Ind. Eng. Chem. Res. 2005, 44, 2879-2886
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Natural Convection Retards Supercritical CO2 Extraction of Essential Oils and Lipids from Vegetable Substrates Juan C. Germain,† Jose´ M. del Valle,*,† and Juan C. de la Fuente‡ Departamento de Ingenierı´a Quı´mica y Bioprocesos, Pontificia Universidad Cato´ lica de Chile, Avenida Vicun˜ a Mackenna 4860, Macul, Santiago, Chile, and Departamento de Procesos Quı´micos, Biotecnolo´ gicos y Ambientales, Universidad Te´ cnica Federico Santa Marı´a, Avenida Espan˜ a 1680, Valparaiso, Chile
External mass-transfer coefficients (kf) during supercritical fluid extraction (SCFE) of highsolubility solutes, under solvent upflow conditions and low superficial velocities, can be small because of the negative influence of natural convection phenomena. A shrinking-core model for mass transfer was used to estimate best-fit values of kf for data on SCFE of lipids from prepressed rapeseeds. Values of kf at a high Reynolds number (Re ) 14.1) were similar when using solvent upflow or downflow, but kf at lower Re (1.57) was 3.6 times smaller when using solvent upflow than that predicted from a literature correlation for downflow conditions. These kf’s are consistent with values estimated by fitting literature data, or gathered from various sources under similar, nonadequate conditions (solvent upflow under low Re) for the extraction of both fatty and essential oils. Care is advisable when employing best-fit values of kf from laboratory data for process design purposes, especially when sizing of the solvent pumps for the experiments is questionable. 1. Introduction Supercritical fluid (SCF) extraction (SCFE) has been intensely explored during the past several years, as an alternative to conventional extraction processes. The use of supercritical carbon dioxide (SC-CO2) as an extraction solvent for vegetable substrates has been especially important for the food, cosmetic, and pharmaceutical industries. Important plant components that can be extracted using SC-CO2 include essential oils1 and lipids2 because SC-CO2 dissolves these two types of solutes relatively well, prevents thermal degradation reactions, and avoids contamination with toxic residues. During the SCFE process, the pretreated vegetable substrate (commonly milled to a suitable particle size) is placed within vertically positioned, cylindrical extraction vessels, and SC-CO2 is pumped through the packed bed either from the bottom to the top of the vessel (upflow conditions) or in the opposite direction (downflow conditions). Upflow is preferred for industrial applications because it can cause particle fluidization and prevent bed compaction. There may exist differences in extraction rates between processes employing solvent upflow or downflow conditions, however, because of the influence of natural convection phenomena. The contributions of natural convection to mass transfer are especially important under near-critical conditions, for a solute exhibiting a large solubility, and when using a small interstitial solvent velocity.3 This has been observed in the SC-CO2 extraction of benzene derivatives on various solid supports, reducing the speed of the extraction process when solvent upflow conditions were employed as compared to downflow conditions.3,4 Data from the literature we examined have shown that the values of the external mass-transfer coefficient (kf) for the SC-CO2 extraction of lipids2 and essential oils5 from plant material are * To whom correspondence should be addressed. Tel.: (562) 3544418. Fax: (56-2) 3545803. E-mail:
[email protected]. † Pontificia Universidad Cato ´ lica de Chile. ‡ Universidad Te ´ cnica Federico Santa Marı´a.
