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Effect of diffusivity on gas-side mass transfer coefficient
ChemicalEngineeringScience,1966,Vol. 21, pp. 361-365. PergamonPress Ltd., Oxford. Printed in Great Britain.
Effect of diffusivity on gas-side mass transfer coefficient V. D. MEHTA and M. M. SHARMA Department of ChemicalTechnology,Universityof Bombay, Matunga, Bombay-19(INDIA). (Received 24 August 1965) Abstract-The effect of diffusivity on gas-side mass transfer coefficient was studied in an experimental bubble column. A fourteen-fold variation of diffusivity was obtained by using a variety of solutes and carrier gases. Both absorption and vaporization experiments were car&d ou< some&es for the same solute. The absorption experiments were unambiguously gas-film controlled. The gas-side mass transfer coefficient varies as 0.5 power of the di&sivity under similar hydrodynamic conditions. Schmidt number is most unlikely to be the pertinent variable. It is also likely that the gas-side mass transfer coefficient varies as 0.33 power of the submergence and 0.75 power of the gas flow rate.
THE EFFECT of diffusivity on gas-side mass transfer coefficient has been the subject matter of a number of publications [l-5]. However, most of the work has been done on the vaporization of solutes in a variety of carrier gases. It is also not clear whether the diffusivity or the Schmidt number is the pertinent variable. In this work a fourteen-fold variation in diffusivity was obtained by using a variety of solutes and carrier gases. Both absorption and vaporization experiments were carried out, sometimes for the same solute. EXPERIMENTAL
Experiments were carried out at essentially atmospheric pressure and a temperature of about 29°C in a 5.2 cm dia. tube, having a 2 mm nozzle at the bottom for gas-inlet, with liquid depths in the range of 4-8 cm. The gas flow rate was varied from about 10 to 23 cm3/sec. The flow of gas through the nozzle is likely to simulate the flow of gas through a slot in a bubble cap column. Hydrogen, nitrogen, Freon-12 (dichlorodifluoromethane) and Freon-l 14 (dichlorotetrafluoroethane) were the carrier gases. The following solutes were used: chlorine, sulphur dioxide, ammonia, n-butylamine, di-n-propylamine, triethylamine, methyl ethyl ketone, n-butyl formate and ethyl propionate. Chlorine and sulphur dioxide were absorbed in aqueous sodium hydroxide solutions (l-6 N) and amines in dilute sulphuric acid solutions (-2N) so
that the liquid side resistance could be completely eliminated. Absorption. Flow rates of the solute gas;NH,, Cl, and SOJ and the carrier gas were adjusted by opening the needle valves to give 3-10 per cent (usually about 5 per cent) of the solute in the gas mixture. The gases were metered by soap-film meters. A known amount of the absorbent was introduced in the bubble column and the stop-watch started. A check was made of the flow rate during the run. The pressure of the gas entering the column and temperatures of the gas entering and leaving the column were recorded. After a definite time (usually 10 min) the liquid was taken out and analysed. For the absorption of amines, carrier gas saturated with an amine at a known temperature entered the column. The static pressure of the gas to be metered was also recorded. The amounts of sulphite and hypochlorite were determined by the iodometric method [6]. In the case of absorption of amines in a known volume and strength of sulphuric acid, the free acid was determined by the standard acidimetric titration using bromophenol blue as an indicator [6]. Vaporization. A known volume of solute was taken and the flow rate of the carrier gas adjusted to a prefixed rate. After two to three minutes the outlet gas was passed through two bottles (in series) of appropriate solutions which completely removed the solute from the carrier gas. After a definite time
361
V. D. MEHTA
and M. M. SHARMA
the above bottles were disconnected and the gas allowed to go to the atmosphere. The temperatures of the liquid before and after a run were also recorded. In the case of amines the sample bottles contained a known volume and strength of sulphuric acid. The amount of amine vaporized was estimated by back titrating the excess free acid (the difference between the initial and final readings gives the amount of amine vaporized in a given time). The outlet concentration of methyl ethyl ketone was determined by absorbing the ketone in a known I I I -5 101 volume of water. The methyl ethyl ketone in water IO I. IO I 30 I 10 I 20 09 was analysed by the hydroxylamine hydrochloride log,,U method. In the case of ethyl propionate and IEbutyl formate the solutes were absorbed in about FIG. 2. Effect of gas flow rate on KGa for the absorption of 50 % aqueous ethanol and estimated by the SOa (carrier gas-Freon-12) in aqueous sodium hydroxide solution (submergence = 4 cm). saponification method. RESULTS
AND DISCUSSION
For the calculation of &a the vapor pressure data of n-butylamine, di-n-propylamine and triethylamine were taken from reference [7], and that for methyl ethyl ketone, n-butyl formate and ethyl propionate from reference [S]. The flow of the gas through the column followed the pattern of chain bubbling, therefore the coalescence of the bubbles, which otherwise could have affected both the values of KG and effective interfacial area, was unimportant. In addition visual observation indicated no difference in the hydrodynamic behaviour for all the systems investigated
( SO2and N,)
0
2.0 "0 x 0
(S&and
Freon-12) 0
x”
“11 IO
Liquid
FIG. 1.
