239
Ind. Eng. Chem. Fundam. 1981, 20, 239-246
Nomenclature C = model output matrix Cc= specialized model output matrix for tout c h = inlet reactant concentration disturbance (dimensionless deviation from steady-state value) cmt = outlet reactant concentration (dimensionless deviation from steady-state value) D = model input-to-output matrix D,, D,' = specialized model input-boutput matrix and scalar for Cout J = quadratic performance functional Kf = estimator gain matrix for feedback of measurements y Kp, K I = feedback controller gain matrices, proportional and integral action respectively P = discrete-time model state matrix Q = discrete-time model input matrix Qc= discrete-time model input vector for c h u = manipulated input vector, [inlet temperature,flow ratelT (dimensionlessdeviations from steady-state values) u' = controller output vector V = covariance matrix of white measurement noise W = covariance matrix of white process noise w ,w' = white noise components x = state vector y = measurement vector
p
= co-input vector for dual regulator corresponding to y
9 = co-state vector for dual regulator corresponding to x
Subscript k = discrete time index Superscripts T = transpose - = estimate = optimal value
*
Literature Cited Anderson, B. D. 0.;Moore, J. B. "Unear Optimal Control"; Prentkx-llall: Englewood Cliffs. NJ, 1971. Astrom, K. J. "Introductlon to Stochastic Control Theory"; Academic Press: New York. 1970. Doyle, J. C.; Stein, G. I€€€ Trans. Autom. Control 1979, AC-24, 607. Kwakarnaak, H.; Sivan, K. "Linear Optimal Control Systems"; Wiley: New York, 1972. Silva, J. M.; Wallman, P. H., Foss, A. S. Ind. Eng. Chem. F h m . 1979 18, 383. Thau, F. E.: Kestenbawn, A. Trans ASME. J . Dyn. Sys. Mae$. confrd1974 986(4), 454. Wallman, P. H., Sliva, J. M.. Foss, A. S., Ind. Eng. Chem. Fundam. 1979, 18, 392. Wallman, P. H. M.D. Thesis, University of California, Berkeley, CA, 1977. Wallman, P. H. I&. Eng. Chem. Fundam. 1979, 18, 327. Wolovich, W. A. "Linear Multivariable Systems"; Springer-Veriag: New York, 1974.
Greek Letters a = radius of circle in the complex plane (design parameter
Received for review July 7, 1980 Accepted April 13, 1981
for pole forcing)
Pure-Component Vapor Pressures Using UNIFAC Group Contribution Torben Jensen, Aage Fredenslund, and Peter Rasmussen Instltuttet for Kemiteknlk, Technical University of Denmark, DK 2800 Lyngby, Denmark
A group-contribution model, in part based on the UNIFAC method for vapor-liquid equilibria, is developed for predicting pure-component vapor pressures. The model is applied to different hydrocarbons, alcohols, ketones, organic acids, and chloroalkanes of molecular weights below 500. Good representation is obtained for vapor pressure data in the region 10-2000 mmtig. The model may be used to estlmate vapor pressures within the above category of compounds for which no experimental data are available.
Introduction "he W A C groupcontribution method was developed for the prediction of excess Gibbs energies of liquid mixtures and hence for the calculation of vapor-liquid equilibria (Fredenslund et al., 1975,1977; Skjold-Jerrgensen et al., 1979). It is a rather new development to use the group-contribution concept for mixtures. Previously, it was only used to predict pure-component properties, for example, heat capacities and critical temperatures and pressures. To date, however, only one group-contribution method for a priori prediction of pure-component vapor pressures has been fully developed (Macknick and Prausnitz, 1979). Equations of state may be used to calculate vapor pressures. However, accurate results can only be expected for relatively small, nonpolar molecules or when information about the vapor pressure directly enters into the model as in the Soave-Redlich-Kwong equation of state via the acentric factor. 0 196-43 1318 11 1020-0239$0 1.2510
Moshfeghian et al. (1979) indicate that their PFGC (Parameters From Group Contribution) equation of state may be used to predict the vapor pressures of heavy hydrocarbons and polar substances such as normal alcohols. Fredenslund and Rasmussen (1979) presented some ideas of how to use the UNIFAC method for the prediction of pure-component properties. However as of yet neither PFGC nor UNIFAC parameters are available for the actual use of these models in vapor pressure predictions. Macknick and Prausnitz (1979) calculate parameters for the AMP equation (Abrams et al., 1974) using group contribution. In developing the model, they emphasized the prediction of vapor pressures of heavy hydrocarbons, and relatively large discrepanciesfrom experimental values are encountered for lighter hydrocarbons. The correlation of Macknick and Prausnitz does not include polar substances. In this work a correlation is developed for the prediction of vapor pressures for polar and nonpolar compounds with 0 1981 American Chemical Society
240
Ind. Eng. Chem. Fundam., Vol. 20,No. 3, 1981 m
+ +
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4
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0
u
uB
Ind. Eng. Chem. Fundam., Vol. 20, No. 3, 1981
+
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Ind. Eng. Chem. Fundam., Vol. 20, No.
