Eulerian Moment Equations for 2-D Stochastic Immiscible Flow

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Abstract
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 one dimension are extended to two dimensions. Comparison to Monte Carlo simulation (MCS) shows that the MDE approach gives a good approximation to total oil production. For such spatially integrated or averaged quantities MDEs may be substantially more efficient than MCS.

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