Ind. Eng. Chem. Res. 1993,32, 2721-2726
2721
Modeling of Supercritical Fluid Extraction from Herbaceous Matrices Ernesto Reverchon,' Giorgio Donsl, and Libero Sesti Oss60 Dipartimento di Zngegneria Chimica e Alimentare, Universith di Salerno, Via Ponte Don Melillo, 84084 Fisciano ( S A ) ,Italy
Experimental results of supercritical fluid extraction from various herbaceous matrices are presented. In optimal extraction conditions, the use of a fractional separation technique allows a nearly complete separation of the extract in cuticular waxes and essential oil. The modeling of these results is proposed starting from the description of the mass transfer from a single spherical particle. The simultaneous extraction of two pseudocompounds is assumed to simulate the two compound families obtained by fractionation. T h e model is then extended t o simulate the whole extractor. The yields of essential oil and cuticular waxes obtained from rosemary, basil, and marjoram leaves are fairly simulated by the model. Intraparticle mass transfer resulted as the controlling stage in supercritical extraction of essential oils.
Introduction Supercritical fluid extraction (SCFE) is receiving broad attention for ita potential application in several industries such as food, pharmaceutical, and petroleum. Although several gases can be used for SCFE, C02 is the most commonly utilized, due to its chemical and physical properties: it is not toxic, it is not flammable, and its critical temperature and pressure are not high (31.1 "C and 73.8 bar). Moreover, many compounds show an appreciable solubility in supercritical C02 a t pressures that are technologically simple to withstand. The work performed in this field is mainly experimental and based on laboratory scale plants, while only few SCFE processeshave so far been applied to industrial production. This is partly due to the difficulties in the experimental set up and in the understanding of the behaviour of supercritical solutions. The tuning of reliable models that are able to support scale-up procedures is another activity that needs to be improved in this field. Most of the available SCFE models have been developed for the extraction of oil from seeds (Brunner, 1984; Bulley et al., 1984; Gangadahra and Mukhopadyay, 1988; Gil et al. 1988). This process is characterized by high oil yields and the extracts are formed by similar compounds. These circumstances simplify the experimental work and the process can be mathematically described by a single stage extraction of one pseudocompound. On the contrary, few systematic works are available for SCFE of essential oils from herbaceous matrices that are characterized by low yields with a complex extraction process. The final product consists of many compounds belonging to some families formed by terpenes and their derivatives (Stahl and Gerard, 1985). All these conditions contribute to make it difficult to explore these processes. The SCFE modeling of essential oils shows similarities with SCFE of caffeine from coffee beans as described by Brunner (1984). Bartle et al. (1990)recently have proposed a SCFE model for small amounts of solutes contained in a matrix and dispersed through it. They also applied this approach to selected essential oil compounds. However, their model only takes into account the internal mass transfer resistance. The model only allows the simulation of the asymptotic trend of the extraction curve. Nguygen et al. (1991) using a simple first-order rate expression tried to model C02 SCFE of vanilla pods and obtained an estimate of the internal diffusion coefficient. Kandiah and Spiro (1990) made a first attempt to describe SCFE kinetics of essential oil from ginger rhizomes.
The present work proposes a model description of SCFE from herbaceous matrices such as rosemary, basil, and marjoram leaves. The SCFE products were precipitated in two separators in series and then analyzed by GC-MS. They were characterized as cuticular waxes and essential oil and then simulated as two pseudocompounds extracted in parallel from a spherical particle by supercritical C02 through mass transfer mechanisms in series that include internal and film resistances. The mathematical model proposed resulted in fair agreement with the experimental evidence obtained on different materials, particle sizes, and experimental scales.
