I n d . Eng. Chem. Res. 1987, 26, 755-759
The ion exchange on the resin involves the interaction between the generated proton (eq 1)and the pyridinium ion on the resin (eq 2). The pyridinium ion is displaced HCI
Ht 4- CI-
(1)
from the ion exchange and then diffuses into the solution and reacts with C1- to form the pyridinium salt (eq 3). The pyridinium salt is not very soluble in xylene and precipitates out, leading to the observed turbidity. Even though the degree of dissociation of HC1 is small (eq l),the equilibrium is shifted by ion adsorption (eq 2), and the originally undissociated HCl molecules are subsequently also adsorbed. This mechanism is similar to the case in which a weak acid, such as acetic acid in water, is brought in contact with an OH-type anion exchanger. The formation of insoluble pyridinium salt (eq 3) assures the technical feasibility of complete exchange of pyridinium ion from the resin. This technique of direct regeneration of cationic resins with HC1 in nonaqueous media is general and should be applicable to other ion exchangers. To demonstrate the principle in the procedures described, solvents were used to dissolve and flush the pyridinium salt from the regenerated resin. It should be apparent that the insoluble pyridinium salt could be flushed out with the hydrocarbon itself in a form of a fine suspension without the use of an additional solvent. The pyridine in the spent eluate can be readily recovered as product by extraction with a solvent, such as water, leading to a simple and environmentally sound process.
755
Summary The nitrogen compounds in hydrocarbon oils can be removed effectively with cationic exchange resins. The treating capacity of the resin is much higher than the conventional clay. The resin loaded with nitrogen compounds can be directly regenerated with an anhydrous acid dissolved in the hydrocarbon oil without switching to an aqueous system. The overall mechanism is based on the fact that the acid dissociates to yield protons which exchange with and replace the pyridinium ions on the resin; these pyridinium ions then form insoluble pyridinium salt with C1. This mechanism is similar to the ion exchange of weak acid in water with an anion exchanger. The direct regeneration technique described here is simple and environmentally sound and lends itself to commercial applications. Acknowledgment We thank Dr. I. J. Heilweil for critical reading of the manuscript. Registry No. HCl, 7647-01-0; pyridine, 110-86-1; xylene, 1330-20-7.
Literature Cited Abrams, I. M.; Benezra, L. Encyclopedia of Polymer Science and Technology; Wiley: New York, 1967; Vol. 7, p 732. Gemant A. Ions in Hydrocarbons; Interscience: New York, 1962; p 45. Saunders, L. Ion Exchangers in Organic and Biochemistry; Calmon, C., Kressman, T. R. E., Eds.; Interscience: New York, 1957; p 545. Vermeulen, T.; Huffman, E. H. Ind. Eng. Chem. 1953,45,1658-1664. Yan, T. Y.; Shu, P. (to the Mobil Oil Corp.) US Patent 4458033, 1984. Received for review February 21, 1986 Accepted December 16, 1986
Characterization Parameters for Petroleum Fractions M o h a m m a d R. R i a z i and T h o m a s
E. D a u b e r t *
Department of Chemical Engineering, The Pennsylvania S t a t e University, University Park, Pennsylvania 16802
A generalized empirical correlation has been proposed to predict physical properties of pure hydrocarbons and undefined petroleum fractions. Properties such as critical temperature ( T J ,critical pressure ( p c )criticd , volume ( molecular weight (M), normal boiling point (Tb),specific gravity ( S ) ,refractive index ( n ) ,carbon-to-hydrogen weight ratio (CH),and heat of vaporization (AH,) may be predicted from any pair of available characterizing parameters (Tb, S),(Tb, I ) , ( T b , CH), ( M , S), ( M ,I), ( M , CH),(vl, S), (vl, I),or (vl, CH) as input parameters. Proposed correlations are generally superior or a t least equivalent t o the existing correlations and are applicable in the molecular weight range 70-300 and normal boiling point range 80-650 O F .
