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Modeling the supercritical fluid extraction of black pepper (Piper nigrum L.) essential oil
Journal of Food Engineering 54 (2002) 263–269 www.elsevier.com/locate/jfoodeng
Modeling the supercritical fluid extraction of black pepper (Piper nigrum L.) essential oil Sandra R.S. Ferreira
a,1
, M. Angela A. Meireles
b,*
a
Departamento de Engenharia Quımica e Engenharia de Alimentos, EQA, Universidade Federal de Santa Catarina, UFSC, Cx. P. 476, 88040-900 Florian opolis, SC, Brazil b LASEFI, Departamento de Engenharia de Alimentos, Faculty of Engineering Alimentos, Unicamp, Cx. P. 6121, 13081-970 Campinas, S~ ao Paulo, Brazil Received 5 July 2001; accepted 3 November 2001
Abstract The fixed bed extraction of black pepper essential oil using supercritical carbon dioxide was modeled by the extended Lack’s plug flow model developed by Sovova (Sovova’s model). The experimental data were obtained for extractions conducted at 30, 40 and 50 °C, and 150, 200, and 300 bar, for two different types of ground black pepper (batches 1 and 2). The model parameters were evaluated from the experimental data. The fluid-phase mass transfer coefficient was obtained from the constant extraction rate (CER) period using a logarithmical solute mass ratio difference. The Sovov a’s model was able to describe the experimental data quite well. The best value for the extraction parameter, which relates the resistances of solid-phase mass transfer to fluid-phase mass transfer, was 0.12 and 0.25 for batches 1 and 2, respectively. The experimental data were well represented by the model for the mass ratio of solute present in ruptured cell to the initial mass ratio of solute equal to 65% and 38% for batches 1 and 2, respectively. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Supercritical fluid extraction; Black pepper oil; Mass transfer model
1. Introduction Brazil is the second largest worldwide producer of black pepper (Piper nigrum L.) and of several other spices and herbs, used in food processing as well as in pharmaceutical and cosmetic products. Black pepper is an important spice, appreciated for both its aroma and its pungency. Studies on supercritical fluid extraction (SFE) to obtain black pepper oil and/or oleoresin have been reported in the literature (Ferreira, Meireles, & Cabral, 1993; Ferreira, Nikolov, Doraiswamy, Meireles, & Petenate, 1999; Vidal & Richard, 1987). The components of the pepper’s extract that contribute to its value as a food additive are the volatile oil for its aroma and the alkaloid compounds for the pungency. Black pepper oil is formed by monoterpenes, sesquiterpenes, and oxygenated compounds (Ferreira, 1996). *
Corresponding author. Tel.: +55-19-788-4033; fax: +55-19-7884027. E-mail addresses: [email protected] (S.R.S. Ferreira), meireles@ fea.unicamp.br (M.AA. Meireles). 1 Tel.: +55-48-331-9448; fax: +55-48-331-9687.
The engineering design of SFE processes, which generally involves putting in contact a packed bed formed by the solid substratum (like ground spices) and a supercritical fluid (SF), requires the knowledge of the thermodynamics constraints (solubility and selectivity) as well as the kinetic constraints (mass transfer rate). In spite of the increased interest in SFE there is still a lack of information about the mass transfer aspects of these processes. Because the flow pattern in a fixed bed is complex, it has been found convenient to develop semi-empirical correlations to describe the mass transfer between the solute dissolved in the solid phase and the solvent phase. Conceivably, the mass transfer coefficient, which is a function of density, viscosity, diffusivity, porosity of the bed, particle size, and solvent flow rate, can be used to describe the kinetic restraints of the system. The influence of the above variables is, in general, expressed using the dimensionless numbers of Sherwood, Reynolds, Schmidt, and Grashof, when natural convection is important (Ferreira, Meireles, & Nikolov, 1997). In the pressure and temperature range where most supercritical extractions are carried out, up to now there has been no
0260-8774/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 0 1 ) 0 0 2 1 2 - 6
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Nomenclature CER mextr h Hb J ðX ; Y Þ K k kXa kYa P MCER N O p QCO2 r S t tCER T U XO
constant extraction rate ðkg oil=sÞ mass of extract (kg) axial coordinate (m) length of bed (m) interfacial mass transfer rate ðkg oil=m3 sÞ initial mass of inaccessible oil (kg oil) extraction parameter (dimensionless) solid-phase mass transfer coefficient (s) fluid-phase transfer coefficient (s) initial mass of easily accessible solute (kg solute) mass extraction rate for the CER period (kg oil/s) mass of cellulosic structure (kg solid) mass of solute in solid phase (kg oil) pressure (bar) solvent flow rate ðkg CO2 =sÞ dimensionless concentration of solute in solid phase (dimensionless) extractor sectional area ðm2 Þ extracting time (s) end of the CER (s) temperature ð°CÞ superficial velocity (m/s) initial solute mass ratio in the solid phase (kg oil/kg cellulosic structure)
generally accepted correlation for the mass transfer coefficient between the SF phase and the natural solid substratum. Results obtained employing low speed flows, where buoyancy forces may play a significant role (Lim, Holder, & Shah, 1989; Lim, Lee, Kim, & Lee, 1995; Mandelbaum & B€ ohm, 1973), are also missing. For SFE the known dimensionless mass transfer equations (Sherwood equations) developed for liquids are probably not able to describe mass transfer kinetics because of the unusual behavior of dense gases. Therefore, the use of a simple model that requires little experimental information can prove to be useful for scale-up design calculations. Besides the empirical models there are several mathematical models available to correlate experimental results, such as models based on heat transfer analogy and differential mass balance integration models (Papamichail, Louli, & Magoulas, 2000). Then, the purpose of this work was to evaluate the kinetic aspects of the black pepper essential oil extraction, with supercritical CO2 as solvent, using the mass transfer model described by Sovov a (1994) to investigate both the spatial and the time dependence of the fluid phase solute concentration. The experimental data selected were the ones partially published by Ferreira et al. (1999).
