Abstract: The permeability of shale gas reservoirs is extremely low,and the formation is stress-sensitive strongly. The hydraulic fracturing is one of the effective exploitation methods. A composite shale gas reservoir model was established by introducing some gas migration mechanisms,such as shale gas adsorption and desorption,Knudsen diffusion,unsteady cross flow and seepage. Mathieu function,Pedrosa variable substitution,regular perturbation theory,Laplace transform and Stehfest numerical inversion methods were used to solve the mathematical model,and then the typical curves of dimensionless pseudo-pressure were plotted. The sensitivity analyses were conducted on the relevant parameters,such as permeability modulus,SRV radius,outer region fracture permeability,diffusion coefficient and desorption compressibility. The results show that the gas flow can be divided into nine stages. A larger permeability modulus resulted in a larger pressure difference required for gas well constant production. The larger the SRV radius and the desorption compressibility are,the smaller the pressure difference is. The larger fracture permeability in outer zone corresponds to a smaller mobility ratio. The larger the diffusion coefficient is,the larger the apparent permeability of the shale matrix is,and the earlier the cross flow occurs. The proposed well test model can improve the accuracy of pressure dynamic analysis of shale gas reservoirs and has certain theoretical guiding significance for fracturing development of shale gas reservoirs.

Key words: shale gas, composite model, pressure, stress sensitivity, elliptical SRV, fractured well