Modeling stochastic multiphase flow in porous media

We present a novel approach to modeling stochastic multiphase now problems, for example NAPL flow, in a heterogeneous subsurface medium with random soil properties. A stochastic numerical model for steady state and transient two-phase and three-phase flow in a random soil property field is developed using the Karhunen-Loeve Moment Equation (KLME) approach and is numerically implemented. An exponential model and van Genuchten model are adopted to define the constitutive relationship between phase relative permeability and capillary. The log-transformed intrinsic permeability, soil pore size distribution, and van Genuchten fitting parameter are assumed to be Gaussian random functions with a separable exponential covariance function. We demonstrate the validity of the proposed KLME model by favorably comparing up to second-order approximations to Monte Carlo simulations, which are considered "true" solutions. The significant computational efficiency of the KLME approach over Monte Carlo simulation is also illustrated.