Influence of Proppant Size on the Proppant Embedment Depth

[Image: see text] Hydraulic fracturing is a well stimulation technique involving the fracturing of bedrock formations by a pressurized liquid, in which proppants are added to keep the fracture open after the fracturing operation. The scale discrepancy between the rock specimen and the proppant may bring deviations in the analysis of proppant embedment depth if the fluid-deteriorated formation is treated as an isotropic medium. This study tries to uncover the origins of these deviations through numerical and analytical analyses. The fluid-deteriorated formation is first modeled as a layered rock to obtain equivalent elastic parameters under isotropic conditions. Then, the equivalent parameters are used in the numerical modeling of proppant embedment. The numerical simulations indicate that the simplification of the fluid-deteriorated formation into an isotropic rock results in an underestimation of the proppant embedment depth, and this deviation increases with the scale contrast between rock specimens and proppants. Hertz contact theory is utilized to explain this deviation. As a promising technique, the nano/micro-indentation is also proposed to depict the fluid-deterioration effect along the depth. This study provides methods for the calibration of mechanical parameters of fluid-deteriorated rocks in the analysis of proppant embedment.