242
3, 1981
Table 11. Parameters for Ag'k (cal/mol)a . I _ _
____ group
CH, CH' g;z(cYc) CH(CYC)
C
3%)
ACCH, ACCH, ACCH AC CH=CH, CH,Cl CH,CO COOH OH
Ak,2
Ak,l
-0.203122 X 0.903611 X -0.383293 X -0.104980 X 0.268196 X -0.870419 X 0.918826 X -0.931797 X -0.562015 X -0.922395 X 0.116462 X 0.202922 X 0.563854 X -0.593885 X -0.237302 X 0.694406 X -0.166798 X
lo5
lo5 lo6 lo6 lo7 lo5
lo5
lo4 lo3 lo6 10'
lo7
lo5 lo6 lo7 lo' lo7
-0.849432 X -0.711573 X 0.119073 X 0.481727 X -0.110942 X 0.130180 X -0.210510 X -0.398271 X -0.680379 X 0.247224 X -0.338009 X -0.531721 X -0.149046 X 0.867711 X 0.512928 X -0.238682 X 0.141393 X
Ak,3
lo4 lo4
lo5 lo4 lo6 lo5 lo4 lo4 lo4
lo5 lo5 lo5 lo5 lo3 lo5
lo6
lo5
Ak,4
0.221895 X -0.788164 0.279668 X -0.125106 X -0.312966 X -0.184980 X -0.118919 X 0.181363 X 0.197934 X 0.394721 X -0.127495 X -0.102153 X -0.158269 X 0.502551 X 0.159570 X -0.371547 X 0.729408 x
10'
0.152689 X 0.111290 X -0.213533 X -0.109249 X 0.191274 X -0.274945 X 0.329737 X 0.573457 X 0.917902 X -0.444217 X 0.524373 X 0.843247 X 0.268735 X -0.220564 X -0.878324 X 0.388440 X -0.229812 X
10' 10' 10' 10' lo* 10' 10'
lo1 10' 10' 10' 10' 10' 10'
10'
lo4 lo4 lo4 lo4
lo5 lo4 lo3 lo3 lo3 lo4 lo4
lo4 lo4 lo3 lo4 lo5 lo4
Note: To ensure the highest possible accuracy, all six digits in the parameters should be used.
molecular weights below about 500. Parameters to be used with the correlation are presented. The correlation is reliable for prediction of vapor pressures not exceeding a few atmospheres. Theoretical Background Based on the solution of groups concept and the UNIFAC model, Fredenslund and Rasmussen (1979) derived the following equation k
k
RT In (cp,"P,")= x V k ( ' ) & k + RTCV,(')In r k ( ' ) (I.) k = 1, 2, ...,N(') In this equation, &k is the difference between the Gibbs energy g k and the reference energy gk0 of group k (2) &k = g k - gko Nc") is the number of different groups in molecule i, the number of groups of type k in component i, p," the fugacity coefficient of component i at temperature T and saturation pressure P,", and rk")is the residual UNIFAC group activity coefficient at a group composition corresponding to a "solution" consisting of pure component i. Equation 1may be used to predict the vapor pressure P," provided one knows the values of T , v,: Vk"), r k " ) , and &k*
The fugacity coefficients D(: may be calculated from second virial coefficients estimated by the Hayden and O'Connell(1975) method as described by Fredenslund et al. (1977). The residual group activity coefficients rp?may be calculated by means of the UNIFAC equations with group interaction parameters presented by SkjoldJerrgensen et al. (1979). It is not possible to estimate A g k values from independent sources. Before eq 1can be used to predict vapor pressures it is therefore necessary to establish a set of &k values from known vapor pressures. Model Development The group Gibbs energy functions &k depend strongly on temperature and, to some extent, on the detailed structure of the molecules. We therefore split the first term in eq 1 into the following expression k xvk(')&k
=
k xvk(')&k
+ AG"'
(3)
where &'k is a structure-independent contribution and AGr" is a structure-dependent term. Several different expressions were tried for Agk. The most satisfactory was &k = A k , i / T i- A k , 2 -t A k , a T A k , * In ( r ) (4)
