Ind. Eng. Chem. Process Des. Dev. 1980, 19, 144-147
144
Literature Cited Basmadjian, D., Ha. K. D., Pan, C. Y., Ind. fng. Chern. Process Des. Dev., 14, 328 (1975a). Basmadiian, D., Ha, K. D., Prouk D. P., Ind. Eng. Chem. Process Des. Dev., 14, 340 (1975b). Carter, J. W., Trans. Inst. Chem. Eng., 46, T213 (1968). Carter, J. W., Barrett, D. J., Trans. Inst. Chem. Eng., 51, 75 (1973). Hiester, N. K., Vermeulen, T., Chem. f n g . Prog., 48, 505 (1952). Linde Corporation, Molecular Sieve Adsorbent Data Sheets No. 22 and SD 22-23. Ma, Y. H., Mancel, C., AIChEJ.. 18, 1148 (1972).
Pan, C. Y., Ph.D. Thesis. University of Toronto, 1970. Pan, C. Y., Basmadjian, D., Chern. Eng. Sci., 22, 285 (1967). sei,, 25, 1653 (1970), Pan, c, y , , Basmadjian, D,, Chem, Pan, C. Y., Basmadjian, D., Chem. f n g . Sci., 26, 45 (1971). Ruthven, D, M,, University Of New Brunswick, Fredericton, New Brunswick, Canada, private communication, 1976. Sargent, R. W. H., Whitford, C. J.. Adv. Chem. Ser., No. 102, 155 (1971). Takeuchi. Y., Kawazoe, K., J . Chern. Eng. Jpn., 9 , 46 (1976).
Received f o r reuieu: March 13, 1979 Accepted October 15, 1979
Infinite Dilution Activity Coefficients of Linear and Branched Alkanes from C, to C9 in n-Hexadecane by Inert Gas Stripping Dominique Richon, Philippe Antoine, and Henrl Renon Centre RBacteurs et Processus, Equipe de Recherche Associge au C.N.R.S. No 768, €cole Nationale Sup6rieure des Mines de Paris, 75006 Paris, France
Determinations of Henry's constants and limiting activity coefficients by inert gas stripping were carried out for a wide range of normal and branched alkanes in n-hexadecane. The apparatus was improved, but limits of validity of the experimental method were found suggesting that a special cell should be designed for high values of Henry's constants.
Introduction It is shown in this paper that the dilution technique proposed by Leroi and al. (1977) is very fast and accurate to obtain limiting activity coefficients of a solute dissolved in a solvent. However, the value of y mcan be extracted from the law of elution only if the solute is volatile enough and, therefore, the elution time is not too long. The extension of the method to Henry's constant measurements is quite easy if special care is taken to utilize a still with a very small vapor phase volume. Experimental Procedure The solute-solvent mixture is introduced in a cell immersed in a constant-temperature bath. A constant carrier gas flow bubbles through the stirred liquid phase and strips the volatile component into the vapor phase. The composition of the gas leaving the cell is periodically sampled and analyzed by gas chromatography by use of a gas-sampling valve. Equilibrium should be reached between the gas leaving the cell and the liquid phase in the cell. The peak area, Si, of solute i decreases exponentially with time if the analysis is made in the linearity range of the detector, assuming a nonvolatile solvent. In these conditions, the limiting activity coefficients, ym,of solute i was shown previously (Leroi et al., 1977) to be dependent on the carrier gas flow rate, D, the total amount of solvent, N , in the cell and the slope of the straight line representing In S against time and related to them by the equation
where Pis is the saturation pressure of the solute i. Equipment. The equipment is the same as described by Leroi et al. (1977) except for the following improvements. The carrier gas is introduced a t the bottom of the cell by capillaries at the extremities of which gas bubbles 00 19-7882/80/ 1 1 19-0 144$0 1 .OO/O
of equal size form slowly. This modification improves mass transfer as shown in the Appendix. A new glass cell (Figure 1) was built with a concentric gas inlet and outlet. The outlet gas collector is conical to prevent liquid entrainment. A three-way valve (Autoclave Engineer with two independent stems) placed between the carrier gas pressure regulator and the flow control needle valve allows one to stop the carrier gas flow rate and replace it by a solute gas flow rate. The needed initial amount of gaseous solute is introduced into the cell in this way.