vc),
Background Riazi (1979), reported by Riazi and Daubert (1980), developed a simple two-parameter equation for prediction of physical properties of undefined hydrocarbon mixtures of the form 6 = aTbbS' (1) where 6 is the property to be predicted, Tb is the normal boiling point ( O R ) and S is the specific gravity a t 60/60 OF. Properties such as molecular weight, refractive index, critical properties, density, and heat of vaporization were successfully correlated to Tb and S through eq 1. This 0888-5885/87/2626-0755$01.50/0
equation was comparable to similar correlations such as those of Kesler and Lee (1976) and was included in API Technical Data Book-Petroleum Refining (1986) for predicting the molecular weights, refractive indexes, and pseudocritical temperatures and pressures of undefined mixtures. This form of correlation was later used by other investigators; for example, Gray (1981) used the form of eq 1 for the molecular weight of coal liquids. Most recently, Riazi and Faghvi (1985) used the form of eq 1 for prediction of thermal conductivity of liquid and vapor hydrocarbon systems. 0 1987 American Chemical Society
756 Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987 Table I. Comparison of Two Families of Cz0Hydrocarbons C,O
paraffin (n-eicosane) aromatic (n-tetradecylbenzene) difference, %
Th, OF 650.8 669.0
M
vl, const.
282.5 274.5
5.63 5.62
2.8
-2.8
-0.1
Table 11. Comparison of Adjacent Members of Paraffin Family n-paraffins Tb, "F M Cla 627.1 268.5 -- (n-nonadecane) C,, (n-eicosane) 650.8 282.5 difference, %
3.8
I
CH
0.265 0.285
5.7 7.1
9
7.5
24.6
vi, const.
S
I
CH
4.87 5.63
0.789 0.792
0.264 0.265
5.70 5.71
0.4
0.4
0.2
15.6
5.2
I t is important to note that the parameters used for vary strongly with carbon number but not with hydrocarbon group. Parameters selected for g2 significantly vary from one group to another. For example, consider properties of CZOin two different families in Table I. For a single family, an example of how the parameters vary from one compound to another is given in Table 11. From analyses similar to those in Tables I and 11, it is clear that parameters such as S , I , or CH characterize hydrocarbon type while Tb, M, or u1 characterize carbon number (or type of compound) in a single family. Similar comparisons may be made for different groups in one family, for example, between mono- and polyaromatics. On the basis of such analysis, the properties in Table I11 were correlated to different pairs of (g1, 92) through eq 2. AHwBis the molar heat of vaporization at normal boiling point. It should be noted that pairs of parameters from one of 9, or 9, do not characterize hydrocarbon properties accurately. For example, pairs such as (S,I)or (S,CH) cannot be used for the purpose of characterization. In addition, these types of two-parameter correlations are suitable only for nonpolar compounds. For polar compounds, a third parameter is usually necessary. For systems containing heteratomic compounds and attached functional groups such as N, NH, and OH, multiproperty correlations are needed to describe behavior of such systems (for example, see: Brule and Starling, 1984). The modification of eq 2 which keeps its simplicity while significantly improving its accuracy was determined to be in the form 9 = a exp[bgl + cB2 + d%182]%le%~ (3) where a-f are constants for each property. Data on the properties of 138 pure hydrocarbons in the carbon number range 1-20, including paraffins, olefins, naphthenes, and aromatics in the molecular weight range 70-300 and the boiling point range 80-650 O F , which are included in API Technical Data Book-Petroleum Refining (extant 19861, were used in obtaining the constants in eq 3. Those properties for which data such as M, I , S , Tb, and ul were available for petroleum fractions were also included in obtaining the constants in eq 3. Tables IV-XI1 present constants and average errors obtained by using the equa-
Table 111. Properties and Pairs of Correlating Parameters
Twu (1984) and Lin and Chao (1984) developed empirical correlations for prediction of critical properties (T,, P,, V,) and molecular weight (M) of hydrocarbon systems. These new correlations were developed by using perturbation theory and contain as many as 33 numerical constants for prediction of a property such as T,. Correlations developed by Lin and Chao are similar to those developed by Kesler et al. (1979). In the Lin-Chao correlations, in addition to Tband S , molecular weight (M) is also needed as an input parameter. Lin and Chao compared their correlations with the work of Riazi and Daubert (1980) and claimed more accurate results. In the correlations developed by Twu, properties such as T,, P,, and V , are interrelated; therefore, an error in predicting one property may be propagated into a much larger error in prediction of another property.
