Theory of Filtration in a Double Porosity Medium
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This paper defines a generalized mathematical model of filtration in a double porosity medium, taking into account recent ideas on liquid and gas flow in rocks with an anomalously low permeability (including nanoporous rocks). The obtained generalized equation takes into consideration, in contrast to the classical model, the integral effects of direct filtration of an energy (or heat) carrier in low-permeable inclusions. The laws of gas flow variations at the discharge point are compared with the classical double porosity model and with the Boussinesq–Leibenzon model.
The general problem setting and the analytical constructions were supported by the Russian Science Foundation, project no. 14-50-00095. The numerical analysis was performed under a state assignment, project no. 0149-2019-005.