Lubrication model of suspension flow in a hydraulic fracture with frictional rheology for shear-induced migration and jamming.

We developed a model for suspension flow in a hydraulic fracture, taking into account frictional rheology to capture the effects of shear-induced particle migration, jamming and transition to close packing. One of the key issues with the existing slurry rheology models is that each of them diverges near the close packing limit, which is typically resolved in numerical simulations via a pragmatic (and mostly unjustified) regularization. Another drawback of the family of existing models for proppant transport in fractures is the assumption of a uniform cross-flow concentration profile, which neglects the effects of shear-induced migration. We developed a self-consistent model for slurry flow with a constitutive relation for suspension rheology, which is applicable in the entire range of particle volume concentration, from dilute suspension through dense suspension to the close packing limit. In addition, we investigated the influence of various constitutive relations for the suspension rheology on the final model for the slurry flow. The selected model for slurry flow was implemented into a two-dimensional lubrication model of proppant transport in a fracture (based on the two-continua approach), and illustrative simulations were conducted in comparison with the family of existing suspension rheology models (having a singularity). Validation against laboratory experiments is discussed.