Nomenclature
p
eigenvalue in Equation 9, given by Equations 12 and 13 = molecular diffusivity of solute in melt, sq. cm./sec. = index. 0 i 1. + 2, etc. = index. 1 . 2. etc. = equilibrium dktribution coefficient, ws/wr - 0 = length of zone. cm. = eigenvalue given by Equation 11 = dimensionless zone size, p = ( L V / D ) ( p , / p J
Q
=
r
= e/(€
R
=
C,?
D
i 1
k
L mj
7,
= duration of initial period during which solid contains
r1
9
= dimensionless time from beginning of terminal period, 71 = ( T - 7,) = dimensionless composition of melt a t 17 and T, q =
&-IJ
= dimensionless composition of melt a t freezing inter-
no solute-i.e.,
=
Tat which pq=ofirst equals
w/w,
face a t
T,
=
wx=o/wo
= dimensionless composition of solid a t
T ? p,,
= m,/w,
m
Literature Cited
F-~P
i=o
C
- I)
m
ipe-iP
*=o
t x
I’ u’
we u, zc,? w,,n z
= = = = =
= = = =
time from initi.ation of freezing: sec. distance from freezing interface into melt, cm. rate of solidification, cm.:sec. weight fraction of solute in melt a t x and t weight fraction of solute in eutectic Lveight fraction of solute originally in melt (uniform) weight fraction of solute in solid a t z weight fraction of solute a t freezing interface distance down solid from first solid frozen out, z = tV: cm.
GREEKLETTERS = dimensionless eutectic composition, e = ZL~,/LL’, = dimensionless ‘distance from freezing interface into melt, 17 = x V p , / D p l p l , p s = density of liquid and solid, respectively, g./cc. 7 = dimensionless time. T = ( t V z / D ) ( p s / p l ) = ( z V / D ) X
e 7
(1) Friedenberg, R. M., “Ultrapurity and Ultrapurification of Pharmaceuticals by Zone Melting,” Ph.D. thesis, University of Connecticut. Storrs, Conn., 1963. (2) Herington, E. F. G.: “Zone Melting of Organic Compounds,” Wiley. New York, 1963. (3) Pfann, W.G., “Zone Melting,” Wiley. New York, 1958. (4) Smith. V. G., Tiller, W.A., Rutter, J. W., Can. J . Phys. 33, 723 (1955). (5) Wilcox. 1.V. R., “Fractional Crystallization from Melts,” Ph.D. thesis, University of California, Berkeley, 1960. (6) 1t:jlcox. \V. R., J . A f f l . Phys. 35, 636 (1964). (7) Wilcox. M’. R., “Solute Redistribution during Solidification of Eutectic-Forming Mixtures,” Aerospace Corp., El Segundo, Calif.. Rept. TDR-169 (3240-10) TN-2 (1963). (8) IVilcox. W.R.? “Zone Melting of Eutectic-Formining Mixtures.” Aerospace Corp., El Segundo, Calif., Rept. ATN64(9236)-Z(1963). (9) \Vilcox, I$-. K., Friendenberg, R . M., Back, N., Chem. Reus. 64, 187 (1964). (10) Lt’ilcox, I V . R., It’ilke, C. R., A.I.Ch.E. J . 10, 160 (1964). (11) Nilcox: h’. R., U’ilke: C. R.: “Ultrapurification of Semiconductor Materials,” p. 481, Macmillan, New York, 1961, RECEIVED for review December 20, 1963 ACCEPTED March 30. 1964
(PSlPJ2
KINETICS OF ABSORPTION OF CARBON DIOXIDE IN MONOETHANOLAMINE SOLUTIONS A T SHORT CONTACT TIMES J .
K. A . C L A R K E
Warren Sprzng Laboratory, Defartment of ScientiJic and Industrial Research, Stevenage, Hertfordshzre, England Work was carried out to measure the absorption rate of a gas, a t short contact times, with a fast chemical reaction taking place simultaneously, and to test the relation between the absorption rates observed and the diffusion coef Ficient, the physical solubility of the gas, and the kinetic rate constant for the homogeneous liquid phase reaction. Measurements are reported of rates of absorDtion of carbon dioxide in laminar jets
of aqueous monoethanolamine solutions a t contact times of 3 to 2 0 msec. and gas pressures of 1 and 0.1 atm.
