An Efficient Method for Correlation of Vapor Pressure of Gaseous Compounds Containing C-H-O

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1 Regula Aticle PHYSICAL CHEMISTRY RESEARCH Published by the Ianian Chemical Society Phys. Chem. Res., Vol. 3, No. 4, , Decembe DOI: /pc An Efficient Method fo Coelation of Vapo Pessue of Gaseous Compounds Containing C-H-O M. Reiszadeh*, E. Sanjai, Z. Jali and M. Saviz Baktash Chemical Engineeing Depatment, Shaheza Banch, Islamic Azad Univesity, Shaheza, Ian (Received 8 May 2015, Accepted 8 August 2015) Pediction of available vapo pessue data in the case of compounds containing C-H-O led to deivations and ecommendations of standad equations fo this popety. The accuacy of vapo pessue estimations is essential to use as a basis to calculate acentic facto, themal and equilibium popeties. In this study, accoding to the pevious wok, an accuate equation to estimate vapo pessue is developed to 130 pue C-H-O compounds as a function of educed tempeatue and citical pessue. With new poposed equation, vapo pessues have been calculated in compaison with expeimental data epoted in liteatue fo 2019 data points of 130 pue C-H-O compounds and the oveall aveage absolute elative deviation is only 0.333%. The accuacy of the developed equation has been compaed to that of Antoine and othe mostly used equations. Ou compaisons show that new equation leads to moe accuate esults than those of liteatue methods. Keywods: Vapo pessue, C-H-O, Pue compounds, Coelation, Antoine INTRODUCTION Reliable liquid vapo pessue pediction is essential to develop equations of state to simulate, evaluate and optimize chemical pocesses. The accuacy of vapo pessue calculations is vey impotant because of using as a basis to calculate acentic facto, themal and equilibium popeties [1]. Authentic vapo pessue data ae impotant in pocess design equipment. Most oil and gas pocessing opeations such as oil efiney equies vapo pessue data fo estimation of phase equilibium. The vapo pessue o equilibium vapo pessue is a good indication of liquid evapoation ate in combustion modeling. In numeical simulations, significant changes in the fuel atomization and evapoation ates lead to change in fuel vapo pessue [2]. Because of absence and limited ange of vapo pessue expeimental data in the liteatue, some eseaches have used diffeent vapo pessue coelations to estimate *Coesponding autho. eiszadeh@iaush.ac.i paametes in equations of state [3-7]. Numeous empiical vapo pessue equations have been published until now. The best known ae those of Wagne [8], Clausius, Antoine, Fost-Kalkwaf, Cox, Gomez- Thodos, Lee-Kesle, Ambose-Walton, Riedel [9,10] and Lemmon-Goodwin [11]. The most common of all vapo pessue coelations is Antoine [12] with thee constant paametes, which is valid only within a limited tempeatue ange. In this wok we extend the pevious equation [13] to 130 pue mostly used C-H-O compounds which ae fomed with only C, H and O elements. Based on this model, a pedictive coelation is developed. The souce of satuated vapo pessue expeimental data used in this study is Ref. [14]. VAPOR PRESSURE CORRELATION MODELS Antoine Coelation The Antoine vapo pessue coelation was modified

