General Strategy for Stability Testing and Phase-Split Calculation in Two and Three Phases

Efficient and robust phase equilibrium computation has become a prerequisite for successful large-scale compositional reservoir simulation. When knowledge of the number of phases is not available, the ideal strategy for phase-split calculation is the use of stability testing. Stability testing not only establishes whether a given state is stable, but also provides good initial guess for phase-split calculation. In this research, we present a general strategy for twoand three-phase split calculations based on reliable stability testing. Our strategy includes the introduction of systematic initialization of stability testing particularly for liquid/liquid and vapor/liquid/liquid equilibria. Powerful features of the strategy are extensively tested by examples including calculation of complicated phase envelopes of hydrocarbon fluids mixed with CO2 in single-, two-, and three-phase regions.

[1]  Hussein Hoteit,et al.  Numerical Modeling of Diffusion in Fractured Media for Gas-Injection and -Recycling Schemes , 2009 .

[2]  C. Floudas,et al.  Global optimization for the phase and chemical equilibrium problem: Application to the NRTL equation , 1995 .

[3]  Mark A. Stadtherr,et al.  Reliable computation of phase stability using interval analysis : Cubic equation of state models , 1998 .

[4]  K. I. M. McKinnon,et al.  A Generic Global Optimization Algorithm for the Chemical and Phase Equilibrium Problem , 1998, J. Glob. Optim..

[5]  John A. Trangenstein,et al.  Customized minimization techniques for phase equilibrium computations in reservoir simulation , 1987 .

[6]  M. Stadtherr,et al.  Interval Analysis for Thermodynamic Calculations in Process Design: A Novel and Completely Reliable Approach , 1999 .

[7]  S. Gómez,et al.  Phase stability analysis with cubic equations of state by using a global optimization method , 2002 .

[8]  C. Floudas,et al.  GLOPEQ: A new computational tool for the phase and chemical equilibrium problem , 1997 .

[9]  Kamy Sepehrnoori,et al.  Three-Phase Flash in Compositional Simulation Using a Reduced Method , 2010 .

[10]  H. H. Rachford,et al.  Procedure for Use of Electronic Digital Computers in Calculating Flash Vaporization Hydrocarbon Equilibrium , 1952 .

[11]  Efficient Phase Equilibrium Calculation for Compositional Simulation: The Direct Reduced Flash , 2007 .

[12]  M. Stadtherr,et al.  Enhanced Interval Analysis for Phase Stability: Cubic Equation of State Models , 1998 .

[13]  Abbas Firoozabadi,et al.  Cubic-Plus-Association Equation of State for Asphaltene Precipitation in Live Oils , 2010 .

[14]  D. Peng,et al.  A New Two-Constant Equation of State , 1976 .

[15]  D. Nichita.  A REDUCTION METHOD FOR PHASE EQUILIBRIUM CALCULATIONS WITH CUBIC EQUATIONS OF STATE , 2006 .

[16]  Abbas Firoozabadi,et al.  Higher-order compositional modeling with Fickian diffusion in unstructured and anisotropic media , 2010 .

[17]  Huanquan Pan,et al.  Fast and Robust Algorithm for Compositional Modeling: Part II - Two-Phase Flash Computations , 2003 .

[18]  D. Nichita,et al.  Multiphase equilibrium calculation using reduced variables , 2006 .

[19]  M. Assael,et al.  Phase-Equilibrium Calculations , 1996 .

[20]  F. Orr,et al.  Phase Behavior of CO2 and Crude Oil in Low-Temperature Reservoirs , 1981 .

[21]  S. Gómez,et al.  Multiphase equilibria calculation by direct minimization of Gibbs free energy with a global optimization method , 2002 .

[22]  Michael L. Michelsen,et al.  Simplified flash calculations for Cubic Equations of State , 1986 .

[23]  Abbas Firoozabadi,et al.  Initialization of phase fractions in Rachford-Rice equations for robust and efficient three-phase split calculation , 2012 .

[24]  Abbas Firoozabadi,et al.  Wax Precipitation in Gas Condensate Mixtures , 2001 .

[25]  W. Seider,et al.  Homotopy-continuation method for stability analysis in the global minimization of the Gibbs free energy , 1995 .

