A 3-D analytical model for multi-stage fractured shale gas reservoirs with damaged fractures

After performing hydraulic fracturing treatments in shale reservoirs, the hydraulic fractures and their adjacent reservoir rocks can be damaged. Typically, the following fracture damage scenarios may occur: (1) choked fractures with near-wellbore damage; (2) partially propped fractures with unpropped or poorly propped sections within the fractures; (3) fracture face damage; and (4) multiple damage cases. The basic equations of fracture skin factors, which are widely used to depict fracture damage, are derived under steady-state conditions. They are not accurate when the damaged length is relatively long and are not applicable for multiple fracture damage and partially propped fractures. In this paper, a new composite linear flow 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 modified from de Swaan-O's spherical element model considering the slip flow, Knudsen diffusion, surface diffusion, and desorption. Natural fractures are idealized as a thin layer that evenly covers the matrix. The reservoir-fracture flow model is extended from the seven-region linear flow model with four additional sub-regions to handle single and multiple fracture damage mechanisms. Specifically, the inner reservoir region near the primary hydraulic fracture is treated as the SRV where the secondary fracture permeability is higher than that of other unstimulated dual-porosity regions and obeys a power-law decreasing trend due to the attenuate stimulation intensity within the SRV. The flows in different regions are coupled through flux and pressure continuity conditions at their interfaces. This model is validated by matching with the Marcellus Shale production data. And the degraded model's calculation matches well with that of the seven-region linear flow model validated by KAPPA software. Type curves with five typical flow regimes 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. Fracture face damage, choked fracture damage, and partially propped fractures all control specific flow regimes but the fracture face damage shows the smallest influence, only dominating the late fracture linear flow regime and the matrix-fracture transient regime. In the multiple fracture damage case, some typical flow regimes can be easily identified except the partially propped fractures. The field application example further ensures the applicability in dealing with real field data.