Fluid flow modeling through pressure-dependent porous media: An analytical solution and a computational fluid dynamics approach

Fluid flow modeling in porous media requires solving relevant governing equations, which are inherently nonlinear. However, some simplifications are usually made to make them linear. One of those common assumptions is invariant rock properties with respect to reservoir pressure. However, there are some situations, including pressure-dependent porous media, where this assumption would not be applicable. Hence, the solution of the nonlinear diffusivity equation shall be sought for such cases. The main goal of this study is to present a new analytical solution to the diffusivity equation and a numerical scheme considering exponential decreases in the petrophysical properties with reservoir pressure. The diffusivity equation was solved using the assumed exponential functions, and analytical solutions are provided in this paper. Besides, Computational Fluid Dynamics methods were utilized to verify the accuracy of the derived equations. The developed analytical equations and numerical scheme were then applied over several pressure-dependent porous media cases, and our comparison study showed that neglecting the pressure-dependency of the petrophysical properties will lead to significant errors (approximately 40%). Based on the introduced solutions, we also proposed a new set of type-curves that can be used in well-testing analyses of the deformable porous media.