NUMERICAL-CALCULATION OF EQUIVALENT GRID BLOCK PERMEABILITY TENSORS FOR HETEROGENEOUS POROUS-MEDIA
NUMERICAL-CALCULATION OF EQUIVALENT GRID BLOCK PERMEABILITY TENSORS FOR HETEROGENEOUS POROUS-MEDIA
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DOI：
10.1029/91wr00107
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发表时间：
1991-05-01
影响因子：
5.4
通讯作者：
DURLOFSKY, LJ
中科院分区：
文献类型：
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作者：
DURLOFSKY, LJ
提出了确定异质多孔介质等效网格块渗透率张量的数值程序。 该方法需要求解受周期性边界条件影响的精细尺度压力方程，以在精细尺度速度场的适当平均时产生粗尺度或等效网格块渗透率。 当计算该粗尺度渗透率的区域构成代表性单元体积（REV）时，所得的等效渗透率可以解释为该区域的有效渗透率。 精细尺度上压力方程的求解是通过应用基于精确三角形的有限元数值程序来完成的，该程序允许对几何复杂特征进行建模。 周期性边界条件的规范显示在所有情况下都会产生对称的正定等效渗透率张量。 该方法通过应用于周期性模型问题进行验证，然后应用于具有分形生成的渗透率场的面积和横截面的放大。 讨论了该方法对于这些更一般的异质性领域的适用性和局限性。
A numerical procedure for the determination of equivalent grid block permeability tensors for heterogeneous porous media is presented. The method entails solution of the fine scale pressure equation subject to periodic boundary conditions to yield, upon appropriate averaging of the fine scale velocity field, the coarse scale or equivalent grid block permeability. When the region over which this coarse scale permeability is computed constitutes a representative elementary volume (REV), the resulting equivalent permeability may be interpreted as the effective permeability of the region. Solution of the pressure equation on the fine scale is accomplished through the application of an accurate triangle-based finite element numerical procedure, which allows for the modeling of geometrically complex features. The specification of periodic boundary conditions is shown to yield symmetric, positive definite equivalent permeability tensors in all cases. The method is verified through application to a periodic model problem and is then applied to the scale up of areal and cross sections with fractally generated permeability fields. The applicability and limitations of the method for these more general heterogeneity fields are discussed.