow: both fluids flow in opposite direction Crossflow: both fluids flow at right angles to each other Mixed flow: one or both fluids are mixed through means of baffles or other geometry

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Chapter 4: Heat Transfer Types of Construction Double pipe: One pipe flows inside of a second larger pipe. TH in

Tc in

Tc out

TH out DOUBLE-PIPE HEAT EXCHANGER Cross-flow: Stacked layers of fluid flow at right angels to each other.

CROSSFLOW HEAT EXCHANGER

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Chapter 4: Heat Transfer Shell-and-tube: Smaller tubes are passed through a larger housing, or shell. This flexible configuration is one of the most common in industry. It allows for varied numbers of tubes or passes. Mixing can be accomplished with baffles. The chart at the end of the chapter shows the standard configurations established by the Tubular Exchanger Manufacturers Association (TEMA). 25 3 2 23 4 20 5 23 11

19

6

7

17

18

16 25 21 25 8 13 14

1

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

4

23

2

9

24

24 11 23 10 12 15 22

STATIONARY HEAD – CHANNEL STATIONARY HEAD FLANGE– CHANNEL OR BONNET CHANNEL COVER STATIONARY HEAD NOZZLE STATIONARY TUBESHEET TUBES SHELL SHELL COVER SHELL FLANGE– STATIONARY HEAD END SHELL FLANGE– REAR HEAD END SHELL NOZZLE SHELL COVER FLANGE FLOATING TUBESHEET

14. FLOATING HEAD COVER 15. FLOATING HEAD FLANGE 16. FLOATING HEAD BACKING DEVICE 17. TIE RODS AND SPACERS 18. TRANSVERSE BAFFLES OR SUPPORT PLATES 19. IMPINGEMENT PLATE 20. PASS PARTITION 21. VENT CONNECTION 22. DRAIN CONNECTION 23. INSTRUMENT CONNECTION 24. SUPPORT SADDLE 25. LIFTING LUG

Example of shell-and-tube heat exchanger (TEMA-type AES), and heat exchanger component nomenclature. Source: Republished with permission of McGraw-Hill, Inc., from Perry's Chemical Engineers' Handbook, 8th ed., Don W. Green and Robert H. Perry, New York, 2008; permission conveyed through Copyright Clearance Center, Inc.

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Chapter 4: Heat Transfer Compact Heat Exchangers Plate-and-Frame: A series of corrugated plates are compressed between two pressure-retaining frame plates, and sealed with elastomeric gaskets. They are useful for this compact size and easily expandable capacity. Spiral-Plate: Two rolled strips of plate with spacer studs are welded onto each other in clock-spring shape. The high shear rates as compared to tubular designs prevent many forms of fouling, and the pure countercurrent flow leads to a LMTD currection factor that is essentially equal to 1.0.

LD T CO ID OU FLU T HO ID IN U FL CARRYING BAR

FIX

ED CO END VE R LD CO ID IN FLU

ATE PL K C PA

MO EN VEAB D C LE OV ER

Y RR CA AR B

CO

T OL

B ION

S

ES

R MP

ING

T T HO ID OU FLU

COLD FLUID HOT FLUID PLATE-AND-FRAME HEAT EXCHANGER

Source: Republished with permission of McGraw-Hill, Inc., from Perry's Chemical Engineers' Handbook, 8th ed., Don W. Green and Robert H. Perry, New York, 2008; permission conveyed through Copyright Clearance Center, Inc.

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Chapter 4: Heat Transfer Types of Evaporators

Evaporators Type and Schematic

Forced-Circulation Evaporator V

S

Description and Applications

Description:

Advantages:

• High heat-transfer coefficients Circulating pump withdraws liquor from the flash chamber and forces it past the heating • Positive circulation surfaces. Typically, heating tubes are submerged and hydrostatic heads prevents boiling­; • Relative freedom from salting, scaling, evaporation occurs in the flash chamber. Higher and fouling heat-transfer rates can be achieved if boiling is allowed in the tubes but then scaling and salt for- Disadvantages: mation may occur. The forced circulation keeps • High cost solids in suspension. Tube velocities are limited by erosion and typically are 4–10 ft/s. • Power required for circulating pump

Applications: G C

• High hold-up and residence time

• Crystalline products

P F

Advantages and Disadvantages

Difficulties:

• Corrosive solutions

• Plugging of tube inlets by detached salt deposits

• Viscous solutions

• Corrosion/erosion • Salting due to boiling in the tubes • Poor circulation due to high head losses

Short-Tube Vertical Evaporator V

G S F P

C

Description:

Advantages:

Circulation past the heating surface is generated by boiling in the tubes. The liquid then returns to the chamber through a central well. For crystallizing solutions, a propeller placed in the lower end of the central well will keep solids in suspension. Best heat transfer is achieved when liquid level is halfway up the tubes. Scaling occurs in the tubes where evaporation takes place but can be mechanically cleaned, because the tubes are relatively wide (2–3") and short (4–6').

• High heat-transfer coefficients • Low head room • Easy mechanical descaling • Relatively inexpensive

Disadvantages: • Poor heat transfer at low DT • High floor space and weight

Applications:

• High hold-up

• Clear liquids • Crystalline products (if using propeller) • Noncorrosive liquids

• Poor heat transfer for viscous liquids

Difficulties: • Large body makes use of corrosionresistant higher alloys cost-prohibitive

• Mild scaling solutions

• Corrosion/erosion • Salting due to boiling in the tubes • Poor circulation due to high head losses ©2020 NCEES

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Chapter 4: Heat Transfer Evaporators Type and Schematic

Long-Tube Vertical Evaporator (Falling Film) F

S

V

Description and Applications

Description:

Advantages:

• Low hold-up Liquid is fed to the top of vertical tubes. Tubes are narrow (1–2") and long (20–35'). The liquid • Cheapest per unit of capacity flows down the walls as a film. Pressure drop in the tubes is low and the temperature of the liquid • Small floor space is essentially the same as that of the vapor head. Vapor-liquid separation typically occurs at the • Good heat-transfer coefficients at all temperatures bottom. To ensure proper wetting of the tubes, external recirculation is usually required unless Disadvantages: feed-to-evaporation rates are high. • High head room

Applications:

G C

• Heat-sensitive materials

• Not suitable for scaling or salting liquids

• Foaming liquids

• External recirculation usually required

Difficulties:

• Low temperature operation

P

Advantages and Disadvantages

• Poor feed distribution

• Large evaporation loads

• Plugging of the feed distributor if solids are present in the liquid

Long-Tube Vertical Evaporator (Rising Film) V

S P

ENT’T

Description:

Advantages:

Liquid enters the long, vertical heating tubes from the bottom and rises up, propelled by the vapors generated by the evaporation. Boiling occurs in the tubes. On top of the tubes is a small vapor head with almost no liquid hold-up, where the liquid and vapor separate. The product line can be connected to the feed line to create recirculation.

Applications: • Black liquid (pulp and paper) • High temperature differences

G

• High evaporation loads

C

• Good heat-transfer coefficients at reasonable temperatures • Simple construction and compactness enables use of corrosion-resistant alloys • Low cost • Low hold-up • Small floor space

Disadvantages: • High head room • Not suitable for scaling or salting liquids

F

• Poor heat-transfer coefficients at lower temperatures

Difficulties: • Sensitivity to changes in operating conditions

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Chapter 4: Heat Transfer Evaporators Type and Schematic

Description and Applications

Horizontal Tube Evaporator

Description: S

V

G C

F

Advantages and Disadvantages

Advantages:

• Large vapor-liquid disengaging area The evaporating liquid is on the shell side and the heating medium on the tube side. This • Good heat-transfer coefficients evaporator is mainly used for boiler feedwater. It has low entrainment and can be designed for • Semiautomatic descaling high steam and vapor temperatures and pres(bent-tube type) sures. Tubes can be designed so that they deform • Low cost (straight-tube type) when shocked (sprayed with cold water while still heated with steam), which causes the scale • Minimal head room required to crack off, making this evaporator suitable for severe scaling applications, such as hard water. Disadvantages:

Applications:

• Not suitable for salting liquids

• Boiler feedwater • Severely scaling liquids (bent-tube type)

• Not suitable for scaling liquids (straighttube type) • High cost (bent-tube type)

Wiped Film (Agitated Film) Evaporator

V

F

• Typically small capacity Advantages:

Description:

S

The liquid is spread on the tube wall by a rotating assembly of blades that maintain close clearance from the wall or ride on the film. The heating surface is one large-diameter tube that may be straight or tapered, horizontal or vertical. The expensive construction limits application to the most difficult materials.

Applications: BLADES

• Heat-sensitive materials in which exposure to high temperature must be minimized

P

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• Ability to handle extremely viscous materials • High feed-to-product ratios without need for recirculation

Disadvantages: • Low heat-transfer coefficients

• Extremely viscous materials C

• Very short residence time

175

• High installation costs • High operating costs

Chapter 4: Heat Transfer Evaporators Type and Schematic

Submerged Combustion Evaporator

Description and Applications

Description:

V+G

P F

Advantages and Disadvantages

Advantages:

Heat transfer is provided by bubbling combustion gases through the liquid; thus no heat-transfer surfaces are used. The evaporator consists of a tank holding the liquid, a burner, and a gas distributor. The vapor from the evaporation is mixed with the combustion gases, making it impossible to recover the heat from the vapor.

Applications:

• No surface on which scale can form • Use of special alloys or nonmetallic materials is possible

Disadvantages: • High entrainment losses • No heat recovery from the vapor, resulting in high fuel costs

• Highly corrosive solutions

• Cannot control crystal size in crystallization applications

• Severely scaling liquids

where C = counterscale F = feed G = vent P = product S = steam V = vapor EWT'T = separated entrainment outlet Source of first 5 schematics: Perry, Robert H. and Cecil H. Chilton, Chemical Engineer's Handbook, 5th ed., New York: McGraw-Hill, 1973. Source of the sixth schematic: Chemical Engineering Research and Design (www.ichemejournals.com), © Institute of Chemical Engineers, published by Elsevier. Source of the seventh schematic: China Manufacturers and Suppliers of Oil, Gas and Petrochemical Equipment, http://www.china-ogpe.com/buyingguide/, January 2016.

Heat-Transfer Calculations for Evaporators While the general heat-transfer equations apply, evaporators have some special considerations:

Heat-transfer coefficient: Depends strongly on the temperature difference. Heat-transfer area: Surface area through which the heat transfer takes place, measured on the liquid side. Apparent temperature difference: The temperature difference can be difficult to determine because it varies along the length of the evaporator tubes. The apparent temperature difference is calculated as the difference between the heating-medium and boilingliquid temperatures. Heating-medium temperature is the saturation temperature of the steam at steam pressure. (Superheat or subcooling are not considered.) Boiling-liquid temperature is the saturation temperature of the liquid at vapor head pressure—thus assuming a negligible boiling-point rise.

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Chapter 4: Heat Transfer Temperature corrected for boiling-point rise: Boiling-point rise is the difference between the boiling point of the solution and the boiling point of the pure solvent at the same pressure. The temperature corrected for the boiling-point rise is the apparent temperature difference minus the boiling-point rise. This is typically used as the basis for the calculation of heat-transfer coefficients and also as a basis for comparing efficiencies of different evaporator types. Multi-Effect Evaporators Multi-effect evaporators reduce the energy needed for evaporation by using the steam generated in one stage as the heating medium for another stage. The temperature difference for heat transfer in each effect is:

DT = Tcond, steam − Tevap, liquid where the condensation temperature of the steam is determined by the pressure in the effect where the steam was generated:

Tcond, steam = Tsat at Pn − 1 The evaporation temperature of the liquid is determined by the pressure in the current effect:

Tevap, liquid = Tsat at Pn Different feed arrangements are common: 1. In the forward feed configuration, the product and vapor flow are parallel. This configuration is used when the feed is near the boiling point or when the product is heat-sensitive or prone to scaling and requires low temperature differences. One additional advantage is that flow of the product from one effect can be achieved by pressure difference alone, so that no intermediate liquor pumps are needed.

Forward Feed Configuration

I

II

III

VAPOR TO CONDENSER IV

STEAM

CONDENSATE THICK LIQUOR

FEED

Source: McCabe, Warren L., Julian Smith, and Peter Harriott, Unit Operations of Chemical Engineering, 5th ed., New York: McGraw-Hill, 1993.

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Chapter 4: Heat Transfer 2. In the backward feed configuration, the product and vapor flow are countercurrent. It is used when the feed is cold, because most of the feed preheating is done by the vapor generated in the previous effect. It is preferred for highly viscous liquor, because the temperature in the effect will be higher as the liquor becomes more concentrated.

Backward Feed Configuration VAPOR TO CONDENSER I

II

III

IV

STEAM

CONDENSATE THICK LIQUOR

FEED

Source: McCabe, Warren L; Julian Smith; and Peter Harriott. Unit Operations of Chemical Engineering, 5th ed., New York: McGraw-Hill, 1993.

4.3.1.6 Insulation Heat loss from cylindrical, insulated pipe:

2 r kins L (T1 − T3) Qo = k r ln d r2 n + h insr 1

3

2

Surface temperature of the insulation:

h r r T1 + T3 3k 2 ln d r2 n 1 T2 = h r r 1 + 3k 2 ln d r2 n 1 dQo

Critical insulation radius (where heat loss is at a minimum): dr = 0 2

(for kins % kpipe)

k r2, crit = hins 3 2 r kins L (T1 − T3) Qo min = k 1 + ln e h insr o 3 1

T2, crit =

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k T1 + T3 ln e h insr o 3 1

k 1 + ln e h insr o 3 1

178

Chapter 4: Heat Transfer where T1 = surface temperature of the pipe T2 = surface temperature of the insulation T∞ = temperature of surroundings r1 = outer radius of the pipe r2 = outer radius of the insulation kins = thermal conductivity of the insulation h∞ = convective heat-transfer coefficient for the surroundings

4.3.2

Heat-Exchange Equipment Analysis

4.3.2.1 Pressure Drop and Surface Temperatures Pressure Drop for Single-Phase Heat Transfer Tube-side pressure drop for incompressible, single-phase flow in a shell-and-tube exchanger (including pressure drop in the tubes, in the heads for a multipass exchanger, and at the inlet and outlet nozzles):

tu DPtubeside = *1.5 + n >2 f c L m d n n + 2.5H4 2 t n D w m

where

2

ut = velocity in the tubes f = friction factor (Darcy-Weisbach, see Moody diagram) m = 0.25 for laminar flow (Re < 2,100) m = 0.14 for turbulent flow (Re > 2,100)

Pressure Drop in Rising Film Evaporators In rising film evaporators, the pressure drop in the tubes is comprised of frictional pressure drop and acceleration pressure drop from the increased velocity of the flow due to volume change during evaporation. If the inlet flow is liquid, the acceleration pressure drop is calculated from: 2 mo 1 1 1 DPa = y d A n d t − t n g vap liq c cross

where DPa = acceleration pressure drop y

= vapor fraction (by weight)

Across = cross-sectional area of the tube

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Chapter 4: Heat Transfer Surface Temperature for Condensation Surface temperature for the condensation of a superheated vapor:

Tsurface = Tcoolant + Tvapor d1 −

Uov n h

where h = sensible heat-transfer coefficient for the vapor Uov = overall heat-transfer coefficient, based on h Condensation occurs only if Tsurface # Tsat .

4.3.2.2 Performance Evaluations (Number of Thermal Transfer Units) Heat-Exchanger Effectiveness (e): Qo actual heat − transfer rate = f= o Q max maximum possible heat − transfer rate C hot (Thot, in − Thot, out) Ccold (Tcold, out − Tcold, in) = f = C (T C min (Thot, in − Tcold, in) min hot, in − Tcold, in) Chot = Cmin

Thot, in − Thot, out f hot = T hot, in − Tcold, in

Ccold = Cmin

Tcold, out − Tcold, in fcold = T hot, in − Tcold, in

Heat-capacity rate is C:

C

= mo c p

Cmin = smaller of Chot and Ccold Cmax = larger of Chot and Ccold Ratio of heat-capacity rates is RNTU:

C RNTU = Cmin max where

0 # RNTU # 1 RNTU = 0 for exchangers with phase change (condensation or evaporation) Number of Transfer Units (NTU) U A NTU = Cov min

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Chapter 4: Heat Transfer Heat-Exchanger Effectiveness and NTU Relations Effectiveness and Transfer Unit Equations, Schematic, and Graphical Solution

Flow Geometry

Double-Pipe e

f=

1 − exp 8− NTU (1 + R NTU )B 1 + R NTU

NTU NTU =

Cocurrent

− ln 81 − f (1 + R NTU )B 1 + R NTU

1.0

0.00

0.8

0.25 0.50 RNTU

0.6

0.75 1.00

0.4

TUBE FLUID

0.2

SHELL FLUID

0.0 0

1

2

3

4

5

NTU

e

f=

1 − exp 8− NTU (1 − R NTU )B 1 − R NTU exp 8− NTU (1 − R NTU )B

− 1 NTU NTU = d f 1 n R NTU − 1 ln R NTU f − 1

NTU RNTU = 1: f = NTU + 1 f RNTU = 1: NTU = 1 − f

1.0

Countercurrent

0.8 1.00 0.75 0.50 RNTU 0.25 0.00

0.6 0.4 0.2 0.0 0

1

2

3

4

5

NTU

©2020 NCEES

181

TUBE FLUID

SHELL FLUID

Chapter 4: Heat Transfer Heat-Exchanger Effectiveness and NTU Relations (cont'd) Flow Geometry Cross-Flow

Effectiveness and Transfer Unit Equations, Schematic, and Graphical Solution

e

f = 1 − exp >

exp (− NTU 0.78 R NTU ) − 1 H − NTU 0.22 R NTU

1.0

COLD FLUID

0.8

Both Fluids, Unmixed

1.00 0.75 R 0.50 NTU 0.25

0.6 0.4

0.00

HOT FLUID

0.2 0.0 0

1

2

3

4

5

NTU

e

R NTU 1 = 1 1 f 1 − exp (− NTU) + 1 − exp (− NTU R NTU ) − NTU 1.0

0.00

Both Fluids, Mixed

0.50 RNTU 0.75

0.6

1.00

0.4 0.2 0.0 0

1

2

3

4

NTU

©2020 NCEES

COLD FLUID

0.25

0.8

182

5

HOT FLUID

Chapter 4: Heat Transfer Heat-Exchanger Effectiveness and NTU Relations (cont'd) Flow Geometry

Effectiveness and Transfer Unit Equations, Schematic, and Graphical Solution e

1 % − f= R 1 exp 8− R NTU (1 − exp − NTU )B/ NTU

NTU NTU = − ln 125°F/50°C) River water (brackish) River water (muddy, silty) Hard water City/well water Untreated boiler feedwater (> 125°F/50°C) Treated boiler feedwater Untreated cooling tower water Treated cooling tower water Distilled water Hydrocarbons Fuel oil Asphalt and residue Vegetable oil and heavy gas oil Light hydrocarbons Heavy hydrocarbons Other Quenching liquids Refrigerating liquids, brines Heat-transfer media Polymer forming liquids Vaporizing liquids (organic and inorganic) Condensing organic liquids Organic vapors and liquids (including condensing) Gases and Vapors Steam (clean) Steam (oil-bearing) Alcohol vapors Industrial air or other dirty (oil-bearing) gases Diesel exhaust (> 125°F/50°C)

©2020 NCEES

192

hr - ft 2 - cF Btu

m2 : K W

0.0005 0.0010 0.0020 0.0030 0.0033 0.0010

0.00009 0.00018 0.00035 0.00053 0.00059 0.00018

0.0010 0.0010 0.0020 0.0010 0.0005

0.00018 0.00018 0.00035 0.00018 0.00009

0.0050 0.0100 0.0030 0.0010 0.0040

0.00088 0.00176 0.00054 0.00018 0.00072

0.0040 0.0010 0.0010 0.0050 0.0020 0.0010 0.0010

0.00070 0.00018 0.00018 0.00090 0.00035 0.00018 0.00018

0.0005 0.0010 0.0005 0.0020 0.0100

0.00009 0.00018 0.00009 0.00035 0.00176

Chapter 4: Heat Transfer 4.4.1.6 Nucleate Boiling Heat-Transfer Data Relative Magnitude of Nucleate Boiling Heat-Transfer Coefficients at 1 atm, ​Referenced to Value for Water h Fluid hwater Water

1.0 0.87 0.94 0.83 0.75 0.61 0.70 0.53 0.36 0.35 0.32

Water with 20% sugar Water with 10% Na2SO4 Water with 26% glycerin Water with 55% glycerin Water with 24% NaCl Isopropanol Methanol Toluene Carbon-tetrachloride n-Butanol

Source: Republished with permission of McGraw-Hill, from Heat Transfer, J.P. Holman, 5th ed., New York, 1981; permission conveyed through Copyright Clearance Center, Inc.

Maximum Heat Flux in Nucleate Boiling (Burnout Heat Flux) Fluid

Water Benzene Propanol Butanol Ethanol Methanol

Surface Copper Chrome-plated copper Steel Copper Aluminum Nickel-plated copper Nickel-plated copper Aluminum Copper Copper Chrome-plated copper Steel

Liquid H2 Liquid N2 Liquid O2

Any metal surface Any metal surface Any metal surface

Heat Flux Btu # -3 10 hr -ft 2

DT °F

Heat Flux

kW m2

DT

°C

200–270 300–400 410 43.5 50.5 67–110 79–105 55 80.5 125 111 125

42–50 54 — — 76–90 60–70 — — — — —

620–850 940–1260 1290 130 160 210–340 250–330 170 250 390 350 390

23–28 30 — — 42–50 33–39 — — — — —

9.53 31.7 47.5

4 20 20

30 100 150

2 11 11

Source: Republished with permission of McGraw-Hill, from Heat Transfer, J.P. Holman, 5th ed., New York, 1981; permission conveyed through Copyright Clearance Center, Inc.

©2020 NCEES

193

Chapter 4: Heat Transfer 4.4.1.7 Solar Radiation Data Maximum Expected Solar Radiation at Various North Latitudes

Month

January February

30° North 24-hr noon avg. 65 240 75 270

March

90

305

April May June July August September October November December

110 120 130 130 125 115 100 80 65

340 360 365 365 360 350 315 270 240

Btu hr-ft 2 40° North 24-hr noon avg. 40 170 55 210 75 255 95 300 120 335 130 345 130 350 125 340 105 315 80 270 60 215 45 175

W m2 45° North 24-hr noon avg. 30 135 45 175

30° North 24-hr noon avg. 205 757 237 852

40° North 24-hr noon avg. 126 536 174 662

45° North 24-hr noon avg. 95 426 142 552

65

230

284

962

237

804

205

726

90 115 130 130 120 100 75 50 35

280 320 335 340 325 300 245 185 140

347 379 410 410 394 363 315 252 205

1073 1136 1151 1151 1136 1104 994 852 757

300 379 410 410 394 331 252 189 142

946 1057 1088 1104 1073 994 852 678 552

284 363 410 410 379 315 237 158 110

883 1009 1057 1073 1025 946 773 584 442

Source: Langhaar, J.W., "Cooling Pond May Answer Your Water Cooling Problem," Chem.Eng. 60(8), 1953, pages 194–198.

4.4.1.8 Emissivity ( f ) Emissivity of Building Materials at Ambient Temperature (Unless Specified Otherwise) Material Asbestos Brick (building) Brick (fireclay) at 2000°F/1100°C Enamel (white) Glass (smooth) Gypsum Marble Oak Oil Plaster Refractory (good radiator) at 1500°F/800°C Refractory (poor radiator) at 1500°F/800°C Roofing paper Rubber (grey, soft) Rubber (hard) Water

©2020 NCEES

194

Emissivity 0.96 0.93 0.75 0.90 0.94 0.90 0.93 0.90 0.82 0.91 0.85 0.70 0.91 0.86 0.95 0.96

Chapter 4: Heat Transfer Emissivity of Metals at Ambient and Elevated Temperatures Material

Emissivity at Ambient Temperatures

Emissivity at ~1000°F/540°C

0.04 0.94 0.22 0.10 0.61 0.08 0.02 0.78 0.02 0.06 0.63 0.25 0.90 0.07 0.15 0.85 0.03 0.05 0.25

0.08 0.60 ­­— — — 0.26 0.18 0.77 0.04 0.13 0.76 0.6 0.85 0.18 0.22 0.85 0.10 0.04 —

Aluminum, polished Aluminum, anodized Aluminum, surface roofing Brass, polished Brass, oxidized Chromium, polished Copper, polished Copper, oxidized Gold, polished Iron, polished Iron, cast, oxidized Iron, galvanized Iron, oxide Magnesium Stainless steel, polished Stainless steel, weathered Tungsten Zinc, polished Zinc, galvanized

©2020 NCEES

195

Chapter 4: Heat Transfer

4.4.2

Charts with Heat-Transfer Data Overall Heat-Transfer Coefficients for Various Applications (U.S. Units):

Btu hr -ft 2-cF

0

u r Bt F h 2 ° ft

CONDENSATION AQUEOUS VAPOURS

0

50

CO

EF F

IC IE NT ,

60

FL

UI D

BOILING AQUEOUS

0

CE SS PR O

DILUTE AQUEOUS BOILING ORGANICS

0

30

CONDENSATION ORGANIC VAPORS

00

OILS AIR AND GAS HIGH PRESSURE

LL C

ERA

OV

400

300

250

200

2

MOLTEN SALTS

D ATE

IM

EST

PARAFFINS HEAVY ORGANICS

150 0

10

RESIDUE

100

50 100 AIR AND GAS LOW PRESSURE

Btu hr 2 F U ov, ft ° , T N CIE I F F 350 OE

40

200

300

400

500

600

700

800

900

THERMAL FLUID BRINES

CONDENSATE BOILING WATER RIVER, WELL, HOT HEAT SEAWATER TRANSFER OIL REFRIGERANTS

AIR AND GAS

STEAM CONDENSING

SERVICE FLUID COEFFICIENT, Btu ft2 °F hr

COOLING TOWER WATER

Source: Reprinted from Chemical Engineering Design, 2nd ed., Gavin Towler and Ray Sinnott, Chapter 19: Heat Transfer Equipment, © 2013, with permission from Elsevier.

Overall Heat-Transfer Coefficients for Various Applications (SI Units):

W m2 : K

FIC

IE

NT ,W

/m

2

°K

CONDENSATION AQUEOUS VAPOURS

CO EF

00

25

ES

S

FL UI

D

BOILING AQUEOUS

OC PR

2

DILUTE AQUEOUS

PARAFFINS HEAVY ORGANICS

RESIDUE

00

E

OV

0

200

750

1

500

0

750

0

50

500 1000

1500

2000

2500

500 AIR AND GAS

0

1

ES

100

10

250 AIR AND GAS LOW PRESSURE

225

0 125

MOLTEN SALTS OILS AIR AND GAS HIGH PRESSURE

D ATE TIM

0

0 15

LC RAL

,W , U ov ENT

CI

FFI

OE

BOILING ORGANICS CONDENSATION ORGANIC VAPORS

2 °K

/m

0 00

BRINES RIVER, WELL, SEAWATER

3000

3500

4000

4500

THERMAL FLUID HOT HEAT TRANSFER OIL

BOILING WATER

CONDENSATE

STEAM CONDENSING

REFRIGERANTS

COOLING TOWER WATER

SERVICE FLUID COEFFICIENT, W/m2°K

Source: Reprinted from Chemical Engineering Design, 2nd ed., Gavin Towler and Ray Sinnott, Chapter 19: Heat Transfer Equipment, © 2013, with permission from Elsevier. ©2020 NCEES

196

Chapter 4: Heat Transfer

4.4.3

Heat-Exchanger Design Information TEMA Heat Exchanger Types FRONT-END STATIONARY HEAD TYPES

REAR-END HEAD TYPES

SHELL TYPES

L

E A

FIXED TUBE SHEET LIKE "A" STATIONARY HEAD

ONE-PASS SHELL

CHANNEL AND REMOVABLE COVER

M

F

FIXED TUBE SHEET LIKE "B" STATIONARY HEAD

PASS SHELL WITH LONGITUDINAL BAFFLE

B

N

G SPLIT FLOW

BONNET (INTEGRAL COVER)

P

H C

REMOVABLE TUBE BUNDLE ONLY

CHANNEL INTEGRAL WITH TUBE SHEET AND REMOVABLE COVER

FIXED TUBE SHEET LIKE ''N" STATIONARY HEAD

OUTSIDE PACKED FLOATING HEAD DOUBLE SPLIT FLOW

S

J

FLOATING HEAD WITH BACKING DEVICE DIVIDED FLOW

T

N

PULL-THROUGH FLOATING HEAD CHANNEL INTEGRAL WITH TUBE SHEET AND REMOVABLE COVER

K KETTLE-TYPE REBOILER

U U-TUBE BUNDLE

D

X SPECIAL HIGH-PRESSURE CLOSURE

©2020 NCEES

W CROSS FLOW

197

EXTERNALLY SEALED FLOATING TUBE SHEET

4.4.4 F-Factor Charts

©2020 NCEES

1.0

0.8 0.1

Chapter 4: Heat Transfer

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1.0

1.2

1.4

1.5

1.6 2.0

2.5

3.0

4.0

6.0

0.7

8.0 R = 10.0

15.0 20.0

198

F = MTD CORRECTION FACTOR

0.9

0.6

0.5

0

0.1

0.2

0.3

0.4 0.5 0.6 P = TEMPERATURE EFFICIENCY

0.7

0.8

MTD CORRECTION FACTOR

T1 1 SHELL PASS

t2

T2

P=

t2 – t1 T1 – t1

R=

T1 – T2 t2 – t1

Q/(Uov A) Δ Tlm

•

t1

2 OR MORE TUBE PASSES F=

0.9

1.0

©2020 NCEES

1.0

0.1

0.2 0.3

0.4

0.5

0.6 0.7 0.9

Chapter 4: Heat Transfer

1.0

1.2

1.4

1.6

1.8

2.0

2.6

3.0

4.0

6.0

8.0

R = 10.0

0.7

0.8

0.8

15.0 20.0

199

F = MTD CORRECTION FACTOR

0.9

0.6

0.5

0

0.1

0.2

0.3

0.4 0.5 0.6 P = TEMPERATURE EFFICIENCY

0.7

0.8

MTD CORRECTION FACTOR

T1 t2

T2

P=

t2 – t1 T1 – t1

4 OR MORE TUBE PASSES R=

T1 – T2 t2 – t1

Q/(Uov A) Δ Tlm

•

t1

2 SHELL PASS

F=

0.9

1.0

©2020 NCEES

1.0

0.2

0.4

0.6 0.8 1.0

1.2

0.8 1.4

Chapter 4: Heat Transfer

1.6

1.8

2.0

2.5

3.0

4.0

5.0

0.7

8.0 R = 10.0

15.0 20.0

200

F = MTD CORRECTION FACTOR

0.9

0.6

0.5

0

0.1

0.2 T1

0.3

0.4 0.5 0.6 P = TEMPERATURE EFFICIENCY

0.7

0.8

MTD CORRECTION FACTOR

t2

6 OR MORE TUBE PASSES

3 SHELL PASSES

•

T2

t1

P=

t2 – t1 T1 – t1

R=

T1 – T2 t2 – t1

F=

Q/(Uov A) Δ Tlm

0.9

1.0

©2020 NCEES

1.0

0.2

0.4

0.6 0.8 1.0

1.2

0.8 1.4

1.6

Chapter 4: Heat Transfer

1.8

2.0

2.5

3.0

4.0

6.0

8.0 R = 10.0

15.0 20.0

201

F = MTD CORRECTION FACTOR

0.9

0.7

0.6

0.5

0

0.1

0.2 T1

0.3

0.4 0.5 0.6 P = TEMPERATURE EFFICIENCY

t2

0.7

0.8

MTD CORRECTION FACTOR

4 SHELLS

8 OR MORE TUBE PASSES

4 SHELL PASSES

Q/(Uov A) Δ Tlm

•

T2

t1

P=

t2 – t1 T1 – t1

R=

T1 – T2 t2 – t1

F=

0.9

1.0

©2020 NCEES

1.0

0.2

0.4

0.6 0.8 1.0

1.2

1.4

1.6

1.8

2.0

2.5

3.0

4.0

6.0

8.0

R = 10.0

0.8

15.0 20.0

Chapter 4: Heat Transfer

202

F = MTD CORRECTION FACTOR

0.9

0.7

0.6

0.5

0

0.1

0.2 T1

0.3

0.4 0.5 0.6 P = TEMPERATURE EFFICIENCY

5 SHELLS

10 OR MORE TUBE PASSES

5 SHELL PASSES P=

t2 – t1 T1 – t1

R=

T1 – T2 t2 – t1

•

T2

0.8

MTD CORRECTION FACTOR

t2

t1

0.7

F=

Q/(Uov A) Δ Tlm

0.9

1.0

©2020 NCEES

1.0

0.2 0.4

0.6 0.8 1.0

1.2

1.4

1.6

1.8

2.0

2.5

3.0

4.0

6.0

8.0 10.0

0.8

15.0 R = 20.0

Chapter 4: Heat Transfer

203

F = MTD CORRECTION FACTOR

0.9

0.7

0.6

0.5

0

0.1

0.2 T1

0.3

0.4 0.5 0.6 P = TEMPERATURE EFFICIENCY

0.7

0.8

MTD CORRECTION FACTOR

t2

12 OR MORE TUBE PASSES

6 SHELL PASSES

•

6 SHELLS t1 T2

P=

t2 – t1 T1 – t1

R=

T1 – T2 t2 – t1

F=

Q/(Uov A) Δ Tlm

0.9

1.0

©2020 NCEES

1.0

0.7 0

0.1

0.2

T1

0.3

0.4 0.5 0.6 P = TEMPERATURE EFFICIENCY

T1

0.8

MTD CORRECTION FACTOR t2

1 DIVIDED FLOW SHELL PASS

2 OR MORE TUBE PASSES Q/(Uov A) Δ Tlm

•

t1 T2

0.7

P=

t2 – t1 T1 – t1

R=

T1 – T2 t2 – t1

F=

0.9

1.0

Chapter 4: Heat Transfer

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1.0

1.2

1.4

1.6 1.8 2.0

2.5

3.0

5.0

6.0

0.8

8.0 R = 10.0

15.0 20.0

204

F = MTD CORRECTION FACTOR

0.9

5 CHEMICAL REACTION ENGINEERING 5.1 Symbols and Definitions Symbols Symbol

CA or [A]

©2020 NCEES

Description Concentration of component A

Units (U.S.)

Units (SI)

lb mole ft 3 Btu lbm - cF

mol liter J kg : K

Cp

Average heat capacity

FA

Molar feed of A

lb mole sec

mol s

DV gr

Gibbs free energy of reaction (molar)

Btu lb mole

J mol

Dht r

Heat of reaction

Btu lb mole

J mol

varies

varies

K

Equilibrium constant

k

Reaction rate constant

M

Molar ratio of initial reactant concentrations (weighted by the stoichiometric constants)

m

Mass of reactor contents

lbm

kg

mo

Mass flow rate of feed

lbm sec

kg s

n

Moles of reactant or product

lb mole

g mol

n

Reaction order

P

Pressure (PA = partial pressure of A)

d

^ - nh

lb mole 1 n ft 3 sec

^1 - nh

c mol m liter s

dimensionless

dimensionless

205

lbf in 2

Pa

Chapter 5: Chemical Reaction Engineering Symbols (con't) Symbol

Description

q

Heat transfer

rA

Rate of reaction – based on component A

Units (U.S.)

Units (SI/metric)

Btu sec

J s

lb mole ft3-sec

g mol L:s

SAB

Selectivity to A relative to B

SV T

Space velocity = space time Temperature

1 sec °F or °R

1 s °C or K

To

Feed temperature

°F or °R

°C or K

t

Time

sec

s

dimensionless

1

θA

Fraction of surface covered by adsorbed species A

V

Reactor volume

XA

Fractional conversion of component A

dimensionless

YA

Yield of A relative to reactant use

dimensionless

eA

Fractional volume change at full conversion of A

dimensionless

x

Space time = space velocity

dimensionless ft3

1

sec

L

s

5.2 Fundamentals 5.2.1

Reaction Rate

5.2.1.1 Rate Constant A chemical reaction may be expressed by the general equation:

aA + bB * cC + dD The rate of reaction of any component is defined as the number of moles of that component formed per unit time per unit volume:

dn − rA = 1 A V dt − rA = −

(negative because A is consumed)

dC A dt if V is constant

The rate of reaction is frequently expressed as

− rA = k f _C A, C B, ... i The fractional conversion XA is defined as the moles of A reacted per mole of A fed:

XA =

©2020 NCEES

C Ao − C A C = 1 − A if V is constant C Ao C Ao

206

Chapter 5: Chemical Reaction Engineering 5.2.1.2 Order of Reaction If − rA = k C Ax C By , then the reaction is x order with respect to A and y order with respect to B. The overall order is n = x + y.

5.2.1.3 Temperature Dependence (Arrhenius Equations) The Arrhenius equation gives the dependence of k on temperature: −E a

k = Ae R T where

A = pre-exponential or frequency factor J cal Ea = activation energy c mol or mol m R = universal gas constant For values of rate constant ki at two temperatures Ti:

Ea =

RT1 T2 k ln e k1 o or − 2 _T1 T2 i

E T1 − T2 k ln e k1 o = Ra T 1 T2 2

5.2.1.4 Half-Life The half-life of a reaction, t 1 , is the batch time required to reach 50% conversion.

dC For − rA = − dt A = kC An

2

1 t 1 occurs when C A = 2 C Ao 2

For n = 1 (first order)

ln 2 t1 = k 2

= 1 For n Y

t1 =

5.2.2

2

− 2n 1 − 1 − (n − 1) k C Ao(n 1)

Rate Equations in Differential Form for Irreversible Reactions

5.2.2.1 Zero-Order (A " R) − rA = −

d CA d XA = C Ao =k dt dt

and

d XA = k C Ao dt

and

d XA k CA = = 1 − XAi C Ao k _ dt

5.2.2.2 First-Order ^A " R h − rA = −

d CA d XA = C Ao = k CA dt dt

5.2.2.3 Second-Order ^2A " R h , One Reactant − rA = −

©2020 NCEES

d CA d XA = C Ao = k C A2 dt dt

and

2 d X A k CA 2 = = k C Ao _1 − X A i C Ao dt

207

Chapter 5: Chemical Reaction Engineering 5.2.2.4 Second-Order _ A + bB " R i , Two Reactants − rA = − and

C d CA = k C A C B = k bC Ao 2 _1 − X A i _ M − X A i when M = Bo ! 1 dt b C Ao

− rA = k bC Ao 2 _1 − X A i

2

when M = 1

Integrated forms of these equations for constant- and variable-volume batch, plug flow, and CSTR reactors are included in Integrated Reaction Equations for Irreversible Reactions section in this chapter.

5.2.3

Yield and Selectivity

Yield Y is defined as the molar ratio of the desired product formed to the reactant that is consumed. Selectivity S is defined as the molar ratio of the desired product to undesired product.

5.2.3.1 Two Irreversible Reactions in Parallel

k

k

A "D D (desired) and A "U U (undesired) d CA − rA = − = kD CA x + kU CA y dt = rD

d CD = kD CA x dt

= rU

d CU = kU CA y dt

dC YD = instantaneous fractional yield of D = − d CD A N YD = overall fractional yield of D = N −D N Ao A

N A and N D are the final values measured at the reactor outlet

where

N = overall selectivity to D over U N D U

S DU

N D and N U are the final values measured at the reactor outlet

where

5.2.3.2 Two First-Order Irreversible Reactions in Series k

k

A "D D "U U (D = desired, U = undesired) − rA = −

d CA = kD CA dt

dC rD = d tD = k D C A − k U C D = rU

d CU = kU CD dt

The yield and selectivity definitions for series reactions are identical to those for parallel reactions, and the equations for overall yield and selectivity are the same as those in the previous subsection.

©2020 NCEES

208

Chapter 5: Chemical Reaction Engineering The maximum concentration of D in a plug flow reactor is

k ln e k U o

kU

C D, max k kU − kD =e Do C Ao kU

D 1 = at time x max = k log mean `kU − kD j

The maximum concentration of D in a CSTR is

C D,max = C Ao

1

2

1 2

>e k U o + 1H k

at time x max =

1 kD kU

D

5.2.4

Pressure Dependence (Gas Phase Reactions)

All of the equations in the previous sections of this chapter can be written in terms of pressure where

P CA = RTA

5.3 Reactor Equations 5.3.1

Types of Reactors

For flow reactors, space time t is defined as the reactor volume divided by the inlet volumetric feed rate. Space velocity SV is the reciprocal of space time, that is, SV = 1/t.

5.3.1.1 Batch Reactor Constant Volume For a well-mixed, constant-volume batch reactor:

− rA = −

d CA d XA = CAo dt dt

t = C Ao

and

#0

XA

d XA − rA

Variable Volume For a well-mixed, variable-volume batch reactor:

− rA =

C Ao d XA _1 + f A X A i d t

and

t = C Ao

#0

XA

d XA

_− rA i_1 + f A X A i

where eA = fractional volume change at full conversion of A

1 − C A C Ao 1−X C A = C Ao e + A o or X A = 1 + f X 1 f A XA A A

5.3.1.2 Plug Flow Reactor For a plug flow reactor, for all values of f A :

C V x = FAo = C Ao Ao

#0

XA

d XA _− rA i

where FAo = moles of A fed per unit time

For a constant volume plug flow reactor ( f A = 0 ): x =−

©2020 NCEES

#C

CA Ao

d CA − rA

209

Chapter 5: Chemical Reaction Engineering 5.3.1.3 Continuous Stirred Tank Reactor (CSTR) For a well-mixed CSTR for all values of eA:

C V C X x = FAo = Ao A Ao _− rA i

where - rA is evaluated at exit stream conditions For a constant volume CSTR ( f A = 0 ):

x=

C Ao − C A _− rA i

5.3.1.4 Equal-Sized Reactors in Series With a first-order reaction A " R , with no change in volume:

x N− reactors = N x individual 1

N N x N - reactors = k >e C Ao o − 1H CA

or

N

N C Ao = d1 + k x N n CA N N

where

N

= number of CSTRs (equal volume) in series

C A N = concentration of A leaving the Nth CSTR N plug flow reactors in series gives the same conversion as a single plug flow reactor with the same total volume.

5.3.1.5 Equal-Sized Reactors in Parallel N identical reactors in parallel give the same conversion as a single reactor of the same total volume. (This is equally true for both plug flow reactors and CSTRs.)

5.3.1.6 Plug Flow Reactors With Recycle First Order (eA = 0) k x = C Ao + RC A R + 1 ln (R + 1) C A Second Order (eA = 0)

k C Ao x C Ao `C Ao − C A j = R+1 C A `C Ao + RC A j

where R = recycle ratio, defined as the fraction of the reactor outlet stream that is recycled

Relationship Between Overall Conversion and Single-Pass Conversion XAo XAs = + ` 1 R 1 − XAo j

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Chapter 5: Chemical Reaction Engineering

5.3.2

Integrated Reactor Equations for Irreversible Reactions

5.3.2.1 Zero-Order Reactions _A " R, − rA = k i Constant Volume Batch reactor:

k t = CAq XA = CAq − CA Plug flow reactor or CSTR:

k x = C Aq X A = C Aq − C A Variable Volume

V = Vq _1 + f A X A i ,

DV = Vq f A X A

Batch reactor:

C C V k t = fAo ln _1 + f A X A i = fAo ln V A A o

Plug flow reactor or CSTR:

k x = C Aq X A

5.3.2.2 First-Order Reactions _ A " R, − rA = k C A i Constant Volume Batch reactor:

C 1 k t = ln CAo = ln 1 − X = − ln _1 − X A i A A

Plug flow reactor:

C 1 k x = ln CAo = ln 1 − X = − ln _1 − X A i A A

CSTR:

kx =

C Ao − C A X = −A CA 1 XA

Variable Volume

V = Vq _1 + f A X A i,

DV = Vq f A X A

Batch reactor:

DV 1 k t = ln 1 − X = − ln _1 − X A i = − ln d1 − f V n A

A o

Plug flow reactor:

k x = − _1 + f A i ln _1 − X A i − f A X A CSTR:

kx =

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Chapter 5: Chemical Reaction Engineering 5.3.2.3 Second-Order Reactions `2 A " R, − rA = k C A2 j , One Reactant Constant Volume Batch reactor:

XA 1 1 kt = C − C = A Ao C Ao _1 − X A i

or

CA 1 = C Ao 1 + k t C Ao

or

CA 1 = C Ao 1 + k x C Ao

Plug flow reactor:

XA 1 1 kx = C −C = A Ao C Ao _1 − X A i CSTR:

kx =

C Ao − C A XA = 2 2 CA C Ao _1 − X A i

Variable Volume V = Vo (1 + eA XA), DV = Vo eA XA Batch reactor:

1 _1 + f A i X A kt = C > + f A ln _1 − X A iH 1 − XA Ao

Plug flow reactor: 2 XA 1 G k x = C =2f A _1 + f A i ln _1 − X A i + f A 2 X A + _f A + 1 i 1 − X Ao A

CSTR:

X A _1 + f A X A i

2

kx =

C Ao _1 − X A i

2

5.3.2.4 Second-Order Reactions _A + bB " R, − rA = k C A C B i , Two Reactants Constant Volume Batch reactor:

CB M − XA = ln k t b C Ao ^ M − 1 h = ln M C A M _1 − X A i k t C Bo = k t b C Ao =

C

when M = b CBo ! 1 Ao



C Ao − C A X = − A when M = 1 CA 1 XA

Plug flow reactor:

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C M − XA k t b C Ao ^ M − 1 h = ln MCB = ln A M _1 − X A i



k x C Bo = k x b C Ao =



C Ao − C A X = −A CA 1 XA

C

when M = b CBo ! 1 Ao

212

when M = 1

Chapter 5: Chemical Reaction Engineering CSTR:

5.3.3

kx =

C Ao − C A XA = − + − ^ h bC A 8C Ao M 1 C AB bC Ao _1 X A i _ M − X A i



when M = b CBo ! 1 Ao

kx =

C Ao − C A XA = 2 2 bCA b C Ao _1 − X A i



when M = 1

C

Complex Reactions

5.3.3.1 First-Order Reversible Reactions (A − rA = −

k1 k2

R)

d CA = k1 C A − k 2 C R dt

k1 C R eq = K= C k 2 C A eq

and

C M = C Ro Ao

d X A k1 ^ M + 1 h = a X A eq − X A k dt M + X A eq − ln f1 −

C A − C A eq ^ M + 1h XA = = − ln p X A eq C Ao − C A eq a M + X k k1 t A eq

At equilibrium, when XA = XAeq , then -ln(0) " ∞ and t" ∞.

5.3.3.2 Reactions of Shifting Order From zero order at high CA to first order at low CA:

k C − rA = +1 A 1 k2 CA C ln e CAo o + k 2 `C Ao − C A j = k1 t A

C ln e CAo o A

C Ao − C A

= − k2 +

k1 t C Ao − C A

where

k1 k 2 = zero-order rate constant k1 = first-order rate constant This form of the rate equation is used for elementary enzyme-catalyzed reactions and for elementary surface-catalyzed reactions in batch reactor. For plug flow reactor replace time, t, with space time, τ. The equation assumes a constant density system.

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Chapter 5: Chemical Reaction Engineering

5.4 Catalytic Reactors Source: Missen, Ronald W., Charles A. Mims, and Bradley A. Saville, Introduction to Chemical Reaction Engineering and Kinetics, New York: John Wiley & Sons, Inc., 1999, pp. 191–192.

5.4.1

Key Assumptions

•

Catalyst surface contains a fixed number of sites.

•

All the catalytic sites are identical.

•

Reactivities of the sites depend only on temperature. They do not depend on the nature or amounts of other materials present on the surface during the reaction.

5.4.2

Surface Reaction Steps

1. Unimolecular surface reaction:

A:s " B:s

A • S is a surface-bound species involving A and site S.

_− rA i = kiA

Rate is given by: 2. Bimolecular surface reaction: Rate:

A:s+B:s " C:s+s

_− rA i = kiA iB

A:s+B " C+s

3. Eley-Rideal reaction:

B is a gas-phase species that reacts directly with an adsorbed intermediate.

_− rA i = kiACB

Rate:

CB is the gas-phase concentration of B.

5.4.3

Enzyme Kinetics: Michaelis-Menten Source: Missen, Ronald W., Charles A. Mims, and Bradley A. Saville, Introduction to Chemical Reaction Engineering and Kinetics, New York: John Wiley & Sons, Inc., 1999. k1

S + E E ES k−1

kr

where

ES " P + E

fast slow

S = substrate E = enzyme ES = enzyme-substrate complex P = product

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Chapter 5: Chemical Reaction Engineering 5.4.3.1 Michaelis-Menten Model Material balance on total enzyme:

CE + CES = CE0

Concentration of complex:

CES =

Define Michaelis constant:

k− KM = k 1 1

k1CsCE kCC CC = 1 s+ E0 = s E0 k−1 k1Cs k−1 k −1 + k1 Cs

kC C rp = krCES = Kr E+0 CS M S krCE0CS0 rP0 = `− rS0 j = K + C M S0

Rate of production of product P: Initial rate:

Limiting Cases

krCE0CS0 KM

Low CS0

CS0 % KM

rP0 = `− rS0 j =

High CS0

CS0 & KM

rP0, max = krCE0 1

maximum rate 1

= Intermediate rP0 2 krCE0 = 2 rP0, max CS0 K= M Michaelis-Menten Equation rP0, maxCS Standard form: rP = K + C M S rP0, maxCS0 rP0 = K + C M S0

Initial rate:

5.4.3.2 Estimation of KM and Vmax Linearized Form

Lineweaver-Burk Plot

K KM 1 1 1 1 Intercept r= Slope r M rP0 = rP0, max + rP0, max = CS0 P0, max P0, max

Linearized Form of Integrated Michaelis-Menten Equation



Constant-volume batch reactor:

C ln e C S o

r S0 t = 1 − P0, max − KM CS0 − CS CS0 CS KM

5.4.3.3 Single-Substrate Inhibition k1

E + S ? ES k−1



k2

ES + S ? ESS k−2

kr

ES " E + P Rate Law

rP =

krCE0CS

C S2

KM + CS + K 2

=

rP0, max CS C S2 + + KM CS K 2

k− K2 = k 2 2

2

C Inhibition occurs due to the term KS in the denominator. 2

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Chapter 5: Chemical Reaction Engineering Maximum Rate

Occurs at CS = _ KMK2 i2 rP0, max, apparent =

1

krCE0

1 + 2e

1 2

KM o K2

rP0, max

=

1 + 2e

1

KM 2 o K2

The maximum rate from the inhibited reaction is lower than rP0, max for the uninhibited reaction.

5.5 Heat Effects in Reactors The reactor design equations in the previous sections assume isothermal operation. For non-isothermal operation, both material and energy balance equations are required.

5.5.1

Batch Reactor

Energy Balance

dT mcp dt = V _− Dhtr i_rA i + q

endothermic reactions q is positive exothermic reactions

q is negative

adiabatic conditions

q is zero

5.5.2

Plug-Flow Reactor

dT mc o p dt = V _− Dhtr i_rA i + q

endothermic reactions q is positive exothermic reactions

q is negative

adiabatic conditions

q is zero

5.5.3

Continuous Stirred Tank Reactor mc o p _To − T j = V _− Dhtr i_rA i + q

endothermic reactions q is positive exothermic reactions

q is negative

adiabatic conditions

q is zero

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6 FLUID MECHANICS 6.1 Symbols and Definitions Symbols Symbol

Units (U.S.) ft2

Units (SI) m2

A

Area

Ar

Archimedes diameter

dimensionless

C

Fitting characteristic

dimensionless

CD

Drag coefficient

dimensionless

Cv

Valve flow coefficient

dimensionless

cp

Specific heat (constant pressure)

Btu lbm -cF

J kg : K

cv

Specific heat (constant volume)

Btu lbm -cF

J kg : K

D DH d F f

Diameter

ft or in.

m

Hydraulic diameter

ft or in.

m

Diameter (minor)

ft or in. lbf

m

fFanning H h hf

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Description

Force Friction factor (Darcy-Weisbach)

dimensionless

Fanning friction factor

dimensionless

N

Total head

ft

m

Height

ft

m

Head loss

ft

m

hf, fitting

Head loss in fitting

ft

m

hL K KE

Head loss (general)

ft

m

Loss coefficient

dimensionless

Kinetic energy

Btu 217

J

Chapter 6: Fluid Mechanics Symbols (con't) Symbol

Units (U.S.)

Units (SI)

k

Ratios of specific heats (cp/cv)

L

Length or thickness

ft or in.

m

MW

Molecular weight

lb lb mole

kg kmol

Ma m m

Mach number

mo

Mass flow rate

n Ns

Specific exponent

dimensionless

dimensionless lbm

Mass

kg Pa • sn

Apparent Viscosity

kg s

lbm hr dimensionless

Specific speed

rpm

rpm

NPSHa

Net positive suction head available

ft

m

NPSHr

Net positive suction head required

ft

m

lbf or psi ft 2

Pa

P

Pressure

P PE

Wetted perimeter

ft

m

Potential energy

Btu

J

Pvap

Vapor pressure

psi

Pa

R R Re r S SG T t

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Description

ft or in.

Radius Universal gas constant

m 3

psi-ft Btu lb mole-cR or lb mole-cR

Reynolds number

J mol : K

dimensionless ft or in. rpm

Radius Rotational speed Specific gravity

m rpm

dimensionless

Temperature Time

°F or °R hr or min or sec

°C or K s

u

Velocity

ft sec

m s

V

Volume

ft3

m3

Vo

Volumetric flow rate

ft 3 sec

m3 s

W

Work

ft-lbf

N•m

Wo X x y Y z a

Power

hp

W

Distance

ft or in.

m

Length, distance, or position

ft or in.

m

Length

m

Expansion factor

ft or in. dimensionless

Length or elevation difference

ft or in.

m

Angle

radian

radian

218

Chapter 6: Fluid Mechanics Symbols (con't) Symbol β

Description Ratio of small to large diameter

Units (U.S.) dimensionless

Units (SI)

N kg m = s2 m m

lbf ft

γ

Surface tension

d e

Thickness of a film

ft ft

h

Absolute roughness Porosity, void fraction, or volume fraction ^0 1 e 1 1 h Efficiency

h

Fluid viscosity

lbm ft - sec

N:s m2

q

Angle

radian

radian

μ

Dynamic viscosity

lbm cP or ft-sec

kg Pa : s or s : m

Infinite, plastic, or high shear viscosity

lbm cP or ft-sec

kg Pa : s or s : m

e

n3

dimensionless dimensionless

n

Kinematic viscosity

ft 2 hr

m2 s

r

Density

lbm ft 3

kg m3

rf

Density of fluid

lbm ft 3

kg m3

rp

Density of particles

lbm ft 3

kg m3

τ

Stress

lbf ft 2

Pa

xt

Shear stress

lbf ft 2

Pa

t0

Yield stress of fluid

lbf ft 2

Pa

Φ

Sphericity of particle (0 < Φ ≤ 1, where Φ = 1 is a perfect sphere)

dimensionless

Physical Constants Symbol

g

Value 32.174 9.8067 32.174

gc

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Units

ft sec 2 m s2 lbm-ft lbf -sec 2 kg : m =1 N : s2

219

Description Gravitational acceleration (Earth)

Gravitational conversion factor

Chapter 6: Fluid Mechanics

6.2 Fundamentals of Fluid Mechanics 6.2.1

Mechanical Energy Balance

6.2.1.1 Conservation of Mass Conservation of mass for flow from Point 1 to Point 2 is

mo 1 = mo 2 The continuity equation is ρ1 A1 u1 = ρ2 A2 u2 For an incompressible fluid, ρ1 = ρ2, therefore:

A1 u1 = A2 u2 and Vo1 = Vo2

6.2.1.2 The Bernoulli Equation

ft -lbf

= The Bernoulli equation states, in energy per unit mass 32.2 lbm P gc u 2 t + 2 + g z = constant

ft 2 N : m m2 = , 2 or kg sec s2

For one-dimensional flows (with uniform velocity profiles) through conduits with flow from Point 1 to Point 2, expressed in:

Energy Per Unit Mass (Energy Basis) P1 gc u12 P2 gc u 22 + + + = g z g w 1 c in t t + 2 + g z 2 + loss 2 where

win = net shaft work in = power/mass flow rate Energy Per Unit Volume (Pressure Basis) u2t t g z u2t t g z P1 + 21g + g 1 + t win = P2 + 22g + g 2 + t ^loss h c c c c Height of Fluid (Head Basis) P1 gc u12 P2 gc u 22 + + + = z h 1 s t g 2g t g + 2g + z 2 + h L where

hs = shaft work head hL = head loss

6.2.1.3 Energy Line and Hydraulic Grade Line Energy Line (or Energy Grade Line) The energy line (EL) represents the total head available to a fluid and can be expressed as: For inviscid incompressible flow:

Pg u2 EL = t gc + 2g + z = constant along a streamline

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Chapter 6: Fluid Mechanics For incompressible flow with losses:

Pg u2 EL = t gc + 2g + z − h L Hydraulic Grade Line (or Hydraulic Gradient Line) The hydraulic grade line (HGL) represents the total head available to a fluid, minus the velocity head, and can be expressed as: For inviscid incompressible flow:

Pg HGL = t gc + z For incompressible flow with losses:

Pg HGL = t gc + z − h L Note: The energy or hydraulic grade lines do not represent "sources" or "sinks" of energy such as the effects of pumps or turbines.

Energy Line and Hydraulic Grade Line for Incompressible Fluid Between Two Points (With Losses) ENERGY

u 12 2g

HYDRAU

LINE

hL

DE LINE

u 22 2g

LIC GRA

P1 gc g

P2 gc g

FLOW z1

1

2 z2

DATUM

6.2.1.4 The Impulse-Momentum Principle The resultant force in a given direction acting on a fluid equals the rate of change of momentum of the fluid, where

/ F = /Vo2 t 2 u2 - /Vo1 t1 u1 /F = result of all external forces acting on the control volume /Vo1 t1 u1 = rate of momentum of the fluid flow entering the control volume in the same direction as the force /Vo2 t 2 u2 = rate of momentum of the fluid flow leaving the control volume in the same direction as the force

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Chapter 6: Fluid Mechanics

6.2.2

Viscosity and Fluid Properties

6.2.2.1 Hydrostatic Head, Stress, Pressure, and Viscosity Definitions: Hydrostatic head is

tgh P= g c Stress is x = lim where

^DA " 0h

DF DA

x = surface stress at a point

Pressure is

P = − xn where

xn = stress normal at a point

Newton's Law of Viscosity relates shear stress (τt = stress tangential to the boundary) to the velocity gradient or shear rate (du/dy), using a constant of proportionality known as the dynamic (absolute) viscosity (μ) of the fluid:

du x t = n dy Kinematic viscosity is

n v=t

FLUID TYPES AND CHARACTERISTICS

M GHA

ID

FLU

IC

BIN

ST

IAN

EU DO

PL A

ON WT

NE

PS

SHEAR STRESS (τt ) τ0

6.2.2.2 Fluid Types and Characteristics

T

N ATA DIL

SHEAR RATE (du/dy)

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Chapter 6: Fluid Mechanics Classifications of Fluids Fluid Classification

Fluid Type

Behavior

Examples

Viscosity is constant. Water, light oil, blood plasma

du x t = n dy

Newtonian

The term μ is reserved for Newtonian fluids. Apparent viscosity (m) decreases with increased shear stress. n

Time-Independent Viscosity

Pseudoplastic (shear thinning)

Dilatant (shear thickening)

du x t = m d dy n

n = power law index, n < 1 m is also known as the consistency coefficient or consistency index Apparent viscosity (m) increases with increased shear stress. n

du x t = m d dy n

Molasses, latex paint, whole blood

Corn starch suspensions

n = power law index, n > 1 Time-Dependent Viscosity

Viscoplastic

Viscoelastic

Thixotropic

Apparent viscosity (m) decreases with duration of stress.

Yogurt, plastisols

Rheopectic

Apparent viscosity (m) increases with duration of stress.

