lune 19sO
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
(4) Goff, J. A,, “Goff Diagram for Moist Air,” American Society of Heating and VentilatingEngineers, 1946. (6) Grimley, 9. S., Tram. Inst. Chem. Enms., 23, 233 (1945). (6) Kowalke, 0. L., Hougen, 0. A.,, and Watson, K. M., B d l . Uniw., lis. Ehg. Ezpt. Bta., No. 68 (June 1925). (7) McAdams, W. H., “Heat Trammiasion,” 2nd ed., p. 229, New York, McGraw-Hill Book Co., 1942. (8) McAdams, W. H., Pohlenz, J. B., and St. John, R. C., C h . Ehg. PTO~TSSS, 45,241 (1949). (9) Mayo, F., Hunter, T. O., and Naah, A. W., J . Soo. Chem. I d . (London), 54,375 (1835). (10) Perry, J. H., “Chemical Engineers Handbook,” pp. 391, 1144, New York, MoGraw-Hill Book Co., 1941.
110s
(11) Sohoenborn, D., and Dougherty, W., Trans. Am. Inst. C h m . Engrs., 36,21 (1940). (12) Surosky, A. E., and Dodge, B. F., IND.ENG.CHEM.,42, l l i 2 (1950). (13) Taecker, R. G., and Hougen, 0. A., C h m . Eng. Promeas, 45,188 (1949). (14) Van Krevelan, D. W., Hoftijrer, P.J., and Van Hooren, C. J., Rec. truu. chim., 66,6U(1947). (15) Weisman, J., “Determination of Effective Interfacial Area in Packed Columns,” M.S.thesis, Columbia Univ. (1949).
R B C ~ V BJanuary D 24, 1960. Contribution No. 3 from the Chemical Engineering Laboratories, Engineering Center, Columbia University, N. Y.
Absorption in Packed Towers Effect of Molecular Diffusivity on Gas Film Coefficient R . W. HOUSTON’
AND
C H A R L E S A. WALKER
Y A L E U N I V E R B I T Y . N I W HAVEN. CONN.
Over-all Coefficients of absorption for various solutes from an air stream by water in a 12-inch column packed to a height of 2 feet with 1-inch Rawhig rings are reported. The solutes chosen for this study are ammonia, methanol, ethanol, and acetone. The range of gas diffuslvities covered is twofold. Gas rates varied from 100 to 900 pounds per hour per square foot and water rates from 500 to 3000 pounds per hour per square foot. Interpretation of the data is bared on the use of the Sherwood and Holloway relation to calculate individual liquid film coefflclents. Individual gas film coefflcients are then calculated by the usual relationship between Individual and over-all coefficients. At liquor rates of 500, IOOO, and 2000 pounds per hour per square foot and a t gas rates up to 600 pounds per hour per square foot the gas film coefficients for the various systems are correlated by the */, power of the gas diffusivity. The Coefficients for a liquor rate of 3000 pounds per hour per square foot and gas rates up to 600 pounds per hour per square foot show much less dependence of kaa on the gas dlffusivity, but the data at this liquor rate are not conclusive.
0
NE of the widely used industrial methods of bringing vapor and liquid phases into intimate contact for purposes of transferring mass or heat is the packed tower. In this device the vapor and liquid atreams are passed usually in countercurent fashion through a tower packed with any one of a variety-of materials intended to increase the interfacial contact area and to increase turbulence. Despite the complexity of flow in packed towers, a very considerable amount of progress has been made in deriving s$isfactory design methods. Except in relatively few instances, however, it is not yet possible to design a tower without a few laboratory or pilot plant runs on the particular system and particular packing to be used. Most of the experimental data on absorption in packed towers have been interpreted in terms of the two-film theory first proposed by Whitman (96). In applying this theory it is considered that the resistance to mass transfer is due t o a film of gas and a film of liquid and that a state of dynamic equilibrium exists a t the interface. Determination of concentrations at the interface by experimental methods has not yet been accomplished. It isusually necessary, therefore, to interpret experimental data by means of an over-all coefficient of mass transfer based on either the gas film or the liquid film. Such over-all coefficients of mass transfer can 1
Present address, General Eleotric Company, Bcheneotady, N. Y.
be shown t o be related to the individual film coefficients by the relation:
Although these over-all coefficientsare of great utility in scaling up pilot plant units to larger she, their use in predicting the effect of operating variables on the absorption is definitely limited. For this purpose individual film coefficients are necessary because the effects of such operating variables as gas rate, liquor rate, and temperature on the two coefficients are considerably different. To obtain general corielations which can be used to predict the effect of operating conditions on the transfer coefficients, several methods have been proposed for splitting the over-all coefficients into individual coefficients.