where Ak,lare contants. The term AGr: takes into account effects arising from details of the molecular structure, for example, the existence of different groups in the molecule, the number of carbon atoms in the longest chain of the molecule, and the location of a branch. In some cases, for example, for nalkanes and 1-chloroalkanes, AG': is zero. When AGr$is not zero it may be a constant or a weak function of temperature. The term AG': is calculated as a sum of contributions &'kj of the different types j of structure dependent contributions in all groups k k
i
(5)
AG'Ii =
where Vkj(i) is the number of contributions of type j in groups of type k. The chosen expressions for &'hi are given in Table I, which also shows for different molecules how to calculate the first term of eq 1. The second term in eq 1 is calculated from the residual part of UNIFAC m
m
m,n = 1, 2, em(i)
=
Qmn
...,N(') n
(i)
= exp(-a,,/T)
Values of the constants Q, (reflecting the surface area of group m) and of the parameters a,,, (reflecting the energetic interactions between groups m and n) are obtained from Skojold-Jargensen et al. (1979) and Fredenslund et al. (1977). It may be noted that if m and n are members of the same main group, the parameter am,nis zero, e.g. ~ C H ~ C= H~ C~ H ~ , C=H ~ C H , C H= 0 (74 ~ A C C H ~ A C C= H ~~ A C C H ~ A C C H =
0
(7b)
In general when m and n are not members of the same main group am,n f an,, (8) The fugacity coefficient is calculated from the virial equation truncated after the second term. The expression becomes In v; = P;Bi(T)/RT (9)
Ind. Eng. Chem. Fundam., Vol. 20, No.
where the second virial coefficient Bi(T)may be predicted from the method of Hayden and O'Connell(l975). This method incorporates the chemical association model for the description of strongly associating components such as organic acids. A computer program for calculating Bi(!l') by Hayden and O'Connell's method is listed by Fredenslund et al. (1977). Estimation of Group Contributions The group contributions &k have been calculated from experimental vapor pressures, which have however not been used directly. Instead an Antoine equation representing the data has been used. This has allowed for the calculation of 20 vapor pressures for each component at evenly distributed points in the temperature range of the experimental data. A g c e and AgcH,. The group contributions &CHs and Agca were estimated from a series of n-alkanes from propane to &decane including a total of 320 data points. This alkane data base covers the temperature range 168 to 625 K, which is representative also for the data base for the other group contributions. For the CH3and CH2group contributions there are no structure-dependent terms,and the residual group activity coefficientsare unity. Equation 1 is therefore reduced to
RT In (P:*,s) = 2&CHs
+ YCH~(~)&CH~
(IO)
The parameters for the group contributions &k were estimated using a modified Levenberg-Marquardt method for the minimization of the function
F = CC[RTjIn (P,S(Tj).(p,B(Tj)) - 2&CH,(Tj) i l
l2
(11)
i = 1, 2, ..., all components j = 1,2, ..., all temperatures for component i
3&CH = 3&bH + 2&'bH,1
(13)
where is the structure-dependent term. The values of the & b H and Ag'bH,l parameters were estimated simultaneously by a minimization of an expression similar to eq 11. The explanations and expressions for the various structure dependent terms are given in Table I. Other Agk)s. The CHzeyegroup contribution was calculated from a series of cycloalkanes from cyclopentane to cyclooctane. It was necessary to build in a structure dependent term Ag'bHlssl to account for the influence on vapor pressures resulting from the differences in bound angles for these components.
+ ACH+,GT)/J'C
0
AN ? 0
I
n
0
rl
X (D
rl Q,
W N
z I
N
0
rl
X N b rl
W N
o!