Interpretation of Results Equation 1cannot be applied when the amount of solute in the vapor space VG of the cell is not small compared to the amount dissolved in the liquid, assuming that the vapor phase is well mixed in the cell. This corresponds to the case of high Henry's constants or a high value of the product yimPiscompared to NRTI V,. Duhem and Vidal (1978) derived another expression which simplifies when the corrective term accounting for the variation of the total gas flow rate due to the vaporization of solute is neglected, into
Experimental Results The chemical products have the following origins. The n-pentane, n-hexane, and n-heptane are from Merck and have a GLC certified minimum purity of 99%. 2Methylpentane, from Fluka, has a GLC certified minimum purity of 98 '3%. n-Hexadecane, 2,2-dimethylbutane, 2,3dimethylbutane, 2-methylbutane, and 3-methylpentane are from Fluka, the GLC minimum purity being 99%. n-
e 1979 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 19,
Table 111. Henry's Constants for Alkanes in n-Hexadecane H" (our results, a t m )
I n
solute
-~
C -
b
220 29.5 7.52 2.01
143.0 26.7 7.32 2 .oo
209 26.4 7.41 2.02
a , b Values in these t w o columns are obtained with dilutor method by using t w o different values of homogeneous vapor phase volume in the equilibrium still (see text).
Figure 1. Equilibrium cell: A, glass still body; B, conical collector of gas outlet; C, gasket; D, plug; E, capillaries; F, Teflon seal; G, magnetic stirrer; H, metallic ring to adjust the depth of the collector, B, in the still; I, tube for carrier gas inlet; J, gas outlet. Table I. Limiting Activity Coefficients of Normal Alkanes in n-Hexadecane at 2 5 "C solute n-pentane n-hexane n-heptane n-octane
a
H" (Lenoir et al., 19711. a t m
~~
methane ethane propane n-butane
F -
No. 1, 1980 145
Two
0.825 0.888 0.931 0.986
Results obtained with this method. et al. ( 197 1).
ym
0.892
From Lenoir
Table 11. Limiting Activity Coefficients for Branched Alkanes in n-Hexadecane a t 25 " C solute 2-met hylbutane 2-methylpentane 3methylpentane 2,2-dimethylbutane 2,3-dimethylbutane
Yrn
0.885 0.91 0.84 0.91 0.85
Our results.
Octane is also from Fluka with a GLC purity 199.5%. 2-Methylbutane, provided by Baker Chemical Co., has a GLC minimum purity of 99%. Methane, ethane, propane, and n-butane were supplied by 1'Air Liquide; the stated purities are 99.95'70, 99.970, 99.570, and 9970, respectively. All of these gaseous and liquid chemicals were used without any further purification. The results for limiting activity coefficients and Henry's constants of hydrocarbons in n-hexadecane are reported in Tables I to 111. The ymobtained for branched alkanes with the dilutor method are similar to those extrapolated from y ( x ) results of Barbe (1977) obtained by a vapor sorption technique. Activity coefficients of Barbe are, however, systematically higher than ours by about 4%. The new results combined with calorimetric data can be used to evaluate the enthalpy-entropy compensation in alkane systems as discussed by Patterson and Barbe (1976).
Limits of Applications of the Dilutor Method. The experiments with the series of normal alkanes give lower and lower slopes, a, of the elution law: In [(S,)/(S,)t=o] = -at with increasing carbon number of the solute molecule. For the system n-octane-n-hexadecane, the experiment takes several hours to produce a sufficient variation of S,. The experiment with n-nonane lasts about four times longer than for n-octane in order to obtain a significant change in S, which remains very small in magnitude. The dispersion in Sivalues in time does not allow a precise enough determination of the slope and activity coefficient. At the other extreme of the range of volatility of alkanes, the dilutor method has been used to measure Henry's constants of four lower alkanes dissolved in n-hexadecane. The results are reported in Table 111, along with data from Lenoir et al. (1971). The value of vapor phase volume VG in the cell to be used in eq 2 should be estimated. It has a larger influence on the value of Hi"when the volatility of the solute increases. Two estimates of VG were taken into account, because it is not clear if all the vapor space is well mixed in the cell because of the presence of conical part at the top of the cell, designed to avoid liquid entrainment. Two limiting cases are considered assuming that either (a) VG, is equal to the whole volume accessible ~ ,smaller to the vapor up to the sampling valve or (b) V G is by all the volumes where a piston flow can be assumed. Comparing the results to those of Lenoir (1971), it appears that the influence of VG becomes very important for the highest values of H," (methane). Values of ITrnethane by Lenoir lie between our two limiting values. When H" > 30 atm are measured, it is necessary to have the smallest possible volume, VG,of vapor space with a simple shape where thorough mixing can be achieved. The still, as it is constructed, is not adapted to the measurement of high Henry's constants, but the method can be adapted to obtain gas solubility data in liquids. The cell for gas solubilities