\

Symposium on Physical Properties of Hydrocarbon Mixtures

Papers presented before the Division of Petroleum Chemistry at the 85th Meeting of the American Chemical Society, Washington, D. C., March 26 to 31, 1933.

Improved Methods for Approximating Critical and Thermal Properties of Petroleum Fractions

K. RI. WATSON AND E. F. NELSON, Universal Oil Products Company, Chicago, Ill.

H E published literature and the files of every petroleum laboratory contain many data on the physical p r o p T erties of petroleum fractions, the value of which is

limited by the difficulty of correlating them into relation- ships of general applicability. Such correlations should permit prediction of difficultly measurable properties from the results of standardized inspections such as the Engler distillation and the specific gravity. I n our present state of knowledge it is necessary to resort to many purely em- pirical relationships which have no apparent theoretical foundation but are valuable in that they correlate existing data with accuracy and permit its extrapolation with some degree of assurance. The relationships presented below are for the most part of the empirical type based on con- sideration of the best data available a t this time. It is recognized that in some cases they are not entirely Iogical and that in all cases the actual numerical values will be subject to revision as more data are collected.

AVERAGE BOILING POINT Several different m e t h o d s

of e s t a b l i s h i n g a so-called average boiling point of petro- leum f r a c t i o n s have been in m o r e o r l e s s g e n e r a l use . By calculating an integrated a v e r a g e o r d i n a t e of the true boiling point curve, an accurate a v e r a g e boiling point may be o b t a i n e d . This average will be weighted on either a volu- m e t r i c o r a weight basis, de- pending on the units in which the distillation curve is plotted. An integrated average of the 100-cc. E n g l e r d i s t i l l a t i o n c u r v e s i m i l a r l y g ives a fair approximation to the volumetric a v e r a g e boiling point with a tendency toward higher values than are obtained by averag-, ing a volumetric true boiling point curve.

As a basis for the correlation of p h y s i c a l p r o p e r t i e s , par- t i c u l a r l y the so-called molal p r o p e r t i e s , a volumetrically weighted average boiling point of fe rs a l e s s logical bas i s

than what may be termed the “molal average boiling point.” The molal average boiling point is less than the volumetric average because of the fact that the ratio of specific gravity to molecular weight is higher for the low-boiling members of a hydrocarbon series. Thus, in determining the average boiling point from a volumetric distillation curve, the lower boiling fractions should be given increased weighting in proportion to the variation with boiling point of this ratio of specific gravity to molecular weight.

I n Figure 1 is presented a curve giving a correction to be subtracted from the volumetric average boiling point of a petroleum fraction in order to obtain an approximation to its molal average boiling point. This correction is expressed as a function of the slope of the 100-cc. Engler distillation curve and becomes zero as the slope of the curve approaches zero, denoting a pure compound. The general form of this curve was derived by plotting the ratio of specific gravity

Two new concepts are introduced f o r correla- tion of the physical properties of petroleum. The molal average boiling point is used in all correlations involving the boiling point of the stock. A chart is presented fo r estimating this value from the Engler distillation. Variations in physical properties with change in the character of the stock are quantitatively expressed by means of a characterization factor de$ned as the ratio of the cube root of the molal average boiling point, in degrees Rankine, to the specific gracity. This factor ranges from 12.5 for purely paraflnic fractions to 10.0 f o r highly cracked, aromatic stocks.

On this basis, methods are presented f o r ap- proximating the molecular weight, critical tem- perature and pressure, specific heats of liquid and vapor, heal of vaporization at atmos- pheric pressure, change of heat of Taporization with pressure, and change of total heat content with pressure, f o r stocks of varying characters and boiling ranges. The only experimental data required are the Engler distillation and the specific gracity. Howez‘er, these relationships cannot be applied with accuracy to such hydro- carbons as undergo chemical change during the analysis used as a basis for the work.

880

t o molecular weight against n o r m a l boiling point for the paraffin h y d r o c a r b o n s . Al- though the numerical values of this ratio change for different series of hydrocarbons, it seems reasonable to assume t h a t i t s variation with boiling tempera- ture will be approximately the same for other series on which complete data are not available. On this basis these ratios were used as w e i g h t i n g factors for correcting the true boiling point curve to a molal basis. The re- lationships between the slopes of the Engler distillation curve and true boiling point curve were approximated from the data of Piroomov and Beiswenger ($1) and Obryadchakoff (20).

The correction to be subtracted from the v o l u m e t r i c average boiling point was found to be practically independent of the magnitude of the boiling tem- perature and could be expressed as a function only of the slope of the Engler d i s t i l l a t i o n curve. However, the curve derived in this manner gave corrections too high for the best agreement with molecular weight and cr i t i c a1 temperature data. This may be

August, 1933 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y aai

explained by the fact that the higher boiling fractions of petroleum stocks tend to be less paraffinic than the low boiling, and have higher values of specific gravity to molcwlar weight ratios than assumed in the derivation. Accordingly, the slope of the correction curve was reduced to bring it into agreement with the available data. This is the relationship plotted in Figure 1. For differences greater than 6 the curve

was merely extended as 2.L 30 , an extrapolation because

of the uncertainty of the data on h igh-boi l ing hydrocarbons. The per- centage error of the cor- rection curve of Figure 1 i s p r o b a b l y high in many cases, but, in view of t h e f a c t t h a t t h e

FIGURE 1. CORRECTION FOR correction term is rela- MOLAL AVERAGE BOILING POINT tively small as compared

to the magnitude of the average boiling temperature, the relationship is fairly satis- factory.

