Model for Calculating Propped Fracture Conductivity in Deep Shale Reservoirs

Abstract

Shale gas is an important unconventional natural gas. Hydraulic fracturing has become one of the effective means in shale gas production and its goal is to form propped fractures with high conductivity. With the increase of shale gas exploitation depth, rock plasticity is stronger and proppant is more easily embedded, which leads to the decrease of propped fracture conductivity. Therefore, According to the elastic-plastic theory of the contact between the sphere and the plane, the formula for calculating the proppant embedment depth is derived from the stress equilibrium condition. Then, Kozeny-Carman equation is used to solve the propped fracture permeability. Finally, the propped fracture conductivity calculation model considering the stress parameters, rock parameters and proppant parameters is established. Based on the established model, the effects of rock yield strength, closure pressure, fracture fluid pressure, layer numbers of proppant filling and proppant size on propped fracture conductivity are analyzed. The results show that the fracture conductivity increases with the increase of rock yield strength in a power function. The smaller fluid pressure, larger closure pressure and less proppant filling layers will result in lower propped fracture conductivity. The conductivity of large-size proppant filling fractures is obviously higher than that of small-size proppant filling fractures. The calculation model provides a basis for fast and effective evaluation of fracture conductivity, and also provides a reference for how to improve the effect of fracturing in deep shale reservoirs.