Yamada&Gunn-RackettEquation

8/6/2019 Yamada&Gunn-RackettEquation

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ava i lab le method. Prev ious ly the authors have shown thatfor pred ic t ing the satura ted l iqu id dens i ty o f pure com-pounds the Racket t equat ion is accura te , s imple , andversat i le ( 3 7 ) . The extension of th is cor re la t ion tomixtures shou ld prove usefu l in numero us app l ica t ions.For t he sys tems of Tables I l l and I V Harmen 's me thodfor predict ing bubble-point densit ies is essent ial ly equiva-l en t i n accu racy to Equat ion 10. In o rde r to mainta in th isaccu racy , howeve r , bo th Ha rmen 's me thod and the p ro -posed me thod requ i re one emp i r i ca l cons tan t ( C for theme thod of Harmens and Z R A for Equation IO). One con -t ras t in the iwo metho ds is the range o f compo unds fo rwh ich they can be app l i ed . Whereas H a rmens ' me thodwas deve loped main ly fo r hydrocarbons in the C1-C7range , t he mod i f i ed Racke t t equa t i on has been shown tobe re l i ab le fo r heav ie r hyd roca rbons , o rgan ic compounds ,and inorgan ic compounds (37).NomenclatureK = corre la t ing param eter of Lu char tN = numb er o f data po in tsPc = c r i t i ca l p ressu re , a tmP r = reduced p ressu re , P / P cR = un ive rsal gas cons tan t , 82 .06 a tm cm 3 / g mo l KT = t empera tu re , KT c = c r i t i ca l t empera tu re , KT c m = pseudoc r i t i ca l t empera tu re of mix tu re , KT r = reduced tempera tu re , T / T c mV b p = bubb le -poin t vo lume , cm 3 / g mo lV c m = pseudoc r i t i ca l vo lume o f m ix tu re , cm 3 / g mo lV s = vo lume o f sa tu ra ted l i quid , cm 3 / g mo lZc = cr i t i ca l compress ib i l i ty fac torZcm = cr i t i ca l compre ss ib i l i ty fac tor fo r mix tu reZ R A = cons tan t o f mo d i f i ed Racke t t equa t i onGreek Let terspbp = bubble-po in t dens i ty , g mol /cm3p c = c r i t i ca l dens i t y , g m o l / cm 3

P r = reduce d dens i ty , p / p cP S = satura ted l iqu id dens i ty , g mo l /c m 3Literature Cited

Amer ican Petro leum Inst i tu te , "Techn ical Data Book, Petro leum Re-f in ing ," 2nd ed. Amer ican Petro leum Inst i tu te , Wash ington, D.C..Chueh, P. L . , Prausn i tz , J . M .. A lChE J.. 13, 099 (1967) .Guggenhe im, E. A., "Thermodynamics." 2nd ed., p. 168, Inter-sc ience. New York, N.Y. . 1949.Gunn, R. D., Chueh. P . L . , Prausn i tz. J . M., A IChE J . , 12, 937( 1 9 6 6 ) .Harmens, A . . Chem. Eng. Sc i . . 20,813-22 (1965)Ha rme n s , A . , ibid. , 21, 725 (1966).Kay. W. B., In d. Eng. Chem., 30, 59 (1938) .Kay, W . B.,b id . . 32, 53 (1940) .Kay, W. B. , ib id.. 33, 90 (1941) .Kay, W. 3.. ibid.. 40 , 1459 (1948)Kay, W. B. , J . Chem. Eng. Data. 1 5 , 46 ( 1 9 7 0 ) .Kay. W. 6.. Albert. R. E ., Ind. Eng. Chem. 48 , 422 (1956) .Kay, W. B. , B ier le in . J . A , , ib id . , 45 , 618 (1953) .Kay, W. B. , Br ice , D . B., bid., 45 , 615 (1953) .Kay, W. 8.. evens, T. D., Chem. Eng. Progr. Symp. Ser. No . 3,48 , 108 (1952) .Kay. W. B ., Rambosek. G. M., Ind. Eng. Chem.. 45 , 221 (1953) .Li. C. C., Can. J . Chem. Eng., 19 , 709 (1971).Lu . B . C.-Y. , Chem. Eng., 6 6 ( 9 ) . 1 3 7 ( 1 9 5 9 ) .Nicho ls, W. B. , Ream er , H. H. . S ag e . 8 . H .. A lCh E J . . 3, 26 2

1971.

