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Contemporary Engineering Sciences, Vol. 10, 2017, no. 11, 503 - 511
HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ces.2017.7334
Thermodynamic Modeling of Microalgae Oil
Extraction Using Supercritical Fluids
Ángel Darío González-Delgado
University of Cartagena
Chemical Engineering Department
Avenida del Consulado Calle 30 No. 48 – 152
Cartagena, Colombia
Yeimmy Yolima Peralta-Ruíz
Universidad del Atlantico
Programa de Ingeniería Agroindustrial
Km. 7 Vía a Puerto Colombia
Barranquilla, Colombia
Copyright © 2017 Ángel Darío González-Delgado and Yeimmy Yolima Peralta-Ruiz. This
article is distributed under the Creative Commons Attribution License, which permits unrestricted
use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this work, a thermodynamic model was developed in three stages in order to
predict the phase equilibrium between the oil extracted from Chlorella sp. and
supercritical CO2, as well as the most favorable conditions of pressure and
temperature to carry out the extraction. Temperatures above room temperature
and at a pressure above the critical pressure of the solvent leads to an increase in
the amount of oil present in the CO2. However, it is necessary to perform an
analysis of the molecular interactions that occur in this operation in order to
strengthen the method of predicting compositions in equilibrium.
Keywords: Oil Extraction, Supercritical Solvent, Thermodynamic Modeling
1. Introduction
In recent years, research on the biofuels production from renewable sources [1,2,3]
has increased considerably due to depletability and severe environmental stress
posed by fuel resources [4] and the importance of improvement general efficiency
504 Á. D. González-Delgado and Y. Y. Peralta-Ruiz
[5]. Third-generation biofuels are also called advanced biofuels because of raw
materials and the technological processes used for their production [6,7,8].
Microalgae only need a liquid medium, some nutrients and sunlight to stimulate
the growth of biomass [9], which makes feasible the use of land not suitable for
cultivation of human and animal food products for the assembly of these. Among
the different methods used for the oil extraction is found the supercritical fluids
(SFE) technology, which emerges as an alternative to the traditional use of large
quantities of toxic solvents, as well as the handling of short extraction times, high
selectivity, economic efficiency and profitability [10,11]. A fluid is called
supercritical when it is forced to remain at pressure and temperature conditions
above its critical conditions. Supercritical fluids extraction has been used in
several species of microalgae to obtain different substances, such as omega-3 fatty
acids[12], beta-carotene [13] and carotenoids [14]. In this paper, thermodynamic
concepts are applied in the oil extraction from Chlorella sp. for biodiesel
production by supercritical CO2. For this, a prediction of the phase equilibrium
was made in order to determine the most favorable operating conditions.
2. Materials and Methods
Phase equilibrium modeling
The complexity of the modeling increases due to the differences in size between
solvent and solute molecules, the molecular interactions and, the saturated and
unsaturated fatty acids and triglycerides mixture that make up the microalgae oil.
Therefore, the supercritical fluid-solid equilibrium modeling was separated into
three major stages.
First stage of modeling: Solvent selection
For solvent selection, it is necessary to take into account the composition of the
oil of microalgae. Table 1 shows that like other vegetable oils, this is a
combination of both polar and non-polar lipids in different concentrations.
Table 1. Composition of lipids obtained from the microalga Chlorella sp.[15]
Fatty acid Percentage in sample
14:0 9.0 ± 0.5
16:0 25.0 ± 1.5
16:1 2.0 ± 0.1
16:2 10.0 ± 0.8
16:3 9.0 ± 0.7
18:0 0.9 ± 0.2
18:1 5.0 ± 0.7
18:2 20.0 ± 1.2
18:3 19.0 ± 0.9
Thermodynamic modeling of microalgae oil extraction 505
From all fatty acids present in the specie Chlorella sp., it is necessary to extract
the non-polar ones, due to lead to the biodiesel production by transesterification,
therefore, a solvent of low polarity is needed.
Second stage of modeling: Calculation of the oil concentration in the phase
equilibrium equilibrium and selection of the Equation of State
To determine the oil concentration in the supercritical fluid at certain pressure and
temperature conditions, it is necessary to start from the phase equilibrium
condition, in which the chemical potential of a species i in the solid matrix must
be equal to the potential of the same species in the supercritical fluid (Equation 1);
however, when it is worked under supercritical conditions (far from ideal gas
behavior), the fugacity of the species in question should be taken into account
(Equation 2). The fugacity of the species i in the solid depends on the saturation
pressure and the molar volume (Equation 3), while the fugacity of the same
species in the supercritical fluid depends on the fugacity factor, pressure and
molar fraction (Equation 4), where μ represents the chemical potential, R is the
universal constant of the gases, T is the temperature, f is the fugacity, Ps is the
saturation pressure, υ is the molar volume of the substance, P is the system
pressure, x is the molar fraction and ф is the fugacity factor.
