Two-Scale Percolation-Difference Method for Simulation of Transport with Trapping in Porous Media
We examine the phenomenon of isolated traps formation during two-phase displacement in porous media. Two main problems are connected with its description. First, the problem of non-locality is an obstacle, which results from the origin of traps. However, some algorithms to solve it are known. In this paper we study the second problem, dealing with the minimum scale of simulation and consisting in the following. A disordered medium generates traps of various sizes. For any finite scale of simulations h, traps, whose length is smaller than h, can not be caught in such a model. This requires to minimize the simulation step to zero.
We propose a solution of this problem in form of two-scale network method, applied to saturation transport equations, which allows to take into account of desired trap volume. It consists of three essential parts: a) involving two steps of different scale for the pressure field and for the saturation field; b) approximation of saturation transport equation by its analytical solution in scale of one step; c) checking for the non-locality condition.
In result, the pressure field is computed by finite difference method and determination of the saturation field is reduced to an invasion percolation algorithm of lgcal fronts tracing.
The method is realized to compute Darcy’s flow in heterogeneous porous medium, as well as Poiseuille motion in capillary network.
KeywordsPorous Medium Capillary Pressure Relative Permeability Capillary Force Pressure Field
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