In this paper, a problem of numerical simulation of hydraulic fractures is considered. An efficient algorithm of solution is proposed for the plain strain model of hydraulic fracturing. The algorithm utilizes a FEM-based subroutine to compute deformation of the fractured material. The flow of generalized Newtonian fluid in the fracture is modeled in the framework of lubrication theory. In this way, the architecture of the computational scheme is relatively simple and enables one to deal with advanced cases of the fractured material properties and configurations as well as various rheological models of fluid. In particular, the problems of poroelasticity, plasticity, and spatially varying properties of the fractured material can be analyzed. The accuracy and efficiency of the proposed algorithm are verified against analytical benchmark solutions. The algorithm capabilities are demonstrated using the example of the hydraulic fracture propagating in complex geological settings.

中文翻译：

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水力压裂数值模拟：基于混合有限元算法

本文研究了水力裂缝的数值模拟问题。针对水力压裂的平面应变模型，提出了一种有效的求解算法。该算法利用基于 FEM 的子程序来计算断裂材料的变形。广义牛顿流体在裂缝中的流动是在润滑理论的框架下建模的。通过这种方式，计算方案的架构相对简单，可以处理断裂材料特性和配置的高级案例以及流体的各种流变模型。特别是，可以分析断裂材料的孔隙弹性、塑性和空间变化特性等问题。针对分析基准解决方案验证了所提出算法的准确性和效率。