viscosity,
3.0
4.0
cp
Effect of liquid viscosity on KGU (gas flow rate = 16 cms/sec submergence = 4 cm).
under a given set of gas flow rate and the submergence. Figure 1 shows that K,a for absorption of SOZ (carrier gas-Freon-12) in aqueous sodium hydroxide solution is independent of viscosity of the solution indicating an absence of liquid side resistance (the viscosity of the sodium hydroxide solution was varied by increasing the normality of the solution from 2-6N). This is also in conformity with the information available in literature that in bubblecap columns for gas-film controlled process the liquid viscosity is unimportant [9]. In the case of the absorption of triethylamine in dilute sulphuric acid an additional experiment was carried out where the acid solution contained about 1.8 g moles/l. of sodium sulphate which increased the viscosity of the solution from 1.19 to 2.22 cp. The K,a values in the two experiments were practically the same indicating absence of liquid-side resistance. The absorption experiments were, therefore, unambiguously gas-film controlled. Figure 2, a log-log plot of K,a for the absorption of SO, (carrier gas-Freon-12) in aqueous sodium hydroxide solution against superficial gas velocity shows that K,a varies as O-75power of gas flow rate (U), cm3/sec. Experimental K,a values corrected to a gas flow rate of 16 cm3/sec are plotted in Figs. 3 and 4. The maximum variation in the gas flow rate around 16 cm3/sec was 7 per cent. 362
Effect of diffusivity on gas-side mass transfer coefficient
FIG. 3.
Effect of diffusivity on KGU(gas flow rate
= 16cm3/sec, submergence = 4 Cm).
Legend 14. Absorption. (1). Ammonia-Freon-l (3). Ammonia-Nitrogen. (4). Chlorine-Freon-12. 14. (6). Sulphur dioxideFreon-l (7). Sulphur dioxide-Freon-12. (9). n-Butylamine-Freon-12. (10). Di-n-propylamine-Freon-114. (12). Di-n-propylamine-Hydrogen. (13). Triethylamine-Freon-114. (15). Triethylamine-Nitrogen. (16). Triethylamine-Hydrogen. Multicomponent absorption. (17). Ammonia-Freon-12 and Hydrogen.
(2). Ammonia-Freon-12. (5). Chlorine-Nitrogen. (8). Sulphur dioxide-Nitrogen. (11). Di-n-propylamine-Freon-12. (14).
Triethylamine-Freon-12.
(18). Sulphur dioxide-Freon-12
and
Hydrogen. Vaporization. (21). n-Butylamine-Nitrogen. (24). Di-n-propylamine-Hydrogen. (27). Triethylamine-Nitrogen. (30). Methyl ethyl ketone-Nitrogen. (33). nButy1 formate-Hydrogen.
Figure
(25): (28). (31). (34).
n-Butylamine-Freon-114. Di-n-propylamine-Freon-114. Triethylamine-Freon-114. TriethylamineHydrogen. n-Butyl formate-Freon-114. Ethyl propionate-Freon-12.
3, a log-log plot of &a against diffusivi-
ties of solutes in various carrier gases, shows that &a varies as the O-5 power of the diffusivity. The diffusion coefficients were calculated by the method of HIRSCHFELDER,BIRD and SPOTZ modified by WILKE and LEE [lo]. The reported value of the diffusion coefficient for ammonia in nitrogen [l l] was corrected for temperature [12]. In the case of
n-ButylamineFreon-12. Di-n-propylarnine-Freon12. Triethylamine-Freon-12. (29). Methyl ethyl ketone-Freon-l 14. (32). n-Butyl formate-Freon-12. (35). Ethyl propionate-Hydrogen.
vaporization the values of the diffusion coefficients refer to the temperature and pressure of the experiment. The range of diffusivities covered was from about O-023to O-32cm’/sec giving about a fourteenfold variation of diffusivity. The maximum value of the diffusion coefficient available at ambient conditions is about 0.9 cm’/sec (ammonia in hydrogen). However, systems with diffusion coefficients
363
V. D. MEHTAand M. M. SHARMA
Table 1.
