SUPERSCRIPTS 9 1
= =
gas state only liquid state only
literature Cited
Allen, G., Gee, G., Wilson, G. J., Polymer 1 (4),456 (1960). IND.ENG. Bagley, E. B., Kelson, T. P., Chen, S-A, Barlow, J. W.) C H l 3 I . F v s D a h I . 9, 93-7 (1970). Beiininga, €I., Scott, R . L., J . C h e ~ nPhys. . 23, 1911 (1955). Blanks, 11. F., Prausnitz, J. &I.,ISD. ENG.CH16RI. FL-ND.W. 3, 1 (1965). Bondi, .4.A , , A.I.Ch.E. J . 8, 610 (1962). Boiidi, A,, “Physical Propertie- of Rlolecular Crystals, Liquids and Glasses,” Wiley, New York, 1968. Roiidi. A. A , . Simkin. I). .J.. A.I.Ch.E. J . 6. 191 11960). Chen,’r\: < I . , ’ j . Chcn;. Eng.‘D& 10, 207 (1666). Eyi,iiig, H., Jhon, 11.S.,“Significant Liquid Structures,’’ Wiley, Xew l o r k , 1969. ~I
Hansen, C. hl., “Three-Dimensional Solubility Parameter and Solvent Diffusion Coefficient,” Danish Technical Press, Copenhagen, 1967. Hildebrand, J. H., Scott, R. L., “Regular Solutions,” PrenticeHall, Englewood Cliffs, N. ,J., 1962a. Hildebrand, J. H., Scott, It. L. , “Regular Solittions,” p. 167, Prentice-Hall, Englewood Cliffs, 3;.J., 1962b. Huisman, JohnYSage, B. H., J . Chem. Eng. Data 9, 233 (1964). Makay, R. A . , Sage, B. H .*, J . Chon. Eno. Data 5 . 21 ilS6O). Moelwyn-Hughes, E. A., “Physical “Chemistry,” Perg:amon Press, London, 1961. Orwoll, R.il., Flory, P. J., J . A m r . Chem. SOP. 89, 6814 (1967). Prigogiiie, I., “JIolecular Theory of Solutions,” with A . Rellemans and T’. RIathot, Chap. XVI, Korth-Holland Publishing Co., Amsterdam, and Interscience, Kew York, 1957. Roberts. J. K.. “Heat and Thermodviiamics.” Rlackie and Son. London aiid‘Glasgow, 1947. TVestwatei, IT.,Fraiitz, I T . IT.,Hildebrand, J. II., Phys. Rev. 31, 13*5(1923). RF,CILIVI:D for review August 1, 1969 ACCEPTEDAugust 28, 1970 I
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N e w Three-Parameter Equation of State Byung-lk l e e and Wayne C. Edmisterl Oklahoma State U~aiversity,Stillwater, Okla. 74074 A new three-parameter empirical equation of state has been developed for hydrocarbons (pure and mixed) in the vapor phase. The parameters are functions of temperature, critical conditions, and acentric factor. An analytical solution for density at a given pressure and temperature i s possible. This new equation i s more accurate than the original and modified forms of the Redlich-Kwong equation and the generalized BenedictWebb-Rubin equation and more easily applied than the latter. It i s recommended for the calculations of fugacities and isothermal changes in the enthalpy of vapor phase mixtures.
E i i i p i i i c a l equations of state are wecl in calculatiiig fugacities as well as deiisitieq, for pure coni1)ounds aiid aiid eiitlid1)ie,~~ niisti~req.The Kedlicli-K~voiig(1949) niid the Ueiiediet-WebbRuhiii (Ikiietlict et al., 1940, 1951) equatioiis are widely used iii swIi therriiodyiianiic calculatioiis! as are niodificatioiis of them (13ai.iier cf ol.> 1966; Ednii,sibilityfactor or (Ieiisity. A dixadvniitage is it.”
