Validação experimental da equação de Hazen-Dupuit-Darcy (HDD) modificada para meios porosos finos

Abstract

The classical pressure-drop equation for porous media flow—the Hazen-Dupuit Darcy equation, or simply HDD—relates the pressure-drop per unit of porous medium length of an isothermal, incompressible, porous médium saturating, Newtonian fluid flow in terms of the two constitutive quantities K and C it defines, which are known as the permeability and the form coefficient of the porous medium, respectively. It has been noted that the HDD equation becomes ambiguous for cases in which the pressuredrop caused by the porous medium no longer bears relation with the porous medium length, such as for the entire class of porous media that are sufficiently thin in the flow direction. To account for pressure-drops on this class of porous media, a modified HDD equation was proposed by Naaktgeboren et al. (2012) based on numerical results of laminar flow through porous media of simplified (collapsed) porous médium geometry and vanishing length. The proposed modified HDD equation is written in terms of modifiedK and C parameters, namely, Km and Cm, that are themselves composed of a linear combination of two pressure-drop terms, one being dependent and the other, independent of porous medium length. This work attempts validating the modification of the HDD equation introduced by Naaktgeboren et al. (2012) with experimentally measured pressure-drops of air flowing across porous mettalic foams of various lengths due to Baril et al. (2008) by means of least squares data modeling. The analysis shows that the modification of the HDD equation proposed by Naaktgeboren et al. (2012) is valid for the analysed experimental dataset. Moreover, expected values of bulk, Darcian porous médium permeability and form coefficients can be recovered from the variable length porous media pressure-drop measurements.