Effect of proppant deformation and embedment on fracture conductivity after fracturing fluid loss

Fracture conductivity after fracturing fluid loss is significant for the optimization of pumping schedule and the productivity modeling. A new model was established to evaluate the fracture conductivity under closure pressure, considering the proppant deformation and the mechanical properties of the shale. The deformation of proppants and formation rock and the embedment of proppants were calculated by the contact mechanics. The average pore radius in the fracture was calculated. After matching the simulated embedment with experimental data, the mechanical properties of shale after fluid loss were obtained. Based on that, a mathematical model combined with Kozeny-Carman correlation was established. The accuracy of this model was also verified by experimental data. The simulation shows that the change of the mechanical properties of shale leads to more nonlinear variation of the fracture conductivity. Improving the fracture aperture is a better way to improve the fracture conductivity compared with raising the fracture permeability.