From the above value of E together with this ratio it follows that log A = 18.4 ( A in min.-l), Even the values for E and A derived from application of Kissinger’s method satisfy this relation. although individually they are incorrect. An explanation for the constancy of E ’In A proposed by Moeltqn-Hughes is considered inadequate and it is anticipated that a more detailed consideration of results of this kind \vi11 be the subject of a forthcoming paper. Acknowledgment
(9) Freeman, E. S., Carroll, B.. J . Phys. Chem. 62, 394 (1938). (10) Hildebrand, F. B.. “Introduction to Sumerical Analysis.” McGraw-Hill>New York. 1956. (11) Kissinger, H. E.. .4naI. Chrrn. 29, 1702 (1957). (12) Kissinger. H. E.; J . R ~ s .Vat/. . Bur. Std. 57, 217 (1956). (13) Mackerizie, K. C.. “Differential Thermal Investigation of C h v s . ” Mineralozical Societv. London. 1957. (14) hoel\ryn-Hu$hes, E. .A,. “.Physical Chemistry,” 2nd rev. ed., p. 1245. Pergamon Press. N e w York. 1961. (1 5) hloel\vyn-Hughes. E. A,: .Johnson. P., Trans. Faraday SOC. 36, 948 (1940). (16) Murphy. C. B.. A n a l . Chem. 30, 867 (1958). (17) Ibid., 32, 168K (1960). 1181 Ibid.. 34. 298K (1962). (l9j Murray. P.. \\.h’ite. .J:. Trans. Brit. Guam. Soc. 54, 204 (1955). (20) Se\vell. E. C . , Cloy .\lrnrra/s Bull. 2, 233 (1955). (21) %\\ell. C. C.. Gt. Brit.. Dept. Sci. Ind. Kes.. Bid. Res.. Series of Notrs (1952 ~1056). (22) Smothers, \V. Chiang. Y.. ”Differential Thermal Analysis. Theory a n d Practice.“ Chemical Publishing Co., New York. ,
‘The authors express their appreciation 10 M. R . J. \Vyllie for being the first to suggest that DTA might be useful in the study of crude oil oxidation, A. B. Hartman for designing the electronic components of the DTA unit. and R . L. Gergins for his valuable assistance with the experimental work. Literature Cited
(1) Allison, E. B., Silicates Ind. 19, 363 (1954). (2) Blumberg. A. A . , J . Phys. Chem. 63, 1129 (1959). (3) Boersma, S. L., J . Am. Cernm. Soc. 38, 281 (1955). i4j Borchardt, H. J.. Ph.D. thesis, Uni;,ersitv of IVisconsin, June 1956. (5) Borchardt. H. J., Daniels, F., J . Am. Chem. SOC.79, 41 (1957). (6) Crossley, M . L., Kienle, R. H.: Benbrook, C. H.: Ibzd., 62, 1400 (1940). (7) Denisov, E. T., Zrcest. Akad. n’auk SSSR, Otdel. Khim. .Vauk 1960, 1298. (8) Ellis, B. G., Mortland, M. M., .4m. itilzn~ral.47, 371 (1962). >
I
1958.
(23) Spiel. S., Berkelhamner, L. €I.>Pask. J. A , . Davies. B.? U. S. Bur. Mi,ies, Tech. Paper 664 (1945). (24) ‘Tadema. H. .1.. Erdol Rohie 12, 140 (1959). (25) Vaughn. F.. Cloy .IllineiuIs B d l . 2, 265 (1955). (26j VOIJ, M. .J,, A n a l . Chem. 21, 683 (1949): (27) Vulis, L. A , . Zh. Tvkhri. Fir. 16, 83 (1946). (28) \\‘ads. G.. .Vi$fion Ragaku Zasshi 1960, 1656.
,
RECEIVED for review February 10, 1964 ACCEPTED June 22, 1964
Di\-ision of Petroleum Chemistry, 144th Meeting, XCS, Los Angeles, Calif.; .April 1963.
