Pressure transient analysis of multistage fracturing horizontal wells with finite fracture conductivity in shale gas reservoirs

A new analytical solution of pressure transient analysis is proposed for multistage fracturing horizontal well (MFHW) with finite-conductivity transverse hydraulic fractures in shale gas reservoirs. The effects of absorption, diffusion, viscous flowing, stress sensitivity, flow convergence, skin damage and wellbore storage are simultaneously considered as well in this paper. Laplace transformation, source sink function, perturbation method and superposition principle are, respectively, employed to solve related mathematical models of reservoir system and hydraulic fracture system. And then boundary element method (BEM) is applied to couple reservoir system and hydraulic fracture system. The transient pressure is inverted from Laplace space into real time space with Stehfest numerical inversion algorithm. Based on this new solution, the distribution of transient pseudo-pressure for MFHW with multiple finite-conductivity transverse hydraulic fractures is obtained. Different flowing regimes are identified, and the effects of relevant parameters are analyzed as well. The essence of this paper is considering the effects of transient gas flowing occurrence in finite-conductivity hydraulic fractures with BEM. Compared with some existing models and numerical simulation model of shale gas reservoirs, this proposed new model can provide a relative more accurate analysis of the relevant parameters, especially for the fracture conductivity. In conclusion, this new model provides the relative accurate and comprehensive evaluation results for multistage fracturing horizontal technology.