Stochastic analysis of two-phase water and oil flow: II. Comparison between perturbation and Monte Carlo results
The first paper (Changet al., 1995) described stochastic analysis of two-phase flow in a fully liquid-saturated system. In this paper, the results of Monte-Carlo simulations are compared with the closed-form expressions obtained using the perturbation approach. We present analytical solutions to the one-dimensional, steady-state oil-and-water flow equations. These solutions are subsequently used in the Monte-Carlo analysis to estimate the statistical properties of the key output processes. The comparison between the results of perturbation and Monte-Carlo approaches shows a good agreement between the two methods over a wide range lnk (k is the intrinsic permeability) variability with three different combinations of input stochastic processes of lnk and soil parameter γ. In particular, a good agreement was obtained for capillary and individual pressure variances and effective phase conductivities. The results showed that as the mean capillary pressure in the profile increased, the variance of capillary pressure increased while the variances of individual pressures decreased. Overall comparison between the two methods showed that the first-order perturbation theory can be successfully used to describe the effective behavior of large-scale, two-phase systems.