Statistical Moment Equations for Flow in Composite Heterogeneous Porous Media

Abstract

We describe a conditional statistical moment equations (CSME) method for quantifying the uncertainty in flow related quantities (pressure and velocity) due to incomplete knowledge (uncertainty) about the permeability field in a composite system. We identify multiple permeability regions in the flow domain. For each region, the mean, variance, and covariance of permeability are specified. We focus on the flow problem; specifically, we study the first two statistical moments of pressure for incompressible systems. The applicability of the method for composite media is demonstrated using several examples. We present and analyze the statistical moments of the pressure for several composite systems with various combinations of the mean, variance and correlation lengths in the different regions. We focus on the predication uncertainty for systems where the overall variance of the log-permeability is (much) larger than unity.