INTRODUCTION

Thermodynamic properties of substancesare vital in process and design calculations. One ofthe most important pure component propertiesneeded in design calculations is the vapor pressureof pure substances, which is not availableexperimentally for a wide range of materials. Anumber of correlations are available in literature toestimate vapor pressure among which those thatare based on group contribution methods can beused as predictive tools1-3.

Nowadays, the DIPPR, DDB, PPDS4 databanks provide a large amount of experimental dataand correlations for estimating vapor pressure ofpure compounds.

Even though, these data banks contains

ORIENTAL JOURNAL OF CHEMISTRY

www.orientjchem.org

ISSN: 0970-020 XCODEN: OJCHEG

2011, Vol. 27, No. (4):Pg. 1331-1335

Est. 1984

An International Open Free Access, Peer Reviewed Research Journal

Vapor Pressure Prediction Using Group Contribution Method

AZAM MARJANI*, MASHALLAH REZAKAZEMI and SAEED SHIRAZIAN

Islamic Azad University, Arak Branch, Department of Chemistry, Arak, Iran*Corresponding author: a-marjani@iau-arak.ac.ir

(Received: July 25, 2011; Accepted: September 04, 2011)

ABSTRACT

A group contribution method was developed for prediction of pure hydrocarbon vapor pressurein the reduced temperature range from 0.45 up to near critical point (0.95 Tc). Experimental vaporpressure data of totally 456 hydrocarbon compounds were collected and used to obtain modelparameters. The developed model employs the combinatorial and the residual UNIFAC terms andfugacity of pure hydrocarbons. The proposed modified model is incomparable accuracy to existingsimilar models that shows an excellent agreement between estimated and experimental data.

Keywords: Vapor pressure; Group contribution; UNIFAC;Pure organic compound; Molecular structure.

thermodynamics properties, such as vapor pressurefor more than 6000 compounds, many substancesare not stable at high temperatures and decomposedue to temperature rise; it is not possible to obtaintheir vapor pressure experimentally and as a result,it is impossible to obtain a correlation for predictingtheir properties like vapor pressure based onexperimental data. This is the reason why groupcontribution methods based on UNIFAC groupshave found great interest in the recent decades.Without having all detailed knowledge of componentphysical properties, the methods can be capable topredict properties. Among these methods is themethod proposed by Fredenslund et al. in 1975 [3].They developed a procedure to estimate the excessGibbs free energy of the solution by decomposingthe component into a set of its characteristic groups(group contribution technique); and then, the non-ideality of the component due to the differences in

1332 MARJANI et al., Orient. J. Chem., Vol. 27(4), 1331-1335 (2011)

the sizes and shapes of component groups, ascompared to the other components in the mixtureis estimated. The residual contribution also iscalculated.

In group contribution method based onUNIFAC groups, the compound is broken down intoconstituent groups which follows the assumption thatvapor pressure is determined by group–groupinteraction parameters, then interaction parametersis used for prediction of vapor pressure of interestcompound.

However, some researchers haveproposed correlations for estimation of purecompound vapor pressure. In this work, a correlationbased on UNIFAC groups using group contributionmethod is developed in which, the focus is on theestimation of vapor pressures in wide – pressureregion.

Theory

Fredenslund and Rasmussen4 haveintroduced a group contribution method based onUNIFAC groups for the prediction of vapor pressureof pure organic compounds by relating UNIFACmolar Gibbs free energy differences to the vaporpressure. In their proposed method the vaporpressure of component i ( ) is obtained from Eq.1.

...(1)

where R is the universal gas constant, T isthe temperature, is the number of groups oftype k in molecule i, is the fugacity coefficient ofmolecule i at vapor liquid equilibrium and N is thetotal number of groups. is the contribution ofgibbs energy due to group k and is the activitycoefficient of group k in molecule i. Based on themethod of Fredenslund is obtained from Eq. 2.The first term on the right hand side of Eq. 2 isrelated to temperature and the second term isrelated to the configuration.

...(2)

The best temperature dependency for is obtainedby Fredenslund is introduced by Eq. 3.

...(3)

is a week function of temperature

[4] and is a function of the structure of the moleculefrom the view point of the presence of differentgroups, the number of carbon atoms in the largestring and the location of the branches in a molecule.Fredenslund and Rasmussen have proposed adifferent correlation for each group. The correlationsare linear functions of temperature for some groups.In this work, a new procedure for obtaining thedependence of is introduced.