(18)
well, in view of the fact that it IVW derived froin :in equation of state and not specific:~llyfor the second viiial coefficient. I11 Table IV culculated comp~es~ibility factors via the proposed and other equatioiii of state are compared with experimentally observed v:ilues of com1)re~aibilityfactors for three methane biiiarie~,tn.o etliane biiixrie., a i d one propaiie binary. The original I3Kli cquatioii n a y ornit ted from ‘l‘able IT’ because 110 q m i f i c roii;t:iiit.s could bc foiuid for n-decaiie vapor. I11 Table 5‘ calculated value?; of the isotlieriiial eiithalpy tliffei,eiice by differelit equatioiis arc coiiipai,ed with experimentally observed values for propaiie~ n-l~eiitaiie, five metliane-1jroljaiie niixtures. and m e iiitrogeii-riiethaiie mixture. 13RK coiistaiiti foi, iiitrogeii are fi,orn Craiii aiid Soniitag (1967). literature Cited
Baiiier, 11. P;., Pigford, I?. L., Schreiiier, N’. C., Proc. , 4 m e r . Pcfrol. Znsf. (Diu. 1it.f.) 46, 244 (19GG). Beiiedict, 11..Webb. G . B.. Itubiii~L. C., J . Chcm. Phiis. ., 8. . 334 (1940):
Evaluations
The proposed equation of state and its derivative expressions are evaluated and compared with other equations in Table:, I through 57. Table I contaiiis the absolute average per ceiit deviations of o u r equation and four other equatioiis of htatc, as referenced, in the prediction of densities for the P-V-T values i l l the tabulations of Canjar and 11miiiiiig (1967), for 13 coniponeiita in the vapor phase. The number of points and the ranges of temperature and pressure are included. ‘These saine five equations of state are compared i l l the predictioiis of the vapor 1)ha.e values of Z , j / P , and AII for five hytlrocarboiiu, also using data from the Canjar and 1Iaiiniiig tabnlatioiis (Table 11). Second virial coefficients from this work-Le., Equation 14-are compared in Table I l l with expeiimeiital values and with calculated value. via two previou.: equations (1IcGlashau aiid Potter, 1962; Pitzer and Curl, 1957) for five hydrocarbons. Our equation for B agrees very
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Benedict, 11.,Webb, ( + .E., 1~ubinj1,. C., Frietid, I,., C h c ~ , Eng. . Progi.. 47, 419, 440, 571, GO9 (1951). Brydoii, J. W., Waleii, S . , Cniijar, L. N.,Chcm. Eng. Progr. ~S’ymp.Scr. 49, 151 (lX13). Canjar, L. N., lIaiitiiiig, F. S.,“Thermochemical Propcrtiw aiid Iteduced Correlatioiis for Gase?,’’ (itilf P\it)li-hitig Co., TIouiton, Tex., 1967. Crain, 11. W.,Jr., S(Jiiiit:l& 13. E., J . Chct,L. Eng. Daia 12, 73 (1967).
11c(;la~haii,11. L., Potter, I ) . J . B,, I’roc. IL)o!J. SOC.(I,ontlo,z) A 267, 478 (196%). lfather, A. E., Ph.1). theyis, Uiiiversitq of lIichig:iii, 1067. Pitzer, K. S,j Ciirl, Jr., 11. F.,J . .lvwr. Chcm. SOC.79, 2:3G!l (1957). Reamer. IT. 11.. Olds. I?. 11.. S:tee. B. IT.. 1,acey. W. T.. fnd.Em. Reamer, II.’€I.,~Skge,6. TI., J . C h o n . Eng. Data 5 , 44 (1060). Reamer, 11. H., Sage, B. IT., J . Choti. Eng. Doln 7, 101 (19W). Reamer, H. €I., Sage, 13. ]I., J . C h t v ~Eng. . Du/u 11, 17 (1966). Iteartier, 11. H., Sage, U. I I . , Laces, IV. K., Zntl. Eng. ( ~ ’ h ( t n42, . 3S4 (19,X).
Itedlich, 0.)Kwoiig, J . X , S., Chc,,z. Ilcv. 44, %3:3 (1949). Sage. B. €1.. Reamer. 11. IT.. Old*. 11. I I . , Lace\, iV. S . .Zni1. Enu.
Ind. Eng. Chem. Fundam., Vol. 10, No. 1, 1971
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