CET 96

DOI: 10.3303/CET2296078

Paper Received: 27 June 2022; Revised: 06 September 2022; Accepted: 17 October 2022
Please cite this article as: Reddy T., Seodigeng T., Rutto H., 2022, Response Surface Analysis and Modeling of Sclerocarya Birrea kernel Oil
Yield in Supercritical Carbon Dioxide, Chemical Engineering Transactions, 96, 463-468 DOI:10.3303/CET2296078

CHEMICAL ENGINEERING TRANSACTIONS

VOL. 96, 2022

A publication of

The Italian Association

of Chemical Engineering
Online at www.cetjournal.it

Guest Editors: David Bogle, Flavio Manenti, Piero Salatino
Copyright © 2022, AIDIC Servizi S.r.l.

ISBN 978-88-95608-95-2; ISSN 2283-9216

Response Surface Analysis and Modeling of Sclerocarya
Birrea kernel Oil Yield in Supercritical Carbon Dioxide

Trishen Reddya, Tumisang Seodigengb,*, Hilary Ruttoa
aDepartment of Chemical and Metallurgical Engineering, Vaal University of Technology, Andries Potgieter Blvd,
Vanderbijlpark, Gauteng, 1900, South Africa
bCentre for Renewable Energy and Water, Vaal University of Technology, Andries Potgieter Blvd, Vanderbijlpark, Gauteng,
1900, South Africa

The response surface methodology (RSM) was used to evaluate the influence of two independent variables
namely extraction temperature and extraction pressure via literature data obtained from supercritical fluid
extraction (SFE) process of Sclerocarya birrea kernel oil. The optimal (custom) option was utilised on Design
Expert Version 13 to optimise the variables taken into consideration. The raw experimental data comprised of 9
experimental runs of which the temperature was varied between 40, 60 and 75 °C and the pressure was varied
between 250, 350 and 450 bar. The reaction time, particle size and carbon dioxide (CO2) flowrate was kept
constant at 30 kg CO2/hour for all experimental runs. Each extraction lasted for 270 minutes and each set of
extraction conditions was repeated in triplicate. The determination coefficient value (R2), adjusted R2 value, p-
values and F-values were considered in determining the effectiveness of the response surface methodology
model. The results from the analysis of variance indicated that the all model terms excluding the quadratic
temperature term are all highly significant with p values less than 0.01. The quadratic term of temperature has
no significant effect on Sclerocarya birrea kernel oil yield. The optimal conditions to obtain the maximum oil yield
from Sclerocarya birrea kernels were at a pressure of 450 bar and temperature of 60 °C. Under these optimal
conditions, the yield of Sclerocarya birrea kernel oil was predicted to be 9.22 g oil/L CO2. The experiment results
obtained from literature agreed with the predicted values as indicated by the R2 and adjusted R2 values which
were 0.98 and 0.97 respectively.

1. Introduction

Sclerocarya birrea is commonly known as marula (English); maroela (Afrikaans); morula (Tswana); and umGanu
(isiZulu). The plant is widely distributed in South Africa, Botswana, Congo, Eritrea, Ethiopia, Gambia, Kenya,
Malawi, Mozambique, Namibia, Niger, Senegal, Somalia, South Africa, Sudan, Swaziland, Tanzania, Uganda,
Zambia and Zimbabwe (Orwa et al., 2009). It is a popular plant species because it provides nutritional
sustenance to the population throughout the year (Mojeremane & Tshwenyane, 2004). For this reason, it is
often referred to as the “tree of life” (Welford, Abad & Gericke, 2008). Almost all of the major constituents of the
marula tree can be utilised (Orwa et al., 2009). The wood of the plant is utilised to produce fencing, erecting
housing, roofing and poles (Mojeremane & Tshwenyane, 2004). The bark of the tree is also utilised by the locals
to treat many ailments viz. fevers, diarrhea, boils, syphilis, leprosy, dysentery, hepatitis, rheumatism,
gonorrhoea, diabetes, dysentery and malaria (Mutshinyalo & Tshisevhe, 2003). The fruits of the plant are
consumed as is or can be processed to manufacture juices and a fermented alcohol beverage whilst the nut of
the marula tree has a diameter of 2-3 cm of which holds 3-4 kernels that are utilised to produce porridges
(Mojeremane & Tshwenyane, 2004). The kernels have a composition that is made up of 5.2 % moisture and
55.9 % oil (Zharare & Dhlamini, 2000). South African marula kernels are rich in fatty acids namely oleic, palmitic
and stearic acid (Mthiyane & Hugo, 2019). Oleic, palmitic, and stearic acid are fatty acids that the human body
naturally produces. (Vermaak et al., 2011). Oilseeds can be processed by mechanical means however the
process is time consuming and labour intensive (Jahirul et al.,2013). Solvent extraction is also utilised in oil
extraction as it is more effective than mechanical processing methods; but the process is hazardous and the
quality of the oil is compromised (Ajila et al., 2011).