Technical Development In development of new correlations for prediction of physical properties of petroleum fractions, some important factors were considered. These factors were accuracy, simplicity, generality, availability of input parameters, extrapolatability, and finally comparability with similar correlations which have been developed in recent years. Equation 1 was derived from the general equation 9 = a81b%zc
S 0.79 0.86
(2)
where 9, and O2 can be any two parameters capable of characterizing molecular forces and molecular size of a compound. The following pairs of parameters were selected as input parameters given as the pair (81, g2): (Tb, S);(M, r); ( u l , CH) where Tb = normal boiling point (OR), M = molecular weight, ul = kinematic viscosity a t 100 OF (constant), S = specific gravity at 60/60 O F , I = (n2- l ) / ( n 2 2), n = refractive index at 20 "C, and CH = carbon-tohydrogen weight ratio. Any pair of (g1, 82) such as (Tb, S), (M, CH), ( u l , S ) ,etc., may be used as input parameters in eq 2.
+
Table IV. Constants in Eauation 3 for T," no.
0,
Tcl Tc2 Tc3 T,4 Tc5 Tc6 Tc7 Tc8 Tc9
Tb Tb Tb M
'M
M
O2
s I CH S I
M
CH
u1 VI
S I
v1
CH
a
10.6443 5.6259 X lo6 2.2452 554.4 2.4254 X lo6 37.332 251.026 4.414 X lo3 4.939 X lo2
= 70-300; Tb = 80-650
O F .
b -5.1747 X lo-' -7.317 X lo-' 1.9152 X -1.3478 X 2.001 x 10-4 1.3848 X -3.177 X lo-' -0.0291 -2.8 X lo-'
C
0.54444 -16.9097 -0.06487 -0.61641 -13.049 -0.1379 1.6587 -1.2664 -8.91 X
d 3.5995 x 10-4 2.5131 X -6.0192 X 0.0 0.0 -2.7 x 10-4 0.0 0.0 0.0
e
0.81067 0.6154 0.7699 0.2998 0.2383 0.3526 0.1958 0.1884 0.1928
f 0.53691 4.3469 0.900 1.0555 4.0642 1.4191 -0.9431 0.7492 0.7744
% av dev.b
0.5 0.6 0.7 0.7 0.8 1.0 1.1
1.0 0.9
3' % av dev. = [(Elpredicted value - experimental value(/experimentalvalue)/no. of data points]100.
Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987 757 Table V. Constants in Equation 3 for P." d no. 0' 8, a -4.725 X Tb 6.162 X lo6 Pcl -6.7041 X Tb I 2.2337 X Pc2
e
s
Pc3 Pc4 Pc5 Pc6 Pc7 P,8 P,9
CH S
Tb
M M M
I CH
s
U'
I
~1 ~1
CH
" M = 70-300;
158.96 4.5203 X lo4 2.9384 X 1017 815.99 1.271 X lo5 6.1475 X loz2 40.9115
= 80-650
Tb
-4.8014 -74.5612 -0.3454 -0.3084 -48.5809 -0.265 -5.6028 -71.905 0.1323
-2.1357 X -1.8078 X -0.01415 -2.139 X -0.2523 -0.4586 0.01906
Tb M M M
CH
S I CH S I CH
u1 u1 ~1
" M = 70-300;
0.2048 1.206 X lo-' 1.016 X lo4 0.2558 1.64424 X 3.219523 X lo-'' 0.245582
= 80-650
Tb
I
Tb Tb u1
CH
~1
S I
u1
CH
~1
~2
U1
s
U1
I
~1
CH
S2 S3 S4 S5 S6
Tb
I
Tb CH M I M CH ~1
I
u1
-1.3051 -6.5236 -3.8093
CH
X X X
lo-'
-2.33 X lo4 -1.01845 X -1.588 X 10" -1.48844 X -6.1406 X lo-' 0.02614
s
M u1 u1
CH S CH
4.239 X lo-' 0.26376 0.08716
" M = 70-300; Tb = 80-650
4.0846 18.43302 3.2223 1.6015 12.9148 2.4004 6.0793 20.7032 1.6306
2.7 2.6 3.5 2.7 2.3 3.1 3.8 3.8 3.9
e 0.7506 0.7687 0.1657 0.20378 0.2556 0.0706 1.19093 X 0.1417 0.046004
lo-'
f
% av dev.