0
I
-
m
0
0
r l r l
x
x
9
0
( D N ( D b
( 0 - 4
d t 0
0
m
-
I
o
o
(14)
n
0
r l r (
rl
x
X N
x
m r l
(12)
(ACHzcyo5
X b
w ( D
RT In (pi'.(ais)- 5&CHs - & C H ~ = 3&CH
=
rl
r l m
The fugacity coefficients (pi" were calculated by means of the Hayden and O'Connell(1975) method as described by Fredenslund et al. (1977). AgCH and Agc. By means of the &CH, and the &cH2 group contributions it is possible to calculate the group contributions for the CH group and the C group from experimental vapor pressures. The CH group contribution is calculated from a series of branched-chain alkanes, and it contains two structure dependent terms. One of these is used when the CH group is located just beside another CH group, and the other is used when the CH group is beside a C group. The estimation of a structure-dependent term can be illustrated by means of 2,3,54rimethylhexane for which eq 1can be written as
&'bH~cyf,l
0
1 *
-
YCHn(i)&CH2(Tj)
*I
t-
W
b
*cn
0
0
0
Q , v )
".* * I
(D
r
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x x x
at-m
WOCD NNb
mbm
maad 9'9p: 000
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l
l
n n n n n
>ooooo -lrlrlrlrlrl
< x x x x x
n u r o e m m
0 rl
X N 0 0 b Q,
".
0
ooaao
* I *
rlrlrlrlrl
x x x x x
m
o
t
n
3000000&0000 -lrlrlrlllrlrlrlrlr(rlrl
< x x x x x x x x x x x
3, I981 243
244
Ind. Eng. Chem. Fundam., Vol. 20, No. 3, 1981
Table IV. Deviations between Experimental Vapor Pressures from the Data Base and Values Calculated from the UNIFAC Correlation class of components group temp range, K pressure range, atm n-alkanes substituted alkanes substituted alkanes cy cloalkanes substituted cycloalkanes substit u ted cy cloalkanes 1-alkenes benzene aromatics substituted benzene substituted benzene substituted benzene alcohols 2 -ketones carboxylic acids 1-chloroal kanes a APsav % =
(l/N)[xNIPsexp- PsdI/Psex,]
C CHZ(cyc) CH( CYC) %-GAH, ACH AC ACCH, ACCH, ACCH OH CH,CO COOH CH,Cl X
168-625 188-462 231-463 2 35-4 6 a 250-634 260-422 160-577 280-377 360-668 280-502 300-487 311-477 270-680 24 1-59 3 290-650 288-600
0.02-2.23 0.01-1.98 0.02-2.57 0.02-2.83 0.02-1.98 0.02-2.17 0.02-2.66 0.07-1.97 0.01-2.07 0.02-2.03 0.02-2.66 0.02-2.07 0.00-3.11 0.01-2.60 0.00-2.88 0.01-2.53
Osav:% 1.69 3.24 5.98 3.48 7.06 4.30 2.37 0.01 5.17 3.94 3.64 2.56 8.73 7.52 3.51 4.26
100. (N is the number of data points.)
Table V. Deviations between Experimental Vapor Pressures N o t Included in the Data Base and Values Calculated from the UNIFAC Correlation component
temp range, K
pressure range, atm
Usav, %
4,4-dimethyl-l-pentene 2,6-dimethyl-4-heptanol 4-methyl-4-heptanol 2-methyl-2-heptanolc 3-methyl-3-heptanolc 2-methyl-1-pentanolc 4-methyl-2-pentanol tetralin phenol 1,3-dihydroxybenzene m-cresol b 1-ethyl-3-hydroxybenzene 1,2-dimethy1-5-hydroxybenzene
301-347 378-452 349-434 347-430 370-424 370-424 356-404 319-481 452-481 424-528 376-480 377-500 435-520
0.21-1.07 0.08-1.01 0.03-0.99 0.03-1.03 0.10-0.7 6 0.15-1.09 0.1 5-1.02 0.00-1.01 0.02-1.95 0.01-0.52 0.03-1.13 0.02-1.27 0.14-1.61
1.87 6.93 9.27 2.59 9.15 6.19 0.84 13.6 4.50 6.34 9.29 4.37 6.26
Usmax, % Ps*? atm 2.65 15.70 19.60 9.69 15.31 8.16 1.38 18.82 5.96 15.80 16.30 5.19 8.03
1.07 1.01 0.03 0.03 0.10 1.09 0.36 0.08 0.03 0.01 0.03 0.07 1.61
a Ps* is the pressure for which the maximum percent deviation is found. Experimental vapor pressures are taken from Reid et al. (1976). Experimental vapor pressures are taken from Dykyj and Repai (1979).