lower than that predicted by literature correlations for packed beds of solid substrates operating with SCFs. We hypothesized in this work that the negative influence of natural convection could be partially responsible for this situation. If this so happens, values of kf could be small for solvent upflow conditions and lower than those when employing solvent downflow. 2. Literature Review Sovova´ et al.6 reported data on SC-CO2 extraction of grape oil from milled seeds in a packed bed (dp ) 0.265 mm; ) 0.33). The extraction temperature (T) and pressure (P) were 313 K and 28 MPa, respectively. The authors used two extraction vessels (150-cm3 capacity and 3.3-cm i.d.; 12-cm3 capacity and 0.8-cm i.d.), and their experimental design considered variations in the height of the packed bed (by changing the substrate load) and the superficial velocity (U) and flow direction of the solvent (Table 1). The height of the packed bed could be estimated based on the reported value of the apparent density of the packed bed of seeds (730 kg/ m3). Sovova´ et al.7 reported data on the extraction of caraway essential oil from a packed bed of milled seeds (dp ) 0.383 mm; ) 0.514) in the 150-cm3 extraction vessel using SC-CO2 at 313 K and 9 or 10 MPa as the solvent. Two extraction curves were reported in this case for each extraction condition only altering the flow direction of the solvent (Table 1). These literature data on SCFE on grape seed lipids and caraway essential oils were analyzed as described in section 3 using a shrinking-core model. Best-fit values of effective diffusivity (De) and kf for extraction of grape oil from milled seeds in the presence of SC-CO2 at 313 K and 28 MPa are shown in Table 1, and experimental data points and model predictions are compared in Figure 1. A single value of De was estimated by fitting the model to downflow extraction curves 1 and 2, for which a reliable value of kf could be estimated. The other six upflow curves represented three different superficial solvent velocities, and a single value of kf was estimated
10.1021/ie049119x CCC: $30.25 © 2005 American Chemical Society Published on Web 03/08/2005
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Table 1. Extraction Conditions and Model Parameters for SCFE Experiments on Lipids from Milled Grape Seeds6 Using SC-CO2 at 313 K and 28 MPa and on Essential Oils from Milled Caraway Seeds7 Using SC-CO2 at 313 K
d
extraction curve
substrate
bed height (cm)
flow direction
SCF velocity (U, mm/s)
Re
De (m2/s)
kf (m/s)
1 2 3 4 5 6 7 8 9e 10e 11f 12 f
grape seed grape seed grape seed grape seed grape seed grape seed grape seed grape seed caraway seed caraway seed caraway seed caraway seed
1.5a 24.1a 5.3a 11.4a 3.2a 0.3d 1.1d 3.1d 5.1 7.5 5.1 7.5
downflow downflow upflow upflow upflow upflow upflow upflow downflow upflow downflow upflow
0.66 0.66 0.66 0.33 0.33 0.039 0.039 0.039 0.072 0.072 0.056 0.056
1.7 1.7 1.7 0.86 0.86 0.10 0.10 0.10 0.38 0.38 0.28 0.28
1.77 × 10-10 b 1.77 × 10-10 b 1.77 × 10-10 1.77 × 10-10 1.77 × 10-10 1.77 × 10-10 1.77 × 10-10 1.77 × 10-10 7.41 × 10-12 b 7.41 × 10-12 5.28 × 10-12 b 5.28 × 10-12
2.76 × 10-5 c 2.76 × 10-5 c 1.66 × 10-6 b 3.70 × 10-7 b 3.70 × 10-7 b 2.55 × 10-7 b 2.55 × 10-7 b 2.55 × 10-7 b 1.14 × 10-4 c 2.57 × 10-7 b 8.14 × 10-5 c 8.40 × 10-8 b
a 12-mL extraction vessel. b Best-fit value employing the QSS-SC model. c Predicted value using the correlation of Puiggene ´ et al.3 150-mL extraction vessel. e Extraction conditions: 313 K and 9 MPa. f Extraction conditions: 313 K and 10 MPa.
Figure 1. Modeling of cumulative oil extraction plots for milled grape seeds in packed beds using SC-CO2 at 313 K and 28 MPa as the solvent. (A) Extraction experiments using solvent downflow [extraction curves 1 (bed height H ) 1.5 cm) and 2 (H ) 24.1 cm)] or upflow (H ) 5.3 cm) conditions for Re ) 1.7. (B) Extraction experiments using solvent upflow conditions for Re ) 0.86: extraction curves 4 (H ) 11.4 cm) and 5 (H ) 3.2 cm). (C) Extraction experiments using solvent upflow conditions for Re ) 0.10: extraction curves 6 (H ) 0.3 cm), 7 (H ) 1.1 cm), and 8 (H ) 3.1 cm).
for each dimensionless Reynolds number (Re). Our results showed that kf for solvent upflow conditions was around 20-100 times smaller than that predicted by using the equation of Puiggene´ et al.3 for downflow conditions. It is unfortunate that Figure 1A cannot give a clearer contrast between upflow and downflow conditions because this effect is confounded with that of the bed height, which was varied in curves 1-3. In contrast with grape seed oil, two different P/T conditions were used for the SCFE of caraway essential oil. A correction factor (F) proposed by Aguilera and Stanley,8 which embodies all microstructural factors affecting internal mass transfer and which indicates how many times bigger the binary diffusion coefficient (D12) is than De, was employed in our analysis. We assumed that the correction factor F is constant when the same substrate and pretreatment are employed and that F is independent of the conditions of the extraction solvent. Under this assumption, the ratio between the values of De for extraction curves 9 and 11 is proportional to the ratio between the values of D12 at 313 K and 9 MPa and at 313 K and 10 MPa (effective diffusivity ratio ) 1.400). This condition was imposed when using the shrinking-core model to estimate the best-fit values of De for these two extraction curves. A single value of kf was estimated for each of the two other upflow extraction curves. Table 1 presents the best-fit values of De and kf, and Figure 2 shows the data points and model predictions for these extraction experiments.