463

For this reason, supercritical fluid extraction has gained popularity recently (Sovova & Stateva, 2011). It is also
a process that is environmentally friendly (Hashemi, Khaneghah & de Souza Sant'Ana, 2017). It is claimed to
be environmentally friendly because the most common solvent that is utilised in SFE is carbon dioxide which is
safe and non-flammable (Chemat, 2017). Carbon dioxide can also be reutilised in the process and hence, it is
a cost effective process (Lavenburg, Rosentrater & Jung, 2021). A maximum recovery of 55 % Sclerocarya
birrea kernel oil under supercritical fluid conditions at 450 bars and 60 °C has been reported (Taseki, 2015).

2. Materials and Methods

2.1. Computational methods: Response surface experimental design

In this study, RSM was utilised to optimise the operating conditions of supercritical carbon dioxide via literature
data obtained from (SFE) process of Sclerocarya birrea kernel oil. Taseski (2015), conducted supercritical fluid
extraction of Sclerocarya birrea kernel oil which comprised of 9 experimental runs for the determination of the
solubility of Sclerocarya birrea kernel oil in supercritical carbon dioxide. The extraction temperature was varied
between 40, 60 and 75 °C and the extraction pressure was varied between 250, 350 and 450 bar. The reaction
time remained constant at 270 minutes for all experimental runs whilst the particle size was kept constant at
850 μm. The carbon dioxide flowrate was maintained at 30 kg CO2/hour for all experimental runs. Each set of
extraction conditions was repeated in triplicate and the average oil yield at each extraction condition was then
utilised for optmisation purposes. The two independent variables were studied namely extraction temperature
(X1) and extraction pressure (X2). The independent variables were coded at three levels to ensure that there is
an equal and even distribution of the intervals and levels (Baş & Boyacı., 2007). The independent variables are
typically coded as it makes it easier to observe their influence on the response (Tirado-Kulieva et al., 2021). The
independent variables were therefore coded using equation 1 below (Nandiwale & Bokade, 2014). The coded
levels and intervals were therefore dispersed between 1-low, 0-medium and 1-high (Tharazi, Sulong & Mohd
Salleh, 2020).

𝑋𝑖 =

𝑥𝑖−𝑥𝑜

(
𝑥𝑚𝑎𝑥𝑖𝑚𝑢𝑚−𝑥𝑚𝑖𝑛𝑖𝑚𝑢𝑚

2
)
(1)

Where xi represents the actual value for temperature and pressure), xo represents the real variable value at
centre point, Xi denotes the variable that has been coded, xmaximum and xminimum are the maximum and minimum
values of the real independent variables. Using equation 1 resulted in the following coded levels as depicted in
table 1.

Table 1: Independent variables and their levels for RSM design.

Factor Description Unit of
measure

Type
-1

Low

Level
0

Medium

High
X1 Temperature °C Numerical 40 60 75
X2 Pressure Bar Numerical 250 350 450

The response surface methodology was conducted to study the effect of the operating parameters on the
solubility of Sclerocarya birrea kernel oil in supercritical carbon dioxide. The optimal (custom) design was utilised
on Design Expert Version 13 to develop a second order polynomial equation as shown in equation 2 was utilised
to express the oil yield (Y) of Sclerocarya birrea kernel oil.

𝑌 = 𝐵𝑂 + ∑ 𝐵𝑖 𝑥𝑖

𝑛
𝑖=1 + ∑ 𝐵𝑖𝑖 𝑥𝑖

2𝑛
𝑖=1 + ∑ ∑ 𝐵𝑥𝑖 𝑥𝑗

𝑛
𝑗=𝑖+1

𝑛
𝑖=1 (2)

Where, Y is the predicted response; B0 is a constant; Bi is the coefficient of the linear terms, Bii is the coefficient
of the quadratic terms, xi and xj is the independent variables.
The coefficients of the second order model was obtained via Design Expert version 13. The goodness of fit was
determined using the analysis of variance and the efficacy of the models was tested by calculating the R2 for
each model and also the average absolute relative deviation.