v”c is the number of carbon atoms in the ring. is a function of temperature. It is seen that Ag’bH Similar structure deDen%nt terms are used in the calculation of Ag‘b+j &d Ag‘k&.. The ACH ETOUD contribution was calculated from vaDor pressures of benzine. With the AgAcH group contribution established it was possible to calculate the ACCH3, ACCH,, and ACCH group contributions from the vapor pressures of a series of methyl- and alkyl-substituted benzenes. The AC group contribution was calculated from anthracene, phenanthrene, pyrene, and naphthalenes. Using the structure dependent terms presented in Table I it is possible to give a good representation of the vapor pressures for these compounds. A special structure-dependent group contribution to be used for the AC group in substituted benzenes was also calculated. This group contribution should only be used when none of the other groups is valid, as for example, for styrene. Group contributions from highly polar components such as the OH, COOH, CH,Cl, and CH&O groups have also been calculated. This is possible in the present model because of the inclusion of group activity coefficients in the second term of eq 1. The second term in eq 1 may contribute from nothing (compounds enclosing only one main group) to about the same amount as the first term, dependent on the pressure and the component. Polar substances will give the highest contributions. The values of the parameters for the calculation of Agk and Ag’kj are given in Tables I1 and 111, respectively.
Results The results from the data reduction are summarized in Table IV. In most cases, the agreement between calculated and experimental vapor pressures is acceptable for engineering purposes. The largest deviations are encountered for the alcohols, 2-ketones, and the substituted cyclohexanes. Table V gives some results for components which were not used for the estimation of the & i s . Noting that nearly all these components are polar, the deviations between experimental and predicted vapor pressures are quite small. Vapor pressures for tetralin were calculated using the ACH, CH,~c,,),and AC group contributions. The deviations between experimental and predicted vapor pressures may be due to the fact that there has not been calculated an AC-CH,( ), structure-dependent term. The vapor pressures ?or the phenols have been calculated using the ACH, AC, and the OH group contributions. The results are quite good considering that no phenols were included in the data base. Table VI shows a comparison between experimental vapor pressures and vapor pressures calculated by the UNIFAC and by the AMP correlation. For 3-ethylheptane, 3-ethyloctane, and 4-ethyloctane the vapor pressures are only calculated at the normal boiling point. The vapor pressures for the other components are calculated at 20 temperatures in the temperature range for which experimental vapor pressures are available. One of the reasons for the discrepancies between UNIFAC and AMP is that UNIFAC contains a structure-dependent
Ind. Eng. Chem. Fundam., Vol. 20, NO. 3, 1981 245
Table VI. Comparison between the UNIFAC and the AMP Correlation UNIFAC component 1-methyl-4-propylbenzenea9 1,2-dimethyl-4-ethylbenzenea* 3-ethylpentaneapb Bethylheptane a*d 3-ethylo~tane~>~ 4ethyloctane a, lethylnaphthalene a * c 2eth~lnaphthalene~9~ 3ethylhexane 2,3,3-trimethylpen tane 2,3,44rimethylpentane 2-methyL3ethylpentane 3-methyl-3-ethylpentane
Q'aw
%
3.52 3.57 12.95 6.40 1.63 8.58 4.92 5.64 2.32 2.81 0.84 6.03 4.75
AMP
M'max, %
Q'av, %
M'max, %
8.52 5.81 14.74 6.40 1.63 8.58 11.89 9.76 2.77 2.94 1.77 7.86 5.09
8.61 8.83 19.74 14.14 12.42 18.16 7.35 8.75 6.77 39.63 38.87 16.22 26.00
20.30 12.62 39.53 14.14 12.42 18.16 11.89 14.87 18.20 71.76 92.29 38.99 43.62
The experimental vapor pressures were not included in the UNIFAC data base. Rep& (1979). Stull et al. (1969).
Table VII. Comparison between the UNIFAC and the AMP Correlation for n-Alkanes AMP
UNIFACa component
AP'av,
O'max,
fl'av,
1.30 1.18 2.94 2.93 2.43 1.06 1.49 2.91 1.97 4.79 8.42
4.89 1.95 4.06 8.35 3.00 1.95 4.56 6.77 5.43 10.50 17.46
9.41 6.32 4.60 2.70 0.27 1.44 2.12 2.72 2.05 2.92 4.29
%
%
%
M'm,, %
26.51 17.95 12.09 3.42 0.36 3.71 5.80 7.21 5.38 7.97 11.59
a For the components C,,H, t o C,H,, the temperature k outside the range used for the estimation of the AgCH3 and &CH, group contributions. For the AMP calculations no extrapolation was needed. For C,H,, t o C,,H,
experimental vapor pressures are taken from Reid et al. (1976). For C,,H, t o C,H,, "experimental" vapor pressures are estimated from the correlation by Kudchadker and Zwolinski (1966).
