79
Ind. Eng. Chem. Fundam. 1983, 22, 79-83
Use of Gas Chromatographic Headspace Analysis in Vapor-Liquid Equilibrium Data Collection Danlel A. Shawl and Thomas
F. Anderson”
Department of Chemical Engineering, University of Connecticut, Storrs, Connecticut 06268
Gas chromatographic headspace analysis is shown to be a rapid and reliable method for determining activity coefficients in binary and higher order systems. With this method the vapor phase in equilibrium with either a pure-component or mixture liquid phase is precisely sampled and analyzed by gas chromatography. Ratios of resolved peak areas yield activities directly. The method is especially suited to mixtures of relatively nonvolatile components.
Introduction Distillation provides the most important method for separating mixtures of volatile components in the chemical process industries. The key to its successful design and operation is a knowledge of vapor-liquid equilibria. Surprisingly, there are many systems of industrial importance for which literature data are either inaccurate or reported at very limited conditions of temperature and pressure, e.g., glycol-amine, alcohol-glycol, organophosphates, and high-molecular weight hydrocarbon systems. This lack of data is due, in part, to the tedious and exacting nature of vapor-liquid equilibrium measurements. Thus, methods proposed recently for obtaining mixture properties are designed to be both fast and reliable (Legret et al., 1980; Martin and Paulaitis, 1979; Turek et al., 1979; Wagner et al., 1980). At low to moderate pressures, the activity coefficient is the key variable in calculating vapor-liquid equilibria. Qualitatively, it is a measure of the nonideality of the liquid mixture. For a perfectly ideal liquid mixture, all the activity coefficients are equal to one at all compositions. For a nonideal system, the activity coefficients are either greater than or less than one. Although methods of estimating activity coefficients have been developed (e.g., Fredenslund et al., 1977), for critical design calculations, estimated values may not be sufficiently accurate. In this case, better estimates of activity coefficients are those determined experimentally and then correlated using one of several semiempirical equations, e.g., Wilson (Wilson, 1964), NRTL (Renon and Prausnitz, 1968), or UNIQUAC (Abrams and Prausnitz, 1975). This work is concerned with determining activity coefficients in liquid mixtures of nonelectrolytes. The procedure used here is known as gas chromatographicheadspace analysis and is based on a method originally reported by Wichterle and Hala (1963); more recently the method has been used by Hachenberg and Schmidt (1977). Using this method, activity coefficients are determined by accurately sampling the vapor phase which is at equilibrium with either a mixture or pure-component liquid phase. Although this method has not previously been widely adopted, it is now very attractive due to the availability of accurate gas chromatographic headspace sampling devices. Principle of Measurement The function of the headspace analyzer is to reproducibly sample the vapor phase that is in equilibrium with Lotepro, 1140 Avenue of the Americas, New York, NY 10038.
either a solid or liquid phase in a closed container. The sample from the headspace analyzer is routed directly to a gas chromatograph GC which separates on a packed column the sample components which are then measured by a suitable detector. The output of the detector yields a series of peaks, each of which corresponds to a different component. Since the area under each peak is proportional to the total moles of that component, we can write Ai = Kini
(1)
where Ai is the peak area for component i, ni is the moles of component i in the sample, and Ki is a constant of proportionality. The value of Ki is different for each component. However, it is a “true” constant for component i, if the GC detector is operated within a linear range and if column and detector operating conditions are maintained constant. For each species i, the number of moles in the vapor sample obtained by the headspace analyzer can also be related to its fugacity fiv, if a suitable equation of state is known. Using the virial equation of state truncated after the second virial coefficient, we find
where V is the sample volume, u is the specific volume, Vfn,, and Bij is the virial coefficient for the i-j pair. Equation 2 states that the fugacity of component i is proportioned to the moles of i in sample volume multiplied by a correction factor. At low pressures the fugacity is essentially the partial pressure and the correction factor becomes unity. Since we ensure that the liquid and vapor phases are in equilibrium, for each component i we can write (3) where f? is the fugacity of i in the liquid phase. Equation 3 must be satisfied for each component that distributes between the two phases. If the liquid phase is a pure component, eq 3 becomes (4) The superscript indicates a pure liquid and the prime is used to distinguish a vapor-phasefugacity corresponding to a component in equilibrium with a pure liquid phase. The vapor phase is not pure, but contains oxygen, nitrogen,
0196-4313/83/1022-0079$01.50/00 1983 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 22, No. 1, 1983
80
GAS CHROMATOGRAPH
.. ..