It has been found that use of the molal average boiling point, as estimated from Figure 1, improves most of the physical correlations in which the boiling point is used. I t is recommended that this average be used in preference to either the 50 per cent point of the Engler curve or the various methods of averaging which have been previously proposed.

In order to determine the volumetric areragc hoiling point, it is ordinarily sufficient to average the temperatures a t \I hch the percentage over plus the distillation loss in the 100-cc. Engler distillation equals 10, 30, 50, 70, and 90 per cent. The slope used in Figure 1 is obtained hy dividing the differ- ence hctn w n the 90 pel cent a i d 10 pel relit poilit: by 80.

111 TVOI hiiig with high-boiling stocks where the vapor temperatures in the 100-cc. Engler distillation exceed 700" F., it is preferable to use the data from a distillation under reduced pressure in order that the liquid temperature does not enter the range of rapid cracking. Ordinarily a dis- tillation under pressure of 10 mm. of mercury is satisfactory. Such data are converted to atmospheric pressure by means of a vapor pressure chart. If low-pressure distillation data are not available on high-boiling stocks, the 50 per cent point probably offers a better approximation to the average boiling point than would be obtained by averaging the temperatures of the atmospheric pressure distillation curve.

*

cH.4R.4CTERIZ.4TIOK FACTOR In attempting any general correlation of the properties

of petroleum, the most difficult factors to take into account are the differences in behavior shown by stocks of different origins and treatments. Several schemes have been pro- posed for quantitatively expressing the differences in char- acter of different oils. Hill and Coates (I5j proposed a viscosity-gravity function as a means of classifying lubri- cating stocks. This relationship has not been developed for the more volatile fractions. Lange and Jewel (17) have proposed a relationship between refractive index and specific gravity but have not sufficiently developed it for immediate usefulness.

From the data contained in the International Critical Tables on the properties of the pure hydrocarbons, it has been noted that the ratio of the cube root of the absolute boiling point to the specific gravity is substantially constant for the paraffin hydrocarbons boiling between 100" and 700" F., if the averages of all the reported isomers are considered. When the boiling point is expressed in degrees Rankine and the specific gravity at 60/60" F., this ratio varies between 12.5 and 12.8 for the paraffinc. For benzene the ratio is 9.8.

It is suggested that the ratio of the cube root of the absolute boiling point to the specific gravity be used as a characteriza- tion factor, denoting what may be termed the '(paraffinicity" of hydrocarbon fractions. Thus:

where K = characterization factor T g = molal av. boiling point, O Rankine s = sp. gr. at 60/60° F.

A characterization factor of 12.5 indicates a stock pre- dominantly paraffinic in nature. Lower values of the factor indicate increasing deviation from the paraffinic toward the naphthenic and aromatic properties. For narrow- boiling fractions from Midcontinent crude oils this ratio varies from approximately 12.4 for the fractions boiling near 100" F. up to a practically constant value of 11.8 for higher boiling fractions up to 700" F. In fractions from highly aromatic or naphthenic stocks the factor is con- siderably louTer, approaching 10 as a minimum value. I n highly cracked stocks the factor is found to vary between 10 and 11, depending on the severity of the conditions t o which the stock has been exposed.

The characterization factor is readily calculated from the measured specific gravity and the molal average boiling point determined from the Engler distillation and Figure 1.

hlOLECULAR ITEIGHT

Methods for relating the molecular weight to any other single physical property of petroleum fractions have proved unreliable except for limited applications. However, by correlation with two other properties, such as specific gravity and boiling point, a relationship can be developed which is satisfactory for most purposes.

MOLAL AVLrUCC BOlLlllC WtNT.1

FIGURE 2. MOLECULAR WEIGHTS OF PETROLEUM FRACTIONS AS A FUNCTION

( T B ) ' / ~ / S . OF CHARACTERIZ.4TION FACTOR, K =

where 8 - ipecific gravity, 60/6O0 Fd T B = molal av. boiling point, Ran-

kine

Such a correlation is presented in Figure 2 where molecular weight is plotted against molal average boiling point for stocks of constant values of the characterization factor K . The upper curve, corresponding to K = 12.5, represents the relationship for predominantly paraffinic stocks. For naphthenic, aromatic, or cracked stocks the lower curves corresponding to the calculated values of K are used. These curves have been established from the data on the pure. hydrocarbons and the results of FitzSimons and Bahlke (11) on fractions of Midcontinent crude, Lange and Jesse1 (17) on stocks of various origins, Brown (4) on a synthetic crude, and data on cracked stocks determined in this laboratory

882 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y Vol. 25, No. 8

by a modified Hoffman method. All these data are repre- sented by the curves of Figure 2 with errors rarely as great as 5 per cent, and it is believed that this chart offers a satis- factory basis for calculations where actual determination of molecular weight cannot be made. However, an experi- mental determination of the molecular weight is to be recom- mended whenever possible for accurate calculations.