term (AG,") whereas AMP does not. Table VI1 shows a calculation of vapor pressures for a series of n-alkanes. The UNIFAC correlation has been extrapolated far beyond the temperature range from which ~ ~ & C H ~ were calculated. the group contributions A g c and Comparison with the AMP equation for which no temperature extrapolation was necessary is also shown. The two correlations seem to be about equally reliable up to about C35H72. This indicates a limit for the UNIFAC extrapolation of about 150 K. An example in the Appendix shows in detail how the method is used. Conclusion The aim of this work was to establish a group-contribution method for the prediction of pure-component vapor pressures based on the UNIFAC model. The result is a correlation which yields acceptable predictions in the pressure range 10-2000 mmHg. The method may be used for both polar and nonpolar components. Only second virial coefficients, easily calculated from generalized correlations, and structural information are needed. The prediction of vapor pressures for a given component can be improved if one knows one experimental value, for example, the normal boiling point. The improvement can be carried out by estimation of a Ag'ij term from the difference between the known vapor pressure and that
Reid et al. (1976).
Dykyj and
predicted by the present method. Using this Ag'ij as a general structure-dependent term will improve the vapor pressure predictions. Supplement The list of components (and references) usef for the calculation of the various group contributions, together with a listing of a program for the calculation of vapor pressures, can be obtained from the authors. Appendix Example. Calculate the vapor pressure for 2,3,3,4tetramethylpentane a t 400 K. Solution. The number of different groups are
vCHa(i) = 6;
vCHW = 2;
=1
From eq 4, Table I, 11, and I11 we find A g h= ~ ~ 0.203122 X 106/400 + (-0.849432 X lo4) 0.221895 X 10' X 400 0.152689 X lo4 In (400) = 1.59235 X 103 cal/mol
+
+
Similarly, one finds AghH= -2.49122
X
lo3 cal/mol
Agh = -4.41276 X 103 cal/mol
It is now possible to calculate the first term in eq 3 k ~vk'"&'k
=6Agh~ + ~2M'CH
+ &h
=
1.58900 X 102 cal/mol The structure dependent contributions are U C H , ~ ( ~ ) & ' ' C H ~ = 2 x (-0.195243 x lo3) = -3.90486 X 10' cal/mol
vc,~(i)Agffc,l = 1 X (-0.116835
X
lo3) = -1.16835
X
lo2 cal/mol
k i
AGtti = c&i""hg''kj= -5.07321
X
102 cal/mol
2,3,3,4Tetramethylpntanecontains only groups from the same main group. The residual activity coefficients are therefore unity and eq 1 reduces to k
R T In (Pr(ci")= = 1.58900 X 10'
&k(i)&k
+ (-5.07321 X 10')
+ AG':
(1A)
=
-3.48421
X
10' cal/mol
If we assume the fugacity coefficient to be unity we find
246
Ind. Eng. Chem. Fundam. 1981, 20, 246-250
= activity coefficient of group k in pure component i = saturation fugacity coefficient of component i = UNIFAC parameter related to am,, = surface area fraction of group m in molecule i Indices and Superscripts i = component, molecule k, m, n = group 1 = parameter number j = structure contribution type number s = saturation rho
* emv
(pi”
The deviation between the calculated pressure 0.6451 atm and the experimental value of 0.6741 atm is 4.3 % . The actual fugacity coefficient can be calculated using the method of Hayden and O’Connell(l975). The information needed is temperature, pressure, and some pure component properties P, = 26.8 atm T, = 607.6 K 2, =0.260 Rd = 4,679 A DMU = 0.00 D ETA 0.00 Equation 1A can be solved by iteration, and a few iterations will lead to a fugacity coefficient (pi” = 0.9589 and a vapor pressure P4, = 0.6728 atm (0.2% deviation). Nomenclature am = UNIFAC group interaction parameter A k l = parameter in Gibbs energy function for group k Bi(T) = second virial coefficient of component i &k = Gibbs energy function for group k AG’; = sum of structure dependent contributions for component i = structure dependent contribution j for group k Vk = number of groups k in molecule i vkj(n = number of structure contributions of type j in groups k = Gibbs energy of one mole of groups k = perfect gas Gibbs energy of one mole of groups k Mi)= number of different groups in molecule i Pi”= vapor pressure of pure component i Q k = van der Wads surface area of group k R = gas constant T = absolute temperature Greek Letters