119571,.Phillips, E. M . , Thodos. G., b id . . 7 , 413 (1961) .Racket t . H. G..J . Chem. Eng. Data , 1 6 , 308 (1971) .Rea. H . R. . SDencer. C. F., Danner , R. P . . b i d . , 1 8 (2 ) , 227 (1973)Reamer . H. H . , Sage, 8. H.. ib id . . 7 , 161 (1962) .Reamer , H. H.. Sage, B . H. . b id . , 8 , 508 (1963) .Re a me r , H . H.. Sage, E. H .. bid.. 11, 17 (1966) .Reamer , H. H . , Sage, B. H., Lacey. W. N.. ;b id . , 1, 29 (1956) .Ritter. R . B. . Leno i r , J . M.. Schweppe. J . L . , Petro l . Ref iner , 37(111, 225 (1 958) .Sage, B . H. . Lace y. W. N. . Monograph fo r API Research Pro jectNo. 37, "Some Properties of the Lighter Hydrocarbons , HydrogenSul f ide and Carbon Diox ide ." Amer ican Petro leum Inst i tu te , Wash-ing ton, D.C., 1955.(29) Sage, B. H. , L a ce y , W. N.. Monograph fo r APi Re search Pro jectN o. 37, "Thermodyna mic Properties of the Lighter Paraffin Hydro-carbons and Nitrogen," American Petroleum Insti tute, Washington,D.C.. 1950.(30) Sage, B . H. , Reamer , H. H. , J . Chem. Eng. Data , 9 , 26 (1964) .(31) Spencer , C. F . . Danner . R. P . , bid., 17, 36 (1972) .Rece ived fo r rev iew June 7, 1972. Accepted January 13, 1973. Worksponsored by the Ame rican Petroleum Insti tute. Division of Refining.

Saturated Liquid Molar Volumes.TheRackett EquationTomoyoshi Yamada and Robert D. Gunn'Chemical Engineer ing, Univers i ty of Wyomi ng , La r am i e , Wyo . 82070A slightly modified form of the generalized Rackettequation is p resented which improves its predictiveaccuracy by about an order of magnitude.

Racket t (7 ) recent ly proposed an unusua l ly s implegenera l ized equat ion for pre d ic t ing l iqu id vo lume s. Theaccura cy o f th is equa t ion, howe ver , is on ly mod erate .Spence r and Danne r ( 9 ) found average dev ia t ions o f2 .40% be tween ca l cu la ted and expe r imen ta l l iqu id vo l -umes. These la t te r invest iga tors have a lso modi f ied th isequat ion to pred ic t l iqu id vo lumes wi th h igh accuracy,but the modi f ied re la t ionsh ip is no longer ent i re ly genera l -ized because i t requ i res one curve f i t ted constant fo re a c h p u r e c o m p o u n d . A genera l ized form of t he Racke t tequat ion is proposed here which is also very accura te .

'To whom correspondence should be addressed

v = V s c r Z c r ( 1 - T R ) 2 / -where

Zc r = 0.29056 - 0.08775 wand where Vscr is def ined asVs c r '= V ' exp [ - (1 - T ' R ) " ' In (0.29056 -

0 .08775 o)] 2 )The or ig ina l Rack et t equat ion used the cr i t i ca l vo lumeand the cr i t i ca l compre ss ib i l i ty fac tor as parame ters .Bo th a re sub jec t to l a rge expe r imen ta l e r ro rs wh i ch ham-per ser ious ly the pred ic t ive accu rac y o f the Racket tequat ion. The proposed re la t ionsh ip c i rcumvents thesep rob lems .One l iqu id dens i ty is requ i red to ca lcu la te the sca l ingvo lume , V s c r , but th is is not a shor tcoming for a gene ra l -ized relat ionship. For eve ry compound for wh ich c r i t i ca lvo lumes have been determined l iqu id molar vo lumes are