Gypsum paste, kaolin clay suspensions

Bingham fluid

Kelvin material Maxwell material

Behaves as a rigid body until a minimum stress (yield stress) is applied, then reacts as a Newtonian fluid at shear stresses above the yield stress.

du x t = x 0 + h dy h = fluid viscosity x 0 = yield stress The materials exhibit both viscous and elastic characteristics during deformation under stress.

6.2.2.3 Surface Tension and Capillary Rise Surface tension g is the force per unit contact length

F c= L where F = surface force at the interface L = length of interface

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Mayonnaise, river mud, slurries

Silicone putty

Chapter 6: Fluid Mechanics The capillary rise, h, is approximated by

h =e

4c gc cos a o tgd

where

h = height of the liquid in the vertical tube α = angle made by the liquid with the wetted tube wall d = the diameter of the capillary tube

6.2.3

Velocity

Velocity is defined as the rate of change of position with respect to time

dx u = dt where x = position Velocity of a Newtonian fluid in a thin film is

y u ^ t h = u d

du = u dy d THIN FILM

δ

u y

BOUNDARY

The velocity distribution for laminar flow in circular tubes or between planes is

u ^ r h = u max =1 − c r m G R 2

where

r

= distance from the centerline

R

= radius of the tube or half the distance between the parallel planes

u

= local velocity at r

umax = velocity at the centerline of the duct u

= average velocity in the duct

Flow Conditions Fully turbulent flow

Circular tubes in laminar flow

Parallel planes in laminar flow

1.18

2

1.5

u max = u The shear stress distribution is

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Chapter 6: Fluid Mechanics

6.2.4

Reynolds Number

Dimensionless number describing flow behavior with the general definition:

inertial forces Re = viscous forces

6.2.4.1 Hydraulic Diameter DH = hydraulic diameter (also known as the characteristic length)

= # cross sectional area 4PA D H 4= wetted perimeter

Hydraulic Diameters for Various Flow Configurations Flow Configuration

Diagram

Hydraulic Diameter DH =

D

D = inside diameter

Through a circular tube

u a

Through a square duct

a

u

a

a

Through a rectangular duct

2ab a+b

u

Through a circular annulus

u

b

D1

D2

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D2-D1

Chapter 6: Fluid Mechanics

Hydraulic Diameters for Various Flow Configurations (cont'd) Flow Configuration

Through a partially filled pipe (tube)

Hydraulic Diameter DH =

Diagram

2 8rl - c _r - h iB l

c

r

where

c = 2 h _2r - h i

h l FLUID APPROACH VELOCITY (uo)

Around a sphere (or sphere through a fluid)

Sphere diameter

PROJECTED AREA (Ap)

FLUID STREAMLINES

FLUID APPROACH VELOCITY (uO)

Around any object (or an any object through a fluid)

4Ap P PROJECTED AREA (Ap) P = PERIMETER OF SHAPE PRESENTED NORMAL TO THE APPROACH VELOCITY

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FLUID STREAMLINES

Chapter 6: Fluid Mechanics 6.2.4.2 Newtonian Fluid Re =

DH u t n

where u = approach velocity

Various Forms of Reynolds Numbers and Their Units in Circular Conduits (Pipes) Fluid Velocity

u

Fluid Density ρ

Fluid Viscosity μ

ft

ft sec

lbm ft 3

lbm ft-sec

Dut n

m

m s

kg m3

N:s Pa : s or m2 kg or m : s

Dut 32.2n

ft

ft sec

lbm ft 3

lbf-sec ft 2

Dut 123.9 n

in.

ft sec

lbm ft 3

cP

Vo t 22, 700 D n

in.

lbm ft3

cP

ft 3 sec

Vo t 50.6 D n

in.

lbm ft 3

cP

gpm

mo 6.31 D n

in.

Vo t 35.42 D n

in.

Du v

ft

ft sec

ft 2 sec

Du v

m

m/s

m2 s

Du 12v

in.

ft sec

ft 2 sec

Du 7740 v

in.

ft sec

cS

Vo 1, 419, 000 D v

in.

ft 3 sec

cS

Vo 3160 D v

in.

gpm

cS

Reynolds Number Form

Diameter

Dut n

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D

Volumetric Flow rate

Vo

cP

227

mo

Kinematic Viscosity

ν

lbm hr

cP

lbm ft 3

Mass Flow rate

barrels hr

Chapter 6: Fluid Mechanics 6.2.4.3 Power Law Fluid Re x =

` D n u (2 − n) t j

f K d _3n + 1 i n 8 (n − 1) p 4n n

where n = power law index K = consistency index

6.2.4.4 Bingham Fluid Bingham fluid flow through a pipe:

ReBP =

4Vo t r D3 x0 gc p r D n3 f1 + 24Vo n3

where

n3 = infinite viscosity, or plastic viscosity, or high shear limiting viscosity x0 = yield stress of the fluid

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Chapter 6: Fluid Mechanics Viscosity as a Function of Temperature for a Variety of Gases and Liquids 100 10 SAE

80

L

60 40

GO

30

IL (2

P I) 1° A

20

10 8 6 4

35 °A PI

3 LA HY ET OL OH LC

) 0% (10

VISCOSITY, CENTIPOISES (cP)

2

DI ST ILL AT E

1 0.8

CA RB

0.6

BE

NZ

0.4 0.3

N-

0.2

AM

MO

0.1

NI

A(

ON TE T

EN

ACE

E

RA CH L

TON E (L PEN IQU TAN ID) E (L IQU ID)

LIQ

OR IDE GASO

WA TE

LINE

R

UI

D)

0.08 0.06

OXYGEN (1 ATM)

0.04 0.03

OSPHERE

AIR AT ATM

0.02

CHLORINE R

IA VAPO

AMMON

0.01

NE

0.008

PROPA

0.006 0.004

0

100

E

PRESSUR

METHANE

E CARBON DIOXID METHANE

HYDROGEN

R WATER VAPO TANE n - PEN

200

R (1 ATM) WATER VAPO

XIDE CARBON DIO

300

400

500

600

TEMPERATURE (°F)

Source: Brown, G. G., et. al., Unit Operations, New York: John Wiley & Sons, Inc., 1951.

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700

Chapter 6: Fluid Mechanics 6.2.4.5 Critical Reynolds Number The critical Reynolds number (Rec ) is the minimum Reynolds number at which flow is expected to become turbulent, as shown in the following table:

Rec 2100 10

Flow Regime Flow through a pipe Flow around a sphere

1708r1 h

Circular flow (rotating cylinder, Taylor-Couette flow)

6.2.5

where the inner cylinder has a diameter (r1) and height (h)

Friction

6.2.5.1 Absolute Roughness and Relative Roughness f Relative roughness is D . Absolute Roughness or Specific Roughness ( f ) of Various Pipes Material PVC and plastic pipes Copper, lead, brass, aluminum (new) Stainless steel Steel commercial pipe Asphalted cast iron Galvanized iron Smoothed cement New cast iron Well-planed wood Ordinary concrete Worn cast iron Coarse concrete Ordinary wood

ε ft 0.0000033 0.000005 0.00005 0.0002 0.0004 0.0005 0.001 0.0016 0.0016 0.0026 0.004 0.0065 0.002

6.2.5.2 Friction Factors for Laminar Flow For laminar flow (Re < 2100)

64 f = Re

6.2.5.3 Friction Factors for Turbulent Flow The Colebrook equation

KJK f 1 =− 2 log10 KKK D + 2.51 f K 3.7 Re f L

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230

in. 0.00004 0.00006 0.0006 0.0024 0.0048 0.006 0.012 0.019 0.019 0.031 0.048 0.078 0.024

m 1.0E–06 1.5E–06 1.5E–05 6.0E–05 1.2E–04 1.5E–04 3.0E–04 5.0E–04 5.0E–04 8.0E–04 1.2E–03 2.0E–03 6.1E–04

mm 0.001 0.0015 0.015 0.06 0.12 0.15 0.3 0.5 0.5 0.8 1.2 2.0 0.6

Chapter 6: Fluid Mechanics The Haaland equation is an empirical approximation of the friction factor that does not require iteration, 10

1 =− 1.8 log10 > 6.9 + c f m 9 H f Re 3.7D for the following conditions

f 4 # 10 4 # Re # 108 and 0 # D # 0.05 For fully turbulent flow

1 = 2f 1.74 − 2 log10 c D m f

Friction Factor Chart 0.1 0.09 0.08

LAMINAR FLOW

CRITICAL ZONE TRANSITION ZONE

COMPLETELY TURBULENT REGIME 0.05

f = 64 Re

0.07

0.04

0.06

0.03

0.05

0.02

0.006

0.03

0.004

f 0.025

0.002

0.02

0.001 0.0008 0.0006 0.0004

0.015

RELATIVE ROUGHNESS

0.01 0.008

Rcr

e D

0.015 0.04

0.0002 0.0001 SMOOTH PIPES

0.01

0.000,001 0.000,005

0.009 0.008

7 9 103

2

3

4 5 67 9 104

2

3

4 5 67 9 2 3 4 5 67 9 105 106 REYNOLDS NUMBER Re

2

3

4 5 67 9

MOODY DIAGRAM. (FROM L.F. MOODY, TRANS. ASME, VOL. 66, 1944.)

6.2.6

Pressure Drop for Laminar Flow

The Hagen-Poiseuille equation for Vo in terms of the pressure drop DPf is

= Vo

r R 4 DP f r D 4 DP = 8n L 128n L

f

This relation is valid only for flow in the laminar region.

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107

2

3

0.000,05

0.000,01 4 5 67 9 108

Chapter 6: Fluid Mechanics

6.2.7

Pressure Drop for Turbulent Flow

6.2.7.1 Head Loss in Pipe or Conduit The Darcy-Weisbach equation is

u2 L u2 = hL f= K D 2g 2g where

f

= friction factor

D

= inside diameter of the pipe or hydraulic diameter (DH) of conduit

L

= length over which the pressure drop occurs

L f D = K = the loss coefficient The total loss coefficient for a system is

K = / Ki where Ki = the loss coefficient for individual fittings, valves, and other components Changes in K for different pipe internal diameter are 4

D Ka = Kb e Da o b

An alternative formulation is

2f Fanning Lu 2 hL = Dg where the Fanning friction factor is

f f Fanning = 4

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Chapter 6: Fluid Mechanics Loss Coefficients and Equivalent Lengths for Fittings and Valves Loss Coefficient Equivalent 1 Length* K = K1 + K d 1 + 3 ID Re

Fitting

90o

Elbows

45o

180o

Used as elbows Tees Run through

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L D

K1

K3

r Standard c d = 1 m , threaded

35

800

0.40

r Standard c d = 1 m , flanged or welded

20

800

0.25

r Long radius c d = 1.5 m

16

800

0.20

Mitered

100

1000

1.15

r Standard c d = 1 m , threaded

16

500

0.20

r Long radius c d = 1.5 m

13

500

0.15

Mitered, 1 weld (45°)

20

500

0.25

r Standard c d = 1 m , threaded

60

1000

0.70

r Standard c d = 1 m , flanged or welded

30

1000

0.35

r Long radius c d = 1.5 m

25

1000

0.30

Standard, threaded

60

500

0.70

Long radius, threaded

35

800

0.40

Standard, flanged or welded

65

800

0.80

Stub-in branch

85

1000

1.00

Threaded

10

200

0.10

Flanged or welded

40

150

0.50

Stub-in branch

5

100

0.05

233

n

Chapter 6: Fluid Mechanics

Loss Coefficients and Equivalent Lengths for Fittings and Valves (cont'd) Loss Coefficient Equivalent 1 Length* K = K1 + K d 1 + 3 ID Re

Fitting

inches

L D

K1

K3

Dopening = 1.0 p Dpipe

10

300

0.10

Gate, ball, or Dopening = 0.9 p Reduced trim f plug Dpipe

12

500

0.15

Dopening = 0.8 p Dpipe

20

1000

0.25

Standard

330

1500

4.00

Angle or Y type

165

1000

2.00

Diaphragm

Fully open

165

1000

2.00

Butterfly

Full open

20

800

0.25

Lift

830

2000

10.00

Swing

125

1500

1.50

Tilting disk

40

1000

0.50

Full line size f

Reduced trim f Valves

Globe

Check

* Approximated from the loss coefficient equation using friction factors for fully turbulent flow for pipe sizes 1" through 24"

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n

Chapter 6: Fluid Mechanics 6.2.7.2 Loss Coefficients for Contraction and Expansion Notes: 1. Reynolds Number (Re) and friction factor (f) are based on inlet velocity.

d

2. b = D Contraction:

CONTRACTION

FLOW

When

D

d

θ

θ < 45° and

i 160 1 Re < 2500, then K = 1.6 c1.2 + Re m e 4 − 1 o sin c 2 m b Re > 2500, then K = 1.6 `0.6 + 1.92f j f When

1 − b2 p sin i 4 2 b

θ > 45° and

1

i 2 160 1 Re < 2500, then K = 1.6 c1.2 + Re m e 4 − 1 o 2500, then K = `0.6 + 0.48f j f 4 p 4000, then K = 2.6 `1 + 3.2f j `1 − b 4 j sin c 2 m When

θ > 45° and

Re < 4000, then K = 2 `1 − b 4 j Re > 4000, then K = `1 + 3.2f j `1 − b 4 j

2

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D

Chapter 6: Fluid Mechanics 6.2.7.3 Loss Coefficients for Pipe Entrance and Exit Loss Coefficients Loss Coefficient Fitting

Type

K 1 n K = Re1 + K3 d1 + ID inches

Configuration

K1

K∞

Inward projecting or reentrant

FLOW

160

1.0

Sharp-edged

FLOW

160

0.5

Entrance

d

FLOW

Rounded

160

r

Exit

All geometries

0.0

r/d 0.02 0.04 0.06 0.10 0.15 & up

K∞ 0.28 0.24 0.15 0.09 0.04

1.0

6.2.7.4 Valve Flow Coefficient (Cv) Valve flow coefficient (Cv ) is a value of the relationship between the pressure drop across a valve and the corresponding flow rate:

Cv = Vo

SG DP

Also:

Cv =

ad 2 K

where

gpm a = constant, 29.9 2 in psi

or

m3 0.0352 2 s m Pa

d = effective diameter of the valve, in inches or meters K = loss coefficient Note: Values of Cv are not interchangeable between unit systems.

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Chapter 6: Fluid Mechanics The estimated flow rate with a known K value is

ad 2 DP Vogpm = K SG where ΔP = pressure drop (psi or Pa)

6.2.8

Flow Through an Orifice

6.2.8.1 Submerged Orifice Submerged Orifice Operating Under Steady-Flow Conditions

V

h 1 – h2 h1

h2

D2

D Vo = A2 u2 = CA 2g _h1 − h2 i where

u2 = velocity of fluid exiting the orifice



A = cross-sectional area at diameter D



A2 = vena contracta cross-sectional area at diameter D2



C = coefficient of discharge

6.2.8.2 Orifice Discharging Freely into Atmosphere Orifice Discharging Into Atmosphere Atm

h

D

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Chapter 6: Fluid Mechanics Torricelli's equation is

u = 2gh Vo = CA 2gh where

h = distance from the liquid surface to the centerline of the orifice opening A = cross-sectional area at diameter D C = coefficient of discharge

6.2.9

Particle Flow

The force exerted by a fluid that opposes the weight of an immersed object (buoyant force) can be expressed in terms of differential densities:

FG = where

`t p − t f j gVp gc

FG = buoyant force rp = particle density rf = fluid density Vp = volume of particle The force exerted by a fluid flowing past a solid body (drag force) can be expressed in terms of a drag coefficient (CD):

FD = where

CD tf u32 AP 2gc

FD = drag force u3 = approach velocity AP = the projected area of object with axes perpendicular to the flow

6.2.9.1 Stokes Law or Stokes Flow For a sphere moving through a fluid at Re 10,000

P=

KT N3 D5 t gc

where KT = empirical constant (fully turbulent)

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Chapter 6: Fluid Mechanics Values of Constants KL and KT for Baffled Tanks Type of Impeller KL

Propeller, square pitch, 3 blades Propeller, pitch = 2, 3 blades Turbine, 6 flat blades Turbine, 6 curved blades Fan turbine, 6 blades Flat paddle, 2 blades Shrouded turbine, 6 curved blades

41.0 43.5 71.0 70.0 70.0 36.5 97.5

KT 0.32 1.00 6.30 4.80 1.65 1.70 1.08

Note: Table is specific to tank configuration and provided as an example only. Power required to suspend particles to a maximum height (Z) using a turbine impeller is

P = g tm Vmut _1 − em i

2 3cT

D

1 2

m e 4.35b

where

b

− = Z E − 0.1, with E = clearance between impeller and tank floor T

rm , Vm = density and volume, respectively, of solid-liquid suspension, not including the clear liquid in zone above height Z (also known as cloud height)

ut

= terminal velocity of particles

e m

= volume fraction of liquid in zone occupied by suspension

and

1 1 1 1 tm = tliquid + xsolids d tsolids − tliquids n with

xsolids =

mass fraction of the solid particles in the solid-liquid suspension

Suspension of Particles in a Tank

CLEAR LIQUID SOLID-LIQUID SUSPENSION

Z

TANK E

D T

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Chapter 6: Fluid Mechanics 6.3.7.2 Blending of Miscible Liquids in a Tank CORRELATION OF BLENDING TIMES FOR MISCIBLE

Correlation of Blending Times for Miscible Liquids in aBAFFLED Turbine-Agitated, Baffled Vessel LIQUIDS IN A TURBINE-AGITATED VESSEL 1000

100 fT 10

1

1

102

10

103

104

105

ND2p Re = _________ μ

Blending time factor (fT) (for miscible Newtonian fluids only):

t _ N D 2 i3 g 6 D 2 2

fT =

1

1

1

3

H2T2

where t = blend time (sec)

6.4 Flow and Pressure Measurement Techniques 6.4.1

Manometers and Barometers

6.4.1.1 Simple Manometer Simple Manometer Patm P2 PA FLUID 1 (ρfluid 1)

zA P1

FLUID 2 (ρfluid 2)

z1

g PA − Patm = PA − P2 = g 9tfluid2 _ z2 − z1 i − tfluid1 _ zA − z1 iC c

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z2

106

Chapter 6: Fluid Mechanics 6.4.1.2 Manometer With Multiple Fluids Manometer With Multiple Fluids FLUID 3 (ρfluid 3) FLUID 1 (ρfluid 1) z2P2 zAPA

z2P2

A z1P1

B

z1P1 z3P3

zBPB

z3P3

FLUID 2 (ρfluid 2)

FLUID 4 (ρfluid 4)

PA − PB = _ PA − P1 i + _ P1 − P2 i + _ P2 − P3 j + _ P3 − PB j g PA − PB = g 9tfluid1 _ z1 − zA i + tfluid2 _ z2 − z1 i + tfluid3 _ z3 − z2 j + tfluid4 _ zB − z3 jC c

6.4.1.3 Inclined U-Tube Manometer Inclined U-Tube Manometer P1

P2

x

∆h MANOMETER FLUID

θ

g g P1 − P2 = g tm x sini = g tm Dh c c where

x = difference in tube fill length rm = density of the manometer fluid (densities of the fluids on each side of the manometer are equal) q = angle of inclination (horizontal = 0°)

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Chapter 6: Fluid Mechanics 6.4.1.4 Barometers Another device that works on the same principle as the manometer is the simple barometer.

tgh tgh Patm = PA = Pv + g = PB + g c c where

Pv = vapor pressure of the barometer fluid

Barometer PV

PB

h

ρ

PA

6.4.2

Flow Measurement Devices (Summary) Flow Measurement Devices

Mechanical

Class Meter Type Description Rotary Rotary piston spins within a chamber of known piston volume. For each rotation, an amount of fluid passes through the piston chamber. The rotations are counted and the flow rate is determined from the rate of rotations.

Gear

Two rotating gears with synchronized, close-fitting teeth. A fixed quantity of liquid passes through the meter for each revolution. Permanent magnets in the rotating gears transmit a signal to a transducer for flow measurement.

OPERATION OF AN OVAL GEAR METER Operation of an oval gear meter

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Advantages • Accurate; suitable for fuel metering • Suitable for low volume metering and laboratory or bench scale testing

• Accurate; suitable for fuel metering • Suitable for low volume metering and laboratory or bench scale testing

Drawbacks • High permanent pressure drop at high flows • Clear liquids only • High cost

• High permanent pressure drop at high flows • Clear liquids only • High cost

Chapter 6: Fluid Mechanics Flow Measurement Devices (cont'd) Mechanical (cont'd)

Class Meter Type Description Nutating Also known as a wobbly plate meter. Fluid enters Disk a chamber of known volume. When the chamber is filled, the fluid is released, which causes the disk to perform a nutating action (wobble in a circular path without actually spinning on its axis). The motion is detected by either gearing or magnetic transducers. The flow rate is determined from the rate of motions. HOLE SHAFT

Rotameter (variable area)

• Good for hot liquids

Drawbacks • Accuracy is adversely affected by viscosities below the meter's designated threshold

NUTATING DISK

INLET

Helical

Advantages • Accurate and repeatable; used for water service metering

OUTLET

Counter-rotation of the gears carries known volumes of liquid axially down the length of the gears. The rotation rate is measured using sensors, which in turn correlates to flow rate.

• Used for heavy and high-viscous liquids • Highest accuracy of any positive displacement flow meter

Source: Flowserve Corp., Irving, TX Fluid flows upward through a clear tapered tube and • Simple operation suspends a bob. The higher the flow rate, the higher with few moving the bob suspends in the tube. The bob is the indicator parts and no exterand the reading is obtained from the scale marked on nal power source the tube. • Inexpensive and FLOW PIPE widely available TAPERED TUBE

• Accurate provided the fluid properties remain unchanged

• Can only measure liquids • Low corrosion allowance • Cannot handle abrasive fluids

• Must be mounted vertically • Changes in fluid properties gives erroneous results • Not suited for large pipes (< 6 inches) • Readout uncertainty near bottom of the scale

• Resistant to shock and chemical action • Some fluids may obscure reading.

BOB

• •

FLOW

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Chapter 6: Fluid Mechanics Flow Measurement Devices (cont'd) Mechanical (cont'd)

Class Meter Type Description Turbine (or Fluid flows past a turbine wheel positioned in the Woltmann center of the pipe with the shaft in line with the pipe. Type) The rotational speed is proportional to the flow rate. Shaft rotation is detected electronically. ELECTRONIC PICKUP METER HOUSING FLOW ROTOR SUPPORT

TURBINE

Advantages • Simple and durable structure; can be installed vertically or horizontally

Drawbacks • Cannot tolerate cavitation • Accuracy adversely affected by entrained gas

• Can be designed to detect flow in either • Sensitive to changes direction in fluid viscosity • Operates under • Long straight runs a wide range of of pipe upstream temperatures and and downstream pressures of the meter are • Low pressure drop across the flow meter

needed

• Bearings are prone to wear (though • Effective in applisome are provided cations with steady, "bearingless") high-speed flows • Not suitable for

• Can be used for gasses but not suitable for steam Paddle Fluid flows past a paddle wheel positioned off-center • Simple and durable Wheel Type of the pipe with the shaft perpendicular with the pipe. structure; can be The rotational speed is proportional to the flow rate. installed vertically Shaft rotation is detected electronically. or horizontally FLOW

ROTATION

PADDLE WHEEL DETECTOR (MOUNTED EXTERNALLY)

• Easy installation into existing systems for insertion models • Can be designed to detect flow in either direction • Operates under a wide range of temperatures and pressures

Other meters in this class: Single Jet Multi Jet Pelton Wheel

• Low pressure drop across the flow meter • Effective in applications with steady, high-speed flows

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steam

• Requires a full pipe of liquid • Not suitable for steam • Bearings are prone to wear

Chapter 6: Fluid Mechanics Flow Measurement Devices (cont'd) Pressure

Class Meter Type Description Venturi The meter constricts the fluid flow and sensors measure the differential pressure before and within the constriction. The differential pressure is then converted to a corresponding flow rate. PRESSURE MEASUREMENT

Advantages • Highly accurate over a wide range of flows

Drawbacks • Flow must be derived from pressure drop

• No moving parts

• Pipe must be full (mostly used for liquid service)

• Low pressure drop

• Occupies space L ( D of approximately 50)

FLOW

Orifice Plate (also squareedge orifice plate)

• Cannot measure fluids in reverse flow • Flow must be derived from pressure drop

Flow is restricted using a plate with a hole drilled • Accurate over a through it. Sensors measure the differential pressure wide range of before and after the meter (two tap configurations are flows, but not suitshown). The differential pressure is then converted to able for trade use • Accuracy a corresponding flow rate. (2–4% of full scale) reduced at low • No moving parts flows dP MEASUREMENT (FOR FLANGE TAP OPTION) dP

FLOW

dP dP MEASUREMENT (FOR VENA CONTRACTA TAP OPTION)

Note: Orifices may be drilled in the middle of the plate (concentric) or off-center (eccentric) to accommodate certain fluid types and flow regimes. Orifices may also be round or segmented.

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• Low cost; price does not drama-tically increase with pipe size

• Plate materials prone to wear and corrosion, which adversely effects accuracy

• Low maintenance (orifice plates can • Accuracy effected be replaced during by high-viscous maintenance operafluids tions) • Moderate to high • Easy to convert to permanent pressure different applicadrop tions or fluids by • Pipe must be full replacing the orifice (for liquids) plate • In common use

Chapter 6: Fluid Mechanics Flow Measurement Devices (cont'd) Pressure (cont'd)

Class Meter Type Description Nozzle Similar to a venturi meter, but the inlet section is in the shape of an ellipse and there is no exit section. dP MEASUREMENT dP

Advantages • More accurate than orifice plates • High flow capacity and high velocity applications

FLOW

Drawbacks • Flow must be derived from pressure drop • More expensive than orifice plates

• Less susceptible to wear and corrosion than orifice plates

• Takes up slightly more room than orifice plates

• Can operate in higher turbulence

• Higher permanent pressure drop than venturi meters

• Tolerant of fluids containing suspended solids

• Pipe must be full (for liquids)

• Less expensive than the venturi meter • Physically smaller than the venturi meter

Dall Tube

Similar to the venturi meter but more compact at the expense of some loss in accuracy and additional permanent pressure loss.

• Can indicate a reverse-flow condition • Similar performance as the venturi meter • Shorter length than the venturi meter

dP

• Low unrecoverable pressure loss

FLOW

• Accurate to within 1% of full scale

• More expensive than orifice plates or flow nozzle meters • Sensitive to turbulence • More complex to manufacture • Accuracy dependent on actual flow data • Cannot indicate a reverse-flow condition

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Chapter 6: Fluid Mechanics Flow Measurement Devices (cont'd) Pressure (cont'd)

Class Meter Type Description Advantages Wedge Similar in principle to the orifice meter, a wedge • Well suited for placed in the flow stream creates the differential pressludge, slurry, or sure element. The fluid is forced downward, similar high-viscous fluid to a segmented orifice plate, but is guided along a service sloping wedge shape rather than a sharp edge. The differential pressure is then converted to a corresponding flow rate. dP

Drawbacks • Differential pressure to flow rate dependent on empirical data unique to each model and application • High permanent pressure drop

FLOW

WEDGE

Pitot Tube

The pitot tube is primarily used for gas or air service. • Essentially no pres- • Low accuracy (difThe Pitot tube measures the total pressure (dynamic sure drop ferential pressure and static pressures combined). The static tube mea- • Easy to install and between static and sures the static pressure only. The difference between dynamic is small use the two measurements reveals that the dynamic presand therefore prone • Instrument can be sure is converted into the flow rate. to error) removed when not • Accuracy dependP in service dent on placement STATIC TUBE • Can be used to within the flow measure gas velocicross-section ties and to establish • Low rangeability FLOW a velocity profile • Requires clean fluids (tube easily PITOT TUBE plugs) Note: The pitot tube (impact tube) and the static tube are sometimes provided within a single element.

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Chapter 6: Fluid Mechanics Flow Measurement Devices (cont'd) Pressure (cont'd)

Class Meter Type Description Annubar The annubar or averaging pitot-tube flow meter measures the difference between the total pressure (upstream) and the static pressure (downstream) to derive the flow rate. dP

ANNUBAR (IMPACT TUBE)

Advantages • Accurate (1% of full scale) • Compact design (sensing lines not required)

Drawbacks • Not suitable for dirty or viscous fluids • Element must be centered within the pipe

FLOW UPSTREAM SENSING PORTS

FLOW

DOWNSTREAM SENSING PORTS SIMPLIFIED CROSS-SECTION OF SENSING (IMPACT) TUBE

Cone (or V-Cone)

Note: Temperature elements can be made integral with the impact tube to provide temperature compensation and corrections. A cone is inserted in the flow stream to create a • Excellent accuracy differential pressure similar to a venturi meter or Dall (0.5% of full scale) tube meter, which is then correlated to the flow rate. • Suitable for fluids dP with suspended solids • Compact design (0–2 pipe diameters)

FLOW

• Suitable for gas flow measurement

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• Moderate permanent pressure drop • Requires extensive calibration to achieve rated accuracy • Must operate within rated β-ratio range

Chapter 6: Fluid Mechanics Flow Measurement Devices (cont'd) Thermal

Class Meter Type Description Advantages Thermal A known amount of heat is applied to the heating • Used primarily for Mass element. Some of this heat is lost to the flowing fluid. gas service (stack Meters As flow increases, more heat is lost. The amount of flow measurement heat lost is sensed using temperature elements (comand emissions paring the upstream and downstream values). The monitoring) fluid flow is derived from the known heat input and • Low pressure drop the temperature measurements. • The temperature and heating HEATING ELEMENT DOWNSTREAM T1 = UPSTREAM elements come in = T2 TEMPERATURE TEMPERATURE a single element ELEMENT ELEMENT assembly for a compact design

Drawbacks • Thermal properties of the gas must be known • Moderate accuracy • Not for steam service

• Detects low flows (laminar flows)

FLOW

Vortex

• Can be used as a velocity meter

Vortex Shedding

Vortices (or eddy currents) created by an obstruction are detected by ultrasonic or optical transducers. The rate of vortex formation and subsequent shedding caused by the bluff body or obstruction is proportional to the fluid velocity. BLUFF BODY (STRUT)

FLOW

RECEIVING TRANSDUCER

EDDYS (VORTICES)

• Results are in true mass flow • Can be used for liquids, gases, and steam • Low wear • Low cost to install and maintain • Low sensitivity to variations in process conditions • Stable long-term accuracy and repeatability • Applicable to a wide range of process temperatures

TRANSMITTING TRANSDUCER

• Available for a wide variety of pipe sizes

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• Not suitable for low flow rates • Minimum length of straight pipe is required upstream and downstream of the meter

Chapter 6: Fluid Mechanics Flow Measurement Devices (cont'd) Magnetic

Class Meter Type Description Advantages Drawbacks Mag Meter The operation of a magnetic flow meter or mag meter • Ideal for dirty water • Does not work is based on Faraday's Law, which states that the voltor other conductive on nonconductive age induced across any conductor as it moves at right fluids fluids (e.g., hydroangles through a magnetic field is proportional to the • Suitable for fluids carbons) velocity of that conductor. with two-phase • Expensive flow • Does not correlate E \ u#B#D • No pressure drop to mass flow until where (models are availfluid or bulk slurry able for full pipe density is known E = voltage generated in a conductor bores) u = velocity of the conductor • Accurate • Measures true volumetric flow

B = magnetic field strength

Ultrasonic

D = length of the conductor The flow meter applies a magnetic field through the entire cross-section of the flow tube. The velocity is then determined by the meter by measuring the magnetic strength. For a simple Doppler system, sound waves are used to determine the velocity of a fluid flowing in a pipe. At zero flow, the frequencies of an ultrasonic wave transmitted into a pipe and its reflections from the fluid are the same. At flow, the frequency of the reflected wave is different because of the Doppler effect. As fluid velocity increases, the frequency shift increases linearly. A transmitter evaluates the frequency shift to determine the flow rate. For a Transit time system, ultrasonic waves are sent and received between transducers in both directions in the pipe. At zero flow, it takes the same time to travel upstream and downstream between the transducers. At flow, the upstream wave travels more slowly and takes more time than the downstream wave. As fluid velocity increases, the difference between the upstream and downstream times also increases. A transmitter evaluates the delay times to determine the flow rate. Note: Either method can be deployed as a clamp-on unit (dry) or be installed integral to the fluid (wet).

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• Sufficiently accurate for custody transfer

• Expensive

• Clamp-on systems suitable for field testing and verification of installed flow meters

• Unwanted attenuation can occur

• Sensitive to stray vibrations

• Fluid must be able to transmit ultrasonic waves

Chapter 6: Fluid Mechanics Flow Measurement Devices (cont'd) Impulse

Class Meter Type Description Advantages Coriolis A Coriolis flow meter uses the natural phenomenon • Suitable for highly in which an object begins to "drift" as it travels from viscous fluids or toward the center of a rotation occurring in the • Insensitive to temsurrounding environment. Coriolis flow meters genperature and fluid erate this effect by diverting the fluid flow through properties a pair of parallel U-tubes with an induced vibration (by an actuator, not shown) perpendicular to the flow. • Measures mass flow rate directly The vibration simulates a rotation of the pipe and the resulting Coriolis "drift" in the fluid causes the U-tubes to twist and deviate from their parallel alignment. The force producing this deviation is proportional to the mass flow rate through the U-tubes. VIBRATION VIBRATION FLOW

NO DEFLECTION

6.4.3

Drawbacks • Not accurate for gases at low flow rates • High permanent pressure drop

DEFLECTION

Orifice, Nozzle, and Venturi Meters

6.4.3.1 Square-Edge Orifice Meter (Vena Contracta Taps) d2 2

d2

0.66 DISCHARGE COEFFICIENT Corifice FOR SQUARE-EDGE ORIFICE METERS

0.64 d1 Corifice

d2

FLOW

0.62

β =

0.60

SQUARE-EDGE ORIFICE METER 0.58 4 10

105

106 Re

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d1 —— = 0.7 d2 0.6 0.5 0.4 0.2

107

108

Chapter 6: Fluid Mechanics Flow Coefficient (C) and Orifice Loss Coefficient C=

Corifice 1 − b4

Incompressible Flow Vo = C Aorifice

2 gc DP t

Compressible Flow 2 g c DP t

Vo = Y C Aorifice

where Y = expansion factor

6.4.3.2 Flow Nozzle Meter 1.00

d2 2

d2

0.2 0.6

0.4

d1

d2

Cnozzle

0.98 d1 β = —— = 0.8 d2

0.96

FLOW

0.94

104

NOZZLE METER

Cnozzle 1 − b4

Incompressible Flow Vo = C Anozzle

2 gc DP t

Compressible Flow Vo = Y C Anozzle

2 gc DP t

where Y = expansion factor

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Flow Coefficient (C) C=

105

DISCHARGE COEFFICIENT Cnozzle FOR NOZZLE METERS

282

107

108

Chapter 6: Fluid Mechanics 6.4.3.3 Venturi Flow Nozzle Meter The venturi discharge coefficient is a function of the specific geometry of the meter. PRESSURE MEASUREMENT

FLOW

Flow Coefficient (C) C=

Cventuri 1 − b4

Incompressible Flow Vo = C Aventuri

2 gc DP t

Compressible Flow Vo = Y C Aventuri

2 gc DP t

where Y = expansion factor

6.4.3.4 Pitot Tube Flow Meter STATIC TUBE

P1

P2

FLOW PITOT TUBE (OR IMPACT TUBE) P1 measures the static pressure. Assuming elevation effects are negligible, P2 is the stagnation pressure:

t u2 P1 + 2 g c

Therefore:

u=

©2020 NCEES

2 gc _ P2 − P1 i t

283

Chapter 6: Fluid Mechanics 6.4.3.5 Permanent Pressure Loss in Flow Meters FLOW RESTRICTION

VENA CONTRACTA PB

PA

FLOW P VC PERMANENT PRESSURE LOSS PA PB

P vc

Pressure Loss Across Restrictive Flow Meters: The permanent pressure loss (or nonrecoverable pressure drop) across a restrictive flow meter (e.g., orifices and nozzles) is the difference between the upstream pressure, PA, (the static pressure not influenced by the device, or roughly one pipe diameter upstream), and the pressure measured downstream of the device where the static pressure recovery is complete, PB (approximately six pipe diameters downstream). For a given measured differential pressure, ΔP (e.g., radius or flange taps for an orifice), the permanent pressure loss can be estimated by:

J N 2 K 1 − b 4 `1 − Cd j − Cd b 2 O PA − PB = DP K K 1 − b 4 `1 − C 2 j + C b 2 OO d d L P where Cd = coefficient of discharge for the device (e.g., Corifice and Cnozzle) For orifice plates and nozzles, the flow coefficient, K, can be approximated

K=f

1 − b 4 `1 − Cd2 j Cd b 2

2

− 1p

Source: ASME MFC-3M-2004, Measurement of Fluid Flow in Pipes Using Orifice, Nozzle, and Venturi

©2020 NCEES

284

Chapter 6: Fluid Mechanics 6.4.3.6 Weir Meters Rectangular Weir—Suppressed L

V-Notch Weir (90o Notch)

L

H

H 5

3

Vo = C L H 2 Vo = C H 2

where

ft 0.5 C = 3.33 sec



C = 1.84

ft 0.5

where C = 2.5 sec

m 0.5 m 0.5 C = 1.4 s s

Rectangular Weir—Contracted

L

H Vo = C _ L − 0.2H i H 2 3



©2020 NCEES

ft 0.5

where C = 3.33 sec

C = 1.84

m 0.5 s

285

Chapter 6: Fluid Mechanics

6.5 Tables Pipe Dimensions and Weights

Pipe Size

OD

inches

inches

1/8

0.405

1/4

0.54

mm

6

mm

10.3

8

13.7

3/8

0.675

10

1/2

15

17.1

0.840

21.3

Weights are based on carbon steel pipe Identification Wall Thickness Weight Steel Stainless lbm kg Steel inches mm Iron Schedule ft m Schedule Pipe No. 10 10S 0.049 0.19 1.24 0.28 STD 40 40S 0.068 0.24 1.73 0.37 XS 80 80S 0.095 0.31 2.41 0.47 STD XS

10 40 80

10S 40S 80S

0.065 0.088 0.119

STD XS

10 40 80

10S 40S 80S

0.065 0.091 0.126

5 10 40 80 160

5S 10S 40S 80S

0.065 0.083 0.109 0.147 0.188 0.294

5 10 40 80 160

5S 10S 40S 80S

0.065 0.083 0.113 0.154 0.219 0.308

5 10 40 80 160

5S 10S 40S 80S

0.065 0.109 0.133 0.179 0.250 0.358

5 10 40 80 160

5S 10S 40S 80S

0.065 0.109 0.140 0.191 0.250 0.382

5 10 40 80 160

5S 10S 40S 80S

0.065 0.109 0.145 0.200 0.281 0.400

STD XS XX

3/4

20

1.050

26.7

STD XS XX

1 25

1.315

33.4

STD XS XX

1-1/4

32

1.660

42.2

STD XS XX

1-1/2

40

1.900

48.3

STD XS XX

©2020 NCEES

286

1.65 2.24 3.02 1.65 2.31 3.20 1.65 2.11 2.77 3.73 4.78 7.47 1.65 2.11 2.87 3.91 5.56 7.82 1.65 2.77 3.38 4.55 6.35 9.09

0.33 0.43 0.54

1.65 2.77 3.56 4.85 6.35 9.70 1.65 2.77 3.68 5.08 7.14 10.15

1.11 1.81 2.27 3.00 3.77 5.22

0.42 0.57 0.74 0.54 0.67 0.85 1.09 1.31 1.72 0.69 0.86 1.13 1.48 1.95 2.44 0.87 1.41 1.68 2.17 2.85 3.66

1.28 2.09 2.72 3.63 4.86 6.41

Inside Diameter inches

mm

0.307 0.269 0.215

7.82 6.84 5.84 10.40 9.22 7.66 13.80 12.48 10.70 18.00 17.08 15.76 13.84 11.74 6.36 23.40 22.48 20.96 18.88 15.58 11.06 30.10 27.86 26.64 24.30 20.70 15.22

0.49 0.63 0.80 0.63 0.84 1.10 0.80 1.00 1.27 1.62 1.95 2.55 1.03 1.28 1.69 2.20 2.90 3.64 1.29 2.09 2.50 3.24 4.24 5.45

0.410 0.364 0.302

1.65 2.69 3.39 4.47 5.61 7.77 1.90 3.11 4.05 5.41 7.25 9.55

1.530 1.442 1.380 1.278 1.160 0.896

0.545 0.493 0.423 0.710 0.674 0.622 0.546 0.464 0.252 0.920 0.884 0.824 0.742 0.612 0.434 1.185 1.097 1.049 0.957 0.815 0.599

1.770 1.682 1.610 1.500 1.338 1.100

38.90 36.66 35.08 32.50 29.50 22.80 45.00 42.76 40.94 38.14 34.02 28.00

Chapter 6: Fluid Mechanics Pipe Dimensions and Weights (cont'd) Weights are based on carbon steel pipe

Pipe Size

OD

inches

inches

mm

2

50

mm

2.375

60.3

Identification Steel Iron Pipe

STD XS XX

2-1/2

65

2.875

73

STD XS XX

3 80

3.5 88.9

STD XS XX

3-1/2

90

4

100

4 101.6

4.5

114.3

STD XS XX

STD XS XX

4-1/2

115

5

125

5

127

5.563

141.3

STD XS XX

STD XS XX

©2020 NCEES

Wall Thickness

Stainless Steel Schedule

inches

mm

5S 10S 40S 80S

0.065 0.109 0.154 0.218 0.344 0.436

5 10 40 80 160

5S 10S 40S 80S

0.083 0.120 0.203 0.276 0.375 0.552

5 10 40 80 160

5S 10S 40S 80S

0.083 0.120 0.216 0.300 0.438 0.600

5 10 40 80

5S 10S 40S 80S

0.083 0.120 0.226 0.318 0.636

5 10 40 80 120 160

5S 10S 40S 80S

0.083 0.120 0.237 0.337 0.438 0.531 0.674

40 80

40S 80S

0.247 0.355 0.710

5 10 40 80 120 160

5S 10S 40S 80S

0.109 0.134 0.258 0.375 0.500 0.625 0.750

1.65 2.77 3.91 5.54 8.74 11.07 2.11 3.05 5.16 7.01 9.53 14.02 2.11 3.05 5.49 7.62 11.13 15.24 2.11 3.05 5.74 8.08 16.15 2.11 3.05 6.02 8.56 11.13 13.49 17.12 6.27 9.02 18.03 2.77 3.40 6.55 9.53 12.70 15.88 19.05

Schedule No. 5 10 40 80 160

287

Weight

lbm ft 1.61 2.64 3.66 5.03 7.47 9.04 2.48 3.53 5.80 7.67 10.02 13.71 3.03 4.34 7.58 10.26 14.34 18.6 3.48 4.98 9.12 12.52 22.87 3.92 5.62 10.8 15.00 19.02 22.53 27.57 12.55 17.63 32.56 6.36 7.78 14.63 20.80 27.06 32.99 38.59

Inside Diameter

kg m

inches

mm

2.39 3.93 5.44 7.48 11.11 13.44 3.69 5.26 8.63 11.41 14.92 20.39 4.52 6.46 11.29 15.27 21.35 27.68 5.18 7.41 13.57 18.64 34.03 5.84 8.37 16.08 22.32 28.32 33.54 41.03 18.67 26.24 48.45 9.46 11.56 21.77 30.97 40.28 49.12 57.43

2.245 2.157 2.067 1.939 1.687 1.503

57.00 54.76 52.48 49.22 42.82 38.16 68.78 66.90 62.68 58.98 53.94 44.96 84.68 82.80 77.92 73.66 66.64 58.42 97.38 95.50 90.12 85.44 69.30 110.08 108.20 102.26 97.18 92.04 87.32 80.06 114.46 108.96 90.94 135.76 134.50 128.20 122.24 115.90 109.54 103.20

2.709 2.635 2.469 2.323 2.125 1.771 3.334 3.260 3.068 2.900 2.624 2.300 3.834 3.760 3.548 3.364 2.728 4.334 4.260 4.026 3.826 3.624 3.438 3.152 4.506 4.290 3.580 5.345 5.295 5.047 4.813 4.563 4.313 4.063

Chapter 6: Fluid Mechanics Pipe Dimensions and Weights (cont'd) Weights are based on carbon steel pipe

Pipe Size

OD

inches

inches

mm

6

150

mm

6.625

168.3

Identification Steel Iron Pipe

STD XS XX

7

175

8

200

7.625

193.7

8.625

219.1

STD XS XX

STD XS

XX 9

225

10

250

9.625

244.5

10.75

273

XX 11

275

©2020 NCEES

11.75

298.5

STD XS XX

Stainless Steel Schedule

Weight

Inside Diameter

inches

mm

lbm ft

kg m

inches

mm

5S 10S 40S 80S

0.109 0.134 0.280 0.432 0.562 0.719 0.864

7.59 9.30 18.99 28.60 36.43 45.39 53.21

40S 80S

0.301 0.500 0.875

5 10 20 30 40 60 80 100 120 140

5S 10S

0.109 0.148 0.250 0.277 0.322 0.406 0.500 0.594 0.719 0.812 0.875 0.906

11.31 13.83 28.26 42.56 54.21 67.57 79.22 35.10 56.69 94.00 14.78 19.97 33.32 36.82 42.55 53.09 64.64 75.92 90.44 100.93 107.93 111.27 50.54 72.60 121.85 22.61 27.78 41.76 51.01 60.29 81.53 95.98 114.71 133.01 155.10 172.27 67.91 89.51 151.46

6.407 6.357 6.065 5.761 5.501 5.187 4.897

40

2.77 3.40 7.11 10.97 14.27 18.26 21.95 7.65 12.70 22.23 2.77 3.76 6.35 7.04 8.18 10.31 12.70 15.09 18.26 20.62 22.23 23.01 8.69 12.70 22.23 3.40 4.19 6.35 7.80 9.27 12.70 15.09 18.26 21.44 25.40 28.58 9.53 12.70 22.23

162.76 161.50 154.08 146.36 139.76 131.78 124.40 178.40 168.30 149.24 213.56 211.58 206.40 205.02 202.74 198.48 193.70 188.92 182.58 177.86 174.64 173.08 227.12 219.10 200.04 266.20 264.62 260.30 257.40 254.46 247.60 242.82 236.48 230.12 222.20 215.84 279.44 273.10 254.04

Schedule No. 5 10 40 80 120 160

40S 80S

160

STD XS XX

STD XS

Wall Thickness

5 10 20 30 40 60 80 100 120 140 160

40S 80S

0.342 0.500 0.875

5S 10S

0.134 0.165 0.250 0.307 0.365 0.500 0.594 0.719 0.844 1.000 1.125

40S 80S

40S 80S

0.375 0.500 0.875

288

23.57 38.08 63.14 9.92 13.41 22.38 24.72 28.58 35.67 43.43 51.00 60.77 67.82 72.49 74.76 33.94 48.77 81.85 15.21 18.67 28.06 34.27 40.52 54.79 64.49 77.10 89.38 104.23 115.75 45.60 60.13 101.72

7.023 6.625 5.875 8.407 8.329 8.125 8.071 7.981 7.813 7.625 7.437 7.187 7.001 6.875 6.813 8.941 8.625 7.875 10.482 10.420 10.250 10.136 10.020 9.750 9.562 9.312 9.062 8.750 8.500 11.000 10.750 10.000

Chapter 6: Fluid Mechanics Pipe Dimensions and Weights (cont'd) Weights are based on carbon steel pipe

Pipe Size

OD

inches

inches

mm

mm

Identification Steel Iron Pipe

STD 12 300

12.75 323.8

XS

XX

STD 14 350

16 400

©2020 NCEES

14 355.6

16 406.4

XS

STD XS

Schedule No.

20 30 40 60 80 100 120 140 160 10 20 30 40 60 80 100 120 140 160 10 20 30 40 60 80 100 120 140 160

Wall Thickness

Stainless Steel Schedule 5S 10S 40S 80S

10S 40S 80S

10S 40S 80S

Weight

Inside Diameter

inches

mm

lbm ft

kg m

inches

mm

0.156 0.180 0.250 0.330 0.375 0.406 0.500 0.562 0.688 0.844 1.000 1.125 1.312

3.96 4.57 6.35 8.38 9.53 10.31 12.70 14.27 17.48 21.44 25.40 28.58 33.32 4.78 6.35 7.92 9.53 11.13 12.70 15.09 19.05 23.83 27.79 31.75 35.71 4.78 6.35 7.92 9.53 12.70 16.66 21.44 26.19 30.96 36.53 40.49

21.00 24.19 33.41 43.81 49.61 53.57 65.48 73.22 88.71 107.42 125.61 139.81 160.42

31.24 35.98 49.71 65.19 73.86 79.71 97.44 108.93 132.05 159.87 186.92 208.08 238.69 41.36 54.69 67.91 81.33 94.55 107.40 126.72 158.11 194.98 224.66 253.58 281.72 47.34 62.65 77.83 93.27 123.31 160.13 203.54 245.57 286.66 333.21 365.38

12.438 12.390 12.250 12.090 12.000 11.938 11.750 11.626 11.374 11.062 10.750 10.500 10.126

315.88 314.66 311.10 307.04 304.74 303.18 298.40 295.26 288.84 280.92 273.00 266.64 257.16 346.04 342.90 339.76 336.54 333.34 330.20 325.42 317.50 307.94 300.02 292.10 284.18 396.84 393.70 390.56 387.34 381.00 373.08 363.52 354.02 344.48 333.34 325.42

0.188 0.250 0.312 0.375 0.438 0.500 0.594 0.750 0.938 1.094 1.250 1.406 0.188 0.250 0.312 0.375 0.500 0.656 0.844 1.031 1.219 1.438 1.594

289

27.76 36.75 45.65 54.62 63.50 72.16 85.13 106.23 130.98 150.93 170.37 189.29 31.78 42.09 52.32 62.64 82.85 107.60 136.74 164.98 192.61 223.85 245.48

13.624 13.500 13.376 13.250 13.124 13.000 12.812 12.500 12.124 11.812 11.500 11.188 15.624 15.500 15.376 15.250 15.000 14.688 14.312 13.938 13.562 13.124 12.812

Chapter 6: Fluid Mechanics Pipe Dimensions and Weights (cont'd) Weights are based on carbon steel pipe

Pipe Size

OD

inches

inches

mm

mm

Identification Steel Iron Pipe

STD 18

450

18

XS

457

STD XS 20 500

22 550

20 508

22 559

STD XS

STD XS 24 600

©2020 NCEES

24 610

Schedule No. 10 20 30 40 60 80 100 120 140 160 10 20 30 40 60 80 100 120 140 160 10 20 30 60 80 100 120 140 160 10 20 30 40 60 80 100 120 140 160

Wall Thickness

Stainless Steel Schedule 10S 40S 80S

10S 40S 80S

10S 40S 80S

10S 40S 80S

Weight

Inside Diameter

inches

mm

lbm ft

kg m

inches

mm

0.188 0.250 0.312 0.375 0.438 0.500 0.562 0.750 0.938 1.156 1.375 1.562 1.781

4.78 6.35 7.92 9.53 11.13 12.70 14.27 19.05 23.83 29.36 34.93 39.67 45.24 5.54 6.35 9.53 12.70 15.09 20.62 26.19 32.54 38.10 44.45 50.01 5.54 6.35 9.53 12.70 22.23 28.58 34.93 41.28 47.63 53.98 6.35 9.53 12.7 14.27 17.48 24.61 30.96 38.89 46.02 52.37 59.54

35.80 47.44 58.99 70.65 82.23 93.54 104.76 138.30 171.08 208.15 244.37 274.48 308.79

53.31 70.57 87.71 105.17 122.38 139.16 155.81 205.75 254.57 309.64 363.58 408.28 459.39 68.61 78.56 117.15 155.13 183.43 247.84 311.19 381.55 441.52 508.15 564.85 75.55 86.55 129.14 171.10 294.27 373.85 451.45 527.05 600.67 672.30 94.53 141.12 187.07 209.65 255.43 355.28 442.11 547.74 640.07 720.19 808.27

17.624 17.500 17.376 17.250 17.124 17.000 16.876 16.500 16.124 15.688 15.250 14.876 14.438

447.44 444.30 441.16 437.94 434.74 431.60 428.46 418.90 409.34 398.28 387.14 377.66 366.52 496.92 495.30 488.94 482.60 477.82 466.76 455.62 442.92 431.80 419.10 407.98 547.92 546.30 539.94 533.60 514.54 501.84 489.14 476.44 463.74 451.04 597.30 590.94 584.60 581.46 575.04 560.78 548.08 532.22 517.96 505.26 490.92

0.218 0.250 0.375 0.500 0.594 0.812 1.031 1.281 1.500 1.750 1.969 0.218 0.250 0.375 0.500 0.875 1.125 1.375 1.625 1.875 2.125 0.250 0.375 0.500 0.562 0.688 0.969 1.219 1.531 1.812 2.062 2.344 290

46.10 52.78 78.67 104.23 123.23 166.56 209.06 256.34 296.65 341.41 379.53 50.76 58.13 86.69 114.92 197.60 251.05 303.16 353.94 403.38 451.49 63.47 94.71 125.61 140.81 171.45 238.57 296.86 367.74 429.79 483.57 542.64

19.564 19.500 19.250 19.000 18.812 18.376 17.938 17.438 17.000 16.500 16.062 21.564 21.500 21.250 21.000 20.250 19.750 19.250 18.750 18.250 17.750 23.500 23.250 23.000 22.876 22.624 22.062 21.562 20.938 20.376 19.876 19.312

Chapter 6: Fluid Mechanics Pipe Dimensions and Weights (cont'd) Weights are based on carbon steel pipe

Pipe Size

OD

inches

inches

26

26

mm

mm

Identification Steel Iron Pipe

650

660

STD XS

28

28

STD

30 762

STD XS

700

30 750

32 800

711

32 813

34 850

34 864

36

36

900

914

42 1050 48 1200

42 1067 48 1219

©2020 NCEES

STD XS

STD XS

STD XS

Schedule No. 10 20 10 20 30 10 20 30 10 20 30 40 10 20 30 40 10 20

Wall Thickness

Stainless Steel Schedule 40S 80S 40S

10S 40S 80S

40S 80S

40S 80S

40S 80S

inches

mm

0.312 0.375 0.500

7.92 9.53 12.70 7.92 9.53 12.70 15.88 7.92 9.53 12.70 15.88 7.92 9.53 12.70 15.88 17.48 7.92 9.53 12.70 15.88 17.48 7.92 9.53 12.70 9.53 12.70 9.53 12.70

0.312 0.375 0.500 0.625 0.312 0.375 0.500 0.625 0.312 0.375 0.500 0.625 0.688 0.312 0.375 0.500 0.625 0.688 0.312 0.375 0.500

30 60

0.375 0.500

30 60

0.375 0.500

291

Weight

Inside Diameter

lbm ft

kg m

inches

mm

85.68 102.72 136.30

127.36 152.88 202.74 137.32 164.86 218.71 272.23 147.29 176.85 234.68 292.2 157.25 188.83 250.65 312.17 342.94 167.21 200.82 266.63 332.14 364.92 176.97 212.57 282.29 248.53 330.21 284.25 377.81

25.376 25.250 25.000

644.16 640.94 634.60 695.16 691.94 685.60 679.24 746.16 742.94 736.60 730.24 797.16 793.94 787.60 781.24 778.04 848.16 844.94 838.60 832.24 829.04 898.16 894.94 888.60 1047.94 1041.60 1199.94 1193.60

92.35 110.74 146.99 182.90 99.02 118.76 157.68 196.26 105.69 126.78 168.37 209.62 230.29 112.36 134.79 179.06 222.99 245.00 119.03 142.81 189.75 166.86 221.82 190.92 253.89

27.376 27.250 27.000 26.750 29.376 29.250 29.000 28.750 31.376 31.250 31.000 30.750 30.624 33.376 33.250 33.000 32.750 32.624 35.376 35.250 35.00 41.250 41.000 47.250 47.000

Chapter 6: Fluid Mechanics Tubing Sizes (U.S.) Size OD (inches) (inches) 1/4 3/8 1/2 5/8 3/4 7/8 1 1.050 1-1/8 1-1/4 1-5/16 1-3/8 1-1/2 1-5/8 1.660 1-3/4 1-7/8 1.900 2 2-1/4 2-3/8 2-1/2 2-7/8 3 3-1/8 3-1/2 3-3/4 4 4-1/2 5 6-1/4

©2020 NCEES

0.2500 0.3750 0.5000 0.6250 0.7500 0.8750 1.0000 1.0500 1.1250 1.2500 1.3125 1.3750 1.5000 1.6250 1.6600 1.7500 1.8750 1.9000 2.0000 2.2500 2.3750 2.5000 2.8750 3.0000 3.1250 3.5000 3.7500 4.0000 4.5000 5.0000 6.2500

24ga

22ga

20ga

18ga

0.022 0.206 0.331

0.028 0.194 0.319 0.444

0.035

0.049

0.430 0.555 0.680 0.805 0.930 0.980 1.055 1.180 1.243 1.305 1.430 1.555 1.590 1.680 1.805 1.830 1.930

0.402 0.527 0.652 0.777 0.902 0.952 1.027 1.152 1.215 1.277 1.402 1.527 1.562 1.652 1.777 1.802 1.902 2.152 2.277 2.402 2.902

Gauge (nominal inches) 16ga 14ga 12ga 11ga Inside Diameter (inches) 0.062 0.083 0.109 0.120

0.376 0.501 0.626 0.751 0.876 0.926 1.001 1.126 1.189 1.251 1.376 1.501 1.536 1.626 1.751 1.776 1.876 2.126 2.251 2.376 2.751 2.876 3.001 3.376

292

0.334 0.459 0.584 0.709 0.834 0.884 0.959 1.084 1.147 1.209 1.334 1.459 1.494 1.584 1.709 1.734 1.834 2.084 2.209 2.334 2.709 2.834 2.959 3.334 3.584 3.834 4.334 4.834

0.532 0.657 0.782 0.832 0.907 1.032 1.095 1.157 1.282 1.407 1.442 1.532 1.657 1.682 1.782 2.032 2.157 2.282 2.657 2.782 2.907 3.282 3.532 3.782 4.282 4.782

0.510 0.635 0.760 0.810 0.885 1.010 1.073 1.135 1.260 1.385 1.420 1.510 1.635 1.660 1.760 2.010 2.135 2.260 2.635 2.760 2.885 3.260 3.510 3.760 4.260 4.760 6.010

9ga

7ga

1/4"

3/8"

0.148

0.180

0.250

0.375

4.000 4.500 5.750

5.500

1.364 1.454 1.579 1.604 1.704 1.954 2.079 2.204 2.579 2.704 2.829 3.204 3.454 3.704 4.204 4.704

1.640 2.015 2.140 2.515 2.640 2.765 3.140 3.390 3.640 4.140 4.640 5.890

Chapter 6: Fluid Mechanics Tubing Sizes (Metric) Size

OD (mm)

1/4" 3/8" 1/2" 5/8" 3/4" 7/8" 1" 1.050" 1-1/8" 1-1/4" 1-5/16" 1-3/8" 1-1/2" 1-5/8" 1.660" 1-3/4" 1-7/8" 1.900" 2" 2-1/4" 2-3/8" 2-1/2" 2-7/8" 3" 3-1/8" 3-1/2" 3-3/4" 4" 4-1/2" 5"

6.4 9.5 12.7 15.9 19.1 22.2 25.4 26.7 28.6 31.8 33.4 35.0 38.1 41.3 42.2 44.5 47.7 48.3 50.8 57.2 60.4 63.5 73.1 76.2 79.4 88.9 95.3 101.6 114.3 127.0

6-1/4"

158.8

©2020 NCEES

24ga

22ga

20ga

18ga

0.600 5.2 8.3

0.700 5.0 8.1 11.3

0.900

1.300

10.9 14.1 17.3 20.4 23.6 24.9 26.8 30.0 31.6 33.2 36.3 39.5 40.4 42.7 45.9 46.5 49.0

10.1 13.3 16.5 19.6 22.8 24.1 26.0 29.2 30.8 32.4 35.5 38.7 39.6 41.9 45.1 45.7 48.2 54.6 57.8 60.9 73.6

Gauge (nominal mm) 16ga 14ga 12ga 11ga Inside Diameter (mm) 1.600 2.100 2.800 3.100

9.5 12.7 15.9 19.0 22.2 23.5 25.4 28.6 30.2 31.8 34.9 38.1 39.0 41.3 44.5 45.1 47.6 54.0 57.2 60.3 69.9 73.0 76.2 85.7

8.5 11.7 14.9 18.0 21.2 22.5 24.4 27.6 29.2 30.8 33.9 37.1 38.0 40.3 43.5 44.1 46.6 53.0 56.2 59.3 68.9 72.0 75.2 84.7 91.1 97.4 110.1 122.8

13.5 16.6 19.8 21.1 23.0 26.2 27.8 29.4 32.5 35.7 36.6 38.9 42.1 42.7 45.2 51.6 54.8 57.9 67.5 70.6 73.8 83.3 89.7 96.0 108.7 121.4

12.9 16.0 19.2 20.5 22.4 25.6 27.2 28.8 31.9 35.1 36.0 38.3 41.5 42.1 44.6 51.0 54.2 57.3 66.9 70.0 73.2 82.7 89.1 95.4 108.1 120.8 152.6

293

9ga

7ga

1/4"

3/8"

3.800

4.600

6.400

9.600

34.6 36.9 40.1 40.7 43.2 49.6 52.8 55.9 65.5 68.6 71.8 81.3 87.7 94.0 106.7 119.4

41.6 51.2 54.3 63.9 67.0 70.2 79.7 86.1 92.4 105.1 117.8

101.5 114.2

149.6

146.0

139.6

7 MASS TRANSFER 7.1 Symbols and Definitions Symbols Symbol

Description

A

Area

A

Absorption factor

Units (U.S.) ft2

or

Units (SI) m2

in2

dimensionless

ft ft 3

m2 m3

lb mole hr lb mole ft 3

mol s mol m3

Heat capacity

Btu lbm -cF

Distillate flow rate

lb mole hr

J = m2 kg : K s 2 : K mol s

DAB

Mass diffusivity (diffusion coefficient)

D, d E

Diameter

ft 2 hr ft or in.

m2 s m

F

Feed flow

f f

Ratio of vapor-phase flow to feed flow (fraction vaporized)

dimensionless

Darcy friction factor

dimensionless

f

Fugacity of a pure component

lbf in 2

= Pa

kg N = 2 m m : s2

fti

Fugacity of a component i in a mixture

lbf in 2

= Pa

kg N = m2 m : s2

a

Effective interfacial mass-transfer area per unit volume

B

Bottom product flow rate

c

Concentration

cp D

©2020 NCEES

2

dimensionless

Efficiency

mol s

lb mole hr

294

Chapter 7: Mass Transfer

Symbols (cont'd) Symbol

Description

G

Gas flow rate (stripper/absorber)

GS

Gas flow rate, solute-free basis

Units (U.S.)

