Model for fracture conductivity considering particle size redistribution caused by proppant crushing

Abstract

Clarifying the dynamic evolution and control mechanisms of fracture conductivity is crucial for optimizing hydraulic fracturing design. Previous studies on fracture conductivity mechanisms in deep shale reservoirs have been insufficient, particularly when considering proppant crushing, rendering existing models inapplicable. Therefore, in this study, the coupled effects of particle size redistribution caused by proppant crushing were considered. A particle crushing model based on fractal theory was introduced. It was combined with the Kozeny–Carman equation, and equations were derived for the evolution of the equivalent diameter of the proppant pile gradation curve and permeability, establishing a new model for predicting the fracture conductivity considering the particle size redistribution caused by proppant crushing. Furthermore, it provides an optimized chart of conductivity that matches the supply conductivity of the reservoir. The results of the study reveal that the fracture conductivity decreases owing to proppant rearrangement, compaction, and crushing, with a more significant decline in the initial compression stage, where the rate of conductivity reduction is 2.5 times that of the compaction stage. Proppant crushing shifts the gradation curve leftward, reducing the equivalent particle diameter and, consequently, the fracture conductivity. By adjusting the crushing ratio, apparent Young's modulus, looseness factor, and proportion of large-particle components of the proppant, the fracture conductivity can be controlled. This provides a theoretical basis for the development of proppant properties and fracturing optimization in deep shale reservoirs.