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Study of the Saffman–Taylor Instability in an Oil Reservoir Formation in Two Dimensions

Authors
  • Bublik, S. A.1
  • Semin, M. A.1
  • 1 Mining Institute of the Ural Branch of the Russian Academy of Sciences, Perm, 614007, Russia , Perm (Russia)
Type
Published Article
Journal
Mathematical Models and Computer Simulations
Publisher
Pleiades Publishing
Publication Date
Mar 01, 2021
Volume
13
Issue
2
Pages
263–273
Identifiers
DOI: 10.1134/S2070048221020046
Source
Springer Nature
Keywords
License
Yellow

Abstract

Abstract—The paper is devoted to the simulation of oil displacement by water and the formation of the Saffman–Taylor instability. The problem is solved in two-dimensional formulation. A circular domain with one injection well and eight production wells located along the contour around the injection well is considered as geometry. To study the patterns of oil displacement by water, hydrostatic pressure, oil and water seepage rates, and oil saturation are calculated. The graphical analysis considers mainly the oil saturation field. The hydrostatic pressure field is calculated by solving the steady-state piezoconductivity equation; the field of the oil-water seepage rate is calculated using the linear Darcy filtration law; and the oil saturation field is calculated from the solution of the advection transport equation. The two-phase nature of the flow considered in the problem lies in the fact that the oil and water phases have their own relative phase permeabilities calculated using the Brooks–Corey model. The equations are solved numerically using the finite volume method. An irregular triangular grid is used to discretize the computational domain. As a result of the simulation, it is established that the type of the Saffman–Taylor instability, due to its randomness, strongly depends on the computational grid. After the production wells are flooded, the displacement front stabilizes. The instability increases as the ratio of dynamic viscosities of oil and water increases.

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