MOLAL A V L I y . L I IOILIff i POIN1.F

FIGURE 3. MOLECULAR WEIGHTS OF PETROLEUM FRACTIONS AS FUNCTION OF BOILIXG POINT AND SPECIFIC

GRAVITY

The relationships of Figure 2 are presented in a form more convenient for ordinary use in Figure 3 where molecular weight is plotted against molal average boiling point and A. P. I. gravity.

CRITICAL TEMPERATURE

Correlations of many of the physical properties of hydro- carbons, especially a t elevated temperatures and pressures, are best expressed by reduced equations containing functions of the critical temperature and pressure. For the use of these relationships simple methods for estimating critical temperature and pressure are invaluable. One of the authors (23) has proposed the following relationship between critical temperature, density, and boiling point of pure compounds:

3 = 0.283 ($) 0.18 T, where T, = abs. critical temp.

T, = abs. temp, at which the substance is in equilibrium with its saturated vapor in a concentration of 1 gram-mole in 22.4 liters

M = molecular weight d = density of liquid at its normal boiling point,

grams/cc.

The relationship between T, and the normal boiling point was also derived and presented in graphical form. For a substance boiling a t 0" C., T, is equal to the boiling point, while for higher boiling substances T, is greater and for lower boiling substances less than the normal boiling point.

This relationship was shown to be in good agreement with the experimentally determined values on practically all nonpolar substances ranging from gases such as nitrogen up to the highest boiling materials on which data have been obtained. It is assumed that this same relationship is applicable to mixtures when the molal average boiling point is used for the determination of T,. Figure 4 was derived by combining the relationship graphically expressed by Figure 3 with Equation 2 and a coefficient of thermal ex-

.pansion table based on the publications of Zeitfuchs (26) and Wilson and Bahlke.(25) and the data on pure aromatic and naphthenic compounds. This chart relates critical temperature to molaI average boiling point and A. P. I. gravity for the hydrocarbons. These curves are in good

agreement with the published data on both petroleum frac- tions and pure hydrocarbons.

A similar chart was developed by Eaton and Porter (9) to correlate their experimental data on critical temperatures. Figure 4 is in close agreement with their chart and equation except in the higher temperature range. It is believed that use of the molal average boiling point gives a more logical correlation on stocks of wide boiling ranges than does the use of the 50 per cent point of the A. S. T. M. distillation as proposed by Eaton and Porter. An illustration of the applicability of the molal average boiling point is found in the data of Bahlke and Kay (2) on a gasoline and close- boiling naphtha of substantially the same specific gravity and molecular weight. The properties of these two stocks are as follows:

GABOLINE NAPHTH.4

Molecular weight (detd.) 109 110 Gravity, O A. P. I. 5 7 . 3 5 7 . 1 A. S. T. M. distillation: 10% 149

230 282 325 37 1 2 . 8 271 586 254

- 230 245 258 272 295

0.81 260 59 1 256

-

These data show that the gasoline is a lighter stock of lower molecular weight and critical temperature than the naphtha. However, both the 50 per cent point and the volumetric average boiling point of the gasoline are con- siderably higher than those of the naphtha. When the boiling point is corrected to a molal average basis by the use of Figure 1, the values of both the average boiling point and

YQAL AVLIAGL WILING mI*r'r

FIGURE 4. CRITICAL TEMPERATURES OF PETROLEUM FRACTIONS

estimated critical temperature fall in the proper order. The critical temperatures for these two stocks estimated from Figure 4 are 584 and 587, respectively.

CRITICAL PRESSURE Unfortunately very few published data are available on

the critical pressures of hydrocarbon mixtures. The de- termination is difficult and susceptible to large errors if special precautions are not followed. Because of the scarcity of data, a highly reliable method of prediction does not seem possible a t this time. The following method has been used by the authors in the absence of a better scheme and seems to offer fair correlation with what data are available.

The method of plotting vapor pressure data proposed by Cox (7) offers a good method for estimating the critical pressure of a pure hydrocarbon whose critical temperature

August, 1933 I N D U S T R 1.4 L A N D E N G I N E E R I N G C H E R.I I S T R Y 883

is known. The vapor pressure curves of the pure hydro- carbons when plotted on the Cox chart form straight lines converging a t a single point. I n order to determine the critical pressure of a compound whose critical temperature is known, it is necessary only to plot a line on the Cox chart connecting the normal boiling point of the compound to the point of hydrocarbon convergency. The critical pressure may be read a t the point where this vapor pressure curve crosses the critical temperature abscissa.

