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Numerical modeling of two-phase fluid flow in deformable fractured porous media using the extended finite element method and an equivalent continuum model

机译:扩展有限元法和等效连续模型对可变形压裂多孔介质中两相流体流动的数值模拟

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In the present paper, a numerical model is developed based on a combination of the extended finite element method and an equivalent continuum model to simulate the two-phase fluid flow through fractured porous media containing fractures with multiple length scales. The governing equations involve the linear momentum balance equation and the flow continuity equation for each fluid phase. The extended finite element method allows for an explicit and accurate representation of cracks by enriching the standard finite element approximation of the field variables with appropriate enrichment functions, and captures the mass transfer between the fracture and the matrix. Due to the high computational cost of X-FEM, this technique is only used to model large fractures. The pre-existing short fractures, which are distributed randomly in the porous medium, contribute to the increase of the effective permeability tensor and are modeled with an equivalent continuum model. Finally, the robustness of the proposed computational model is demonstrated through several numerical examples, and the effects of crack orientation, capillary pressure function, solid skeleton deformation, and existence of short cracks on the pattern of fluid flow are investigated. It is shown that the developed model provides a correct prediction of flow pattern for different crack configurations. (C) 2016 Elsevier Ltd. All rights reserved.
机译:在本文中,基于扩展有限元方法和等效连续体模型的组合,建立了一个数值模型,以模拟两相流体流经包含多个长度尺度裂缝的裂缝性多孔介质。控制方程涉及每个流体相的线性动量平衡方程和流动连续性方程。扩展的有限元方法通过使用适当的富集函数丰富场变量的标准有限元近似值,从而可以清晰,准确地表示裂缝,并捕获裂缝和基体之间的传质。由于X-FEM的计算成本很高,因此该技术仅用于建模大型裂缝。在多孔介质中随机分布的预先存在的短裂缝有助于有效渗透率张量的增加,并使用等效连续模型进行建模。最后,通过几个数值例子证明了所提出的计算模型的鲁棒性,并研究了裂纹取向,毛细压力函数,固体骨架变形以及短裂纹的存在对流体流动模式的影响。结果表明,所开发的模型为不同的裂纹形态提供了正确的流型预测。 (C)2016 Elsevier Ltd.保留所有权利。

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