XP Xk y Y DY Y Yin YCER z Z W e qCO2 qCS s
mass ratio of easily accessible solute (kg oil/ kg cellulosic structure) mass ratio of solute inside un-ruptured cells (kg oil/kg cellulosic structure) dimensionless concentration of solute in solvent phase (dimensionless) mass ratio of solute in solvent phase ðkg oil=kg CO2 Þ mean mass ratio difference in bed during the CER period ðkg oil=kg CO2 Þ solubility of the solute in the solvent phase ðkg oil=kg CO2 Þ solvent phase solute mass ratio at bed inlet ðkg oil=kg CO2 Þ solvent phase solute mass ratio at bed outlet ðkg oil=kg CO2 Þ dimensionless coordinate parameter of fast extraction period (dimensionless) mass transfer parameter in the solid phase (dimensionless) total porosity (dimensionless) solvent density ðkg=m3 Þ solid density ðkg=m3 Þ dimensionless time
2. Mass transfer model The mass transfer mechanism of the high-pressure extraction of complex mixtures, like essential oils, is not yet fully understood (Brunner, 1994; Sovova, Komers, Kucera, & Jez, 1994). The difficulties in modeling complex systems come from the fact that the number of components in the mixture is elevated. There are also problems in establishing the interactions between the extract’s components, the solvent and the solid phase (black pepper particles). In the extraction of black pepper essential oil with supercritical CO2 it was observed that the fluid phase concentration of the soluble components began to decrease after a portion of the solute had been removed (decreasing extraction rate period). This effect may be explained by the combination of increased solute-fluid mass transfer resistance and the decrease in the ‘‘effective’’ length of the fixed bed, due to the exhaustion of the extract in the solid substratum in the direction of the flow (Schaeffer, Zalkow, & Teja, 1989). SFE operations can be related to the time of extraction, by the evaluation of the extraction curve. According to the literature, the extraction curves are clearly divided into three sections (Bulley, Fattory, Meisen, &
S.R.S. Ferreira, M.A.A. Meireles / Journal of Food Engineering 54 (2002) 263–269
Moyls, 1984; Ferreira et al., 1993; Lee, Bulley, Fattory, & Meisen, 1986): 1. Constant extraction rate (CER): the external surface of the particles is covered with solute (easily accessible solute) – the mass transfer resistance is in the solvent phase. 2. FER (FER): failures in the external surface oil layer appear. The easily accessible solute is completely depleted at the extractor’s entrance – the diffusion mechanism starts. 3. Diffusion-controlled: mass transfer occurs only by the diffusion in the bed and inside the solid substratum particles.
These definitions lead to an analytical solution of Eqs. (1) and (2) that divided the overall extraction curve into three regions: constant extraction rate period (CER), falling extraction rate (FER) period and diffusion controlled period. The initial and boundary conditions were set as: X ðh; t ¼ 0Þ ¼ X0 and Y ðh ¼ 0; tÞ ¼ 0. For this evaluation, the Sovova’s model, in spite of the uniformity of the solute in the solid phase, divides the total amount of solute ðOÞ into two fractions: the easily accessible fraction or the most superficial one ðP Þ and the difficult access fraction or inside un-ruptured cells one ðKÞ (Berna et al., 2000). Employing the following dimensionless variables: r¼
Literature data (Ferreira et al., 1993, 1999; Vidal & Richard, 1987) indicate that the overall extraction curves for SFE from ground black pepper show the three regions described previously. A literature model that describes the process as above is the extended Lack’s plug flow model discussed by Sovov a (1994) that takes into account the solute solubility in the solvent phase ðY Þ and the mass transfer coefficient both in the fluid ðkYa Þ and in the solid ðkXa Þ phases, and neglects the accumulation of the solute in the fluid phase. It is a very convenient model for design purposes since it possesses an analytical solution and has just one adjustable parameter that considers the solid phase resistance. The model also assumes pseudo steady state and plug flow, and the temperature, the pressure and the solvent velocity are kept constant throughout the extraction. The bed is homogeneous with respect to the solute and particle size distributions. Therefore, the mass balance for a bed element is given by (Berna, T arrega, Blasco, & Subirats, 2000; Papamichail et al., 2000; Reis-Vasco, Coelho, Palavra, Marrone, & Reverchon, 2000): Solid phase: qCS ð1 eÞ
oX ¼ J ðX ; Y Þ: ot
ð1Þ
Fluid phase: qF U
oY ¼ J ðX ; Y Þ; oh
ð2Þ
where X and Y are the solute mass ratio in the solid and fluid phases, respectively, t is time, U is the superficial velocity, qCS and qF are the solid and fluid phases densities, respectively, e is the total porosity (bed and particles), h is the axial direction, and J ðX ; Y Þ is the interfacial mass transfer rate. Usually, for SFE the fluid phase can be treated as a diluted solution, therefore the solvent density ðqCO2 Þ can replace the fluid phase density. To solve Eqs. (1) and (2) Sovov a (1994) defined J ðX ; Y Þ as a function of the concentration difference using a local mass transfer coefficient for both phases.
