An Efficient Boundary Integral Formulation for Flow Through Fractured Porous Media
An Efficient Boundary Integral Formulation for Flow Through Fractured Porous Media
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DOI：
10.1006/jcph.1998.5858
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发表时间：
1998-07
影响因子：
4.1
通讯作者：
M. F. Lough;Seong H. Lee;J. Kamath
中科院分区：
文献类型：
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作者：
M. F. Lough;Seong H. Lee;J. Kamath
本文提出了一种新的裂隙多孔介质渗流模型。我们制定我们的模型在边界积分方程的耦合系统，并提出了一个有效的程序，使用边界元法求解方程。在新模型中，基质中的流动由通常的达西定律的多孔介质，与裂缝被视为嵌入在基质中的平面源。在一个单独的裂缝流量是由一个二维达西定律（如在一个Hele？肖氏细胞），与相关的平面水槽分布。这种方法的基本特点是，裂缝被视为特殊的平面，而不是窄间隙的空隙。所得方程组中的误差是内在无量纲参数（裂缝间隙尺寸与所考虑的体积尺度的比率）的量级。我们还描述了我们如何适应新的模型来计算有效的网格块渗透率。这是发展新模式的主要动机。使用有效网格块渗透率来模拟裂缝性油气藏中的流动是比在精确表示每个裂缝时模拟流动有效得多的过程。我们提出了一些数值例子，说明了新的流动模型，以及它是如何被用来模拟水库中的流动。
In this paper we present a new model for flow in fractured porous media. We formulate our model in terms of a coupled system of boundary integral equations and present an efficient procedure for solving the equations using the boundary element method. In the new model, the flow in the matrix is governed by the usual Darcy law for porous media, with the fractures being treated as planar sources embedded in the matrix. The flow in an individual fracture is governed by a two-dimensional Darcy law (as in a Hele?Shaw cell), with an associated planar sink distribution. The essential feature of this approach is that the fractures are treated as special planes rather than narrow-gap voids. The error in the resulting system of equations is on the order of an intrinsic dimensionless parameter (the ratio of the fracture gap size to the scale of the volume under consideration). We also describe how we adapt the new model to compute effective grid block permeabilities. This was the principal motivation behind the development of the new model. Using effective grid block permeabilities to model flow in fractured oil and gas reservoirs is a much more efficient process than modeling the flow when every fracture is precisely represented. We present some numerical examples that illustrate the new flow model and how it is used to model flow in a reservoir.