...(4)

The second term of Eq. 1 is the residualcontribution, which is calculated by UNIFAC methodas below:

...(5)

...(6)

...(7)

In Eqs. 5-7 Q is the constant representingthe group surface, is the summation of the areafraction of group m in molecule i, is the groupinteraction parameter and is a measure of theinteraction energy between groups and is energeticinteraction between group m and n.

1333MARJANI et al., Orient. J. Chem., Vol. 27(4), 1331-1335 (2011)Ta

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1334 MARJANI et al., Orient. J. Chem., Vol. 27(4), 1331-1335 (2011)

Optimization of the parameters of the modelTo optimize the parameters of the model

the Root Mean Square Deviation (RMSD) of therelative error in predicting the vapor pressure of 456number of pure compounds have been minimized.The RMSD is defined by Eq.15. Subscripts i and jstand for the number of pure compounds andnumber of experimental data points for eachcompound, respectively.

...(8)

The range of reduced temperature hasbeen chosen to be 0.45-0.95 with 0.1 intervals. Themaximum pressure for the correlation is 35 atm,which is higher than the maximum pressure of whichis 3 atm.

The minimum value produced byoptimization depends on the initial guess. For othergroups, initial guess is chosen randomly. In orderto provide confidence that obtained minimum valueis the true global minimum of the optimization, allgroups is again optimized by initial random guesses.The fitting function was minimized using “Nedler-Mead simplex direct search” algorithm. This is adirect search method that does not use numericalor analytic gradients. On the other hands, thealgorithm find minimum of unconstrainedmultivariable function using derivative-free method.

RESULTS AND DISCUSSION

Based on the criteria proposed by Marrero,a comprehensive set of first-order groups basedon UNIFAC groups has been defined. The mostimportant issue in determining first-order groups isthat atom of the molecule should not be included inmore than one group groups. On the other hands,no group should not be overlapped to any other

first-order group. The contributions from first-ordergroups that construct a wide variety of hydrocarboncompounds including aliphatic, aromatic,heterocyclic, cycloaliphatic and many other differentclasses of hydrocarbon compounds are introducedin Table 1.

First, the Gibbs free energy withoutconsidering the molecular structure is obtained. Inthis one, the Gibbs free energy is only function oftemperature. After that, besides to the temperatureconsequence, effect of molecular structure isconsidered.

As it is observed, the error is reducedwhich is attr ibuted to using PR EOS, thecombinatorial term for the groups and fugacitycoefficient. Optimization is performed respectivelybased on our No. in Table 1.

CONCLUSIONS

In this study, group contribution methodbased on UNIFAC groups has been developed forprediction of pure hydrocarbon vapor pressure asfunction of temperature and molecular structure.The method requires knowledge of only themolecular structure.

According to the result presented, theproposed method yielded results that compared toexisting similar models, is more accurate inpredicting the vapor pressure of pure hydrocarboncompound when the effect of material structure tobe considered. The method finds most usefulapplication in the wide-pressure region. Equationsrelated to the gas - liquid equilibrium with regard tomolecular structure of compounds was developed.Considering molecular structure of compound wasincreased model accuracy and decreased error lessthan 15 percent. It is worth noting that in previoussimilar models due to withdraw from theseparameters, vapor pressure prediction errorsignificantly is higher than the present model.

1335MARJANI et al., Orient. J. Chem., Vol. 27(4), 1331-1335 (2011)

1. C. Crampon, L. Trassy, L. Avaullée, E. Neau,L. Coniglio, Simplification and extension ofa predictive group contribution method forestimating heavy organic pure compoundvapor pressures: I. Hydrocarbons, FluidPhase Equilibria, 216: 95-109 (2004).

2. P. Li, P.-S. Ma, S.-Z. Yi, Z.-G. Zhao, L.-Z. Cong,A new Corresponding-States Group-

Contribution method (CSGC) for estimatingvapor pressures of pure compounds, FluidPhase Equilibria, 101: 101-119 (1994).

3. C.-H. Tu, Group-contribution method for theestimation of vapor pressures, Fluid PhaseEquilibria, 99: 105-120 (1994).

4. DIPPR 801 project data, in: Design Institutefor Physical Property Data, AIChE (1995).

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