Units (SI)

lb mole hr lb mole hr ft sec 2 Btu lb mole

mol s

g

Gravitational acceleration

gt

Molar Gibbs free energy

H

Henry's Law constant

lbf in 2

Heat input

Btu hr

mol s m s2 J mol kg N = m2 m : s2

= Pa

h h

Height

ft or in.

Head loss, pressure drop

ft or in.

2 J kg : m W= s= 3 s m m

h

Specific enthalpy

Btu lbm

J = m2 kg s 2

ht

Molar specific enthalpy

Btu lb mole

J mol

Dh

Specific enthalpy change

Btu lbm

J = m2 kg s 2

Dhvap

Latent heat of vaporization

Btu lbm

J = m2 kg s 2

HTU

Height of a transfer unit

ft or in.

m

DH

j

Colburn Factor

jA

Molar flux of component A per area

K

Distribution coefficient for phase equilibrium

L

Liquid flow (for a flash, in a column, stripper, or absorber)

LS

Liquid flow rate, solute-free basis

l

Length, distance

m m m

Mass

dimensionless

lb mole ft 2- hr

mol m2 : s dimensionless

lb mole hr lb mole hr ft or in.

mol s

lbm

kg

mol s m

General phase equilibrium coefficient

dimensionless

Slope of the operating line or slope of the equilibrium line

dimensionless

lbm lb mole

kg mol

MW

Molecular weight

N n

Number of stages Number of moles

lb mole

mol

no

Molar flow per area, molar flux

lb mole ft 2- hr

mol m2 : s

NTU P ©2020 NCEES

dimensionless

Number of transfer units

lbf in 2

Pressure 295

dimensionless

= Pa

kg N = 2 m m : s2

Chapter 7: Mass Transfer

Symbols (cont'd) Symbol

Description

Units (U.S.)

lbf in 2

Units (SI)

kg N = m2 m : s2

Pc

Critical pressure

Pr

Reduced pressure

P*

Three-phase equilibrium pressure

lbf in 2

Partial pressure

lbf in 2

kg N = m2 m : s2 kg = N = Pa m2 m : s2

psat

Saturation pressure, or vapor pressure

lbf in 2

= Pa

/

Poynting correction factor

dimensionless

q

Ratio of liquid-phase flow to feed flow

dimensionless

Qo

Heat duty

q

Ratio of liquid-phase flow to feed flow (fraction not vaporized)

dimensionless

R

Reflux ratio

dimensionless

R

Universal gas constant

S

Boil-up ratio

S T Tc Tr

Stripping factor

u

Velocity

V

Volume

V

p

= Pa dimensionless

Btu hr

= Pa

kg N = m2 m : s2

2 J kg : m W= s= 3 s

Btu J mol : K lb mole -cR dimensionless dimensionless

Temperature

°R or °F

K or °C

Critical temperature

°R or °F

K or °C dimensionless

Reduced temperature

m s

ft sec ft3

m3

Vapor flow (for a flash, in a column, stripper, or absorber)

lb mole hr

mol s

vt

Molar volume

ft 3 lb mole

m3 mol

v

Specific volume

ft 3 lbm

m3 kg

ft 3 lb mole

m3 mol

Dv

Specific volume change during phase change

X x Y y Z z z

Mole ratio in liquid phase (solute-free basis)

dimensionless

Mole fraction in liquid phase

dimensionless

Mole ratio in vapor phase (solute-free basis)

dimensionless

Mole fraction in vapor phase

dimensionless

Compressibility factor

dimensionless

Mole fraction in the feed

dimensionless

a ©2020 NCEES

Distance or length

ft or in.

m

ft ft 3

m2 m3

2

Interfacial area per unit volume 296

Chapter 7: Mass Transfer

Symbols (cont'd) Symbol

Description

Units (U.S.)

aij

Relative volatility for components i and j

dimensionless

d

Film thickness

g

Activity coefficient

g

Surface tension, interfacial tension

e

Void fraction

m

Dynamic viscosity

r

Density

zi

Fugacity coefficient i of a pure component in the vapor phase

dimensionless

zt i

Fugacity coefficient i of a component in a mixture in the vapor phase

dimensionless

zd

Volume fraction of the dispersed phase (holdup)

dimensionless

ft or in.

N kg m = s2

lbf in. dimensionless

Diffusion Fick's Law of Diffusion: Molar Flux dc j A = − D AB dzA

Mass transport due to diffusion and bulk flow:

dx no A = no x A + j A = (no A + no B) x A − c D AB dzA dx no B = no x B + j B = (no A + no B) x B − c D BA dzB where

no A = molar flux of species A no = bulk flow

©2020 NCEES

m dimensionless

7.2 Fundamentals of Mass Transfer 7.2.1

Units (SI)

297

lbm cP or ft -sec

kg Pa : s = m : s

lbm ft 3

kg m3

Chapter 7: Mass Transfer Rules of Thumb for Diffusion Coefficients at 25°C

In Gases Air Hydrogen Carbon dioxide In Liquids Gases in water Acids in water Organics in water Organic solvents

ft 2 m D AB c sec

D AB c ms m

0.43 × 10–4 – 2.4 × 10–4 1.8 × 10–4 – 8.1 × 10–4 0.32 × 10–4 – 1.7 × 10–4

0.4 × 10–5 – 2.2 × 10–5 1.7 × 10–5 – 7.5 × 10–5 0.3 × 10–5 – 1.6 × 10–5

0.75 × 10–8 – 2.2 × 10–8 1.3 × 10–8 – 3.2 × 10–8 0.43 × 10–8 – 1.5 × 10–8 1.6 × 10–8 – 3.2 × 10–8

0.7 × 10–9 – 2.0 × 10–9 1.2 × 10–9 – 3.0 × 10–9 0.4 × 10–9 – 1.5 × 10–9 1.5 × 10–9 – 3.0 × 10–9

2

Diffusion Coefficient (Pressure and Temperature Dependence) For dilute, binary gas systems, changes in the diffusion coefficient can be predicted at any temperature and at any pressure below 25 atm by:

P T 2 XD _T1 i DAB _T2, P2 i = DAB _T1, P1 ie P1 oe T2 o 2 1 XD _T2 i 3

where

DAB(T, P) = diffusion coefficient as a function of pressure and temperature ΩD(T) = the "collision integral" for molecular diffusion, which is a dimensionless function of temperature and of the intermolecular potential field for one molecule of A and one molecule of B.

Collision Integral for Diffusion as a Function of Dimensionless Temperature

Collision integral, ΩD

3.0 2.5 2.0 1.5 1.0 0.5 0.0

0.0

2.0

4.0

6.0

8.0

10.0

Dimensionless temperature, kT/εAB

Source: Fundamentals of Momentum, Heat, and Mass Transfer, James R. Welty, Gregory L. Rorrer, and David G. Foster. Copyright © 2015 John Wiley & Sons, Inc. Reproduced with permission of John Wiley & Sons, Inc. where

k

= Boltzmann constant

εAB = Leonard-Jones force constant ©2020 NCEES

298

Chapter 7: Mass Transfer Integrated Fick's Law

Steady-state equimolar counterdiffusion of two components (No bulk flow, DAB = DBA, ideal gas):

no A =

D AB c D AB (c A − c A, i) = (x A − x A, i) d d

For an ideal gas:

no A =

D P D AB (p − p A, i) = AB (y A − y A, i) d RT A d RT

where i = conditions at the interface d = film thickness Steady-state diffusion of A through a stagnant film ( no B = 0 )

no A =

c D AB 1−x ln f − A p 1 x A, i d

where

xA,i = concentration of A at the interface xA = concentration of A at distance z from the interface Concentration profile:

1−x 1−x z ln f − A p = ln f − A, b p 1 x A, i d 1 x A, i

where

xA,b = concentration of A in the bulk fluid z

= distance from the interface

For an ideal gas:

no A = ylm =

D AB P D P y A, i − y A 1−y ln f − A p = AB ylm 1 y A, i d RT d RT `1 − y A j − `1 − y A, i j

ln where

`1 − y A j

`1 − y A,i j

, p lm =

` P − p A j − ` P − p A, i j

ln

` P − pAj

` P − p A,i j

ylm = logarithmic mean of the mole fractions in the gas phase and at the interface plm = logarithmic mean of the partial pressures in the gas phase and at the interface For diffusion of one component through a multicomponent mixture, the equation above with an effective diffusion coefficient can be used:

D A, mix =

©2020 NCEES

1 − yA yj j ! A D Aj

/

299

Chapter 7: Mass Transfer

7.2.2

Mass-Transfer Coefficients Definitions of the Mass-Transfer Coefficient System

Equimolar counter-diffusion, liquid

Equimolar counter-diffusion, ideal gas

Diffusion through a stagnant film, liquid

Diffusion through a stagnant film, ideal gas Diffusion through a stagnant film, ideal gas, mass-basis where

clm =

Mole Fraction

Concentration

no A = k x Dx A c D AB kx = d no A = k y Dy A D P k y = AB d RT no A = k xl Dx A c D AB k xl = d clm = no A k yl Dy A D AB P k yl = d RT ylm = mo A k yl Dy A D P MWA k yl = AB d RT ylm

no A = kc Dc A D kc = AB d no A = kc Dc A D kc = AB d no A = kcl Dc A D kcl = AB d clm = no A kc Dc A D kc = AB d clm

c Ao − c A c −c ln cAo − c Ai A Ai

kc = mass-transfer coefficient for liquid (concentration basis) kG = mass-transfer coefficient for gas (pressure basis) kx = mass-transfer coefficient for liquid (mole fraction basis) ky = mass-transfer coefficient for gas (mole fraction basis) kc' = mass-transfer coefficient for liquid (concentration basis), corrected for inert component kG' = mass-transfer coefficient for gas (concentration basis), corrected for inert component kx' = mass-transfer coefficient for liquid (mole fraction basis), corrected for inert component ky' = mass-transfer coefficient for gas (mole fraction basis), corrected for inert component

©2020 NCEES

300

Pressure

no A = kG Dp A D kG = AB d RT

no A = kGl Dp A D AB kG l = d RT plm

Chapter 7: Mass Transfer

7.2.3

Convective Mass Transfer

Reynolds analogy between momentum, heat, and mass transfer with Colburn correction:

jM =

2/3 kG n dt D n Gl AB

2/3

c n h jH = c G d p n k p M

For flow through straight tubes and across plane surfaces:

f = j= jM H 8 For turbulent flow around cylinders:

f jM = jH # 8 where

f

= Darcy friction factor

GM = mass flux in

kg lbm or 2 ft 2 - hr m :s

G' = molar flux Btu W or 2 hr - ft 2 - o F m :K jH = Colburn heat-transfer factor h = heat-transfer coefficient in

jM = Colburn mass-transfer factor k = thermal conductivity in

W Btu or m : K hr - ft - o F

kG = gas-phase mass-transfer coefficient

©2020 NCEES

301

Chapter 7: Mass Transfer Other correlations for the mass-transfer coefficient:

Mass Transfer1 for Simple Situations Fluid Motion Inside circular pipes

Range of Conditions

Re = 4000–60,000 Sc = 0.6–3000 Re = 10,000–400,000 Sc > 100 Transfer begins at leading edge Rex < 50,000

Rex = 5 × 105–3 × 107 Unconfined flow parallel to Pr = 0.7–380 flat plates2 Rex = 2 × Pr = 0.7–380

104–5

×

105

Equation

Re–0.17

jM = 0.023 Sh = 0.023 Re0.83 Sc1/3 jM = 0.0149 Re–0.12 Sh = 0.0149 Re0.88 Sc1/3 jM = 0.664 Rex–0.5 0.25

Pr Nu = 0.037 Re x0.8 Pr 00.43 e Pr0 o i

Between above equation and 0.25

Pr Nu = 0.0027 Re x Pr 00.43 e Pr0 o i

Confined gas flow parallel to a flat plate in a duct Liquid film in wetted-wall tower, transfer between liquid and gas

Perpendicular to single cylinders

Ree = 2600–22,000

jM = 0.11 Ree–0.29

4C = 0–1200 n

See note 4.

ripples suppressed

4C = 1300–8300 n Re = 400–25,000 Sc = 0.6–2.6 Rel = 0.1–105 Pr = 0.7–1500

1.506

− Sh = (1.76 # 10 5) c 4nC m

Sc 0.5

kG P 0.56 = 0.281 ^ Relh0.4 Sc Gl Nu = 80.35 + 0.34 ^ Relh0.5 + 0.15 ^ Relh0.58B Pr 0.3

Sh = Sh0 + 0.347 _ Rell Sc 0.5 i

0.62

Past single spheres

Through fixed beds of pellets3

Rell Sc 0.5 = 1.8–600,000 Sc = 0.6–3200

Sh0 = *

2.0 + 0.569 (GrM Sc) 0.250 2.0 + 0.0254 (GrM Sc) 0.333 Sc 0.244

Rell = 90–4000 Sc = 0.6

−0.575 2.06 j M = j H = f ^ Rellh

Rell = 5000–10,300 Sc = 0.6

−0.815 20.4 j M = 0.95j H = f ^ Rellh

Rell =0.0016–55 Sc = 168–70,600

−2/3 1.09 j M = f ^ Rellh

Rell = 5–1500 Sc = 168–70,600

jM =

GrM Sc < 10 8 4 GrM Sc 2 10 8

0.250 ^ Rellh−0.31 f

1. Average mass-transfer coefficients throughout, for constant solute concentrations at the phase surface. Generally, fluid properties are evaluated at the average conditions between the phase surface and the bulk fluid. The heatmass-transfer analogy is valid throughout. 2. Mass-transfer data for this case scatter badly but are reasonably well represented by setting jM = jH.

©2020 NCEES

302

Chapter 7: Mass Transfer

3. For fixed beds, the relation between e and dp is a = volume of bed. For mixed sizes:

6 ^1–f h d p , where a is the specific solid surface, surface per

n



dp =

/ ni d pi3

i=1 n

/ ni d pi2

i=1

4. For small rates of flow or long contact times:

k L, av d = D AB Shav . 3.41

For large Reynold numbers of short contact times: 1



6D C 2 kl, av = e AB o rtdl



2 3 d Shav = c 2r l Re Sc m

1

Total absorption rate from the average kL:

ur y d N A, av = l `crA, l − c A0 j = k L, av `c A, i − crA jM



`c A, i − crA jM =

where

a



cA,i = concentration of A at the interface



cA0 = concentration of A at the approach, or initial, value



cA



c A , l = bulk-average concentration of A across length l



DAB = molecular diffusivity of A in B

dc

©2020 NCEES

`c A, i − c A0 j − `c A, i − crA, l j RS V SS `c A, i − c A0 j WWW W ln SS SS`c A, i − crA, l jWWW T X

= specific surface of a fixed bed of pellets, pellet surface/volume of bed

= bulk-average concentration of A

= diameter of a cylinder



de

= equivalent diameter of a noncircular duct = 4 (cross-sectional area)/perimeter



dp

= diameter of a sphere; for a nonspherical particle, diameter of a sphere of the same surface as the particle



GrM = Grashof number for mass transfer



k



kl,av = average mass-transfer coefficient across length l



l



NA,av = average mass-transfer flux of A at, and relative to, a phase boundary

gl 3 Dt t 2 t dn n

= mass-transfer coefficient

= length

303

Chapter 7: Mass Transfer ni



= a number, dimensionless

hd

Nu

= Nusselt number k



Pr

= Prandtl number k



Pr0 = Prandtl number at the approach, or initial, value



Pri

= Prandtl number at the interface



Re

= Reynolds number

cp n

dG lG n or n

d G Re' = Reynolds number for flow outside a cylinder cn dp G Re'' = Reynolds number for flow past a sphere n d G Ree = Reynolds number for flow in a noncircular duct en xG Rex = Reynolds number with x as the length dimension n n Sc = Schmidt number t D AB



kl



Sh



Sh0 = Sherwood number at the approach, or initial, value



Shi = Sherwood number at the interface



u y = bulk average velocity in the y direction (parallel to the direction of flow)



C

= mass flow rate per unit width



d

= thickness of a layer



e

= void fraction

= Sherwood number D AB

Source: Republished with permission of McGraw-Hill, from Mass Transfer Operations, Robert Treybal, 3rd ed., New York,1987; permission conveyed through Copyright Clearance Center, Inc.

7.2.4

Mass Transfer Between Phases for Dilute Systems no A = k L (x − xi) = kG (yi − y) = k lL (c − ci) = k lG (pi − p)

LIQUID PHASE

INTERFACE

= lL tr L and kG k lG P k L k= yi − y k L k lL tr L Ll HTUG = = = x − xi kG k lG P Gl HTU L

x

where

G'

= molar flux (gas phase)

HTUG = height of a transfer unit based on vapor-phase resistance i = subscript meaning concentration at interface

©2020 NCEES

yi y

HTUL = height of a transfer unit based on liquid-phase resistance

kL

xi

VAPOR PHASE T, ptot

= liquid-phase mass-transfer coefficient (mole fraction basis) 304

CONCENTRATION OF X APPROACHING THE INTERFACE

CONCENTRATION OF Y APPROACHING THE INTERFACE

Chapter 7: Mass Transfer k lL = liquid-phase mass-transfer coefficient (concentration basis) kG

= gas-phase mass-transfer coefficient (mole fraction basis)

k lG

= gas-phase mass-transfer coefficient (partial pressure basis)

L'

= molar flux (liquid phase)

pi

= partial pressure

tr L

= average molar density of liquid phase

In most types of separation equipment, the interfacial area for mass transfer cannot be accurately determined, and transfer coefficients based on volume of the device are used:

1 = 1 + m KG a kG a kL a

and

1 = 1 + 1 KL a m kG a kL a

where

a = effective interfacial mass-transfer area per unit volume, in

ft 2 m2 3 or ft m3

KG = overall gas-phase mass-transfer coefficient KL = overall liquid-phase mass-transfer coefficient m = slope of equilibrium line Overall Mass-Transfer Coefficients KL and KG for Dilute Systems no A = K L (x − x eq) = KG (y eq − y) where

xeq = liquid mole fraction in equilibrium with vapor phase yeq = vapor mole fraction in equilibrium with liquid phase

Overall Mass-Transfer Coefficients for Dilute Systems Equilibrium: y = m • x Use for:

7.2.5

Gas Phase

Liquid Phase

1 = 1 +m KG kG k L

1 = 1 + 1 K L m kG k L

High solubility, low m; gas-phase resistance is controlling

Mass Transfer Between Phases for Concentrated Systems no A =

ktL (x − xi) ktG (yi − y) Kt L (x − x eq) Kt G (y eq − y) = eq eq x BM = y BM = x BM y BM

x BM =

y BM =

©2020 NCEES

(1 − x) − (1 − xi) _1 − x i ln _1 − xi j (1 − y) − (1 − yi) `1 − y j ln `1 − yi j

eq = x BM

eq = y BM

(1 − x) − (1 − x eq) _1 − x i ln _1 − x eq i (1 − y) − (1 − y eq) `1 − y j ln `1 − y eq j 305

Low solubility, high m; liquid-phase resistance is controlling

Chapter 7: Mass Transfer = ktG k= k lG P y BM G y BM = ktL k= k lL tL x BM L x BM yi − y k L ktL y BM L M HTUG y BM = = = x − xi kG ktG x BM G M HTU L x BM where

ktG

= gas-phase mass-transfer coefficient for concentrated systems

Kt G

= overall gas-phase mass-transfer coefficient for concentrated systems

ktL

= liquid-phase mass-transfer coefficient for concentrated systems

Kt L

= overall liquid-phase mass-transfer coefficient for concentrated systems

x BM = logarithmic-mean solvent concentration between bulk and interface y BM = logarithmic-mean gas concentration between bulk and interface L'

= molar flux (liquid phase)

G' = molar flux (gas phase) HTUL = height of a transfer unit based on liquid-phase resistance HTUG = height of a transfer unit based on vapor-phase resistance tr L

= average molar density of liquid phase

Overall Mass-Transfer Coefficients Kt L and Kt G for Concentrated Systems eq 1 = y BM 1 + x BM 1 (y − yi) eq eq Kt G y BM ktG y BM ktL (x − xi) eq 1 = x BM 1 + y BM 1 (xi − x ) eq eq Kt L x BM ktL x BM ktG (yi − y)

7.2.6

Height of a Transfer Unit Gl Gl = HTUG k= G a y BM ktG a Ll Ll = HTU L k= t a x L BM kL a

©2020 NCEES

HTUOG =

Gl Gl = y BM mGl x BM eq = t eq HTU G + eq HTU L Ll y BM KG a y BM KG a y BM

HTUOL =

Ll Ll = x BM Ll y BM eq = t eq HTU L + eq HTU G l x BM mG x K L a x BM KL a BM

306

Chapter 7: Mass Transfer where

HTUG = height of a transfer unit based on vapor-phase resistance HTUOG = height of an overall vapor-phase mass-transfer unit HTUL = height of a transfer unit based on liquid-phase resistance HTUOL = height of an overall liquid-phase mass-transfer unit Height Equivalent to One Theoretical Plate (HETP) If equilibrium line and operating line are parallel c mG = 1 m , then: l

L

l

HETP = HTU If equilibrium line and operating line are straight, but not parallel, then:

HTUOG = HETP

7.2.7

mGl − 1 Ll l ln c mG m Ll

Mass Transfer with Reaction

Consider a reaction between a dissolving gas A and a liquid-phase reactant B, with q moles of B reacting per mole of A, so that:

nA + mB " Products m q= n where

q = number of moles of B reacting per mole of A CAL and CBL = molar concentrations of A and B, respectively, in the liquid The rate of reaction of A, JL, is then given by n m J L = k nm C AL C BL m+n−1

3 where knm = reaction velocity constant, in d m n

mol JL has units, moles/sec/unit volume of liquid. Alternatively, n m J = k nm C AL C BL fL

mol , n and m are the orders of reaction in A and B, and f L is the liquid s : m3 hold-up fraction. A "reaction time" tR can be defined as JL is the rate of reaction and has units of

tR =

(n + 1) ( n − 1) m 2k nm C AL C BL

The mass transfer of A in the liquid is given by * − C AL) J = k L a (C AL

©2020 NCEES

307

Chapter 7: Mass Transfer where

J

= reaction rate in moles/sec/unit volume of reactor

* = dissolved gas concentration in liquid bulk in C AL

m k L = interphase mass-transfer coefficient in s a

mol m3 1

= gas-liquid interphase surface area/unit dispersion volume in m

mol J is the rate of reaction and has units of . A mass-transfer "diffusion time," tD, can be defined as s : m3 D t D = AL k L2 where DAL = diffusivity of A in the liquid If a fast reaction is occurring near the interface within the "diffusion film," it will enhance the mass-transfer rate, and the equation for the mass transfer of A into liquid, above, becomes * − C AL) J = k L* a (C AL

k L* where

©2020 NCEES

* (n = = 2D AL k nm (C AL − C AL) n+1

− 1)

1

m 2 C BL G

m k L* = enhanced liquid-film mass-transfer coefficient in s

308

Chapter 7: Mass Transfer Various Gas-Liquid Reaction Regimes and Parameters of Importance Conditions

Important Variables

I Kinetic control

Rate

Slow reaction

\ \ \

tD t R 1 0.02

0.02 1

Rate

tD tR 1 2

Design so that

III Fast reaction

Rate

21

tD C BL t R 1 qC * AL

IV Very fast reaction

LIQUID FILM

BULK CBL

* CAL

21

a kL

\

* C AL

CAL

CBL

* CAL

\

CAL

a CBL

k nm

n+1 * c 2 m `C AL j

* CAL CAL

Independent of kL Independent of e L Rate

tD tR

\

a

CBL * CAL

depends on * k L k nm C AL C BL Independent of e L

V Instantaneous reaction

J \ kL a

m

\ \

\

* C BL + C AL

Reaction at interface; controlled by transfer of B to interface from bulk,

* `C BL j

\

* C BL 22 C AL

General case of III

* n `C AL j

Independent of knm Independent of e L (if e L is adequate)

D AL eL a 2 100 k L

Reaction in film, C AL . 0 (pseudo first order in A' )

eL knm

Independent of a (if a is adequate) Independent of kL

II Diffusion control Moderately fast reaction in bulk of liquid, C AL . 0

\

Concentration Profiles

GAS

Regime

Rate

\ \

a kL

* Independent of C AL Independent of knm Independent of e L

tD C BL t R 22 qC * AL

CAL

CBL

* CAL

CAL

Reprinted from Mixing in the Process Industries, 2nd ed., N. Harnby, M.F. Edwards, and A.W. Nienow, "Gas-Liquid Dispersion and Mixing," p. 352, © 1992, with permission from Elsevier.

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Chapter 7: Mass Transfer

7.3 Vapor-Liquid Separations 7.3.1

Batch Distillation

Rayleigh Equation

#n n

f

0

dn = nf = n ln n0

#x x

f

0

dx y−x

where

nf = moles in still at end of run n0 = initial moles in still xf = mole fraction in liquid phase at end of run x0 = initial mole fraction in liquid phase in still Relative Volatility Equation

where

c ym x a AB = − d1 y n 1−x aAB = relative volatility

y

= mole fraction of light component in vapor phase

Rearranging:

a x y = 1 + (a AB − 1) x AB

Therefore,

n n ln n A = a AB ln n B 0A

0B

where

nA = moles of liquid "A" left in the still at any time nB = moles of liquid "B" left in the still at any time 0

= time zero

aAB = relative volatility

Operating Line for Batch Distillation With Reflux RD x yn + 1 = R + x n + R D+ 1 D 1 D where

RD = reflux ratio based on the distillate rate x = liquid composition

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Chapter 7: Mass Transfer Batch Distillation Apparatus •

Batch Distillation Apparatus

QC

CONDENSER

N N-1

DISTILLATE ACCUMULATOR

N-2 1 2

COLUMN

3 REBOILER •

QR

7.3.2

Continuous Distillation

7.3.2.1 Theoretical Stage An ideal theoretical stage has the following characteristics: 1. It operates in steady state and has a liquid product and a vapor product. 2. All vapor and liquid entering the stage are intimately contacted and perfectly mixed. 3. Total vapor leaving the stage is in equilibrium with total liquid leaving the stage. For a single binary distillation stage, the following balances and equilibrium relationships apply. Overall mass balance:

Fn

Component mass balance:

(zn)

z n Fn + y n + 1 Vn + 1 + x n − 1 L n − 1 = y n Vn + x n L n

311

(xn–1)

(yn) STAGE n (yn+1) Vn+1

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Ln–1

Vn

Fn + Vn + 1 + L n − 1 = Vn + L n

(xn) Ln

ΔHn

Chapter 7: Mass Transfer Energy balance:

ht f, n Fn + ht V, n + 1 Vn + 1 + ht L, n − 1 L n − 1 + DH n = ht V, n Vn + ht L, n L n where

ht

= molar specific enthalpy

Fn

= feed flow to stage n

Vn

= vapor flow leaving stage n

Ln

= liquid flow leaving stage n

DH n = heat input to stage n

7.3.2.2 Constant Molal Overflow When the molar heats of vaporization of the components are nearly equal, the molar flow rates of the vapor and liquid are nearly constant in each section of the column. In the rectifying section, the following assumptions then apply:

= = L L= L1 L= and V V1 = Vn 0 n And in the stripping section, the following assumptions then apply:

= l L= L Lm N

and

l V= V= Vm N

where

L = liquid flow in the rectifying section V = vapor flow in the rectifying section Ll = liquid flow in the stripping section V l = vapor flow in the stripping section N = total number of stages m = stage in stripping section n = stage in rectifying section

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Chapter 7: Mass Transfer 7.3.2.3 Column Material Balance Stage Model for Distillation

CONDENSER STAGE 0

•

Qc

V1

RECTIFYING SECTION

L0

F zF

V1

L0

V2

L1

Vn

Ln-1

Vn+1

Ln

Vf

Lf-1

D XD

STAGE 1

STAGE n

STRIPPING SECTION

STAGE f (FEED)

Vf+1

Lf

VM

L M- 1

VM+1

LM

VN

LN-1

STAGE M

STAGE N

LN

VN+1

LN

•

QR

REBOILER STAGE N+1

B XB

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Chapter 7: Mass Transfer Overall mass balance:

F=D+B Component mass balance:

zF F = xD D + xB B Ratios:

D = zF − xB F xD − xB B = xD − zF F xD − xB For the rectifying section, the following balances apply:

D = V1 − L0 = Vn + 1 − L n x D D = y1 V1 − x0 L0 = y n + 1 Vn + 1 − x n L n For the stripping section, the following balances apply:

B = L N − 1 − VN = L m − Vm + 1 x B B = x N − 1 L N − 1 − y N VN = x m L m − y m + 1 Vm + 1

7.3.2.4 Graphical Solution for Binary Distillation (McCabe-Thiele Diagram) McCabe-Thiele Diagram for Binary Distillation With Constant Molal Overflow and Constant Relative Volatility 1

y1

x - INTERCEPT (y = 1) EQUILIBRIUM CURVE

xD E

A

y'

D

y = MOLE FRACTION IN VAPOR

y - INTERCEPT (x = 0)

C x'

yN+1

y=x

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STRIPPING OPERATING LINE

xB 0

q LINE

zF

yN B

0

RECTIFYING OPERATING LINE

xN x = MOLE FRACTION IN LIQUID

314

1

Chapter 7: Mass Transfer Equations for the McCabe-Thiele Diagram Name

Equations

Equilibrium Line

ax y = 1 + x (a − 1)

Operating Line for the Rectifying Section

x D x x D R L L L L yn + 1 = V xn + DV = L + D xn + L D+ D = R + 1 xn + R +D 1 = V xn + c1 − V m xD

A

Slope:

Operating Line for the Stripping Section

B

L= R V R+1

Reflux Ratio:

x L V−D R = D = D = y D −1 x=0 Ll xB xB B Ll − xB B = Ll S + 1 − xB = B = − = ym + 1 x x x − S xm S Ll − m Ll − Vl m Vl Ll − B m Ll − B B 1 B 1 Ll = ` − j + ` + − j x F − x B 1 f R 1 f x −x B D F x-Intercept (y = 1):

Slope:

Ll = S + 1 S Vl Feed Line

C

y-Intercept (x = 0): x x D y x = 0 = R +D 1 = L D+ D

Boil-up Ratio: l L xy = 1 − xB xB + B − 1 = V l = Ll − 1 = − S B B 1 xy = 1 xy=1 = Ll B − f 1 q z z y = f x + fF = q − 1 x − q −F 1

Feed Condition:

q = mole fraction liquid in feed mqlar enthalpy to cqnvert feed to saturated vapqr = molar enthalpy of vaporization f = mole fraction vapor in feed q+f=1 Slope:

f−1 q = − f q 1

Intercept: For z F $ `1 − f j

z z x y = 0 = 1 −Ff = qF

For z F # `1 − f j

yx = 1 = Intersection of Feed Line/ Operating Lines

D

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xI = e

zF + f − 1 q − zF = − f q 1

f ^R + 1h zF x − D o f R+1 1+R−f

` f − 1j ^R + 1h z z x y I = fF + e F − +D o 1 + R − f f R 1

315

Chapter 7: Mass Transfer Equations for the McCabe-Thiele Diagram (cont'd) Name Intersection of Feed Line/ Equilibrium Line

E

Equations For constant a: 2

af zF 1 1 H+ xl = − 2 > a − 1 + f − 1 − _a − 1 i ` f − 1 j

af zF 1 > 1 + zF − H − − − f 1 1 a 4 _a − 1 i ` f − 1 j _a − 1 i ` f − 1 j

f − 1 + zF o yl = xl e f f Operating Line for Total Reflux Operating Line for Minimum Reflux

y=x x − yl R min = Dl − l y x

Circled A, B, C, D, and E in table above refer to the previous graph, "Binary Distillation With Constant Molal Overflow."

7.3.2.5 Feed Conditions The feed condition is defined by

Ll = L + q F = L + `1 − f j F

V = V l + `1 − q j F = V l + f F

Feed Conditions Feed Condition Subcooled Liquid

Values for f and q

f1 cpL (Tb − TF) q = 1+ Dhvap

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L

316

Feed Line in McCabe-Thiele

Chapter 7: Mass Transfer Feed Conditions (cont'd) Feed Condition

Values for f and q

Flows at Feed Location

f=0

Bubble Point (Saturated Liquid)

q=1

L

V

L'

V'

F

0 8 ft) columns Extremely low-flow Capacity revamps where conditions; where efficiency and turndown can be leakage must be sacrificed; highly fouling and minimized corrosive services

Source: Republished with permission of McGraw-Hill, from Distillation Design, Henry Z. Kister, New York, 1992; permission conveyed through Copyright Clearance Center, Inc.

7.4.1.4 Hydraulic Model for Trays The Hydraulic Model for Trays TRAY ABOVE AN ADT

FROTH

hcl ADB

hw

AB LIQUID AND GAS

LIQUID WITH BUBBLES TRAY BELOW

Source: Republished with permission of McGraw-Hill, from Distillation Design, Henry Z. Kister, New York, 1992; permission conveyed through Copyright Clearance Center, Inc.

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Chapter 7: Mass Transfer Tray Area Definitions Tray Area Total tower crosssectional area

Symbol

AT

Definition The inside cross-section area of the empty tower without downcomers or trays Total cross-section area minus the area at top of the downcomer; also referred to as free area; represents smallest area available for vapor flow in the intertray spacing Total tower cross-section area minus total downcomer area, downcomer seal area, and any other nonperforated regions; also referred to as the active area (Aa); represents the area available to vapor flow near the tray floor

Net area

AN

Bubbling area

AB

Hole area

Ah

Slot area

AS

Total vertical curtain area for all valves through which vapor passes in a horizontal direction as it leaves the valves, based on the narrowest opening of the valves; smallest area available for vapor flow on a valve tray

Open slot area

ASo

Slot area when all valves are fully opened

Fractional hole area

Af

Downcomer top area

ADT

Area at top of downcomer

ADB

Area at bottom of downcomer

Downcomer bottom area

Total area of perforations on the tray; smallest area available for vapor passage

Ratio of hole area to bubbling area (in sieve trays) or slot area to bubbling area (in valve trays)

7.4.1.5 Definitions of Vapor Load Several different parameters are used for characterization of the vapor load.

ft 3

m3

The vapor load (Vload), in sec or s , is

Vload = CFS

tG tL − tG

where

CFS

ft 3

m3

= vapor flow rate at conditions, in sec or s

rL, rG = densities of the liquid and gas phases, respectively 0.5

ft The F-factor for gas loading, in sec d 3 n ft lbm

F = u tG

0.5 m kg or s e 3 o , is m

where u = superficial linear gas velocity

ft

m

The C-factor for gas loading, in sec or s , is

C=u

tG tL − tG

In practice, the F-factor and the C-factor may be based on bubbling area AB, net area AN, or some other area, depending on the source of data and correlations. Care must be taken to use the correct area basis, depending on the source. These terms are related as follows:

V = C = load A

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F tL − tG

329

Chapter 7: Mass Transfer 7.4.1.6 Definitions of Liquid Load gpm

m3

The tray liquid load QL, in in. or hr : m , is

Vo QL = L L W

where

gal m3 VoL = liquid volumetric flow rate, in min or s LW = outlet weir length, in inches or meters gpm ft m The downcomer liquid load QD, in 2 or sec or s , is ft VoL QD = A DT

7.4.1.7 Flow Regimes on Trays Flow Regimes

Cs, VAPOR LOAD / A, ft/ s

FLOODING

SPRAY FROTH EMULSION BUBBLE LIQUID FLOW RATE PER WEIR LENGTH

Source: Republished with permission of McGraw-Hill, from Distillation Design, Henry Z. Kister, New York, 1992; permission conveyed through Copyright Clearance Center, Inc. .

VAPOR FLOW RATE

ENTRAINMENT F LOODI NG

AREA OF SATISFACTORY OPERATION

INT

WEEP PO

EXCESSIVE WEEPING

ING FLOOD MER NCO DOW

E EN XCES TR SI AIN VE ME NT

Tray Performance Diagram

DUMP POINT

LIQUID FLOW RATE

Source: Republished with permission of McGraw-Hill, from Distillation Design, Henry Z. Kister, New York, 1992; permission conveyed through Copyright Clearance Center, Inc. ©2020 NCEES

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Chapter 7: Mass Transfer 7.4.1.8 Column Flooding Effect of Design Parameters on Flooding Design Parameters That Lower Flooding Point Low bubbling area Low fractional hole area (< 8%) Low tray spacing High weirs (> 4 in) Small weir length Small clearance under downcomer Small downcomer top area

Spray Entrainment Flooding X

Froth Entrainment Flooding X

Downcomer Backup Downcomer Choke Flooding Flooding X

X

X

X

X

X X X

X X X X X

Source: Republished with permission of McGraw-Hill, from Distillation Design, Henry Z. Kister, New York, 1992; permission conveyed through Copyright Clearance Center, Inc.

7.4.1.9 Entrainment Flooding The correlations for entrainment given below are based on C-factors, specifically the Souders and Brown constant

ft m CSB at the entrainment flood point, in sec or s . CSB, flood = uS, flood

tG tL − tG

where uS,flood = superficial gas velocity at the entrainment flood point

Fair's Entrainment Flooding Correlation ft m CSB at the entrainment flood point, in sec or s 0.5

0.2 t e −G o m CSB, flood = u N, flood c 20 c tL tG

where uN,flood = superficial gas velocity at the entrainment flood point based on the net area AN

γ

= surface tension, in dyne/cm

CSB,flood and uN,flood are based on the net area AN. The correlation is applicable to sieve trays, valve trays, and bubble cap trays. These restrictions apply: 1. System is nonfoaming or low-foaming. 2. Weir height is less than 15 percent of tray spacing. 3. Sieve-tray perforations are 13 mm (1/2 in.) or less in diameter. 4. Ratio of slot (bubble cap), perforation (sieve), or full valve opening (valve plate) area Ah to active area Aa is 0.1 or greater. Otherwise the value of uN,flood should be corrected using the following table:

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Chapter 7: Mass Transfer Ah Aa

uN,flood Correction Factor

0.10 0.08 0.06

1.00 0.90 0.80

0.7 0.6 0.5

PLATE SPACING 36"

0.4

24"

0.3

18" 12"

0.2

9" 6"

CSB, flood = uN, flood

20 0.2 γ

ρG ρL – ρG

0.5

, ft/sec

Fair's Entrainment Flooding Correlation

0.1 0.07 0.06 0.05 0.04 0.03

0.01

0.02

0.03

0.05

0.07

0.1

L FLV = _ G

0.2 ρG

0.3

0.5

0.7

1.0

2.0

0.5

ρL

Source: Republished with permission of McGraw-Hill, from Distillation Design, Henry Z. Kister, New York, 1992; permission conveyed through Copyright Clearance Center, Inc.

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Chapter 7: Mass Transfer 7.4.1.10 Downcomer Backup Flooding The downcomer backup is determined by a pressure balance for the downcomer:

hdc = ht + hw + how + hhg + hda where

hdc = height of clear liquid in downcomer, in inches liquid or mm liquid ht = total tray pressure drop, in inches liquid or mm liquid hw = height of weir at tray outlet, in inches liquid or mm liquid how = height of liquid crest over weir, in inches liquid or mm liquid hhg = liquid hydraulic gradient across tray, in inches liquid or mm liquid hda = head loss due to liquid flow under downcomer apron, in inches liquid or mm liquid The height of aerated liquid in the downcomer is determined by:

hldc = where

hdc z dc

hldc = height of aerated liquid froth in downcomer, in inches froth or mm froth z dc = relative froth density (froth density to liquid density) To prevent downcomer backup flooding, the following criterion must be met:

hldc 1 S + h W where

S = tray spacing, in inches or millimeters

Downcomer Choke Flooding Glitsch Correlation The maximum clear liquid velocity at the downcomer entrance to avoid downcomer choke flooding is the lowest of the three following correlations: `QD, max j1 = 250 SF

`QD, max j2 = 41 tL − tG SF

where

`QD, max j3 = 7.5 S `tL − tG j SF

S

= tray spacing, in inches or millimeters

SF

= derating factor

QD,max = maximum downcomer liquid load, in

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gpm ft m or sec or s ft 2

333

Chapter 7: Mass Transfer Generalized Criteria for Maximum Downcomer Velocity

Maximum Downcomer Velocities ft

Foaming Tendency Low Medium High

Clear Liquid Velocity in Downcomer, sec 18-in. 24-in. 30-in. Spacing Spacing Spacing

Example Low-pressure (< 100 psia) light hydrocarbons, stabilizers, air-water simulators Oil systems, crude oil distillation, absorbers, midpressure (100–300 psia) hydrocarbons Amines, glycerine, glycols, high-pressure (> 300 psia) light hydrocarbons

0.4–0.5

0.5–0.6

0.6–0.7

0.3–0.4

0.4–0.5

0.5–0.6

0.2–0.25

0.2–0.25

0.2–0.3

Source: From H.Z. Kister, Distillation Operation, Copyright © 1990, McGraw-Hill, Inc. As shown in Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992; permission conveyed through Copyright Clearance Center, Inc.

System Factors

Capacity Discount Factors for Foaming Systems System Type Nonfoaming Fluorine systems Moderate foaming Heavy foaming Severe foaming

Examples Freon, BF3 Oil absorbers, amine, and glycol regenerators Amine and glycol absorbers MEK units

Foam-stable

Caustic regenerators

Factor 1.00 0.90 0.85 0.73 0.60 0.30

Source: Copyright ©2008. From Albright's Chemical Engineering Handbook by Lyle F. Albright. Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa plc.

7.4.1.11 Tray Hydraulic Parameters

Hydraulic Parameters

h ow

h hg h t + h w + h ow + h da + h hg

hw 1

h d + h w + h ow + –2 h hg h da 1 β ( h w + h ow ) + –2 h hg

SIEVE TRAY h hg P 2

h ow

hw

P1 P1 – P2 = h d

Source: Republished with permission of McGraw-Hill, Inc., from Perry's Chemical Engineers' Handbook, 8th ed., Don W. Green and Robert H. Perry, New York, 2008; permission conveyed through Copyright Clearance Center, Inc. ©2020 NCEES

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Chapter 7: Mass Transfer where

hd = dry tray pressure drop, in inches liquid or mm liquid hda = head loss due to liquid flow under downcomer apron, in inches liquid or mm liquid hhg = liquid hydraulic gradient across tray, in inches liquid or mm liquid how = height of liquid crest over weir, in inches liquid or mm liquid ht = total tray pressure drop, in inches liquid or mm liquid hw = height of weir at tray outlet, in inches liquid or mm liquid b = tray aeration factor in pressure drop equation, dimensionless

7.4.1.12 Tray Pressure Drop The total pressure drop across a tray, ht:

ht = hd + hl where hl = pressure drop through the aerated liquid on the tray, in inches liquid or mm liquid

7.4.1.13 Efficiency The point efficiency is the ratio of the change of composition at a point to the change that would occur on a theoretical stage:

EOG = f

yn − yn − 1 p eq y n − yn − 1 po int

The Murphree tray efficiency applies to an entire tray instead of to a single point on a tray:

EMV = f

yn − yn − 1 p y neq − yn − 1 tray

Overall column efficiency:

N EOC = Nt a The overall column efficiency is related to the Murphree efficiency by:

EOC =

ln 81 + EMV _m − 1 iB ln m

V with m = m L

where

EOC = overall column efficiency EOG = point efficiency for a tray EMV = Murphree tray efficiency Nt = number of theoretical stages in a column Na = number of actual stages in a column y neq = vapor mole fraction in equilibrium with the liquid l ©2020 NCEES

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Chapter 7: Mass Transfer

7.4.2

Packed Columns

7.4.2.1 Primary Packing Design Parameters • Type of tower separation • Packing height • Packing type and packing factors • Tower pressure drop • Flooding velocity calculation

7.4.2.2 Absorption and Stripping Gas Absorption With Countercurrent Flow Gi , YAi

Li , XAi h=h PACKING

dh G, YA

L, XA h=o Go , YAo Lo , XAo

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Chapter 7: Mass Transfer Operating Line Above Equilibrium Line BOTTOM OF TOWER YAo

PINCH POINT SLOPE = L G MIN

YA

EQUILIBRIUM LINE (SLOPE = m) OPERATING LINE SLOPE = L G

YAi

XAo

(YAo / m) = ( XAo ) MAX

XA where

G = mass velocity of gas phase L = mass velocity of liquid phase XA = mass ratio A in liquid phase YA = mass ratio A in gas phase h = height of packing i

= dilute end

o = rich end

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Chapter 7: Mass Transfer Desorption or Stripping With Countercurrent Flow Go , YAo

Lo , XAo h=h PACKING

dh G, YA

L, XA h=o Gi , YA i L i , XA i

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Chapter 7: Mass Transfer Operating Line Below Equilibrium Line Y eq(XAo) EQUILIBRIUM LINE YAo (MAX)

YAo

OPERATING LINE FOR MINIMUM GAS FLOW SLOPE = L G MAX

PINCH POINT

YA

TOP OF TOWER

OPERATING LINE

YAi

XAi

XAo XA

Gas Absorption With Concurrent Flow Go, YAo

Lo, XAo h=h

dh L, XA

G, YA

h=o Gi , YAi Li , XAi

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Chapter 7: Mass Transfer Absorption Operation With Concurrent Flow TOP OF TOWER YAo

YA

OPERATING LINE SLOPE = – L G

YAi (YAi ) MAX

–

L G MIN

EQUILIBRIUM LINE

XAo

XAi XA

Desorption or Stripping With Concurrent Flow Go, YAo

Li , XAi

h=h

dh

h=o Gi , YAi Lo, XAo

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Chapter 7: Mass Transfer Desorption or Stripping Operation With Concurrent Flow

EQUILIBRIUM LINE

YA

YAo OPERATING LINE

– YAi

L G

MIN

(YAi ) MAX

XAi

XA

7.4.2.3 Mass-Transfer Coefficients NA = ky (yA – yAs) NA = kx (xAs – xA) NA = Kx (xA* – xA) NA = Ky (yA – yA*) where

NA

= molar flux of A

kx, ky

= individual mass-transfer coefficients

Kx, Ky = overall mass-transfer coefficients xAs, yAs = solute mole fraction at interface in liquid and gas phase, respectively xA*

= mole fraction of solute in the liquid phase at equilibrium

yA*

= mole fraction of solute in the gas phase at equilibrium

(NA)AVG Ai = (ky)AVG (yA – yAs) Ai where Ai = total interfacial area

Ai =a A h

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XAo

Chapter 7: Mass Transfer where

a = interfacial area per unit volume, in ft2 A = cross-sectional area, in ft2 h = height of packing, in ft

7.4.2.4 Packing Design Operating Line The equation for the operating line is

Go y Ao − Gy A = Lo x Ao − Lx A

1 L y A = G x A + G (Gy Ao − Lo x Ao)

or

Packing Height of Transfer Unit The height of packing is

yAo (1 − y ) dy h = HG #yAi (1 − y )A(ylm − yA ) A A As

and

h = nG HG

where

nG = number of gas-phase transfer units lm = log mean The number of gas-phase transfer units is yAo (1 − y ) dy nG = #yAi (1 − y )A(ylm − yA ) A A As

where

(1 − yA) lm =

(1 − yA) + (1 − yAs) as an approximation 2

For dilute solutions, assume L, G, and slope m are constant.

mG mG HOG = HG + L HL = L HOL where HOG and HOL = height of overall transfer units in gas and liquid phases, respectively

L = mG A = absorption factor, which ranges from 1.0 to 1.4 1 = A S = stripping factor Hl m= P where P = absolute pressure

H l = Henry's constant

HOL HOG = A nOG =

©2020 NCEES

yAo − yAi ` yA − y A* jlm

and

nOL =

xAo − xAi ` x A* − xA jlm 342

Chapter 7: Mass Transfer

where

` yA −

y A* jlm

` yA − y A* jo − ` yA − y A* ji = RS V SS` yA − y A* jo WWW W ln SS SS ` yA − y A* ji WWW T X

and similarly for ` x A* − xA jlm For dilute solutions:

nOL =

x Ao − x Ai ` x A − x A* jlm

Packing HETP For gas absorption: h = nOG HOG For gas stripping: h = nOL HOL Also, h = NTP HETP where

NTP

= number of theoretical plates

HETP = height of an equivalent theoretical plate JK N SRS WVW KK y − H xAi OOO SS W Ao p O H G WW HG OO + p L W ln SSSd1 − p L nKKK WW KK y − H xAi OO SS WW Ai p S L P NTP = T X pL ln H G H L = = A m m p G 1= H G = S A pL RS JK SS K SSc − 1 m KK xAo − ln S 1 S K KK x − SS Ai S L NTP = T ln (S)

pL A= HG

VW yAi NOO WW m OO + 1 WW yAi OO S WW WW m O P X

where

A = absorption factor S = stripping factor Note: For absorption and stripping, calculations for tower height are the same, although the operating line slope will differ.

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Chapter 7: Mass Transfer Height of Packing = = h NTU NTUOL HTUOL = NT HETP OG HTUOG where HETP

= height equivalent of a theoretical stage

HTUOG = height of an overall vapor-phase mass-transfer unit HTUOL = height of an overall liquid-phase mass-transfer unit NTUOG = overall number of transfer units based on gas phase NTUOL = overall number of transfer units based on liquid phase NT

= number of theoretical stages

h

= height of packing

Height of Overall Transfer Unit G HOG = K a (1 −s y ) y A lm where

(1 − yA) lm =

(1 − y A* ) − (1 − yA) 1 − y* ln f − A p 1 yA

L HOL = K a (1 −s x ) x A lm where

(1 − xA) lm =

(1 − xA) − (1 − x A* ) 1 − xA p ln f 1 − x A*

Number of Gas-Phase Transfer Units nOG =

#y y

A0

A1

`1 − yA jlm

* `1 − yA j ` yA − y A j

dyA

Using the log-mean average:

1−y nOG = 0.5 ln 1 − yAi + Ao

#y y

Ao

Ai

dyA ` yA − y A* j

In dilute solutions:

nOG =

yAo − yAi ` yA − y A* jlm

* jlm = where ` yA − y A

©2020 NCEES

` yA − y A* jbottom − ` yA − y A* jtop

ln

` yA − y A* jbottom ` yA − y A* jtop

344

Chapter 7: Mass Transfer Number of Liquid-Phase Transfer Units nOL =

#x x

Ao

Ai

_1 − xA ilm

_1 − xA i ` x A* − xA j

1−x nOL = 0.5 ln 1 − xAo + Ai

#x x

Ao

Ai

dxA

dxA x A* − xA

Absorption With Reaction Dissolved solute reacts with solvent in liquid phase if irreversible reaction:

y nOG = ln yAo Ai

7.4.2.5 Correlations for Mass-Transfer Coefficients For insoluble gases that do not react chemically with the liquid: 0.5

h

n 1 G H x = a d n x n e t Dx o x x vx where

Hx = individual liquid-phase HTU Gx = mass velocity of liquid mx = viscosity of liquid

Dvx = diffusivity of liquid rx = liquid density a and h = constants given in the table below

Values of a and h in Equations1 for Various Packing Materials at 77°F Packing Type Rings

Saddles

Tile

Packing Size (in.) 2

a 80

h 0.22

1.5

90

0.22

1

100

0.22

0.5

280

0.35

0.375 1.5

550 160

0.46 0.28

1

170

0.28

0.5 3

150 110

0.28 0.28

1. All quantities in equations must be expressed in fps units if these values of a are used. Source: McCabe, W.L., and J.C. Smith, Unit Operations of Chemical Engineering, 3rd ed., New York: McGraw-Hill, 1976. ©2020 NCEES

345

Chapter 7: Mass Transfer The temperature effect of liquids on the HTU can be evaluated as:

H x = H xo e

−0.013 (T − To)

where

Hx = HTU at T °F Hxo = HTU at To °F T

= final temperature in °F

To = initial temperature in °F Henry's Law: y* = m x

y x* = m

where

m = Henry's Law Constant/Total Pressure

7.4.2.6 Packing Factors Selection of packing is based primarily on packing factors and avoidance of flooding.

Packing Factors (ft–1) PACKING FACTORS** (WET AND DUMP PACKED)

NOMINAL PACKING SIZE (INCHES)

TYPE OF PACKING

MAT’L.

SUPER INTALOX

CERAMIC

60

30

SUPER INTALOX

PLASTIC

33

21

16

INTALOX SADDLES

CERAMIC

40

22

18

15

HY-PAK RINGS

¼

725

⅜

330

½

¾

⅝

200

145

METAL

1

1¼

98

1½

52

42

2

3

3½

PALL RINGS

PLASTIC

97

52

40

25

16

PALL RINGS

METAL

70

48

28

20

16

170

110

65

45

125

95

65

37

110

83

57

32

BERL SADDLES

CERAMIC

900

RASCHIG RINGS

CERAMIC

1600

1000

580

380

255

155

RASCHIG RINGS 1/32” WALL

METAL

700

390

300

170

155

115

RASCHIG RINGS 1/16” WALL

METAL

410

290

220

137

EXTRAPOLATED

1/8” WALL

1/32” WALL

3/16” WALL

1/16” WALL

1/4” WALL

3/32” WALL

3/8” WALL

240

3

F

OBTAINED IN 16" AND 30" I.D. TOWER

DATA BY LEVA

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001). ©2020 NCEES

346

Chapter 7: Mass Transfer Packing Factors: Stacked Packings & Grids

1000 800 600

SINGLE SINGLESPIRAL SPIRALRINGS RINGS(

PACKING FACTOR– F

400

200

CHECKER BRICK, 55% FREE SPACE

DIAMOND PITCH SQUARE PITCH DIAMOND PITCH SQUARE PITCH

CROSS PARTITION

GRID TILE (CERAMIC)

1/4'' WALL 3/16'' WALL

RASCHIG RINGS (CERAMIC)

CROSS PARTITION RINGS (SQUARE PITCH) 5/16'' WALL

RASCHIG RINGS

100 80

(CERAMIC)

1'' x 1'' x 1/4''

60

1'' x 2'' x 1/4''

40

3/8'' WALL

11/2'' x 11/2'' x 3/16''

RASCHIG RINGS

(METAL 1/8'' WALL)

2'' x 2'' x 3/8''

WOO

METAL GRID

20

D GR

(1'' x 1'' x 1/16'')

10

2''

1''

IDS

4'' x 4'' x 1/2''

3''

4''

NOMINAL PACKING SIZE – INCHES

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).

Packing Factors: Screen Packing & Random Dumped Packing

1000 800

STEDMAN

600

PACKING FACTOR– F

400

200 100 80

CANNON

QUARTZ ROCK 2'' SIZE GOODLOE CROSS PARTITION RINGS

60 40

TELLERETTES

20 10

PANAPAK

MAS PAC FN-200

FROM MANUFACTURERS DATA EXCEPT AS NOTED 2'' 3'' 1'' NOMINAL PACKING SIZE - INCHES

MAS PAC FN-90 4''

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001). ©2020 NCEES

347

Chapter 7: Mass Transfer 7.4.2.7 Flooding and Pressure Drop Generalized Pressure Drop Correlation

0.60

GENERALIZED PRESSURE DROP CORRELATION

0.40

G 2 F µ 0.1 ρG ( ρL ρG ) g

0.20

FLOODIN

G LINE

0.10

1.50 1.50 1.00

.060

0.50

.040 .020

PARAMETER OF CURVES IS PRESSURE PARAMETER OF CURVES IS PRESSURE DROP IN INCHES OF WATER/FOOT OF DROP IN INCHES OF WATER/FOOT PACKED HEIGHT

0.25 0.10

.010 .006 .004

0.05

.002 .001 .01

.02

.04 .06

0.1

L G

0.2

ρG

ρL ρG

0.4 0.6

1.0

2.0

4.0 6.0 10.0

1 2

lbm L = LIQUID RATE, sec-ft2 G = GAS RATE, lbm 2 sec-ft lbm ρL = LIQUID DENSITY, ft3 ρG = GAS DENSITY, lbm3 ft F = PACKING FACTOR µ = VISCOSITY OF LIQUID, cP g = GRAVITATIONAL ACCELERATION

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001). Determination of column diameter D:

D=

©2020 NCEES

G c 4 m d A n where GA = actual gas flow rate of the packed column r G

348

Chapter 7: Mass Transfer Pressure Drop Versus Gas Rate

5/8 RASCHIG RINGS (METAL) (1/32" WALL) COLUMN DIA. = 15 in. PACKING HEIGHT = 5.1 ft.

L=

0.6

F = 190

L=

0.4

DRY

1.0 0.8

L= 12, 000 15,00 0 L L = = 10,0 L= 80,000 00 00 20,00 000 L = 40,000 00 L = 6 0,00000

L=

30 ,00 0 25 , 00 20 ,00 0 0

2.0

L=

∆P~INCHES WATER / FT. PACKING

4.0

0.2

0.1

100

2

3

lbm LIQUID RATE AS PARAMETER ft2-hr

4 500

1000

AIR MASS VELOCITY,

2000

5000

lbm ft2-hr

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).

1/4-in. INTALOX SADDLES (CERAMIC) COLUMN DIA. = 8 in. PACKING HEIGHT = 4.4 ft.

2.0

0.4

50,00 L = 000 3,000 L = 000 1 L = 0,00000 100 DR Y

10,0 0

0.6

L=

0

1.0 0.8

L=

∆P~INCHES WATER / FT. PACKING

4.0

F = 725

0.2

0.1

LIQUID RATE lbs./ft lbm 2,hr. LIQUID RATE R AS PARAMETER AS PARAMETE ft2-hr 20

40

60

80 100

200

AIR MASS VELOCITY,

400

600

1000

lbm ft2-hr

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).

