The Permeability Distribution (PD) Method for Filter Media Characterization

Abstract

Cake filtration is frequently used for the removal of particulate solids from fluids in industrial processes. The build up of a filter cake is usually accompanied by a decrease in overall permeability of the filter leading to an increased pressure drop over the filter medium. For an incompressible filter cake that builds up on a homogeneous filter cloth (surface filtration mode), a linear pressure drop profile is expected over time. However, occasionally experiments show curved pressure drop profiles. Whereas pressure drop profiles with increasing slope are generally ascribed to cake compression and/or depth filtration, pressure drop profiles with decreasing slopes are only ascribed to inhomogeneities in the filter. Such inhomogeneities can arise due to filter cake patches and/or an inhomogeneous filter cloth itself. In this work a method is proposed that transforms the pressure drop profile of a filter into a permeability distribution (PD) of the filter medium, thus accounting for possible inhomogeneities of the medium. The determination of the PD is looked at as an inverse problem of an integral transformation. The method is applied to experimental filter pressure drop data of laboratory scale jet-pulse cleaned bag filter plants. It is found that even clean filter media can exhibit a significant permeability profile.

Acknowledgments

The authors thank Harald Hanche-Olsen from the Department of Mathematics at NTNU for invaluable hints concerning the mathematical background of the model, namely for noting that the present problem can be formulated as a Stieltjes transform. Financial support from the Austrian Science Foundation (FWF) under the project no. P16313-N07 and the Austrian Energy and Environment AG & Co KG is gratefully acknowledged.