Can filter cake porosity be estimated based on the Kozeny–Carman equation?

Application of the Kozeny–Carman equation for estimating the porosity of filter cakes formed in filtration is examined. It is shown that the Kozeny–Carman equation belongs to a class of relationships relating the pressure gradient and flow rate for fluid flow through porous media and is applicable to unconsolidated randomly packed media composed of spherical or nearly spherical particles. In contrast, filter cakes formed under pressure may be compressible and are not homogeneous. Furthermore, the question whether filter cakes may be considered as unconsolidated remains unresolved. These complicating factors plus the fact that the calculated porosity values based on the Kozeny–Carman equation tend to be exceedingly low as compared with those obtained from independent measurements strongly suggest that using the Kozeny–Carman equation for determining cake porosity is questionable and not appropriate.

Graphical abstractExperimental measurements of the dependence of porosity on the compressive stress on filter cakes (calcium carbonate and bentonite). A very large variation in porosities shows that the structures are significantly different. This implies that a unique functional relation between porosity and compressive stress (a unique constitutive law) is not universally valid nor obtainable.Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► Filter cake porosities have been estimated using the Kozeny–Carman equation. ► This sometimes yields unrealistically low porosities. ► The Kozeny–Carman equation is restricted in applicability. ► These factors suggest the Kozeny–Carman relation must be used with caution.