Supercritical carbon dioxide extraction of essential oils:: Modeling and simulation

J. of Supercritical Fluids 39 (2007) 338–346 Supercritical carbon dioxide extraction of essential oils from plants with secretory ducts: Mathematical modelling on the micro-scale Irena Zizovic ∗ , Marko Stamenić, Aleksandar Orlović, Dejan Skala University of Belgrade, Faculty of Technology and Metallurgy, Karnegijeva 4, P.O. Box 3503, 11120 Belgrade, Serbia and Montenegro Received 20 September 2005; received in revised form 20 January 2006; accepted 16 March 2006 Abstract In this study, the supercritical carbon dioxide extraction of essential oils from plants which contain secretory ducts as essential oil reservoirs was investigated and modelled. Supercritical carbon dioxide extraction of essential oils from Asteraceae family species, marigold and chamomile, indicated that particle size had no significant influence on the extraction rate in two outermost cases: fine milled plant material and plant material cut to particle length of 5 mm. This confirmed previously reported phenomenon that in some cases particle size had no influence on the rate of supercritical extraction process. In order to explain this behavior, the mathematical model which took into consideration the phenomena occurring on the secretory duct scale, was developed and applied to simulate experimental data of marigold and chamomile supercritical carbon dioxide extraction. Proposed model was also applied to the literature experimental data of fennel fruit supercritical fluid extraction where the same phenomenon had been observed. To obtain information regarding secretory structure, scanning electron microscopy investigation of the plant material was performed. Very good agreement of the model results and experimental data in the case of different plant species, extraction conditions and particle sizes, confirmed the basic hypothesis of the model. © 2006 Elsevier B.V. All rights reserved. Keywords: Supercritical fluid; Mathematical modelling; Extraction; Essential oil; Natural products 1. Introduction Essential oils with or without resins and gums are found in special secretory structures located within plant tissues or on the surface of the plant (trichomes). The type of secretory structure is specific to the plant family or species [1]. Process of the essential oil isolation, either by extraction or distillation, should be dependent on the oil storage and the type of secretory structure. Secretory structures within plant tissue can be secretory cells, secretory cavities or secretory ducts. Secretory ducts are elongated cavities and they often branch to create network extending from the roots through the stem to the leaves, flowers and fruits [1]. They can be found in all species of the family Apiaceae (Umbelliferae) including angelica, ajowan, celery, parsley, caraway, cumin, dill, coriander and anise as well as in the largest family of plants Asteraceae (Compositae) comprising approximately 23,000 known species including chamomile, marigold, yarrow, tarragon, wormwood, arnica and mugwort. ∗ Corresponding author. Tel.: +381 11 3303 795; fax: +381 11 3370 387. E-mail address: [email protected] (I. Zizovic). 0896-8446/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.supflu.2006.03.009 Secretory ducts are also present in Hypericaceae, Pinaceae and Coniferae families. In fruits they are called vittae (fennel, caraway, parsely, cumin, celery). Recently, techniques involving nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) have been used increasingly to study plant physiology and metabolism including localization of triglyceride and essential oil accumulation in Apiaceae family fruits [2,3]. Results of these investigations showed that the fruit was shizocarp with two single-seeded mericarps (units of structure of the female portion of flower). The mericarps had six oil canals (vittae), which were associated with essential oil accumulation in Apiaceae. Reserve oil (triglycerides) was located in the seeds. Therefore, it was observed that the essential oil and triglycerides were located in separate, well-defined compartments, mericarp channels and seed endosperm. This is the fact of interest from the point of both, essential and fatty oil extraction. Supercritical fluid extraction (SFE) of essential oils with carbon dioxide has certain advantages over steam distillation. Steam distillation can lead to thermal degradation and partial hydrolysis of some essential oil compounds. SFE with carbon dioxide can be performed at temperatures around 313 K, thereby preserving original oil