138
Ind. Eng. Chem. Process Des. Dev. 1981, 20, 138-143
If necessary a second iteration can be done by recalculation of qo for the T value obtained from eq 4 or the graph in Figure 11. 1.4. The adiabatic induction time for the homogeneous self-heating is given by the relation
The solution can be written in the form
2. Heat Balance. Conservation of energy enables one to write down an overall equation for the heat balance. For strongly dilute products a simplified equation can be used (7)
Equation 5 expresses the fact that the heat of decomposition of the peroxide is consumed by the solvent to raise its temperature and to evaporate. Allowing total evaporation of the solvent eq 5 yields for TMPH-CD37.5, using the numerical values given in Appendix I, 326-kJ = 2kJ X AT + 0.625 X 315 kJ so that AT = 65 K is available for product temperature rise. 3. Fluid Ejection. 3.1. Liquid Flow. The flow of a liquid through an orifice is given by the equation
w=
= A
(8)
when friction is neglected. 3.2. Gas Flow. A maximum in gas flow through an opening is attained for a supersonic flow, given by the equation
Nomenclature T = temperature, K t = time, s p = pressure, Pa
Ap = pressure difference, Pa = density, kg/m3 Cp = specific heat at constant temperaure, J / k g Y = C,/G q = heat production, W/kg AH = heat of decomposition, J/kg X = heat conductivity, W/m K k = heat transfer coefficient, W/m2 K E = activation energy, J/mol C = heat production factor, J R = gas law constant, 8.3144 J/mol K M = molecular mass, kg/mol e = base of natural logarithms, 2.718... 6, = Frank-Kamenetzk parameter V = volume of tank, mP S = surface area of tank, m2 r = radius of tank, m A = surface of vent area, m2 W = mass flow, kg/s p
Subscripts c = critical referred to product conditions 0 = critical referred to ambient conditions
Literature Cited ADR “European Agreement concerning the intematbnal carriage of dangerous goods by road (AM)”, Appendix Bib; Unked Nations: Geneva, 1974. Barzykin, V.; Merzhanov, A. 0.;Dubovitsky, F. 1. “Thermal Explosion of Expioslves in the Liquid State”. Second Symposium on Problems Connected with the Stabilily of Explosive Substances, Sweden, 1970. p 180. Boyie, W. J. Chem. Eng. Frog. 1967, 63,61. Fauske, H. K. Chem. Eng. Frog. Symp. Ser. 1986, 61, 59. Frank-Kamenetzky, D. Acta Phys. Chim. (USSR) 1939, 70, 365. Gray, P.; Lee, P. R. “ ” a i Explosion Theory” In “Oxldation and Combustion Reviews“, Vol. 2, Tlpper, C. F. H.,ed.; Elsevier: Amsterdam, 1967. Grmthuizen, Th. M.; Pasman, H. J. Loss Rev. 1975, 9 , 91. Merzhanov, A. G.; Dubovttsky, F. I. Rws. Chem. Rev. 1088, 35(4), 278. NRC CommMee on Hazardous Matdais, “Ressure Reiievlng Systems for Marine Bulk Uquld Cargo”, AD744 681; Dlstr. NTIS U.S. Department of Commerce: Springfield, Va., 1971. Schb, G. Thesis, Technische UnkersMt Hannwer, Braunschweig, 1957. Schultz-Forberg, B. G&hrilche fadung 1977, 70, 31. Semenov, N. N. “Chemical Kinetlcs and Chain Reactions”, The Clarendon Press: Oxford, 1935; p 79. Stone, J. P.; Wililams, F. W.; Hezlett, R. N. J. Fke FkrmmaMfy1976, 7, 303. “Transport of Dangerous Qoods”, Recommendations prepared by the com mittee of experts on the transport of dangerous goods, Unlted Nations: New York, 1977, Chapters 11 and 12.
Received for review January 11, 1980 Accepted August 28, 1980
Estimation of Vapor Pressures of High-Boiling Fractions in Liquefied Fossil Fuels Containing Heteroatoms Nitrogen or Sulfur Douglas Edwards,’ Catherlne G. Van de Rostyne,’ Jack W l n n l ~ k and , ~ John M. Prausnltr’ ch8rniCal Engineering Depafiment, Universw of Callfornia, Berireky, California 94720
The SWAP (Smith-Winnick-Abrams-Prausnitz) correlation is extended to include the effect of bound nitrogen and sulfur. Also, evidence is presented showing that the correlation is applicable to narrow-boiling petroleum fractions. The extended correlation is for the region 1300-260 000 Pa. By use of a minimum of experimental information including approximate characterization and one vapor-pressure datum, vapor pressures can be calculated within
*lo%.