Experimental Technique and Apparatus The majority of SCFE experiments was performed on the apparatus schematically shown in Figure 1. It consisted in a thermostated extractor (400 cm3 internal volume) and two separators operated in series (200 cm3 internal volume). Both separators had internal devices to collect the precipitated material accurately. C02 was pumped by a high-pressure diaphragm pump (Milton Roy, Milroyal B) capable of liquid C02 flow rates in the range from 0.5 to 5 dm3/h and able to operate at pressures up to 500 bar. The flow rate of C02 was measured by a rotameter (Matheson 304) and ita volume was totalized by a dry test meter (Sim Brunt B10). Temperatures and pressures were measured by calibrated Fe-Const thermocouples (accuracy f0.1 OC) and Bourdon test gauges (Salmoiraghi SC-3200), accuracy h0.25 bar, respectively. A charge of about 230 g of dried and comminuted material was used in each run. Different mean particle sizes resulted from comminution (see Table I). This operation was not forced to avoid thermal degradation of the starting material. The C02 mass flow rate was 1.2 kg/h. Some extraction tests were performed on a SCFE pilot plant scale apparatus designed as the scale-up of the laboratory one. I t mainly consists of a thermostated extraction vessel (20 dm3) and three separation stages in series. It is equipped with two pumps capable of a maximum C02 flow rate of 50 kg/h each, a Coriolis mass flow meter and cold and warm utilities. The operating conditions performed on the laboratory apparatus were reproduced on the pilot one, with the only exception of process conditions of the last separation stage because the laboratory apparatus operates at open loop while the pilot one recycles the C02 at the exit of the last separation
Q8SS-5SS5/93/2632-2721~Q4.o0/00 1993 American Chemical Society
2722 Ind. Eng. Chem. Res., Vol. 32, No. 11,1993
o m
0
/r
0
*"
1.20
0.80 A
R
W
s 2
Figure 1. Schematic representation of the laboratory apparatus used in SCFE experiments: E, extractor; S1,S2 separators; FM, flow measurement devices.
stage. The last separation stage was operated at 40 bar, 15 OC. Pilot plant tests were performed on basil leaves using charges of about 6 kg of comminuted material with a mean particle size of 0.55 mm. GC-MS analysis was performed by a Finnigan Model 800 ion trap detector connected to a Varian Model 3400 GC. Also a Carlo Erba supercritical chromatograph series 3000,was used to analyze solid extracts that presented some separation difficulties on GC-MS due to the high molecular weight of their constituting compounds. In a typical laboratory extraction test, after the extractor charge and the preliminary start-up operations, the valve located downstream from the extractor was closed and the pump started. Within a few minutes the pressure in the extractor reached the set value; the valve was then opened allowing the COz circulation in the whole apparatus. Pressure and temperature in the two separators were regulated by metering valves and by heating/cooling elements. Typical temperature and pressure in the extractor ranged from 35 to 50 "C and from 80 to 120 bar. Temperature and pressure in the separatorswere selected to reach the complete recovery of waxes in the first separator and of essential oil in the second one. In all experimental tests, operating conditions of the first separator were 0 OC and 80 bar.
Experimental Results The above described procedure allowed the precipitation of a white solid material in the first separator. GC-MS results revealed that this material was mainly made up of n-paraffins ranging from C25 to C35 for all the vegetable matrices tested. The mean molecular weight has been evaluated for each material studied and ranged from 408 to 430 (see Table I). In the second separator the precipitated matter was formed by a low viscosity liquid and a small quantity of water that was separated by centrifugation. GC-MS analysis confirmed that the remaining product can be considered as an essential oil. For example, in the case of rosemary oil, it was made up of hydrocarbon terpenes, oxygenated terpenes, and small amounts of sesquiterpenes (Reverchon and Senatore, 1992). The average molecular weight of the compounds collected in the second separator ranged from 148 to 160. The molecular weight of these products was independent of extraction time. A further series of runs was performed to assess the optimal extraction conditions for the various vegetable species considered. GC-MS analysis was used to characterize the extracted essential oils. Since oxygenated terpenes are considered the most desired essential oil flavor constituents (Coppella and Barton, 19871,optimum extraction was fixed so that the maximum percentage of oxygenated terpenes with respect to the other compounds was produced. It was found that the optimum extraction pressure and temperature for rosemary, marjoram, and
>I 0.40
0.00
t (min) Figure 2. Superposition of experimentaland modelextraction yields for essential oil and cuticular waxea from rosemary leavea: A,eesential oil;
Figure 3. Superposition of experimental and model extraction yields for essential oil and cuticular waxes from basil leaves: 0, essential oil; 0,cuticular waxes.