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s im i l a r l y ava i l ab le . Fo r a number o f compounds , how-eve r , t he c r i t i ca l t empera tu re and a t l eas t one l i qu id den -s i ty have been me asu red expe r imen ta l l y , bu t no t t he c r i t i -c a l v o l u m e .In ca l cu la t i ng the sca l i ng vo lume , T ' R shou ld be cho -sen in a reg ion in wh ich l iqu id dens i ty is kno wn wi th theg rea tes t accu racy . Th i s t empera tu re w i l l o f t en be a t t heno rm al bo i l ing po in t or in the range o f 20-25C. Fre-quent ly , there w i l l be a number o f measurements by d i f -f e ren t i nves t i ga to rs at t hese tempe ra tu res , and the abso -l u te accu racy o f t hese mea su remen ts ca n be es t ima ted .These cons ide ra t i ons a re impo r tan t because the p red i c -t ive capab i l i ty o f Equat ion 1 is d i rec t l y p ropo r t i ona l to th ea c c u r a c y o f V s c r , I f h igh p rec i s i on da ta a re ava i l ab le overa w ide range o f t empera tu re , a l eas t squa res f i t t i ng p ro -c e d u r e m a y b e u s e d to ca l cu la te V s c r ; and th is has beendone i n t he p resen t case . For th is purpose the tabu la t iono f c r i t i ca l cons tan ts by Kudchadke r e t a l . ( 4 ) has beenused fo r c r i t i ca l t empera tu res . Because Equa t i on 1 i sve ry accu ra te , t he va lue o f VScr mus t be cons i s ten t w i thTc . T h u s e a c h t i m e n e w r e c o m m e n d e d v a lu e s fo r t h ec r i t i ca l t empera tu re a re comp i l ed , new va lues fo r V s c rm u s t also be ca l cu la ted f rom Equa t ion 2 .Equat ion 1 has been tes ted w i th t he i den t i ca l da ta se temp loyed by the au tho rs in a p rev ious i nves t i ga t i on (2).For 26 nonpo la r compoun ds the ave rage abso lu te dev ia -

t ion be tween ca l cu la ted and expe r imen ta l l i qu id vo lumesi s 0 .286 %. Th is com pare s w i th an ave rage dev ia t ion o f0 .206% fo r t he same da ta se t f o r t he co r re la t ion p resen t -ed prev ious ly (2). ab le I shows the compar i son fo r t heind i v i dua l compounds . To tes t t he two co r re la t i ons on acomparab le bas i s , i den t i ca l f i t t i ng p rocedu res we readopted. O pt imized va lues of V s c r were used in Equat ion1 ; and , t he re fo re , op t im ized Vsc va lues were used in theco r re la t i on o f Gunn and Yamada (2). This opt imizat ionreduced the ave rage dev ia t ion f rom 0 .22% repo r ted i nthe or ig ina l re ference to 0 .206% repo r ted he re . Obv ious -ly , the Vsc va lues employed here are s l igh t ly d i f fe rentthan those or ig ina l ly repor ted and both sets are s l igh t lyd i f fe rent than the V s c r va lues . I t is emphas i zed , howeve r ,that the var ia t ions between a l l th ree sets o f Vsc,a r e c o n -s iderab ly less than that normal ly encountered betweenexpe r imen ta l c r i t i ca l vo lume measu remen ts by d i f f e ren tinvest igators.Th is invest iga t ion shows that the cor re la t ion o f Gunna n d Y a m a d a ( 2 ) has average dev ia t ions about 25% lowerthan Equa t i on 1. Th is conc lus ion may be m is lead ing ,howeve r , because bo th co r re la t i ons p robab l y a re w i th inexpe r imen ta l accu racy . The abso lu te d i f f e rence i n dev ia -t ions for the two cor re la t ions is on ly 0 .08%, and there iscons iderab le quest ion as to how m eaning fu l th is d i f fe r -en ce is . Even for a com poun d as w ide ly s tud ied as

Table I. Deviations Between C alculated and Expe rimental Saturated Liquid VolumesVo i YOdeviation

