统一管道–界面单元法的构建及其在水力压裂模拟中的应用

Development of an unified pipe-interface element method and its application in hydraulic fracturing simulation

为了模拟可渗透性孔隙裂隙介质中的水力压裂,提出了一种新的数值计算方法,即统一管道-界面单元法(UP-IEM)。该方法提出了2个"统一"的概念:(1)将二维平面中的裂隙劈裂和流体流动统一为一维管道问题;(2)将岩体基质管道和裂隙管道统一为具有不同导水系数的相同管道,使用同一套数学方程计算流体流动。解决了传统的离散裂隙网络介质模型难以考虑岩体基质渗透性的难点。同时,该方法引入界面单元计算裂隙扩展,与传统有限单元法以及离散单元法相比,既不需要局部裂纹扩展准则,也不需要跟踪算法,具有计算速度快,计算效率高的优点。采用孔隙弹性理论和有效应力概念描述岩体基质的变形,在界面单元中采用黏聚性区域模型描述水力裂隙扩展,采用接触-摩擦模型模拟自然裂隙的闭合和滑移,基于达西流流动理论计算孔隙介质和裂隙中的流体流动。针对流-固强耦合计算过程,建立了半显式求解的计算框架。模拟了经典的Terzaghi固结测试、非对称四点梁弯曲测试和KGD裂隙扩展模型,通过将数值结果与解析解和物理试验结果进行对比,分别验证了UP-IEM模拟流体流动、裂纹扩展以及水力压裂问题的准确性及适用性。此外,建立单一自然裂隙和复杂裂隙网络模型,分析水力裂隙与预存在裂隙之间的相互作用,获得原岩应力对裂隙扩展路径的影响。研究表明,UP-IEM能够有效模拟离散裂隙岩体中的水力压裂过程。

This paper proposes a novel method,named as unified pipe-interface element method(UP-IEM),for modelling the hydraulic fracture propagation in a permeable porous medium. There are two unified processes including the combination of the fluid flow and the fracture propagation into 1 D pipe element and the unification of the matrix pipe and the fracture pipe as a same pipe with different hydraulic conductivities for solving the fluid flow using the same mathematical equations. UP-IEM overcomes the difficulties to consider the rock matrix permeability of traditional discrete fracture network model. The interface element is introduced to simulate the fracture propagation. For UP-IEM which has high efficiency,neither local crack propagation criteria nor tracking algorithms are required compared with traditional FEM and DEM. The deformation of the rock matrix is described by poroelasticity theory and effective stress concept. The cohesive zone model is used to simulate hydraulic fracture propagation and the contact-frictional model is utilized to model closure and slip of natural cracks.Besides,the fluid flow in porous medium and fractures is solved using Darcy law. A semi-explicit frame is built to solve the hydro-mechanical coupling problems. Three typical examples,including Terzaghi’s consolidation test,unsymmetric four-points bending test and KGD model,are simulated. The simulation results are compared with analytical solutions and experimental results,verifying the accuracy and applicability of UP-IEM simulating fluid flow,fracture propagation and hydraulic fracturing. Furthermore,the hydraulic fracturing in models with single natural fracture and complex fracture network is simulated,analyzing the interaction between hydraulic fractures and pre-existing fractures and discussing the influence of in-suit stresses on the fracture propagation path. These examples show that UP-IEM could effectively simulate the hydraulic fracturing in discrete fractured rock.