I
J. B. MAXWELL and L. S. BONNELL Esso Research and Engineering Co., Linden, N. J,
Derivation and Precision of a New Vapor Pressure Correlation for Petroleum Hydrocarbons reference basis which is useful in design work, for quality specifications, and as an important correlating variable for other physical properties. Normal boiling points are commonly used in typifying crude petroleum fractions and for reference in contractual negotiations. The type of vapor pressure chart required fully covers extremes of both pressure and boiling point. Published vapor pressure charts are generally inadequate in one or both of these respects. As a result, large and dubious extrapolations are often made far beyond the limits for which the charts are valid or acceptably reliable. Even more important, extrapolations of this sort have caused confusion because predicted normal boiling points reported by different workers have been too inconsistent. Wide use of a suitable correlation would help eliminate such confusion. One of the chief aims of the present work, therefore, was to develop a generally useful and practicable correlation.
An improved linear correlation for the vapor pressure of hydrocarbons and hydrocarbon mixtures \
b
Accounts for effect of chemical type
b
Provides charts and conversion tables covering wide extremes of temperature and pressure
b
Shows excellent agreement with recent data
CHEMISTS
and chemical engineers, especially in the petroleum industry, have had increasing need in the past few years for improved hydrocarbon vapor pressure correlations that can be extrapolated with confidence far beyond the actual data. The inadequacy of existing correlations has led to recent intensive effort to gather and correlate new data on high boiling hydrocarbons (7, 2, 6, 7, 72, 74, 76, 20, 27, 25). The present report describes a new, generalized vapor pressure correlation that appears to meet today’s exacting requirements fully. The petroleum industry’s need for more reliable and extensive vapor pressure correlations has stemmed mainly from increasing use of deep vacuum distillation in evaluating and processing crude oil. This has inspired intensive efforts to learn more about the properties of high-boiling petroleum fractions and some o f , their derivatives. Many laboratory studies have been undertaken involving distillation under high vacuum, often below 0.1 mm. of mercury. Low pressure is required, of course, to avoid thermal decomposition. I n order to interpret the boiling point data so obtained, a suitable vapor pressure correlation, or chart, is usually essential. By using such a chart, atmospheric or normal boiling points are customarily predicted from observed boiling points. This provides a common
Survey of Existing Correlations
Generally speaking, the main objective in correlating vapor pressure data has been to establish some type of a linear relation that could be extrapolated well beyond the limited range of the experimental data. The methods commonly used may be divided into two broad categories :
,
Those in which some function of either the temperature or the vapor pressure of one compound is plotted against the corresponding function of a reference compound to obtain a relationship that is linear over a wide pressure range. Those which express the vapor pressure of individual compounds as some function of temperature with characteristic parameters for each individual compound. . The following review points out the advantages of certain published correlation methods in these categories. I n the first of these categories, Duhring’s rule is one of the earliest and more widely used methods. Duhring proposed a linear relationship between the boiling points, each at the same vapor pressure, for any two similar compounds. Actually, Diihring’s rule is linear over only a very limited pressure range. By using recipnocal boiling point
(absolute), Cox ( 7 7 ) established a linear relationship far superior to Duhring’s. He found that the data on normal paraffins could be represented by a family of lines intersecting at a common point. His idea of a single intersection point is highly valuable for developing a generalized correlation. The Othmer (23) type of correlation also falls in the first category. For any two compounds, Othmer established a linear relationship between the logarithm of pressure plotted a t the same boiling point. Another well known correlation is Brown and Coates’ (G), in which the scope of Duhring’s rule was extended by adding a squared temperature term. Although Cox proposed the use of reciprocal temperatures, his published chart for normal paraffins is actually an Othmer type of correlation, as the pressure scale is logarithmic. Consequently, the temperature scale is a modified reciprocal relationship. Calingaert and Davis (70) showed that the Cox temperature scale is nearly proportional to 1/(T - 43) with T in ’ F. Lamb, Sitar, and Goen (74) improved the linearity of this type of relationship for high boiling normal paraffins by varying the constant in the temperature scale. I n the second category, one of the more widely accepted and practical correlation methods is the well-known Antoine (3) equation : B LogP=A+-
T+C
’
where P is the absolute pressure, T is the absolute temperature, and A , B, and C are parameters characteristic of any compound. Equation 1 is a great improvement over the simple relation, log P = A + B / T , derived from the Clausius-Clapeyron equation. Thodos (25) recently proposed the following equation for individual compounds : Log P = A $- B
(+) + C($)* D
- - l n
-I(2)
(fd
The constants A , B, C, D, and n are characteristic of the compound. The last term in Equation 2 is insignificant a t atmospheric pressure or below for hydrocarbons with normal boiling points I
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JULY 1957
1 1 87
Table I. Confirmation of Pressure Scale Extrapolation by Thermal Properties of n-Hexane Boiling Point of n-Hexane, R. Integration Pressure, Calcd. of Clapeyron equation Mm. Hg by Eq. 4
...
