THE EFFECTIVE DIFFUSIVITY OF CLOVE(Eugenia caryophyllus) ESSENTIAL OIL IN PRESSURIZED CO2

THE EFFECTIVE DIFFUSIVITY OF CLOVE (Eugenia caryophyllus) ESSENTIAL OIL IN PRESSURIZED CO2¹

Caciano ZAPATA NOREÑA², M. Angela A. MEIRELES³,^*

SUMMARY

The effective diffusivity of clove essential oil in subcritical liquid CO₂ was estimated. The experimental apparatus employed was a fixed-bed extractor. The fixed bed was formed with grounded (mesh -32 + 65) and compacted clove buds which were considered a solid element. The effective diffusion coefficient was evaluated by fitting the experimental concentration profile to the unsteady state mass balance equation for unidirectional diffusion in a finite solid medium. The diffusion coefficient was related to the concentration of oil in the solid by an exponential function. The estimated values of the effective diffusion coefficient varied from 3.64 to 5.22x10^-10 m²/s. The average relative errors were lower than 3.1%.

Key words: Diffusion coefficient, mass transfer, finite difference, clove essential oil, supercritical extraction.

RESUMO

ESTIMATIVA DA DIFUSIVIDADE MÁSSICA EFETIVA DO ÓLEO ESSENCIAL DE CRAVO-DA-ÍNDIA (Eugenia caryophyllus), EM CO₂ PRESSURIZADO. O coeficiente de difusão efetivo do óleo essencial de cravo-da-índia em CO₂ líquido subcrítico foi estimado. O equipamento experimental usado foi um extrator de leito fixo. O leito fixo foi formado por cravo-da-índia moído (mesh -32 + 65) e compactado, sendo assim considerado como um meio sólido. O coeficiente de difusão efetivo foi estimado pelo ajuste do perfil de concentração experimental à equação de balanço de massa em estado transiente, para difusão unidirecional em um meio sólido. A dependência do coeficiente de difusão com a concentração de óleo no sólido, foi descrita por uma função exponencial. O coeficiente de difusão determinado variou de 3,64 a 5,22x10^-10m²/s. Os erros médios relativos foram menores do que 3,1%.

Palavras chave: Difusividade mássica, transferência de massa, diferenças finitas, óleo essencial de cravo-da-índia, extração supercrítica.

1 — INTRODUCTION

Among the studies on estimation of effective diffusion coefficient of natural product essential oils using pressurized CO₂, is one by Goto et al [5]. These authors proposed a mathematical model to evaluate extraction rate considering local equilibrium adsorption of mint essential oil by lipids and mass transfer. The intraparticle diffusion coefficient of -menthol, the main constituent of mint oil, in supercritical solvent varied from 0.17x10^-8 to 1.46x10^-8 m²/s.

Reverchon et al [9] measured the mass diffusivity of basil, marjoram and rosemary essential oils in CO₂ for particles of different sizes at 100 bar and 313 K. They found that the effective diffusion coefficient varied from 1.4x10^-13 to 2.8x10^-13 m²/s. These authors indicated that internal resistance in herbaceous matters controls the mass transfer process.

Roy et al [10] used experimental data obtained for the extraction of ginger essential oil at different CO₂ flow rates to estimate the effective diffusion coefficient. They found that the value of effective diffusivity was 2.5x10^-10 m²/s.

Nevertheless, the effect of bed compactness, has not been studied to date, with the exception of the work by Del Valle and Aguilera [3]. For mushroom powder, bed compaction prior to extraction with supercritical fluids resulted in a solubilization rate apparently controlled by solid matrix solute diffusion; therefore, extraction rate could be predicted by solid diffusion models. These authors evaluated mushroom oleoresin extraction for CO₂ densities from 538.3 to 678.7 kg/m³ and temperatures from 336 to 363.3 K. They determined that oleoresin fractions located in pores were easily extracted and the diffusion coefficient varied from 1.0x10^-8 to 1.5x10^-8 m²/s. Remaining oleoresin located inside the solid matrix was extracted at a rate controlled by a diffusivity 100 to 150 times lower.

The diffusion of solutes in biological system during extraction is a phenomenon which is difficult to explain because it is influenced by the interaction among components and structure. Thus, it is possible that the diffusion coefficient depends on concentration.

The present work objective was to estimate the effective mass diffusion coefficient of clove essential oil in CO₂ for supercritical extraction in a fixed-bed extractor. Operational conditions employed were pressures of 64.7 and 69.7 bar and temperatures of 10 and 12^oC. The effective mass diffusion coefficient dependence of essential oil concentration in solid phase was also investigated.

