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food and bioproducts processing 9 0 ( 2 0 1 2 ) 199–204
Contents lists available at ScienceDirect
Food and Bioproducts Processing
journal homepage: www.elsevier.com/locate/fbp
Solvent extraction of vegetable oils: Numerical and
experimental study
Myriam Lorena Melgarejo Navarro Cerutti, Antonio Augusto Ulson de Souza,
Selene Maria de Arruda Guelli Ulson de Souza∗
Federal University of Santa Catarina, Chemical Engineering Department, Laboratory of Mass Transfer, PO Box 476, 88040-900
Florianópolis, SC, Brazil
a b s t r a c t
A process for the extraction of vegetable oils from soybean seeds with a solvent was developed experimentally. The
extraction was carried out in a continuous, fixed-bed extractor. A non-dimensional transient model was applied
to simulate the mass transfer process which occurs during the extraction in a packed bed column. The governing
dimensionless differential equations were numerically solved using the method of finite volumes. The numerical
results were compared with data obtained from the experimental extraction, presenting good agreement. The val-
ues obtained numerically for the total oil mass extracted in the fluid phase presented a maximum error of 20%,
when compared to the experimental data. The greatest discrepancy was observed at the end of the extraction. This
maximum error can be considered small due to the use of a simple numerical model.
© 2011 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Keywords: Extraction; Vegetable oils; Modeling; Simulation; Mass transfer
1. Introduction
The processing and commercialization of vegetable oils
from soybean, rice, cotton, and sunflower seeds represent
important economic activities in Brazil and worldwide. Veg-
etable oils, besides being an important and widely exploited
source of lipids, vitamins, waxes, pigments and lecithins,
are among the most promising sources of hydrocarbons
for energy and chemical needs, with a view to replac-
ing petroleum which is non-renewable and highly polluting
(Amarasinghe and Gangodavilage, 2004; Amarasinghe et al.,
2009).
Vegetable oil is generally extracted by employing the hex-
ane fraction of petroleum as the solvent in a continuous
process in which the stages for the removal of residual sol-
vent from the solid and the extracted oil are onerous and
not always efficient. Consequently, more appropriate pro-
cesses have been sought. Prominent amongst the contenders
is extraction with carbon dioxide under supercritical con-
ditions, which in recent decades has generated important
experimental information. However, when compared to the
conventional process, this presents numerous problems that
∗
Corresponding author. Tel.: +55 48 3721 9448x207; fax: +55 48 3721 9687.
E-mail address: selene@enq.ufsc.br (S.M.d.A.G.U. de Souza).
Received 10 June 2010; Received in revised form 27 January 2011; Accepted 16 March 2011
hinder its implantation due to the high cost involved (Rezende
and Filho, 2000; Rosenthal et al., 1998).
The literature contains a variety of studies on the subject
of extractors (Karnofsky, 1986, 1987) and on the modeling of
extraction (Abraham et al., 1988; Martinho et al., 2008; Thomas
et al., 2007) based on the overall mass balance and experimen-
tal data. The mathematical model proposed by Majumdar et al.
(1995), for the fixed-bed extractor, provided important results
which contributed to later studies with specific extractors,
such as the De Smet, Rotocell and Crown-Model, conducted by
Veloso (1999), Thomas (1999) and Benetti (2001), respectively.
The mass transfer that occurs during solvent extraction
in a packed column was analyzed in this study using the
mathematical model proposed by Majumdar et al. (1995). The
following phenomena were considered:
- transient regime in the process;
- transfer of oil from the pore phase to the fluid phase by
concentration difference;
- transfer of oil by diffusion, in the opposite direction to the
flow of the micelle;
- passage of oil between the phases, solid and pores;
0960-3085/$ – see front matter © 2011 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
doi:10.1016/j.fbp.2011.03.002
200 food and bioproducts processing 9 0 ( 2 0 1 2 ) 199–204
Nomenclature
ap interface area of the particle, cm−1
C mass fraction of oil in the fluid phase, dimen-
sionless
Cp mass fraction of oil in the solid phase, dimen-
sionless
dp diameter of the particle, cm
D diameter of the column, cm
Dab diffusion coefficient, cm2/s
kf coefficient of mass transfer, cm/s
L length of the column, cm
N mass fraction of oil in the solid phase of the
particle, dimensionless
Pe Peclet number, dimensionless
Q Hexane flow rates, mL/min
Re Reynolds number, dimensionless
Sc Schmidt number, dimensionless
Sh Sherwood number, dimensionless
t extraction time, s
Vs interstitial velocity of the fluid phase, cm/min
Z vertical co-ordinate of the bed, cm
εb porosity of the bed, dimensionless
εp porosity of the particle, dimensionless
density of hexane, g/mL
viscosity of hexane, g/cm s
and the following hypotheses:
- oil as a single component;
- solid with macro-pores filled with oil (stationary phase);
- absence of radial concentration gradients in the fluid phase;
- constant and uniform porosity of the particle and of the bed;
- constant and uniform temperature (27 ◦C);
- nil heat generation;
- constant viscosity and density of the micelle.
With the objective of studying the mass transfer that occurs
during the process of oil extraction from layers of soybean, in
a fixed-bed column, experimental data are obtained and used
in the development of a mathematical model.
2. Experimental methodology
In order to determine the efficiency of the extraction process
on a fixed bed, extraction runs were carried out with layers
of soybean seed and an equilibrium constant obtained for the
fluid and solid phases at LABMASSA – Mass Transfer Labo-
ratory of the Department of Chemical Engineering and Food
Engineering, UFSC.
