Rod-Shaped Proppant Conductivity of a Hydraulic Fracture Considering Elastic-Plastic Deformation and Embedment: An Analytical Model

Hydraulic fracturing with a proppant is widely employed to create fracture networks and enhance the conductivity of unconventional oil and gas reservoirs. However, the proppant conductivity tends to decrease due to the increasing closure pressure and temperature during long-term production. Hence, it is of great significance to quantitatively characterize the effects of thermal expansion and mechanical behaviors of proppant deformation and embedment on hydraulic fracture conductivity. In this paper, an analytical model is proposed for revealing physical relations between rod-shaped proppant conductivity and various impacting factors, and the model is validated against available experimental data. Results show that with increasing closure pressure and temperature, the rod-shaped proppant experiences pure elastic, elastic-plastic, pure plastic deformation, and linear thermal expansion, which leads to a declining proppant conductivity. Effects of critical parameters on the proppant deformation and proppant conductivity evolution are also investigated. Specifically, the proppant conductivity shows a positive relationship with the proppant aspect ratio. It is also found that with increasing closure pressure, the proppant conductivity variation can be divided into five stages. This model provides insights into the proppant deformation, embedment, and productivity, by which suggestions can be offered to optimize the parameter design in the hydraulic fracturing process, helping to realize the efficient extraction of unconventional oil and gas reservoirs.