Ind. Eng. Chem. Process Des. Dev. 1985, 24, 498-500
498
Literature Cited
Yu, C. Y. MS Thesis, University of Abbama, Tuscaloosa, AL, 1983.
Abrams, D. S.;Prausnitz, J. M. AICh.6 J. 1975, 27, 118. De Fre, R. M.; Verhoeye. L. A. J. Appl. Chem. Blotechnol. 1978, 26, 469. Fredenslund. Aa.; Jones, R. L.; Prausnh, J. M. AIChE J. 1975, 27, 1086. Heidemann, R. A.: Mandhane, J. M. Chem. Eng. Sci. 1973, 28. 1213. Marquardt, D. W. J. Soc.Ind. Appl. Math. 1963, 7 1 . 431. Micheisen, M. L. fluid Phase Equilb. 1980, 4 , 1. Renon, H.: Prausnltz, J. M. AIChE J. 1968, 14, 135. Simonetty, J.: Yee, D.; Tassios, D. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 174. S0rensen. J. M. Ph.D. dissertation, Instituttet for Kemiteknik, Lyngby, Den. . mark, 1980. Ssrensen, J. M.; Magnussen, T.: Rasmussen, P.: Fredensiund. Aa. FlUM Phase Equilib. 1979, 3 47. Sarensen, J. M.; Ark, W. "Liquid-Liquid Equilibrium Data Collection": Chemical Data Series, voi. v., Parts 2 and 3, DECHEMA, Schon & Wekel GmbH: Frankfurt, W. Germany, 1980.
Department of Chemical and Metallurgical Engineering The University of Alabama University, Alabama 35486
Chang-Yu Yu
David W . Arnold*
Received for review December 17, 1982 Revised manuscript received May 21, 1984 Accepted June 4, 1984
Supplementary Material Available: Tables IV, V, VI, VII. NRTL and UNIQUAC parameters from adjustable and fixed penalty method (4pages). Ordering information is given on any current masthead page.
Estimating the Molecular Welght of Petroleum Fractions A set of simple equations is presented derived from an earlier chart method for estimating the molecular weights of petroleum fractions boiling at different temperatures from a blend such as gasoline. The only data needed for the computations are the ASTM distillation curve and the specific gravity of the blend.
Introduction In the course of an investigation on fuellair mixture formation in spark ignition engines, it became necessary to estimate the molecular weight of the fuel vapor as a function of the extent of evaporation of the liquid petroleum fuel. A need of this nature may also arise in other situations of engineering interest. The only available data for the liquid fuel, in most cases, would usually be comprised of the ASTM distillation curve and the specific gravity. With a knowledge of these two alone, it is then desirable to devise a method of estimating the molecular weights of the vapor at different percentages of evaporation of the fuel. A survey of the relevant published literature revealed that the most expedient way of doing this is by using the U.O.P. (Universal Oil Products) characterization factor proposed by Watson and Nelson (1933) and now commonly referred to as the Watson K factor. The molecular weight of petroleum fractions cannot be satisfactorily correlated with any single property. However, it can be correlated with two properties with an accuracy sufficient for most purposes. This is found to be the case with other properties too. Watson and co-workers (1935) developed a series of charts to evaluate various properties of petroleum fractions. Each property is related to two parameters such as,for example, the Watson K factor and the A.P.I. gravity. Watson et al. state that the molecular weight of petroleum fractions can be estimated with errors rarely exceeding 5% with the help of their chart. Winn (1957) later converted the data in these charts to the form of a nomograph in which the values of any two properties determine the values of the rest. The U.O.P. characterization factor or the Watson K factor is defined by the relation (Tb,R)1'3 K=-
S
(1)
where Tb,R = molal average boiling point, OR,and s = specific gravity at 60/60OF. The value of K and the molal average boiling point uniquely determine the average molecular weight of any petroleum fraction and can be determined from the Watson chart or the Winn nomograph. It is stated that the Watson K factor is a measure of "paraffinicity" and has approximately the same value 01 96-43051a51 1i24-0498$01 .solo
