Numerical simulation of proppant transport in hydraulic fractures with length-dependent variable aperture

Hydraulic fracturing is vital for enhancing oil and gas production. Proppant transport governs fracture conductivity and is therefore critical. Most studies simplify fractures as constant-width structures, inconsistent with real variable-width fractures.This paper establishes numerical models for proppant transport in variable-width fractures and networks via a solid-liquid two-phase flow method.The results show that, compared to constant-width fractures, variable-width fractures exhibit abrupt changes (reduction) in proppant bank height at width transition points, and the proppant bank trailing edge length is significantly shorter. Proppant particle size has a significant impact: smaller particle sizes increase the leading-edge length by up to 6.7 times and reduce the leading-edge inclination angle by up to 0.22 times. Perforation location greatly influences proppant vortices: when space near the fracture entrance is limited, only a counterclockwise vortex forms near the bottom perforation; if sufficient space exists between the proppant bank and the fracture entrance, besides counterclockwise vortices near the bottom and top perforations, a clockwise vortex forms slightly away from the entrance along the outer edge of the proppant bank; no vortices form in regions far from the fracture entrance. This study provides a new approach for researching proppant transport laws in irregularly shaped fractures.