Ind. Eng. Chem. Res. 1999, 38, 3069-3075
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SEPARATIONS Supercritical Fractional Extraction of Fennel Seed Oil and Essential Oil: Experiments and Mathematical Modeling E. Reverchon,*,† J. Daghero,‡ C. Marrone,† M. Mattea,‡ and M. Poletto† Dipartimento di Ingegneria Chimica a Alimentare, Universita` di Salerno, Via Ponte Don Melillo, 84084 Fisciano (SA), Italy, and Facultad de Ingenieria, Universidad Nacional de Rio Cuarto, Ruta 36, km 601, 5800 Rio Cuarto, Argentina
Supercritical CO2 extraction of fennel seeds has been performed in two steps; the first step was performed at 90 bar and 50 °C to obtain the selective extraction of essential oil. The second one was performed at 200 bar and 40 °C and allowed the extraction of vegetable oil. The experiments were performed using the fractional separation of the extracts using three different CO2 flow rates (0.5, 1.0, and 1.5 kg/h). On the basis of the extraction results and of the analysis of scanning electron microscopy (SEM) images of the vegetable matter, mathematical models of the two extraction processes have been proposed. The extraction of fennel vegetable oil has been modeled using a model based on differential mass balances and on the concept of broken and intact cells as evidenced by SEM. Only one adjustable parameter has been used: the internal mass-transfer coefficient kt. A fairly good fitting of the experimental data was obtained by setting kt ) 8 × 10-8 m/s. The fennel essential oil extraction process was modeled as desorption from the vegetable matter plus a small mass-transfer resistance. The same internal mass-transfer coefficient value used for vegetable oil extraction allowed a fairly good fitting of the essential oil extraction data. Introduction Vegetable oils and essential oils are two of the most interesting products proposed for supercritical fluids extraction (SFE). Indeed, in these two cases supercritical fluid processing is very promising for improving traditional industrial techniques that are based on hexane extraction for vegetable oils and steam distillation for essential oils. Supercritical fluid extraction of seed oil has been studied by several authors from the processing point of view, and a wide range of seed species has been explored: wheat germ,1 oats,2 corn germ,3 cottonseed,4,5 soybean,5-7 evening primrose,8 jojoba,9 rice bran,10 rapeseed,7 peanut5 and grape seed.11 Despite the large number of species processed, only some models of the SFE of seed oil have been published. They all agree with the fact that at least the first part of the SFE process is governed by the solubility equilibrium between the oil and the fluid phase. From the mathematical point of view, the models proposed are based on differential mass balance integration. Bulley et al.,12 Lee et al.,13 and Fattori et al.14 assumed that mass-transfer resistance was only in the solvent phase. King and Catchpole15 used a shrinking core model to describe a variable external resistance where the solute balance on the solid phase determines the thickness of the mass-transfer layer in the external * To whom correspondence should be addressed. Telephone: 0039089964116.Fax: 0039089964057.E-mail: reverch@ dica.unisa.it. † Universita ` di Salerno. ‡ Universidad Nacional de Rio Cuarto.