The average boiling points of mixtures of hydrocarbons usually plot as approximately straight lines on the Cox chart haT-ing the same point of convergency as the pure hydrocarbons. Similarly the lines representing conditions of initial equilibrium vaporization are also approximately straight on the Cox chart for stocks which do not contain large quantities of dissolved gases. However, the elope of the initial vaporization curve is considerably less than that of the average boiling point curve so that these two lines inter- sect a t a point beyond the critical temperature of the fraction. It has been found that this point of intersection may be as- sumed with fair approximation to lie a t a point beyond the intersection of the average boiling point line and the critical temperature abscissa by a distance equal to two-tenths times the distance between the latter intersection and the atmos- pheric average boiling point. The temperature of initial equilibrium vaporization a t atmospheric pressure may be taken as the Engler distillation 10 per cent point as pointed out by Bridgeman, Aldrich, and White (3). By these assumptions an approximation to the initial vaporization line is established on the Cox chart. The critical pressure is then taken as the pressure corresponding to the inter- section of this initial vaporization line mith the critical temperature abscissa.

The above method may be made clear by an illustration dealing with the naphtha C used in the experiments of Weir and Eaton (24) . The characteristics of this naphtha were as follows:

A. P. I. gravity -4. S. T. A I . distillation: 10% " _ M

5 8 . 2

157 n. 1 du 70 i l l 269 303 353 2 56 241

507, __ 70% 90%

Volumetric av. v . p , , F. Molal av. v. p. (Figure l), ' F.

The critical temperature of this stock is estimated as 571 " F. from Figure 4.

The procedure for graphically estimating the critical pressure of this stock is shown on the Cox chart of Figure 5. The slanting lines on this chart are the vapor pressure curves of the paraffin hydrocarbons having the number of carbon atoms indicated a t the tops of the lines. Line FC is the critical temperature abscissa a t 571" F. A B is the average boiling point line drawn through the atmospheric average boiling point, A , a t 241" F. and the point of convergence of the pure hydrocarbon lines. Point D is located kiy measuring along line A B a distance equal to two-tenths times the distance of AC. Point E is the A. S. T. hl. 10 per cent point, 157" F. The critical temperature and pressure are repre- sented by point F , corresponding t o a temperature of 571 " F. and an absolute pressure of 530 pounds per square inch. These values are in agreement with those roughly predicted by Weir and Eaton from the thermal behavior of this dis- tillate, respectively, 575" F. and 500 pounds per square inch.

The above graphical method is equivalent to expressing the critical pressure as a function of average boiling point, critical temperature, and the slope of the A . 8 . T. M. distilla- tion curve, and can be developed into a mathematical or a graphical expression if future data indicate that the method has satisfactory accuracy.

SPECIFIC HEAT (LIQUID STATE) In comparing the results of different investigators of the

specific heats of petroleum fractions, it is apparent that differences exist which cannot be attributed entirely to experimental error and that these data cannot be correlated by any simple relationship to specific gravity and tempera- ture alone, such as proposed by Cragoe (8). However, if these results are compared from the standpoint of the char- acterization factors of the stocks, it will be noted that the differences of the various investigators follow more or less

TLMPUATURC IN ENLI r.wncwmr

FIGLRE 5 . hfETHOD FOR ESTIMATING CRITIC4L PRES- SURES O F PETROLEUM FRACTIOM

consistent trends with the characterization factor. As the characterization factor of the stock diminishes, indicating a less paraffinic nature, the specific heat tends to decrease. Also, the rate of change of specific heat with specific gravity appears to decrease as does the temperature coefficient of the specific heat.

A quantitative expression for the relationship between characterization factor and specific heat was estimated from the specific heat data on the pure hydrocarbons of the paraf- fin, naphthene, and aromatic series. These data are available for only a few compounds so that the relationship cannot be considered as highly exact. The estimated specific heats of the hydrocarbons of each series corresponding to a specific gravity of 0.88 and a temperature of 75" F. were plotted against the corresponding characterization factors. From the slope of this curve the following function was derived by which specific heat data for a stock having a characteri- zation factor of 11.8 may be multiplied in order to take into account the variation of specific heat as a function of char- acterization factor:

f ( K ) = 0.055K + 0.35 (3) This function was selected to equal unity where K = 11.8 in order that no correction to the conventional specific heat charts will be necessary when working with Midcontinent fractions.