2 Reiszadeh et al./phys. Chem. Res., Vol. 3, No. 4, , Decembe based on Clapeyon equation. It is widely used to estimate vapo pessues ove limited tempeatue ange [12]. The Antoine coelation is shown below: B ln P vp A (1) T C whee P vp is the vapo pessue (mmhg), T is the tempeatue ( C) and the constant values of A, B and C fo some species ae pesented in Appendix A in [9]. Lee-Kesle s Method Lee-Kesle equation [9] is one of the successful methods to pedict vapo pessue using six-paamete fomulations. lnp f f (0) vp (0) (1) f ( T ) f ( T ) (2) (3) ln T T T (1) ln T T (4) T Whee P vp is the educed vapo pessue which is equal to P/P c. P c is the citical pessue (pascal), ω is the acentic facto, T is the educed tempeatue which is equal to T/T c, and T c is the citical tempeatue (K) of the fluid. Values fo T c and P c can be found in the liteatue fo many pue substances [10,15]. Ambose-Walton Coesponding States Method Ambose and Walton [10] developed anothe epesentation of the Pitze expansion with an additional tem f (2) (T ). (0) ln ( Pc / ) f ( Tb ) (9) (1) f ( T ) b Whee ω is the acentic facto, P c is the citical pessue (bas) of the fluid, and τ = 1-T. Riedel Coelation Method Riedel [16] poposed a vapo pessue equation in following fom: ln P vp B 6 A C ln T DT (10) T 6 the T tem allows desciption of the inflection point of the vapo pessue cuve in the high-pessue egion. Paametes A, B, C and D ae functions of T, T c, T b and P c. Wagne Equation Wagne [8] used an elaboate statistical method to pesent an equation fo epesenting the vapo pessue behavio of nitogen and agon ove the wide tempeatue ange. The esulting equation is: Psat A B C D ln (11) Pc 1 whee τ = 1 T/T c, P c is the citical pessue and T c is the citical tempeatue. Luis et al. [1] detemined Wagne equation paametes fo 257 substances with low deviations. Howeve, thee ae a few joint substances with the pesent wok fo a coect compaison with Wagne [8] and Luis [1] wok. ln P vp (0) (1) 2 (2) f ( T ) f ( T ) f ( T ) (5) ( 0) f ( 1) f T T (6) (7) ( 2) f T (8) 280 Sanjai Equation Sanjai [13] tied to find a new simple equation fo the vapo pessue of pue substances. It is a fou-constant nonlinea coelation that epoduces vapo-liquid equilibium data with high accuacy even at low educed tempeatues. Sanjai [13] empiical coelation was pesented as follow: ln P vp b 2 a c ln T d T (12) T whee P vp is educed vapo pessue which is equal to P/P c, T = T/T c is the educed tempeatue, and the coefficients a,

3 An Efficient Method fo Coelation of Vapo Pessue of/phys. Chem. Res., Vol. 3, No. 4, , Decembe b, c and d ae constant paametes. DEVELOPED EQUATION This wok ties to develop a new model to estimate vapo pessue of pue C-H-O compounds by the help of vapo pessue expeimental data moe accuate than othe models in tems of educed tempeatue and citical pessue. Thee ae many available data in souces [14] to allow the poposition of a model fo vapo pessue of pue substances. Afte multiple egession analysis, the coefficients A, B, C and D ae constant paametes and thei values fo 130 C-H-O substances ae pesented in Table 1. Also fo moe infomation about obtained constant paametes, (R 2 ) of each substance in fitting pocedue is pesented in Table 1. The obtained equation pesented in this study is: ln P vp A B T C T BT 1.9 (13) Also Table 1 shows the numbe of data points, citical tempeatues, citical pessues, and tempeatue anges of expeimental data fo each substance. RESULT AND DISCUSSION We caied out calculations fo 130 pue C-H-O Table 1. Citical Popeties, Tempeatue Range, and Tuned Coefficients to be Used in Eq. (13) Name Fomula No of data T min T max T c (K) P c (ba) A B C D R 2 1 Methane CH Methanol CH 4O Acetylene C 2H Ketene C 2H 2O Ethylene C 2H Ethylene oxide-1 C 2H 4O Acetic acid C 2H 4O Ethane C 2H Dimethyl ethe C 2H 6O Ethanol C 2H 6O Ethylene glycol C 2H 6O Popyne C 3H Cyclopopane C 3H Popylene C 3H Popen-3-ol C 3H 6O Acetone-1 C 3H 6O Acetone-2 C 3H 6O Popylene oxide C 3H 6O Ethyl fomate C 3H 6O Methyl acetate C 3H 6O Popanoic acid-1 C 3H 6O Popane C 3H

4 Reiszadeh et al./phys. Chem. Res., Vol. 3, No. 4, , Decembe Table 1. Continued 23 1-Popanol C 3H 8O Popanol C 3H 8O Methyl ethyl ethe C 3H 8O Ethyleneglycol monomethyl ethe C 3H 8O Methylal C 3H 8O Glyceol C 3H 8O Methylpopane C 4H Butane C 4H Butanol C 4H 10O Diethyl ethe C 4H 10O Isobuatol C 4H 10O Methyl popyl - 34 C ethe 4H 10O Tet-butanol C 4H 10O Ethoxyethanol C 4H 10O Diethylene glycol C 4H 10O Diacetylene C 4H Diacetylene C 4H Fuan C 4H 4O ,2-Butadiene C 4H ,3-Butadiene C 4H Butyne C 4H Cyclobutene C 4H Vinyl acetate C 4H 6O Acetic anhydide C 4H 6O Butene C 4H Methylpopene C 4H Cis-2-butene C 4H Cyclobutane C 4H Tans-2-butene C 4H Butyaldehyde C 4H 8O Isobutyaldehyde C 4H 8O Methyl ethyl ketone C 4H 8O Tetahydofuane C 4H 8O ,4-Dioxane C 4H 8O Butyic acid C 4H 8O Ethyl acetate C 4H 8O Methyl popionate C 4H 8O