Eflect
of
diJiisivity
vs.
Schmidt
number on gas-side mass transfer coeflcient.
Run No.
Solute
Carrier gas
Nature of experiment
& (cm2/sec)
Schmidt no.
2.
Ammonia Sulphur dioxide
Freon-l 2 Nitrogen
Absorption Absorption
Ammonia Triethylamine Triethylamine Ammonia Methyl ethyl ketone
Hydrogen Nitrogen Hydrogen Freon-l 14 Nitrogen
Absorption Vaporization Absorption Vaporization
0.125 0.141 0.254 0.3075 0.296 0.1075 0.115
0.206 1.12 0.63 364 3.78 0.161 1.39
16: :* 28. 1. 30.
higher than O-3 cm2/sec were not used as the outlet concentration of the solute, becomes very low in the case of absorption and approaches saturation in the case of vaporization and in both the cases a small error in analysis could give very misleading results. A number of solutes were considered to And out whether diffusivities substantially lower than O-023 cm2/sec at ambient conditions (atmospheric pressure and 30°C) could be obtained. With Freon-l 14 as the carrier gas, diffusion coefficients (cm2/sec) for some of the solutes that are likely to be useful are: tetrachloroethylene-O-0232, sulphuryl chloride0.028, silicon tetrachloride-O.0265, paraldehyde -0.022 etc. which shows that none of these solutes provide diffusivities lower than O-022 cm2/sec. The diffusion coefficient of triethylamine in Freon-C318 (C,Fs, mol. wt. = 200) is 0*0227 cm2/sec. In the case of n-butylamine, di-n-propylamine and triethylamine both absorption and vaporization experiments were carried out. &a values obtained from the two sets agreed closely. Table
2.
E#ect
of d@iivity
vs. Schmidt
(Triethylamine Run no.
13 14 ‘15 16 25 26 27 28 -
Solute
Triethylamine Triethylamine Triethylamine Triethylamine Triethylamine Triethylamine Triethylamine Triethylamine
Carrier gas
Nature of experiment
Freon-l 14 Freon-l 2 Nitrogen Hydrogen Freon-l 14 Freon-12 Nitrogen Hydrogen
Absorption
Vaporization
Experimental Kca x 105 (g-mole&c cm3 atm at gas flow rate of 16 cm”/sec) 2.06 2.24 2.86 3.22 3.07
The &a values for multi-component systems, where a given solute with a binary mixture of carrier gases were used, agree well with those for binary systems having the same diffusivities. The diffusivity of a solute in multi-component systems was calculated by the method of WILKE and LEE [13]. Table 1 indicates that systems having the same diffusivities show practically the same mass transfer coefficient in spite of variation of the Schmidt number by factors up to about eight. This clearly shows that Schmidt number is most unlikely to be a correlating factor and the data are very well correlated with D o’5, When the pressure is increased for a particular system, the Schmidt number remains substantially the same but the diffusivity varies inversely as the pressure, and therefore according to our findings the mass transfer coefficient should decrease with increase in pressure at a given superficial velocity. The proportionality of &a to D8”’ may not hold for other type of transfer equipment, such as packed columns. number on gas-side mass transfer coefficient.
in a variety of carrier gases).
:&sec)
L P D
0.0248 0.0288 0.0752 0.3075 O-0231 0.0271 0.072 0.296
0*70 090 2.13 364 0.75 0.955 222 3.78
364
K,a x lo5 g-moles/ Values of Kca x lo5 set cm3atm at gas based on -0.5 flow rate of 16 Dg’J.5 cms/sec 0.935 0.972 1.76 3.22 0.89 1.02 1.63 3.07
0.935 1.01 1.61 3.29 0.89 0.965 1.57 3.18
0.935 0.824 0.533 0.410 0.890 0.790 0.518 0.398
Effect of ditTusivity on gas-side mass transfer coefficient
‘W,,
equally marked when a single solute is absorbed or vaporised with a variety of carrier-gases (as was done in the A.1.Ch.E. programme [l-4]). See Table 2. Figure 4 shows that &a for the absorption of SO2 (Carrier gas-Freon-12) in aqueous sodium hydroxide solution is likely to vary as one third power of submergence (S). Work is in progress to determine the effect of various variables on &a in a model bubble-cap column. The work reported in this paper indicates that the following relationship is likely to hold :
s
FIG. 4. Effect of submergence on KGa for the absorption of SOa (carrier gas-Freon-12) in aqueous sodium hydroxide solution (gas flow rate = 16 cm3/sec).
