Yi yz

Equation (7.33) demonstrates that one overall gas-transfer 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 half-way 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

Liquid-film 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 * 10-3

0.22

1,800-68,000

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

3-in. partition rings

(stacked staggered)

0.0168

0.09

13,000-63,000

Spiral rings (stacked

staggered):

3-in. single spiral

1.95 * 10-3

0.28

1,800-68,000

3-in. triple spiral

2.49 * 10"3

0.28

13,000-63,000

Drip-point grids

(continuous flue):

No. 6146

3.51 ' 10"3

0.23

15,000-135,000

No. 6295

1.50* 10"3

0.31

11,000-100,000

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.

Absorption Factor Mass Transfer
Figure 7.13. Graphical determination of transfer units (absorption).

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 non-diffusing 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 liquid-foam 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 so-called 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

Gas-film 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

900-2,300

2,300-6,800

1 in.

9.31

0.39

0.58

900-3,600

1,800-2,300

8.53

0.32

0.51

900-2,700

2,300-20,000

1.5 in.

26.4

0.38

0.66

900-3,200

2,300-6,800

2.66

0.38

0.40

900-3,200

6,800-20,000

2 in.

4.06

0.41

0.45

900-3,600

2,300-20,000

4 in

1.80

0.40

0.40

5,000-10,000

2,500-20,000

Berl saddles:

1/2 in.

62.8

0.30

0.74

900-3,200

2,300-6,800

0.741

0.30

0.24

900-3,200

6,800-20,000

1 in.

2.09

0.36

0.40

900-3,600

1,800-20,000

1.5 in.

6.14

0.32

0.45

900-4,500

1,800-20,000

3-in. partition rings

(stacked staggered)

1338

0.58

1.06

700-4,100

13,000-20,000

Spiral rings

(stacked staggered):

3-in. single

2.17

0.35

0.29

600-3,200

13,000-45,000

spiral

3-ln. triple

21.7

0.38

0.60

900-4,500

2,300-13,000

spiral

Drip-point

(continuous flue):

No. 6146

4.02

0.37

0.39

600-4,500

13,000-30,000

No. 6295

5.40

0.17

0.27

450-4,500

600 300

60 30

2

1 /

0.01

0.03

Figure 7.14. Plot for determination of flooding point. (1) Grids. (2) Stacked rings. (3) Random packing of rings.

The flooding point represents the upper limit for the operation of the tower. Operating conditions of the tower can be improved by increasing the gas flow. Usually a gas flow of 50-60% of the flow corresponding to the flooding point is used. The diameter of the tower is found by the following procedure:

1.Based on L, G the specific gravity of the liquid and the gas, l and Fig. 7.14, is found (1w/dh2/3 * 103). dh2/3 is shown in Table 7.4 for different packing materials.

2.lw and dh must be chosen so, that lw is greater than 0.08 m3/m/h for common packing including raschig rings less than 7.5 cm, and greater than 0.12 m3/h for raschig rings larger than 7.5 cm.

3.Generally, 0.4 m3/m/h can be considered as the upper limit for all types of packing.

4.Based on equation (7.39) and the total flows (kg/m2) it is possible to find the area of cross-section of the absorption stripping tower.

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