Conductivity analysis of tortuous fractures filled with non-spherical proppants

Abstract

Hydraulic fracturing is a widely used technique to exploit unconventional oil and gas reservoirs. Hydraulic fractures are naturally tortuous and rough in the formation, which has a significant impact on their permeability and conductivity. For a better understanding of this issue, a method combining the normal distribution random function and the quartet structure generation set was proposed to construct the 3D tortuous fracture. This method included three main steps of fracture seeding, fracture growing and geometric loft. The normal distribution random function was used in the seeding process to control the orientation and tortuosity of fractures. And then, four spheres were overlapped to form the non-spherical proppant, whose sphericities could be adjusted by the center distance and radius of these spheres. Random packings of these proppants in tortuous fractures were simulated by the discrete element method. Finally, the flowing pressure and velocity of fluid in fractures were calculated by the coupling model of elasticity and lattice-Boltzmann method. Also the accuracy of this model was verified by the classical Kozeny-Carman equation. The results show that the deformation of fracture surface under the closure pressure is larger in the area supported by less proppants. The permeability and conductivity of tortuous fractures decrease with the increase of the fracture tortuosity and the decrease of the size and sphericity of proppants, which are all related to the porosity and pore specific area of fractures. In terms of increasing the permeability and conductivity of fractures, there is an optimum value of the proppant sphericity, which is about 0.91 in this study. Although the fracture permeability decreases with the increase of the fracture width, its stress sensitivity becomes weaker. Therefore a higher fracture conductivity can be obtained in the fracture with larger width, especially under the high closure pressure. The findings of this study can help for better understanding of influence of fracture tortuosity and proppant sphericity on the fracture conductivity.