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Food Science and Technology (Campinas)
Print version ISSN 01012061Online version ISSN 1678457X
Ciênc. Tecnol. Aliment. vol. 17 n. 4 Campinas Dec. 1997
http://dx.doi.org/10.1590/S010120611997000400027
HIGH PRESSURE PHASE EQUILIBRIUM: PREDICTION OF ESSENTIAL OIL SOLUBILITY^{1 }
Lúcio CARDOZOFILHO^{2}, Fred WOLFF^{2}, M. Angela A.^{ }MEIRELES^{3, *}
SUMMARY
This work describes a method to predict the solubility of essential oils in supercritical carbon dioxide. The method is based on the formulation proposed in 1979 by Asselineau, Bogdanic and Vidal. The PengRobinson and SoaveRedlichKwong cubic equations of state were used with the van der Waals mixing rules with two interaction parameters. Method validation was accomplished calculating orange essential oil solubility in pressurized carbon dioxide. The solubility of orange essential oil in carbon dioxide calculated at 308.15 K for pressures of 50 to 70 bar varied from 1.7± 0.1 to 3.6± 0.1 mg/g. For same the range of conditions, experimental solubility varied from 1.7± 0.1 to 3.6± 0.1 mg/g. Predicted values were not very sensitive to initial oil composition.
Keywords: Essential oil; phase equilibria; supercritical extraction; PengRobinson; SoaveRedlichKwong
RESUMO
EQUILÍBRIO DE FASES A ALTAS PRESSÕES  PREDIÇÃO DA SOLUBILIDADE DE ÓLEOS ESSENCIAIS. Este trabalho descreve uma metodologia para o cálculo da solubilidade de óleos essenciais em dióxido de carbono a altas pressões baseada na formulação proposta em 1979 por Asselineau, Bogdanic e Vidal. Foram utilizadas as equações cúbicas de estado de PengRobinson e SoaveRedlichKwong com regras de mistura de van der Waals com dois parâmetros de interação. O cálculo da solubilidade do óleo essencial de laranja em dióxido de carbono pressurizado foi usado para validação do método. A solubilidade calculada a 308,15 K para pressões entre 50 e 70 bar variou entre 1,5 e 4,1 mg/g. Valores experimentais para as mesmas condições variam entre 1,7± 0.1 a 3,6± 0.1 mg/g. Os valores preditos não são muito sensíveis à composição inicial do óleo essencial.
Palavraschave: Óleo essencial; equilíbrio de fases; extração supercrítica; PengRobinson; SoaveRedlichKwong
1 INTRODUCTION
The process of supercritical extraction, using carbon dioxide as solvent, is an efficient method for obtaining essential oils starting from a solid matrix, and recently it has been considered a possible substitute for conventional methods.
Essential oil solubility in carbon dioxide is an important parameter in economic viability studies and in supercritical extraction projects. Knowledge of solubility permits calculation of the distribution coefficient, a parameter used in mass transfer models [3].
Modeling of supercritical processes is strongly dependent on thermodynamic methods used for phase equilibria calculations. Even if mass transfer limitations are neglected, simplified models still involve great challenges to be faced. In this work the "ff" approach was used for essential oil and carbon dioxide vaporliquid equilibria calculation. PengRobinson (PR) and SoaveRedlichKwong (SRK) equations were used, since in spite of their simplicity, they have been presenting satisfactory results [1].
Essential oils are a complex mixture in which terpenes and their derived compounds are responsible for some of its main characteristics [6]. Experimental information on the physical properties of essential oil components is scarce in the literature so that, it is already possible to foresee the need to predict properties such as critical temperature and pressure and acentric factor (Tc, Pc and w), which are required for solubility calculations.
The aim of this work was to develop a methodology for calculation of essential oil solubility in carbon dioxide using the PR and SRK equations of state.
2 METHODOLOGY
A methodology was developed for the calculation of solubility based on the formulation by Asselineau et al [2].
Heidemann [7] reviewed methodologies developed for high pressure phase equilibria calculation and observed that there are several ways of approaching the theme. More recent publications [9, 10] do not present significant progress in relation to the Asselineau et al [2] work. In addition, a large part of the work found in the literature is limited to the solution of problems in the petroleum industry problems.
An advantage of the Asselineau et al [2] methodology is the use of only one algorithm to solve any of the basic phase equilibria problems (dew point, bubble point and flash).
