High-Pressure Fluid Phase Equilibria: Phenomenology and Computation

Description

The book begins with an overview of the phase diagrams of fluid mixtures (fluid = liquid, gas, or supercritical state), which can show an astonishing variety when elevated pressures are taken into account; phenomena like retrograde condensation (single and double) and azeotropy (normal and double) are discussed. It then gives an introduction into the relevant thermodynamic equations for fluid mixtures, including some that are rarely found in modern textbooks, and shows how they can they be used to compute phase diagrams and related properties. This chapter gives a consistent and axiomatic approach to fluid thermodynamics; it avoids using activity coefficients. Further chapters are dedicated to solid-fluid phase equilibria and global phase diagrams (systematic search for phase diagram classes). The appendix contains numerical algorithms needed for the computations. The book thus enables the reader to create or improve computer programs for the calculation of fluid phase diagrams. introduces phase diagram classes, how to recognize them and identify their characteristic features presents rational nomenclature of binary fluid phase diagrams includes problems and solutions for self-testing, exercises or seminars 0i_Edited-by High-Pressure Fluid Phase Equilibria 0iii_Series-Editor Supercritical Fluid Science and Technology 0iv_Copyright-page Copyright 0v_Dedication Dedication 0xiii_Symbols Symbols 0xix_Preface Preface 0xvii_Foreword Foreword 01_Chapter-1-Introduction 1 Introduction 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 07_Chapter-2-Phenomenology-of-Phase-Diagrams 2 Phenomenology of Phase Diagrams 2.1 Basic Considerations 2.1.1 Phase Diagrams — Cuts and Projections 2.1.2 Subcritical Vapor–Liquid Equilibria 2.1.3 The Lever Rule 2.1.4 Supercritical Vapor–Liquid Equilibria 2.1.5 Volumetric Behavior 2.2 Experimentally Known Binary Phase Diagram Classes 2.2.1 Class I 2.2.1.1 Variants of Class I: Critical Curve with a Pressure Minimum or an S-shape 2.2.1.2 Variants of Class I: (Positive) Azeotropy 2.2.1.3 Variants of Class I: Negative Azeotropy 2.2.1.4 Variants of Class I: Phase Diagrams with Bancroft Points 2.2.2 Class II 2.2.2.1 Variants of Class II: l=l Critical Curves withPositive Slopes 2.2.2.2 Variants of Class II: l=l Critical Curveswith a Temperature Minimum 2.2.2.3 Variants of Class II: Azeotropy 2.2.3 Class III 2.2.3.1 Variants of Class III: Monotonously DecreasingMajor Critical Curve 2.2.3.2 Variants of Class III: Gas–Gas Equilibria 2.2.3.3 Variants of Class III: Critical Curve with a Pressure and a Temperature Minimum 2.2.3.4 Variants of Class III: Azeotropy and Heteroazeotropy 2.2.3.5 Variants of Class III: Heteroazeotropywithout Azeotropy 2.2.4 Class IV 2.2.5 Class V 2.2.6 Class VI 2.2.7 Class VII 2.2.8 Class VIII 2.3 Rational Nomenclature of Phase Diagram Classes 2.4 Ternary Phase Diagrams 2.4.1 One Immiscible Binary Subsystem 2.4.2 Two Immiscible Binary Subsystems 2.4.3 Three Immiscible Binary Subsystems 2.4.4 No Immiscible Binary Subsystems 2.4.5 The Ternary Lever Rule 2.4.6 Three-Dimensional Representations 2.4.7 Miscibility Windows and Cosolvency 2.5 Phase Diagrams of Polymer Solutions 2.6 Problems 073_Chapter-3-Experimental-Observation-of-Phase-Equilibria 3 Experimental Observation of Phase Equilibria 3.1 Warning 3.2 Overview 3.3 Synthetic Methods 3.4 Analytic Methods 3.5 Transient Methods 3.5.1 Methods Using Flow of Matter 3.5.2 Methods Using Heat Flow 3.6 Problems 083_Chapter-4-Thermodynamic-Variables-and-Functions 4 Thermodynamic Variables and Functions 4.1 Fundamentals 4.2 Energy Functions and the Equation of State 4.3 Residual, Excess, and Partial Molar Quantities 4.3.1 Residual Quantities 4.3.2 Excess Quantities 4.3.3 Partial Molar Quantities 4.4 Jacobian Determinants 4.5 Variables of Historical Importance 4.6 Problems 099_Chapter-5-Stability-and-Equilibrium 5 Stability and Equilibrium 5.1 Criteria of Equilibrium 5.2 Thermodynamic Stability and Equilibrium Criteria Based on the Second Law 5.3 Phase Equilibria of Pure Substances 5.3.1 Differential Equations 5.3.2 Algebraic Equations 5.4 Critical Points of Pure Fluids 5.5 Phase Equilibria of Binary Mixtures 5.5.1 Differential Equations 5.5.2 Algebraic Equations Based on the Gibbs Energy 5.5.3 Vapor–Liquid Equilibria at Infinite Dilution 5.5.4 Mixtures in the Vicinity of Pure-Fluid Critical Points 5.5.5 The Isobaric Phase Diagram of an Ideal Mixture 5.5.6 Azeotropy 5.6 Critical Curves 5.6.1 Differential Equations 5.6.2 Algebraic Equations 5.6.3 Critical Endpoints 5.7 Three-Phase Curves 5.8 Isochoric Thermodynamics 5.8.1 Isochoric