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A method for evaluating the flow of fluids in a porous medium with sources and sinks. (English) Zbl 0669.76118

Steady-state filtration of a homogeneous fluid in a rectangular region containing sources and sinks is analyzed. The computational domain is a two-dimensional model of a homogeneous oil-bearing stratum, penetrated by a system of injection and production wells. The problem reduces to a solution of the Laplace equation for stream functions in a multiply- connected domain which is transformed into a simply-connected domain by means of sections. The Laplace equation, written in the form of finite differences, is solved by an iteration method with relaxation from the top. Streamlines of percolation flows with different arrangements of sources and sinks are derived for two types of boundary conditions.

MSC:

76S05 Flows in porous media; filtration; seepage
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