Figure 2. Modeling of cumulative essential oil extraction plots for milled caraway seeds in packed beds using SC-CO2 at 313 K and (A) 9 MPa (Re ) 0.38) or (B) 10 MPa (Re ) 0.28) as the solvent and using solvent (-b-) downflow or (‚‚‚O‚‚‚) upflow conditions.
Literature data on SCFE of caraway seed essential oil allowed a better comparison between solvent upflow and downflow conditions than the data on the extraction of lipids. At each considered P/T combination, the couple of upflow/downflow experiments were performed almost at identical conditions. Only a slight difference in the bed height was considered for upflow by increasing the sample load. All other variables were identical except for the solvent flow direction. De values that we esti-
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mated for each P/T combination using curves 9 and 11 agreed with those in the literature on SCFE of terpenoids5 (F ) 2700). The external mass-transfer coefficient estimated using the correlation of Puiggene´ et al.3 for solvent downflow conditions was between 400 (Re ) 0.36) and 900 times (Re ) 0.28) higher than the corresponding best-fit value of kf for the experiments using solvent upflow conditions. The experimental data points that were available to carry out our analysis for SCFE of essential oils were more limited than those for SCFE of lipids. Also the differences between the two flow directions can be within a presumed experimental error, particularly the extractions carried out at 9 MPa. Overall, a picture emerges from Figures 1 and 2 that indicates that external mass transfer may be affected negatively when opposed by gravity (solvent upflow conditions). However, this picture is blurred because of the noted limitations in the literature data and some others that will be discussed in section 4. In this work, we gathered our own data on the extraction of lipids from prepressed oilseeds under carefully selected conditions to best analyze the contribution of natural convention to external mass transfer. The data were modeled to determine if and when best-fit values of kf are smaller when employing solvent upflow rather than downflow conditions. 3. Materials and Methods 3.1. Substrate. Prepressed rapeseeds (Brassica napus) were used as the substrate in our work. The seeds were processed at the Technical University of Hamburgs Harburg (Germany) using a Komet oil press (type C402NGO 160AW30, Oekotec GmbH & Co., Mo¨nchengladbach, Germany), and the prepressed vegetable substrate was later ground in a hammer mill fitted with a mesh with 5-mm openings (model M2, Assa Tecnologı´a S. A., Santiago, Chile) and size-classified in a Ro-Tap test sieve shaker (W. S. Tyler, Mentor, OH). The -14/ +24 mesh Tyler fraction (dp ) 0.95 mm) was employed for further analysis. The apparent density of the pellets in a packed bed (Fb ) 514 kg/m3) was determined using the gravimetric procedure of del Valle et al.,9 whereas the true density (Fs ) 1366 kg/m3) and inner porosity (p ) 0.344) of the pellets were determined by mercury porosimetry in a Micromeritics Pore Sizer 9420 Autopore III (Micromeritics Instrument Corp., Norcross, GA). Finally, the porosity of the packed bed () was estimated according to eq 1.