The differences between values of &a predicted on the basis of Schmidt number and diffusivity are
KGa cc D/5
uo.75 So.33
ANDREW[14] has shown that the above equation correlates the data reported in Bubble-Tray Design Manual [l].
REFERENCES
PI
Bubble-Tray Design Manual A.1.Ch.E. New York 1958. from Universitv of Delaware A.1.Ch.E. New York 1958. from University of Michigan A.1.Ch.E. New York 1958. from North Carolina State College A.1.Ch.E. New York 1959.
121 Trav Efficiencies in Distillation Columns Final Reoort [31 Tra; Ekciencies in Distillation Columns Final Report [41 Tray efficiencies in Distillation Columns Final Report PI GERSER J. A., Chem.Engng Prog. 1963 59 35. Kl VOGEL, Text book of Quantitative Inorganic Analysis
Longman, Green and Co., New York (2nd Ed.) p. 354. Bulletin on Alkyd and Alkylene Amines Union Carbide Chemicals Co. New York. :;; PERRYJ. H. Chemical Engineers’ Hand Book (4th Ed. pp. 3-55) McGraw Hill Book Co. Inc., New York 1963. [91 GERSTERJ. A., Znd. Engng Chem. ind. (int’.) Edn. 1960 52 645. 1101 WILKE C. R. and LEE C. Y., Znd.Engng Chem. ind. (int.) Edn 1955 47 1253. [111 TRAUTZ M., and MULLER, W. Ann. Phys. 1935 22 333. 1121 CHEN N. H. and OTHMBRD. F. J. them. and Engng Dara 1963 8 168. 1131 WILKE C. R. Chem. Engng Prog. 1950 46 95. P41 ANDREW S. P. S. Alta Technoligia Chemica Processi di Scambia p. 153 Academia Nationale dei Lincei, Rome 1961. R&um&I_es auteurs de cet article &udient l’influence, sur le coefficient de transfert de masse, c&k gaz, de la diffusivitk d’un mklange gazeux bullant &travers un liquide dam une colonne. 11srkussirent & faire varier la diiusivite dans le rapport. 1 & 14 en utilisant une varif& de gaz dissous dans certains gaz servant de gaz d’entrainement; ils effect&rent des essais g la fois d’absorption et de vaporisation, exp&iences rkalis&es quelquefois sur le meme gaz dissous. Les essais d’absorption furent contra& d’une man&e nette et p&&se, par la thkorie du film gazeux. IX coefficient de transfert de masse varie comme la racine car& daladiiusivite dans des conditions hydrodynamiques simiiaires. Les auteurs nous montrent que certains syst&mes prksentant les msmes diffusivitcs prbentaient pratiquement le meme coefficient de transfert de masse mais une variation tr& accu& du nombre de Schmidt: il est done t&s peu probable que le nombre de Schmidt soit la variable adequate. Le coefficient de transfert de masse c&b gaz varie t&s certainement comme la hauteur du liquide dans la colonne g la puissance 0,33, et, comme la vkesse de passage du melange gazeux & travers le liquide g la puissance 0,75. Zusammenfassung-In einer Biasenkolonne wurde der EinfluR des Diffusionskoeffizienten auf den gasseitigen StoffiibertragungskoelTizienten bei Absorption+ und Verdampfungsvorangen (bisweilen mit dem gleichen Liisungsmittel) untersucht. Die Absorptionsgeschwindigkeit wurde zweifelsfrei durch den ubertragungs-Widerstand der Gasphase bestimmt, wobei Kc*a unter gleichen hydrodynamischen Bedingungen von der Wurzel aus dem Diffusionskoeffizienten abhing. Es ist sehr unwahrscheinlich, da13 die Sc-Zahl als kennzeichnende Variable gelten kann. Der ubertragungskoeffizient war vom Gasdurchsatz in der 0,75’c” Potenz abhlngig.
