Analytical model of hydraulic fracturing horizontal well gas production capacity of a water-bearing tight sandstone reservoir considering planar heterogeneity

Previous models of the gas-production rate of hydraulic fracturing horizontal wells were by assuming permeability heterogeneity, which is unrealistic in water-bearing tight gas reservoirs because of sandstone-mudstone crossover. Therefore, we develop an analytical model to describe the gas-production dynamics of hydraulic fracturing horizontal wells that considers permeability heterogeneity. In addition, threshold pressure gradient, stress sensitivity, and slippage are incorporated into the model. To solve this model analytically, the elliptical flow is transformed to radial flow by conformal transformation. The gas-production rate, reservoir pressure distribution, and average formation pressure are obtained by superposition principle, boundary pressures are calculated by material balance method, and the dynamic supply boundary propagation is modeled by steady-state sequential replacement. Actual field production data from Ordos Basin, China is used to verify the new model, which increases accuracy by 11.3% over previous models (98.6% versus 87.3%). The propagation distance of the dynamic supply boundary is predicted (in the fracture direction it is 109.3 m and in the vertical fracture direction it is 44.2 m). We analyze how stress sensitivity, the dynamic threshold pressure gradient, matrix permeability, pressure difference, and initial water saturation affect gas production rate and dynamic supply boundary. Based on orthogonal experimentation, the factors affecting the gas production rate and dynamic supply boundary of tight gas reservoirs can ranked in the following order: pressure difference > permeability > initial water saturation. This analytical model can accurately characterize gas production and pressure response, it is easy to use and rapid to calculate.