After the volume fracturing of shale gas reservoirs

due to the abrupt variations in the pore scale of the gas seepage and the severe difference between the characteristics of shale matrix and fractures

the seepage velocity field showed a sharp discontinuity

resulting in the failure of continuum assumption. In order to accurately understand the flow pattern of shale gas reservoirs and analyze the productivity

based on the trilinear flow model of fractured horizontal wells in shale gas reservoirs and coupled with the anomalous diffusion equation of fractal porous media

we established a fractured horizontal well productivity model of shale gas reservoirs. The dimensionless production was obtained by Laplace transform and Stehfest numerical inversion. Finally

we analyzed its result combining specific example and obtained a dimensional production curve. The analysis results showed that five flow regions for shale gas could be identified

including the linear flow stage of hydraulic fractures

the bilinear flow in hydraulic fractures and natural fractures

the linear flow stage of natural fractures

the bilinear flow in natural fractures and matrices

and the phase of matrix linear flow. Based on the production model

we also studied the influence of anomalous diffusion exponent

pseudo-permeability

storability ratio

fracture spacing and the like. on the production of shale gas reservoirs. The results indicated that the smaller abnormal diffusion exponent and the stronger matrix heterogeneity were

the more obvious decrease of productivity would be

and the natural fractures pseudo-permeability had great impact on the length of time in the linear flow of the natural fractures. Furthermore

the hydraulic fracture pseudo-permeability could influence the productivity in the whole middle-late production cycle. The larger the storability ratio was

the more obvious increase amplitude of productivity would be. The research provided a new idea and method for productivity analysis and evaluation of shale gas reservoirs.