Multiparameter equations of state: an accurate source of thermodynamic property data

Cover......Page 1
Title page......Page 4
Preface ......Page 6
Contents ......Page 8
Nomenclature ......Page 12
1 Introduction ......Page 20
2.1 A Brief History ......Page 24
2.2 Publications on Thermodynamic Reference Data ......Page 30
2.3 Current Work and Future Challenges ......Page 31
3.1 Different Kinds of Multiparameter Equations of State ......Page 34
3.1.1 Equations in Terms of the Helmholtz Energy ......Page 35
3.1.1.1 Correlations for the Helmholtz Energy of the Ideal Gas ......Page 37
3.1.1.2 Common Formulations for the Residual Helmholtz Energy ......Page 42
3.1.2 Equations in Terms of Pressure ......Page 44
3.1.2.1 Integration of Pressure Explicit Equations ......Page 45
3.1.3 Special Functional Forms ......Page 47
3.1.3.1 Hard Sphere Terms ......Page 48
3.1.3.2 Critical Region Terms ......Page 50
3.2 Calculating Thermodynamic Properties from the Helmholtz Energy ......Page 54
3.2.1 Properties in the Homogeneous Region ......Page 55
3.2.2 Properties of the Vapour-Liquid Equilibrium Phases ......Page 61
3.2.3 Properties in the Vapour-Liquid Two Phase Region ......Page 64
3.3 Iterative Procedures ......Page 65
3.3.1 Calculations Based on Temperature and Pressure ......Page 67
3.3.2 Calculations Based on Pressure and Density ......Page 70
3.3.3 Calculations Based on Pressure and Enthalpy ......Page 71
3.3.5 Calculation of Phase Equilibria ......Page 73
3.3.5.1 Multiple Maxwell Loops ......Page 75
4. Setting Up Multiparameter Equations of State for Pure Substances ......Page 80
4.1 Linear and Nonlinear Fitting ......Page 81
4.2 Describing the Helmholtz Energy of the Ideal Gas ......Page 85
4.3.1 The Multiproperty Approach ......Page 93
4.3.2 Defining Residua for Linear Algorithms ......Page 96
4.3.3 Defining Residua for Nonlinear Algorithms ......Page 99
4.3.4 Assigning Weights to Experimental Data ......Page 104
4.4 Optimising the Functional Form ......Page 109
4.4.1 Defining a Bank of Terms ......Page 110
4.4.1.1 Hard Sphere Terms ......Page 112
4.4.2 Setting Up a Regression Matrix ......Page 116
4.4.3 The Stepwise Regression Analysis (SEEQ) ......Page 117
4.4.3.1 Introduction of a Pairwise Exchange ......Page 122
4.4.4 The Evolutionary Optimisation Method (EOM) ......Page 125
4.4.5 The Optimisation Algorithm by Setzmann and Wagner (OPTIM) ......Page 126
4.4.5.1 Adapting OPTIM to Equations of State ......Page 133
4.4.5.2 Introduction of a Pairwise Exchange ......Page 135
4.4.6 The Nonlinear Optimisation Algorithms by Tegeler et al ......Page 136
4.4.6.1 The Nonlinear Quality Criterion ......Page 137
4.4.6.2 The Nonlinear Stepwise Regression Analysis (NLREG) ......Page 140
4.4.6.3 The Nonlinear Optimisation Algorithm (NLOPT) ......Page 144
4.4.6.4 Speeding Up Nonlinear Optimisation Algorithms ......Page 145
4.4.7 Automated Optimisation Algorithms ......Page 147
4.4.7.1 Optimisation of Simplified Equations for Mixtures with Constant Composition ......Page 148
4.4.8 Independent Developments and Future Perspectives ......Page 150
4.5 Describing Properties in the Critical Region ......Page 152
4.5.1 Predictions from Theory ......Page 153
4.5.1.1 Theoretically Founded Equations of State ......Page 157
4.5.2 Capabilities of Empirical Multiparameter Equations of State ......Page 160
4.5.3 Setting Up Equations with Modified Gaussian Bell Shaped Terms ......Page 170
4.5.4 Setting Up Equations with Nonanalytic Terms ......Page 171
4.5.5 Semiempirical Approaches ......Page 175
4.5.5.1 The Use of Switching Functions ......Page 176
4.5.5.2 The Transformation Approach ......Page 177
4.5.5.3 The Approach of Kiselev and Friend ......Page 178
4.6 Consideration of the Extrapolation Behaviour ......Page 180
4.6.1 Comparisons with Data Beyond the Range of Primary Data ......Page 182
4.6.2 The Influence of the Functional Form ......Page 185
4.6.3 The Representation of Ideal Curves ......Page 187
5 The Performance of Multiparameter Equations of State ......Page 192
5.1 Comparisons with Thermal Properties ......Page 196
5.2 Comparisons with Caloric Properties ......Page 210
5.3 Properties at Vapour-Liquid Phase Equilibrium ......Page 225
5.4 Some General Assessments ......Page 233
6 Generalised Functional Forms ......Page 238
6.1 Simultaneous Optimisation of Functional Forms ......Page 242
6.2 Simultaneously Optimised Equations for Technical Applications ......Page 246
6.2.1 Accuracy Versus Numerical Stability - A Compromise ......Page 254
6.2.1.1 An Investigation of Numerical Stability ......Page 256
6.2.1.2 The Influence of Uncertain Critical Parameters ......Page 261
6.2.1.3 Conclusions Regarding Required Data Sets ......Page 264
6.2.2 Results for Non- and Weakly Polar Fluids ......Page 267
6.2.3 Results for Polar Fluids ......Page 281
6.3 Simultaneously Optimised Reference Equations of State ......Page 294
7 Generalised Equations of State ......Page 296
7.1 BACKONE Equations of State ......Page 298
7.1.1 Fitting BACKONE Equations of State to Data ......Page 300
7.1.2 Some Results ......Page 304
7.2 Generalised Empirical Equations of State ......Page 310
7.2.1 The Approach by Platzer and Maurer ......Page 311
7.2.1.1 Some Results ......Page 312
7.2.2 The Approach by Span and Wagner ......Page 319
7.2.2.1 Fitting the Substance Specific Parameters ......Page 322
7.2.2.2 Results for Non- and Weakly Polar Fluids ......Page 325
7.2.2.3 Numerical Stability ......Page 333
8 Describing Mixtures with Multiparameter Equations of State ......Page 338
8.1 Using Composition Dependent Sets of Coefficients ......Page 339
8.1.1 The AGA8-DC92 Equation of State for Natural Gases ......Page 343
8.2 Extended Corresponding States Approaches ......Page 346
8.2.1 Interpolation Between Reference Fluids ......Page 347
8.2.2 The Shape Factor Concept ......Page 348
8.3 Helmholtz Models with Departure Functions ......Page 351
8.3.1 Mixture Specific Departure Functions ......Page 354
8.3.2 Generalised Departure Functions ......Page 355
References ......Page 360
Index ......Page 382