100
10 1 0.I 0.01 0.001 0.0001 0.00001
446.6 393.7 353 .o 320.8 294.6 273.2 254.7
520.2" 446.2 392.9 352.8 321.0 295. Z b 273.8' 255.5*
From API Research Project 44 (2) selected values; used as starting point of integration. Heat capacity of liquid extrapolated below melting point. a
above 400' F. Using Equation 2, Lillard (76) developed a correlation for normal paraffins u p to a 1500" F. normal boiling point. He then conconstructed a chart (the Lillard-Thodos correlation) covering the subatmospheric pressure range down to 0.01 micron of mercury. Modifications of both the Cox and Othmer relationships involve, respectively, reduced pressures and temperatures. This method of using corresponding states should show some improvement over the original correlations. However, substitution of reduced conditions is not desirable for two reasons: The necessary conversion to and from reduced conditions is impracticable; and for a high boiling hydrocarbon, inaccuracies tend to be introduced because extrapolation is required to find its critical temperature or pressure. The Cox method is significantly more reliable for wide extrapolations than the Othmer plot and far better than Duhring's rule. I n the second category, the Lillard-Thodos correlation was a marked improvement over the Antoine equation. All of these basic methods have been used by others to develop generalized vapor pressure correlations, or charts, and some are widely used in the petroleum industry. Certain of these charts were carefully studied in order to establish which type of correlation would be most acceptable from the standpoints of precision, consistency, scope, and general utility. Special attention was paid to those published by Nelson (22), Brown and Badger (8),Myers and Fenske (20, 27), and two similar ones suggested by Maxwell (77, 78). Development of Generalized Correlation It is clear that the type of generalized correlation desired should meet the following requirements :
1 188
I t should be a linear relationship of a type that fits the data over wide extremes of vapor pressure and normal boiling point and can thus be extrapolated with confidence far beyond the actual data. I t should fit the mass of recent data over the range they cover with a high degree of precision. The correlation developed in 1932 by Maxwell (78) appeared on the surface to be one of the best possibilities for meeting these requirements. Figure 1 represents the subatmospheric portion of this correlation extrapolated to much lower pressures than were originally used. It proved to be the most convenient and reliable correlation among several examined. A set of large working charts and conversion tables for precise readings derived from Figure 1 and other correlations presented here was recently published (19). The general equation for Figure 1 is: 1
- = A" Tn Ti
+ B, (when P, = Ps),
(3)
where T, = absolute boiling point of any hydrocarbon above propane T6 = absolute boiling point of n-hexane, taken as the standard reference compound P, = P6 = vapor pressure corresponding respectively to T,and Tg A,, and B, = constants characteristic of each compound (n) The method of constructing the scales for Figure 1 has been described in some detail (78). However, certain features are worth recounting here. Pressure Scale. The ordinate scale is equivalent to the reciprocal temperature of the reference compound, n-hexane. This reciprocal temperature scale was converted to a pressure scale using the extensive data on n-hexane above 1 mm. of mercury. In order to extend this conversion to lower pressures, an Antoine equation was fitted to the n-hexane,data below 50 mm. of mercury, which reduced to :
where P is pressure in millimeters of mercury and T is absolute temperature, ' R. The resulting converging lines in Figure 1 intersected at a common point according to the method suggested by cox. Because of the large extrapolation of Equation 4 as the pressure scale was extended to lower and lower presures, some question arose about its validity in the lower pressure regions. However, the boiling point of n-hexane in the very low pressure range can be established thermodynamically by the
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Clapeyron equation as described below. Boiling points so established are compared in Table I with those computed from Equation 4. The agreement is amazingly good, and Equation 4 was thus fully verified. I n the low pressure region where R T / P may be substituted for AV, the Clausius approximation is very nearly identical with the exact Clapeyron equation. The approximate equation can be expressed as follows : Ad T d (In P) = .-
R T2
(5)
where X is the heat of vaporization. From any known value ho, the latent heat of vaporization may be calculated from the equation :