Choice of System. Theoretical considerations indicate that in the absorption of very slight1 soluble gases the liquid film might be expected to offer most ofthe resistance to mass transfer. Sherwood and Hollowa (81) have shown that this is the case in the abso tion of hydkgen, oxyQen, and carbon dioxide by water. ‘8ey have derived an emplrical equation for calculating the individual liquid film coefficient. The equation is based on a wide range of liquor rates. Its final form is
where the values of a,n,and s are dependent on the nature of the packing. The physical properties in this equation are those of the liquid. Theoretical considerations also indicate that in the absor tion of highly soluble vapors the gas film might be expected to of& most of the resistance to mass transfer. Experimental data on numerous systems indicate that few cases of pure gas film in absorption have yet been studied. Graphical Method. On the basis that the individual gas film coefficient might be proportional to the gas rate to a constant power it has been suggested that individual gas film coefficients might be obtained by extrapolating plots of l / K o a us. 1/Gn to obtain an intercept which, according to Equation 1, should be equal b l/HkLa. This method has been used succeasfully by Brinsmade and Bliss (5) in interpreting data on liquid-liquid extraction. These authors give a comprehensive statement of the limitations of the method. Its use in absorption studies has been limited, however, by the fact that the value of the exponent on G is not definitely established. Brinsmade and Bliss were able to determine the value of this exponent in their liquid-liquid extraction studies by noting which value gave a straight line on the lot. Data of s a c i e n t accuracy to accom lish thia in the cam ofabsorption apparently are not availaile. The data appear to scatter so much that no clear indication of the correct value of the exponent is given.
1106
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Vaporization of Pure Liquids. The va orization under adiabatic conditions of ure liquids in packec!towers into a stream of carrier gas woult be expected to yield over-all coefficients essentially e ual to the gas film coefficient. Despite experimental difficulties, a i s method has been ap lied by Mehta and PaTekh (21) to the determina!ion of the e d c t of molecular diffuslvity on the gas film coefficient. More recently, Surosky and Dodge (22) have reported a similar study. Both papers report that the effect of molecular diffusivity is small. In the light of present knowledge it is possible to obtain individual film coefficients from over-all coefficients by either using the Sherwood and Holloway correlation to calculate kLa and then a Equation 1, or using the graphical method. calculating k ~ from One of the most important contributions which remains to be made in the field of absorption in packed towers is a relation between the individual gas film coefficient and the operating variables. The variables of greatest interest in their effects on the individual film coefficients of mass transfer in packed towers are: Liquor rate Physical properties of the liquid Gas rate Physical properties of the gas Temperature Nature of the packing 7. Diffusion coefficient for the solute in the liquid 8. Diffusion coefficient for the solute in the inert gas
1. 2. 3. 4. 5. 6.
Vol. 42, No. 6
The remaining variable in this tabulation, the, diffusion coefficient for the solute in the inert gas, has been studied by various authors, but no definite correlation has yet been achieved. Gilliland (IO)correlated gas film coefficientsin wetted-wall towers by a simple exponential function of the diffusion coefficient using the 0.56 power. Chilton and Colburn ( 5 ) have suggested the exponent 0.67 for the effect of diffusivity on the gas fdm mass transfer coefficient, basing their suggestion on an analogy between heat transfer and mass transfer, Sherwood (20)extended the K h m h analogy t o mass transfer and indicated that for wider ranges of variables than were covered by Gilliland, a more complexfunction of diffusivity is involved in wetted-wall towers. It seems reasonable to suppose that the proper function would be evenmore complex in the case of packed towers because of the greater complexity of the flow pattern. Mehta and Parekh ( 2 1 )successfully correlated data on vaporization of pure liquids in packed towers by the 0.17 power of diffusivity. Surosky and Dodge (22) have interpreted a similar experimental study in the same way, using a slightly lower power of the diffusivity. In interpreting absorption data, however, i t appears that the effect of diffusivity is much greater. Othmer and Scheibel (18)suggest that data on various systems appear to be correlated best by the first power of diffusivity. The present study was undertaken in an attempt to shed some light on the question of the effect of diffusivity on the gas film coefficient. The particular method of attack chosen for this study is based on the consideration that all independent variables except the diffusion coefficients should remain constant. This condition appears to be satisfied only by restricting the study to one inert gas and one solvent and using various solutes. The physical properties of the flowing streams are changed to only a slight extent by the small quantities of solute present. By selecting a single operating temperature and a single type of packing, all the variables listed above except gas and liquor rates will have unique values for any particular solute. Then a t any given gas and liquor rates the individual coefficientsof mass transfer for various solutes should change only as a result of changes in diffusion coefficients. Because some of the existing absorption data indicate effects of such factors as the packing height and the liquid distributor design, these factors should also be fixed.