2 — MATERIALS AND METHODS

Clove buds were bought from a local store (Campinas, São Paulo, Brazil). Material was cleaned manually with the use of sieves with meshes of 6 and 8 (Granutest Tyler series, Brazil) to remove branches, leaves, stones, powder and other foreign materials. Cleaned and selected clove buds were placed in plastic containers which were hermetically closed and stored in a domestic freezer (Metalfrio, 620 L, horizontal, Brazil).

The amount of material required for each experimental run was ground in a laboratory helix-type mill (Marconi, Model MA-345, Brazil) with water circulation. The solid was ground in a frozen state to avoid thermal degradation of the volatile oil. Solid particles were sifted in a sieve shaker for 25 min. to obtain particles with meshes of -32 and +65. Solid material was manually compacted with the aid of a glass rod (1 cm of diameter) into a surgical tubular cloth (T. M. Orthopaedic, 100% cotton) which was placed into a hollow cylindrical matrix made of disposable hypodermic syringes. Solids with a cylindrical shape of approximately 2.17 cm diameter and 6.8 cm length and a uniform density were obtained. Each experiment required 7 cylinders that were weighed in an analytic balance (Sartorius, Model A 200 S, + 0.001 g, USA) and placed inside of an extractor (with length of 60.5 cm and inside diameter of 2.16 cm).

2.1 – Experimental procedure

A flow sheet of the experimental apparatus is shown in Figure 1. Valves V₁ and V₂ were always open to guarantee that reservoir-II was always full of CO₂ (Liquid Carbonic do Brazil, 99% pure). System pressure was controlled with the aid of a heating tape (Fisaton, Model -5.5 cm width, Brazil) wrapped around reservoir-I and linked to an automatic temperature controller (Dyna-sense, Model 2156-00, USA). One hour before connecting the extractor to the extraction line, the recirculating water bath (Tecnal, Model TE-184, +1K, Brazil) for reservoir-II was turned on. Ninety minutes later, having reached preselected operational conditions, valve V₃ was opened and CO₂ began to flow through the bed. Up to this point valve V₄ was kept closed. Once extractor pressure was equilibrated, its upper end was isolated by closing valve V₄. Thereafter, valve V₅ and the micrometering valve used to expand and to control the CO₂ flow rate were opened. These valves were heated with a heating tape (Fisaton, Model -5, of 2.5 cm width, Brazil) linked to an electronic temperature controller (Dyna-Sense, Model 2156-00, USA). These valves (V₅ and micrometering) were opened in such a way so as to maintain constant and at a minimum the CO₂ flow rate. This care was taken to avoid the possibility of oil accumulation in the fluid phase. Oil was collected in 20 cm³ glass flasks. CO₂ flow was maintained for seven hours. After this valve V₃ was closed and CO₂ was completely removed from the extracting line.

FIGURE 1.
Flowsheet of the Experimental Unit.

After complete depressurization (0 bar of pressure), cylinders formed with compacted solid were removed from the extractor and placed in a dessecator until they reached room temperature; afterwards, they were weighed and the solid phase concentration profile was calculated.

2.2 – Composition of the extract

The composition of clove oil was determined by gas chromatography using the procedure described by Rodrigues et al [11].

2.3 – Mass transfer in a finite solid with a concentration dependent mass diffusivity

To study oil extraction kinetics using CO₂ as solvent in a fixed bed formed with compacted clove particles, compacted substratum was considered as a solid, in agreement with Del Valle and Aguilera [3]. For the experimental system employed (see Figure 2), diffusion occurred only in the axial direction. Therefore, mass balance for the solid phase is given by the unidirectional, nonstationary mass transfer equation, or Fick’s Second Law, and can be written as [12]:

FIGURE 2.
Experimental conditions.

(1)

Where the diffusion coefficient depends on oil concentration in the solid:

(2)

The initial and boundary conditions are given by:

C.I.: Initially the oleoresin content was evenly distributed within the solid:

(3)

C.C.: During extraction, the solid surface concentration is:

(4)

C.C.: The finite solid condition is:

(5)

The following dimensionless groups will be defined:

(6)

(7)

(8)

where D⁺ is the value of the variable diffusivity that corresponds to the initial concentration [2, 6].

For the concentration-dependent diffusion coefficient for the solution of the mass transfer equation the following dimensionless variable may be used [1, 6]:

(9)

Expressing Equation (1) in terms of dimensionless groups, we have:

(10)

Introducing the transformation variable defined as [2]:

(11)

Substituting Equation (11) into Equation (10) results in:

(12)

To solve Equation (12) we have assumed that the solute concentration dependence of the diffusion coefficient follows an exponential function as given by the relationship [6]:

(13)

Where D_o is the diffusion coefficient when X = X_oand D⁺ is the variable diffusion coefficient in X = X_o, defined by [6]:

(14)

Therefore, variable D of Equation (9) is defined as:

(15)

Thus:

(16)

Initial and boundary conditions for Equations (3), (4) and (5) of this model are expressed, in terms of variable S as:

