Improved Flow Material Balance Equation for Dynamic Reserve Calculation Considering Variable Gas Drainage Radius in Shale Gas Reservoirs

Based on the nonlinear relationship between the cumulative gas production and the total pressure difference, a segmental material balance equation was applied, and an improved flow material balance (FMB) equation was proposed to calculate the dynamic reserves of shale gas reservoirs with a variable gas drainage radius. In the early stage, the shale gas well drainage radius gradually increased. The spread range of the formation pressure increased, but fractures gradually closed because of the enhancement of the effective stress. This resulted in stress sensitivity. In the middle to late stages, the gas drainage radius can be regarded as unchanged. The rate of increase in the pressure spreading range decreased, and the rate of decrease in the fracture closure decreased. The stress sensitivity can be ignored. To explain these phenomena, a segmental material balance equation was established. Furthermore, an improved FMB equation was obtained based on the productivity equation using the potential superposition theorem, and the drainage radius of horizontal wells was regarded as a variable for the last dynamic reserve calculation. Finally, the dynamic reserves of four shale gas wells were calculated. The comparison indicated that the proposed improved equation predictions agreed more closely with actual development experience than the conventional models based on the dynamic recovery rate calculation and the correlation coefficient obtained by data fitting. The proposed method improves the dynamic reserve calculations and contributes to well productivity evaluation.