A Finite Difference, Semi-implicit, Equation-of-State Efficient Algorithm for the Compositional Flow Modeling in the Subsurface: Numerical Examples

摘要

The mathematical model that has been recognized to have the more accurate approximationto the physical laws govern subsurface hydrocarbon flow in reservoirs isthe Compositional Model. The features of this model are adequate to describe notonly the performance of a multiphase system but also to represent the transport ofchemical species in a porous medium. Its importance relies not only on its currentrelevance to simulate petroleum extraction processes, such as, Primary, Secondary,and Enhanced Oil Recovery Process (EOR) processes but also, in the recent years,carbon dioxide (CO2) sequestration.The purpose of this study is to investigate the subsurface compositional flow underisothermal conditions for several oil well cases. While simultaneously addressingcomputational implementation finesses to contribute to the efficiency of the algorithm.This study provides the theoretical framework and computational implementation subtleties of an IMplicit Pressure Explicit Composition (IMPEC)-Volume-balance(VB), two-phase, equation-of-state, approach to model isothermal compositional flowbased on the finite difference scheme. The developed model neglects capillary effectsand diffusion. From the phase equilibrium premise, the model accounts for volumetricperformances of the phases, compressibility of the phases, and composition-dependentviscosities. The Equation of State (EoS) employed to approximate the hydrocarbonsbehaviour is the Peng Robinson Equation of State (PR-EOS).Various numerical examples were simulated. The numerical results captured the complexphysics involved, i.e., compositional, gravitational, phase-splitting, viscosity andrelative permeability effects. Regarding the numerical scheme, a phase-volumetric-flux estimation eases the calculation of phase velocities by naturally fitting to phase-upstream-upwinding. And contributes to a faster computation and an efficient programmingdevelopment.