)1-
Fb Fs(1 - p)
) 0.425
(1)
3.2. Extraction Experiments. Experiments were carried out using a SFE-1L process development unit from Thar Technologies (Pittsburgh, PA), which is equipped with a computer-controlled system to adjust the extraction pressure and solvent flow rate. A 500cm3 capacity, 54-mm-i.d. extraction vessel (model 500mL-ph), fitted with an external jacket, was employed. The temperature inside the extraction vessel was controlled by passing hot water from a PolyScience (Niles, IL) 8205 thermostated bath through the external jacket. The system was equipped with a P-200A-220V pump and a Micro Motion (Boulder, CO) CMF010M324NU mass flow sensor, which allowed one to maintain the desired solvent flow rate. The extraction pressure was
Table 2. Extraction Conditions and Model Parameters for SCFE Experiments on Lipids from Prepressed Rapeseeds in a Packed Bed of 3-cm Thickness Using SC-CO2 at 313 K and 30 MPa SCF extraction flow velocity curve direction (U, mm/s) 13 14 15 16
downflow upflow downflow upflow
1.53 1.53 0.17 0.17
Re
De (m2/s)
kf (m/s)
14.1 14.1 1.57 1.57
1.78 × 10-9 a 1.78 × 10-9 1.78 × 10-9 a 1.78 × 10-9
1.91 × 10-5 b 1.91 × 10-5 a 7.44 × 10-6 b 2.04 × 10-6 a
a Best-fit value employing the QSS-SC model. b Predicted value using the correlation of Puiggene´ et al.3
maintained by a BPR-A-200B1 back-pressure regulator (BPR) placed at the outlet of the extractor. The outlet line of the BPR was connected to the inlet port of a Swagelock (Solon, OH) SS-43YF2 six-port, two-way valve that allowed periodic switching of oil collection between two 200-cm3 cyclone separators (model CS-200mL). The extraction experiments were carried out using prepressed rapeseed samples as the substrate and liquid CO2 (g99.8% pure) from AGA S. A. (Santiago, Chile) as the solvent. All extractions were carried out using 20 or 180 g/min of CO2 at 313 K and 30 MPa and were analyzed in upflow and downflow modes. In every case, the prepressed seeds were placed inside the extraction vessel in the extreme nearest to the solvent exit (the top of the vessel for upflow conditions or the bottom of the vessel for solvent downflow conditions), forming a thin packed-bed layer (3-cm thickness) to avoid mass transfer being controlled by solubility and minimize possible axial dispersion effects while at the same time maximizing the sample load into the extractor. The rest of the extraction vessel (solvent inlet extreme) was filled with glass beads. Two data points were obtained in each experimental run, with at least three runs being carried out at each of the four conditions in the experimental design (Table 2). In all experimental runs, the amount of oil recovered in each cyclone separator, as well as the initial and final weight and composition of the substrate, was determined gravimetrically, where the moisture and oil contents of the substrate and treated samples were determined using the methods of del Valle and Uquiche.10 In each experimental run, the amount of oil in cyclone separators was corrected by the experimentally assessed solute recovery10 to determine the cumulative yield of oil. 3.3. Literature Correlation for the External Mass-Transfer Coefficient. Equation 1 from Puiggene´ et al.3 was used in this work to estimate values of kf. This correlation takes into account natural convection in an explicit fashion and distinguishes between mass transfer in favor or against gravity. It employs Churchill’s superposition rule for heat transfer but expressed in terms of Sherwood (Sh) numbers instead of Nusselt numbers: 3
ShT ) xShF3 ( ShN3
(1a)
ShF ) 0.395Re0.58Sc0.33
(1b)
ShN ) 2 + 0.0011(Gr × Sc)0.368
(1c)
where the subscripts T, F, and N indicate total, forced, and natural (or free) convection, respectively. The plus sign in eq 1a is employed when the mass transfer is
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Table 3. Physical Properties of the SCF Phase under Extraction Conditions in Experiments of SCFE of Grape Seed Oil,6 Caraway Essential Oil,7 and Rapeseed Oil solute
extraction conditions
dp (mm)
F (kg/m3)
µ (Pa s × 105)
D12 (m2/s × 109)
Csat. (kg/m3 CO2)
∆F (kg/m3)
Sc
Gr
triglycerides triglycerides essential oils essential oils
28 MPa/313 K 30 MPa/313 K 9 MPa/313 K 10 MPa/313 K
0.265 0.95 0.383 0.383
899 910 486 629
9.10 9.38 3.48 4.78
3.08 3.00 20.9 14.9
6.16 6.85 2.73 13.2
0.59 0.49 236 309
32.9 34.4 3.44 5.11
11.6 429 35 100 31 400