Heavy hydrocarbons and their derivatives are of increasing interest in fossil-fuel technology, including coal Union Carbide Co., S. Charleston, W. Va. TRW, Redondo Beach, Calif. Georgia Institute of Technology, Atlanta, Ga. 0196-4305/81/1120-0138$01.00/0
liquefaction and gasification. Following primary liquefaction or gasification, separation operations are required for purifying the product. Design of separation equipment requires quantitative data for physical properties: in particular, vapor pressures. However, little is known about the vapor pressures of heavy hydrocarbons and their de0 1980 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981
130
Table I. Parameters in Eq 3
D A B C
E
5.4224 X l o 5 4.6512 x lopz3 2.6646 X lo''
F 9.0692 x 2.0617 x 1.0278 x
-3.326 X 10' 1.3450 x 10' -1.8775 X 10'
rivatives, especially those that are aromatic. In 1976, Smith et al. (1976) correlated vapor-pressure data for heavy hydrocarbons in the region 1300-260000 Pa; the resulting SWAP correlation is reliable to f10% and can be extrapolated with good results to lower pressures (Macknick et al., 1978). The SWAP correlation is based on Prigogine's (1957) theory of polysegmented molecules. One of its main advantages is that in characterizing the hydrocarbon, critical properties are not used; fractions of aromaticity, naphthenicity, branching, and heteroatomicity are used rather than specific structural information which is required to estimate critical properties. This is important especially for mixtures of complex hydrocarbons where structure is difficult, if not impossible, to determine. Currently available methods for estimating critical properties, based on results for fluids of low and intermediate molecular weight, may not be reliable for high-molecular-weight materials. In this work we extend SWAP to include hydrocarbon derivatives containing either nitrogen or sulfur as heteroatoms and present evidence showing that the extended correlation is applicable to narrow-boiling petroleum fractions. SWAP Correlation For the region 1300-260000 Pa, Smith et al. (1976) proposed that vapor pressure P is related to absolute temperature T by 1nP= A +B / p + C / p (1) where reduced pressure P and reduced temperature p are given by P = P/P*; = T / P (2) Here PC and T* are parameters characterizing the fluid. Coefficients A , B, and C are functions only of molecular flexibility c/n, where n is the number of carbon atoms and 3c is the number of external degrees of freedom (density-dependent rotations and vibrations, in addition to translation) per molecule. These functions are of the form A , B or C = ( l / r ) In ((DXE)r+ (FXG)'J
(3)
where X = ( c / n - 0.167)-'. Parameters D, E, F, G, and r are shown in Table I. Equation 1 was originally applied to large normal paraffins, where experimental data are relatively plentiful. Vapor pressures of other hydrocarbons are correlated as perturbations about a closely related normal paraffin. We first determine the number of carbon atoms in the normal paraffin which would have a normal boiling point (T760) equal to that of the hydrocarbon in question. This is the effective carbon number (n,ff) of the hydrocarbon neff
=
[
3.03191 - [In (1078 - T760)]/2.303 0.04999
11.5
(4)
where T760is in kelvins. If the normal boiling point is not known, it can be estimated for normal paraffins as shown by Macknick et al. (1978) from another vapor-pressure datum, at a temperature below, possibly far below, the normal boiling point. For compounds other than paraffins, two methods are outlined in Appendix I1 to estimate normal boiling point.
loo loo
G
r
6.4197 x -2.1884 X l o - ' -7.5590 X lo-'
-0.53853 0.17427 -0.11956
Table 11. Parameter A ( c / n ) Obtained from Vapor-Pressure Data" for Nitrogen-Containing Compounds ~
compound 2,5-dimethylpyrrole pyrrole 2,4-dimethylquinoline quinaldine quinoline isoquinoline 2-methyl-5-ethylpyridine 3-methylpyridine 4-methylpyridine 2-methylpyridine pyridine diethylamine dimethy lamine methylamine a
~
range of data, Pa 9 300-226 600 9 300-266 600 1 2 000-106 600 1 4 700-101 300 1 4 700-101 300 14 700-101 300 2 700-101 300 9 300-266 9 300-266 20 000-266 20 000-266 40 000-120 670-101 530-101
600 600 600 600 000 300 300
~~~~
-103 x A(Ch)H
133 169 8.94 32.8 -36.3 -1.97 6.74 57.3 57.2 62.1 90.9 115 244 375
Taken from Boublik et al. (1973).