365
Effect of diffusivity on gas-side mass transfer coefficient V. D. MEHTA and M. M. SHARMA Department of ChemicalTechnology,Universityof Bombay, Matunga, Bombay-19(INDIA). (Received 24 August 1965) Abstract-The effect of diffusivity on gas-side mass transfer coefficient was studied in an experimental bubble column. A fourteen-fold variation of diffusivity was obtained by using a variety of solutes and carrier gases. Both absorption and vaporization experiments were car&d ou< some&es for the same solute. The absorption experiments were unambiguously gas-film controlled. The gas-side mass transfer coefficient varies as 0.5 power of the di&sivity under similar hydrodynamic conditions. Schmidt number is most unlikely to be the pertinent variable. It is also likely that the gas-side mass transfer coefficient varies as 0.33 power of the submergence and 0.75 power of the gas flow rate.
THE EFFECT of diffusivity on gas-side mass transfer coefficient has been the subject matter of a number of publications [l-5]. However, most of the work has been done on the vaporization of solutes in a variety of carrier gases. It is also not clear whether the diffusivity or the Schmidt number is the pertinent variable. In this work a fourteen-fold variation in diffusivity was obtained by using a variety of solutes and carrier gases. Both absorption and vaporization experiments were carried out, sometimes for the same solute. EXPERIMENTAL
Experiments were carried out at essentially atmospheric pressure and a temperature of about 29°C in a 5.2 cm dia. tube, having a 2 mm nozzle at the bottom for gas-inlet, with liquid depths in the range of 4-8 cm. The gas flow rate was varied from about 10 to 23 cm3/sec. The flow of gas through the nozzle is likely to simulate the flow of gas through a slot in a bubble cap column. Hydrogen, nitrogen, Freon-12 (dichlorodifluoromethane) and Freon-l 14 (dichlorotetrafluoroethane) were the carrier gases. The following solutes were used: chlorine, sulphur dioxide, ammonia, n-butylamine, di-n-propylamine, triethylamine, methyl ethyl ketone, n-butyl formate and ethyl propionate. Chlorine and sulphur dioxide were absorbed in aqueous sodium hydroxide solutions (l-6 N) and amines in dilute sulphuric acid solutions (-2N) so
that the liquid side resistance could be completely eliminated. Absorption. Flow rates of the solute gas;NH,, Cl, and SOJ and the carrier gas were adjusted by opening the needle valves to give 3-10 per cent (usually about 5 per cent) of the solute in the gas mixture. The gases were metered by soap-film meters. A known amount of the absorbent was introduced in the bubble column and the stop-watch started. A check was made of the flow rate during the run. The pressure of the gas entering the column and temperatures of the gas entering and leaving the column were recorded. After a definite time (usually 10 min) the liquid was taken out and analysed. For the absorption of amines, carrier gas saturated with an amine at a known temperature entered the column. The static pressure of the gas to be metered was also recorded. The amounts of sulphite and hypochlorite were determined by the iodometric method [6]. In the case of absorption of amines in a known volume and strength of sulphuric acid, the free acid was determined by the standard acidimetric titration using bromophenol blue as an indicator [6]. Vaporization. A known volume of solute was taken and the flow rate of the carrier gas adjusted to a prefixed rate. After two to three minutes the outlet gas was passed through two bottles (in series) of appropriate solutions which completely removed the solute from the carrier gas. After a definite time
361
V. D. MEHTA
and M. M. SHARMA
the above bottles were disconnected and the gas allowed to go to the atmosphere. The temperatures of the liquid before and after a run were also recorded. In the case of amines the sample bottles contained a known volume and strength of sulphuric acid. The amount of amine vaporized was estimated by back titrating the excess free acid (the difference between the initial and final readings gives the amount of amine vaporized in a given time). The outlet concentration of methyl ethyl ketone was determined by absorbing the ketone in a known I I I -5 101 volume of water. The methyl ethyl ketone in water IO I. IO I 30 I 10 I 20 09 was analysed by the hydroxylamine hydrochloride log,,U method. In the case of ethyl propionate and IEbutyl formate the solutes were absorbed in about FIG. 2. Effect of gas flow rate on KGa for the absorption of 50 % aqueous ethanol and estimated by the SOa (carrier gas-Freon-12) in aqueous sodium hydroxide solution (submergence = 4 cm). saponification method. RESULTS
AND DISCUSSION
For the calculation of &a the vapor pressure data of n-butylamine, di-n-propylamine and triethylamine were taken from reference [7], and that for methyl ethyl ketone, n-butyl formate and ethyl propionate from reference [S]. The flow of the gas through the column followed the pattern of chain bubbling, therefore the coalescence of the bubbles, which otherwise could have affected both the values of KG and effective interfacial area, was unimportant. In addition visual observation indicated no difference in the hydrodynamic behaviour for all the systems investigated
( SO2and N,)
0
2.0 "0 x 0
(S&and
Freon-12) 0
x”
“11 IO
Liquid
FIG. 1.
