Kozeny s constant

K" is generally known as Kozeny s constant and a commonly accepted value for K" is 5. As will be shown later, however, K" is dependent on porosity, particle shape, and other factors. Comparison with equation 4.2 shows that B the permeability coefficient is given by ... 

Figure 4.2. Variation of Kozeny s constant AT" with voidage for various shapes...

Calculate the minimum velocity at which spherical particles of density 1600 kg/m3 and of diameter 1.5 mm will be fluidised by water in a tube of diameter 10 mm. Discuss the uncertainties in this calculation. The viscosity of water is 1 mN s/m2 and Kozeny s constant is 5. 

The dimensionless constant K is known as Kozeny s constant and has a value of approximately 5.0 although strictly it is a function of both intraparticle porosity and particle shape. Assuming now that the bed... 

Kozeny s Equation—The equations thus far presented show that the flow is proportional to the square of the particle-diameter and to some power of the porosity. The shape of the particles is also of some consequence, but this factor is contained in the proportionality constant. The most important of these variables is the porosity since, as we have shown, the flow may vary from the 3.3-power (Slichter)-to the 7.0-power (Buckingham) of this factor. Next in importance is a concept of the size-distribution. We have shown in Chapter 6 that some relation exists between pore-space and particle-size but obviously the methods used heretofore for expressing particle-size make small allowance for size-distribution and inadequately take cognizance of the shapes of the particles themselves. The general problem of the relationship of these variables was first made empirically by Kruger (1918-1920), but its exact mathematical formulation is due to Kozeny (1927). His equation may be stated as follows ... 

Flux of component i, mol/m s Flux of solute, mol/m s Flux of solvent, mol/m s Kozeny-Carman constant Distribution constant of solute Membrane thickness, m Phenomenological coefficients... 

A) Kozeny s shape factor Fs and Kozeny constant Kz In Eq. (2.58), a shape factor Fs for different shaped conduits (Table 2.9) is implemented ... 

Where parameter c is known as the Kozeny constant, which is interpreted as a shape factor that is assigned different values depending on the configuration of the capillary (as a point of reference, c = 0.5 for a circular capillary). S is the specific surface area of the chaimels. For other than circular capillaries, a shape factor is included ... 

Equation (7,17) is called the Kozeny-Carman equation and is applicable for flow through beds at particle Reynolds numbers up to about 1.0. There is no sharp transition to turbulent flow at this Reynolds number, but the frequent changes in shape and direction of the channels in the bed lead to significant kinetic energy losses at higher Reynolds numbers. The constant 150 corresponds to = 2.1, which is a reasonable value for the tortuosity factor. For a given system, Eq. (7,17) indicates that the flow is proportional to the pressure drop and inversely proportional to the fluid viscosity. This statement is also known as Darcy s law, which is often used to describe flow of liquids through porous media. 

We can determine the value of the Kozeny constant as given by Happel s permeability (Eq. 8.5.6) by equating it to the Kozeny-Carman permeability, which from Eq. (4.7.16) may be written... 

In the permeability methods a known quantity of air is forced through a small bed of the fine solids under a constant pressure drop, and the flow time is recorded. The theory is based on the laminar flow of fluids through porous beds, and the specific surface area S (m g ) of the material is calculated from the Kozeny equation... 

---