Gilliland. E. R., Sullivan, T. E.. Chem. Eng. Prog.. Symp. Ser., 48 (2), 18
Subscripts d = dissociation
(1952).
i = componenti ref = reference
Literature Cited Alesandrini, C. G.. Lynn, S..Prausnitz. J. M.. ind. Eng. Chem., Process Des. Dev., 11, 253 (1972). Antezana, F. J., doctoral dissertation, Columbia University, New York, N.Y.,
1974 Antezana. F. J., Cheh, H. Y., ind. Eng. Chem., Fundam., 14, 224 (1975) Benedict, M., Webb, G. B.. Rubin. L. C., J. Chem. Phys., 8, 334 (1940). Black, C., Ind. Eng. Chem., 5 0 , 391 (1958). Field, T. E., J. Am. Chem. SOC.,56, 2535 (1934). Gillespie, L. J., Proc. Am. Acad. Arts Sci., 66, 153 (1940). Gillespie, L. J., Gerry, H. T.. J. Am. Chem. SOC.,53, 3962 (1931). Gillespie, L. J , Lurie, E., J. Am. Chem. SOC.,53, 2978 (1931).
Groenier, W. S.,Thcdos. G., J. Chem. Eng. Data, 5 , 285 (1960). Huttig, G. F., Martin, W., 2.Anorg. Chem., 125,269 (1922). Kazarnovskii, Ya. S.,Simonov, G. 0.. Aristov, G. E., Russ. J. Phys. Chem. 14, 774 (1940). Lurie, E., Gillespie, L. J., J. Am. Chem. SOC.,49, 1146 (1927). Martin, J. J., Hou, Y. C., A.i.Ch.E. J., 1, 142 (1955). Onnes, H. K.. Proc. Acad. Sci. (Amsterdam), 4, 125 (1902). Perkins, A. J., J. Chem. Phys., 5 , 180 (1937). Poynting. J. H., Phil. Mag., 12(4).32 (1881). Reamer, H. H., Sage, B. H., J. Chem. Eng. Data, 4,152 (1959). Redlich, O.,Kwong, J. N. S.,Chem. Rev., 44, 233 (1949). Walter, L. S.,Am. J. Sci., 261, 151 (1963).
Received for reuiew October 21,1974 Accepted January 19,1976
Absorption of Ethylene in Bromine Solutions in a Packed Column Aminul Huq
'
Department of Chemical Engineering, University of Sydney, Sydney, Australia
Rates of chemical absorption in a 2-in. diameter column packed with '/&in. ceramic Raschig rings at normal atmospheric conditions in the temperature range of 20 to 30 OC indicated that the ethylene-bromine-water reaction is in accord with the penetration theory. The effective interfacial area, calculated from the theory of a pseudo first-order reaction, was found to b e consistent with values extrapolated from other reported values.
Introduction I t is desirable to know the values of the true mass transfer coefficients and the effective interfacial area, separately, in order to have a better understanding of the various factors which affect these values and also for prediction of effects of the chemical reaction on the rate of mass transfer. Supplementary to the physical and chemical absorption measurements in the laminar liquid jet apparatus (Huq and Wood, 1968, 1974; Huq, 1969), a series of aborption runs were carried out with ethylene gas and aqueous solutions of bromine in a small, pilot-scale packed column. The objective of these experiments was to see the extent to which the behavior of the scaled-up equipment can be explained in terms of the data obtained on the kinetics of the system in the laminar liquid jet absorber. The results were analyzed in terms of current theories (Danckwerts, 1951, Brian, 1964) to examine their applicability to large-scale equipment. Experimental Section The experiments were carried out a t normal atmospheric conditions in a 2-in. internal diameter column packed with I/4-in. ceramic Raschig rings to a height of 19 in. The pressure varied from 760 to 769 mmHg and the temperature from 20 to 30 O C . The liquid and the gas flowed countercurrently, entering the column from the top and the bottom, respectively. The gas velocity varied from 65 to 95% of the flooding velocity of 418 lb/(ft2)(h),while the liquid velocity was maintained a t 1210 lb/(ft*)(h). (See Table I.) Industries Division, Planning Commission, Government of the People's Republic of Bangladesh, Dacca, Bangladesh; also Adviser on Intra-Regional Training, Colombo Plan Bureau, P.O. Box 596, Colombo 4,Sri Lanka.