Sherwood and Holloway included most of these variables in their study of individual liquid film coefficients and their final correlation includes items 1 , 2 , 5 , 6 , and 7 of the above tabulation. Gas rate (item 3) wm shown to have no effect below the loading point. This implies that item 4 will not be a significant variable in determining kLa. Item 8 is, of course, not a variable of importance in this case. With regard to the individual gas film coefficient, however, definite and dependable correlations of a similar nature are not available. The case is slightly more complicated than the preceding one, in that the value of koa is known to be dependent on both the liquor rate and the gas rate. The liquor rate (item 1)is a variable in this case in its effect on the interfacial contact area as well as in the effect of holdup (which is a function of liquor D rate) on the true gas velocity. The physical properties of the liquid (item 2) are of importance in so far as they affect the flow pattern in the tower. The effect of gas rate (item 3) is somewhat simpler in that holdup ia not a function of gas rate in the range below loading (8). The effect of the physical properties of the gas (item 4) has received very little attention in the case of packed towers, despite the industrial importance of cases where the carrier gas is something other than air. The effect of temperature (item 5) has not been definitely established, although it is known to be relatively small. The effect of the nature of the packing (item 6 ) remains to be established definitely, although there are enough data on variC ous packings to permit a t least a rough comparison. Item 7 is not a variable of significance with Figure 1. Schematic Diagram of Absorption Apparatus regard to koa.
?
DESCRIPTION OF APPARATUS
The tower used for this investigation had an inside diameter of 12 inches, and was packed w i t h 1-inch c a r b o n Ritschig rings by dumping into water. The measured height was 1.94 feet, and the measured dry voids was 0.72. The liquid distributor, shown at A in Figure 1, consisted of 14 sections of '/(-inch copper tubing bent out and down from a short length of 1 - i n c h p i p e . Ten tubes discharged at equal intervals on a 10-inch circle, while four tubes discharged on it 4-inch circle. The ends of all tubes were about 0.5 inch from the top of the packing. Air mas drawn through the column by a blower, B, rated at 400 cubic feet per minute. The slow steady temperature rise of its exhaust precluded its use to maintain the column at a positive pressure. To vaporize the organic solvents, an e l e c t r i c a l l y h e a t e d vaporizer, C, was used. This consisted of a jacketed vessel
lune 1950
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
with the liquid boiling on each side of the jacket to cut down the heat loss from the center tank. The rate of power input to the center tank was thus used as a means of controlling the rate of vaporization into the air stream. Vapor from the outer jacket was condensed and reused.
1107
EQUILIBRIUM DATA
Ammonia. The equation given by Kowalke, Hougen, and
Watson (I4 ) was used to determine the solubility data of ammonia in water: (3)
EXPERIMENTAL PROCEDURE
City water was drawn from the constant-head tank D,and the rate set by observing one of two rotameters shown in kigure 1. The air rate was set b the globe valve, F, and measured by means of a sharp-edgedrorifice. The power in ut to the center tank of the vaporizer was adjusted to give an inyet concentration of 1to 2 mole %. For the ammonia runs li uid from a standard cylinder was throttled directly into a double pipe heat exchan er and vaporized with steam. After passin through a surge tan!, it was metered by means of an orifice a d m i x e d with the air stream. Temperatures and pressures at the points indicated in Figure 1 were recorded. Liquid samples were taken at the two points indicated by SL on Figure 1. T o account for the absorption that occurred in the spray section beneath the packing, a three-trough collecting device, a waa laced flush under the packing plate. The trouehs were tdangul% in shape in an attempt to secure a representative Sam le over the entire crom section. The ratio of the trough area to t i e cross-sectional area waa 0.18. Samples were taken of the li uid sent to the drain in order that material balances could be c&ulated. It ww considered unnecessary to correct for any absorption that might have occurred between the packing and the li uid distributor. %wo gas samples were also taken at the points marked SO on Figure 1. It was considered that entrainment difficulties would prevent accurate sampling of the gas immediately beneath the acking. The gas samples were drawn through one or two bub- ' flers into a large gas buret by means of an aspirator. The buret was calibrated so that samples of 600, 1O00, or 1500 ml. could be drawn at measured static pressures. For ammonia, the sample ww absorbed in 2% boric acid solution. Both alcohols were absorbed in water, while acetone was absorbed in a saturated sohtion of 2 4-dinitrophenylhydrarine in 2 N hydrochloric acid. In almost ail cases it was found that virtually complete absorption occurred in the fist bubbler. Fritted-glass gas dispersing tubes were used in the bubblers except for the acetone samples, in which case drawn glms tubes were used. Before taking samples the lines were flushed for several minutes. In all runs a t least 30 minutea of steady-state operation were observed before samples were taken. In a few runs, du h a t e liquid samplea were taken at 15-minute intervals and alp were found to agree within 1%of the mean.
