STOCHASTIC-ANALYSIS OF MULTIPHASE FLOW IN POROUS-MEDIA .1. SPECTRAL PERTURBATION APPROACH

Stochastic analysis of steady-state multiphase (water, oil, and air) Row in heterogeneous porous media was performed using the perturbation theory and spectral representation techniques. The gas phase is assumed to have constant pressure. The governing equations describing the how of oil and water are coupled and nonlinear. The key stochastic input variables are intrinsic permeability, k, and the soil grain size distribution index, alpha. Three different stochastic combinations of these two input 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 derivation of the mean Row equations and estimation of the effective Row properties. The impact of the spatial variability of k and alpha on the effective conductivities and the variances of pressures and specific discharges was examined.