Determination of Effective Interfacial Area Because of complications involved in the theory of gas absorption accompanied by a second-order chemical reaction, as is the case with the ethylene-bromine-water system (Huq and Wood, 1974), the values of the mass transfer coefficient and the effective interfacial area of packing under flow conditions were obtained by using the method of absorption with fast, pseudo-first-order reaction (Brian, 1964; Vidwans and Sharma, 1967; Jhaveri and Sharma, 1969). The absorption flux, the mass transfer coefficient, and the ratio of chemical to physical absorption rates are listed in Table 11. The conditions are those for pseudo first-order reaction, based on absorption studies in a laminar liquidjet apparatus with jet lengths varying from 6.39 to 15.14 cm a t 20 O C , from 4.36 to 15.47 cm a t 25 "C, and from 7.12 to 10.04 cm a t 30 "C. I t may be seen that the assumptions for a pseudo-first-order reaction are valid under the experimental conditions. Note that the conditions for pseudofirst-order behavior could also have been tested using the kinetic constants obtained from the laminar-jet studies. However, since these constants were thought to be uncertain because they were derived from experiments carried out under widely differing conditions, the assumptions made in treating the packed column data were tested from the absorption measurements themselves. The effective interfacial area was calculated from the calculated capacity coefficient, K L U , and the liquid-side transfer coefficient, ~ L = R ( D ~ & B ) ~ /The * . rate constant, h2, and the diffusion coefficient, D , were taken from the absorption measurements in the laminar jet (Huq and Wood, 1968, 1974), and are listed in Table 111. The derived values of the interfacial area are given in Table IV. Ind. Eng. Chem., Fundam., Vol. 15, No. 2, 1976
99
Table I. Absorption of Ethylene Gas into Bromine-Water in a Packed Columna Temp, "C
Gas flow rate, 1b/(h )( f t 2)
Table 111: Diffusion Coefficients and Rate Constants of Ethylene Gas in Bromine-Water
HTU, f t
20
280.88 0.57 290.54 0.44 362.03 0.36 339.98 0.45 368.88 0.41 25 290.54 0.45 339.98 0.47 384.09 0.39 399.30 0.33 389.41 0.38 30 389.41 0.41 384.09 0.42 362.03 0.41 399.30 0.35 339.98 0.33 a Column diameter: 2 in.; packing: 1/4-in. ceramic Raschig rings; packed height: 19 in.; liquid rate: 1210 lb/(h)(ft2); liquid concentratim of bromine: 3.5 x l o + g-mol/cm3.
Discussion Table V shows the slopes of straight lines relating the values of log (HTU)OLvs. log ( D ) a t temperatures of 20, 25, and 30 'C, a t constant liquid rate of 1210 lb/(h)(ft2) and the varying gas flow rates of 290,340,362,384,389, and 499 lb/(h)(ft2). The straight lines on the logarithmic plots have been statistically fitted to the data. The slopes are nearly constant over the range of flow conditions; the average value is equal to -0.50 within expected deviations of 8 to 14%. Since, for a pure gas, the gas-side resistance is negligible, it may be reasonably concluded that (HTU)L varies as D-0.50 and h ~ varies a as over the entire range of flow conditions studied. This is in agreement with the prediction of the penetration theory that k~ varies as the square root of diffusivity. This square-root variation characterizes the unsteady-state molecular diffusion of solute into an element of fluid without a velocity gradient, and this appears to be the case for liquid-gas flow ratios of 3:l to 4:l and for flow conditions corresponding to 65 to 95% flooding. Furthermore, there is no indication that the mass transfer process becomes less dependent on molecular diffusivity as flooding is approached. Theories based on turbulent transport occurring in parallel with molecular diffusivity either do not predict an exponent of 0.50 on diffusivity or suggest that the exponent on D should vary widely with flow conditions. Thus to the
Temp, "C 20 25 30
Diffusion Coefficient, D, cmz s 1.40 x 10-5 1.51 x 10-5 1.78 x 10-5
Rate constant, l./(g-rnol )(s1 97 000 164 000 260 000
