Analytical solutions for multi-stage fractured shale gas reservoirs with damaged fractures and stimulated reservoir volumes

After performing hydraulic fracturing in shale reservoirs, the hydraulic fractures and their adjacent rocks can be damaged. Typically, the following fracture damage scenarios may occur: (1) choked fractures; (2) partially propped fractures with unpropped or poorly propped sections at the middle or tail of fractures; (3) fracture face damage; and (4) multiple damage cases. The classical fracture skin factors are derived under steady-state conditions. They are not accurate when the damaged length is relatively long and are not applicable for multiple damage and partially propped fractures. In this article, a new analytical model is established considering all above-mentioned fracture damage mechanisms, complex gas transport mechanisms, and the stimulated reservoir volume (SRV) of shale gas reservoirs. The matrix model is a spherical element model considering the slip flow, Knudsen diffusion, surface diffusion, and desorption. Natural fractures are idealized as a thin layer that evenly envelops the matrix. The reservoir-fracture flow model is a ten-region linear flow model which can handle fracture damage mechanisms. Specifically, the inner reservoir region is treated as an SRV where the secondary fracture permeability obeys a power-law decreasing trend due to the attenuate stimulation intensity. This model is validated by matching with the Marcellus Shale production data. And the degraded model's calculation matches well with that of a published linear flow model. New type curves are generated and sensitivity analyses are conducted. Results indicate that the presence of the SRV diminishes pressure and derivative values in certain flow regimes depending on the SRV properties. Different damage mechanisms all control specific flow regimes but the fracture face damage shows the slightest influence. In the multiple fracture damage case, some typical flow regimes can be easily identified except those induced by the partially propped fractures. The field application example further ensures the applicability in dealing with real field data.