Ind. Eng. Chem. Process Des. Dev. 1983, 22, 433-436
433
Extension of the UNIFAC Group-Contribution Method for the Prediction of Pure-Component Vapor Pressures Osnat Ben Yair and Aage Fredenslund' Instituttet for Kemifeknik, Technical Unlversm of D e m r k , DK 2800 Lyngby, Denmark
A group-contribution model, in part based on the UNIFAC method for vapor-liquid equilibria, has been developed for predicting pure-component vapor pressures. In this work, the method is extended to include amines, pyridines, nitriles, ethers, esters, and ketones. In addition, the accuracy of the method is tested by prediction of heats of vaporization via the Clauslus-Clapeyron equation. The predicted heats of vaporizatlon agree wlth the experimental values within a few percent.
Introduction Jensen et al. (1981) have introduced a correlation, based in part on the UNIFAC method for vapor-liquid equilibria, for the prediction of pure-component vapor pressures. The purpose of this contribution is to extend the correlation of Jensen et al. and further test its validity by applying it to the prediction of heats of vaporization. We state here very briefly the basic equations used in the correlation and summarize the results. For further details we refer the reader to the work of Jensen et al. (1981) and to the supplement (see paragraph a t the end of this article). The range of application of the correlation is the same as that stated by Jensen et al. (1981): pressures up to about 3 bar and molar masses up to 500. The temperature range is given in Table IV for the individual groups. Theory The equation used to calculate the vapor pressures of pure components is
RT In (I$tpf)=
k &k(i)&k
k
+ R T E v k c i ' In rk(i)
(1)
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 cvk(i)&k
=
k Evk'"&k
+ AG':
=Ak,i/T
Ak,2
+ Ak,sT+
Ak,4
m
m
h
rkC0
= Q k [ I - ln
Eemc')+,k
- E(em(i)+k~/~en(i)+mn)] (5)
m,n = 1, 2, ...,
$mn
= exp(-amn/lr)
Values of the constants Q, reflecting the surface area of group m)and of the parameters amn(reflecting the energetic interactions between groups m and n) are obtained from (Gmehling et al., 1982). The fugacity coefficient is calculated from the virial equation truncated after the second term. The expression becomes In I$; = P,"Bi(T)/RT
In T
(3)
The term AGrritakes 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, or the location of a branch. In some cases, for example, for nalkanes and 1-chloroalkanes, AG is zero. When AG '< is not zero it may be a constant or a weak function of temperature. The term AG': is calculated as a sum of contributions, &'i. Index j refers to the type of structure-dependent contribution and k refers to the group in question
':
(4) 0198-4305/83/1122-0433$01.50/0
(6)
The heat of vaporization for a pure component is given by the Clausius-Clapeyron equation
(2)
where Agk is a structure-independent contribution and AGt\ is structure-dependent. For the structure-independent term we use the following expression with 4 parameters,
&k
where vkj(i' k the number of contributions of type j in group of type k. The chosen expressions for &"kj 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 1is calculated from the residual part of UNIFAC
(7)
d In P,S/dT is found from eq 1.
Estimation of Group Contributions The groups considered in this work are given in Table I. The group contributions &k have been calculated from experimental vapor pressures, which have, however, not been used directly. Instead the Antoine equation representing the data has been used. This allowed for the calculation of 20 vapor pressures for each component a t evenly distributed points in the temperature range of the experimental data. Details regarding the groups taken into account in this work are described in Table I and in the supplement. Results of Data Reduction The parameters for the structure-independent part and for the structure-dependent part, A k j , are given in Tables I1 and 111. Examples of application of these parameters are shown for a number of components in Table I. Table @ 1983 American Chemical Society
434
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 3, 1983
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Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 3, 1983 455
Table 11. Parameters for Ag'k (cal/mol)"
a
group k Ak,i Ak,z Ak,3 CH,NH, 0.104766 x l o 7 -0.546368 x l o 5 -0.592314 X CH,NH 0.806988 x lo6 -0.416873 x l o s -0.754669 X CH,N -0.354410 x l o 7 0.123499 x lo6 0.355438 x CH,N -0.158143 X l o 7 0.446149 x l o 5 0.121605 X CH,NH -0.161010 x l o 7 0.355340 x l o 5 0.140934 x 0.107739 x lo* -0.325447 X lo6 -0.533593 X CSHJ -0.147266 X 10' 0.432234 X lo6 0.106877 x CsH4N CPSN -0.242963 X l o 6 -0.234952 x l o 5 0.116452 X CH'CN -0.977179 X lo6 -0.326107 x l o 4 0.458306 x CH,O -0.204191 x l o 7 0.713658 x l o 5 0.243411 x CH,O 0.533539 x lo7 -0.275639 X lo6 -0.102255 x CH,CO, 0.128660 x l o 7 -0.694162 x l o 5 -0.975105 X CH,CO, -0.330264 x l o 7 0.966894 x l o 5 0.281759 X CH,CO 0.120918 x l o 8 -0.385661 X l o 6 -0.766927 X To ensure highest possible accuracy, all six digits in the parameters should be used.