On the above basis the following general equation is proposed as an improved correlation of the specific heat data of liquid fractions from varying sources:

cp = [0.6811 - 0.308s + t(0.000815 - 0.000306~)] X [0.055K + 0.351 (4)

where cp = sp. heat s = sp. gr. a t 60/60" F. t = temp., F. K = characterization factor (Equation 1)

The coefficient of s in the above equation is similar to that of the Bureau of Standards' equation (8) and is slightly

884 I N D U S T R I A L A N D E N G I N E E R I N G C H E l M I S T R Y Vol. 23, No. 8

smaller than that proposed for Fortsch and Whitman ( I d ) and considerably smaller than that of Weir and Eaton (24). The high specific gravity coefficient found by Weir and Eaton can be attributed to the fact that the heaviest stock on which they worked was a lubricating oil fraction having a relatively low characterization factor of 11.2, indicating that it was a less paraffinic stock than normal fractions of hlid-

I I I ~

I

IC4 Po0 SCO 90 504 bo0 m0 9m ELLIPER*TURC.I

FIGURE 6. SPECIFIC HEATS OF LIQUID PETROLEUM OILS, WHERE K = 11.8 (MIDCONTINENT STOCKS)

For other stocks multiply by (0.055K + 0.38).

continent crude. The temperature coefficient of Equation 4 is an average of those proposed for Midcontinent stocks by all the investigators cited above. Neither Weir and Eaton nor Lange and Jesse1 ( I ? ) found the variation of temperature coefficient with specific gravity which was reported by Fortsch and Whitman (IW), the Bureau of Standards (8) , and Gary, Rubin, and Ward ( I S ) .

For convenient use, Equation 4 is plotted in Figure 6. The lines as plotted are applicable to fractions from hfid- continent crude or other sources having a characterization factor of approximately 11.8. For other types of stock the specific heats read from the curves should be multiplied by the function of K expressed in Equation 3. The data cal- culated from Equation 4 or Figure 6 are in satisfactory agreement with the experimentally observed values of the investigators cited above, including the cracked gas oils of Weir and Eaton (24) and Gary, Rubin, and Ward (13).

In the use of Equation 4 a t conditions near the critical state, considerable error may be encountered, owing to variation of specific heat with pressure. The equation applies where the pressure is well above that required to prevent vaporization but may give results much too low a t lower pressures.

SPECIFIC HEAT (VAPOR STATE) Data on the specific heats of petroleum fractions in the

vapor state are less plentiful than those dealing with the liquid state. Bahlke and Kay ( I ) , Weir and Eaton ( 2 4 , and Gary, Rubin, and Ward (1s) have made the most ex- tensive investigations of this property. On fractions from Midcontinent crudes the work of the three investigators is in exact agreement. Weir and Eaton (24) also obtained specific heat data on a highly cracked gas oil in the vapor state. These results were lower than for Midcontinent fractions of the same specific gravity. Gary, Rubin, and Ward (IS), on the other hand, found that the specific heats of the vapors of cracked stocks were but little lower than those of Midcontinent fractions of the same specific gravity.

I n order to establish a basis for estimating the specific heats of vapors differing widely in nature from Midcontinent fractions, a correction factor was derived from the data on

pure hydrocarbons as a function of the Characterization factor in the same manner as described above for the liquid state. The function is mathematically expressed as follows:

(5 ) f ( K ) = 0.12K - 0.41

This function is also adjusted to equal unity for Midcontinent fractions having a characterization factor of 11.8. The equation proposed by Bahlke and Kay (1) is accordingly modified to apply to other stocks merely by multiplying by the function derived from Equation 5:

4.0 - s c p = 6450 ( t f 670) (0.12K - 0.41)

where c, = sp. heat of vapors t - = temp., F. s = s . gr. at 60/60° F. K = cRaracterixation factor

The results of Equation 6 are slightly higher than the data of Weir and Eaton (24) on the highly cracked gas oil and iuncr then those of Gary, Rubin, and Ward ( I S ) . Suffi- cient data are not available for completely verifying the applicability of the equation, and it is presented merely as a form which expresses the expected trends and should be more accurate than any equation entirely neglecting changes in the character of the stock.

In Figure 7 the equation of Bahlke and Kay is presented graphically together with specific heat curves for the paraffin gases. These curves for gases were derived by interpolation between the data of Bahlke and Kay and the measurements of Eucken and Lude ( I O ) on the specific heat of methane a t temperatures up to 400" F. The data on methane indicate that the curves of Figure 7 should curre downward at the

Teu-nme'I

FIGURE 7. SPECIFIC HEATS OF PARAFFIN GASES A R D PETROLEUM VAPORS AT ATMOSPHERIC PRESSURE, WHERE

K = 11.8 (MIDCONTINEXT STOCKS) For other stocks multiply by (0.12K - 0 41) .

higher temperatures, but the curvature is slight and has been neglected in view of the straight-line relationships found by Bahlke and Kay and substantiated by Weir and Eaton at temperatures up to 1000" F In Figure 7 the data on gases are correlated with the specific gravity of the gas referred t o air. For the heavier hydrocarbons the A. P. I. gravity of the liquid is used.

HEAT OF S'APORIZATIOIY AT ATMOSPHERIC PRESSURE The older experimental data on heats of vaporization of

petroleum fractions show wide variations and inconsistencies which, it seems, must be attributed to experimental errors on the parts of the different investigators. From considera- tion of the data available in 1929 Cragoe (8) concluded that latent heats of vaporization estimated from modifications of Trouton's rule are consistently too high for petrcleum

August, 1933 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y

I I

fractions. However, the more recent measurements by Weir and Eaton (24) and Gary, Rubin, and Ward ( I S ) are not in agreement with this conclusion and indicate that the average values arrived a t by Cragoe are very much too low.