basil leaves were in the same ranges from 80 to 100 bar and from 40 to 50 "C. Operating conditions of 100bar and 40 O C were selected for all runs performed to evaluate process yields against time. The extraction results are summarized in Figures 2,3,and 4 for rosemary, basil, and marjoram, respectively. Hollow and filled symbols refer to cuticular waxes and essential oil experimental points, respectively. The yield data show that the initial extraction rate of essential oils is high but tends to zero when solute concentration decreases, while the extraction rate of cuticular waxes remains almost constant in the experimental range explored. Also some longer duration experiments (5 h) were performed to assess the initial essential oil content in the vegetable matrices. These experiments where carried out to extract all the essential oil from the solid particles. Thus, it was possible to calculate essential oil concentrations that were reported in Table I. The same experiments did not give similar information for waxes, indeed for these it was impossible to reach the asymptotic trend for yield. The high concentration of waxes on the external part and their low solubility in supercritical COa (Reverchon,1992) led us to hypothesize a spherical particle shell only
Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 2723 1.20
1.20
0.80
0.80
n
n
W
W
R
I
R
*
*
0.40
0.40
0.00
0.00
Figure 4. Superpositionof experimentaland model extractionyields for essentialoil and cuticular waxes from marjoram leaves: W, essential oil; 0,cuticular waxes.
Figure 5. Superpositionof experimentaland model extractionyields for basil essential oil extracted at two different mean particle sizes: 0 , 0.17 mm; W, 0.55 mm.
Table I. Simulation Conditions and Results. basil marjoram rosemary d, = 0.17 mm d, = 0.15 mm d, = 0.23 mm E C E C E C 430 151 428 148 408 M(g/mol) 160 0.075 2.16 co (kmol/m3) 0.063 2.265 0.053 2.37 D, (mZ/s) 1.5 X 1.6 X 1.4 X 3.7 X 2.8 X 9.4 X 10-13 10-17 10-13 10-1' 10-13 10-17
the locations of essential oil in the internal structure and cuticular waxes on the leaf surface allow a simultaneous extraction of both compounds classes (Reverchon, 1992). Moreover, essential oil concentrations in the fluid phase are always very low if compared with the equilibrium value.
a E = essential oil; C = cuticular waxes. All experiments on the laboratory apparatus have been performed at the following conditions: extraction pressure = 100 bar; extraction temperature = 40 O C ; first separator,80 bar and 0 O C ; second separator,25 bar and -5 O C ; COz flow rate = 1.2 kg/h; void fraction = 0.4.
constituted of wax, in cuticular waxes extraction model calculations. The essential oil yield obtained by SCFE was compared with that obtainable by hydrodistillation. In the case of marjoram, maximum SCFE yield was 0.82% while hydrodistillation produced about 0.9% of essential oil. Of course the two products are not completely comparable, as demonstrated for rosemary (Reverchon and Senatore, 1992). Experiments on the pilot plant followed the same procedure used for the ones on the laboratory apparatus. C02 flow rate was scaled-up to operate at the same contacting time (12 min). The same basil cultivar as in laboratory tests was used, with a mean particle size of 0.55 mm. Due to the higher mean particle size tested, longer extraction times were used. The basil essential oil yields obtained from the pilot plant are reported in Figure 5 where they are compared to those of the laboratory apparatus. It is evident that by using a 0.55-mm mean particle size, 5 h is definitely not adequate to extract all the basil essential oil contained in the charge. The measurement of solubilities of essential oil and cuticular wax compounds in supercritical C02 could be of interest in comparing the value of the actual concentration of these compounds with respect to equilibrium conditions. Solubilities of some terpenes and oxygenated terpenes are available in literature (Stahl and Gerard, 1985; Stahl et al., 1986). The solubilities on octacosane and triacontane, assumed as reference compounds representative of cuticular waxes, have been measured by Reverchon et al. (1993). Solubilities of essential oil compounds are over 2 orders of magnitude higher than those of cuticular wax compounds in the described process conditions. However,