Rates c f gas take-up observed a t the lower pressure are in agreement with the “penetration” theory
for pseudo-first-order reactions developed by Danckwerts. Absorption a t atmospheric pressure corresponds to a less ameriable kinetic condition, since the concentration of unreacted monoethanolamine at the interface becomes seriously depleted during even the shortest attainable contact time of gas and liquid, and heat of reaction appears to influence the observed rates of absorption.
of considerable interest to relate rates of gas absorption with simultaneous fast chemical reaction in liquids to the physicochemical parameters of the system concerned. For this purpose the laminar liquid jet technique (6, 24,25) is particularl>- valuable. Contact times of gas and liquid of 3 to 30 msec. can be achieved: and simple hydrodynamic conditions in the jet permit the c’ontact rime to be directly related to the flow rate of liquid. T h e technique was applied by Nijsing. Hendriksz, and Kramers (25) to a study of the absorption of COz in laminar streams of aqueous alkali-metal hydroxide solutions
I
T IS
Present address, Department of Chemistry, University College, Dublin.
and agreement with the theory of diffusion Lvith chemical reaction was found. Empirical methods ”err used to evaluate the diffusion coefficient and the physical solubility of C 0 2 in the liquids. A number of studies have been made by different techniques, of “transient” absorption rates of CO? in monoethanolamine and its aqueous solutions which are important in industrial practice as carbon dioxide absorbents (2, 73: 75. 76). The present work was designed to permit measurement of rates of COS absorption in aqueous monoethanolamine under conditions such that the “penetration” theory of diffusion accompanied by pseudo-first-order chemical reaction (8)could be applied with VOL. 3
NO. 3 A U G U S T 1 9 6 4
239
confidence, and thereby to test whether the observed absorption rates could be related to the physicocht-mica1 quantities characteristic of the system-viz., the diffusion coefficient and physical solubility of COS in monoethanolamine solutions and the kinetic rate constant for the homogeneous liquid phase reaction. I n estimating the first and second of these quantities. advantage has been takm nl th,. \iiiiilarity in molecular properties of COn and NZO T h e third quantity has been determined experimentally by Jensen, Jqrgensen, and Faurholt (22). Experimental and Results
Materials. Distillers Co. 99.9% pure C 0 2 and British Oxygen Co. medical grade NsO were used. the latter in additional experiments described below. Mbnoethanolamine was a Cnion Carbide 99.97, product having a freezing point of 10.5’ C. Solutions of monoethanolamine were freshly prepared in distilled water partially deaerated by boiling. Concentration was controlled by titrimetric analysis of the amine and boiling in orthophosphoric acid to expel C o n , which was determined by vapor-phase chromatography. Apparatus and Procedure. Figure 1 shows schematically the main part of the absorption apparatus. T h e solution was fed from a n air-stripping column located 30 feet above ground level. through temperature-regulating stages set a t 25 C., metered in a rotameter. A , and led into the absorption cell, B. Within the cell a jet is formed in a nozzle designed to minimize boundary-layer formation (see below) and is caught cleanly in a glass receiver tube which leads into a storage container. A screw clip, VI, balances the jet a t the top of the receiving tube, in such a way that overflow or gas entrainment does not occur during a determination of absorption rate. T h e carbon dioxide flow from a cylinder was thermostated, C, saturated with water vapor a t the experimental temperature, D ,and passed through a ballast volume, E, to the soap-film flowmeter. F: and the absorption cell. B. After the cell had been purged for several minutes. stopcock SIwas closed and a soap film introduced into the lo\ver section of the flowmeter buret. leaving a sealed charge of gas in contact with the jet. As gas is absorbed in the jet. the gas volume decreases and the soap film moves upward a t a rate equal to the rate of gas absorption a t the contact time chosen. For measurements a t atmospheric pressure stopcock S2 \vas opened to the atmosphere during the movement of the soap film. I n the experiments at reduced pressure a stable pressure was produced by pumping through a needle valve, I.’?. to a further ballast volume. Gas inlet flow was controlled by valve V 3 , Any pressure fluctuations \vere detectable to 0.01 m m . of H g on a \ v a t u manometer, G. having as reference side a 1-liter bulb. H. and linked to the absorption cell. In practice it was possible to hold the pressure constant (to zkO.01 cm. of water) for times sufficient to permit measurements of the slowest gas take-up rates. Temperature of the absorption cell \vas held constant to 1 0 . 0 2 O C. in an air thermostat box. J . T h e materials used in the construction of the liquid-handling system wrre restricted to glass. a stainless steel with a 3% molybdenum content. polytetrafluoroethylene. and a minor amount of neoprene rubber. Figure 2 sho\vs details of the absorption cell. The jet delivery assembly \vas mounted on top of a glass pipe section and consisted of a stainless steel tube, K . of 3,’s-inch internal diameter. held within a tlvo-dimensional traverse mechanism by means of an O-ring gland seal. Contact pressure of the sliding surfaces of the traverse )vas provided by a ring of steel springs. For linear velocities of floiv in the range 3 to 5 meters per second a glass capillary receiver. M . having a n internal diameter 20 to 307, greater than the jet diameter was found most satisfactory [cf. Nijsing ( 2 . i ) ] . Gas-liquid contact time was varied by variation of jet length a t a constant liquid flow rate. Jet length \vas ad,justed by slackening the jet delivery tube in the O-ring seal and sliding it into the appropriate posit ion. T h r contact time of liquid and surrounding gas is calculated most easily if plug flow in the ,jet--i,e,, a “flat” velocity distribution.-~can be assumed. Considerable attention was given to this requiremrnt. a number of nozzle ( L ) designs being tested 240
IBEC FUNDAMENTALS
lo storage
t o boNast vofumms and vacuum pump
Figure 1.
