This short monograph focuses on the theoretical backgrounds and practical implementations concerning the thermodynamic modeling of multiphase equilibria of complex reservoir fluids using cubic equations of state. It aims to address the increasing needs of multiphase equilibrium calculations that arise in the compositional modeling of multiphase flow in reservoirs and wellbores.
It provides a state-of-the-art coverage on the recent improvements of cubic equations of state. Considering that stability test and flash calculation are two basic tasks involved in any multiphase equilibrium calculations, it elaborates on the rigorous mathematical frameworks dedicated to stability test and flash calculation. A special treatment is given to the new algorithms that are recently developed to perform robust and efficient three-phase equilibrium calculations.
This monograph will be of value to graduate students who conduct research in the field of phase behavior, as well as software engineers who work on the development of multiphase equilibrium calculation algorithms.
Author(s): Huazhou Li
Series: Petroleum Engineering
Publisher: Springer
Year: 2021
Language: English
Pages: 221
City: Cham
Preface
Contents
About the Author
1 Introduction
1.1 First and Second Laws of Thermodynamics
1.2 Fundamental Thermodynamic Relations
1.3 Phase Stability and Phase Equilibrium Conditions
1.4 Fugacity and Fugacity Coefficients
1.5 Gibbs Phase Rule
1.6 Phase Behavior of Pure Fluids
1.7 Phase Behavior of Binary Mixtures
1.8 General Phase Behavior of Complex Reservoir Fluids
1.9 Example Questions
References
2 Cubic Equation of State
2.1 Brief Overview of Most Popular EOSs
2.2 vdW EOS
2.3 RK EOS
2.4 SRK EOS
2.5 PR EOS
2.6 Volume Translation Models in CEOS
2.6.1 Historical Development
2.6.2 Impact of Using Volume Translation on Phase Equilibrium Calculations
2.6.3 Distance-Function-Based Volume Translation Model for PR EOS and SRK EOS
2.6.4 Pressure–Volume Crossover Issue Caused by Temperature-Dependent Volume Translation Models
2.7 Huron-Vidal Mixing Rule
2.8 Further Readings
2.9 Example Questions
References
3 Phase Stability Test
3.1 Gibbs Free Energy Analysis of Phase Equilibria
3.2 Derivation of the TPD Function
3.3 Solution Methods
3.3.1 Equation Solving Approach
3.3.2 Trust-Region-Based Minimization Approach
3.4 Example Questions
References
4 Two-Phase Equilibrium Calculations
4.1 Equal Fugacity Condition
4.2 Derivation of RR Equation
4.3 Other Forms of RR Equation
4.4 Numerical Algorithm of Two-Phase Equilibrium Calculations
4.5 Example Questions
References
5 Multiphase Equilibrium Calculations
5.1 Multiphase Flash Calculation Theories
5.1.1 RR Equation for Multiphase Flash
5.1.2 Multiphase Flash Approach Proposed by Michelsen (1994)
5.1.3 Multiphase Flash Approach Proposed by Leibovici and Nichita (2008)
5.1.4 Multiphase Flash Approach Proposed by Okuno et al. (2010)
5.1.5 Multiphase Flash Approach Proposed by Petitfrere and Nichita (2014) and Pan et al. (2021)
5.2 General Trust-Region-Based Three-Phase Equilibrium Calculation Algorithm
5.3 Vapor–Liquid-Liquid Three-Phase Equilibrium Calculation Algorithms
5.4 Vapor–Liquid-Aqueous Three-Phase Equilibrium Calculation Algorithms
5.5 Free-Water and Augmented Free-Water Three-Phase Equilibrium Calculation Algorithms
5.6 Vapor–Liquid-Asphaltene Three-Phase Equilibrium Calculation Algorithms
5.7 Further Discussion
5.8 Further Readings
5.9 Example Questions
References