Extraction Model Different approaches can be adopted in SCFE modeling. The successful approach adopted in modeling SCFE of seeds (Bulley et al., 1984;Schaeffer et al., 1989)represents the overall fixed bed behavior by the differential mass balance for the solute in the supercritical phase and in the solid phase. These balances are coupled with an equilibrium relationship to evaluate the mass transfer coefficient of the extraction process. This approach can be adopted when solubility equilibria or external diffusion are the limiting stages. When intraparticle or internal diffusion controls the mass transfer process, it is opportune to start studying mass transfer between a singleparticle and the supercritical solvent and then extend the results to the whole bed. Although typical vegetable particles do not conform to these assumptions, we elected to develop a simplifiedmodel based on the hypothesis of a bed formed by spherical particles of the same shape and size. Bartle et al. (1990) utilized a similar approach and based their solution on the hypothesis that mass transfer resistance on the fluid side is equal to zero. In this work, the extraction process from a single particle has been described by the following stages in series: (1) C02 diffusion in the SCF film around the particle; (2) C02 penetration and diffusion in the particle; (3) compound solubilization; (4) product diffusion through the solid; (5) product diffusion through the SCF film. In stages 2 and 4 we presumed equimolar counterdiffusion. Moreover, because information about the kinetics of the single processes is missing, the same stages have been considered together through the definition of an overall solid diffusivity. Similarly steps 1and 5 have been represented as an overall solid-supercritical fluid diffusivity. Moreover we assumed that (a) the particle diameter is the weight mean diameter of the measured size distribution, (b) extraction of essential oils and of cuticular waxes are parallel and noninteracting processes, (c) diffusivities
2724 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993
of essential oils and cuticular waxes in the vegetable matrix are independent from particle radius, and (d) oils and waxes are both considered as a single chemical compound. Hypothesis b is particularly well suited in SCFE of essential oils due to the fact that essential oil concentration is very low if compared with equilibrium solubilities.
Mathematical Representation The material balance across an internal particle surface of radius r, referred to component i, results in the first Fick's law, that for constant density and diffusivity in the solid and in spherical coordinates ( r , 8, $1 is Ni = -cigrni X
where N = N ( t ) is the material flux, co is the initial concentration in the solid matrix, X r , xg, and x+ are the dimensionless concentrations, functions of the extraction time, along coordinates r, 8, and $, respectively, and D , is the diffusivity in the solid matrix. If the concentration of component i is independent from coordinates 8 and $, eq 1 can be reduced to Ni =-Cismi
(--a:: ) 2:
Ni = kei(ci - cif)
(3)
where ci is the concentration of component i at the particle surface, Cif is the concentration of component i in supercritical phase, and kei is the particle to supercritical phase mass transfer coefficient. From eq 2 and the boundary condition 3, applying the Fourier transforms and the heat-mass transfer analogy, the following general solution is obtained (Wong, 1977) (Cif-
io)
Uei
(7)
Tan et al. (1988)estimated an external diffusivity of about 1 X lo4 m2/s for the same range of pressure and temperature investigated in the present work and for the P-naphthollCO2 system. Since P-naphthol has a similar molecular weight to essential oils, we assumed this value for Dei of oils. The same value was considered for waxes as well. Relationship 4, coupled to the particular solution obtained from eq 5, allows the quantitative calculation for the extraction of component i from the single particle against extraction time. The extension of the model results to the whole bed can be made on the assumption that all the particles in it behave in the same way. The number of particles that constitute the bed are
- 6V(1nP
-
e)
ird;
where V is bed volume, e is void fraction, and np is the number of particles; the total amount of product extracted is thus
ir
The same material flux must fit the transport equation on the external surface
Ni = 4R
2Rkei Sh=-fF-
X
where R is the particle radius. Equation 4 is a general allow the particularization solution of eq 2; the terms for a given system. The value of each term of the series is defined by the periodic equation
where &i are the k solutions related to the compound i. In order to calculate phi from eq 5, kei and D,i have to be evaluated. Dmi will be used as the model parameter to obtain the best fit of the experimental data. The external mass transfer coefficients can be obtained from semiempirical correlations that connect mass transfer to the other process parameters through convenient dimensionless numbers. We used the relationship proposed by Tan et al. (1988) for solid-fluid mass transfer in a supercritical fluid extractor.
