Abstract: 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 41.81×10-17 m2 to 5.43×10-17 m2 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 S&D model, but showing a bad match with P&M model.

Key words: shale in coal measures, matrix shrinkage, dual porosity medium, fracture permeability, fracture normal stiffness