H = 3.18 at 80' F. Acetone. The ex erimental data of Othmer et al. ( 1 7 ) were used to determine t i e following empirical equat,ion: log-e
P
Ammonia. Liquid samples were determined by direct titration with 2 N and 0.5 N sulfuric acid, using a mxed indicator consisting of 1.250 grama of methyl red and 0.825 gram of methylene blue in lo00 ml. of 95% alcohol. A very sharp color change a t the end oint was observed in all cases. The aisorbed ammonia from the gas sample was determined by direct titration with 0.03 N hydrochloric acid using a mixed indicator consistin of 5 parts of 0.1% bromocresol green and 1part of 0.1% methA red in 95% alcohol (16 . A microburet of 10.0ml. capacity was used for very dilute so utions. Acetone. All samples were determined gravimetrically by precipitating the derivative of 2 4dinitrophenylhydrarine. The optimum conditions found by Iddles and Jackson (12) pYefe followed. however, analysis of known solutions here indicated eps.entially 100% precipitation of the theoretical yield within the limits of concentration of sample from 4 x 10-0 to 10 X 10-6 gram mole per ml., the rea ent concentration beisg about 18 X 10-6 gram mole per ml. ft was assumed that the theoretical yield was also obtained with the gas samples. Methanol and Ethanol. A colorimetric procedure for the alcohols was develo ed for this investi ation, based on the method of Webb (94). TS I! method depeng on the controlled oxidation of the alcohols with an excess of potassium dichromate in nitric acid. The resulting decrease in optical density waa used as a measure of the concentration of alcohol in the sample. An Evelyn photoelectric colorimeter was used for all readings. Preliminary investigation indicated that maximum light absorp tion occurred with a filter passing a eak wave len h of 420 nw. Two calibration curves were establisied covering a coho1 concentrations from 3 to 90 X 10-4 gram mole per liter. Reproducibility of the calibration curves for these anelyeas indicated average deviations of the order of = 1%from the mean.
1
?
(4)
H = 1.37 at 80" F. Methanol. Data for this system were obtained from two sources. Those of Baller et al. ( 9 ) at 25" C. were used in conjunction with x / p values reported by Chalov and Tsvetaeva ( 4 ) a t varying temperatures. As the former were considered more reliable, greater weight was placed on them to determine the following equation: logP
2324 - 7.199 T
I?
= 12.2 a t 80" F.
(5)
Ethanol. Data of Baller et al. (I?), Dobson ( 6 ) , Shaw and Butler (19), and Thomas (93) were employed to determine the following expression for the ethanol system: c 2250 log- = - - 6.469
P
T
H = 10.7 at 80" F. All the equations represent the experimental data within *3% in the temperature range from 20" to 30"C. and for solute partial pressures to 0.02 atmosphere. DIFFUSION CONSTANTS
Values of the diffusion constants used in this investigation are shown in Table I.
Table I.
METHODS OF ANALYSIS
- 7.364 T
2250
Diffusion Constants
DL
Erstern
sq.aFt O80 O ~ ~F. /HOW
Ammonia-air-water Acetone-air-water Methanol-air-water Ethanol-air-water
9 . 3 0 X 10-6 4.81 X 106.86 X 105.27 x 10-8
sq.at Dv SOo F. 0.710
0.368 0.618 0.475
Measured liquid diffusion constants for the ammonia, methanol, and ethanol systems (1, 19) were correlated by the method of by means of the relation Wilke (M),
F=- T Dh
c7 1
Values of F thus found were: For ammonia For methanol For ethanol
F = 1.45x 107 F = 1.97 X l o 7 F = 2.55 X 10'
In the absence of experimental data for acetone, Wilke's method was used to determine F = 2.80 X 10'. Lacking experimental data for the diffusivities of ammohis and aogtone in air, the Gilliland equation ( 9 ) waa employed for these systems. The constants for the diffusivities of methanol and ethanol in air were taken from the International Critical Tables (IS). The constants reported in Table I are believed to be reliable within *lo%.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1108
Vol. 42, No. 6
20 . .
I
I-
'16 F-:
LL
3
2 12
e Y,
Y 8 0
H
03
J 4 d
20 G,LB./HR. Figure 2.
0
0 Q
@
-
SC?.FT.
Comparison of Acetone Data
Figure 3.
