Watson and Nelson (7) introduced the following boiling point and gravity ratio, t e r m e d the “characterization factor,” aa an indication of the chemical character of a hydrocarbon and as a correlative factor:
where K
= characterization factor = specific gravity a t G O O F. T E = atmosph:rjc b o i 1 i n g point, Rankine
d
This factor is valuable in that it is reasonably constant for chemically similar hydrocarbons. It is useful as a quantitative means for expressing the effect of variation in chemical type and, in conjunction R. L. SMITH AMI) K. M. WATSON with one other property, serves as a basis for correlating properties U n i v e d Oil F’roducts Company, Riverside, Ill. of pure componenL9 of widely varying c h e m i c R 1 types and boiling points. Application of the characterization factor was extended to KOWLEDGE of the critical properties of hydrocarbon mixtures by considering the boiling point of the whole mixmistures, particularly as a function of properties readily ture to be the “molal average boiling point,” which was less determinnble, is of great value for estimating the physithan the volumetric average by a correction which was a cal snd thermal properties necessary for inteligent deeiqn of petroleum refining equipment. Many of these properties are function of the Engler distillation curve slope. It was pointed out that the boiling point so obtained was actually directly correlntable on the basis of the criticaI temperature higher than the true molal average boiling point and was and pressure by r pplication of the theorem of corresponding established in an effort to obtain a single, simple average states. boiling point which would eliminate dependence on width of The most easily determined properties definitive of a hydrocarbon are the specific gravity and the boiling point. Many boiling range from the characterization factor and correlations other properties, such as molecular weight, chemical charof other physical properties. However, more complete dnta acter, cracking reaction velocity constants, hydrogen content and apF.lcation of the principle of additivity of the properties and heats of combustion, are correlatable as functions of these of mixtures indicate that for wide boiling mixtures the Watsimple inspection data. However, petroleum problems alson-Nelson “molal average boiling point” represents an unmost always invoIve m.:stures of great numbers of components satisfactory approximation to the proper variable for corwhich it is usually impracticable to treat separately, even to relation of many properties. the extent of determining individual bailing points and If components of the same chemical character or charncterigravities. I n such cases it 2s custDmary to measure the zation factor, IC, are mixed, the resultant blend should have gravity of the entire mixture and to report the boiling point the same K . From the above definition of K , since d varies in the form of a batch distilla’ion curve. For the higher linearly with volume per cent, ( T ~ ) 1 /must 3 also ~ a linearly q boiling substances, the distillation must be carried out a t with volume per cent. sufficiently lorn tempernturas to avoid decomposition, necessitating prcssures lower than atmospheric and correction to the equivalent atmospheric pressure values by means of where j v l = volume fraction of component 1 in mixture vapor pressure relations. Since the true boiling point distillation is nat yet in general use by the industry, boiling point Thus, the proper boiling point to use for calculation of li is: curves obtained by the A. S . T. M. and h a l e r distillations will be considered in the lollowing discussion and correlations. T s b v . ) lfv*(To)‘’ I fvdTo*)”* * * 1
-
Additive Properties of Mixtures LIany properties of mistures niay be estimated by assuming that the propertics of the individud components are directly d d i t i v e . For example, such properties as the weight or hydrogen content of a mixture are equal to the sums of the corresponding properties of the componenta. Siqilnrly, it mny be satisfactorily assumed that in liquid hydrocarbon mixtures a t atmospheric temperature and pressure the volume of the mixture is equal to the sum of the volumes of the componcnk, neglecting volume changes in mixing. On the basis of these principles of additivity, it is possible to establish conditions which must be met by correlations of various properties that are to be mutually applicable to mixtures and pure components.
+
+ -
4
This boiling point will be termed the “cubic avcrnge boiling point.” For petroleum fractions i t m n y be obtained by subtracting from the volumetric average a correction cspresscd n8 a function of Engler distillation curve slope and volumctric average I~oilingpoint. This correction is prcsc&A grepliicnlly by the scrics of curves in Figure I , dtxignatd ~8 cubic average. If two componeots of diffcrcnt K and thc samc or different i>oilingpointsare mixed,
INDUSTRIAL AND ENGINEERING CHEMISTRY
DECEMBER, 1937
+
or Kdx. = fmKi /wr& where fwi = woight frnction of component 1
(8)
Therefore, the characterization factor, K, when based on the correct cubic average boiling point, is additive with weight fraction in all mixtures where changes in volume with mixing (arenegligible. It may be similarly demonstrated that A. P. I. gravity is also d d i t i v e with weight fraction in all mixtures where volume changes in mixing are negligible: A. P.I.mix. = /mi X A. P. 1,i $- j w ? X A. P. 1.2
+ ... .