Extraction: The experiments were carried out in a cylindri-
cal column made of borosilicate in the laboratory, with 15 cm
length and 1.6 cm diameter, containing a glass screen with
holes to secure the bed. The upper end of the column has a
wide opening to allow the bed loading and the lower end is fun-
neled to carry out the sampling. The column was filled with
layers of soybeans 0.357 cm in diameter, 0.035 cm in thickness
and with a 24.33% fat content (determined by the method of
Soxhlet), previously packed, provided by Ceval Alimentos S/A
(SC). The quantity of 5.3 g of soybean layers was manually
loaded with a funnel up to 6.3 cm of the total length of the
column, aiming at obtaining a constant packing for each run.
The solvent hexane (analytical quality) was introduced into
the column via a peristaltic pump (Gilson, Miniplus 3 model)
at a constant flow of 10 mL/min. After totally filling the column
the micelle was collected at the outlet at time intervals of 30 s
(after the first micelle collection at 15 s).
The micelle samples were collected in glass tubes of known
dry weight, before being evaporated in a heater (Fisatom), with
the accumulated mass being calculated by the difference in
mass on an analytical balance (Mettler Toledo, model AB204-S,
precision 10−4 g). The volume of empty space contained in the
column (εb), or the packing degree of the bed, was measured
by the solvent volume required to fill the packed bed divided
by the total volume of the empty column.
All experimental runs were performed three times. The
diameter of the layers of soybean was determined by granulo-
metric analysis (Perry, 1996), using sieves of the ASTM series,
available at LABMASSA/UFSC.
Equilibrium constant: The equilibrium relationship between
the residual oil content in the solid sample and the quantity
of oil in the micelle trapped in its pores was determined by
the tangent to the curve obtained from the collected mass
fractions (wet basis) for both phases. Each point on the curve,
which was obtained in a glass Erlenmeyer, belonged to a mass
variable in a constant volume of 50 mL, measured after 10 h of
shaking in a bath (Nova Ética, model 304) at 27 ◦C. The filter-
carrier device for polycarbonate syringes (Sartorius, model
16514/17E) was used for sampling and the total residual mass
of oil in the solid was further obtained from the difference
between the initial mass and the mass after evaporation using
glass sampling tubes (Navarro, 2002). All analyses were carried
out according to the AOAC (1997).
3. Numerical formulation
Taking into account the phenomena involved and the
hypotheses cited above, a model was developed in order to
simulate the performance of a fixed-bed extractor. This model
is based on the study presented by Majumdar et al. (1995),
which uses the equations of conservation of mass and of
chemical species (oil – in the fluid and solid phases).
3.1. Governing equations
(a) Equation of conservation of mass – fluid phase
∂Vs
∂Z
=
1 − εb
εb
kf ap(Cp − C) (1)
where Vs is the interstitial velocity of the fluid phase; C
is the mass fraction of oil in the fluid phase; Cp is the
mass fraction of oil in the solid phase; Z is the vertical
co-ordinate of the bed; εb is the porosity of the bed; kf is
the coefficient of mass transfer; ap is the interface area of
the particle.
(b) Equation of conservation of chemical species, oil – fluid
phase
∂C
∂t
+
∂(VsC)
∂Z
= Dab
∂2C
∂Z2
+
1 − εb
εb
apkf (Cp − C) (2)
where Dab is the diffusion coefficient.
food and bioproducts processing 9 0 ( 2 0 1 2 ) 199–204 201
(c) Equation of conservation of chemical species, oil – solid
phase
∂Cp
∂t
εp + (1 − εp)
∂N
∂Cp
= −apkf (Cp − C) (3)
where εp is the porosity of the particle; t is the extraction
time; N is the mass fraction of oil in the solid phase of the
particle.
3.2. Initial and boundary conditions
Vs(0, t) = Vsi 0 ≤ t ≤ tf (4)
C(z, 0) = Ci 0 ≤ z ≤ L (5)
Cp(z, 0) = Cpi 0 ≤ z ≤ L (6)
∂C
∂Z
(L, t) = 0 0 ≤ t ≤ tf (7)
VsC
Vsi
−
Dab
Vsi
∂C
∂Z
(0, t) = Ci 0 ≤ t ≤ tf (8)
In Eqs. (1)–(3), the following apply:
V s =
Vs
Vsi
t =
Vsit
L
Z =
Z
L
(9)
Sh =
kf dp
Dab
Pei =
Vsidp
Dab
(10)
where L is the length of the column; dp is the diameter of the
particle; Sh is the Sherwood number; Pe is the Peclet number.
The dimensionless equations become:
∂V s
∂Z
=
1 − εb
εb
(apL)
Sh
Pei
(Cp − C) (11)
∂C
∂t
+
∂(VsC)
∂Z
=
1
Pei
dp
L
∂2C
∂Z 2
+
1 − εb
εb
(apL)
Sh
Pei
(Cp − C) (12)
∂Cp
∂t
1 +
1 − εp
εp
∂N
∂Cp
+
1
εb
Sh
Pei
(apL)(Cp − C) = 0 (13)
where the lower index “i” refers to the initial state and the
upper index ( ) to the dimensionless parameters.
To determine the coefficient of mass transfer, kf, the Sher-
wood number is used according to the correlations proposed
by Treybal (1981),
Sh = 2.4Re0.34
Sc0.42
0.08 < Re < 0.125 (14)
Sh = 0.442Re0.69
Sc0.42
0.125 < Re < 5000 (15)
The Reynolds number (Re) and the Schmidt number (Sc) are
defined in the following way:
Re =
Vsdp
Sc =
Dab
(16)
where Re is the Reynolds number; Sc is the Schmidt number;
is the specific mass and is the viscosity of hexane.
In order solve the equations of the model the following
must be known: the initial state of the bed and the profile
Fig. 1 – Discretization of the fixed bed model.
conditions given by Eqs. (4)–(8), as well as the equilibrium
relationship between Cp and N.
The numerical solution is developed by dividing the bed
into a series of discrete elements, of length dz, as shown in
Fig. 1, employing the finite volumes method (Maliska, 1995).
