SciELO - Scientific Electronic Library Online

 
vol.17 issue4THE GENERALIZED MAXIMUM LIKELIHOOD METHOD APPLIED TO HIGH PRESSURE PHASE EQUILIBRIUMUSO DA EQUAÇÃO DE ESTADO DE PENG-ROBINSON COM REGRA DE MISTURA DEPENDENTE DA COMPOSIÇÃO NA PREDIÇÃO DO EQUILÍBRIO DE FASES DO SISTEMA TERNÁRIO CO2-LIMONENO-CITRAL author indexsubject indexarticles search
Home Pagealphabetic serial listing  

Services on Demand

Article

Indicators

Related links

Share


Food Science and Technology (Campinas)

On-line version ISSN 1678-457X

Ciênc. Tecnol. Aliment. vol. 17 n. 4 Campinas Dec. 1997

http://dx.doi.org/10.1590/S0101-20611997000400027 

HIGH PRESSURE PHASE EQUILIBRIUM: PREDICTION OF ESSENTIAL OIL SOLUBILITY1

 

Lúcio CARDOZO-FILHO2, Fred WOLFF2, M. Angela A. MEIRELES3, *

 

 


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 Peng-Robinson and Soave-Redlich-Kwong 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; Peng-Robinson; Soave-Redlich-Kwong


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 Peng-Robinson e Soave-Redlich-Kwong 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.

Palavras-chave: Óleo essencial; equilíbrio de fases; extração supercrítica; Peng-Robinson; Soave-Redlich-Kwong


 

 

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 "f-f" approach was used for essential oil and carbon dioxide vapor-liquid equilibria calculation. Peng-Robinson (PR) and Soave-Redlich-Kwong (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    17n4a26i1.jpg (1280 bytes) 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,...,nc -1 (1)

 

(2)

Solubility will be defined as:

(3)

where mi, Mi and yi 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*nc + 4; specified data are T *, NV* = 1, , and P; and unknowns are , 17n4a26i5.jpg (410 bytes), NV, NL, 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 pressure-increasing 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,...,nc-1

; i = nc

Equilibrium relationship

; i = 1,¼ ,nc

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 Newton-Raphson 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

Teb (K)

Tc (K)

Pc (bar)

w

Ethanol

0.0886

351.65a

513.92d

61.48d

0.6452d

Linalool

0.00586

472.15a

635.99e

25.82b

0.7617f

a-Terpineol

0.00055

493.15a

675.59e

29.50 b

0.7133f

trans-2,Hexenal

0.00012

419.65a

615.15e

35.94 b

0.4199f

Octanal

0.00361

444.15a

620.10 e

27.35 b

0.5558f

Nonanal

0.00053

464.15a

637.67 e

24.80 b

0.6053f

Decanal

0.00287

481.65a

651.94 e

22.59 b

0.6536f

Dodecanal

0.00027

484.94b

675.98 b

18.97 b

0.7585*

Citronelal

0.00050

480.65a

663.86 e

24.05 b

0.5570f

Neral

0.00051

502.15c

699.97

25.25 b

0.7174*

Geranial

0.00125

502.15a

699.97e

25.25 b

0.7174*

b-Simensel

0.00012

592.58b

782.72 b

17.64 b

0.6853f

a-Simensel

0.00015 

600.06b

794.25 b

17.79 b

0.6749f

Ethyl butyrate

0.00100

369.15a

571.00d

30.60b

0.4190d

a-Pinene

0.00421

429.35a

630.87 e

28.90 b

0.3242f

D-3-Carene

0.00102

440.15b

646.74 b

28.90 b

0.3242f

b-Mircene

0.01620

440.15a

642.32 e

28.08 b

0.3425f

Valencene

0.00342

564.52b

780.55 b

18.97 b

0.4324f

d-Limonene

0.94895

451.15a

661.11 e

27.56 b

0.3170f

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.

 

 

TABLE 3. Molar composition of orange essential oil determined by Santana [14] and pure components properties.

Component

Teb (K)

Tc (K)

Pc (bar)

w

Linalool

0.00727

472.15a

635.99e

25.82b

0.7617f

a-Pinene

0.00610

429.35a

630.87 e

28.90 b

0.3242f

b-Mircene2

0.00726

440.15a

642.32 e

28.08 b

0.3425f

Sabinene

0.00177

437.15

640.12

29.35

0.3547

Limonene

0.97760

451.15a

661.11 e

27.56 b

0.3170f

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/CO2.

                                                       PR                                     SRK

                                         kij x102           k"ij x102        kij x102       k"ij x102

CO2/Etanol

9.048

-1.414

8.543

-1.412

CO2/Linalool

4.281

-3.156

4.363

-3.249

CO2/a-Pinene

9.482

-2.820

10.28

-2.805

CO2/d-Linomene

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 CO2 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
bar

T
K

Sb ± 0.1
(mg/g)

PR

D
abs.

SRK

D
abs.

PR

D
abs.

SRK

D
abs.

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

1Initial oil composition as given by Marques [8]; 2Initial oil composition as given by Santana [14].

 

4 — CONCLUSIONS

The proposed methodology for solubility calculation did not present the usual convergence difficulties mentioned for high pressure phase equilibria problems.

The PR and SRK equations had the same performance in orange essential oil solubility calculation. Similar behavior may be expected for other essential oils since, in general, these mixtures are formed from the same family of substances.

Comparison of experimental the and calculated results showed that methodology to be satisfactory.

Even though the orange essential oil used by Marques [8] and that used by Santana [14] have different compositions, the calculated solubility for both compositions did not differ very much from the experimental data measured by Santana [14].