u CARRIEP GAS
,
5 G N A 3 CAE ~HROKPTCGRAP*
HELIUM,
hC' ZONE
Figure 1. Schematic of experimental apparatus.
and other light components which are only slightly soluble in the liquid phase. By definition the activity coefficient, yi, is given by (5)
F L O W RESTRICTOR Ah6 N E E D L E VALVE
Figure 2. Detailed schematic of Perkin Elmer Model HS-6headspace analyzer.
Table I. Wilson and Margules Parameters for Binarv Svstems Wilson parameters
where x i and ai are the mole fraction and activity, respectively, for component i. With eq 5 we can calculate the activity coefficient at a predetermined liquid composition if we can determine the ratio of fugacities. Using eq 1-4, this fugacity ratio can be related to the peak area obtained from headspace analysis. Making the appropriate substitutions, we find that the activity coefficient is given as
In eq 6, Ai is the peak area that results from sampling the vapor phase in equilibrium with a liquid mixture in which component i has a mole fraction xi. The other peak area, A:, corresponds to a vapor sample in equilibrium with pure liquid i. The summations in the exponential terms include all the gaseous components. Since the liquids we are concerned with are relatively nonvolatile, their mole fractions in the vapor phase are quite small. Most of the gas in the vapor phase is either oxygen or nitrogen which is trapped in the sample container when the liquid samples are prepared. As a result, the exponential terms in eq 6 not only tend to cancel each other but are also each nearly unity. Thus, to a very good approximation the ratio of exponential terms is unity and we obtain a simple and practical expression for the activity coefficients. X i 4
Equation 7 is the key equation which we use to determine activity coefficients from headspace analysis.
Experimental Apparatus and Procedure Figure 1shows the essential features of the experimental apparatus. Liquid samples of known composition are sealed in 6-mL glass vials; these are placed in the Perkin-Elmer Model HS-6 headspace analyzer. The headspace analyzer controls the temperature of the sample vials and automatically monitors the vapor-phase sampling process. Vapor samples are analyzed with a Perkin-Elmer Sigma 3, temperature-programmable, gas chromatograph; either a flame-ionization or thermal conductivity detector may be selected. Output from the detector is routed first to a Perkin-Elmer Model M-2 integrator and then to a Linear Model 252A 1-mV chart recorder. Helium is used as a carrier gas. The carrier gas pressure at the column entrance is set with a pressure regulator and the flow is
Ah,,,
Ah,,,
system
calimol
calimol
acetone (1)-ethanol ( 2 ) 4 0 ° C acetone (1)-water ( 2 ) 40 "C ethanol (1)-water ( 2 ) 40 "C ethanol (1)-n-heptane ( 2 ) 50 "C propanol (1)-n-heptane ( 2 ) 8 0 "C
-173.6 145.3 69.6 2232.6 2397.1
928.7 1585.1 948.7 359.2 851.6
Margules parameters acetone (1)-ethanol ( 2 ) 40 " C acetone (1)-water ( 2 ) 40 "C ethanol (1)-water ( 2 ) 40 "C ethanol (1)-n-heptane ( 2 ) 5 0 ° C propanol (1)-n-heptane ( 2 ) 80 " C
A*,
'421
0.82 1.82 1.21 2.24 2.31
0.57 2.04 1.22 2.37 2.54
checked with a bubble flowmeter. Retention times for each of the components in a binary mixture are first determined by on-column injections of liquid samples. Operating conditions which are established during the on-column injections are then used during vapor-phase sampling to ensure proper identification of peaks obtained during the vapor-phase analysis. Mixtures of varying composition are prepared by weight covering the complete composition range. Small amounts (2 mL) of each mixture and each pure component are placed in the 6-mL sample vials. The vials are sealed with Teflon-coated, silica-rubber septa and aluminum, crimped caps.1 They are inserted into a thermostated (Figure 2) and allowed to equilibrate for usually 0.5 h. For more viscous solutions more time must be allowed for equilibration. The analysis of the vapor phase is initiated by manually positioning the desired vial to the sampling position. A t this time, the sampling needle penetrates the septum and the carrier gas pressurizes the vial. After pressurization, injection is electronically initiated by closure of Valve SV-1 (Figure 2). The carrier-gas cutoff results in sample passing from the head space to the injector. Sampling is terminated and analysis is initiated when valve 1reopens. The time that valve SV-1 is closed is precisely controlled, and thus the injected gas volumes are precisely reproduced. The vapor sample is analyzed on the GC. Areas of all peaks detected in the vapor phase are calculated. Similar analyses of all the prepared samples provide the necessary data for calculating activity coefficients. Results and Discussion Several binary systems, which have been previously studied, and one ternary system were selected to test the proposed method of measuring activity coefficients. Each system was tested for thermodynamic consistency using the equal area test. In addition, data for each binary
Ind. Eng. Chem. Fundam., Vol. 22, No. 1, 1983 81
1
Ethonol ( I I-n-Heptane ( 2 ) at
50.C
I
I
36
'I
n-Propanol(l1- n'Heptane(2)at 80°C
32
-\ I
2 8 r .
