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

Stochastic analysis of steady-state multiphase (water, oil, and air) R ow in heterogeneous porous media was performed using the perturbation theory and spectral representation techniques. The gas phase is assume d to have constant pressure. The governing equations describing the ho w of oil and water are coupled and nonlinear. The key stochastic input variables are intrinsic permeability, k, and the soil grain size dist ribution index, alpha. Three different stochastic combinations of thes e two input parameters were considered. The perturbation/spectral anal ysis was used to develop closed-form expressions that describe stochas tic variability of key output processes, such as capillary and individ ual phase pressures and specific discharges. The analysis also include d the derivation of the mean Row equations and estimation of the effec tive Row properties. The impact of the spatial variability of k and al pha on the effective conductivities and the variances of pressures and specific discharges was examined.