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.

中文翻译：

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二维油藏地层中Saffman-Taylor失稳研究

摘要—

本文致力于模拟水驱油和萨夫曼-泰勒不稳定性的形成。该问题通过二维公式解决。沿着注入井周围的轮廓具有一个注入井和八个生产井的圆形区域被认为是几何形状。为了研究油在水中的驱替方式，计算了静水压力，油和水的渗透率以及油的饱和度。图形分析主要考虑油饱和度场。通过求解稳态压电系数方程来计算静水压力场；利用线性达西滤波定律计算出油水渗流率场。根据对流输运方程的解计算出油饱和度场。问题中考虑的流动的两相性质在于，油相和水相具有各自的相对相渗透率，这是使用Brooks-Corey模型计算得出的。使用有限体积法对方程进行数值求解。不规则三角形网格用于离散计算域。仿真的结果表明，Saffman-Taylor不稳定性的类型由于其随机性而在很大程度上取决于计算网格。生产井注满后，驱替锋稳定。随着油和水的动态粘度之比的增加，不稳定性增加。使用有限体积法对方程进行数值求解。不规则三角形网格用于离散计算域。仿真的结果表明，Saffman-Taylor不稳定性的类型由于其随机性而在很大程度上取决于计算网格。生产井注满后，驱替锋稳定。随着油和水的动态粘度之比的增加，不稳定性增加。使用有限体积法对方程进行数值求解。不规则三角形网格用于离散计算域。仿真的结果表明，Saffman-Taylor不稳定性的类型由于其随机性而在很大程度上取决于计算网格。生产井注满后，驱替锋稳定。随着油和水的动态粘度之比的增加，不稳定性增加。