five systems the agreement is very good. Furthermore, a comparison between Figure 3 of the work of Joy and Kyle (1969)) where the value of a was obtained by fitting the binary data, and Figures 1, 5, and 6 of this study suggests equally good performance. In addition the LEMF equation predicts ternary VLE from binary VLE data with accuracy comparable to that of the NRTL equation; it predicts binary VLE data from mutual solubility data with accuracy better than that of the NRTL equation (Marina and Tassios, 1973). It seems, hence, that the LEMF equation represents a real twoparameter equation applicable t o both miscible and partially miscible systems. Turning to the computational techniques, the LSQ2 subroutine seems to work reasonably well, the error of convergence being 0.00 in most cases. In some cases, however, erroneous results were obtained due to extraneous minimas in the function E (eq 7). We have found no explanation for this phenomena. Nomenclature
G GE
gil a J
= degrees of freedom = excess free energy of mixing = residual Gibbs energy of component = pertaining to component i = pertaining to component J
i in a j cell
n = number of components in the system €$ = gas constant T = temperature, OC X = liquid composition
GREEKLETTERS a = nonrandomness parameter in the NRTL equation 7 = activity coefficient 4 = number of phases in the system literature Cited
Bancroft, W. D., Hubard, S. S., J. Amer. Chem. Soc., 64, 347 (1942).
Gardner, R. S., Inside Publication No. 2698, U. S. Naval Ordnance Test Station, China Lake, Calif., 1967. Griswold, J., Chu, P. L., Znd. Eng. Chem., 41, 10, 2352 (1949). Hala, E., Wichterle, I., Polak, J., Boublik, T., “Vapor-Liquid Equilibrium Data at Normal Pressure,’’ Pergamon Press, New York, N. Y., 1968. Joy, D. S., Kyle, B. G., AZChE J., 15, 298 (1969). Katayama, T., Sung, E. K., Lightfoot, E. N., AZChE J., 11, 5. 925 (1965).
Marina, J, M.‘, Tassios, D. P., Znd. Eng. Chem., Process Des. Develop., 12, 67 (1973). McCants, J. F., Jones, J. H., Hopson, W. H., Ind. Eng. Chem., 45, 454 (1953).
Pennington, E. N., Marwil, S. J., Ind. Eng. Chem., 45, 1371 (1953).
Renon, H. Prausnitz, J. M., AZChE J., 14, 135 (1968). Severns, Ib. H., Sesonske, A., Perry, R. H., Pigford, R. L., AIChE J., 1, 401 (1955). Stephen, H., Stephen, T., “Solubility of Inorganic and Organic Compounds,” Macmillan, New York, N. Y., 1963. Venkataratnam, R., Jagannadha, R., Venkata, R. C., Chem. Eng. Sci., 7, 102 (1957). RECEIVED for review June 22, 1972 ACCEPTED February 26, 1973 Presented at the AIChE Meeting in Houston, Texas, February, 1971.
Prediction of Gas-liquid Equilibrium through Gas-liquid Chromatography Andrew S. Bogeatzes*’ and Dimitrios P. Tassios Newark College of Engineering, Newark, New Jersey 07109
A rapid, simple, and reliable experimental technique, employing gas-liquid chromatography, is proposed for the determination of infinite dilution activity coefficients of gases in solvents. The method has been successfully tested for SO2 in a number of organic solvents. The yo measured by glc was combined with the oneparameter Tassios-Wilson equation to generate equilibrium data on finite compositions for two different SOY solvent systems. The predicted data compared very well with experimental values obtained using conventional techniques.
w i t h the increasing emphasis on the removal of gaseous pollutants from stationary sources, the selection of the appropriate solvent, if gas-scrubbing is to be employed, becomes very important. It can be easily shown that when a solvent exhibits strong affinity for a given gas, then the activity coefficient of the gas in this solvent is very low. Determination of activity coefficients of gases in liquid through conventional vapor-liquid equlibrium measurements is rather cumbersome and time consuming and hence evaluation of several solvents is rather expensive. 1 Present address, Central Research Laboratories, American Smelting and Refining Co., South Plainfield, K. J. 07080.