5 An Efficient Method fo Coelation of Vapo Pessue of/phys. Chem. Res., Vol. 3, No. 4, , Decembe Table 1. Continued 60 Popyl fomate C 4H 8O Popyl fomate C 4H 8O Pentene C 5H Methyl-1-butene C 5H Methyl-2-butene C 5H Methyl-1-butene C 5H Cis-2-pentene C 5H Cyclopentane C 5H Tans-2-pentene C 5H Diethyl ketone C 5H 10O Methyl popyl ketone C 5H 10O Butyl fomate C 5H 10O Ethyl popanoate C 5H 10O Popyl acetate C 5H 10O Sec butyl fomate C 5H 10O Iso pentane C 5H Neopentane C 5H Pentane C 5H Pentanol C 5H 12O Pentanol C 5H 12O Ethyl popyl ethe C 5H 12O Methyl butyl ethe C 5H 12O Diethoxymethane C 5H 12O Popyl cellosive C 5H 12O Isopeene C 5H Spiopentane C 5H ,3-Dimethyl-1,3- butadien C 6H Hexyne C 6H Hexene C 6H ,3-Dimethyl-2- butene 3,3-Dimethyl-1- butene C 6H C 6H Cyclohexane-1 C 6H Cyclohexane-2 C 6H Cyclohexanol C 6H 12O Butyl acetate C 6H 12O ,2-Dimethyl butane 2,3-Dimethyl butane C 6H C 6H

6 Reiszadeh et al./phys. Chem. Res., Vol. 3, No. 4, , Decembe Table 1. Continued 96 2-Methyl pentane C 6H Methyl pentane C 6H Hexane C 6H Hexanol C 6H 14O Hexanol C 6H 14O Methyl-1-pentanol C 6H 14O Methyl-4-pentanol C 6H 14O Hexanol C 6H 14O DiIsopopyl ethe C 6H 14O Dipopyle ethe C 6H 14O Ethyl butyl ethe C 6H 14O Benzene C 6H Phenol C 6H 6O Resocinol C 6H 6O Pyogallol C 6H 6O ,1- Dimethylcyclopentane C 7H heptene C 7H Cis-1,2- dimethylcyclopentane Cis-1,3- dimethylcyclopentane C 7H C 7H Cycloheptane C 7H Ethylcyclopentane C 7H Methylcyclohexane C 7H tans-1,2- Dimethylcyclopentane Tans-1,3- dimethylcyclopentane 2,4-Dimethyl-3- pentanone C 7H C 7H C 7H 14O Butyl popanoate C 7H 14O Heptanoic acid C 7H 14O ,2-Dimethylpentane C 7H ,3-Dimethylpentane C 7H ,4-Dimethylpentane C 7H Methylhexane C 7H Ethylpentane C 7H Methylhexane C 7H Heptane C 7H Toluene C 7H

7 An Efficient Method fo Coelation of Vapo Pessue of/phys. Chem. Res., Vol. 3, No. 4, , Decembe compounds. The values of the vapo pessue, tempeatue, citical pessue, citical tempeatue, boiling point, and acentic facto, (used fo calculation of liteatue models) wee taken fom data bank [15]. To compae the accuacy of the pesented empiical model, calculated vapo pessues fo all substances vesus coesponded values of expeimental data ae pesented in Fig. 1. In Table 2, aveage absolute elative deviation (AARD%) of the calculated vapo pessue fom poposed model and liteatue methods fo all 130 substances with espect to the values given by expeimental data ae pesented. It shows that new pesented model is moe Calculated educed vapo pessue Expeimental educed vapo pessue Fig. 1. Accuacy of pesented model vs. expeimental data. Table 2. Aveage Absolute Relative Deviation of Fou Liteatue Equations Compaed to New Method Name Fomula Lee kesle Antoine Ambose Riedel This study Methane CH Methanol CH 4O Acetylene C 2H Ketene C 2H 2O Ethylene C 2H Ethylene oxide-1 C 2H 4O Acetic acid C 2H 4O

