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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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