The equations are spatially and temporarily integrated over
the various control volumes, applying the Central Differences
Scheme (CDS) as an interpolation function, obtaining one
equation for each elemental volume. The set of resulting alge-
braic equations is solved by the Jacobi Method (Maliska, 1995).
It is assumed that the variables are uniform within each ele-
ment.
4. Results and discussion
4.1. Analysis and comparison with the experimental
data
The numerical solution for the solvent extraction process in a
packed fixed-bed was obtained under the experimental oper-
ation conditions shown in Table 1, and the parameters of the
model, using a computational algorithm written in the FOR-
TRAN language.
The equilibrium relationship between the solid and
fluid phases of the particles was obtained experimentally,
as described previously. The value of the ∂N/∂Cp ratio is
0.5071 (R2 = 0.9978) and this value is used in Eq. (3), giving
(1 − εp)∂N/∂Cp = 0.35.
The results obtained numerically and the experimental
data for the mass of oil extracted in the fluid phase are shown
in Fig. 2. The experimental data were analyzed three times and
the discrepancy between the three values was less than 12%.
It can be seen that the numerical results obtained with the
application of the previously described mathematical model
are able to predict the behavior of the experimental extrac-
tion with good agreement. The values for the peak mass of
extracted oil in the fluid phase obtained experimentally and
numerically were 0.21 g and 0.23 g, respectively, for the same
extraction time.
Table 1 – Operational data and numerical parameters
required for the simulation.
L = 6.3 cm Q = 10 mL/min
D = 1.6 cm Ci = 0%
dp = 0.357 cm Cpi = 24.33%
ap = 11.20 cm−1a
= 0.6759 g/mL
εb = 0.43 = 0.0071 g/cm s
εp = 0.3 Dab = 1.3 × 10−5
cm2
/sb
a
ap = 4/dp.
b
Krioukov and Iskhakova (2001).
202 food and bioproducts processing 9 0 ( 2 0 1 2 ) 199–204
Fig. 2 – Mass of oil extracted in the fluid phase at each time
interval.
It can also be noted that the greatest discrepancy between
the measured and the simulated values is found at the end of
the extraction, where the curve obtained by the model exhibits
a comparatively greater slope than that of the experimental
extraction.
As reported in the literature (Majumdar et al., 1995), it
should be noted that the highest experimental extraction yield
was achieved at the start of the process when the pure solvent
extracts the free oil originating from the cells ruptured during
the pre-treatment of the raw material, in this case in the form
of layers. At the end of the process, the extraction is more diffi-
cult probably due to the diffusion through the pores, which can
cause a decrease in solubility of the last oil fractions extracted
(Majumdar et al., 1995), as suggested by the last two points in
the figure. After the last sampling, the extracted oil mass is
basically insignificant, indicating the end of the extraction.
Fig. 3 presents the simulated profile and the experimental
data related to the mass accumulated at the end of the extrac-
tion. Once again a high level of agreement was found between
the two situations presented, where in the numerical extrac-
tion 0.78 g of mass was accumulated in 410 s, the time at which
the operation was terminated, and in the experimental extrac-
tion the mass accumulated was 0.98 g. Thus, on comparing the
total oil mass in the fluid phase obtained numerically with
the experimental data, a maximum error of 20% is obtained,
the greatest discrepancy occurring at the end of the extrac-
Fig. 3 – Accumulated oil mass at the end of the extraction
in the fluid phase.
Fig. 4 – Extraction of oil in both phases at the column outlet.
tion. The discrepancy observed between the experimental and
numerical values can be attributed to the fact that the exper-
imental curve represents the sum of the experimental errors
obtained at each point of the analysis. The amount of residual
oil in the soybean layers obtained at the end of the extraction
process was 0.31 g.
The differences between the numerical curve and the
experimental results, observed in Figs. 2 and 3, may be related
to the hypotheses assumed in the simplification of the math-
ematical model proposed herein. The constant and uniform
characteristics of the bed and of the particles adopted in the
equations of the model may have a greater influence at the end
of the extraction process in relation to the real experimental
condition.
The differences obtained between the numerical results
and those found in the experiments indicate that it is neces-
sary further investigation for explanation the limitation of this
model. In practice the overall effect on oil recovery is limited
to a very small proportion of the total quantity of oil extracted,
permitting to use this model to predict the overall yield of oil
recovered.
Fig. 4 shows the profiles for the mass fractions in the
solid and fluid phases at the column outlet obtained from the
numerical solution of the equations of the model. The pre-
dicted profile for the solid phase begins with the maximum
value and falls rapidly, the peak mass transfer for the fluid
phase being obtained in the first 300 s of the extraction. The
liquid phase, from an initial oil quantity of nil, reaches a peak
value 30 s after the start of the extraction and soon falls rapidly.
This behavior results from the presence of a gradient between
the mass fractions C and Cp which is initially large due to
the low value of C and then decreases over time. After 300 s
of extraction the quantity of oil extracted is considered to be
insignificant.
Through the analysis of the behavior of the extraction pro-
cess at three different positions on the column, shown in Fig.
5, it can be concluded that at positions L/3, 2L/3 and at the
end of the column (L) the profiles of the mass fractions reach
a peak, before falling rapidly over time. Thus, at position L/3,
the peak is identified at 10 s, with a mass fraction of 0.03; for
2L/3 at 20 s with a mass fraction of 0.052; and for L at 30 s with a
mass fraction of 0.067. This behavior was to be expected since
the hexane, on leaving the column, had run the whole length
of the column, extracting a greater quantity of oil.
food and bioproducts processing 9 0 ( 2 0 1 2 ) 199–204 203
Fig. 5 – Profile for the mass fraction of oil at three positions
on the column.
Fig. 6 – Profiles for the mass fraction in both phases for
different hexane flow rates.
