基于ABAQUS平台的水力裂缝扩展有限元模拟研究

随着扩展有限元理论的深入研究，利用扩展有限元方法模拟水力压裂具有了一定的可操作性。相比于常规有限元方法，XFEM方法具有计算结果精度高和计算量小的优点。但是，如何模拟射孔孔眼、如何模拟流体与岩石相互作用以及分析水力裂缝的扩展规律仍然是难题。以研究水力压裂裂缝扩展规律为目的，建立了岩石多孔介质应力平衡方程、流体渗流连续性方程和边界条件。通过有限元离散化方法对耦合方程矩阵进行处理。通过富集函数定义初始裂缝（射孔孔眼），选择最大主应力及损伤变量D分别作为裂缝起裂和扩展判定准则，利用水平集方法模拟水力裂缝扩展过程。数值模拟结果显示：增加射孔方位角、压裂液排量和减小水平地应力差，起裂压力上升；黏度对起裂压力无明显影响。增加射孔方位角、压裂液排量、黏度和减小水平地应力差值有助于裂缝宽度的增加。增加水平地应力差值、压裂液排量和减小射孔方位角以及压裂液黏度有助于裂缝长度增加，反之亦然。基于ABAQUS的水力裂缝扩展有限元法可对不同井型和诸多储层物性参数及压裂施工参数进行分析，且裂缝形态逼真，裂缝面凹凸程度清晰，结果准确。此研究可作为一种简便有效研究水力压裂裂缝扩展规律的方法为油田水力压裂设计与施工提供参考与依据。

Extended finite element simulation of hydraulic fracture based on ABAQUS platform

With the further study of the extended finite element theory, the extended finite element method (XFEM) has been widely used to simulate hydraulic fracturing. In comparison with the conventional FEM, the XFEM method has substantial advantages, such as high precision and low computational complexity. However, there are still many difficult challenges including how to simulate the perforation and the interaction between fluid and rock and to analyze propagation law of hydraulic fracturing. In this paper, to study the propagation law of hydraulic fracturing, the stress equilibrium equation of rock porous medium, fluid continuity equation and boundary conditions are established. Through finite element discretization method, the coupling equation matrix is treated. The initial fracture (or propagation) is defined through enrichment functions, and the maximum principal stress and damage variable D are selected respectively as the criterion of fracture initiation and propagation. Hydraulic fracturing propagation process is simulated by using the level set method. Numerical results show that the increase of perforation azimuth, fracture fluid displacement and the reduction of the horizontal stress difference cause the increase of the fracture initiation pressure, and the viscosity has no obvious effect on the fracture initiation pressure. It helps to widen the fracture width by increasing the perforation azimuth, the fracturing fluid displacement, the fracturing fluid viscosity and decreasing the horizontal stress difference. Increasing the horizontal stress difference, fracturing fluid displacement and decreasing the perforation azimuth and the viscosity of fracturing fluid can help to increase the fracture length and vice versa. Different well types and parameters of reservoir and fracturing operation are analyzed by hydraulic fracture XFEM based on ABAQUS platform. The fracture shape is lifelike and the image of degree of concave-convex on the fracture surface is clear. In consequence the result is accurate. As a simple and effective research method for studying the criterion of hydraulic fracturing propagation, this study provides the reference for hydraulic fracturing design and operation in oil field.