Two satisfactory methods are available for estimating the latent heats of yaporization of pure nonpolar compounds. The method of Hildebrand (Id) has been found applicable to practically all pure compounds a t relatiyell. low pres- sures. A modification of this method has been suggested by Lewis and Weber (19). Kistyakowskii (16') proposed the following equation fcir predicting the heat of vaporization a t atmospheric pressure which he states has a thermo- dynamic basis:

.. , _ I *

L = 5 (7.58 + 4.571 log TB) (7) M where L = latent heat of vaporizaotion, B. t. u./pound

Tg = normal boiling point, Rankine M = molecular Tyeight

This equation represents the data on pure compounds as well as does the method of Hildebrand and is somewhat more simple to use.

The definition of the latent heat of vaporization of a mixture is the subject of considerable confusion. Vaporization of a mixture may proceed under a constant pressure with varying temperature or a t a constant temperature with varying pressure. Some definitions of heat of vaporization include the sensible heat absorbed with change in temperature during vaporization. However, i t seems most logical for engineer- ing calculations to define the latent heat of vaporization of a mixture as the difference between the total heat content of the vapor and the sensible heat absorbed by both liquid and vapor in being heated from the reference to the existing state under a constant pressure. Using this conception of heat of vaporization, Turner and Harrell (22:1 have de- veloped a refined method for calculating the total heat absorbed in vaporizing a mixture under constant pressure. However, it seems sufficient to assume for purposes of cal- culation that such a mixture is heated as a liquid to the

l l l i l l r l +---ik- 2m ,b, ,b, ,bo b W -

MOLAL AVERAGE BOILING POINT'?

FIGURE 8. LATENT HEAT OF VAPORJZATIO~ AT ATMOSPHERIC PRESSURE

temperature of the average boiling point, vaporized at this temperature, and heated as a vapor to the temperature of actually complete vaporization. The error introduced by this assumption in calculating the heat content of the vapor is ordinarily negligible because of the small differences be- tween specific heats of the hydrocarbons in the liquid and vapor states.

Because of the wide applicability of the equation of Kist- yakowskii to pure compounds, it seems reasonable to expect that it should also apply to the heavier hydrocarbons. If the equation is assumed to apply to the pure hydrocarbons, i t should also apply with good approximation to estimating

885

the heat of vaporization of a mixture of hydrocarbons, provided the correct average values of molecular weight and boiling point are used. The molal average boiling point is the logical average to use in this calculation. Assuming the applicability of Equation 7 , Figure 8 is plotted relating the latent heat of vaporization of petroleum fractions to the molal average boiling point and either the molecular weight or the characterization factor. Where actually determined

T L = r L g - T R -

where L = latent heat of vaporization at temperature T ,

L g = latent heat of vaporization at normal boiling point

This method is believed to be more reliable than that of Hildebrand a t high pressures, but in the region of the critical state its applicability becomes uncertain for mixtures of wide boiling ranges. The method described in the following section for estimating the variation of heat content of super- heated vapors with pressure is recommended as a means for obtaining the heat content of vapors a t high pressures in preference to any method involving estimation of the change of heat of vaporization with pressure.

EFFECT OF PRESSURE ON HEAT CONTENT OF HYDROCARBON VAPORS

Cope, Lewis, and Weber (6) and Bahlke and Kay (2 ) have presented methods for estimating the change of heat content of superheated hydrocarbon vapors with change of pressure

O Rankine

T g , O Rankine

886 I N D U S T R I A L A N D E N G

from the pressure-volume-temperature relationships of the vapors. These calculations are made by rigorous thermo- dynamic relationships and are reliable where accurate P-V-T data are available. Cope, Lewis, and Weber (6) and Brown, Souders, and Smith (5) have presented a modi- fication of the reduced equation of state in which compressi- bility factors are expressed as a function of only the reduced temperature and pressure. This function is shown to be approximately constant for different hydrocarbon vapors. From the P-V-T relationship thus established, Cope, Lewis, and Weber (6) and Lewis and Luke (18) have developed

PR

FIGURE 10. HEAT CONTENT CORREC- TION FOR CHANGING PRESSURE OF

HYDROCARBON VAPORS A H = heat content a t atrnoapheric presaure

minus heat content at pressure P, B. t. u. Der Ib.

P R = reduced pressure T R = reduced temperature = molec. 1.- .... ._II :umr weigub T = absolute temperature, O Rankine

a method for estimating change of heat content with pressure which gives results in excellent agreement with the experi- mental data on the lower hydrocarbons.

From the few data available it appears that the reduced equation of state applies with fair approximation to pe- troleum fractions. However, because of the uncertain accu- racy of this equation, it seems that some simplification of the method of Lewis and Luke is justifiable for approxi- mating the change of heat content with pressure.

