3D model and numerical algorithm for gas filtration in porous media

The article presents a three-dimensional mathematical model of the gas filtration process in porous media and a numerical algorithm for solving the initial-boundary value problem.  The developed model is described using the nonlinear differential equation in partial derivatives with the appropriate initial and boundary conditions.  The proposed mathematical apparatus makes it possible to carry out hydrodynamic calculations taking into account changes in the main factors affecting the process under consideration: permeability, porosity, and thickness of layers, gas recovery coefficient, viscosity, etc.  Computer implementation of the model provides an opportunity to solve practical problems of analysis and forecasting of the gas production process under various conditions of impact on the productive reservoir, as well as making decisions on the development of existing and design of new gas fields.

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Mathematical Modeling and Computing, Vol. 9, No. 3, pp. 637–646 (2022)