265
X ; Xk
y ¼1
ð3Þ Y ; Y
ð4Þ
kYa h; U kYa qCO2 Y s¼ t; ð1 eÞqCS Xk
ð5Þ
z¼
ð6Þ
where Xk is the solute mass ratio for the un-ruptured cells in the solid phase, Y is the solubility of the extract in the solvent (kg/kg), kYa is the fluid-phase mass transfer coefficient ðs1 Þ, then the fluid-phase solute profile is given by the following set of equations (Sovova, 1994): For s < sCER y ¼ expðzÞ:
ð7Þ
For sCER 6 s < sFER and z > zw y¼
sCER expðzw zÞ : fr0 exp½kðsCER sÞg
ð8Þ
For sCER 6 s < sFER ; z 6 zw and also for s P sFER y¼
r0 exp½kðs sCER Þ ; fexpðr0 kzÞ þ r0 exp½kðs sCER Þ 1g
ð9Þ
where the subscripts CER and FER indicate the beginning of the extraction from inside the un-ruptured cells and the end of the easily accessible oil, respectively. From Eq. (5) it is clear that the parameter z represents a dimensionless coordinate. The subscript w indicates the limit between the CER and FER extraction periods and k represents an extraction parameter defined by the Lack’s plug flow model (Sovova, 1994) to take into account the diffusion mechanism. The extraction curves are obtained according to the following relation: mextr ¼ QCO2
tTOTAL Z
yðtÞ dt;
ð10Þ
0
tTOTAL stands for the total extraction time. The overall extraction curve given by Sovova (1994), can be written as (Pasquel, Meireles, Marques, & Petenate, 2000):
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For the CER period, t < tCER
mextr ¼ Y ½1 expðZÞQCO2 t:
ð11Þ
For the FER period, tCER 6 t < tFER mextr ¼ Y ½t tCER expðzW ZÞQCO2 : For the diffusion controlled period, t P tFER Y WXO ln 1 þ exp mextr ¼ N XO 1 W Y W QCO2 Xk exp ; ðtCER tÞ N XO
ð12Þ
3.2. Model parameter evaluation ð13Þ
with the following restrictions: Z¼
N kYa qCO2 ; QCO2 ð1 eÞqCS
tCER ¼
ð14Þ
XO Xk N ; Y Z QCO2
ð15Þ
ð16Þ XP ¼ X0 Xk ; zW Y XO expbðW QCO2 =N Þðt tCER Þc Xk ¼ ln ; Z WXO XO Xk ð17Þ
N kXa ZY ¼k ; W ¼ QCO2 ð1 eÞ Xk N tFER ¼ tCER þ QCO2 W Xk þ ðXO Xk Þ expðWXO =Y Þ ln ; XO
spheres and the diameters were 0.11 and 0.08 mm for batches 1 and 2, respectively. The compositions of the extracts obtained by gas chromatography–mass spectrometry (GC–MS) analysis were constant during the CER period. This condition is required in order to treat the system black pepper/CO2 as a pseudo ternary system formed by cellulosic structure þ solute þ CO2 .
ð18Þ
ð19Þ
where mext is the mass of extract (kg), N is the mass of cellulosic structure (kg), kXa is the solid-phase mass transfer coefficient ðs1 Þ, XP is the solute mass ratio for the easily accessible solute also in the solid phase, and k is the extraction parameter.
3. Methodology 3.1. The experimental data The experimental data of Ferreira (1996) were used. The data were obtained for temperatures of 30, 40, and 50 °C, and pressures of 150, 200 and 300 bar and two different batches of grounded black pepper (batches 1 and 2) that were partially published by Ferreira et al. (1999). The solubility for the system black pepper (cellulosic structure + solute)/CO2 were determined at interstitial velocity varying from 4:77 105 to 10:71 105 m=s for batches 1 and 2 at different operational conditions. The solvent interstitial velocity for the modeled curves varied from 15 105 to 71 105 m=s. The particles that formed the fixed bed were treated as
The total amount of oil ðOÞ was obtained considering the theoretical maximum amount of oil presented in the black pepper (Buckle, Rathnawathie, & Brophy, 1985; Ferreira, 1996; Parry, 1969). The Sovova’s model considers the total amount of solute in the solid phase ðOÞ as formed by the sum of the easily accessible oil ðP Þ and the solute inside the un-ruptured cells of the solid particles ðKÞ. The solute concentration in the solid phase ðX Þ is related to the amount of solute-free solid phase ðN Þ, as follows (Sovova, 1994): XO ¼
O ; N
Xk ¼
K ; N
XP ¼
P : N
ð20Þ
Sovova (1994) used the local mass transfer coefficient. Nevertheless, this information is hardly available and probably cannot be accessed due to the difficulties associated with the sampling along a fixed bed subjected to high pressures as in the case of SFE. To overcome these difficulties an overall mean mass transfer coefficient was used by Pasquel et al. (2000). The reasoning behind this is the fact that several authors verified that during the first two periods (CER and FER) more than 70% of the solute is extracted (Dean & Kane, 1993). The same behavior has been observed for black pepper (Ferreira et al., 1993, 1999) and other systems (Rodrigues, Marques, & Meireles, 2001; Zancan, Marques, Meireles, & Petenate, 2001). Therefore, the extraction process will be modeled using the mass transfer coefficient of the solvent phase for the CER period, defined as (Pasquel et al., 2000): kYa ¼
MCER ; qCO2 S Hb DY
ð21Þ
where the mass ratio difference was calculated as (Ferreira et al., 1999): DY ¼
YCER : ln½Y =ðY YCER Þ
ð22Þ
In Eq. (22) the solute solubility was the one measured for the pseudo-ternary system formed by CO2 þ cellulosic structure þ solute, where the cellulosic structure + solute represents the solid phase. This definition represents in a better way the thermodynamic restriction for the SFE performed in fixed beds.
S.R.S. Ferreira, M.A.A. Meireles / Journal of Food Engineering 54 (2002) 263–269
267
Table 1 Parameters for the Sovova’s model based on experimental results for Figs. 1–3 Ya (kg/kg)
QCO2 106 ðkg=sÞ
kYa 104 ðs1 Þ
tCER =60 ðsÞ
kXa 105 ðs1 Þ
Xk
Z
k
W
Temperature of 30 °C 2 200 2 300
0.0416 0.0605
9.4336 12.073
3.8108 3.9538
17.5 11.7
6.48 16.68
0.0239 0.0239
0.9060 0.8019
0.16 0.25
0.2523 0.5075
of 40 °C 150 150 150 300 300 300
0.0932 0.0932 0.0353 0.1365 0.1365 0.0477
1.2306 9.6506 1.5545 0.88391 10.537 10.446
1.9465 5.9118 1.6377 2.0948 4.7403 5.3944
36.5 36.5 16.9 9.8 9.8 14.1
0.38 8.25 0.00618 7.43 28.84 17.75
0.0173 0.0173 0.0239 0.0173 0.0173 0.0239
2.9715 1.1508 1.9792 5.5235 1.0485 1.2036
0.007 0.05 0.0005 0.07 0.12 0.26
0.1123 0.3107 0.0015 3.0578 0.9951 0.6245
Temperature of 50 °C 2 300
0.1255
12.954
4.0977
11.8
0.0173
0.6991
0.04
0.2033
Pepper (batch)
Temperature 1 1 2 1 1 2
a
P (bar)
7.24
Fitted using Y and X in mass ratio of solute in the fluid and solid phases.
