Pore-scale modelling for fluid transport in 2D porous media
Date
2006-12
Authors
Cloete, Maret
Journal Title
Journal ISSN
Volume Title
Publisher
Stellenbosch : University of Stellenbosch
Abstract
In the present study, a model to predict the hydrodynamic permeability of viscous
flow through an array of solid phase rectangles of any aspect ratio is derived. This
also involves different channel widths in the streamwise and the transverse flow
directions which may be chosen irrespectively to the rectangular shape itself. It
is shown how, with the necessary care taken during description of the interstitial
geometry, a volume averaged approach can be used to obtain results identical to a
direct method. Insight into the physical situation is gained during the modelling of
the two-dimensional interstitial flow processes and resulting pressure distributions
and this may prove valuable when the volume averaging method is applied to more
complex three-dimensional cases. The analytical results show close correspondence
to numerical calculations, except in the higher porosity range for which a more
realistic model is needed.
Tortuosity is studied together with its inverse. Correspondences and differences
regarding the definitions for the average straightness of pathlines, expressed in
literature, are examined. A new definition, allowing different channel widths in
the streamwise and the transverse flow directions, for the tortuosity is derived from
first principles.
A general relation between newly derived permeability and tortuosity expressions
was obtained. This equation incorporates many possible geometrical features for a
two-dimensional unit cell for granules. Three possible staggering configurations of
the solid phase along the streamwise direction are also included in this relation.
Description
Thesis (MScEng (Applied Mathematics))--University of Stellenbosch, 2006.
Keywords
Dissertations -- Applied mathematics, Theses -- Applied mathematics, Fluid dynamics -- Mathematical models, Viscous flow -- Mathematical models, Porous materials -- Fluid dynamics -- Mathematical models