Modelling of time-dependent proppant embedment and its influence on tight gas production

Abstract

Hydraulic fracturing is typically used to exploit underground gas/oil resources. However, most commercial fracture-design programs and reservoir simulators neglect proppant embedment issues when calculating hydraulic the fracture width, and the majority of previous studies regarding proppant embedment treat the reservoir rocks as time-independent materials–elastic or elastoplastic. In this study, the time dependent deformation of tight reservoir rocks is validated through laboratory experiments, and the fractional Maxwell model is utilized to characterize the viscoelastic deformation of tight sandstones. Combining the fractional rheological model with the Hertz contact theory, an analytical model of fracture width, which considers the time-dependent embedment depth of proppants, is established. Utilizing this analytical model of fracture width, numerical simulations are conducted to study the viscoelastic deformation of tight sandstones on the long-term accumulative production of tight gas. Numerical simulations of a fifteen-year cumulative production tight gas well indicate the long-term gas production, which considers the creep characteristics of a tight sandstone reservoir, experiences a 40% reduction when compared to the production of a linear elastic reservoir. Therefore, consideration of the viscoelastic characteristics of reservoir rocks to predict the long-term oil/gas production is extremely significant.