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Chemical Engineering Communications, Vol.150, 653-732, 1996
Single fluid flow in porous media
A comprehensive study on single fluid flow in porous media is carried out. The volume averaging technique is applied to derive the governing flow equations. Additional terms appear in the averaged governed equations related to porosity epsilon, tortuosity tau, shear factor F and hydraulic dispersivity D-h. These four parameters are uniquely contained in the volume averaged Navier-Stokes equation and not all of them are independent. The tortuosity can be related to porosity through the Brudgemann equation, for example, for unconsolidated porous media.The shear factor models are reviewed and some new results are obtained concerning high porosity cases and for turbulent flows. It is known that there are four regions of flow in porous media : pre-Darcy's flow, Darcy's flow, Forchheimer flow and turbulent flow. The transitions between these regions are smooth. The first region, the pre-Darcy's flow region represents the surface-interactive flows and hence is strongly dependent on the porous media and the flowing fluid. The other flow regions are governed by the flow strength of inertia. For Darcy's flow, the pressure gradient is found to be proportional to the flow rate. The Forchheimer flow, however, is identified by a strong inertial effects and the pressure gradient is a parabolic function of flow rate. Turbulent flow is unstable and unsteady flow characterized by chaotic flow patterns. The pressure drop is slightly lower than that predicted using the laminar flow equation.The hydraulic dispersivity is a property of the porous media. It may be considered as the connectivity of the pores in a porous medium. It characterizes the dispersion of mementum, heat and mass transfer. In this paper, only the dispersion of momentum is studied.Single fluid flow through cylindrical beds of fibrous mats and spherical particles has been used to show how to solve the single fluid flow problems in porous media utilizing the knowledge developed in this communication. Both the pressure drop and axial how velocity profiles are computed using the developed shear factor and hydraulic dispersion models. Both the predicted velocity profile and pressure drop compare fairly well with the published experimental data.
Keywords:VOID FRACTION DISTRIBUTIONS;PARTICLE-SIZE DISTRIBUTION;HARD-SPHERE PACKINGS;PACKED FIXED-BEDS;TRANSPORT-PROPERTIES;EFFECTIVE VISCOSITY;BRINKMAN EQUATION;REYNOLDS-NUMBER;CYLINDRICAL CONTAINERS;LIQUID PERMEATION