Investigation of Fracture Width Change under Closure Pressure in Unconventional Reservoir Based on the Hertz Contact Theory

To describe the fracture width is crucial for the flow conductivity evaluation, which influences the exploitation efficiency of unconventional oil and gas resources. Commonly, as the proppants fill in the fracture, the deformation will happen under the closure pressure to resist the fracture width change. Therefore, it is significant to develop the theoretical model to predict the variation. In this work, the mathematical model for the propping behavior of proppants in the fracture under closure pressure is established based on the Hertz contact theory. Compared with the existing models, the developed model considers both the proppant insertion and the elastic compression among the proppants, which is closer to the actual physical process. Furthermore, the experimental cases with different proppant sizes are taken to verify the model, and the good conformity presents its rationality. The parameter sensitivity analysis of this model shows that the fracture width change increases with the increase of the average diameters of proppants ( D ) and it declines with the improving of proppant elasticity modulus ( E 1 ) and Poisson’s ratio ( v 1 ).