Calculation model of shale fracture compressibility and evolution of permeability under water-bearing conditions

Water saturation of shale reservoirs significantly influences the permeability and compressibility of propped fractures. This study focused on the Longmaxi Formation shale reservoir in northern Guizhou, China, where the permeability of water–saturated shale under varying gas and confining pressures was measured. A compressibility model for proppant embedment and compaction deformation was developed and validated against the experimental results. This study examined the compressibility of supported fractures considering water–rock interactions and elucidated the intrinsic relationship between compressibility and water saturation. The findings demonstrated a decreased trend in shale fracture permeability with increasing water saturation under identical conditions. Compared to dry shale, the permeability decreased by 1.2%–16.4% and 2.0%–17.8% at water saturation of 15% and 50%, respectively. The results of the model calculations demonstrate that fracture compressibility is contingent on the degree of variation of the fracture width. Prolonged water–rock interactions intensified the variation in the fracture width increasing the compressibility under the same stress conditions. As the water saturation increased from 0% to 50%, the fracture closure rate increased from 0.034 to 0.179 with the increase in effective stress. Increased water saturation also increases the sensitivity of the fracture compressibility to effective stress while decreasing the elastic modulus of the rock, thereby enhancing the proppant embedment depth and significantly increasing the fracture compressibility. This study provides critical insights into the dynamic evolution of fracture permeability during hydraulic fracturing and offers valuable implications for gas production forecasting.