464

3. Results and Discussion

3.1. Model Fitting

Sclerocarya birrea kernel oil yield obtained from literature is presented in table 2. The experimental data was
utilised to determine the coefficients of the second order polynomial equation. For each of the responses under
investigation, a second-order polynomial equation was obtained using the multiple regression analysis and the
partial sum of squares. The Fisher's test was used to determine the model coefficients' significance. The Fisher
test considers the residual error and the F-value, which is a portion of the average square of the model (Rassem
et al., 2019). As a function of the independent variables in terms of coded components, the second-order
polynomial equation was used to express the solubility of Sclerocarya birrea kernel oil in supercritical carbon
dioxide and is provided in equation 3.

𝑌 (

𝑔 𝑜𝑖𝑙

𝐿 𝐶𝑂2
) = 8.05 − 0.6058𝑋1 + 2.58𝑋2 + 1.15𝑋1𝑋2 − 0.0704𝑋1

2 − 1.66𝑋2
2 (3)

Equation 3 can also be expressed in terms of uncoded factors and is given in equation 4.

𝑌 (

𝑔 𝑜𝑖𝑙

𝐿 𝐶𝑂2
) = −6.89065 − 0.238031𝑥1 + 0.104401𝑥2 + 0.000657𝑥1𝑥2 − 0.000230𝑥1

2 − 0.000166𝑥2
2 (4)

3.2. Response surface analysis

The overall F value of 208.6 indicates that the model is significant. The linear model terms of temperature and
pressure, as well as the interaction model term and quadratic pressure term all have p-values that are less 0.01;
which is an indication that these model terms are very significant. The quadratic term of temperature however
had no significant effect on Sclerocarya birrea kernel oil yield as indicated by the p value of 0.6753. Figures. 1a
and figure 1b show how the independent factors and oil yield relate to one another as shown in figure 1a and
figure 1b depicting the response surface curve and its contour plot. From figure 1a and figure 1b, it can be seen
that the extraction pressure showed a quadratic effect on the response. The higher solvent-solute interaction is
a result of the high concentrations of CO2 at the elevated pressure levels which can be attributed to the high
negative yet substantial quadratic pressure term (Bala et al., 2016). Similar patterns were seen in the extraction
of mango seed kernel oil using SFE, according to Cerón-Martnez et al. (2021). The quadratic pressure term was
observed by the authors to be both negative and extremely significant. According to Nandiwale and Bokade
(2014), positive values for the linear variables show that the yield increases immediately as the positive variable
rises. The fact that the coefficient of pressure is greater than both the coefficient of temperature and the
interaction term suggests that pressure controls how much oil is produced. The similar patterns were seen by
Peng, Setapar, and Nasir (2020) when they optimized the supercritical CO2 extraction of roselle oil using RSM.
From figure 1b, it can be seen that the yield for the concentration can be optimised, as there is a continual linear
increase on oil yield pertaining to the lower extraction pressure range corresponding to a decrease in extraction
temperature. It can also be observed that as the extraction pressure increases, the yield also increases with an
increasing temperature. The yield however reaches a maximum with an increase in pressure and thereafter
decreases in a parabolic manner. The maximum/minimum oil yield can therefore be located using a partial
derivative of equation 4 with respect to pressure.

𝜕𝑌
𝜕𝑋2

= 0.10440057568066 + 0.00065669012459622𝑥1 − 0.000332582𝑥2 = 0 (5)

The plot of the optimised concentration is depicted in figure 2a. The variance inflation factors for each model
term are all relatively close to 1, which shows that the components are orthogonal. The robust agreement
between the projected R2 value and the adjusted R2 value demonstrates the model's appropriateness. The parity
plot as shown in figure 2b demonstrates that the predicted values and experimental values are on par. The oil
yield is dependent on both temperature and pressure, according to the response surface plot, but pressure has
a far greater impact than temperature. This is demonstrated by the unimportant temperature quadratic model
term, which had a p-value of 0.6753. The results are in line with Rassem et al. (2019) in which the authors
emphasize that pressure was the most significant factor influencing the output of essential oil from jasmine
flowers. The authors go on to explain that pressure can interact with temperature indefinitely because of its
polarity. The response surface plot shows that the maximum oil yield was attained at 60 °C for the midpoint
temperature and 450 bar for the maximum pressure. As a result, pressure has a significant impact on the oil
yield, and the two variables are directly related. dos Santos Garcia, da Silva, and Cardozo Filho (2013) also
noted that the corresponding temperature and pressure that produced the best oil yield were 40 °C and 60 °C,