8 Reiszadeh et al./phys. Chem. Res., Vol. 3, No. 4, , Decembe Table 2. Continued Ethane C 2H Dimethyl ethe C 2H 6O Ethanol C 2H 6O Ethylene glycol C 2H 6O Popyne C 3H Cyclopopane C 3H Popylene C 3H Popen-3-ol C 3H 6O Acetone C 3H 6O Popylene oxide C 3H 6O Ethyl fomate C 3H 6O Methyl acetate C 3H 6O Popanoic acid-1 C 3H 6O Popane C 3H Popanol C 3H 8O Popanol C 3H 8O Methyl ethyl ethe C 3H 8O Ethyleneglycol monomethyl ethe C 3H 8O 2 Methylal C 3H 8O Glyceol C 3H 8O Methylpopane C 4H Butane C 4H Butanol C 4H 10O Diethyl ethe C 4H 10O Isobuatol C 4H 10O Methyl popyl ethe C 4H 10O tet-butanol C 4H 10O Ethoxyethanol C 4H 10O Diethylene glycol C 4H 10O Diacetylene C 4H Diacetylene C 4H Fuan C 4H 4O ,3-Butadiene C 4H ,3-Butadiene C 4H Butyne C 4H Cyclobutene C 4H Vinyl acetate C 4H 6O Acetic anhydide C 4H 6O Butene C 4H

9 An Efficient Method fo Coelation of Vapo Pessue of/phys. Chem. Res., Vol. 3, No. 4, , Decembe Table 2. Continued 2-Methylpopene C 4H Cis-2-butene C 4H Cyclobutane C 4H Tans-2-butene C 4H Butyaldehyde C 4H 8O Isobutyaldehyde C 4H 8O Methyl ethyl ketone C 4H 8O Tetahydofuane C 4H 8O ,4-Dioxane C 4H 8O Butyic acid C 4H 8O Ethyl acetate C 4H 8O Methyl popionate C 4H 8O Popyl fomate C 4H 8O Pentene C 5H Methyl-1-butene C 5H Methyl-2-butene C 5H Methyl-1-butene C 5H Cis-2-pentene C 5H Cyclopentane C 5H Tans-2-pentene C 5H Diethyl ketone C 5H 10O Methyl popyl ketone C 5H 10O Butyl fomate C 5H 10O Ethyl popanoate C 5H 10O Popyl acetate C 5H 10O Sec butyl fomate C 5H 10O Iso Pentane C 5H Neopentane C 5H Pentane C 5H Pentanol C 5H 12O Pentanol C 5H 12O Ethyl popyl ethe C 5H 12O Methyl butyl ethe C 5H 12O Diethoxymethane C 5H 12O Popyl cellosive C 5H 12O Isopeene C 5H Spiopentane C 5H ,3-Dimethyl-1,3-butadien C 6H Hexyne C 6H

10 Reiszadeh et al./phys. Chem. Res., Vol. 3, No. 4, , Decembe Table 2. Continued 1-Hexene C 6H ,3-Dimethyl-2-butene C 6H ,3-Dimethyl-1-butene C 6H Cyclohexane-1 C 6H Cyclohexane-2 C 6H Cyclohexanol C 6H 12O Butyl acetate C 6H 12O ,2-Dimethyl butane C 6H ,3-Dimethyl butane C 6H Methyl pentane C 6H Methyl pentane C 6H Hexane C 6H Hexanol C 6H 14O Hexanol C 6H 14O Methyl-1-pentanol C 6H 14O Methyl-4-pentanol C 6H 14O Hexanol C 6H 14O DiIsopopyl ethe C 6H 14O Dipopyle ethe C 6H 14O Ethyl butyl ethe C 6H 14O Benzene C 6H Phenol C 6H 6O Resocinol C 6H 6O Pyogallol C 6H 6O ,1-Dimethylcyclopentane C 7H Heptene C 7H Cis-1,2-dimethylcyclopentane C 7H Cis-1,3-dimethylcyclopentane C 7H Cycloheptane C 7H Ethylcyclopentane C 7H Methylcyclohexane C 7H Tans-1,2- dimethylcyclopentane C 7H Tans-1,3- dimethylcyclopentane C 7H ,4-Dimethyl-3-pentanone C 7H 14O Butyl popanoate C 7H 14O Heptanoic acid C 7H 14O ,2-Dimethylpentane C 7H ,3-Dimethylpentane C 7H

