A coupled extended finite element approach for modeling hydraulic fracturing in consideration of proppant

Due to its influence on the stress field around the propped fractures in horizontal well and the final conductivity of the created fracture network, the transport and packing of proppant plays a significant role in hydraulic fracturing. Therefore, it is important to describe the distribution of proppant in fractures and to accurately model the propped fractures. To this aim, a two-dimensional fully coupled model based on the extended finite element method (XFEM) is established, which takes into account some crucial physical processes, including rock deformation, fracturing fluid flow, fracturing fluid leak-off, propagation of fractures, proppant transport and proppant packing. The fluid-solid coupling equations are solved by the Newton-Raphson method and the proppant transport is evaluated by the upwind scheme. The hexagonal close packing of proppant is used to calculate the width of propped fracture. By taking advantage of the characteristic features of XFEM, an efficient strategy to model the propped fracture is proposed by directly enforcing the displacement boundary conditions on relevant enriched degrees of freedom without adding additional elements. The proposed coupled approach is validated by comparison with existing literature. The results of the sequential fracturing show that the propagation path of the subsequently created fracture is strongly affected by the boundary conditions (i.e., sliding contact, filled with constant pressure fluid, or propped open by proppant) imposed on the previously propped fracture, and the proposed XFEM-based strategy to model the propped fracture is an accurate and efficient alternative. Further sensitivity analysis reveals that the fracture spacing and the proppant concentration of the injected slurry also have significant influence on propagation path of the subsequently created fracture. The advantages of XFEM make the proposed coupled approach an attractive tool for the design of hydraulic fracturing.