composition and properties. Along with I. Zizovic et al. / J. of Supercritical Fluids 39 (2007) 338–346 SFE investigations, mathematical models of these processes were developed. Mathematical model widely used in the literature, was introduced by Sovová [4]. Basic assumption of the model is that part of the cells (the hypothetical oil containing units) was opened by milling. The easily accessible solute from the cells opened by milling is extracted first, and the slower extraction of the solute protected by the cell walls follows. Advantages of this model are that it can be applied on any type of herbaceous material, and on the SFE of both, essential and fatty oils. Significant contribution to the modelling of essential oil SFE was given by Reverchon et al. [5–8] who introduced models based on the differential mass balance for the extractor vessel and heat transfer analogy. Essential oil SFE processes were modelled on the macro-scale by many authors, and experimental results were described well by the proposed models [4–14]. Recently, Sovová [14] has introduced new model for SFE of natural products, also based on the concept of broken and intact cells with two extraction periods, the first one governed by phase equilibrium and the second one governed by internal diffusion in particles. A detailed description of the first period was given where different types of phase equilibrium and solvent flow patterns were taken into account. The number of model parameters was from four to seven depending on the process complexity. Zizovic et al. [15–17] introduced micro-scale mathematical models of essential oil SFE process based on the hypothesis that essential oil extraction process should be dependent on the type of secretory structure. The aim of these studies was to verify the phenomena on the micro-scale and to optimize the SFE process according to the behavior of specific secretory structure during the extraction. In the case of Lamiaceae family species, it was found that peltate glands (essential oil reservoirs) underwent break-up due to the influence of supercritical carbon dioxide (SC CO2 ) on the gland membrane. The model was successful in simulating literature experimental data and it enabled SFE process optimization of Lamiaceae family species (mint, basil, rosemary, marjoram, sage, oregano, lavender, thyme) [16]. Mathematical modelling on the micro-scale of the essential oil SFE processes should therefore take into account the type of secretory structure (oil reservoir), the phenomena occurring on the micro-scale and the impact of these phenomena on the macro-scale process. In this study, the previously reported phenomenon [18,19] that in certain cases particle size had no influence on the SFE process is investigated on the micro-scale. Coelho et al. [18] studied SFE of essential oil from fennel fruits (Apiaceae) and reported that for different particle sizes, no significant change in evolution of extraction yield was observed, in fact the extraction yield curves overlapped for different particle sizes as a function of the extraction time at a fixed flow rate. Bocevska and Sovová [19] studied the SFE of essential oil from yarrow flower (Asteraceae) and reported that the pretreatment of yarrow flowers (fine milled or cut with scissors) did not affect the extraction rate. These results can be explained by the consideration of the phenomena taking place on the secretory structure scale, which is in both cases a secretory duct. The influence of particle size on the SFE yield was observed only during the SFE of seed oils from parsley fruits (Apiaceae) [20]. The authors reported the effect of particle size on the evolution of extraction yield at 10 MPa, 339 318 K and at SC CO2 flow rate of 1.1 kg/h. For the particle size of 495 ␮m reported yield at the end of extraction process was 5.5 wt.%, and for the particle size of 293 ␮m reported yield at the end of the extraction process was 8 wt.%. However, the essential oil content determined by hydrodistillation was 4.5 wt.%. This indicates that, especially in the case of SFE from very small particles of 293 ␮m, some compounds from the damaged seed endosperm were probably extracted as well. In order to investigate SFE from secretory ducts and the influence of particle size on the evolution of extraction yield, two herbs from Asteraceae family, marigold and chamomile, have been chosen. The proposed mathematical model was applied to simulate SFE processes from marigold and chamomile. The model was also applied to the previously published data [18] in order to simulate SFE from fennel fruits. 