Computation model of proppant embedment depth based on dimensional analysis

Abstract

Hydraulic fracturing is designed to form a high-conductivity fracture. The proppant will embed into the formation rock, especially in soft rock, owing to the interaction between proppant and fracture surface after fracture closure. Proppant embedment would reduce the fracture width and then lower the fracture conductivity. According to dimensional analysis, the rock is assumed to be an elastic material. Using the theory of elasticity to describe the stage of elastic deformation and analysis of the corresponding simplified embedding process, the study establish the static computation model of the two-dimensional infinite half plane and three-dimensional infinite half space model of the proppant embedment. According to laboratory results, the calculation model was modified, got an effective correction factor and analyzed the causes of errors, then discussed the factors which have impact on proppant embedment. The result calculated by the model in this paper can be reference of proppant optimization in on-site fracturing for a certainty degree.