The compressibility factors for the higher hydrocarbons, estimated from the chart of Brown, Souders, and Smith, may be represented with a fair degree of approximation up to a reduced temperature of 1.5 by the following equations for converging families of straight lines:

For low values of reduced pressure, p = 1.0 - [ 0 . 7 3 ( T ~ ) - ~ - 0 . 1 8 ] P ~ (9)

(10)

For high values of reduced pressure, p = 1.0 - (0.24 - 0.14 T R ) (8 - P R )

where p = compressibility factor TR = reduced temperature, T / T , P R = reduced pressure, P/Pe

The above equations are not recommended for P-V-T calculations but should be fairly satisfactory for estimating heat content a t high pressures, where the values sought are relatively small corrections to be applied to a large total heat content.

The relationship between heat content and pressure is expressed by the following thermodynamic equation:

(11) . -

where H = heat content V = volume T = abs. temp. P = abs. pressure

The general equation of state is obtained by substituting the values of p from Equations 9 and 10 in the general

I N E E R I N G C H E M I S T R Y Vol. 25, No. 8

equation PI' = pRT. The resulting equation of state may be solved for V and differentiated with respect to T, and the results substituted in Equation 11. In this manner the following equations were derived:

For low values of reduced pressure,

For high values of reduced pressure,

where AH = change in heat content with change in pressure from zero to P R , where PR is any pressure in the range of applicability of Equation 9

AH' = change in heat content with change in pressure from P R ~ to P'R, where P R ~ is the reduced pres- sure at the limit of applicability of Equation 9 and P'R is any pressure above PRO in the range of Equation 10

By using each of these equations in the range of its appli- cability, a general chart may be derived expressing the change in heat content resulting from a change in pressure from zero to any elevated value. For ordinary calculations the difference between heat content a t zero and atmospheric pressures may be disregarded. This relationship is expressed graphically in Figure 10 where the ratio AHMIT is plotted against reduced temperature and reduced pressure.

The use of Figure 10 gives values for the change of heat content with pressure which are lower than those found experimentally by Weir and Eaton and higher than those of Bahlke and Kay ( 2 ) .

By means of Figure 10 it is possible to predict the heat content of a petroleum vapor a t any temperature and pressure from its heat content a t atmospheric pressure and the same temperature. For this calculation, values of the molecular weight, critical temperature, and critical pressure are neces- sary. These may be estimated by the methods described above.

EXAMPLE OF USE OF RELATIONSHIPS The use of the above relationships may be made clear by

the solution of a typical problem dealing with a stock on which experimental data are available for verification of the calculations. The so-called naphtha C of Weir and Eaton is convenient for this purpose. The boiling characteristics of this stock were given above, and the critical temperature and pressure estimated from Figures 4 and 5. These results may be summarized as follows:

Sp. gr. A-. P. I. gravity Molal av. b. p., F. Critical temo.. O F. Critical preisure, lh./sq. in.

0,7469 58

241 671 530

The characterization factor is calculated as follows:

This stock is therefore a typical Midcontinent fraction and the specific heat charts, Figures 7 and 8 , may be used directly as plotted. The molecular weight is estimated from Figure 2 or 3 to be 108.

As an illustration, suppose that it is desired to calculate the heat content above 32" F. of this naphtha in the vapor state a t a temperature of 800" F. and a gage pressure of 1000 pounds per square inch.

The mean specific heat of the liquid between 32" and 241" F. is obtained from the curves of Figure 6 at the mean temperature, 137" F., as 0.532.

The procedure is as follows:

August, 1933 I X D U S T R I A L A N D E N G I N E E R I K G C H E M I S T R Y 887

The mean specific heat of the vapor between 241' and 800" F. is estimated from the curves of Figure 7 at the mean temperature, 520" F., as 0.600.

B. t . u /Ib. 111

Heat of vaporization (Figure 8) 133

Total heat (atm pressure) 579

Heat of liquid = 0 532 (241-32)

Heat of vapor 0 600 (800-241) 33;,

From the average curve through Weir and Eaton's experi- mental data on the heat content of this stock the corresponding value is 580 B. t. u. per pound.

To estimate the total heat content at a gage pressure of 1000 pounds per square inch, Figure 10 is used:

TR = 1260/1031 = 1 2 2 PR = 1015/530 = 1 9 2 A H lf (Figure 10) = 4 65

" = 54 B. t u /Ib 108 A H =

Total heat content at 800' F , IOOOlb /sq in = 579 - 54 = 525 B t u /lb

The value e-timated from Weir and Eaton's experimental

The methods outlined above may be utilized for the prepa- ration of more convenient combined charts where many calculations are to be made on a particular type of stock. For example, a chart may be prepared relating total heats of liquid and vapor to temperature and pressure for a par- ticular stock. In other cases, a chart relating total heats of vapor and liquid a t a constant pressure to temperature and A. P. I. gravity for fractions of a constant characterization factor is more convenient. By preparing a set of such charts corresponding to different characterization factors and pressures, a majority of thermal calculation problems

chart is 520

can be solved directly by graphical methods. The use of nomographic charts is also desirable for some types of work.