Sh = 0.38Re0.a3Sc'/3
(6) Then the external mass transfer coefficient can be calculated using the Sherwood number definition if a value of Dei is available
Equation 9 holds in the hypothesis that all the particles in the bed have reached the same extraction stage during the whole process, thus neglectingthe concentration profile that occurs along the bed when supercritical COZflows through it. This approach is consistent with the aim of providing a model more than a precise description of the systems to which it is applied. I t can be regarded in the same manner as the hypothesis that the particles are spherical and of the same size. Moreover, modeling caffeine extraction from coffee beans, Brunner (1984) adopted an enhancement factor that was empiricallyfound by Schlunder (1981) for heat transfer in packed beds. This assumption is equivalent to the one that holds for eq 9. It is then possible to model yield (y) against time ( t ) , by defining
where W is the total weight of herbaceous matter in the fixed bed. The yield curves obtainable from eq 10can be compared to the experimental data by applying the least-squares method in which the solid diffusivity Dmi is assumed as the adjustable parameter. Moreover, it is possible to evaluate the concentration profile of the extractable material along the particle radius at different extraction times. For this purpose the differential material balance on a component i located in a particle can be written as follows: aci rar
1 aci) = D m i[ -1- X + vg -1r aci - + V d -r2 ar ae r s m $ a$
Equation 11has been developed, according to Bird et al. (19601, including the unsteady term and mass fluxes across each coordinate. The velocity vr of the compound i can be considered equal to zero because compounds of interest do not change their position with respect to the
coordinate system. Moreover, when concentration of component i is independent from C$ and 0 and its diffusivity does not depend from radius r, as hypothesized above, eq 11 can be reduced to
Ind. Eng. Chem. Res., Vol. 32, No. 11,1993 2725 1 .o 0.8
X oil 0.6
This equation is mathematically analogous to the representation of the unsteady cooling of a hot sphere suddenly immersed into a cold fluid and its solution has been proposed by several authors for different boundary conditions (Carslaw and Jaeger, 1959;Crank, 1975;So and Mcdonald, 1986). The general solution of eq 12, obtained by applying the Fourier transforms and the heat and mass transfer analogy (Wong, 1977) is
(13) where xi is the dimensionless concentration of compound i in the solid particle. If the same particular solution obtained for eq 5 is applied to 13, it is possible to evaluate the concentration profiles of the extracting compound against particle radius and time.
Comparison between Model and Experimental Results Experimental results showed two distinct trends of extraction yield against time for essential oils and cuticular waxes. Essential oils showed a faster extraction rate at low extraction times and a subsequent progressivedecrease up to an asymptotic value that corresponds to complete depletion of the essential oil in the vegetable matrix. On the contrary, cuticular waxes showed an approximately linear extraction rate in the whole range of experimental conditions explored. These behavior differences can be explained by the different location of the considered compounds in the herbaceous matrices. Cuticular waxes are mainly located within a thin layer that covers the leaves. On the contrary, essential oils are located in the internal part of the leaves in cellular organelles called vacuoles and in epidermal hairs (Reverchon, 1992). These behaviors can be simulated by different hypotheses about the initial distribution of the extractable materials. It is assumed that essential oil compounds are uniformly distributed within the matrix, whereas cuticular waxes are supposed to be located in a narrow layer on the particle surface. These assumptions and the results of exhaustive extraction tests allowed us to evaluate concentration of the pseudocompounds that simulates essentialoils (see Table I). Concentration of cuticular waxes has been arbitrarily set at the value of pure compound particle since no asymptotic trend has been observed. The best fit between the model and the experimental data has been evaluated starting from the material balance of eq 1. Model results are shown by a continuous line in Figures 2, 3, and 4 for rosemary, basil, and marjoram, respectively. The evaluated yields of both essential oils and cuticular waxes, showed a good fit for the vegetable matrices tested. The multiple correlation parameter (R2) ranged between 0.98 and 0.99.