C.I.:

(17)

C.C.(1):

(18)

C.C.(2):

(19)

Equation (12), with Equations (17), (18) and (19) as initial and boundary conditions was solved using the explicit finite differences method. Diffusion equation discretization can be accomplished by the following approach for its first and second order derivatives [2]:

(20)

(21)

Combining Equations (20) and (21) with Equation (12) we have:

(22)

For , and

(23)

The initial and boundary conditions expressed as finite differences for the exponential model are given by:

C.I.:

(24)

C.C. (1):

(25)

C.C. (2):

(26)

As a result of discretization, the system of simultaneous equations generated was solved by means of matrix direct multiplication outline. Once S_i values were obtained, concentration values in each position could be calculated by:

(27)

Average concentration in each segment was determined by:

(28)

For estimation of X_s, k₁ and D_o parameters, the modified simplex method of Nelder and Mead [7] was used. Quality of model fitting was evaluated through average relative errors given by:

(29)

where N_p is number of experimental points, and predicted and experimental concentrations are expressed dimensionless.

3 — RESULTS AND DISCUSSION

Initial solute concentration in solid phase, X₀, was taken to be oleoresin content as determined by Rosengarten’s hexane extraction method as described by Germer [4]. This value was 25.0 + 0.3% and is in agreement with results shown in the literature [4]. The composition of the clove oil is given in Table 1.

TABLE 1
. Composition of clove essential oil (mass %).

64.7 bar
T oC	Eugenol	b- caryophyllene	a-humulene	Eugenol acetate	Unidentified
10	50.14	19.77	2.10	27.60	0.39
12	58.62	19.81	1.60	19.50	0.47
69.7 bar
10	48.41	19.86	2.49	28.19	1.05
12	49.34	19.91	2.23	27.64	0.88

For the solution of equations using the explicit method, 5 second increments, with 60 nodal points were used. Intervals for Fourier number were on the order of magnitude of 10^-5. This size was chosen to avoid numerical oscillations that make the method unstable [8]. In this work the stability criterion was: where D is given by Equation (23).

FIGURE 3.
Experimental and calculated concentration profile at 69.7 bar and 10^oC.

FIGURE 4.
Experimental and calculated concentration profile at 64.7 bar and 12^oC

FIGURE 5.
Experimental and calculated concentration profile at 69.7 bar and 12^oC.

Table 2 shows estimated values of parameters k₁, X_s and D_o. Mean relative deviations are smaller than 3.1%. Figures 3, 4, 5 and 6 show the concentration profile for the pressure and temperature conditions studied. There is a good agreement between predicted curves and experimental data. At 10^oC the effective diffusion coefficient did not change when pressure increased 5 bar. At 12^oC, as pressure increased from 64.7 bar to 69.7 bar, the effective diffusion coefficient decreased as much 27%. At a constant pressure the following behavior was observed as temperature increased from 10 to 12^oC: at 64.7 bar the effective diffusion coefficient was 4.97x10^-10 m²/s and it was 3.64x10^-10m/s² at 69.7.

Several phenomena acted upon the system. An explanation of observed behavior can only be achieved if all combined effects are considered. For instance, the effective diffusion coefficient is associated with solute interaction in the solid phase, as well as in the fluid phase. Therefore, system thermodynamic limitations can, to a certain extent, interfere with effective diffusion coefficient determination. But this phenomena was not explicitly considered in the model. The possibility also exits that the operational conditions employed are near the crossover region, since results shown in the literature detected a minimum in the solubility at 16^oC for pressures of 60.5 to 70 bar [11]. Another phenomena that should be considered is the modification of extract composition (see Table 1) observed at these pressures and temperatures. Composition was strongly affected by temperature at a pressure of 64.7 bar, but this was not observed at 69.7 bar. Therefore, eugenol conversion to eugenol acetate may be partially responsible for the observed behavior of the effective diffusion coefficient. An understanding of the role of the interaction of each solute with the solid matrix, as well as with the solvent, would probably help in explaining the behavior of the effective diffusion coefficient calculated for the mixture.

TABLE 2.
Estimated parameters for the exponential model

64.7 bar				69.7 bar
Temp. (oC)	k1x106 g. m.l.o/g. oil	Xs g. oil/g. m.l.o*	Dox1010 (m2/s)	% er	k1x106 g. m.l.o/g. oil	Xs g. oil/g. m.l.o	Dox1010 (m2/s)	% er
10	1.93	0.155	4.97	3.05	1.93	0.155	4.97	2.74
12	1.93	0.155	4.97	1.83	1.32	0.155	3.64	0.81

* m.l.o = oil free base

4 — CONCLUSIONS

The clove oil diffusion coefficient for compacted bed was predicted using the mass transfer equation for a finite solid.