For the normal paraffin (n-par.) which has the same T760 as that of the compound of interest (c/n)n7pu.= 0.167
+ 1.022/neff- 0.189/nZefl
(5)
To correct for aromaticity, naphthenicity, and branching, Smith et al. write c / n = (C/n)n-par. + A(c/n) (6) where A ( c / ~ )= (0.1319F~+ 0.2429FN + 0.1992FB) exp(-2.532 X 10-3T,60) (7) where FA= fraction of carbon atoms which are part of an aromatic ring, FN= fraction of carbon atoms which are naphthenic (part of a saturated ring), F B = fraction of carbon atoms which are in a terminal branch F B = (lCHs - 2)/1 where is the number of CH3 groups and 1 is the total number of carbon atoms, per molecule (FB1 0). [For example, for toluene, lcH3 = 1and 1 = 7. However, we use FB= 0 for toluene.] For parameter PC, a similar procedure is followed (8) p" = PCn-par.+ bpr
P*,.,.
= 7.70
X
lo7 e ~ p ( - 4 . 7 2 2 2 / ( T-~ loo)] ~~ (9)
+
AP* = (0.72FA 0.27FN- 0.65FB)1.33X lo7 (10) where the units of P" are Pa. Parameter T* is evaluated from eq 1 by use of one vapor-pressure datum. Extension to Hydrocarbon Derivatives Containing Either Nitrogen or Sulfur To achieve the desired extension, experimental vaporpressure data were studied for 21 sulfur-containing and 14 nitrogen-containing fluids (Van de Rostyne, 1978; Edwards, 1980); these fluids are identified in Tables I1 and 111. The primary effect of introducing a heteroatom like S or N into a hydrocarbon is on the flexibility c/n. Therefore, for each fluid shown in Tables I1 and 111, vaporpressure data were fit to the SWAP method letting c/n be the adjustable parameter to obtain the best fit. By use of eq 6, values of Acln were found; these are also shown in Tables I1 and 111.
140
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981
Table 111. Parameter A ( c / n ) Obtained from Vapor-Pressure Data for Sulfur-Containing Compounds compound methanethiol 1-propanethi01 2-propanethiol 1-hexanethiol 1-heptanethiol 2-methyl-1butanethiol 2-methyl-2butanethiol 3-methyl-2butanethiol 2-methyl-2pentanethiol 2-methyl-2propanethiol thioanisole l-undecanethiol l-eicosanethiol thiophenol 2-methylbenzenethiol 3-methylbenzenethiol 4-methylbenzenethiol ethanethiol thiophene %-methylthiophene 3-methylthiophene
data -lo3 x sourcea A ( c / n ) ,
range of data, Pa
000 600 600 600 300 600
2 1 1 1 1 1
294 97.3 130 27.3 19.9 43.9
40000-266600
1
37.6
9 300-266 600
1
47.0
9 300-266 600
1
29.4
40 000-266 600
1
95.3
9 300-120 000 1300-200000
1 2
52.4 12.1
1300-200000
2
1300-200 000 1300-200 000
2 2
55.1 24.6
1 300-200 000
2
36.3
1 300-200 000
2
21.6
1300-200 000 1 300-200 000 1300-200 000
2 2 2
160 83.8 64.4
1300-200 000
2
63.7
1300-200 40 000-266 24 000-266 9 300-266 9 300-173 9 300-266
5.31
a 1 : Boublik et al. (1973); 2: Wilhoit and Zwolinski (1971).
