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Dispersion of solids in fracturing flows of yield stress fluids

Published online by Cambridge University Press:  29 September 2017

S. Hormozi Open the ORCID record for S. Hormozi [Opens in a new window]  and
I. A. Frigaard Open the ORCID record for I. A. Frigaard [Opens in a new window]
S. Hormozi*
Affiliation:
Department of Mechanical Engineering, Ohio University, 251 Stocker Center, Athens, OH 45701, USA
I. A. Frigaard
Affiliation:
Departments of Mathematics and Mechanical Engineering, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, Canada V6T 1Z2
*
†Email address for correspondence: hormozi@ohio.edu
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Abstract

Solids dispersion is an important part of hydraulic fracturing, both in helping to understand phenomena such as tip screen-out and spreading of the pad, and in new process variations such as cyclic pumping of proppant. Whereas many frac fluids have low viscosity, e.g. slickwater, others transport proppant through increased viscosity. In this context, one method for influencing both dispersion and solids-carrying capacity is to use a yield stress fluid as the frac fluid. 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. In using shear-thinning viscous frac fluids, flows may vary significantly on the particle scale, from Stokesian behaviour to inertial behaviour across the width of the fracture. Equally, according to the flow rates, Hele-Shaw style models give way at higher Reynolds number to those in which inertia must be considered. We develop a model framework able 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. This model framework also predicts the transverse distributions of the solid volume fraction and velocity profiles as well as their evolutions along the flow part.

JFM classification

Low-Reynolds-number flows: Hele-Shaw flows Non-Newtonian Flows: Plastic materials Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 830 , 10 November 2017 , pp. 93 - 137
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© 2017 Cambridge University Press 

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