Kozeny equation

The detailed consideration of these equations is due largely to Kozeny [50] the reader is also referred to Collins [51]. However, it is apparent that, subject to assumptions concerning the topology of the porous system, the determination of K provides an estimate of Ao- It should be remembered that Ao will be the external area of the particles and will not include internal area due to pores (note Ref. 52). Somewhat similar equations apply in the case of gas flow the reader is referred to Barrer [53] and Kraus and co-workers [54]. 

Ca.rma.n-KozenyEfjua.tion, Flow through packed beds under laminar conditions can be described by the Carman-Kozeny equation in the... 

The specific resistance coefficient for the dust layer Ko was originally denned by Williams et al. [Heat. Piping Air Cond., 12, 259 (1940)], who proposed estimating values of the coefficient by use of the Kozeny-Carman equation [Carman, Trans. Inst. Chem. Fng. (London), 15, 150 (1937)]. In practice, K and Ko are measured directly in filtration experiments. The K and Ko values can be corrected for temperature by multiplying by the ratio of the gas viscosity at the desired condition to the gas viscosity at the original experimental conditions. Values of Ko determined for certain dfists by Williams et al. (op. cit.) are presented in Table 17-5. 

Clearly, the factors determining Ko are far more complex than is indicated by a simple application of the Kozeny-Carman equation, and when possible, filter design should be based on experimental determinations made under conditions approximating those expected in the planned installation. 

Replacing 2/8 with shape parameter c and with a specific surface, the Kozeny equation is obtained. 

Tortuosity t is basically a correction factor applied to the Kozeny equation to account for the fact that in a real medium the pores are not straight (i.e., the length of the most probable flow path is longer than the overall length of the porous medium) ... 

Thus the Carman-Kozeny equation appiicabie for the increment dx is given by... 

The specific cake resistance r(nr ) depends on particulate bed characteristics e and According to the Carman-Kozeny equation for packed beds (Chapter 2)... 

In principle, filter bed permeabilities can be calculated using the Carman-Kozeny equation 2.53. For slurries containing irregular particles, however, cake filtrabilities together with filter medium resistance are determined using the Leaf Test (Figure 4.13). In this technique, a sample of suspended slurry is drawn through a sample test filter leaf at a fixed pressure drop and the transient volumetric flowrate of clear filtrate collected determined. 

It was shown in Chapter 2 that the simplest models of solid-liquid separation are those based of the Carman-Kozeny equation for filtration in whieh the bed permeability (filtrability), F, may be expressed by... 

Estimation of the pressure-drop The system is designed to work within a given pressure limit thus, one needs a relation giving the pressure-drop in the column (per unit length). Darcy s law gives the relation of AP/L versus the mobile phase velocity u. However, the Kozeny-Carman equation is best adapted for laminar flows as described ... 

Kovats RI scale 176 Kozeny-Carman equation 11 Kubelka-Hunk equation (TLC) 705 Kuderna-Danish concentrator 763... 

The determination of the specific surface area of a powder by air permeability methods essentially involves the measurement of the pressure drop across a bed of the powder under carefully controlled flow conditions. The data obtained are substituted in the Kozeny-Carman equation to estimate the specific surface area. Permeability methods have certain advantages, one of them being that the equipment used for carrying out the measurements is cheap and robust. Another advantage is that sample problems are minimized because a large sample of powder is required to be used for analysis. 

This is known as the Blake-Kozeny equation and, as noted, applies for A/e.PM < 10-... 

This equation with a value of 150 instead of 180 is called the Ergun equation and is simply the sum of Eqs (13-15) and (13-16). (The more recent references favor the value of 180, which is also more conservative.) Obviously, for ARcRM < 10 the first term is small relative to the second, and the Ergun equation reduces to the Blake-Kozeny equation. Likewise, for A Re PM > 1000 the first term is much larger than the second, and the equation reduces to the Burke-Plummer equation. 

If the Blake-Kozeny equation for laminar flow is used to describe the friction loss, which is then equated to AP/p from the Bernoulli equation, the resulting expression for the flow rate is... 

The permeability, K, is characteristic of the medium and can be related to measurable properties by the Carman-Kozeny equation ... 

Strictly, the value 5 in the Carman-Kozeny equation should be treated as an empirical constant, which has to be determined experimentally. However, for many systems of interest, the value is very close to 5. 

The specific resistances obtained are independent of applied load, suspension concentration and membrane type, as expected for non-compressible filter cakes. Tests with uniform latex particles have given permeabilities in very good agreement with Equation 2, using a value of 5 for the Carman-Kozeny constant. 

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 on the assumption that the Carman-Kozeny equation is applicable. Discuss the uncertainties in this calculation. Repeat the calculation using the Ergun equation and explain the differences in the results obtained. 

As noted in Section 6.1.3 of Volume 2, the Carman-Kozeny equation applies only to conditions of laminar flow and hence to low values of the Reynolds number for flow in the bed. In practice, this restricts its application to fine particles. Approaches based on both the Carman-Kozeny and the Ergun equations are very sensitive to the value of the voidage and it seems likely that both equations overpredict the pressure drop for fluidised systems. 

Obtain a relationship for the ratio of the terminal falling velocity of a particle to the minimum fluidising velocity for a bed of similar particles. It may be assumed that Stokes Law and the Carman-Kozeny equation are applicable. What is the value of the ratio if the bed voidage at the minimum fluidising velocity is 0.4 ... 

The use of the Carman-Kozeny equation is discussed in Section 4.2.3 of Chapter 4. It is interesting to note that if e = 0.48, which was the value taken in Problem 6.1, then up/uf = 47.5, which agrees with the solution to that problem. 

Equation 9.33 is the Carman-Kozeny equation [Carman (1937)]. The parameter Kc has a value which depends on the panicle shape, the porosity and particle size range. The value lies in the range 3.5 to 5.5 but the value most commonly used is 5. 

In cake filtration, the filter medium acts as a strainer and collects the solid particles on top of the initial layer. A filter cake is formed and the flow obeys the Carman-Kozeny equation for packed beds. 

---