Since T* is a function of the single vapor-pressure datum, for the fluids studied here, we chose the temperature corresponding to 39990 Pa for determining the best Acln. To find and subsequently correlate Ac/n, it was necessary to exercise care in the definitions of parameters T760, F A , FN,and FB. We preserve the original SWAP method by perturbing about an effective normal paraffin. However, to obtain good vapor-pressure predictions for heteroatom-containing hydrocarbons, it is necessary further to perturb the model about a structural homomorph of the heteroatom-containing hydrocarbon. This homomorph is obtained by replacing all heteroatoms with equivalent carbon atoms. For example, the homomorph for pyridine is benzene and that for thiophenol is toluene. Then T760, FA, FN,and F B are determined from the homomorph. Unfortunately, equivalent carbon atoms cannot always be substituted for the heteroatoms; e.g., for aromatic five-membered rings containing nitrogen and/or sulfur, it is impossible to obtain an aromatic five-membered ring containing only carbon atoms. Hence, for such rings, a true homomorph does not exist. In this case we still replace all heteroatoms with carbons even if they are not equivalent carbons. We then determine T760 as the normal boiling point of this approximate homomorph. F A is determined as if all substituted carbon atoms are equivalent, whether they are or not. For example, while the homomorph of thiophene contains one nonaromatic carbon atom, F A is set equal to 1.0. To obtain the best estimate of the effective carbon number, the approximate homomorph should resemble the true homomorph to as large an extent as possible. We encounter another obstacle here, however, if we consider, for instance, thiophene. Our preference, using the rules
described above, would be to replace the sulfur atom with carbon and use the normal boiling point of cyclopentadiene to represent T760.However, cyclopentadiene exists only as a dimer and we cannot easily obtain a value for T7w Instead, we use the next closest approximation to the true homomorph-cyclopentene. Fortunately, normal boiling point is not sensitive to degree of aromaticity. For example, TyWfor cyclopentane is 322 K and that for cyclopentene is 317 K; also, T760for toluene is 384 K whereas that for methylcyclohexaneis 374 K. Further, the SWAP method is not sensitive to small inaccuracies in T760, as shown by Macknick et al. (1978). To illustrate the use of the SWAP method for the case of five-membered rings, we present an example calculation for thiophene in Appendix I. Within the scatter of the data, the results shown in Tables I1 and I11 correlate with F H , the fraction of heteroatomaticity. For nitrogen-containing compounds FH
=
[
1
(no. of N atoms) (no. of N atoms) + (no. of c atoms) per molecule (11)
A similar definition is used for sulfur-containing compounds. For both types of compounds, A(c/n) becomes increasingly negative as FHrises; molecular flexibility for a nitrogen- or sulfur-containing hydrocarbon derivative is lower than that of a corresponding heteroatom-free hydrocarbon. Introduction of the heteroatom tends to stiffen the molecule. For nitrogen-containing compounds 0 5 F H < 0.073 A(C/n)H = 0; AC/nH = 0.9285FH
4-
0.6773;
FH 2
0.073 (12)
For sulfur-containing compounds A(C/n)H
0.7847FH3 - 1.635FH2- 0.02029FH (13)
Equations 12 and 13 are used in addition to eq 7 to determine the total Ac/n used in eq 6. Appendix I gives illustrative calculations showing how the extended SWAP correlation can be used to calculate vapor pressures of hydrocarbon derivatives containing either nitrogen or sulfur heteroatoms. Discussion When eq 12 and 13 are used, the vapor pressures of all compounds shown in Tables I1 and 111are reproduced with an average error of less than 10% over the experimentally available range. Maximum errors are also less than 10% except for pyrrole (12%) and dimethyl pyrrole (17%). For fluids whose molecules contain both sulfur and nitrogen, a reasonable approximation may be provided by adding the contributions from eq 12 and 13 to determine Ac/n. Experimental data for such fluids are extremely rare. However, deta are available for thiazole and methyl 2-thiazole (Boublik et al., 1973) in the range 1330-101 300 Pa. When SWAP is used for these fluids, the maximum error in the predicted vapor pressure is 4%. To gain some perspective on the accuracy of SWAP compared to that of other methods, we have calculated maximum and average errors for two representative compounds, one containing nitrogen (2,4-dimethylquinoline) and one containing sulfur (thiophenol) over the available range of data. In addition, we have calculated maximum and average errors for these compounds supposing that their true structures were not known, to simulate the usefulness of the three methods on mixtures where
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981
141
Table IV. Accuracies of Three Vapor-Pressure Correlations Used For Estimation For Compounds of Unknown Structure (Range 1330-200 000 Pa) deviation from experiment, % thiophenol
method SWAP Lee-Kesler Riedel-Plank-Miller SWAP wlo heteroatom correction
correct structure max av 6.9 6.1
7.2 16.0
2.1 4.8
1.1 4.5