5. Parametric sensitivity analysis
The parametric sensitivity analysis was carried out in terms
of the effect of the variation in the feed rate over the profile of
the mass fraction. To investigate the influence of the flow rate
of hexane on the extraction process, the operational flow was
altered by +50% and −50%.
Fig. 6 illustrates the profiles for the mass fraction of oil
at the column outlet, for different feed rates. The passage
of the solvent over the column is slower with lower flow
rates, increasing the time spent in the column and decreas-
ing the extraction time. Similarly, for greater flow rates, the
total extraction time is greater because of the shorter time
spent in the column. It is worth noting that the peaks of the
greatest mass fraction of oil at the outlet are obtained with
the shortest extraction time when the inlet flow of solvent is
lowest.
6. Conclusions
Through a comparison between the results obtained for
the experimental and the simulated extractions, it can be
concluded that the model described predicts, with good agree-
ment, the behavior of the extraction process. Under the
conditions studied, the values obtained numerically for the
total oil mass extracted in the fluid phase presented a maxi-
mum error of 20%, when compared to the experimental data.
The greatest discrepancy occurs at the end of the extraction.
This maximum error can be considered as small and the dis-
crepancies between the numerical and experimental results
may be related to the hypothesis assumed in the application
of a simple numerical model.
Through the parametric sensitivity analysis, it was found
that a variation in the inlet flow rate of the solvent influenced
the total extraction time due to a change in the time spent by
the solvent on the column.
Acknowledgements
This study was carried out with the financial support of Con-
selho Nacional de Desenvolvimento Científico e Tecnológico,
CNPq/MCT – Brazil. The authors are grateful to LABMASSA –
Laboratory of Mass Transfer, for financial support and to the
Research Group – Numerical Simulation of Chemical Systems,
for technical support.
References
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extraction of oilseeds. J. Am. Oil Chem. Soc. 65, 129–135.
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(Modelagem Matemática nos Trechos Horizontais do Extrator
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Steady-state Regimes of the Extractor “Crown-Model”
(Pesquisa Numérica dos Regimes Estacionários do Extrator
“Crown-Model”). XXII CILAMCE, Campinas-SP, Brazil.
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solvent extraction of vegetable oil in a packed bed. J. Am. Oil
Chem. Soc. 72, 971–979.
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Mechanics. LTC - S. A., Brazil.
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Food Bioprod. Process. 86, 87–95.
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Perry, R.H., 1996. Chemical Engineer Manual (Manual del
Ingeniero Químico). McGraw-Hill, México.
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Rio Grande do Sul (Unijuí), Brazil.
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Dissertation, Universidade Regional do Noroeste do Estado do
Rio Grande do Sul (Unijuí), Brazil.
Myriam Lorena Melgarejo Navarro
Cerutti Graduate in Chemical Engineer-
ing – National Universidad of Asunción –
UNA (1999); Master’s degree in Chemical
Engineering – Federal University of Santa
Catarina – UFSC (2002); and Doctorate in
Chemical Engineering – Federal Univer-
sity of Santa Catarina – UFSC (2007). She
has experience in the area of Chemical
Engineering, with emphasis on Auto-
motive Fuels, Mass Transfer, Transport
Phenomena, Industrial Operations, Extraction, Adsorption,
Modeling and Simulation.
Antônio Augusto Ulson de Souza Grad-
uate in Chemical Engineering, UFRJ,
1982; Master’s degree in Chemical Engi-
neering, UNICAMP, 1985; Doctorate in
Mechanical Engineering, UFSC, 1992; and
Post-doctorate in Chemical Engineering,
UCDavis-USA, 1997. He is a Professor at
the Chemical Engineering Department at
UFSC and has published 52 papers in
international journals and 319 papers in
congress proceedings. He has supervised
36 Master’s degree and 17 Doctorate students. He acts as a
reviewer for 12 international journals and carries out research
in the area of Food, Textiles, Petroleum, Environment, Natu-
ral Products, Biodegradation, Adsorption, Dyeing, Enzymatic
Processes, and Water Reutilization.
Selene Maria de Arruda Guelli Ulson de
Souza Graduate in Chemical Engineer-
ing, UNICAMP, 1982; Master’s degree in
Chemical Engineering, UNICAMP, 1985;
Doctorate in Mechanical Engineering,
UFSC, 1992; and Post-doctorate in Chem-
ical Engineering, UCDavis-USA, 1997. She
is Professor and Chairman of the Chemi-
cal Engineering Department at UFSC and
has published 53 papers in international
journals and 329 papers in congress pro-
ceedings. She has supervised 36 Master’s degree and 18
Doctorate students. She acts as a reviewer of 25 international
journals and carries out research in the areas of Food, Natu-
ral Products, Bioprocesses, Textiles, Petroleum, Environment,
Adsorption, and Water Reuse.

