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首页> 外文期刊>International Journal for Numerical Methods in Fluids >A higher resolution edge-based finite volume method for the simulation of the oil-water displacement in heterogeneous and anisotropic porous media using a modified IMPES method
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A higher resolution edge-based finite volume method for the simulation of the oil-water displacement in heterogeneous and anisotropic porous media using a modified IMPES method

机译：基于改进的IMPES方法的基于边缘的有限体积方法，用于非均质和各向异性多孔介质中油水驱替的模拟

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In this article, we present a higher-order finite volume method with a 'Modified Implicit Pressure Explicit Saturation' (MIMPES) formulation to model the 2D incompressible and immiscible two-phase flow of oil and water in heterogeneous and anisotropic porous media. We used a median-dual vertex-centered finite volume method with an edge-based data structure to discretize both, the elliptic pressure and the hyperbolic saturation equations. In the classical IMPES approach, first, the pressure equation is solved implicitly from an initial saturation distribution; then, the velocity field is computed explicitly from the pressure field, and finally, the saturation equation is solved explicitly. This saturation field is then used to re-compute the pressure field, and the process follows until the end of the simulation is reached. Because of the explicit solution of the saturation equation, severe time restrictions are imposed on the simulation. In order to circumvent this problem, an edge-based implementation of the MIMPES method of Hurtado and co-workers was developed. In the MIMPES approach, the pressure equation is solved, and the velocity field is computed less frequently than the saturation field, using the fact that, usually, the velocity field varies slowly throughout the simulation. The solution of the pressure equation is performed using a modification of Crumpton's two-step approach, which was designed to handle material discontinuity properly. The saturation equation is solved explicitly using an edge-based implementation of a modified second-order monotonic upstream scheme for conservation laws type method. Some examples are presented in order to validate the proposed formulation. Our results match quite well with others found in literature. Copyright (C) 2016 John Wiley & Sons, Ltd.
机译：在本文中，我们提出了一种高阶有限体积方法，采用了“修正的隐式压力显式饱和”（MIMPES）公式，以模拟油和水在非均质和各向异性多孔介质中的二维不可压缩和不可混合的两相流。我们使用基于边的数据结构的中位数-双顶点为中心的有限体积方法来离散化椭圆压力和双曲饱和方程。在经典IMPES方法中，首先，从初始饱和度分布隐式求解压力方程;然后，根据压力场显式计算出速度场，最后，明确求解饱和度方程。然后将该饱和场用于重新计算压力场，然后继续进行该过程，直到达到模拟结束为止。由于饱和方程的明确解，对模拟施加了严格的时间限制。为了解决此问题，开发了Hurtado及其同事的MIMPES方法的基于边缘的实现。在MIMPES方法中，通常在整个模拟过程中速度场变化缓慢，这一事实可解决压力方程，并且速度场的计算频率低于饱和度场。压力方程的求解是使用Crumpton两步法的改进方法来完成的，该方法旨在正确处理材料的不连续性。饱和方程可使用守恒律类型方法的改进二阶单调上游方案的基于边的实现来明确求解。提出了一些例子，以验证所提出的配方。我们的结果与文献中的其他结果非常吻合。版权所有（C）2016 John Wiley＆Sons，Ltd.

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