CONDENSATION OF WATER VAPOR FROM A NONCONDENSING GAS ON VERTICAL TUBES IN A BANK J A M E S T. SCHRODT A N D E A R L R . G E R H A R D Chrmical E n p e e r i n g Ilepartment. C n i i e r s l t y of Louzsriile. Louisr / / l e , Ky
Data are presented on the condensation of water vapor from saturated air streams. under turbulent transverse flow to short cylindrical condensing surfaces. were varied from 2000 to 20,000.
Tests were conducted
Gas-phase Reynolds numbers
Values of JD and JH obtained are expressed graphically as functions
of the appropriate Reynolds numbers, and are shown to agree reasonably well with data from the literature.
s
of cooler-condenser problems are approached in various \cays. I n principle they all follow the accepted theory that the cooling and change of phase occur in three simultaneous steps: removal of sensible heat of the mixture, condensation and removal of latent heat, and removal of the sensible heat of the condensed phase. Colburn and Hougen (2) expressed the heat removal mathematically as OLUTIOSS
+
(1) h , ( t , - ti) k,‘Z.Z, x ( p , - p l ) = h o ’ ( t , - t w ) but because of the lack of diffusion data they relied upon Chilton’s and Colburn‘s J factor correlation ( 7 ) JH
=
Jn
for its solution. T h e resolution of partial condenser problems is therefore greatly dependent upon the reliability of this analogy. 46
I&EC FUNDAMENTALS
Recent studies ( d , 7: 8) on condensing pure vapors from saturated noncondensable gases have substantiated the analogy for streams flo\ving parallel to the condensing surface. but there appeared to be no such data for the more practical situationi.e.. flokc transverse to the cooling surface. This note presents the results of a study of the air-water vapor system \chere condensation occurred from saturated streams at 90’ F. flowing a t right angles to vertical tubes. Five 10.0- X 0.75-inch o.d. brass tubes were aligned in a staggered manner behind 7 ro\vs of false tubes in a 3.25- Y 10.0-inch insulated duct. A vertical rather than a horizontal arrangement \vas chosen after preliminary investigations indicated that condensed liquid falling from horizontal tubes was re-entrained in the air stream. Furthermore. Comings. Clapp. and Taylor ( 3 ) indicated that induced turbulence generated by the false tubes \\.odd providc comparable conditions a t each tube surface for the transfer phenomena. T\centy-fow runs were conducted a t free stream velocities of 0..56 to 47.0 feet per srcond. T h e nearly constant temperatures. concentrations. and mass flow rates in the bulk stream passing through the compact tube bundle justified the
use of averaged stream properties. A Lucite \\indo\\, installed adjacent to the tubes provided close inspection of the liquid phase film enveloped by the gaseous boundary layer containing the temperature and concentration gradients.
place), the upstream and do\vnstream \vet- and dry-bulb temperatures ivere measured Lvith calibrated thermometers graduated to 0.05' F. I n general, the gai mixture streams were cooled about 1.5' to 3.0' F. I'he mixture floiv rates lvere determined, as \\-ere the condenjate temperatures and condensate iveights from each tube. T h e latter sho\ved negligible variations. \vhich siiggested that the I b l v tubes \\ere providing adeq[iate turbiileiice to induce e q t d conditions a t all five tube sLirfaces. 'l'he sen.;ible heat lo+ from the gas phase \vas evaliiated by subtracting the latcnt heat and sensible heat loss of the condensed phase from the t o t a l heat picked u p by the \vater coolant. .I-his value sho\\cd f'iir q r e c i n e n t it-ith the measkired sensible hear loss and \vds felt to be the more
Prior to the investigation of the condensing system t\vo series of runs \cere conducted on the test unit ivith dry aif: (1) \\-here the false tubes \vere in position and (2) \vithout the false tubes. These resulted in t\vo distinct J I I factor correlations: series 1 corresponding to curve 0 . and 2 to curve 6 of Figure 1. ~I'he data of Hughes (7) for a single tube, arid Snyder ( 9 ) for roivs 8, 9, and 10 of a vertic,.iI tube bank have been plotted i n the figure to indicate the elrect of tiirbulence 011 the heat transfer. I n the tests under condrncing conditions !false tubes in
-\
2 . 5 IO3 ~
Figure 1 .
