THE FIRST-ORDER RELIABILITY METHOD OF PREDICTING CUMULATIVE MASS FLUXIN HETEROGENEOUS POROUS FORMATIONS

Previous studies have proposed the first-order reliability method (FOR M) as an approach to quantitative stochastic analysis of subsurface tr ansport. Most of these considered only simple analytical models of tra nsport in homogeneous media. Studies that looked at more-complex, hete rogeneous systems found FORM to be computationally demanding and were inconclusive as to the accuracy of the method. Here we show that FORM is poorly suited for computing point concentration cumulative distribu tion functions (cdfs) except in the case of a constant or monotonicall y increasing solute source. FORM is better equipped to predict transpo rt in terms of the cumulative mass flux across a control surface. As a demonstration, we use FORM to estimate the cumulative mass flux cdf i n two-dimensional, random porous media. Adjoint sensitivity theory is employed to minimize the computational burden. In addition, properties of the conductivity covariance and distribution are exploited to impr ove efficiency. FORM required eight times less CPU time than Monte Car lo simulation to generate the results presented. The accuracy of FORM is found to be minimally affected by the size of the initial solute bo dy and the solute travel distance. However, the accuracy is significan tly influenced by the degree of heterogeneity, providing an accurate e stimate of the cdf when there is mild heterogeneity (sigma(lnK) = 0.5) but a less accurate estimate when there is stronger heterogeneity (si gma(lnK) = 1.0).