(4)
Application of Pure-Component Correlations to Mixtures
If B correlation of any dependent vnrinblc is developed ns a function of two definitive properties, it may be validly applied to both mixtures and pure components only if the average definitive properties or the mixture are so defined that the dependent variable for any mixture is the same as that of a pure component having the Fame definitive properties as the average definitive properties of the mixture. This principle may be used to determine directly the proper average definitive properties for mixtures when pure-component dntn arc available. When only data on mixtures are available, the principle may be applied, by trial-and-error assumptions of average property, to determine the correct average d e finitive property and consequently establish a valid purecomponent correlntion if the range of variation in each misturc is small relative to the total range covered by the correlation. As an npplicntion of the above principle, the correlation of Iuu!cnulnr weight with boiling point and A. P. I. gravity may be ccnsidered. The molecular weight of a mixture is additive with the mole fractions of its components as is nlso
Consideration of the principles of additivity of mixtures shows that, for the application to mixtures of correlations of properties of pure components with ~ p e cific gravity and boiling point, no one type OS average bailing point is suitable for all properties. The following different average boiling points have been developed for application to correlation= of the various physical properties: (a) cubic average boiling point-characteri;cation factor, viscosities; (6)true molal average boiling point-pseudocritical temperature ; (c) mean average boiling point-molecular weight, hydrogen content, heat of combustion, pseudocritical pressure ; (4 weight average boiling point-true critical temperaturee, Using these average boiling points, new correlations of true and pseudocritical temperature and pressure datir, are presented which a m applicable both to pure components and wide boiling mixtures.
1409
its true molal average boiling point. However, if inolecuhr weights of pure components are plotted against boiling points with lines uf confitrtik A. P. I. gravity, i t is found that the molecular weight of a pure component, having an A. 1’. 1. gravity and boiling point the same as the A. P. I. gravity and true molal average boiling point of a mixture, is not the same as the molecular weight of the mixture. Therefore, the true molal average boiling point cannot be the proper definitive property for applying the pure-component correlation to mixtures. Similar consideration shows that the cubic average boiling point is also unsound as a correlating variable. However, an average boiling point which is the arithmetic average of the true molal and cubic averages does form a sound bash for correlntion of molecular weights. This average, which will be termed the “mean avorngc boiling point” of n blend, corresponds to n molecular weight on the pure-component correlation, which is equal to the actunl molecular weight of the mixture. In Figure 1 nre plotted curves for obtaining true niolal avernge boiling points of petroleum fractions from Enyler distillation curve slopes and volumetric average boiling points. Midway between thcse curves and those estnblishing the cubic average boiling point are plotted similar corrections for obtaining the mean average boiling point. When working with mixtures of pure components or narrow cuts, fur which the distillntion curve slope is meaningless, the menn average boiling point is directly calculated as the arithmetic average of the true molal and cubic average boiling points of the components. A similar analysis may bc applied to the published correlation ( 8 ) of hydrogen contcnt with boiling point and specific gravity. Again i t is found thnt the mean average boiling point is the proper dcfinitivc variable for npplicntion of this purc-component correlation to mixtures and that correlntions involving the characterization factor and cubic nverage or true molal average boiling point nre not sound for misttires of wide boiling range. Examination of the mean average boiling point shows i t to approximate closely the original Watson-Nelson “molal average,” which was developed initially for molecular weight correlations. In general, the previously published correlations employing the Watson-h’elson average boiling point are satisfactory for the pure components and relrttively nnrrow cuts for which they were developed, but break down when applied to mistures of extremely wide boiling rnnge, escept where the proper correlating vnrinble is the mean Rvernge boiling point ns defined above. The viscosities of blends of petroleum fractions c n n w t be cnlculatcci by directly additive methods, ns are molecular weights and hydrogen contents. IIowcver, the recornmended A. S. T. hL viscosity blending procedure, togetherwith th‘e unpublished results of a fuel oil blending investigation, hnve been used for predicting empirically the rclntions between the viscosities of components and their blends. These rclntions indicate thnt the cubic average boiling point is the proper vnrinblc for iisc in the correlation of viscosity with grnvity nncl boiling point. Therefore, the published corrcln tioiis between charncterixntion factor and viscosity are sound and indcpcndent of width of boiling rnngc when the chnrnctcrizntioti factor is based on the correct cubic Rvernge boiling point. Irowever, rnensurcmcnt of viscosity nlono pcrniih ~stiiiiiition of only thc cubic nverngo boiling point, and d a h r t w & be avnilnble on the Engler distillntion curve slope to pcrinit cnlcirhtion of either menn or true molal average boiling poinb.
