Th. Skaggs et Da. Barry, THE FIRST-ORDER RELIABILITY METHOD OF PREDICTING CUMULATIVE MASS FLUXIN HETEROGENEOUS POROUS FORMATIONS, Water resources research, 33(6), 1997, pp. 1485-1494
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).