Pore-scale modelling for fluid transport in 2D porous media
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.