Mathematical Modeling of Supercritical Carbon Dioxide Extraction Kinetics of Bioactive Compounds from Mango Ginger (Curcuma amada Roxb)

Abstract

The main goal of this work was to study the extraction kinetics aspects of the Supercritical carbon dioxide(SC-CO 2) extraction by modeling the extraction curves. Extraction of mango ginger was performed at the different level of the pressure (100-350 bar) and temperature (40-60 º C) to evaluate the effect of process parameters on the extraction kinetics. The mass transfer models used to describe the extraction curves were simple exponential model and Ficks's diffusion model. Based on the experimental data, extraction rate constant and diffusion coefficients were estimated. Results showed good agreement between calculated and experimental data with higher values of coefficient of determination (R 2). The extraction rate and diffusivity increased with increase in pressure and decreased with increase in temperature. But at higher pressure and temperature the yield increased significantly due to vapor pressure effect.

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Sciknow Publications Ltd. OJOC 2014, 2(3):36-40
Open Journal of Organic Chemistry DOI: 10.12966/ojoc.07.01.2014
©Attribution 3.0 Unported (CC BY 3.0)
Mathematical Modeling of Supercritical Carbon Dioxide
Extraction Kinetics of Bioactive Compounds from Mango Ginger
(Curcuma amadaRoxb)
Thirupathihalli Pandurangappa Krishna Murthy1,* and Balaraman Manohar2
1Department of Biotechnology, Sapthagiri College of Engineering, Bangalore-560057, India
2Department of Food Engineering, CSIR-Central Food Technological Research Institute, Mysore- 570020. India
*Corresponding author (Email: crishna@live.in)
Abstract - The main goal of this work was to study the extraction kinetics aspects of the Supercritical carbon dioxide(SC-CO2)
extraction by modeling the extraction curves. Extraction of mango ginger was performed at the different level of the pressure
(100-350 bar) and temperature (40-60 ºC) to evaluate the effect of process parameters on the extraction kinetics. The mass
transfer models used to describe the extraction curves were simple exponential model and Ficks’s diffusion model. Based on the
experimental data, extraction rate constant and diffusion coefficients were estimated. Results showed good agreement between
calculated and experimental data with higher values of coefficient of determination (R2). The extraction rate and diffusivity
increased with increase in pressure and decreased with increase in temperature. But at higher pressure and temperature the yield
increased significantly due to vapor pressure effect.
Keywords - Supercritical Carbon Dioxide, Mango Ginger, Bioactive Components, Fick’s Diffusion Model, Exponential Model
1. Introduction
Curcuma amadaRoxb commonly known as mango ginger
belongs to the family Zingiberaceae. The plant is widely
cultivated in India apart from Malaysia, China, Bangladesh,
Myanmar, Thailand, Japan and Australia[1]. It is a unique
spice morphologically similar to ginger but, imparts mango
flavor and because of its exotic aroma they are extensively
used in the preparation of culinary items especially pickles,
sauces etc in Indian subcontinent. The essential oil and
nonvolatile components of rhizome exhibited antimicrobial,
antifungal and antihelmintic activity against tape worms.
Mango ginger is also an unconventional source of starch [2].
A pure component is considered to be in a supercritical
state if its temperature and pressure are higher than the critical
values [3]. In a supercritical state, liquid like densities are
approached, while viscosity is near that of normal gases and
diffusivity is about two orders of magnitude higher than in
typical liquid. Compared with the conventional solvent
extraction supercritical fluid extraction offers advantages due
to its relatively low environmental impact. [4]. The extraction
can be selective by controlling the density of the medium and
the extracted material is effortlessly recovered by simply
depressurizing, allowing the Supercritical fluid to return to the
gas phase and evaporatesleaving little or even no solvent
residue [5]. Carbon dioxide, nitrous oxide, ethane, propane,
n-pentane and water are widely used as supercritical fluids.
Carbon dioxide is commonly used in food and bioprocess
industries as it is inexpensive, nontoxic, nonflammable, easily
removed from extracts and has high interpenetration in solid
matrices [6-7].
The effectiveness of supercritical fluid extraction process
may affected by many variables such as pressure, temperature,
time, particle size, solvent flow rate, density etc.
[8].Mathematical modeling may be helpful for better
understanding the experimental results obtained and then
developing design scaling up procedures. These models are
based on mass transfer mechanisms and equilibrium
relationships. Some of the process parameters like solvent
flow rate, equipment dimensions, particle size etc. need to be
determined for process design by simulation of extraction
curves [9-10].
The objective of this investigation was to study the effect
of process parameters such as pressure, temperature on the
extraction rate and mass transfer during the supercritical
carbon di oxide extraction of bioactive compounds from
mango ginger.
2. Materials and Methods
2.1. Preparation of Plant Material
Fresh and matured mango ginger rhizomes were procured
from local market, Mysore, Karnataka, India. Toluene

