在煤砂岩叠置储层中，通过水力压裂技术在纵向上沟通煤岩和砂岩储层成为该类气田高效开发的一种方式。针对煤砂互层中水力裂缝纵向延伸问题，综合应用Biot孔弹性理论、渗流力学、相场法理论建立了多孔介质中水力裂缝扩展计算非线性方程组，并采用有限元法对该非线性方程组进行离散。其中渗流-应力耦合方程组采用Newton-Raphson(NR)法迭代求解，裂缝相场演化方程采用Picard法迭代求解。本文模型将断裂力学中的强不连续裂缝转化为扩散型裂缝，不需要额外的规则来追踪裂缝界面，且裂缝延伸后不需要重新剖分网格。将数值模型计算得到的裂缝宽度与解析模型计算得到的裂缝宽度进行对比，验证了模型的正确性。基于建立的数值模型，研究了煤砂互层中水力裂缝纵向延伸影响因素。研究表明，在煤层中射孔压裂时，上覆地应力与顶底板最小水平地应力差越小、层间界面胶结强度越小、层间界面渗透率越大，水力裂缝越不容易穿过界面而延伸至顶底板砂岩层。注入速率对裂缝延伸轨迹影响很小。当水力裂缝到达层间界面时，会出现憋压现象，从而使得水力裂缝开启层间界面或延伸到顶底板。在顶板砂岩层中射孔压裂时，水力裂缝会穿过上界面而延伸到煤层中，但是水力裂缝难以穿过下界面而延伸到底板砂岩层。在顶板砂岩中射孔压裂比煤层中射孔压裂破裂压力高。

In the coal sandstone interbedded reservoir,it is an efficient exploit way to connect the coal and sandstone reservoir vertically by hydraulic fracturing technology.Therefore,Aiming at the problem of hydraulic crack vertical extension in the coal-sand interbedding formation,the nonlinear equations for calculating hydraulic crack propagation in porous media are established based on the poro-mechanics theory proposed by Biot,seepage mechanics and the phase field method,and the nonlinear equations are discretized by the finite element method.The coupled mechanical equilibrium and fluid flow equation is linearized and solved using Newton-Raphson (NR) method,while the phase field is solved by the Picard iteration method.In this model,the sharp fracture in fracture mechanics is transformed into diffusive fracture,no additional rules are needed to trace the fracture shape,and no re-meshing is needed after fracture extension.By comparing the fracture width calculated by the numerical model with that calculated by the analytical model,the correctness of the model is verified.Based on the established numerical model,the factors affecting the hydraulic crack vertical extension in the coal-sand interbedded formation are studied.Numerical results show that when perforating in the coal seam,the smaller the difference between the overburden in-situ stress and the minimum horizontal in-situ stress of the upper and lower sandstone layers,the smaller the interlayer interface cementation strength and the greater the interlayer interface permeability,the more difficult for the hydraulic crack to penetrate the interlayer interface and extend to the upper and lower sandstone layers.Injection rate has little effect on the fracture extension trajectory.When the hydraulic crack reaches the interlayer interface,the pressure will rise,so that the hydraulic crack will opens the interlayer interface or extends to the upper and lower sandstone layers.When perforating in the upper sandstone layer,the hydraulic crack will extend to coal seam through the upper interlayer interface,but it is difficult for the hydraulic crack to extend to lower sandstone layer through the lower interlayer interface.Perforation in the upper sandstone layer has higher crack initiation pressure than that perforation in the coal seam.

1 模型建立

   1.1 尖锐裂缝的相场法近似

   1.2 水力裂缝相场演化控制方程

   1.3 多孔弹性介质应力与渗流控制方程

   1.4 边界条件

   1.5 数值求解

2 模型对比与验证

3 数值算例与分析

   3.1 地应力差

   3.2 层间界面强度

   3.3 层间界面渗透率

   3.4 注入速率

   3.5 射孔位置

4 结论