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Chapter 7: Mass Transfer Pressure Drop Versus Gas Rate (cont'd) 3/8 INTALOX SADDLES (PORCELAIN)

1.0

60,000 00

0.6 0.4

L= 50,00 30,00 000 0 0 1,000 0 DR 000 L = Y L = 5 20,00000 00

L=8

,000000

0.8

8 in. COLUMN DIA. = 8'' 4.4 ft PACKING HEIGHT = 4.4' F =330 330 F= lbm LIQUID RATE AS PARAMETER ft2-hr

L=

L=

L=

∆P~INCHES WATER / FT. PACKING

2.0

0.2

0.1

50

100

200

300

500

AIR MASS VELOCITY,

1000

2000

lbm ft2-hr

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).

4.

COLUMN DIA. = 30 in. PACKING HEIGHT = 10 ft. NO.2 HY-PAK (METAL)

60 ,00 L= 0 50 ,00 0 L= 40 ,00 0 L= 30, 000 L= 20, 000 L= 10,0 L= 5,0000 00 0 DRY 0

1. 0.8 0.6

L=

∆P~INCHES WATER / FT. PACKING

2.

0.4

0.2

0.1

FF==18 18

lbm LIQUID RATE AS PARAMETER ft2-hr 100

2

3

4 500

1000

AIR MASS VELOCITY,

2000

5000

lbm ft2-hr

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).

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350

Chapter 7: Mass Transfer Pressure Drop Versus Gas Rate (cont'd)

4.0

3" X 3" CROSS PARTITION RINGS – DUMPED (CERAMIC)

35 ,0 30 00 L= ,00 L = 25,0 0 0 L = 20,0 0 15, 00 L = 000 12 L = ,000 90,000 L = 00 6,0000 00 L=4 5,50000 L=1 ,550000 DR Y

1.0 0.8 0.6

L=

0.4

L=

∆P~INCHES WATER / FT. PACKING

2.0

F = 78

0.2

lbm LIQUID RATE AS PARAMETER ft2-hr 0.1 100

2

3

1000

4 500

AIR MASS VELOCITY,

2000 lbm ft2-hr

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).

4.0

COLUMN DIA. = 16 in. PACKING HEIGHT = 6.0 ft. COCURRENT FLOW CO-CURRENT FLOW

0.4

L= L = 70,0 00 L 60 L = = 50 ,00 0 , 40 000 L = ,000 30 ,00 L= 0 20 L = ,000 1 DR 0,000 YL INE

∆P~INCHES WATER / FT. PACKING

2.0

2 in. RASCHIG RINGS (CARBON STEEL)

0.2

F = 57

1.0 0.6

0.1 100

lbm LIQUID RATE AS PARAMETER ft2-hr 2

3

4 5

1000

AIR MASS VELOCITY,

2000

5000

lbm ft2-hr

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).

©2020 NCEES

351

Chapter 7: Mass Transfer Pressure Drop Versus Gas Rate (cont'd) 1-1/2" INTALOX SADDLES (PORCELAIN) 1-1/2-in. COLUMN DIA. = 16 in. PACKING HEIGHT = 6.2 ft. "COCURRENT CO-CURRENT"FLOW FLOW

000 80, 000 70, 0 L= ,00 60 00 = L ,0 50 L= 00 0,0 4 L=

2.0

1.0

30 ,00 0

0.6

20, 000 10, 000 DR Y L=5 ,00000 0

L=

0.4

L=

L=

L=

∆P~INCHES WATER / FT. PACKING

4.0

lbm LIQUID RATE AS PARAMETER ft2-hr

0.2

0.1

100

2

3

4 500

1000

2000

5000

10,000

lbm

AIR MASS VELOCITY,

ft2-hr

Source: Eckert, Foote, Nemunaitis, and Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).

COLUMN DIA. = 16 in. PACKING HEIGHT = 6.0 ftft. CO-CURRENTFLOW FLOW COCURRENT

00

0,0

6 L=

1.0

L= 0.6

L= L = 20,00 DR 10,00 0 YL 0 INE

∆P~INCHES WATER / FT. PACKING

2.0

1 in. INTALOX SADDLES (POLYPROPYLENE)

50 L= ,00 40 ,00 0 L= 0 30 ,00 0

4.0

0.4

F = 57

0.2

LIQUID RATE AS PARAMETER 0.1 100

2

3

4 5

1000

AIR MASS VELOCITY,

2000

lbm ft2-hr 5000

lbm ft2-hr

Source: Eckert, Foote, Nemunaitis, and Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).

©2020 NCEES

352

Chapter 7: Mass Transfer Pressure Drop Versus Gas Rate (cont'd) 2 in. INTALOX SADDLES (POLYPROPYLENE)

COLUMN DIA. = 16 in. PACKING HEIGHT = 6.0 ft. COCURRENT CO-CURRENTFLOW FLOW

2.0

L L =1 L = = 90 00,0 L 80 ,00 00 L = = 70 ,000 0 L = 60 ,00 L = 50, ,000 0 L = 40, 000 L = 30,0 000 L 20 00 DR= 10, 0,000 Y L 00 INE

∆P~INCHES WATER / FT. PACKING

4.0

1.0 0.6 0.4

0.2

0.1

F = 21 LIQUID RATE AS PARAMETER

100

2

3

4 5

1000

AIR MASS VELOCITY,

2000

lbm ft2-hr

5000

lbm ft2-hr

Source: Eckert, Foote, Nemunaitis, and Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).

1-1/2 1-1/2-in. in. PALL PALL RINGS RINGS (CARBON (CARBON STEEL) STEEL)

4.0 COLUMN DIA. = 16 in. PACKING HEIGHT = 6.0 ft. COCURRENT FLOW

0 ,00 70 00 = L 0,0 6 L=

L=

50 ,00 0 4 0,0 L= 00 30 ,00 L= 0 20, 0 00 L= 10, 000 DRY LIN E

1.0 0.6

L=

∆P~INCHES WATER / FT. PACKING

2.0

0.4

0.2

0.1 100

FF=28 = 28

2 LIQUID ,- HR. LIQUIDRATE RATELBS./FT.lbm AS PARAMETER ft2-hr AS PARAMETER

2

3

4

5

1000

2000

5000

lbm AIR MASS VELOCITY, 2 ft -hr

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).

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353

Chapter 7: Mass Transfer Pressure Drop Versus Gas Rate (cont'd) 2 in. PALL RINGS (POLYPROPYLENE) COLUMN DIA. = 16 in. PACKING HEIGHT = 5.6 ft. "CO-CURRENT" FLOW COCURRENT FLOW

2.0

1.0

50 ,00 L= 0 40 ,00 L= 0 30 , L = 000 20, L = 000 10, 000

0.6

DRY

0 ,00 120 = L 00 0 , 110 0 00 L = 0,00 0,0 0 8 1 L = 000 L = , 90 L= 0 ,00 0 70 = ,00 L 60 = L

0.4

L=

∆P~INCHES WATER / FT. PACKING

4.0

0.2

0.1 100

2

3

LIQUID RATE LBS./FT.2, HR. AS PARAMETER lbm LIQUID RATE 2 AS PARAMETER ft -hr

4

500

1000

AIR MASS VELOCITY,

2000

5000

10,000

lbm ft2-hr

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).

7.5 Liquid-Liquid Extraction 7.5.1

Fundamentals of Liquid-Liquid Extraction

7.5.1.1 Partition Ratio The equilibrium partition ratio in mole fraction units is

yi c iraffinate o K= i x= i c iextract

where yi = mole fraction of solute i in the extract phase xi = mole fraction of solute i in the raffinate phase gi = activity coefficient of solute i in the indicated phase The equilibrium partition ratio in mass ratio units Kil is

Yil = Kil = Xil

e

extract m solute

mextraction solvent

e

raffinate m solute

m raffinate solvent

o

o

where

Yi l = ratio of mass solute i to mass extract solvent in extract phase Xil = ratio of mass solute i to mass raffinate (feed) solvent in raffinate phase kg lbm m = mass flow rate, in hr or s ©2020 NCEES

354

Chapter 7: Mass Transfer The advantage of using the solute-free basis is that the feed solvent and extraction solvent flows do not change during the extraction.

7.5.1.2 Extraction Factor On a McCabe-Thiele type of diagram, E is the slope of the equilibrium line divided by the slope of the operating

F

line S .

S E i = mi F

where

E i = extraction factor mi = local slope of the equilibrium line

kg lbm S = mass flow rate of the solvent phase, in hr or s kg lbm F = mass flow rate of the feed phase, in hr or s For dilute systems with straight equilibrium lines, the slope of the equilibrium line is equal to the partition ratio:

mi = Kil

7.5.1.3 Separation Factor The separation factor indicates the relative enrichment of a given component in the extract phase after one theoretical stage of extraction.

Yl Yl f il p f ilp Y j extract Xi Kl = = i a ijl = l l l K Yj X j f il p f p X j raffinate X jl where

a ijl = separation factor for solute i with respect to solute j (mass ratio basis)

7.5.1.4 Interfacial Mass Transfer no = k y (yint − y) no = k x (xint − x)

no = koy (y * − y) no = kox (x − x *)

where

no = molar flow per area xint = mole fraction of solute i in the raffinate phase at the interface x* = mole fraction of solute i in the raffinate phase in equilibrium with the extract phase yint = mole faction solute i in the extract phase at the interface y* = mole fraction of solute i in the extract phase in equilibrium with the raffinate phase NTUG =

©2020 NCEES

#y y s

e

(1 − y)1m dy (1 − y) (yint − y)

355

Chapter 7: Mass Transfer For dilute solutions:

NTUOL =

x f − xr (x − x *)1m

where

xf

= mole fraction of solute i in the feed

xr

= mole fraction of solute i in the raffinate

NTUG = number of transfer units based on gas phase NTUOL = number of transfer units based on liquid phase (

7.5.2

)lm = log mean

Theoretical (Equilibrium) Stage Calculations Countercurrent Extraction Cascade F 'X f FEED STAGE

E 'Ye or Y1 1

X1

Y2 2

X n–1

Yn n

Xn

Y n+1

r –1

X r–1 RAFFINATE STAGE

Yr r

R'X r

S' Ys

Source: Republished with permission of McGraw-Hill, Inc., from Perry's Chemical Engineers' Handbook, 8th ed., Don W. Green and Robert H. Perry, New York, 2008; permission conveyed through Copyright Clearance Center, Inc.

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356

Chapter 7: Mass Transfer 7.5.2.1 McCabe-Thiele Method McCabe-Thiele Graphical Stage Calculation Using Bancroft Coordinates 2

WT. SOLUTE Y ' WT. EXTRACTION-SOLVENT

1

2 E

r 0

3

R LIB

UI

EQ

M IU 4

LIN

G

IN AT ER

E LIN

X f ' Ye

OP

SLOPE =

F' S'

PARTIAL STAGE X r ' Ys

0

X

WT. SOLUTE ' WT. FEED-SOLVENT

2

Source: Republished with permission of McGraw-Hill, Inc., from Perry's Chemical Engineers' Handbook, 8th ed., Don W. Green and Robert H. Perry, New York, 2008; permission conveyed through Copyright Clearance Center, Inc. For immiscible feed and extraction solvents, the operating line for the feed end (stage 1 to stage n) is

Y ln + 1 =

F l l+ E l Yel− F l Xf l X Sl Sl n

where

Xfl = mass ratio of solute in feed Yel = mass ratio of solute in extract E l = mass flow rate of extraction solvent only F l = mass flow rate of feed solvent only S l = mass flow rate of extraction solvent only For immiscible feed and extraction solvents, the operating line for the raffinate end (stage n to stage r) is

Ynl=

F l l + S l Ysl− Rl X rl X Sl Sl n − 1

where

X rl = mass ratio of solute in raffinate Ysl = mass ratio of solute in solvent Rl = mass flow rate of raffinate solvent only

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357

Chapter 7: Mass Transfer The overall material balance is

Yel=

F l Xf l+ S l Ysl− Rl X rl El

7.5.2.2 Kremser-Souders-Brown (KSB) Theoretical Stage Equation For straight equilibrium and operating lines, the number of theoretical stages N is approximated by:

N=

ln >f

X f l− Ysl /ml 1 m+ 1 pc1 − E H E l l − l X r Ys /m ln E

Sl =1 for E = ml l , E Y F

where

N = number of theoretical stages ml = local slope of equilibrium line in mass ratio units lbm S l = mass flow rate of the solvent only (solute-free basis), in hr or F l = mass flow rate of the feed solvent (solute-free basis), in lbm or hr An alternate form is Xf l− Ysl /ml E N − 1/E = − 1 1/E X rl− Ysl /ml

kg s kg s

=1 for E Y

Xf l− Ysl /ml = N+1 for E = 1 X rl− Ysl /ml Graphical solutions to the KSB equation are shown below. Note that the term for the abscissa is the inverse of the term used in the KSB equation.

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358

Chapter 7: Mass Transfer Graphical Solutions to the KSB Equation 1.0 0.8 0.6 0.4

N=1

0.2

2

0.1 .08 .06 .04

3

.02

X'r X'f

4

.01 .008 .006 – Y' /m' .004 s – Y's /m' .002

6

.001 .0008 .0006 .0004 .0002

8

.0001 .00008 .00006 .00004

10

.00002

15

.00001 1

2

4

ε, EXTRACTION FACTOR

6

8

10

Source: Republished with permission of McGraw-Hill, Inc., from Perry's Chemical Engineers' Handbook, 8th ed., Don W. Green and Robert H. Perry, New York, 2008; permission conveyed through Copyright Clearance Center, Inc.

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Chapter 7: Mass Transfer In general, these equations are valid for any concentration range in which equilibrium can be represented by a linear relationship Y = m X + b (written here in general form for any system of units). For applications that involve dilute feeds, the section of the equilibrium line of interest is a straight line that extends through the origin where Yi = 0 at Xi = 0. In this case, b = 0, and the slope of the equilibrium line is equal to the partition ratio where m = K. The KSB equation also may be used to represent a linear segment of the equilibrium curve at higher solute concentrations. In this case, the linear segment is represented by a straight line that does not extend through the origin, and m is the local slope of the = equilibrium line, so b Y 0= and m Y K. Furthermore, a series of KSB equations may be used to model a highly curved equilibrium line by dividing the analysis into linear segments and matching concentrations where the segments meet. For equilibrium lines with moderate curvature, an approximate average slope of the equilibrium line may be obtained from the geometric mean of the slopes at low and high solute concentrations:

maverage . m geometric mean = m low m high

7.5.2.3 Stage Efficiency p o (%) = p md

=

p o (%) =

theoretical stages # 100 actual stages cd, n + 1 − cd, n cd, n + 1 − c d* ln [1 + p md (E − 1)] # 100 ln E

where

p o = overall stage efficiency p md = Murphree stage efficiency based on the dispersed phase

7.5.3

Rate-Based Calculations With Mass-Transfer Units

In most cases, the dominant mass-transfer resistance resides in the feed (raffinate) phase because the slope of the equilibrium line usually is greater than one. In that case, the overall mass-transfer coefficient based on the raffinate phase may be written:

where

1 =1 + 1 kor kr mervol ke m

ft

ke

= extract-phase mass-transfer coefficient, in hr or s

kr

= raffinate-phase mass-transfer coefficient, in hr or s

ft

m

m ft kor = overall mass-transfer coefficient based on the raffinate phase, in hr or s mervol = local slope of equilibrium line (volumetric concentration basis)

©2020 NCEES

360

Chapter 7: Mass Transfer The required contacting height of an extraction column is related to the height of a transfer unit and the number of transfer units by:

V Z t = k ra or where

#

x in

x out

dX = HTUor NTUor X − X eq

Zt

= total height of extractor

Vr

= liquid velocity of raffinate phase, in sec or s

a Xeq

ft

m

2 2 = interfacial area per unit volume, in ft 3 or m3

ft m = mass ratio in equilibrium with composition of extract phase

HTUor = height of overall transfer units (based on raffinate phase) NTUor = number of transfer units (based on raffinate phase) For straight equilibrium and operating lines, the number of transfer units is approximated by the Colburn equation:

where

RS J VW SS KK l Ysl NOO WW − SS KK X f ml OO W 1 1 OO c1 − m + WW ln SS KK E E WW SS KK X l− Ysl OO WW K O r S ml P NTUor = T L X 1 1−E

l = lS , EY1 E m= Fl An alternate form is

1 1 Yl Xf l− s l exp 2:

Re n uso = d t c p c

where

Re = 0.94H0.757 − 0.857 P0.149

H # 59.3

Re = 3.42H0.441 − 0.857 P0.149

H 2 59.3

t c2 c3 n c4 g Dt

P

=

H

2 n = f 4d p g Dt p d w n nc 3c

0.14

P0.149

P, H = dimensionless groups mw = reference viscosity equal to 0.9 cP or 9 × 10–4 Pas The slip velocity at higher holdup is estimated from:

us . uso `1 − zd j

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Chapter 7: Mass Transfer Flooding Velocity It is generally recommended that flow velocities be limited to 50 percent of the calculated flooding velocities.

ucf =

0.178uso u 1 + 0.925 d udf n cf

where

ucf = continuous-phase flooding velocity udf = dispersed-phase flooding velocity Drop Coalescence Rate Problems with coalescence are most likely when the superficial dispersed-phase flooding velocity udf is greater than about 12 percent of the characteristic slip velocity.

Mass-Transfer Coefficients and Efficiency

vol koc a = m dc kod a = 0.08 #

zd `1 − zd j f e

1/4

g 3 Dt 3 p c t c2

1/2

1/2

nc n o + d m1 n e d o tc Dc t dc d Dd

where

Dc

= solute diffusion coefficient for the continuous phase

Dd

= solute diffusion coefficient for the dispersed phase

koc

= overall mass-transfer coefficient based on the continuous phase

kod

= overall mass-transfer coefficient based on the dispersed phase

mdc = local slope of equilibrium line for dispersed-phase concentration plotted versus continuous-phase concentration vol = local slope of equilibrium line for dispersed-phase concentration plotted versus continuous-phase m dc concentration on volumetric concentration basis

γ

= interfacial tension

μc

= viscosity of continuous phase

μd

= viscosity of dispersed phase

ρc

= density of continuous phase

ρd

= density of dispersed phase

φd

= volume fraction of dispersed phase (holdup)

With the height of one transfer unit (based on the continuous phase):

u HTUqc = k ca oc

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Chapter 7: Mass Transfer 7.5.4.2 Packed Columns Liquid Redistribution Little benefit is gained from a packed height greater than 10 ft (3 m). Redistributing the dispersed phase about every 5 to 10 ft (1.5 to 3 m) is recommended to generate new droplets and constrain backmixing. Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 15-64.

Minimum Packing Size For a given application, a minimum packing size or dimension exists below which random packing is too small for good extraction performance. The critical packing dimension dc is

dc = 2.4 where

c Dt g

γ = interfacial tension

Packing Holdup For standard commercial packings of 0.5 in (1.27 cm) and larger, fd varies linearly with the liquid velocity of the dispersed phase (ud) up to values of fd = 0.10 (for low values of ud). As ud increases further, fd increases sharply up to a "lower transition point" resembling loading in gas-liquid contact. At still higher values of ud, an upper transition point occurs, the drops of dispersed phase tend to coalesce, and ud can increase without a corresponding increase in fd. This regime ends in flooding. Below the upper transition point, the dispersed-phase holdup is

ud uc + = f uso `1 − zd j zd 1 − zd Packing Flooding: Siebert, Reeves, and Fair Correlation ucf =

©2020 NCEES

0.178f uso _b Z] 1 ] b udf ]] b 2b `b 1 + 0.925 d u n [] rg = G c m bb cf ] cos ]] 4 b \ a

ap dp g= 2

367

Chapter 7: Mass Transfer Packing Flooding: Modified Crawford-Wilke Correlation

Flooding Velocities 104

LIQUID – LIQUID PACKED TOWERS A MODIFIED CRAWFORD-WILKE CORRELATION

2

Vc l + V D 0.5 ρ C VC

6 4

=

α

C

0.5

2

6 4 2

α

C

2

VC 0.5 ρ C +

VD0.5

103

102 6 4 2 10

1

2

4

6

10

'c

2

γ

ρ ρc

4

0.2

10

6 F

V = ft./hr. (SUPERFICIAL VELOCITY) C = CONTINUOUS PHASE D = DISPERSE PHASE α = sq. ft. AREA OF PACKING/ c ft. = DIFFERENCE = VOID FRACTION IN PACKING

2

1.5

2

2

4

6

10

3

µ'c = VISCOSITY IN (CENTIPOISE)

ρ = DENSITY (POUNDS PER / CUBIC FOOT)

γ = INTERFACIAL SURFACE TENSION (DYNES / cm) F = PACKING FACTOR (DIMENSIONLESS)

Pressure Drop In general, the pressure drop through a packed extractor is due to the hydrostatic head pressure. The resistance to flow caused by the packing itself normally is negligible; typical packings are large and flooding velocities are much lower than those needed to develop significant DP from resistance to flow between the packing elements.

Mass-Transfer Coefficients 1

U=

2 n e d o td Dd

n d1 + nd n c

For Φ < 6:

kd =

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0.00375us n d1 + nd n c

368

Chapter 7: Mass Transfer For Φ > 6:

−1 2

nd o kd = 0.023us e t D d d

2

1

kc dp n 5 d ut 2 = 0.698 e c o e p s c o `1 − zd j Dc tc Dc nc vol 1 = 1 + m dc kod kd kc

where

kc = continuous-phase mass-transfer coefficient kd = dispersed-phase mass-transfer coefficient Packing Data

Random and Structured Packings Used in Packed Extractors Packing Koch-Glitsch IMTP® 25 Koch-Glitsch IMTP® 40 Koch-Glitsch IMTP® 50 Koch-Glitsch IMTP® 60 Sulzer I-Ring #25 Sulzer I-Ring #40 Sulzer I-Ring #50 Nutter Ring® NR 0.7 Nutter Ring® NR 1 Nutter Ring® NR 1.5 Nutter Ring® NR 2 Nutter Ring® NR 2.5 HY-PAK® #1 in. HY-PAK® #1-1/2 in. HY-PAK® #2 in. FLEXIRING® 1 in. FLEXIRING® 1-1/2 in. FLEXIRING® 2 in. CMR® 1 CMR® 2 CMR® 3 BETARING® #1 BETARING® #2 FLEXIMAX® 200 FLEXIMAX® 300 FLEXIMAX® 400

©2020 NCEES

Surface Area ap1 Metal Random Packing 224 151 102 84 224 151 102 226 168 124 96 83 172 118 84 200 128 97 246 157 102 186 136 189 148 92

369

m2 m3

Void Fraction1 (e) 0.964 0.980 0.979 0.983 0.964 0.980 0.979 0.977 0.977 0.976 0.982 0.984 0.965 0.976 0.979 0.959 0.974 0.975 0.973 0.970 0.980 0.963 0.973 0.973 0.979 0.983

Chapter 7: Mass Transfer Random and Structured Packings Used in Packed Extractors (cont'd) Packing

Surface Area ap1

m2 m3

Plastic Random Packing 204 105 167 114 93 205 119 99 Ceramic Random Packing INTALOX® Saddles 1 in. 256 INTALOX® Saddles 1-1/2 in. 195 INTALOX® Saddles 2 in. 118 Ceramic Structured Packing FLEXERAMIC® 28 282 FLEXERAMIC® 48 157 FLEXERAMIC® 88 102 Metal Structured Packing2 Koch-Glitsch SMV-8 417 Koch-Glitsch SMV-10 292 Koch-Glitsch SMV-16 223 Koch-Glitsch SMV-32 112 Sulzer SMV 2Y 205 Sulzer SMV 250Y 256 Sulzer SMV 350Y 353 INTALOX® 2T 214 INTALOX® 3T 170 INTALOX® 4T 133 Plastic Structured Packing2 Koch-Glitsch SMV-8 330 Koch-Glitsch SMV-16 209 Koch-Glitsch SMV-32 93 Sulzer SMV 250Y 256 Super INTALOX® Saddles #1 Super INTALOX® Saddles #2 BETARING® #1 BETARING® #2 SNOWFLAKE® FLEXIRING® 1 in. FLEXIRING® 1-1/2 in. FLEXIRING® 2 in.

Void Fraction1 (e) 0.896 0.934 0.942 0.940 0.949 0.922 0.925 0.932 0.730 0.750 0.760 0.720 0.770 0.850 0.978 0.985 0.989 0.989 0.990 0.988 0.983 0.989 0.989 0.987 0.802 0.875 0.944 0.875

1. Typical value for standard wall thickness. Values will vary depending upon thickness. 2. SMV structured packings also are available with horizontal dual-flow perforated plates installed between elements (typically designated SMVP packing). These plates generally reduce backmixing and improve mass-transfer performance at the expense of a reduction in the open cross-sectional area and somewhat reduced capacity. Source: Republished with permission of McGraw-Hill, Inc., from Perry's Chemical Engineers' Handbook, 8th ed., Don W. Green and Robert H. Perry, New York, 2008; permission conveyed through Copyright Clearance Center, Inc.

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Chapter 7: Mass Transfer 7.5.4.3 Sieve Tray Columns Sieve Tray Perforated Area Perforations usually are in the range of 0.125 to 0.25 in (0.32 to 0.64 cm) in diameter, set 0.5 to 0.75 in (1.27 to 1.81 cm) apart, on square or triangular pitch. Hole size appears to have relatively little effect on the mass-transfer rate except that, in systems of high interfacial tension, smaller holes produce somewhat better mass transfer. The entire hole area is normally set at 15 to 25 percent of the column cross-section, although adjustments may be needed. It is common practice to set the velocity of liquid exiting the holes to correspond to a Weber number between 8 and 12. This normally gives velocities in the range of 0.5 to 1.0 ft sec (15 to 30 cm ).

s The velocity of the continuous phase in the downcomer (or upcomer) udow, which sets the downcomer cross-sectional area, should be set lower than the terminal velocity of some arbitrarily small droplet of dispersed phase, such as a diameter of 1/32 or 1/16 in (0.08 or 0.16 cm). Otherwise, recirculation of entrained dispersed phase around a tray will result in flooding. The terminal velocity ut of these small drops can be calculated using Stokes' Law: g d p2 Dt ut = 18n c Downcomer area typically is in the range of 5 to 20 percent of the total cross-sectional area, depending upon the ratio of continuous- to dispersed-phase volumetric flow rates. For large columns, tray spacing between 18 and 24 in. (45 and 60 cm) is generally recommended. LIGHT LIQUID OUT OPERATING INTERFACE

HEAVY LIQUID IN

PERFORATED PLATE DOWNCOMER COALESCED DISPERSED LIGHT LIQUID IN HEAVY LIQUID OUT

Source: Republished with permission of McGraw-Hill, Inc., from Perry's Chemical Engineers' Handbook, 8th ed., Don W. Green and Robert H. Perry, New York, 2008; permission conveyed through Copyright Clearance Center, Inc. The height of the coalesced layer at each tray, h, is

h=

DPo + DPdow − zd g Dt L `1 − zd j g Dt

DPo

= orifice pressure drop

where

DPdow = pressure drop for flow through a downcomer (or upcomer)

L

©2020 NCEES

= downcomer (or upcomer) length

371

Chapter 7: Mass Transfer The orifice pressure drop DPo is 0.2

−2

2 c 0.71 1 DPo = 2 d1 − log Re n td uo2 + 3.2 e do g Dt o d c o

where

for Re =

uo do td nd

do = diameter of orifice in ft

The pressure drop through the downcomer is

DPdow = where udow

2 4.5udow tc 2

= velocity in downcomer (or upcomer)

For large columns, the design should specify that the height of the coalesced layer is at least 1 in. (2.5 cm) to ensure that all holes are adequately covered. For segmental downcomers, the area of the downcomer is

H A = 6S _3H 2 + 4S 2 i where A

= area of segmental downcomer (or upcomer)

H

= height of segmental downcomer (or upcomer)

S

= chord length of segmental downcomer (or upcomer)

Chord length S is

S = =8H d

1

Dcol H 2 − nG 2 2

where Dcol = column diameter

Sieve Tray Flooding Velocity Velocity of the continuous phase at the flood point is

where

RS V0.5 SS L − A WWW WW ucf = SSS udf 2 WW + d n B C SS ucf W T X A=

6c do Dt g

B=

1.11td g Dt f ha2

C=

2.7tc 2g Dt fda2

where fha = fractional hole area fda = fractional downcomer area The cross-flow velocity of the continuous phase uc flow is

Lfp ucflow . z − h uc

where Lfp = length of flow path z ©2020 NCEES

= sieve tray spacing 372

Chapter 7: Mass Transfer Sieve Tray Efficiency The sieve tray efficiency is approximated by

po = 0.21 f

0.42

ud z0.5 0.35 p d u n c do c

7.6 Adsorption 7.6.1

Adsorption Equilibrium

For a single adsorbate in a gas stream, the equilibrium capacity of the adsorbent may be related to the concentration of the adsorbate in the bulk stream by the Freundlich equation: W = a p1/n where

mass qf adsqrbate

W = unit mass of adsorbent p

= partial pressure of adsorbate in the bulk gas stream

a, n = empirical coefficients derived from log-log plot of data for W vs. p Both coefficients are a function of temperature. The Freundlich equation can be used for liquid-solid adsorption by entering concentration instead of partial pressure.

MASS ADSORBATE/MASS ADSORBANT

Typical Adsorption Isotherms TYPICAL ADSORPTION ISOTHERMS INCREASING TEMPERATURE

LOG PARTIAL PRESSURE OF ADSORBATE

7.6.2

Adsorption Operation

Adsorption in typical commercial operations is conducted by passing the gas or liquid stream through a usually vertical fixed bed of adsorbent particles. Adsorption beds are usually oriented vertically. Adsorption beds have three zones that characterize the operation: 1. Equilibrium zone where adsorbate is in equilibrium with inlet concentration 2. Mass transfer zone where adsorbate is diffusing into adsorbent 3. Active zone where no adsorption has occurred The length of the mass transfer zone (MTZ) is a function of the fluid velocity along with adsorbent porosity and uniformity of pore size. ©2020 NCEES

373

Chapter 7: Mass Transfer Adsorption Concentration Profiles Across Bed EQUILIBRIUM ZONE

VAPOR-PHASE CONCENTRATION

y IN

ACTIVE ZONE

MASSTRANSFER ZONE

y OUT

O

L

BED LENGTH CONCENTRATION PROFILE AT A GIVEN TIME DURING ADSORPTION OPERATION

Three performance regimes for adsorption beds characterize the operation. Considering a given point in a bed: 1. Dry, when the mass transfer zone is below the point in the bed and the concentration has a low value 2. Break-through, when the mass transfer zone reaches the point in the bed and the concentration increases 3. Saturated, when the concentration at the point in the bed increases to the value of the inlet concentration

Adsorption Outlet Composition Versus Time LIGHT LIQUID OUT

DRY y IN

SATURATED INTERFACE

HEAVY LIQUID IN

VAPOR-PHASE CONCENTRATION y OUT

BREAK-THROUGH

REDISTRIBUTOR PACKING

LIGHT LIQUID IN

HEAVY LIQUID OUT

0

TIME

CONCENTRATION PROFILE AS A FUNCTION OF TIME AT A GIVEN POINT IN THE BED. ADSORPTION STEP. ©2020 NCEES

374

Chapter 7: Mass Transfer

7.6.3

Adsorption Regeneration

Adsorption processes can be nonregenerative or regenerative. Nonregenerative adsorption is a batch process. For regenerative adsorption, adsorbent beds are cycled between adsorption and desorption (regeneration) modes and multiple beds are required for continuous operation. During regeneration, stripping the adsorbate is accomplished by passing a pure fluid through the bed at a lower pressure for pressure swing adsorption (PSA) or at a higher temperature for temperature swing adsorption (TSA). For TSA, the pressure may be slightly lowered in addition to the temperature increase. Often a split stream from the fluid exiting the adsorbing bed is used as the pure fluid for regenerating adsorption beds. The regeneration of adsorption beds leaves a residual concentration of adsorbate in the adsorbent. This reduces the working capacity of regenerated adsorbent in comparison with the capacity of fresh adsorbent. Working capacity W l = Wsat − Wregen where Wsat = amount adsorbed on the bed at break-through Wregen = amount of adsorbate remaining on the bed after regeneration

Characteristics of Typical Adsorption Systems

Adsorption System Characteristics TSA

System Type:

Gas Phase

PSA Gas Phase

Liquid Phase

Configuration of system Number of beds Time on adsorption Flow direction on adsorption

2 to 4 4 to 8 hours Down

Flow direction on regeneration

Up

2 to 4 4 to 8 hours Up Down; treated vaporized liquid when feasible

2 to 16 Minutes to hours Up Down

Common adsorbents Hydrophobic

Activated carbons for removing VOCs from gas

Hydrophilic

Silica gel, activated alumina, mol sieve for dehydration and removing slightly polar organics

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Activated carbons for water purification

Activated carbon for air separations; heavy hydrocarbons from light hydrocarbons

Chapter 7: Mass Transfer

7.7 Humidification and Drying 7.7.1

Adiabatic Humidification and Cooling Adiabatic Humidification and Cooling FLOW MODEL O

LENGTH OR HEIGHT dZ

Z

G's1 Y'1 TG1

G's1 Y' TG

G's1 Y '+ dY ' TG + dTG

G's1 Y'2 TG2

L'1 Tas

L' Tas

L'+ dL' Tas

L'2 Tas

MATERIAL BALANCE dL' = G'sdY'

L'2 – L'1 = G's (Y '2 – Y '1) INTERFACIAL SERVICE ds = adz

ABS HUMIDITY

MASS TRANSFER Y'as

GAS INTERFACE

BULK

Y'1

Y'

GAS

Y 'as

RATE OF MASS TRANSFER

Y'2

G'sdY ' = kYa (Y 'as – Y ')dz

dY '

TEMPERATURE

SENSIBLE HEAT TRANSFER BULK

TG1

SENSIBLE RATE OF TRANSFER

GAS

G's Cs1 dT G = hg a (T G – T as) dz

dTG

TG

TG2 Tas

INTERFACE AND BULK LIQUID

Tas

dz

O

z

PSYCHOMETRIC RELATIONS

ABS HUMIDITY

SATURATION HUMIDITY

ADIABATIC SATURATION

Y 'as Y '2 Y '1 Tas TG2

TG1

TEMPERATURE

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Chapter 7: Mass Transfer where

Ll = solute-free liquid flow rate Gls = dry-gas mass flow rate Y 1l = initial humidity Y l2 = final humidity Y las = saturation humidity at liquid-gas interface TG = temperature of bulk gas Tas = temperature at liquid-gas interface Cs1 = specific heat capacity at the liquid-gas interface hg = gas heat-transfer coefficient Since Y las is constant:

ky a z Yl − Yl ln f las − l1 p = Gls Y as Y 2 where ky = overall mass-transfer coefficient a

= interstitial surface per unit volume, in

z

= height, in ft

ft 2 ft 3

Gls _Y l2 − Y 1l i = ky a z ^DY lhlm where

^DY lhlm = logarithmic mean of humidity difference

or

NTUtG = and

Y l2 − Y 1l Y l − Y 1l = ln > as H Y las − Y l2 ^DY lhlm

Gls z = = HTU tG ky a NTUtG where

NTUtG = number of gas-phase transfer units HTUtG = height of transfer unit Air-Water Systems yw

= mole fraction of water

ya

= mole fraction of air

y y y Yw = yw = 1 −wy = 1 −ay = molal humidity = mole water vapor/mole dry air a w a 18 = = Yw 29 : Yw mass humidity = mass water vapor/mass dry air ©2020 NCEES

377

Chapter 7: Mass Transfer Pw

Relative humidity = 100 P w where

P w = partial pressure of water at a given temperature Pw = vapor pressure of water at a given temperature Yw=

where

Pw Patm − P w

Pw Y ws = P − atm Pw

Y ws = saturation humidity Patm = atmospheric pressure (14.696 psia or 0.1013 MPa) % saturation = 100

Y w = P w `Patm − Pw j (100) at total pressure of one atmosphere Y ws Pw ` Patm − P w j

Humid heat CPH = 0.24 + 0.46Yw where

CPH = humid heat capacity, Btu/lb Adiabatic Saturation Temperature m tAS = ty0 − C R `YwS − Yw0 j PH

where

tAS = adiabatic saturation temperature ty0 = initial inlet temperature lR = latent heat of vaporization at reference temperature

Yw0 = initial inlet humidity CPH = humid heat capacity YwS = humidity at saturation m tWB = ty − C R `YWB − Yw j PH

where

YWB = humidity at wet bulb temperature tWB = wet bulb temperature

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Chapter 7: Mass Transfer Humidity Chart for the Air-Water System at One Atmosphere HUMID HEAT, BTU/LB DRY AIR (°F) 0.26

0.30

0.28

0.15

14104°0

17

20%

40%

30%

135°

130°

MID

18

°AADDR IABA TIC S ITUA TION LINE S

100% 90% 80% 70% 60% 50%

UM HEA TV SH

19

125°

HU

VOLUME, CU FT/LB DRY AIR

20

PER SATU CENT RATI ON

IDIT Y

21

0.14

0.12

0.10

16 15 14 13

TED URA

SAT

12

IFIC

SPEC

P

. TEM

E VS

UM VOL

ME VOLU

120°

E TUR ERA

115°

TURE PERA

M

VS TE

0.08

0.06

110° 105°

100° 95°

55° 60° 50° 45°

65°70°

80° 75°

0.04

90° 85° 0.02

0 25

40

60

80

100

120

160

140

180

200

220

TEMPERATURE, F°

Source: Brown, G.G., et. al., Unit Operations, New York: John Wiley & Sons, Inc., 1950.

Cooling Tower Operating Diagram Hy8 vs t4 80 Hy vs tx

H, BTU/LB DRY AIR

60 40 20 0 50

Hy0 TOP OF TOWER

CpxL GB max

t x0 CpxL SLOPE = GB

HY1 t 1 BOTTOM OF x TOWER 60

70

80 t, °F

C Px L o : _t x − t x0 j + H y0 Hy = e G B ©2020 NCEES

379

90

100

110

240

250

HUMIDITY, LB WATER VAPOR/LB DRY AIR

0.24

10%

22

0.22

Chapter 7: Mass Transfer where

Hy = enthalpy of vapor phase CPx = specific heat of liquid phase L

= liquid-phase mass velocity

GB = dry air mass velocity tx = liquid-phase temperature Hy0 = initial enthalpy of vapor phase tx0 = liquid-phase inlet temperature

7.7.2

Drying of Solids

Moisture (Solvent) Percentage Content Typically calculated on a dry solid/dry air basis:

m X = % moisture in solid = mw s where

X

= moisture (solvent) content in solid, moisture mass/dry solid mass

mw = moisture (solvent) content, mass of water or solvent, in lbm ms = mass of dry solid, in lbm m Y = % moisture in air = mw a where

Y

= moisture (solvent) content in air, moisture mass/dry air mass

mw = moisture (solvent) content, mass of water or solvent, in lbm ma = mass of dry air, in lbm Rate of Drying Rate of drying is dictated by the state of the solvent, such as: • "Free" solvent on surface of solids • "Bound" solvent, which must reach the surface through diffusion or capillary action • "Solvated" solvent, which is chemically bound to the solids (sometimes labile to removal, sometimes not) that are not generally considered in drying analyses

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380

Chapter 7: Mass Transfer Drying Curve FALLING RATE I

CONSTANT RATE

N, DRYING RATE

FALLING RATE II

X*

XC

X, MOISTURE (SOLVENT) CONTENT lb/lb DRY SOLID where X* = equilibrium moisture content: the moisture content of the solid when it reaches equilibrium with the surrounding air; depending upon the specific conditions of the surrounding air Xc = critical moisture content: the moisture content that marks the instant when the liquid content on the surface of the solid is no longer sufficient to maintain a continuous liquid film on the surface Constant Rate: Rate of drying independent of moisture content. During this period the solid is so wet that the entire surface of the solid is covered with a continuous film of liquid. Falling Rate I: Only part of the solid surface is saturated as the entire solid surface can no longer be maintained at saturation conditions by the movement of moisture within the solid. The rate of drying is linear with regard to X. Falling Rate II: The entire solid surface is unsaturated and the drying rate is limited by the rate of internal moisture movement. Source: McCabe, Warren L., and Julian C. Smith, Unit Operations of Chemical Engineering, 3rd ed., New York: McGraw-Hill, 1976.

Specific Drying Applications Drying of slab using gas from one side only: 1. For drying during the constant rate period Rate of drying can be determined based on the balance between the heat transfer to the material and the rate of vapor removal from the surface.

= NC

h t DT = k g Dp m

where DT = gas dry bulb temperature—temperature at surface of solid Dp = vapor pressure of water at surface temperature—partial pressure of water vapor in the gas

lbm hr-ft 2-atm lbm NC = constant drying rate, in 2 ft - hr kg = mass-transfer coefficient, in

©2020 NCEES

381

Chapter 7: Mass Transfer Btu

l = latent heat of evaporation, in lbm

ht = total heat-transfer coefficient, in

Btu hr-ft 2-cF

When the air is flowing parallel to the surface:

ht = 0.0128 G0.8 When the air is flowing perpendicular to the surface, the equation is

ht = 0.37 G0.37 where G = mass velocity, in

t=

lbm ft 2-hr

ms (X1 − X 2) A NC

where

t

= drying time

X1 = moisture content in solid at time 1 X2 = moisture content in solid at time 2 2. For linear falling rate period I

t=>

N ms (X1 − X 2) H ln 1 − N A (N1 N 2) 2

where

lb ft 2-hr lb = drying rate at time 2, in 2 ft -hr = mass of dry solids, in lb

N1

= drying rate at time 1, in

N2 ms

If falling rate I extends all the way to X* and drying starts at the critical moisture content:

t=

ms ` XC − X * j X −X* o : ln e C − A : NC X2 X *

3. For falling rate period II, rate curve must be integrated:

t =d = NC

ms n A

#x x

1

2

dX N

h t DT = k g Dp m

Dryer Design and Performance 1. Tray dryers To determine the tray area for a specific production rate:

A=

©2020 NCEES

P (t + td) LT

382

Chapter 7: Mass Transfer where

P

= production rate, in mass of dry solids per hour

t

= drying time

td

= downtime for loading and unloading trays

LT

= tray loading in mass of dry solids per square area of tray, in

2. Continuous through-circulation dryers To determine required conveyor length: Required dryer holding capacity C in pounds is

C=Pt where

P = production rate, in

lbm dry solid hr

t = drying time, in hr Pt A= L where

A = conveyor area, in ft2 lbm dry sqlid L = bed loading, in 2 ft cqnveyqr area A B=W where

B = effective dryer length, in ft W = conveyor width, in ft 3. Rotary dryers The residence time can be determined empirically using: for countercurrent flow, sign in the expression below is positive for concurrent flow, sign in the expression below is negative −

t=

5D p0.5 LG 0.23L ! 0 . 6 F SN 0.9 D

where

t = retention time, in min L = dryer length, in ft

D = diameter of shell, in ft Dp = weighted average particle size of material, in micrometers

©2020 NCEES

383

lbm ft 2

Chapter 7: Mass Transfer rev N = speed, in min

ft S = slope of shell, in ft G = air mass velocity in F = feed rate in

lbm hr - ft 2

lbm dry material hr-ft qf dryer crqss-sectional area 2

4. Spray dryers An estimate of the drying time can be found using:

t= where

mWt s d p2 12Kf `Ta − Ts j

t

= drying time, in min

dp

= drop diameter in ft

W

= moisture content in the drop in lbm dry solid

Kf

= thermal conductivity of the gas film in

lbm

Btu hr -ft -cF

Ta – Ts = temperature difference between drop and gas in °F rs

= density of the solid

Typical Critical Moisture Content of Various Materials

Approximate Critical Moisture Contents Obtained on the Air Drying of Various Materials, Expressed as Percentage Water on the Dry Basis Material

Thickness (in.)

Barium nitrate crystals, on trays Beaverboard Brick clay Carbon pigment Celotex Chrome leather Copper carbonate, on trays English china clay Flint clay refractory brick mix Gelatin, initially 400% water Iron blue pigment, on trays Kaolin Lithol red

©2020 NCEES

1.0 0.17 0.62 1 0.44 0.04 1–1.5 1 2.0 0.1–0.2 (wet) 0.25–0.75 1

384

Critical Moisture (% Water) 7 Above 120 14 40 160 125 60 16 13 300 110 14 50

Chapter 7: Mass Transfer Approximate Critical Moisture Contents Obtained on the Air Drying of Various Materials, Expressed as Percentage Water on the Dry Basis (cont'd) Material

Thickness (in.)

Lithopone press cake, in trays

0.25 0.50 0.75 1.0

Niter cake fines, on trays Paper, white eggshell Fine book Coated Newsprint Plastic clay brick mix Poplar wood Prussian blue Rock salt, in trays Sand, 50–150 mesh 200–325 mesh through 325 mesh Sea sand, on trays

0.0075 0.005 0.004 2.0 0.165 1.0 2.0 2.0 2.0 0.25 0.50 0.75 1.0 2.0 2.0 0.25 1

Silica brick mix Sole leather Stannic tetrachloride sludge Subsoil, clay fraction 55.4% Subsoil, much higher clay content Sulfite pulp Sulfite pulp (pulp lap) White lead Whiting Wool fabric, worsted Wool, undyed serge

0.25–0.75 0.039 0.25–1.5

Critical Moisture (% Water) 6.4 8.0 12.0 16.0 Above 16 41 33 34 60–70 19 120 40 7 5 10 21 3 4.7 5.5 5.9 6.0 8 Above 90 180 21 35 60–80 110 11 6.9 31 8

Source: McCabe, W.L., and J.C. Smith, Unit Operations of Chemical Engineering, 3rd ed., New York: McGraw-Hill, 1976.

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Chapter 7: Mass Transfer

7.8 Filtration Types of filters: 1. Discontinuous pressure filters 2. Continuous filters 3. Centrifugal filters 4. Cartridge filters 5. Bag filters

Factors for Selection of Filter Media The filter media in any process filter need to meet the following requirements to be of value in a chemical process: • The septum must obviously be able to retain the solids to be filtered, producing a reasonably clear filtrate • The removed solids must not plug off the media upon initial or subsequent use. • The media must be chemically resistant to the chemicals in the filtrate and the filter cake. • The septum must be strong enough physically to withstand the operating conditions. • The media must allow the cake to be discharged cleanly and completely. • The cost of the media must be reasonable enough not to add significantly to the overall plant or production cost.

Filtration Equations Total pressure drop:

Dp = pa − p b = (pa − pl ) + (pl − p b) = Dpc + Dp m where Dp = overall pressure drop

pa

= filter inlet pressure

p'

= septum inlet pressure

pb

= filter outlet pressure

Dpc = pressure drop over cake Dpm = pressure drop over medium Filter cake pressure drop:

dp 150nu (1 − f) 2 = dL gc (z s D p) 2 f 3 where

dp dL = pressure gradient at thickness L µ

= viscosity of filtrate

u = linear velocity of filtrate, based on filter area e = porosity of cake ©2020 NCEES

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Chapter 7: Mass Transfer Dp = nominal diameter of solid particles 6v p z s = D s for nonspherical particles p p z s = 1 for spherical particles or

2

dp = dL

s 4.17n u (1 − f) 2 f v p p p

gc f

3

where

sp = surface of single particle vp = volume of single particle Filter medium resistance:

Rm =

` pl − p b j gc

nu

=

− Dp m g c nu

7.9 Membrane Separation Processes General Background

Fluid Stream Schematic TMP

PERMEATE OR FILTRATE RETENTATE

FEED FEED CHANNEL ΔP

Normal flow filtration (NFF) refers to the situation in which retentate flow is zero and all the feed stream flows to the membrane surface are normal. Tangential flow filtration (TFF) refers to the situation in which the feed stream flows are tangential to the membrane surface and exit the module as a retentate stream, creating a velocity gradient at the membrane surface. Permeation flux J in

J=

ft 3 mol or 2 indicates the productivity of a membrane: ft day m s 2

volumetric permeate flow rate membrane area

Permeability L indicates the sensitivity of productivity or flux to transmembrane pressure (TMP):

flux L = transmembrane pressure Transmembrane pressure (TMP) may refer to a module average. Pure-component permeability (e.g., water permeability) refers to membrane properties, while the more industrially relevant process permeability includes fouling and polarization effects. The recovery or conversion ratio CR indicates the efficiency of a membrane module:

CR =

permeate flow rate feed flow rate

Solutes entrained by the permeate flow are retained by the membrane. They accumulate on the membrane surface and form a region of high concentration called the polarization boundary layer. A steady state is reached between back transport away

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Chapter 7: Mass Transfer from the membrane surface, tangential convective transport along the membrane surface, and normal convective flow towards the membrane. The local transmission or sieving coefficient S indicates the passage of a single component through a membrane. The concentrations may change within a module:

c p (local) S = c (local) f

The observed passage Sobs indicates the transmission coefficient based on the concentration in the permeate stream exiting a module and in the feed stream entering a module. The observed passage characterizes the module:

c p (mod ule) Sobs = c (mod ule) f

The intrinsic passage Sint indicates the transmission coefficient based on the concentration in the permeate stream exiting a module and in the feed stream at the membrane wall. The intrinsic passage characterizes the membrane:

cp Sint = c w

where

cf = concentration in feed cp = concentration in permeate cw = concentration at wall of membrane The retention or rejection R is the complement to the transmission coefficient or passage:

R=1–S The multiple-component separation factor aij defines the selectivity for component separation:

where

c f ip p cif S = a ij = S i j c f jp p c jf cif = concentration of component i in feed cip = concentration of component i in permeate

Component transport through membranes can be considered as mass transfer in series: 1. Transport through a polarization layer above the membrane that may include static or dynamic cake layers 2. Partitioning between the upstream polarization layer and membrane phases at the membrane surface 3. Transport through the membrane 4. Partitioning between the membrane and the downstream fluid

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Chapter 7: Mass Transfer A simplified model of polarization can be used as the basis for analysis:

Polarization in Tangential Flow Filtration REGIONS:

CONCENTRATIONS:

BULK SOLUTIONS POLARIZATION BOUNDARY LAYER PERMEATE

Cb

FLOW VECTORS: TANGENTIAL FLOW PERMEATE NORMAL FLOW

Cw Cp

Source: Republished with permission of McGraw-Hill, Inc., from Perry's Chemical Engineers' Handbook, 8th ed., Don W. Green and Robert H. Perry, New York, 2008; permission conveyed through Copyright Clearance Center, Inc.

Gas Separation The flux for permeation is

t Ji = c zi m` pi, feed − pi, permeate j where:

Ji = permeation flux of component i, in ri = permeability of component i, in

ft 3 mol or 2 ft 2 hr m s

ft 3 ft mol or 2 ft 2 hr psi m s Pa

z = membrane thickness pi = partial pressure of component i Stage cut q is defined by V permeate volume flow rate = i L= feed volume flow rate where

mol lb mole hr or s mol lb mole L = molar feed flow rate, in hr or s V = molar permeate flow rate, in

Selectivity is

aij = where

y e yi o j

x e xi o j

aij = separation factor

xi = mole fraction of component i in the feed or reject yi = mole fraction of component i in the permeate The pressure ratio U is

P U = P feed permeate

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Chapter 7: Mass Transfer The ratio of permeation flux for two components i and j is

RS V SS x − d yi n WWW S i U WW Ji W = a ij SSS Jj SS − e y j oWWW x SS j U WW T X = At stage cut U 0 , the permeate composition as a function of feed composition is U 1 1 yi = c 2 m>c xi + + a − 1 m − U

2 4ax i H c xi + 1 + 1− m − 1 a U _a − 1 i U

For membrane modules, the partial pressure driving force is a point function dependent on the partial pressures at a point on the membrane and is not constant. To take this into account, the equation may be used in iterative calculations for approximating the performance of membrane modules. The limiting case for a >> F is

P yi , xi P feed = xi U permeate The limiting case for a J 1 _ ii

avg

H

_ Ji iavg = c t i m c 1 m 9` x n − 1 PF − y n − 1 PP j + ` x n PF − y n PP jC = c t i m c 1 m 9_ x n − 1 + x n i PF − ` y n − 1 + y n j PPC z 2 z 2

The overall module area can be approximated as

AN =

where

y n Vn _ Ji iavg

_ Ji iavg = c t i m c 1 m 9` x0 PF − y0 PP j + ` x N PF − y n PP jC = c t i m c 1 m 9_ x0 + x n j PF − ` y0 + y n j PPC z 2 z 2

Procedure for Incremental Calculation Given aij, PF, PP, L0, and x0: 1. Select increment Dx 2. For the initial point 0, calculate y0 and (Ji)0 3. Determine xn ©2020 NCEES

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Chapter 7: Mass Transfer 4. Calculate yn and y n 5. Calculate DVn and Vn 6. Calculate y n DVn 7. Calculate Ln 8. Calculate (Ji)n, (Ji)avg, and An 9. After the final increment, calculate (Ji)N and AN

Membrane Separation Processes—Reverse Osmosis Osmotic Pressure The osmotic pressure ps of a solution is ps = Fs is cs R T where ps = osmotic pressure in psi or Pa Fs = osmotic coefficient

is = number of ions formed by solute molecules cs = concentration of the solute in

lb mole mol or ft3 m3

R = universal gas constant T = absolute temperature in °R or K

Concentration Gradients SKIN awF awP = c wP

c wF

c wi POROUS SUPPORT PERMEATE P c si

FEED F

c sP c sm c sP

Source: McCabe, Warren L., Julian C. Smith, and Peter Harriott, Unit Operations of Chemical Engineering, 5th ed., New York: McGraw-Hill, 1993. ©2020 NCEES

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Chapter 7: Mass Transfer where

aw = activity of water cs = concentration of solute Flux Across Membrane The flux of solvent JW (water, for example) is

Jw =

c w D w v w DP − Dr c m RT z

where

J = permeation flux in c = concentration in

ft 3 m3 or 2 2 ft hr m s

lb mole mol or ft 3 m3

m2 ft 2 D = effective diffusivity in hr or s ft 3 m3 v = partial specific volume in lbm or kg DP = friction losses in psi or Pa

z = membrane thickness in ft or m Dp = differential osmotic pressure in psi or Pa The flux of solute is

Dc Js = Ds Ss c z s m where:

Ss = distribution coefficient of the solute Polarization Factor The polarization factor is the relative concentration difference across the polarization boundary layer and is

C=

csi − cs J w f cs = k c

where

f = fraction of solute rejected m ft kc = mass-transfer coefficient based on concentration, in hr or s Pressure Drop The internal flow in a hollow-fiber membrane is laminar, and the internal pressure drop DPf with one closed end is

DPf =

128 J w n L2 2 D3

where

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Chapter 7: Mass Transfer

7.10 Crystallization Saturation and Supersaturation

The Solubility-Supersolubility Diagram

C'

CONCENTRATION

LABILE

C" B"

B'

D C A

B

M

LE

TAB

S ETA

STABLE

TEMPERATURE

Diagram regions: • Stable (unsaturated) zone, where crystallization is impossible. • Metastable (supersaturated) zone, between the solubility and supersolubility curves, where spontaneous crystallization is improbable. However, if a crystal seed were placed in such a metastable solution, growth would occur on it. • Unstable or Labile (supersaturated) zone, where spontaneous crystallization is probable, but not inevitable.

Expressions of Supersaturation Dc = c – c* where

c = concentration c* = saturation concentration Dc = driving-force concentration

c S = c* where S = supersaturation ratio

Dc s = c* = S − 1 where s = relative supersaturation (100s is % supersaturation) Dq = q* – q ©2020 NCEES

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Chapter 7: Mass Transfer where q = temperature of the solution q* = saturation temperature of the solution The supersaturation and supercooling are related by the local slope of the solubility curve

d c* Dc = c d i m D i Nucleation

d c* by di

Diagram of Nucleation NUCLEATION

PRIMARY

HOMOGENEOUS (SPONTANEOUS)

SECONDARY (INDUCED BY CRYSTALS)

HETEROGENEOUS (INDUCED BY FOREIGN PARTICLES)

Gibbs Energy of Nucleation DGcrit =

4r c r c2 3

DGcrit =

4r c r c2 = Gibbs free energy for the critical radius of a stable nucleus 3

where

g = interfacial tension between the developing crystal surface and the supersaturated solution

rc = critical radius of a stable nucleus Homogeneous Nucleation Rate (Arrhenius Form) J = A EXP >−

16r c 3 v 2 H 3k 3 T 3 (ln S) 2

where

J = nucleation rate A = rate constant R k = Boltzmann constant ( k = Nc , where N is Avogadro's number) v = number of moles of ions produced from one mole of electrolyte (for non­electrolytes, v = 1) T = absolute temperature S = supersaturation ratio

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Chapter 7: Mass Transfer Crystal Growth 1 dm 3= a 3a dL 6= a dr 6a g = = RG K= t G = t t t vr G Dc A dt b c b c dt b c dt b c where

kg m2 : s m KG = mass-transfer coefficient with units that are dependent on g (if g = 1), in s RG = mass deposition rate, in

g = the order (a fitting parameter) Dcg = concentration driving force for mass transfer, in

kg m3

A = b L2 = particle area, in m2 m = a rc L3 = particle mass, in kg t

= time, in s

a = volume shape factor b = surface shape factor

m G = overall linear growth rate, in s kg rc = crystal density, in 3 m L = some characteristic size of the crystal, in m r

= radius corresponding to the equivalent sphere, in m

m vr = mean linear velocity of growth, in s

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Chapter 7: Mass Transfer Some Mean Overall Crystal Growth Rates Expressed as a Linear Velocity1 Crystallizing Substance

cC

S

vr b m sl

(NH 4) 2 SO 4 : Al 2 (SO 4) 3 : 24H 2 O

15 30 30 40 40 30 60 90 20 30 30 40 20 30 30 25 25 25 15 30 30 40 20 40 20 40 20 20 30 50 50 30 30 40 40 50 50 70 70 30 30 25 30 30

1.03 1.03 1.09 1.08 1.05 1.05 1.05 1.01 1.06 1.02 1.05 1.02 1.02 1.01 1.02 1.03 1.09 1.20 1.04 1.04 1.09 1.03 1.02 1.01 1.05 1.05 1.09 1.18 1.07 1.06 1.12 1.07 1.21 1.06 1.18 1.002 1.003 1.002 1.003 1.02 1.08 1.05 1.01 1.05

  1.1 × 10–8*   1.3 × 10–8*   1.0 × 10–7*   1.2 × 10–7* 8.5 × 10–7   2.5 × 10–7* 4.0 × 10–7 3.0 × 10–8 6.5 × 10–8 3.0 × 10–8 1.1 × 10–7 7.0 × 10–8   4.5 × 10–8*   8.0 × 10–8*   1.5 × 10–7* 5.2 × 10–9 2.6 × 10–8 4.0 × 10–8    1.4 × 10–8*   2.8 × 10–8*   1.4 × 10–7*   5.6 × 10–8* 2.0 × 10–7 6.0 × 10–7 4.5 × 10–8 1.5 × 10–7   2.8 × 10–8*   1.4 × 10–7*   4.2 × 10–8*   7.0 × 10–8*   3.2 × 10–7*  3.0 × 10–8 2.9 × 10–7 5.0 × 10–8 4.8 × 10–7 2.5 × 10–8 6.5 × 10–8 9.0 × 10–8 1.5 × 10–7 1.1 × 10–7 5.0 × 10–7 3.0 × 10–8 1.0 × 10–8 4.0 × 10–8

NH4NO3

(NH 4) 2 SO 4 NH4H2PO4

MgSO 4 : 7H 2 O NiSO 4 : (NH 4) 2 SO 4 : 6H 2 O K 2 SO 4 : Al 2 (SO 4) 3 : 24H 2 O

KCl KNO3 K2SO4

KH2PO4

NaCl

Na 2 S 2 O 3 : 5H 2 O Citric acid monohydrate

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Chapter 7: Mass Transfer Some Mean Overall Crystal Growth Rates Expressed as a Linear Velocity1 (cont'd) Crystallizing Substance Sucrose

1

cC

S

vr b m sl

30 30 70 70

1.13 1.27 1.09 1.15

  1.1 × 10–8*   2.1 × 10–8* 9.5 × 10–8 1.5 × 10–7

c

The supersaturation is expressed by S = l with c and c' as kg of crystallizing substance per kg of free water. The c 1 significance of the mean linear growth velocity, vr c = 2 G m , is explained by equation 6.61 and the values recorded here refer to crystals in the approximate size range 0.5–1 mm growing in the presence of other crystals.