The methodology discussed is not limited to equations of state used in this work. In principle, any equation of state can be applied to developed algorithm.

 

5 — REFERENCES

[1] ARAÚJO, M. E. Estudo do Equiliíbrio de Fases para Sistemas Óleo Vegetal/Dióxido de Carbono Empregando a Equação de Peng-Robinson (Phase Equilibria Study Using the Peng-Robinson Equation of State for Systems: Vegetable Oil/Carbon Dioxide). Campinas, São Paulo, Brazil, 1997. 314pp. Ph.D. Dissertation, (Doctor in Food Engineering) - Faculdade de Engenharia de Alimentos, Universidade Estadual de Campinas (UNICAMP). 

[2] ASSELINEAU, L.; BOGDANIC, G.; VIDAL, J. A Versatile Algorithm for Calculating Vapor-Liquid Equilibria. Fluid Phase Equilibria. vol. 3, pp. 273-290, 1979.

[3] BRUNNER, G. Gas Extraction: An Introduction to Fundamentals of Supercritical Fluids and the Applications to Separation Process. Darmstadt, Alemanha: Steinkopff., 1994.

[4] CARDOZO, L. F., STRAGEVITCH, L., WOLFF, F., MEIRELES, M. A. A. The Generalized Maximum Likelihood Method Applied to High Pressure Phase Equilibrium. Ciência e Tecnologia de Alimentos. vol. 17, no. 4, pp. 481-484, 1997.

[5] DANNER, R. P.; DAUBERT, T. E. Data Compilation Tables of Properties of Pure Compounds. DIPPR. The Pennsylvania State University, 1984.

[6] FUNDAÇÃO CARGILL. 1o Simpósio de Óleos Essenciais (1st Symposium on Essential Oil), Campinas, S.P., Brazil, March 27 - 28, 1986.

[7] HEIDEMANN, R. A. Computation of High Phase Equilibria. Fluid Phase Equilibria. vol. 14, pp. 55-78, 1983.

[8] MARQUES, D. S. Desterpenação de Óleo Essencial de Laranja por Cromatografia Preparativa de Fluido Supercrítico (Terpene Reduction in Orange Essential Oil by Preparative Chromatography and Supercritical Carbon Dioxide Extraction). Campinas, São Paulo, Brazil, 1997. 331pp. Master’s thesis (Master in Food Engineering), Faculdade de Engenharia de Alimentos, Universidade Estadual de Campinas (UNICAMP). 

[9] MICHELSEN M. L., Multiphase Isenthalpic and Isentropic Flash Algorithms. Fluid Phase Equilibria. vol. 33, pp. 13-27, 1987.

[10] MICHELSEN M. L. Phase Equilibrium Calculations. What is Easy and What is Difficult? Fluid Phase Equilibria. vol. 17, no. 5/6, pp. 431-439, 1993.

[11] PERRY, CHILTON, Manual de Engenharia Química, 5ed., Editora Guanabara Dois, Rio de Janeiro, Brazil, 1980.

[12] PRESS, W. H.; VETTERLING, W. T; TEUKOLSKY, S. A.; FLANNERY, B. P. Numerical Recipes in FORTRAN: The Art of Scientific Computing. Cambridge University Press, Cambridge, 1992.

[13] REID, R.C., PRAUSNITZ, J.M.; POLING, B.E. The Properties of Gases and Liquids, 4ed., McGraw-Hill Co., New York, USA, 1987.

[14] SANTANA, H. B. Desenvolvimento de uma Metodologia para a Determinação da Solubilidade de Componentes de Óleo Essencial em Dióxido de Carbono (Determination of the Solubility of Essential Oil in Carbon Dioxide). Campinas, São Paulo, Brazil, 1996. 119pp. Master’s thesis (Master in Food Engineering), Faculdade de Engenharia de Alimentos, Universidade Estadual de Campinas (UNICAMP).

[15] WEAST, R. C.; ASTLE, M. J. CRC - Handbook of Data on Organic Compounds, CRC Press, Inc., Florida, 1992, vol. 1 and 2.

 

6 — NOMENCLATURE

a, b PR and SRK equation parameters;
kij k"ij binary interaction parameters for PR and SRK equations;
mi mass of component i; 
Mi molecular mass of component i;
nc number of components of oil; 
Nl total number of moles in carbon dioxide poor phase; 
Nv total number of moles in carbon dioxide rich phase;
P pressure; 
Pc critical pressure; 
Sb solubility; 
T temperature; 
Teb normal boiling temperature; 
Tc critical temperature; 
xi molar fraction of component i in carbon dioxide poor phase;
yi molar fraction of component i in carbon dioxide rich phase;
molar fraction of component i in essential oil; 
w acentric factor.

 

Greek letters 

a molar fraction of essential oil completely dissolved in carbon dioxide rich phase; 
wpe4.jpg (877 bytes) fugacity coefficient of component i in carbon dioxide poor phase;
wpe5.jpg (867 bytes) fugacity coefficient of component i in carbon dioxide rich phase.

 

1 Received for publication in 8/5/97. Accepted for publication in 9/12/97.

2 DEQ / UEM, Av. Colombo, 5790 Bloco D-90 Campus Universitário, 87020-900 Maringá, PR, Brazil.  cardozo@cybertelecom.com.br 

3 LASEFI - DEA, FEA - UNICAMP, Cx. Postal 6121, 13083-970 Campinas, SP - Brazil. Meireles@ceres.fea.unicamp.br.

* To whom correspondence should be addressed.