274 Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
Everet and Stoddart (1961) and Martire and Pollara (1965) obtained infinite dilution activity coefficients by gasliquid chromatography (glc) that were thermodynamically reliable and compared quite favorably with those obtained by extrapolation from static measurements under welldefined equilibrium conditions. This technique has been employed mainly for liquid solutes and requires that for each solvent a separate chromatographic column is prepared. Sheets and Marchello (1963) suggested that extractive distillation solvents can be qualitatively rated by employing direct injection of each solvent in a chromatograph containing a column packed with a solid substrate only. Later Tassios
(1970) showed that infinite dilution relative volatilities of liquid binary mixtures in higher boiling point solvents can be reliably obtained through glc by employing direct solvent injection. I n this paper, i t is shown that direct solvent injection can be employed in evaluating infinite dilution activity coefficients (70) of gases in liquid solvents. The technique is simple and rapid requiring 2-4 hr per solvent. The accuracy of the method is demonstrated with sulfur dioxide in several solvents a t temperatures of 25-93'. It is also shown that the method can be applied to mixtures of solvents. Tassios (1971) has proposed a one-parameter form of the equation developed by Wilson (1964) that can predict activity coefficients for the whole concentration range of a binary system from knowledge of one yo value alone. This expression was employed in this study, along with the yo value of SO2 obtained through glc, to evaluate partial pressures of SO2 a t finite SO2 concentrations in the systems S02-N,N-dimethylaniline and S02-N,N-dimethylacetamide. The results are very good for engineering applications and indicate that the glc technique can be employed not only for solvent screening but also for predicting equilibrium data to be used for design purposes.
Table 1. Parameter Values in Eq 9 Comprerribility factor,
A
Compound
so2
N,N-Dimethylaniline N,N-Dimethylacetamide
B
Z
C
7 . 7 5 -1279.90
0
0.94
8 . 3 5 -2527.41
0
1
+7.53
1
-13.79
-1350.96
Hence there is only one adjustable parameter per binary system (gij), which can be obtained from one yo value per binary (Tassios, 1971; Hankinson, et al., 1972). Values for the heat of vaporization a t the temperature of the system were calculated through the Clausius-Clapeyron equation d1nPiO -dT
AHi -~
(7)
RT2
Hence, eq 6 becomes,
Infinite Dilution Activity Coefficients through Glc
James and Martin (1952), Kwantes and Rijnders (1958), and Porter, et al. (1956), have extensively discussed determination of infinite dilution activity coefficients through glc. The solvent is employed as the partitioning liquid in a chromatographic column, and a small amount of the solute is injected into the column. Then, according to Porter et al. (1956)
M,RT HioPio
The following equation for the dependency a t the vapor pressure on temperature was employed log Pio (mm) = A
yo =
1.704 X lo7 MP ioVgo
where
Partial Pressures at Finite Gas Concentration from yo Values
Starting with the Wilson equation (1964)
where
-5
-d/RT
Vi
(5)
gji but Aij # Aji
gij =
Tassios proposed a one adjustable parameter form of this equation by replacing the constants gii and gji, through the energies of vaporization 9 11 ..
gjj
- -AU =
i
- -(AHi
-AUj = -(AH,
- ZiRT) - ZjRT)
gii = RT2 BT+ [
" I
+T- log e
- ZiRT
(10)
Values for the constants A, B, and C were obtained by regressing the vapor pressure data available in the literature (Perry, 1963; Stull, 1947) for SO2 and N,N-dimethylaniline. Vapor pressure data for N,N-dimethylacetamide was obtained directly from Dupont Co. (1971). The values of the constants are presented in Table I. The compressibility factor, eq 6 and 6a, is evaluated a t the temperature and pressure of the solution (Tassios, 1971). Evaluation of Z a t the temperature of the solution and the saturation pressure of the pure component a t this temperature was also used in this study. The values of 2, obtained through the method of Hougen and Watson (1947), are presented in Table I. Equipment and Procedure
(4) Aij -1
(9)
Evaluation of [d In Pio/dT] through eq 9 and substitution into eq 8 yields
yo = -
I n eq 1 it is assumed that infinite dilution conditions prevail in the column. This is discussed later. It has been shown by Martire and Pollara (1965) that eq 1 can be written as
+ B-T + Clog T
(6) (64
An F & M Model 500 gas chromatograph equipped with a 10-ft (0.25 in. 0.d.) column constructed of stainless steel was used in this study. The column was packed with high-performance Chromosorb G Mesh 80-100, which has a recommended maximum liquid limit of 5% (approximately 1.5 g of solvent for 28.6 g of chromosorb contained in the column). The inert gas employed was helium with flow rate ranging from 54 to 61 cc/min over the total number of tests conducted. Helium flow for a particular run, measured with a soap-film flowmeter, was maintained constant within *0.2%. Column temperature was maintained constant within * l o . The sulfur dioxide-nitrogen gas mixture used was cylinder gas, with composition analyzed by mass spectrometer as being 89.9% SO2 and 9.9% N2. A gas sampling valve injected a constant volume of gas into the carrier gas (this volume being Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
275
0.05
I
0.04
-
0.08
-
I
,
,
,
,
I
I
I
I
I
I
I
I
Solvent
,
temp,
Dimethylaniline Nitrobenzene Trimethylpyridine Triethylenetetramine Dimethylacetamide Dimethylacetamide Dimethylacetamide
OM*"
I'
.. .