* Denotes that the growth rate is probably size-dependent. Source: Mullin, J.W., Crystallization, 4th ed., Woburn, MA: Reed Educational and Professional Publishing Ltd., 2001.

7.11 Leaching Leaching is the removal of a soluble substance from an insoluble solid via liquid extraction. The desired component diffuses into the solvent by mass transfer. Two common methods of leaching are: • Percolation of liquids through stationary solid beds • Dispersion of solids in each leaching stage by mechanical agitation

Multistage Leaching For multistage leaching processes, the most common setup is continuous countercurrent leaching, where a liquid solvent overflows from stage to stage in a direction opposite to the flow of the solid. The stages are numbered in the direction of flow of the solid. • The flow rates of contained liquid in the solid slurry streams are shown as L-values. • The concentrations of solute in the solid slurries are shown as x-values. • Feed solid slurries enter at stage 1, containing a liquid flow of La with a solute concentration of Xa. • Leached solid slurries exit at stage N, containing a liquid flow of Lb with a solute concentration of Xb. • It is assumed that the solids flow rate is constant from stage to stage. • The flow rates of overflow solvent from each stage are shown as V-values. • The concentrations of solute in the solvent streams are shown as y-values. • Lean solvent enters the process at stage N, at a mass flow rate of Vb and a solute concentration of Yb. • The concentrated solvent, or leachate, exits at a mass flow rate of Va and a solute concentration of Ya.

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Chapter 7: Mass Transfer Multistage Leaching Diagram LEACHATE FEED SOLIDS

Va Ya

STAGE

La

ONE

xa

V2

Vn

Y2 L1

Yn Ln-1

x1

xn-1

STAGE n

Vn+1 Yn+1 Ln xn

Vn+2

STAGE Yn+2 Ln+1 n+1 xn+1

VN YN LN-1 xN-1

STAGE N

Vb Yb Lb xb

LEAN SOLVENT LEACHED SOLIDS

Inputs = Outputs:

La + Vn+1= Va + Ln Component balance:

La (xa) + Vn + 1 (y n + 1) = Va (ya) + L n (x n) Leaching Operating Line V Y −L X L Yn + 1 = V n X n + a aV a a n+1

n+1

Note: If the density of liquid Ln is constant from stage to stage, then the overflow and underflow rates are both constant and the operating line is straight.

Calculation of the Number of Required Stages in Leaching With Constant Overflow The equilibrium line for leaching is

Xe = Ye The first stage of the leaching process is calculated initially as a mass balance to set up the flow of slurried solids through the rest of the stages. Therefore, the following calculation determines the total number of stages N, in the format of N–1:

N−1 =

ln e

yb − xb o ya − xa

ln e

yb − y a o xb − x a

Langmuir Adsorption of Undissociated Single Species Reversible adsorption of species A:

Rate of adsorption of A:

kaA

A+s ? A:s kdA

raA = kaACA _1 − iA i

Rate is proportional to the rate at which molecules strike the surface, concentration in bulk gas, and fraction of unoccupied sites (1–θA) Rate of desorption of A: At equilibrium, raA = rdA Langmuir adsorption isotherm:

k

where KA = kaA dA

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rdA = kdA iA

_ kaA/kdA i CA k C K C = +A A iA = k +aAk AC = 1 KACA dA aA A 1 + _ kaA/kdA i CA

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Chapter 7: Mass Transfer Langmuir Adsorption of Dissociated Single Species

kaB2

Adsorption of a dissociating diatomic molecule:

B2 + 2s ? 2B : s



Rate of adsorption of B:

raB2 = kaB2CB2 _1 − iB i



Rate of desorption of B:

rdB2 = kdB2 iB2



Langmuir adsorption isotherm:



where KB2 = k 2 dB2

kdB2

2

kaB

1*

iB =

` KB2CB2 j2

1*

1 + ` KB2CB2 j2 * If n sites are required for n fragment, the exponent becomes 1/n.

Source: Missen, Ronald W., Charles A. Mims, and Bradley A. Saville, Introduction to Chemical Reaction Engineering and Kinetics, New York: John Wiley & Sons, Inc., 1999.

7.12 Particle Settling and Cyclonic Separation 7.12.1 Particle Settling Free Settling: Particle-to-particle interactions are negligible. Hindered Settling: Particle settling is at a reduced rate relative to the settling velocity of a single particle caused by interactions with neighboring particles.

Approximate Regions of Free and Hindered Settling for Given Solids' Concentration and Density 50

wt. % SOLIDS

40 HINDERED

30

20 FREE

10

0

0.1

0.2

0.3

0.4

PARTICLE

—

0.5

0.6

0.7

0.8

FLUID

PARTICLE

If upwards fluid velocity ( uf ) is less than the settling velocity of the particle (us ), then the particles will settle.

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Chapter 7: Mass Transfer For settling operations, the settling velocity (us ) equals the terminal velocity (ut). For Stokes flow, the smallest diameter spherical particle (Dp ) that will settle is

18nuf g `tp − tf j

Dp =

For general flow up to Re < 2×105, the smallest diameter spherical particle that will settle is

Re n Dp = u t f f where the Reynolds number can be estimated using

1 =d 0.00433 + 0.203 Re

1

CD 2 − n 0.0658 Re

where

CD 4n g `tp − tf j = Re 3tf2 u t3

7.12.2 Cyclone Separators Cyclone Separator FINES + AIR



where

a = height of tangential inlet

De IMMERSION TUBE (OR GAS OUTLET TUBE)

b = width of tangential inlet De = diameter of immersion tube

FEED (DIRTY AIR)

s = immersion length of outlet tube D = cyclone diameter

s a

h = length of cylindrical section

h

D

z = length of conical section

CYCLONE BODY

b

H = cyclone height H

CONICAL SECTION

z

B = diameter of tail outlet



Particle Removal Efficiency 1 h = 2 Dpc p 1 +f Dp

where

Dpc = diameter of particle collected with 50% efficiency B

TAILS

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Dp = diameter of particle of interest



401

h = fractional particle collection efficiency

Chapter 7: Mass Transfer Effective Number of Turns 1 z Ne = a c h + 2 m where Ne = number of effective turns the gas makes in the cyclone h

= length of body of cyclone

z

= length of cone of cyclone

Cyclone 50% Particle Efficiency for Particle Diameter 9n b H Dpc = > 2 r Ne ui `tp − tg j

0.5

where Dpc = diameter of particle that is collected with 50% efficiency, in meters µ = dynamic viscosity of gas ui = inlet velocity into cyclone ρp = density of particle ρg = density of gas

CYCLONE EFFICIENCY (%)

Cyclone Collection Efficiency CYCLONE COLLECTION EFFICIENCY 100

10

1

0.1

PARTICLE SIZE RATIO

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1

402

Dp Dpc

Chapter 7: Mass Transfer Cyclone Ratio of Dimensions to Body Diameter (D) Capacity Dimension

High Efficiency

Conventional

High Throughput

Inlet height, a

0.44

0.50

0.80

Inlet width, b

0.21

0.25

0.35

Cylindrical section length, h

1.40

1.75

1.70

Cone length, z

2.50

2.00

2.00

Immersion length, s

0.50

0.60

0.85

Gas exit diameter, D

0.40

0.50

0.75

Tails outlet diameter, B

0.40

0.40

0.40

Cyclone height, H

3.90

3.75

3.70

Source: Adapted from Cooper, C. David, and F.C. Alley, Air Pollution Control: A Design Approach, 4th ed., Illinois: Waveland Press, 2011.

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8 PLANT DESIGN AND OPERATIONS 8.1 Terms and Definitions Definitions Term Boiling point

Combustible dust Combustible liquid

Description The temperature at which the vapor pressure of a liquid equals the atmospheric pressure of 14.7 pounds per square inch (psia), 101 kPa, or 760 mm of mercury. For purposes of this classification, when an accurate boiling point is not available for a material or when a mixture does not have a constant boiling point, use the 20%-evaporated point of a distillation performed in accordance with ASTM D 86. Boiling point is commonly expressed in °F or °C. A finely divided solid material that is 420 microns or less in diameter and that, when dispersed in air in the proper proportions, can be ignited by a flame, spark, or other source of ignition. Will pass through a U.S. No. 40 standard sieve. A liquid having a closed-cup flash point at or above 100°F (38°C). Subdivided into: Class II: Closed-cup flash point at or above 100°F (38°C) and below 140°F (60°C) Class IIIA: Closed-cup flash point at or above 140°F (60°C) and below 200°F (93°C) Class IIIB: Closed-cup flash point at or above 200°F (93°C)

Deflagration

Detonation

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This category does not include compressed gases or cryogenic fluids. An exothermic reaction, such as the extremely rapid oxidation of a flammable dust or vapor in air, in which the reaction progresses through the unburned material at a rate less than the velocity of sound. A deflagration can have an explosive effect. An exothermic reaction characterized by the presence of a shock wave in the material that establishes and maintains the reaction. The reaction zone progresses through the material at a rate greater than the velocity of sound. The principal heating mechanism is one of shock compression. A detonation has an explosive effect.

404

Chapter 8: Plant Design and Operations Definitions (cont'd) Term Explosion

Description An effect produced by the sudden, violent expansion of gases, which may be accompanied by a shock wave, a disruption of enclosing materials or structures, or both. An explosion could result from: • Chemical changes such as rapid oxidation, deflagration or detonation, decomposition of molecules, or runaway polymerization (usually detonations) • Physical changes such as pressure tank ruptures

• Atomic changes such as nuclear fission or fusion Flammable gas A material that is a gas at 68°F (20°C) or less at 14.7 psia (101 kPa) of pressure—therefore a material that has a boiling point of 68°F (20°C) or less at 14.7 psia (101 kPa)—and which either: • Ignites at 14.7 psia (101 kPa) when in a mixture of 13% or less by volume with air • Has a flammable range mixed in air at 14.7 psia (101 kPa) and 63°F (20°C) These levels shall be determined at the specified pressure and temperature in accordance with ASTM E 681. Flammable liq- A liquefied compressed gas that, under a charged pressure, is partially liquid at a temperature of 68°F uefied gas (20°C) and that is flammable. Flammable A liquid having a closed-cup flash point below 100°F (38°C). Flammable liquids are further categorized liquid into a group known as Class I liquids and subdivided into: Class IA: Closed-cup flash point below 73°F (23°C) and boiling point below 100°F (38°C) Class IB: Closed-cup flash point below 73°F (23°C) and boiling point at or above 100°F (38°C)

Flammable material Flammable solid

Class IC: Closed-cup flash point at or above 73°F (23°C) and boiling point below 100°F (38°C). The category of flammable liquids does not include compressed gases or cryogenic fluids. A material capable of being readily ignited from a common source of heat or at a temperature of 600°F (316°C). A solid, other than a blasting agent or explosive, that: Is capable of causing fire through friction, absorption or moisture, spontaneous chemical change, or retained heat from manufacturing or processing or Has an ignition temperature below 212°F (100°C) or Burns so vigorously and persistently when ignited as to create a serious hazard

A chemical shall be considered a flammable solid in accordance with the test method of CPSC 16 CFR: Part 1500.44 if it ignites and burns with a self-sustained flame at a rate greater than 0.1 inch (2.5 mm) per second along its major axis. Flammable va- The concentration of flammable constituents in air that exceeds 25% of their lower flammable limit (LFL). pors or fumes Flash point The minimum temperature in degrees Fahrenheit (or Centigrade) at which a liquid will give off sufficient vapors to form an ignitable mixture with air near the surface or in the container, but will not sustain combustion. The flash point of a liquid shall be determined by appropriate test procedure and apparatus as specified in ASTM D 56, ASTM D 93, or ASTM D 3278.

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Chapter 8: Plant Design and Operations Definitions (cont'd) Term Highly toxic

Description A material that produces a lethal dose or lethal concentration that falls within any of these categories: • A chemical that has a median lethal dose (LD50) of 50 milligrams or less per kilogram of body weight when administered orally to albino rats weighing between 200 and 300 grams each • A chemical that has a median lethal dose (LD50) of 200 milligrams or less per kilogram of body weight when administered by continuous contact for 24 hours (or less if death occurs within 24 hours) with the bare skin of albino rabbits weighing between 2 and 3 kilograms each • A chemical that has a median lethal concentration (LC50) in air of 200 parts per million by volume or less of gas or vapor, or 2 milligrams per liter or less of mist, fume, or dust when administered by continuous inhalation for 1 hour (or less if death occurs within 1 hour) to albino rats weighing between 200 and 300 grams each

Immediately dangerous to life and health (IDLH) Organic peroxide

Mixtures of these materials with ordinary materials, such as water, may not warrant classification as highly toxic. The concentration of air-borne contaminants that poses a threat of death, immediate or delayed permanent adverse health effects, or effects that could prevent escape from such an environment. This concentration level of contaminants is established by the National Institute for Occupational Safety and Health (NIOSH) based on both toxicity and flammability. Generally it is expressed in parts per million by volume (ppm/v) or milligrams per cubic meter (mg/m3). An organic compound that contains the bivalent -O-O- structure and that may be considered a structural derivative of hydrogen peroxide in which one or both of the hydrogen atoms have been replaced by an organic radical. Organic peroxides can pose an explosion hazard (detonation or deflagration) or can be shock sensitive. They also can decompose into various unstable compounds over an extended period of time. Class I: Formulations that are capable of deflagration but not detonation Class II: Formulations that burn very rapidly and pose a moderate reactivity hazard Class III: Formulations that burn rapidly and pose a moderate reactivity hazard Class IV: Formulations that burn in the same manner as ordinary combustibles and pose a minimal reactivity hazard Class V: Formulations that burn with less intensity than ordinary combustibles or do not sustain combustion and pose no reactivity hazard Unclassified detonable: Organic peroxides that are capable of detonation. These pose an extremely high explosion hazard through rapid explosive decomposition.

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Chapter 8: Plant Design and Operations Definitions (cont'd) Term Oxidizer

Description A material that readily yields oxygen or other oxidizing gas or that readily reacts to promote or initiate combustion of combustible materials and, if heated or contaminated, can result in vigorous self-sustained decomposition. Class 4: An oxidizer that can undergo an explosive reaction due to contamination or exposure to thermal or physical shock and that causes a severe increase in the burning rate of combustible materials with which it comes into contact. Additionally, the oxidizer causes a severe increase in the burning rate and can cause spontaneous ignition of combustibles. Class 3: An oxidizer that causes a severe increase in the burning rate of combustible materials with which it comes into contact. Class 2: An oxidizer that causes a moderate increase in the burning rate of combustible materials with which it comes into contact.

Oxidizing gas Physical hazard

Class 1: An oxidizer that does not moderately increase the burning rate of combustible materials. A gas that can support and accelerate combustion of other materials more than air does. A chemical for which there is evidence that it is one of the following: • Combustible liquid • Cryogenic fluid • Explosive or flammable solid, liquid, or gas • Solid or liquid organic peroxide • Solid or liquid oxidizer • Oxidizing gas • Pyrophoric solid, liquid, or gas • Unstable (reactive) solid, liquid, or gas material

Toxic

• Water-reactive solid or liquid material A chemical falling within any of these categories: • Has a median lethal dose (LD50) of more than 50 milligrams per kilogram but not more than 500 milligrams per kilogram of body weight when administered orally to albino rats weighing between 200 and 300 grams each. • A chemical that has a median lethal dose (LD50) of more than 200 milligrams per kilogram but not more than 1000 milligrams per kilogram of body weight when administered by continuous contact for 24 hours (or less if death occurs within 24 hours) with the bare skin of albino rabbits weighing between 2 and 3 kilograms each. • A chemical that has a median lethal concentration (LC50) in air of more than 200 parts per million but not more than 2000 part per million by volume or less of gas or vapor, or more than 2 milligrams per liter but not more than 20 milligrams per liter of mist, fume, or dust, when administered by continuous inhalation for 1 hour (or less if death occurs within 1 hour) to albino rats weighing between 200 and 300 grams each.

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Chapter 8: Plant Design and Operations Definitions (cont'd) Term Description Unstable (reac- A material, other than an explosive, that in the pure state or as commercially produced will vigorously tive) material polymerize, decompose, condense, or become self-reactive and undergo other violent chemical changes, including explosion, when it is either: • Exposed to heat, friction, or shock • In the absence of an inhibitor • In the presence of contaminants • In contact with incompatible materials Unstable (reactive) materials are subdivided into: Class 4: Materials that in themselves are readily capable of detonation or explosive decomposition or explosive reaction at normal temperatures and pressures. Includes materials that are sensitive to mechanical or localized thermal shock at normal temperatures and pressures Class 3: Materials that in themselves are capable of detonation or of explosive decomposition or explosive reaction but which require a strong initiating source or which must be heated under confinement before initiation. Includes materials that are sensitive to thermal or mechanical shock at elevated temperatures and pressures Class 2: Materials that in themselves are normally unstable and readily undergo violent chemical change but do not detonate; includes materials that can undergo chemical change with rapid release of energy at normal temperatures and pressures and that can undergo violent chemical change at elevated temperatures and pressures

Water-reactive material

Class 1: Materials that in themselves are normally stable but that can become unstable at elevated temperatures and pressures A material that explodes; violently reacts; produces flammable, toxic, or other hazardous gases; or evolves enough heat to cause autoignition or ignition of combustibles upon exposure to water or moisture. Waterreactive materials are subdivided into: Class 3: Materials that react explosively with water without requiring heat or confinement Class 2: Materials that react violently with water or have the ability to boil water. Materials that produce flammable, toxic, or other hazardous gases, or evolve enough heat to cause autoignition or ignition of combustibles upon exposure to water or moisture Class 1: Materials that react with water with some release of energy, but not violently

Source: 2015 International Building Code, Country Club Hills, Illinois: International Code Council.

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Chapter 8: Plant Design and Operations

8.2 Safety, Health, and Environment 8.2.1

Hazard Identification

8.2.1.1 Definition of Safety Safety is the condition of protecting people from threats or failure that could harm their physical, emotional, occupational, psychological, or financial well-being. Safety is also the control of known threats to attain an acceptable level of risk. The United States relies on public codes and standards, engineering designs, and corporate policies to ensure that a structure or place does what it should do to maintain a steady state of safety—that is, long-term stability and reliability. Some safety/regulatory agencies that develop codes and standards commonly used in the United States are shown below.

Insurance, Safety, and Regulatory Agencies Abbreviation ANSI CGA CSA FAA FMG IEC

Jurisdiction Nonprofit standards organization Nonprofit trade association Nonprofit standards organization U.S. federal regulatory agency Insurance Nonprofit standards organization

MSHA

Name American National Standards Institute Compressed Gas Association Canadian Standards Association Federal Aviation Administration FM Global International Electrotechnical Commission Intertek Testing Services NA (formerly Edison Testing Labs) Mine Safety and Health Administration

NFPA

National Fire Protection Association

Nonprofit trade organization

OSHA UL USCG USDOT USEPA

Occupational Health and Safety Administration Underwriters Laboratories United States Coast Guard United States Department of Transportation United States Environmental Protection Agency

Federal regulatory agency Nationally recognized testing laboratory Federal regulatory agency Federal regulatory agency Federal regulatory agency

ITSNA

Nationally recognized testing laboratory Federal regulatory agency

8.2.1.2 Definition of Risk A traditional preventive approach to both accidents and occupational illness involves recognizing, evaluating, and controlling hazards and work conditions that may cause physical injuries or adverse health effects.

Hazard is the capacity to cause harm. It is an inherent quality of a material or a condition. For example, a rotating saw blade or an uncontrolled high-pressure jet of water has the capability (hazard) to slice through flesh. A toxic chemical or a pathogen has the capability (hazard) to cause illness. Risk is the chance or the probability that a person will experience harm and is not the same as a hazard. Risk always involves both probability and severity elements. The hazard associated with a rotating saw blade or the water jet continues to exist, but the probability of causing harm, and thus the risk, can be reduced by installing a guard or by controlling the jet's path. Risk is expressed by the equation: Risk = Severity/Consequence # Probability When people discuss the hazards of disease-causing agents, the term exposure is typically used more than probability. If a certain type of chemical has a toxicity hazard, the risk of illness rises with the degree to which that chemical contacts your body or enters your lungs. In that case, the equation becomes: Risk = Hazard # Exposure Organizations evaluate hazards using multiple techniques and data sources.

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Chapter 8: Plant Design and Operations 8.2.1.3 Job Safety Analysis Job safety analysis (JSA) is known by many names, including activity hazard analysis (AHA), or job hazard analysis (JHA). Hazard analysis helps integrate accepted safety and health principles and a specific task. In a JSA, each basic step of the job is reviewed, potential hazards identified, and recommendations documented as to the safest way to do the job. JSA techniques work well when used on a task that the analysts understand well. JSA analysts look for specific types of potential accidents and ask basic questions about each step, such as these: Can the employee strike against or otherwise make injurious contact with the object? Can the employee be caught in, on, or between objects? Can the employee strain muscles by pushing, pulling, or lifting? Is exposure to toxic gases, vapors, dust, heat, electrical currents, or radiation possible?

8.2.1.4 OSHA Highly Hazardous Chemicals The following is from 29 CFR 1910.119, Appendix A. It contains a list of toxic and reactive highly hazardous chemicals that present a potential for a catastrophic event at or above the threshold quantity.

Highly Hazardous Chemicals Chemical Name Acetaldehyde Acrolein (2-Propenal) Acrylyl Chloride Allyl Chloride Allylamine Alkylaluminum Ammonia, Anhydrous Ammonia solutions (greater than 44% ammonia by weight) Ammonium Perchlorate Ammonium Permanganate Arsine (also called Arsenic Hydride) Bis (Chloromethyl) Ether Boron Trichloride Boron Trifluoride Bromine Bromine Chloride Bromine Pentafluoride Bromine Trifluoride 3-Bromopropyne (also called Propargyl Bromide) Butyl Hydroperoxide (Tertiary) Butyl Perbenzoate (Tertiary) Carbonyl Chloride (see Phosgene) Carbonyl Fluoride Cellulose Nitrate (concentration greater than 12.6% nitrogen) Chlorine Chlorine Dioxide Chlorine Pentrafluoride Chlorine Trifluoride

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CAS* 75-07-0 107-02-8 814-68-6 107-05-1 107-11-9 Varies 7664-41-7 7664-41-7 7790-98-9 7787-36-2 7784-42-1 542-88-1 10294-34-5 7637-07-2 7726-95-6 13863-41-7 7789-30-2 7787-71-5 106-96-7 75-91-2 614-45-9 75-44-5 353-50-4 9004-70-0 7782-50-5 10049-04-4 13637-63-3 7790-91-2

TQ** 2500 150 250 1000 1000 5000 10,000 15,000 7500 7500 100 100 2500 250 1500 1500 2500 15,000 100 5000 7500 100 2500 2500 1500 1000 1000 1000

Chapter 8: Plant Design and Operations Highly Hazardous Chemicals (cont'd) Chemical Name Chlorodiethylaluminum (also called Diethylaluminum Chloride) 1-Chloro-2,4-Dinitrobenzene Chloromethyl Methyl Ether Chloropicrin Chloropicrin and Methyl Bromide mixture Chloropicrin and Methyl Chloride mixture Cumene Hydroperoxide Cyanogen Cyanogen Chloride Cyanuric Fluoride Diacetyl Peroxide (concentration greater than 70%) Diazomethane Dibenzoyl Peroxide Diborane Dibutyl Peroxide (tertiary) Dichloro Acetylene Dichlorosilane Diethylzinc Diisopropyl Peroxydicarbonate Dilauroyl Peroxide Dimethyldichlorosilane 1,1-Dimethylhydrazine Dimethylamine, Anhydrous 2,4-Dinitroaniline Ethyl Methyl Ketone Peroxide (also Methyl Ethyl Ketone Peroxide; concentration greater than 60%) Ethyl Nitrite Ethylamine Ethylene Fluorohydrin Ethylene Oxide Ethyleneimine Fluorine Formaldehyde (Formalin) Furan Hexafluoroacetone Hydrochloric Acid, Anhydrous Hydrofluoric Acid, Anhydrous Hydrogen Bromide Hydrogen Chloride Hydrogen Cyanide, Anhydrous Hydrogen Fluoride Hydrogen Peroxide (52% by weight or greater) Hydrogen Selenide ©2020 NCEES

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CAS* 96-10-6 97-00-7 107-30-2 76-06-2 None None 80-15-9 460-19-5 506-77-4 675-14-9 110-22-5 334-88-3 94-36-0 19287-45-7 110-05-4 7572-29-4 4109-96-0 557-20-0 105-64-6 105-74-8 75-78-5 57-14-7 124-40-3

TQ** 5000 5000 500 500 1500 1500 5000 2500 500 100 5000 500 7500 100 5000 250 2500 10,000 7500 7500 1000 1000 2500

97-02-9

5000

1338-23-4

5000

109-95-5 75-04-7 371-62-0 75-21-8 151-56-4 7782-41-4 50-00-0 110-00-9 684-16-2 7647-01-0 7664-39-3 10035-10-6 7647-01-0 74-90-8 7664-39-3 7722-84-1 7783-07-5

5000 7500 100 5000 1000 1000 1000 500 5000 5000 1000 5000 5000 1000 1000 7500 150

Chapter 8: Plant Design and Operations Highly Hazardous Chemicals (cont'd) Chemical Name Hydrogen Sulfide Hydroxylamine Iron, Pentacarbonyl Isopropylamine Ketene Methacrylaldehyde Methacryloyl Chloride Methacryloyloxyethyl Isocyanate Methyl Acrylonitrile Methylamine, Anhydrous Methyl Bromide Methyl Chloride Methyl Chloroformate Methyl Ethyl Ketone Peroxide (concentration greater than 60%) Methyl Fluoroacetate Methyl Fluorosulfate Methyl Hydrazine Methyl Iodide Methyl Isocyanate Methyl Mercaptan Methyl Vinyl Ketone Methyltrichlorosilane Nickel Carbonyl (Nickel Tetracarbonyl) Nitric Acid (94.5% by weight or greater) Nitric Oxide Nitroaniline (para Nitroaniline) Nitromethane Nitrogen Dioxide Nitrogen Oxides (NO; NO(2); N2O4; N2O3) Nitrogen Tetroxide (also called Nitrogen Peroxide) Nitrogen Trifluoride Nitrogen Trioxide Oleum (65% to 80% by weight; also called Fuming Sulfuric Acid) Osmium Tetroxide Oxygen Difluoride (Fluorine Monoxide) Ozone Pentaborane Peracetic Acid (concentration greater 60% Acetic Acid; also called Peroxyacetic Acid) Perchloric Acid (concentration greater than 60% by weight) Perchloromethyl Mercaptan

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CAS* 7783-06-4 7803-49-8 13463-40-6 75-31-0 463-51-4 78-85-3 920-46-7 30674-80-7 126-98-7 74-89-5 74-83-9 74-87-3 79-22-1 1338-23-4 453-18-9 421-20-5 60-34-4 74-88-4 624-83-9 74-93-1 79-84-4 75-79-6 13463-39-3 7697-37-2 10102-43-9 100-01-6 75-52-5 10102-44-0 10102-44-0 10544-72-6 7783-54-2 10544-73-7 8014-95-7 20816-12-0 7783-41-7 10028-15-6 19624-22-7

TQ** 1500 2500 250 5000 100 1000 150 100 250 1000 2500 15,000 500 5000 100 100 100 7500 250 5000 100 500 150 500 250 5000 2500 250 250 250 5000 250 1000 100 100 100 100

79-21-0

1000

7601-90-3 594-42-3

5000 150

Chapter 8: Plant Design and Operations Highly Hazardous Chemicals (cont'd) Chemical Name Perchloryl Fluoride Peroxyacetic Acid (concentration greater than 60% Acetic Acid; also called Peracetic Acid) Phosgene (also called Carbonyl Chloride) Phosphine (Hydrogen Phosphide) Phosphorus Oxychloride (also called Phosphoryl Chloride) Phosphorus Trichloride Phosphoryl Chloride (also called Phosphorus Oxychloride) Propargyl Bromide Propyl Nitrate Sarin Selenium Hexafluoride Stibine (Antimony Hydride) Sulfur Dioxide (liquid) Sulfur Pentafluoride Sulfur Tetrafluoride Sulfur Trioxide (also called Sulfuric Anhydride) Sulfuric Anhydride (also called Sulfur Trioxide) Tellurium Hexafluoride Tetrafluoroethylene Tetrafluorohydrazine Tetramethyl Lead Thionyl Chloride Trichloro (chloromethyl) Silane Trichloro (dichlorophenyl) Silane Trichlorosilane Trifluorochloroethylene Trimethyoxysilane

CAS* 7616-94-6

TQ** 5000

79-21-0

1000

75-44-5 7803-51-2 10025-87-3 7719-12-2 10025-87-3 106-96-7 627-3-4 107-44-8 7783-79-1 7803-52-3 7446-09-5 5714-22-7 7783-60-0 7446-11-9 7446-11-9 7783-80-4 116-14-3 10036-47-2 75-74-1 7719-09-7 1558-25-4 27137-85-5 10025-78-2 79-38-9 2487-90-3

100 100 1000 1000 1000 100 2500 100 1000 500 1000 250 250 1000 1000 250 5000 5000 1000 250 100 2500 5000 10,000 1500

* Chemical abstract service number ** Threshold quantity in pounds (amount necessary to be covered by OSHA CFR 1910.119 standard)

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Chapter 8: Plant Design and Operations 8.2.1.5 Hazardous Classification Based on NFPA 70 NFPA Hazardous Classification CLASS I GASES OR VAPOR

DIVISION 1 HAZARDOUS VAPORS PRESENT ZONE 0, 1, OR 2

CLASS III FIBERS

CLASS II COMBUSTIBLE DUST

DIVISION 1 HANDLED, MANUFACTURED OR USED

DIVISION 2 HAZARDOUS VAPORS CONTAINED BUT MAY BE PRESENT

DIVISION 2 STORED OR HANDLED OTHER THAN MANUFACTURE

DIVISION 2 SURFACE ACCUMULATED – NON AIR SUSPENDED

DIVISION 1 AIR SUSPENDED

GROUP A ACETYLENE GROUP E COMBUSTIBLE METAL DUSTS

GROUP B FLAMMABLE GAS, FLAMMABLE OR COMBUSTIBLE VAPOR MESG ≤ 0.45 MM MIC RATIO ≤ 0.40

GROUP F COMBUSTIBLE CARBONACEOUS DUSTS CONTAINING >8% AND TRAPPED VOLATILES

GROUP C FLAMMABLE GAS, FLAMMABLE OR COMBUSTIBLE VAPOR 0.45 MM ≤MESG ≤ 0.75 MM 0.45 MM ≤ MIC RATIO ≤ 0.80 GROUP D FLAMMABLE GAS, FLAMMABLE OR COMBUSTIBLE VAPOR 0.75MM ≤ MESG 0.80MM ≤ MIC RATIO MSEG: MAXIMUM EXPERIMENTAL SAFE GAP MIC: MINIMUM IGNITING CURRENT RATIO

GROUP G COMBUSTIBLE DUSTS NOT INCLUDED ELSEWHERE

CLASS 1, ZONE 0: IGNITABLE CONCENTRATIONS PRESENT CONTINUOUSLY OR FOR LONG PERIODS OF TIME CLASS 1, ZONE 1: IGNITABLE CONCENTRATIONS LIKELY TO EXIST UNDER NORMAL OPERATION CLASS 1, ZONE 2: IGNITABLE CONCENTRATIONS NOT LIKELY TO EXIST UNDER NORMAL OPERATION

Source: Reproduced with permission from NFPA 70®, National Electric Code®, © 2011, National Fire Protection Association. This is not the complete and official position of the NFPA on the referenced subject, which is represented only by the standard in its entirety. National Electrical Code and NEC are registered trademarks of the National Fire Protection Association, Quincy, MA. Maximum Experimental Safe Gap (MESG): The maximum clearance between two parallel metal surfaces that has been found, under specified test conditions, to prevent an explosion in a test chamber from being propagated to a secondary chamber containing the same gas or vapor at the same concentration. Minimum Igniting Current (MIC) Ratio: The ratio of the minimum current required from an inductive spark discharge to ignite the most easily ignitable mixture of a gas or vapor, divided by the minimum current required from an inductive spark discharge to ignite methane under the same test conditions. ©2020 NCEES

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Chapter 8: Plant Design and Operations 8.2.1.6 Flammability Flammable describes any solid, liquid, vapor, or gas that will ignite easily and burn rapidly. A flammable liquid is defined by NFPA and USDOT as a liquid with a flash point below 100°F (38°C). Flammability is further defined with lower and upper limits: LFL = lower flammability limit (volume % in air) UFL = upper flammability limit (volume % in air) A vapor-air mixture will only ignite and burn over the range of concentrations between LFL and UFL. Flammability data is shown at the end of this chapter. Predicting Lower Flammable Limits of Mixtures of Flammable Gases (Le Chatelier's Rule) Based on an empirical rule developed by Le Chatelier, the lower flammable limit of mixtures of multiple flammable gases in air can be determined. A generalization of Le Chatelier's rule is

/d n

i=1

Ci n LFLi $ 1

where Ci

= the volume percent of fuel gas i in the fuel/air mixture

LFLi = the volume percent of fuel gas i at its lower flammable limit in air alone If the indicated sum is greater than unity, the mixture is above the lower flammable limit. This can be restated in terms of the lower flammable limit concentration of the fuel mixture (LFLm):

LFLm =

100 C / d fi n i = 1 LFLi n

Cfi = the volume percent of fuel gas i in the fuel gas mixture.

where

Predicting Lower Flammable Limits

COMBUSTIBLE CONCENTRATION

SATURATED VAPORAIR MIXTURES

UPPER LIMIT

FLAMMABLE MIXTURES

MIST

B A

TL

AUTOIGNITION

LOWER LIMIT AIT

TU TEMPERATURE

* THE SFPE HANDBOOK OF FIRE PROTECTION ENGINEERING, NATIONAL FIRE PROTECTION ASSOCIATION. 1988.

WITH PERMISSION FROM THE SOCIETY OF FIRE PREVENTION ENGINEERS. Source: DiNenno, Philip J., The SFPE Handbook of Fire Protection Engineering, 1st ed., Gaithersburg: Society of Fire Protection Engineers, 1988.

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Chapter 8: Plant Design and Operations 8.2.1.7 Fundamental Burning Velocities Fundamental Burning Velocities of Selected Gases and Vapors Gas Acetone Acetylene Acrolein Acrylonitrile Allene (propadiene) Benzene

n-butyltert-butyl1,2-dimethyl1,2,4-trimethyl1,2-Butadiene (methylallene) 1,3-Butadiene 2,3-dimethyl2-methyl-

n-Butane 2-cyclopropyl2,2-dimethyl2,3-dimethyl2-methyl2,2,3-trimethylButanone 1-Butene 2-cyclopropyl2,3-dimethyl 2-ethyl2-methyl3-methyl2,3-dimethyl-2-butene 2-Buten 1-yne (vinylacetylene) 1-Butyne 3,3-dimethyl2-Butyne Carbon disulfide Carbon monoxide

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Fundamental Burning Velocity

a cm s k 54 166* 66 50 87 48 37 39 37 39

Gas Cyclobutane ethylisopropylmethylCyclohexane methylCyclopentadiene Cyclopentane methylCyclopropane

68 64 52 55 45 47 42 43 43 42 42 51 50 46 46 46 49 44 89 68 56 61 58 46

cis-1,2-dimethyltrans-1,2-dimethylethylmethyl1,1,2-trimethyltrans-Decalin (decahydronaphthalene)

n-Decane 1-Decene Diethyl ether Dimethyl ether Ethane Ethene (ethylene) Ethyl acetate Ethylene oxide Ethylenimine Gasoline (100-octane) n-Heptane Hexadecane 1,5-Hexadiene n-Hexane 1-Hexene 1-Hexyne 3-Hexyne HFC-23 (Difluoromethane)

416

Fundamental Burning Velocity

a cm s k 67 53 46 52 46 44 46 44 42 56 55 55 56 58 52 36 43 44 47 54 47 80* 38 108 46 40 46 44 52 46 50 57 53 6.7

Chapter 8: Plant Design and Operations Fundamental Burning Velocities of Selected Gases and Vapors (cont'd) Gas HFC-143 (1,1,2-Trifluoroethane) HFC-143a (1,1,1-Trifluoroethane) HFC-152a (1,1-Difluoroethane) Hydrogen Isopropyl alcohol Isopropylamine Jet fuel, grade JP-1 (average) Methane diphenylMethyl alcohol Methylene 1,2-Pentadiene (ethylallene) cis-1,3-Pentadiene trans-1,3-Pentadiene (piperylene) 2-methyl-(cis or trans) 1,4-Pentadiene 2,3-Pentadiene

n-Pentane 2,2-dimethyl2,3-dimethyl2,4-dimethyl2-methyl3-methyl2,2-trimethyl-

Fundamental Burning Velocity

a cm s k

Gas

Fundamental Burning Velocity

a cm s k

13.1 7.1 23.6

1-Pentene 2-methyl4-methyl-

50 47 48

312* 41 31 40 40* 35

1-Pentene 4-methylcis-2-Pentene 2-Pentyne 4-methylPropane

63 53 51 61 54 46*

56 61 61 55 54 46 55 60 46

2-cyclopropyl1-deutero1-deutero-2-methyl2-deutero-2-methyl2,2-dimethyl2-methyl2-cyclopropyl2-methylPropionaldehyde

50 40 40 40 39 41 53 44 58

41 43

Propylene oxide (1,2-epoxypropane) 1-Propyne

82 82

42 43 43 41

Spiropentane Tetrahydopyran Tetralin (tetrahydronaphthalene) Toluene (methylbenzene)

71 48 39 41

* Gases that were critically examined as to their fundamental burning velocities, in studies by Andrews and Bradley (Andrews, G.E., and D. Bradley, "Determination of Burning Velocities: a Critical Review," Combustion and Flame, Vol. 18, New York: Elsevier Scientific Publishing Co., 1972, pp. 133–153) or by France and Pritchard (France, D.H., and R. Pritchard, "Burning Velocity Measurements of Multicomponent Fuel Gas Mixtures," Gas Warnie International, Vol. 26, No. 12, 1977). Source: Reproduced with permission from NFPA 68, Standard on Explosion Protection by Deflagration Venting, © 2013, National Fire Protection Association. This is not the complete and official position of the NFPA on the referenced subject, which is represented only by the standard in its entirety.

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Chapter 8: Plant Design and Operations The table below compares values from the Andrews/Bradley and France/Pritchard studies to those in the preceding table.

Comparison of Fundamental Burning Velocities for Selected Gases Fundamental Burning Velocity a s k Andrews and Bradley From Table Above In Air In Oxygen 166 158 1140 80 79 -

cm

Gas Acetylene Ethylene Hydrogen Methane Propane

312 40 46

310 45

1400 450 -

-

Flammability Properties of Gases Gas Volume: 5L (0.005 m3) Sphere Energy of the Ignition Source : E = 10J Flammable Material Pmax (bar-g) Acetophenonea Acetylene Ammoniab b-Naphtholc Butane Carbon disulfide Diethyl ether Dimethyl formamidea Dimethyl sulfoxidea Ethanea Ethyl alcohol Ethyl benzenea Hydrogen Hydrogen sulfide Isopropanola Methane Methanola Methylene chloride Methyl nitrite Neopentane Octanola

7.6 10.6 5.4 4.4 8.0 6.4 8.1 8.4 7.3 7.8 7.0 7.4 6.8 7.4 7.8 7.1 7.5 5.0 11.4 7.8 6.7

Octyl chloridea

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France and Pritchard (in Air) 0 347 43 46

Chapter 8: Plant Design and Operations Flammability Properties of Gases Gas Volume: 5L (0.005 m3) Sphere Energy of the Ignition Source : E = 10J (cont'd) Flammable Material Pmax (bar) Pentanea Propane South African crude oil Toluenea

7.8 7.9 6.8–7.6 7.8

a. Measured at elevated temperatures and extrapolated to 25°C (77°F) at normal conditions b. E = 100J - 200J c. 200°C (392°F) Source: Reproduced with permission from NFPA 68, Standard on Explosion Protection by Deflagration Venting, © 2013, National Fire Protection Association. This is not the complete and official position of the NFPA on the referenced subject, which is represented only by the standard in its entirety.

8.2.1.8 Combustible Dust Combustible dust is a solid material composed of distinct particles or pieces, regardless of size, shape, or chemical composition, that presents a fire or deflagration hazard when suspended in air or some other oxidizing medium over a range of concentrations. Combustible dusts are often either organic or metal dusts that are finely ground into very small particles, fibers, fines, chips, chunks, flakes, or a small mixture of these. According to OSHA's Safety and Health Information Bulletin (SHIB) "Combustible Dust in Industry: Preventing and Mitigating the Effects of Fire and Explosions," dust particles with an effective diameter of less than 420 microns (those passing through a U.S. No. 40 standard sieve) should be deemed to meet the criterion of the definition. However, larger particles can still pose a deflagration hazard (for instance, as larger particles are moved, they can abrade each other, creating smaller particles). In addition, particles can stick together (agglomerate) due to electrostatic charges accumulated through handling, causing them to become explosible when dispersed. Types of dusts include, but are not limited to: •

Metal dust, such as aluminum and magnesium

•

Wood dust

•

Plastic or rubber dust

•

Biosolids

•

Coal dust

•

Organic dust, such as flour, sugar, paper, soap, and dried blood

•

Dusts from certain textiles

Kst is the dust deflagration index, which measures relative explosion severity compared to other dusts. The larger the value for Kst, the more severe the explosion. Kst provides the best "single number" estimate of the anticipated behavior of a dust deflagration. MIE, the minimum ignition energy, predicts the ease and likelihood of ignition of a dispersed dust cloud. MEC, the minimum explosible concentration, measures the minimum amount of dust dispersed in air required to spread an explo­sion. The MEC is analogous to the Lower Flammable Limit (LFL) or Lower Explosive Limit (LEL) for gases and vapors in air. ©2020 NCEES

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Chapter 8: Plant Design and Operations Examples of Kst Values for Different Types of Dusts Dust Explosion Class* St 0 St 1 St 2 St 3

m Kst c bar : s m * 0 > 0 and < 200 > 200 and < 300 > 300

Characteristic

Typical materials**

No explosion Weak explosion Strong explosion Very strong explosion

Silica Powered milk, charcoal, sulfur, sugar, zinc Cellulose, wood flour, poly methyl acrylate Anthraquinone, aluminum, magnesium

* OSHA CPL 03-00-008 - Combustible Dust National Emphasis Program ** NFPA 68, Standard on Explosion Prevention by Deflagration Venting Source: OSHA 3371-08: Hazard Communication Guidance for Combustible Dust: Occupational Safety and Health Administration, 2009, p. 8-9. The actual class is sample-specific and will depend on varying characteristics of the material, such as particle size or moisture. Source for next five tables: Reproduced with permission from NFPA 68, Standard on Explosion Protection by Deflagration Venting, © 2013, National Fire Protection Association. This is not the complete and official position of the NFPA on the referenced subject, which is represented only by the standard in its entirety.

Agricultural Products Material

Cellulose Cellulose pulp Cork Corn Egg white Milk, powdered Milk, nonfat, dry Soy flour Starch, corn Starch, rice Starch, wheat Sugar Sugar, milk Sugar, beet Tapioca Whey Wood Flour

©2020 NCEES

Mass Median Diameter (mm) 33 42 42 28 17 83 60 20 7 18 22 30 27 29 22 41 29

Minimum Flammable Concentration

g l m3 60 30 30 60 125 60 200 60 30 200 60 60 125 125 -

b

420

Pmax _ bar i

Kst c bar : m sm

Dust Hazard Class

9.7 9.9 9.6 9.4 8.3 5.8 8.8 9.2 10.3 9.2 9.9 8.5 8.3 8.2 9.4 9.8 10.5

229 62 202 75 38 28 125 110 202 101 115 138 82 59 62 140 205

2 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 2

Chapter 8: Plant Design and Operations Carbonaceous Dusts

Material

Mass Median Diameter (mm)

Charcoal, activated Charcoal, wood Coal, bituminous Coke, petroleum Lampblack Lignite Peat, 22% H2O

28 14 24 15

QmRgT×106 H (kQVPM)

where T = absolute ambient temperature k

= nonideal mixing factor

QV = ventilation rate P = absolute ambient pressure

Sweep-through concentration change in a vessel: C –C QVt = V ln =C1 –C0 G 2

0

where

QV = volumetric flow rate t

= time

V = vessel volume ©2020 NCEES

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Chapter 8: Plant Design and Operations C0 = inlet concentration C1 = initial concentration C2 = final concentration

8.3 Protective Systems 8.3.1

Overpressure Protection/Pressure Relief

8.3.1.1 Major Types of Relief Devices Relief Devices CAP

Conventional pressure relief valve (PRV)/ Pressure Safety Valve (PSV) with a single adjusting ring for blowdown control

STEM SPINDLE ADJUSTING SCREW BONNET SPRING

Source: "Sizing, Selection, and Installation of Pressure-relieving Devices in Refineries: Part 1—Sizing and Selection," API Standard 520, 8th ed., December 2008, Figure 1. Courtesy of the American Petroleum Institute.

VENT (PLUGGED)

DISK SEATING SURFACE ADJUSTING RING BODY NOZZLE

CAP STEM SPINDLE ADJUSTING SCREW BONNET SPRING

VENT (UNPLUGGED)

BELLOWS DISK SEATING SURFACE ADJUSTING RING BODY ©2020 NCEES

NOZZLE

460

ADJUSTING RING BODY

Chapter 8: Plant Design and Operations

NOZZLE

CAP

Balance-Bellows PRV/PSV

STEM SPINDLE ADJUSTING SCREW

Source: "Sizing, Selection, and Installation of Pressure-relieving Devices in Refineries: Part 1—Sizing and Selection," API Standard 520, 8th ed., December 2008, Figure 2. Courtesy of the American Petroleum Institute.

BONNET SPRING

VENT (UNPLUGGED)

BELLOWS DISK SEATING SURFACE ADJUSTING RING BODY NOZZLE SET PRESSURE ADJUSTMENT SCREW SEAT

SPINDLE

PILOT VALVE

EXTERNAL BLOWDOWN ADJUSTMENT

PILOT EXHAUST

PILOT SUPPLY LINE

OPTIONAL PILOT FILTER

OUTLET PISTON SEAT

INTERNAL PRESSURE PICKUP INLET

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MAIN VALVE

461

Pop-Action Pilot-Operated Valve (Flowing Type)

Source: "Sizing, Selection, and Installation of Pressure-relieving Devices in Refineries: Part 1—Sizing and Selection," API Standard 520, 8th ed., December 2008, Figure 10. Courtesy of the American Petroleum Institute.

Chapter 8: Plant Design and Operations

Rupture Disc Assembly DISC

Source: Crowl, Daniel A., and Louvar, Joseph F., Chemical Process Safety: Fundamentals with Applications, 2nd ed., New York: Pearson Education 2002. With permission.

CARRIER ASSEMBLY

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Chapter 8: Plant Design and Operations 8.3.1.2 Pressure-Level Relationships for Pressure Relief Valves Pressure-Level Relationships for PRVs PRESSURE VESSEL REQUIREMENTS

VESSEL PRESSURE

MAXIMUM ALLOWABLE ACCUMULATED PRESSURE (FIRE EXPOSURE ONLY)

121

MULTIPLE VALVES AND MAXIMUM RELIEVING PRESSURE FOR PROCESS SIZING

116 115

SINGLE–VALVE MAXIMUM RELIEVING PRESSURE FOR PROCESS SIZING PERCENT OF MAXIMUM ALLOWABLE WORKING PRESSURE (GAUGE)

MAXIMUM ALLOWABLE WORKING PRESSURE OR DESIGN PRESSURE (SEE NOTE 4)

MAXIMUM RELIEVING PRESSURE FOR FIRE SIZING

120

MAXIMUM ALLOWABLE ACCUMULATIVE PRESSURE FOR MULTI-VALVE INSTALLATION (OTHER THAN FIRE EXPOSURE)

MAXIMUM ALLOWABLE ACCUMULATED PRESSURE FOR SINGLE–VALVE INSTALLATION(OTHER THAN FIRE EXPOSURE))

TYPICAL CHARACTERISTICS OF PRESSURE RELIEF VALVES

THE MAXIMUM ALLOWABLE SET PRESSURE FOR SUPPLEMENTAL VALVES (FIRE EXPOSURE)

110

OVERPRESSURE (MAXIMUM)

105

MAXIMUM ALLOWABLE SET PRESSURE FOR ADDITIONAL VALVES (PROCESS)

100

SIMMER (TYPICAL)

MAXIMUM ALLOWABLE SET PRESSURE FOR SINGLE VALVE

BLOWDOWN (TYPICAL) (SEE NOTE 6) 95

CLOSING PRESSURE FOR A SINGLE VALVE MAXIMUM EXPECTED OPERATING PRESSURE (SEE NOTES 5 AND 6)

90

LEAK TEST PRESSURE (TYPICAL)

85 NOTES: 1. THIS FIGURE CONFORMS WITH THE REQUIREMENTS OF SECTION VIII OF THE ASME BOILER AND PRESSURE VESSEL CODE FOR MAWPS GREATER THAN 30 PSIG. 2. THE PRESSURE CONDITIONS SHOWN ARE FOR PRESSURE RELIEF VALVE INSTALLED A PRESSURE VESSEL. 3. ALLOWABLE SET-PRESSURE TOLERANCES WILL BE IN ACCORDANCE WITH THE APPLICABLE CODES. 4. THE MAXIMUM ALLOWABLE WORKING PRESSURE IS EQUAL TO OR GREATER THAN THE DESIGN PRESSURE FOR COINCIDENT DESIGN TEMPERATURE. 5. THE OPERATING PRESSURE MAYBE HIGHER OR LOWER THAN 90%. 6. SECTION VIII, DIVISION 1, APPENDIX M OF THE ASME CODE SHOULD BE REFERRED TO FOR GUIDANCE ON BLOWDOWN AND PRESSURE DIFFERENTIALS.

Source: "Sizing, Selection, and Installation of Pressure-relieving Devices in Refineries: Part 1—Sizing and Selection," API Standard 520, 8th ed., December 2008. Courtesy of the American Petroleum Institute.

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Chapter 8: Plant Design and Operations 8.3.1.3 Relief Vent Sizing Relief-Venting Flammable Liquids

HEAT ABSORPTION, Q (BTU/HR)

.82

Q

14,090,000

0 (A) 0 0 1,0 =2

8

0.33

9,950,000

.

566

Q=

4,000,000

Q

0 (A) 0 0 ,3 199

Q

0 (A) 3,40 6 9 =

Q = 14,090,000

0A ,00 0 =2

400,000 20

200 1000 2800 2 EXPOSED WITH A SURFACE AREA, A (FT )

Source: Reproduced with permission from NFPA 30, Flammable and Combustible Liquid Code, © 2015, National Fire Protection Association. This is not the complete and official position of the NFPA on the referenced subject, which is represented only by the standard in its entirety.

Estimation of Emergency Relief Venting for Specific Liquids CFH =

70.5Q L M

where

CFH = cubic feet of free air per hour 70.5 = factor for converting pounds of gas to ft3 of air

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Q

= total heat input per hour (Btu)

L

Btu = latent heat of vaporization c lb m

M

= molecular weight

464

Chapter 8: Plant Design and Operations 8.3.1.4 Pressure Relief Variables and Constants Pressure Relief Variables and Constants Symbol

Description

Units (U.S.)

Units (metric)

in2

mm2

lbm-lb mole-cR lbf -hr

A

Required effective discharge area of the device

C

o of the A function of the ratio of the ideal gas-specific heats e k = Cv gas or vapor at inlet-relieving temperature

Cp

Specific heat at constant pressure

Btu lb cF

kg : kg mol : K mm 2 : hr : K Pa KJ kg K

Cv

Specific heat at constant volume

Btu lb cF

KJ kg K

F2

Coefficient of subcritical flow

Gl

Specific gravity of a liquid at flowing temperature referred to water at standard conditions

k

Ratio of the specific heats e

Kb

Kc

Kd for liquid

Cp

Cp o for an ideal gas at relieving temperaCv

ture. The ideal-gas to specific-heat ratio is independent of pressure. Capacity correction factor due to back pressure; can be obtained from manufacturer's literature or estimated for preliminary sizing. The backpressure correction factor applies to balanced-bellows valves only. For conventional and pilot-operated valves, use a value for Kb equal to 1.0. Combination correction factor for installations with a rupture disc upstream of the pressure relief valve. Equals 1.0 when a rupture disc is not installed; equals 0.9 when a rupture disc is installed in combination with a PRV and the combination does not have a certified value. Rated coefficient of discharge that should be obtained from the valve manufacturer. For preliminary sizing, an effective discharge coefficient can be used as follows: • 0.65 when a PRV is installed with or without a rupture disc in combination • 0.62 when a PRV is not installed and sizing is for a rupture disc with minimum net flow area

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dimensionless

dimensionless

dimensionless

dimensionless

Chapter 8: Plant Design and Operations Pressure Relief Variables and Constants (cont'd) Symbol

Kd for gas, vapor, steam

Description Effective coefficient of discharge. For preliminary sizing, use the following values:

Units (U.S.)

• 0.975 when a PRV is installed with or without a rupture disc in combination

Units (metric)

dimensionless

• 0.62 when a PRV is not installed and sizing is for a rupture disc with minimum net flow area

KN

Correction factor for the Napier equation (KN = 1.0)

dimensionless

KSH

Superheat correction factor; can be obtained from the "Superheat Correction Factors" table in this section. For saturated steam at any pressure, KSH = 1.0. For temperatures above 1200°F, use the critical vapor sizing equations.

dimensionless

Kv

Correction factor due to viscosity

dimensionless

KW

M

Correction factor due to back pressure. If the back pressure is atmospheric, use a value for KW of 1.0. Balanced-bellows valves in backpressure service require the correction determined from the figure "Capacity Correction Factor, KW, Due to Back Pressure on BalancedBellows PRVs in Liquid Service." Conventional and pilot-operated valves require no special correction. Molecular weight of the gas or vapor at inlet-relieving conditions. Various handbooks carry tables of molecular weights of materials; however, the composition of the flowing gas or vapor is seldom the same as that listed in such tables. This composition should be obtained from the process data.

dimensionless

P1

Upstream relieving pressure; set pressure plus allowable overpressure plus atmospheric pressure

psia

kPa

P2

Back pressure

psia

kPa

Q

Flow rate

U.S. gal min

L min

r

Ratio of back pressure to upstream relieving pressure, P2 1

dimensionless

Reynolds number

dimensionless

Re T m U V

P

Relieving temperature of the inlet gas or vapor

°R (°F + 460)

Absolute viscosity at the flowing temperature

cP

Viscosity at the flowing temperature

Saybolt universal seconds

Required flow through the device

W

Required flow through the device.

Z

Compressibility factor for the deviation of the actual gas from a perfect gas, evaluated at inlet-relieving conditions.

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K (°C + 273)

466

scfm at 14.7 psia and 60°F

normal m3 at 0°C min

lb h

kg h

and 101.325 kPa

dimensionless

Chapter 8: Plant Design and Operations Pressure Relief Equations Description

Coefficient C

Units (U.S.) (units per previous table) ^k + 1 h

2 ^k − 1 h kc k + 1 m

C = 520

Units (metric) (units per previous table)

C = 0.03948

KN = 1.0

KN = 1.0

where P 1 # 1, 500 psia Correction Factor KN

where P1 # 10, 339 kPa

0.1906 P − 1, 000 KN = 0.2292 P1 − 1, 061 1 where P1 > 1,500 psia and # 3, 200 psia

F2 =

Coefficient F2

0.02764 P − 1, 000 KN = 0.03324 P1 − 1, 061 1 where P1 > 10,339 kPa and # 22, 057 kPa

2 ck 1m c −k m rc k m >1 − r k H k 1 1−r −

W A=CK PK K d 1 b c

Sizing for Gas or Vapor Service at Critical Flow Conditions

^k + 1 h

2 ^k − 1 h kc k + 1 m

TZ M

Sizing for Subcritical Flow: Gas or Vapor, Conventional and Pilot-Operated PRVs When the ratio of back pressure to inlet pressure exceeds the critical pressure ratio Pcf /P1, the flow through the pressure-relief device is subcritical. These equations may be used to calculate the required effective discharge area for a conventional PRV whose spring setting is adjusted to compensate for superimposed back pressure. Equations may also be used for sizing a pilot-operated PRV. Sizing for Steam-Relief Operating at Critical Flow Conditions

©2020 NCEES

W A = 735 F K K 2 d c

TZ M P1 (P1 − P2)

W A = 51.5 P K K K K K 1 d b c N SH

467

17.9W A= F K K 2 d c

TZ M P1 (P1 − P2)

190.5W A= PK K K K K 1 d b c N SH

Chapter 8: Plant Design and Operations Pressure Relief Equations (cont'd) Description Sizing for Liquid Relief: PRVs Requiring Capacity Certification

Units (U.S.)

Units (metric)

The ASME Code requires that capacity certification be obtained for PRVs designed for liquid service. The procedure for obtaining capacity certification includes testing to determine the rated coefficient of discharge for the liquid PRVs at 10% overpressure. The sizing equations for pressure-relief devices in liquid service provided here assume that the liquid is incompressible (i.e., the density of the liquid does not change as the pressure decreases from the relieving pressure to the total back pressure).

Q A = 38 K K K K d w c v

G1 P1 − P2

11.78 Q A= K K K K d w c v

Kv = d 0.9935 +

2.878 + 342.75 1 0 n Re0.5 Re1.5

Valves in liquid service that are designed in accordance with the ASME Code may be initially sized using these area equations.

Kv: Correction Factor Due to Viscosity

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− .

G1 P1 − P2

Chapter 8: Plant Design and Operations Pressure Relief Equations (cont'd) Description

Units (U.S.)

Units (metric)

Re = Reynolds Number When a PRV is sized for viscous liquid service, it should first be sized as if it were for a nonviscous application (i.e., Kv = 1.0), so that a preliminary required discharge area A can be obtained from the liquid relief area equations above. From API 526 standard orifice sizes, use the next orifice size larger than A to determine the Reynolds Number, Re, from either of the following relationships:

Re =

Second equation is not recommended for viscosities less than 100 Saybolt universal seconds (SSU)

Q (2, 800 Gl) n A

Re =

12, 700 Q U A

After determining the Reynolds Number, Re, obtain the factor KV. Apply KV in the liquid relief area equations above to correct the preliminary required discharge area. If the corrected area exceeds the chosen standard orifice area, repeat the above calculations using the next larger standard orifice size. Source: Sizing, Selection, and Installation of Pressure-Relieving Devices in Refineries: Part 1—Sizing and Selection, API Standard 520, 8th ed., December 2008. Courtesy of the American Petroleum Institute.

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Chapter 8: Plant Design and Operations Superheat Correction Factors, KSH

Superheat Correction Factors Set Pressure psig (kPag) 15 (103) 20 (138) 40 (276) 60 (414) 80 (551) 100 (689) 120 (827) 140 (965) 160 (1103) 180 (1241) 200 (1379) 220 (1516)

300 (149) 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

400 (204) 0.98 0.98 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99

500 (260) 0.93 0.93 0.93 0.93 0.93 0.94 0.94 0.94 0.94 0.94 0.95 0.95

600 (316) 0.88 0.88 0.88 0.88 0.88 0.89 0.89 0.89 0.89 0.89 0.89 0.89

240 (1654) 260 (1792) 280 (1930) 300 (2068) 350 (2413) 400 (2757) 500 (3446) 600 (4136) 800 (5514) 1000 (6893) 1250 (8616) 1500 (10,339) 1750 (12,063) 2000 (13,786) 2500 (17,232) 3000 (20,679)

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

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 ---------

0.95 0.95 0.96 0.96 0.96 0.96 0.96 0.97 1.00 1.00 1.00 ------

0.90 0.90 0.90 0.90 0.90 0.91 0.92 0.92 0.95 0.96 0.97 1.00 1.00 1.00 1.00 --

Temperature °F (°C) 700 800 (371) (427) 0.84 0.80 0.84 0.80 0.84 0.81 0.84 0.81 0.84 0.81 0.84 0.81 0.84 0.81 0.85 0.81 0.85 0.81 0.85 0.81 0.85 0.81 0.85 0.81 0.85 0.85 0.85 0.85 0.86 0.86 0.86 0.87 0.88 0.89 0.91 0.93 0.94 0.95 0.95 1.00

0.81 0.81 0.81 0.81 0.82 0.82 0.82 0.82 0.83 0.84 0.85 0.86 0.86 0.86 0.85 0.82

900 (482) 0.77 0.77 0.77 0.77 0.77 0.77 0.78 0.78 0.78 0.78 0.78 0.78

1000 (538) 0.74 0.74 0.74 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75

1100 (593) 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72 0.72

1200 (649) 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70

0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.79 0.79 0.78 0.80 0.81 0.81 0.80 0.78 0.74

0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.76 0.76 0.77 0.77 0.77 0.76 0.73 0.69

0.72 0.72 0.72 0.72 0.72 0.72 0.73 0.73 0.73 0.73 0.74 0.74 0.73 0.72 0.69 0.65

0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.71 0.71 0.71 0.70 0.69 0.66 0.62

Source: Sizing, Selection, and Installation of Pressure-Relieving Devices in Refineries: Part 1—Sizing and Selection, API Standard 520, 8th ed., December 2008. Courtesy of the American Petroleum Institute.

