Macrodispersion for two-phase, immiscible flow in porous media

Abstract Two-phase immiscible flow in a heterogeneous porous media is studied. The permeability is given as a log-normal random function with a given mean, variance and correlation. A set of up-scaled model equations with a new effective macrodispersion tensor is derived for such models. The macrodispersion solution is compared with high-resolution solutions of the original equations, based on several realizations in the permeability. It is shown that the average solution gives a very accurate approximation of the flow. A model with a two-scale permeability field is also studied where the variation on the largest scale is kept in the averaged equations. Here too the macrodispersion solution is compared with high-resolution solutions and the result is very promising. Capillary diffusion effects on the macrodispersion is also discussed.

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