A finite element model for three dimensional hydraulic fracturing
A finite element model for three dimensional hydraulic fracturing
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DOI：
10.1016/j.matcom.2006.06.020
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发表时间：
2006-11
期刊：
影响因子：
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通讯作者：
P. Devloo;P. Fernandes;S. Gomes;Cedric Marcelo Augusto Ayala Bravo;Renato Gomes Damas
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文献类型：
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作者：
P. Devloo;P. Fernandes;S. Gomes;Cedric Marcelo Augusto Ayala Bravo;Renato Gomes Damas
本文致力于开发具有 3d 裂缝扩展的水力压裂过程数值模拟模型。它考虑了裂缝内流体流动、流体通过裂缝壁泄漏以及周围多孔介质的弹性响应的影响。采用有限元技术对流体流动守恒定律以及与牵引力和裂缝张度相关的奇异积分方程进行离散化。奇异积分方程的离散模型是使用模板矩阵结构实现的，可以有效地实现流固耦合问题。牛顿法与 GMRES 线性求解器相结合，用于求解所得的非线性方程组。提出了一种裂缝扩展算法，该算法基于输送到某一点的流体量与可能因泄漏而损失的流体量的平衡。为了说明该模型的可行性，我们给出了典型运行参数的仿真结果。
This paper is devoted to the development of a model for the numerical simulation of hydraulic fracturing processes with 3d fracture propagation. It takes into account the efects of fluid flow inside the fracture, fluid leak-off through fracture walls and elastic response of the surrounding porous media. Finite element techniques are adopted for the discretization of the conservation law of fluid flow and the singular integral equation relating the traction and the fracture opening. The discrete model for the singular integral equation is implemented using a stencil matrix structure allowing an efficient implementation of the fluid–structure interaction problem. Newton’s method combined with GMRES linear solver are used to solve the resulting nonlinear set of equations. An algorithm for fracture propagation is proposed which is based on the balance of the amount of fluid transported to a certain point with the amount of fluid that could be lost by leak-off. To illustrate the feasibility of the model, we present simulation results for typical operational parameters.