determination does not need a conical collector required to avoid entrainment of liquid droplets a t high carrier gas flow rate, because the carrier gas flow rate is then very small ( < l o cm3/min). The tubing between the still and the sampling valve must be as short as possible. Conclusion An improved dilutor method has been used to determine limiting activity coefficients of some hydrocarbons in nhexadecane. It has been noted that, a t 25 "C, the activity coefficient measurement of n-nonane is very difficult and inaccurate because of the very small amount in the vapor phase. However, for a hydrocarbon solute of less than 9 carbon atoms, the experiment is quite simple and yields accurate determination of limiting activity coefficients. The method is easily extended to Henry's constant determinations by taking into account the influence of the volume of the vapor phase in the equilibrium cell. Measurement of the Henry's constants higher than 30 atm requires another design of the cell with a small and ho-
146
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 1, 1980
mogeneous vapor phase in the cell. Appendix Mass Transfer in the Equilibrium Cell. A condition of validity of the present method is that thermodynamical equilibrium is reached between the saturated gas leaving the cell and the liquid. The following calculation of mass transfer of solute helped to design the cell. When carrier gas bubbles through the solvent, the solute is transferred from the solvent to the gas through the interface of the bubbles in two steps. (1) Mass Transfer in the Liquid Phase. The number of moles of solute, dn,, passing through the interface during a time d t is given by dn, = 4 k ~ x R b ' ( C ,-~ C,,sL)dt
(AI)
C: is the concentration in the liquid phase and C,,: is the interfacial concentration. kL is the mass transfer coefficient calculated by means of the correlation of Cheh and Tobias (1968). For computation of hL, it is necessary to know the liquid diffusion coefficient Dl,L of solute, i, in solvent, j , estimated here from the correlation of Wilke and Chang (1955). At the interface, concentrations C,,: and ClsGare related by the equilibrium relation (A2) written at infinite dilution.
1 02
therefore dn, - MG p _ -dt
p~
RT
dCIG Vb
dt
Assuming that diffusion in the gas phase of the bubble is very fast C,G(t) = C,,,G(t)
(A51
Eq A2, A4, and A5 combined with eq A1 lead to the following differential equation
B is assumed constant because variations of k,, P and physical constants of the gas and liquid are negligible for bubbles going up in the cell. Taking account of all those hypotheses, the integration of eq A6 between 0 and C i G ( t )gives
Results of calculations are given in Figure 2 in the case of an n-heptane-n-methylpyrrolidone (NMP) mixture at 25 "C a t 1 atm; n-heptane is the solute, NMP is the solvent, and the carrier gas is helium. The bubble diameter is taken as 1.5 mm. It appears from Figure 2 that viscosity is not a limiting factor because even with F~ = 40 cP, the
I 08
I
hlcmi
.
k r cm/s*
u r n , cm/s
1.5 0.351 17.2 2 .o 0.369 23.9 2.5 0.355 27.1 3.0 0.342 29.7 4.0 0.322 34.3 5.0 0.306 38.3 a KL has been estimated f r o m Cheh-Tobias correlation (1968).
equilibrium is reached at 99% after only passing through h = 1 cm of solution. The small influence of p on T is due to compensating effects; when p increases, kL increases but the velocity of the bubble in solution decreases and time spent in solution increases. The liquid mass transfer coefficient is not very sensitive to the bubble diameter (Table IV), being much less than the velocity of bubbles. Figure 3 shows the behavior of T against the path length h of the bubbles in solution for different bubble diameters. Even for the larger diameters Db 4.5 mm it is close to 1 if h = 5 cm. (2) Diffusion in the Gas Phase. Crank (1956) gives the following relation for the solute concentration in gaseous bubbles not being stirred by convection movements at a distance r from a bubble center at time t
xr 7L is an estimation of the approach to equilibrium between bubbles and solution as a function of the time spent by bubbles in solution. vffiis obtained through the equation for the intermediate law = 7.2 X 10-2vL-0.6Db'~6g
I
06
Figure 2. Influence of viscosity of liquid phase (n-heptane-NMP) on transfer rate, T L is plotted vs. path length of helium bubbles in the liquid at 25 "C and 1 atm for several values of viscosity in centipoises. Table IV. K L and urn as a Function of Db for n-Heptane in a Solvent with a Viscosity of 1 CP
Dh.mm
niis related to the average concentration in a bubble by
I
04
i=1
1
sin k! Rb exp( -
DijG l2 x2 t Rb2
)]
(A8)
DijG,the diffusion coefficient of solute i in gas j , is given by Slattery and Bird (1958). Mass of solute in bubble at time t is given by integration
M ( t ) = 4x M i
LRb
r2CiG(r,t)dr
(A91
(A101
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 1, 1980 147
Table V. Diffusion Coefficient of n-Heptane in Several Gases at 2 5 "C and 1 Atm helium
Azote argon
0.348 0.075 0.067
that the best way to form bubbles of small and even sizes is to use well spaced capillaries.