where Cv and C, are the molal heat capacities of the saturated vapor and liquid, respectively. The Clausius-Clapeyron equation may be integrated to predict the vapor pressure-temperature relation for any compound over the range for which the necessary thermal data are available. Fortunately, low temperature heat capacity data exist for n-hexane (2, 73) and Equation 6 could be integrated over the desired temperature range. A curve was developed from Equation 6, so Equation 5 could then be integrated graphically. I n terms of the vapor pressure-temperature relationship, this is equivalent to :
where To is the boiling point at 100 mm. of mercury, Po. Both the boiling point, 520.2' R. ( 2 ) , and heat of vaporization, 13,500 B.t.u. per mole (78), are accurately known for n-hexane at this vapor pressure. The graphical integration is carried on starting with these values.
Temperature Scale. The temperature scale of Figure 1 and its counterpart. Figure 6, presented later, is a 1/' R. scale converted to " F. I n 1950, a chart like Figure 1 was published by Maxwell (77). This chart has the same temperature scale below 650' F. as Figure 1, and the pressure scales for both are identical. Above 650' F., the 1/' R. scale of the 1950 chart was purposely distorted to satisfy the Beale and Docksey ( 5 ) data on high boiling hydrocarbons. Later study indicated that these data might be partly in error because of questionable corrections for the effect of thermal decomposition. Consequently, these data were ignored in the present work. For certain practical purposes, the 1950 chart (77) and Figure 1 are equally good. For example, subatmospheric vapor pressures predicted for high boiling materials via the normal boiling point
V A P O R PRESSURE OF HYDROCARBONS
lines are identical below 650' F. and practically the same a t temperatures somewhat above 650' F. For many uses, therefore, the distortion in the 1/'R. scale of the 1950 chart had little or no effect. Actually, it affected only the level of normal boiling points predicted for compounds boiling above! 650' F. as shown below. Normal Boiling Point 1950 Chart, ' F.
Figure 1,
650 750 1000 1250
650 743 967 1186
O
F.
Difference, O
F. 0
7 33 64
The predicted normal boiling points from the 1950 chart were markedly higher than those from other wellknown correlations. This was one reason for undertaking the present work.
Referring again to Figure 1, the approximate scope of the data used in the present work is indicated for convenient reference. I t is apparent that the dQta on hydrocarbons boiling above 800' F. are sparse or nonexistent, and even defy procurement. Additional data on higher boiling compounds would be valuable in confirming the extrapolated regions of Figure 1. The data from the American Petroleum Institute ResearcH Project 42 (7) (API-42 data) were especially useful in establishing the effect of hydrocarbon chemical type on vapor pressure and converted normal boiling point. The Myers and Fenske (27) data were valuable because they cover a fairly large pressure range and a wide variety of hydrocarbon types. Data on the Cj4CI6hydrocarbons (7, 2, 7, 24) also were important because of their large pressure range. The Blodgett-Langmuir data (6) on two extremely narrow-boiling
(about I O o 17. range) petroleum fractions were considered about the most valuable in verifying the extrapolated low pressure region of the correlation. These data were obtained by a unique method, giving results a t the lowest pressures ever reported. The method used by Blodgett and Langmuir in determining vapor pressures a t very low pressures would probably be most useful in obtaining data on high boiling fractions in future investigations of this subject. The vapor pressure of a very narrow-boiling petroleum oil is (determined by allowing it to evaporate a t constant temperature in a high vacuum, condensing the vapor on a metal surface cooled by liquid air. The thickness of the thin film of condensate is determined from the interference color which it reflects, and thus the weight of the condensate is known. The vapor pressure is calculated from the relationship among mass, molecular weight, and pressure as suggested by Langmuir (75). The data a t 10 mm. VOL. 49,
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The other data noted in Figure 1 were used in a manner equivalent to that just mentioned-that is, the normal boiling points predicted by the different correlations corresponded in effect to two readings, each representing the data at the extremes of the observed vapor pressures. This procedure gave results accurate enough for checking the different vapor pressure correlations. Effect of Characterization Factor
