Eulerian Moment Equations for 2-D Stochastic Immiscible Flow

摘要

We solve statistical moment differential equations (MDEs) 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, in which a bimodal profile is less evident. Mean and variance of (water) saturation exhibit a bimodal 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 MDE approach gives a good approximation of the location and magnitude of uncertainty is sufficient, MDEs may be substantially more efficient than MCS.