viscosity,
3.0
4.0
cp
Effect of liquid viscosity on KGU (gas flow rate = 16 cms/sec submergence = 4 cm).
under a given set of gas flow rate and the submergence. Figure 1 shows that K,a for absorption of SOZ (carrier gas-Freon-12) in aqueous sodium hydroxide solution is independent of viscosity of the solution indicating an absence of liquid side resistance (the viscosity of the sodium hydroxide solution was varied by increasing the normality of the solution from 2-6N). This is also in conformity with the information available in literature that in bubblecap columns for gas-film controlled process the liquid viscosity is unimportant [9]. In the case of the absorption of triethylamine in dilute sulphuric acid an additional experiment was carried out where the acid solution contained about 1.8 g moles/l. of sodium sulphate which increased the viscosity of the solution from 1.19 to 2.22 cp. The K,a values in the two experiments were practically the same indicating absence of liquid-side resistance. The absorption experiments were, therefore, unambiguously gas-film controlled. Figure 2, a log-log plot of K,a for the absorption of SO, (carrier gas-Freon-12) in aqueous sodium hydroxide solution against superficial gas velocity shows that K,a varies as O-75power of gas flow rate (U), cm3/sec. Experimental K,a values corrected to a gas flow rate of 16 cm3/sec are plotted in Figs. 3 and 4. The maximum variation in the gas flow rate around 16 cm3/sec was 7 per cent. 362
Effect of diffusivity on gas-side mass transfer coefficient
FIG. 3.
Effect of diffusivity on KGU(gas flow rate
= 16cm3/sec, submergence = 4 Cm).
Legend 14. Absorption. (1). Ammonia-Freon-l (3). Ammonia-Nitrogen. (4). Chlorine-Freon-12. 14. (6). Sulphur dioxideFreon-l (7). Sulphur dioxide-Freon-12. (9). n-Butylamine-Freon-12. (10). Di-n-propylamine-Freon-114. (12). Di-n-propylamine-Hydrogen. (13). Triethylamine-Freon-114. (15). Triethylamine-Nitrogen. (16). Triethylamine-Hydrogen. Multicomponent absorption. (17). Ammonia-Freon-12 and Hydrogen.
(2). Ammonia-Freon-12. (5). Chlorine-Nitrogen. (8). Sulphur dioxide-Nitrogen. (11). Di-n-propylamine-Freon-12. (14).
Triethylamine-Freon-12.
(18). Sulphur dioxide-Freon-12
and
Hydrogen. Vaporization. (21). n-Butylamine-Nitrogen. (24). Di-n-propylamine-Hydrogen. (27). Triethylamine-Nitrogen. (30). Methyl ethyl ketone-Nitrogen. (33). nButy1 formate-Hydrogen.
Figure
(25): (28). (31). (34).
n-Butylamine-Freon-114. Di-n-propylamine-Freon-114. Triethylamine-Freon-114. TriethylamineHydrogen. n-Butyl formate-Freon-114. Ethyl propionate-Freon-12.
3, a log-log plot of &a against diffusivi-
ties of solutes in various carrier gases, shows that &a varies as the O-5 power of the diffusivity. The diffusion coefficients were calculated by the method of HIRSCHFELDER,BIRD and SPOTZ modified by WILKE and LEE [lo]. The reported value of the diffusion coefficient for ammonia in nitrogen [l l] was corrected for temperature [12]. In the case of
n-ButylamineFreon-12. Di-n-propylarnine-Freon12. Triethylamine-Freon-12. (29). Methyl ethyl ketone-Freon-l 14. (32). n-Butyl formate-Freon-12. (35). Ethyl propionate-Hydrogen.
vaporization the values of the diffusion coefficients refer to the temperature and pressure of the experiment. The range of diffusivities covered was from about O-023to O-32cm’/sec giving about a fourteenfold variation of diffusivity. The maximum value of the diffusion coefficient available at ambient conditions is about 0.9 cm’/sec (ammonia in hydrogen). However, systems with diffusion coefficients
363
V. D. MEHTAand M. M. SHARMA
Table 1.
