标题： 液压压裂的数值模拟：一种基于有限元法的混合算法 显示英文标题

标题： Numerical simulation of hydraulic fracturing: a hybrid FEM based algorithm

摘要： 本文考虑了水力裂缝数值模拟的问题。 提出了一个用于水力压裂平面应变模型的高效求解算法。 该算法利用基于有限元方法的子程序来计算裂缝材料的变形。 裂缝中的广义牛顿流体流动在润滑理论框架内进行建模。 这样，计算方案的结构相对简单，能够处理裂缝材料性质和配置的高级情况以及各种流体的流变模型。 特别是，可以分析多孔弹性、塑性和裂缝材料的空间变化性质的问题。 通过与解析基准解进行比较，验证了所提出算法的准确性和效率。 通过水力裂缝在复杂地质条件下的传播示例，展示了该算法的能力。 显示英文摘要

摘要： 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 modelled 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.