页岩储层裂隙渗透率模型和试验研究

Fracture permeability model and experiments of shale gas reservoirs

页岩储层的裂隙渗透率是评价页岩气开采的重要参数,基于裂隙法向刚度的概念,考虑页岩储层变形过程中裂隙系统和基质系统之间的相互作用以及页岩气解吸引起的体应变,提出了与有效应力相关的页岩储层的渗透率模型。然后分别分析了页岩气藏在单轴应变和常体积条件下的渗透率模型,分析表明,单轴应变和常体积条件下(3个方向的总应变都为0)的裂隙渗透率模型完全一致。采用脉冲衰减渗透率仪测试了煤系页岩的裂隙渗透率,当有效应力从0.7 MPa增加到14.5 MPa时,渗透率从41.81×10-17m2降到5.43×10-17m2。为了阐述渗透率模型的有效性,利用煤系页岩的渗透率数据对有效应力-渗透率模型进行拟合。结果表明,当裂隙的法向刚度、张开度和煤系页岩的初始渗透率分别为57 922.5 MPa/m、0.000 17 m和50.15×10-17m2时,有效应力-渗透率模型和煤系页岩的渗透率拟合程度较好。然后利用现场渗透率数据对该模型进行拟合,结果表明,当裂隙的法向刚度和张开度的关系符合反比例函数时,拟合程度非常好。该渗透率模型适合于单轴应变、常体积和常围压条件,可用于描述页岩气开采过程中页岩储层裂隙渗透率随孔隙压力的变化规律。同时,该渗透率模型和P&M模型以及S&D模型进行了比较,结果表明,该渗透率模型的拟合结果与S&D模型基本一致,但与P&M模型存在一定的差别。

The fracture permeability of shale gas reservoirs is an important parameter when estimating the shale gas extraction. On the basis of the fracture normal stiffness concept, the effective stress-dependent permeability model for shale gas reservoirs is proposed, which considers fracture-matrix interaction and gas desorption induced volumetric strain during shale formation deformation processes. Then, the models for gas shale under uniaxial strain and constant volume conditions are analyzed. Theoretical analysis indicates that the fracture permeability model under uniaxial strain conditions is consistent with the one under constant volume conditions（the total strains in all directions are equal to zero）. The fracture permeability of shale in coal measures is measured with pulse decay permeameter. Permeability decreases from 41.81×10-17m2 to 5.43×10-17m2 while effective stress increases from 0.7 MPa to 14.5 MPa. To verify the effective stress-dependent permeability model, first, the effective stress-permeability model is calibrated with fracture permeability data. Results indicate a good match with the permeability of shale while the fracture normal stiffness, the aperture and the initial fracture permeability are 57 922.5 MPa/m, 0.000 17 m, and 50.15×10-17 m2, respectively. Then,the permeability model is calibrated with field measured permeability. Results show a remarkable match with the field permeability when the relationship between the fracture normal stiffness and the fracture aperture conforms to the inverse proportional function.The proposed permeability model is adaptable to uniaxial strain, constant volume and constant confining stress conditions. It can describe the changes of the fracture permeability of shale formation with pore pressure during shale gas extraction. And then, the comparison between the proposed model and other models is made. Results demonstrate that the match results of the permeability model are basically consistent with SD model, but showing a bad match with PM model.