2. Materials and methods 2.1. Materials and equipment Dried flowers of marigold (Calendula officinalis) and chamomile (Matricaria recutita) grown in central Serbia were used for SFE experimental studies. Conventional method of marigold essential oil production is the extraction with organic solvents. Therefore, as a characterization of plant material extraction of the dry marigold flowers with n-hexane in Soxlet apparatus was performed and 6.11 wt.% of extract was obtained. Hydrodistillation of marigold flowers yielded 0.11 wt.% of volatile oil while hydrodistillation of chamomile flowers yielded 0.7 wt.% of deep blue oil. Moisture contents were determined on a Metrohm 737 Karl Fischer Coulometer equipped with 832 KF Thermo trap. Samples of plant material were treated at 378 K for 1 h. Determined moisture values were 10.62 and 10.25 wt.% for marigold and chamomile flowers, respectively. For the purpose of secretory structure analysis and mathematical modelling, dried fruits of fennel (Foenicum vulgare) grown in northern Serbia were used. Extractions with SC CO2 were carried out in an Autoclave Engineers Screening System shown in Fig. 1. The Supercritical Extraction Screening System is designed for small batch research runs using CO2 as the supercritical medium with Fig. 1. Schematic presentation of the autoclave engineers screening system—T: CO2 storage tank; C: cryostat; LP: high pressure liquid pump; E: extractor vessel; S: separator vessel. 340 I. Zizovic et al. / J. of Supercritical Fluids 39 (2007) 338–346 maximum allowable working pressure of 41.3 MPa at 511 K. Liquid CO2 is supplied from CO2 cylinder by a siphon tube. The liquid CO2 is cooled in cryostat between the cylinder outlet and the pump to prevent vaporization. The pump is liquid metering pump with a maximum output pressure of 41.3 MPa and an adjustable flow rate from 38 to 380 ml/h. The CO2 is pumped into the system until the required pressure is obtained. Back pressure regulators are used to set the system pressure (in extractor and separator). The extractor vessel (150 ml) is filled with the plant material from which a substance is to be extracted. Heaters are supplied on the extractor vessel for temperature elevation. The SC CO2 flows through the extractor and enters the separator vessel (500 ml). Samples of the extracted substance can be taken by opening the ball valve located at the bottom of the vessel. A flowmeter is provided to indicate the flow rate of CO2 being passed through the system and the flow can be adjusted by micrometering valve. The CO2 continues to flow out of the separator through the flowmeter/totalizer and out to atmosphere. Plant tissue images were obtained on a scanning electron microscope (SEM) JSM-T20 (Japan). 2.2. Methods Flowers of marigold and chamomile were fine milled and sieved to particle diameter of 0.7 mm or cut to an average particle length of 5 mm for the determination of the influence of particle size on the SFE process. In order to suppress co-extraction of undesired higher molecular-weight compounds, Reverchon [21] recommends to carry out SFE of essential oils at SC CO2 densities which correspond to temperatures from 313 to 323 K and pressures from 7.8 to 10 MPa. The influence of SFE conditions on obtained yield was investigated for marigold and extractions of milled and cut material were performed at temperatures of 313 and 323 K and pressures of 9 and 10 MPa. In the case of chamomile, extractions of milled and cut material were carried out at 313 K and 10 MPa. The amount of total extract was measured during the extraction. SC CO2 flow rate was 0.3 kg/h in all the experiments and the mass of marigold and chamomile samples was 19 and 30 g, respectively. SEM analysis was performed in order to investigate marigold, chamomile and fennel fruit secretory ducts. The samples were mounted onto metal cylinders using collodial silver paste (Dell Pena, Inc.). The tissue samples were gold coated with alloy Au–Pd (85:15). 