0.2
0.5 I 2 VAPOR PRESSURE, Figure 2.
I n checking the correlation considered here, certain simplifications were found both expedient and desirable, especially in using the API-42 data. First, it was considered logical to make all comparisons on the basis of a common reference pressure; otherwise too much confusion would have resulted, The particular pressure level used for this purpose is of no importance in itself. The normal boiling point basis was adopted, therefore, because it is such a I
I
1
I
20
common reference. I n general, the accuracy of the correlations examined was judged largely from the consistency of the normal boiling points predicted by each correlation from two or mor? observations at subatmospheric pressures. The largest and most useful group of data at hand was the API-42 data on 135 pure hydrocarbons of different types, with boiling points measured at 0.5, 1, 2, 5, and 10 mm. of mercury. The possibility was explored of using the data at only two of these pressures to represent all of them for any one compound. The data obtained at 0.5 and 5 mm. of mercury proved entirely adequate for this purpose.
Interpretation a n d Use of Data
u: t10 I
5 IO MERCURY
API data on 135 pure compounds
of mercury pressure on the two narrow fractions were obtained by conventional means (72).
0
mm
I
I
I
I n the initial phase of the present work. a detailed comparison was made between the correlation in Figure 1 and the Lillard-Thodos correlation, as they appeared to be the best available. It became evident that neither correlation was adequate for all types of higher boiling hydrocarbons, judging from the API-42 data. O n the average, Figure 1 agreed with these data better than the Lillard-Thodos correlation, but the latter was superior for paraffinic hydrocarbons. I n view of this, the precision of each of these correlations was evaluated in considerable detail to discover the factor or factors responsible for the disparities between them. As a preliminary step, normal boiling points were first predicted from all of the API-42 data, using both Figure 1 and the Lillard-Thodos correlations. Algebraic averages of the differences between the normal boiling points predicted from the data at 0.5 mm. of mercury and those predicted from data a t higher pressures were plotted against pressure as in Figure 2. This established two things: The results from each of the above correlations gave good linear relation-
l
I
,
I
’ REGRESSION FOR 135 PURE COMPOUNDS
$5
. si’;”’
0
+
-
- BOILING POINT RANGE,
-5 -
OF.
500-650
0 650-750 ~~
E
n
9
~
IC
II
12
Figure 3.
\ 4L
0
4 7 5 0 - 000 0 000- 900
+
0
1
-10 14 9 IO GHA R AGTE R IZ AT ION FACTO R
13
4
BOILING POINT RANGE, “E
II
12
13
14
independence of boiling point level
Unit for ordinate scale i s difference between normal boiling points, converted by Figure 1, per tenfold change in pressure corresponding to observed vapor pressure data
1 190
INDUSTRIAL AND ENGINEERING CHEMISTRY
V A P O R PRESSURE ships representing the data between 0.5 and 5 mm. of mercury pressure. The results from the data at 10 mm. of mercury pressure were definitely inconsistent with the others, implying that the original data a t this pressure are questionable.