structure is unlikely to be well defined. These are shown in Table IV. The nitrogen-containing compound was altered to be 3-methyl-1-naphthalenamineand the sulfur-containing compound was altered to be 1-ethylthiophene. These perturbations change primarily the position and character of the heteroatoms and leave fraction aromaticity nearly unchanged. Since Macknick et al. (1978) have previously shown that SWAP is a superior method in the face of uncertainties in aromaticity, we want here to show SWAP’S advantages in terms of uncertainties in the position of heteroatomicity. We assume that fraction heteroatomicity can be determined with good accuracy. For both compounds the accuracy of the SWAP method either equals or exceeds that of the Riedel-Plank-Miller method and that of the Lee-Kesler method (Reid et al., 1977). More important, when structure is perturbed, the accuracy of the SWAP method is affected less. Note that the percent error for the SWAP method hardly changes when molecular structure is misrepresented in contrast to that for the methods of Riedel-Plank-Miller or Lee-Kesler. We also include in Table IV the maximum and average percent errors calculated for 2,4-dimethylquinoline and thiophenol when the correction to cln for heteroatomicity is not included. In both cases, error increases. The small change in error for 2,4-dimethylquinoline is due to its relatively small fraction heteroatomicity, relative to that for thiophenol. This points out the relative insensitivity of SWAP to small errors in the fractions used and the necessity to make corrections €or heteroatom content. Each method requires input data to determine applicable constants. The SWAP method needs only approximate structure expressed through fractions of aromaticity, naphthenicity, branching, and heteroatomicity, and one vapor-pressure datum. On the other hand, the Lee-Kesler and Riedel-Plank-Miller methods both require critical temperature and critical pressure as well as one vaporpressure datum. Since critical properties are often not available, they were estimated using Lydersen’s group contribution method (Reid et al., 1977) which requires detailed structural information and molecular weight. Mixtures Perhaps the major utility of the SWAP correlation lies in its applicability to narrow-boiling mixtures of heavy hydrocarbons (cuts or fractions), where detailed molecular structure is not known. To illustrate, we compare calculations using SWAP for the petroleum-cut data of Myers and Fenske (1955), who studied four sets of narrow-boiling petroleum fractions, designated OLA tar,Sovaloid C, Wax I, and Wax 11. Both OLA tar and Sovaloid C were characterized as predominantly alkylated anthracenes and phenanthrenes, also possibly containing some four-ring, polynuclear aromatics. The degree of alkylation was small. The two waxes were stated to be typical high-boiling normal paraffins. Based on these structures, we set FA = 1 for the OLA tar and for Sovaloid C; we set FA = 0 for
2,4 -dimethylquinoline
incorrect structure max av
correct structure max av
incorrect structure max av
7.7
2.4
1.7
0.4
1.8
0.4
8.7 10.0
1.8
2.6
0.9
10.5
2.1
4.5
1.9
10.0
4.7 4.5
2.0
0.9
__
_-
__
--
Table V. Calculated Vapor Pressures Using SWAP, Lee-Kesler, and Riedel-Plank-Miller for Petroleum Fractions (Range 27.0-13 330 Pa) deviation from experiment, % SWAP OLA tar Sovaloid C Wax I Wax I1
LeeKesler
RiedelPlank-Miller
max
av
inax
av
max
av
18.7 22.9
8.0 7.8 6.6
18.4
10.1
10.0
23.7 24.9
10.8 8.2
15.4 20.8
3.3
58.6
21.2
19.5 6.8
30.0
9.1 8.6
64.0
23.1
the waxes. All other characterization factors (FB, F N , FH) were set to zero. T760 was estimated from an extrapolation of the experimental data. Table V shows maximum and average errors through the range of experimental data, generally 27 to 1330 Pa. Agreement is good, especially considering the rough quality of the characterizations of the compounds and considering that the maximum deviations occur at 27 Pa where we expect the largest experimental uncertainty. For comparison, we have also used the Lee-Kesler and Riedel-Plank-Miller methods to estimate the vapor pressures of the petroleum-cut data of Myers and Fenske. These methods require critical constants; Lydersen’s method (Reid et al., 1977) was used to estimate the critical properties. Lydersen’s method requires knowledge of exact molecular structure and molecular weight. Since molecular structure was not known, it was estimated as follows: OLA tar and Sovaloid C were assumed to be 1,6-diethyl-4methylanthracene (chosen because it is a “typical” alkylated anthracene); Wax I was assumed to be n-tricosane; Wax I1 was assumed to be n-octacosane (the structural equivalents of the waxes were chosen so that their normal boiling points were close to those of the waxes). Table V presents maximum and average calculated relative errors. In all cases the accuracy of the SWAP method either equals or exceeds that of the Riedel-Plank-Miller and Lee-Kesler methods. This is particularly true for Wax I1 where the maximum and average errors of the SWAP method are approximately one-tenth those of the other two methods. The advantage of SWAP results from its use of rough characterizations rather than exact structure to characterize the properties of a given compound or mixture. These characterizations (FA, FN, FH) are often easy to determine experimentally; they tend to give a sufficiently accurate representation of the character of unknown compounds. Extrapolation of a rough characterization to exact structure can lead to large errors in that structure, especially for mixtures. Translation of the estimated structure to critical properties using a group-contribution method magnifies those errors. Finally, use of the incorrect critical properties leads to larger errors in vapor pressure, especially far from the available vapor-pressure datum. SWAP
142
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981
avoids these problems by using the rough characterization directly. Unfortunately, no published data are presently available for narrow-boiling fractions of hydrocarbons containing nitrogen and/or sulfur heteroatoms. However, the evidence presented here suggests that the extended SWAP method, as discussed here, should provide good estimates for the vapor pressures of such fractions.
