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# High-Pressure Fluid Phase Equilibria

## Phenomenology and Computation

- 2nd Edition, Volume 2 - December 1, 2023
- Authors: Ulrich K Deiters, Thomas Kraska
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 1 3 2 8 0 - 3
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 1 3 2 8 1 - 0

High pressures play a more and more important role in modern technology. Examples are the supercritical fluid extraction of medical drugs and dyes from biological material, the ha… Read more

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Request a sales quoteHigh pressures play a more and more important role in modern technology. Examples are the supercritical fluid extraction of medical drugs and dyes from biological material, the handling of compressed or liquefied gases (including natural gas or hydrogen), the operation of modern thermal power plants, and various technical processes for controlled particle formation. *High-Pressure Fluid Phase Equilibria, Second Edition* enables understanding of the complicated phase behavior that fluid or fluid mixtures (liquids, gases, or supercritical phases) can exhibit at elevated pressures. The underlying thermodynamic equations are explained, and robust algorithms for the computation of such equilibria (including solid–fluid equilibria) are proposed.

Since the publication of the first edition of this book, there have been many new developments, for instance, differential equation methods for the computation of phase equilibria, accurate numerical differentiation, and high-precision equations of state (e.g., the GERG model). Moreover, more detail and explanation has been added on important topics that were only briefly examined in the original book to better assist the reader, such as expansion processes and chemical reactions).

The book remains invaluable as a single resource for grasping the intricacies of fluid phase behavior. It enables the readers to write or improve their own computer programs for the calculation of phase equilibria. It will appeal to graduate students of chemical engineering and university research staff involved in chemical engineering of supercritical fluids or the physical chemistry of fluids; the book can also serve as the basis of lectures or advanced students’ seminars.

- Comprehensively presents the complex world of phase equilibria (binary and ternary) and the various methods for computing phase equilibria, whilst carefully considering the relevant pressure and temperature ranges
- Introduces phase diagram classes, how to recognize them, and how to identify their characteristic features
- Presents rational nomenclature of binary fluid phase diagrams
- Includes problems and solutions for self-testing, exercises, or seminars

- Presentation of the phase equilibria models is extended and expanded
- There are now more descriptions on more equations of state, especially the PCSAFT EoS
- Features new chapter on nonisothermal applications and chemically reactive systems and extensive updates and additions to all existing chapters

- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- List of symbols
- Biography
- Preface
- Chapter 1: Introduction
- Abstract
- 1.1. What are fluids?
- 1.2. Why should you read this book?
- 1.3. What is the scope of this book?
- 1.4. Do you have to read the whole book?
- 1.5. Some conventions
- Further Reading
- Chapter 2: Phenomenology of phase diagrams
- Abstract
- 2.1. Basic considerations
- 2.2. Experimentally known binary phase diagram classes
- 2.3. Rational nomenclature of phase diagram classes
- 2.4. Ternary phase diagrams
- 2.5. Phase diagrams of polymer solutions
- 2.6. Problems
- Further Reading
- Chapter 3: Experimental observation of phase equilibria
- Abstract
- 3.1. Warning
- 3.2. Overview
- 3.3. Synthetic methods
- 3.4. Analytic methods
- 3.5. Transient methods
- 3.6. Problems
- Further Reading
- Chapter 4: Thermodynamic variables and functions
- Abstract
- 4.1. Fundamentals
- 4.2. Energy functions and the equation of state
- 4.3. Residual, excess, and partial molar quantities
- 4.4. Jacobian determinants
- 4.5. Other useful relations between partial derivatives
- 4.6. Variables of historical importance
- 4.7. The ideal-gas reference state
- 4.8. Problems
- Further Reading
- Chapter 5: Stability and equilibrium
- Abstract
- 5.1. Criteria of equilibrium
- 5.2. Thermodynamic stability and equilibrium criteria based on the Second Law
- 5.3. Perturbations of equilibrium states
- 5.4. Phase equilibria of pure substances
- 5.5. Critical points of pure fluids
- 5.6. Widom lines
- 5.7. Phase equilibria of binary fluid mixtures
- 5.8. Critical curves
- 5.9. Three-phase curves
- 5.10. Isochoric thermodynamics: definitions and algebraic equations for phase equilibria
- 5.11. Isochoric thermodynamics: differential equations for phase equilibria
- 5.12. Final remarks
- 5.13. Problems
- Further Reading
- Chapter 6: Non-isothermal applications and chemically reactive systems
- Abstract
- 6.1. Scanning calorimetry
- 6.2. The isochoric heat capacity of pure substances in two-phase equilibrium
- 6.3. Adiabatic compression and expansion
- 6.4. Chemical reactions
- 6.5. Problems
- Further Reading
- Chapter 7: Solid–fluid equilibrium
- Abstract
- 7.1. Thermodynamic functions of solids
- 7.2. Equilibrium of a pure solid and a mixed fluid phase
- 7.3. Remarks on phase diagrams of binary mixtures
- 7.4. Impure solids
- 7.5. Problems
- Further Reading
- Chapter 8: Equations of state for pure fluids
- Abstract
- 8.1. Fundamentals
- 8.2. The ideal gas
- 8.3. The virial equation of state
- 8.4. Cubic equations of state
- 8.5. Equations of state based on molecular theory
- 8.6. Reference equations of state
- 8.7. The corresponding-states principle
- 8.8. Near-critical behavior
- 8.9. Which equation of state is best?
- 8.10. How to obtain the parameters
- 8.11. Problems
- Further Reading
- Chapter 9: Equations of state for mixtures
- Abstract
- 9.1. Fundamentals
- 9.2. The random mixing approximation
- 9.3. 1-fluid theory
- 9.4. Combining rules
- 9.5. n-fluid theories
- 9.6. The mean-density approximation
- 9.7. Advanced theory
- 9.8. The GERG model
- 9.9. GE-based mixing rules
- 9.10. Anything goes?
- 9.11. Fuzzy components
- 9.12. Problems
- Further Reading
- Chapter 10: Global phase diagrams
- Abstract
- 10.1. The concept
- 10.2. The coordinates of global phase diagrams
- 10.3. Boundary states
- 10.4. Global phase diagrams for specific models
- 10.5. Applications of global phase diagrams
- 10.6. Ternary systems
- 10.7. Problems
- Further Reading
- Appendix A: Algebraic and numeric methods
- Abstract
- A.1. Errors
- A.2. Roots of nonlinear functions
- A.3. Interpolation
- A.4. Numerical differentiation
- A.5. Numerical integration
- A.6. Ordinary differential equations
- A.7. Linear algebra
- A.8. Parameter fitting and systems of nonlinear equations
- Further Reading
- Appendix B: Theorems and proofs
- Abstract
- B.1. Legendre transformation
- B.2. Euler relations
- B.3. The slopes of isochores
- B.4. The expansion theorem of Jacobian determinants
- B.5. The commutation rule for matrix–vector products
- B.6. Directional derivatives
- Further Reading
- Appendix C: Equations of state: auxiliary equations for programming
- Abstract
- Conventions:
- C.1. The van der Waals equation of state
- C.2. The Redlich–Kwong equation of state
- C.3. The Soave–Redlich–Kwong equation of state
- C.4. The Peng–Robinson equation of state
- C.5. The Carnahan–Starling–van der Waals equation of state
- C.6. The simplified perturbed-hard-chain equation of state
- C.7. The PC-SAFT equation of state
- Further Reading
- Appendix D: Solutions of the problems
- Chapter 2—Phenomenology of phase diagrams
- Chapter 3—Experimental techniques
- Chapter 4—Thermodynamic variables and functions
- Chapter 5—Stability and equilibrium
- Chapter 6—Nonisothermal applications and chemically reactive systems
- Chapter 7—Solid–fluid equilibrium
- Chapter 8—Equations of state for pure fluids
- Chapter 9—Equations of state for mixtures
- Chapter 10—Global phase diagrams
- Further Reading
- References
- References
- Index

- No. of pages: 474
- Language: English
- Edition: 2
- Volume: 2
- Published: December 1, 2023
- Imprint: Elsevier
- Paperback ISBN: 9780443132803
- eBook ISBN: 9780443132810

UD

### Ulrich K Deiters

Ulrich Deiters was born in 1953. He studied chemistry at the Ruhr University of Bochum (Germany), where he, under the supervision of Gerhard M. Schneider, obtained his doctorate in physical chemistry in 1979. He then joined the groups of Keith E. Gubbins and William B. Streett at the Cornell University, Ithaca (USA). After his return to Bochum he founded his own research group. He served for many years as chairman of the IUPAC Subcomittee on Thermodynamic Data. In 1993 he became a professor of physical chemistry at the University of Cologne, from where he formally retired in 2018. His main research fields are the thermodynamics and statistical thermodynamics of fluid mixtures, Monte Carlo simulation, prediction of thermodynamic data *ab initio *from quantum mechanical calculations, and the development of mathematical methods for the prediction of phase diagrams.

TK

### Thomas Kraska

Thomas Kraska was born in 1964. He studied chemistry at the Ruhr University of Bochum (Germany), where he, under the supervision of Ulrich K. Deiters, obtained his doctorate in physical chemistry in 1992. He then joined the group of Keith E. Gubbins at Cornell University, Ithaca (USA) for two years, followed by a research stay for 6 months in the group of Kenneth S. Pitzer at UC Berkeley (USA). He returned to Cologne University in Germany and founded his own research group. In 1999 he obtained his habilitation and continued in Cologne with research on molecular thermodynamics, MD simulation, and the nucleation and growth of metallic and pharmaceutical nanoparticles. At present he is active in the field of chemical education, fostering physical chemistry, mathematization, and molecular simulation in secondary chemistry education.

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