part of the particles. Sovova´16 and Sovova´ et al.17,18 considered the solid phase as divided between broken and intact cells. The merit of this model is to use a realistic description of the vegetable structure. Its major drawback is the large number (5) of adjustable parameters it contains. Moreover, the authors only tested simplified forms of this model. Recently, Marrone et al.19 demonstrated that it is possible to fix all parameters but one in the Sovova` model using SEM image analysis of the vegetable matter to measure the number and the dimension of broken and intact cells. These authors applied this technique in the modeling of almond oil supercritical extraction. Supercritical extraction of essential oil from vegetable matter has also been widely studied (see for a review ref 20). However, essential oil isolation from the other coextracted material has only been successfully performed when a fractional separation technique has been coupled to supercritical extraction.20-22 Until now, only a few papers have been published on the modeling of supercritical fluid extraction of essential oils. Some authors used the heat-transfer analogy of the cooling of a single sphere to describe the extraction process.23,24 However, this model describes an idealized situation, and the description of the fixed bed of particles is, as a rule, overestimated. Other authors described the extraction process through the integration of differential mass balances. Goto et al.25 described the extraction of peppermint essential oil as a desorption process characterized by the attainment of an instantaneous equilibrium. Sovova´ et al.18 extracted essential oil from caraway seed and used an extension of the previous model used to model vegetable oil extraction. Roy et al.26
10.1021/ie990015+ CCC: $18.00 © 1999 American Chemical Society Published on Web 07/15/1999
3070 Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999
described the ginger rhizomes supercritical extraction using a shrinking core model. Effective diffusivity and solubility were considered as model parameters. However, the model was unable to describe the experimental results obtained at different particle sizes. Catchpole et al.27 described the SFE of coriander seed, sage, and celery, proposing the solid mass balance on a single particle. An analytical solution of the simplified model was proposed, and intraparticle diffusion was found to control the extraction process. Reverchon,28 studying the SFE of sage leaves’ essential oil, found that internal mass transfer controlled the extraction process. The shape of the particles (slabs) had to be taken into account to obtain a fairly good description of experimental data when large particles were considered. Reverchon and Marrone29 for the SFE of clove bud essential oil found that a small external mass-transfer resistance controlled the extraction process in this case. Goodarznia and Eikani30 used the mass balance on a single particle coupled with a fluid phase balance on a differential section of the bed; internal diffusivity and axial dispersion were also taken into account. In conclusion, very different models have been used to take into account the various structures of vegetable matter and the different locations where essential oil can be located. In some cases vegetable oil and essential oil coexist in the same vegetable matter: various seeds contain both these materials. Only Catchpole et al.27,31 studied this problem when they considered the simultaneous extraction of seed oil and essential oil from coriander seed. Until now, no attempt has been made at the fractional extraction of vegetable and essential oil. In this work we studied the fractional extraction of essential oil and vegetable oil from fennel seeds by supercritical CO2. Two consecutive extraction steps performed by increasing the extraction pressure were used with the scope of isolating the two different products. On the basis of the experimental evidence, we propose the mathematical modeling of the two extraction processes with the general objective of assessing whether similar or different mathematical models can be used to describe the two extraction processes. Mathematical Modeling General Hypotheses. The modeling of the extraction processes was based on the following hypotheses: (a) Several components are involved in the extraction of seed oil and essential oil. However, we suppose that their behaviors with respect to the mass-transfer phenomena are similar and can be described by a single pseudocomponent. (b) The commonly accepted continuous description of the extraction bed has been assumed with the implicit hypothesis that concentration gradients in the fluid phase develop at larger scales than the particle size. The solute concentration in the fluid phase depends only on time t and on the axial coordinate z. Its value C is given in terms of solid mass per unit of solvent mass. (c) The solvent flow rate, with interstitial velocity u, is uniformly distributed in all the sections of the extractor. The pressure drop can be neglected as well as temperature gradients within the column. The axial dispersion is negligible. (d) The volume fraction of the fluid is not affected by the reduction of the solid mass during extraction;
