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

[摘要] In the present study, a model to predict the hydrodynamic permeability of viscousflow through an array of solid phase rectangles of any aspect ratio is derived. Thisalso involves different channel widths in the streamwise and the transverse flowdirections which may be chosen irrespectively to the rectangular shape itself. Itis shown how, with the necessary care taken during description of the interstitialgeometry, a volume averaged approach can be used to obtain results identical to adirect method. Insight into the physical situation is gained during the modelling ofthe two-dimensional interstitial flow processes and resulting pressure distributionsand this may prove valuable when the volume averaging method is applied to morecomplex three-dimensional cases. The analytical results show close correspondenceto numerical calculations, except in the higher porosity range for which a morerealistic model is needed.Tortuosity is studied together with its inverse. Correspondences and differencesregarding the definitions for the average straightness of pathlines, expressed inliterature, are examined. A new definition, allowing different channel widths inthe streamwise and the transverse flow directions, for the tortuosity is derived fromfirst principles.A general relation between newly derived permeability and tortuosity expressionswas obtained. This equation incorporates many possible geometrical features for atwo-dimensional unit cell for granules. Three possible staggering configurations ofthe solid phase along the streamwise direction are also included in this relation.

[发布机构] Stellenbosch University