STOCHASTIC-ANALYSIS OF 2-PHASE FLOW IN POROUS-MEDIA .2. COMPARISON BETWEEN PERTURBATION AND MONTE-CARLO RESULTS

The first paper (Chang et 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 e xpressions obtained using the perturbation approach. We present analyt ical solutions to the one-dimensional, steady-state oil-and-water flow equations. These solutions are subsequently used in the Monte-Carlo a nalysis to estimate the statistical properties of the key output proce sses. The comparison between the results of perturbation and Monte-Car lo approaches shows a good agreement between the two methods over a wi de range ln kappa (kappa is the intrinsic permeability) variability wi th three different combinations of input stochastic processes of ln ka ppa and soil parameter Gamma. In particular, a good agreement was obta ined for capillary and individual pressure variances and effective pha se conductivities. The results showed that as the mean capillary press ure in the profile increased, the variance of capillary pressure incre ased while the variances of individual pressures decreased. Overall co mparison between the two methods showed that the first-order perturbat ion theory can be successfully used to describe the effective behavior of large-scale, two-phase systems.