STOCHASTIC FLUID TRAVEL-TIMES IN HETEROGENEOUS POROUS-MEDIA

An analytic approach is developed for quantifying the distribution of fluid passage times in a heterogeneous porous medium. The basic method ology employed utilizes a diffusion theory description for the displac ement of a purely advected fluid subject to a random field of hydrauli c conductivity. Within this framework, a governing model is formed usi ng the backward form of the statistical Kolmogorov equation, which yie lds the inverse Gaussian distribution as a solution to the fluid passa ge time problem. In proposing the methodology, a rationale is presente d for quantifying the associated model parameters using a simple appli cation of the mean and variance to Darcy's law, with subsequent compar isons being made to previous results obtained for perturbation solutio ns of the associated stochastic partial differential equations. In add ition, the validity of the model is discussed within the bounds of a M arkovian description for ground-water flow under a continuum-based mod eling framework. Here, it is argued that acceptably accurate results m ay be achieved for a statistical Peclet number in excess of 70.