that is, the solid does not change its volume during the extraction process. Further hypotheses regard the natural matrix. Such kinds of hypotheses are not easily exchangeable among different kinds of matrixes and should be adapted to the specific microscopic structure. (e) The solute in the solid can be present in two separate phases. One phase includes the solute contained inside the particles (the “tied solute” phase). It fills a fraction φt of the overall volume occupied by the seed particles. This value, according to the above hypothesis (d), does not change with time during the extraction process and therefore, φt is considered constant. The average tied solute concentration, in terms of mass of solute per mass of nonsoluble solid, is called P. The other phase is made of the solute freely available on the particle surface. The concentration here is always the same, and according to our hypotheses, it is equal to the pure oil density qo. (f) The fraction of the seed volume filled by the free solute is φf ) 1 - φt. (g) The fraction of the seed occupied by the free solute during the extraction is ψφf, where we always have ψ e 1. (h) Linear equilibrium relationships apply between phases. During the extraction, both the free solute and the tied solute move from the seed particles to the solvent. This flux might reduce the volume occupied by the seed particles and probably change the φf and φt values. In particular, during the extraction, the volume occupied by the free solute phase in the untreated particles is filled by the solvent. Nevertheless, we believe that the external volume of the particle is essentially determined by the structure of the insoluble solids, which is not affected by the extraction. Furthermore, the small value of φf makes negligible the effective increase due to the reduction of the volume occupied by the free solute phase during the extraction. Taking into account that the inclusion of such and φ changes in a mathematical model would make its resolution considerably harder, we avoided it according to hypothesis (d). According to the above hypotheses, the mass balance on the solute in the extractor is
∂C ∂P ∂ψ ∂C Ff + Ffu + (1 - )φtFs + (1 - )φfqo ) 0 ∂t ∂z ∂t ∂t (1) where Ff is the fluid density, which we suppose is not affected by the presence of the solute, and Fs is the bulk density of the nonsoluble solid, which is the mass of nonsoluble solids in the seeds per unit of particle volume. The mass balance on the phase of the tied solute alone is
Jta ∂P )∂t (1 - )φt
(2)
where a is the specific surface of the seed particles and Jt is the mass transfer rate between the tied phase and the fluid phase. The mass balance on the free solute phase alone is
Jfa ∂ψ )∂t (1 - )φf
qo
(3)
Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999 3071
where Jf is the mass-transfer rate between the free solute phase and the fluid phase per unit of surface. In both eqs 2 and 3 the same mass-transfer area a was included. This is not strictly true because fluxes Jf and Jt might affect different area partitions of the particle surface. This model, however, is unable to make a distinction between the effect of a mass-transfer area change and that of a mass flux J change. For this reason, the exchange area was conventionally put equal to a. The system of equations from 1 to 3 has a unique solution when the initial conditions (i.c.) for C, P, and ψ and the boundary condition (b.c.) for C are given:
i.c.: C|t)0 ) C0; P|t)0 ) P0; ψ|t)0 ) ψ0
(4)
b.c.: C|z)0 ) 0
(5)
Moreover, we suppose that the loading time of the solvent into the extractor was long enough to enable the fluid to reach the equilibrium concentration before the extraction started. Therefore, in light of hypothesis (h) we have
qo ) KψC0
(6)
where Kψ is the equilibrium constant between the solvent and the free solute phase. This means that before the extraction starts, a part of the solute present in the seed saturates the fluid. This condition, together with eq 6, implies that the tied solute phase and the solvent are at equilibrium at the extraction start and that, therefore, after hypothesis h:
P0 ) KpC0
(7)
where Kp is the equilibrium constant between these two phases. As a consequence of this hypothesis, free solute alone participates to the initial saturation of the solvent. This condition is necessary for eq 6 to apply. Therefore, the volume fraction ψ0 of the free solute at the extraction start is different from the value of ψ in the untreated seed. The free oil mass balance relates C0 and ψ0 to the loading of the untreated solid:
qo(1 - )φf ) qo(1 - )φfψ0 + C0Ff
(8)
Both equations 6 and 7 are valid under the hypothesis of a linear equilibrium relationship between the solvent and any of the solute phases. This provides a simplified view of the system. However, we do not have more accurate information regarding its thermodynamic behavior, to confidently assume more complex equilibrium models. Experimental Section Apparatus and Experimental Methods. The extraction apparatus mainly consisted of an extractor with an internal volume of 400 cm3 (Di ) 5.5 cm) and two 200 cm3 separators operated in series. The second separator was equipped with a device that allows the discharge of the extracts at fixed time intervals. CO2 was delivered by a high-pressure diaphragm pump (Milton Roy, Milroyal B) capable of operating at pressures up to 500 bar and flow rates up to 4 kg/h of CO2. The instantaneous CO2 flow rate and the total quantity