Thermodynamics and Phase Equilibrium 5.8.2 Local Stability 5.8.3 Mechanical Stability 5.8.4 Computation 5.9 Heat Effects of Phase Transitions 0157_Chapter-6-Solid-Fluid-Equilibrium 6 Solid–Fluid Equilibrium 6.1 Thermodynamic Functions of Solids 6.2 Equilibrium of a Pure Solid and Mixed Fluid Phase 6.3 Remarks on Phase Diagrams of Binary Mixtures 6.4 Impure Solids 6.4.1 Continuous Miscibility 6.4.2 Continuous Solubility on Interstitial Sites (Clathrates) 6.4.3 Formation of Stoichiometric Compounds 6.5 Problems 0177_Chapter-7-Equations-of-State-for-Pure-Fluids 7 Equations of State for Pure Fluids 7.1 Fundamentals 7.2 The Ideal Gas 7.3 The Virial Equation Of State 7.4 Cubic Equations of State 7.4.1 The van der Waals Equation of State 7.4.2 The Redlich–Kwong Equation 7.4.3 The Redlich–Kwong–Soave Equation 7.4.4 The Peng–Robinson Equation 7.4.5 Generalized Cubic Equations of State 7.5 Equations of State Based on Molecular Theory 7.5.1 Hard-Sphere Equations of State 7.5.2 Attraction Terms 7.5.3 Perturbed-Hard-Chain Theories 7.5.4 Perturbation Theories 7.5.4.1 Nonspherical Pair Potentials 7.5.4.2 Scaled-particle Theory 7.5.4.3 Soft Repulsion 7.5.4.4 Hard Convex Bodies 7.5.4.5 Hard Flexible Chains 7.5.4.6 Polar Molecules 7.5.5 Chemical Association Theories 7.6 Reference Equations Of State 7.7 The Corresponding-States Principle 7.8 Near-Critical Behavior 7.9 Which Equation of State is Best? 7.10 How To Obtain The Parameters 7.11 Problems 0211_Chapter-8-Equations-of-State-for-Mixtures 8 Equations of State for Mixtures 8.1 Fundamentals 8.2 The Random Mixing Approximation 8.3 One-Fluid Theory 8.4 Combining Rules 8.5 n-Fluid Theories 8.6 The Mean-Density Approximation 8.7 Advanced Theory 8.8 GE-Based Mixing Rules 8.9 Anything Goes? 8.10 Fuzzy Components 8.10.1 Continuous Thermodynamics 8.10.2 Pseudocomponents 8.11 Problems 0231_Chapter-9-Global-Phase-Diagrams 9 Global Phase Diagrams 9.1 The Concept 9.2 The Coordinates of Global Phase Diagrams 9.3 Boundary States 9.3.1 Double Critical Endpoints 9.3.2 Tricritical Points 9.3.3 Border Azeotropy 9.3.4 Critical Azeotropic Endpoints 9.3.5 Zero-Kelvin Endpoints 9.3.6 Critical Pressure Step Points 9.4 Global Phase Diagrams for Specific Models 9.4.1 The van der Waals Equation of State 9.4.2 The Redlich–Kwong Equation of State 9.4.3 The Carnahan–Starling–Redlich–Kwong Equation of State 9.4.4 The Carnahan–Starling–van der Waals Equation of State 9.4.5 Lattice Gas Models 9.4.6 Other Equations of State 9.4.7 Are Shield and Sword Regions Realistic? 9.5 Applications of Global Phase Diagrams 9.6 Ternary Systems 9.7 Problems 0267_Appendix-A-Algebraic-and-Numeric-Methods Appendix A: Algebraic and Numeric Methods A.1 Errors A.1.1 Round-off Errors A.1.2 Termination Errors A.2 Root of a One-Dimensional Function: Substitution Methods A.3 Root of a One-Dimensional Function: Regula Falsi A.4 Root of a One-Dimensional Function: Newton's Method A.5 Roots of Cubic Polynomials A.5.1 Cardano's Method A.5.2 Fast Numeric Method A.6 The Roots of Quartic Polynomials A.7 The Roots of Quintic Polynomials A.8 Numerical Differentiation A.8.1 Symmetric Differentiation Methods A.8.2 Asymmetric Differentiation Methods A.9 Numerical Integration A.9.1 Simpson's/Newton's Method A.9.2 Gauss' and Chebyshev's Methods A.9.3 Romberg's Method A.9.4 Improper Integrals A.10 Ordinary Differential Equations: Runge–Kutta Method A.11 Linear Algebra A.12 Eigenvalues of a Symmetric Matrix A.13 Parameter Fitting and Systems of Nonlinear Equations 0295_Appendix-B-Proofs Appendix B: Proofs B.1 Legendre Transformation B.2 The Slopes Of Isochores B.3 The Expansion Theorem of Jacobian Determinants 0301_Appendix-C-Equations-of-State-Auxiliary-Equations-for-Programming Appendix C: Equations of State: Auxiliary Equations for Programming C.1 The van der Waals Equation of State C.2 The Redlich–Kwong Equation of State C.3 The Redlich–Kwong–Soave 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 0305_Appendix-D-Solutions-of-the-Problems Appendix D: Solutions of the Problems Chapter 2 – Phenomenology of Phase Diagrams Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Chapter 3 – Experimental Techniques Problem 1 Problem 2 Chapter 4 – Thermodynamic Variables and Functions Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Chapter 6 – Solid–Fluid Equilibria Problem 1 Problem 2 Problem 3 Chapter 7 – Equations of State Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Chapter 8 – Equations of State for Mixtures Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Chapter 9 – Global Phase Diagrams Problem 1 Problem 2 Problem 3 Problem 4 0327_References References 0339_Index Index A B C D E F G H I L M O P Q R S T V