A Model for Steady Fluid Flow in Random Three‐Dimensional Networks of Disc‐Shaped Fractures
A Model for Steady Fluid Flow in Random Three‐Dimensional Networks of Disc‐Shaped Fractures
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DOI：
10.1029/wr021i008p01105
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发表时间：
1985-08
影响因子：
5.4
通讯作者：
J. Long;Peggy Gilmour;P. Witherspoon
中科院分区：
文献类型：
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作者：
J. Long;Peggy Gilmour;P. Witherspoon
建立了三维随机裂缝网络中流体稳定流动的模型。在这个模型中，裂缝是不可渗透基质中的盘状不连续性。压裂盘可以任意地位于岩石体积内，并且可以具有任何期望的孔分布、半径取向和密度。因此，当圆盘模型合适时，可以计算通过裂缝网络的流量，这些裂缝网络在统计上与自然界中发生的裂缝网络相似。在指定边界条件和所需的裂缝之后，识别这些盘（元素）之间的交叉点（节点）。然后，通过网络的稳定流计算使用混合的分析-数值技术。在每个裂缝中，作为每个节点处的平均水头的函数的流入或流出每个节点的解析方程被开发。该方程是基于镜像理论和假设，每个节点是一个源（或汇）的均匀强度。构造了一组质量平衡方程，其将从其相关联的裂缝之一流入节点的流量等同于流出节点进入另一相关联的裂缝。求解这些方程以获得每个节点处的平均水头，然后可以通过将平均水头值代入分析方程来计算裂缝之间的通量。该模型已成功地检查了两个和三个交叉骨折的几种情况下的分析结果。我们计划使用这些技术来测量裂缝网络的渗透率。
A model for steady fluid flow in three-dimensional, random networks of fractures has been developed. In this model the fractures are disc shaped discontinuities in an impermeable matrix. The fracture discs can be arbitrarily located within the rock volume and can have any desired distribution of aperture, radius orientation, and density. Thus where the disc model is appropriate it is possible to calculate flow through fracture networks which are statistically similar to those that occur in nature. After the boundary conditions and the desired fractures are specified, the intersections (nodes) between these discs (elements) are identified. Then steady flow through the network is calculated using a mixed analytical-numerical technique. In each fracture, analytic equations for flow into or out of each node as a function of the average head at each node are developed. The equations are based on image theory and the assumption that each node is a source (or sink) of uniform strength. A set of mass balance equations is constructed which equate flow into a node from one of its associated fractures to flow out of the node into the other associated fracture. These equations are solved for the average head at each node, and flux between fractures can then be calculated by substituting the average head values back into the analytical equations. The model has been successfully checked against analytical results for several cases of two and three intersecting fractures. We plan to use these techniques to measure the permeability of fracture networks.