2.3. Mathematical modelling To simulate SFE from caraway fruits secretory ducts, Zizovic et al. [17] developed mathematical model without fitting parameters. In this study, the proposed model was applied to simulate SFE from marigold and chamomile flowers as well as from the fennel fruits [18]. The following assumptions describing the secretory ducts behavior during SFE process and the process itself, were used to derive the essential oil extraction model: - The system is isothermal and isobaric and the properties of supercritical CO2 are constant. - The axial mixing of SC CO2 exists in the extractor and the flow rate of SC CO2 is constant during extraction process. - The essential oil is represented by a single pseudo component and it is stored in the secretory ducts as essential oil reservoirs. Pseudo components are ␣-bisabolol, methylhexadecanoate and anethole, for chamomile, marigold and fennel, respectively. - An average duct diameter is adopted according to SEM images and the duct length is equal to an average particle diameter. - The ducts are opened on both sides by grinding pretreatment and SC CO2 dissolves in the oil causing the oil volume increase, which leads to the essential oil (oil phase containing dissolved CO2 ) pouring out from the ducts and external wetting of the particle. - All particles are spherical and equally wetted and in the case of 5 mm particles (cut plant material) volume-average particle diameter was used. - SC CO2 penetrating and dissolving into the oil phase inside the duct are instantaneous processes that occurred during pressurization of the system prior to the extraction. - SFE of the oil that embeds the particles takes place first, and diffusion through the film around the oil phase controls the extraction process during this period of SFE. - Subsequent to the extraction of the essential oil embedding the particles, the SFE of the oil from secretory ducts starts. As the essential oil contained in the duct is discharged due to the extraction process, the oil front is moving towards the centre of the duct and diffusion of the oil through the supercritical phase inside the duct is present. Diffusion through the film around the particle is present as well. - Diffusion through the duct is not obstructed by the duct diameter and it is represented by the molecular diffusion of the essential oil through SC CO2 . Material balance for the supercritical phase in the extractor vessel, for isothermal and isobaric system can be written as: ∂csf ∂2 csf ∂csf = Dl + ST −u 2 ∂t ∂x ∂x (1) Where csf is the essential oil concentration in supercritical phase, t the extraction time, x the axial coordinate along the extractor, Dl the axial dispersion coefficient, u the superficial supercritical fluid velocity and ST the is Source and Transfer term which describes essential oil transfer from specific secretory structure to supercritical fluid phase. The corresponding initial and boundary conditions are: t = 0, 0 ≤ x ≤ L, t > 0, x = 0, t > 0, x = L, csf = 0 csf = 0 ∂csf = 0, ∂x where L is the extractor length. (1a) (1b) (1c) I. Zizovic et al. / J. of Supercritical Fluids 39 (2007) 338–346 According to the basic hypothesis of the model, the following mathematical equations describing the secretory duct Source and Transfer term (ST) can be written as: 341 ST = aw k(c∗ − csf ), for t ≤ tw (2a) where D is the binary diffusion coefficient of the oil in SC CO2 phase, cd the oil concentration in the SC CO2 phase inside the duct and z is the axial coordinate of the secretory duct and cd (z = 0) = ce . Initial condition of Eq. (8) for each space increment was: ST = ad k(ce − csf ), for t > tw (2b) ce = c∗ where tw is the time when the oil that embedded the particles is extracted, c* the equilibrium concentration of the essential oil in SC CO2 on SC phase–essential oil interface, ce the essential oil concentration in SC phase at the duct end, aw the specific surface of wetted particles referred to SC fluid volume and it is dependant on time, position in the extractor and the quantity of oil that surrounds the particles, ad the specific surface of open duct ends available for mass transfer referred to SC fluid volume and k is the mass transfer coefficient through the SC film surrounding the particles. Eq. (1) was solved using the finite difference method in explicit form [22]. For this purpose the extractor was divided into twenty space increments. Specific surface for SFE from the ducts was calculated from: 2 ad = 2N(dd /2) π VE ε (3) where N is the number of secretory ducts, dd the secretory duct diameter, ε the void fraction of the bed and VE is the volume of extractor vessel. Specific surface of wetted particles was calculated from: aw = 3(1 − ε) Rw ε (4) where Rw is the radius of wetted particle which is a function of time, position in the extractor and the quantity of oil that surrounded the particle. All particles are equally wetted and the oil film thickness around each particle is the same at the beginning of SFE. Decrease of the wetted particle volume due to the extraction from the oil film can be defined as: d(csat Vw ) = 4πR2w k(c∗ − csf ) dt for t = tw when duct discharging starts. 