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Chapter 8: Plant Design and Operations Capacity Correction Factor, KW, Due to Back Pressure on Balanced-Bellows PRVs in Liquid Service 1.00 0.95 0.90 0.85

Kw

0.80 0.75 0.70 0.65 0.60 0.55 0.50

0

10 20 30 40 PERCENT OF GAUGE BACKPRESSURE = (PB /PS) x 100

50

Kw = CORRECTION FACTOR DUE TO BACK PRESSURE. PB = BACK PRESSURE, IN PSIG. PS = SET PRESSURE, IN PSIG. NOTE: THE CURVE ABOUT REPRESENTS VALUES RECOMMENDED BY VARIOUS MANUFACTURERS. THIS CURVE MAY BE USED WHEN THE MANUFACTURER IS NOT KNOWN. OTHERWISE, THE MANUFACTURER SHOULD BE CONSULTED FOR THE APPLICABLE CORRECTION FACTOR.

Source: Sizing, Selection, and Installation of Pressure-Relieving Devices in Refineries: Part 1--Sizing and Selection, API 520, 8 ed., December 2008. Courtesy of the American Petroleum Institute

8.3.1.5 Discharge Location The discharge piping connected to the pressure relief device must be no smaller than the discharge opening of the device. The device must be piped to a point of safe discharge while keeping the run of discharge piping as short as possible. Discharge piping connected to the device must be supported so as not to impact any loadings on the body of the device. For multiple devices discharging into a discharge manifold or header, the discharge manifold or header must be sized so the cross-sectional area is equal to or greater than the sum of the discharge cross-sectional areas of all the devices connected to the discharge manifold or header.

8.3.2

Other Protections

8.3.2.1 Inerting and Blanketing Inerting, or blanketing, is the long-term maintenance of an inert atmosphere in the vapor space of a container or vessel during operation. This practice is used to control the concentration of oxygen, thereby reducing fire and explosion hazards.

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Chapter 8: Plant Design and Operations 8.3.2.2 Secondary Containment Secondary containment systems prevent migration of wastes or accumulated liquid out of the system to the soil, groundwater, or surface water during the use of the tank system. Federal hazardous waste storage regulations require the secondary containment system to have sufficient capacity to contain at least 10% of the total volume of the primary containers or 100% of the volume of the largest container, whichever is greater.

8.3.2.3 Safety Instrumented Systems Safety Instrumented Systems (SIS) are used where mechanical protection devices are not effective or not economically attractive. The SIS includes all the Safety Instrumented Functions in a process area. A Safety Instrumented Function (SIF) is a single shutdown loop with a sensor, a logic solver, and a final acting element. For example, a high temperature shutdown loop could consist of a temperature indicating transmitter, a programmable logic controller, and an automatically operated isolation valve to shut off a fuel source. Typically, the SIS will include a logic solver with sufficient reliability to support multiple SIFs that protect against the same undesired event. Safety Integrity Level (SIL) is a measure of reliability of a SIF. The SIL requirement for each SIF is generally set during Layer of Protection Analysis (LOPA). SIL sets the redundancy and testing requirements. In detailed design, the specific instrumentation, control device(s), and logic solver are selected for each SIF. Then, the Probability of Failure on Demand (PFD) for the SIF is calculated using data for the failure rate of each component and the proposed testing frequency. The resulting PDF is checked against the SIL required. The SIF design or testing frequency can then be modified to meet requirements if necessary.

8.4 Environmental Considerations 8.4.1

Air Pollution

Concentrations in air can be converted from ppb to

P _ MW i ng 3 = ppb RT m

ng as follows: m3

where ppb = parts per billion P = pressure, in atm

liter : atm

R = ideal gas law constant = 0.0821 mol : K T = absolute temperature, K = 273.15 + °C

g

MW = molecular weight, in mol

8.4.1.1 Atmospheric Dispersion Modeling σy and σz are functions of downwind distance and stability class: 2 Q ^z − H h ^z + H h 1 y p + exp f − 12 pH C = 2ruv v exp f − 2 2 p>exp f − 1 2 2 y z vy vz v 2z 2

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2

472

Chapter 8: Plant Design and Operations where C = steady-state concentration at a point (x, y, z) in

ng

ng m3

Q = emissions rate in s

σy = horizontal dispersion parameter, in meters σz = vertical dispersion parameter, in meters

m

u

= average wind speed at stack height in s

x

= downwind distance along plume center line, in meters

y

= horizontal distance from plume center line, in meters

z

= vertical distance from ground level, in meters

H = effective stack height (m) = h + ∆h where

h



∆h = plume rise

= physical stack height

Maximum concentration at ground level and directly downwind from an elevated source: 2 Q 1 _H i Cmax = ruv v exp f − 2 2 p y z vz

where variables are as above except for Cmax = maximum ground-level concentration

vz =

H for neutral atmospheric conditions 2

Atmospheric Stability Under Various Conditions Surface Wind m Speeda in s 6

Strongb

Day: Solar Insulation Moderatec

Slightd

A A-B B C C

A-Bf B B-C C-D D

B C C D D

Night: Cloudinesse Cloudy ( 0.05 IN. PER YR. MONEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

AIR FREE

AERATED

ACID, HYDROFLUORIC

50

ACID, FORMIC

0

CONCENTRATION, %

ACID, CITRIC

0

ACID, CHROMIC

100

ACID, BORIC

200

ACID, HYDROCHLORIC

300

ACID, ACETIC

TEMPERATURE, °F

KEY TO CHARTS

AIR FREE

AIR FREE

AIR FREE

AIR FREE

AIR FREE

AIR FREE

NEOPRENE = SATISFACTORY = FOR LIMITED USE ONLY = UNSATISFACTORY NICKEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

AIR FREE

AERATED

PHENOLIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY POLYETHYLENE = COMPLETE RESISTANCE = SOME ATTACK = ATTACK OR DECOMPOSITION RUBBER (NATURAL, GR-S)

HARD RUBBER

HARD RUBBER

= SATISFACTORY = SATISFACTORY FOR LIMITED USE = GENERALLY UNSATISFACTORY

HARD RUBBER

RUBBER, BUTYL = SATISFACTORY = SATISFACTORY FOR LIMITED USE = GENERALLY UNSATISFACTORY

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SOFT GR-S CANNOT BE USED

517

Chapter 8: Plant Design and Operations Detailed Corrosion Data on Construction Materials (cont'd)

100

CONCENTRATION, % STAINLESS STEEL, 18-8 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, TYPE 316 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 12% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 17% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

STRESS CORROSION

STEEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STYRENE COPOLYMERS, HIGH IMPACT = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY ZIRCONIUM = < 0.002 IN. PER YR. = 0.002 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

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ACID, HYDROFLUORIC

50

ACID, FORMIC

0

ACID, CITRIC

0

ACID, CHROMIC

100

ACID, BORIC

200

ACID, HYDROCHLORIC

300

ACID, ACETIC

TEMPERATURE, °F

KEY TO CHARTS

Chapter 8: Plant Design and Operations Detailed Corrosion Data on Construction Materials (cont'd)

100

ALUMINUM = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

IN ETHANOL

ASPHALTIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = UNSATISFACTORY

AIR FREE

COPPER, AL BRONZE, TIN BRONZE = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. EPOXY RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = NOT RECOMMENDED

AERATED

DRY

IN ETHANOL

GLASS = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

300

400 F

200 TECH NOT RECOMMENDED 600 F

HASTELLOY C = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

TECH

HASTELLOY D = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

©2020 NCEES

AIR FREE

AERATED, NO VELOCITY

IN ETHANOL

FURANE RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY

HASTELLOY B = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

AMMONIA, AQUEOUS

50

ALUMINUM POTASSIUM SULFATE (ALUM)

0

CONCENTRATION, %

ACID, SULFURIC

0

ACID, OXALIC

100

ACID, PHOSPHORIC

200

ALUMINUM CHLORIDE

300

ACID, NITRIC

TEMPERATURE, °F

KEY TO CHARTS

519

SLUDGEHCI AND 250 PSI

Chapter 8: Plant Design and Operations Detailed Corrosion Data on Construction Materials (cont'd)

50

100

IRON, CAST = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. MONEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

AIR FREE, NO VELOCITY

AIR FREE

AERATED, NO VELOCITY

AIR FREE

AERATED

NEOPRENE = SATISFACTORY = FOR LIMITED USE = UNSATISFACTORY NICKEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

AERATED

IN ETHANOL

PHENOLIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY POLYETHYLENE = COMPLETE RESISTANCE = SOME ATTACK = ATTACK OR DECOMPOSITION RUBBER (NATURAL, GR-S) = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY RUBBER, BUTYL = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY

©2020 NCEES

AERATED, NO VELOCITY

520

AMMONIA, AQUEOUS

0

CONCENTRATION, %

ALUMINUM POTASSIUM SULFATE (ALUM)

0

ALUMINUM CHLORIDE

100

ACID, OXALIC

200

ACID, SULFURIC

ACID, PHOSPHORIC

300

ACID, NITRIC

TEMPERATURE, °F

KEY TO CHARTS

Chapter 8: Plant Design and Operations Detailed Corrosion Data on Construction Materials (cont'd)

100

STAINLESS STEEL, 18-8 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, TYPE 316 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 12% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 17% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STEEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

STRESS AIR FREE, NO VELOCITY CRACKS

IN ETHANOL

STYRENE COPOLYMERS, HIGH IMPACT = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY ZIRCONIUM = < 0.002 IN. PER YR. = 0.002 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

©2020 NCEES

521

AMMONIA, AQUEOUS

50

ALUMINUM POTASSIUM SULFATE (ALUM)

0

CONCENTRATION, %

ALUMINUM CHLORIDE

0

ACID, SULFURIC

100

ACID, OXALIC

200

ACID, PHOSPHORIC

300

ACID, NITRIC

TEMPERATURE, °F

KEY TO CHARTS

Chapter 8: Plant Design and Operations Detailed Corrosion Data on Construction Materials (cont'd)

0

0

50

100

CONCENTRATION, % ALUMINUM = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. ASPHALTIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY COPPER, AL BRONZE, TIN BRONZE = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. EPOXY RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = NOT RECOMMENDED FURANE RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY GLASS = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY B = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY C = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY D = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

©2020 NCEES

522

CALCIUM HYPOCHLORITE

100

CALCIUM CHLORIDE

200

AMMONIUM CHLORIDE

300

AMMONIUM CARBONATE

TEMPERATURE, °F

KEY TO CHARTS

Chapter 8: Plant Design and Operations Detailed Corrosion Data on Construction Materials (cont'd)

0

0

50

100

CONCENTRATION, % IRON, CAST = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. MONEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. NEOPRENE = SATISFACTORY = FOR LIMITED USE ONLY = UNSATISFACTORY

AVOID HCI AND Fe, NI IONS

NICKEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. PHENOLIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY POLYETHYLENE = COMPLETE RESISTANCE = SOME ATTACK = ATTACK OR DECOMPOSITION RUBBER (NATURAL, GR–S) = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY RUBBER, BUTYL = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY

©2020 NCEES

523

CALCIUM HYPOCHLORITE

100

CALCIUM CHLORIDE

200

AMMONIUM CHLORIDE

300

AMMONIUM CARBONATE

TEMPERATURE, °F

KEY TO CHARTS

Chapter 8: Plant Design and Operations Detailed Corrosion Data on Construction Materials (cont'd)

0

0

50

100

CONCENTRATION, % STAINLESS STEEL, 18-8 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, TYPE 316 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 12% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 17% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STEEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

pH > 7

STYRENE COPOLYMERS, HIGH IMPACT = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY ZIRCONIUM = < 0.002 IN. PER YR. = 0.002 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

©2020 NCEES

524

pH > 7

CALCIUM HYPOCHLORITE

100

CALCIUM CHLORIDE

200

AMMONIUM CHLORIDE

300

AMMONIUM CARBONATE

TEMPERATURE, °F

KEY TO CHARTS

Chapter 8: Plant Design and Operations Detailed Corrosion Data on Construction Materials (cont'd)

100

FERROUS SULFATE

50

FERROUS CHLORIDE

0

CONCENTRATION, %

FERRIC CHLORIDE

0

ETHANOL

100

ETHYLENE GLYCOL

200

ALUMINUM = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. ASPHALTIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY AIR FREE

COPPER, AL BRONZE, TIN BRONZE = < 0.002 IN. PER YR. = 0.002 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. EPOXY RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = NOT RECOMMENDED FURANE RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY GLASS = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY B = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY C = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY D = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

©2020 NCEES

0.09% HCI

525

GLYCERINE

300

COPPER SULFATE

TEMPERATURE, °F

KEY TO CHARTS

Chapter 8: Plant Design and Operations Detailed Corrosion Data on Construction Materials (cont'd)

100

IRON, CAST = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. MONEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. NEOPRENE = SATISFACTORY = FOR LIMITED USE ONLY = UNSATISFACTORY PITS

NICKEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. PHENOLIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY POLYETHYLENE = COMPLETE RESISTANCE = SOME ATTACK = ATTACK OR DECOMPOSITION RUBBER (NATURAL, GR–S) = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY RUBBER, BUTYL = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY

©2020 NCEES

526

FERRIC CHLORIDE

50

FERROUS SULFATE

0

CONCENTRATION, %

FERROUS CHLORIDE

0

ETHANOL

100

ETHYLENE GLYCOL

200

GLYCERINE

300

COPPER SULFATE

TEMPERATURE, °F

KEY TO CHARTS

Chapter 8: Plant Design and Operations Detailed Corrosion Data on Construction Materials (cont'd)

100

STAINLESS STEEL, 18-8 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, TYPE 316 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 12% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 17% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STEEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STYRENE COPOLYMERS, HIGH IMPACT = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY

DRY

ZIRCONIUM = < 0.002 IN. PER YR. = 0.002 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

©2020 NCEES

527

FERROUS SULFATE

50

FERROUS CHLORIDE

0

CONCENTRATION, %

FERRIC CHLORIDE

0

ETHANOL

100

ETHYLENE GLYCOL

200

GLYCERINE

300

COPPER SULFATE

TEMPERATURE, °F

KEY TO CHARTS

DISCOLORS

Chapter 8: Plant Design and Operations Detailed Corrosion Data on Construction Materials (cont'd)

ALUMINUM = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. ASPHALTIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY COPPER, AL BRONZE, TIN BRONZE = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. EPOXY RESINS

AIR FREE

AIR FREE

= SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY FURANE RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY GLASS = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY B = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY C = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY D = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

©2020 NCEES

528

AIR FREE

POTASSIUM HYDROXIDE

100

PHENOL

50

NICKEL SULFATE

0

CONCENTRATION, %

NICKEL CHLORIDE

0

METHANOL

100

MAGNESIUM SULFATE

200

MAGNESIUM CHLORIDE

300

HYDROGEN PEROXIDE

TEMPERATURE, °F

KEY TO CHARTS

Chapter 8: Plant Design and Operations Detailed Corrosion Data on Construction Materials (cont'd)

IRON, CAST = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. MONEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. NEOPRENE

ALKALINE

DISCOLORS

DRY AIR FREE

= SATISFACTORY = FOR LIMITED USE ONLY = UNSATISFACTORY DRY

NICKEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. PHENOLIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY POLYETHYLENE = COMPLETE RESISTANCE = SOME ATTACK = ATTACK OR DECOMPOSITION RUBBER (NATURAL, GR-S) = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY RUBBER, BUTYL = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY

©2020 NCEES

529

AIR FREE, SULFER FREE PITS

POTASSIUM HYDROXIDE

100

PHENOL

50

NICKEL SULFATE

0

CONCENTRATION, %

NICKEL NITRATE

0

METHANOL

100

MAGNESIUM SULFATE

200

MAGNESIUM CHLORIDE

300

HYDROGEN PEROXIDE

TEMPERATURE, °F

KEY TO CHARTS

AIR FREE

Chapter 8: Plant Design and Operations Detailed Corrosion Data on Construction Materials (cont'd)

STAINLESS STEEL, 18-8 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, TYPE 316 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 12% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 17% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STEEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STYRENE COPOLYMERS, HIGH IMPACT = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY

800 F.

800 F.

ALKALINE

pH > 7

pH > 7

STRESS CRACKS

PITS

DISCOLORS, SULFUR FREE

AIR FREE

STRESS CRACKS

ZIRCONIUM = < 0.002 IN. PER YR. = 0.002 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

©2020 NCEES

POTASSIUM HYDROXIDE

100

PHENOL

50

NICKEL SULFATE

0

CONCENTRATION, %

NICKEL NITRATE

0

METHANOL

100

MAGNESIUM SULFATE

200

MAGNESIUM CHLORIDE

300

HYDROGEN PEROXIDE

TEMPERATURE, °F

KEY TO CHARTS

530

Chapter 8: Plant Design and Operations Detailed Corrosion Data on Construction Materials (cont'd)

100

ZINC SULFATE

50

ZINC CHLORIDE

0

CONCENTRATION, %

SODIUM NITRATE

0

SODIUM HYDROXIDE

100

SODIUM CHLORIDE

200

SODIUM CARBONATE

300

POTASSIUM SULFATE

TEMPERATURE, °F

KEY TO CHARTS

ALUMINUM = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. ASPHALTIC RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY PITS

COPPER, AL BRONZE, TIN BRONZE = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. EPOXY RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY FURANE RESINS = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY GLASS = < 0.005 IN. PER YR. = 0.005 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

10 20 30

HASTELLOY B = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY C = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. HASTELLOY D = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

©2020 NCEES

531

AIR FREE

Chapter 8: Plant Design and Operations Detailed Corrosion Data on Construction Materials (cont'd)

100

ZINC SULFATE

50

ZINC CHLORIDE

0

CONCENTRATION, %

SODIUM NITRATE

0

SODIUM HYDROXIDE

100

SODIUM CHLORIDE

200

SODIUM CARBONATE

300

POTASSIUM SULFATE

TEMPERATURE, °F

KEY TO CHARTS

DRY

= < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

AIR FREE

= < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

1300 F.

400 F.

= SATISFACTORY = FOR LIMITED USE ONLY = UNSATISFACTORY 600 F.

= < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

1300 F.

= SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY = COMPLETE RESISTANCE = SOME ATTACK = ATTACK OR DECOMPOSITION = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY = SATISFACTORY = SATISFACTORY FOR LIMITED SERVICE = GENERALLY UNSATISFACTORY

©2020 NCEES

532

STRESS CRACKS

950 F.

DRY

AIR FREE

Chapter 8: Plant Design and Operations Detailed Corrosion Data on Construction Materials (cont'd)

100

STAINLESS STEEL, 18-8 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, TYPE 316 = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 12% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STAINLESS STEEL, 17% Cr = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR. STEEL = < 0.002 IN. PER YR. = < 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

DRY

pH > 7 STRESS CRACKS STRESS CRACKS AT HIGHER TEMPS.

STYRENE COPOLYMERS, HIGH IMPACT = SATISFACTORY = SATISFACTORY FOR LIMITED USE = UNSATISFACTORY ZIRCONIUM = < 0.002 IN. PER YR. = 0.002 - 0.02 IN. PER YR. = 0.02 - 0.05 IN. PER YR. = > 0.05 IN. PER YR.

©2020 NCEES

533

ZINC SULFATE

50

ZINC CHLORIDE

0

CONCENTRATION, %

SODIUM NITRATE

0

SODIUM HYDROXIDE

100

SODIUM CHLORIDE

200

SODIUM CARBONATE

300

POTASSIUM SULFATE

TEMPERATURE, °F

KEY TO CHARTS

Chapter 8: Plant Design and Operations 8.6.2.1 Galvanic Corrosion Galvanic Corrosion 0.2

0

–0.2

–0.4

–0.6

–0.8

–1.0

–0.2

–1.4

–1.6

MAGNESIUM ZINC BERYLLIUM ALUMINUM ALLOYS CADMIUM MILD STEEL & CAST IRON LOW ALLOY STEEL AUSTIENITIC CAST IRON ALUMINUM BRONZE NAVAL BRASS, YELLOW BRASS & RED BRASS TIN COPPER 50/50 LEAD TIN SOLDER ADMIRALTY BRASS, ALUMINUM BRASS MANGANESE BRONZE SILICON BRONZE STAINLESS STEEL – GRADES 410, 416 NICKEL SILVER 90/10 COPPER NICKEL 80/20 COPPER NICKEL STAINLESS STEEL – GRADE 430 LEAD 70/30 COPPER NICKEL NICKEL ALUMINUM BRONZE NICKEL CHROMIUM ALLOY 600 NICKEL 200 SILVER STAINLESS STEEL – GRADES 302, 304, 321 & 347 NICKEL COPPER ALLOYS – 400, K500 STAINLESS STEEL – GRADES 316 & 317 ALLOY 20 STAINLESS STEEL NICKEL IRON CHROMIUM ALLOY 825 TITANIUM GOLD, PLATINUM GRAPHITE

MOST NOBLE – CATHODIC

LEAST NOBLE – ANODIC

Note: Unshaded symbols show ranges exhibited by stainless steels in acidic water such as may exist in crevices or in stagnant, low-velocity, or poorly aerated water. Source: Davis, J.R., ASM Specialty Handbook on Stainless Steel, 2nd ed.: American Society for Metals, 1996, p. 139. Reprinted with permission of ASM International. All rights reserved. www.asminternational.org.

8.6.2.2 Electrochemistry Electrochemical Terms

©2020 NCEES

Term Cathode

Definition The electrode at which reduction occurs

Anode Oxidation Reduction Cation Anion

The electrode at which oxidation occurs The loss of electrons The gaining of electrons Positive ion Negative ion

534

Chapter 8: Plant Design and Operations 8.6.2.3 Standard Oxidation Potentials Standard Oxidation Potentials for Corrosion Reactions* Potential (Eo) Volts vs. Corrosion Reaction Normal Hydrogen Electrode + − Au " Au3 + 3e

-1.498

+ − 2H2O " O2 + 4H + 4e

-1.229

+ − Pt " Pt 2 + 2e

-1.200

+ − Pd " Pd 2 + 2e

-0.987

+ − Ag " Ag + e

-0.799

+ − 2Hg " Hg 22 + 2e

-0.788

+ + − Fe 2 " Fe3 + e

-0.771

4 ^OH h " O2 + 2H2O + 4e −

-0.401

−

+ − Cu " Cu 2 + 2e

-0.337

+ + − Sn 2 " Sn 4 + 2e

-0.150

+ − H2 " 2H + 2e

+0.000

+ − Pb " Pb 2 + 2e

+0.126

+ − Sn " Sn 2 + 2e

+0.136

+ − Ni " Ni 2 + 2e

+0.250

+ − Co " Co 2 + 2e

+0.277

+ − Cd " Cd 2 + 2e

+0.403

+ − Fe " Fe 2 + 2e

+0.440

+ − Cr " Cr3 + 3e

+0.744

+ − Zn " Zn 2 + 2e

+0.763

+ − Al " Al3 + 3e

+1.662

+ − Mg " Mg 2 + 2e

+2.363

+ − Na " Na + e

+2.714

+ − K " K +e

+2.925

*Measured at 25°C. Reactions are written as anode half-cells. Arrows are reversed for cathode half-cells. Note: In some chemistry texts, the reactions and the signs of the values (in this table) are reversed; for example, the half-cell + − potential of zinc is given as –0.763 volt for the reaction Zn 2 + 2e " Zn . When the potential Eo is positive, the reaction proceeds spontaneously as written. Source: Republished with permission of John Wiley and Sons, from Engineering Materials and Their Applications, Richard A. Flinn and Paul K. Trojan, 3rd ed., 1986; permission conveyed through Copyright Clearance Center, Inc.

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Chapter 8: Plant Design and Operations

8.7 Process Equipment Design Installation Practices for Equipment Relief System

Recommendations

For rupture disc in corrosive service, or for highly toxic materials where spring-loaded reliefs may weep.

VESSEL

P

For two rupture discs in extremely corrosive service. The first may need to be replaced periodically.

For rupture disc and spring-loaded relief. Normal relief may go through spring-loaded device and rupture disc is backup for larger reliefs.

For two reliefs in series. The rupture disc protects against toxicity or corrosion. The springloaded relief closes and minimizes losses.

P

For two rupture discs with 3-way valve that keeps one valve always directly connected to vessel. This design is good for polymerization reactors that require periodic cleaning.

C

A

B VESSEL

A. Pressure drop not more than 3% of set pressure. B. Long radius elbow. C. If distance is greater than 10 feet, support weight and reaction forces below the long radius elbow.

For orifice area of a single safety relief in vapor service; should not exceed 2% of the crosssectional area of the protected line. May require multiple valves with staggered settings. PIPE

A. Process lines; should not be connected to safety-valve inlet piping. A ©2020 NCEES

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Chapter 8: Plant Design and Operations Installation Practices for Equipment Relief (cont'd) System

Recommendations A. Turbulence-causing device. B. Dimension shown below:

A

Device Causing the Turbulence B

Regulator or valve 2 ells or bends not in same plane 2 ells or bends in same plane 1 ell or bend Pulsation damper

Minimum Number of Straight-Pipe Diameters 25 20 15 10 10

Source: Jennet, Eric, "Components of Pressure-Relieving Systems," Equipment Relief Installation Practices: Chemical Engineering Magazine, 1963, pp. 151–158.

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Chapter 8: Plant Design and Operations

8.8 Instrumentation and Process Control 8.8.1

Sensors

Commonly Used Process Instruments

Measured Variable

Instrument Type

Operating Principle

Pressure (gauge)

Differential pressure (DP) cell

Pressure difference causes displacement of a diaphragm. The displacement can be transmitted mechanically to a bellows to register a pneumatic signal or converted to an electrical signal by a strain gauge or by movement of the diaphragm relative to a static capacitor plate. Gauge pressure is measured relative to atmospheric pressure.

Pressure difference

DP cell

As above. Pressure difference is measured between two points in the process.

Temperature

Thermocouple

Wires of different metals joined together to form a circuit with one joint hotter than the other will develop an EMF through the Seebeck effect. If one joint is at a reference temperature the other temperature can be found from the EMF. The reference temperature is usually ambient temperature, which is determined by measuring the electrical resistance of a platinum wire. Different combinations of metal wire are used depending on the temperature range. See Love (2007) for details of thermocouple types.

Temperature

RTD

Resistance is measured in a length of pure metal wire. The relationship between temperature and resistance is known for the given metal, and the measurement can be used to calculate the temperature.

Volumetric flow

Orifice meter

Flow passes through a restriction orifice. Pressure difference across the orifice is measured with a DP cell. Flow rate is calculated from pressure drop.

Volumetric flow

Venturi meter

Flow passes through a shaped pipe restriction. Pressure difference across the restriction is measured with a DP cell. Flow rate is calculated from pressure drop.

Mass flow

Coriolis meter

Flow through a shaped vibrating pipe loop causes it to twist due to the Coriolis effect. The extent of twist is measured optically. These instruments can be used for multiphase flow, but are expensive, particularly for large flow rates.

Level

DP cell

A DP cell placed between the top and bottom of a vessel can indicate level if there is no internal pressure drop in the vessel.

Level

Capacitance probe

The capacitance between a probe in the center of the vessel and the wall is affected by the dielectric constant of the material between them, and so varies with level.

Level

Radar

The sensor sends a radio wave emission out into the vessel and measures how long it takes for the signal to be reflected back. The return signal can be used to accurately calculate the level.

Interface level

DP cell

A DP cell can determine the interface level between immiscible fluids if they are in a vessel that has an internal weir (so that overall level remains constant).

pH

Glass electrode

The glass electrode and a reference electrode (usually silver/silver chloride) form an electrochemical circuit allowing EMF to be measured.

Composition

Chromatograph

Gas chromatography (GC ) can be used to separate simple mixtures and generate a signal through a thermal conductivity detector (TCD) or flame ionization detector (FID). GC methods are difficult to use for online control because the chromatography typically takes a few minutes, but they can be used in cascade control schemes to adjust set points on other controllers.

Source: Reprinted from Chemical Engineering Design, 2nd ed., Gavin Towler and Ray Sinnott, "Table 5.2, Instrumentation and Process Control," p. 258, ©2013, with permission from Elsevier, www.elsevier.com. ©2020 NCEES

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Chapter 8: Plant Design and Operations

8.8.2

Controller Actions

In order to determine the action of a controller, it is first necessary to understand the final control element, which is typically a control value. Control valves are designed to fail in the wide-open position or completely shut. The fail-open (FO) valves require increased air pressure to close, or are air-to-close (AC). The fail-closed (FC) valves require increased air pressure to open (AO). Less commonly, some control valves are fail-last (FL) position. The decision of which type to use depends on the process and safety considerations. The action of the feedback controller will depend on the action of the transmitter (typically direct), the action of the valve (FO/FC), and the effect of the manipulated variable on the process variable. If the proportional gain of the controller is negative, i.e. the controller output increases when the process variable increases, then it is called a direct-acting controller. If the proportional gain is positive, i.e. the controller output decreases when the process variable increases, then it is called a reverseacting controller. Source: Republished with permission of McGraw-Hill, Inc., from Process Modeling, Simulation and Control for Chemical Engineers, William L. Luyben, 2nd ed., 1990; permission conveyed through Copyright Clearance Center, Inc.

8.8.2.1 First-Order Control System Models The transfer function model for a first-order system is

Y (s) = K R (s) xs + 1 where K = steady-state gain t = time constant

Y (s) Laplace transforms of output, in deviation form = R (s) Laplace transforms of input, in deviation form The step response of a first-order system to a step input of magnitude M is

y (t) = y0 e

−t/x

+ KM (1 − e −t/x)

In the chemical process industry, y0 is typically taken to be zero, and y(t) is referred to as a deviation variable. For systems with time delay (dead time or transport lag) q, the transfer function is

Y (s) Ke − is = R (s) xs + 1 The step response for t ≥ q to a step of magnitude M is

y (t) = 8 y0 e − (t − i)/x + KM (1 − e − (t − i)/x)Bu (t − i) where

u(t) = unit step function

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Chapter 8: Plant Design and Operations 8.8.2.2 Second-Order Control System Models One standard second-order control system model is

Y (s ) K~ 2n = 2 R (s) s + 2g~ n s + ~ 2n

where K = steady-state gain z = the damping ratio wn = the undamped natural (z = 0) frequency

~ d = ~ n 1 − g 2 , the damped natural frequency ~ r = ~ n 1 − 2g 2 , the damped resonant frequency If the damping ratio z is less than unity, the system is said to be underdamped; if z is equal to unity, it is said to be critically damped; and if z is greater than unity, the system is said to be overdamped. For a unit step input to a normalized, underdamped, second-order control system, the time required to reach a peak value tp and the value of that peak Mp are determined by

tp =

r ~n 1 − g 2

Mp = 1 + e

− rg/ 1 − g 2

The percent overshoot (%OS) of the response is determined by

%OS = 100e

− rg/ 1 − g 2

For an underdamped, second-order system, the logarithmic decrement is

2rg x 1 d = m 1n d x k n = k+m 1 − g2 where xk and xk+m are the amplitudes of oscillation at cycles k and k + m, respectively. The period of oscillation t is related to wd by wdt = 2p The time required for the output of a second-order system to settle to within 2% of its final value (2% settling time) is defined to be

Ts =

4 g~ n

An alternative form commonly employed in the chemical process industry is

Y (s ) K = R (s) x 2 s 2 + 2gxs + 1 where K = steady-state gain z = the damping ratio t = the inverse natural frequency

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Chapter 8: Plant Design and Operations Feedback Control CONTROLLER TIC

COLD PROCESS FLUID

TEMPERATURE TT TRANSMITTER

STEAM

HOT PROCESS FLUID

Feed Forward Control CONTROLLER FIC COLD PROCESS FLUID

FT

FLOW TRANSMITTER

STEAM

HOT PROCESS FLUID

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Chapter 8: Plant Design and Operations Feed Forward Plus Feedback Control FEED FORWARD CONTROLLER FIC

SUMMING CONTROLLER QIC

FEEDBACK CONTROL TIC

FT

COLD PROCESS FLUID

FLOW TRANSMITTER TT

TEMPERATURE TRANSMITTER

STEAM

HOT PROCESS FLUID

Cascaded Feedback Control TIC PRIMARY CONTROLLER COLD PROCESS FLUID SECONDARY CONTROLLER

TEMPERATURE TT TRANSMITTER

FIC

FT STEAM

8.8.3

HOT PROCESS FLUID

FLOW TRANSMITTER

Alarms

Alarms are tools to help operators quickly identify conditions that are abnormal or threaten process or personal safety. Alarms may be accompanied by audible or visible cues on control panels or SCADA systems. Alarms are often communicated to plant operators to allow rapid response to undesirable conditions. Where a response within the necessary time to prevent a catastrophic failure is either unlikely or impossible, a system should be installed with an automatic trip or interlock to prevent failure. Alarms are typically generated within a computer or programmable logic device that perform a logical operation based on the system instrumentation and controls. These setpoints are often user configurable and set by the plant operators. Source: Reprinted from Chemical Engineering Design, 2nd ed., Gavin Towler and Ray Sinnott, "Alarms, Safety Trips and Interlocks," pp. 270–272, and "Layers of Plant Safety," pp. 433–435, ©2013, with permission from Elsevier, www.elsevier.com. ©2020 NCEES

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Chapter 8: Plant Design and Operations

8.8.4

Safety Instrumented Systems Definitions of Safety Integrity Terms Term

Definition Arrangement of hardware and/or software elements in a system; for example:

Architecture

Average Probability of Failure on Demand (PFDavg) Basic Process Control System (BPCS) Common Cause Failure MooN Mean Time to Fail (MTTF) Mean Time to Trip Spurious (MTTFS) Safe Failure Fraction (SFF) Safety Instrumented System (SIS) Safety Integrity Level (SIL) Safety Instrumented Function (SIF) Systematic Failure Tolerable Risk Validation

Verification

(1) Arrangement of safety instrumented system (SIS) subsystems (2) Internal structure of an SIS subsystem (3) Arrangement of software programs Average probability that a safety-instrumented function will fail in such a way that it cannot respond to a potentially dangerous condition. PFD or PFDavg is applied to repairable systems. System that responds to input signals from the process, its associated equipment, other programmable systems, and/or an operator and generates output signals causing the process and its associated equipment to operate in the desired manner but that does not perform any safety-instrumented functions with a claimed SIL $ 1. Failure that is the result of one or more events and that causes failure of two or more separate channels in a multiple-channel system, leading to system failure. Safety instrumented system, or part thereof, made up of N independent channels that are so connected that M channels are sufficient to perform the safety-instrumented function. Mean time to random failure for a component population. MTTF is applied to items that are not repaired, such as bearings and transistors. Mean time for a safety function to fail in a mode that causes a spurious trip. Fraction of the overall random hardware failure rate of a device that results in either a safe failure or a detected dangerous failure. Instrumented system used to implement one or more safety-instrumented functions. A SIS is composed of any combination of sensor(s), logic solver(s), and final element(s). Discrete level (one out of four) for specifying the safety integrity requirements of the safety-instrumented functions to be allocated to the safety instrumented systems. SIL 4 has the highest level of safety integrity; SIL 1, the lowest. Safety function with a specified safety integrity level that is necessary to achieve functional safety and that can be either a safety instrumented protection function or a safety instrumented control function. Failure related in a deterministic way to a certain cause, which can only be eliminated by a modification of the design or of the manufacturing process, operational procedures, documentation, or other relevant factors. Risk that is accepted in a given context based on the current values of society. Activity of demonstrating that the safety-instrumented function(s) and safety instrumented system(s) under consideration after installation meet in all respects the safety requirements specification. Activity of demonstrating for each phase of the relevant safety life-cycle, by analysis and/or tests, that for specific inputs the outputs meet in all respects the objectives and requirements for the specific phase.

Source: With thanks to the International Electrotechnical Commission (IEC) for permission to reproduce information from its International Standards. All such extracts are copyright of IEC, Geneva, Switzerland. All rights reserved. Further information on the IEC is available from www.iec.ch. IEC has no responsibility for the placement and context in which the extracts and contents are reproduced by the author, nor is IEC in any way responsible for the other content or accuracy therein. IEC 61511-1 ed.2.0. Copyright (c) 2016 IEC Geneva, Switzerland. www.iec.ch. ©2020 NCEES

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Chapter 8: Plant Design and Operations 8.8.4.1 Functional Safety Life Cycle SIS Safety Life-Cycle Phases and Functional Safety Assessment Stages MANAGEMENT OF FUNCTIONAL SAFETY IN FUNCTIONAL SAFETY ASSESSMENT AND AUDITING

SAFETY LIFE-CYCLE STRUCTURE AND PLANNING

1

HAZARD AND RISK ASSESSMENT CLAUSE 8

VERIFICATION

ALLOCATION OF SAFETY FUNCTIONS TO PROTECTION LAYERS CLAUSE 9 2 SAFETY REQUIREMENTS SPECIFICATION FOR SAFETY INSTRUMENTED SYSTEM 3 CLAUSES 10 AND 11 STAGE 1 DESIGN AND ENGINEERING OF SAFETY INSTRUMENTED SYSTEM CLAUSES 11 AND 12

4

DESIGN AND DEVELOPMENT OF OTHER MEANS OF RISK REDUCTION CLAUSE 9

STAGE 2 INSTALLATION, COMMISSIONING AND VALIDATION 5 CLAUSES 14 AND 15 STAGE 3

OPERATION AND MAINTENANCE CLAUSE 16 6

STAGE 4

CLAUSE 5

10

CLAUSE 6.2

7

MODIFICATION CLAUSE 17

8

DECOMMISSIONING CLAUSE 18

STAGE 5

11

9

CLAUSES 7, 12.4, AND 12.7

KEY: TYPICAL DIRECTION OF INFORMATION FLOW. NO DETAILED REQUIREMENTS GIVEN IN THIS STANDARD. REQUIREMENTS GIVEN IN THIS STANDARD. NOTE 1 STAGES 1 THROUGH 5 INCLUSIVE ARE DEFINED IN 5.2.6.1.3. NOTE 2 ALL REFERENCES ARE TO PART 1 UNLESS OTHERWISE NOTED.

Source: With thanks to the International Electrotechnical Commission (IEC) for permission to reproduce information from its International Standards. All such extracts are copyright of IEC, Geneva, Switzerland. All rights reserved. Further information on the IEC is available from www.iec.ch. IEC has no responsibility for the placement and context in which the extracts and contents are reproduced by the author, nor is IEC in any way responsible for the other content or accuracy therein. IEC 61511-1 ed.2.0. Copyright (c) 2016 IEC Geneva, Switzerland. www.iec.ch.

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Chapter 8: Plant Design and Operations 8.8.4.2 SIS Safety Life-Cycle Overview The Safety Instrumented System (SIS) Safety Life-Cycle Safety Life-Cycle Phase or Activity Box # in Previous Title Image 1 Hazard and Risk Assessment

2

Allocation of Safety Functions to Protection Layers

3

SIS Safety Requirements Specification

4

SIS Design and Engineering

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Requirements Clause or Subclause

Objectives

Inputs

Outputs

To determine the hazards and hazardous events of the process and associated equipment, the sequence of events leading to the hazardous event, the process risks associated with the hazardous event, the requirements for risk reduction, and the safety functions required to achieve the necessary risk reduction Allocation of safety functions to protection layers and the associated safety integrity level for each safety-instrumented function

8

Process design, layout, work force arrangements, safety targets

Description of hazards of the required safety function(s) and their associated risk reduction(s)

9

Description of allocation of safety requirements (see Clause 9)

To specify the requirements for each SIS, in terms of the required safety-instrumented functions and their associated safety integrity, in order to achieve the required function-al safety To design the SIS to meet the requirements for safety-instrumented functions and safety integrity

10

Description of required safetyinstrumented function(s) and associated safety integrity requirements Description of allocation of safety requirements (see Clause 9)

SIS safety requirements; software safety requirements

Design of the SIS in conformance with the SIS safety requirements; planning for the SIS integration test

545

11, 12.4

SIS safety requirements; software safety requirements

Chapter 8: Plant Design and Operations SIS Safety Life-Cycle Overview (cont'd) Safety Life-Cycle Phase or Activity Box # in Previous Title Image 5 SIS Installation Commissioning and Validation

Requirements Clause or Subclause

Objectives

To integrate and test the SIS

12.3, 14, 15

To validate that the SIS meets in all respects the requirements for safety in terms of the required safety-instrumented functions and the required safety integrity

SIS safety requirements

SIS Operation and To ensure that the functional Maintenance safety of the SIS is maintained during operation and maintenance

16

7

SIS Modification

17

8

9

SIS Verification

10

SIS Functional Safety Assessment

To test and evaluate the outputs of a given phase to ensure correctness and consistency with respect to the products and standards provided as inputs to that phase To investigate and arrive at a judgment on the functional safety achieved by the SIS

SIS design SIS integration test plan

6

To make corrections, enhancements, or adaptations to the SIS, ensuring that the required safety integrity level is achieved and maintained Decommissioning To ensure proper review and sector organization, and to ensure SIF remains appropriate

Inputs

18

7, 12.7

5

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Fully functioning SIS in conformance with the SIS design results of SIS integration tests

Results of the installation, Plan for the safety commissioning, and validation of the validation activities SIS SIS requirements Results of the operation and mainSIS design tenance activities Plan for SIS operation and maintenance Revised SIS Results of SIS safety requiremodification ments

As-built safety requirements and process information Plan for the verification of the SIS for each phase

SIF placed out of service

Planning for SIS functional safety assessment

Results of SIS functional safety assessment

SIS safety requirement

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Outputs

Results of the verification of the SIS for each phase

Chapter 8: Plant Design and Operations 8.8.4.3 Safety Integrity Levels: Probability of Failure on Demand Safety Integrity Level (SIL) 4

Demand Mode of Operation Target Average Probability Target Risk Reduction of Failure on Demand

$ 10

-5

to 1 10

-4

2 10, 000 to # 100, 000

3

$ 10

-4

to 1 10

-3

2 1000 to # 10, 000

2

$ 10

-3

to 1 10

-2

2 100 to # 1000

1

$ 10

-2

to 1 10

-1

2 10 to # 100

8.8.4.4 Functional Safety Equations Average Probability of Failure on Demand (PFDavg) 1 PFavg = T

T

#

PF (t) dt

(Rigorous version)

0

mt PFavg = 2

(Approximation)

Safe Failure Fraction (SFF) SFF =

mSD + mSU + mDD mSD + mSU + mDD + mDU

where l = failure rate (failures/year) and subscripts indicate failure mode: SD = safe detected SU = safe undetected DD = dangerous detected DU = dangerous undetected

8.9 Operation 8.9.1

Operating Procedures

The main types of process operating procedures are 1. Standard Operating Procedures (SOP)—Written instructions documenting step-by-step instructions for safely performing a task within operating limits. The SOP covers all modes of operation. The purpose of the standard operating procedure is to ensure operations are always carried out correctly and in the same manner. An SOP should be available at the place where the work is done. 2. Startup/Shutdown Procedures—Written procedures for startup and shut-down phased so that interlinked plant operations can resume or stop in a safe and controlled manner. 3. Emergency or Abnormal Operating Procedures—Written instructions documenting step-by-step instructions for reaching a safe state following a process in an upset condition. The emergency procedures should cover the PPE, the level of intervention which is safe, and when to evacuate. The procedures will also need to tie in with site emergency plans. ©2020 NCEES

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Chapter 8: Plant Design and Operations 4. Temporary Operating Procedures—Written instructions for a finite period of time. At the conclusion of this time, the facility returns to using the Standard Operating Procedures. Temporary operating procedures should include an expiration date. 5. Maintenance Procedures—Written instructions that address material control and maintenance practices needed to ensure system operability and integrity. These procedures specify the required maintenance, testing, and inspection frequencies. Source: Guidelines for Engineering Design for Process Safety, 2nd ed., New York: John Wiley & Sons, Inc., 2012. The zones for safe operation of process equipment are defined as 1. Normal Operating Zone: The minimum or maximum values of an operating parameter that define the boundaries of normal operations. Some examples of operating parameters to be defined include •

High and low pressure

•

High and low temperature

•

High and low level

•

High and low pH

•

High and low flow

2. Troubleshooting Zone: An area that provides time for troubleshooting, so that operations personnel can make adjustments in time to return the operating parameters to the Normal Operating Zone. Human factors and process response time generally indicate zone size. Immediate actions, and in some cases predetermined actions, to avoid Safe Operating Limit (SOL) deviation are taken in this zone. 3. Buffer Zone: The upper and lower area of the known safe zone provides a buffer to ensure no operating parameter can reach the Unknown/Unacceptable Operation Zone. Factors that influence Buffer Zone size may include engineering judgment, reliability of instrumentation, operating experience, probability and consequence of human error, and so on. A process will not be operated intentionally in this zone. 4. Safe Operating Limit (SOL): A value for an operating parameter that defines the equipment or process unit's safeoperating envelope, beyond which a process will not intentionally be operated due to the risk of imminent, catastrophic equipment failure or loss of containment. Operational or mechanical corrective action ceases and immediate predetermined actions are taken at these operating parameter values in order to bring equipment and process units to a safe state. Each SOL should be documented in the plant's Process Safety Information. 5. Unacceptable or Unknown Operating Zone: An area beyond the Safe Operating Limit. A process will not be intentionally operated in this zone.

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Chapter 8: Plant Design and Operations Operation Zones for Process Equipment EQUIPMENT LIMIT UNACCEPTABLE/UNKNOWN OPERATING ZONE SAFE OPERATING LIMIT

INSTRUMENT RANGE

BUFFER ZONE

NEVER EXCEED LIMIT

TROUBLESHOOTING ZONE MAXIMUM NORMAL OPERATING LIMIT NORMAL OPERATING ZONE MINIMUM NORMAL OPERATING LIMIT TROUBLESHOOTING ZONE NEVER EXCEED LIMIT BUFFER ZONE

SAFE OPERATING LIMIT

UNACCEPTABLE/UNKNOWN OPERATING ZONE

INSTRUMENT RANGE EQUIPMENT LIMIT

Source: Smith, David J., Reliability, Maintainability and Risk - Practical Methods for Engineers, 5th ed., "Appendix A1: Terms Related to Failure," Amsterdam: Elsevier, 1997. www.elsevier.com.

8.9.2

Start-up and Shutdown

Start-up, operation, and shutdown of most different types of plants included the following modes: 1. normal start-up 2. normal operation 3. normal shutdown 4. emergency shutdown There are further relevant distinctions of shutdowns including: 1. normal shutdown condition 2. hot standby condition 3. emergency shutdown condition 4. major scheduled shutdown, or turnaround, condition 5. prolonged shutdown, or mothballing condition Source: Adapted from Less, Frank, Lees' Loss Prevention in the Process Industries, 4th ed., Chapter 20, Amsterdam: Elsevier, 2012. www.elsevier.com.

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8.10 Process Equipment and Reliability 8.10.1 Testing and Inspection Maintenance and Reliability Term

Definition

Example or Application

Up Time

Availability (%) = Total Time Availability

Diversity

Failure Modes and Effects Analysis (FMEA)

Mean Time Between Failures (MTBF)

The availability of a gas turbine generator was The proportion of time that an item is ca- increased to 95% by minimizing the schedpable of operating to specification within a uled maintenance duration. large time interval. In-line check valves of two different technoloThe same performance of a function by gies or separate manufacturers are two or more independent and dissimilar installed to decrease the likelihood of means. reverse flow from waste-water treatment back to the process. An FMEA identifies internal spring failure A qualitative tool for analysis identifying from excessive wear on a solenoid valve. The all the ways a particular component can local and system consequences are documentfail and the effects of the failure on the ed. A recommendation is made for regular system. inspection to prevent this point of failure. The total cumulative functioning time of a population divided by the number of failures, MTBF is used for items that involve For 10,000 total hours of recorded uptime, the MTBF for 4 power supplies is 2500 hours. repair and excludes downtime.

Total Up Time MTBF = Number of Failures Predictive Maintenance

Preventive Maintenance

Redundancy

Reliability

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The aim of predictive maintenance is, first, to predict when equipment failure may occur and, second, to prevent occurrence of that failure by performing maintenance.

A plant predictive maintenance program could use regular vibration analyses and motor current signature analyses to determine equipment conditions and predict failure. A preventive maintenance program for a cenActions carried out for the purpose of trifugal pump at a plant could include monthly keeping equipment or instrumentation in a inspection of the gland packing, bearing specified condition. lubrication, and pump mountings. The provision of more than one means of achieving a function. An active pump runs continuously for long Active/Duty: All items remain operating prior to failure. Standby: Replicated items do not operate until needed. The probability that the system will not leave the operational state. The availability for a given system is always greater than or equal to the reliability.

550

periods of time without having to go through the start-up process. The standby pump remains dormant and is tested regularly to ensure reliability.

Safety-instrumented function; probability of failure on demand.

Chapter 8: Plant Design and Operations

8.10.2 Maintenance Decision Tree for Optimum Maintenance IS IMPACT AND FREQUENCY OF FAILURE ON AVAILABILITY AND COST ACCEPTABLE?

NO

YES

IS FAILURE PREDICTABLE

NO

YES

UNSCHEDULED MAINTENANCE

YES * PREDICTIVE MAINTENANCE

PREVENTIVE MAINTENANCE

CALENDAR TIME BASIS

IS IMPENDING FAILURE DETECTABLE?

USAGE BASIS

CONTINUOUS MONITORING

NO

UNSCHEDULED MAINTENANCE

PERIODIC MANUAL MONITORING

* predictive maintenance based on precursor to failure Source: Reprinted from Manufacturing Engineer's Reference Book, D. Koshal, pages 18 and 20, 1993, with permission from Elsevier. www.elsevier.com. TYPICAL EQUIPMENT FAILURE DIAGRAM Failure Equipment

FAILURE RATE (λ)

DURING EXTREME EVENTS

DURING NORMAL OPERATION INFANT MORALITY

USEFUL LIFE PERIOD

TIME

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WEAROUT PERIOD

Chapter 8: Plant Design and Operations

8.11 Process Improvement and Troubleshooting The variety and complexity of modern processing industries requires that engineers be able to find ways to improve the processes of their facilities for the benefit of their employers or clients. Process improvement allows for the optimization of utilities, raw materials, and other resources to maximize production and minimize the cost per unit produced. Engineers who are tasked with process improvement and troubleshooting focus their knowledge and training to make a facility or process work more efficiently and economically. Work in this area will focus on one of the following types of activities: • Optimum balance of process variables • Increased capacity—Debottleneck and/or add equipment • Improved product quality—Control contamination and deterioration • Improved mechanical performance—Reduce corrosion and fouling • Decreased utility and raw material consumption—Steam, power, water, chemicals, and so on • More efficient maintenance • Improved safety practices The use of data is paramount to any of the activities listed above. The modern process-industries plant typically has an abundance of data that is part of the control systems. This data is collected from all aspects and areas of the facility. One of the most common methods of using data to improve a process is the DMAIC method. The five phases in the DMAIC method are 1. Define the problem and system by setting goals and understanding the requirements of the customer and the system. 2. Measure the key aspects of the process and gather the data that is available and relevant to the issue, project, or problem to be solved. This data can be used to determine the "as is" state of the process. 3. Analyze the data to investigate the process and determine the cause-and-effect relationships in the process. Seek out the root cause(s) of the problem being evaluated. 4. Improve or optimize the current process based on data analysis techniques to create a new, future-state process and run pilot trials to establish the process capability. 5. Control the new process to ensure that any deviations are corrected quickly before they result in defects or issues. Data analysis can be a complex activity and techniques in this area include 5 Whys Regression analysis Cause-and-effect diagraming Design of experiments Taguchi loss function General linear modeling Cost-benefit analysis Failure modes, effects, and diagnostic analysis (FMEDA)

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Analysis of variance Correlation Control/run charts Pareto analysis Value stream mapping Axiomatic design Root-cause analysis

Chapter 8: Plant Design and Operations One of the most useful techniques for troubleshooting is root-cause analysis (RCA). RCA is a method of problem-solving used to identify the root cause(s) of faults or problems. A factor is considered a root cause if removal from the problem-fault sequence prevents the final undesirable event from recurring. A causal factor is one that affects an event's outcome and, if removed, might benefit the process but does not prevent the recurrence of the problem being addressed. RCA is applied to methodically identify and correct the root causes of events, rather than to simply address the symptomatic result. Focusing correction on root causes has the goal of entirely preventing problem recurrence. RCA is typically used as a reactive method for identifying event causes, revealing problems, and solving them. Analysis is most typically done after an event has occurred; however, it can also be used as a predictive tool. The basic steps in root-cause analysis are: 1. Define the problem or describe the event to prevent in the future. 2. Gather data and evidence, classifying it along a time line. 3. Data-mine for clusters of similar problems that are close to the problem or event. 4. Ask why this happens and identify the causes, giving each sequential step toward the problem or event. 5. Classify all causes into either "causal" or "root." 6. Identify any other items that affect the problem or event. 7. Identify the corrective action(s) that will, with certainty, prevent recurrence of each harmful effect. 8. Identify solutions that prevent recurrence and that are within the control of the institution. 9. Implement the recommended root-cause corrections. 10. Ensure effectiveness by observing the implemented solutions in operation. Observation is one of the best ways to identify issues that need to be addressed when working and troubleshooting in any type of plant.

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©2020 NCEES

8.12 Flammability Data

Chemical Acetaldehyde Acetic Acid

Class I Division Typea Group

Flash Point (°C)

AIT (°C)

% LFL 4

75-07-0

Cd

I

−38

175

64-19-7

Dd

II

39

426

67-64-1 74-86-2 79-10-7 107-13-1 107-18-6 107-05-1 7664-41-7 62-53-3 71-43-2 3583-47-9 106-99-0 71-36-3 25167-67-3 630-08-0 98-82-8 110-82-7 75-19-4

Dd

–20

D Dd Cd D Dd,f D Dd Dd,g B(D)d,e Dd D Cd D D Dd

I GAS II I I I GAS IIIA I GAS GAS I I GAS I I I

465 305 488 481 378 485 651 615 498 288 420 343 385 609 424 245 503

60-29-7

Cd

I

−45

74-84-0 64-17-5 74-85-1 107-06-2 75-21-8 141-78-6 64-17-5 100-41-4 75-00-3

Dd Dd Cd Dd B(C)d,e Dd Dd D D

GAS I GAS I I I I I GAS

−29 13

Ad

54 0 22 −32 70 –11

36

36 −17

13 −20 −4 13 15 −50

Vapor Vapor Class % Density Pressureb 1 Zone UFL (Air=1) (mm Hg) Groupc

MIE (mJ)

MIC MESG Ratio (mm)

0.37

0.98

0.92

2.67

1.76 1.02 0.25 0.86 0.87 0.84 1.17 3.17

60

1.5

874.9

IIA

19.9

2.1

15.6

IIA

2.5 2.5 2.4 3 2.5 2.9 15 1.2 1.2 1.9 2 1.4 1.6 12.5 0.9 1.3 2.4

12.8 100 8 17 18 11.1 28 8.3 7.8 8.5 11.5 11.2 10 74 6.5 8 10.4

2 0.9 2.5 1.8 2 2.6 0.6 3.2 2.8 2 1.9 2.6 1.9 0.97 4.1 2.9 1.5

230.7 36,600 4.3 108.5 25.4 366 7498 0.7 94.8

1.15 0.017

1 0.28

0.16

0.78

680

1.33 6.85

0.2 0.25 0.13

1 0.94 0.76

4.6 98.8 5430

IIA IIC IIB IIB IIB IIA IIA IIA IIA IIA IIB IIA IIA IIB IIA IIA IIA

0.22 0.17

1 0.84

0.99 1.07 0.79 0.91 0.94 0.54 1.05 0.94 0.91

160

1.9

36

2.6

538

IIB

0.19

0.88

0.83

472 363 490 413 429 427 363 432 519

3 3.3 2.7 6.2 3 2 3.3 0.8 3.8

12.5 19 36 16 100 11.5 19 6.7 15.4

1 1.6 1 3.4 1.5 3 1.6 3.7 2.2

0.24

59.5

IIA IIA IIB

0.82 0.88 0.53

0.91 0.89 0.65

IIB IIA IIA

0.065 0.46

0.47

0.59 0.99 0.89

7 2214.6

79.7 1314 93.2 59.5 9.6

0.07

0.88

Chapter 8: Plant Design and Operations

554

Acetone Acetylene Acrylic Acid Acrylonitrile Allyl Alcohol Allyl Chloride Ammonia Aniline Benzene n-Butane 1,3-Butadiene 1-Butanol Butylene Carbon Monoxide Cumene Cyclohexane Cyclopropane Diethyl Ether (Ethyl Ether) Ethane Ethanol (Ethyl Alcohol) Ethylene Ethylene Dichloride Ethylene Oxide Ethyl Acetate Ethyl Alcohol Ethyl Benzene Ethyl Chloride

CAS No.

©2020 NCEES

Chemical

CAS No.

Ethyl Mercaptan Formaldehyde (Gas) Formic Acid

75-08-1 50-00-0 64-18-6

Fuel Oil 1 (Jet Fuel)

8008-20-6

Fuel Oil 2 (Diesel)

Flash Point (°C) −18

Vapor Vapor Class 1 % Density Pressureb Zone UFL (Air=1) (mm Hg) Groupc 18 2.1 527.4 IIB 73 1 IIB 57 1.6 42.7 IIA

AIT (°C)

% LFL

50

300 430 434

2.8 7 18

38–72k

210

0.7

5

52–96k

257

−46 −4 −23

280 204 225 500 260

1.4 1 1.1 4 4

7.6 6.7 7.5 75 44

3 3.5 3 0.1 1.2

555

Gasoline n-Heptane n-Hexane Hydrogen Hydrogen Sulfide

8006-61-9 142-82-5 110-54-3 1333-74-0 7783-06-4

Isobutane Isoprene Isopropyl Ether Kerosene Liquefied Petroleum Gas Methanol (Methyl Alcohol) Methyl Chloride Methyl Ether Methyl Ethyl Ketone Naptha (Petroleum) n-Octane n-Pentane Process Gas > 30% H2 Propane 1-Propanol Propylene Styrene Tetrahydrofuran Toluene

75-28-5 78-79-5 108-20-3 8008-20-6 68476-85-7

Dg Dd Dd D D

GAS I I II I

−54 −28 72

460 220 443 210 405

1.8 1.5 1.4 0.7

8.4 8.9 7.9 5

2 2.4 3.5

550.6 148.7

67-56-1

Dd

I

12

385

6

36

1.1

126.3

74-87-3 115-10-6 78-93-3 8030-30-6 111-65-9 109-66-0 1333-74-0 74-98-6 71-23-8 115-07-1 100-42-5 109-99-9 108-88-3

D Cd Dd Dd,h Dd,g Dd,g Bi Dd Dd Dd Dd Cd Dd

GAS GAS I I I I GAS GAS I GAS I I I

−46 −41 −6 42 13 −40

632 350 404 288 206 243 520 450 413 460 490 321 480

8.1 3.4 1.4 1.1 1 1.5 4 2.1 2.2 2.4 0.9 2 1.1

17.4 27 11.4 5.9 6.5 7.8 75 9.5 13.7 10.3 6.8 11.8 7.1

1.7 1.6 2.5 2.5 3.9 2.5 0.1 1.6 2.1 1.5 3.6 2.5 3.1

15 31 −14 4

45.5 152

IIA IIA IIC IIB

MIE (mJ)

0.24 0.24 0.019 0.68

MIC MESG Ratio (mm) 0.9

0.9 0.57 1.86

0.88 0.88 0.25

0.91 0.93 0.28 0.9

IIA

92.4 14 513

20.7 6.1 161.6 28.53

0.95

IIA IIA

1.14

IIA

0.14

IIA IIB IIB IIA IIA IIA IIA IIA IIA IIA IIB IIA

0.53

0.28 0.019 0.25

0.94

0.82

0.92

0.85 0.92

1 0.84 0.84

0.97 0.45 0.82

0.28

0.94 0.93 0.97 0.89 0.91

1.21 0.54 0.24

0.87

Chapter 8: Plant Design and Operations

Class I Division Typea Group Cd I B GAS D II II or D IIIAk II or IIIAk Dd I Dd I d,g D I d B GAS Cd GAS

©2020 NCEES

Chemical

CAS No.

