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