An efficient SGBEM–FEM framework for predicting transient hydrocarbon production by coupling transient Darcy flow and channel flow is proposed, which extends the steady state analysis framework developed in Hu and Mear (2022). The governing equation of transient Darcy flow in the matrix is formulated by an integral equation method, and that of channel flow in the fracture is cast in a weak form suitable for treatment with the standard finite element method. An asymptotic analysis is conducted for the transient flux field around the crack front in porous media, and a special tip element is developed to capture the dominant asymptotic field. Cracks in an unbounded domain as well as a layered domain are treated. For the layered domain simulation, a fast algorithm is developed for evaluating the bounded layer kernel based upon Ewald summation. The numerical implementation is verified with the solution to the decoupled transient Darcy flow equation and the coupled equations, respectively. Numerical examples consisting of sequential circular cracks, sequential long cracks and petal cracks are presented to demonstrate the capability of the proposed framework. The proposed framework could potentially be a useful basis for extensions to model related engineering processes involving fluid flows in fractured subsurfaces (such as contaminant transport, nuclear waste disposal, and carbon capture).

中文翻译：

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用于油井生产模拟的计算框架：通过 SGBEM-FEM 耦合瞬态达西流和通道流


提出了一种高效的 SGBEM-FEM 框架，通过耦合瞬态达西流和通道流来预测瞬态碳氢化合物的产生，该框架扩展了 胡 和 Mear （2022） 开发的稳态分析框架。基质中瞬态达西流的控制方程由积分方程法公式化，裂缝中通道流的控制方程以适合使用标准有限元法处理的弱形式铸造。对多孔介质中裂纹前沿周围的瞬态磁通场进行了渐近分析，并开发了一种特殊的尖端元件来捕获主要的渐近场。处理无界域和多层域中的裂缝。对于分层域仿真，开发了一种基于 Ewald 求和的有界层内核的快速算法。分别通过解耦瞬态达西流方程和耦合方程来验证数值实现。给出了由序列圆形裂纹、序列长裂纹和花瓣裂纹组成的数值实例，以证明所提出的框架的能力。拟议的框架可能成为扩展涉及裂隙地体流动的相关工程过程（例如污染物运输、核废料处理和碳捕获）的有用基础。