Reduced NO . Of G u n n -Y a ma d a 1 2) This work Eq . 1t e mp . r a n g e , data V s c r , Da taCompound "C po in ts Av. Max. Av. Max. cc/ mo l sourceArgonNitrogenCarbon monoxideCarbon dioxideMethanePropanelsobutanen-Pentanen-Hexane2,3-Dimethyl butanen-Heptane2,2,3-Trimethylbutanen-OctaneCyclohexaneEthyleneBenzeneTolueneo-XyleneEthylbenzeneChlorobenzeneBromobenzeneMethanolaEthanola1-Propanol"Ethyl etherAcetic acid"Methyl formateaEthyl acetateMethyl butyrateAcetoneAcetonitri le"Ethyl mercaptan

0.56 to 1.O0.50 to 0.950.51 to 1.O0.86 to 1 .00.47 to 0.970.22 to 0.990.74 to 0.980.291 to 1.00.56 to 0.950.55 to 0.970.34 to 0.990.53 to 0.570.48 to 0.940.52 to 0.680.45 to 0.990.49 to 0.990.56 to 0.670.54 to 0.610.29 to 0.650.36 to 0.860.56 to 0.810.53 to 0.980.53 to 0.990.66 to 0.990.32 to 0.990.46 to 0.980.56 to 0.990.36 to 0.980.56 to 0.990.56 to 0.640.89 to 0.980.55 to 0.99

27142692040555212265327814304526341824

251937342236255616

0.320.200.380.330.400.180.430.180.1 70.340.170.020.180.160.380.240.040.050.090.080.091.921.810.710.100.670.390.220.210.062.800.32

1.400.561.081.071.770.600.651.030.370.660.810.020.640.401.910.690.060.070.330.420.353.844.241.900.471.421.211.310.650.114.530.75

0.730.180.350.400.330.240.410.270.320.450.310.010.440.150.380.180.030.060.290.170.1 12.672.681.370.211.110.300.200.280.032.520.19

2.810.370.882.340.880.900.720.860.711.011.040.020.770.272.440.860.050.100.620.300.226.205.493.260.532.161.700.490.470.074.370.43

75.7489.9591.9493.7899.53199.53256.44310.87367.50359.26429.08412.97490.22309.42130.77255.92314.53367.58369.34305.38320.47118.36173.55224.24281.27175.77169.92284.35338.65208.40159.24202.28

Gran d av. dev 592 0.206compon ents no t inc luded in over -a l l average deviat ion . Cr i t i ca ltempera tures taken from K u d ch a d ke r e t al . (4). Cr i t ica l tempera turesused for argon and nitrog en are 150.72an d 1 2 6 . 2 K , respect ive ly (3 ) .

0.75 0.286 0.86

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argon, the h igh ly regarded exper imenta l repor t o f Miche lset al . ( 5 ) gives a satura ted l iqu id molar vo lume of 37.49at 130.03K. The co mpi la t ion o f argon data by D in ( 7 )recommends a va lue o f 37.20 a t the same cond i t ions .Th is represents a var ia tion o f 0 .77% in exper imenta lmeas ureme nts for argon.Spence r and Danne r (9) epor t an average dev ia t ion o f0 .38 % for the i r nongenera l ized m odi f ica t ion o f the Rack-ett equat ion. This result is no t comparab le to that givenhere, because these authors used a d i f fe rent and morecomple te data set . Exper imenta l e r ror is probably higheralso in their data set than in the careful ly selected andl im i ted da ta used he re .H igh accuracy is ach ieved wi th the Racket t equat ionpr imar i ly th rough the use o f the sca l ing vo lume. V sc isbased on a l iqu id dens i ty wh ich is usua l ly known to within0.25%. Cr i t ica l vo lumes are f requent ly in er ror by severa lpe rcen t , and even the g roup R T c / P c wil l f requently vary 1to 2% between d i f fe rent exper imenta l invest iga tors , p r i -mar i ly because o f the var iab i l i ty in the cr i t i ca l pressuremeasu remen ts .Com pared wi th a nongenera l ized equat ion, a genera l -ized re la tionsh ip such as E quat ion 1 has three advan-tages. The on ly parameters requ i red, Tc , w , and V s c r , a rethose used to pred ic t any o f the conf igura t iona l thermo-dynamic proper t ies ; and no add i t iona l parameter is re-qu i red spec i f ica l ly to ca lcu la te l iqu id vo lumes. The sca l -ing vo lume, def ined by Equat ion 2 , is mo re accura te thanthe cr i t i ca l vo lume for pred ic t ing both l iqu id phase andgas phase proper t ies ( 7 7 ) . I f fo r a par t icu lar compo*undthe cr i t i ca l constants are unknown, then accura te dens i tymeasurements in con junct ion w i th Equat ion 1 may beused to make good es t ima tes o f t he c r i t i ca l pa rame te rs( 2 ) .Fina l ly , var ious co r re la t ions for the cr i t i ca l compre ss-ib i li ty fac tor are c ompa red:[Fro m Equat ion 11 Zc = 0.29056 - 0.08775 w (3 )[Gunn and Yamada ( 2 ) ] (4 )(5 )Because o f the la rge exper imenta l e r rors in repor tedvalues of Z c , i t does not appear poss ib le a t th is t ime to