assisted by the gravity force (solvent downflow conditions, for solutes denser than the solvent), whereas the minus sign is employed when the mass transfer is opposed by gravity (typically, under solvent upflow conditions). In eq 1, Re is the dimensionless Reynolds number, Sc is the dimensionless Schmidt number, and Gr is the dimensionless Grashof number. The equation should be valid for 10 < Re < 100, Sc < 20, and 2.0 × 106 < Gr < 4.8 × 107, corresponding to the experimental region that was investigated by Puiggene´ et al.3 For calculations, the density (F) and viscosity (µ) of the SCF phase under process conditions were assumed to be unaffected by the dissolved solute and were calculated as a function of the extraction temperature and pressure using NIST Standard Database v5.011 for pure CO2, whereas D12 was estimated as a function of the reduced temperature (Tr ) T/Tc, where Tc ) 304.3 K) and reduced density (Fr ) F/Fc, where Fc ) 468 kg/ m3) of the SC-CO2 and the molecular weight (MW2) and critical volume (Vc2) of the solute (component 2) using the equation of Catchpole and King.12 Adopted values were MW2 ) 885.4 g/mol and Vc2 ) 3200 cm3/mol for lipids12 and MW2 ) 144.3 g/mol and Vc2 ) 500.5 cm3/ mol for essential oils.5 The solubility of lipids in SCCO2 (Csat) was estimated as a function of F and T using the equation of del Valle and Aguilera.13 Sovova´ et al.7 correlated the solubility of caraway essential oil at 313 K as a function of P and the ratio between essential oils and lipids present in the liquid mixture. Because the solubility changed during SCFE, it was concluded by parameter adjustment that a mean solubility for a mixture that contains 4.7% of essential oils was suitable for describing extraction at both 9 and 10 MPa. The difference in density between the SCF saturated with solute and pure SC-CO2 (∆F) was estimated by using the Peng-Robinson equation of state (PR-EoS) with quadratic mixing rules.2 Representative values of PREoS parameters ac, b, and κ adopted for the lipids were calculated from critical temperature and pressure and an acentric factor as reported by de la Fuente et al.14 for sunflower oil. Best-fit values of binary interaction parameters for a mixture of CO2 and triglycerides were obtained for solubilities predicted by the correlation of del Valle and Aguilera13 for 313-333 K and 16-30 MPa. These values were k12 ) 0.01 and l12 ) 0.09. In the case of essential oils, PR-EoS parameters ac, b, and κ and best-fit values of k12 and l12 were adopted from the report of Gamse and Marr15 for the subsystems limonene-CO2 and carvone-CO2. Limonene and carvone represent ca. 98% of the hydrodistilled essential oil from caraway seeds.7 The calculated values of physical properties of the SCF under process conditions reported in Tables 1 and 2 are summarized in Table 3. 3.4. SCFE Model and Fitting Procedure for Model Parameters. The quasi-steady-state version of a shrinking-core model16 was employed in this work to fit the literature data and our experimental data. This model describes the situation where a sharp boundary develops at a radial position r ) rc between a solute-
rich core in the porous particle and an extracted outer region and where the core shrinks as the extraction proceeds. The model neglects the axial dispersion of the solute in the fixed bed and is based on a differential mass balance for the extractor (eq 2) coupled with a differential equation for solute diffusion in the outer region of each particle (eq 3). The position rc inside each particle is located by a total mass balance of solute inside the solid matrix, which leads to differential equation 4, where C and Ci are the solute concentrations
3kf 1 - ∂C U ∂C + )(C - Ci|R) ∂t ∂z R
( )
(2)
De ∂ 2 ∂Ci r )0 ∂r r2 ∂r
(3)
∂rc R2kf ) 2 (C - Ci|R) ∂t r C
(4)
c
so
in the SCF phase in the bed and inside the pores of the solid particle, respectively, t is the extraction time, z is the axial coordinate of the extractor vessel, R ()dp/2) is the particle radius, and Cso is the initial concentration of the solute in the solid. For mathematical implementation, approximate values of spatial derivatives of the model were estimated using finite differences, and the resulting temporary differential equations were numerically solved using a modified Rosembrock formula of order 2 set in MATLAB 6.0 (The MathWorks, Natick, MA). The following initial and boundary conditions were considered for numerical solution:
C(z,0) ) 0
(0 e z e L)
(5a)
rc(z,0) ) R
(0 e z e L)
(5b)
|
(t g 0)
(5c)
∂C )0 ∂z L,t Ci(rc,t) ) Csat De
|
∂Ci ∂r
R
(t g 0)
) kf(C - Ci|R)
(t g 0)
(5d) (5e)
Parameter adjustment was performed by minimization of the quadratic errors between experimental data points and simulated values using the model. Two adjustable parameters were used, namely, kf and De. Values of kf for downflow extraction curves were calculated using eq 1 and employed as input in the model to determine a single best-fit value of De for each substrate and P/T combination. The corresponding values of De were then used to find the best-fit value of kf for each upflow extraction curve. A unique value of kf was fitted to represent all curves using the same superficial
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Figure 3. Dimensionless plot of Sh/Sc1/3 versus Re for the external mass-transfer coefficient in a packed bed of a solid substrate operating with a SCF. Lines represent predictions using the model of Puiggene´ et al.3 under typical conditions for the SCCO2 extraction of essential oils (Sc ) 2.13) and triglycerides (Sc ) 34.4) using solvent downflow (assisting flow) and upflow (opposing flow) conditions for Gr values ranging from 10 (dotted lines) to 38 000 (full lines).