Open Journal of Organic Chemistry (2014) 36-40 37
distillation method was used to estimate moisture content of
fresh rhizome and found to be 90±0.5 % (wet basis). The
rhizomes were washed and sliced using a slicing machine
(M/s Robot coupe, USA, Model: CL 50 Gourmet). The slices
were dried at 45±2 oC in Low temperature Low humidity
(LTLH) dryer. The dried material was powdered in hammer
mill (M/s Apex, USA) and the mean particle diameter was
480±40 µm as measured by Particle size analyzer (Model:
CIS-100, M/s Galai production, Israel). Food grade CO2
(99.99 % pure) was used as solvent for extraction supplied by
Ms.Kiran Corporation, Mysore, Karnataka, India.
2.2. Supercritical Carbon dioxide Extraction
For all the extraction experiments, high-pressure SCF
extractor(NOVA Swiss WERKE AG, EX 1000-1.4-1.2 type,
Switzerland) designed to working pressures of up to 1000 bar
and temperature up to 100°C was used. The mango ginger
powder was loaded into the extraction vessel which is of 1.1
lit in capacity. Set of experiments were conducted at different
pressures (100-350 bar) and temperatures (40-60 oC). After
attaining the desired temperature, the CO2 which had been
compressed to the set pressure was allowed into the extractor.
A fraction has been collected from the separator at definite
time intervals and the weight of the extract would be noted.
The average flow rate was maintained around 1.8-2.0 kg/hr.
2.3. Mathematical Modeling
2.3.1. Exponential function
The mathematical relationship between the yield and
extraction time gives better insight into the kinetics of the
process. Exponential function is the simple mathematical
function to describe the extraction kinetics. The amount of the
extracted yield at time from exponential model is given below
Eq.1
where Y is the extraction yield in weight percent, Yh is the
highest yield, and kEis extraction rate constant [11].
2.3.2. Diffusion Model
During the migration of solute from the solid matrix to the
bulk of the fluid there are several mass transfer steps involved
[12]. The Fick’s second law is widely used to describe the
mass transferis given below:
Eq. 2
Where C is the concentration of the solute, t is the
extraction time, De is the effective diffusivity, r is the radius of
diffusion. The extraction process parameters strongly affect
the effective diffusivity under which the extraction process is
carried out. The extraction from food materials is generally
controlled by internal diffusion [13]. Solutions of Fick’s
second law are therefore used to determine De assuming that
De is constant with the concentration. YD is defined as the
ratio between extract concentration at time, t and the initial
extract concentration of the matrix. The following boundary
conditions will be employed for solving above equation:
YD = 0, r ± R, t ≥ 0; YD = 1, 0 < r < R, t = 0.
The solution to eq. (1) is given by:
Eq. 3
For extraction from plant matrix where external resistance
is negligible, it is generally assumed that the first term of the
series solution can usually be used with little error [14].
Therefore, when the logarithm of YD is plotted against time, a
straight line must be obtained and the diffusivity can be
calculated from its slope.
Eq. 4
3. Results and Discussion
3.1. Effect of Pressure and temperature on extraction rate
Experimental yield values of supercritical carbon dioxide
extract of mango ginger were regressed against the time
according to the exponential equation (Eq.1) by nonlinear
least square method using the SOLVER tool based on the
Generalized Reduced Gradient (GRG) method of iteration
available in Microsoft Excel (Microsoft Office 2010, USA).
Coefficient of determination (R2) was used as a criterion to
check the fitness of experimental value with the model
predicted values. The kinetic rate constant kE values along
with the R2 values are presented in Table .1 and graphically
shown in Fig .1 (a), (b) and (c) shows the plot of extraction
yield vs extraction time at different extraction conditions. At
constant temperature, as pressure increases density of CO2
increases and at constant pressure as temperature increases
density of CO2 decrease. In the present investigation kE values
increased with increase in pressure at constant temperature
and decrease with increase in temperature at constant pressure.
Solubility of the mango ginger extract mainly effected by the
density of CO2. But higher pressure and higher temperature
there is sudden increase in yield due to the higher solute vapor
pressure at higher temperatureeven though density of CO2 is
less. Extraction rate also increase with increase in pressure in
the SCF extraction and decreases with increase in temperature
[15-16].