Triethylamine Vinyl Acetate Vinyl Chloride Xylene

121-44-8 108-05-4 75-01-4 1330-20-7

Class I Division Typea Group Cd I Dd I d D GAS d D I

Flash Point (°C) –9 −6 −78 25

AIT (°C)

% LFL

249 402 472 464

1.2 2.6 3.6 0.9

Vapor Vapor Class 1 % Density Pressureb Zone UFL (Air=1) (mm Hg) Groupc 8 3.5 68.5 IIA 13.4 3 113.4 IIA 33 2.2 IIA 7 3.7 IIA

MIE (mJ)

MIC MESG Ratio (mm)

0.75 0.7 0.2

1.05 0.94 0.96 1.09

a. Type designates whether the material is a gas, flammable liquid, or combustible liquid. b. Vapor Pressure is reflected in units of mm Hg at 25°C (77°F), unless stated otherwise.

d. Material has been classified by test. e. When all conduits run into explosion-proof equipment are provided with explosion-proof seals installed within 450 mm (18 in.) of the enclosure, equipment for the group classification shown in parentheses is permitted.

556

f. For classification of areas involving ammonia, see ASHRAE 15, Safety Code for Mechanical Refrigeration, and ANSI/ CGA G2.1, Safety Requirements for the Storage and Handling of Anhydrous Ammonia. g. Commercial grades of aliphatic hydrocarbon solvents are mixtures of several isomers of the same chemical formula (or molecular weight). The autoignition temperatures of the individual isomers are significantly different. The electrical equipment should be suitable for the AIT of the solvent mixture. h. [deleted] i.

Petroleum naphtha is a saturated hydrocarbon mixture whose boiling range is 20°C to 135°C (68°F to 275°F). It is also known as benzine, ligroin, petroleum ether, and naphtha.

j.

Fuel and process gas mixtures found by test not to present hazards similar to those of hydrogen may be grouped based on the test results.

k. [deleted] Source: Reproduced with permission from NFPA 497, Recommended Practice for the Classification of Flammable Liquids, Gases, or Vapors and of Hazardous (Classified) Locations for Electrical Installations in Chemical Process Area, © 2012, National Fire Protection Association. This is not the complete and official position of the NFPA on the referenced subject, which is represented only by the standard in its entirety.

Chapter 8: Plant Design and Operations

c. Class I Zone Groups are based on 1996 IEC TR3 60079-20, Electrical apparatus for explosive gas atmospheres—Part 20: Data for flammable gases and vapors, relating to the use of electrical apparatus, which contains additional data on MESG and group classifications.

9 PHYSICAL PROPERTIES 9.1 Symbols and Definitions Symbols Symbol

Units (U.S.)

Units (SI)

cp

Heat capacity (at constant pressure)

Btu lbm -cF

J = m2 kg : K s 2 : K

cv

Heat capacity (at constant volume)

Btu lbm -cF

h

Specific enthalpy

Btu lbm

J = m2 kg : K s 2 : K J kg

Dhfusion

Enthalpy of fusion

Btu lbm

J kg

Enthalpy of vaporization

Btu lbm

J kg

Btu hr -ft -cF lbm lb mole

W m:K g mol

Dhvap

k MW

©2020 NCEES

Description

Thermal conductivity Molar mass (molecular weight)

lbf or psi in 2

kg m : s2

P

Pressure

r

Ratio of heat capacities = c v

s

Specific entropy

Btu lbm -cF

J kg : K

T

Temperature

cF or cR

cC or K

v

Specific volume

ft 3 lbm

m3 kg

a

Thermal diffusivity

ft 2 sec

m2 s

cp

Pa =

dimensionless

557

Chapter 9: Physical Properties Symbols (cont'd) Description

Symbol

Units (U.S.)

Units (SI)

dyne cm lbm ft -sec

N m kg Pa : s = m : s

g

Surface tension

m

Dynamic viscosity

ν

Kinematic viscosity

ft 2 sec

m2 s

r

Density

lbm ft 3

kg m3

r

Electrical resistivity

X - ft

X:m

9.2 Physical Properties of Metals 9.2.1

U.S. Customary Units

Thermal Conductivity

Thermal Diffusivity

lbm ft 3

Btu lbm-cF

Btu hr -ft -cF

ft 2 hr

26.98

168

0.214

136.35

3.55

532.0 540.0 95.5 449.1 557.0 557.7 1203.7 491.5 455.0 708.1 33.3 108.5 466.5 845.7 638.2 556.1 530.0 748.8 1339.1 53.8 775.4

0.091 0.082 0.152 0.097 0.098 0.093 0.031 0.109 0.100 0.031 1.093 0.250 0.120 0.034 0.065 0.105 0.106 0.055 0.032 0.180 0.058

61.80 15.00

1.27

Aluminum Brass 70%Cu, 30%Zn Bronze 75%Cu, 25%Sn Calcium Chromium Constantan Copper Gold Iron Iron, cast Lead Lithium Magnesium Manganese Mercury (liquid) Molybdenum Nickel Nichrome V Palladium Platinum Potassium Rhodium ©2020 NCEES

40.08 52.00 63.54 196.97 55.85 207.20 6.94 24.31 54.94 200.59 95.94 58.69 106.40 195.08 39.09 102.91

558

55.75 13.10 232.84 184.31 48.24 29.60 20.80 49.69 90.71 4.62 4.51 80.31 54.31 7.06 41.60 41.60 60.09 87.24

Heat of Fusion

Heat Capacity

lbm lb mole

Melting Point

Density

U.S. Unit:

Electrical Resistivity (0°C)

Property:

Molar Mass

Physical Properties of Metals at 68°F (U.S. Units)

cF

Btu lbm

1220

138.2 72.2

5.09 6.73 29.20

1700 1200 1544 2939 2336 1983 1947 2804

62.99 28.05 12.93 452.75 308.72 16.40 20.34

621 356 1202 2282 –38 4748 2651

32.81 32.18 20.01 14.11

2829 3222 145 3565

X -ft : 10 8.20

10.50 41.67 0.24 3.98 4.52 0.83 0.65 0.80 3.68

0.87 0.12 0.09

−8

83.58 215.4 89 28.8 114.7 41.4 10.62 147.4 114.6 5.08 186.3 132.8

43.3 25.0

Chapter 9: Physical Properties

247.28 82.04

6.42

118.69 47.88 183.85 238.03 65.38

488.0 488.0 454.8 281.4 1202.0 1189.3 445.4

0.113 0.110 0.055 0.126 0.034 0.028 0.094

24.80 9.40 39.29 12.71 102.26 15.60 67.60

0.45 0.17 1.57 2.44 0.53 1.55

Heat of Fusion

Thermal Diffusivity

0.056 0.295

lbm lb mole

Melting Point

Thermal Conductivity

ft 2 hr

U.S. Unit:

Electrical Resistivity (0°C)

Heat Capacity

Btu hr -ft -cF

Molar Mass

Btu lbm-cF

107.87 22.99

lbm ft 3 655.5 60.3

Property:

Silver Sodium Steel, carbon Steel, mild (1%C) Steel, stainless Tin Titanium Tungsten Uranium Zinc

9.2.2

Density

Physical Properties of Metals at 68°F (U.S. Units) (cont'd)

cF

Btu lbm

4.82 13.78

1762 208

45.0 37.8

37.73 127.95 16.08 91.86 18.04

450 3038 6129 2075 786

25.2 122.6 109.7

X -ft : 10

−8

43.9

SI Units

©2020 NCEES

63.54 196.97 55.85 207.20 6.94 24.31 54.94 200.59 95.94

W m:K

m2 s

896 381 343 636 407 410 389 130 456 419 130 4576 1047 502 142 272

236.0 107.0 26.0

91.61 32.77

96.5 22.7 403.0 319.0 83.5 51.2 36.0 86.0 157.0 8.0 7.8 139.0

559

Electrical Resistivity (0°C)

J kg : K

Heat of Fusion

40.08 52.00

kg m3 2698 8522 8650 1530 7194 8922 8933 19,281 7873 7288 11,343 533 1738 7473 13,547 10,222

Melting Point

26.98

Thermal Diffusivity

Aluminum Brass 70%Cu, 30%Zn Bronze 75%Cu, 25%Sn Calcium Chromium Constantan Copper Gold Iron Iron, cast Lead Lithium Magnesium Manganese Mercury (liquid) Molybdenum

Thermal Conductivity

g mol

Heat Capacity

SI Unit:

Density

Property:

Molar Mass

Physical Properties of Metals at 20°C (SI Units)

cC

kJ kg 321.5 167.9

1.55 2.05 8.90

660 927 649 840 1615 1280 1084 1064 1540

19.20 8.55 3.94 138.00 94.10 5.00

327 180 650 1250 –39 2620

X -m : 10 2.50

3.20 12.70 6.19 102.71 116.64 21.42 16.77 20.64 94.97

−8

194.4 501.1 207.0 67.0 266.7 96.3 24.7 342.9 266.6 11.8 433.3

Chapter 9: Physical Properties

Density

Heat Capacity

Thermal Conductivity

Thermal Diffusivity

SI Unit:

g mol

kg m3

J kg : K

W m:K

m2 s

X -m : 10

58.69

440 444 230 134 754 243 235 1235

94.0 12.2 72.0 72.0 104.0 151.0 428.0 142.0

22.45 3.10

106.40 195.08 39.09 102.91 107.87 22.99

8907 8490 11,995 21,450 862 12,420 10,500 966

118.69 47.88 183.85 238.03 65.38

7817 7817 7285 4508 19,254 19,050 7135

473 461 230 528 143 117 394

42.9 16.3 68.0 22.0 177.0 27.0 117.0

165.67

11.61 4.39 40.52 62.97 13.68 40.00

Heat of Fusion

2.32

Melting Point

Nickel Nichrome V Palladium Platinum Potassium Rhodium Silver Sodium Steel, carbon Steel, mild (1%C) Steel, stainless Tin Titanium Tungsten Uranium Zinc

Electrical Resistivity (0°C)

Property:

Molar Mass

Physical Properties of Metals at 20°C (SI Units) (cont'd)

cC

kJ kg

6.20

1455

308.9

10.00 9.81 6.10 4.30 1.47 4.20

1554 1772 63 1963 961 98

11.50 39.00 4.90 28.00 5.50

232 1670 3387 1135 419

−8

9.3 Physical Properties of Plastics 9.3.1

U.S. Customary Units Physical Properties of Plastics (U.S. Units) Property:

Density

Heat Capacity

Thermal Conductivity

U.S. Unit:

lbm ft 3 64–75 64–71 57–78 57–60 69–125 77–97 1.0–2.0 109–117 134 130–140 134 106

Btu lbm-cF 0.361–0.370 0.330–0.399 0.279–0.301 0.499–0.549 0.320–0.499 0.251

Btu hr -ft -cF 0.092–0.156 0.098–0.196 0.110–0.127 0.243–0.283 0.191–0.526 0.081–0.110 0.017–0.023 0.083–0.110 0.113 0.142–0.375 0.113 0.138

ABS Nylon Polycarbonate Polyethylene Polyester PVC Polystyrene foam PVDF PFA PTFE FEP ETFE

©2020 NCEES

0.28–0.36 0.28 0.28 0.28

560

100.8 58.1 104.7 87.9

58.6 285.1 255.1 102.1

Chapter 9: Physical Properties

9.3.2

SI Units Physical Properties of Plastics (SI Units) Property: SI Unit: ABS Nylon Polycarbonate Polyethylene Polyester PVC Polystyrene foam PVDF PFA PTFE FEP ETFE

©2020 NCEES

Density

Heat Capacity

Thermal Conductivity

kg m3 1020–1200 1030–1140 910–1250 913–968 1100–2010 1240–1550 16–32 1746–1874 2150 2082–2243 2150 1700

J kg : K

W m:K

1510–1550 1380–1670

0.16–0.27 0.17–0.34

1170–1260

0.19–0.22

2090–2300 1340–2090 1050

0.42–0.49 0.33–0.91 0.14–0.19 0.03–0.04 0.14–0.19 0.20 0.25–0.65 0.20 0.24

1172–1507 1172 1172 1172

561

Chapter 9: Physical Properties

9.3.3

Chemical Resistance of Plastics Acrylonitrile Butadiene Styrene Polymer (ABS)

Polyvinyl Chloride, Type I (PVC)

Saran

Polyester Glass

Epoxy Glass

Phenolic Asbestos

Fluorocarbons

Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Poor Excel. Poor Poor Poor Poor Poor

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Excel. Excel. Excel. Excel. Excel. Good Excel. Excel. Excel. Excel. Excel. Excel. Excel. Good Excel. Excel. Poor Fair Poor Excel.

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Polycarbonate

Cellulose Acetate Butyrate (CAB)

10% H2SO4 50% H2SO4 10% HCl 10% HNO3 10% Acetic 10% NaOH 50% NaOH NH4OH NaCl FeCl2 CuSO4 NH4NO3 Wet H2S Wet Cl2 Wet SO2 Gasoline Benzene CCl4 Acetone Alcohol

Chlorinated Polyether (Penton)

Plastic:

Polypropylene, Polyethylene

Chemical Resistance of Plastics

Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel. Excel.

Excel. Fair Poor Good Excel.

Source: Republished with permission of McGraw-Hill, Inc., from Perry's Chemical Engineers' Handbook, R.H. Perry and D. Green, 6th ed., New York, 1984; permission conveyed by Copyright Clearance Center, Inc.

©2020 NCEES

562

Chapter 9: Physical Properties

9.4 Physical Properties of Liquids and Gases—Temperature-Independent Properties 9.4.1

U.S. Customary Units

Triple Point

Heat of Vaporization at NBP

Critical Temperature

Critical Pressure

cF

Btu lbm

cF

psia

C2H4O C2H4O2 C3H6O C2H2   NH3 Ar C6H6 C4H10

iso-Butane 1-Butene 1-Butanol

C4H10 C4H8 C4H10O

1,3-Butadiene 1,2-Butadiene Carbon dioxide Carbon monoxide Carbonyl sulfide Carbon tetrachloride Chlorine Cumene (isopropylbenzene) Cyclohexane n-Decane Diethyl ether Ethane Ethanol Ethyl acetate Ethylbenzene Ethylene

C4H6 C4H6 CO2 CO COS CCl4 Cl2 C9H12

120.192

306.2

–140.8

131.9

676.4

462.2

17.78

C6H12 C10H22 C4H10O C2H6 C2H6O C4H8O2 C8H10 C2H4

84.160 142.282 74.122 30.069 46.068 88.105 106.165 28.053

177.3 345.4 94.0 –127.4 172.9 170.7 277.1 –154.8

44.1 –21.4 –177.3 –297.0 172.9 –118.4 –138.9 –272.5

153.2 118.8 154.2 210.4 365.7 156.9 144.2 207.4

536.8 652.2 380.4 89.9 465.5 482.3 651.2 48.6

591.8 305.0 527.9 706.7 890.1 562.7 525.4 731.3

16.94 14.57 16.52 12.87 17.11 19.23 18.17 13.37

©2020 NCEES

$

Chemical

563

Critical Density

Normal Boiling Point (NBP)

cF

Acetaldehyde Acetic Acid Acetone Acetylene Air Ammonia Argon Benzene n-Butane

lbm lb mole 44.053 60.052 58.079 26.037 28.965 17.031 39.948 78.112 58.122 58.122 56.106 74.1216 54.090 54.090 44.010 28.010 60.075 153.823 70.906

Property:

Formula

Molar Mass

Temperature-Independent Properties of Liquids and Gases (U.S. Units)

69.8 244.2 455.1 –114.7 –317.6 –28.0 –302.5 176.1 31.1

–190.1 62.0 –138.5 564.4 –352.1 –107.8 –301.7 41.9 –216.9

253.2 167.4 219.3 270.5   588.8 69.3 169.3 165.7

379.1 605.8 455.1 95.4 –221.1 270.1 –188.4 552.0 305.5

807.8 839.2 681.7 900.1 549.1 1643.7 724.1 711.7 550.6

10.9 20.6 245.8

–255.0 –301.6 –128.7

157.0 167.5 249.6

274.4 295.4 553.9

526.3 583.1 640.2

23.8 51.7 –109.2 –312.7 –58.3 170.0 –29.2

–164.0 –213.2 –69.8 –337.0 –217.9 –9.1 –149.7

178.1 190.4 246.5 92.3 132.8 83.0 121.5

305.5 362.0 87.8 –220.5 222.1 541.8 290.7

619.4 702.9 1070.0 506.8 923.7 661.4 1157.1

lbm ft 3 17.85 21.17 17.34 13.82 21.39 14.05 33.44 19.02 14.23 14.08 14.54 16.95 15.16 15.45 29.19 18.97 27.78 34.79 34.01

Chapter 9: Physical Properties

62.000 37.997 30.026 4.003 100.202 86.175 2.016 36.461 34.081 16.043 32.042 74.07854 31.057 72.106 20.180 123.109 28.013 128.255 114.229

387.0 –306.6 –2.7 –781.7 209.1 155.7 –423.0 –121.0 –76.5 –258.7 148.5 134.5 20.6 175.4 –410.9 411.5 –320.4 303.4 258.1

7.9 –363.4 –180.4 –788.4 –131.1 –139.6 –434.6 –173.5 –121.8 –296.4 –143.8 –144.4 –136.2 –124.0 –415.5 42.4 –346.0 –64.2 –70.2

C8H18

114.229

210.6

O2 C5H12 C5H12 C3H8 C3H8O C3H6 SO2 C8H8 C7H8 H2O C8H10 C8H10 C8H10

31.999 72.149 72.149 44.096 60.095 42.080 64.064 104.149 92.138 18.015 106.165 106.165 106.165

–297.3 82.1 96.9 –43.8 207.0 –53.7 14.0 293.5 231.1 212.0 281.0 282.3 291.9

564

Critical Density

C2H6O2 F2 CH2O He C7H16 C6H14 H2 HCl H2S CH4 CH4O C3H6O2 CH5N C4H8O Ne C6H5NO2 N2 C9H20 C8H18

Critical Pressure

cF

Critical Temperature

Triple Point

cF

Heat of Vaporization at NBP

Normal Boiling Point (NBP)

Ethylene glycol Fluorine Formaldehyde Helium n-Heptane n-Hexane Hydrogen Hydrogen chloride Hydrogen sulfide Methane Methanol Methyl acetate Methyl amine Methyl ethyl ketone Neon Nitrobenzene Nitrogen n-Nonane n-Octane iso-Octane (2,2,4trimethylpentane) Oxygen iso-Pentane n-Pentane Propane 1-Propanol Propylene Sulfur dioxide Styrene Toluene Water p-Xylene m-Xylene o-Xylene

©2020 NCEES

lbm lb mole

$

Chemical

Formula

Property:

Molar Mass

Temperature-Independent Properties of Liquids and Gases (U.S. Units) (cont'd)

Btu lbm

cF

psia

lbm ft 3

  75.0 329.7 8.8 136.2 144.0 192.9 190.7 234.9 219.6 473.1 176.7 361.0 188.5 36.9 190.0 85.6 124.1 129.9

  –199.7 296.3 –450.3 512.6 453.8 –400.0 124.5 211.9 –116.7 462.8 452.1 314.4 504.2 –379.6

  770.2 955.8 33.1 396.8 436.9 188.0 1202.1 1305.3 667.1 1172.5 688.9 1082.0 601.9 398.9

  37.01 22.02 4.34 14.48 14.56 1.95 26.86 21.68 10.15 17.09 20.28 12.59 16.85 30.09

–232.5 610.5 564.2

492.5 330.8 360.7

19.56 14.49 14.66

–161.3

115.3

519.5

373.0

15.12

–361.8 –256.9 –201.4 –305.7 –195.2 –301.4 –103.8 –23.2 –139.3 32.0 55.9 –54.1 –13.3

91.6 147.6 153.7 183.0 297.5 188.7 167.3 151.2 155.1 970.1 144.6 146.2 147.3

–181.4 369.0 385.8 206.1 506.6 195.9 315.5 683.7 605.5 705.1 649.4 650.7 674.8

731.4 489.9 488.8 616.6 749.7 660.6 1143.5 563.2 598.5 3200.1 512.2 512.7 542.1

27.23 14.73 14.48 13.76 17.13 14.33 32.77 18.24 18.23 20.10 17.85 17.66 17.79

Chapter 9: Physical Properties

9.4.2

SI Units

Triple Point

Heat of Vaporization at NBP

Critical Temperature

Critical Pressure

cC

cC

kJ kg

cC

MPa

C2H4O C2H4O2 C3H6O C2H2   NH3 Ar C6H6 C4H10 C4H10 C4H8 C4H10O C4H6 C4H6 CO2 CO COS CCl4 Cl2

44.053 60.052 58.079 26.037 28.965 17.031 39.948 78.112 58.122 58.122 56.106 74.1216 54.090 54.090 44.010 28.010 60.075 153.823 70.906

21.0 117.9 235.1 –81.5 –194.2 –33.3 –185.8 80.1 –0.5 –11.7 –6.35 118.75 –4.6 11.0 –78.5 –191.5 –50.2 76.6 –34.0

–123.4 16.7 –94.7 295.8 –213.4 –77.7 –185.4 5.5 –138.3 –159.4 –185.35 –89.3 –108.9 –136.2 –56.6 –205.0 –138.8 –22.82 –100.9

C9H12

120.192

152.3

–96.0

306.8

C6H12 C10H22 C4H10O C2H6 C2H6O C4H8O2 C8H10 C2H4 C2H6O2 F2 CH2O He C7H16 C6H14

84.160 142.282 74.122 30.069 46.068 88.105 106.165 28.053 62.000 37.997 30.026 4.003 100.202 86.175

80.7 174.1 34.4 –88.6 78.3 77.1 136.2 –103.8 197.2 –188.1 –19.3 –452.1 98.4 68.7

6.7 –29.7 –116.3 –182.8 78.3 –83.6 –95.0 –169.2 –13.4 –219.7 –118.0 –455.8 –90.6 –95.3

356.3 276.3 358.6 489.4 850.6 365.0 335.4 482.4   174.4 767.0 20.6 316.8 334.9

565

Critical Density

Normal Boiling Point (NBP)

Acetaldehyde Acetic Acid Acetone Acetylene Air Ammonia Argon Benzene n-Butane Isobutane 1-Butene 1-Butanol 1,3-Butadiene 1,2-Butadiene Carbon dioxide Carbon monoxide Carbonyl sulfide Carbon tetrachloride Chlorine Cumene (isopropylbenzene) Cyclohexane n-Decane Diethyl ether Ethane Ethanol Ethyl acetate Ethylbenzene Ethylene Ethylene glycol Fluorine Formaldehyde Helium n-Heptane n-Hexane

©2020 NCEES

g mol

$

Chemical

Formula

Property:

Molar Mass

Temperature-Independent Properties of Liquids and Gases (SI Units)

5.57 5.79 4.70 6.21 3.79 11.33 4.99 4.91 3.80 3.63 4.02 4.414 4.27 4.85 7.38 3.49 6.37 4.56 7.98

kg m3 286 339 278 221 343 225 536 305 228 226 233 272 243 247 468 304 445 557 545

358.0

3.19

285

280.5 344.6 193.6 32.2 240.9 250.2 344.0 9.2   –128.7 146.9 –268.0 267.0 234.3

4.08 2.10 3.64 4.87 6.14 3.88 3.62 5.04   5.31 6.59 0.23 2.74 3.01

271 233 265 206 274 308 291 214

588.8 192.9 389.3 318.8 510.0 235.1 629.3 35.2   –140.6 1,369.5 132.3 161.2 –122.5 393.8 288.9 385.5 152.0 365.2 134.7 389.7 146.35 580.573 289.95 414.3 151.9 442.9 183.4 573.4 31.0 214.7 –140.3 308.9 105.6 193.1 283.2 282.6 143.7

  593 353 70 232 233

Chapter 9: Physical Properties

kJ kg

cC

MPa

Critical Density

cC

Critical Pressure

Triple Point

cC

Critical Temperature

Normal Boiling Point (NBP)

g mol

Heat of Vaporization at NBP

Molar Mass

Property:

Formula

Temperature-Independent Properties of Liquids and Gases (SI Units) (cont'd)

H2 HCl H2S CH4 CH4O C3H6O2 CH5N C4H8O

2.016 36.461 34.081 16.043 32.042 74.07854 31.057 72.106

–252.8 –85.0 –60.3 –161.5 64.7 56.9 –6.3 79.6

–259.2 –114.1 –85.5 –182.5 –97.7 –98.0 –93.5 –86.7

448.7 443.6 546.4 510.8 1100.5 411.1 839.8 438.3

–240.0 51.4 100.0 –82.6 239.4 233.4 156.9 262.4

1.30 8.29 9.00 4.60 8.08 4.75 7.46 4.15

Neon Nitrobenzene Nitrogen n-Nonane n-Octane iso-Octane (2,2,4-trimethylpentane) Oxygen iso-Pentane n-Pentane Propane 1-Propanol Propylene Sulfur dioxide Styrene Toluene Water p-Xylene m-Xylene o-Xylene

Ne C6H5NO2 N2 C9H20 C8H18

20.180 123.109 28.013 128.255 114.229

–246.0 210.9 –195.8 150.8 125.6

–248.6 5.8 –210.0 –53.5 –56.8

85.8 442.7 199.2 288.7 302.1

–228.7

2.75

482

–147.0 321.4 295.7

3.40 2.28 2.49

313 232 235

C8H18

114.229

99.2

–107.4

268.2

270.9

2.57

242

O2 C5H12 C5H12 C3H8 C3H8O C3H6 SO2 C8H8 C7H8 H2O C8H10 C8H10 C8H10

31.999 72.149 72.149 44.096 60.095 42.080 64.064 104.149 92.138 18.015 106.165 106.165 106.165

–183.0 27.8 36.1 –42.1 97.2 –47.6 –10.0 145.3 110.6 100.0 138.3 139.1 144.4

–218.8 –160.5 –129.7 –187.6 –126.2 –185.2 –75.5 –30.7 –95.2 0.0 13.3 –47.9 –25.2

213.1 343.3 357.5 425.7 692.0 438.9 389.1 351.7 360.8 2256.5 336.3 340.1 342.6

–118.6 187.2 196.6 96.7 263.7 91.1 157.5 362.1 318.6 705.1 343.0 343.7 357.1

5.04 3.38 3.37 4.25 5.17 4.55 7.88 3.88 4.13 22.06 3.53 3.53 3.74

436 236 232 220 274 230 525 292 292 322 286 283 285

$

Hydrogen Hydrogen chloride Hydrogen sulfide Methane Methanol Methyl acetate Methyl amine Methyl ethyl ketone

kg m3 31 430 347 163 274 325 202 270

Chemical

Source for tables in Section 8.4: "Table of Physical Properties for Hydrocarbons and Other Compounds of Interest to the Natural Gas and Natural Gas Liquids Industries," GPS Standard 2145-16, Tulsa, OK: GPA Midstream Association, 2016, pp. 4–9, and NIST Chemistry Web Book, NIST Standard Reference Database Number 69, P.J. Linstrom and W.G. Mallard, eds.

©2020 NCEES

566

Chapter 9: Physical Properties

9.5 Physical Properties of Liquids and Gases—Temperature-Dependent Properties 9.5.1

U.S. Customary Units Temperature-Dependent Physical Properties of Gases at 14.7 psia (U.S. Units) Gas

Temperature

cF

Nitrogen

Oxygen

Carbon Monoxide

Carbon Dioxide

Sulfur Dioxide

Air

©2020 NCEES

0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000

Density

lbm ft 3 0.0835 0.0582 0.0446 0.0362 0.0304 0.0263 0.0955 0.0664 0.0510 0.0414 0.0348 0.0300 0.0835 0.0581 0.0446 0.0362 0.0304 0.0263 0.131 0.0914 0.0701 0.0569 0.0479 0.0413 0.195* 0.134 0.102 0.0829 0.0697 0.0601 0.0864 0.0601 0.0461 0.0374 0.0315 0.0272

Heat Thermal Capacity (Cp) Conductivity

Btu lbm - cF 0.248 0.249 0.251 0.256 0.262 0.269 0.218 0.222 0.230 0.239 0.246 0.252 0.248 0.249 0.253 0.259 0.266 0.273 0.190 0.219 0.239 0.255 0.268 0.279 0.143 0.158 0.171 0.182 0.190 0.196 0.239 0.240 0.244 0.249 0.256 0.262

567

Btu ft - hr -cF 0.0129 0.0175 0.0217 0.0256 0.0294 0.0331 0.0133 0.0184 0.0231 0.0276 0.0318 0.0359 0.0126 0.0172 0.0213 0.0251 0.0286 0.0320 0.00763 0.0127 0.0179 0.0230 0.0279 0.0325 0.00443 0.00738 0.0107 0.0142 0.0177 0.0208 0.0132 0.0178 0.0220 0.0259 0.0297 0.0333

Thermal Diffusivity 2

ft hr 0.624 1.21 1.93 2.76 3.69 4.68 0.637 1.24 1.97 2.79 3.71 4.74 0.608 1.18 1.88 2.68 3.54 4.47 0.307 0.632 1.07 1.59 2.18 2.82 0.159 0.349 0.612 0.945 1.34 1.76 0.639 1.23 1.95 2.78 3.69 4.68

Viscosity

lbm ft - sec 10.6E–6 13.9E–6 16.8E–6 19.5E–6 22.0E–6 24.3E–6 12.2E–6 16.3E–6 19.9E–6 23.1E–6 26.1E–6 28.8E–6 10.5E–6 13.9E–6 16.8E–6 19.4E–6 21.7E–6 23.9E–6 8.65E–6 12.2E–6 15.3E–6 18.2E–6 20.8E–6 23.2E–6 7.38E–6 10.7E–6 13.8E–6 16.6E–6 19.3E–6 21.8E–6 11.06E–6 14.5E–6 17.5E–6 20.1E–6 22.5E–6 24.7E–6

Prandtl Number 0.730 0.713 0.704 0.701 0.704 0.709 0.722 0.710 0.714 0.721 0.727 0.730 0.745 0.727 0.719 0.721 0.726 0.733 0.774 0.760 0.739 0.723 0.716 0.715 0.856 0.823 0.791 0.764 0.746 0.741 0.716 0.705 0.698 0.697 0.698 0.698

Chapter 9: Physical Properties Temperature-Dependent Physical Properties of Gases at 14.7 psia (U.S. Units) (cont'd) Temperature Gas

cF

Hydrogen

Ammonia

Helium

Neon

Argon

Fluorine

©2020 NCEES

0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000

Density

lbm ft 3 0.00600 0.00420 0.00320 0.00260 0.00220 0.00190 0.0514 0.0355 0.0272 0.0220 0.0185 0.0160 0.0119 0.00830 0.00640 0.00520 0.00440 0.00380 0.0601 0.0419 0.0321 0.0261 0.0219 0.0189 0.119 0.0830 0.0636 0.0516 0.0434 0.0375 0.113 0.0789 0.0605 0.0491 0.0413 0.0356

Heat Thermal Capacity (Cp) Conductivity

Btu lbm - cF

Btu ft - hr -cF

3.37 3.45 3.47 3.47 3.48 3.51 0.484 0.529 0.581 0.630 0.677 0.722 1.24 1.24 1.24 1.24 1.24 1.24 0.246 0.246 0.246 0.246 0.246 0.246 0.124 0.124 0.124 0.124 0.124 0.124 0.192 0.204 0.214 0.220 0.225 0.229

0.0911 0.121 0.148 0.174 0.199 0.222 0.0117 0.0193 0.0278 0.0371 0.0471 0.0577 0.0802 0.102 0.123 0.142 0.160 0.178 0.0253 0.0325 0.0390 0.0449 0.0505 0.0558 0.00903 0.0121 0.0148 0.0173 0.0196 0.0217 0.0127 0.0179 0.0229 0.0279 0.0328 0.0376**

568

Thermal Diffusivity 2

ft hr 4.50 8.34 13.3 19.3 25.9 33.4 0.471 1.03 1.76 2.67 3.76 4.99 5.43 9.94 15.5 22.0 29.4 37.8 1.71 3.15 4.93 7.00 9.38 12.0 0.609 1.17 1.87 2.69 3.63 4.66 0.585 1.11 1.77 2.58 3.53 4.62

Viscosity

lbm ft - sec 5.38E–6 6.89E–6 8.27E–6 9.54E–6 10.7E–6 11.9E–6 5.76E–6 8.48E–6 11.2E–6 13.9E–6 16.6E–6 19.3E–6 12.0E–6 15.4E–6 18.5E–6 21.4E–6 24.2E–6 26.8E–6 19.0E–6 24.3E–6 29.1E–6 33.5E–6 37.6E–6 41.5E–6 13.4E–6 18.0E–6 22.1E–6 25.8E–6 29.2E–6 32.4E–6 13.6E–6 18.4E–6 22.7E–6 26.7E–6 30.4E–6 33.9E–6

Prandtl Number 0.718 0.708 0.697 0.685 0.678 0.675 0.857 0.837 0.843 0.851 0.860 0.869 0.669 0.671 0.672 0.672 0.672 0.672 0.664 0.662 0.660 0.660 0.659 0.659 0.663 0.666 0.667 0.667 0.667 0.667 0.740 0.758 0.763 0.759 0.751 0.741

Chapter 9: Physical Properties Temperature-Dependent Physical Properties of Gases at 14.7 psia (U.S. Units) (cont'd) Temperature Gas

cF

Chlorine

Methane

Ethane

Propane

Acetylene

©2020 NCEES

0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000

Density

lbm ft 3 0.215 0.148 0.113 0.0918 0.0772 0.0666 0.0480 0.0333 0.0256 0.0207 0.0174 0.0150 0.0907 0.0627 0.0480 0.0389 0.0327 0.0282 0.135 0.0923 0.0705 0.0571 0.0480 0.0414 0.0784 0.0542 0.0415 0.0337 0.0283 0.0244

Heat Thermal Capacity (Cp) Conductivity

Btu lbm - cF

Btu ft - hr -cF

0.112 0.118 0.121 0.123 0.124 0.125 0.512 0.578 0.673 0.772 0.866 0.953

0.00429 0.00649 0.00861 0.0106 0.0126 0.0144 0.0164 0.0256 0.0360 0.0475 0.0599** 0.0731**

0.377 0.485 0.599 0.700 0.787 0.863 0.353 0.470 0.589 0.690 0.773 0.844 1.60 0.442 0.494 0.531 0.558 0.581

0.00939 0.0179 0.0282 0.0399 0.0526 0.0663 0.00777 0.0151 0.0242 0.0348 0.0467 0.0597 0.0193 0.0171 0.0241 0.0309 0.0375 0.0441

569

Thermal Diffusivity 2

ft hr 0.178 0.372 0.629 0.943 1.31 1.73 0.667 1.33 2.09 2.97 3.97 5.11 0.275 0.590 0.981 1.46 2.04 2.72 0.163 0.348 0.583 0.884 1.26 1.71 0.0377 0.715 1.18 1.73 2.37 3.11

Viscosity

lbm ft - sec

Prandtl Number

7.72E–6 11.0E–6 14.1E–6 17.0E–6 19.8E–6 22.5E–6 6.57E–6 8.93E–6 11.0E–6 12.9E–6 14.6E–6 16.3E–6

0.724 0.720 0.713 0.708 0.705 0.704 0.739 0.727 0.741 0.755 0.762 0.763

5.43E–6 7.59E–6 9.56E–6 11.4E–6 13.1E–6 14.7E–6 4.87E–6 6.74E–6 8.56E–6 10.3E–6 12.1E–6 13.8E–6 9.36E–6 8.38E–6 10.6E–6 12.7E–6 14.6E–6** 16.4E–6**

0.786 0.739 0.731 0.720 0.706 0.691 0.797 0.757 0.750 0.738 0.720 0.702 0.774 0.778 0.786 0.787 0.783 0.777

Chapter 9: Physical Properties Temperature-Dependent Physical Properties of Gases at 14.7 psia (U.S. Units) (cont'd) Temperature Gas

cF

Ethylene

Propylene

Hydrogen Sulfide

0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000

Density

lbm ft 3 0.0844 0.0584 0.0447 0.0363 0.0305 0.0263 0.128 0.0880 0.0673 0.0545 0.0458 0.0395 0.1027 0.0711 0.0544 0.0441 0.0371 0.0320

Heat Thermal Capacity (Cp) Conductivity

Btu lbm - cF

Btu ft - hr -cF

0.332 0.424 0.515 0.595 0.665 0.725 0.329 0.428 0.518 0.600 0.674 0.738 0.237 0.246 0.258 0.272 0.286 0.300

0.00930 0.0170 0.0266 0.0380 0.0508** 0.0651** 0.00765 0.0146 0.0229 0.0323 0.0425 0.0535 0.0065 0.0108 0.0144 0.0184 0.0229** 0.0279**

Thermal Diffusivity 2

ft hr 0.332 0.685 1.16 1.76 2.51 3.41 0.182 0.386 0.656 0.986 1.38 1.84 0.267 0.616 1.03 1.53 2.16 2.90

Viscosity

lbm ft - sec 5.90E–6 8.31E–6 10.5E–6 12.4E–6 14.2E–6 15.8E–6 4.94E–6 7.10E–6 9.08E–6 10.9E–6 12.6E–6 14.2E–6 7.27E–6 10.5E–6 13.7E–6 16.9E–6** 20.2E–6** 23.4E–6**

Prandtl Number 0.758 0.749 0.730 0.702 0.669 0.635 0.763 0.751 0.741 0.730 0.718 0.703 0.956 0.862 0.884 0.901 0.908 0.908

* The vapor pressure of sulfur dioxide at 0˚F is 10.2 psia. Hypothetical vapor density at 0˚F and 14.7 psia is reported in the table. ** Extrapolated values Sources: These data are provide courtesy of the American Institute of Chemical Engineering (AIChE) and its thermophysical property research consortium, the Design Institute for Physical Properties (DIPPR®) using DIPPR® 2016 version. Vapor densities were obtained using SRK equation of state with DIPPR 801 values for critical temperature, critical pressure, and acentric factor. These data are provided for the sole purpose of the preparation for and taking of NCEES engineering exams with no warrantee expressed or implied.

©2020 NCEES

570

Chapter 9: Physical Properties

9.5.2

SI Units Temperature-Dependent Physical Properties of Gases at 0.1 MPa (SI Units) Temperature Gas

cC

Nitrogen

Oxygen

Carbon Monoxide

Carbon Dioxide

Sulfur Dioxide

Air

©2020 NCEES

0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500

Density

kg m3 1.23 0.903 0.712 0.588 0.500 0.436 1.41 1.03 0.813 0.671 0.572 0.498 1.23 0.903 0.712 0.588 0.500 0.436 1.94 1.42 1.12 0.924 0.786 0.685 2.87 2.08 1.63 1.35 1.15 0.997 1.28 0.933 0.736 0.608 0.517 0.450

Heat Thermal Capacity (Cp) Conductivity

Thermal Diffusivity

Viscosity

kJ kg : K

W m:K

m hr

nPa : s

1.04 1.04 1.05 1.07 1.09 1.12 0.914 0.933 0.963 0.995 1.02 1.05 1.04 1.04 1.06 1.08 1.11 1.13 0.816 0.924 1.00 1.06 1.11 1.15 0.609 0.664 0.714 0.756 0.788 0.813 1.00 1.01 1.02 1.04 1.06 1.09

0.0237 0.0307 0.0372 0.0434 0.0494 0.0551 0.0244 0.0323 0.0397 0.0466 0.0533 0.0597 0.0231 0.0301 0.0365 0.0425 0.0481 0.0535 0.0145 0.0224 0.0306 0.0386 0.0464 0.0536 0.00843 0.0131 0.0183 0.0238 0.0292 0.0343 0.0242 0.0312 0.0377 0.0439 0.0498 0.0556

0.0665 0.117 0.179 0.249 0.326 0.408 0.0682 0.121 0.182 0.251 0.328 0.412 0.0650 0.115 0.175 0.241 0.313 0.390 0.0331 0.0617 0.0985 0.142 0.192 0.245 0.0174 0.0342 0.0565 0.0842 0.117 0.152 0.0681 0.120 0.181 0.250 0.326 0.408

16.6 21.0 24.9 28.5 31.8 35.0 19.2 24.6 29.4 33.8 37.8 41.5 16.5 20.9 24.8 28.3 31.5 34.5 13.8 18.4 22.6 26.5 30.0 33.3 11.8 16.2 20.3 24.2 27.8 31.2 17.2 21.8 25.8 29.4 32.7 35.7

571

2

Prandtl Number 0.727 0.712 0.704 0.701 0.703 0.707 0.718 0.710 0.713 0.720 0.725 0.729 0.741 0.726 0.719 0.720 0.725 0.731 0.772 0.758 0.740 0.725 0.717 0.715 0.851 0.821 0.792 0.767 0.749 0.741 0.714 0.704 0.698 0.697 0.697 0.698

Chapter 9: Physical Properties Temperature-Dependent Physical Properties of Gases at 0.1 MPa (SI Units) (cont'd) Temperature Gas

cC 0 Hydrogen

Ammonia

Helium

Neon

Argon

Fluorine

©2020 NCEES

100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500

Density

kg m3 0.0887 0.0649 0.0512 0.0423 0.0360 0.0314 0.758 0.551 0.434 0.358 0.304 0.265 0.176 0.129 0.102 0.0840 0.0715 0.0623 0.888 0.650 0.513 0.423 0.361 0.314 1.76 1.29 1.02 0.838 0.714 0.621 1.67 1.22 0.966 0.797 0.679 0.591

Heat Thermal Capacity (Cp) Conductivity

kJ kg : K

W m:K

14.2

0.166

14.5 14.5 14.5 14.6 14.6 2.05 2.23 2.42 2.61 2.79 2.96 5.19 5.19 5.19 5.19 5.19 5.19 1.030 1.030 1.030 1.030 1.030 1.030 0.520 0.520 0.520 0.520 0.520 0.520 0.812 0.858 0.893 0.919 0.938 0.953

0.212 0.255 0.295 0.334 0.371 0.0222 0.0342 0.0475 0.0618 0.0772 0.0934 0.145 0.179 0.211 0.241 0.270 0.298 0.0459 0.0570 0.0670 0.0764 0.0852 0.0935 0.0165 0.0212 0.0254 0.0293 0.0329 0.0364 0.0235 0.0314 0.0393 0.0470 0.0547 0.0623*

572

Thermal Diffusivity 2

m hr 0.475 0.814 1.23 1.73 2.29 2.91 0.0516 0.100 0.163 0.238 0.327 0.429 0.571 0.964 1.44 1.99 2.62 3.32 0.181 0.306 0.457 0.630 0.826 1.04 0.0649 0.114 0.173 0.242 0.319 0.405 0.0622 0.108 0.164 0.231 0.309 0.398

Viscosity

nPa : s

Prandtl Number

8.39

0.716

10.4 12.2 13.9 15.6 17.1 9.21 12.9 16.5 20.1 23.7 27.4 18.7 23.2 27.3 31.3 35.0 38.6 29.6 36.6 43.0 48.9 54.5 59.8 21.1 27.1 32.6 37.6 42.2 46.6 21.5 27.8 33.6 38.9 43.9 48.7

0.708 0.697 0.687 0.679 0.675 0.849 0.837 0.843 0.850 0.858 0.866 0.669 0.671 0.672 0.672 0.672 0.672 0.663 0.661 0.660 0.660 0.659 0.659 0.663 0.666 0.667 0.667 0.667 0.667 0.744 0.759 0.763 0.760 0.753 0.745

Chapter 9: Physical Properties Temperature-Dependent Physical Properties of Gases at 0.1 MPa (SI Units) (cont'd) Temperature Gas

cC

Chlorine

Methane

Ethane

Propane

Acetylene

Ethylene

©2020 NCEES

0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500

Density

kg m3 3.17 2.30 1.81 1.49 1.27 1.10 0.708 0.517 0.408 0.337 0.287 0.250 1.34 0.973 0.765 0.631 0.537 0.468 1.98 1.43 1.125 0.927 0.788 0.686 1.16 0.842 0.663 0.547 0.465 0.405 1.24 0.907 0.714 0.589 0.501 0.436

Heat Thermal Capacity (Cp) Conductivity

kJ kg : K

W m:K

0.473 0.494 0.506 0.514 0.519 0.523 2.17 2.44 2.80 3.17 3.53 3.87 1.64 2.06 2.49 2.88 3.21 3.51 1.55 2.00 2.45 2.83 3.16 3.44 1.60 1.87 2.06 2.20 2.31 2.40 1.45 1.80 2.14 2.45 2.72 2.95

0.00803 0.0115 0.0148 0.0179 0.0210 0.0239 0.0307 0.0453 0.0615 0.0793 0.0983 0.119* 0.0184 0.0320 0.0481 0.0661 0.0857 0.107 0.0152 0.0270 0.0412 0.0575 0.0757 0.0955 0.0193 0.0304 0.0412 0.0518 0.0622 0.0724 0.0180 0.0303 0.0453 0.0628 0.0824* 0.104*

573

Thermal Diffusivity 2

m hr 0.0193 0.0363 0.0581 0.0844 0.115 0.149 0.0720 0.129 0.194 0.267 0.350 0.442 0.0301 0.0575 0.0908 0.131 0.179 0.234 0.0178 0.0339 0.0539 0.0788 0.109 0.146 0.0377 0.0696 0.109 0.155 0.208 0.268 0.0359 0.0668 0.107 0.157 0.218 0.290

Viscosity

nPa : s 12.3 16.7 20.8 24.8 28.5 32.1 10.4 13.5 16.3 18.8 21.2 23.4 8.62 11.5 14.1 16.6 18.9 21.1 7.70 10.2 12.6 15.0 17.4 19.7 9.36 12.7 15.7 18.5 21.1 23.5* 9.38 12.6 15.5 18.1 20.5 22.8

Prandtl Number 0.724 0.720 0.714 0.709 0.706 0.704 0.733 0.727 0.741 0.754 0.761 0.764 0.772 0.738 0.731 0.722 0.709 0.696 0.785 0.756 0.750 0.740 0.724 0.708 0.774 0.778 0.786 0.788 0.785 0.779 0.755 0.748 0.731 0.706 0.677 0.646

Chapter 9: Physical Properties Temperature-Dependent Physical Properties of Gases at 0.1 MPa (SI Units) (cont'd) Temperature

Density

Gas

kg m3 1.89 1.37 1.07 0.884 0.752 0.655 1.51 1.10 0.868 0.716 0.609 0.530

cC

Propylene

Hydrogen Sulfide

0 100 200 300 400 500 0 100 200 300 400 500

Heat Thermal Capacity (Cp) Conductivity

kJ kg : K

W m:K

1.44 1.82 2.15 2.47 2.75 3.00 1.00 1.03 1.08 1.13 1.18 1.24

0.0150 0.0260 0.0390 0.0535 0.0692 0.0860 0.0126 0.0190 0.0247 0.0308 0.0376* 0.0452*

Thermal Diffusivity 2

m hr 0.0198 0.0376 0.0608 0.0882 0.120 0.158 0.0302 0.0601 0.0949 0.137 0.188 0.248

Viscosity

nPa : s 7.88 10.7 13.4 15.9 18.1 20.3 11.6 15.9 20.2 24.5* 28.9* 33.2*

Prandtl Number 0.760 0.751 0.741 0.732 0.722 0.709 0.911 0.862 0.883 0.899 0.907 0.909

* Extrapolated values Sources: These data are provide courtesy of the American Institute of Chemical Engineering (AIChE) and its thermophysical property research consortium, the Design Institute for Physical Properties (DIPPR®) using DIPPR® 2016 version. Vapor densities were obtained using SRK equation of state with DIPPR 801 values for critical temperature, critical pressure, and acentric factor. These data are provided for the sole purpose of the preparation for and taking of NCEES engineering exams with no warrantee expressed or implied.

9.6 Physical Properties of Air 9.6.1

Dry Atmospheric Air Composition Composition of Dry Atmospheric Air Component Nitrogen Oxygen Argon Carbon dioxide Neon Helium Methane Krypton Hydrogen Nitrous oxide Carbon monoxide Xenon

Total

©2020 NCEES

Mole Fraction 0.780848 0.209390 0.009332 0.000400 18.2 × 10–6 5.2 × 10–6 1.5 × 10–6 1.1 × 10–6 0.5 × 10–6 0.3 × 10–6 0.2 × 10–6 0.1 × 10–6

1.0

574

d

Molar Mass

g lb n lb mole or mol 28.0134 31.9988 39.948 44.0095 20.1797 4.0026 16.0325 83.798 2.01588 44.0128 28.0101 131.294 28.96546

Chapter 9: Physical Properties

9.6.2

Dry Atmospheric Air Properties Properties of Dry Atmospheric Air Property Molar mass NBP temperature Triple point temperature Critical temperature Critical pressure Critical density

Density of liquid at NBP

U.S. Units*

lb

28.965 lb mole –317.64 °F –352.12 °F –221.12 °F 549.11 psia

g

28.965 mol 78.903 K 59.75 K 132.53 K 3.7860 MPa

lbm ft 3

342.68

kg m3

lbm ft 3 lbm 7.3039 gal

875.21

kg m3

21.393 54.637

gal

Volume of liquid at NBP

0.13691 lbm

Density of ideal gas

0.07633

Volume of ideal gas

13.101 lbm

Speed of sound in air p = 14.696 psia, T = 32°F p = 0.1 MPa, T = 0°C Speed of sound in air p = 14.696 psia , T = 68°F p = 0.1 MPa, T = 20°C

SI Units**

lbm ft 3 ft 3

m3

0.0011426 kg 1.2250

kg m3 m3

0.81631 kg

m

ft

330 s

ft

343 s

1090 sec 1130 sec

m

* U.S. unit values are given at 60°F and 14.696 psia, except where noted otherwise. ** SI unit values are given at 15°C and 0.101325 MPa, except where noted otherwise.

©2020 NCEES

575

Chapter 9: Physical Properties

9.6.3

Temperature-Dependent Properties of Air (U.S. Customary Units)

©2020 NCEES

lbm ft -sec

Btu hr - ft -cF

9.98E–06 1.09E–05 1.15E–05 1.28E–05 1.44E–05 1.60E–05 1.74E–05 1.89E–05 2.01E–05 2.14E–05 2.25E–05

576

0.0120 0.0132 0.0140 0.0156 0.0179 0.0202 0.0225 0.0247 0.0268 0.0288 0.0307

Thermal Diffusivity

1.40 1.40 1.40 1.40 1.40 1.39 1.39 1.38 1.38 1.37 1.37

Thermal Conductivity

Heat Capacity Ratio

(cp)

Heat Capacity

Btu lbm-cF 0.2400 0.2400 0.2400 0.2400 0.2401 0.2424 0.2452 0.2476 0.2507 0.2533 0.2567

Prandtl Number

–50 0 32 100 200 300 400 500 600 700 800

lbm ft 3 0.094 0.086 0.081 0.071 0.060 0.052 0.046 0.041 0.0374 0.034 0.0286

Viscosity

°F

Density

Temperature

Temperature-Dependent Properties of Air at 14.7 psia (U.S. Units)

0.719 0.714 0.710 0.708 0.701 0.692 0.685 0.681 0.678 0.677 0.679

ft 2 hr 0.530 0.642 0.726 0.917 1.233 1.599 1.989 2.415 2.857 3.323 4.173

Chapter 9: Physical Properties

9.6.4

Temperature-Dependent Properties of Air (SI Units)

–50 0 20 40 60 80 100 120 140 160 180 200 250 300 350 400

©2020 NCEES

1.005 1.005 1.005 1.005 1.009 1.009 1.009 1.013 1.013 1.017 1.022 1.026 1.034 1.047 1.055 1.068

1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.39 1.39 1.39 1.38 1.38 1.37 1.37

W m:K

14.6 17.2 18.2 19.1 20.2 20.9 21.8 22.7 23.5 24.3 25.2 25.8 27.8 29.5 31.2 32.8

577

0.0204 0.0243 0.0257 0.0271 0.0285 0.0299 0.0314 0.0328 0.0343 0.0358 0.0372 0.0386 0.0421 0.0454 0.0485 0.0515

Thermal Diffusivity

nPa : s

Prandtl Number

Heat Capacity Ratio

(cp)

Heat Capacity

kJ kg : K

Thermal Conductivity

kg m3 1.534 1.293 1.205 1.127 1.067 1.000 0.946 0.898 0.854 0.815 0.779 0.746 0.675 0.616 0.566 0.524

Viscosity

°C

Density

Temperature

Temperature-Dependent Properties of Air at 0.1 MPa (SI Units)

m2 s 0.722 0.711 0.712 0.709 0.714 0.707 0.701 0.700 0.695 0.691 0.691 0.687 0.683 0.680 0.678 0.679

1.32E–05 1.87E–05 2.12E–05 2.39E–05 2.65E–05 2.96E–05 3.29E–05 3.61E–05 3.96E–05 4.32E–05 4.67E–05 5.04E–05 6.03E–05 7.04E–05 8.12E–05 9.20E–05

©2020 NCEES

9.6.5

Psychrometric Chart (U.S. Customary Units)

wet bulb, dry bulb, saturation temperature, relative humidity

∞

∞ ∞

578 Source: American Society of Heating, Refrigerating, and Air-Conditioning Engineers, 1992.

Chapter 9: Physical Properties

∆ ∆

©2020 NCEES

9.6.6

Psychrometric Chart (SI Units)

wet bulb, dry bulb, saturation temperature, relative humidity

∞

∞

∞

579 Source: American Society of Heating, Refrigerating, and Air-Conditioning Engineers, 1992.

Chapter 9: Physical Properties

∆ ∆

Chapter 9: Physical Properties

9.7 Physical Properties of Water 9.7.1

U.S. Customary Units

©2020 NCEES

Density

Heat Capacity

Viscosity

Thermal Conductivity

psia

32.02 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 320 340

0.08872 0.12173 0.17814 0.2564 0.36336 0.50747 0.69904 0.95051 1.2767 1.695 2.2259 2.893 3.7232 4.7472 5.9998 7.5195 9.3496 11.538 14.136 17.201 20.795 24.986 29.844 35.447 41.878 49.222 57.574 67.029 89.667 118.02

lbm ft 3 62.415 62.423 62.406 62.364 62.299 62.213 62.110 61.991 61.857 61.710 61.549 61.377 61.193 60.998 60.793 60.578 60.354 60.120 59.877 59.626 59.366 59.097 58.820 58.535 58.241 57.940 57.630 57.312 56.650 55.955

Btu lbm-cF 1.0086 1.0055 1.0028 1.0010 0.9999 0.9993 0.9990 0.9989 0.9991 0.9993 0.9998 1.0003 1.0009 1.0016 1.0025 1.0035 1.0046 1.0059 1.0073 1.0088 1.0106 1.0125 1.0147 1.0170 1.0196 1.0224 1.0254 1.0287 1.0362 1.0449

lbm ft -sec 1.204E–03 1.038E–03 8.776E–04 7.533E–04 6.552E–04 5.761E–04 5.114E–04 4.577E–04 4.127E–04 3.744E–04 3.417E–04 3.134E–04 2.888E–04 2.673E–04 2.484E–04 2.316E–04 2.168E–04 2.035E–04 1.916E–04 1.808E–04 1.712E–04 1.624E–04 1.544E–04 1.471E–04 1.405E–04 1.344E–04 1.288E–04 1.236E–04 1.144E–04 1.065E–04

Btu hr-ft -cF 0.3244 0.3293 0.3353 0.3413 0.3471 0.3527 0.3579 0.3628 0.3672 0.3713 0.3750 0.3783 0.3813 0.3839 0.3862 0.3881 0.3898 0.3912 0.3924 0.3934 0.3941 0.3947 0.3951 0.3953 0.3953 0.3952 0.3949 0.3944 0.3931 0.3912

580

Surface Tension

Vapor Pressure

°F

Prandtl Number

Temperature

Physical Properties of Liquid Water (U.S. Units)

13.47 11.42 9.45 7.95 6.79 5.88 5.14 4.54 4.04 3.63 3.28 2.98 2.73 2.51 2.32 2.16 2.01 1.88 1.77 1.67 1.58 1.50 1.43 1.36 1.30 1.25 1.20 1.16 1.09 1.02

dyne cm 75.65 75.02 74.22 73.40 72.57 71.71 70.84 69.96 69.05 68.13 67.19 66.24 65.27 64.28 63.28 62.26 61.23 60.19 59.13 58.05 56.96 55.86 54.74 53.62 52.47 51.32 50.16 48.98 46.59 44.16

Chapter 9: Physical Properties

Heat Capacity

Viscosity

lbm ft 3 55.225 54.458 53.652 52.804 51.912 50.971 49.976 48.920 47.795 46.590 45.290 43.876 42.318 40.572 38.566 36.152 32.936 27.283 26.085 24.196 20.102

Btu lbm-cF 1.0550 1.0666 1.0802 1.0959 1.1143 1.1358 1.1612 1.1916 1.2285 1.2740 1.3317 1.4072 1.5100 1.6588 1.8958 2.3480 3.5861 15.5790 28.2960 97.4060

lbm ft -sec 9.958E–05 9.354E–05 8.820E–05 8.343E–05 7.913E–05 7.523E–05 7.165E–05 6.833E–05 6.521E–05 6.225E–05 5.940E–05 5.661E–05 5.382E–05 5.097E–05 4.796E–05 4.463E–05 4.054E–05 3.399E–05 3.268E–05 3.180E–05 3.333E–05

360 380 400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 700 702 704 705.1

©2020 NCEES

153.03 195.74 247.26 308.76 381.48 466.75 565.95 680.55 812.10 962.24 1132.7 1325.5 1542.5 1786.2 2059.2 2364.9 2707.3 3093.0 3134.5 3176.6 3200.1

581

Btu hr-ft-cF 0.3888 0.3857 0.3819 0.3776 0.3725 0.3666 0.3599 0.3522 0.3436 0.3340 0.3233 0.3118 0.2995 0.2867 0.2735 0.2600 0.2461 0.2547 0.2765 0.3584

0.97 0.93 0.90 0.87 0.85 0.84 0.83 0.83 0.84 0.85 0.88 0.92 0.98 1.06 1.20 1.45 2.13 7.48 12.04 31.11

Surface Tension

Density

psia

Prandtl Number

Vapor Pressure

°F

Thermal Conductivity

Temperature

Physical Properties of Liquid Water (U.S. Units) (cont'd)

dyne cm 41.69 39.19 36.66 34.10 31.52 28.92 26.30 23.69 21.08 18.47 15.89 13.35 10.846 8.415 6.078 3.876 1.877 0.2565 0.1375 0.0375

Chapter 9: Physical Properties

9.7.2

SI Units

©2020 NCEES

kJ kg : K

Pa : s

W m:K

4.2199 4.2055 4.1955 4.1888 4.1844 4.1816 4.1801 4.1795 4.1796 4.1804 4.1815 4.1831 4.1851 4.1875 4.1902 4.1933 4.1969 4.2008 4.2053 4.2102 4.2157 4.2283 4.2435 4.2615 4.2826 4.3071 4.3354 4.3678 4.4050 4.4474

1.791E–03 1.518E–03 1.306E–03 1.138E–03 1.002E–03 8.901E–04 7.974E–04 7.193E–04 6.530E–04 5.961E–04 5.468E–04 5.040E–04 4.664E–04 4.332E–04 4.039E–04 3.777E–04 3.543E–04 3.333E–04 3.144E–04 2.973E–04 2.817E–04 2.547E–04 2.321E–04 2.129E–04 1.965E–04 1.825E–04 1.702E–04 1.596E–04 1.501E–04 1.418E–04

0.5610 0.5705 0.5800 0.5893 0.5984 0.6072 0.6155 0.6233 0.6306 0.6373 0.6436 0.6492 0.6544 0.6590 0.6631 0.6668 0.6700 0.6728 0.6753 0.6773 0.6791 0.6817 0.6832 0.6837 0.6833 0.6820 0.6800 0.6771 0.6733 0.6688

582

Surface Tension

kg m3 999.79 999.92 999.65 999.06 998.16 997.00 995.61 993.99 992.18 990.17 988.00 985.66 983.16 980.52 977.73 974.81 971.77 968.59 965.30 961.88 958.35 950.95 943.11 934.83 926.13 917.01 907.45 897.45 887.00 876.08

Prandtl Number

0.000612 0.000873 0.001228 0.001706 0.002339 0.00317 0.004247 0.005629 0.007385 0.009595 0.012352 0.015762 0.019946 0.025042 0.031201 0.038595 0.047414 0.057867 0.070182 0.084608 0.10142 0.14338 0.19867 0.27028 0.36154 0.47616 0.61823 0.79219 1.0028 1.2552

Thermal Conductivity

0.01 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190

Viscosity

MPa

Heat Capacity

Vapor Pressure

°C

Density

Temperature

Physical Properties of Liquid Water (SI Units)

N −3 m : 10 13.47 11.19 9.45 8.09 8.09 6.13 5.42 4.82 4.33 3.91 3.55 3.25 2.98 2.75 2.55 2.38 2.22 2.08 1.96 1.85 1.75 1.58 1.44 1.33 1.23 1.15 1.09 1.03 0.98 0.94

75.65 74.94 74.22 73.49 72.74 71.97 71.19 70.40 69.60 68.78 67.94 67.10 66.24 65.37 64.48 63.58 62.67 61.75 60.82 59.87 58.91 56.96 54.97 52.93 50.86 48.74 46.59 44.41 42.19 39.95

Chapter 9: Physical Properties

©2020 NCEES

1.5549 1.9077 2.3196 2.7971 3.3469 3.9762 4.6923 5.503 6.4166 7.4418 8.5879 9.8651 11.284 12.858 14.601 16.529 18.666 21.044 21.297 21.554 21.814 22.064

kJ kg : K

Pa : s

W m:K

4.4958 4.5512 4.6146 4.6876 4.7719 4.8701 4.9856 5.1230 5.2889 5.4931 5.7504 6.0848 6.5373 7.1863 8.2080 10.1160 15.0040 45.1550 62.3510 102.1500 243.7800

583

1.343E–04 1.276E–04 1.215E–04 1.160E–04 1.109E–04 1.061E–04 1.017E–04 9.750E–05 9.351E–05 8.966E–05 8.590E–05 8.217E–05 7.841E–05 7.454E–05 7.043E–05 6.588E–05 6.033E–05 5.207E–05 5.075E–05 4.908E–05 4.781E–05 4.854E–05

0.6633 0.6570 0.6497 0.6413 0.6319 0.6212 0.6092 0.5959 0.5812 0.5650 0.5474 0.5288 0.5092 0.4891 0.4685 0.4474 0.4257 0.4250 0.4384 0.4674 0.5479

Surface Tension

kg m3 864.66 852.72 840.22 827.12 813.37 798.89 783.63 767.46 750.28 731.91 712.14 690.67 667.09 640.77 610.67 574.71 527.59 451.43 438.64 422.26 398.68 322.00

Prandtl Number

Thermal Conductivity

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 371 372 373 373.94

Viscosity

MPa

Heat Capacity

Vapor Pressure

°C

Density

Temperature

Physical Properties of Liquid Water (SI Units) (cont'd)

N −3 m : 10 0.91 0.88 0.86 0.85 0.84 0.83 0.83 0.84 0.85 0.87 0.90 0.95 1.01 1.10 1.23 1.49 2.13 5.53 7.22 10.72 21.27

37.68 35.38 33.07 30.74 28.39 26.04 23.69 21.34 18.99 16.66 14.36 12.09 9.864 7.703 5.626 3.665 1.877 0.388 0.269 0.160 0.065

Chapter 9: Physical Properties

9.7.3

Properties of Water Properties of Water Property Molar mass Boiling temperature Triple point temperature Triple point pressure Critical temperature Critical pressure Critical density Maximum density of liquid (4°C = 39°F)

U.S. Units

lb

18.01528 lb mole 212°F 32°F 0.0887 psia 705.1°F 3200.1 psia 20.102

lbm ft 3

lbm ft 3 lbm 8.3455 gal

SI Units

g

18.01528 mol 373.15 K 273.15 K 611.657 Pa 647.09 K 22.06 MPa 322.00

62.426

gal

1000

kg m3 kg m3 m3

Minimum volume of liquid (4°C = 39°F)

0.11983 lbm

Heat of vaporization (100°C = 212°F)

970.17 lbm

Density of ice (0°C = 32°F)

57.227

Latent heat of fusion (0°C = 32°F)

143.38 lbm

333.55 kg

87.90

87.90

55.53

55.53

1.3333

1.3333

Dielectric constant of liquid (0°C = 32°F) Dielectric constant of liquid (100°C = 212°F) Refractive index of liquid (20°C = 68°F)*

Btu

lbm ft 3 Btu

0.001 kg

kJ

2257 kg 916.7

kg m3 kJ

*Refractive index at Sodium D line Source: Harvey, Allan H., and Eric W. Lemmon, NIST/ASME Steam Properties, Version 3.0, Gaithersburg: National Institute of Standards and Technology, 2013.

