SCALES OF FLUCTUATION AND THE PROPAGATION OF UNCERTAINTY IN RANDOM POROUS-MEDIA

The mechanics of transport and flow in a random porous medium are addr essed 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 stat istically uncorrelated. The stochastic process making up a hydraulic p roperty is thus represented as a linear combination of normalized dete rministic 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 con straint. The solution process will thus consist of the original scales used to represent the porous medium as well as various interaction be tween these scales. The objective of this paper is to develop a proced ure for quantifying the uncertainty in the field variables using the s cales of fluctuation of the porous medium as the measuring stick.