-
Data of Othrner and Scheibel (18) for 1-Inch rings a t L = 650 Data of Hutchings et a/. 7 7 ) for 1.25-inch rings a t L 490 Data of Hutchingset al. ( 1 7 ) for 1.25-inch rings at L = 915 Data of Hutchings et a/. ( 1 1 ) for 1.25-inch rings a t L = 1080 Representative of data of authors
RESULTS
Experimental data recorded for each run included the gas and liquor rates, the composition of the gas mixture entering the bottom of the tower, the composition of the gas mixture leaving the tower, the composition of the liquid leaving the packing, and the composition of the liquid leaving the bottom of the tower. Although it was possible to calculate the material balance for the entire tower from these data, it was not possible to calculate the material balance over the packed section. The spray section below the packing support plate was responsible for as much as 50% of the total absorption occurring, as revealed by sampling the liquid leaving the packed section and the liquid leaving the bottom of the tower. Hence, calculation of the material balance
0 0
-
-
Comparison of Ammonia Data
Data of Dwyer and Dodge (7) a t L 500 Data of Molstad et a/. (76) a t L = 3000 Representative of data of authors
over the packed section would require that the gas entering the packed section be analyzed. Such sampling is accompanied by very difficult experimental problems and was not attempted in this work. The material balance reported is therefore a check only on the over-all operation of the tower and not on that portion (the packed section) used in calculating coefficients. In order to perform this calculation it was necessary to calculate the composition of the gas entering the packed section by a material balance using the measured flow rates, exit gas composition, and composition of the liquid leaving the packing. That the general scheme was satisfactory in the case of ammonia absorption and acetone absorption is shown by a comparison of the present data with those of other workers (Figures 2 and 3). The data on methanol appear also to be satisfactory, as indicated by the consistency of the material balances. Some diffi-
I
---
0. 0
280 G , h I /HRSQ.Fr Figure 4.
Absorption of Ammonia
G, Figure 5.
200 500 LE. /HR.SQ.FT.
1000
Absorption of Acetone
INDUSTRIAL A N D ENGINEERING CHEMISTRY
June 1950
1109
Table I I, Absorption of Various Solutes in Water Run No.
Lo
Bo
P
of Total eaistance in Gas Film
Run No.
100.2 99.6 102.0 101.3 101.1 105.0 94.3 103.0 101.0 101.8 108.0 104.7 99.6 102.3 94.8 100.4 99.0 90.6 90.6 105.7 103.1
85 87 91
Ethanol 4 3 , 2 42
90.8 97.4 100.2 90.0 108.1 103.0 104.1 93.2
84 85
Material Balanoeb,
%
Koac
k p 4 8
koaCt/
Ammonia
78
1 41 8 7 40 6 46 47 38 44 40 22 31 12 21 29 30 37 10 11 20 28 9 19 27 17 36 16 34 36 15 33 14 23 32 61 60
79 80 90 72 07 00
68 69 71 78 84 67 73 48 68 63 69
Acetone
103.0
Methanol 23 502 22 993 21 ZOO0 19 502 18 987 17 2000 I0 3020 11 502 10 loo0 14 Zoo0 13 3020 9 602 8 987 7 ZOO0 12 3020 4 502 3 987 2 2000 1 3020
106 102 100 187 182 187 175 412 409 411 429 692 641 000 615 879 949 943 930
75 76
82 81 64 68
71
100.8 99.0 90.3 97.2 107.0 98.3 103.6 93.2 104.9 97.1
68
101 .o 97.6 97.5 103.2 100.5 103.1 96,6 101.7 102.0 102.9 107.6 104.2 96.1 106.7 90.6 97.8 106.4 106.9 106.9
97 97 99 90 90 97 97 94 94 96 95 91 91 93 96 80 87 89 89
80
61 00 05 66 38 41 40 40
culty was experienced in the case of ethanol, however, where the material balances based on chemical analysis of the various streams were very poor. The fact that material balances based on an inlet gas stream composition calculated from the energy input to the central tank of the vaporizer were much better than those based on chemical analysis of the inlet gasindicated that this stream represented the source of the disorepancies in the material balances. Hence material balances for the ethanol runs were based on the following procedure. Thirteen of the ethanol runs showed over-all material balances within * 10% on the basis of chemical analysis of all streams. In all runs the energy input to the center tank waa measured with a wattmeter. Based on the thirteen runs showing satisfactory material balances, it was possible to derive a relation between the wattmeter reading and the inlet concentration-Le,, to estimate the heat loss from the vaporizer. Calculation of inlet gas compositions from the wattmeter readings and this relation gave six additional runs with material balances of *lo%, seven additional runs with material balances of * 15%, and eleven additional runs with material balances of *25%, leaving only six runs with poorer material balances. These were regarded as satisfactory in view of the facta that, calculation of the mass transfer coefficient
48 49
La 499 994 2000 2000 3020 3020 600 994 970 2000 2000 2000 3020 3020 3020 502 502 994 994 987 994 987 2000 2000 2000 ZOO0 3020 3020 3020 502 602 987 987 945 2000 2000 3020 3020 3020 602 987 2000 3020
G" 103 103 104 102 104 103 180 181 175 181 180 181 179 182 179 398 392 394 399 392 390 391 390 397 398 390 390 398 393 604 559 564 556 569 564 560 573 564 658 868 861 846 830
'7 Resistance 0of Total
Material Balanceb,
%
&ac
h a d * ' k&bf
in Gas Film 97
.,
97 98 97 98 97
..
95 90 97
I
.
90
90
.. ..
96 97 96 98 93 94 93 93 94 93 90 95
.. ..
