STOCHASTIC-ANALYSIS OF MULTIPHASE FLOW IN POROUS-MEDIA .2. NUMERICAL SIMULATIONS

The first paper (Chang et al., 1995b) of this two-part series describe d the stochastic analysis using spectral/perturbation approach to anal yze steady state two-phase (water and oil) flow in a, liquid-unsaturat ed, three fluid-phase porous medium. In this paper, the results betwee n the numerical simulations and closed-form expressions obtained using the perturbation approach are compared. We present the solution to th e one-dimensional, steady-state oil and water flow equations. The stoc hastic input processes are the spatially correlated logk where k is th e intrinsic permeability and the soil retention parameter, alpha. Thes e solutions are subsequently used in the numerical simulations to esti mate the statistical properties of the key output processes. The compa rison between the results of the perturbation analysis and numerical s imulations showed a good agreement between the two methods over a wide range of logk variability with three different combinations of input stochastic processes of logk and soil parameter alpha. The results cle arly demonstrated the importance of considering the spatial variabilit y of key subsurface properties under a variety of physical scenarios. The variability of both capillary pressure and saturation is affected by the type of input stochastic process used to represent the spatial variability. The results also demonstrated the applicability of pertur bation theory in predicting the system variability and defining effect ive fluid properties through the ergodic assumption.