PNNL

Abstract

We solve statistical moment differential equations for immiscible flow in porous media in the limit of zero capillary pressure, with application to secondary oil recovery. Closure is achieved by Taylor expansion of the fractional flow function and a perturbation argument. Previous results in 1-D are extended to 2-D are extended to 2-D, in which bimodal profile is less evident. Mean and variance of (water) saturation exhibit a bimodel character; two shocks replace the single shock front evident in the classical Buckley-Leverett saturation profile. Comparison to Monte Carlo simulations (MCS) shows that the moment equations approach gives a good approximation to total oil production.