38 Open Journal of Organic Chemistry (2014) 36-40
0
0.4
0.8
1.2
1.6
0 3 6 9 12 15 18
Yield, %
Tme, hr
0
1
2
3
0 3 6 9 12 15 18
Yield, %
Time, hr
0
1
2
3
4
0 3 6 9 12 15 18
Yield, %
Time, hr
Fig. 1. Yield vs time at different temperature (▲-40oC■
-50oC●-60oC---- Model predicted) and Pressure(a) 100 bar
(b) 225 bar (c) 350 bar
0.055
0.105
0.155
0.205
0.055 0.105 0.155 0.205
Predicted k, s-1
Experimental k, s-1
Fig. 2. Regression Model predicted extraction rate constant vs
exponential model extraction rate constant values.
Table 1. Extraction rate constant (kE) at different temperature
and pressure
Exponential Model
Regression model
P
T
kE
R2
kE
Relative
error
100
40
0.1705
0.993
0.1699
0.31
100
50
0.1226
0.980
0.1325
8.11
100
60
0.0943
0.918
0.0848
9.99
225
40
0.1218
0.987
0.1116
8.35
225
50
0.1163
0.965
0.1188
2.20
225
60
0.1082
0.983
0.1158
7.02
350
40
0.0900
0.928
0.1007
11.8
350
50
0.1651
0.992
0.1526
7.58
350
60
0.1923
0.970
0.1942
0.94
*P-Pressure, T-Temperature, kE-extraction rate constant,
R2-Coefficient of Determination.
Table 2. Statistical analysis of the selected quadratic model
for extraction rate constant (kE)
Regression Statistics
Multiple R
0.969
R Square
0.939
Adjusted R
Square
0.838
Standard Error
0.0145
Observations
9
ANOVA
df
SS
MS
F
Significance F
Regression
5
0.0098
0.0020
9.297
0.048
Residual
3
0.0006
0.00022
Total
8
0.0104
Coefficients
Standard
Error
t Stat
P-value
A0
0.4401
0.2612
1.685
0.1905
A1
-0.0023
0.00041
-5.73
0.0105
A2
-0.0026
0.01035
-0.25
0.8130
A3
1.52E-6
6.6E-07
2.313
0.1036
A4
-5.16E-5
0.000102
-0.50
0.6498
A5
3.60E-5
5.8E-06
6.155
0.0086
To study the dependency of kE on Temperature (T) and
pressure (P), the values of kE values obtained from
exponential equation was regressed according to response
equation (Eq.5)
Eq. 5
The kE values fitted best to the model equation with R2
value of 0.969. The ANOVA for the selected model have
significance value. From the p-value, pressure is having
significant effect on the extraction rate and interaction
between the temperature and pressure is also significantly
effected the extraction process. The developed regression
model for dependent variable (kE) and independent variable
(Pressure and Temperature) is given in Eq. 6
Eq. 6
(a)
(b)
(c)
(d)

Open Journal of Organic Chemistry (2014) 36-40 39
The regression statistics and ANOVA is presented in
Table 2. The regression model predicted values along with the
relative error are shown in Table 1. In Fig 2, exponential
model predicted values were plotted against the regression
equation predicted values shows the good correlation between
values. The interaction effect of pressure and temperature on
the extraction rate constant was given in Fig.3.
3.2. Effect of Pressure and temperature on mass transfer
The diffusivity was calculate from the slope of ln(YD) vs t
(Eq.4). The average particle size of the mango ginger was 480
µm. The experimental data shows the linearity with high
coefficient of determination.
Fig. 3. Effect of Temperature and pressure on extraction rate
(s-1)
Table 3. Diffusivity values (De, m2/s) at different temperature
and pressure
Pressure
(bar)
Temperature
(oC)
Diffusivity, x10-12
(m2/sec)
100
40
0.799
100
50
0.717
100
60
0.546
225
40
2.550
225
50
1.650
225
60
0.669
350
40
1.690
350
50
3.560
350
60
18.50
The diffusivity values for the experimental conditions are
tabulated in Table 3. At the lower pressures the diffusivity is
low due to the less density of carbon dioxide. As the
temperature increases the diffusivity also decreased. But at
350 bar pressure trend has changed. Diffusivity is higher
athigher pressure. Also it has increased with increase in
temperature. Although the solubility of the carbon dioxide is
less at higher temperature, the vapor pressure played a
significant role here. The estimated diffusivity values were in
the range of 0.5 -19 x 10-12m2/sec.
4. Conclusion
The extraction kinetics of mango ginger extract in
supercritical carbon dioxide was explored experimentally at
different extraction conditions, and the results were checked
by using two models. The experimental data correlated well
with the model predicted values of the selected models. The
extraction rate constant obtained from the exponential model
shows there is significant effect of pressure and interaction
between temperature and pressure. Effective diffusivity
calculated using Fick’s law of diffusion increased with
increase in pressure. At higher temperature and pressure both
extraction rate and diffusivity values are very high. This
shows the vapor pressure effect dominates solvent density.
The values of mass transfer coefficients determined could
provide good information especially on design or sizing of
actual extractor and provides the information during industrial
operation to evaluate the extraction time required for given
yield at different pressure and temperature.
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