of CO2 used were measured with a calibrated rotameter (Matheson, 604) and a dry test meter (Sim Brunt, B10), respectively. More details on the apparatus were published elsewhere.22 The experiments were performed on fennel seeds (Foeniculum vulgare Mill.) cultivated in Egypt. Seeds were milled down to a mean particle size of 0.37 mm. Fennel seed particles loaded in the extractor were 281, 304, and 275 g, when the experiments were performed at 0.5, 1.0, and 1.5 kg/h CO2 flow rates, respectively. The asymptotic yields of fennel essential oil and fennel oil were 1.8 and 9.1 wt % of the charged material. A key feature of the extraction process is the fractional separation of the extracts used to isolate seed oil and essential oil from waxes. It is necessary to use the fractional separation, since supercritical CO2 coextracts cuticular waxes that are located on the surface of every vegetable structure (seeds included). Due to their location, it is not possible to use a selective extraction procedure to eliminate waxes. However, selectivity can be recovered during the separation stages, taking advantage of the fact that waxes have near zero solubilities in liquid CO2 at around 0 °C.20,22 Therefore, the first separator was operated at the same pressure of the extraction step and at -2 °C during all the experiments performed. Thermodynamic Feasibility of the Process. Essential oils are typically formed by terpenes and sesquiterpenes (C10 and C15 structures) that are very soluble in supercritical CO2 even at near critical pressures and temperatures. For example, limonene is completely miscible at about 100 bar and 50 °C.32 The main components of vegetable oils are triglycerides whose solubility in supercritical CO2 becomes appreciable at 40 °C for pressures around 200 bar.33 For a comparison of solubilities in supercritical CO2 for these two compound families, see Reverchon.20 Therefore, from a thermodynamic point of view, a fractional extraction of these compounds from vegetable matter using supercritical CO2 is feasible at 40 °C if the first step of the process is performed at 75-90 bar and the second one is performed at pressures of 200 bar or larger. However, process feasibility depends also on the kinetics of the extraction process, that is on the masstransfer resistances in the liquid and solid phases. Essential Oil Supercritical Extraction. The first step of the extraction process was performed at 90 bar and 50 °C with the aim of selectively extracting fennel essential oil. Waxes elimination was demanded from the first separator, as described in the previous section. The extraction and simultaneous isolation of fennel essential oil was successful. In the first separator paraffinic waxes were collected with carbon atom numbers between 25 and 37; this waxes composition agrees well with that of various other vegetable matter extracted by supercritical CO2.20 In the second separator fennel essential oil was collected. It is mainly formed by estragole (about 80%), anethole, fenchone, and limonene and was not contaminated by waxes and by higher molecular weight compounds. The corresponding yield data obtained at different CO2 flow rates are reported in Figures 1 and 2 against the specific mass of CO2 used and against the extraction time, respectively. We obtained an essential oil asymptotic yield of 1.8 wt % of the loaded material. Seed Oil Supercritical Extraction. The second step of the extraction process was performed at 40 °C
3072 Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999
Figure 1. Fennel essential oil extraction yield as a function of the specific mass of solvent used ms/m0. Continuous lines ) model results: (0) 1.5 kg/h; (O) 1.0 kg/h; (4) 0.5 kg/h.
Figure 3. Fennel oil extraction yield as a function of the specific mass of solvent used ms/m0. Continuous lines ) model results: (0) 1.5 kg/h; (O) 1.0 kg/h; (4) 0.5 kg/h.
Figure 2. Fennel essential oil extraction yield as a function of time. Continuous lines ) model results: (0) 1.5 kg/h; (O) 1.0 kg/h; (4) 0.5 kg/h.
Figure 4. Fennel oil extraction yield as a function of time. Continuous lines ) model results: (0) 1.5 kg/h; (O) 1.0 kg/h; (4) 0.5 kg/h.
and 200 bar and was aimed at the extraction of fennel vegetable oil. Also in this case the first separator was used to precipitate coextracted waxes. This stage of the process was also successful. The white mass collected in the first separator was again formed by paraffins, though their molecular weight was slightly larger (carbon atoms from 25 to 41). Fennel oil was collected in the second separator. The corresponding yield data are reported in Figures 3 and 4 against the specific mass of solvent used and against the extraction time, respectively. Some experiments were also performed by a one-step extraction at 200 bar and 40 °C and fractional separation in three separators in series with the aim of separating waxes in the first one, vegetable oil in the second one, and essential oil in the third. However, when we used this procedure, we obtained a lower precipitation selectivity, and small quantities of the vegetable oil were collected together with the essential oil. We obtained an oil asymptotic yield of about 9.2 wt % of the loaded matter.
