Material and Energy

iii

Prefaces

HANDBOOK ON

MATERIAL AND ENERGY

BALANCE CALCULATIONS

MATERIALS PROCESSING

THIRD EDITION

By Arthur E. Morris

Gordon Geiger

and

H. Alan Fine

Prefaces

Acknowledgements

This Handbook was prepared under Subcontract 00014529, with Bechtel BWXT Idaho, LLC. We are grateful for the assistance of Simon Friedrich of OIT-DOE in obtaining the contract.

Several people made substantial contributions to the Handbook. First, Chapter 3 is largely the work of two graduate students from Texas A and M University, Mr. Blair Sterba-Boatwright and Mr. Peng-lin Huang. Both are candidates for the PhD. in statistics, and made what was a very rough draft into a polished product. Second, Mr. Semih Perdahcioglu developed FlowBal and MMV-C, and revised FREED to include a reaction tool. Semih is now a research assistant at University of Twente, Netherlands. Third, Mr. Knut Lindqvist wrote the code for Super Goal Seek and Super Solver, and Robert Baron wrote U-Converter.

We are obligated to three faculty members for miscellaneous advice with various topics. Professor Eric Grimsey (WASM Kalgoorlie) provided valuable suggestions, encouragement, and help, especially with the application of the degree-of freedom concept. Professor David Robertson (Missouri University of Technology) cleared up a number of points regarding the material on continuously-mixed and unsteady-state processes. Professor Mark Schlesinger (Missouri University of Technology) permitted use of several of his examples and exercises.

Finally, no text is generated in isolation. Appendix C contains a number of general references that provided background information and material data, and other texts that influenced the structure of this edition of the Handbook. Some of the problem-solving strategies of those texts were modified to fit the computationally-intensive approach used in this edition.

Prefaces

Preface to the First Edition

We live in a day and age when realization of the “limits to growth” and the finite extent of all of our natural resources has finally hit home. Yet our economy and our livelihoods depend on successful operation of industries that require and consume raw materials and energy. This success depends, in turn, on efficient use of the available resources, which not only allows industry to conserve materials and energy, but also allows it to compete successfully in the world markets that exist today.

The duties of the metallurgical engineer include, among many other things, development of information concerning the efficiency of metallurgical processes, either through calculation from first principles, or by experimentation. The theory of the construction of material and energy balances, from which such knowledge is derived, is not particularly complicated or difficult, but the practice, particularly in pyrometallurgical operations, can be extremely difficult and expensive.

In this Handbook we have tried to review the basic principles of physical chemistry, linear algebra, and statistics which are required to enable the practicing engineer to determine material and energy balances. We have also tried to include enough worked examples and suggestions for additional reading that a novice to this field will be able to obtain the necessary skills for making material and energy balances. Some of the mathematical techniques which can be used when a digital computer is available are also presented. The user is cautioned, however, that the old computing adage “garbage in, garbage out” is particularly true in this business, and that great attention must still be paid to setting up the proper equations and obtaining accurate data. Nevertheless, the computer is a powerful ally and gives the engineer the tool to achieve more accurate solutions than was possible just twenty-five years ago.

It is hoped that readers, particularly those who are out of practice at these kinds of calculations will ultimately be able to perform energy balances in processes for which they are responsible, and as a result be able to improve process efficiencies. A bibliography of past work on this subject is presented in an appendix to provide reference material against which results of studies can be checked. Hopefully, results reported in the future will reflect increases in efficiency.

H. Alan Fine

University of Kentucky

Lexington, Kentucky

Gordon H. Geiger

University of Arizona

Tucson, Arizona

Preface to the Third Edition

Because the fundamental bases on which the laws of conservation of mass and energy depend remain the same, users of this edition will find an essential similarity between this edition and the slightly revised (second) edition of 1993. Two noteworthy changes in the professional engineer’s practice have occurred since 1993, however. First, in the last 20 years, a dramatic shift has occurred away from metallurgical engineering and the extractive industry towards materials engineering. A large and growing number of recent graduates are employed in such fields as semiconductor processing, environmental engineering, and the production and processing of advanced and exotic materials for aerospace, electronic and structural applications. Second, in the same time frame the advance in computing power and software for the desktop computer has significantly changed the way engineers make computations.