extent that the present experimental results tend to indicate a constant exponent of 0.50 on D, a mechanism other than unsteady-state penetration into an element of the surface liquid with negligible velocity gradient and with negligible transport zone adjacent to the interface does not appear reasonable. This conclusion does not preclude an effect of larger scale turbulence on the frequency of surface renewal, as distinct from smaller scale eddies which act in parallel with molecular diffusion during a given surface exposure. The observed effect of diffusivity indicates the penetration mechanism without flow-induced small-scale turbulence for transfer a t the gas-liquid interface. A characteristic of this mechanism is the life-time during which the average fluid surface element is exposed. Each packing produces a distribution of liquid surface lifetimes which can be expected to be dependent on packing geometry. Insofar as the packing geometry is assumed to be the only factor affecting lifetime distribution, penetration theory with its assumption of surface renewals predicts that (HTU)L will be proportional to the liquid flow rate per unit wetted perimeter to the % power (Sherwood and Pigford, 1952). Surface renewal by gross turbulence in the course of flow over a continuous length of packing is a factor in the performance of packing and becomes more and more important as the flow rate increases and flooding is approached. These renewals occur without simultaneous appearance of smaller scale eddies near the interface such as would provide an eddy diffusivity to affect the molecular transport process during a given surface exposure. The variations of KLU might have been the effect of surface renewals by gross turbulence and, to some extent, by eddy diffusivity, since the gas velocity varied up to 95% of the flooding velocity. The observed effect of temperature upon (HTU)L indicates an exponential factor with an exponent of -0.016T, where T is in degrees Centigrade. This may be compared with exponents of -0.019 to -0.0202' reported for other systems (Sherwood and Pigford, 1952).
gmol/cm3 ) Table 11. Validity of Pseudo-First-Order Behavior (Liquid Concentration of Bromine: 3.5 X Equilibrium Chemical concn, g-mol/ Physical sorption. cm3, sorption flux, n/(cm2) Temp, n/c* k L a "C c* x lo6 q = c/c* flux g mol (s) x l o 7 k L , cm/s 20 5.32 6.6 1.54 7.05 0.0288 4.57 1.30 6.49 0.0245 4.98 1.19 6.35 0.0223 5.35 1.07 5.98 0.0200 5.60 0.0198 5.76 1.05 6.06 25 4.70 7.45 1.48 7.57 0.0316 5.12 1.01 6.49 0.0215 6.41 0.88 6.00 0.0185 6.85 0.95 6.33 0.0203 6.70 0.87 5.97 0.0184 6.89 30 4.19 8.38 1.29 8.25 0.0308 6.38 7.02 0.0272 1.14 7.98 a Since in all cases n/c*KL is greater than 3 but less than q values, essentially pseudo-first-order behavior holds under such conditions. 100
Ind. Eng. Chern., Fundarn., Vol. 15, No. 2, 1976
Table IV. Gas-Liquid Interfacial Area in Packed Column (Total Surface Area: 7.84 f t 2 ; Packed Volume: 978.15 cm3) Interfacial area Capacity Mass transfer Fraction surface Run no. coeff., ft3/h coeff., f t / h area wetted Ft2 Cm2/cm3 PC-1 PC-2 PC-3 PC-4 PC-5 PC-6 PC-7 PC-8 PC-9 PC-10 PC-11 PC-12 PC-13 PC-14 PC-1 5
34.16 44.16 53.83 42.71 47.42 42.81 41.07 50.30 59.44 51.26 47.24 46.68 47.56 54.81 58.34
25.44 25.44 25.44 25.44 25.44 34.02 34.02 34.02 34.02 34.02 44.90 44.90 44.90 44.90 44.90
Table V. Determination of Slope of HTU as a Function of Solute Diffusivitv Constant liquid rate, Ib/(h)(ft2) 1210
Gas flow rate, Ib/(h)(ft2 290.54 362.03 339.98 384.09 389.41 399.30
Slope, d In (HTU)/d In D -0.46 -0.53 -0.57 -0.46 -0.48 -0.50
The effect of the wall of the column is not significant. Visual observation indicated that only a small fraction of the wall surface was effective for mass transfer; most of the effective interfacial area, a , was in the packing. Values of the effective interfacial area, evaluated from the capacity coefficient and the liquid-side chemical transfer coefficient on the basis of the pseudo first-order theory, scatter widely from 0.99 to 2.01 cm2/cm3. The variations in diffusivity and kinetic constants corresponding to the three temperatures would affect the liquid-side transfer coefficients, while the variations in KLa are explained by packing geometry and surface renewals with gross turbulence. The scatter in the values of the effective interfacial area may be explained by these variations. In particular, scatter in KLa values accounts for scatter in a values a t any particular temperature. The mean of the values of the effective interfacial area, when statistically averaged, is 1.37 cm2/cm3. All the measured values are within f30% of this mean value, with one exception. No values of the effective interfacial area for y4in. Raschig rings are reported in the literature; hence no comparative analysis of the observed interfacial area with literature values is possible. However, by extrapolation from the data of Vidwans and Sharma (1967) and Jhaveri and Sharma (1969) the interfacial area for Y4-in. Raschig rings is estimated to be 1.38 cm2/cm3. The observed values of the interfacial area are consistent with this value and indicate 20 to 25% wetting, similar to values for other packings (Perry, 1963).