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Artigo 2

  • 1. food and bioproducts processing 9 0 ( 2 0 1 2 ) 199–204 Contents lists available at ScienceDirect Food and Bioproducts Processing journal homepage: www.elsevier.com/locate/fbp Solvent extraction of vegetable oils: Numerical and experimental study Myriam Lorena Melgarejo Navarro Cerutti, Antonio Augusto Ulson de Souza, Selene Maria de Arruda Guelli Ulson de Souza∗ Federal University of Santa Catarina, Chemical Engineering Department, Laboratory of Mass Transfer, PO Box 476, 88040-900 Florianópolis, SC, Brazil a b s t r a c t A process for the extraction of vegetable oils from soybean seeds with a solvent was developed experimentally. The extraction was carried out in a continuous, fixed-bed extractor. A non-dimensional transient model was applied to simulate the mass transfer process which occurs during the extraction in a packed bed column. The governing dimensionless differential equations were numerically solved using the method of finite volumes. The numerical results were compared with data obtained from the experimental extraction, presenting good agreement. The val- ues obtained numerically for the total oil mass extracted in the fluid phase presented a maximum error of 20%, when compared to the experimental data. The greatest discrepancy was observed at the end of the extraction. This maximum error can be considered small due to the use of a simple numerical model. © 2011 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Extraction; Vegetable oils; Modeling; Simulation; Mass transfer 1. Introduction The processing and commercialization of vegetable oils from soybean, rice, cotton, and sunflower seeds represent important economic activities in Brazil and worldwide. Veg- etable oils, besides being an important and widely exploited source of lipids, vitamins, waxes, pigments and lecithins, are among the most promising sources of hydrocarbons for energy and chemical needs, with a view to replac- ing petroleum which is non-renewable and highly polluting (Amarasinghe and Gangodavilage, 2004; Amarasinghe et al., 2009). Vegetable oil is generally extracted by employing the hex- ane fraction of petroleum as the solvent in a continuous process in which the stages for the removal of residual sol- vent from the solid and the extracted oil are onerous and not always efficient. Consequently, more appropriate pro- cesses have been sought. Prominent amongst the contenders is extraction with carbon dioxide under supercritical con- ditions, which in recent decades has generated important experimental information. However, when compared to the conventional process, this presents numerous problems that ∗ Corresponding author. Tel.: +55 48 3721 9448x207; fax: +55 48 3721 9687. E-mail address: selene@enq.ufsc.br (S.M.d.A.G.U. de Souza). Received 10 June 2010; Received in revised form 27 January 2011; Accepted 16 March 2011 hinder its implantation due to the high cost involved (Rezende and Filho, 2000; Rosenthal et al., 1998). The literature contains a variety of studies on the subject of extractors (Karnofsky, 1986, 1987) and on the modeling of extraction (Abraham et al., 1988; Martinho et al., 2008; Thomas et al., 2007) based on the overall mass balance and experimen- tal data. The mathematical model proposed by Majumdar et al. (1995), for the fixed-bed extractor, provided important results which contributed to later studies with specific extractors, such as the De Smet, Rotocell and Crown-Model, conducted by Veloso (1999), Thomas (1999) and Benetti (2001), respectively. The mass transfer that occurs during solvent extraction in a packed column was analyzed in this study using the mathematical model proposed by Majumdar et al. (1995). The following phenomena were considered: - transient regime in the process; - transfer of oil from the pore phase to the fluid phase by concentration difference; - transfer of oil by diffusion, in the opposite direction to the flow of the micelle; - passage of oil between the phases, solid and pores; 0960-3085/$ – see front matter © 2011 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.fbp.2011.03.002
  • 2. 200 food and bioproducts processing 9 0 ( 2 0 1 2 ) 199–204 Nomenclature ap interface area of the particle, cm−1 C mass fraction of oil in the fluid phase, dimen- sionless Cp mass fraction of oil in the solid phase, dimen- sionless dp diameter of the particle, cm D diameter of the column, cm Dab diffusion coefficient, cm2/s kf coefficient of mass transfer, cm/s L length of the column, cm N mass fraction of oil in the solid phase of the particle, dimensionless Pe Peclet number, dimensionless Q Hexane flow rates, mL/min Re Reynolds number, dimensionless Sc Schmidt number, dimensionless Sh Sherwood number, dimensionless t extraction time, s Vs interstitial velocity of the fluid phase, cm/min Z vertical co-ordinate of the bed, cm εb porosity of the bed, dimensionless εp porosity of the particle, dimensionless density of hexane, g/mL viscosity of hexane, g/cm s and the following hypotheses: - oil as a single component; - solid with macro-pores filled with oil (stationary phase); - absence of radial concentration gradients in the fluid phase; - constant and uniform porosity of the particle and of the bed; - constant and uniform temperature (27 ◦C); - nil heat generation; - constant viscosity and density of the micelle. With the objective of studying the mass transfer that occurs during the process of oil extraction from layers of soybean, in a fixed-bed column, experimental data are obtained and used in the development of a mathematical model. 2. Experimental methodology In order to determine the efficiency of the extraction process on a fixed bed, extraction runs were carried out with layers of soybean seed and an equilibrium constant obtained for the fluid and solid phases at LABMASSA – Mass Transfer Labo- ratory of the Department of Chemical Engineering and Food Engineering, UFSC. Extraction: The experiments were carried out in a cylindri- cal column made of borosilicate in the laboratory, with 15 cm length and 1.6 cm diameter, containing a glass screen with holes to secure the bed. The upper end of the column has a wide opening to allow the bed loading and the lower end is fun- neled to carry out the sampling. The column was filled with layers of soybeans 0.357 cm in diameter, 0.035 cm in thickness and with a 24.33% fat content (determined by the method of Soxhlet), previously packed, provided by Ceval Alimentos S/A (SC). The quantity of 5.3 g of soybean layers was manually loaded with a funnel up to 6.3 cm of the total length of the column, aiming at obtaining a constant packing for each run. The solvent hexane (analytical quality) was introduced into the column via a peristaltic pump (Gilson, Miniplus 3 model) at a constant flow of 10 mL/min. After totally filling the column the micelle was collected at the outlet at time intervals of 30 s (after the first micelle collection at 15 s). The micelle samples were collected in glass tubes of known dry weight, before being evaporated in a heater (Fisatom), with the accumulated mass being calculated by the difference in mass on an analytical balance (Mettler Toledo, model AB204-S, precision 10−4 g). The volume of empty space contained in the column (εb), or the packing degree of the bed, was measured by the solvent volume required to fill the packed bed divided by the total volume of the empty column. All experimental runs were performed three times. The diameter of the layers of soybean was determined by granulo- metric analysis (Perry, 1996), using sieves of the ASTM series, available at LABMASSA/UFSC. Equilibrium constant: The equilibrium relationship between the residual oil content in the solid sample and the quantity of oil in the micelle trapped in its pores was determined by the tangent to the curve obtained from the collected mass fractions (wet basis) for both phases. Each point on the curve, which was obtained in a glass Erlenmeyer, belonged to a mass variable in a constant volume of 50 mL, measured after 10 h of shaking in a bath (Nova Ética, model 304) at 27 ◦C. The filter- carrier device for polycarbonate syringes (Sartorius, model 16514/17E) was used for sampling and the total residual mass of oil in the solid was further obtained from the difference between the initial mass and the mass after evaporation using glass sampling tubes (Navarro, 2002). All analyses were carried out according to the AOAC (1997). 3. Numerical formulation Taking into account the phenomena involved and the hypotheses cited above, a model was developed in order to simulate the performance of a fixed-bed extractor. This model is based on the study presented by Majumdar et al. (1995), which uses the equations of conservation of mass and of chemical species (oil – in the fluid and solid phases). 3.1. Governing equations (a) Equation of conservation of mass – fluid phase ∂Vs ∂Z = 1 − εb εb kf ap(Cp − C) (1) where Vs is the interstitial velocity of the fluid phase; C is the mass fraction of oil in the fluid phase; Cp is the mass fraction of oil in the solid phase; Z is the vertical co-ordinate of the bed; εb is the porosity of the bed; kf is the coefficient of mass transfer; ap is the interface area of the particle. (b) Equation of conservation of chemical species, oil – fluid phase ∂C ∂t + ∂(VsC) ∂Z = Dab ∂2C ∂Z2 + 1 − εb εb apkf (Cp − C) (2) where Dab is the diffusion coefficient.