5 . 0 IO ~'
Correlation of #
Figure 2 .
JH
Authors
Re
2 . 0 io4 ~
1.0 104 ~
with Reynolds number for transfer of heat to cylinders A
Authors
X
Snyder ( 9 ) 0
Hughes (5)
Comparison of J m with Jn for transfer of heat and mass to cylinders X
Authors' Jx
0
Authors' J l i
A
Maisel's and Sherwood's J D (6)
VOL. 4
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1
FEBRUARY 1965
47
Table 1.
1 2 3
4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Q
1540 1490 1420 1330 1330 1220 785 852 852 485 582 555 545 510 440 420 420 410 365 355 320 275 230 190
92.10 92.25 91.25 92,70 72.75 72,20 90.10 89.15 89.55 88,90 90.20 88,45 88.65 88.75 85.80 90.40 90.10 90,30 90.60 88.20 86.00 86.10 86,65 86.70
90.00 90.25 89.35 90.30 90.50 87.90 87.65 87.30 87.70 87.40 88.35 86.70 86.65 86.65 84.15 86.75 86.40 88.25 88.40 86,45 84.10 84,OO 84.35 84.25
Re 18,900 18,220 17,400 4 16,250 16?250 5 15,000 6 7 12,100 8 10,100 10,100 9 10 6,890 11 6,820 12 6,560 13 6,400 6,100 14 5,320 15 16 5,160 17 5,160 5,000 18 19 4,420 20 4,210 21 3,880 22 3,330 23 2 790 24 2,300 Differenced calue, Qs = Q r - Q r Run h‘o. 1 2 3
~
44.2 45,l
58,6 59.3 58.2 58.2 58.3 57.8 55.7 70.5 70.9 73.4 66.8 65 .O 65.6 64.7 64.7 51.2 51.2 66.7 66.6 72.5 64.4 63.8 64.3 64.0
45 . O 44.6 44.7 44.7 42.6 64.9 65.1 68.2 61 , I 59.7 60.4 59.5 60.6 42.2 42.2 61.8 61.8 68.2 60.6 60.3 60.2 60.2
1.855 1.820 1.721 1.750 1.765 1.647 1.385 0.758 0.745 0.670 1.015 0 914 0,895 0.900 0.724 0,916 0.929 0.873 0.846 0,580 0,645 0.595 0.550 0.507
72.1 71.3 72 0 73 . O 72.1 72,8 71 . O 75.0 73.0 74.0 68.0 63.0 63.0 61.0 65.0 59.0 59 0 64.5 64.2 76.5 63.0 62.0 62.0 63.0
-
I&EC
FUNDAMENTALS
Calculated Data
QS,a h,,b B.t.u./Hr. B.t.u./Hr. sq. Ft. F . 30,1 570 27.2 589 28.6 608 27.4 600 27.4 577 26.1 607 22.8 570 19.5 228 19.5 274 16.7 246 16.7 274 16.4 295 16.1 273 272 15.6 14.2 230 13.5 398 13.5 347 13.3 236 12.9 244 12.7 157 11.6 206 10.7 186 9.55 172 8.65 137 Qc. b Obtainedjrom a , Figure 1.
reliable. Using this value and curve a of Figure 1, the interface temperature, ti, was calculated. T h e vapor to liquid phase change produced what appeared to be a “ripple-free” film on the surfaces. T h e film was thicker on the sides than on the upstream faces of the tubes. If the intensity of the heat and mass transfer varied from a maximum on the front, decreased, and then increased slightly in the \vake as TVinding and Cheney (10)found in their studies, it does not seem too improbable that the liquid was forced there from shear stress. T h e film appeared very thin in the wake region. This cannot be explained and differs from the cited findings ( 7 0 ) . T h e film-type condensation was maintained by polishing and cleaning the tubes with caustic. 48
180 177 185 180 180 180 155 185 185 185 240 240 240 240 230 152 152 240 240 185 235 235 184 184
Acerage subcooled temperature.