Using the fluid-phase mass transfer coefficient and Eq. (14) the values of XP and Xk were obtained from Eq. (15). The parameter sCER , the dimensionless time, indicates the end of the CER period that is for t ¼ tCER , s ¼ sCER was estimated from the experimental data as described by Ferreira et al. (1999). The parameter sFER was estimated from Eq. (19). The experimental values for U, qCO2 , qCS , Hb , Y , and e as reported by Ferreira et al. (1999) were also used to model the overall extraction curves.
4. Results and discussion The solubility and the composition of the extracts indicated that batch 1 presented higher solubility values and an oil composition that is richer in lower molecular weight components, as compared to the pepper extracts from batch 2. Ferreira et al. (1999) attributed this behavior to the fact that the pepper from batch 2 could have been previously exhausted from the easily accessible solute by using steam-distillation. Therefore, one may expect the diffusion mechanism to play a more important role for the pepper from batch 2 as compared to the pepper from batch 1. Table 1 shows the values for the model parameters obtained using the experimental data for black pepper batches 1 and 2 of Ferreira (1996) and using the equations listed above. For black pepper batch 1 the ratio XP =XO is 0.65 for N equal to 27.63 g and for batch 2 the values are 0.38 and 27.92 g, respectively. Fig. 1 compares the experimental and the predicted overall extraction curves for the pepper from batch 2. From Eqs. (14) and (18) it is seeing that the k-value is directly proportional to the ratio of solid-phase and the fluid phase mass transfer coefficients, i.e., k ¼ kYa qCS Xk =kYa qCO2 Y . Therefore, the k-value is a measure of the relative importance of diffusion (diffusion-controlled
Fig. 1. Experimental and predicted overall extraction curves for pepper batch 2, at 30 °C. : 200 bar and 9:43 106 kg=s; N: 300 bar and 12:07 106 kg=s.
period) with respect to convection (CER period) during the process. The higher the k-value the greater is this relative importance. At the higher pressure, tCER was 11.70 min and the k-value was 0.25. The first parameter is smaller than the value at the lower pressure ðtCER ¼ 17:50 minÞ, while the k-value was larger. Also, at the higher pressure the solvent flow rate was larger, and so the CER ended earlier at this pressure, and the falling and diffusion controlled extraction periods lasted longer. On the other hand, the parameter tCER is directly proportional to the amount of ruptured cells (Eq. (15)), a quantity determined by the pretreatment imparted to the raw material, which was the same for every experimental run (Table 1). Therefore, the results of Fig. 1 imply that maintaining Xk constant imposes a severe restriction on the predictive ability of the Sovova’s model. Fig. 2 compares predicted and experimental overall extraction curves at 40 °C for various conditions. In Fig. 2 the effects of solvent flow rate and raw material can be appreciated. At 300 bar and upper level of flow rate, for pepper from batch 2 the k-value was larger ðk ¼ 0:26Þ
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Fig. 3. Experimental and predicted overall extraction curves for pepper batch 1 at 50 °C, 300 bar, and 12:95 106 kg=s.
Fig. 2. Experimental and predicted overall extraction curves at 40 °C: (a) 150 bar, N: 1:23 106 kg=s, batch 1, : 9:65 106 kg=s, batch 1, : 1:55 106 kg=s, batch 2; (b) 300 bar, N: 0:88 106 kg=s, batch 1, : 10:54 106 kg=s, batch 1, : 10:45 106 kg=s, batch 2.
than for pepper from batch 1 ðk ¼ 0:12Þ, as expected, due to the larger value of Xk for pepper from batch 2. Additionally, for pepper from batch 1 at the low flow rate ð0:88 106 kg=sÞ, the k-value was smaller ðk ¼ 0:07Þ and tCER was equal compared to the higher flow rate ð10:537 106 kg=sÞ, also as expected. Since Xk was maintained constant to accommodate an equal value of tCER (estimated using a spline as explained) at the low solvent flow rate, the relative weight of diffusion to convection must be diminished through the k-value. The behavior of the system was different at 150 bar. At low flow rate the k-value for pepper from batch 1 was larger by one order of magnitude as compared to pepper from batch 2. The explanation lies in the fact that at this pressure the solvent flow rate for the run with pepper from batch 2 was 26% larger than the corresponding run for pepper from batch 1. In addition, at 300 bar, the solvent flow rates differ by less than 7%. The larger the k-value, the greater is the relative importance of diffusion with respect to convection. Therefore, when diffusion inside the solid particles plays an important role in the SFE process, the k-values that best describe the experimental data will increase. Values of k equal to the unity indicate that diffusion would be more important than convection. To verify the sensitivity of the overall extraction curve to the values of k, these curves were calculated using k-values differing by at least one order of magnitude. Fig. 3 compares experimental
data to predicted extraction curves for pepper from batch 1, at 300 bar and 40 °C. The predicted curves were obtained using different k-values. For k ¼ 0:12 the predicted curve quantitatively described the experimental data. At lower values of k we observe a deviation from the experimental points after the CER period. The procedure employed to evaluate the model parameters failed, for some conditions, to describe the system behavior for the falling rate period at 300 bar for pepper from batch 1 (Fig. 2(a)). This can be improved if Xk were allowed to vary as a function of pressure and temperature. Or even better, an experimental procedure should be developed to determine Xk .
5. Conclusion The procedure used to evaluate the parameters of the Sovova’s model from experimental data quantitatively described the experimental data for the majority of conditions analyzed. The simplicity of parameters evaluation lies in the fact that the fluid-phase mass transfer coefficient ðkYa Þ and tCER are estimated from the slope and the intercept of two straight lines used to describe the experimental overall extraction curve. The other required parameters were directly evaluated from experimental data. Thus only one adjustable parameter, the extraction parameter k, was required to describe the overall extraction curve. Further work will be required to evaluate the effects of the operational conditions in the model parameters. This procedure will provide a powerful tool for scale-up purposes.