-1.2028 -0.72011 -1.4439 -1.3036 -4.60413 -1.3362 -3.801261 -10.65067 -1.028488
1.8 1.8 2.4 1.9 2.1 2.6 1.6 1.7 2.1
d 1.11056 X 0.0 -2.87657 X 10 0.16247 0.0 0.0 -5.704 X
e 0.97476 2.0935 1.6736 0.56370 0.6675 0.5596 0.051
f
% av dev.
6.51274 -1.9985 -0.68681 6.89383 -10.6 0.65815 0.8411
2.1 2.3 2.2 3.4 3.5 3.6 2.2
C
2.984036 0.0 -4.5707 X -1.68759 14.9371 -7.7305 X
lo-'
d
e
f
% av dev.
-4.25288 X 0.0 9.22926 X lo4 -2.1247 X lo-' 6.029 X lo-' 0.0
6.77857 136.395 36.45625 4.28375 X lo3 9.1133 X lo-, 444.377
4.01673 X lo-' 0.4748 5.12976 X lo-' 2.62914 X lo-' 0.3228 0.2899
1.0 1.1 1.1 1.7 1.6 1.5
C
-23.5535 -8.1635 X lo-, -20.594 -7.925 X -26.3934 -0.10966
e
f
% av dev.
2.9806 X 10' 1.69916 X 10" 1.1284 X lo6 6.84403 X lo-, 3.8083 X lo7 0.18242
-0.3418 8.90041 X lo-' -7.71 X lo-' 2.89844 X lo-' -0.02353 0.05245
0.5 1.0 0.5 1.3 0.5 1.0
f
% av dev.
d 2.2152 X 3.60649 X 7.344 X 4.921118 X 0.2533 -5.654 X
OF.
Table X. Constants in Eauation 3 for Z " b 8, a no. 8, I1 T b 0.022657 3.9052 X lo4 12 T b CH 4.307 x -9.8747 x 0.422375 3.18857 X I3 M S I4 I5 I6
-0.4844 -1.0303 -0.1801 -0.8063 -0.8097 -0.6616 -0.5913 -0.6395 0.471
OF.
6.9195 7.3238 X lo-' 6.3028 9.19255 X lo-' 8.04224 1.17777
" M = 70-300; Tb = 80-650
d 1.095 X 4.425 X 1.4805 X 2.6012 X 4.5318 X 3.826 X lo4 2.12365 X lo-' 0.4608 0.016031
-9.53384 4.2376 7.9113 X lo-' -9.63897 38.106 -0.10741 -0.7311
X
Table IX. Constants in Equation 3 for S " no. 0, 8, a b
s1
% av dev.
OF.
1.34890 -3.8798 0.6056
" M = 70-300; Tb = 80-650
0.0 0.0451 0.0 0.355 1.8854 0.0
C
8.6574 X lo4 5.3305 X -1.95411 X lo-' -8.9854 X lo-' -5.976 X 0.1380
Table VIII. Constants in Equation 3 for Tha 8, a b no. el Tbl M S -1.58262 3.77409 X Tb2 M I 0.4283 0.0 Tb3 M CH 4.72372 X lo-' -1.57415 X lo4 Tb4 Tb5 Tb6
0.0
C
OF.
2.606 X lo4 3.06584 X lo-' 1.51723 X lo6 4.0 X lo4 84.1505 288.916
" M = 70-300; Tb = 80-650
c
-0.26404 -3.5349 0.05345 0.5287 14.1853 0.1082 3.513392 36.09011 0.086387
-9.2189 X -2.657 X -2.0208 X -2.3533 X -2.04563 X lo-' -1.63181 X lo-' -0.11261
Table VII. Constants in Equation 3 for M " no. 8, 0, a b MI Tb S 581.96 5.43076 M2 M3 M4 M5 M6 M7
3.1939 X 0.0190
b
OF.
