Stochastic Flowpath Analysis of Multiphase Flow in Random Porous Media

Abstract

Multiphase flow in random porous media is studied by means of a stochastic flowpath approach, which is built upon concepts of differential geometry. This approach replaces the partial differential equations of flow by a set of ordinary differential equations along the flowpaths. Geo- metrical characterization of multiphase flow involves space transformations. The stochastic flowpath approach accounts for heterogeneity and allows for random initial or boundary conditions. It does not require perturbative approximations, and it does not involve Green's functions. The differential geometric formulation involves tracking the flowpath trajectories of the different phases within the flow domain. We discuss the solution of the two-phase flow equation within a random permeability medium by numerical simulation.