𝜇𝑖𝑠𝑜𝑙 = 𝜇𝑖
𝑓𝑠𝑐
(1)
𝑑𝜇𝑖 = 𝑅𝑇𝑙𝑛(𝑓𝑖)
(2)
𝑓𝑖𝑠𝑜𝑙 = 𝑃𝑖
𝑠 exp 𝜐𝑖
𝑠𝑜𝑙 (𝑃 − 𝑃𝑖𝑠)
𝑅𝑇
(3)
𝑓𝑖𝑓𝑠𝑐
= 𝜙𝑖𝑓𝑠𝑐
𝑥𝑖𝑓𝑠𝑐
𝑃
(4)
As can be seen in Equation 4, to find the molar fraction of species i, in the
supercritical fluid under phase equilibrium conditions, it is necessary to find the
fugacity factor at determined pressure and temperature conditions. This is
achieved using Equation 5, in which the fugacity factor is a function of the
compressibility factor Z, the volume and number of moles of species i and j at
temperature conditions.
𝑅𝑇𝑙𝑛 𝜙 𝑖 = − 𝜕𝑃
𝜕𝑁𝑖 𝑇,𝑉,[𝑁𝑗 (𝑖)]
−𝑅𝑇
𝑉 𝑑𝑉
𝑉
∞
− 𝑅𝑇𝑙𝑛𝑍
(5)
If the Helmholtz energy is obtained at specific temperature, pressure and
composition conditions, all the information necessary to calculate the phase
equilibrium can be obtained. This residual energy is a quantifiable measure of
departure from ideal behavior, and can be evaluated as the sum of an attractive
506 Á. D. González-Delgado and Y. Y. Peralta-Ruiz
and repulsive term. Equations 6 to 20 show in detail the thermodynamic model
used.
(𝐴𝑅/𝑅𝑇)𝑇,𝑉,𝑛 = (𝐴𝑅/𝑅𝑇)𝑎𝑡𝑡 + (𝐴𝑅/𝑅𝑇)𝑓𝑣
(6)
(𝐴𝑅/𝑅𝑇)𝑓𝑣 = 3 𝜆1𝜆2
𝜆3 𝑌 − 1 +
𝜆23
𝜆32 𝑌
2 − 𝑌 − 𝑙𝑛𝑌
+ 𝑛𝑙𝑛𝑌
(7)
𝜆𝑘 = 𝑛𝑗𝑑𝑗𝑘
𝑁𝐶
𝑖
(8)
𝑌 = 1 −𝜋𝜆3
6𝑉 −1
(9)
𝑑𝑐 = 0.08943𝑅𝑇𝐶
𝑃𝐶
1/3
(10)
𝑑 = 1.065655𝑑𝑐 1 − 0.12 exp −2𝑇𝐶
3𝑇
(11)
(𝐴𝑅/𝑅𝑇)𝑎𝑡𝑡 = − 𝑍
2 𝑛𝑖 𝑞𝑗𝑣𝑗
𝑖𝑁𝐺𝑗
𝑁𝐶𝑖 𝜃𝑘
𝑔𝑘𝑗 𝑞 𝜏𝑘𝑗
𝑅𝑇𝑉 𝑁𝐺𝑘
𝜃𝑖𝜏𝑙𝑗𝑁𝐺𝑙
(12)
𝜃𝑗 = 𝑞𝑗
𝑞 𝑛𝑖𝑣𝑗
𝑖
𝑁𝐶
𝑖
(13)
𝑞 = 𝑛𝑖
𝑁𝐶
𝑖
𝑞𝑗𝑣𝑗𝑖
𝑁𝐺
𝑗
(14)
𝜏𝑗𝑖 = exp 𝛼𝑗𝑖 ∆𝑔𝑗𝑖 𝑞
𝑅𝑇𝑉
(15)
Thermodynamic modeling of microalgae oil extraction 507
∆𝑔𝑗𝑖 = 𝑔𝑗𝑖 − 𝑔𝑖𝑖
(16)
𝑔𝑖𝑗 = 𝑘𝑖𝑗 𝑔𝑖𝑖𝑔𝑗𝑗 12 , ( 𝑘𝑖𝑗 = 𝑘𝑗𝑖 )
(17)
𝑔𝑗𝑗 = 𝑔𝑗𝑗∗ 1 + 𝑔𝑗𝑗
′ 𝑇
𝑇𝑗∗ − 1 + 𝑔𝑗𝑗
′′ 𝑙𝑛 𝑇
𝑇𝑗∗
(18)
𝑘𝑖𝑗 = 𝑘𝑖𝑗∗ 1 + 𝑘𝑖𝑗
′ ln 𝑇
𝑇𝑖𝑗∗
(19)
𝑇𝑖𝑗∗ = 0.5(𝑇𝑖
∗ + 𝑇𝑗∗)
(20)
Where n is the total number of moles, ni is the number of moles of component i,
NC is the number of components, NG is the number of functional groups, dj is the
hard sphere diameter per mole of species j, dc is diameter of hard sphere under
critical conditions, z is the coordinate number assumed to be equal to 10, qj is the
number of surface segments assigned to group j, q is the total number of surface
segments, vij is the number of groups type j in molecule i, Ѳj is the surface
fraction of group j, gjj is the attractive energy between equal segments, gij is the
attractive energy between different segments, kij is the binary interaction
parameter αij is the non-randomness parameter, V is the total volume of the
mixture, T is the temperature of the mixture, Tc is the critical temperature of the
pure component, Pc is the critical pressure of the pure component and Tj* is a
reference temperature for group j. Therefore, the GC-EOS relationship is given by
Equation 21, which was selected due to the molecular structure of the microalgae
oil can be characterized by a few functional groups, besides being a versatile
method for calculating the phase equilibrium of multicomponent systems
𝑙𝑛𝜙𝑖 = 1
𝑅𝑇
𝜕𝐴𝑅
𝜕𝑛
𝑇,𝑉,𝑛
− 𝑙𝑛𝑍
(21)
3. Results and Discussion
Parameters of thermodynamic model
Table 2 shows the number of functional groups CH2 and CH=CH present in the
microalgae oil based on composition showed. The molecular weights of the fatty
508 Á. D. González-Delgado and Y. Y. Peralta-Ruiz
acids were obtained from the literature and are the basis for the calculation of the