96
96 95 96 95 95 92 90
.. ....
91
91 92 93 93 94 92 91 80
..
..
87
88 87
Lb./(hour)(aq. foot). solute absorbed in water. Materi.l balanoe solute removed from air Lb. moles/(hour)(au. foot)(atm.). d Lb. rnolea/(hour)(au. foot) (-t). a Calculated by Sherwood and Holloway relation. I Caloulated by equation -!4- 1 KQa koa HkLa' Temperaturea of KW and liquid 77O to 8 3 O F. Inlet gss concentration, 1.0 to i.6% by volume. ~
-
does not depend on using the inlet gas concentration; the valuee of the coefficients calculated for duplicate runs show reasonable consistency; and a similar relation between inlet gas composition and wattmeter readings could be used for runs with acetone and methanol. Over-all coefficientsof mass transfer were calculated by the rate equation in terms of the logarithmic mean driving force, since the equilibrium lines are substantially straight when plotted in stoichiometric units and concentrations of the various solutes were low. These coefficients are reported in Table 11. The Sherwood and Holloway relation was employed to calculate the individual liquid film coefficientsat 20" C . These were corrected to 80 O F. by the relation suggested by Sherwood and Holloway. Individual gas film coefficients were then calculated by means of Equation 1. The data of Table I1 indicate that in the absorption of both ammonia and acetone the liquid film represents an appreciable portion of the total resistance to mass transfer. This film constitutes as much as 52% of the total resistance in some cases of ammonia absorption and as much as 60% of the total resiatanw in some cases of acetone absorption. Thus, any error due to the use of the Sherwood and Holloway relation may lead to B very large
1110
INDUSTRIAL A N D ENGINEERING CHEMISTRY I
I
Bo
Vol. 42, No. 6 1
I
I
,
)
o L = 500 LWHR .SQ.FT.
C, LE. /HR. SQ.FT. Figure 7.
error in the value of the individual gas film coefficient. In the absorption of methanol and ethanol, on the other hand, not more than 14% of the total resistance to mass transfer is indicated to be due to the liquid film. In these cases a relatively large error in the value of the individual liquid film coefficient leads to a much smaller error in the individual gas film coefficient. The gas rates used here are greater than those used in the derivation of the Sherwood and Halloway relation. There is reason to believe that under most of the conditions of this work the equation of these authors should be satisfactory. It was shown by Sherwood and Holloway that in a tower packed with 1.5-inch Raschig rings operated a t a liquor rate of 2000 pounds per hour per square foot the individual liquid film coefficient was independent of gas rate up to the loading point. The available data on 1-inch Raschig
Absorption of Ethanol
rings indicate that the loading point for liquor rates of 2000 and 3000 pounds per hour per square foot is near a gas rate of 700 pounds per hour per square foot. Hence the appli.cation of the correlation for individual liquid film coefficients at the highest gas rates used in this work is questionable. The calculated individual gas film coefficients are shown a s functions of the gas rate in Figures 4,5,6,and 7 . The data for gas rates up to 600 pounds per hour per square foot may be represented reasonably well by straight lines of slope 0.8 on these loglog plots. The data are somewhat better represented by the curves shown than by straight lines, however, and are accordingly represented in this way. The slopes of the curves a t high gas rates are seen to be somewhat less in the case of ethanol and
D, Figure 8. DependenceIof koa on Solute Gas
,SQ.F T/H R.
Figure 9. Dependence of koa on Solute Gas
lune 1950
INDUSTRIAL A N D ENGINEERING CHEMISTRY
1111
50
f 40 a t:
5 30 0
a I
c
3 20 J
0
I
- o i 0.3
04
0, ,Sa.FT/ HR.
0.5
0.6
Q8
1.0
D,, SQ.FTJHR.