Eflect
of
diJiisivity
vs.
Schmidt
number on gas-side mass transfer coeflcient.
Run No.
Solute
Carrier gas
Nature of experiment
& (cm2/sec)
Schmidt no.
2.
Ammonia Sulphur dioxide
Freon-l 2 Nitrogen
Absorption Absorption
Ammonia Triethylamine Triethylamine Ammonia Methyl ethyl ketone
Hydrogen Nitrogen Hydrogen Freon-l 14 Nitrogen
Absorption Vaporization Absorption Vaporization
0.125 0.141 0.254 0.3075 0.296 0.1075 0.115
0.206 1.12 0.63 364 3.78 0.161 1.39
16: :* 28. 1. 30.
higher than O-3 cm2/sec were not used as the outlet concentration of the solute, becomes very low in the case of absorption and approaches saturation in the case of vaporization and in both the cases a small error in analysis could give very misleading results. A number of solutes were considered to And out whether diffusivities substantially lower than O-023 cm2/sec at ambient conditions (atmospheric pressure and 30°C) could be obtained. With Freon-l 14 as the carrier gas, diffusion coefficients (cm2/sec) for some of the solutes that are likely to be useful are: tetrachloroethylene-O-0232, sulphuryl chloride0.028, silicon tetrachloride-O.0265, paraldehyde -0.022 etc. which shows that none of these solutes provide diffusivities lower than O-022 cm2/sec. The diffusion coefficient of triethylamine in Freon-C318 (C,Fs, mol. wt. = 200) is 0*0227 cm2/sec. In the case of n-butylamine, di-n-propylamine and triethylamine both absorption and vaporization experiments were carried out. &a values obtained from the two sets agreed closely. Table
2.
E#ect
of d@iivity
vs. Schmidt
(Triethylamine Run no.
13 14 ‘15 16 25 26 27 28 -
Solute
Triethylamine Triethylamine Triethylamine Triethylamine Triethylamine Triethylamine Triethylamine Triethylamine
Carrier gas
Nature of experiment
Freon-l 14 Freon-l 2 Nitrogen Hydrogen Freon-l 14 Freon-12 Nitrogen Hydrogen
Absorption
Vaporization
Experimental Kca x 105 (g-mole&c cm3 atm at gas flow rate of 16 cm”/sec) 2.06 2.24 2.86 3.22 3.07
The &a values for multi-component systems, where a given solute with a binary mixture of carrier gases were used, agree well with those for binary systems having the same diffusivities. The diffusivity of a solute in multi-component systems was calculated by the method of WILKE and LEE [13]. Table 1 indicates that systems having the same diffusivities show practically the same mass transfer coefficient in spite of variation of the Schmidt number by factors up to about eight. This clearly shows that Schmidt number is most unlikely to be a correlating factor and the data are very well correlated with D o’5, When the pressure is increased for a particular system, the Schmidt number remains substantially the same but the diffusivity varies inversely as the pressure, and therefore according to our findings the mass transfer coefficient should decrease with increase in pressure at a given superficial velocity. The proportionality of &a to D8”’ may not hold for other type of transfer equipment, such as packed columns. number on gas-side mass transfer coefficient.
in a variety of carrier gases).
:&sec)
L P D
0.0248 0.0288 0.0752 0.3075 O-0231 0.0271 0.072 0.296
0*70 090 2.13 364 0.75 0.955 222 3.78
364
K,a x lo5 g-moles/ Values of Kca x lo5 set cm3atm at gas based on -0.5 flow rate of 16 Dg’J.5 cms/sec 0.935 0.972 1.76 3.22 0.89 1.02 1.63 3.07
0.935 1.01 1.61 3.29 0.89 0.965 1.57 3.18
0.935 0.824 0.533 0.410 0.890 0.790 0.518 0.398
Effect of ditTusivity on gas-side mass transfer coefficient
‘W,,
equally marked when a single solute is absorbed or vaporised with a variety of carrier-gases (as was done in the A.1.Ch.E. programme [l-4]). See Table 2. Figure 4 shows that &a for the absorption of SO2 (Carrier gas-Freon-12) in aqueous sodium hydroxide solution is likely to vary as one third power of submergence (S). Work is in progress to determine the effect of various variables on &a in a model bubble-cap column. The work reported in this paper indicates that the following relationship is likely to hold :
s
FIG. 4. Effect of submergence on KGa for the absorption of SOa (carrier gas-Freon-12) in aqueous sodium hydroxide solution (gas flow rate = 16 cm3/sec).