Figure 1. Infinite dilution activity coefficients for SO2 vs. solvent weight: (a) DMA,, N,N-dimethylacetamide; (b) DMA, N,N-dimethylaniline
O c
41.0 25.0 39.0 40.0 41.5 66.0 93.0
yo
YO
Yo
0.027 0.913 0.123 1.580 0.036 0.071 0.077
3.7 3.2 3.3 8.9 5.5 2.8 19.5
12 3 3 3 13 4 10
amount of solute charged into the column must be as small as possible. Under these conditions, infinite dilution activity coefficients have been evaluated and are in very good agreement with values obtained through vapor-liquid equilibrium measurements (Kwantes and Rijnders, 1958; Porter, et al., 1956). Tassios (1972) has shown that infinite dilution conditions can be established with lower solvent amounts (5% of column content). Infinite dilution relative volatilities thus measured agreed very well with those from conventional vapor-liquid equilibrium measurements. This subject was further investigated in this study. Figures l a and l b include the results for the dependence of infinite dilution activity coefficient on solvent amount using hT,Ndimethylaniline and N,N-dimethylacetamide. I t can be seen that there is an apparent effect of solvent amount, and that the results show that infinite dilution conditions are obtained a t approximately 0.3 g of solvent. This solvent amount is 1.05$&by weight of solvent carrier, which is much less than the amount required as suggested by Kwantes and Rijnder (1958) for solvent independency of partition coefficients. A minimum of 0.8 g for each solvent was used hereafter.
close to 0.25 cc). All solvents used in the experiment had greater than 99 mol % purity. The solvent was injected a t a rate of 1-2 ml/min into the injection port, which was kept a t a sufficiently high enough temperature above the boiling point of the solvent to permit complete vaporization. A period of 30 min was allowed between solvent injection and first gas sample injection to permit even distribution of solvent on the substrate, for it was found by Tassios (1972) that measurements of infinite dilution relative volatilities in this interval gave abnormally high values. A t least two measurements for each solvent were made. The solvent loss was evaluated by weighing the column before the first solute injection and after the end of the experiment. The solvent amount used in calculating yo was the average amount between solute injection and SO2 peak occurance. The obtained values for the losses agree rather closely with those calculated by employing the vapor pressure of the solvent. For example, for dimethylaniline the measured loss was 0.0009 g/min against a calculated value of 0.00096 g/min.
Results and Discussion
Solvent Requirement for lnflnite Dilution Conditions
The reproducibility of this technique is demonstrated in Table 11. Except for N,Ndimethylacetamide a t 93", the reproducibility of this technique can be considered very good. Table I11 presents the obtained yo values of SO2 in four different solvents along with the literature values. Also yo
In order that infinite dilution conditions prevail in the column, it is suggested by Kwantes and Rijnders (1958) that the amount of immobile solvent on the solid support must be a t least 15% by weight and by Porter, et al. (1956), that the
Table 111. Infinite Dilution Activity Coefficients for SO2
% deviation This study Solvent
T,
O C
YO
T,
O C
literature YO
of exmrimental fro; literature value
$8.0 40 0.025. N,N-Dimethylaniline 40 0.030 - 10 N,N-Dimethylformamide 40.5 0.081 38 0.084 -3.6 38 0.0390 $7.7 0.036 41.5 N,N-Dimethylacetamide 38 0.042 -14.3 66 0.070 66 0,062. $12.9 0.080 -12.4 66 93 0.077 93 0.091a -15.3 93 0.120 -35.8 Nitrobenzene 25.5 0.910 25 0.784 $16.1 a Values obtained by actual extrapolation of partial pressure data given in the literature. 41
276
0.027
Ind. Eng. Chem. Process Des. Develop., Vol. 12, NO.3, 1973