Critical Temperatures Several methods of correlation of the criticnl tcmperatures of pure hydrocnrbons have been proposed, based on evtrapola-
1410
INDUSTRIAL AND ENGINEEII INC CCIEICI1Sl’ll Y
tioils oi iiietisurctiieiits of low-boiling materials togcthcr with exi)erinicntsl dnta on petroleum fractions. In attempting to apply tticsc correlations to mixtures, the problem is coniplictltcti by ttie lnck of Rdditivity of critical properties. It has loxlg L)cen recognizcrl that tlic true critical pressure of a mixture mny be much grwter than the critical prcssure of a pure component having tlic same definitivc properties, and ordinarily is grcnter thnn tlic criticnl prcssure of a11j‘ component present in it. It hns been assuincd, liowcwr, that thc critical temperature of mi.\turc wns the snnic ns that of n pure componetlt of the same gravity, i n conjunction with cithcr c h w nctrrization fnctor, nioleculnr \wight, or molal n\‘cragc boiling point, lIo\revcrJ tlie recctit itivcstigntions of Ilocss (6) tiitlicntc t h t the triic criticnl tciiipcrntuw c$ tlic mixture is n l w higher tlinn tlint of n corrcsponding pure component Iinvitig tlic w i i c grnvity niitl niolcculnr n’ciglit. Trite c*riticd propcrtics of mixtures nrc of pnrticular w l u c i n the cnlculntion uf 1)linsc rclatiotis ntitl viiporizntion cquiIibriritii dntn. IIoivc~.er,for tlic cq~rallyimportiint problerii of t-npor volutiic niid ccnipwssibility cnl) .ilntirinq, it has long bccii rccogtiized that u9c of tlic true criticril properties of a mixtui.c for cnlcrilntiiig ~~crlr~cccl tcmpcrnturw nnci pressures retitlcrs tlir tticorcni of corrcspoiitli--s statcs inttpplicnble. T’tiris the coiiiprcssi1,ility fnctor of n nlisture n t specified rc(luccd conditions is gcnctxlly gi*cntcr than thc corresponding vnlue for n purc cotnponctit n t tlir wine reduccd conclitions. Tility ftictor correlation :IS tlirit of pure conipoiictits. :\]thoiigli tlicrr is no t1icorctic:il ccrtiriiity of the csisteiice of such n point, Iiny provcti its csistencc, within csj)cr.inicntnl accuracy, for those inisturcs t l i n t lie studied; it will be RFsumed that cvery misturc lins a clcfinite pseudocritical point, and it is the sniiic ns tlie criticnl point of n pure componcnt having the same t1cfiiiitii.c pro,,crtics ns sonic type of average definitive proprrtic~(Jf toe mixture. Thc corrclntion prcscntcd by l i r ~ yplots pcudocritical tcrnpeiaturc npinst rnolcculnr IrciKIit for lincs of constant chnrnctcrizntion fnctor, K . 8cscrnI considerations indicate that the estrnpolntccl portion i.: iticoncct, and that K and rriolccukir tvcipht are probnbly not the proper corrclating vnriaLIes. If, HS ICny Pbtetl, pseudocritical tempernture is additive with inolc fraction, his constant K lines must be straight since niolcculnr weiglit is also additive with mole fraction, but tlic plot nctunlly s h o ~ sdeviations from linearity of triorc than 100” F . Also, since it has bccn shown in the foregoing discussion t l i n t Zi is properly :L function of the cubic n n d moieculnr weiKIi t of the riicnn nvcrngc boiling point, it :ippcnrs thnt two different average boiling points hnvc bccn iiscd i n the p~ecutlocriticnltcmpcrnturc corrclntion. Fiirtlicrmore, comLnn t-boiling-point 1 incs tiiroii g h the cxtrapoln tcd portion of I= log tP.
- log pPe
log tP, may be plotted against (tT,/pT,) for various constant values of pP,, the slope of these constant pP, lines may be calculated,
FIQURE 4
from a direct extrapolation of the function as calculated from Roess'data. It may be that the relation between (tPJpP,) and (tT,/ pT,) is not the same for all types of mixtures. The assumption that it is the same is tantamount to any one of the following statements, and verification of any one of these statements would validate the assumption: (a) The compressibility factor must be the same at the true critical point for
VOL. 29, NO. 12
INDUSTRIAL AND ENGINEERING CHEMISTRY
1414
all mixtures with the same value of ( t T c / p T c ) ;(b) the compressibility factor isotherms for the true critical temperature, when plotted against log P, must be exactly similar a t the true critical point for all mixtures with the same value of (tT,/pT,); and ( c ) the true critical temperature isotherms
on the true reduced basis must coincide for all mixtures with the same value of (tT,/pT,). All of these statements seem reasonable. They are similar in nature to the assumption of the theorem of corresponding states and of the existence of pseudocritical properties as defined by Kay.