Acknowledgements The authors are grateful to EQA-UFSC, FAPESP (1995/0562-3 and 1999/01962-1), CNPq, and CAPES for providing the financial support to develop this work.
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Modeling the supercritical fluid extraction of black pepper (Piper nigrum L.) essential oil Sandra R.S. Ferreira
a,1
, M. Angela A. Meireles
b,*
a
Departamento de Engenharia Quımica e Engenharia de Alimentos, EQA, Universidade Federal de Santa Catarina, UFSC, Cx. P. 476, 88040-900 Florian opolis, SC, Brazil b LASEFI, Departamento de Engenharia de Alimentos, Faculty of Engineering Alimentos, Unicamp, Cx. P. 6121, 13081-970 Campinas, S~ ao Paulo, Brazil Received 5 July 2001; accepted 3 November 2001
Abstract The fixed bed extraction of black pepper essential oil using supercritical carbon dioxide was modeled by the extended Lack’s plug flow model developed by Sovova (Sovova’s model). The experimental data were obtained for extractions conducted at 30, 40 and 50 °C, and 150, 200, and 300 bar, for two different types of ground black pepper (batches 1 and 2). The model parameters were evaluated from the experimental data. The fluid-phase mass transfer coefficient was obtained from the constant extraction rate (CER) period using a logarithmical solute mass ratio difference. The Sovov a’s model was able to describe the experimental data quite well. The best value for the extraction parameter, which relates the resistances of solid-phase mass transfer to fluid-phase mass transfer, was 0.12 and 0.25 for batches 1 and 2, respectively. The experimental data were well represented by the model for the mass ratio of solute present in ruptured cell to the initial mass ratio of solute equal to 65% and 38% for batches 1 and 2, respectively. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Supercritical fluid extraction; Black pepper oil; Mass transfer model
1. Introduction Brazil is the second largest worldwide producer of black pepper (Piper nigrum L.) and of several other spices and herbs, used in food processing as well as in pharmaceutical and cosmetic products. Black pepper is an important spice, appreciated for both its aroma and its pungency. Studies on supercritical fluid extraction (SFE) to obtain black pepper oil and/or oleoresin have been reported in the literature (Ferreira, Meireles, & Cabral, 1993; Ferreira, Nikolov, Doraiswamy, Meireles, & Petenate, 1999; Vidal & Richard, 1987). The components of the pepper’s extract that contribute to its value as a food additive are the volatile oil for its aroma and the alkaloid compounds for the pungency. Black pepper oil is formed by monoterpenes, sesquiterpenes, and oxygenated compounds (Ferreira, 1996). *
Corresponding author. Tel.: +55-19-788-4033; fax: +55-19-7884027. E-mail addresses: [email protected] (S.R.S. Ferreira), meireles@ fea.unicamp.br (M.AA. Meireles). 1 Tel.: +55-48-331-9448; fax: +55-48-331-9687.
The engineering design of SFE processes, which generally involves putting in contact a packed bed formed by the solid substratum (like ground spices) and a supercritical fluid (SF), requires the knowledge of the thermodynamics constraints (solubility and selectivity) as well as the kinetic constraints (mass transfer rate). In spite of the increased interest in SFE there is still a lack of information about the mass transfer aspects of these processes. Because the flow pattern in a fixed bed is complex, it has been found convenient to develop semi-empirical correlations to describe the mass transfer between the solute dissolved in the solid phase and the solvent phase. Conceivably, the mass transfer coefficient, which is a function of density, viscosity, diffusivity, porosity of the bed, particle size, and solvent flow rate, can be used to describe the kinetic restraints of the system. The influence of the above variables is, in general, expressed using the dimensionless numbers of Sherwood, Reynolds, Schmidt, and Grashof, when natural convection is important (Ferreira, Meireles, & Nikolov, 1997). In the pressure and temperature range where most supercritical extractions are carried out, up to now there has been no
0260-8774/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 0 1 ) 0 0 2 1 2 - 6
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Nomenclature CER mextr h Hb J ðX ; Y Þ K k kXa kYa P MCER N O p QCO2 r S t tCER T U XO
constant extraction rate ðkg oil=sÞ mass of extract (kg) axial coordinate (m) length of bed (m) interfacial mass transfer rate ðkg oil=m3 sÞ initial mass of inaccessible oil (kg oil) extraction parameter (dimensionless) solid-phase mass transfer coefficient (s) fluid-phase transfer coefficient (s) initial mass of easily accessible solute (kg solute) mass extraction rate for the CER period (kg oil/s) mass of cellulosic structure (kg solid) mass of solute in solid phase (kg oil) pressure (bar) solvent flow rate ðkg CO2 =sÞ dimensionless concentration of solute in solid phase (dimensionless) extractor sectional area ðm2 Þ extracting time (s) end of the CER (s) temperature ð°CÞ superficial velocity (m/s) initial solute mass ratio in the solid phase (kg oil/kg cellulosic structure)
generally accepted correlation for the mass transfer coefficient between the SF phase and the natural solid substratum. Results obtained employing low speed flows, where buoyancy forces may play a significant role (Lim, Holder, & Shah, 1989; Lim, Lee, Kim, & Lee, 1995; Mandelbaum & B€ ohm, 1973), are also missing. For SFE the known dimensionless mass transfer equations (Sherwood equations) developed for liquids are probably not able to describe mass transfer kinetics because of the unusual behavior of dense gases. Therefore, the use of a simple model that requires little experimental information can prove to be useful for scale-up design calculations. Besides the empirical models there are several mathematical models available to correlate experimental results, such as models based on heat transfer analogy and differential mass balance integration models (Papamichail, Louli, & Magoulas, 2000). Then, the purpose of this work was to evaluate the kinetic aspects of the black pepper essential oil extraction, with supercritical CO2 as solvent, using the mass transfer model described by Sovov a (1994) to investigate both the spatial and the time dependence of the fluid phase solute concentration. The experimental data selected were the ones partially published by Ferreira et al. (1999).