o
-
Experlmental,Head.Space Anal
- Margules E q u a t i o n -- - Wilson E q u o t i o n
MOLE FRACTION ETHANOL, x ,
Figure 3. Comparison of calculated, experimental, and literature values of activity coefficients for the system ethanol (1)-n-heptane (2) at 50 OC. Ethanol I l l - n - H e p t a n e ( 2 I at 50°C Experimental Data Best Smaath Curve
M O L E FRACTION
n - PROPANOL , x I
Figure 5. Comparison of calculated and experimental activity coefficients for the system 1-propanol (1)-n-heptane (2) at 80 O C . n - Proponollll-n-Heptane (2) at 8 0 ° C Experimental, Head Space Analysis -Best Smooth Curve 0
-24
-3 2
t
I
,
1
I
I
0
02
04
06
08
10
1
MOLE FRACTION ETHANOL, x i
Figure 4. Area test for the system ethanol (1)-n-heptane (2) at 50 "C.
-20 Difference in areas = 2 8 %
- 3 4 0
system were fitted to the three-suffix Margules equation and the Wilson equation; the estimated parameters for both equations are given in Table I for all the binary systems studied. Figure 3 shows experimental activity coefficients for the ethanol-n-heptane systems at 50 "C. This system exhibits large positive deviations from Raoult's law as shown by the moderate values for the activity coefficients. The smooth curve shows the activity coefficients recommended by Van Ness et al. (1967))the the broken line gives activity coefficients calculated using the Wilson equation with parameters fitted to our data. Agreement is quite good. An area test, based on the Gibbs-Duhem equation, is shown in Figure 4 for the ethanol-n-heptane systems. The requirement for thermodynamic consistency is met if the area under the curve is zero; i.e., the area above the x axis is equal to the area below the x axis. Although it is difficult to know how close the areas should be, it is generally agreed that if the difference in areas divided by the sum of the areas is less than 0.02, the data are thermodynamically consistent. For this system, the data are well within this limit. Data for the 1-propanol-n-heptane system are shown in Figure 5. Also shown are the calculated activity
0
02
C4
06
08
I O
M O L E FRACTION n-proponol, x 1
Figure 6. Area test for thermodynamic consistency for the system 1-propanol (1)-n-heptane (2) at 80 "C.
