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Dontsov, E. V.; Peirce, Anthony

The goal of this study is to analyze the steady flow of a Newtonian fluid mixed with spherical particles in a channel based on a continuum model, where the constitutive behaviour of the slurry is approximated by an empirical formula. In order to account for the gravitational settling of particles, two-dimensional flow needs to be considered as the pressure gradient and gravity may not always be collinear. It is shown that the problem under consideration features a boundary layer, whose size is on the order of the particle radius. The expressions for both the outer (i.e. outside the boundary layer) and inner (i.e. within the boundary layer) solutions are obtained in terms of the particle concentration, particle velocity, and fluid velocity. Unfortunately, these solutions require numerical solution of an integral equation, depend on the ratio between the pressure gradient and the gravity force, and the orientation of the pressure gradient relative to the gravity. Consequently, the development of a proppant transport model for hydraulic fracturing based on these results is not practical. For this reason, an approximate solution is introduced, where the effect of gravity is accounted for in an approximate fashion, reducing the complexity of the slurry flow solution. To validate the use of this approximation, the error is estimated for different regimes of flow. The approximate solution is then used to calculate the expressions for the slurry flux and the proppant flux, which are the basis for a model that can be used to account for proppant transport with gravitational settling in a fully coupled hydraulic fracturing simulator.

Text

2014-08-13

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/50000

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/