LITERATURE CITED (1) Bahlke and Kay, ISD. EKG. CHEM., 21, 942 (1929). (2) Ibid., 24, 291 (1932). (3) Bridgeman, Aldrich, and White, Bull. Am. Petroleum Inst., 11,

(4) Brown, G. G., private communication, 1932. (5 ) Brown, Souders, and Smith, IND. ENG. CHEM., 24, 513 (1932). (6) Cope, Lewis, and Weber, Ibid., 23, 887 (1931). (7) Cox, E. R., Ibid., 15, 592 (1923). (8) Cragoe, Bur. Standards, Miscellaneous Pub. 97 (1929). (9) Eaton and Porter, ISD. ENG. &EM., 24, 819 (1932).

(10) Eucken and Lude, 2. physik. Chem., B5, 413 (1929). (11) FitzSimons and Bahlke, Bull. Am. Petroleum Inst., 11;Ko. 1,

(12) Fortsch and Whitman, IKD. ESG. CHEM., 18, 795 (1926). (13) Gary, Rubin, and Ward, Ibid., 25, 178 (1933). (14) Hildebrand, J . Am. Chem. Soc., 37, 970 (1915). (1.5) Hill and Coates, ISD. EKG. CHEY., 20, 641 (1928). (16) Kistyakowskii, 2. physik. Chem., 107, 65 (1923). (17) Lange and Jessel, J . Inst. Petroleum Tech., 16, 783 (1930);

(18) Lewis and Luke, Trans. Am. Sac. Mech. Eng., Petroleum Mech.

(19) Lewis and Weber, J. IXD. ESG. C H E Y . , 14, 485 (1922). (20) Obryadchakoff, Ibid., 24, 1155 (1932). (21) Piroomov and Beiswenger, Bull. Am. Petroleum Inst., 10, So. 2,

(22) Turner and Harrell, Chem. ck M e t . Eng., 37, 98 (1930). (23) Watson, K. M., IND. ESG. CHEY., 23, 360 (1931). (24) Weir and Eaton, Ibid., 24, 211 (1932). (25) Wilson and Bahlke, Ibid., 16, 115 (1924). (26) Zeitfuchs, E. H., Ibid., 17, 1280 (1925).

RECEIVED April 10, 1933

KO. 1, 4 (1930).

70 (1930).

17, 572 (1931); 18, 850 (1932).

Eng., 54, 55 (1932).

52 (1929).

Entropy and Free Energy Relations among Hydrocarbons GEORGE S. PARKS, Stanford University, Calif.

KS0WLEI)C:E of the magnitudes of the free A energy changes in the

various reactions which a given compound can conceivably un- dergo is of great value to the re- search chemist. H e can thereby determine which of these reac- t io n s a r e thermodynamically feasible and thus avoid the waste of time, effort, and money in- volved in an attempt to carry out impossible processes . More- over, in the case of a reaction which does not go to virtual completion, he can thereby pre- dict the conditions of tempera-

The importance of a knowledge of free energy magnitudes to the industrial research chemist is stressed, and the methods fo r determining fhe free energy changes in reactions incolning the hydrocarbons are briefly gicen.

The work of Research Project 29 of the Ameri- can Petroleum Institute is reviewed. The en- tropy and free energy relationships obtained f o r the four typical classes of hydrocarbons (paraf- fins, olefins, benzenoids, and polymethylenes) are summarized. A f ew examples of the appli- cation of these free energy data to hydrocarbon reactions, both real and hypothetical, are con- sidered.

by the application of Equation 1 to equilibrium data obtained at one or more temperatures. Two n o t e w o r t h y e x a m p l e s of this method are the investi- gation by Pease a n d D u r g a n (13) of the equilibria between e t h a n e , ethylene, and hydro- gen, and the recent investiga- tion by Frey and Huppke (2 ) of the equilibrium dehydrogena- tions of ethane, propane, and the b u t a n e s . However, such studies are necessarily limited t o r e a c t i o n s wh ich a r e not u n d u l y complicated by other side r e a c t i o n s and in wh ich

ture, pressure, and concentra- tion that will produce the most favorable shift of the equilib- rium point, since at any absolute temperature, T, the change in free energy at unit activity, AF", is related to the equi- librium constant by the simple equation:

AF" = - R T h K (1) [The notation of Lewis and Randall (8) will be used throughout

this paper. ]

METHODS OF DETERMINING AF O FOR HYDROCARBOX REACTIONS

Conversely, for reactions involving the hydrocarbons, AF" has been determined experimentally in some instances

r e a d i l y m e a s u r a b l e q u a n - tities of the reacting substances are present under equilib- rium conditions. These requirements apparently preclude the extensive application of this method to hydrocarbon reactions within the near future, although the development of specific catalysts and improvements in the methods of analyzing for relatively small amounts of compounds may eventually lead to its more extensive applicability.

A more generally available method for the experimental evaluation of AF O in reactions pertaining to hydrocarbons involves the utilization of the so-called third law of thermo- dynamics and the fundamental thermodynamic equation:

(2) AF = A H - TAS