Table II.
a
Measured Data
t,,
F.
68.0 66.8 64.4 64.8 66.0 62.7 58.3 74.0 71.4 74.8 67.9 63.7 65.5 64.9 65.3 52.8 57.5 68.5 66.3 72.2 63.7 64.9 63.5 65.9
L o , Lh. M o l e / Hr. Sq. Ft. Atm. 5.20 4.49 4.52 4.12 4.30 3.76 3.27 3.19 2.66 2.49 2.74 3.09 2.63 2.60 2.46 2 .oo 2.12 2,56 2.30 2.28 2.08 2.10 1.75 1.77
k g expri
ko Ea ~ c d
1 12 1.04 1.06 0.969 0.950 0.885 0.916 0.922 0.825 0,910 1.04 1.22 1.02 1.06 1 11 0,960 1.02 1 .30 1.05 1.08 1.18 1.19 1.19 1.19
Entrained water droplets were removed from the mixture stream prior to its entrance into the tube bundle, and none could be detected in the outlet stream. This latter observation might suggest that a combination of a laminar boundary layer or sublayer and a ripple-free liquid film prevents bloLving of the liquid from the tubes, but this was not made a point of further investigation. Values of k , were calculated from the experimental data as well as from the analogy. T h e experimental results are plotted in Figure 2 d, Ivhere values of J Hfrom Figure 1 and J D are expressed as functions of the appropriate Reynolds number. T h e results of hfaisel’s and Sherwood’s evaluation of J D (6) for evaporation of water from a single cylinder are also plotted and,
as expected, fall beloxi the present data T h e measured and calculated data for the investigation are reported in Tables I and 11. T h e standard deviation between k , ellcc, and k , e x p t l was 0.31 and the average per cent error based upon k , ex,,tl wds 9 4%. Some of this variation can be attributed to error resulting from the calculation of t l T h e results of the study presented as dimensionless J factor correlations suggest that the analogy holds reasonably well for flo\v transverse to vertical tubes in a bundle Nomenclature
C
pBJf
pt p,,
= mean partial pressure of noncondensable, atm. = partial pressure of vapor a t interface, a t m .
t,
= =
ti
=
t, = Re = p p
A
W
= = =
.Y
= =
Qs
=
partial pressure of vapor in bulk stream, atm. temperature of bulk stream, ’ F. temperature of liquid-gas interface, ’ F. temperature of coolant, F. Reynolds number of mixture, doG,lp density of mixture, lb./cu. ft. viscosity of mixture, lb.ift,-hr. latent heat of condensation, B.t.u./lb. coolant flow rate, Ib./hr. condensate flow rate, Ib./hr. sensible heat transferred, B.t.u./hr.