Figure 10. Dependence of kola on Solute Gas
Figure 11. Dependence of koa on Solute Gas
methanol than in the case of acetone and ammonia. This is interpreted as being related to the question of whether the Sherwood and Holloway equation can be properly applied a t the highest gas rates used in this work. If the gas rate is above the loading point in these cases, the value of the liquid film coefficient calculated by the equation will be lower than the true value and the calculated value of the individual gas film coefficient accordingly will be too high. This effect would be most pronounced in the case of ammonia and acetone. Smoothed values of the calculated individual gas film coefficients read from Figures 4 to 7 are plotted against diffusivity in Figure 8 to 11. Because of the questions introduced above, the maximum gas rate used in preparing the last four figures is 600 pounds per hour per square foot. The values of koa a t liquor rates of 500, 1000, and 2000 pounds per hour per square foot are represented reasonably well by straight lines of slope 2/3, the value suggested by Chilton and Colburn for unpacked tubes. Ths values of LGU at a liquor ratc of 3000 pounds per hour per square foot show essentially no dependence on molecular diffusivity, the values for the various systems at a constant gas rate being represeiitcd to i:10% by horizontal lines. No theoretical justification for such an otmwvation has been found. It may be noted, however, that evpressing the individual gas film coefficientsas simple exponential f mations of the molecular diff usivity has no basis in theory. The actual mechanism is one of mass transfer through a laminar film miti a turbulent core. The relative rates a t which these resistances decrease with increasing turbulence cannot be prcvlicted at the present time. It is possible that laminar film resistance decrettsw somewhat more rapidly than turbulent core resistance, in which case the effect of molecular diffusivity would become increasingly less as turbulence is increased, by increasing either gas rate or liquor rate. In brief, expressing the effect of molecular diff usivity on mass transfer coefficients in packed towers by a simple exponential function is an entirely empirical method of correlation. Mehta and Parekh ( $ 1 ) a;dd Surosky and Dodge (22) found little effect of molecular diffusivity on gas film coefficients, whereas Othmer and Scheibel (18) found a much greater effect. The former groups performed studies at relatively high liquor ratesand the latter a t lower liquor rates. Thus thereis an indication that the exponent on molecular diffusivity, if such a method of correlation can be used, is dependent on the liquor rate. Unfortunately, the present data are not conclusive with regard to the effect of diffusivity on mass transfer coefficients. In the
first place, the necessity for studying a number of different solutes and for developing methods of analysis for each required sacrifices in the number of data points obtained for each system. The fact that the magnitude of the error due to analytical methods is different for each system may result in a final comparison which is erroneous, Secondly, the choice of ammonia as one of the solutes may have been incorrect although it was desircd to include one such material in the investigation. It will be apparent from Figures 8 to 11 that the koa values for ammonia lie well above the lines a t a liquor rate of 500 pounds per hour per square foot, approximately on the lines at liquor rates of 1000and 2000 pounds per hour per square foot and somewhat below the lines a t a liquor rate of 3000 pounds per hour per square foot. This regularity in the behavior of ammonia suggests that this case of absorption may be more complex than the other cmes. Omitting the ammonia points in Figures 8 to 11 would lead to the conclusion that the corredt exponent on diffusivity is in some cases smaller than 2/3. Finally inspection of Figure 5 indicates that the increase in koa for acetone when the liquor rate is increased from 2000 to 3000 pounds per hour per square foot is larger than the increase which results when the liquor rate is increased from 1000 to 2000 pounds per hour per square foot. This suggests that the acetone coefficientsat 1, = 3000 may be too high. If this were the case i t would be of importance in drawing Figure 11 and would lead to a correlating line of slope greater than zero. ACKNOWLEDGMENT
Acknowledgment is hereby made to E. I. du Pont de Nemours 8: Company for a fellowship granted R. W. Houston for the 1948-49 school year. NOMENCLATURE
e
D, DL DL F ff
= concentration of solutc, Ib. moles/cu. foot of solution = diffusion coefficient for solute in air, sq. foot/hour = diffusion coefficient for solute in water, sq. foot/hour
= diffusion eoefficiet$ for solute in water, sq. cm./sec.
diffusion factor,
K. sec./(sq. cm.)(cp.)
= gas rate, Ib. air/(hour)(sq. foot) fl = Henry’s law constant, Ib. moles/cu. foot/atm. Koa = over-all gas film coefficient, lb. moles/(hour)(cu. foot)
atm. koa = individual gas film coefficient, Ib. moles/(hour)(cu. foot)(atm.), KLa = over-all liquid film coefficient, lb. moles/(hour)(eu. foot)(lb. mole/cu. foot)
INDUSTRIAL AND ENGINEERING CHEMISTRY
1112
= individual liquid film coefficient, Ib. moles/(hour')(cu. =
= = = =
= = * = =
(9) Gilliland, Ibid., 26, 681 (1934). (IO) Gilliland and Sherwood, Ibid., 26, 516 (1934). (11) Hutchings, Stuteman, and Koch, Chem. Eng. Propress, 45, 253
foot)(lb. mole/cu. foot) liquid rate, Ib. water/(hour)(sq. foot) logarithm, base e logarithm, base 10 molality of solute, Ib. moles/1000 Ib. solution solute partial pressure in air, atm. temperature, R. mole fraction of solute in water density, Ib./cu. foot viscosity, Ib./(hour)(foot) viscosity, centipoises
(1949). (12) Iddles and Jackson, IND. ENG.CHEM.,ANAL.ED.,6,459 (1934). (13) International Critical Tables, Vol. 5, New York, McGraw-Hill Book Go., 1929. (14) Kowaike, Hougen, and Watson, U n i ~ Vis. . Eng. E@. Sta., 68 (June 1925). (15) Ma and Zuazaga, IND. ENG.CHEM.,ANAL.ED., 14, 280 (1942). (16) Molatad, McKinney, and Abbey, Trans. Am. Inst. C h . Engrs., 39, 605 (1943). (17) Othmer, Kollman, and White, IND. ENG.CHEM.,36, 965 (1944). (18) Othmer and Scheibel, Trano. Am. Inst. Chem. Enprs., 40, 611 (1944).