0.4
0.2
0.0
Figure 6. Dimensionless concentration profile of essential oil along a basil particle, against radius (r). Concentration curves are spaced at 12-min intervals that is the contacting time during SCFE process. Two successive curves can be regarded also as the concentration profile along two different particles located at top and at bottom of the bed (see text). The insert in semilogarithmic scale depicb interface concentration.
As a consequence of the hypothesis on initial concentrations of the pseudocompounds, only the diffusivities related to essential oils have a physical significance. They range between (1.5 and 2.8) X 10-13 m2/s. This is a reasonable result because the tested herbaceous matrices are botanically similar and extracted compounds approximately have the same mean molecular weight (see Table I). Nguyen et al. (1991) obtained a similar value for diffusion coefficient in SCFE of vanilla pods (3 X 10-13 m2/8 ) . The comparison of diffusivities calculated for essential oils, with the values given by Brunner (1984) for rapeseed oil extraction, shows that our values are lower by some orders of magnitude. This result could be related to the higher mass transfer resistance offered by herbaceous matrices. It can be supposed that in seed particles the oil is readily available next to the surface (Lee et al., 1986). In other words, in the extraction of essential oil the mass transfer controlling stage is related to intraparticle diffusion. Different correlations have been tested in the evaluation of the external mass transfer coefficient, but all resulted in values of the external resistance some orders of magnitude lower than those for the internal mass transfer resistance. Thus their influence on the modeling results is limited. SCFE extraction tests were performed on basil leaves and on the pilot plant described in the Experimental Section with the aim of providing the extension of the model to different particle sizes and different processes scales. Results are shown in Figure 5. The same diffusivity has been used for both the experimental seta modeled. Again there is a fair agreement between experimental data and modeled results. Therefore, not only different materials but also different particle sizes and experimental scales are fairly modeled. Figure 6 reports the basil essential oil concentration along the particle radius at different extraction times, as obtained from eq 13. Surface concentration reaches much lower values than the initial one, confirming that external mass transfer resistance is significantly lower than the internal one. However, the interface concentration is not
2726 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993
equal to zero as from the insert in Figure 6, proposed in semilogarithmic scale. Further considerations can be formulated about the hypotheses in the model. We considered all particles in the extractor at the same concentration during the whole extraction process. It is possible to take into account the different concentrations that occur in the particles at different bed heights by introducing differential mass balances, This implies the transformation of the mathematical model in a distributed parameters problem. During COz charge and pressurization in the extractor all particles in the bed are in similar conditions. After this first stage, different particle concentration profiles establish along the bed. Also Figure 6 shows the concentration profile into particles at different quotes along the extractor at fixed times. Each curve is spaced at 12 min, that is the contacting time between supercritical fluid and the bed. Then, two subsequent curves can be the representation of particle concentration profile at the bottom and at the top of the bed. Surface concentration differences against the bed height tend to decrease with extraction time; the overall difference is not negligible but does not significantly affect the proposed description.
Conclusions The extraction of essential oils from herbaceous matrices cannot be adequately described by the same model developed for the extraction of oil seeds. The proposed model, based on a single particle approach and on the definition of an internal diffusivity, allows a fair fitting of the available experimental data for different materials, mean particle sizes,and experimental scales. Intraparticle diffusion resulted as the controlling stage for all the analized matrices. Further refinements of the model are possible in order to take into account particle shape and size distribution.
Acknowledgment The work was partly developed within the Progetto Finalizzato Chimica Fine, supported by C.N.R. (National Research Council), Roma, Italy.