To take advantage of the methodology, essential oil solubility in carbon dioxide was treated as a dew point problem. Essential oil solubility in carbon dioxide was considered to be the amount of carbon dioxide required for a given oil sample solubilization, according to the process represented in Figure 1.
FIGURE 1. Stages of solubilization process of essential oil sample in carbon dioxide at constant temperature and pressure.
Let be the original essential oil molar composition and let a be the essential oil molar fraction in the final mixture (essential oil and carbon dioxide). Thus, the composition on the carbon dioxide rich phase at the instant the oil phase disappears is given by:
; i=1,...,n_{c} 1 (1)
(2)
Solubility will be defined as:
(3)
where m_{i}, M_{i} and y_{i} are mass, molecular mass and molar fraction of essential oil components, respectively.
Given these definitions, the main subject can be summarized by:" Given T, P and calculate a , and Sb."
Using the Asselineau et al [2] methodology, the problem can be presented as given in Table 1. Carbon dioxide rich phase will be represented by V and carbon dioxide poor phase by L. Fugacity coefficients () will be determined using PR and SRK equations with the following mixing rules:
(4)
(5)
The total number of equations is 2*n_{c} + 4; specified data are T *, N^{V*} = 1, , and P; and unknowns are , , N^{V}, N^{L}, T and a .
At high pressures, solution of the above system is nonlinear, therefore strongly depending on initial estimates. A way of guaranteeing convergence is to begin calculations at low pressures and to continue them in a pressureincreasing direction, using equilibrium points which have already been calculated as the initial estimates for the following ones. The convergence can be guaranteed selecting sufficiently small increments of P. This procedure allows us to obtain solubility isotherms as a function of pressure.
TABLE 1. System of equation based on Asselineau et al. [2] work.
Component mass balance  ; I = 1,...,n_{c}1 ; i = n_{c } 
Equilibrium relationship  ; i = 1,¼ ,n_{c } 
Restriction 

Global mass balance 

Specified equations 

The nonlinear system of equations (Table 1) was solved using the Broyden numeric method [12], because its convergence is faster than the NewtonRaphson method since the Jacobian is not recalculated for each iteration. A diagram for the solution of the nonlinear system of equations is represented in Figure 2.
FIGURE 2. Block diagram of proposed algorithm.
3 RESULTS AND DISCUSSION
To exemplify the use of the proposed methodology, it was decided to use data for orange essential oil whose composition was determined by Marques [8] and Santana [14] and whose solubility was determined by Santana [14]. In Tables 2 and 3 the oil molar composition, as well as critical pressure and temperature, normal boiling temperature and acentric factor for pure components, is given.
TABLE 2. Molar composition of orange essential oil determined by Marques [8] and pure component properties.
Component 
 T_{eb }(K)  T_{c} (K)  P_{c} (bar)  w 
Ethanol  0.0886  351.65^{a }  513.92^{d }  61.48^{d }  0.6452^{d } 
Linalool  0.00586  472.15^{a }  635.99^{e }  25.82^{b }  0.7617^{f } 
aTerpineol  0.00055  493.15^{a }  675.59^{e }  29.50^{ b }  0.7133^{f } 
trans2,Hexenal  0.00012  419.65^{a }  615.15^{e }  35.94^{ b }  0.4199^{f } 
Octanal  0.00361  444.15^{a }  620.10^{ e }  27.35^{ b }  0.5558^{f } 
Nonanal  0.00053  464.15^{a }  637.67^{ e }  24.80^{ b }  0.6053^{f } 
Decanal  0.00287  481.65^{a }  651.94^{ e }  22.59^{ b }  0.6536^{f } 
Dodecanal  0.00027  484.94^{b }  675.98^{ b }  18.97^{ b }  0.7585^{* } 
Citronelal  0.00050  480.65^{a }  663.86^{ e }  24.05^{ b }  0.5570^{f } 
Neral  0.00051  502.15^{c }  699.97  25.25^{ b }  0.7174^{* } 
Geranial  0.00125  502.15^{a }  699.97^{e }  25.25^{ b }  0.7174^{* } 
bSimensel  0.00012  592.58^{b }  782.72^{ b }  17.64^{ b }  0.6853^{f } 
aSimensel  0.00015  600.06^{b }  794.25^{ b }  17.79^{ b }  0.6749^{f } 
Ethyl butyrate  0.00100  369.15^{a }  571.00^{d }  30.60^{b }  0.4190^{d } 
aPinene  0.00421  429.35^{a }  630.87^{ e }  28.90^{ b }  0.3242^{f } 
D3Carene  0.00102  440.15^{b }  646.74^{ b }  28.90^{ b }  0.3242^{f } 
bMircene  0.01620  440.15^{a }  642.32^{ e }  28.08^{ b }  0.3425^{f } 
Valencene  0.00342  564.52^{b }  780.55^{ b }  18.97^{ b }  0.4324^{f } 
dLimonene  0.94895  451.15^{a }  661.11^{ e }  27.56^{ b }  0.3170^{f } 
^{a }T_{eb} from CRC [15]; ^{b}P_{c} calculated using JOBACK [13]; ^{c}Data from PERRY and CHILTON [11]; ^{d}Data from DIPPR [5]; ^{e}T_{c} calculated using JOBACK [13] and T_{eb} from CRC [15]; ^{f}Lee Kesler [13] method used to calculate acentric factor.