465

respectively. According to Louaer et al. (2018), operating at lower pressures and at an elevated temperature
simultaneously reduced the solvent power, which in turn decreased the oil output. This is clear when the oil
output is at its lowest, 1.85 g.L-1, at the lowest pressure of 250 bar and the maximum temperature of 75 °C.
Montesantos et al. (2019) state that an increase in the solvents density results in an increase in the oil extraction.
Lachos-Perez et al. (2020) also agrees in which the authors found that the highest yield was obtained at higher
CO2 density on the SFE process using CO2 of lipophilic molecules from sugarcane straw.

Table 2: Optimal (custom) design and response for the oil yield of Sclerocarya birrea kernels.

Run X1
(°C)

X2
(bar)

Coded
Temperature

variable

Coded
Pressure
variable

Observed response
(g oil/L CO2)

Predicted response
(g oil/L CO2)

1 40 250 -1 -1 5.808 5.515
2 60 250 0 -1 3.5415 3.580
3 75 250 1 -1 1.8512 2.007
4 40 350 -1 0 8.1345 8.623
5 60 350 0 0 7.8533 8.002
6 75 350 1 0 7.7568 7.415
7 40 450 -1 1 8.4825 8.412
8 60 450 0 1 9.2213 9.104
9 75 450 1 1 8.9301 9.502

Table 3: Analysis of variance for the fitted quadratic polynomial model.

Source Sum of
Squares

Degree of
freedom

Mean Square F-value p-value

Model 104.88 5 20.98 208.36 < 0.0001 significant
X1-Temperature 2.69 1 2.69 26.71 0.0004
X2-Pressure 60.43 1 60.43 600.2 < 0.0001
X1X2 6.13 1 6.13 60.84 < 0.0001
X1² 0.0187 1 0.0187 0.1862 0.6753
X2² 10.11 1 10.11 100.41 < 0.0001
Residual 1.01 10 0.1007
Lack of Fit 1.01 3 0.3356
Pure Error 0 7 0
Total 105.89 15
Standard deviation 0.3173 R2 0.9905
Mean 6.45 Adj R2 0.9857
C.V % 4.92 Adeq precision 38.3409

Table 4: Regression coefficient of polynomial function of response surface oil yield.

Factor Coefficient
Estimate

Degree of
freedom

Standard
Error

95% CI
Low

95% CI
High

Variance
inflation factor

Intercept 8.05 1 0.1555 7.7 8.39
X1-Temperature -0.6058 1 0.1172 -0.867 -0.3446 1.03
X2-Pressure 2.58 1 0.1051 2.34 2.81 1.07
X1X2 1.15 1 0.1473 0.8209 1.48 1.08
X1² -0.0704 1 0.1631 -0.4338 0.2931 1.01
X2² -1.66 1 0.1659 -2.03 -1.29 1.03

466

Figure 1: a) Contour plot for the effects of temperature and pressure on oil yield b) Response surface for the

effects of temperature and pressure on oil yield.

Figure 2: a) Optimisation of pressure and temperature b) Predicted values versus actual response.

4. Conclusions

RSM was successfully used to optimize the supercritical fluid extraction parameters to increase the production
of Sclerocarya birrea kernel oil. The two variables namely extraction pressure and extraction temperature both
had a significant effect on the oil yield, both alone and in conjunction, according to the response surface plots.
A higher fluid density results from an increase in pressure, which raises the solubility. When it comes to
temperature, the opposite is observed because an increase in temperature at a fixed pressure reduces the
density of the CO2 in the supercritical state, thus reducing the solubility. The quadratic temperature term however
had no significant effect on Sclerocarya birrea kernel oil yield. The coefficient of pressure is also much larger
in comparison to the coefficient of temperature and the interaction term which is an indication that pressure is
an indispensable variable on the yield of Sclerocarya birrea kernel oil.

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Response Surface Analysis and Modeling of Sclerocarya Birrea kernel Oil Yield in Supercritical Carbon Dioxide