An Analytical Model of Artificial Fracture Closure Under Elastoplastic Deformation

Abstract

The closure of artificial fractures is one of the most complicated problems in the development of unconventional oil and gas reservoirs. Aiming at modifying the current theoretical models, an analytical model of the contact process was proposed with due regard for elastoplastic deformation. The constructed model is based on Hertz’s elastic contact equations and can be used to interpolate an exponential function. A numerical analysis method was used to derive the equation of state to determine the rigidity and asperity of the alastoplastic phase for all the deformation phases. The correlation between average contact pressure and fracture closure of the entire rough surface was established using probability statistics. Compared with the classical models, this analytical model is easier to consruct and use. As the new model takes into account all the deformation phases, it describes the fracture surface contact behavior well with increasing normal stress. Comparison has shown that the results calculated by the developed model are in agreement with the finite-element-based Kogut-Etison (KE) model.