祝贺李辉的论文《A hydro-mechanical-damage fully coupled cohesive phase field model for complicated fracking simulations in poroelastic media》在CMAME上接受发表!

论文链接：https://doi.org/10.1016/j.cma.2022.115451

A hydro-mechanical-damage fully coupled cohesive phase field model for complicated fracking simulations in poroelastic media

基于水力粘性损伤相场多场耦合模型的孔弹性介质复杂水力压裂模拟

 Hui Li, Hongwu Lei, Zhenjun Yang*, Jianying Wu, Xiaoxian Zhang, Shouding Li* 

Abstract：A hydro-mechanical-damage fully coupled numerical method is developed for simulations of complicated quasi-brittle fracking in poroelastic media. A unified fluid continuity equation with crack-width dependent permeability, based on the Biot’s poroelastic theory, is used for simultaneous modeling of fluid flow in both fractures and porous media. The fluid pressure is coupled into the governing equations of the phase-field regularized cohesive zone model, which can automatically predict quasi-brittle multi-crack initiation, nucleation, and propagation without remeshing, crack tracking, or auxiliary fields as needed by other methods. An alternate minimization Newton–Raphson iterative algorithm is implemented within the finite element framework to solve the above three-fields coupled problem with nodal degrees of freedom of displacements, fluid pressures, and damages. The method is first validated by three problems with analytical solutions, a problem with experimental results, and a two-crack merging problem with numerical results in published literature, in terms of time evolutions of injected fluid pressures, crack widths and lengths, and final crack paths. Horizontal wellbore fracking problems with parallel hydraulic cracks and random natural fractures are then simulated, with the effects of spacing, number, and angle of perforations investigated in detail. It is found that the developed method is capable of modeling complex multi-crack fracking in both homogeneous media and heterogeneous media with natural fractures, and is thus promising for fracking design optimization of practical exploitation of shale gas and oil.

摘要：文中提出了一种水-力-粘性损伤相场多场耦合数值方法，用于准脆性多孔介质材料的复杂水力压裂模拟。基于Biot多孔介质理论，该方法将裂缝模拟为渗透系数较大的连续单元，推导了可同时模拟流体在多孔介质和裂缝中的统一形式控制方程。通过将流体压力引入相场正则化粘聚裂缝模型，从而实现水力作用下的多裂缝起裂、成核和扩展模拟，无需引入网格重划分技术和裂缝追踪技术。基于有限元框架，开发了交替式Newton-Raphson迭代算法求解位移场、流体压力场和损伤相场的控制方程。文中模拟了一系列经典算例，通过与解析解、数值解和试验数据等进行对比，验证了方法在预测裂缝扩展、流体压力变化等的正确性。之后，模拟了均质储层模型和天然裂缝网络储层模型的复杂水平井多缝水力压裂问题，分析了射孔间距、数量和角度等参数的影响，展示了该方法应用于工程实际的潜力。

图1.  准脆性水力压裂几何构形

图2.  多缝同步压裂模拟的损伤云图

图3.  初始射孔角度对天然裂缝网络水力压裂的影响

图4.  不同时刻下天然裂缝网络中多缝同步压裂模拟的损伤和流体压力云图

该项研究工作得到了中国科学院重大专项项目（No. IGGCAS-201903）、国家自然科学基金（No. 51974202 和No. 51779222）、武汉大学-曼彻斯特大学先进材料与结构多尺度研究联合科研平台（No. WHUZZJJ202208）等资助。

This study is funded by the IGGCAS Key Deployment Project (No. IGGCAS-201903) of Chinese Academy of Sciences, National Natural Science Foundation of China (No. 51974202 and No. 51779222) and Key Seed Fund Program for Sino-Foreign Joint Scientific Research Platform of Wuhan University (No. WHUZZJJ202208).