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Although great success has been achieved in the shale gas industry, accurate production dynamic analyses is still a challenging task. Long horizontal wells coupling with mass hydraulic fracturing has become a necessary technique to extract shale gas efficiently. In this paper, a comprehensive mathematical model of a multiple fractured horizontal well (MFHW) in a rectangular drainage area with a rectangular stimulated reservoir volume (SRV) has been established, based on the conceptual model of “tri-pores” in shale gas reservoirs. Dimensionless treatment and Laplace transformation were employed in the modeling process, while the boundary element method was used to solve the mathematical model. The Stehfest numerical inversion method and computer programing techniques were employed to obtain dimensionless type curves, production rate, and cumulative production. Results suggest that 9 flow stages can be observed from the pseudopressure derivative type curve when the reservoir and the SRV are large enough. The number of fractures, SRV permeability, and reservoir permeability have no effect on the total production when the well is abandoned. As SRV and reservoir permeability increases, the production rate is much higher in the middle production stage. Although the SRV scale and its permeability are very important for early and intermediate production rates, the key factors restricting the shale gas production rate are the properties of the shale itself, such as adsorbed gas content, natural fractures, and organic content. The proposed model is useful for analyzing production dynamics with stimulated horizontal wells in shale gas reservoirs.

A Model for a Multistage Fractured Horizontal Well with Rectangular SRV in a Shale Gas Reservoir