01 - Eq. Fases Ol Essen

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Fl uid Phme Equil ibri a, 59 (1990) 135-145Elsevier Science Publishers B.V., Amsterdam 135

PH SE EQUILIBRI OF ESSENTI L OIL COMPONENTSND SUPERCRITIC L C RBON DIOXIDE

VINCENZO BRANDANI, GIOVANNI DEL RE, GABRIELE DI GIACOMOand VITTORIA MUCC IANTEDipartimento di Chimi ca, Ingegneri a Chimi ca e Materi ali, Uni versitri de L Aquil a,Z-67040 Monteluco di Roio, L Aquil a I tab)(Received June 18, 1989; accepted in final form M arch 8; 1990)

ABSTRACT

Brandani, V., Del Re, G., Di Giacomo, G. and M ucciante, V., 1990. Phase equilibria ofessential oil components and supercritical carbon dioxide. Fluid Phase Equil ibri a, 59:135-145.The solubility of pure essential oil comp onents and their binary mixture s in supercritica l

carbon dioxide was correlated using an equation of state with density-dependent mixingrules. This equation was then used to predict the phase diagram of the two binary carbondioxide-limonene and carbon dioxide-citral systems at temperatures from 308.2 to 323.2 Kand over the whole range of pressure and composition. In addition, the phase behaviour ofthe ternary carbon dioxide-limonene-citral system was calculated at pressures from 9.0 to10.9 MPa at 323.2 K and over the whole range of composition.

INTRODUCTIONUsing a simple single pass flow apparatus we measured the solubilities of

limonene, citral and their mixtures in supercritical carbon dioxide

aFig. 1. Mole cular structure of limonene, a, and citral, b.0378-3812/90/ 03.50 0 1990 - Elsevier Science Publishers B.V.


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(Di Giacomo et al., 1989). The molecular structures of limonene and citralare shown in Fig. 1. The experimental results prove the technical feasibilityof supercritical deterpenation of lemon oil with carbon dioxide. However,for optimal design and operation of such a process it is necessary to knowthe phase behaviour of the system over the whole range of operatingconditions.

We illustrate here how vapour phase solubility data can be used to predictequilibrium liquid phase composition for both binary and ternary systems.EQUATION OF STATE

All the experimental data were correlated using an EOS, which, followingLiidecke and Prausnitz (1985), was obtained using the equation of Mansooriet al. (1971) for the repulsive term and that of Soave (1972) for the attractiveterm.Using the Mansoori et al. (1971) form for the reference system, thereduced molar residual Helmholtz energy is:

where D, E and F are defined as:m m m

D = c yq; E= cw ia ; ; F= c ~ ,a ,3 (2)i=l i = l i

Here w is either x or y, a, is the hard-sphere diameter of molecule and mis the number of components. The reduced density is defined as:5 = bp/4 (3)with

m mb = c c wiwjbij

i=l j=l

whereb = (b;i3 + b;p)3/8The Soave perturbation term is:

A Pert = gPet = _ f . In (1 + bp)NRT b RT (6)where a is an equation-of-state parameter which reflects attractive inter-molecular forces.


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For pure componentsR2T2

a=P,-a +aT20 lr

1 r2 (7)RT

b = b. - + cThe pure component parameters ao, a, and b, are determined by fitting

the PUT data from 308.2 to 328.2 K and from 0.1 to 15.0 MPa for carbondioxide (Casci et al., 1972) and the vapour pressures of pure limonene from287.2 to 448.2 K (Perry and Chilton, 1973). For the citral we used the AMPequation (Abrams et al., 1974; Ma nick et al., 1977) to extrapolate theavailable experimental vapour pressure data from 334.9 to 501.2 K (Perryand Chilton, 1973) to the temperatures of interest. This equation, in additionto two adjustable parameters (E, and s), requires the van der Waals volumedetermined from Bondis group-contribution correlation (Bondi, 1968). Theirvalues are E,/R = 9920.92 K, s = 9.978 and Vw = 103.57 cm3 mol-, re-spectively.

Average absolute errors, S, were calculated using

where W represents in turn vapour pressures of limonene and citral andtotal pressure of carbon dioxide.

The values of S - 100 obtained by fitting the above-mentioned experimen-tal data are 0.85 for carbon dioxide, 1.21 for limonene and 1.77 for citral.

Critical properties of limonene and citral have been calculated with theLydersen group-contribution method (Reid et al., 1977). Their values arereported in Table 1, while all pure component parameters of the EOS arereported in Table 2.