Acknowledgment For financial support, the authors are grateful to the Fossil Energy Program, Assistant Secretary Energy Technology, U.S. Department of Energy. We also thank R. C. Reid and P. R. Westmoreland for their helpful suggestions in preparing this manuscript. Appendix I Sample Calculations. To illustrate the extended SWAP correlation for predicting vapor pressures of sulfurand nitrogen-containing hydrocarbons, we present calculations for two representative pure liquids: thiophene and quinoline. Required data for the estimations are approximate mole fractions of n-paraffinic, branched paraffinic, naphthenic, aromatic, sulfur, and nitrogen atoms in the sample. Also needed are the normal boiling point of the structural homomorph and a single vapor-pressure datum. Nitrogen-ContainingHydrocarbon. Quinoline: FN = 0; FB = 0;FA = 1.0; FH = 0.1; T,P datum, 471.4 K, 39990 Pa; homomorph = naphthalene (T760 = 491.1 K). 1. nefffrom eq 4 neff= [(3.03191 - {ln (1078 491.1))/2.303)/0.04999]'.5= 12.12 2. c/n,-par.from eq 5
c/n,.p,.
= 0.167
+ 1.022/12.12 - 0.189/(12.12)2 = 0.2500
3. A(c/n) from eq 7 A(c/n) = [0.1319(1) + 0.2429(0) + 0.1992(0)] exp[-O.OO2532(491.1)]= 0.03804
4. A(c/n)H from eq 12 A ( c / ~ ) H= -0.9285(0.1) + 0.06773 = -0.0251 5. P*n-par. from eq 9
Pln.par. = 7.70
X
lo7 exp[-4.7222/(491.1 - loo)] = 7.613 X lo7 Pa
C = -2.861
10. T* can now be obtained by solving eq 1 using the vapor pressure datum 0 = 2.027 - In (39990/8.571 X lo7) - 6.149T*/471.4 2.861T*'/(471.4)' Only one solution is possible: r" = 498.3 K. 11. As a test, calculate the vapor pressure at 485.8 K In (P/8.571 X lo7) = 2.027 - 6.149/(485.8/498.3) 2.861/(485.8/498.3)2; P = 58460 Pa The reported vapor pressure at this temperature is 57390 Pa; the error is 1.9%. Sulfur-Containing Hydrocarbon. The method for sulfur-containing hydrocarbons is analogous to that used for nitrogen-containing hydrocarbons. Thiophene: FN = 0; FB = 0;FA = 1.0; FH = 0.2; T,P datum, 329.8 K, 39990 Pa; homomorph = cyclopentane (T760= 317 K). 1. nefffrom eq 4 neff = [(3.03191 - {In (1078 - 317.)l/2.303)/0.04999]1.5 = 5.252 2. (cln),.,,. from eq 5 (c/n)n.par,= 0.167 + 1.022/5.252 - 0.189/(5.252)2 = 0.3547 3. A(c/n) from eq 7 A(c/n) = [0.1319(1) 0.2429(0) + 0.1992(0)] exp [-0.002532(317)] = 0.0591
+
4. A ( c / ~ ) Hfrom eq 13 A(C/n)H = 0.7847(0.2)3- 1.635(0.2)' - 0.02029(0.2) = -0.0632 5 . P*n.par. from eq 9 P*n-par. = 7.70 X 10' exp[-4.7222/(317 -loo)] = 7.534 x io7 P a 6. hpc from eq 10
AP* = [0.72(1) + 0.27(0) - 0.65(0)]1.33 X lo7 = 9.576 X lo6 Pa 7. Summing the contributions to c/n and Pr c/n = 0.3547 + 0.0591 - 0.0632 = 0.3506
Pr
= 7.538 x
lo7 + 9.597 X
lo6 = 8.492 X lo7 Pa
8. From c/n = 0.3506 X = (0.3506 - 0.167)-' = 5.447
6. apC from eq 10 [0.72(1) + 0.27(0) - 0.65(0)]1.33 X lo7 = 9.599 x
lo6 P a
7. Summing the contributions to c l n and P* c / n = 0.25 + 0.03804 - 0.0251 = 0.2629
Pr = 7.612 X
B = -6.149;
lo7 + 9.597 X lo6 = 8.572 X lo7 Pa
8. From c/n = 0.2629
