Numerical prediction of the decline of the shale gas production rate with considering the geomechanical effects based on the two-part Hooke's model

The production rate of a typical shale gas well generally has steep decline trend at the initial stage but small declines at later times. Some empirical relationships have been proposed to describe the declining production rates and thus forecast the final cumulative production of a shale gas well. However, these empirical relationships can hardly elucidate the mechanisms that cause the special shale gas production trend. In this study, a novel two-part Hooke's model (TPHM) for the permeability and effective stress relationship is developed and incorporated into the hydro-mechanical COMSOL solver to determine the production rate of shale gas wells against time. The TPHM conceptualizes shale rock into soft part and hard part, which comply with the natural-strain-based and engineering-strain-based Hooke's laws, respectively, and contribute differently to the decreasing permeability with increasing effective stresses. The simulation results are analyzed and compared with those for which the permeability change effect is not considered. The analysis indicates that the decrease in stress-induced permeability plays a non-negligible part in the decline of the production rate.