Assessment of Forchheimer's Equation to Predict the Permeability of Ceramic Foams

Correct estimation of the pressure drop in filtration processes that involve fluid velocity variations is of major importance, because it allows the filtration rate and/or the energy consumed on fluid flow to be more accurately controlled. Permeability of porous filters has been often described by Forchheimer's equation, which establishes a nonlinear dependence between pressure drop and fluid velocity. Two constants, k ₁ and k ₂, dependent only on the medium, quantify the viscous and inertial effects on the pressure drop curve. In this work, experimental data of airflow through 10 pores per linear inch ceramic foam filters are used to show that a single sample may have completely distinct permeability constants depending on the data range chosen for analysis. The Darcian permeability constant k ₁ displays higher variation than the non-Darcian permeability constant k ₂. The conclusion is that special attention must be taken to represent permeability of highly porous structures in a large velocity range. The predictability of Forchheimer's equation generally worsens when less data are included in the curve fitting, particularly at low velocities. Careful consideration should be made if constants k ₁ and k ₂ are intended to be used for permeability estimation beyond the fitting range.