Theoretical Investigation of Unconditionally Stable Sequential Algorithms of Coupled Flow and Geomechanics for Hydraulically Fractured Systems

Jihoon Kim
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Abstract

We investigate unconditionally stable sequential algorithms for coupled hydraulically fractured geomechanics and flow systems, which can account for poromechanics behavior within the fractures. We focus on modifying the concepts of the fixed stress and undrained sequential methods properly for the coupled systems by taking appropriate stabilization terms for stability and convergence with energy analyses. Specifically, an apparent fracture stiffness is used for for numerical stabilization. Because this fracture stiffness depends on the fracture length, the stabilization term needs to be updated dynamically, different from the drained bulk modulus used for typical poromechanics problems. For numerical tests, we take the extended finite element method for geomechanics while the piecewise constant finite element method is used for flow within an existing hydraulic fracture. The numerical results support a priori stability analyses.
水力压裂系统流动与地质力学耦合无条件稳定序列算法的理论研究
我们研究了水力-裂缝地质力学和流动耦合系统的无条件稳定序列算法,该算法可以解释裂缝内的孔隙力学行为。我们着重于修正耦合系统的固定应力和不排水顺序方法的概念,采用适当的稳定性和收敛性稳定化项与能量分析。具体来说,断裂表观刚度用于数值稳定。由于裂缝刚度取决于裂缝长度,因此稳定项需要动态更新,这与典型孔隙力学问题中使用的排水体模量不同。数值试验采用扩展有限元法进行地质力学分析,采用分段常数有限元法进行水力裂缝内渗流分析。数值结果支持先验稳定性分析。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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