2000 4000 6000 10,000 20,000 Average <?, (Ib.)/(hn)(sq.ft.)

2000 4000 6000 10,000 20,000 Average <?, (Ib.)/(hn)(sq.ft.)

FIG. 14-78 Mass-transfer coefficients versus average gas velocity—HCl absorption, wetted-wall column. To convert pound-moles per hour-square foot-atmosphere to kilogram-moles per second-square meter-atmosphere, multiply by 0.00136; to convert pounds per hour-square foot to kilograms per second-square meter, multiply by 0.00136; to convert feet to meters, multiply by 0.305; and to convert inches to millimeters, multiply by 25.4. [Dobratz et al., Chem. Eng. Prog., 49, 611 (1953).]

Gaylord and Miranda [Chem. Eng. Prog., 53,139M (1957)] using a multitube cocurrent-flow falling-film hydrochloric acid absorber for hydrogen chloride absorption found

Mi75

DtubeG

where Kg = overall mass-transfer coefficient, (kg mol)/(s m2 atm) Mm = mean molecular weight of gas stream at inlet to tube Dtube = diameter of tube, m

G = mass velocity of gas at inlet to tube, kg/(sm2) | = viscosity of gas, Pas

Note that the group DubeG/l is dimensionless. This relationship also satisfied the data obtained for this system, with a single-tube fallingfilm unit, by Coull, Bishop, and Gaylor [Chem. Eng. Prog., 45, 506 (1949)].

The rate of mass transfer in the liquid phase in wetted-wall columns is highly dependent on surface conditions. When laminar-flow conditions prevail without the presence of wave formation, the laminar-penetration theory prevails. When, however, ripples form at the surface, and they may occur at a Reynolds number exceeding 4, a significant rate of surface regeneration develops, resulting in an increase in mass-transfer rate.

If no wave formations are present, analysis of behavior of the liquidfilm mass transfer as developed by Hatta and Katori [J. Soc. Chem. Ind., 37, 280B (1934)] indicates that k, = 0.422 .

Dl = liquid-phase diffusion coefficient, m2/s p = liquid density, kg/m3 Z = length of surface, m kl = liquid-film-transfer coefficient,

(kg-mol)/[(s-m2)(kg-mol)/m3] r = liquid-flow rate, kg/(sm) based on wetted perimeter | = viscosity of liquid, Pa- s g = gravity acceleration, 9.81 m/s2

FIG. 14-79 Liquid-film resistance in absorption of gases in wetted-wall columns. Theoretical lines are calculated for oxygen absorption in water at 55°F. To convert feet to meters, multiply by 0.3048; °C = % (°F — 32). (Sherwood and Pigford, Absorption and Extraction, 2d ed., McGraw-Hill, New York, 1952. )

FIG. 14-79 Liquid-film resistance in absorption of gases in wetted-wall columns. Theoretical lines are calculated for oxygen absorption in water at 55°F. To convert feet to meters, multiply by 0.3048; °C = % (°F — 32). (Sherwood and Pigford, Absorption and Extraction, 2d ed., McGraw-Hill, New York, 1952. )

When Z is large or r/pBF is so small that liquid penetration is complete, and kf = 11.800 Df/BF

A comparison of experimental data for carbon dioxide absorption obtained by Hatta and Katori (op. cit.), Grimley [Trans. Inst. Chem. Eng., 23, 228 (1945)], and Vyazov [Zh. Tekh. Fiz. (U.S.S.R.), 10, 1519 (1940)] and for absorption of oxygen and hydrogen by Hodgson (S.M. thesis, Massachusetts Institute of Technology, 1949), Henley (B.S. thesis, University of Delaware, 1949), Miller (B.S. thesis, University of Delaware, 1949), and Richards (B.S. thesis, University of Delaware, 1950) was made by Sherwood and Pigford (Absorption and Extraction, McGraw-Hill, New York, 1952) and is indicated in Fig. 14-79.

In general, the observed mass-transfer rates are greater than those predicted by theory and may be related to the development of surface rippling, a phenomenon which increases in intensity with increasing liquid path.

Vivian and Peaceman [Am. Inst. Chem. Eng. J., 2, 437 (1956)] investigated the characteristics of the CO2-H2O and Cl2-HCl, H2O system in a wetted-wall column and found that gas rate had no effect on the liquid-phase coefficient at Reynolds numbers below 2200. Beyond this rate, the effect of the resulting rippling was to increase significantly the liquid-phase transfer rate. The authors proposed a behavior relationship based on a dimensional analysis but suggested caution in its application concomitant with the use of this type of relationship. Cognizance was taken by the authors of the effects of column length, one to induce rippling and increase of rate of transfer, one to increase time of exposure which via the penetration theory decreases the average rate of mass transfer in the liquid phase. The equation is kh j u,

where Dt = diffusion coefficient of solute in liquid, ft2/h g = gravity-acceleration constant, 4.17 X 108 ft/h2 h = length of wetted wall, ft ke = mass-transfer coefficient, liquid phase, ft/h

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