2.4. Parameter identification and correlations Total number of secretory ducts (N) was calculated on the basis of the essential oil quantity in plant tissue and the average volume of secretory duct. Volume of the essential oil from secretory duct after saturation with CO2 and the quantity of dispensed oil was calculated using Peng Robinson Equation of State [23]. Solubility of SC CO2 in the essential oil phase was calculated from the empirical correlation given by Gaspar et al. [24]: oil cCO = k1 P 6 + k 2 P 5 + k 3 P 4 + k 4 P 3 + k 5 P 2 + k 6 P 2 Sh = 0.38Re0.83 Sc1/3 Re = ρdp u , µ (12) Sc = µ ρD (13) ShD dp (14) where csat is the essential oil concentration in the oil film around particle which is constant and equal to the concentration of the oil in liquid phase saturated with CO2 and Vw is the wetted particle volume. The volume of the wetted particle is: k= 4 3 πR 3 w (6) According to Eqs. (5) and (6), for each time and space increment Rw can be obtained from: − k ∗ dRW = (c − csf ) dt csat (7) The essential oil concentration in SC phase at the duct end was calculated from the equal fluxes on the duct end–SC phase interface for each time and space increment: −D dcd = k(ce − csf ) dz (8) (11) where Re, Sc and Sh are Reynolds, Schmidt and Sherwood numbers, respectively, defined as follows: and Vw = (10) where P is pressure and constants k1 –k6 are empirical coefficients. On the basis of this solubility value the concentration of the oil phase saturated with SC CO2 (csat ) in the oil film around the particles can be calculated. Mass transfer coefficient (k) in the SC film around the particles was estimated using empirical correlation given by Tan et al. [25]: (5) − (9) where dp is the particle diameter, ρ the density of SC CO2 , µ the viscosity of SC CO2 and D is the binary diffusion coefficient of essential oil in SC CO2 phase. The viscosity of SC CO2 was estimated using empirical correlation [26]. The binary diffusion coefficient for essential oil/SC CO2 system in SC film around the particle was calculated from the equation given by Catchpole and King [27]. The axial dispersion coefficient in SC phase was calculated using correlation given by Tan and Liou [28]: Pe = 1.634Re0.265 Sc−0.919 (15) where Pe is Peclet number, and Dl = udp Pe (16) The solubility of essential oil in SC CO2 phase was estimated on the basis of literature data on solubility of pseudo-components 342 I. Zizovic et al. / J. of Supercritical Fluids 39 (2007) 338–346 in SC CO2 [5,6,29–31]. The void fraction of the bed was estimated on the basis of its dependence on the particle diameter to extractor tube diameter ratio [32]. For the purpose of mathematical modelling of SFE from non-spherical particles of cut plant material the volume-average particle diameter was calculated [33] and its value was adopted as particle diameter:  1/3 6V (17) dp = π where V is the mean particle volume. 3. Results and discussion Experimental data of the SFE from fine milled and cut marigold flowers at different pressures (9 and 10 MPa) and temperatures (313 and 323 K) are presented in Figs. 2 and 3. Results of the SFE from fine milled and cut chamomile flowers at 313 K Fig. 4. Yield of total extract as a function of the specific amount of solvent mCO2 /msolid (kg CO2 /kg herbaceous material) for SFE from chamomile flowers at 10 MPa and 313 K. Fig. 2. Yield of total extract as a function of the specific amount of solvent mCO2 /msolid (kg CO2 /kg herbaceous material) for SFE from marigold flowers at 9 MPa and 313 and 323 K. Fig. 3. Yield of total extract as a function of the specific amount of solvent mCO2 /msolid (kg CO2 /kg herbaceous material) for SFE from marigold flowers at 10 MPa and 313 and 323 K. and 10 MPa are shown in Fig. 4. As can be seen, no significant change in the evolution of extraction yield can be observed besides the reasonable scatter of experimental data. Particle size had no influence on the extraction rate in two outermost cases: fine milled material and cut material to particle length of 5 mm. Results of SFE of marigold flowers indicate that the same phenomenon was observed at different SFE conditions (313–323 K and 9–10 MPa). SEM images of marigold and chamomile flowers and fennel fruits are shown in Fig. 5. On the basis of SEM images of marigold and chamomile samples and on the basis of an investigation of secretory structures in Asteraceae performed by Lotocka and Geszprych [34], the values of secretory duct diameters were estimated as follows: 2.3 ␮m for marigold and 2 ␮m for chamomile. According to the published micrographs [34] secretory duct diameter in sepals, petals and leaves varied from 1.3 to 12 ␮m. Secretory ducts as