Ref
(Balej and Regner, 1956) (Batelle, 1969) (Batelle, 1969) (de Carli, 1926) (Batelle, 1969) (de Carli, 1926) (Batelle, 1969) (de Carli, 1926) (Batelle, 1969) (Batelle, 1969)
~~~~
Table
O'OD
t
~~~~~
IV. Infinite Dilution Activity Coefficients for SOz Solvent
r, o c
Yo
Dimethylformanide Trimethylpyridine Xylidine Benzonitrile 3-Methylsulfolane 3-Methoxysulfolane N,N-Bismethylamine Triethylenetetramine Xylidine-Dimethylaniline (1: 1)
40 39 40 39 40 39 42 41
0.081 0.123
40
0.040
0.140 0.532 0.609 1.090 1.590 1 580
LlOUlD PHASE-MOLES SOI PER MOLE N. N DIMETHYLANILINE
Figure 2. The system SOz-N,N-dimethylaniline, temperature 40°, total gas pressure 1 atm: 0,experimental data (Balei and Regner, 1956); X, Tassios-Wilson equation, Z = 1 ;-, Tassios-Wilson equation, Z = 0.94
values obtained by our extrapolation of the literature data are included. The agreement must be considered very satisfactory if the uncertainty in the literature values, obtained by extrapolation of low concentration activity coefficients, is taken into account. This uncertainty results from the extrapolation technique employed and the experimental error involved in establishing and measuring equilibrium compositions a t very low concentrations. The two different literature values for SO2in N,N-dimethylaniline demonstrate this point. New data for y o values of SO2 in several other solvents are presented in Table IV. Of all the new solvents tested, none compared with dimethylaniline in its capacity for SOz absorption a t 40". The method was also used in determining infinite dilution activity coefficients for SO2 in a mixture of organic solvents. The value of yofor SO2 was measured in an equimolar mixture of xylidine and N,N-dimethylaniline a t 40". The value of yo measured for the mixture is shown in Table IV as 0.040. This is a reasonable value since the yo values for SO2 in pure dimethylaniline and xylidine are 0.027 and 0.140, respectively. The yo values for SO2 in two different solvents, N,N-dimethylaniline and N,N-dimethylacetamide, were employed in evaluating the parameter glZin the Tassios form of the Wilson equation. The obtained value, along with the values for gli calculated from eq 10, are presented in Table V. Figures 2 and 3 present calculated and experimental partial pressures
I LlOUlD PHASE -MOLES
Sq
PER MOLE N , N DIMETHYLACETAMIDE
Figure 3. The system SO2-N,N-dimethylacetamide, temperature 40", total gas pressure 1 atm: 0,experimental data (de Carli, 1926); X I Tassios-Wilson equation, Z = 1 ; -, Tassios-Wilson equation, Z = 0.94
for SO2in the aforementioned solvents. Two sets of calculated values are shown to emphasize the difference resulting from the assumption of 2 = 1. The calculated values of 2 = 0.94 are in excellent agreement with the experimental results, especially a t the low concentrations of interest for design purposes. Even though this technique has been applied to SO*,it should be applicable to all gaseous solutes (YO,, HzS, etc.) and, of course, liquid solutes, too. Hence, it can be employed in screening solvents for the removal of any gas or mixture of gases. Conclusions
The proposed technique is simple, reliable, and by comparison to conventional measurements extremely rapid. The method, applied only to SO2in this study, should be applicable to all gaseous and, of course, liquid solutes. Combined with
Table V. Parameters in the Tassios-Wilson Equation System
SOz (1)-N,N-dimethylaniline (2) SO2 (1)-iV,N-dimethylacetamide (2)
r, o c 40 40
YI O
0.027 0.036
gll
-5271.22 -5271.22
g22
-10,978.92 -10,279.80
912
-9166.87 - 8617.02
Ind. Eng. C.hem. Process Des. Develop., Vol. 1 2 , No. 3, 1973
277
the Tassios form of the Wilson equation, it can provide equilibrium data a t finite gaseous concentrations for design purposes.