  • 3. food and bioproducts processing 9 0 ( 2 0 1 2 ) 199–204 201 (c) Equation of conservation of chemical species, oil – solid phase ∂Cp ∂t εp + (1 − εp) ∂N ∂Cp = −apkf (Cp − C) (3) where εp is the porosity of the particle; t is the extraction time; N is the mass fraction of oil in the solid phase of the particle. 3.2. Initial and boundary conditions Vs(0, t) = Vsi 0 ≤ t ≤ tf (4) C(z, 0) = Ci 0 ≤ z ≤ L (5) Cp(z, 0) = Cpi 0 ≤ z ≤ L (6) ∂C ∂Z (L, t) = 0 0 ≤ t ≤ tf (7) VsC Vsi − Dab Vsi ∂C ∂Z (0, t) = Ci 0 ≤ t ≤ tf (8) In Eqs. (1)–(3), the following apply: V s = Vs Vsi t = Vsit L Z = Z L (9) Sh = kf dp Dab Pei = Vsidp Dab (10) where L is the length of the column; dp is the diameter of the particle; Sh is the Sherwood number; Pe is the Peclet number. The dimensionless equations become: ∂V s ∂Z = 1 − εb εb (apL) Sh Pei (Cp − C) (11) ∂C ∂t + ∂(VsC) ∂Z = 1 Pei dp L ∂2C ∂Z 2 + 1 − εb εb (apL) Sh Pei (Cp − C) (12) ∂Cp ∂t 1 + 1 − εp εp ∂N ∂Cp + 1 εb Sh Pei (apL)(Cp − C) = 0 (13) where the lower index “i” refers to the initial state and the upper index ( ) to the dimensionless parameters. To determine the coefficient of mass transfer, kf, the Sher- wood number is used according to the correlations proposed by Treybal (1981), Sh = 2.4Re0.34 Sc0.42 0.08 < Re < 0.125 (14) Sh = 0.442Re0.69 Sc0.42 0.125 < Re < 5000 (15) The Reynolds number (Re) and the Schmidt number (Sc) are defined in the following way: Re = Vsdp Sc = Dab (16) where Re is the Reynolds number; Sc is the Schmidt number; is the specific mass and is the viscosity of hexane. In order solve the equations of the model the following must be known: the initial state of the bed and the profile Fig. 1 – Discretization of the fixed bed model. conditions given by Eqs. (4)–(8), as well as the equilibrium relationship between Cp and N. The numerical solution is developed by dividing the bed into a series of discrete elements, of length dz, as shown in Fig. 1, employing the finite volumes method (Maliska, 1995). The equations are spatially and temporarily integrated over the various control volumes, applying the Central Differences Scheme (CDS) as an interpolation function, obtaining one equation for each elemental volume. The set of resulting alge- braic equations is solved by the Jacobi Method (Maliska, 1995). It is assumed that the variables are uniform within each ele- ment. 4. Results and discussion 4.1. Analysis and comparison with the experimental data The numerical solution for the solvent extraction process in a packed fixed-bed was obtained under the experimental oper- ation conditions shown in Table 1, and the parameters of the model, using a computational algorithm written in the FOR- TRAN language. The equilibrium relationship between the solid and fluid phases of the particles was obtained experimentally, as described previously. The value of the ∂N/∂Cp ratio is 0.5071 (R2 = 0.9978) and this value is used in Eq. (3), giving (1 − εp)∂N/∂Cp = 0.35. The results obtained numerically and the experimental data for the mass of oil extracted in the fluid phase are shown in Fig. 2. The experimental data were analyzed three times and the discrepancy between the three values was less than 12%. It can be seen that the numerical results obtained with the application of the previously described mathematical model are able to predict the behavior of the experimental extrac- tion with good agreement. The values for the peak mass of extracted oil in the fluid phase obtained experimentally and numerically were 0.21 g and 0.23 g, respectively, for the same extraction time. Table 1 – Operational data and numerical parameters required for the simulation. L = 6.3 cm Q = 10 mL/min D = 1.6 cm Ci = 0% dp = 0.357 cm Cpi = 24.33% ap = 11.20 cm−1a = 0.6759 g/mL εb = 0.43 = 0.0071 g/cm s εp = 0.3 Dab = 1.3 × 10−5 cm2 /sb a ap = 4/dp. b Krioukov and Iskhakova (2001).
