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Proppant embedment mainly accounts for diminishing fracture aperture and conductivity. The conductivity decrease could greatly restrict fluid flow, thereby affecting the well performance. In this paper, new mathematical models are derived to calculate the proppant embedment and fracture conductivity after hydraulic fracturing. These models take three crucial factors into consideration, including proppant instantaneous elastic deformation, the conductivity change over time, and effective fracture geometry and corresponding proppants amount. Fitting correction is performed for the new theoretical model based on the experimental data. The results show that the theoretical model proposed matches well with the experimental data. The fracture conductivity is in proportion to proppant viscosity, elastic modulus of proppant and in inverse proportion to closure pressure, while elastic modulus of rock and large value of formation rock viscosity have slight impact on fracture conductivity. Moreover, with the increase of proppant viscosity, it takes longer for the conductivity to come to the steady state. These new mathematical models can provide some insights for proppant size selection and sand ratio optimization of fracturing treatment, and it is also a good method to predict the proppant embedment and the fracture conductivity.

Theoretical Analysis of Proppant Embedment and Fracture Conductivity in Fractured Reservoir