total number of moles present and the molar percentage. On the other hand, total
fatty acids are the sum of all contributions of the number of functional groups
present in each fatty acid multiplied by the molar fraction. Finally, the triglyceride
functional group (TG) was included [16] in order to refine the thermodynamic
modeling, and it was calculated as three times the total fatty acids.
Table 2. Group composition of microalgae oil
Fatty acid %
weight
Molecular
mass
%
molar
N° of
CH=CH
groups
N° of CH2
groups
14:0 9.0 228 10.25 0 12
16:0 25.0 256 25.37 0 14
16:1 2.0 254 2.05 1 12
16:2 10.0 252 10.31 2 10
16:3 9.0 250 9.35 3 8
18:0 0.9 284 0.82 0 16
18:1 5.0 282 4.61 1 14
18:2 21.0 280 19.48 2 12
18:3 19.0 278 17.76 3 10
Fatty acid 100.9 - 100.00 1.48 11.70
Triglycerides - - - 4.44 35.10
0
5
10
15
20
25
0.75 0.80 0.85 0.90 0.95 1.00
Pre
ssur
e, M
Pa
x, CO2
40 °C60 °C70 °C
Figure 1. Pressure-composition diagram for the supercritical CO2-microalgae oil
mixture at different temperatures
Thermodynamic modeling of microalgae oil extraction 509
The model calculations and the phase equilibrium curve as a function of pressure
values were performed using Excel. Figure 1 shows the results obtained at three
temperatures (40, 60 and 70 ºC), which will allow to have information regarding
the third part of the phase equilibrium modeling: the location and selection of the
most favorable conditions to carry out the supercritical extraction. It can be
noticed that increases in temperature lead to 1) an increase in the operating
pressure for a same molar fraction of CO2 in the mixture and, 2) an increase in the
amount of oil present in the supercritical CO2. Also, the higher temperature from
the ambient temperature, the second change is more pronounced.
4. Conclusions
A thermodynamic model was developed in order to predict the phase equilibrium
between the extracted oil of Chlorella sp. and supercritical CO2. Due to its
complexity because of the size differences between the solvent and solute
molecules, the molecular interactions and the saturated and unsaturated fatty acids
and triglycerides mixture that make up the microalgae oil, the modeling was
separated into three stages: In the first one the CO2 was selected as solvent due to
its polar affinity with the fatty acids that favor the biodiesel production, in the
second, the GC-EOS group contribution equation was chosen due to the ease it
provides for performing the phase equilibrium calculations in systems where there
is little information reported or difficult to find compared to using a cubic state
equation. Finally, in the third stage, the most favorable conditions of pressure and
temperature were analyzed by means of the equilibrium curve to carry out the
supercritical extraction, where it was found that increases in these conditions lead
to an increase in the amount of oil present in the solvent.
Acknowledgements. Authors thank to University of Cartagena and Universidad
del Atlántico for the supply of equipment and software necessary to conclude
successfully this work.
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Received: April 15, 2017; Published: June 6, 2017