©2020 NCEES

584

Chapter 9: Physical Properties

9.8 Steam Tables Source for all tables in this section: GPSA Engineering Data Book, 13th ed., Vol. 2, Tulsa, OK: GPSA, 2012, Figures 24-30 and 24-31 on pp. 24-35 through 24-38.

9.8.1

Properties of Saturated Steam (U.S. Customary Units) Saturated Steam (U.S. Units)—Temperature Table Specific Volume, v

Temperature

Pressure

cF 32.018 35 40 45 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200 210 212 220 230 240

psia

Liquid

0.08865 0.09991 0.12163 0.14744 0.17796 0.21392 0.25611 0.30545 0.36292 0.42964 0.50683 0.59583 0.69813 0.81534 0.94294 1.2750 1.6927 2.2230 2.8892 3.7184 4.7414 5.9926 7.5110 9.3400 11.5260 14.1230 14.6960 17.1860 20.7790 24.9680

0.016022 0.016020 0.016019 0.016020 0.016023 0.016027 0.016033 0.016041 0.016050 0.016060 0.016072 0.016085 0.016099 0.016114 0.016130 0.016165 0.016204 0.016247 0.016293 0.016343 0.016395 0.016451 0.016510 0.016572 0.016637 0.016705 0.016719 0.016775 0.016849 0.016926

©2020 NCEES

Specific Enthalpy, h

Specific Entropy, s

Btu lbm

Btu lbm - cF

3

ft lbm Vapor

Liquid

3302.4 2948.1 2445.8 2037.8 1704.8 1432.0 1207.6 1022.1 868.4 740.3 633.3 543.6 468.1 404.4 350.4 265.39 203.26 157.33 122.98 97.07 77.27 62.08 50.225 40.957 33.639 27.816 26.799 23.148 19.381 16.321

0.000 3.002 8.027 13.044 18.054 23.059 28.060 33.057 38.052 43.045 48.037 53.027 58.018 63.008 67.999 77.98 87.97 97.96 123.00 117.95 127.96 137.97 148.00 158.04 168.09 178.15 180.17 188.23 198.33 208.45

585

Vapor 1075.5 1076.8 1079.0 1081.2 1083.4 1085.6 1087.7 1089.9 1092.1 1094.3 1096.4 1098.6 1100.8 1102.9 1105.1 1109.3 1113.6 1117.8 1122.0 1126.1 1130.2 1134.2 1138.2 1142.1 1146.0 1149.7 1150.5 1153.4 1157.1 1160.6

Liquid

Vapor

0.0000 0.0061 0.0162 0.0262 0.0361 0.0458 0.0555 0.0651 0.0745 0.0839 0.0932 0.1024 0.1115 0.1206 0.1295 0.1472 0.1646 0.1817 0.1985 0.2150 0.2313 0.2473 0.2631 0.2787 0.2940 0.3091 0.3121 0.3241 0.3388 0.3533

2.1872 2.1767 2.1594 2.1426 2.1262 2.1102 2.0946 2.0794 2.0645 2.0500 2.0359 2.0221 2.0086 1.9954 1.9825 1.9577 1.9339 1.9112 1.8895 1.8686 1.8487 1.8295 1.8111 1.7934 1.7764 1.7600 1.7568 1.7442 1.7290 1.7142

Chapter 9: Physical Properties Saturated Steam (U.S. Units)—Temperature Table (cont'd) Temperature

cF 250 260 270 280 290 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600 620 640 660 680 700 702 704 705.47

©2020 NCEES

Pressure psia 29.8250 35.4270 41.8560 49.2000 57.5500 67.0050 89.6430 117.9920 153.01 195.73 247.26 308.78 381.54 466.87 566.15 680.86 812.53 962.79 1133.38 1326.17 1543.2 1786.9 2059.9 2065.7 2708.6 3094.3 3135.5 3177.2 3208.2

Specific Volume, v

Specific Enthalpy, h

Specific Entropy, s

ft 3 lbm

Btu lbm

Btu lbm - cF

Liquid 0.017066 0.017089 0.017175 0.017264 0.01736 0.01745 0.01766 0.01787 0.01811 0.01836 0.01864 0.01894 0.01926 0.01961 0.02000 0.02043 0.02091 0.02146 0.02207 0.02279 0.02364 0.02466 0.02595 0.02768 0.03037 0.03662 0.03824 0.04108 0.05078

Vapor

Liquid

13.819 11.762 10.060 8.644 7.4603 6.4658 4.9138 3.7878 2.9573 2.3353 1.8630 1.4997 1.2169 0.99424 0.81717 0.67492 0.55956 0.46513 0.38714 0.32216 0.26747 0.22081 0.18021 0.14431 0.11117 0.07519 0.06997 0.06300 0.05078

218.59 228.76 238.95 249.17 259.4 269.7 290.4 311.3 332.3 353.6 375.1 396.9 419.0 441.5 464.5 487.9 512.0 536.8 562.4 589.1 617.1 646.9 679.1 714.9 758.5 825.2 835.0 854.2 906.0

586

Vapor 1164.0 1167.4 1170.6 1173.8 1167.8 1179.7 1185.2 1190.1 1194.4 1198.0 1201.0 1203.1 1204.4 1204.8 1204.1 1202.2 1199.0 1194.3 1187.7 1179.0 1167.7 1153.2 1133.7 1107.0 1068.5 991.7 979.7 956.2 906.0

Liquid

Vapor

0.3677 0.3819 0.3960 0.4098 0.4236 0.4372 0.4640 0.4902 0.5161 0.5416 0.5667 0.5915 0.6161 0.6405 0.6648 0.6890 0.7133 0.7378 0.7625 0.7876 0.8134 0.8403 0.8686 0.8995 0.9365 0.9924 1.0006 1.0169 1.0612

1.7000 1.6862 1.6729 1.6599 1.6473 1.6351 1.6116 1.5892 1.5678 1.5473 1.5274 1.5080 1.4890 1.4704 1.4518 1.4333 1.4146 1.3954 1.3757 1.3550 1.3330 1.3092 1.2821 1.2498 1.2086 1.1359 1.1210 1.1046 1.0612

Chapter 9: Physical Properties Saturated Steam (U.S. Units)—Pressure Table Pressure Temperature psia 0.1 0.2 0.3 0.4 0.6 0.8 1 2 3 4 6 8 10 20 30 40 50 60 70 80 90 100 150 200 250 300 350 400 450 500 600 700 800 900 1000 1200 1400 1600 1800 ©2020 NCEES

cF 35.02 53.16 64.48 72.87 85.22 94.38 101.74 126.07 141.47 152.96 170.05 182.80 193.21 227.96 250.34 267.25 281.02 292.71 302.93 312.04 320.28 327.82 358.43 381.80 400.97 417.35 431.73 444.60 456.28 467.01 486.20 503.08 518.21 531.95 544.58 567.19 587.07 604.87 621.02

Specific Volume, v

Specific Enthalpy, h

Specific Entropy, s

Btu lbm

3

Liquid

Vapor

Btu lbm - cF Liquid Vapor

3.03 21.22 32.54 40.92 53.25 62.39 69.73 94.03 109.42 120.92 138.03 150.87 161.26 196.27 218.9 236.1 250.2 262.2 272.7 282.1 290.7 298.5 330.6 355.5

1076.8 1084.7 1089.7 1093.3 1098.7 1102.6 1105.8 1116.2 1122.6 1127.3 1134.2 1139.3 1143.3 1156.3 1164.1 1169.8 1174.1 1177.6 1180.6 1183.1 1185.3 1187.2 1194.1 1198.3

0.0061 0.0422 0.0641 0.0799 0.1028 0.1195 0.1326 0.1750 0.2009 0.2199 0.2474 0.2676 0.2836 0.3358 0.3682 0.3921 0.4112 0.4273 0.4411 0.4534 0.4643 0.4743 0.5141 0.5438

2.1766 2.1060 2.0809 2.0562 2.0215 1.9970 1.9781 1.9200 1.8864 1.8626 1.8294 1.8060 1.7879 1.7320 1.6995 1.6765 1.6586 1.6440 1.6316 1.6208 1.6113 1.6027 1.5695 1.5454

376.1 394.0 409.8 424.2 437.3 449.5 471.7 491.6 509.8 526.7 542.6 571.9 598.8 624.2 648.5

1201.1 1202.9 1204.0 1204.6 1204.8 1204.7 1203.7 1201.8 1199.4 1196.4 1192.9 1184.8 1175.8 1164.5 1152.3

0.5679 0.5882 0.6059 0.6217 0.6360 0.6490 0.6723 0.6928 0.7111 0.7279 0.7434 0.7714 0.7966 0.8199 0.8417

1.5264 1.5105 1.4968 1.4847 1.4738 1.4639 1.4461 1.4304 1.4163 1.4032 1.3910 1.3683 1.3474 1.3274 1.3079

ft lbm Liquid 0.016020 0.016025 0.016040 0.016056 0.016085 0.016112 0.016136 0.016230 0.016300 0.016358 0.016451 0.016527 0.016592 0.016834 0.017009 0.017151 0.017274 0.017383 0.017482 0.017573 0.017659 0.01774 0.01809 0.01839 0.01865 0.01889 0.01912 0.01934 0.01954 0.01975 0.02013 0.02050 0.02087 0.02123 0.02159 0.02232 0.02307 0.02387 0.02472

Vapor 2,945.5 1,526.3 1,039.7 792.1 540.1 411.69 333.60 173.76 118.73 90.64 61.98 47.35 38.42 20.087 13.744 10.4965 8.5140 7.1736 6.2050 5.4711 4.8953 4.4310 3.0139 2.2873 1.84317 1.54274 1.32554 1.16095 1.03179 0.92762 0.76975 0.65556 0.56896 0.50091 0.44596 0.36245 0.30178 0.25545 0.21861 587

Chapter 9: Physical Properties Saturated Steam (U.S. Units )—Pressure Table (cont'd) Pressure Temperature psia 2000 2200 2400 2600 2800 3000 3100 3200 3208.2

9.8.2

cF 635.80 649.45 662.11 673.91 684.96 695.33 700.28 705.08 705.47

Specific Volume, v

Specific Enthalpy, h

Specific Entropy, s

Btu lbm

Btu lbm - cF

3

ft lbm Liquid

Vapor

0.02565 0.02669 0.02790 0.02938 0.03134 0.03428 0.03681 0.04472 0.05078

0.18831 0.16272 0.14076 0.1211 0.10305 0.08500 0.07452 0.05663 0.05078

Liquid

Vapor

Liquid

Vapor

672.1 695.5 719.0 744.5 770.7 801.8 824.0 875.5 906.0

1138.3 1122.2 1103.7 1082.0 1055.5 1020.3 993.3 931.6 906.0

0.8625 0.8828 0.9031 0.9247 0.9468 0.9728 0.9914 1.0351 1.0612

1.2881 1.2676 1.2460 1.2225 1.1958 1.1619 1.1373 1.0832 1.0612

Properties of Saturated Steam (SI Units) Saturated Steam (SI Units)—Temperature Table Temperature

cC 0.01 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 ©2020 NCEES

Pressure kPa 0.6113 0.8721 1.2276 1.7051 2.339 3.169 4.246 5.628 7.384 9.593 12.349 15.758 19.94 25.03 31.19 38.58 47.39 57.83 70.14 84.55 101.35 120.82

Specific Volume, v

Specific Enthalpy, h

Specific Entropy, s

kJ kg

kJ kg : K

3

m kg Liquid

Vapor

Liquid

Vapor

Liquid

Vapor

0.001000 0.001000 0.001000 0.001001 0.001002 0.001003 0.001004 0.001006 0.001008 0.001010 0.001012 0.001015 0.001017 0.001020 0.001023 0.001026 0.001029 0.001033 0.001036 0.001040 0.001044 0.001048

206.14 147.12 106.38 77.93 57.79 43.36 32.89 25.22 19.52 15.26 12.03 9.568 7.671 6.197 5.042 4.131 3.407 2.828 2.361 1.982 1.6729 1.4194

0.01 20.98 42.01 62.99 83.96 104.89 125.79 146.68 167.37 188.45 209.33 230.23 251.13 272.06 292.98 313.93 334.91 355.90 376.92 397.96 419.04 440.15

2501.4 2510.6 2519.8 2528.9 2538.1 2547.2 2556.3 2565.3 2574.3 2583.2 2592.1 2600.9 2609.6 2618.3 2626.8 2635.3 2643.7 2651.9 2660.1 2668.1 2676.1 2683.8

0 0.0761 0.151 0.2245 0.2966 0.3674 0.4369 0.5053 0.5725 0.6387 0.7038 0.7679 0.8312 0.8935 0.9549 1.0155 1.0753 1.1343 1.1925 1.2500 1.3069 1.3630

9.1562 9.0257 8.9008 8.7814 8.6672 8.5580 8.4533 8.3531 8.2570 8.1648 8.0763 7.9913 7.9096 7.8310 7.7553 7.6824 7.6122 7.5445 7.4791 7.4159 7.3549 7.2958

588

Chapter 9: Physical Properties Saturated Steam (SI Units)—Temperature Table (cont'd) Temperature

Pressure

cC 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 205 210 215 220 225 230 235 240 245 250 255 260 265 270 275 280 285 290 295 300

kPa

©2020 NCEES

143.27 169.06 198.53 232.1 270.1 313.0 361.3 415.4 475.8 543.1 617.8 700.5 791.7 892.0 1002.1 1122.7 1254.4 1397.8 1553.8 1723.0 1906.2 2104 2318 2518 2795 3060 3344 3618 3973 4319 4688 5081 5499 5942 6412 6909 7436 7993 8581

Specific Volume, v

Specific Enthalpy, h

Specific Entropy, s

kJ kg

kJ kg : K

3

m kg Liquid 0.001052 0.001056 0.001060 0.001065 0.001070 0.001075 0.001080 0.001085 0.001091 0.001096 0.001102 0.001108 0.001114 0.001121 0.001127 0.001134 0.001141 0.001149 0.001157 0.001164 0.001173 0.001181 0.001190 0.001199 0.001209 0.001219 0.001229 0.001240 0.001251 0.001263 0.001276 0.001289 0.001302 0.001317 0.001332 0.001348 0.001366 0.001384 0.001404

Vapor

Liquid

Vapor

Liquid

Vapor

1.2102 1.0366 0.8919 0.7706 0.6685 0.5822 0.5089 0.4463 0.3928 0.3468 0.3071 0.2727 0.2428 0.2168 0.194005 0.174009 0.156054 0.141005 0.127036 0.115021 0.104041 0.094079 0.086019 0.078049 0.071058 0.065037 0.059076 0.054071 0.050130 0.045098 0.042021 0.038077 0.035064 0.032079 0.030017 0.027077 0.025057 0.023054 0.021067

461.30 482.48 503.71 524.99 546.31 567.69 589.13 610.63 632.20 653.84 675.55 697.34 719.21 741.17 763.22 785.37 807.62 829.98 852.45 875.04 897.76 920.62 943.62 966.78 990.12 1013.62 1037.32 1061.23 1085.36 1109.73 1134.37 1159.28 1184.51 1210.07 1235.99 1262.31 1289.07 1316.3 1344.0

2691.5 2699.0 2706.3 2713.5 2720.5 2727.3 2733.9 2740.3 2746.5 2752.4 2758.1 2763.5 2768.7 2773.6 2778.2 2782.4 2786.4 2790.0 2793.2 2796.0 2798.5 2800.5 2802.1 2803.3 2804.0 2804.2 2803.8 2803.0 2801.5 2799.5 2796.9 2793.6 2789.7 2785.0 2779.6 2773.3 2766.2 2758.1 2749.0

1.4185 1.4734 1.5276 1.5813 1.6344 1.6870 1.7391 1.7907 1.8418 1.8925 1.9427 1.9925 2.0419 2.0909 2.1396 2.1879 2.2359 2.2835 2.3309 2.3780 2.4248 2.4714 2.5178 2.5639 2.6099 2.6558 2.7015 2.7472 2.7927 2.8383 2.8838 2.9294 2.9751 3.0208 3.0668 3.1130 3.1594 3.2062 3.2534

7.2387 7.1833 7.1296 7.0775 7.0269 6.9777 6.9299 6.8833 6.8379 6.7935 6.7502 6.7078 6.6663 6.6256 6.5857 6.5465 6.5079 6.4698 6.4323 6.3952 6.3585 6.3221 6.2861 6.2503 6.2146 6.1791 6.1437 6.1083 6.0730 6.0375 6.0019 5.9662 5.9301 5.8938 5.8571 5.8199 5.7821 5.7437 5.7045

589

Chapter 9: Physical Properties Saturated Steam (SI Units)—Temperature Table (cont'd) Temperature

cC 305 310 315 320 330 340 350 360 370 374.14

Pressure kPa 9202 9856 10,547 11,274 12,845 14,586 16,513 18,651 21,030 22,090

Specific Volume, v

Specific Enthalpy, h

Specific Entropy, s

kJ kg

kJ kg : K

3

m kg Liquid 0.001425 0.001447 0.001472 0.001499 0.001561 0.001638 0.001740 0.001893 0.002213 0.003155

Vapor

Liquid

Vapor

Liquid

Vapor

0.019948 0.018350 0.016867 0.015488 0.012996 0.010797 0.008813 0.006945 0.004925 0.003155

1372.4 1401.3 1431.0 1461.5 1525.3 1594.2 1670.6 1760.5 1890.5 2099.3

2738.7 2727.3 2714.5 2700.1 2665.9 2622.0 2563.9 2481.0 2332.1 2099.3

3.3010 3.3493 3.3982 3.4480 3.5507 3.6594 3.7777 3.9147 4.1106 4.4298

5.6643 5.6230 5.5804 5.5362 5.4417 5.3357 5.2112 5.0526 4.7971 4.4298

Saturated Steam (SI Units)—Pressure Table Pressure

Temperature

kPa

cC 0.01 6.98 13.03 17.50 21.08 24.08 28.96 32.88 40.29 45.81 53.97 60.05 64.97 69.10 75.87 81.33 91.78 99.63 105.99 111.37 116.06 120.23

0.6113 1 1.5 2 2.5 3 4 5 7.5 10 15 20 25 30 40 50 75 100 125 150 175 200 ©2020 NCEES

Specific Volume, v

Specific Enthalpy, h

Specific Entropy, s

kJ kg

kJ kg : K

3

m kg Liquid 0.001000 0.001000 0.001001 0.001001 0.001002 0.001003 0.001004 0.001005 0.001008 0.001010 0.001014 0.001017 0.001020 0.001022 0.001027 0.001030 0.001037 0.001043 0.001048 0.001053 0.001057 0.001061

Vapor 206.14 129.21 87.98 67 54.25 45.67 34.8 28.19 19.24 14.67 10.02 7.649 6.204 5.229 3.993 3.24 2.217 1.694 1.3749 1.1593 1.0036 0.8857 590

Liquid 1 29.3 54.71 73.48 88.49 101.05 121.46 137.82 168.79 191.83 225.94 251.4 271.93 289.23 317.58 340.49 384.39 417.46 444.32 467.11 486.99 504.7

Vapor

Liquid

Vapor

2501.4 2514.2 2525.3 2533.5 2540.0 2545.5 2554.4 2561.5 2574.8 2584.7 2599.1 2609.7 2618.2 2625.3 2636.8 2645.9 2663.0 2675.5 2685.4 2693.6 2700.6 2706.7

0 0.1059 0.1957 0.2607 0.3120 0.3545 0.4226 0.4764 0.5764 0.6493 0.7549 0.8320 0.8931 0.9439 1.0259 1.0910 1.2130 1.3026 1.3740 1.4336 1.4849 1.5301

9.1562 8.9756 8.8279 8.7237 8.6432 8.5776 8.4746 8.3951 8.2515 8.1502 8.0085 7.9085 7.8314 7.7686 7.6700 7.5939 7.4564 7.3594 7.2844 7.2233 7.1717 7.1271

Chapter 9: Physical Properties Saturated Steam (SI Units)—Pressure Table (cont'd) Pressure

Temperature

kPa

cC 124.00 127.44 130.60 133.55 136.30 138.88 141.32 143.63 147.93 151.86 155.48 164.97 167.78 170.43 172.96 175.38 177.69 179.91 184.09 187.99 191.64 195.07 198.32 205.76 212.42 218.45 223.99 233.90 242.60 250.40 263.99 275.64 285.88 295.06 303.40 311.06 318.15 324.75 330.93

225 250 275 300 325 350 375 400 450 500 550 700 750 800 850 900 950 1000 1100 1200 1300 1400 1500 1750 2000 2250 2500 3000 3500 4000 5000 6000 7000 8000 9000 10,000 11,000 12,000 13,000 ©2020 NCEES

Specific Volume, v

Specific Enthalpy, h

Specific Entropy, s

kJ kg

kJ kg : K

3

m kg Liquid

Vapor

0.001064 0.001067 0.001070 0.001073 0.001076 0.001079 0.001081 0.001084 0.001088 0.001093 0.001097 0.001108

0.7933 0.7187 0.6573 0.6058 0.5620 0.5243 0.4914 0.4625 0.4140 0.3749 0.3427 0.2729

0.001112 0.001115 0.001118 0.001121 0.001124 0.001127 0.001133 0.001139 0.001144 0.001149 0.001154 0.001166 0.001177 0.001187 0.001197 0.001217 0.001235 0.001252 0.001286 0.001319 0.001351 0.001384 0.001418 0.001452 0.001489 0.001527 0.001567

0.2556 0.2404 0.2270 0.2150 0.2042 0.194044 0.177053 0.163033 0.151025 0.140084 0.131077 0.113049 0.099063 0.088075 0.079098 0.066068 0.057007 0.049078 0.039044 0.032044 0.027037 0.023052 0.020048 0.018026 0.015987 0.014263 0.01278 591

Liquid

Vapor

Liquid

Vapor

520.72 535.37 548.89 561.47 573.25 584.33 594.81 604.74 623.25 640.23 655.93 697.22

2712.1 2716.9 2721.3 2725.3 2729.0 2732.4 2735.6 2738.6 2743.9 2748.7 2753.0 2763.5

1.5706 1.6072 1.6408 1.6718 1.7006 1.7275 1.7528 1.7766 1.8207 1.8607 1.8973 1.9922

7.0878 7.0527 7.0209 6.9919 6.9652 6.9405 6.9175 6.8959 6.8565 6.8213 6.7893 6.7080

709.47 721.11 732.22 742.83 753.02 762.81 781.34 798.65 814.93 830.30 844.89 878.50 908.79 936.49 962.11 1008.42 1049.75 1087.31 1154.23 1213.35 1267.00 1316.64 1363.26 1407.56 1450.1 1491.3 1531.5

2766.4 2769.1 2771.6 2773.9 2776.1 2778.1 2781.7 2784.8 2787.6 2790.0 2792.2 2796.4 2799.5 2801.7 2803.1 2804.2 2804.2 2801.4 2794.3 2784.3 2772.1 2758.0 2742.1 2724.7 2705.6 2684.9 2662.2

2.0200 2.0462 2.0710 2.0946 2.1172 2.1387 2.1792 2.2166 2.2515 2.2842 2.3150 2.3851 2.4474 2.5035 2.5547 2.6457 2.7253 2.7964 3.9202 3.0267 3.1211 3.2068 3.2858 3.3596 3.4295 3.4962 3.5606

6.6847 6.6628 6.6421 6.6226 6.6041 6.5865 6.5536 6.5233 6.4953 6.4693 6.4448 6.3896 6.3409 6.2972 6.2575 6.1869 6.1253 6.0701 5.9734 5.8892 5.8133 5.7432 5.6772 5.6141 5.5527 5.4924 5.4323

Chapter 9: Physical Properties Saturated Steam (SI Units)—Pressure Table (cont'd) Pressure

Temperature

kPa 15,000 16,000 17,000 18,000 19,000 20,000 21,000 22,000

cC 336.75 342.24 347.44 352.37 357.06 361.54 365.81 369.89 373.80

22,090

374.14

14,000

©2020 NCEES

Specific Volume, v

Specific Enthalpy, h

Specific Entropy, s

kJ kg

kJ kg : K

3

m kg Liquid

Vapor

Liquid

Vapor

Liquid

Vapor

0.001611

0.011485

1571.1

2637.6

3.6232

5.3717

0.001658 0.001711 0.001770 0.001840 0.001924 0.002036 0.002207 0.002742

0.010337 0.009306 0.008364 0.007489 0.006657 0.005834 0.004952 0.003568

1610.5 1650.1 1690.3 1732.0 1776.5 1826.3 1888.4 2022.2

2610.5 2580.6 2547.2 2509.1 2464.5 2409.7 2334.6 2165.6

3.6848 3.7461 3.8079 3.8715 3.9388 4.0139 4.1075 4.3110

5.3098 5.2455 5.1777 5.1044 5.0228 4.9269 4.8013 5.5327

0.003155

0.003155

2099.3

2099.3

4.4298

4.4298

592

©2020 NCEES

9.8.3

Superheated Steam (U.S. Customary Units) 3 Btu Btu Superheated Steam (U.S. Units) v = d ft n h = c lbm m s = c lbm - cF m lbm

300 452.3 1195.8 2.1153 90.25 1195.0 1.9370 45.00 1193.9 1.8595

400 512.0 1241.7 2.1720 102.26 1241.2 1.9942 51.04 1240.6 1.9172

500 571.6 1288.3 2.2233 114.22 1288.0 2.0456 57.05 1287.5 1.9689

600 631.2 1335.7 2.2702 126.16 1335.4 2.0927 63.03 1335.1 2.0160

1 (101.74) 5 (162.24) 10 (193.21) 14.696 (212)

v h s v h s v h s v h s v h s v h s

                                   

30.53 1192.8 1.8160 22.36 1191.6 1.7808 11.04 1186.8 1.6994 7.259 1181.6 1.6492            

34.68 1239.9 1.8743 25.43 1239.2 1.8396 12.628 1236.5 1.7608 8.357 1233.6 1.7135 6.220 1230.7 1.6791 4.937 1227.6 1.6518

38.78 1287.1 1.9261 28.46 1286.6 1.8918 14.168 1284.8 1.8140 9.403 1283.0 1.7678 7.020 1281.1 1.7346 5.589 1279.1 1.7085

42.86 1334.8 1.9734 31.47 1334.4 1.9392 15.688 1333.1 1.8619 10.427 1331.8 1.8162 7.797 1330.5 1.7836 6.218 1329.1 1.7581

46.94 1383.2 2.0170 34.47 1382.9 1.9829 17.198 1381.9 1.9058 11.441 1380.9 1.8605 8.562 1379.9 1.8281 6.835 1378.9 1.8029

593 20 (227.96) 40 (267.25) 60 (292.71) 80 (312.03) 100 (327.81)

v h s v h s v h

51.00 1432.3 2.0576 37.46 1432.1 2.0235 18.702 1431.3 1.9467 12.449 1430.5 1.9015 9.322 1429.7 1.8694 7.446 1428.9 1.8443

900 809.9 1482.7 2.3923 161.95 1482.6 2.2148 80.95 1482.4 2.1383

1000 869.5 1533.5 2.4283 173.87 1533.4 2.2509 86.92 1533.2 2.1744

1200 988.7 1637.7 2.4952 197.71 1637.7 2.3178 98.84 1637.6 2.2413

1400 1107.8 1745.7 2.5566 221.60 1745.7 2.3792 110.77 1745.6 2.3028

1600 1227.0 1857.5 2.6137 245.40 1857.4 2.4363 122.69 1857.3 2.3598

55.07 1482.3 2.0958 40.45 1482.1 2.0618 20.20 1481.4 1.9850 13.452 1480.8 1.9400 10.077 1480.1 1.9079 8.052 1479.5 1.8829

59.13 1533.1 2.1319 43.44 1533.0 2.0978 21.70 1532.4 2.0212 14.454 1531.9 1.9762 10.830 1531.3 1.9442 8.656 1530.8 1.9193

67.25 1637.5 2.1989 49.41 1637.4 2.1648 24.69 1637.0 2.0883 16.451 1636.6 2.0434 12.332 1636.2 2.0115 9.860 1635.7 1.9867

75.37 1745.5 2.2603 55.37 1745.4 2.2263 27.68 1745.1 2.1498 18.446 1744.8 2.1049 13.830 1744.5 2.0731 11.060 1744.2 2.0484

83.48 1857.3 2.3174 61.34 1857.2 2.2834 30.66 1857.0 2.2069 20.440 1856.7 2.1621 15.325 1856.5 2.1303 12.258 1856.2 2.1056

Chapter 9: Physical Properties

s

200 392.6 1150.4 2.0512 78.16 1148.8 1.8718 38.85 1146.6 1.7927

Temperature (°F) 700 800 690.8 750.4 1383.8 1432.8 2.3137 2.3542 138.10 150.03 1383.6 1432.7 2.1361 2.1767 69.01 74.98 1383.4 1432.5 2.0596 2.1002

Pressure (psia) Saturated Temp. (°F)

©2020 NCEES

3 Btu Btu Superheated Steam (U.S. Units) (cont'd) v = d ft n h = c lbm m s = c lbm - cF m lbm

300              

400 4.081 1224.4 1.6287 3.468 1221.1 1.6087 3.008

500 4.636 1277.2 1.6869 3.954 1275.2 1.6683 3.443

600 5.165 1327.7 1.7370 4.413 1326.4 1.7190 3.849

120 (341.25) 140 (353.02) 160 (363.53)

h s v h s v h s v h s v h s v

                             

                             

1217.6 1.5908 2.649 1214.0 1.5745 2.361 1210.3 1.5594 2.125 1206.5 1.5453 1.9276 1202.5 1.5319  

1273.1 1.6519 3.044 1271.0 1.6373 2.726 1268.9 1.6240 2.465 1266.7 1.6117 2.247 1264.5 1.6003 2.063

1325.0 1.7033 3.411 1323.5 1.6894 3.060 1322.1 1.6767 2.772 1320.7 1.6652 2.533 1319.2 1.6546 2.330

1375.7 1.7491 3.764 1374.7 1.7355 3.380 1373.6 1.7232 3.066 1372.6 1.7120 2.804 1371.5 1.7017 2.582

1426.4 1.7911 4.110 1425.6 1.7776 3.693 1424.8 1.7655 3.352 1424.0 1.7545 3.068 1423.2 1.7444 2.827

1477.5 1.8301 4.452 1476.8 1.8167 4.002 1476.2 1.8048 3.634 1475.5 1.7939 3.327 1474.8 1.7839 3.067

1529.1 1.8667 4.792 1528.6 1.8534 4.309 1528.0 1.8415 3.913 1527.5 1.8308 3.584 1526.9 1.8209 3.305

1634.5 1.9344 5.466 1634.1 1.9212 4.917 1633.7 1.9094 4.467 1633.3 1.8987 4.093 1632.9 1.8889 3.776

1743.2 1.9962 6.136 1742.9 1.9831 5.521 1742.6 1.9713 5.017 1742.3 1.9607 4.597 1742.0 1.9510 4.242

1855.5 2.0535 6.804 1855.2 2.0404 6.123 1855.0 2.0287 5.565 1854.7 2.0181 5.100 1854.5 2.0084 4.707

180 (373.06) 594

200 (381.79) 220 (389.86) 240 (397.37) 260 (404.42)

h s v h s

         

         

         

1262.3 1.5897 1.9047 1260.0 1.5796

1317.7 1.6447 2.156 1316.2 1.6354

1370.4 1.6922 2.392 1369.4 1.6834

1422.3 1.7352 2.621 1421.5 1.7265

1474.2 1.7748 2.845 1473.5 1.7662

1526.3 1.8118 3.066 1525.8 1.8033

1632.5 1.8799 3.504 1632.1 1.8716

1741.7 1.9420 3.938 1741.4 1.9337

1854.2 1.9995 4.37 1854.0 1.9912

280 (411.05)

900 6.702 1478.8 1.8625 5.738 1478.2 1.8451 5.015

1000 7.207 1530.2 1.8990 6.172 1529.7 1.8817 5.396

1200 8.212 1635.3 1.9664 7.035 1634.9 1.9493 6.152

1400 9.214 1743.9 2.0281 7.895 1743.5 2.0110 6.906

1600 10.213 1856.0 2.0854 8.752 1855.7 2.0683 7.656

Chapter 9: Physical Properties

v h s v h s v

200              

Temperature (°F) 700 800 5.683 6.195 1377.8 1428.1 1.7822 1.8237 4.861 5.301 1376.8 1427.3 1.7645 1.8063 4.244 4.631

Pressure (psia) Saturated Temp. (°F)

©2020 NCEES

3 Btu Btu Superheated Steam (U.S. Units) (cont'd) v = d ft n h = c lbm m s = c lbm - cF m lbm

Pressure (psia) Saturated Temp. (°F) 300 (417.33) 350 (431.72)

450 (456.28) 595

500 (467.01) 550 (476.94) 600 (486.21) 700 (503.1) 800 (518.23) 900 (531.98)

200                                                            

300                                                            

400                                                            

500 1.7675 1257.6 1.5701 1.4923 1251.5 1.5481 1.2851 1245.1 1.5281 1.1231 1238.4 1.5095 0.9927 1231.3 1.4919 0.8852 1223.7 1.4751 0.7947 1215.7 1.4586                  

600 2.005 1314.7 1.6268 1.7036 1310.9 1.6070 1.477 1306.9 1.5894 1.3005 1302.8 1.5735 1.1591 1298.6 1.5588 1.0431 1294.3 1.5451 0.9463 1289.9 1.5323 0.7934 1280.6 1.5084 0.6779 1270.7 1.4863 0.5873 1260.1 1.4653

900 2.652 1472.8 1.7582 2.266 1471.1 1.7403 1.9767 1469.4 1.7247 1.7516 1467.7 1.7108 1.5715 1466.0 1.6982 1.4241 1464.3 1.6868 1.3013 1462.5 1.6762 1.1082 1459.0 1.6573 0.9633 1455.4 1.6407 0.8506 1451.8 1.6257

1000 2.859 1525.2 1.7954 2.445 1523.8 1.7777 2.134 1522.4 1.7623 1.8928 1521.0 1.7486 1.6996 1519.6 1.7363 1.5414 1518.2 1.7250 1.4096 1516.7 1.7147 1.2024 1513.9 1.6963 1.0470 1511.0 1.6801 0.9262 1508.1 1.6656

1200 3.269 1631.7 1.8638 2.798 1630.7 1.8463 2.445 1629.6 1.8311 2.1700 1628.6 1.8177 1.9504 1627.6 1.8056 1.7706 1626.6 1.7946 1.6208 1625.5 1.7846 1.3853 1623.5 1.7666 1.2088 1621.4 1.7510 1.0714 1619.3 1.7371

1400 3.674 1741.0 1.9260 3.147 1740.3 1.9086 2.751 1739.5 1.8936 2.4430 1738.7 1.8803 2.1970 1737.9 1.8683 1.9957 1737.1 1.8575 1.8279 1736.3 1.8476 1.5641 1734.8 1.8299 1.3662 1733.2 1.8146 1.2124 1731.6 1.8009

1600 4.078 1853.7 1.9835 3.493 1853.1 1.9663 3.055 1852.5 1.9513 2.7140 1851.9 1.9381 2.4420 1851.3 1.9262 2.2190 1850.6 1.9155 2.0330 1850.0 1.9056 1.7405 1848.8 1.8881 1.5214 1847.5 1.8729 1.3509 1846.3 1.8595

Chapter 9: Physical Properties

400 (444.59)

v h s v h s v h s v h s v h s v h s v h s v h s v h s v h s

Temperature (°F) 700 800 2.227 2.442 1368.3 1420.6 1.6751 1.7184 1.898 2.084 1365.5 1418.5 1.6563 1.7002 1.6508 1.8161 1362.7 1416.4 1.6398 1.6842 1.4584 1.6074 1359.9 1414.3 1.6250 1.6699 1.3044 1.4405 1357.0 1412.1 1.6115 1.6571 1.1783 1.3038 1354.0 1409.9 1.5991 1.6452 1.0732 1.1899 1351.1 1407.7 1.5875 1.6343 0.9077 1.0108 1345.0 1403.2 1.5665 1.6147 0.7833 0.8763 1338.6 1398.6 1.5476 1.5972 0.6863 0.7716 1332.1 1393.9 1.5303 1.5814

©2020 NCEES

3 Btu Btu Superheated Steam (U.S. Units) (cont'd) v = d ft n h = c lbm m s = c lbm - cF m lbm

1000 (544.61) 1100 (556.31)

200      

300      

400      

500      

600 0.5140 1248.8 1.4450

v h s v h s v h s v h s v h s v h s v h s v h s

                                               

                                               

                                               

                                               

0.4532 1236.7 1.4251 0.4016 1223.5 1.4052 0.3174 1193.0 1.3639                              

0.5445 1318.3 1.4989 0.4909 1311.0 1.4843 0.4062 1295.5 1.4567 0.3417 1278.7 1.4303 0.2907 1260.3 1.4044 0.2489 1240.0 1.3783 0.1686 1176.8 1.3073 0.0984 1060.7 1.1966

1400 (587.1) 1600 (604.9) 1800 (621.03) 2000 (635.82) 2500 (668.13) 3000 (695.36)

0.6191 1384.3 1.5535 0.5617 1379.3 1.5409 0.4714 1369.1 1.5177 0.4034 1358.4 1.4964 0.3502 1347.2 1.4765 0.3074 1335.5 1.4576 0.2294 1303.6 1.4127 0.1760 1267.2 1.3690

900 0.7604 1448.2 1.6121

1000 0.8294 1505.1 1.6525

1200 0.9615 1617.3 1.7245

1400 1.0893 1730.0 1.7886

1600 1.2146 1845.0 1.8474

0.6866 1444.5 1.5995 0.6250 1440.7 1.5879 0.5281 1433.1 1.5666 0.4553 1425.3 1.5476 0.3986 1417.4 1.5301 0.3532 1409.2 1.5139 0.2710 1387.8 1.4772 0.2159 1365.0 1.4439

0.7503 1502.2 1.6405 0.6843 1499.2 1.6293 0.5805 1493.2 1.6093 0.5027 1487.0 1.5914 0.4421 1480.8 1.5752 0.3935 1474.5 1.5603 0.3061 1458.4 1.5273 0.2476 1441.8 1.4984

0.8716 1615.2 1.7130 0.7967 1613.1 1.7025 0.6789 1608.9 1.6836 0.5906 1604.6 1.6669 0.5218 1600.4 1.6520 0.4668 1596.1 1.6384 0.3678 1585.3 1.6088 0.3018 1574.3 1.5837

0.9885 1728.4 1.7775 0.9046 1726.9 1.7672 0.7727 1723.7 1.7489 0.6738 1720.5 1.7328 0.5968 1717.3 1.7185 0.5352 1714.1 1.7055 0.4244 1706.1 1.6775 0.3505 1698.0 1.6540

1.1031 1843.8 1.8363 1.0101 1842.5 1.8263 0.8640 1840.0 1.8083 0.7545 1837.5 1.7926 0.6693 1835.0 1.7786 0.6011 1832.5 1.7660 0.4784 1826.2 1.7389 0.3966 1819.9 1.7163

Chapter 9: Physical Properties

1200 (567.22)

596

v h s

Temperature (°F) 700 800 0.6084 0.6878 1325.3 1389.2 1.5141 1.5670

Pressure (psia) Saturated Temp. (°F)

©2020 NCEES

3 Btu Btu Superheated Steam (U.S. Units) (cont'd) v = d ft n h = c lbm m s = c lbm - cF m lbm

Pressure (psia) Saturated Temp. (°F) 3206.2 (705.4)

3500

597

4500

5000

5500

200                                    

300                                    

400                                    

500                                    

600                                    

900 0.1981 1355.2 1.4309 0.1762 1340.7 1.4127 0.1462 1314.4 1.3827 0.1226 1286.5 1.3529 0.1036 1256.5 1.3231 0.0880 1224.1 1.2930

1000 0.2288 1434.7 1.4874 0.2058 1424.5 1.4723 0.1743 1406.8 1.4482 0.1500 1388.4 1.4253 0.1303 1369.5 1.4034 0.1143 1349.3 1.3821

1200 0.2806 1569.8 1.5742 0.2546 1563.3 1.5615 0.2192 1552.1 1.5417 0.1917 1540.8 1.5235 0.1696 1529.5 1.5066 0.1516 1518.2 1.4908

1400 0.3267 1694.6 1.6452 0.2977 1689.8 1.6336 0.2581 1681.7 1.6154 0.2273 1673.5 1.5990 0.2027 1665.3 1.5839 0.1825 1657.0 1.5699

1600 0.3703 1817.2 1.7080 0.3381 1813.6 1.6968 0.2943 1807.2 1.6795 0.2602 1800.9 1.6640 0.2329 1794.5 1.6499 0.2106 1788.1 1.6369

Chapter 9: Physical Properties

4000

v h s v h s v h s v h s v h s v h s

Temperature (°F) 700 800   0.1583   1250.5   1.3508 0.0306 0.1364 780.5 1224.9 0.9515 1.3241 0.0287 0.1052 763.8 1174.8 0.9347 1.2757 0.0276 0.0798 753.5 1113.9 0.9235 1.2204 0.0268 0.0593 746.4 1047.1 0.9152 1.1622 0.0262 0.0463 741.3 985.0 0.9090 1.1093

©2020 NCEES

9.8.4

Superheated Steam (SI Units) m3 o h d kJ n s = d kJ n = Superheated Steam (SI Units) v e= kg kg : K kg

Pressure (MPa) Saturated Temp. (°C) v h s

0.05 (81.33)

v h s v h s v h s v h s v h s v h s v h s v h s

                                               

0.1 (99.63) 0.2 (120.23) 598

0.3 (133.55) 0.4 (143.63) 0.5 (151.86) 0.6 (158.85) 0.8 (170.43)

100 17.1960 2687.5 8.4479

150 19.5120 2783.0 8.6882

200 21.8250 2879.5 8.9038

250 24.1360 2977.3 9.1002

Temperature (°C) 300 400 500 26.4450 31.0630 35.6790 3076.5 3279.6 3489.1 9.2813 9.6077 9.8978

600 40.2950 3705.4 10.1608

700 44.9110 3928.7 10.4028

800 49.5260 4159.0 10.6281

900 54.1410 4396.4 10.8396

3.41800 2682.5 7.6958 1.69580 2676.2 7.3614                                    

3.88900 2780.1 7.9401 1.93640 2776.4 7.6134 0.95960 2768.8 7.2795 0.63390 2761.0 7.0778 0.47080 2752.8 6.9299                  

4.35600 2877.7 8.1580 2.17200 2875.3 7.8343 1.08030 2870.5 7.5066 0.71630 2865.6 7.3115 0.53420 2860.5 7.1706 0.42490 2855.4 7.0592 0.35200 2850.1 6.9665 0.26080 2839.3 6.8158

4.82000 2976.0 8.3556 2.40600 2974.3 8.0333 1.19880 2971.0 7.7086 0.79640 2967.6 7.5166 0.59510 2964.2 7.3789 0.47440 2960.7 7.2709 0.39380 2957.2 7.1816 0.29310 2950.0 7.0384

5.28400 3075.5 8.5373 2.63900 3074.3 8.2158 1.31620 3071.8 7.8926 0.87530 3069.3 7.7022 0.65480 3066.8 7.5662 0.52260 3064.2 7.4599 0.43440 3061.6 7.3724 0.32410 3056.5 7.2328

8.05700 3705.1 9.4178 4.02800 3704.7 9.0976 2.01300 3704.0 8.7770 1.34140 3703.2 8.5892 1.00550 3702.4 8.4558 0.80410 3701.7 7.3522 0.66970 3700.9 8.2674 0.50180 3699.4 8.1333

8.98100 3928.5 9.6599 4.49000 3928.2 9.3398 2.24400 3927.6 9.0194 1.49570 3927.1 8.8319 1.12150 3926.5 8.6987 0.89690 3925.9 8.5952 0.74720 3925.3 8.5107 0.56010 3924.2 8.3770

9.90400 4158.9 9.8852 4.95200 4158.6 9.5652 2.47500 4158.2 9.2449 1.64990 4157.8 9.0576 1.23720 4157.3 8.9244 0.98960 4156.9 8.8211 0.82450 4156.5 8.7367 0.61810 4155.6 8.6033

10.8280 4396.3 10.0967 5.41400 4396.1 9.7767 2.70600 4395.8 9.4566 1.80410 4395.4 9.2692 1.35290 4395.1 9.1362 1.08220 4394.7 9.0329 0.90170 4394.4 8.9486 0.67610 4393.7 8.8153

6.20900 3278.9 8.8642 3.10300 3278.2 8.5435 1.54930 3276.6 8.2218 1.03150 3275.0 8.0330 0.77260 3273.4 7.8985 0.61730 3271.9 7.7938 0.51370 3270.3 7.7079 0.38430 3267.1 7.5716

7.13400 3488.7 9.1546 3.56500 3488.1 8.8342 1.78140 3487.1 8.5133 1.18670 3486.0 8.3251 0.88930 3484.9 8.1913 0.71090 3483.9 8.0873 0.59200 3482.8 8.0021 0.44330 3480.6 7.8673

Chapter 9: Physical Properties

0.01 (45.81)

50 14.8690 2592.6 8.1749

©2020 NCEES

m3 o h d kJ n s = d kJ n = Superheated Steam (SI Units) (cont'd) v e= kg kg : K kg Pressure (MPa) Saturated Temp. (°C) 1.0 (179.91) 1.2 (187.99) 1.4 (195.07)

599

1.8 (207.15) 2.0 (212.42) 2.5 (223.99°C) 3.0 (233.90) 3.5 (242.60) 4.0 (250.40)

50

100

150

200

250

300

400

500

600

700

800

900

v h s v h s v h s v h s v h s v h s v h s v

                                           

                                           

                                           

0.20600 2827.9 6.6940 0.16930 2815.9 6.5898 0.14302 2803.3 6.4975                          

0.23270 2942.6 6.9247 0.19234 2935.0 6.8294 0.16350 2927.2 6.7467 0.14184 2919.2 6.6732 0.12497 2911.0 6.6066 0.11144 2902.5 6.5453 0.08700 2880.1 6.4085 0.07058

0.25790 3051.2 7.1229 0.21380 3045.8 7.0317 0.18228 3040.4 6.9534 0.15862 3034.8 6.8844 0.14021 3029.2 6.8226 0.12547 3023.5 6.7664 0.09890 3008.8 6.6438 0.08114

0.30660 3263.9 7.4651 0.25480 3260.7 7.3774 0.21780 3257.5 7.3026 0.19005 3254.2 7.2374 0.16847 3250.9 7.1794 0.15120 3247.6 7.1271 0.12010 3239.3 7.0148 0.09936

0.35410 3478.5 7.7622 0.29460 3476.3 7.6959 0.25210 3474.1 7.6027 0.22030 3472.0 7.5390 0.19550 3469.8 7.4825 0.17568 3467.6 7.4317 0.13998 3462.1 7.3234 0.11619

0.40110 3697.9 8.0290 0.33390 3696.3 7.9435 0.28600 3694.8 7.8710 0.25000 3693.2 7.8080 0.22200 3691.7 7.7523 0.19960 3690.1 7.7024 0.15930 3686.3 7.5960 0.13243

0.44780 3923.1 8.2731 0.37290 3922.0 8.1881 0.31950 3920.8 8.1160 0.27940 3919.7 8.0535 0.24820 3918.5 7.9983 0.22320 3917.4 7.9487 0.17832 3914.5 7.8435 0.14838

0.49430 4154.7 8.4996 0.41180 4153.8 8.4148 0.35280 4153.0 8.3431 0.30860 4152.1 8.2808 0.27420 4151.2 8.2258 0.24670 4150.3 8.1765 0.19716 4148.2 8.0720 0.16414

0.54070 4392.9 8.7118 0.45050 4392.2 8.6272 0.38610 4391.5 8.5556 0.33770 4390.8 8.4935 0.30010 4390.1 8.4386 0.27000 4389.4 8.3895 0.21590 4387.6 8.2853 0.17980

h s v h s v h s

               

               

               

               

2855.8 6.2872 0.05872 2829.2 6.1749      

2993.5 6.5390 0.06842 2977.5 6.4461 0.05884 2960.7 6.3615

3230.9 6.9212 0.08453 3222.3 6.8405 0.07341 3213.6 6.7690

3456.5 7.2338 0.09918 3450.9 7.1572 0.08643 3445.3 7.0901

3682.3 7.5085 0.11324 3678.4 7.4339 0.09885 3674.4 7.3688

3911.7 7.7511 0.12699 3908.8 7.6837 0.11095 3905.9 7.6198

4145.9 7.9862 0.14056 4143.7 7.9134 0.12287 4141.5 7.8502

4385.9 8.1999 0.15402 4384.1 8.1276 0.13469 4382.3 8.0647

Chapter 9: Physical Properties

1.6 (201.41)

Temperature (°C)

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m3 o h d kJ n s = d kJ n = Superheated Steam (SI Units) (cont'd) v e= kg kg : K kg Pressure (MPa) Saturated Temp. (°C) 4.5 (257.49) 5.0 (263.99 6.0 (275.64)

600

8.0 (295.06) 9.0 (303.40) 10.0 (311.06) 12.5 (327.89) 15.0 (342.24)

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250

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400

500

600

700

800

900

                                                     

                                                     

                                                     

                                                     

                                                     

0.05135 2943.1 6.2828 0.04532 2924.5 6.2084 0.03616 2884.2 6.0674 0.02947 2838.4 5.9305 0.02426 2785.0 5.7906                        

0.06475 3204.7 6.7047 0.05781 3195.7 6.6459 0.04739 3177.2 6.5408 0.03993 3158.1 6.4478 0.03432 3138.3 6.3634 0.02993 3117.8 6.2854 0.02641 3096.5 6.2120 0.02000 3039.3 6.0417 0.01565 2975.5 5.8811

0.07651 3439.6 7.0301 0.06857 3433.8 6.9759 0.05665 3422.2 6.8803 0.04814 3410.3 6.7975 0.04175 3398.3 6.7240 0.03677 3386.1 6.6576 0.03279 3373.7 6.5966 0.02560 3341.8 6.4618 0.02080 3308.6 6.3443

0.08765 3670.5 7.3110 0.07869 3665.5 7.2589 0.06525 3658.4 7.1677 0.05565 3650.3 7.0894 0.04845 3642.0 7.0206 0.04285 3633.7 6.9589 0.03837 3625.3 6.9029 0.03029 3604.0 6.7810 0.02491 3582.3 6.6776

0.09847 3903.0 7.5631 0.08849 3900.1 7.5122 0.07352 3894.2 7.4234 0.06283 3888.3 7.3476 0.05481 3882.4 7.2812 0.04857 3876.5 7.2221 0.04358 3870.5 7.1687 0.03460 3855.3 7.0536 0.02861 3840.1 6.9572

0.10911 4139.3 7.7942 0.09811 4137.1 7.7440 0.08160 4132.7 7.6566 0.06981 4128.2 7.5822 0.06097 4123.8 7.5173 0.05409 4119.3 7.4596 0.04859 4114.8 7.4077 0.03869 4103.6 7.2965 0.03210 4092.4 7.2040

0.11965 4380.6 8.0091 0.10762 4378.8 7.9593 0.08958 4375.3 7.8727 0.07669 4371.8 7.7991 0.06702 4368.3 7.7351 0.05950 4364.8 7.6783 0.05349 4361.2 7.6272 0.04267 4352.5 7.5182 0.03546 4343.8 7.4279

Chapter 9: Physical Properties

7.0 (285.88)

v h s v h s v h s v h s v h s v h s v h s v h s v h s

Temperature (°C)

©2020 NCEES

m3 o h d kJ n s = d kJ n = Superheated Steam (SI Units) (cont'd) v e= kg kg : K kg Pressure (MPa) Saturated Temp. (°C) 17.5 (354.75) 20.0 (365.81) 25.0

601

35.0

40.0

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100

150

200

250

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500

600

700

800

900

                                   

                                   

                                   

                                   

                                   

                                   

0.01245 2902.9 5.7213 0.00994 2818.1 5.5540 0.00604 2580.2 5.1418 0.00279 2151.1 4.4728 0.00210 1987.6 4.2126 0.00191 1930.9 4.1135

0.01736 3274.1 6.2383 0.01477 3238.2 6.1401 0.01112 3162.4 5.9592 0.00868 3081.1 5.7905 0.00693 2994.4 5.6282 0.00562 2903.3 5.4700

0.02106 3560.1 6.5866 0.01818 3537.6 6.5048 0.01414 3491.4 6.3602 0.01145 3443.9 6.2331 0.00953 3395.5 6.1179 0.00894 3346.4 6.0114

0.02434 3824.6 6.8736 0.02113 3809.0 6.7993 0.01665 3777.5 6.6707 0.01366 3745.6 6.5605 0.01153 3713.5 6.4631 0.00994 3681.2 6.3750

0.02738 4081.1 7.1244 0.02385 4069.7 7.0544 0.01891 4047.1 6.9345 0.01562 4024.2 6.8332 0.01328 4001.5 6.7450 0.01152 3978.7 6.6662

0.03031 4335.1 7.3507 0.02645 4326.4 7.2830 0.02145 4309.1 7.1680 0.01745 4291.9 7.0718 0.01488 4274.9 6.9886 0.01296 4257.9 6.9150

Chapter 9: Physical Properties

30.0

v h s v h s v h s v h s v h s v h s

Temperature (°C)

Chapter 9: Physical Properties

9.9 Diagrams for Water and Steam Pressure-Enthalpy (p-H) Diagram (U.S. Customary Units)

Source: ASME Steam Tables, 4th ed., New York: American Society of Mechanical Engineers, 1979.

©2020 NCEES

602

Chapter 9: Physical Properties Temperature-Entropy (T-S) Diagram (U.S. Customary Units)

Source: ASME Steam Tables, 4th ed., New York: American Society of Mechanical Engineers, 1979.

©2020 NCEES

603

Chapter 9: Physical Properties Pressure-Enthalpy (p-H) Diagram (SI Units) ,

,

,

,

,

,

,

,

,

,

Source: ASME Steam Tables, 4th ed., New York: American Society of Mechanical Engineers, 1979.

©2020 NCEES

604

Chapter 9: Physical Properties Temperature-Entropy (T-S) Diagram (SI Units)

Source: ASME Steam Tables, 4th ed., New York: American Society of Mechanical Engineers, 1979.

©2020 NCEES

605

Chapter 9: Physical Properties Mollier (h, s) Diagram for Steam (English Units)

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606

Chapter 9: Physical Properties Mollier (h, s) Diagram for Steam (Metric Units)

©2020 NCEES

607