考虑虚拟边界与应力耦合的页岩渗透率模型

Shale permeability model considering virtual boundary and stress coupling

为探讨页岩气开采过程中页岩渗透率的变化情况,基于毛细管层序模型,采用虚拟边界与应力耦合相结合的方法,按照一定权重系数将应力推导黏性流动和克努森扩散相加,建立了页岩纳米孔体相气体传输模型。结果表明:新建渗透率模型计算曲线与试验实测值吻合较好,可以较好揭示页岩纳米孔体相气体流动情况;与Lu模型和S&D模型相比,新建模型考虑虚拟边界与应力的耦合,表观渗透率模型计算曲线与试验结果更为吻合,且能很好地反映实测值与孔隙压力所呈现的变化规律,具有较好的优越性;页岩力学参数(弹性模量、泊松比)、Langmuir应变常数及裂隙压缩系数对页岩渗透率起抑制作用,主要表现为其值越大,页岩渗透率越小;初始渗透率对页岩渗透率起促进作用,表现为其值越大,页岩渗透率越大。研究成果可为页岩气开发提供理论支撑。

In order to study shale permeability variation during shale gas production,based on capillary layered se-quence model,a shale nanopore bulk gas transport model is established by combining virtual boundaries and stress coupling and adding stress-derived viscous flow and Knudsen diffusion according to certain weighting factors.The results show that the calculated curve of new established permeability model is in good agreement with measured value,which can better reveal gas flow in shale nanopore bulk phase.Compared with Lu model and S&D model,the newly model in this paper considers coupling of virtual boundary and stress,and calculated curve of apparent permeability model is more consistent with experimental results,and it can well reflect variation law of measured values with pore pressure,showing much advantages.Mechanical parameters of shale(elastic modulus and Poisson’s ratio),Langmuir strain constant and fissure compressibility factor have inhibitory effect on shale permeability,mainly manifesting that the higher the values are,the lower the shale permeability is.Initial permeability has pro-moting effect on shale permeability,manifesting that the higher its value is,the higher the shale permeability is.The research provides theoretical support for shale gas development.