Numerical Modeling of Proppant Embedment in Viscoelastic Formations with the Fractional Maxwell Model

Abstract

Hydraulic fracturing is often used to exploit unconventional hydrocarbons, and proppants are usually added during hydraulic fracturing to keep the fractures induced open. Nevertheless, time-dependent proppant embedment has often been neglected in previous studies. In this survey, the fractional Maxwell model is first proposed to describe the viscoelastic deformation of tight sandstones. Then, the fractional rheological model is incorporated into the finite element framework in ABAQUS to establish a numerical model to investigate the time-dependent embedment of proppants in viscoelastic formations. Parameter sensitivity studies are also performed to investigate the influences of the mechanical characteristics of proppants and formation on the embedment depth. Several factors that influence proppant embedment are also discussed.