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Transport and dispersion of particles in visco-plastic fluids

University of British Columbia

This thesis focuses on development of a model to predict “spreading” of the solids (i.e. proppant) fraction during the fracturing operation. We develop a 1D model that allows us to estimate dispersion of solid particles along a vertical pipe in a fully turbulent flow of a shear thinning yield stress fluid (i.e., visco-plastic fluid), as well as slip relative to the mean flow. In dimensionless form, this results in a quasilinear advection-diffusion equation. Advection by the mean flow, particle settling relative to the mean, in the direction of gravity, turbulent particle dispersivity and Taylor dispersion are the 4 main transport phenomena modelled in the 1D model. We provide a simple analysis of the 1D model, suitable for spreadsheet-type field design purposes, in which we estimate “mixing lengths” due to both settling and dispersion. Secondly, we provide an accurate numerical algorithm for solution of the 1D model and show how pulses of proppant (i.e. slugs) may or may not interact for typical process parameters.

Text

2013-09-03

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/45002

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/