An algorithm for the simulation of curvilinear plane‐strain and axisymmetric hydraulic fractures with lag using the universal meshes
An algorithm for the simulation of curvilinear plane‐strain and axisymmetric hydraulic fractures with lag using the universal meshes
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DOI：
10.1002/nag.2896
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发表时间：
2019-01
影响因子：
4
通讯作者：
Benjamin E. Grossman‐Ponemon;A. Lew
中科院分区：
文献类型：
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作者：
Benjamin E. Grossman‐Ponemon;A. Lew
提出了一种平面应变轴对称曲线水力裂缝的数值模拟方法。我们限制我们的注意力传播的各向同性，线性弹性介质和驱动的层流，牛顿流体的润滑理论的注射，尖锐的裂缝，我们需要存在一个有限的滞后区域之间的流体前沿和裂纹尖端。我们的方法的关键新奇在于我们如何离散不断发展的裂纹和流体域：我们利用通用网格（UM），一种技术来创建符合问题域的三角剖分，只扰动边界附近的通用背景网格的节点。通过这种方式，我们构建了网格，它符合裂纹和流体前缘。这使我们能够建立标准的分段线性有限元空间，并整体解决准静态水力压裂问题的位移场在岩石和流体中的压力。我们证明了我们的算法的性能，通过三个例子：在平面应变的收敛性研究，在轴对称实验的比较，和一个新的情况下，在一个狭窄的产层断裂。
We present an algorithm to simulate curvilinear hydraulic fractures in plane strain and axisymmetry. We restrict our attention to sharp fractures propagating in an isotropic, linear elastic medium and driven by the injection of a laminar, Newtonian fluid governed by lubrication theory, and we require the existence of a finite lag region between the fluid front and the crack tip. The key novelty of our approach is in how we discretize the evolving crack and fluid domains: we utilize universal meshes (UMs), a technique to create conforming triangulations of a problem domain by only perturbing nodes of a universal background mesh in the vicinity of the boundary. In this way, we construct meshes, which conform to the crack and to the fluid front. This allows us to build standard piecewise linear finite element spaces and to monolithically solve the quasistatic hydraulic fracture problem for the displacement field in the rock and the pressure in the fluid. We demonstrate the performance of our algorithms through three examples: a convergence study in plane strain, a comparison with experiments in axisymmetry, and a novel case of a fracture in a narrow pay zone.