6
As Figure 2 shows, the relationship with pressure could be defined well within the accuracy desired for. the present work by using only the data at 0.5 and 5 mm. of mercury pressure. Further study of the API-42 data indicated that the trend with pressure in Figure 2 probably resulted from an effect of hydrocarbon chemical type. I t developed that the Watson and Nelson characterization factor, K , was satisfactory for measuring this effect. The fact that IC can be readily computed from ordinary physical properties is an advantage. T o establish the effect of K, a linear regression was made against K of the differences, At, between the normal boiling points predicted by Figure 1 from the data at 5 and 0.5 mm. of mercury on each of the 135 compounds. The following equation resulted : Ai = -2.5 ( K - 12.0) (8) By using the Lillard-Thodos chart in the same manner, a similar equation was obtained : At = -2.5
h
(K -
13.5)
(9)
T o study other variables that might affect the vapor pressure correlations, it was desirable at this point to use the API-42 data grouped to reduce the number of normal boiling point predictions necessary to represent them, and to use averages of selected small groups of these data to minimize the effect of chance errors in individual observations. One of the groupings comprised data on similar compounds of limited boiling point range. Data grouped in this manner were used in the analysis discussed below. This grouping method proved statistically sound as later explained. The API-42 data were next examined to find out whether there was a trend with boiling point as well as with K. The results are plotted in Figure 3, which also includes the regression line established from Equation 8. No significant trend with boiling point level was indicated. The possible effect of boiling point itself was also examined by another regression analysis. At the same time, coefficients were introduced in the regression to establish whether a curvilinear relationship involving both X and boiling point would better fit the data. As judged by conventional statistical tests, the effect of boiling point was insignificant. The linear relation in Figure 3 was thus found valid with respect to boiling points above 400' F.
O F HYDROCARBONS AVERAGE PRESS RANGE, mm.
-
DESCRIPTION
0 20 COMP. MYERS & FENSKE
a
I K
o z
0 3 NORMAL PARAFFINS,
+
C14
0.5 - 30.0
- Cte
0.03 - 7 6 0
3
2 NARROW PETROLEUM FRACTIONS
x
10"
- 10
+io
3
0
L
0 0
REGRESSION FOR
z w
135 PURE COMPOUNDS
8
LL
k
n
-5
9
Figure 4.
12
II
IO
14
13
CHARACTERIZATION FACTOR Independence of pressure interval
,
Unit for ordinate scale is difference between normal boiling points, converted by Figure 1 , per tenfold change in pressure corresponding to observed vapor pressure data
are expressed per tenfold pressure change. The data representing wide pressure ranges agree well with the regression for the API-42 data. Of the data represented in Figure 4, those for the CI4-C16 hydrocarbons, (7,2, 27, 24) and the Blodgett-Langmuir data (6) on the narrow-boiling petroleum fractions are especially significant. They were 'considered the most precise at very low pressures, and they cover very large pressure ranges, especially the Blodgett-Langmuir data. The fact that the latter were obtained a t extremely low pressures provides the most severe test
Finally, other data covering large pressure intervals were examined to find out whether Equation 8 could be extended to cover large pressure ranges. Experience in handling vapor pressure data on various kinds of pure compounds has indicated that most data produce very nearly linear relationships on a Cox-type plot, even though the slope may be far different for different compounds. Thus, it appeared likely that Equation 8 could be modified to include a logarithmic pressure factor. This was born out by Figure 4 in which the predicted normal boiling point differences
-CHARACTERIZATION 'lo-
FACTOR
t
I
P -
I
0.001
0.0 I 0. I I OBSERVED VAPOR PRESSURE,
I
I
I
IO
IO0
760
mm. OF
MERCURY
Figure 5. Boiling point correction for characterization factor, subatmospheric pressure range Gives correction to b e added to normal boiling points r e a d from Figure 1
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of the K correlation. The Myers and Fenske data also supported the correlation in Figure 4. They were especially valuable, because they covered wide ranges of both pressure and K. Myers and Fenske reported a large number of observations on each hydrocarbon which tended to offset the inconsistencies detected among their data. From the foregoing analysis, the final form established for Equation 8 is: At
-2.5
(K
-
12.0) X logto (PZ/Pl)
(10) where Pf and PI are, respectively, the upper and lower limits of the vapor pressure interval in question. For convenience in use, Equation 10 is presented in graph form in Figure 5. This plot shows that the magnitude of the correction for K is small for petroleum hydrocarbons commonly of interest, if the observed pressure is not much below about 5 mm. of mercury. This makes it possible for most purposes, therefore, to use Figure 1 {or its equivalent) to predict normal boiling points. The following readings based on Figures 1 and 5 indicate the magnitude of the correction for K over fairly wide ranges of pressure and K.
I
Vapor pressure at 600' F., mm. mercury
0.01
0.01
0.01
10
10
10
Characterization factor, I