essential oil reservoirs in Apiaceae fruits are clearly visible and their position in fruit is well known [2,3]. SEM images of fennel fruits are shown in Fig. 5c and d. where fennel fruit secretory ducts (vittae) are clearly visible. In Fig. 5c, the cross-section of fennel fruit with six oil channels is shown. In Fig. 5d, the longitudinal section of secretory duct is visible. On the basis of statistical analysis of 20 scanned secretory ducts, an average value of 70 ␮m for the duct diameter was determined. These estimated values of secretory duct diameters are large enough to enable unobstructed essential oil extraction from the oil channels (effects of tortuosity and diameter constriction can be neglected) regardless of the duct length, which is by the model equal to the particle size. This is, also, in accordance with the basic hypothesis of the model by which diffusion through the duct is not significant resistance to the mass transfer and is represented by the molecular diffusivity through the SC CO2 . Calculated parameters of the model are presented in Table 1 and the results of mathematical modelling and simulation 343 I. Zizovic et al. / J. of Supercritical Fluids 39 (2007) 338–346 Fig. 5. SEM images of plant tissue: (a) cross-section of marigold petal, bar = 70 ␮m; (b) cross-section of chamomile petal, bar = 70 ␮m; (c) cross-section of fennel fruit, six oil channels are visible, bar = 700 ␮m; (d) longitudinal section of fennel fruit, one oil channel is visible, bar = 700 ␮m. are shown in Figs. 6–9. As can be seen, the presented model simulates experimental data of SFE from secretory ducts with high accuracy. Change of the extraction mechanism from the first period, in which the oil is being extracted from the film embedding the particles, to the second one, in which the oil is being extracted form the ducts, is clearly visible on the simulated curves (curve bending in Figs. 6–9). This mechanism transition is relatively fast and therefore the resulting simulation curve is not smooth. The normalized oil concentration in SC CO2 phase (NOC) calculated by the model, defined as the essential oil concentration in SC CO2 divided by the solubility of the oil in SC CO2 at SFE conditions, along the dimensionless extractor length during the SFE of grinded chamomile is shown in Fig. 10. As can be seen from Fig. 10, the first extraction period (t < tw ) is characterized by relatively fast mass transfer resulting in significant increase of the oil concentration in SC CO2 over narrow extractor axial distance. This step increase of csf is “moving” along the extractor length with extraction time, as the oil embedding the particles is being extracted (NOC profiles for 1, 5 and 8 min). As the film surrounding the particles is being extracted from consecutive cross-sections of the vessel, the second mechanism of the extraction from externally dried Table 1 Parameters of the SFE processes and calculated parameters of the model Herb P (MPa) T (K) qCO2 (kg/h) dp (mm) u × 104 (m/s) k × 105 (m/s) Dl × 107 (m2 /s) c* × 103 (kmol/m3 ) ε Marigold Marigold Marigold Marigold Chamomile Chamomilea Fennel 9 9 10 10 10 10 9 313 323 313 323 313 313 313 0.3 0.3 0.3 0.3 0.3 0.3 2.3 0.70 0.70 0.70 0.70 0.70 1.68b 0.55 1.73 1.73 1.73 1.73 1.73 1.73 7.76 3.35 2.34 2.58 3.63 2.94 4.97 16.0 2.40 2.34 2.91 2.26 2.91 5.20 4.22 5.7 3.9 12.0 6.0 15.0 15.0 6.0 0.47 0.47 0.47 0.47 0.47 0.53 0.43 a b Cut chamomile. Volume-average particle diameter. 344 I. Zizovic et al. / J. of Supercritical Fluids 39 (2007) 338–346 Fig. 6. Comparison of the experimental data and model simulation for grinded marigold SFE at 9 MPa and temperatures of 313 and 323 K. Fig. 8. Comparison of the experimental data and model simulation for chamomile SFE at 313 K and 10 MPa for grinded () and cut () plant material. particles commences (extraction from the ducts). This start of the second mechanism can be seen on the NOC profiles for 1, 5 and 8 min, as the low slope monotonous increase of NOC preceeding the step increase that is due to the first extraction mechanism (extraction from the embedding film). During this period of SFE both of the extraction mechanisms, from the surrounding film as well as from the ducts, are present in the extraction vessel. After certain time of extraction, the films of surrounding oil are extracted along entire vessel length, and the extraction is now proceeding by the second mechanism in the entire vessel (extraction from the ducts). NOC profiles shown in Fig. 10 indicate that the extraction from the embedding film is a much faster process than the extraction from ducts. Since