The Effect of Inlet and Exit Pressure-Drop on the Determination of Porous Media Permeability and Form Coefficient

The determination of permeability and form coefficient, defined by the Hazen-Dupuit-Darcy (HDD) equation of flow through a porous medium, requires the measurement of the pressure-drop per unit length caused by the medium. The pressure-drop emerging from flow adjustment effects between the porous medium and the surrounding clear fluid, however, is not related to the porous medium length. Hence, for situations in which the entrance and exit pressure-drops are not negligible, as one would expect for short porous media, the determination of the hydraulic parameters using the HDD equation is hindered. A criterion for determining the relative importance of entrance and exit pressure-drop effects, as compared to core effect, is then of practical and fundamental interest. This aspect is investigated analytically and numerically considering flow through a thin planar restriction placed in a circular pipe. Once the pressure-drop across the restriction is found, the results are then compared to the pressure-drop imposed by an obstructive section having the same dimension as the restriction but finite length, playing the role of the least restrictive porous medium core. This comparison yields a conservative estimate of the porous medium length necessary for neglecting entrance and exit pressure-drop effects. Results show that inlet and exit pressure-drop effects become increasingly important compared to core effects as the porosity decreases and Reynolds number increases for both laminar and turbulent flow regimes. (Correlations based on experimental results available in the literature are employed for turbulent pipe flow). The analysis also shows why the HDD equation breaks down when considering flow through porous media where the entrance and exit pressure-drop effects are not negligible, and how modified permeability and form coefficients become necessary to characterize this type of porous media. Curve-fits accurate to within 2.5% were obtained for the modified permeability and form coefficients of the planar restriction with Reynolds number ranging from 0.01 to 100 and porosity from 0.0625 to 0.909.