Shear-induced volumetric response and particle normal stress partitioning in proppant sand dunes within a single-wing fracture

Abstract

Fluid-induced shear acting on proppant particles affects their transport distribution. It also influences the morphological evolution of sand dunes. However, the role of shear-induced contraction/dilatancy responses in this evolution remains insufficiently understood. Therefore, an existing solid-phase dilatancy/contraction formulation is incorporated into an Eulerian two-phase flow framework to investigate the effects of injection velocity and particle size on proppant transport and sand dune morphological evolution, with particular emphasis on the relationship between shear-induced volumetric response and the partitioning of particle normal stress between the shear-induced and permanent-contact components. The results show that, with increasing injection velocity, sand dune morphological evolution is closely associated with an increasingly dilated packing state in the surface layer. As the injection velocity increases from 0.25 to 1.0 m/s, the surface layer packing state becomes increasingly dilated relative to the local critical packing condition, with the corresponding surface averaged response metric reaching approximately 11.1 times its value at 0.25 m/s, while the local permanent-contact stress in the surface layer decreases by approximately 18.9%. These results indicate that the intensified surface layer response, associated with this increasingly dilated packing state, is accompanied by a reduced permanent-contact contribution to the local particle normal stress and enhanced downstream particle redistribution. Under a fixed injection velocity, decreasing particle size shifts the depositional region farther downstream, while the locally averaged permanent-contact normal stress in the surface layer decreases by approximately 49.8%. Taken together, these results further elucidate the relationship between shear-induced volumetric response and continuum scale particle normal stress partitioning, as well as the association of stress partitioning with variations in sand dune morphology.