coefficients using the Margules and Wilson equations. The Wilson equation obviously gives a superior fit to this data. Figure 6 shows the area test for this system. The area quotient was found to be 0.028; thus, a fair amount of confidence may be placed in the consistency of the data. Activity coefficients were also measured for each of the binaries in the ternary system ethanol-water-acetone. Figures 7,8, and 9 show the experimental and calculated activity coefficients. For the ethanol-water systems, the area test is also shown in Figure 10. These data are found to be consistent. For the systems including acetone (Figures 8 and 9), there is somewhat more scatter to the data. We suspect that this higher random error is due to the higher volatility of acetone, which results in a larger uncertainty in the liquid composition. Thus, this method is not recommended for highly volatile components. In fact, it is most
82
Ind. Eng. Chem. Fundam., Vol. 22, No. 1, 1983
Table 11. Comparison of Experimental and Predicted Activity Coefficients for the Acetone (1)-Water (2)-Ethanol ( 3 ) System at 40 " C . Predicted Values Are Those of the Wilson Equation with Parameters Estimated from Binary Data Alone ~-
Y2
71
-y 1
X2
0.189 0.117 0.51 3 0.023
exptl 2.01 2.08 1.40 5.92
x3
0.558 0.553 0.375 0.929
0,253 0.330 0.112 0.048
7 3
calcd
exptl
calcd
exptl
calcd
2.46 2.62 1.40 6.92
1.46 1.42 2.05 1.02
1.38 1.36 1.91 1.01
1.66 1.43 1.46 3.38
1.56 1.40 1.68 3.51
___-
, 6 ,I. i 6-
0
il
---
i
E t h a n o l i l : - W a t e r l Z i a l 40'C
2 0 1 I
--___
Experimental Dolo Smooth Curve
- Best
Excerimental. Head Soace Anolysis WilsonEquotion Margules E q u a t i o n
A
ib7 -
L Acetonelil Water'2lot 4 0 - C
i
1
2 0t
o
t
Eaperimental Heod Space Anal
MOLE FRACTiOk ACETONE, x ,
Figure 8. Comparison between calculated and experimental activity coefficients for the system acetone (1)-water (2) at 40 O C . 161
I
1
1 12
1(3
lo
I
1
Ethonol(l)-Acetone( 2 ) a f 4 O 0 C
---
/
E x p e r i m e n t a l , Heod Space A n a l y s i s Wllson Equotlon
Margules Equation
MOLE FRACTION ETHANOL, x l
Figure 9. Comparison between experimental and calculated activity Coefficients for the system ethanol (1)-acetone (2) at 40 O C .
useful for mixtures of components with relatively low volatilities. Activity coefficients can also be measured in multicomponent systems nearly as easily as in binary systems. To illustrate, activity coefficients were determined for the
-
02
i
L 04
2
06
08
I
IO
MOLE FRACTION ETHANOL, x i
Figure 10. Area test for the system ethanol (1)-water (2) a t 40 "C. ethanol-water-acetone systems. The experimental values are given in Table 11; also shown are activity coefficients calculated from the Wilson equation using parameters obtained from fitting our binary data. The generally good agreement between the predictions of the Wilson equation and the experimental values is encouraging. The errors are largest for acetone, but are of no greater magnitude than those encountered with either of the two binary acetone systems. Conclusions Experimental values of activity coefficients can be obtained simply and reliably by gas chromatographic headspace analysis. For a binary system, data spanning the complete composition range can be measured in one day. Since the determination of activity coefficients in ternary or higher order systems is no more difficult than in binary systems, this method offers a fast method for screening solvents for azeotropic or extractive distillates and for testing liquid-phase models. The method is especially useful for mixtures of relatively nonvolatile components. Acknowledgment The authors are grateful to the University of Connecticut Research Foundation for financial support and to the Computer Center, University of Connecticut, for the use of its facilities. This paper was presented at the AIChE Annual Meeting, Chicago, IL, November 1980. Nomenclature A, = chromatogram peak area a, = activity B , = second virial coefficient for i-j interaction f, = fugacity of component i f," = pure-component reference fugacity of component i K , = constant of proportionality
Ind. Eng. Chem. Fundam.
