Yi yz
Equation (7.33) demonstrates that one overall gastransfer unit is obtained when the change in gas composition equals the average of the overall driving forces causing the change. Let us consider the diagram shown in Fig. 7.13. The line (3) is vertically halfway between the operating line (2) and the equilibrium curve (1). The step CFD, which corresponds to one transfer unit, has been constructed by drawing the horizontal line CEF, so that CE is equal to EF, and continuing vertically to D.
TABLE 7.2
Liquidfilm height of transfer unit
HtL = m, L=kg/h/m2, L = kg/m/h, ScL = dimensionless (Schmidt number)
Packing 
<P 
n 
Range of L 
Raschig rings:  
3/8 in. 
3.15 ' 10'4 
0.46  
1/2 in. 
7.05 ' 10"4 
0.35  
1 in. 
2.30 * 103 
0.22 
1,80068,000 
1.5 in. 
2.56* 10"3 
0.22  
2 in. 
2.88 * 10"3 
0.22  
Berl saddles:  
1/2 in. 
1.43* 10'3 
0.28  
1 in. 
1.26* 10"3 
0.28  
1.5 in. 
1.34 * 10"3 
0.28  
3in. partition rings  
(stacked staggered) 
0.0168 
0.09 
13,00063,000 
Spiral rings (stacked  
staggered):  
3in. single spiral 
1.95 * 103 
0.28 
1,80068,000 
3in. triple spiral 
2.49 * 10"3 
0.28 
13,00063,000 
Drippoint grids  
(continuous flue):  
No. 6146 
3.51 ' 10"3 
0.23 
15,000135,000 
No. 6295 
1.50* 10"3 
0.31 
11,000100,000 
From the data of Sherwood et al. (1940), and Molstad et al. (1943)
Yg  Yh may be considered as the average driving force for the exchange in gas composition yo  y f corresponding to this step. As GE is equal to EH and if the operating line is straight DF = 2 * GE = GH, and the step CFD corresponds to one transfer unit. In a similar way the other transfer units are stepped off.
The resistance to mass transfer in absorption and stripping processes in the case both the gas film and liquid film are controlling factors can be calculated on the basis of the following equation:
Ky * a Kg* a Kl * a where m = the slope of the equilibrium solubility curve (mole fraction in the gas/mole fraction in the liquid).
By comparing equation (7.26) with (7.29), Htog can be expressed by the contribution of individual phase resistances, HtG and HtL:
For diluted solutions, the ratio of concentrations of nondiffusing substances will be nearly unity, and:
Stripping of very insoluble gases such as oxygen, hydrogen or carbon dioxide, is controlled by resistance to mass transfer in the liquid, for which HtL is a direct measure. HtL can be found for common packing material from the empirical expression
0.31 * fjl where tp and n can be found from Table 7.2 for different packings. L = the flow rate kg/h/m2
Scl = the dimensionless Schmidt number = pUpi * Dl fji = the viscosity (kg/m/h) PL = specific gravity Dl = diffusion coefficient.
In some instances Htog « HtG. This almost obtains for the stripping of ammonia from water into air, but in this case the liquidfoam resistance is still not completely negligible although ammonia is very soluble in water. It is possible to calculate HtG from empirical data:
a*GB
where a, B and y are empirical constants, Scg = the dimensionless Schmidt number, Scg = /vg / pg*Dg, G and L = the gas and liquid flow rates respectively measured in kg /h / m2. pG is the specific gravity of the gas. The diameter of the tower is calculated on the basis of the minimum liquid rate for wetting and on the socalled flooding point.
Values of the empirical constants are listed in Table 7.3.
The minimum liquid rate for wetting lw, can be calculated from the following equation:
dL* a where dL = the density of the liquid kg/m3 a = surface area of the packing m2 / m3 L = See Table 7.2
The flooding point has been defined as the gas velocity at which a liquid layer forms on top of the packing. Based on experimental data, the following equation can be used for the determination of lw at the flooding point:
L pa
dh2/3 G pl where dh = the hydraulic diameter of the packing and yL = the viscosity in kg/m*s.
Table 7.3 is based on data of Fellinger and Pigford (1952) and Molstad et al. (1943).
The function is shown in Fig. 7.14, where
2 = lw * (1000 ¿/l)° 1 is expressed as a function of Q.
TABLE 7.3
Gasfilm height of transfer unit
HtG=m, G=kg/h/m2, L =kg/h/m2, ScG=dimensionless (Schmidt number)
_Ranged
Packing a I) y
Raschig rings:  
3/8 in. 
.39 
0.45 
0.47 
9002,300 
2,3006,800  
1 in. 
9.31 
0.39 
0.58 
9003,600 
1,8002,300  
8.53 
0.32 
0.51 
9002,700 
2,30020,000  
1.5 in. 
26.4 
0.38 
0.66 
9003,200 
2,3006,800  
2.66 
0.38 
0.40 
9003,200 
6,80020,000  
2 in. 
4.06 
0.41 
0.45 
9003,600 
2,30020,000  
4 in 
1.80 
0.40 
0.40 
5,00010,000 
2,50020,000  
Berl saddles:  
1/2 in. 
62.8 
0.30 
0.74 
9003,200 
2,3006,800  
0.741 
0.30 
0.24 
9003,200 
6,80020,000  
1 in. 
2.09 
0.36 
0.40 
9003,600 
1,80020,000  
1.5 in. 
6.14 
0.32 
0.45 
9004,500 
1,80020,000  
3in. partition rings  
(stacked staggered) 
1338 
0.58 
1.06 
7004,100 
13,00020,000  
Spiral rings  
(stacked staggered):  
3in. single 
2.17 
0.35 
0.29 
6003,200 
13,00045,000  
spiral  
3ln. triple 
21.7 
0.38 
0.60 
9004,500 
2,30013,000  
spiral  
Drippoint  
(continuous flue):  
No. 6146 
4.02 
0.37 
0.39 
6004,500 
13,00030,000  
No. 6295 
5.40 
0.17 
0.27 
4504,500 
600 300 60 30

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