for all fractions of a given stock (Hougen and Watson, 1947). The assumption of a constant K over the boiling range necessarily implies that the method can be applied with confidence only to straight-run cuts. Watson et al. provide corrections to the volumetric average boiling point determined from the distillation curve to estimate the molal average boiling point. If the distillation curve is symmetrical, the volumetric average boiling point is close to the 50% evaporation temperature. Further, unless the slope of the distillation curve is steep, the value of K is not significantly altered if the volumetric average boiling point is used instead of the molal average boiling point. Present Work It was felt desirable to develop a mathematical relationship among the properties-characterization factor, average boiling point, and molecular weight-in order to facilitate machine computations. Mair and Willingham (1936) and Lucy (1938) proposed that molecular weights of heavy hydrocarbons of low volatility could be estimated from the relation
M = (T1/35)2'276 (2) where M = molecular weight TI= uncorrected distilling temperature at 1 mmHg, K. If the vapor pressure/temperature relationship of hydrocarbons can be approximated by the Clapeyron equation as is usually done, then T I can be related to the normal boiling point. It was therefore decided to investigate whether the correlation of Watson et al. presented in chart form could be approximated by the following expression M = (Tb/A)B (3) where M = molecular weight, T b = boiling point, K, and A and B are functions of K , the characterization factor. Equation 1 can also be written as In M = B In Tb - B In A (4) A large number of sets of values of M , Tb, and K were read off from the chart of Watson et al. (1935). A linear regression analysis between values of h M and In T b showed that they indeed vary linearly, the correlation coefficient in all cases being in excess of 0.99. The analysis also 0 1985 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985 499
showed that A and B in eq 3 can be related to the characterization factor K by
Table I. ASTM Distillation Curve for the Example Mixture ?& evaporated temp, OC 5 63 10" 75 20 100 30 115 40 125 50" 135 60 143.5 70 155 80 173.5 90" 196 95 210
+ 1.68~ B = 1.27 + 0 . 0 7 1 ~ A = 22.31
Example Experimental data on the variation of molecular weight with progressive evaporation of specific petroleum fuels are rare in the literature. One set of data is given by Bridgeman (1934) for a particular gasoline. Table I shows the distillation temperatures for this fuel. Table I was constructed from the three values given by Bridgeman for l o % , 50%, and 90% evaporated and computing the other temperatures such that the 1 6 1 equilibrium air distillation curve for the fuel agreed with that given by Bridgeman. Using eq 3,5, and 6 in conjunction with the data in Table I, the molecular weights of the fuel components evaporating at different temperatures were determined. Assuming that equal volumes of the liquid fuel give rise to equal moles of vapor, the molecular weight distribution curve was integrated to obtain the variation of average vapor molecular weight with percentage of evaporation by weight. Figure 1shows the result. As may be seen, the agreement between the computed values and the experimental data of Bridgeman is satisfactory, in spite of the approximation.
13"1
I
/E(
190;0/yp/B 3 100
0
BRIDGEMAN'S MEASURED VALUES
A
WEMCIED VALUES
80 70-
60
-
0
10
20
30
40
50
60
70
80
(6)
Equations 3 , 5 , and 6 provide a quick and simple means of estimating the molecular weight of vapor formed by liquid hydrocarbon fuels evaporating over a finite temperature range.
"Values given in Bridgeman's paper. Other values listed were computed to obtain agreement with the 16:l E.A.D. curve for the fuel given by Bridgeman.
Y 0
(5)
90
Id0
Other Correlations There exist other correlations which relate the physical properties of pure hydrocarbons and undefined hydro-
Figure 1. Comparison of predicted molecular weight to the data of Bridgeman.
Table 11. Molecular Weights of Selected P u r e Hydrocarbons: Actual Values and Estimates C, H vinylcyclopentane 7, 1 2 5-propylnonane 12, 26 4,9-dipropyldodecane 18, 38 7-butyldocosane 26, 54 1-phenylhentriacontane 37, 68 1-cyclohexylhexatriacontane 42, 84 4,8,13,17,22,26,31,35-octamethyloctatriacontane 46, 94 compound
1 2 3 4 5 6 7
bP, "C 100.3 197 293 400 502 533 540
formula spgr 0.7835 0.7559 0.7913 0.8042 0.8543 0.8402" 0.8287"
wt
96.17 170.34 254.5 366.72 512.95 589.13 647.2
prepd. mol w t eq 7 eq 8 94.53 94.87 108.81 170.53 163.16 166.26 259.6 234.22 242.15 400.93 336.97 372.65 536.00 432.00 543.1 612.91 478.88 623.66 642.2 494.9 647.70 eq 3
" Supercooled liquid below the normal freezing point.
-PRESENT AUTHORS: E O U A T I O N ( 3 l RIA21 8 DAUBERT: EQUATlON(71
-- -. AMERICAN PETROLEUM -----. WlNN
INSTITUTE: EQUATION 18)
NOMOGRAPH
SP. GR. 0.3
200-
r 0
200
400 600 BOO BOILING POINT F
1000
(a)
Figure 2. Variation of molecular weight with boiling point.
