A simple mathematical model for determining the equivalent permeability of fractured porous media
A simple mathematical model for determining the equivalent permeability of fractured porous media
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DOI：
10.1016/j.icheatmasstransfer.2008.11.010
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发表时间：
2009-03
影响因子：
7
通讯作者：
Jianjun Liu;Y. Sano;A. Nakayama
中科院分区：
文献类型：
--
作者：
Jianjun Liu;Y. Sano;A. Nakayama
提出了一个简单的数学模型来确定裂缝性多孔介质的等效渗透率。该模型由放置在阵列中的方形块组成，块之间存在垂直和水平裂缝。本文推导了裂缝性多孔介质的等效渗透率的解析表达式，该表达式适用于所有宏观流动方向，假设水平流动通过放置在多孔介质中的块体。解析表达式与已有方程吻合较好，也与采用具有周期边界条件的单元结构进行的微观数值计算结果吻合较好。上述二维模型已推广到三维情况下，其中立方岩石排列成一个立方阵列。所得的等效渗透率三维解析表达式与现有公式和微观数值模拟结果吻合较好。
A simple mathematical model has been proposed so as to determine the equivalent permeability of fractured porous media. The model consists of square blocks placed in an array with vertical and horizontal fractures between the blocks. An analytical expression valid for all macroscopic flow directions has been derived for the equivalent permeability of the fractured porous media, assuming a horizontal flow through the blocks placed in a porous medium. The analytical expression agrees well with the existing equations and also with the microscopic numerical results carried out using a unit structure with periodic boundary conditions. The foregoing two-dimensional model has been extended to a three dimensional case in which the cubic rocks are arranged in a cubic array. The resulting three-dimensional analytical expression for the equivalent permeability is found to agree very well with both existing formula and microscopic numerical simulation.