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

• Published in: Powder technology Vol. 237; pp. 233 - 240
• Main Authors: Tien, Chi, Ramarao, Bandaru V.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.03.2013; Elsevier
• Subjects: Applied sciences; Cake porosity; Chemical engineering; equations; Exact sciences and technology; Filter cake; Filtration; Flow through porous media; Fluid dynamics; Fluid flow; Fluids; Hydrodynamics of contact apparatus; Kozeny–Carman equation; Liquid-liquid and fluid-solid mechanical separations; Mathematical analysis; Media; Miscellaneous; Porosity; porous media; Powder technology; Relationship between pressure drop and flow rate; Solid-solid systems; Flow through porous media; Filtration; Cake porosity; Relationship between pressure drop and flow rate; Kozeny–Carman equation; Pressure drop; Porous medium; Hydrodynamics; Pressure gradient; Spherical particle; Porosity; Kozeny―Carman equation; Filter cake
• ISSN: 0032-5910; 1873-328X
• DOI: 10.1016/j.powtec.2012.09.031

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. Experimental 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. [Display omitted] ► 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.