1200
0
200
400 800 800 BOILING POINT F
Ib l
1000
1200
500
Ind. Eng. Chem. Process Des. Dev. 1985,2 4 , 500-506
carbon mixtures to two independent properties. In particular, molecular weight is related to boiling point and specific gravity by the two equations cited below: (a) the equation proposed by Riazi and Daubert (1980)
M = a(Tb,R)b(s)C
M = (Tb/A)B (9) where M = molecular weight of the component boiling at temperature Tb (K) of the distillation curve 2.04 (TM)' 1 A = 22.31 +
(7)
S
with u = 4.5673 X b = 2.1962, and c = -1.0164, and (b) the equation recommended by the American Petroleum Institute (1983) M = 2.0438 X lo2 eXp(0.00218Tb,R) exp(-3.07S)(Tb,R)0'118(S)1'88... (8)
B = 1.27 +
0.086(TM)1'3 S
TM= molal average boiling point of the mixture, K, and s = specific gravity of the mixture. TM,the molal average boding point (K), can be estimated from Tv, the volumetric average boiling point (K), from the following relation TM = Tv - 5.85(S)'.33 (12)
Figure 2a compares the variation of molecular weight with boiling point for a value of specific gravity of 0.8 estimated according to eq 3, 7, and 8 with that obtained from the Winn nomograph. Figure 2b is a similar plot for a value of specific gravity of 0.9. It is seen that in both cases the results obtained with eq 3 conform most closely to the Winn nomograph. Finally, Table I1 presents a few examples comparing the molecular weights of some pure hydrocarbons with boiling points ranging from about 100 to 550 O C computed according to eq 3,7, and 8 with the formula weights of the compounds. The boiling point and the specific gravity of each of these compounds were taken from the work of Ferris (1955). It may be pointed out that both eq 7 and 8 use boiling temperature and specific gravity as the independent parameters to which molecular weight is related. Equation 3, on the other hand, uses boiling temperature and the Watson K factor as the independent parameters. Equation 3 is therefore more reliable for determining the variation of molecular weight with the extent of evaporation of an undefined mixture of hydrocarbons with the attendant unknown variation in specific gravity.
where S = average slope of the distillation curve, 10% to 90%; Co/liq. vol. %. Equation 12 is derived from a graph provided by Watson and Nelson (1933). 2. Equation 3 presented here appears to predict the molecular weight by hydrocarbons more accurately than eq 7 presented by Riazi and Daubert. It is likely that a correlation similar to eq 3 may serve as a better predictor for other properties too (with M representing the property under consideration) than the general equation proposed by those authors in the form of eq 7. Literature Cited American Petroleum Institute: Technical Data Book-Petroleum Refining, 4th Edition. 1983; pp 2-13. Brldgeman, 0. C. Research Paper RP694, National Bureau of Standards, US. Department of Commerce, 1934. Ferris, S. W. "Handbook of Hydrocarbons"; Academic Press Inc.: New Ywk, 1955. Hougen, 0. A,; Watson, K. M. "Industrial Chemical Calculatlons"; Wlley: New York, 1947. Lucy, F. A. Ind. Eng. Chem. 1938, 3 0 , 959. Malr, 6. J.; Willingham, C. 6. I d . Eng. Chem. 1936, 28, 1452. Rlazl, M. R.; Daubert, T. E. Hydrocarbon Process. 1980, 59, 115. Watson, K. M.; Nelson, E. F. Ind. Eng. Chem. 1933, 25, 880. Watson, K. M.; Nelson, E. F.; Murphy, G. B. Ind. Eng. Chem. 1935, 2 7 , 1460.
Conclusions
1. The method presented here provides a simple and quick procedure for estimating the molecular weight of any fraction of a multicomponent hydrocarbon blend, given the distillation curve and specific gravity of the original mixture. The relevant equations have been recast in the following form to facilitate their use.
Department of Mechanical Engineering V. Kuppu Rao Royal Military College of Canada Michael F. Bardon* Kingston, Ontario K7L 2W3 Received for review December 27, 1983 Accepted June 15, 1984
Alternative Distillation Conflguratlons for Separating Ternary Mixtures with Small Concentratlons of Intermediate in the Feed Single sidestream columns are shown to be inefficient for removing small amounts of the intermediate-boiling component In a ternary mixture. However, a sidestream column coupled with a sidestream stripper is shown to consume up to 30% less energy than the conventional two-column system.
sidestream column configuration. Tedder studied a range of feed compositions, using higher product purities (9&99%), and several configurations, including a sidestream column/stripper configuration. Both of these workers reported significantly lower energy consumption using nonconventional, complex configurations for some ranges of feed compositions. Elaahi and Luyben (1983) have explored four-component systems. A complex configuration, using two prefractionators and a two-sidestream third column, was shown to consume 25-35% less energy than the conven-
Introduction
Reduction of energy consumption in distillation has been actively studied in recent years as energy prices have increased sharply. Three-component systems have been explored by Doukas and Luyben (1978) and Tedder and Rudd (1978). Doukas studied systems where the feed had a small amount of either the lightest or the heaviest component. His study assumed low product purities (90-95%). He explored conventional two-column configurations as well as a simple sidestream column and a prefractionator/ 0196-4305/05/1124-0500$01.50/0
0
1985 American Chemical Society
