Stochastic analysis of two-phase flow in porous media: I. Spectral/perturbation approach

Stochastic analysis of steady-state two-phase (water and oil) flow in heterogeneous porous media is performed using the perturbation theory and spectral representation techniques. The governing equations describing the flow are coupled and nonlinear. The key stochastic input variables are intrinsic permeability,k, and the soil and fluid dependent retention parameter, . Three different stochastic combinations of these two imput parameters were considered. The perturbation/spectral analysis was used to develop closed-form expressions that describe stochastic variability of key output processes, such as capillary and individual phase pressures and specific discharges. The analysis also included the estimation of the effective flow properties. The impact of the spatial variability ofk and on the variances of pressures, effective conductivities, and specific discharges was examined.