0.171 0.221 0.269 0.214 0.237 0.160 0.153 0.188 0.222 0.192 0.134 0.1 32 0.135 0.155 0.165
1.34 1.74 2.12 1.68 1.86 1.26 1.21 1.48 1.75 1.51 1.05 1.04 1.06 1.22 1.30
1.28 1.65 2.01 1.59 1.77 1.20 1.15 1.40 1.66 1.43 0.99 0.99 1.01
1.16 1.23
Conclusions The absorption of ethylene gas into aqueous solutions of bromine-water in a packed absorber is found to be consistent with the penetration theory: the operating conditions satisfy the conditions of the pseudo-first-order reaction model. The effective interfacial area and the mass transfer coefficients are calculated by using the method of absorption with fast pseudo-first-order reaction and data from the laminar liquid jet experiments. The measured values of the effective interfacial area are consistent with the value extrapolated from other reported values. Nomenclature a = interfacial area, cm2/cm3 c * = equilibrium concentration, g-mol/cm3 CB = concentration of reacting solvent, g-moUcm3 D = diffusion coefficient, cm2/s k2 = reaction rate constant, l./(g-mol) (s) k~ = liquid side physical transfer coefficient, cm/s ~ L R= liquid side chemical transfer coefficient, cm/s K L = overall absorption coefficient, lb/(h)(ft2)(atm) N = overall absorption rate, g-mol/s n = instantaneous rate of absorption, g-mol/(cm2)(cm) HTU = height of transfer unit, f t NTU = number of transfer unit q = c/c*, ratio of liquid to equilibrium gas concentration L i t e r a t u r e Cited Brian, P. L. T., AlChEJ., 10, 5 (1964). Danckwerts,P. V., lnd. Eng. Chem., 43, 1460 (1951). Danckwerts,P. V., Sharma, M. M., Trans. Inst. Chem. Eng., 44, 284 (1966). Huq, A,, Ph.D. Thesis, University of Sydney, 1969. Huq. A,, Wood, T.. J. Chem. Eng. Data, 13, 256 (1968). Huq, A,, Wood, T.. Chem. Eng. Sci., 29,31 (1974). Jhaveri. A. S., Sharma, M. M., Chem. Eng. Sci., 23, 669 (1968). Jhaveri, A. S., Sharma, M. M.. Chem. Eng. Sci., 24, 189 (1969). Perry, R. H. et al.. "Chemical Engineers' Handbook," 1963. Sherwood, T. K., Holloway, A. W., Trans. Am. Inst. Chem. Eng., 36, 39 (1940). Sherwood, T. K., Pigford, R. L.. "Absorption and Extraction," McGraw-Hill, New York, N.Y., 1952. Vivian, J. E., King, C. J.. A./.Ch.E.J., I O , 220(1964). Vidwans, A. D., Sharma, M. M., Chem. Eng. Sci., 22, 673 (1967).
Receiued for review November 18,1974 Accepted December 15,1975
Ind. Eng. Chem., Fundam., Vol. 15, No. 2, 1976
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