Discussion Seed Oil. From Figures 3 and 4 it appears that in this case the yield data are quasi-overlapped when reported against the specific mass of CO2, showing the set up of equilibrium extraction particularly in the first part of the extraction. The slope of the yield curves shows solubility values near to those of pure triglycerides in supercritical CO2. Therefore, we think that fennel vegetable oil is freely available for extraction at least during the first linear part of the extraction process. Figure 5 shows the surface of an extracted fennel particle as it appears by scanning electron microscopy (SEM). It shows that the particle surface is formed by a sequence of broken cavities that we call “cells” and that we think contained the fennel vegetable oil which is freely available for extraction. In the inner portion of the particles, the remaining part of the vegetable oil is contained inside closed cells. In a previous work on almond oil extraction,19 SEM analysis of the vegetable structures showed that cells containing the seed oil were almost spherical. In the present case Figure 5 shows
Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999 3073 Table 1. Values of the Parameters Used in Mathematical Modeling of Fennel Vegetable Oil Extraction for the Different Solvent Flow Rates W W (kg h-1)
Kp
Kψ (kg m-3)
ψ0
P0
Fs (kg m-3)
0.5 1 1.5
49.7 52.4 49.7
474 500 474
0.41 0.37 0.43
0.93 0.95 0.93
0.09 0.09 0.09
1120 1100 1100
effective density Fe with a mass balance on the nonsoluble solids:
Fsφt ) Fe(1 - Y∞)
Figure 5. Scanning electron microscopy image of the surface of a fennel particle extracted with supercritical CO2. Broken vegetable structures (cells) that contained the free oil phase are evident. There is no evidence of a specific location of essential oil in the vegetable structure.
hexagonal cell structures with L ) 90 µm and D ) 10 µm with a wall thickness of about 3 µm. We calculated φf ) 0.02. This value is obtained from the broken cells to particle volume ratio. To evaluate the total volume of the broken cells (those which are on the particle surface), we first determined their number, say N, as the ratio between the area of the particle surface and the mean area of the single broken cell appearing on the particle surface. This latter was estimated from the microscope image of the particle (Figure 5). From this value, making a simple geometry consideration and averaging between the results obtained with different hypotheses on the cell geometry, we evaluated the mean volume of the cell V. The total volume of the broken cells is, then, approximately equal to 0.5NV, where the 0.5 factor accounts for the fact that only a portion of the broken cells is available on the particle surface. The particle volume is evaluated from the particle size distribution. We think that, at the start of extraction, the bed height is more than sufficient for the fluid phase to become saturated with seed oil. The rate of extraction is effectively limited by the solubility of the oil in the fluid phase. This situation continues until the depletion of oil from the lower portion of the bed has reduced the effective bed height to the point where the fluid is no longer saturated when it leaves the top of the bed. The rate of extraction then becomes limited by the equilibrium between the solid and fluid phases and the rate of diffusion from the interior of the particle to the particle surface. The initial oil concentration in the fluid C0 can be evaluated from the experimental plot of the oil yield as a function of the mass of solvent flowed ms:
C0 )
me me m0 ms ) ‚ ) Y/ ms m0 ms m0
(9)
where me is the mass of the extracted oil and m0 is the initial mass of seed. The last term of eq 9 can be obtained from the slope of the linear section of the yield curve. Our model also requires the values of the bulk density of the nonsoluble solids Fs and the initial values P0 and ψ0. The value of Fs can be obtained from the particle
(10)
where Y∞ is the ultimate value of the extraction yield, that is, the value of Y at long extraction times. Using the value of C0 obtained from eq 9, eq 8 can be used to evaluate ψ0. A mass balance on the free oil allows us to evaluate P0:
qoφf + P0Fsφt ) FeY∞
(11)
The equilibrium constants Kp and Kψ can be calculated according to eqs 7 and 8. The mass-transfer rates Jt and Jf of oil from the two solid phases were modeled with the constant masstransfer coefficients kt and kf, respectively, and with the hypothesis of solute activity being proportional to the oil concentration in the phases:
Jt ) kt(P - KpC)
(12)
and