For mixtures, we chose for the attractive parameter a the density-depen-dent mixing rules proposed by Panagiotopoulos and Reid (1986)a = t f wiwj a ia j )1 2 (1 -kij) + g f f wiw, wix,j + wjhji)

00)i=lj=l i=lj=l

TABLE 1Molecular weight and critical constants of limonene and citralComponent Mw T, WLimonene 136.23 661.0Citral 152.24 694.6

p, MPa)2.762.29


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138TABLE 2Pure component parameters of the EOSComponentLimoneneCitralCarbon dioxide

=0 01 bo0.399 0.173 0.05540.801 0.039 0.09370.687 0.226 0.1022

where k A i j and Aji are adjustable parameters. Parameter k j is dimen-sionless while Xij and hji are non-dimensionalized by:xii=Xijbii/ai 01)iii =Xjibjj/aZ (12)where bi i ai i bj j and ajj are calculated at the critical temperature.The three binary interaction parameters for the carbon dioxide-limoneneand carbon dioxide-citral systems were calculated from the solubility datareported by Di Giacomo et al. (1989) by minimizing the following objectivefunction:

Q= i hp-Ycdf 03)i=l

whereyexpnd y,, are, respectively, the experimental and the calculatedvalues of the mole fraction of carbon dioxide in the vapour phase and n isthe number of experimental values measured (n = 26 for limonene-carbondioxide and n = 29 for citral-carbon dioxide). The fugacity coefficients Qiderived from the proposed EOS are:

mIn Qi = 2 + (aAr/ ~~),,~,+,, ~~lwl a~/aw,)~,,,*+z-l-ln Cz) 14)where

= 2 ~ wl(aiaj)12(1 - k i j )j=l


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f WiW j i WjXjk + wkxkj)j=l k=l

+b 2 wi W h j i 2 f W wi Xi j + W, Xj i )j=l j=l

. ln(l+ b) + 2a C wjbijj=lb bZ [bp/ l+ bp) -ln l +bdl +ois

+ 2 2 Wjbij P/4). [ - E3/F2 + 1)/(1 - t) + 3DE/F- E3/F2)j=l/(l - 0 + (2E3/F2)/(l - 03] (16)

and z is the compressibility factor.To find the numerical value of the binary parameters for the limonene-

citral system we used the experimental data (Di Giacomo et al., 1989) of theternary carbon dioxide-limonene-citral system. The following objectivefunction:

07)was minimized only for k,,. Here, u,, and ycal are experimental andcalculated values of the mole fraction of carbon dioxide in the vapour phase,YeXP nd Y4 are experimental and calculated values of the mole fraction oflimonene in the vapour phase on a carbon dioxide-free basis in the ternarysystem carbon dioxide-limonene-citral and n is the number of experimen-tal value? measured.

TABLE 3Binary interaction parametersSystemCarbon dioxide l)-limonene 2) 0.047 -0.011 - 0.0069Carbon dioxide l)-citral 3) 0.085 - 0.097 - 0.0102Limonene 2)-citral 3) 0.154


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6.07.56.04.53.01.50 0

.

t

0.0 0.2 0.4 0.6 0.8

r II = 315.0

0 de f t fwado 313 2 KA Stahl Gerard 313 2 K

0.0 a.2 0.4 0.6 0.8

0.992 0 996

8.8

6. A*4. aL

.2.

00.992 0.996

10 . T = 23 2 K8.

0.0 0.2 0.4 0.6 0.8

10 - .8.

,6.

,4.2.0

0.950 0.975mole fraction CO2

Fig. 2. Phase behaviour of the carbon dioxide l)-limonene 2) binary system at temperaturesof 308.2, 315.0 and 323.2 K.

The two interaction parameters x2, and x,, for the limonene-citralsystem were set equal to zero, since limonene and citral have similarmolecular structures and only few experimental data are available. All thebinary interaction parameters are reported in Table 3.


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.7.6 .T = 08.2 K

6.0 _

4.6 .

D 0.0 0.2 0.4 0.6 0.8E.fii 8B 7 - 315.0 KLQ 6

4

2

0

1086

7 = 323.2 K86

0.0 0.2 0.4 0.6 0.8 0.98 0.99

10

7.56.0

4.53.01.50.0

8

6

4

2

0

mole fraction CO 2Fig. 3 . Phase behaviour of the carbon dioxide l)-citral 3) binary system at temperatures of308.2, 315.0 and 323.2 K.

Figures 2 and 3 show the calculated phase diagrams for the carbondioxide-limonene and carbon dioxide-citral systems at three different tem-peratures, together with the measured values of solubility. In Fig. 2 middle),


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Fig. 4.

A ----0 --- 10.0 nP*-.- 10.6 nP* ._

-.-. 10.9 IlPm. alrs aL 9.S Ill*

00 0.2 0.4 0.6 0.8Xl i onene

Y X diagram, solvent-free basis, for the carbon dioxide(l)-limonene(2)-citral(3)system at 323.2 K.

0.80.60.4

fe 0.2- 0.06 0.0 0.2 0.4 0.6 0.8

Il.0 0.2 0.4 0.6 0.8

0.0025

I...0.0000

0 9960 0 9975

0.05

0.00IA.90 0.95mole fraction CO2Fig. 5. Phase behaviour o f the carbon dioxide(l)-limonene(2)-citral(3) ternary system at323.2 K and pressures of 9.0 and 10.9 MP a. Dotted curves were obtained with k,, = x2, =K,, = 0.


