Geodesic
Study on the formation of Saffman--Taylor instability in oil reservoir in two-dimensional formulation
Matematičeskoe modelirovanie, Tome 32 (2020) no. 7, pp. 127-142

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The article is devoted to simulation of oil displacement by water and the formation of Saffman–Taylor instability. A circular domain with one injection well and 8 production wells located along the contour around the injection well is considered. To study the patterns of oil displacement by water, hydrostatic pressure, seepage velocity of oil and water, oil saturation are calculated. The graphical analysis of the solution considers mainly the oil saturation field. The calculation of the pressure field is done by means of solving the steady-state seepage equation. The oil-water seepage velocity is calculated using the linear Darcy's law. The oil saturation field is calculated by means of the solution of the advection transport equation. The two-phase nature of the flow lies in various relative phase permeabilities for oil and water. The Brooks–Corey model is used to calculate the relative phase permeabilities. The equations are solved numerically using the finite volume method. An irregular triangular grid is used to discretize the computational domain. As a result, it was established that the form of the Saffman–Taylor instability, by virtue of its randomness, strongly depends on the computational grid. After flooding of producing wells, the phase boundary stabilizes. Instability increases with increasing ratio of dynamic viscosities of oil and water.
Keywords: Saffman–Taylor instability, viscous fingering, seepage flow, porous media, finite volume method, Darcy's law, two-phase flow, Brooks–Corey model. 
@article{MM_2020_32_7_a7,
     author = {S. A. Bublik and M. A. Semin},
     title = {Study on the formation of {Saffman--Taylor} instability in oil reservoir in two-dimensional formulation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {127--142},
     publisher = {mathdoc},
     volume = {32},
     number = {7},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2020_32_7_a7/}
}
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S. A. Bublik; M. A. Semin. Study on the formation of Saffman--Taylor instability in oil reservoir in two-dimensional formulation. Matematičeskoe modelirovanie, Tome 32 (2020) no. 7, pp. 127-142. http://geodesic.mathdoc.fr/item/MM_2020_32_7_a7/