The differences between values of &a predicted on the basis of Schmidt number and diffusivity are
KGa cc D/5
uo.75 So.33
ANDREW[14] has shown that the above equation correlates the data reported in Bubble-Tray Design Manual [l].
REFERENCES
PI
Bubble-Tray Design Manual A.1.Ch.E. New York 1958. from Universitv of Delaware A.1.Ch.E. New York 1958. from University of Michigan A.1.Ch.E. New York 1958. from North Carolina State College A.1.Ch.E. New York 1959.
121 Trav Efficiencies in Distillation Columns Final Reoort [31 Tra; Ekciencies in Distillation Columns Final Report [41 Tray efficiencies in Distillation Columns Final Report PI GERSER J. A., Chem.Engng Prog. 1963 59 35. Kl VOGEL, Text book of Quantitative Inorganic Analysis
Longman, Green and Co., New York (2nd Ed.) p. 354. Bulletin on Alkyd and Alkylene Amines Union Carbide Chemicals Co. New York. :;; PERRYJ. H. Chemical Engineers’ Hand Book (4th Ed. pp. 3-55) McGraw Hill Book Co. Inc., New York 1963. [91 GERSTERJ. A., Znd. Engng Chem. ind. (int’.) Edn. 1960 52 645. 1101 WILKE C. R. and LEE C. Y., Znd.Engng Chem. ind. (int.) Edn 1955 47 1253. [111 TRAUTZ M., and MULLER, W. Ann. Phys. 1935 22 333. 1121 CHEN N. H. and OTHMBRD. F. J. them. and Engng Dara 1963 8 168. 1131 WILKE C. R. Chem. Engng Prog. 1950 46 95. P41 ANDREW S. P. S. Alta Technoligia Chemica Processi di Scambia p. 153 Academia Nationale dei Lincei, Rome 1961. R&um&I_es auteurs de cet article &udient l’influence, sur le coefficient de transfert de masse, c&k gaz, de la diffusivitk d’un mklange gazeux bullant &travers un liquide dam une colonne. 11srkussirent & faire varier la diiusivite dans le rapport. 1 & 14 en utilisant une varif& de gaz dissous dans certains gaz servant de gaz d’entrainement; ils effect&rent des essais g la fois d’absorption et de vaporisation, exp&iences rkalis&es quelquefois sur le meme gaz dissous. Les essais d’absorption furent contra& d’une man&e nette et p&&se, par la thkorie du film gazeux. IX coefficient de transfert de masse varie comme la racine car& daladiiusivite dans des conditions hydrodynamiques simiiaires. Les auteurs nous montrent que certains syst&mes prksentant les msmes diffusivitcs prbentaient pratiquement le meme coefficient de transfert de masse mais une variation tr& accu& du nombre de Schmidt: il est done t&s peu probable que le nombre de Schmidt soit la variable adequate. Le coefficient de transfert de masse c&b gaz varie t&s certainement comme la hauteur du liquide dans la colonne g la puissance 0,33, et, comme la vkesse de passage du melange gazeux & travers le liquide g la puissance 0,75. Zusammenfassung-In einer Biasenkolonne wurde der EinfluR des Diffusionskoeffizienten auf den gasseitigen StoffiibertragungskoelTizienten bei Absorption+ und Verdampfungsvorangen (bisweilen mit dem gleichen Liisungsmittel) untersucht. Die Absorptionsgeschwindigkeit wurde zweifelsfrei durch den ubertragungs-Widerstand der Gasphase bestimmt, wobei Kc*a unter gleichen hydrodynamischen Bedingungen von der Wurzel aus dem Diffusionskoeffizienten abhing. Es ist sehr unwahrscheinlich, da13 die Sc-Zahl als kennzeichnende Variable gelten kann. Der ubertragungskoeffizient war vom Gasdurchsatz in der 0,75’c” Potenz abhlngig.
365