Nakanishi, K., "Practical Infrared Absorption Spectroscopy." pp 14, 20, 26. Holden-Day, San Francisco, Calif.. 1966. Rall, H. T., Smith, H. M.,Ind. Eng. Chem., Anal. Ed., 8, 324, 436 (19361. , - - - /
Rice, H.T.. Lieber, E., Ind. Eng. Chem., 16, 107 (1944). Roberts, J. D., "Nuclear Magnetic Resonance: Application to Organic Chemistry." pp 20, 22, 23, McGraw-Hill. New York, N. Y., 1959.
Ruh. E. L., Walker. R. W., Dean, E. W.. Ind. Eng. Chem., Anal. Ed., 13, 346 (1941). Shell International Research, Neth. Pat. Appl., 6,413,449; Chem. Abstr.. 65. 12106a (1966).
Received for review October 23,1973 Accepted April 16,1974
Design of Direct Contact Humidifiers and Dehumidifiers Using Tray Columns Everett C. Barrett* and Stephen G. Dunn Hatch Associates Ltd.. Toronto. Ontario. Canada M4T 7L9
Simultaneous mass and heat transfer equations for dehumidifying or humidifying in direct contact tray towers are presented and a solution procedure outlined which is readily adapted to a digital computer. T h e mass transfer coefficients are calculated from t h e penetration theory and t h e Chilton-Colburn analogy is used for heat transfer coefficients. T h e equations apply to a wide range of systems without t h e limitations of previous methods and can be used for both superheated and supersaturated (fogging) vapors. Analysis of plant data for a hydrogen sulfide-water dehumidifier on sieve trays shows good agreement between measured and calculated values. Design of a hydrogen-water h u midifier/dehumidifier system on grid trays indicates the presence of fogging in t h e dehumidifier. If 50% or more of t h e fog is scrubbed out below each tray, only a small amount of fog remains in the exit gas.
The success of the Canadian nuclear power program is accelerating the growth of Canada's heavy water industry. Direct contact cooling, dehumidification, heating, and humidification of very large gas flows are an important part of heavy water production processes now in use or being developed (Rae, 1971). These involve mass and heat transfer performance of direct contact sieve and grid tray contactors under more severe conditions than treated by previous design methods. The new method reported here was developed during studies of heavy water processes undertaken for Atomic Energy of Canada Limited. Direct gas-liquid contact for gas cooling and dehumidification is used where fouling or pressure drop considerations are of importance or where a low heat transfer resistance is required. With dusty or corrosive gases or with corrosive cooling water, fouling in a tubular heat exchanger may be unacceptable while in applications such as barometric condensers, the pressure drop resulting from a velocity needed to provide a reasonable heat transfer coefficient would be higher than allowed. Problems associated with direct contact heat transfer are the potential incompatibility of the gas and liquid and the absorption of the gas in the cooling liquid. Design methods for direct contact dehumidifying incorporating varying degrees of simplification have been proposed. The enthalpy potential method first developed by Merkel in 1925 and also used in cooling water tower design has been reported by Kern (1950), Bras (1956a), and Olander (1961). The approach is only valid for systems with a vapor mole fraction in the gas below 0.15 as it assumes that mass transfer is proportional to the humidity driving force rather than the vapor partial pressure driving force. It is also restricted to systems such as air-water with a Lewis number of unity. Additional restrictions are detailed by Bras and Olander. In a further article Bras (1956b) developed a method for saturated gas-vapor mixtures with a small gas-liquid A t while Kern (1950) ex-
panded the enthalpy potential method for Le # 1 but still retained the humidity driving force which limits the method to low humidities. Fair (1972a,b) based his method on overall mass transfer coefficients and related them to heat transfer by analogy. To apply this method to tray columns the Carey temperature efficiency must be assumed equal to the Murphree mass transfer efficiency. This approach is not practical for a tray by tray calculation. Olander (1961) proposed a design method based on material and enthalpy balances assuming a constant height of gas phase transfer unit and appropriate heat and mass transfer analogies. His method applies to superheated vapors only. None of these previous methods accounted for the solubility effects of the gas in the liquid phase as they were concerned with relatively insoluble gases in low-pressure systems Because mass and heat transfer performance of direct contact sieve and grid tray contactors under more severe conditions than treated by previous methods was to be examined, a new approach was necessary. The systems to be studied were water-hydrogen at lo00 psia and temperatures of 100 to 625°F and water-hydrogen sulfide a t 200300 psia and temperatures of 80 to 270°F. Because the vapor phase Lewis number of the water-hydrogen system a t high temperatures is greater than 1 the possibility of supersaturation or fog formation had to be considered. In the water-hydrogen sulfide system the solubility of hydrogen sulfide in water and the resulting heat effects had to be accounted for. Mass and heat transfer rate equations for these conditions are developed and applied using the penetration theory for mass transfer coefficients and the Chilton-Colburn analogy for heat transfer coefficients. Mass and Heat Transfer Equations The mass and heat transfer relations developed are based on the gas and liquid flows on the tray shown in Figure 1, and the gas-liquid interface shown in Figure 2. Ind. Eng. Chem.. P r o c e s s Des. Develop., Vol. 13, No. 4 , 1 9 7 4
353
IT
1
p2
(c) the heat balance on the gas and liquid phases W
g
2
LiHli + Ei(He1 - H I i ) + Ez(H12 - He2
- GiHgi = L2H12
-
(d) the water vapor mass balance
G2Y2 - GiYi = k g ( f i - f g 2 ) a r A a h f (e) the dissolved gas mass balance
G’i - GC2 = LIXi - L2Xz
The gas and liquid enthalpies were evaluated from a physical property program for the appropriate gas-liquid system.
Figure 1. Tray stream parameters. LIQUID
I
(5)
GAS
Avapor fugacity coefficient of unity has been used so that
P*Y
f g
for t, =in
2
t,
or P*Ys f g
Figure 2. Conditions at the gas-liquid interface on a tray.
The case illustrated in Figure 2 depicts gas cooling and dehumidification but the model can be used for heating and humidification as well. The relations used are based on the following principal assumptions. (1) Both gas and liquid phases are assumed to be perfectly mixed so that the conditions of the gas and liquid streams leaving a tray are representative of conditions on the tray. (2) Entrained liquid leaving a tray is assumed to be at the same temperature as the liquid on the tray. (3) All liquid streams are assumed saturated with gas a t their temperature and pressure. (4)The dissolved gas in the entrained liquid is negligible and may be omitted. (5) The entrained liquid entering a tray will be scrubbed out by the vigorous gasliquid contact on that tray. (6) Fog droplet nucleation will occur immediately so that any gas-phase supersaturation results in fog. (7) The fog formed is a t the same temperature as the gas phase. (8) The interfacial areas available for heat and mass transfer are equal. The main equations are: (a) the heat balance across the gas-liquid interface
(b) the overall heat balance on the liquid phase 354
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 4, 1974
=
14.7 for
t,
