Scales of fluctuation and the propagation of uncertainty in random porous media

Abstract

The mechanics of transport and flow in a random porous medium are addressed in this paper. The hydraulic properties of the porous medium are modeled as spatial random processes. The heterogeneity of the medium is modeled as a superposition of scales of heterogeneity that are statistically uncorrelated. The stochastic process making up a hydraulic property is thus represented as a linear combination of normalized deterministic shapes multiplied by a set of uncorrelated random variables. The Karhunen-Loeve expansion is used to formalize this representation. The uncertainty contained in each of these scales is then propagated through the system using the governing differential equation as a constraint. The solution process will thus consist of the original scales used to represent the porous medium as well as various interaction between these scales. The objective of this paper is to develop a procedure for quantifying the uncertainty in the field variables using the scales of fluctuation of the porous medium as the measuring stick.