Rate Decline Analysis of Vertically Fractured Wells in Shale Gas Reservoirs

Based on the porous flow theory, an extension of the pseudo-functions approach for the solution of non-linear partial differential equations considering adsorption-desorption effects was used to investigate the transient flow behavior of fractured wells in shale gas reservoirs. The pseudo-time factor was employed to effectively linearize the partial differential equations of the unsteady flow response. The production performance of vertically fractured wells in shale gas reservoirs under either constant flow rate or constant bottom-hole pressure conditions was analyzed using the composite flow model. The calculation results indicate that the non-linearities that develop in the gas diffusivity equation have significant effects on the unsteady response, leading to a larger pressure depletion and rate decline in the late-time period. In addition, gas desorption from the shale acts as a recharge source, which relieves the gas production rate of decline. Greater values for the Langmuir volumes or Langmuir pressures provide additional pressure support, leading to a lower rate decline while the flowing well bottom-hole pressure is maintained. The reservoir size mainly affects the duration of the pressure depletion and rate decline. In the case of ignoring the non-linearity and adsorption-desorption effect in the differential equation, a greater rate decline under constant bottom-hole pressure production can be obtained during the boundary-dominated depletion. This work provides a better understanding of gas desorption in shale gas reservoirs and new insight into investigating the production performances of fractured gas well.