the fraction of essential oil embedding the particles is small compared to the fraction remaining within the ducts, the extraction mechanism transition occurs in relatively short time. This fast mechanism transition results in the bended form of the simulated integral extraction yield curves. For example, in the case of grinded chamomile this curve bending occurs around 9th minute of the SFE (Fig. 8) and this mechanism transition is also visible in Fig. 10. (NOC profiles for 8th and 9th minute of SFE.) The mathematical model was also used to simulate SFE from cut chamomile (average particle length around 5 mm) and the simulation curve for the cut plant material is presented in Fig. 8. The simulation results depicted in Fig. 8 confirmed the negligible effect of grinding on the yield evolution during SFE. Slightly increased rate of extraction for the fine milled material can be observed during the extraction period corresponding to approximately 60% of recovered overall yield. In this period of SFE the overall process is governed by the oil extraction from the secretory ducts. The recession of the oil front deeper in the ducts during this period is in the case of longer ducts accompanied by the decrease of ce (concentration at the duct end) and consequently Fig. 7. Comparison of the experimental data and model simulation for grinded marigold SFE at 10 MPa and temperatures of 313 and 323 K. Fig. 9. Comparison of the experimental data [18] and model simulation for fennel fruit SFE at 313 K and 9 MPa. I. Zizovic et al. / J. of Supercritical Fluids 39 (2007) 338–346 345 References Fig. 10. Normalized oil concentration (NOC) in SC CO2 along the dimensionless extractor length as a function of time for SFE from grinded chamomile at 313 K and 10 MPa according to the proposed model. by the decrease of mass transfer rate and SFE yield. Negligible difference of the extraction yield for the fine milled and cut material verifies the basic assumptions of the developed model. 4. Conclusion Marigold and chamomile essential oil SC CO2 extraction confirmed previously reported phenomenon that particle size does not affect the evolution of extraction yield of some Asteraceae and Apiaceae family species. These species are characterized by the specific type of essential oil secretory structure known as secretory duct. SFE from marigold flowers at different pressure and temperature conditions confirmed the same phenomenon. Suggested micro-scale mathematical model was applied to simulate essential oil SFE from marigold and chamomile flowers as well as from the fennel fruits for which the same phenomenon was previously reported in the literature. Secretory duct diameters were determined by statistical analysis of SEM micrographs and from published investigations referred to Asteraceae family species. The determined values were large enough to allow unobstructed extraction from secretory ducts disregarding the duct length and the model described experimental data with high accuracy for the investigated species, different extraction conditions and particle sizes. The knowledge of secretory structure makes possible prediction of herbaceous material behavior during the SFE of essential oils. In the case of SFE of species with secretory ducts, it can be expected that particle size will have no influence on evolution of extraction yield, which is the fact of interest from the point of industrial scale SFE of essential oils. Acknowledgement Financial support of this work by the Serbian Ministry of Science and Environmental Protection (Project No. 142073) is gratefully acknowledged. [1] K.P. Svoboda, T.G. Svoboda, Secretory Structures of Aromatic and Medicinal Plants. A Review and Atlas of Micrographs, Microscopix Publications, Knighton, UK, 2000, pp. 7–12. [2] V. Sarafis, H. Rumpel, J. Pope, W. Kuhn, Non-invasive histochemistry of plant materials by magnetic resonance microscopy, Protoplasma 159 (1990) 70. [3] P.V. Gersbach, N. Reddy, Non-invasive localization of thymol accumulation in Carum copticum (Apiaceae) fruits by chemical shift selective magnetic resonance imaging, Ann. Bot. 90 (2002) 253. [4] H. Sovová, Rate of vegetable oil extraction with supercritical CO2 —modelling of extraction curves, Chem. Eng. Sci. 49 (1994) 409. [5] E. Reverchon, G. Donsi, O. Sesti, Modeling of supercritical fluid extraction from herbacous matrices, Ind. Eng. Chem. Res. 32 (1993) 2721. [6] E. Reverchon, O. Sesti, D. Gorgoglione, Supercritical CO2 extraction of basil oil: characterization of products and process modeling, J. Supercrit. Fluids 7 (1994) 185. [7] E. Reverchon, O. Sesti, Modelling