An XFEM-based numerical model to calculate conductivity of propped fracture considering proppant transport, embedment and crushing

The accurate conductivity evaluation of propped hydraulic fracture is crucial for the design and optimization of hydraulic fracturing treatments to achieve economic production of hydrocarbon. In this paper, a coupled numerical model in consideration of transport, placement, deformation, embedment and crushing of proppant is proposed to calculate the conductivity within the framework of the extended finite element method (XFEM). In the model, the fluid-solid coupling equations are simultaneously solved. The proppant transport is modeled using the upwind method. The Hertz contact model is used to obtain the width of propped fracture considering the deformation and embedment of proppant. A damage model is proposed to describe the conductivity reduction of the proppant pack due to grain failure. Size effects on the strength of proppant are considered using Weibull distribution and Griffith theory. After comparison with experimental data, the proposed model is employed to conduct sensitivity studies of several parameters on fracture conductivity. Results show that the most sensitive factor is proppant size, followed by proppant concentration, pumping rate of slurry, elastic modulus of proppant, and pumping strategy of proppant. The effects of elastic modulus of formation and Poisson's ratios of proppant and formation are negligible in comparison to other factors. It is also found that with the increase of proppant size, the fracture conductivity increases initially and decreases after reaching a peak. This paper contributes to a better understanding of the effects of related factors on fracture conductivity and provides a useful numerical tool for proppant selection in hydraulic fracturing design.