Laminar flow through isotropic granular porous media
Date
2006-12
Authors
Woudberg, Sonia
Journal Title
Journal ISSN
Volume Title
Publisher
Stellenbosch : University of Stellenbosch
Abstract
An analytical modelling procedure for predicting the streamwise pressure gradient for
steady laminar incompressible flow of a Newtonian fluid through homogeneous isotropic
granular porous media is introduced. The modelling strategy involves the spatial volume
averaging of a statistical representative portion of the porous domain to obtain measurable
macroscopic quantities from which macroscopic transport equations can be derived. A
simple pore-scale model is introduced to approximate the actual complex granular porous
microstructure through rectangular cubic geometry. The sound physical principles on
which the modelling procedure is based avoid the need for redundant empirical coefficients.
The model is generalized to predict the rheological flow behaviour of non-Newtonian
purely viscous power law fluids by introducing the dependence of the apparent viscosity
on the shear rate through the wall shear stress. The field of application of the Newtonian
model is extended to predict the flow behaviour in fluidized beds by adjusting the Darcy
velocity to incorporate the relative velocity of the solid phase. The Newtonian model
is furthermore adjusted to predict fluid flow through Fontainebleau sandstone by taking
into account the effect of blocked throats at very low porosities. The analytical model as
well as the model generalizations for extended applicability is verified through comparison
with other analytical and semi-empirical models and a wide range of experimental data
from the literature. The accuracy of the predictive analytical model reveals to be highly
acceptable for most engineering designs.
Description
Thesis (MScEng (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2006.
Keywords
Dissertations -- Applied mathematics, Theses -- Applied mathematics, Laminar flow -- Mathematical models, Newtonian fluids -- Mathematical models, Porous materials -- Fluid dynamics -- Mathematical models