Jf ) kf(qo - KψC) for ψ > 0; Jf ) 0 for ψ ) 0 (13) In eq 12, for the tied phase, the driving force is expressed with the use of the average oil concentration P to account for the reduction of the mass-transfer rate at longer extraction times. In eq 13 the pure oil density appears because the oil is considered to be present in a pure phase and, therefore, its activity does not change until it is present. Values of kf = 10-4 m s-1, which are close to the film mass transfer in the fluid phase in the fluid dynamic conditions tested, were used in our calculations. Higher values of kf are not realistic but tend to reproduce results obtained with models which apply the hypothesis of the initial equilibrium regime.34 When our model was tested with such values, no marked differences were observed in the results, suggesting that equilibrium is controlling in the initial stages of extraction. The set of differential eqs 1-7 was solved using a finite difference method. An explicit numerical cell of the Wendroff type was adopted with the Courant number ) 1.35 The proved numerical stability of this cell made the implemented algorithm fairly robust. Since the values of the other parameters have been evaluated directly from experimental measurements (Table 1), the model developed has only one adjustable parameter: the mass-transfer coefficient for the tied oil kt. Furthermore, since the prevailing resistance for the extraction of the oil from the inner cell of the particle depends on the internal mass transfer, kt should be independent of the solvent flow rate. Therefore, we looked for a kt value that, independent from the CO2 flow rate, provided the best fit between the model curves and the experimental data. The best value was kt ) 8 × 10-8 m s-1. Model curves obtained using this value
3074 Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999
of kt are shown by continuous lines in Figures 3 and 4. The general agreement between model and experimental data is fairly good for all the tested conditions. Essential Oil. Essential oil yield data when reported against the specific mass of solvent used are quasioverlapping (Figures 1 and 2). This experimental evidence suggests that also in this case a quasi-equilibrium extraction process has been performed that only slightly depends on CO2 flow rate. The initial slope of the yield curve that can be used to calculate the equilibrium constant (Kp′ ) 9) gives solubility values that are very far from those of the pure terpenes in supercritical CO2 at the used process conditions (90 bar, 50 °C).20 This is coherent with the quasi-equilibrium model according to which essential oil is partitioned between the fluid and solid phases. In the case of fennel essential oil, no specific structures containing these compounds were observed in SEM images. From this observation and experimental results, we assumed that fennel essential oil is adsorbed in the solid vegetable structure forming the seed. The quasi-equilibrium behavior is thus related to the partition of essential oil between the solid and the fluid phases, and the deviation from equilibrium extraction can be attributed to a mass-transfer resistance in the solid phase. As a consequence of all these argumentations, the model that we adopted to describe the SFE of fennel essential oil does not contain the distinction between free and tied solute as in the case of vegetable oil; that is, all the solute related to this part of the extraction was considered as uniformly distributed in the solid phase. Therefore, we used only eqs 1 and 2 with the boundary and initial conditions described by eqs 4 and 5 with φt ) 1 and φf ) 0. In this case, the variables C and P are referred to the concentrations of the essential oil in the fluid and solid phases, C0 ) 0.002, and Kp′ substitutes Kp. Also in this case, the adopted model has only one adjustable parameter: the internal masstransfer resistance. To extract essential oil, the supercritical solvent has to go through the vegetable structure, which is the same situation as that for the case of vegetable oil extraction. Though compounds to be solubilized have very different molecular weights in the case of essential oil and vegetable oil, the solubilization process can be supposed as instantaneous. Therefore, we decided to test the fitting between the essential oil yield data and the model using the same value of the particle mass-transfer coefficient used for the extraction of vegetable oil. Indeed, a fairly good fitting of the experimental results on fennel essential oil extraction has been obtained by least-squares fitting using kt ) 8 × 10-8 ms-1. The comparison between the modeling results and the experimental data is reported in Figures 1 and 2 against the specific mass of solvent used and the extraction time, respectively. Model results are reported as continuous curves. Conclusions The general model proposed has been successfully adapted to the extraction processes of essential oil and seed oil from fennel. Moreover, the same value of the internal resistance allowed us to describe the masstransfer processes in the vegetable structure during extraction.