This edition of the text reflects these changes. The text now includes examples that involve environmental aspects, processing and refining of semiconductor materials, and energy-saving techniques for the extraction of metals from low-grade ores. But the biggest change comes from the computational approach to problems. The spreadsheet program Excel is used extensively throughout the text as the main computational “engine” for solving material and energy balance equations, and for statistical analysis of data. A large thermodynamic database (FREED) replaces the thermodynamic tables in the back of the previous Handbook. A number of specialized add-in Excel programs were developed specifically to enhance Excel’s problem-solving capability. And finally, on-line versions of two commercial programs for steam-table and psychrometric calculations were identified and demonstrated. These programs simplify the rather difficult calculations heretofore required. The use of Excel and the introduction of the add-in programs have made it possible to study the effect of a range of variables on critical process parameters. More emphasis is now placed on multi-device flowsheets with recycle, bypass and purge streams whose material and heat balance equations were previously too complicated to solve by the normally-used hand calculator. Appendix A has a brief description of these programs.

The Excel-based program FlowBal is the most important addition to this Edition. FlowBal helps the user set up material and heat balance equations for processes with multiple streams and units. FlowBal uses the thermodynamic database program FREED for molecular mass and enthalpy data. FlowBal’s purpose is to introduce the increasingly important subject of flowsheet simulation. FlowBal and all other software and supplementary reference material is on a CD included with the Handbook. A text file on the CD describes its contents.

Additional changes have been made throughout the text. There are now ten chapters instead of six, which reflects a desire to organize the material in non-reactive vs. reactive material and energy balance sections. The concept of degree-of-freedom analysis has been introduced to provide a basis for analyzing the adequacy of information presented in a flowsheet. The concepts of extent-of-reaction and the equilibrium constant are presented as ways to designate how far a given chemical reaction will (or can) proceed. The introduction of the equilibrium constant requires the Handbook user to have completed a course in Chemistry which contains lectures on thermochemistry, or at least to have available the chemistry text book used in the freshman year of their engineering education. Chapter 3 has been completely revised to emphasize the statistical analysis of experimental data, while de-emphasizing the descriptive material on chemical analysis and techniques for sampling process streams. A final chapter has been added on case studies, showing the application of computational techniques and software to more complex processes.

This edition frequently uses web citations and Wikipedia as references and suggestions for further reading. Wikipedia has well-written articles on many Handbook topics, and more are being added. Wikipedia is a work in progress, so readers are encouraged to search it for additional information even if a Wikipedia reference is not listed in the text. The web pages cited as Chapter references may change after publication, and other sites may appear.

Finally, a web page has been created where changes and additions to the Handbook are posted. The web page contains updates to the Handbook software, error corrections, references to new software, and links to other sites having useful information on material/energy balances and process simulation. We encourage all Handbook users to alert the authors to useful information and to submit material for posting on the page.