XP Xk y Y DY Y Yin YCER z Z W e qCO2 qCS s
mass ratio of easily accessible solute (kg oil/ kg cellulosic structure) mass ratio of solute inside un-ruptured cells (kg oil/kg cellulosic structure) dimensionless concentration of solute in solvent phase (dimensionless) mass ratio of solute in solvent phase ðkg oil=kg CO2 Þ mean mass ratio difference in bed during the CER period ðkg oil=kg CO2 Þ solubility of the solute in the solvent phase ðkg oil=kg CO2 Þ solvent phase solute mass ratio at bed inlet ðkg oil=kg CO2 Þ solvent phase solute mass ratio at bed outlet ðkg oil=kg CO2 Þ dimensionless coordinate parameter of fast extraction period (dimensionless) mass transfer parameter in the solid phase (dimensionless) total porosity (dimensionless) solvent density ðkg=m3 Þ solid density ðkg=m3 Þ dimensionless time
2. Mass transfer model The mass transfer mechanism of the high-pressure extraction of complex mixtures, like essential oils, is not yet fully understood (Brunner, 1994; Sovova, Komers, Kucera, & Jez, 1994). The difficulties in modeling complex systems come from the fact that the number of components in the mixture is elevated. There are also problems in establishing the interactions between the extract’s components, the solvent and the solid phase (black pepper particles). In the extraction of black pepper essential oil with supercritical CO2 it was observed that the fluid phase concentration of the soluble components began to decrease after a portion of the solute had been removed (decreasing extraction rate period). This effect may be explained by the combination of increased solute-fluid mass transfer resistance and the decrease in the ‘‘effective’’ length of the fixed bed, due to the exhaustion of the extract in the solid substratum in the direction of the flow (Schaeffer, Zalkow, & Teja, 1989). SFE operations can be related to the time of extraction, by the evaluation of the extraction curve. According to the literature, the extraction curves are clearly divided into three sections (Bulley, Fattory, Meisen, &
S.R.S. Ferreira, M.A.A. Meireles / Journal of Food Engineering 54 (2002) 263–269
Moyls, 1984; Ferreira et al., 1993; Lee, Bulley, Fattory, & Meisen, 1986): 1. Constant extraction rate (CER): the external surface of the particles is covered with solute (easily accessible solute) – the mass transfer resistance is in the solvent phase. 2. FER (FER): failures in the external surface oil layer appear. The easily accessible solute is completely depleted at the extractor’s entrance – the diffusion mechanism starts. 3. Diffusion-controlled: mass transfer occurs only by the diffusion in the bed and inside the solid substratum particles.
These definitions lead to an analytical solution of Eqs. (1) and (2) that divided the overall extraction curve into three regions: constant extraction rate period (CER), falling extraction rate (FER) period and diffusion controlled period. The initial and boundary conditions were set as: X ðh; t ¼ 0Þ ¼ X0 and Y ðh ¼ 0; tÞ ¼ 0. For this evaluation, the Sovova’s model, in spite of the uniformity of the solute in the solid phase, divides the total amount of solute ðOÞ into two fractions: the easily accessible fraction or the most superficial one ðP Þ and the difficult access fraction or inside un-ruptured cells one ðKÞ (Berna et al., 2000). Employing the following dimensionless variables: r¼
Literature data (Ferreira et al., 1993, 1999; Vidal & Richard, 1987) indicate that the overall extraction curves for SFE from ground black pepper show the three regions described previously. A literature model that describes the process as above is the extended Lack’s plug flow model discussed by Sovov a (1994) that takes into account the solute solubility in the solvent phase ðY Þ and the mass transfer coefficient both in the fluid ðkYa Þ and in the solid ðkXa Þ phases, and neglects the accumulation of the solute in the fluid phase. It is a very convenient model for design purposes since it possesses an analytical solution and has just one adjustable parameter that considers the solid phase resistance. The model also assumes pseudo steady state and plug flow, and the temperature, the pressure and the solvent velocity are kept constant throughout the extraction. The bed is homogeneous with respect to the solute and particle size distributions. Therefore, the mass balance for a bed element is given by (Berna, T arrega, Blasco, & Subirats, 2000; Papamichail et al., 2000; Reis-Vasco, Coelho, Palavra, Marrone, & Reverchon, 2000): Solid phase: qCS ð1 eÞ
oX ¼ J ðX ; Y Þ: ot
ð1Þ
Fluid phase: qF U
oY ¼ J ðX ; Y Þ; oh
ð2Þ
where X and Y are the solute mass ratio in the solid and fluid phases, respectively, t is time, U is the superficial velocity, qCS and qF are the solid and fluid phases densities, respectively, e is the total porosity (bed and particles), h is the axial direction, and J ðX ; Y Þ is the interfacial mass transfer rate. Usually, for SFE the fluid phase can be treated as a diluted solution, therefore the solvent density ðqCO2 Þ can replace the fluid phase density. To solve Eqs. (1) and (2) Sovov a (1994) defined J ðX ; Y Þ as a function of the concentration difference using a local mass transfer coefficient for both phases.