LITERATURE CITED
(1) Arnold, Sc.D. thesis, Massachusetts Institute of Technology,
),!j:;
1931.
:kw$,F&: ~ ~ ~ ~ ~ . ~ ~~ ~ ~ ~f ~ ~ . ' ~ ~ ~ ) i
(21) Sherwood and Holloway, Ibid., 36, 21, 39 (1940).
Baller, Thomson, and MaoLennan, J. Chem. Soc., 1933, 674. (3) Brinsmade and Bliss, Trans. Am. Inst. Chem. Engrs., 39, 679 (2)
(1944). (4) Chalov, N. V., and Tsvetaeva, 19,945 (1946).
Vol. 42, No. 0
,E ::t B , l d ~ ~ , P " , p , ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ [ii; $ ,: ~ ~ ~ ~ ~ ~ ~ ~ f ; , 21923), ~ ~ 6 ( ~ ~ ~ ~ ) ) 2 3 (26) Wilke, Chem. Eng. Progress, 45, 218 (1949).
$!&f::zl:
J. Applied Chem. (U.S.S.R.),
(6) Chilton and Colburn. IND. ENG.CHEM.,26,1183 (1934). (6) Dobson, J. Chem. Soc., 127,2871 (1925). (7) Dwyer and Dodge, IND. ENG.CEEM.,33,485 (1941).
R E C E I V ~November D 80,1949. Based on a diwertation pmented by R. W. Houeton in June 1950 to the faculty of the School of Engineering of Yale University, in candidaoy for the degree of doctor of engineering.
(8) Elgin and W e b , Ibid., 31, 435 (1939).
Effect of Diffusivity on Gas-Film Absorption Coefficients in Packed Towers ALAN E. S U R O S K Y '
AND
BARNETT F. DODGE
YALE UNIVERSITY. N E W HAVEN. CONN.
T h e molecular diffusivity in the gas phase is one of the variables commonly used in correlating the results of gas rbsorptlon experiments, but l i t t l e quantitative informa. t l o n on i t s effect has been available, especially In packed towers. The main objective of t h e present investigation wasto studytheeffect of diffusivity in a packed tower by as direct a method as possible. To eliminate the possibility of any liquid-phase resistance t o mass transfer, the method of vaporizing pure liquids i n t o an air stream was adopted. Three organic liquids and water were used, giving a 3.7-fold range of diffusivities. A special effort was expended in the design of gas and liquid distributors t o minimize end effects. Experiments were conducted a t Substantially atmospheric pressure and temperature in an &inch diameter tower packed w i t h 1-inch rings. Resist-
ance t o heat transfer in t h e liquid phase was assumed t o be negligible on the basis of previous work. Packed height was varied f r o m 4 t o 12 inches, liquor rate from 435 t o 5OOO pounds per hour per square foot, w i t h the bulk of t h e runs a t 1600, and the gas rate from 140 t o 500 pounds per hour per square foot. The main results of t h e Investigation may be summarized as follows: End effects were equlvalent t o 2.2 inches of packing. Gas-film coefficient koa was independent of liquor rate above a liquor rate of about 1OOO. koa varied as the 0.72 power of the gas-flow rate. koa varied as diffusivity t o the 0.15 power. The small effect of diffusivity in a packed tower indicates t h a t the main resistance is due t o eddy diffusion in t h e t u r b u l e n t core. This result is in close agreement w i t h t h e only other published data on the subject.
A
Similar equations have been proposed for packed towers, the one of Van Krevelen and Hoftijier (16)being aa follows:
SATISFACTORY correlation of gas film absorption coeffi-
cients in packed towers, comparable to that available for liquid film coefficients, has not yet been made. Some years ago, Gilliland and Sherwood (6) proposed the following correlation for their results on the evaporation of liquids into gas streams in a wetted-wall tower
;- c (4)" ($)"
(1)
where the values of the constants were C = 0.023, n = 0.83, and m = 0.44. From the relation between ka, D,and z,this equation may be modified to
D kad I
C'
i
r;)'
($)%
Preaent address, 126 Market St., Patereon, N. J .
(2)
kod D
c (")"'($)'" ad#
(3)
Chilton and Colburn (9)extended the Reynolds analogy between fluid friEtion and heat transfer to include mass transfer in diffusionalprocesses and arrived at an equation for the mass tram-
fer coefficient involving the group, &, to the o.67 power. PD When comparing the performance of a given absorption tower in which gas film is controlling, with different gas system, the diffusivity is assumed to be the main correlating variable. With B reliable correlation for the effdct of diffusivity and data on the diffusivities of various solute gases in a variety of inert or carrier
