About one spatial filtration model with non-classical law of motion in hydrate-containing environment

A. E. Bakeer ; Yu. A. Poveshchenko ; V. O. Podryga ; P. I. Rahimly

Matematičeskoe modelirovanie, Tome 36 (2024) no. 2, pp. 77-98.

Résumé

The work proposes a spatial two-component (H2O, CH4) three-phase (hydrate, free water and gas) filtration model taking into account the dissociation of gas hydrates, based on splitting by physical processes, using a non-classical law of motion (considering its non-linearity). The presented mathematical model makes it possible to calculate two-dimensional flows in areas with an irregular strata structure. With its help, it is possible to carry out both profile and areal calculations, taking into account the complex geometry of sedimentary basins. When testing it to solve problems of the theory of filtration in sed-imentary basins, the method of support operators was applied and implemented. This method makes it possible to calculate filtration processes in media with discontinuous physical properties, which is achieved by using irregular meshes. As a result, it becomes possible to model the shear zones and obtain a numerical solution under conditions of different scales of the problem. At the same time, on meshes with large cells, where there are discontinuities in material properties, a qualitative approximation of the transfer of saturations and gradients of thermodynamic quantities is preserved. The constructed mesh model also approximates the identities of the support operator method on different time layers. Based on the developed computing technology, a software package has been created, the tools of which are capable of solving two-dimensional problems of multiphase and multicomponent modeling of gas hydrate dissociation processes in the porous environment of sedimentary basins of lithologically complex structure on meshes of irregular structure. To test the software package, model calculations of piezoconductive processes in a three-phase medium with hydrated solid-phase inclusions in a two-dimensional case on irregular meshes were carried out. Calculations have shown a decrease in the depression value within spatial regions when using nonlinear filtration laws of motion in the medium compared to the classical Darcy law, which makes it possible to correctly describe the physics of low-permeability reservoirs.

Détail

Keywords: mathematical modeling, gas hydrates, support operator method, irregular meshes, nonlinear filtration law.

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