Abstract
This paper describes an implicit-pressureexplicit-composition and explicit-compositionalmodel. The model uses an equation of state(Peng-Robinson)for phase equilibrium and densitycalculations. Interfacial tension effects areconsidered also. The formulation of the pressureequation yields a symmetric and diagonally dominantmatrix that allows the use of the iterative conjugategradiate method for large systems. Simulation oflaboratory CO2 displacements shows good agreementbetween calculated and experimental results. Theinfluence of interfacial tension is investigated.Physically reasonable results also have beenobtained for hypothetical areal and cross-sectional problems.
Introduction
The design of high-pressure gas, enriched-gas, orCO2, injection schemes requires an accurate predictionof the vapor-liquid equilibrium between the oil-in-placeand the injected fluid. In recent years, vapor-liquid equilibrium calculations have been enhanced by theintroduction of many two-constant equations of statethat can be applied to both the vapor and liquid phases.The application of these equations of state to petroleum reservoir fluids was made possible by the ability toevaluate the parameters of these equations from propertiesof the heavy fraction-i.e., density, average boilingpoint, and molecular weight-which can be measuredeasily.Two compositional models that utilize an equation ofstate for phase equilibrium properties calculation aredescribed by Fussell and Fussell and Coats. Whenboth gas and oil are present in every grid block, the formulation of Fussell and Fussell requires thesimultaneous solution of nb (v+1) nonlinear equations, where nb, is the number of grid blocks and v is thenumber of components in the hydrocarbon system. Theexplicit treatment of the transmissibilities limits thesize of the allowable time step. On the other land, Coatsproposed a fully implicit equation-of-state compositionalmodel. His formulation requires the simultaneous solution of nb (2v+4) equations. Although the stability ofCoat's model is better than that of Fussell and Fussell'smodel, the computational cost of Coat's implicit modelmay become prohibitive for systems containing a largenumber of grid blocks and components.This paper presents an implicit-pressure explicit-composition and saturation equation of statecompositional model that is a variation of that proposedby Kazemi et al. The formulation of the pressure equationyields a symmetric and diagonally dominant matrix that allows the use of the iterative conjugate gradientmethod for large systems. The diagonal dominance isalso a desirable feature for the numerical stability ofdirect elimination methods.A new model for relative permeabilities that isdependent on interfacial tension is proposed and thesensitivity of the recovery to interfacial tension isdiscussed.A well model that allows the simulation of constantvolume, constant injection/production wells and multiblockwell completions is provided.The Peng-Robinson equation of state is used in allexamples, although the solution method is general andapplicable for any other equation of state.
SPEJ
P. 687^
Calculation of thermodynamic properties of mixtures in two-phase equilibrium