Table VI. Constants in Equation 3 for V." b no. 81 62 a -1.4679 X 6.233 x v, 1 Tb s vi2 T b I -1.799 X 1.3077 x iow3 vc3
f
-5.6946 X 1.7458 X 6.1396 X
lo4
C
2.468316 -6.0737 x -0.200996 -6.836 X lo-' 2.31043 X lo-' -7.019 X lo-'
d -5.70425 t -4.414 X -4.24514 X lo-' 0.0 -1.8441 X lo-' -2.5935 X
e 5.7209 X lo-' 0.4470 -8.43271 X 0.1656 -1.1275 X lo-' 0.05166
-0.719895 0.9896 1.117818 0.8291 7.70779 X 0.84599
lo-'
0.5 0.5 0.5 0.9 0.6 0.4
OF.
tions. Note that relationships based on eq 2 and 3 are derived for one particular set of units. Improvements beyond the results of this study may be possible for properties such as density and heat of vaporization if the
equations were made dimensionless and end points were set a t their required limits a t the critical point. Data for undefined mixtures have been taken from the bank of data which have been collected over the past year
758 Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987 Table XI. Constants in Eauation 3 for CH a no. 8, 8, a d CH1 Th S 17.22022 8.24983 X 1.8866 X lo-'* 4.2873 X TL I CH2 CH3 M S 2.35475 9.3485 X CH4 A4 I 2.9004 X 7.8276 X CH5 CH6
u,
S
irL
I
" M = 70-300;
Tb
2.523 X lo-'' 2.143 X lo-''
= 80-650
0.482811 0.2832
0,
Os
ab
8.20613 AH1 T b s 8.7718 AH2 Tb I 8.19521 AH3 Tb CH 2252.1 AH4 M I AH5 M CH 344.44
-6.93931 -0.0116 -8.01719 -0.02445 -0.55768 -0.91085
X X
b
C
% av dev.
-2.72522 -1.3773 -0.68418 -0.37884 -0.146565 -0.17158
-6.79769 -13.6139 -0.7682 -12.34051 -20.31303 -10.88065
2.5 1.7 2.6 1.7 2.5 1.6
OF.
Table XII. Constants in Equation 2 for AHva no.
f
e 16.9402 71.6531 4.74695 60.3484 29.98797 53.7316
e
1.14086 1.13529 1.1355 0.5379 0.72511
f 9.77089 X 0.024139 0.01788 0.48021 0.15676
90 av dev., 1.6 1.6 2.7 2.6 2.7
" M = 70-300; T b = 80-650 OF. bConstants b, c, and d are all zero. % av dev. = [(Elpredictedvalue - experimental valuel/experimental value)/no. of data points1100. Table XIII. Comparison of Several Methods for Prediction of Critical Properties of Pure Hydrocarbons" T , % dev.b P, % dev. method av max av max eq 3 using Tb,S 0.5 2.2 2.7 13.2 Twu, 1984 0.6 2.4 3.9 16.5 Lin and Chao, 1984 1.0 4.2 3.8 33 4.0 12.4 Kesler and Lee, 1976 0.7 3.2 Cavett, 1964 3.0 5.9 5.5 31.2 4.5 22.8 Winn, 1957 1.0 3.8 138 data points were used. bDefined in Table IV.
a t The Pennsylvania State University, a description of which is available from us. Private, open literature, and government sources have been used to establish the data base. Fractions which were chosen for the development of these correlations basically have narrow boiling ranges with maximum Engler slopes of 1.5 OF. Therefore, the 50% ASTM D86 temperature was used for Tb. Equation 3 in terms of Tb and S can also be written or plotted using Watson K and API gravity rather than boiling point and specific gravity and can be located in API Technical Data Book-Petroleum Refining. All predictors presented are accurate with the data bases available at this time. As more data become available, rederivation of the regression constants should result in more accurate predictions. Evaluation and Comparison Equation 3 was evaluated and compared with other similar correlations for critical properties and molecular weight. Table XI11 shows a summary of evaluations for T , and P, as well as comparisons with other methods. Correlations used for T,and P, are in terms of Tband S. Results of evaluation of eq 3 using Tband s for prediction of molecular weights of petroleum fractions are given in Table XIV. Note that for petroleum fractions, the mean-average boiling point (MeABP) is used for Tb. For prediction of heats of vaporization at the normal boiling point, A H V N B , constants for eq 3 were given in Table XII. In order to determine how well the proposed correlation predicts heats of vaporization of undefined mixtures, experimental data for five different coal liquids were taken from Gray (1981) for the purpose of evaluation. Equation 3 (iwl)was used to predict molar heat of vaporization using mixture input parameters of Tb and s. The results are summarized in Table XV and show an
Table XIV. Comparison of Several Methods for Prediction of Molecular Weights of Petroleum Fractions method av a max eq 3 using Tb, S 2.2 18.7 Twu, 1984 5.0 16.1 Kesler and Lee, 1976 8.2 28.2 Winn, 1957 5.4 25.9 API data book, 1983 7.1 32.5 ~~
a Defined
in Table IV.