literature Cited
specific heat of mixture, B.t.u./lb. F. do = diameter of tubes, ft. D, = diffusion coefficient, sq. ft. ‘hr. G = mass flow rate of mixture, lb.!’hr, sq. ft. min. cross section G M = molar flow rate. lb. mole,’hr. sq. ft. min. cross section = gas film heat transfer coefficient, B.t.u./hr. sq. ft. F. h, h,’ = total heat transfer coefficient less that provided by gas film, B.t.u./’hr. sq. f t . F. J o = diffusion J factor = heat transfer J factor J H k = thermal conductivity of mixture, B.t.u.;’hr. sq. ft. ’ F.:’ft. k, = mass transfer coefficient! lb. molejhr. sq. ft. a t m . M , = molecular Iveight of vapor, Ib./mole =
(1) Chilton, T. H., Colburn. A. P., Ind. Eng. Chem. 26, 1183 (1934). (2) Colburn, A. P.: Hougen. 0. A , Ibid.,p. 1178. (3) ~, Comings, E. LV.. Clapp, . . J. T., Taylor, J . F., Ibid., 40, 1076
(1948). (4) Dailey, C. E., thesis. Carnegie Institute of Technology, 1954. (5) Hughes, J. .4., Phil. .\fag. 31, 118 (1916). (6) ,Maisel, D. S.,Sherwood, T. K.? Chem. Eng. Pryer. 46, 131 (1 950). (T) Mizushina, T.. Chem. En!. Sct. 13, 7 (1960). (8) Robson, H . T.. thesis, Cornel1 University, 1950. (9) Snyder, N. JV., Chem. En?. Progr. Symp. Ser. 49, 1, KO. 5. 11 (1953). (10) LVinding, C. C., Cheney, A. J., Ind. Eng. Chem. 40, 1087 (1948). RECEIVED for review September 3 , 1963 ACCEPTED November 9: 1964
M E C H A N I S M OF I N T E R F A C I A L R E S I S T A N C E IN G A S ABSORPTION FRANCIS
GOODRIDGE
AND
IAN
D .
ROBB’
Department of Chemical E n p e e r i n g , Cnntuerszty of -Vewcastle upon Tyne, .Veucastle upon T i n e , England
Interfacial resistance caused b y insoluble surfactants has been studied experimentally in order to determine the mechanism of the phenomenon. The system investigated was that of carbon dioxide-water, the surfactants used being long-chain alcohols and acids. The considerable reduction in the rate of absorption can b e explained quantitatively in terms of a potential energy barrier and a hydrodynamic effect, Values of transfer coefficients and energies of activation showed in most cases good agreement with those of other workers.
HE study of interfacial resistance in gas-liquid systems, Tcaused by monomolecular films of insoluble surfactants, began as early as 1925, but it is only within the last ten years that techniques became sufficiently- refined to produce results of quantitative significance. Early investigations Lvere confined in the main to the evaporation of water and culminated in the recent lvork by La Mer e t ~ l (7:. 3. 20). \vho showed that previous results \\.ere of doubtful quantitative value because of the presence of occluded solvent molecules in the film. His own results he interpreted in terms of a potential energy barrier. but found difficulty in reconciling high experimental energies of activation \vith a simple collision mechanism. This concept of a potential energy barrier \vas extended to the field of gas absorption by Blank ( 4 ) and Goodridge and Bricknell ( 7 7 ) . Blank \vas faced lvith the paradox that although energies of activation appeared to be loLver than those found by Archer and La M e r ( 7 ) . the reduction in the rate of gas absorption was greater. Blank explained this discrepancy by postulating
Present address, Formica, Ltd.: Tynemouth, England.
that in the case of gas absorption holes in the film Lvere blocked by water molecules. Goodridge and Bricknell investigated the absorption of carbon dioxide by water in the presence of a variety of filmforming compounds. They sholved that calculated energies of activation based on energies of hole formation: together with a simple collision theory. gave resistances in close agreement with observed values. This agreement \vas not considered sufficient in itself to establish the validity of the postulated mechanism, but did indicate that the order of magnitude of interfacial resistance could be accounted for in terms of a potential energy barrier. T h e present paper is a n extension of this Lvork. It is shown that results can be explained only if more effects than just that of a potential energy barrier are taken into consideration. Experimental
Equipment and Procedure. Pure carbon dioxide is absorbed into water agitated by a Turbine srirrer in a cylindrical vessel. To avoid any disturbance of the liquid surface. rhe VOL. 4
NO. 1
FEBRUARY
1965
49
