In this paper, a computationally efficient framework capable of modeling well production simulation with general shaped fractures embedded in three dimensional porous matrix is presented. The flow in the matrix is modeled by classical theory of Darcy flow, whereas flow in hydraulic fractures is treated as channel flow. Governing equations of the Darcy flow are formulated in terms of weakly singular, weak-form boundary integral equations, whereas those of channel flow are cast in a weak form using Galerkin method of weighted residuals. We develop a special tip element to capture the dominant $\mathcal{O}\left(\frac{1}{\sqrt{r}}\right)$ asymptotic field of Darcy flow near the crack tip in porous media. We elaborate a unified transformation technique to overcome the difficulty with singular and nearly singular integrals. The numerical implementation is comprehensively verified through decoupled Darcy flow equation, decoupled channel flow equation and coupled equations, respectively. We show three steady state examples, which are sequential circular cracks case, sequential long cracks case and petal cracks case, to demonstrate the capability of the proposed framework.

在本文中，提出了一种计算高效的框架，该框架能够对嵌入在三维多孔基质中的一般形状裂缝进行油井生产模拟进行建模。基质中的流动由经典的达西流动理论建模，而水力裂缝中的流动被视为通道流动。达西流的控制方程用弱奇异的弱边界积分方程表示，而通道流的控制方程则使用加权残差的伽辽金方法以弱形式表达。我们开发了一种特殊的尖端元素来捕捉主导地位$\mathcal{○}\left(\frac{1}{\sqrt{r}}\right)$多孔介质裂尖附近达西流的渐近场。我们制定了一种统一的变换技术来克服奇异积分和近似奇异积分的困难。分别通过解耦达西流方程、解耦通道流方程和耦合方程对数值实现进行了综合验证。我们展示了三个稳态示例，即连续圆形裂纹情况、连续长裂纹情况和花瓣裂纹情况，以展示所提出框架的能力。