  • 4. 202 food and bioproducts processing 9 0 ( 2 0 1 2 ) 199–204 Fig. 2 – Mass of oil extracted in the fluid phase at each time interval. It can also be noted that the greatest discrepancy between the measured and the simulated values is found at the end of the extraction, where the curve obtained by the model exhibits a comparatively greater slope than that of the experimental extraction. As reported in the literature (Majumdar et al., 1995), it should be noted that the highest experimental extraction yield was achieved at the start of the process when the pure solvent extracts the free oil originating from the cells ruptured during the pre-treatment of the raw material, in this case in the form of layers. At the end of the process, the extraction is more diffi- cult probably due to the diffusion through the pores, which can cause a decrease in solubility of the last oil fractions extracted (Majumdar et al., 1995), as suggested by the last two points in the figure. After the last sampling, the extracted oil mass is basically insignificant, indicating the end of the extraction. Fig. 3 presents the simulated profile and the experimental data related to the mass accumulated at the end of the extrac- tion. Once again a high level of agreement was found between the two situations presented, where in the numerical extrac- tion 0.78 g of mass was accumulated in 410 s, the time at which the operation was terminated, and in the experimental extrac- tion the mass accumulated was 0.98 g. Thus, on comparing the total oil mass in the fluid phase obtained numerically with the experimental data, a maximum error of 20% is obtained, the greatest discrepancy occurring at the end of the extrac- Fig. 3 – Accumulated oil mass at the end of the extraction in the fluid phase. Fig. 4 – Extraction of oil in both phases at the column outlet. tion. The discrepancy observed between the experimental and numerical values can be attributed to the fact that the exper- imental curve represents the sum of the experimental errors obtained at each point of the analysis. The amount of residual oil in the soybean layers obtained at the end of the extraction process was 0.31 g. The differences between the numerical curve and the experimental results, observed in Figs. 2 and 3, may be related to the hypotheses assumed in the simplification of the math- ematical model proposed herein. The constant and uniform characteristics of the bed and of the particles adopted in the equations of the model may have a greater influence at the end of the extraction process in relation to the real experimental condition. The differences obtained between the numerical results and those found in the experiments indicate that it is neces- sary further investigation for explanation the limitation of this model. In practice the overall effect on oil recovery is limited to a very small proportion of the total quantity of oil extracted, permitting to use this model to predict the overall yield of oil recovered. Fig. 4 shows the profiles for the mass fractions in the solid and fluid phases at the column outlet obtained from the numerical solution of the equations of the model. The pre- dicted profile for the solid phase begins with the maximum value and falls rapidly, the peak mass transfer for the fluid phase being obtained in the first 300 s of the extraction. The liquid phase, from an initial oil quantity of nil, reaches a peak value 30 s after the start of the extraction and soon falls rapidly. This behavior results from the presence of a gradient between the mass fractions C and Cp which is initially large due to the low value of C and then decreases over time. After 300 s of extraction the quantity of oil extracted is considered to be insignificant. Through the analysis of the behavior of the extraction pro- cess at three different positions on the column, shown in Fig. 5, it can be concluded that at positions L/3, 2L/3 and at the end of the column (L) the profiles of the mass fractions reach a peak, before falling rapidly over time. Thus, at position L/3, the peak is identified at 10 s, with a mass fraction of 0.03; for 2L/3 at 20 s with a mass fraction of 0.052; and for L at 30 s with a mass fraction of 0.067. This behavior was to be expected since the hexane, on leaving the column, had run the whole length of the column, extracting a greater quantity of oil.
  • 5. food and bioproducts processing 9 0 ( 2 0 1 2 ) 199–204 203 Fig. 5 – Profile for the mass fraction of oil at three positions on the column. Fig. 6 – Profiles for the mass fraction in both phases for different hexane flow rates. 5. Parametric sensitivity analysis The parametric sensitivity analysis was carried out in terms of the effect of the variation in the feed rate over the profile of the mass fraction. To investigate the influence of the flow rate of hexane on the extraction process, the operational flow was altered by +50% and −50%. Fig. 6 illustrates the profiles for the mass fraction of oil at the column outlet, for different feed rates. The passage of the solvent over the column is slower with lower flow rates, increasing the time spent in the column and decreas- ing the extraction time. Similarly, for greater flow rates, the total extraction time is greater because of the shorter time spent in the column. It is worth noting that the peaks of the greatest mass fraction of oil at the outlet are obtained with the shortest extraction time when the inlet flow of solvent is lowest. 