yipi
3
Acknowledgment The authors thank Mr. Klaus Heide for his collaboration in the initial stages of this project. In addition, the authors thank the Danish Statens Teknisk-Videnskabelige Forskningsrid for financial assistance. Literature Cited Abrams, 0.S.; Massaldi, H. A.; Prausnitr, J. M. Ind. Eng. Chem. Fundam. 1974, 13, 259. Dykyj, J.; Rep%, M. “Tlak nas@nej pary organickfkh zK&nln”; Vydavatelstvo Sbvenskej Akademle Vied 8ratidSva: Bratkiava, 1979. Fredenslund, Aa.; Jones, R. L.; Rausnltz, J. M. AIChEJ. 1975, 27, 1088. Fredenshmd, Aa.; Gmehllng, J.; l?a”, P. “Vapor-Liqukl EquiRbrle udng UNIFAC”; Elsevler: Amsterdam, 1977. Fredenslund, Aa.; Rasmussen, P. AIChEJ. 1979, 25, 203. Hayden, J. 0.; OConnel, J. P. Ind. Eng. Chem. Rmss Des. Dev. 1975, 14, 209. Kudchadker, P.; Zwollnskl, 6. J. J. Chem. €ng. Data 1960. 1 7 , 352. Macknick, A. 6.;Prausnih, J. M. Id.Eng. Chem. Fum.%” 1979, 78, 348. Moshfsghian, M.; Sharlet, A.; Erbar, J. H. 86th AICM Natlonal Meeting, Houston, 1979. Reid, R. C.; Prausnltz, J. M.; Shanvood, T. K. “The Propertles of Gases and Liqulds”; McGrawHHI: New York, 1976. SkjoW~rgensen. S.; Kolbe, B.; G m h h g , J.; Rasmussen, P. Ind. Eng. Chem. Roc& Dw. Dev. 1979, 18, 1979. Stull, D. R.; Westrum, E. F.; Sinke, 0. C. ”The Chemical Thermodynemics of Organic Compounds”; Wley: New York, 1969.
Received for review July 24, 1980 Accepted March 17, 1981
Ammonia Synthesis as a Catalytic Probe of Supported Ruthenium Catalysts: the Role of the Support and the Effect of Chlorine Woodrow K. Shlfletl and James A. Dumeslc’ Department of Chemical Engimdng, University of Wisconsin-Madbon,
Madison, Wlsconsin 53706
Ammonia synthesis has been used as a probe reaction to investigate how the properties of highly dispersed slllcaand alumina-supported ruthenium are affected by the nature of the support and the presence of chlorhe. The rate of ammonia synthesis was M b b d by ammonia more strongly on ahina-wpporW Ru than on sillcaappotW catalysts. This indicates that the Ru is electron deficient when supported on alumina, compared to Ru on silica. Chlorine was introduced onto the catalysts either as a ligand component of the precursor salt used for support impregnation, as a support constituent, or as a combination of these. No effect was seen for the silica-supported catalysts due to minimal chlorine retention after catalyst reduction. Chlorlne as an alumina support COnStbnt suppressed the synthesis rate, increasing both the apparent activation energy and the inhibiting influence of ammonia. on the rea& rate. These results, tn w t of prevlous ammonia synthesrs studies, were consistent wtth an additional decrease in electron density on the akKninasupportedruthenium induced by the presence of chloride on the support. Chlorine as a precursor component had a substantially different effect: the apparent activation energy decreased while the inhlbtting influence of ammonk was minimally affected. These findings show that the role of chlorine in supported Ru catalysts is twofold and dependent upon the manner in which It is introduced into the catalyst.
Previous studies dealing with ammonia synthesis over ruthenium catalysts (Aika et al., 1972; Aika and Ozaki, 1970; Ozaki et al., 1978, 1975; Urabe et al., 1978) have shown a variety of activities and kinetic behavior de0196-4313/81/1020-0246$01.25/0
pendent upon catalyst support materials and use of promoters. Our earlier work (Holzman et al., 1980) suggested that ammonia synthesis kinetic parameters are indeed sensitive to changes in support materials. Our current 0 1981 American Chemical Society