m = number of components N = number of data points P = total pressure R = gas constant T = absolute temperature V = total volume u = molar volume x i = liquid-phase mole fraction of component i yi = vapor-phase mole fraction of component i
83
1983,22, 83-86
V = vapor phase Literature Cited
Subscripts i , j = component
Abrams, D. S.; Prausnitz, J. M. AIChe J. 1075, 27, 116. Fredenslund, A; Gmehling, J.; Rasmussen, P. "Vapor-Liquid Equilibria Using UNIFAC"; Elsevier: Amsterdam, 1977; Chapter 1. Hachenberg, H.; Schmidt, A. P. "Gas Chromatographic Headspace Analysis"; Heyden: New York, 1977; p 10. Legret, D.; Richon, D.; Renon, H. Ind. Eng. Chem. Fundam. 1080, 19, 122. Martln, W. R.; Paulaitis, M. E. Ind. Eng. Chem. Fundam. 1979, 78, 423. Renon, H.; Prausnltz, J. M. AIChE J. 1968, 74, 135. Turek, E. A,; Arnold, D. W.; Greenhorn, R. A.; Chas, K. C. Ind. Eng. Chem. Fundam. 1970, 78, 426. Van Ness, H. C.; Soczek, C. A.; Kochar, N. K. J. Chem. Eng. Data 1967, 72, 346. Wagner, M.; Alexander, A,; Abraham, T. Paper presented at the 5th International Congress in Scandlnavia on Chemical Engineering, Copenhagen, Denmark, April 1980. Wlchterle, I.; Hala, E. Ind. Eng. Chem. Fundam. 1963, 2 , 1955. Wilson, G. M. J. Am. Chem. SOC. 1964, 86, 127.
Superscripts L = liquid phase
Receiued for reuiew December 21, 1981 Accepted July 20, 1982
Greek Letters yi = activity coefficient of component i
AXij = Wilson binary parameter
Correlations for Predicting Azeotropic Heat of Vaporization of Multicomponent Mixtures Abraham Tamlr Department of Chemical Engineering, Ben Gurion Universiv of the Negev, Beer Sheva, Israel
+
+
+
The new correlations, L(J/kg-mol) = 8.345 X 103T,(K)[(11.944 - 11.476Tr 11.459T:) 4-1.9778 15.456T, - 21.057T;)I for 0.5 I T, I 0.85,with a mean relative deviation from observed values of 3.5%, and L(J/kg-mol) = 8.345 x 10-V,(~) [(:0.52277(Tr - I) - 5.600(~,7- I)) w{9.1047(Tr - I) - IO.IOI(T,~ - I))] for 0.5 5 T , I1, with a mean relative deviation of 4.7%, are recommended for predicting the azeotropic latent heat of vaporization, L , of multicomponent mixtures. The correlations were derived solely on the basis of 81 binary azeotropic mixtures, but they predicted extremely well the azeotropic latent heat for 14 ternary mixtures.
+
Introduction Multicomponent azeotropic mixtures, where X i = Yi,i = 1,2, ..., c , may be considered in some respects as a single component. For example: (a) They possess one kind of latent heat, namely, the differential heat is identical with the integral heat, which is the heat required for a complete vaporization of a mixture. This is in contrast to nonazeotropic mixtures which exhibit both kinds of latent heats. (b) The Clausius-Clapeyron equation (C.C.) for multiazeotropes becomes identical with the C.C. equation for a single substance. This can be shown as follows. According to Malesinski (1965), the Clausius-Clapeyronequation for a multiazeotropic mixture reads
i=l
where c is the number of components in the mixture. Denoting the azeotropic latent heat of vaporization by
assuming a perfect gas mixture, and neglecting V / ,gives
Equation 3 is identical with the C.C. equation for a pure substance. The major conclusion drawn from the above behaviors is that it is possible to apply the same kind of equations originally developed for a pure substance so as to obtain the behavior of a multicomponent azeotropic mixture. In the present case, we make use of the Riedel vapor-pressure correlation (eq 4) and apply eq 3 to obtain the correlation for the azeotropic latent heat. The parameters of the correlation are determined from available data of the azeotropic latent heat of binary mixtures provided by Tamir (1980/81).
Correlations for the Latent Heat and Estimations of Mixture Properties Many correlations have been compiled by Reid et al. (1977) for the vapor pressure of pure substances. In the present study, the Riedel correlation has been arbitrarily chosen. Acceptance of the Pitzer idea that, in addition to the critical properties, the acentric factor can be used as an additional correlating parameter leads to the following correlation for the vapor pressure on the basis of the Riedel equation In PI = ( a l + pl/TI
+ y1 In TI + SlT,6) +
w(aZ
(3) 0196-4313/83/1022-0083$01.50/0
+ & / T , + yZ In T, + hTr6)
The application of eq 3 gives the following result 0 1983 American Chemical Society
(4)