Ak,4
10'
10' 10, 10' 10, 10'
lo3
10' 10' 10,
lo3 10' 10' 10'
lo4 lo4 lo5 lo4 lo4 lo5 lo5 lo4 lo3 lo5 lo5 lo5 lo5 lo5
0.908672 x 0.685048 x -0.220609 x -0.779660 x -0.617380 x 0.526413 x -0.734930 x 0.328253 x 0.425371 x -0.128908 x 0.505727 X 0.116031 x -0.170763 x 0.639894 x
Table 111. Parameters for A G " (cal/mol) ~ ~
group k CH,NH, CH,NH CH,N CH,N CH,NH CSHJ CsH4N CH,CN CH,O CH,O CHiCO, CH'CO, CH,CO
Ak,s
-0.556528 -0.715620 -0.129186 -0.441480 -0.148039 0.367985 0.775002 -0.355668 -0.635386 0.138187 -0.578352 -0.379594 0.143959
Ak,6
X
x x X
x x x x x x x x x
lo3 lo3 lo4 10' lo4 lo3 lo3 10' lo3 lo4 lo3 lo3 lo4
Ak,8
Ak,7
-0.742498
X
lo3 10' lo3 lo7
0.117292 x -0.335568 X
lo3 lo3
-0.303065 X 10' 0.100284 x 10'
-0.503338 X 10' 0.926968 x l o 3
0.124560 x 10' -0.262270 x 10'
0.151224 x 10' 0.251008 x lo-' 0.194803 x 10'
-0.627769 -0.878395 0.360922
X X X
x 10' x lo3 X 10' X 10' x 10'
0.113201
0.217696 -0.130782 -0.957089 -0.477272 0.159364 -0.553397 0.155927 0.484397 -0.313380
Table IV. Deviations between Experimental Vapor Pressures from the Data Base and Values Calculated from the UNIFAC Correlation class of temp Apav, components group range, K %a primary amines CH,NH, 215-390 3.0 secondary amines CH,NH, CH,NH 218-676 2.9 CH,N, CH,N 215-671 3.0 tertiary amines CAN 348-460 2.1 disubstituted pyridines 300-460 3.2 monosubstituted CsH4N pyridines 1-nitriles CH,CN 270-555 3.0 aliphatic ethers CH,O, CH,O 225-460 2.4 aliphatic esters CH,CO,, CH,CO, 246-432 3.5 ketones CH,COb 292-451 3.1 a A P a v % = (1/N)[2~ i p e x p ~ - PSc&d I / p , , p + ~ ] X 100. (N is the number of data points.) The group CH,CO was included in Jensen et al. (1981). IV summarizes the results from the data reduction. In most cases, the agreement between calculated and experimental vapor pressures is acceptable for engineering purposes.
Heats of Vaporization It is not possible to test the parameters shown in Tables I1 and I11 with respect to prediction of vapor pressures of components not used in the data base. We have included all relevant vapor pressure data we could find in the data reduction. However, one may get some idea as to the validity of the method when it is applied to the prediction of heats of vaporization as shown in eq 7. No heat of vaporization data were used in the data reduction. Table V shows experimental heats of vaporization and predicted values using eq 7 with Pi" calculated by the UNIFAC method. The predictions are usually within 5% of the experimental values. This indicates that within the temperature range of this investigation, the UNIFAC
10' X 10' x 10" x 10' X
0.253440 x 10' X
10'
Table V. Experimental and Predicted Heats of VaDorization Icallmoll at the Normal Boiling Point %
component AHv(calcd ) A Hv(exptl) ethylamine 67 00 67 20 7670 butylamine 7570 diethylamine 6650 6970 11760 11690 n-butylaniline methylpyridine 8940 8950 7 300 7710 propionitrile 7935 8220 butyronitrile ethyl ether 6290 6380 dibutyl ether 8900 8820 methyl acetate 7200 7285 isobutyl acetate 8 605 8570 methyl butyrate 7845 8145 propyl proprionate 8850 8690 (AHv(exptl)- AHV(dcd)X 100/AHv(exptl).
devu -0.3 1.3 -4.6 -0.5 0.1 5.3 3.4 1.4 1.o
-1.2 -0.4 3.7 -1.8
method yields vapor pressures which are accurate enough for many design purposes. Equations 1and 7 may readily be extended to yield the vapor pressure and differential heat of vaporization of mixtures. Examples of such predictions are shown in the supplement.