Aij
=
= constants for log Pioequation constants for one-parameter Tassios-Wilson equa-
tion
= distance on recorder chart between Nz peak and solute peak, in. AH = heat of vaporization ALr = energy of vaporization F = carrier gas flow rate measures with soap-film flowmeter a t column outlet, cc/min gii = energy of interaction between molecules of type i equal to energy of vaporization, cal/g mol = energy of interaction between an i-j pair of molegij cules, cal/lb mol Hi0 = infinite dilution partition coefficient M = molecular weight of solvent M , = moles of s t a t i k a r y liquid phase per unit volume Pi0 = vapor pressure of pure i, mm, absolute Pi, = column inlet pressure, mm, absolute Pout = column outlet pressure, mm, absolute P , = vapor pressure of water a t Tf, mm, absolute R = gasconstant T = temperature, O K Tr = temperature of soap-film flowmeter V,” = corrected retention volume; volume of mobile phase passed into the column, ml/g of liquid v i , uj = molar volume, ml/g mol W = weight of stationary solvent liquid, g 2: = mole fraction of solute in solvent phase z = recorder chart speed, in./min 2 = gas compressibility factor
D
activity coefficient at infinite dilution
=
Ti0
literature Cited
Nomenclature
A, B, C
GREEKLETTERS
Balej, J., Regner, A., Collect. Czech. Chem. Commun., 21, 1545 (1956).
Batelle Memorial Institute, “Applicability of Organic Liquids to Gases,” Report No. PB-183513 (1969). de Carli, I?., Atti, Accad. Lincei, 6 , 523 (1926); Chem. Abstr.,
21,1449 (1926). E. I. Du Pont de Nemours and Co., personal communications, 1971. Everet, D. H., Stoddart, C. T. H., Trans. Faraday Soc., 57, 746 (1961). Hankinson, R., Lagfitt, B., and Tassios, D. P., Can. J. Chem., 50, 511 (1972). Hougen, 0. A., Watson, K. M. “Chemical Process Principles, Part 2, Thermodynamics,” Whey, New York, N. Y., 1947, p 489. James, A. T., Martin, A. J. P., Biochem. J., 50, 679 (1952). Kwantes, A., Rijnders, G.. W. A., “GM Chromatography,” D. H. Desty, Ed., Academic Press, London, 1958. Martire. D.. Pollara. L.. J . Chem. Ena. Data. 10.40 , - (1965). - -, Perry, J. H., “Chemical Engineering Handbook,” 4th ed, McGraw-Hill, New York, N.Y., 1963, pp 3-188. Porter, P. D., Deal, C. H., Stross, F. H., J. Amer. Chem. Soc., 78,2999 (1956). Sheets, M. R., Marchello, J. M., Hydrocarbon Process., 42, 99 \
,
,.
(1Qfi9\ L Y “Y
Stull, D. R., Ind. Eng. Chem., 39,517 (1947). Tassios, D. P., Hydrocarbon Process., 49, 7, 114 (1970). Tassios, D. P., AIChE J., 17, 1367 (1971). Tassios, , n-0 \ D. P., Ind. Eng. Chem., Process Des. Develop., 11, 43 3
(LYIL).
Wilson, G. M., J. Amer. Chem. SOC.,86,127 (1964). RECEIVED for review June 26, 1972 ACCEPTED February 22, 1973
A Computer Design Method for Vertical Thermosyphon Reboilers N. V. 1. S. Sarma,’ P. J. Reddy, and P. S. Murti” Regional Research Laboratory, Hyderabad-9, India
Recent improvements in fluid flow correlations have been incorporated in the design procedure for the vertical thermosyphon reboilers. A general purpose computer program has been developed for the design.
V e r t i c a l thermosyphon reboilers play a wide role in chemical industry and require rational design procedures to develop truly optimal equipment. Several flow patterns manifest themselves during heat transfer to a flowing two-phase boiling mixture in a thermosyphon reboiler depending upon the flow rates, physical properties of the components, pipe diameter, and orientation. This complicates the design to be based on sound, theoretical considerations of heat and momentum transfer, and prohibits any great accuracy. A fair amount of empiricism still becomes unavoidable in spite of the tremendous amount of work on two-phase flow that has been reported in the last two decades. 1 Present address, Reactor Research Centre, Kalpakkam, Tamil Nadu, India.
278
Ind. Eng. Chem. Process Des. Develop., Vol. 12,
No. 3, 1973
The various types of flow patterns that are encountered during the upward flow of cocurrent vapor-liquid mixture through a vertical thermosyphon reboiler tube are (i) bubble, (ii) slug, (iii) annular, and (iv) mist. These flow regimes occur in the order of increasing vaporization but are not sharply demarcated. Slug flow prevents the steady-state operation of the reboiler by sending alternate layers of liquid and vapor forcing the system to unsteady state operation and, for this reason, it is desirable to minimize the slug flow region. In mist flow, which is the extreme regime of two-phase flow, heat transfer rates are very poor due to the continuous gas phase and therefore is to be again avoided. A thorough knowledge of the various types of flow regimes, conditions of their onset, and the regions of occurrence is essential for a sound design.
