致密砂岩气水两相流固耦合裂缝动态闭合分析半解析模型

A semi-analytical model coupled gas-water two-phase flow and geomechanics for dynamic closure analysis of fractures in tight sandstone

在致密砂岩气井压裂液返排和早期生产阶段,由于支撑剂回流和储层压降易于造成裂缝不同程度的闭合,从而导致产能的部分损失。为了分析这一关键问题,提出了用于预测压裂液返排和致密气藏早期开发产能的渗流—地质力学方程组完全耦合的半解析数学模型及求解方法,该方法可用于捕捉裂缝的动态行为并获取相关重要参数,以优化致密气开发策略。其中,结合致密气井普遍产水的矿场实际,建立了裂缝系统气水两相渗流方程组;根据裂缝表面不同受力关系,分别建立了人工裂缝与天然裂缝的力学方程,采用了裂缝开度与作用于裂缝壁面的接触应力间的非线性关系描述裂缝闭合;以迭代耦合方式求解渗流—地质力学耦合系统,采用了有限差分法对裂缝内流动求取数值解,获取裂缝的传导率初始分布,通过位移不连续法计算裂缝开度变化,并在渗流方程组中更新迭代以得到气水两相的流体压力与饱和度分布。将该模型与经典解析解及商业模拟软件的计算结果进行对比,验证了解的准确性。将其应用于鄂尔多斯盆地东缘某致密气田的实例井分析,研究表明:在返排及开发早期阶段,裂缝开度随着缝内压力降低而逐渐减小,在井筒射孔点、裂缝相交处、裂缝尖端更容易趋于闭合;由于裂缝成因不同,人工裂缝与天然裂缝有着不同的闭合机制,受支撑剂作用的影响,人工裂缝闭合程度要明显小于天然裂缝;通过拟合实测生产历史数据,能有效评估裂缝的关键参数。该研究对于综合利用早期生产数据准确预测气井产能及控压生产理念的提出具有重要的理论和现实意义。

During fracturing fluid flowback and the early production stage of tight sandstone gas wells,proppant flowback and reservoir pressure drop are possible to cause fracture closure to varying degrees,resulting in par⁃tial loss of productivity.To analyze this key problem,a fully coupled semi-analytical mathematical model and solution method of flow and geomechanical equations were proposed for predicting fracturing fluids flowback and early development productivity of tight gas reservoirs.This method can be used to capture the dynamic be⁃havior of fractures and obtain relevant important parameters to optimize development strategies for tight gas res⁃ervoirs.Among them,the gas-water two-phase flow equations of fracture systems are established based on the field practice of water production in tight gas wells.According to the different stress relationships on the fracture surface,the mechanical equations of artificial and natural fractures are established respectively.The nonlinear re⁃lationship between the fracture aperture and the contact stress acting on the fracture wall is used to describe the fracture closure.The coupling system of flow and geomechanics is solved by the iterative coupling method.The finite difference method is used to obtain the numerical solution of the flow in fractures and obtain the initial dis⁃tribution of fracture conductivity.The change of fracture aperture is solved by the displacement discontinuity method,and updating the iteration in the fluid flow equation group to obtain the pressure and saturation distribu⁃tion of gas and water phases.The model results in this paper are compared with the classical analytical solutions and the commercial simulation software Abaqus to verify the accuracy of solutions.It is applied to the case analy⁃sis of tight gas fields in the eastern margin of Ordos Basin.The research result shows that:in the early stage of flowback and development,the fracture aperture gradually decreases with the decrease of the pressure inside the fracture,and tends to close more easily at the wellbore perforation point,fracture intersection,and fracture tip.Due to the different causes of fractures,artificial fractures and natural fractures have different closure mecha⁃nisms.Affected by the effect of proppant,the closure degree of artificial fractures is smaller than that of natural fractures.By fitting the measured production history data,the key parameters of fractures can be effectively evalu⁃ated.This study has important theoretical and practical significance for accurately predicting gas well productivity and proposing the concept of controlled-pressure production by comprehensively utilizing early production data.