The equations describing the transient flow of a fluid with low compresibility through a series of connected porous media with contrasting geometries and/or properties were coupled into one single vector equation. That equation describes pressure and flow velocity at any point in that composite medium and in the Laplace domain. Numerical symmetric transforms are used to obtain solutions in terms of time.

A distinction is made between actual composite geometries in which flow is delimited by actual boundaries in different configurations; and virtual composite geometries, in which flow geometries are observed in pressure plots though no physical boundaries guide the flow.

The formulation was validated through applications to cases presenting composite geometry flow patterns that have been analyzed previously through approaches different from the one presented.

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