*

Zc = 0.2920 - 0 .0967 wZc = 0.291 - .0 8 wPitzer et al . ( 6 ) ]

determine which o f the three equat ions above is moreaccu ra te .The results of this invest igat ion in dica te that the corr e-la t ion o f Gunn and Yam ada ( 2 ) i s more accu ra te thanEquat ion 1 , a mod i f ied Racket t equation, for pred ic t ingsatura ted l iqu id vo lumes. The d i f fe rence is smal l , how-ever . Equat ion l s very s imple and, there fore , h igh ly rec-o m m e n d e d .NomenclatureR = g a s c o n s t a n tPc = c r i t i ca l p ressu reT c = c r i t i ca l t empera tu reTR = reduced temperature , T / T cT ' R = reduced tempera tu re i n reg ion o f max imum ac -V = l iqu id molar vo lumeV' = exper imenta l l iqu id molar vo lume used to define

V s c r (measu red a t T ' R )V s c = sca l ing vo lume, def ined by Gunn and Yamada ( 2 )Vscr = sca l ing vo lume, def ine d by Equat ion 2Zc = cr i t i ca l com press ib i l i ty fac tor

Zcr = cr i t i ca l compre ss ib i l i ty fac tor fo r the Racke t t

curacy for l iqu id dens i ty measurem ents

equationw = acentr ic factor, def ined by Pitzer et al . (6)Literature Cited(1 ) D in, F . , "Thermodynamic Funct ions of Gases," But terwor ths . Lon-don, 1959.( 2 ) Gunn , R. D . , Yamada , T . ,A /C hEJ . , 17 , 1341 ( 1971 ) .( 3 ) Kobe , K. A,, Lynn, R. E. Chem. Rev. , 5 2 , 117 ( 1953 ) .( 4 ) Kudc hadk e r , A. P., Alani , E. H., Zwol insk i , 8 . J . , i b id . , 68 , 54 9( 1968) .( 5 ) M i c he l s , A , , Level t , J . M . , de Graaf f , W. , Physica, 2 4 , 659 ( 1958 ) .(6 ) Pitzer, K . S., L ippman, D. Z., ur l , R. F., r . , Huggins , C . M. , Peter -sen, D . E. , J . Amer . C hem. Soc., 77 , 3433 ( 1955 ) .( 7 ) R ac k e t t , H . G ., J. Chem. Eng. Data, 15 , 514 ( 1970 )(8) Ross in i , F . D . , "Selec ted Va lues of Phys ica l and ThermodynamicProper t ies of Hydrocarbons and Related Compounds," CarnegiePress, P i t tsburgh, Pa . . 1953.(9) Spencer , C . F . , Danner . R. P. . J . Chem. Eng. Data, 1 7 , 236 ( 1972 ) .(10) T immerm ans, J . , "Phys ico-chemical Constants of Pure OrganicCompounds," E lsevier, New Yo rK, 1950.(11) Yamada, T .. A l C h E J . , i n press , 1973.( 12 ) Young , S ., Sci. Proc . Roy . Dubl in Soc., 12 , 374 (1909-1910)

Received for rev iew July 27, 1972. Accepted January 3, 1973.

23 6 Journal of Chemical and Engineering Data, Vol. 18, No. , 1973

Yamada&Gunn-RackettEquation

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