基于水平集法的非均质岩石建模及水力压裂传播特性研究

基于水平集法的基本思想，讨论了含有不同类型包裹体分布的岩石的二维和三维有限元建模方法。对于二维有限元模型的建立，考虑了以椭圆形为例的规则包裹体的周期分布、位置及包裹体大小均随机变化的多种情况。建议了包裹体和基岩之间界面的材料特性过渡处理方法。同时给出了含有非规则形状包裹体的建模方法。对于三维有限元模型的建立，则考虑了以任意大小椭球体为例的包裹体分布情况。该种建模方法的优点是对于不同的含有任意分布的包裹体的岩石试件，均可以采用相同的有限元网格，即，材料特性的变化不受有限元网格的制约。该法缺点是增加了计算资源。最后结合基于弥散裂缝模型的水力压裂数值计算方法，模拟了含有不同包裹体分布的岩石试件的水力压裂传播特点。

Modelling method of heterogeneous rock material based on level set method and hydraulic fracture propagation features

This paper explores a modelling approach for two-dimensional (2D) and three-dimensional (3D) heterogeneous rock sample containing different types of inclusions base on the level set method (LSM). Taking the elliptical inclusion as an example, its distribution is considered as periodical and random, and the dimension is the same or random in the 2D finite element mesh. The interface between the matrix and inclusions is described by the functions suggested in this paper. Meanwhile, the modelling method for irregular inclusions is also provided using LSM for both 2D and 3D finite element mesh. In the 3D modelling, inclusions are assumed to be spheroid and the distribution also can be periodical or random. The main advantage of this modelling method is that the finite element mesh can remain the same without considering material distributions. In other words, the features of material distribution are separated from the mesh. But it should be pointed out that this method requires high computational resource. Finally, using LSM, the smeared crack model can be used to simulate the features of hydraulic fracture propagation in the heterogeneous rock materials with the same mesh.