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The formation of a complex fracture network with sufficient proppant conductivity is crucial for the efficient development of deep shale gas. Due to cost considerations, quartz sand has commonly replaced ceramic proppant in the field. However, the significant crushing of quartz sand and its distribution as multiple particle sizes both before and after crushing, termed as particle size redistribution, raises concerns about its ability to meet the demands of the fracture network. Based on contact mechanics, we developed an evolutionary equation for fracture width that considers particle size redistribution. The particle crushing is described using a fragmentation replacement method, and changes in specific surface area before and after crushing are used to correct the permeability model of the fracture. By integrating models of fracture width and permeability evolution, we have established an analytical model for proppant conductivity that accounts for quartz sand crushing and its particle size redistribution. Numerical simulations further validate the predictive accuracy of our model. Sensitivity analyses investigate the impact of quartz sand degree of crushing, compressive strength, particle size, particle combination ratio, and closure pressure on fracture conductivity, demonstrating the reliability of quartz sand as a substitute for ceramic proppant in deep shale applications.
Liu et al. (Mon,) studied this question.