6. Conclusions Through a comparison between the results obtained for the experimental and the simulated extractions, it can be concluded that the model described predicts, with good agree- ment, the behavior of the extraction process. Under the conditions studied, the values obtained numerically for the total oil mass extracted in the fluid phase presented a maxi- mum error of 20%, when compared to the experimental data. The greatest discrepancy occurs at the end of the extraction. This maximum error can be considered as small and the dis- crepancies between the numerical and experimental results may be related to the hypothesis assumed in the application of a simple numerical model. Through the parametric sensitivity analysis, it was found that a variation in the inlet flow rate of the solvent influenced the total extraction time due to a change in the time spent by the solvent on the column. Acknowledgements This study was carried out with the financial support of Con- selho Nacional de Desenvolvimento Científico e Tecnológico, CNPq/MCT – Brazil. The authors are grateful to LABMASSA – Laboratory of Mass Transfer, for financial support and to the Research Group – Numerical Simulation of Chemical Systems, for technical support. References Abraham, G., Hron, R.J., Koltun, S.P., 1988. Modeling the solvent extraction of oilseeds. J. Am. Oil Chem. Soc. 65, 129–135. Amarasinghe, B.M.W.P.K., Gangodavilage, N.C., 2004. Rice bran oil extraction in Sri Lanka: data for process equipment design. Food Bioprod. Process. 82, 54–59. Amarasinghe, B.M.W.P.K., Kumarasiri, M.P.M., Gangodavilage, N.C., 2009. Effect of method of stabilization on aqueous extraction of rice bran oil. Food Bioprod. Process. 87, 108–114. AOAC – Association of Official Analytical Chemists, 1997. Official Methods of Analysis of AOAC International. 16a. ed. 3a. rev. AOAC International, Gaithersburg, MD. Benetti, R.C., 2001. Mathematical modelling in Horizontal Passages of Crown-Models Extractor and the Identification (Modelagem Matemática nos Trechos Horizontais do Extrator Crown-Model e sua Identificac¸ão). Dissertation, Universidade Regional do Noroeste do Estado do Rio Grande do Sul (Unijuí), Brazil. Karnofsky, G., 1986. Design of oilseed extractors. I. Oil extraction. J. Am. Oil Chem. Soc. 63, 1011–1014. Karnofsky, G., 1987. Design of oilseed extractors. I. Oil extraction (supplement). J. Am. Oil Chem. Soc. 64, 1533–1536. Krioukov, V.G., Iskhakova, R.L., 2001. Numerical Research of the Steady-state Regimes of the Extractor “Crown-Model” (Pesquisa Numérica dos Regimes Estacionários do Extrator “Crown-Model”). XXII CILAMCE, Campinas-SP, Brazil. Majumdar, G.C., Samanta, A.N., Sengupta, S.P., 1995. Modeling solvent extraction of vegetable oil in a packed bed. J. Am. Oil Chem. Soc. 72, 971–979. Maliska, C.R., 1995. Computational Heat Transfer and Fluid Mechanics. LTC - S. A., Brazil. Martinho, A., Matos, H.A., Gani, H., Sarup, B., Youngreen, W., 2008. Modelling and simulation of vegetable oil processes. Food Bioprod. Process. 86, 87–95. Navarro, M.L.M., 2002. Study of the Mass Transfer in the Extraction Process using Solvent of Vegetable Oils in Fixed Bed Column. Dissertation, Universidade Federal de Santa Catarina (UFSC), Brazil. Perry, R.H., 1996. Chemical Engineer Manual (Manual del Ingeniero Químico). McGraw-Hill, México. Rezende, D.F., Filho, R.M., 2000. Proportional Classic control and for Dynamic Matrix for the Extraction of Grape Oil (Controle Clássico Proporcional e por Matriz Dinâmica para a Extrac¸ão de Óleo de Uva). COBEQ, Águas de São Pedro-SP, Brazil.
  • 6. 204 food and bioproducts processing 9 0 ( 2 0 1 2 ) 199–204 Rosenthal, A., Pyle, D.L., Niranjan, K., 1998. Simultaneous aqueous extraction of oil and protein from soybean: mechanisms for process design. Food Bioprod. Process. 76, 224–230. Thomas, G.C., 1999. Mathematical Model of the Oil Extraction in Installation of the Type “Rotocell” (Modelo Matemático da Extrac¸ão de Óleo em Instalac¸ão do Tipo “Rotocell”). Dissertation, Universidade Regional do Noroeste do Estado do Rio Grande do Sul (Unijuí), Brazil. Treybal, R.E., 1981. Mass-Transfer Operations. McGraw-Hill Kogakusha Ltd., Singapore. Thomas, G.C., Veloso, G.O., Krioukov, V.G., 2007. Mass transfer modelling in counter-current crossed flows in an industrial extractor. Food Bioprod. Process. 85, 77–84. Veloso, G.O., 1999. Mathematical Model of Vegetable Oil Extraction for Solvent in Industrial Extractor of the Type “De Smet” (Modelo Matemático de Extrac¸ão de Óleo Vegetal por Solvente em Extrator Industrial do Tipo “De Smet”). Dissertation, Universidade Regional do Noroeste do Estado do Rio Grande do Sul (Unijuí), Brazil. Myriam Lorena Melgarejo Navarro Cerutti Graduate in Chemical Engineer- ing – National Universidad of Asunción – UNA (1999); Master’s degree in Chemical Engineering – Federal University of Santa Catarina – UFSC (2002); and Doctorate in Chemical Engineering – Federal Univer- sity of Santa Catarina – UFSC (2007). She has experience in the area of Chemical Engineering, with emphasis on Auto- motive Fuels, Mass Transfer, Transport Phenomena, Industrial Operations, Extraction, Adsorption, Modeling and Simulation. Antônio Augusto Ulson de Souza Grad- uate in Chemical Engineering, UFRJ, 1982; Master’s degree in Chemical Engi- neering, UNICAMP, 1985; Doctorate in Mechanical Engineering, UFSC, 1992; and Post-doctorate in Chemical Engineering, UCDavis-USA, 1997. He is a Professor at the Chemical Engineering Department at UFSC and has published 52 papers in international journals and 319 papers in congress proceedings. He has supervised 36 Master’s degree and 17 Doctorate students. He acts as a reviewer for 12 international journals and carries out research in the area of Food, Textiles, Petroleum, Environment, Natu- ral Products, Biodegradation, Adsorption, Dyeing, Enzymatic Processes, and Water Reutilization. Selene Maria de Arruda Guelli Ulson de Souza Graduate in Chemical Engineer- ing, UNICAMP, 1982; Master’s degree in Chemical Engineering, UNICAMP, 1985; Doctorate in Mechanical Engineering, UFSC, 1992; and Post-doctorate in Chem- ical Engineering, UCDavis-USA, 1997. She is Professor and Chairman of the Chemi- cal Engineering Department at UFSC and has published 53 papers in international journals and 329 papers in congress pro- ceedings. She has supervised 36 Master’s degree and 18 Doctorate students. She acts as a reviewer of 25 international journals and carries out research in the areas of Food, Natu- ral Products, Bioprocesses, Textiles, Petroleum, Environment, Adsorption, and Water Reuse.