SIAM Journal on Applied Mathematics, Volume 81, Issue 2, Page 454-484, January 2021.
We propose a reduced model taking account of the capillary trapping to simulate oil migration in geological basins made of several rock types. Our model is derived from Darcy type models thanks to Dupuit approximation and a vertical integration in each geological layer. We propose a time-implicit finite volume scheme which is shown to be unconditionally stable and to admit discrete solutions. Numerical outcomes are then provided in order to illustrate the behavior of our reduced model.

中文翻译：

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毛细管捕集重力流模型在多层地​​质盆地中的油运移

SIAM应用数学杂志，第81卷，第2期，第454-484页，2021年1月。
我们提出了一种简化模型，其中考虑了毛细管捕集以模拟由几种岩石类型构成的地质盆地中的油运移。由于Dupuit近似和每个地质层的垂直整合，我们的模型是从Darcy类型模型派生而来的。我们提出了一个时间隐式有限体积方案，该方案被证明是无条件稳定的并且可以接受离散解。然后提供数值结果，以说明我们简化模型的行为。