265
X ; Xk
y ¼1
ð3Þ Y ; Y
ð4Þ
kYa h; U kYa qCO2 Y s¼ t; ð1 eÞqCS Xk
ð5Þ
z¼
ð6Þ
where Xk is the solute mass ratio for the un-ruptured cells in the solid phase, Y is the solubility of the extract in the solvent (kg/kg), kYa is the fluid-phase mass transfer coefficient ðs1 Þ, then the fluid-phase solute profile is given by the following set of equations (Sovova, 1994): For s < sCER y ¼ expðzÞ:
ð7Þ
For sCER 6 s < sFER and z > zw y¼
sCER expðzw zÞ : fr0 exp½kðsCER sÞg
ð8Þ
For sCER 6 s < sFER ; z 6 zw and also for s P sFER y¼
r0 exp½kðs sCER Þ ; fexpðr0 kzÞ þ r0 exp½kðs sCER Þ 1g
ð9Þ
where the subscripts CER and FER indicate the beginning of the extraction from inside the un-ruptured cells and the end of the easily accessible oil, respectively. From Eq. (5) it is clear that the parameter z represents a dimensionless coordinate. The subscript w indicates the limit between the CER and FER extraction periods and k represents an extraction parameter defined by the Lack’s plug flow model (Sovova, 1994) to take into account the diffusion mechanism. The extraction curves are obtained according to the following relation: mextr ¼ QCO2
tTOTAL Z
yðtÞ dt;
ð10Þ
0
tTOTAL stands for the total extraction time. The overall extraction curve given by Sovova (1994), can be written as (Pasquel, Meireles, Marques, & Petenate, 2000):
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For the CER period, t < tCER
mextr ¼ Y ½1 expðZÞQCO2 t:
ð11Þ
For the FER period, tCER 6 t < tFER mextr ¼ Y ½t tCER expðzW ZÞQCO2 : For the diffusion controlled period, t P tFER Y WXO ln 1 þ exp mextr ¼ N XO 1 W Y W QCO2 Xk exp ; ðtCER tÞ N XO
ð12Þ
3.2. Model parameter evaluation ð13Þ
with the following restrictions: Z¼
N kYa qCO2 ; QCO2 ð1 eÞqCS
tCER ¼
ð14Þ
XO Xk N ; Y Z QCO2
ð15Þ
ð16Þ XP ¼ X0 Xk ; zW Y XO expbðW QCO2 =N Þðt tCER Þc Xk ¼ ln ; Z WXO XO Xk ð17Þ
N kXa ZY ¼k ; W ¼ QCO2 ð1 eÞ Xk N tFER ¼ tCER þ QCO2 W Xk þ ðXO Xk Þ expðWXO =Y Þ ln ; XO
spheres and the diameters were 0.11 and 0.08 mm for batches 1 and 2, respectively. The compositions of the extracts obtained by gas chromatography–mass spectrometry (GC–MS) analysis were constant during the CER period. This condition is required in order to treat the system black pepper/CO2 as a pseudo ternary system formed by cellulosic structure þ solute þ CO2 .
ð18Þ
ð19Þ
where mext is the mass of extract (kg), N is the mass of cellulosic structure (kg), kXa is the solid-phase mass transfer coefficient ðs1 Þ, XP is the solute mass ratio for the easily accessible solute also in the solid phase, and k is the extraction parameter.
3. Methodology 3.1. The experimental data The experimental data of Ferreira (1996) were used. The data were obtained for temperatures of 30, 40, and 50 °C, and pressures of 150, 200 and 300 bar and two different batches of grounded black pepper (batches 1 and 2) that were partially published by Ferreira et al. (1999). The solubility for the system black pepper (cellulosic structure + solute)/CO2 were determined at interstitial velocity varying from 4:77 105 to 10:71 105 m=s for batches 1 and 2 at different operational conditions. The solvent interstitial velocity for the modeled curves varied from 15 105 to 71 105 m=s. The particles that formed the fixed bed were treated as
The total amount of oil ðOÞ was obtained considering the theoretical maximum amount of oil presented in the black pepper (Buckle, Rathnawathie, & Brophy, 1985; Ferreira, 1996; Parry, 1969). The Sovova’s model considers the total amount of solute in the solid phase ðOÞ as formed by the sum of the easily accessible oil ðP Þ and the solute inside the un-ruptured cells of the solid particles ðKÞ. The solute concentration in the solid phase ðX Þ is related to the amount of solute-free solid phase ðN Þ, as follows (Sovova, 1994): XO ¼
O ; N
Xk ¼
K ; N
XP ¼
P : N
ð20Þ
Sovova (1994) used the local mass transfer coefficient. Nevertheless, this information is hardly available and probably cannot be accessed due to the difficulties associated with the sampling along a fixed bed subjected to high pressures as in the case of SFE. To overcome these difficulties an overall mean mass transfer coefficient was used by Pasquel et al. (2000). The reasoning behind this is the fact that several authors verified that during the first two periods (CER and FER) more than 70% of the solute is extracted (Dean & Kane, 1993). The same behavior has been observed for black pepper (Ferreira et al., 1993, 1999) and other systems (Rodrigues, Marques, & Meireles, 2001; Zancan, Marques, Meireles, & Petenate, 2001). Therefore, the extraction process will be modeled using the mass transfer coefficient of the solvent phase for the CER period, defined as (Pasquel et al., 2000): kYa ¼
MCER ; qCO2 S Hb DY
ð21Þ
where the mass ratio difference was calculated as (Ferreira et al., 1999): DY ¼
YCER : ln½Y =ðY YCER Þ
ð22Þ
In Eq. (22) the solute solubility was the one measured for the pseudo-ternary system formed by CO2 þ cellulosic structure þ solute, where the cellulosic structure + solute represents the solid phase. This definition represents in a better way the thermodynamic restriction for the SFE performed in fixed beds.
S.R.S. Ferreira, M.A.A. Meireles / Journal of Food Engineering 54 (2002) 263–269
267
Table 1 Parameters for the Sovova’s model based on experimental results for Figs. 1–3 Ya (kg/kg)
QCO2 106 ðkg=sÞ
kYa 104 ðs1 Þ
tCER =60 ðsÞ
kXa 105 ðs1 Þ
Xk
Z
k
W
Temperature of 30 °C 2 200 2 300
0.0416 0.0605
9.4336 12.073
3.8108 3.9538
17.5 11.7
6.48 16.68
0.0239 0.0239
0.9060 0.8019
0.16 0.25
0.2523 0.5075
of 40 °C 150 150 150 300 300 300
0.0932 0.0932 0.0353 0.1365 0.1365 0.0477
1.2306 9.6506 1.5545 0.88391 10.537 10.446
1.9465 5.9118 1.6377 2.0948 4.7403 5.3944
36.5 36.5 16.9 9.8 9.8 14.1
0.38 8.25 0.00618 7.43 28.84 17.75
0.0173 0.0173 0.0239 0.0173 0.0173 0.0239
2.9715 1.1508 1.9792 5.5235 1.0485 1.2036
0.007 0.05 0.0005 0.07 0.12 0.26
0.1123 0.3107 0.0015 3.0578 0.9951 0.6245
Temperature of 50 °C 2 300
0.1255
12.954
4.0977
11.8
0.0173
0.6991
0.04
0.2033
Pepper (batch)
Temperature 1 1 2 1 1 2
a
P (bar)
7.24
Fitted using Y and X in mass ratio of solute in the fluid and solid phases.