the supercritical extraction of basil oil, in: M. Perrut, G. Brunner (Eds.), Proceedings of the Third Symposium on Supercritical Fluids, vol. 2, 1994, p. 189. [8] E. Reverchon, Mathematical modelling of supercritical extraction of sage oil, AIChE J. 42 (1996) 1756. [9] K.D. Bartle, A.A. Clifford, S.B. Hawthorne, J.J. Langenfeld, D.J. Miller, R. Robinson, A model for dynamic extraction using a supercritical fluid, J. Supercrit. Fluids 3 (1990) 143. [10] M. Goto, M. Sato, T. Hiroshe, Extraction of peppermint oil by supercritical carbon dioxide, J. Chem. Eng. Jpn. 26 (1993) 401. [11] I. Goodarznia, M.H. Eikani, Supercritical carbon dioxide extraction of essential oils: modeling and simulation, Chem. Eng. Sci. 53 (1998) 1387. [12] E.M.C. Reis-Vasco, J.A.P. Coelho, A.M.F. Palavra, C. Marrone, E. Reverchon, Mathematical modelling and simulation of pennyroyal essential oil supercritical extraction, Chem. Eng. Sci. 55 (2000) 2917. [13] F. Gaspar, T. Lu, R. Santos, B. Al-Duri, Modelling the extraction of essential oils with compressed carbon dioxide, J. Supercrit. Fluids 25 (2003) 247. [14] H. Sovová, Mathematical model for supercritical fluid extraction of natural products and extraction curve evaluation, J. Supercrit. Fluids 33 (2005) 35. [15] I. Zizovic, M. Stamenic, A. Orlovic, D. Skala, Mathematical modelling of Lamiaceae family extraction by supercritical carbon dioxide, in: 16th International Congress of Chemical and Process Engineering—CHISA 2004, Praha, Czech Republic, 2004, Summaries 2, C8.4, 498, Full Text CD Rom. [16] I. Zizovic, M. Stamenic, A. Orlovic, D. Skala, Supercritical carbon dioxide essential oil extraction of Lamiaceae family species—mathematical modeling on the micro-scale and process optimization, Chem. Eng. Sci. 60 (2005) 6747. [17] I. Zizovic, M. Stamenic, A. Orlovic, D. Skala, Supercritical carbon dioxide extraction of essential oils from aromatic and medicinal plants—mathematical modelling and simulation, in: 7th World Congress of Chemical Engineering, Glasgow, Scotland, 2005, Book of Abstracts, C10-001, 208, Full Text CD Rom. [18] J.A.P. Coelho, A.P. Pereira, R.L. Mendes, A.M.F. Palavra, Supercritical carbon dioxide extraction of Foenicum vulgare volatile oil, Flavour Fragr. J. 18 (2003) 316. [19] M. Bocevska, H. Sovová, Supercritical CO2 extraction of essential oil from yarrow, in: 16th International Congress of Chemical and Process Engineering—CHISA 2004, Praha, Czech Republic, 2004, Summaries 2, P3.93, 712, Full Text CD Rom. [20] V. Louli, G. Folas, E. Voutsas, K. Magoulas, Extraction of parsley seed oil by supercritical CO2 , J. Supercrit. Fluids 30 (2004) 163. [21] E. Reverchon, Supercritical fluid extraction of essential oils and related products, J. Supercrit. Fluids 10 (1997) 1. [22] B. Carnahan, H.A. Luther, J.O. Wilkes, Applied Numerical Methods, John Wiley & Sons, Inc., New York, 1969, p. 432. [23] D.Y. Peng, D.B. Robinson, A new two-constant equation of state, Ind. Eng. Chem. Fundam. 15 (1976) 59. 346 I. Zizovic et al. / J. of Supercritical Fluids 39 (2007) 338–346 [24] F. Gaspar, G.A. Leeke, B. Al-Duri, R. Santos, Modelling the disruption of essential oils glandular trichomes with compressed CO2 , J. Supercrit. Fluids 25 (2003) 233. [25] C.S. Tan, S.K. Liang, D.C. Liou, Fluid-solid mass transfer in supercritical fluid extractor, Chem. Eng. J. 38 (1988) 17. [26] J.A. Jossi, L.I. Stiel, G. Thodos, The viscosity of pure substances in the dense gaseous and liquid phases, AIChE J. 8 (1962) 59. [27] O.J. Catchpole, M.B. King, Measurement and correlation of binary diffusion coefficients in near critical fluids, Ind. Eng. Chem. Res. 33 (1994) 1828. [28] C.S. Tan, D.C. Liou, Axial dispersion of supercritical carbon dioxide in packed beds, Ind. Eng. Chem. Res. 28 (1989) 1246. [29] E. Reverchon, Fractional separation of SCF extracts from marjoram leaves: mass transfer and optimization, J. Supercrit. Fluids 5 (1992) 256. [30] E. Reverchon, F. Senatore, Isolation of rosemary oil: comparison between hydrodistillation and supercritical CO2 extraction, Flavour Fragr. J. 7 (1992) 227. [31] K.H. Kim, J. Hong, Equilibrium solubilities of spearmint oil components in supercritical carbon dioxide, Fluid Phase Equilib. 164 (1999) 107. [32] R.H. Perry, C.H. Chilton, Chemical Engineers’ Handbook, fifth ed., McGraw Hill, New York, 1973, pp. 5–53. [33] H.S. Fogler, Elements of Chemical Reaction Engineering, second ed., Prentice-Hall Inc., 1992, p. 571. [34] B. Lotocka, A. Geszprych, Anatomy of the vegetative organs and secretory structures of Rhaponticum carthamoides (Asteraceae), Bot. J. Linden Soc. 144 (2003) 207.