Dispersion of solids in fracturing flows of yield stress fluids

Abstract eng:
Recent trends in the hydraulic fracturing have included the use of cyclic pumping of solid particles (proppant) interspersed with yield stress fracturing fluid, which is found to increase the subsequent productivity. We propose a model framework for this scenario and analyse one of the simplifications. A key effect of including a yield stress is to focus high shear rates near the fracture walls. In typical fracturing flows this results in a large variation in shear rates across the fracture. With shear-thinning viscous frac fluids, suspensions may vary on the particle scale from Stokesian behaviour to inertial behaviour across the width of the fracture. Equally, according to the bulk flow rates, Hele-Shaw style models give way at higher Reynolds number to those in which inertia must be considered. We develop the Suspension Balance Model of Nott and Brady [1] to include this range of flows, while still representing a significant simplification over fully three-dimensional computations. In relatively straight fractures and for fluids of moderate rheology, this simplifies into a one-dimensional model that predicts the solids concentration along a streamline within the fracture. We use this model to make estimates of the streamwise dispersion in various relevant scenarios.

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