solvent velocity in the case of grape seed oil extraction, where more than one curve was reported for the same Re. 4. Results and Discussion Figure 3 presents a sensitivity analysis for eq 1 as a function of Sc and Gr. Values of kf are shown in a dimensionless plot of Sh/Sc1/3 versus Re depending on the flow mode and under typical conditions employed for the SCFE of essential oils (T ) 323 K; P ) 9 MPa)1 and lipids (T ) 313 K; P ) 30 MPa)2 from vegetable substrates using SC-CO2 as the solvent, cases for which Sc ) 2.13 and 34.4, respectively. Selected values of Gr bracketed those experimentally observed (cf. Table 3). We estimated unusually low values of kf for all cumulative extraction curves of grape seed oil and caraway essential oil carried out in upflow conditions (Table 1). When we compared these values with those that can be derived from Figure 3, we concluded that they are not as low as predicted by eq 1. In fact, it appears as if the effect of natural convection is somewhat overemphasized by eq 1 and that it is not feasible to use it to estimate values of kf under upflow conditions in the Re range where experiments were done. In contrast, we obtained reasonable estimates of kf by using the correlation for downflow extraction curves. These values appeared to be adequate because kf remained virtually constant below a Sc-dependent Re value (cf. Figure 3), and we previously determined that best-fit values of De were nearly independent of external masstransfer conditions for kf g 10-5 m/s (data not shown). The value of F corresponding to the best-fit value of De for grape seed lipids in Table 1 (F ) 19) obtained using our model to simulate cumulative extraction curves 1 and 2 agrees with the literature values for the SCFE of seed triglycerides with SC-CO2.2 We forced curves 6-8 in Figure 1C to converge to the same horizontal asymptote because this asymptote corresponds to the oil content in the seed that can be extracted with SC-CO2, which should depend only on the substrate and extraction conditions and which remained unchanged in these experiments. That is why we employed only those
experimental data points at the beginning of curve 8 for modeling purposes. We used the same assumption to model curve 5 in Figure 1B. The data on grape seed oil extraction presented some additional limitations. The particle size was determined by sieving following extraction, which can lead to an underestimation of dp because of separation of particles during extraction and particle breakage during subsequent decompression. Larger particle sizes than the ones reported would result in increased values of Gr numbers. Also, the reported bulk density of the packed bed (730 kg/m3) seems large when compared with typical values for most ground seeds (400-500 kg/m3). This can give errors in the estimation of packed-bed heights. Gr numbers for the extraction of essential oils in Table 3 seem to be highly overestimated, particularly when compared with those estimated for triglycerides. Additionally, a remarkable increase in the density of 200-300 kg/m3 for the saturated SCF phase when dissolving 3-13 kg/m3 of essential oils was observed. The explanation resides in the fact that a mixture of 4.7% essential oil and 95.3% lipids is actually being extracted from caraway seed, whereas Gr was calculated for pure essential oil components. Indeed, limonene and carvone are fully miscible in SC-CO2 at 313 K and >8.8 MPa,15 but there is a pronounced decrease in solubility in the presence of fatty oils because of the partition of the essential oil components between a liquid, lipid-rich phase and a gaseous, CO2-rich phase.7,17 Budich and Brunner18 reported that values of ∆F for orange peel essential oil were highly dependent on the density of pure SC-CO2 (230-400 kg/m3) and nearly independent of the temperature (323-343 K). On the basis of the correlation of these authors, extrapolated values of ∆F range from 289 kg/m3 (for F ) 486 kg/m3) to 763 kg/m3 (for F ) 629 kg/m3), which are of the same order of magnitude as those estimated in our study (Table 3). Overestimation of ∆F would cause an overestimation of Gr, but Figure 3 shows that for 10 < Gr < 38 000 there are small changes (