Nomenclature a ) specific surface of the solid, m-1 C ) solute concentration in the solvent in terms of mass of solute per unit mass of solvent, kg kg-1 C0 ) solute concentration in the solvent at the extraction start, kg kg-1 dp ) particle diameter, m Jf ) volumetric mass-transfer fluxes from the free oil phase to the solvent, kg m-2 s-1 Jt ) volumetric mass-transfer fluxes from the tied oil phase to the solvent, (kg/kg) m s-1 kf ) mass-transfer coefficient from the free oil phase to the solvent, m s-1 kt ) mass-transfer coefficient from the tied oil phase to the solvent, m s-1 Kp ) seed oil equilibrium constant between the tied oil phase and the solvent, dimensionless Kp′ ) essential oil equilibrium constant between the crushed seed phase and the solvent, dimensionless Kψ ) seed oil equilibrium constant between the free oil phase and the solvent, kg m-3 m0 ) mass of the seed charge, kg me ) mass of the extracted oil, kg ms ) mass of the flowed solvent, kg P ) solute concentration in the solid in terms of mass of solute per unit mass of nonsoluble solid, kg kg-1 P0 ) solute concentration in the solid at the extraction start, kg kg-1 qo ) vegetable oil density, kg m-3 t ) extraction time, s u ) interstitial velocity of the solvent, m s-1 Y ) extraction yield, dimensionless Y∞ ) maximum extraction yield, dimensionless z ) axial coordinate in the extractor, m Greek Letters ) voidage of the extraction bed, dimensionless φf ) fraction of the particle volume filled by the free oil phase, dimensionless φt ) fraction of the particle volume filled by the tied oil phase, dimensionless Fe ) density of the untreated particles, kg m-3 Ff ) solvent density, kg m-3 Fs ) density of the nonsoluble solid, kg m-3 ψ ) fraction of free oil content to free oil content in untreated seeds, dimensionless ψ0 ) fraction of free oil content to free oil content in untreated seeds at the extraction start, dimensionless
Literature Cited (1) Taniguki, M.; Tsuji, T.; Shibata, M.; Kobayashi, T. Extraction of wheat germ with supercritical carbon dioxide. Agric. Biol. Chem. 1985, 49, 2367. (2) Fors, S. M.; Ericksson, C. E. Characterization of oils extracted from Oats by supercritical carbon dioxide. Food Sci. Technol. (London) 1990, 23, 390. (3) Christianson, D. D.; Friedrich, J. P.; List, G. R.; Warner, K.; Bagley E. B.; Stringfellow, A. C.; Inglett, G. E. SFE of dry milled corn germ with carbon dioxide. J. Food Sci. 1984, 49, 229. (4) List, G. R.; Friedrich, J. P.; Pominski, J. Characterization and processing of cottonseed oil obtained by extraction with supercritical carbon dioxide. J. Am. Oil Chem. Soc. 1984, 61, 1847. (5) Snyder, J. M.; Friedrich, J. P.; Christianson, D. D. Effect of moisture and particle size on the extractability of oils from seeds with supercritical CO2. J. Am. Oil Chem. Soc. 1994, 61, 1851. (6) Friedrich, J. P.; List, G. R. Characterization of soybean oil extracted by supercritical CO2 and hexane. J. Agric. Food Chem. 1982, 30, 192. (7) Eggers, R.; Sievers, U.; Stein, W. High-pressure extraction of oil seed. J. Am. Oil Chem. Soc. 1985, 62, 1222.
Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999 3075 (8) Favati, F.; King, J. W.; Mazzanti, M. Supercritical carbon dioxide extraction of evening primrose oil. J. Am. Oil Chem. Soc. 1991, 68, 422. (9) Stahl, E.; Quirin, K.-W.; Blagrove, R. Extraction of seed oils with supercritical carbon dioxide: effect on residual proteins. J. Agric. Food Chem. 1984, 32, 930. (10) Ramsay, M. E.; Hsu, J. T.; Novak, R. A.; Reigtler, W. J. Processing rice bran by SFE. Food Technol. 