Table XV. Prediction of Heat of Vaporization of Undefined Coal Liquids exptlad pred.b fractiona Tb, O F S A H ~ B AHVNB % dev: 5HC 8HC llHC 16HC 17HC
320 476 643 726 787
0.8827 0.9718 1.0359 1.091 1.1204
133.0 121.0 115.9 105.5 102.9
134.1 126.2 110.6 107.6 102.8
0.8 4.3 -4.6 2.0 -0.1 2.36 av 0.48 bias
T,O F exptl AHJ pred. AHv % error Fraction: 5HC, T,= 708.6 O F , ' (MvNB)pred= 134.1 Btu/lb 200 300 400 500
146.7 134.5 127.4 102.6
148.5 136.7 122.9 105.9
1.2 1.6 -3.5 3.2 2.4 av 0.6 bias
Fraction: 8HC, T, = 886.8 O F , (mVm)pred = 126.2 Btu/lb 400 500 600 700
127.6 119.0 110.9 96.5
134.6 123.3 110.1 93.9
5.5 3.6 -0.7 -3.1 3.2 av 1.3 bias
"Experimental data from Gray (1981). *Calculated from eq 2 (AHl). 'Defined in Table IV. d A H =~heat ~ of ~ vaporization at normal boiling point, Btu/lb. 'Values of T, are calculated by using correlation TJ in Table I. 'Values of AHv are calculated by using AHw = A H ~ B [ ( T - ,7')/(Tc - Tb)Io.%where A H ~ is B calculated by correlation AH1 in Table XII. Experimental values of AHv are taken from Gray (1981).
average error of 2.4% and a bias error of 0.5%. If AHv at other temperatures is required, T , can be estimated by using eq 3 (with Table IV) and the Watson equation may be used to predict AHv. In the latter case, the average error for AHv a t other temperatures was 2.8%, while the bias error was 0.9%. It is expected that the proposed correlations will give even lower errors when they are applied to petroleum fractions. Conclusions The equations presented provide a relatively simple method for prediction of several physical properties using two readily available parameters. Various pairs of input parameters have been used in the development of the correlations, allowing different properties to be directly predicted using the minimum number of available parameters. In selection of input parameters (if such choice
Ind. Eng. Chem. Res. 1987,26, 759-762 exists), generally S is preferable to I as a parameter, while both S and I are superior parameters to the CH ratio. Tb is superior to M , while M is superior to v. Acknowledgment Financial aid from the Refining Department of the American Petroleum Institute is greatly appreciated. Nomenclature a-f = constants in eq 2 and 3 CH = carbon-to-hydrogenweight ratio d = liquid density at 20 "C, g/cm3 I = Huang characterization factor, (n2- l ) / ( n 2 + 2) M = molecular weight n = sodium D-line refractive index at 20 "C and 1 atm P, = critical pressure, psia S = specific gravity at 60160 "F Tb= normal boiling point, "R T , = critical temperature, "R V , = critical volume, ft3/lb Greek Symbols p = correction factor 0 = physical property 01,e, = input parameters in eq 2 and 3 v 1 = kinematic viscosity at 100 "F, constant v2 = kinematic viscosity at 210 "F, constant AHVNB= heat of vaporization at normal boiling point, Btu/(lb-mol)
759
Registry No. Eicosane, 112-95-8;tetradecylbenzene, 1459-10-5; nonadecane, 629-92-5.