An exponential relationship was used to describe diffusion coefficient dependence on oil concentration.

For this model, mean relative deviations between experimental and predicted data were smaller than 3.1%.

The effective diffusion coefficient and extract composition varied with both temperature and pressure, but further studies are required to explain the observed behavior.

5 — REFERENCES

[1] CHU, S. T.; HUSTRULID, A. General Characteristics of Variable Diffusivity Process and the Dynamic Equilibrium Moisture Content. Transactions of the American Society of Agricultural Engineers, vol. 11, no. 5. pp. 709-710, 1968.

[2] CRANK, J. The Mathematics of Diffusion. 2nd ed. London: Oxford University Press, 1975.

[3] DEL VALLE, J. M.; AGUILERA, J. M. Effects of Substrate Densification and CO₂ Conditions on Supercritical Extraction of Mushroom Oleoresins. Journal of Food Science, vol. 54, no. 1, pp. 135-141, 1989.

[4] GERMER, S. P. M. Extração de Óleo Essencial de Cravo-da-Índia em Leito Fixo com Dióxido de Carbono Líquido Subcrítico (Extraction of Clove Essential Oil with Subcritical Carbon Dioxide). Campinas, 1989. 140 p. Master’s thesis (Master in Food Engineering) - Faculdade de Engenharia de Alimentos, Universidade Estadual de Campinas (UNICAMP).

[5] GOTO, M.; SATO, M.; HIROSE, T. Extraction of peppermint oil supercritical carbon dioxide. Journal of Chemical Engineering of Japan, vol. 26, no. 4, pp. 401-407, 1993.

[6] HSU, K. H. A Diffusion Model with a Concentration Dependent Diffusion Coefficient for Describing Water Movement in Legumes During Soaking. Journal of Food Science, vol. 48, no. 2, pp. 618-622, 1983.

[7] KUESTER, J. L.; MIZE, J. H. Optimization Techniques with Fortran. New York: McGraw-Hill Book Company, 1973. 500 p.

[8] MYERS, G. E. Analytical Methods in Conduction Heat Transfer. New York: McGraw-Hill Book Company, 1971. 508 p.

[9] REVERCHON, E.; OSSÉO, L. S.; DONSI, G. Modeling of Supercritical Fluid Extraction from Herbaceous Matrices. Industrial and Engineering Chemistry Research, vol. 32, no. 11, pp. 2721-2726, 1993.

[10] ROY, C. B.; GOTO, M.; HIROSE, T. Extraction of Ginger Oil with Supercritical Carbon Dioxide: Experiments and Modeling. Industrial and Engineering Chemistry Research, vol. 35, no. 2, pp. 607-611, 1996.

[11] RODRIGUES, V. M.; MARQUES, M. O.; MEIRELES, M. A. Evaluation of the Chemical Composition of Clove (Eugenia caryophyllus) Essential Oil Obtained by SCFE. The 4th International Symposium on Supercritical Fluids, vol. A, pp. 215-218, 1997.

[12] WHITAKER, T.; BARRE, H. J.; HAMDY, M. Y. Theoretical and Experimental Studies of Diffusion in Spherical Bodies with a Variable Diffusion Coefficient. Transactions of the American Society of Agricultural Engineers, vol. 12, no. 5, pp. 668-672, 1969.

6 — NOMENCLATURE

D dimensionless diffusivity D(x) variable diffusion coefficient (m2/s) Def effective diffusion coefficient (m2/s) Do effective diffusion coefficient when X = Xo (m2/s) D+ variable diffusion coefficient in X = Xo (m2/s)

Fourier number defined by D+ k1 constant defined by equation (13) k2 constant defined by equation (16) equilibrium distribution coefficient L length N nodal points X concentration of oleoresins in the solid phase (kg (oil)/kg (oil free base) ) Xo initial concentration in clove Xs concentration of oleoresins on the surface of solid Y concentration of oleoresins in the fluid (kg (oil)/kg (CO2)) S variable of transformation defined by equation (11) t time (s) Z dimensionless coordinate z axial coordinate (m) dimensionless concentration

7 — ACKNOWLEDGMENT

The authors wish to express their gratitude to Dr. Marcia O. M. Marques for her assistance in the CGMS analysis. They are also grateful to FAPESP and CNPq for their financial support. CAPES has provided the scholarship for C.Z.N. and Liquid Carbonic S/A provided the carbon dioxide.

[e-mail]

^*

To whom correspondence should be addressed.

¹

Received for publication on 5/08/97. Accepted for publication on 9/12/97.

²

LASEFI — DEA, FEA — UNICAMP, Cx. Postal 6121, 13083-970 Campinas, SP - Brazil.

Publication Dates

• Publication in this collection
  17 Dec 1998
• Date of issue
  Dec 1997

History

• Received
  05 Aug 1997
• Accepted
  09 Dec 1997