from the same figure, using the true molal average boiling point. The ratio of these two critical temperatures on a n . absolute scale is then used to obtain (tPc/pPo)from Figure 3. The pseudocritical pressure is read from Figure 4 or 5 and multiplied by this ratio to determine the true critical pres/' sure. The correlations and methods presented here have the advantage over previous correlations of being based on and applicable to both pseudocritical and true critical properties for all widths of boiling range and any type of mixture. The correlation of true critical pressures presented by Roess does not include the limiting case of the pseudocritical and is, in any case, limited only to those mixtures with a uniform distillation curve where slope is significant. Moreover, values read from his correlation deviate rather widely from his experimental values. A tabulation of some representative data, with the corrected distillations of Roess, is presented in Table I, along with comparisons of values given by different correlations. Deviations from all the available experimental data of the various correlations are as follows : --Roeas-Max. Av. 130 126.7
tPo, lk./sq. in. P T O , F. pPo, Ib./sq. in. a
... b
..
...
...
Above butane.
--Kay--Max. Av. 29 36
...
*vi
---AuthorsMax. Av. 94 19.0 15 13.9
110.2
a6.5
{igi]
Below butane.
Pure components are included with the pseudos.
Vapor Pressure Relations
Pseudocritical Pressure
For high-boiling materials the Brown-Coats and all other vapor pressure extrapolations become uncertain and cannot be used with confidence to determine pseudocritical pressure from pseudocritical temperature. Comparison of the pseudocritical pressures of Figure 4 with those estimated from the Brown-Coats chart (2) indicate that the extrapolated pressures are too low for the higher boiling materials a t high temperatures and pressures on the chart. For substances with a characterization factor of about 12.0, critical pressures from Figure 4 agree almost exactly with those of Kay for the highboiling materials. Critical pressures for aromatic substances predicted from Figure 4 are higher than those of Kay in the high-boiling region; they are closer to, but still higher than, those predicted from the Brown-Coats chart. Recently data were obtained (1) on the vapor pressures of n-dodecane from very low pressures to the critical point. These data indicate that the va-aor Dressure lines 150n160nComponent CHI C B H ~ C ~ H P ClHs C8Hs CaHs C4Hs CdHs CdHla C,Hio On the Brown-Coats chart are' straight Or A. P. I. 440 167 213 213 138 145 104 QQ 114 llo horizontal, but should slope first upward a t very s p . gr. o 247 o 473 o 41 0.41 0 526 0 511 0.600 0.613 0.576 0.585 low pressures with increasing pressure and temperature, and then downward to the critical, in I n using Figure 5 , the A. P. I. gravity of a mixture must be agreement with predictions of the present critical pressure calculated as the weight average of these same values for the correlation. components. It may be that Kay's method of using the Literature Cited molal average of the criticals of the pure components, when known, is as satisfactory as any Other for substances lighter (1) Beale and Docksey, J. Inst. Petroleum Tech., 21,860 (1935). than pentane. (2) Brown and Coats, Univ. of Mich., Dept. Eng. Research, Circ. There is some indefinite indication from Roess' data that a t constant (tT,/pT,), (tPc/pPc) may increase somewhat with increasing boiling point. However, in the absence of any definitely invalidating evidence, the single-line relation was used to calculate pseudocritical from Roess' true critical pressures, and the correlation of the former with pure component data and Kay's pseudocritical pressures is presented in Figures 4 and 5 as a function of mean average boiling point and A. P. I. gravity, or molecular weight and A. P. I. gravity for the lighter components. Molecular weight was not used for the higher boiling substances, since such a correlation would depend on another. The three sets of data correlate consistently within themselves and with one another. The correlation for the lighter components was based on the following extrapolated values of A. P. I. and specific gravities a t 60 F. : O
0
Series 2 (1928).
Calculation of Complete Critical Data By means of Figures 1 to 5 the critical prop,ezties, both true and-pseudo, of any mixture are readily calculated. The true molal, m_e_an,and weight average boiling- points and A**' T*-Favity are first determined. The true perature is then read from Figure 2, using the weight average boiling -- - point. The pseudocritical temperature is then read _.*-
I-.
(3) Cummings, Stones, and Volante, IND.ENG.CREM., 25,728 (1933).
(4) Kay, Ibid., 28, 1014 (1936).
E: ;
~
~
~
~
~
~
~
~
~
~
~
n
~ 214 ~ (1934). ~ ~ ~
(7) Watson and Nelson, Ibid.,25, 880 (1933). (8) Watson, Nelson, and Murphy, Ibid., 27, 1460 (1935). R ~ c p , ~ vAugust ~n 10, 1937. Presented before the Division of Petroleum Chemistry a t the 94th Meeting of the American Chemical Society, Rochester. N. Y . , September 6 t o io, 1937.
~
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