11 An Efficient Method fo Coelation of Vapo Pessue of/phys. Chem. Res., Vol. 3, No. 4, , Decembe Table 2. Continued 2,4-Dimethylpentane C 7H Methylhexane C 7H Ethylpentane C 7H Methylhexane C 7H Heptane C 7H Toluene C 7H Table 3. Statistical Paametes of the Poposed Equation Against Othe Methods AARD% RMSD Antoine Ambos-walton Riedel Lee-kesle This study Cumulative fequency This study Antoine 0.2 Lee-Kesle 0.1 Ambos-Walton Riedel AARD% Fig. 2. Cumulative fequency of liteatue and new method as a function of AARD%. 289

12 Reiszadeh et al./phys. Chem. Res., Vol. 3, No. 4, , Decembe accuate than all liteatue methods fo all of the pue substances consideed in this wok. Table 3 pesents the statistical paametes including aveage absolute elative deviation (AARD%) and oot mean squae deviation (RMSD) of the liteatue coelations and new developed equation. Figue 2 shows the cumulative fequency of the poposed model and diffeent liteatue methods vesus aveage absolute elative deviations. Figue 2 also shows the accuacy of all consideed methods in pediction of vapo pessue of 130 substances. As shown in Fig. 2, developed equation is moe accuate than fou commonly used models in vapo pessue pediction. The new method has successfully pedicted 85% of all expeimental data with AARD% less than 0.5, and 96.3% of the data with AARD% less than 2. Only 1% of the vapo pessue data wee pedicted with AARD% of moe than 3 by the new method. Antoine equation, that is the second accuate method, pedicted 73% of the data with AARD (%) less than 0.5, and 86% of the data with AARD (%) less than 1. Hence the supeioity of this new method ove the liteatue coelations has been veified fo all data existing in data bank. CONCLUSIONS In this study, vaious vapo pessue coelations in liteatue and a new developed model ae evaluated and compaed with each othe. It is found that undesiable pedicting deviations ae obtained using the Antoine equation, Lee-Kesle method, Ambose-Walton method, and Riedel Method ove a wide anges of tempeatue. The Antoine method geneally gives good pediction accuacy elative to the othe liteatue models. Fou liteatue nonlinea coelations wee used to estimate the vapo pessue of C-H-O pue substances, being a function of educed tempeatue and citical pessue. To validate the poposed method, the vapo pessues of 130 C-H-O pue substances with moe than 2019 expeimental data points wee examined and an oveall aveage absolute elative deviation of 0.333% was achieved. ACKNOWLEDGEMENTS The suppots of Shaheza banch of Islamic Azad 290 Univesity fo suppoting this wok ae gatefully acknowledged. REFERENCES [1] A. Luis, G. Foeo, A. Joge, J. Velásquez, Wagne Liquid-Vapou Pessue Equation Constants fom a Simple Methodology. J. Chem. Themodynamics 43 (2011) 1235, DOI: /j.jct [2] H. An, W. Yang, A New Genealized Coelation fo Accuate Vapo Pessue Pediction. Chem. Phys. Lett. 543 (2012) 188. DOI: /j.cplett [3] K. Mejbi, A. Bellagi, Coesponding States Coelation fo the Satuated Vapo Pessue of Pue Fluids. Themochimica Acta 436 (2005) 140, DOI: /j.tca [4] J. Lielmezs, K.G. Astley, J.A. McEvoy, New Satuated Vapo Pessue-Tempeatue Relation. Themochimica Acta 52 (1982) 9, DOI: / (82) [5] F.L. Figueia, L. Lugo, C. Olivea-Fuentes, Genealized Paametes of the Styjek-Vea and Gibbons-Laughton Cohesion Functions fo Use with Cubic EOS of the Van De Waals Type. Fluid Phase Equilib. 259 (2007) 105, DOI: /j.fluid [6] L.A. Foeo, J.A. Velásquez, A Method To Estimate the Patel-Teja Equation of State Constants. J. Chem. Eng. Data 55 (2010) 5094, DOI: /je100656d. [7] M. Azna, A. Silva-Telles, J.O. Valdeama, Paametes fo the Attactive Coefficient of the Patel-Teja-valdeama Equation of State. Chem. Eng. Commun. 190 (2003) 1411, DOI: / [8] W. Wagne, New Vapou Pessue Measuements fo Agon and Nitogen and a New Method fo Establishing Rational Vapo Pessue Equations. Cyogenics 13 (1973) 470, DOI: / (73) [9] R.C. Reid, J.M. Pausnitz, B.E. Poling, The Popeties of Gases and Liquids, 4 th ed., McGaw- Hill, [10] B.E. Poling, J.M. Pausnitz, J.P. O Connell, The

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