TABLE 3. Molar composition of orange essential oil determined by Santana [14] and pure components properties.
Component 
 T_{eb} (K)  T_{c} (K)  Pc (bar)  w 
Linalool  0.00727  472.15^{a }  635.99^{e }  25.82^{b }  0.7617^{f } 
aPinene  0.00610  429.35^{a }  630.87^{ e }  28.90^{ b }  0.3242^{f } 
bMircene^{2 }  0.00726  440.15^{a }  642.32^{ e }  28.08^{ b }  0.3425^{f } 
Sabinene  0.00177  437.15  640.12  29.35  0.3547 
Limonene  0.97760  451.15^{a }  661.11^{ e }  27.56^{ b }  0.3170^{f } 
^{a Teb from CRC [15]; bPc calculated using JOBACK [13]; cData from PERRY and CHILTON [11]; dData from DIPPR [5]; eTc calculated using JOBACK [13] and Teb from CRC [15]; fLee Kesler [13] method used to calculate acentric factor. }
In Table 4 interaction parameters obtained by Cardozo et al [4] are presented for binary systems (orange essential oil component/carbon dioxide) whose equilibrium data are known from the literature. For binary systems (orange essential oil component/carbon dioxide or essential oil component/essential oil component ) where experimental data is missing, interaction parameters were set equal to zero. With this choice, we are by no means implying that there is no interaction between these binary systems. The choice was made to let the problem to be solved.
TABLE 4. Binary interaction parameters available for the system: Orange oil/CO_{2}.
PR SRK  
k_{ij} x10^{2 } k"_{ij} x10^{2 } k_{ij} x10^{2 } k"_{ij} x10^{2}  
CO_{2}/Etanol  9.048  1.414  8.543  1.412 
CO_{2}/Linalool  4.281  3.156  4.363  3.249 
CO_{2}/aPinene  9.482  2.820  10.28  2.805 
CO_{2}/dLinomene  10.15  1.960  9.921  1.415 
Orange essential oil solubility was calculated at conditions used by Santana [14] for experimental determination (Figure 3). Orange essential oil solubility in carbon dioxide was also determined as a function of pressure for a temperature of 308.15 K using orange essential oil composition given by Marques [8] and Santana [14]. The results are presented in Figure 3. Table 5 contains experimental data for orange essential oil solubility in carbon dioxide determined by Santana [14], as well as the experimental error for the temperature and pressures used in the experiments. Comparing results shown in Table 5 and Figure 3, we can conclude that PR EOS has a performance similar to that of SRK EOS.
FIGURE 3. Predicted solubility of orange essential oil in CO_{2} according to PR and SRK equations of state. ¨ Experimental solubility determined by Santana [14] at 308.15 K. Calculated using orange essential oil molar composition determined by Marques [8];  Calculated using orange essential oil molar composition determined by Santana [14].
TABLE 5. Solubility of orange essential oil in carbon dioxide measured experimentally by Santana [14] and calculated using the proposed methodology.
Solubility (mg/g)^{1 } Solubility (mg/g)^{2 }  
P  T  Sb ± 0.1  PR  D  SRK  D  PR  D  SRK  D 
50  308.15  1.7  1.4  0.3  1.3  0.4  1.8  0.1  1.51  0.2 
60  308.15  2.8  2.2  0.6  2.0  0.8  2.6  0.2  2.1  0.8 
65  308.15  3.1  2.9  0.2  2.7  0.4  3.3  0.2  2.7  0.4 
70  308.15  3.6  4.1  0.5  4.0  0.4  4.6  1.0  3.8  0.2 
Global deviation 0.40 0.5 0.4 0.4 