Conclusions The UNIFAC method has been extended to yield reliable predictions of vapor pressures for amines, ethers, esters, and other components; see Table I. The correlation may be used a t pressures up to about 3 bar and for molar masses up to about 500. The temperature range in which the parameters were fitted is shown in Table IV. The correlation is shown to yield reliable predictions of heats of vaporization. Supplement A supplement containing detailed information regarding the data used for this investigation and the results is
Ind. Eng. Chem. Process Des. Dev. 1983, 22, 436-447
436
available upon request from the authors. Acknowledgment The authors are grateful to the Danish Consul for Scientific and Technical Research for financial support and to the Ben Gurion University of the Negev, Israel, for granting Osnat Ben Yair leave of absence for this investigation. In addition, we thank Torben Jensen and Peter Rasmussen of Instituttet for Kemiteknik for many helpful discussions. Nomenclature am,,= UNIFAC group interaction parameter Ah = parameter in Gibbs energy function for group k B,(T) = second virial coefficient of component i Agk = Gibbs energy function for group k AG ", = sum of structure-dependent contributions for component i M'k, = structure dependent contribution j for group k AHvi = heat of vaporization of component i N(') = number of different groups in molecule i P,"= vapor pressure of pure component i Qk = van der Waals surface area of group k R = gas constant
HYdW
T = absolute temperature Greek Letters rk(i)= activity coefficient of group k in pure component i 4; = saturation fugacity coefficient of component i $m = UNIFAC parameter related to a,,,,, omfi = surface area fraction of group m in molecule i vk(i) = number of groups k in molecule i vkj(i) = number of structure contributions of type j in groups
k Indices and Superscripts i = component molecule k , m, n, = group 1 = parameter number j = structure contribution type number s = saturation
Literature Cited Jensen, T.; Fredenslund, Aa.; Rasmwsen, P. I n d . Eng. Chem. Fundam. 1961, 20, 239. Gmehllng, J.; Rasmussen P.; Fredenslund, Aa. Ind. Eng. Chem. Process BS. B V . i982,21, i t a .
Received for review May 10,1982 Accepted January 3, 1983
atlon of Heavy Oils Dennis E. Walbh and NaEYuen Chen' Mob11 Research and Development Corporation, prlnceton, New Jersey 08540
Thermal hydrogasiflcatkm of heavy petraleum oils was lnvestlgated under conditions of short reaction tlme (0.5-15 s products residence tlme) and varied heating rates to elevated temperatures (50-850 OC/s to >550 "C). Total pressures and hybogen partial pressures up to 1500 psig were examined. Products consisted of a residual carbon fraction, light gases (primarily CH,), and BTX. Carbon residue was minimized by increasing hydrogen pressure up to 700 psig, final reaction temperature up to 700 O C , and the oil reaction time up to 8 s. The amount of carbon residue produced is a function of the C/H ratio of the charge. For San Ardo crude, the highest carbon conversion to light products was 82 wt % corresponding to 18 wt % carbon as residue, 67 wt % carbon as gas, and 15 wt % as BTX. Over a wMe range of conversion, gas and BTX were produced in fairly fixed proportions (-82% gas, 18% BTX).
-
-
Introduction It has long been recognized that raw coal can provide substantial yields of gaseous hydrocarbons under conditions of high temperature and hydrogen pressure (Dent, 1944). It has also been established that substantial liquid yields can be realized from the hydrogasification of coal under purely thermal conditions or in the presence of a catalyst (Schroeder, 1962). An extensive review of coal devolatilization and hydrogasification was presented by Anthony and Howard (1976). Pelofsky e t al. (1977) presented data on the influence of heating rate, product vapor residence time, and reaction temperature on the yield and quality of gas and liquid products obtained in the thermal hydrogasification of coal. Graff et al. (1976) and Dobner et al. (1976) reported data indicating thermal gasification conditions which yielded essentially methane, ethane, and BTX as the sole light hydrocarbon products, the balance of the coal carbon becoming char. Finn et al. (1980) studies the production of C8 and lighter aromatics from the hydropyrolysis of coal, noting that volatiles evolution and their cracking to BTX were se-
-
quential reactions. By optimizing separately both the cracking temperature and vapor residence time, they obtained yields of up to 12 wt % benzene from a high volatile bituminous coal. Fynes et al. (1980) reviewed work carried out at various laboratories on the production of BTX from the thermal hydroconversion of coal. Assessing the impact of the several process variables on product yields, they noted that the maximum production of BTX obtained from bituminous coal and lignite was about 15 w t %. Coproduction of BTX is quite desirable since it reduces hydrogen consumption, and the BTX products have value both for blending into the gasoline pool and as chemicals. Consequently, a substantial yield of BTX from a proposed hydrogasification process can enhance its economic attractiveness. Information obtained from the references cited above indicates that the most desirable operating conditions for maximum conversion of coal carbon to light produds with maximum production of BTX include: (1)rapid heating of the material to be hydrogasified (several hundred degrees centigrade per second); (2) final reaction tempera-
0796-430518311122-0436801.5010 0 1983 American Chemical Society