9. Evaluate A, B, and C from eq 3 using the appropriate constants from Table I A = [1/(-0.53853)] In {[(5.4224X lo5) X (5.447)-3.326x'074'.63853 [(9.0692 X 100)(5.447)6.4197X10~2 14.53863) = 2.207
+
and similarly
X = (0.2629 - 0.167)-' = 10.43
B = -6.434; C = -1.544
9. We now calculate A , B, and C from eq 3 using the appropriate constants from Table I and similarly
10. T* is obtained by solving eq 1using the single vapor pressure datum 0 = 2.207 In (39990/8.492 X lo7) - 6.434T*/329.8 1.544P' / (329.8)'
A = [1/(-0.53853)] In ([(5.4224 X lo5) X (10.43)-3.326xx'0 7 4 ' 1 + [(9.0692 ~ ~ X~ ~ ~ 100)(10.43)6.41~X10~2 -0.53853) = 2.027 1
Only one solution is possible: T* = 393.3 K.
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 1, 1981 143
11. Finally, as a test, calculate the vapor pressure at 337.8 K
In (P/8.492
X
lo7) = 2.207 - 6.434/(337.8/393.3) 1.544/(337.8/393.3)2; P = 53140 Pa
The reported vapor pressure at this temperature is 53320 Pa; the error is 0.3%. Appendix I1 Estimation of T760 for Determination of SWAP Parameters. In many cases T7@,the normal boiling point, neff,or Ac/n. will not be available for calculating P*n-par., Fortunately, since the SWAP method is relatively insensitive to the value of we can estimate it with little loss in accuracy. We suggest one of the following two methods. I. Molecular weight (M) and fraction aromaticity (FA) are known. T760 = (1- FA)PAR + FAAR (11-1)
PAR = 65.09Mo.417- 139.5M4.139 AR = 41.87Mo.564- 28.25Mo.370 If sulfur is present Mmeasd Mhomomorph - (1 - FH)+ F~(32/12)
(11-2) (11-3)
(11-4)
is in Kelvins. No correction is needed for nitrogen. 11. One vapor pressure datum (Td, Pd), fraction aromaticity (FA),and fraction heteroatomicity (FH)are known. T760 = (1- FA)(A + BTd CTd2) + FA(D ETd + FTd2)+ GFH HFH’ (11-5) T760
+
C = -1.92
X
+
+
X
Method 11. From eq 11-6 through 11-11 A = 28.4 - 5.22 In (666.5/133.3) = 20.00
B = 1.51 - 0.0709 In (666.5/133.3) = 1.40
+ 2.38 X
(11-6)
B = 1.51 - 0.0709 In (P/133.3)
(11-7)
+ 2.38 X In (P/133.3) D = -142 + 22.2 In (P/133.3)
(11-8)
In (666.5/133.3) = -1.54 x 10-4 D = -142 + 22.2 In (666.5/133.3) = -106
(11-9)
E = 2.39 - 0.210 In (666.5/133.3) = 2.05
+ 1.71 X
In (P/133.3)
(11-10)
(11-11)
G and H depend on whether the heteroatom is N or S. For nitrogen G = 52.1 In (P/133.3) - 558 (11-12)
+ 749
(11-13)
G = -2.10 In (P/133.3) - 386 H = 8.48 In (P/133.3) + 394
(11-14)
H = -99.7 In (P/133.3) For sulfur
(11-15)
in Kelvins and P is in Pa. Method I has been derived (Macknick, 1978) for pure hydrocarbons with no heteroatomicity and is preferred for these compounds because of its better accuracy. Method I also estimates quite well the homomorph T760of compounds containing the heteroatom S, provided the measured molecular weight is corrected for sulfur content using eq 11-4. Since nitrogen and carbon have almost the same molecular weights, there is no correction for nitrogencontaining compounds when using Method I. Often it is difficult or inconvenient to determine the molecular weight of an unknown compound. In this case, method 11is recommended. When the compound is a pure hydrocarbon and a vapor pressure datum above 1330 Pa is available, T760can be estimated within 10 K (Gonzalez, 1979). The homomorph normal boiling point for comT760 is