http://thermart.net/

Arthur E. Morris

Thermart Software

San Diego, California

Gordon H. Geiger

University of Arizona

Tucson, Arizona

Table of Contents

Handbook Table of Contents

1. Dimensions, Units, and Conversion Factors

1.1 The SI System of Units -

1.2 The American Engineering System (AES) of Units -

1.3 Conversion of Units -

1.4 Unit Conversions Using the U-Converter Program -

1.5 Amount of Substance — the Mole Unit -

1.6 Density and Concentration -

1.7 Electrical Units -

1.8 Calculation Guidelines -

1.9 Summary -

References and Further Reading -

Chapter 1 Exercises -

2. Thermophysical and Related Properties of Materials

2.1 Properties and State of a Substance -

2.2 Gibbs Phase Rule -

2.3 The Gas Phase -

2.4 Condensed Phases -

2.5 Vapor Saturation -

2.6 Effect of Pressure on Phase Transformation Temperatures -

2.7 Steam and Air Property Calculations -

2.8 Properties of Solutions -

2.9 Summary -

References and Further Reading -

Chapter 2 Exercises -

3. Statistical Concepts Applied to Measurement and Sampling

3.1 Basic Statistical Concepts and Descriptive Tools -

3.2 Distributions of Random Variables -

3.3 Basic Applications of Inferential Statistics to Measurement -

3.4 Curve Fitting -

3.5 Experimental Design -

3.6 Summary -

References and Further Reading -

Chapter 3 Exercises -

4. Fundamentals of Material Balances with Applications to Non-Reacting Systems

4.1 System Characteristics -

4.2 Process Classification -

4.3 Flowsheets -

4.4 The General Balance Equation -

4.5 Material Balances on Simple Non-Reactive Systems -

4.6 Strategy for Making Material Balance Calculations -

4.7 Degree-of-Freedom Analysis -

4.8 Using Excel-based Calculational Tools -

4.9 Balances on Systems with Multiple Devices -

4.10 Extension of Excel’s Calculational Tools for Repetitive Solving -

4.11 Special Multiple-Device Configurations I — Recycle and Bypass -

4.12 Special Multiple-Device Configurations II — Counter-Current Flow -

4.13 Using FlowBal for Material Balance Calculations -

4.14 Continuously-Mixed Reactors -

4.15 Graphical Representation of Material Balances -

4.16 Measures of Performance -

4.17 Controllers -

4.18 Summary -

References and Further Reading -

Chapter 4 Exercises -

5. Stoichiometry and the Chemical Equation

5.1 Atomic and Molecular Mass -

5.2 Composition of Compounds and the Gravimetric Factor -

5.3 Writing and Balancing Chemical Equations -

5.4 Calculations Involving Excess and Limiting Reactants -

5.5 Progress of a Reaction -

5.6 Practical Indicators of the Progress of Reactions and Processes -

5.7 Parallel, Sequential and Mixed Reactions -

5.8 Practical Examples of Reaction Writing and Stoichiometry -

5.9 Use of Chemical Reactions in FlowBal -

5.10 Balancing Aqueous (Ionic) Reactions -

5.11 Summary and Conclusions -

References and Further Reading -

Chapter 5 Exercises -

6 Reactive Material Balances

6.1 Balances Using Molecular and Atomic Species

6.2 The Use of Excel-based Computational Tools in Reactive System Balances

6.3 Combustion

6.4 The Production of Gases of Controlled Oxygen and Carbon Potential

6.5 Gas-Solid Oxidation-Reduction Processes

6.6 Processes Controlled by Chemical Reaction Kinetics

6.7 The Reconciliation of an Existing Materials Balance

6.8 The Use of Distribution Coefficients in Material Balance Calculations

6.9 Time-Varying Processes

6.10 Systems Containing Aqueous Electrolytes

6.11 Summary

References and Further Reading

Chapter 6 Exercises

7 Energy and the First Law of Thermodynamics

7.1 Principles and Definitions

7.2 General Statement of the First Law of Thermodynamics

7.3 First Law for an Open System

7.4 Enthalpy, Heat Capacity, and Heat Content

7.5 Enthalpy Change of Phase Transformations

7.6 Enthalpy Change During Chemical Reactions

7.7 Thermodynamic Databases for Pure Substances

7.8 Effect of Temperature on Heat of Reaction

7.9 The Properties of Steam and Compressed Air

7.10 The Use of FREED in Making Energy Calculations

7.11 Heat of Solution

7.12 Summary

References and Further Reading

Chapter 7 Exercises

8 Energy Balances in Non-Reactive Systems

8.1 General Energy Balances

8.2 Heat Balances in Adiabatic Systems

8.3 Psychrometric Calculations

8.4 Energy Efficiency

8.5 Recovery and Recycling of Heat

8.6 Multiple-Device System Balances

8.7 Use of FlowBal for Heat Balance Calculations

8.8 Energy Balances Involving Solution Phases

8.9 Aqueous Processes

8.10 Graphical Representation of Energy Balance

8.11 Summary

References and Further Reading

Chapter 8 Exercises

9 Heat and Material Balances on Reactive Systems

9.1 Thermal Constraints on a Material Balance

9.2 Heat of Combustion of Fuels

9.3 Adiabatic Processes

9.4 Heat Balances Using FlowBal

9.5 Quality of Heat and Thermal Efficiency

9.6 System Balances for Reacting Systems With Heat Exchangers

9.7 Aqueous Processes

9.8 Electrolytic Processes

9.9 Summary

References and Further Reading

Chapter 9 Exercises

10 Case Studies

10.1 Material Balance Simulation of an H-Iron Process with Gas Tempering and Recycle

10.2 A Mass and Heat Balance Simulation for the Use of DRI in EAF Steelmaking

10.3 Natural Gas Combustion Control and the Wobbe Index

10.4 Reduction of Hematite to Magnetite

10.5 Conversion of Quartz to Cristobalite in a Fluidized bed

Appendix A Computational Tools for Making Material and Energy Balance Calculations

CD Table of Contents

1. Enhanced Excel Tools

Super Goal Seek

Super Solver

Unit Conversions

U-C.xla

U-C.rtf

FREED

2. FlowBal and MMV-C

Selected Examples

3. Statistical Analysis Examples: StatTools.xls

4. Supplementary Information

Reference data

Steam and air

AirPVT.xls

Documents

Table of Contents

General References

1. General Chemistry

Zumdahl, S. S, and Zumdahl, S. A., Chemistry, 7th Edition, Houghton Mifflin, 2007.

2. Substance Properties and Thermodynamic Data

Haynes, William M., Ed., CRC Handbook of Chemistry and Physics, 91st Edition. CRC Press, 2010.