Nomenclature c = concentration in the solid (kmol/m3) co = starting concentration in the solid (kmol/m3)
cf = concentration in the supercritical phase (krnol/mS)
D, = diffusivity in the solid matrix (m2/s) De = diffusivity in the film surrounding the particle (m2/s) d, = spherical particle diameter (m) E,,&) = total extracted product (kmol/s) k , = external mass transfer coefficient (m/s) M = average molecular weight (g/mol) N = material flux of componet i from a single particle (kmol/ (m28 ) ) np = number of particles in the bed r = particle radius variable (m) R = particle radius (m) R e = Reynolds number Sc = Schmidt number Sh = Sherwoood number t = time (s) v = convection velocity (m/s) V = bed volume (m3) W = bed mass (kg) x = concentration (CJCio, dimensionless) Y = extraction yield ('3% )
Greek symbols
fl = solution of eq 5 c = void fraction 0 = spherical coordinate 4 = spherical coordinate Subscripts
i = compound index k = vector index of the solutions of eq 5
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Carslaw, H. S.; Jaeger, J. C. Conduction of Heat in Solids; Clarendon: Oxford, 1959,233 pp. Coppella, S. J.; barton, P. Supercritical Carbon Dioxide Extraction of Lemon Oil. ACS Symp. Ser. 1987, No. 329,202. Crank, J. The Mathematics of Diffusion;Clarendon: Oxford, 1975, p 89.
Gangadahra Rao, V. S.; Mukhopadhyay, M. Mass Transfer Studies for Supercritical Fluid Extraction of Spices. First Int. Symp. Supercrit. Fluids 1988, 643. Gil, M. G. B.; King, M.; Bott, T. R. Extraction of Rape-Seed Oil using Compressed COz: Evaluation of Mass Transfer Coefficients. First Int. Symp. Supercrit. Fluids 1988, 651. Kandiah, M.; Spiro, M. Extraction of Ginger Rhizomes: Kinetic Studies with Supercritical Carbon Dioxide. Znt. J. Food Sci. Technol. 1990,25, 328. Lee, A. K. K.; Bulley, N. R.; Fattori, M.; Meisen, A. Modelling of SupercriticalCarbon Dioxide Extraction of Canola Oilseed in Fixed Beds. JAOCS, J . Am. Oil Chem. SOC.1986,63, 921. Nguyen, K.; Barton, P.; Spencer, J. S. Supercritical Carbon Dioxide Extraction of Vanilla, J. Supercrit. Fluids. 1991,4, 40. Reverchon, E. Fractional Separation of SCFE Extracts from Marjoram Leaves: Modeling and Optimization. J. Supercrit. Fluids 1992, 5 , 256. Reverchon, E.; Senatore, F. Isolation of Rosemary Oil: Comparison between Hydrodistillation and Supercritical COz Extraction. Flavour Fragrance J . 1992, 7 , 227. Reverchon, E.; Russo, P.; Stassi, A. Solubilities of Solid Octacosane and Triacontane in Supercritical Carbon Dioxide. J. Chem. Eng. Data 1993,38,458. Schaeffer, S. T.; Zalkow, L. H.; Teja, A. S. Modelling of the Supercritical Fluid Extraction of Monocrotaline from Crotalaria Spectabilis. J. Supercrit. Fluids 1989,2, 15. Schlunder, E. U. Einfuhrung in die Warmeubertragung; Vieweg: Braunschweig, 1981. So, G. C.; Mcdonald, D. G. Kinetics of Oil Extraction from Canola (rapeseed), Can. J . Chem. Eng. 1986,64, EO. Stahl, E.; Gerard, D. Solubility Behaviour and Fractionation of Essential Oils in Dense Carbon Dioxide, Perfum. Flavor. 1985,10, 29. Stahl, E.; Quirin, K. W.; Gerard, D. Verdichtete Gasen zur Extraktion und Raffination; Springer Verlag: Berlin, 1986.
Tan, C. S.; Liang, S. K.; Liou, D. C. Fluid-Solid Mass Transfer in a Supercritical Fluid Extractor. Chem. Eng. J. 1988,38, 17. Wong, H. Y. Heat Transfer for Engineers; Longman Group. Ltd.: Birmingham, AL, 1977; p 36. Received for review May 17, 1993 Accepted July 30, 1993' Abstract published in Advance ACS Abstracts, October 1, 1993.