1991, 98. (11) Molero Gomez, A.; Huber, W.; Pereyra Lopez, C.; Martinez de la Ossa, E. Extraction of grape seed oil with liquid and supercritical carbon dioxide. Proceedings of the 3rd International Symposium on Supercritical Fluids; Perrut, M., Brunner, G., Eds.; Strasbourg, 1994; Vol. 2, p 413. (12) Bulley, N. R.; Fattori, M.; Meisen, A.; Moyls, L. Supercritical fluid extraction of vegetable seeds. J. Am. Oil Chem. Soc. 1984, 61, 1362. (13) Lee, A. K. K.; Bulley, N. R.; Fattori, M.; Meisen, A. Modelling of supercritical carbon dioxide extraction of canola oilseed in fixed beds. J. Am. Oil Chem. Soc. 1986, 63, 921. (14) Fattori, M.; Bulley, N. R.; Meisen, A. Carbon dioxide extraction of canola seed: oil solubility and effect of seed treatment. J. Am. Oil Chem. Soc. 1988, 65, 968. (15) King, M. B.; Catchpole, J. R. Physicochemical data required for the design of near critical fluid extraction process. In Extraction of natural products using near-critical solvents; King, M. B., Bott, T. R., Eds.; Chapman and Hall: New York, 1993; p 184. (16) Sovova´, H. Rate of the vegetable oil extraction with supercritical CO2sI. Modelling of extraction curves. Chem. Eng. Sci. 1994, 3, 409. (17) Sovova´, H.; Kucera, J.; Jez, J. Rate of the vegetable oil extraction with supercritical CO2sII. Extraction of grape oil. Chem. Eng. Sci. 1994, 49, 415. (18) Sovova´, H.; Komers, R.; Kucera, J.; Jez, J. Supercritical carbon dioxide extraction of caraway essential oil. Chem. Eng. Sci. 1994, 49, 2499. (19) Marrone, C.; Poletto, M.; Reverchon, E.; Stassi, A. Almond oil extraction by supercritical CO2: experiments and modelling, Chem. Eng. Sci. 1998, 53, 3711. (20) Reverchon, E. Supercritical fluid extraction of essential oils and related materials. J. Supercrit. Fluids 1997, 10, 1. (21) Stahl, E.; Quirin, K.-W.; Gerard, D. Dense gases for extraction and refining; Springer-Verlag: Berlin, 1987. (22) Reverchon, E. Fractional separation of SCF extracts from marjoram leaves: mass transfer and optimization. J. Supercrit. Fluids 1992, 5, 256. (23) Reverchon, E.; Donsı`, G.; Sesti Osse`o, L. Modeling of supercritical fluid extraction from herbaceous matrixes. Ind. Eng. Chem. Res. 1993, 32, 2721.
(24) Santos, R.; Lu, T.; Schlieper, L.; King, M. B.; Bastos, J. Extraction of useful components from herbs using supercritical CO2: experimental findings and data modelling. 3rd International Symposium On high-pressure engineering; von Rohr, Ph. R., Trepp, Ch., Eds.; Elsevier: Amsterdam, 1996; p 399. (25) Goto, M.; Sato, M.; Hirose, T.; Extraction of peppermint oil by supercritical carbon dioxide. Jpn. J. Chem. Eng. 1993, 26 (4), 401. (26) Roy, B. C.; Goto, M.; Hirose, T. Extraction of ginger oil with supercritical carbon dioxide: experiments and modelling. Ind. Eng. Chem. Res. 1996, 35, 607. (27) Catchpole, O. J.; Grey, J. B.; Smallfield, B. M. Near-critical extraction of sage, celery, and coriander seed. J. Supercrit. Fluids 1996, 9, 273. (28) Reverchon, E. Mathematical modelling of supercritical extraction of sage oil. AIChE J. 1996, 42 (6), 1765. (29) Reverchon, E.; Marrone, C. Supercritical extraction of clove bud: Essential oil isolation and mathematical modelling. Chem. Eng. Sci. 1997, 52 (20), 3421. (30) Goodarznia, I.; Eikani, M. H. Supercritical carbon dioxide extraction of essential oils: modeling and simulation. Chem. Eng. Sci. 1998, 53 (7), 1387. (31) Catchpole, O. J.; Andrews, E. W.; Toikka, G. N.; Wilkinson, G. T. Mathematical models for the extraction of oils from plant matrixes using near-critical solvent. Proceedings of the 3rd International Symposium On Supercritical Fluids; Perrut, M., Brunner, G., Eds.; 1994; Vol. 2, p 47. (32) Matos, H. A.; Gomes de Azavedo, E.; Nunes da Ponte, M.; Simoes, P. C.; Carrondo, M. T. Phase equilibria of natural flavours and supercritical solvents. Fluid Phase Equilib. 1989, 52, 357. (33) Bamberger, T.; Erikson, J. C.; Cooney, C. L.; Kumar, S. K. Measurement and model predicition of solubilities of pure triglycerides in supercritical carbon dioxide. J. Chem. Eng. Data 1988, 33, 327. (34) Reverchon, E.; Poletto, M. Mathematical modelling of supercritical CO2 fractionation of flower concretes. Chem. Eng. Sci. 1996, 51, 3741. (35) Lapidus, L.; Pinder, G. F. Numerical solution of partial differential equations in science and engineering; Wiley: New York, 1982.
Received for review January 4, 1999 Revised manuscript received May 20, 1999 Accepted May 28, 1999 IE990015+