Nomenclature C? = solute concentration in liquid, mol/cm3
0 2
04
06
08
10
1 2
14
16
18 h lcmi
-
Figure 3. Influence of bubbles diameter on transfer rate,
iL is plotted versus path length of bubbles in liquid at 25 "C and 1 a t m for several values of bubble diameters. Viscosity is taken as 1.0 cP, and other parameters are those of (n-heptane-NMP) mixture and helium gas.
k1
Ci,: = solute concentration in liquid at interface, mol/cm3 Ci = solute concentration in bubble at interface, mol/cm3 Cp(r,t) = solute concentration in bubble, function of time and distance D = carrier gas flow (at pressure P, temperature T ) , cm3/min Di,L,Dip = diffusion constant of solute i in solvent j (in liquid and gas), cm2/s g = gravitational constant, cm s-* h = path length of bubbles in solution, cm H = Henry's constant, atm kL = transfer coefficient in liquid M,,, = molar mass of component m, g/mol N = amount of solvent in the still, g-mol P = total pressure P, = critical pressure of component m, atm = vapor pressure of pure solute, atm r = distance from center of bubble, cm R = gas constant, cm3 atm g-mol-' K-' Rb, Db, Vt, = radius, diameter, and volume of bubbles Si= GLC solute i peak area t = time, min; t is in seconds in Appendix T = temperature, K Tcm= critical temperature of component m, K urn = limiting speed for bubbles in solution, cm/s = volume of vapor phase in dilutor still up to sampling valve, cm3 Greek Letters pm =
I
I
I
I
I
I
I
I
I
02
04
06
08
10
12
14
16
18
hlcml
Figure 4. Influence of bubble diameters on diffusion rate, T ~ con, ditions are the same as for Figure 3. The approach to equilibrium, TG, is defined as the ratio of M ( t ) over M"
In Figure 4, TG is plotted vs. path length, h. DijG is taken for n-heptane in helium (Table V). If R b C 1.25 mm, time for gas phase diffusion can be neglected compared to time for liquid mass transfer. But if Rb > 2 mm, the previous calculation of i Lis not valid because the hypothesis Ci,,G(t) = CiG(t)does not hold, and gaseous diffusion becomes a limiting factor for transfer. In conclusion, the calculations indicate that bubbles must have a diameter lower than 2 mm and a path length in solution higher than 3 cm. Glass fritted disks which cannot be made in a perfect manner allow the formation of big bubbles. As coalescence must be avoided, we found
density of component or phase m, g/cm3
y = activity coefficient F L = dynamic viscosity V L = kinematic viscosity, CP T L = ratio of mass transfer in the cell to mass transfer to reach
equilibrium taking into account liquid phase resistance only = same as T~ taking into account gas phase diffusion only Subscripts i = solute j = solvent s = at interface Superscripts or subscripts L = liquid G = gas TG
Literature Cited Barbe, M., Patterson, D., private communication, McGill University, Montreal, 1977. Cheh, Y. H., Tobias, C. W., Ind. Eng. Chem. Fundam., 7, 48 (1968). Crank, J., "The Mathematics of Diffusion", Oxford University Press, Chapter VI, p 86, Oxford, 1956. Duhern, P., Vidal, J., Fluid Phase €qui/., 2(3), 231 (1978). Lenoir, J. Y., Renault, P., Renon, H., J . Chem. Eng. Data., 16, 340 (1971). Leroi, J. C., Masson, J. C., Renon, H., Fabries, J. F., Sannier, H., Ind. Eng. Chem. Process Des. Dev., 16, 139 (1977). Patterson, D., Barbe. M., J . Phys. Chem., 80,2435 (1976). Slattery, J. C., Bird, R. B., AIChE J . , 4, 137 (1958). Wilke, C. R., Chang, P., AIChE J . , 1, 264 (1955).
Received for review March 22, 1979 Accepted July 25, 1979