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corresponding to 315.0 K for the carbon dioxide-limonene system, thesolubility measured by Stahl and Gerard (1985) and by de Azevedo et al.(1988) is also shown for purposes of comparison. Figure 4 shows thecalculated diagram Y-X for the ternary system carbon dioxide-limonene-citral at 323.2 K and at pressures ranging from 9.0 to 10.9 MPa. Y and Xrepresent the mole fraction, on a carbon dioxide-free basis, of limonene inthe vapour phase and in the liquid phase, respectively. Figure 5 shows thecalculated phase diagrams for the ternary system carbon dioxide(l)-limonene(2)-citral(3) at 323.2 K and 9.0 MPa and at 323.2 K and lo.? MPa;in both these diagrams the predicted curves obtained with k = A = A = 0are also reported.CONCLUSIONS

Phase behaviour of binary and ternary systems of lemon oil componentsand carbon dioxide has been calculated using experimental solubility data inthe vapour phase, along with an equation of state with density-dependentmixing rules. The results show that accurate calculation of phase behaviourfor the carbon dioxide(l)-limonene(2)-citral(3) system can only be obtainedif binary interactions between the two solutes are taken into account.ACKNOWLEDGEMENTS

This work was supported by the Italian Minister0 della Pubblica Istruz-ione.LIST OF SYMBOLS

Ai iD, E, FEok jmMWNnP

Rs

Helmholtz free. energyequation of state parameterequation of state parameterconstants defined by eqns. (2)parameter of AMP equationbinary adjustable parameternumber of componentsmolecular weighttotal number of molesnumber of experimental data pointspressureobjective functiongas constantaverage absolute error


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144sTVW

X

Z

parameter of AMP equationabsolute temperaturevolumemole fractionliquid-phase mole fraction, solvent-free basisliquid-phase mole fractionvapour-phase mole fraction, solvent-free basisvapour-phase mole fractioncompressibility factor

Greek symbolsi j binary adjustable parameter

t reduced densityP molar densityrJ hard-sphere diameter@ fugacity coefficientSuperscriptspertrref

perturbation part of equation of stateresidual part of equation of statereference part of equation of statedimensionless quantity

SubscriptsCCdeXPij;J123

criticalcalculated quantityexperimental quantitycomponent icomponent jreducedvan der Waalscomponent 1component 2component 3

REFERENCESAbrams, D.S., Massaldi, H.A. and Prausnitz, J.M., 1974. Vapor pressurei of liquids as a

function of temperature. Two -parameter equation based on kinetic theory of fluids. Ind.Eng. Chem. Fundam., 13: 259-262.


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145Bondi, A., 1968. Physical Properties of Molecular Crystals, L iquids and Glasses. Wiley, New

York.Casci, C., Mac& i, E. and Angelino, G., 1972. Proprieta Term odinamiche dellAnidride

Carbonica. Tamburini, Milan.de Azevedo , E.G., Mato s, H .A., da Ponte, M.N . and Simoe s, P.C., 1988. Phase equilibria of

system s containing limonene, cineole and supercritica l carbon dioxide . Proc . Int. Sym p. onSupercritical Fluids, Nice, October 17-19. Societd Fran9aise de Chimie, 1: 135-142.

Di Giacomo, G., Brandani, V., Del Re, G. and Mucciante, V., 1989. Solubility of essential oilcomponents in compre ssed supercritical carbon dioxide. Fhtid Phase Equilibria, 52:405-411.

Kalra, H., Chung, S.Y.-K. and Chen, C .-J., 1987. Phase equilibrium data for supercriticalextraction of lemon flavors and palm oils with carbon dioxide. Fluid Phase Equilibria, 36:263-278.

Ltidecke, D. and Prausnitz, J.M., 1985. Phase equilibria of strongly nonideal mixtures froman equation of state with density dep endent mixing rules. Fluid Phase Equilibria, 22:1-19.

Ma&n ick, A.B., Winmck, J. and Prausnitz, J.M., 1977. Vapo r pressures of liquids as afunction of temperature. Two-param eter equation based on kinetic theory of fluids. Ind.Eng. Chem . Fundam., 16: 392.Mansoori, G.A., Camahan , N.F., Starling, K.E. and Leland, T.W., 1971. Equilibrium thermo-dynamic properties of the mixtures of hard spheres. J. Chem . Phys., 54: 1523-152 5.

Panagiotopoulos, A.Z. and Reid, R.C., 1986. Muhiph ase high pressure equilibria in ternaryaqueous systems. Fluid P hase Equilibria, 29: 525-534.

Perry, H.R. and Chilton, C.H., 1973. Chemical Engineers Handbook, 5th edn. McGraw -Hill,New York.

Reid, R.C., Prausnitz, J.M. and Sherwo od, T.K., 1977. The Properties of Gases and Liquids,2nd edn. McGraw -Hill, New York.

So&e , G., 1972. Equilibrium constants from a modified R edlich-Kwong equation of state.Chem . Eng. S ci., 27: 1197-120 3.

Stahl, E. and Gerard, D., 1985. Solubihty behavior and fractionation of essential oils in densecarbon dioxide. P erf. Flavor., 10: 29-37.

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