[26]  E. Hendriks,et al.  Application of a reduction method to phase equilibria calculations , 1992 .

[27]  A. Lucia,et al.  Thermodynamically consistent quasi‐Newton formulae , 1985 .

[28]  Improved two-sided tangent plane initialization and two-phase-split calculations , 2007 .

[29]  Curtis H. Whitson,et al.  The negative flash , 1989 .

[30]  A New Algorithm for Rachford-Rice for Multiphase Compositional Simulation , 2010 .

[31]  Michael L. Michelsen,et al.  Calculation of multiphase equilibrium , 1994 .

[32]  N. Saber,et al.  Rapid and robust phase behaviour stability analysis using global optimization , 2008 .

[33]  Michael Locht Michelsen,et al.  Thermodynamic Modelling: Fundamentals and Computational Aspects , 2004 .

[34]  D. Nichita,et al.  A new look at multiphase Rachford–Rice equations for negative flashes , 2008 .

[35]  E. Hendriks,et al.  Reduction theorem for phase equilibrium problems , 1988 .

[36]  L. E. Baker,et al.  Gibbs energy analysis of phase equilibria , 1982 .

[37]  Dan Vladimir Nichita,et al.  Efficient Phase Equilibrium Calculation in a Reduced Flash Context , 2008 .

[38]  Kamy Sepehrnoori,et al.  Application of a reduced method in compositional simulation , 2010 .

[39]  Kamy Sepehrnoori,et al.  Fluid Characterization of Three-Phase CO2/Oil Mixtures , 1992 .

[40]  Claude F. Leibovici,et al.  A solution of Rachford-Rice equations for multiphase systems , 1995 .

[41]  Donald B. Robinson,et al.  The development of the Peng - Robinson equation and its application to phase equilibrium in a system containing methanol , 1985 .

[42]  Two-Phase Isentropic Compressibility and Two-Phase Sonic Velocity for Multicomponent-Hydrocarbon Mixtures , 2000 .

[43]  H. Renon,et al.  The isothermal flash problem: New methods for phase split calculations , 1987 .

[44]  K. Gasem,et al.  Multiphase Equilibrium Calculations Using Gibbs Minimization Techniques , 2003 .

[45]  Huanquan Pan,et al.  Complex Multiphase Equilibrium Calculations by Direct Minimization of Gibbs Free Energy by Use of Simulated Annealing , 1998 .

[46]  François Montel,et al.  Calculation of convergence pressure/temperature and stability test limit loci of mixtures with cubic equations of state , 2007 .

[47]  Christodoulos A. Floudas,et al.  Global optimization for the phase stability problem , 1995 .

[48]  Christodoulos A. Floudas,et al.  Global Optimization and Analysis for the Gibbs Free Energy Function Using the UNIFAC, Wilson, and ASOG Equations , 1995 .

[49]  Zhidong Li,et al.  Three-Phase Compositional Modeling of CO2 Injection By Higher-Order Finite Element Methods With CPA equation of state , 2011, ANSS 2011.

[50]  C. M. Crowe,et al.  Convergence promotion in the simulation of chemical processes—the general dominant eigenvalue method , 1975 .

[51]  P. A. Nelson,et al.  Rapid phase determination in multiple-phase flash calculations , 1987 .

[52]  Abbas Firoozabadi,et al.  Modeling Asphaltene Precipitation by n-Alkanes from Heavy Oils and Bitumens Using Cubic-Plus-Association Equation of State , 2010 .

[53]  Shuyu Sun,et al.  Compositional modeling of three‐phase flow with gravity using higher‐order finite element methods , 2011 .

[54]  Abbas Firoozabadi,et al.  Thermodynamics of Hydrocarbon Reservoirs , 1999 .

[55]  Mark A. Stadtherr,et al.  Reliable prediction of phase stability using an interval Newton method , 1996 .

[56]  Solution of the multiphase equilibrium problem for pure component, binary and ternary systems using the area method , 1996 .

[57]  L. Yarborough,et al.  Multiple Phase Behavior in Porous Media During CO2 or Rich-Gas Flooding , 1977 .

[58]  Hussein Hoteit,et al.  Simple phase stability-testing algorithm in the reduction method , 2006 .