Froth Density

First, an effective froth density (j) (dimensionless) is calculated ... 

Lj= length of flow path across plate, m q = hquid-flow rate, mVs = froth density on plate, dimensionless M-l = hquid viscosity, Pa s or kg/(m s)... 

For evafuating the residence time 0g of gas in the froth, the volume of the froth is taken as Aohf, where the height of the froth hj is obtained by first determining effective froth density [Eq. (14-117)]. The dimensionless froth density is defined by... 

FIG. 14-118 Aerodynamic cut diameter for a single-sieve-plate scrubber as a function of bole size, bole-gas velocity, and froth density, F, g/cm. To convert meters per second to feet per second, multiply by 3.281 to convert grams per cubic centimeter to pounds per cubic foot, multiply by 62.43. [Calveti, J. Air Pollut. Control Assoc., 24, 929 (1974).]... 

Determine Cq from Figure 8-129 [193]. Note that determining froth density is by experiment and/or best judgment based on similar or related systems. Usually <[) s 1.0 to 0.50. The method checks literature and industrial tests about 15%. 

Figure 8-149. Correlation for aerated-tray-liquid pressure drop developed from published data for various valves. Note (j> = relative froth density. Reference numbers are from original article [201 ]. Used by permission, Klein, G. F., Chem. Eng. V. 89, No. 9 (1982), p. 81 all rights reserved.

A f = Liquid gradient per row of caps, uncorrected, in. if) = Relative froth density, ratio of froth density to clear liquid density ... 

A simple additive model is normally used to predict the total pressure drop. The total is taken as the sum of the pressure drop calculated for the flow of vapour through the dry plate (the dry plate drop hj) the head of clear liquid on the plate (hw + how) and a term to account for other, minor, sources of pressure loss, the so-called residual loss hr. The residual loss is the difference between the observed experimental pressure drop and the simple sum of the dry-plate drop and the clear-liquid height. It accounts for the two effects the energy to form the vapour bubbles and the fact that on an operating plate the liquid head will not be clear liquid but a head of aerated liquid froth, and the froth density and height will be different from that of the clear liquid. 

Methods have been proposed for estimating the residual head as a function of liquid surface tension, froth density and froth height. However, as this correction term is small the use of an elaborate method for its estimation is not justified, and the simple equation... 

To predict the height of aerated liquid on the plate, and the height of froth in the downcomer, some means of estimating the froth density is required. The density of the aerated liquid will normally be between 0.4 to 0.7 times that of the clear liquid. A number of correlations have been proposed for estimating froth density as a function of the vapour flow-rate and the liquid physical properties see Chase (1967) however, none is particularly reliable, and for design purposes it is usually satisfactory to assume an average value of 0.5 of the liquid density. 

This criterion is, if anything, oversafe, and where close plate spacing is desired a better estimate of the froth density in the downcomer should be made. The method proposed by Thomas and Shah (1964) is recommended. 

The work of Calderbank and Rennie (C4) has been criticized by Sargent and Macmillan (S2) on the basis that the liquid flow conditions used by Calderbank and Rennie (C4) are not found in distillation columns. They (S2) consider that cellular foams are formed for dilute aqueous solutions only when low gas flow rates are employed. By using an n-pentane-isopentane system, Macmillan (Ml) found that for all gas flow rates, froths with densities less than 0.15 were formed and the froth densities were independent of the factor vs(pg)112 but dependent on tray geometry. The associated problem of foam stability has also attracted considerable attention (Al, D3, Zl). 

Figure 6.3-1. Empirical correlation for downcomer froth-density [1],...

Calculation of the froth height in the downcomer requires consideration of two aspects, the clear liquid back-up and, the so called froth-density, which is actually the volume fraction of liquid in the froth. 

In the absence of a fundamental understanding, the prediction of froth density relies on empirical correlation. Figure 6.3-1 shows a simple graphical correlation of mean downcomer froth density as a function of the density difference between liquid and vapour. Brierley [1] indicates that the correlation was produced from relatively few data. Therefore, it is preferable to obtain a value from operating data close to flooding on the same system. 

The clear liquid backup is divided by the froth-density to give the froth height if this exceeds the tray spacing plus the outlet weir height, the tray is deemed to be flooded. 

Some trial and error is required in this calculation because the clear liquid height hc and the froth density 0, depend on each other, and the weep fraction f. depends on the clear liquid height hc. Clear liquid height is related to froth height and froth density By... 

Sieve trays, troth regime. Most dear liquid height and froth density correlations (35,68,81-86) are based on the Francis weir formula. A correlation by Colwell (68), based on a model of froth flow over the weir, was demonstrated to agree with experimental data better than other published correlations. Colwell s correlation is recommended by the author and by Lockett (12), and was successfully used as a building block in weeping correlations (56,63,69) and in froth regime entrainment correlation (40). Colwell s correlation is... 

The Chan and Fair correlation uses the Bennett et al. correlation i Sec. 6.3.3) for calculating the clear liquid height hc and the froth density [Eqe. (6.56) and (6.58)]. For calculating kLait Chan and Fair use a correlation by Foss and Gerster (133),... 

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