Using the fluid-phase mass transfer coefficient and Eq. (14) the values of XP and Xk were obtained from Eq. (15). The parameter sCER , the dimensionless time, indicates the end of the CER period that is for t ¼ tCER , s ¼ sCER was estimated from the experimental data as described by Ferreira et al. (1999). The parameter sFER was estimated from Eq. (19). The experimental values for U, qCO2 , qCS , Hb , Y , and e as reported by Ferreira et al. (1999) were also used to model the overall extraction curves.
4. Results and discussion The solubility and the composition of the extracts indicated that batch 1 presented higher solubility values and an oil composition that is richer in lower molecular weight components, as compared to the pepper extracts from batch 2. Ferreira et al. (1999) attributed this behavior to the fact that the pepper from batch 2 could have been previously exhausted from the easily accessible solute by using steam-distillation. Therefore, one may expect the diffusion mechanism to play a more important role for the pepper from batch 2 as compared to the pepper from batch 1. Table 1 shows the values for the model parameters obtained using the experimental data for black pepper batches 1 and 2 of Ferreira (1996) and using the equations listed above. For black pepper batch 1 the ratio XP =XO is 0.65 for N equal to 27.63 g and for batch 2 the values are 0.38 and 27.92 g, respectively. Fig. 1 compares the experimental and the predicted overall extraction curves for the pepper from batch 2. From Eqs. (14) and (18) it is seeing that the k-value is directly proportional to the ratio of solid-phase and the fluid phase mass transfer coefficients, i.e., k ¼ kYa qCS Xk =kYa qCO2 Y . Therefore, the k-value is a measure of the relative importance of diffusion (diffusion-controlled
Fig. 1. Experimental and predicted overall extraction curves for pepper batch 2, at 30 °C. : 200 bar and 9:43 106 kg=s; N: 300 bar and 12:07 106 kg=s.
period) with respect to convection (CER period) during the process. The higher the k-value the greater is this relative importance. At the higher pressure, tCER was 11.70 min and the k-value was 0.25. The first parameter is smaller than the value at the lower pressure ðtCER ¼ 17:50 minÞ, while the k-value was larger. Also, at the higher pressure the solvent flow rate was larger, and so the CER ended earlier at this pressure, and the falling and diffusion controlled extraction periods lasted longer. On the other hand, the parameter tCER is directly proportional to the amount of ruptured cells (Eq. (15)), a quantity determined by the pretreatment imparted to the raw material, which was the same for every experimental run (Table 1). Therefore, the results of Fig. 1 imply that maintaining Xk constant imposes a severe restriction on the predictive ability of the Sovova’s model. Fig. 2 compares predicted and experimental overall extraction curves at 40 °C for various conditions. In Fig. 2 the effects of solvent flow rate and raw material can be appreciated. At 300 bar and upper level of flow rate, for pepper from batch 2 the k-value was larger ðk ¼ 0:26Þ
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Fig. 3. Experimental and predicted overall extraction curves for pepper batch 1 at 50 °C, 300 bar, and 12:95 106 kg=s.
Fig. 2. Experimental and predicted overall extraction curves at 40 °C: (a) 150 bar, N: 1:23 106 kg=s, batch 1, : 9:65 106 kg=s, batch 1, : 1:55 106 kg=s, batch 2; (b) 300 bar, N: 0:88 106 kg=s, batch 1, : 10:54 106 kg=s, batch 1, : 10:45 106 kg=s, batch 2.
than for pepper from batch 1 ðk ¼ 0:12Þ, as expected, due to the larger value of Xk for pepper from batch 2. Additionally, for pepper from batch 1 at the low flow rate ð0:88 106 kg=sÞ, the k-value was smaller ðk ¼ 0:07Þ and tCER was equal compared to the higher flow rate ð10:537 106 kg=sÞ, also as expected. Since Xk was maintained constant to accommodate an equal value of tCER (estimated using a spline as explained) at the low solvent flow rate, the relative weight of diffusion to convection must be diminished through the k-value. The behavior of the system was different at 150 bar. At low flow rate the k-value for pepper from batch 1 was larger by one order of magnitude as compared to pepper from batch 2. The explanation lies in the fact that at this pressure the solvent flow rate for the run with pepper from batch 2 was 26% larger than the corresponding run for pepper from batch 1. In addition, at 300 bar, the solvent flow rates differ by less than 7%. The larger the k-value, the greater is the relative importance of diffusion with respect to convection. Therefore, when diffusion inside the solid particles plays an important role in the SFE process, the k-values that best describe the experimental data will increase. Values of k equal to the unity indicate that diffusion would be more important than convection. To verify the sensitivity of the overall extraction curve to the values of k, these curves were calculated using k-values differing by at least one order of magnitude. Fig. 3 compares experimental
data to predicted extraction curves for pepper from batch 1, at 300 bar and 40 °C. The predicted curves were obtained using different k-values. For k ¼ 0:12 the predicted curve quantitatively described the experimental data. At lower values of k we observe a deviation from the experimental points after the CER period. The procedure employed to evaluate the model parameters failed, for some conditions, to describe the system behavior for the falling rate period at 300 bar for pepper from batch 1 (Fig. 2(a)). This can be improved if Xk were allowed to vary as a function of pressure and temperature. Or even better, an experimental procedure should be developed to determine Xk .
5. Conclusion The procedure used to evaluate the parameters of the Sovova’s model from experimental data quantitatively described the experimental data for the majority of conditions analyzed. The simplicity of parameters evaluation lies in the fact that the fluid-phase mass transfer coefficient ðkYa Þ and tCER are estimated from the slope and the intercept of two straight lines used to describe the experimental overall extraction curve. The other required parameters were directly evaluated from experimental data. Thus only one adjustable parameter, the extraction parameter k, was required to describe the overall extraction curve. Further work will be required to evaluate the effects of the operational conditions in the model parameters. This procedure will provide a powerful tool for scale-up purposes.
Acknowledgements The authors are grateful to EQA-UFSC, FAPESP (1995/0562-3 and 1999/01962-1), CNPq, and CAPES for providing the financial support to develop this work.
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