Gas-absorption apparatus
1 1 1 1 1 0 2 4 6 8
Figure 2. Absorption cell
using the absorption of 'carbon dioxide in water as a known system. Values of the solubility and diffusion coefficient for carbon dioxide in water are available in the literature. T h e criteria used for uniform velocity distribution in the jet were: constancy of the (derived diffusion coefficient for CO? in water at 25' C . a s determined from measured rates of absorption a t jet lengths of 1 to 10 cm. and consistency with the best literature values: and a substantially cylindrical shape of the jet, I n the first instance a stainless steel nozzle with a converging (bell-shaped) throat was tested. .4s far as possible the throat was machined to the shape of the free streamline published by Southwell (6,29) for flow through a small hole in a plate blocking off the end of a long straight tube. For physical absorption, if the depth of penetration into the liquid of absorbed gas is small relative to the jet diameter, Fick's law predicts that a plot of q 2 5 , / L 1 against 1' should yield a straight line through the origin of slope 4(298/273) C*D','? [Cullen and Davidson (6)1. Lvhere q 2 5 is the rate of absorption of gas a t 25' C. in cubic centimeters per second and C* is the solubility of CO2 in cubic centimeters (:
-
d, W
*)
Q 3.0X
8 -2.0
1.0
0
-
/y
/.O
2.0
3.0
4.0
5.0
6.0
7.0
8.0
f (cm.) Figure 6. Absorption of COS in monoethanolamine solutions at reduced pressure
the orifice face. This substantiates the conclusion that jets produced by the thin diaphragm orifice have a flat velocity distribution, whereas the former type of nozzle, within the range of designs tested, produces a surface retardation which gives rise to rates of absorption a t short jet lengths, smaller than predicted. T h e diaphragm type of nozzle was used in the measurements of absorption rates with jets of monoethanolamine solutions. Absorption Rates in Monoethanolamine Solutions. T h e results of measurements of COZ absorption rates in monoethanolamine aqueous solutions a t 2 5 " C. and 1 atm. a r r shown in Figure 5 as a plot of &, the amount of gas absorbed per second us. the jet length. Although rates of removal of C O Zwere greater than in the corresponding experiments with water and could be measured more accurately, corrections to measured rates due to absorption on the cell walls were also greater and decreased slowly with time of gas purging. Consequently the over-all scatter of points is comparable to that of Figures 3 a n d 4 . Examination of the results of Figure 5 on the basis of considerations outlined in the discussion prompted extension of measurements to a lower pressure of CO?. I n the runs a t reduced pressure a platinum diaphragm nozzle was used to ensure complete immunity from chemical attack. Results of experiments a t a COZ pressure of 8.00 c m . of Hg and a t the highest feasible flow rate of monoethanolamine solutions are shown in Figure 6. T h e diffusion coefficients of K z O were measured in monoethanolamine solutions of concentrations similar to those employed in the jet absorption studies. Results obtained using stirred sintered-disk diaphragm cells (74, 3 0 ) , a n d carrying out NZO analysis by vapor-phase chromatography, are given in Table I . Diffusion proceeded in the cells from NIO-saturated solution in the upper compartments into initially gas-free solutions in the lower compartments. Following the recom242
I&EC FUNDAMENTALS
mendations of Geddes (74) as to calibration conditions. analyses were carried out when the difference in concentration of gas in upper and lower compartments was about 5OgZ of the initial concentration in the upper compartments. Values given in Table I are integral diffusion coefficients referred to this concentration condition and are accurate to about 10yG,T h e determining factors in accuracy of measurement were the efficiency in sampling gas-charged liquid from the cells and the chromatographic analysis itself. T h e solubilities of NZO in similar solutions a t 25' C. were determined to * 5 Y , using the constant-volume method described by Loprest (23) (Table I, column 3).
Table 1.
Diffusion Coefficients and Solubilities of N 2 0 in Monoethanolamine Solutions (25.0" C.)
Solu bzlz ty Monoelhanolamine Concn., Moles/Liter 1.637 3.283 4.877 Water ( 2 0 )
DL x 706, Sq. Cm. /Sec. 1.52 1.39 1.20
x
105,
Mo/es/Gram at 1 Atm. 2.52 2.33 2.26 2.43
Discussion
I n the absorption of a gas, A , in a liquid containing a chemical reagent, B: a simple limiting kinetic condition exists if the rate of diffusion of reagent to the reaction zone in the liquid is rapid relative to the rate of consumption of reagent by chemical reaction with molecules of A . If the chemical reaction is fast. this condition may be observed only a very short contact times, attainable by the laminar jet technique. Danckwerts (8) has solved the governing differential equation for this pseudo-first-
order kinetic condition making the well knoll n penetration theory assumption of a semi-infinite nonturbulent liquid medium and equilibriun~saturation by A of the liquid surface T h e solution rnay be expressed a t T>O. -,
-
1 II
where Q is the amount
