Effect of Walls in Modeling Flow through Porous Media

A study has been undertaken to determine the effect of walls in the modeling of flow through porous media. Two primary influences of the wall are identified: packing effects for an unconsolidated porous medium and viscous effects on the flow. The packing effect is considered through a series of experiments to arrive at an expression for the bulk porosity as a function of the ratio of particle diameter to pipe diameter. From this expression, and assuming that the region of greater haphazard packing occurs at a distance approximately one particle radius from the wall, a porosity of the wall region is determined. The viscous effects are accounted for by incorporating the Brinkman's extension term in the momentum equation. The combined effects are considered by employing a two region model for the fluid mechanics.