From eq 11-1 7’760 = (1- 0.74)(556.3) + (0.74)(677.4) = 645.9 K
A = 28.4 - 5.22 In (P/133.3)
E = 2.39 - 0.210 In (P/133.3) F = -1.15
pounds containing nitrogen or sulfur can be estimated within 40 K when the vapor-pressure datum is above 1330 Pa. The combined resulh of eq 11-11through 11-14were used to estimate the homomorph normal boiling point from the data of two compounds containing both nitrogen and sulfur (thiazole and methyl-2-thiazole). Simple addition of the two contributions yielded results of accuracy comparable to that obtained for compounds containing only one heteroatom. This suggests that Method I1 can be used to estimate the homomorph normal boiling point of compounds containing both nitrogen and sulfur. To illustrate the use of Methods I and I1 for estimating T7@,we present calculations for OLA tar. Since molecular weight is not known for this petroleum fraction, we assume that its molecular weight can be represented by that of 1,6-diethyl-4-methylanthracene(224.3). A convenient vapor pressure datum is 474.3 K at 666.4 Pa. Method I. From eq 11-2 PAR = 65.09(224.3)0’417 - 139.5(224.3)4.’39= 556.3 From eq 11-3 A R = 41.87(224.3)0.564 - 28.25(224.3)0.370 = 677.4 FA = 14/19 = 0.74
C = -1.92
X
+ 1.71 X
In (666.5/133.3) = -8.75 x 10-4 Since the cut exhibits no heteroatomicity, it is not necessary to calculate G or H . From eq 11-5 T760 = [1 - 0.741 x [20 + 1.40(474.3) - 1.54 X 10-4(474.3)2]+ [0.74] X [-lo6 + 2.05(474.3) - 8.75 X 10-4(474.3)2]= 664.2 K
F = -1.15
X
The extrapolated value of T760 used in the calculations for Table V was 652 K. Literature Cited Boubik, T.; Fried, V.; %la, E. “The Vapor Pressures of Pure Substances”, Eisevier Scientiflc Publlshing Co.: Amsterdam, 1973. Edwards, D. M.S. Thesis, Unhrersity of California, Berkeley, 1980. Gonzalez, C.. Chemical Engineering Department, University of California, Berkeley, personal communication, 1979. Macknick, A. B. Dissertation, University of Californla, Berkeley, 1978. Macknick, A. B.; Winnick, J.; Prausnitz, J. M. AIChE J . 1978, 24(4), 731. Myers, H. S.; Fenske. M. R. I d . Eng. Chem. 1955, 47(8), 1652. Prlgogine, I. “Molecular Theory of Solutions”, North-Holland: Amsterdam, 1957. ReM, R. C.; Prausnltz, J. M.; Sherwood, T. K. “The Properties of Gases and LiquMs”, 3rd ed.; McGraw-Hill: New York, 1977. Smlth, 0.;Winnick, J.; Abrams, D. S.; Prausnltz, J. M. Can. J . Chem. Eng. 1876, 54. 337. Van de Rostyne, C. G. M.S. Thesis, University of California, Berkeley, 1978. Wiiholt, R. C.; Zwolinski, B. J. “Handbook of Vapor Pressures and Heats of Vaporization of Hydrocarbons and Related Compounds”, (APIRP 44). Thermodynamics Research Center, Department of Chemistry, Texas ABM University, College Station, Texas, 1971.
Received for review January 17,1980 Accepted August 19,1980