Literature Cited American Petroleum Institute (API) Technical Data BookPetroleum Refining, 4th ed.; Daubert, T. E., Danner, R. P., Eds.; American Petroleum Institute: Washington, DC, extant 1986. Brule, M. R.; Starling, K. E. Ind. Eng. Chem. Process Des. Dev. 1984, 23, 833. Cavett, R. H. Presented at the 27th Midyear Meeting, API Division of Refining, San Francisco, CA, May 15, 1964. Gray, J. A. Report DOE/ET/10104-7,April 1981; Department of Energy, Washington, DC. Kesler, M. G.; Lee, B. I. Hydrocarbon Process. 1976, 55(3), 153. Kesler, M. G.; Lee, B. I.; Sandler, S. I. Ind. Eng. Chem. Fundam. 1979, 18, 49. Lin, H. M.; Chao, K. C. AIChE J . 1984, 30, 981. Riazi, M. R. Ph.D. Thesis, Department of Chemical Engineering, The Pennsylvania State University, University Park, 1979. Riazi, M. R.; Daubert, T. E. Hydrocarbon Process. 1980,59(3) 115. Riazi, M. R.; Faghvi, A. Ind Eng. Chem. Process Des. Deu. 1985,24, 398. Twu, C. H. Fluid Phase Equilib. 1984, 16, 137. Winn, F. W. Pet. Refiner 1957, 36(2), 157.
Received for review April 29, 1986 Accepted January 13, 1987
The Martin Equation Applied to High-pressure Systems with Polar Components Joseph Joffe* Department of Chemical Engineering and Chemistry, New Jersey Institute Newark, New Jersey 07102
of
Technology,
T h e Martin equation of state may be applied t o a polar substance provided t h a t the equation parameter a is made to fit the vapor pressure data a t the temperature of interest. Instead of Martin's procedure for adjusting parameters b and c by means of the value of the experimental critical compressibility factor, it is best t o use with a polar compound a liquid density datum point as close t o the temperature of interest as possible and t o obtain values of b and c by volume translation. This procedure is illustrated with the ethylene-chloroform system. Other high-pressure systems studied are the ethane-acetone system, the hydrogen sulfide-water system, and the carbon dioxide-methanol system. Some of the results are compared with those obtained by Guo and co-workers with the cubic chain-of-rotators equation. The Martin form of the Clausius equation of state (Martin, 1979) is the simplest of the three-constant cubic equations of state. In common with other three-constant equations, such as the Schmidt-Wenzel (1980) and the Patel-Teja (19821, it is capable of representing liquid densities of pure fluids and mixtures over a greater range of fluid types than is possible for two-constant equations, such as the Redlich-Kwong-Soave (Soave, 1972) or the Peng-Robinson (1976). The Martin equation may be written
P = R T / ( V - b ) - a / ( V + c)'
(1)
The equation may also be written in reduced form PR = TR/(z,VR - B ) - A/(z,VR + C)' (2) where B = bP,/RT,, C = cP,/RT,, A = aP,/R2TT,2,and 2, is the compressibility factor a t the critical point. The van der Waals conditions at the critical point yield the relations *Present address: 77 Parker Avenue, Maplewood, NJ 07040.
A = 27/64
B = 2,
- 1/4
B
+ C = 1/8
(3)
Martin proposed that the critical point of the Clausius equation be shifted so as to cause coincidence with the experimental critical isotherm at about twice the critical density. This is accomplised by setting B = 0.8572, - 0.1674 (4) where z, is the experimental critical compressibility factor. It follows from eq 3 that C = 0.2924 - 0.85'72, (5) As proposed by Martin, B and C are to be taken as constants for a given substance, while A is made into a temperature function. When the Martin equation is applied to vapor-liquid equilibria, A is best represented by a Soave-type temperature function (Joffe, 1981): A = (27/64)[1 + m ( l - TR1'2)]2 (6) In previous work, the Martin equation with a Soave-type temperature function was applied by me and co-workers to the study of vapor-liquid equilibria and fugacity coef-
0888-5885/87/2626-0159$01.50/0 0 1987 American Chemical Society
