Laminar flow through isotropic granular porous media

[摘要] An analytical modelling procedure for predicting the streamwise pressure gradient forsteady laminar incompressible flow of a Newtonian fluid through homogeneous isotropicgranular porous media is introduced. The modelling strategy involves the spatial volumeaveraging of a statistical representative portion of the porous domain to obtain measurablemacroscopic quantities from which macroscopic transport equations can be derived. Asimple pore-scale model is introduced to approximate the actual complex granular porousmicrostructure through rectangular cubic geometry. The sound physical principles onwhich the modelling procedure is based avoid the need for redundant empirical coefficients.The model is generalized to predict the rheological flow behaviour of non-Newtonianpurely viscous power law fluids by introducing the dependence of the apparent viscosityon the shear rate through the wall shear stress. The field of application of the Newtonianmodel is extended to predict the flow behaviour in fluidized beds by adjusting the Darcyvelocity to incorporate the relative velocity of the solid phase. The Newtonian modelis furthermore adjusted to predict fluid flow through Fontainebleau sandstone by takinginto account the effect of blocked throats at very low porosities. The analytical model aswell as the model generalizations for extended applicability is verified through comparisonwith other analytical and semi-empirical models and a wide range of experimental datafrom the literature. The accuracy of the predictive analytical model reveals to be highlyacceptable for most engineering designs.

[发布机构] Stellenbosch University