Numerical investigation of the gas-condensate mixture flow in a porous medium

In the last decades, the development of methods for increasing the efficiency of hydrocarbon extraction in fields with unconventional reserves containing large amounts of gas condensate is of great importance. This makes important the development of methods of mathematical modeling that realistically describe physical processes in a gas-condensate mixture in a porous medium.
In the paper, a mathematical model which describes the dynamics of the pressure, velocity and concentration of the components of a two-component two-phase mixture entering a laboratory model of plast filled witha porous substance with known physicochemical properties is considered. The mathematical model is based ona system of nonlinear spatially one-dimensional partial differential equations with the corresponding initial andboundary conditions. Laboratory experiments show that during a finite time the system stabilizes, what givesa basis to proceed to the stationary formulation of the problem.
The numerical solution of the formulated system of ordinary differential equations is realized in the Maple environment on the basis of the Runge-Kutta procedure. It is shown that the physical parameters of the gas-condensate mixture, which characterize the modeled system in the stabilization regime, obtained on this basis, arein good agreement with the available experimental data. This confirms the correctness of the chosen approachand the validity of its further application and development for computer modeling of physical processes ingas-condensate mixtures in a porous medium. The paper presents a mathematical formulation of the system ofpartial differential equations and of respective system stationary equations, describes the numerical approach, and discusses the numerical results obtained in comparison with experimental data.