Carman-Kozeny correlation

Mauran S., Rigaud L., and CoudeviUe O., Application of the Carman-Kozeny correlation to a high-porosity anisotropic consolidated medium The compressed expanded natural graphite. Transport in Porous Media 43 2001 355-376. 

To calculate the reduction in the concentration of surfactant in the fluid by adsorption it is necessary to have an estimation of the inner surface area of the reservoir. This parameter is related to the porosity of the medium and to its permeability. Attempts have been made to correlate these two quantities but the results have been unsuccessful, because there are parameters characteristic of each particular porous medium involved in the description of the problem (14). For our analysis we adopted the approach of Kozeny and Carman (15). These authors defined a parameter called the "equivalent hydraulic radius of the porous medium" which represents the surface area exposed to the fluid per unit volume of rock. They obtained the following relationship between the permeability, k, and the porosity, 0 ... 

Traditionally filterability is correlated to particle size by the Kozeny-Carman equation expressed as a specific cake resistance, r as a function of particle specific surface area Sq, solids density p, and cake porosity e ... 

For a Newtonian fluid, m = 1, both equations (5.46) and (5.47) reduce to the well known Kozeny-Carman equation. Equation (5.47) correlates most of the literature data on the flow of power-law fluids through beds of spherical particles up to about Re 1, though most work to date has been carried out... 

Carman showed that for many materials the constant B, could be taken as 5. However, Carman stated clearly that the universal use of the value 5 will lead to error in certain cases [6, 7]. Because of the lack of alternative values, however, commercially available permeameters such as the Fisher Subsieve Sizer are calibrated for operation on the assumption that the value B = 5 is used in the Kozeny-Carman equation [8]. The unknown value of B for any specific powder is an immediate source of discrepancy between the surface area measured by permeability with that measured by other techniques. The only way to determine B exactly is to use an independent method of analysis to measure the surface area of the powder. B is sometimes called a tortuosity factor but it is my opinion that it is better to call the factor B a correlation factor and in this way firmly state the true nature of the adjustment being made to the equation. 

In order to estimate the rate of fluid flow through a porous material--e.g. the rate of water uptake in an absorbent polymer-either equation 1 or 4 can be used. In either case, the permeability of the material must be known or estimated. In most cases, no detailed knowledge of the geometry of the porous material is available. Therefore, general correlations between pore structure and permeability are often used. Dullien [5] and Happel and Brenner [10] present many of the functional forms that have been used to correlate permeability and porosity. The Kozeny-Carman equation, and its extension for Inertial effects, the Ergun equation, is the most widely encountered correlation. Detailed discussions of the derivation and application of Kozeny s original equation and Carman s modification are available [9, 5, 12]. 

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