In this study, response surface methodology applying Doehlert experimental design was used to optimise decolourisation parameters of crude yellow shea butter. The decolourisation process was significantly influenced by three independent parameters: contact time, decolourisation temperature and adsorbent dose. The responses of the process were oil loss, acid value, peroxide value and colour index. Contour plots of the decolourisation responses were superimposed and well defined the optimum zone. The optimum decolourisation conditions were found to be: contact time (30 min), decolourisation temperature (80℃ - 95℃) and adsorbent dosage (1 - 2 mass%). These conditions gave decolourised shea butter with the following responses; oil loss (6.2% ± 0.2%), peroxide value (1.7 ± 0.1 meq O2/kg), colour (0.21 ± 0.05 Lovibond yellow) and acid value (25.6 ± 0.7 mg KOH/g).
Vegetable oils contain numerous pigments, including chlorophyll, carotenoids, xanthophylls and their derivatives, and these are removed to give the oil a colour that is acceptable to the consumer [
Efficiency of decolourisation process depends on many parameters like temperature, contact time, agitation rate, adsorbent dosage, adsorbent particle size, and variety of oils [
Response surface methodology is based on polynomial surface analysis and it is a collection of mathematical and statistical techniques that are useful for the modeling and analysis of problems in which a response of interest is influenced by several variables [
Bike Mbah et al. (2005) [
Crude yellow traditionally aqueous extracted shea butter was purchased from Penie village-South of Chad in January 2008. The method of extraction was described by (Adoum, 1996) [
The response surface methodology using the Doehlert experimental matrix was used to investigate the relationship existing between the process responses and the independent parameters and to optimise the process conditions as mentioned early [
where yi.exp and yi.cal are the experimental and calculated responses respectively, Z is the number of experimental run.
Three independent variables namely contact time (X1: 5 - 120 min), decolourisation temperature (X2: 50 - 95ºC), and adsorbent dose (X3: 1 - 6 mass %) were used as main independent parameters based on literature review and preliminary studies. A total of 13 different experiments were enough to study the decolourisation process according to the experimental design. Each experiment was repeated twice and the average values were calculated and used. The experiments are presented in
Independent variable | Contact time (5 - 120 min) | Temperature (50˚C - 95˚C) | Adsorbent dose (1 - 6 mass %) |
---|---|---|---|
Exp. No | x1 | x2 | x3 |
1 | 0.000 | 0.000 | 0.000 |
2 | 1.000 | 0.000 | 0.000 |
3 | −1.000 | 0.000 | 0.000 |
4 | 0.500 | 0.866 | 0.000 |
5 | −0.500 | −0.866 | 0.000 |
6 | 0.500 | −0.866 | 0.000 |
7 | −0.500 | 0.866 | 0.000 |
8 | 0.500 | 0.289 | 0.816 |
9 | −0.500 | −0.289 | −0.816 |
10 | 0.500 | −0.866 | −0.816 |
11 | 0.000 | 0.577 | −0.816 |
12 | −0.500 | 0.289 | 0.816 |
13 | 0.000 | −0.577 | 0.816 |
oil loss was expressed as a mass ratio of decolourised oil to that of crude one, while acid and peroxide values were evaluated using the method described in AFNOR (1981) [
The coefficients of the polynomial were represented by b0 (constant term), bi (linear effects), bii (quadratic effects) and bij (interaction effects). Xi and Xj are the independent variables. The analyses of variance (ANOVA) were generated and the effect and regression coefficients of individual, quadratic and interaction terms were determined. The significances of all terms in the polynomial were judged statistically at a probability (P) of 0.001, 0.01 and 0.05. The regression coefficients were then used to make statistical calculation to generate contour map and response surface graphs from the regression models.
The decolourisation apparatus was composed of a 250 ml conical flask equipped with a mechanical agitator of model (Heidolph, RZR1, Germany). The flask was immersed in a thermostated water bath. In each experiment, 30 g of crude shea butter was heated and maintained at the desired temperature for 15 min before adding the adsorbent, and then the mixture was continuously heated and stirred. The agitation rate used was that just enough to keep the clay dispersed (150 rpm). After decolourisation, the mixture was immediately filtered using Whatman no 1 filter paper on a layer of celite 545 and a vacuum pump of model (960101, Osi-DVD-Bolong, Italy). Each experiment was repeated twice and the results reported are the means of three measurements.
This technique as described by (ISO 15305, 1998) [
The data in
Run | X1 | X2 | X3 | Yloss | YAv | YPv | YColour |
---|---|---|---|---|---|---|---|
1 | 62.50 | 72.50 | 3.50 | 10.4 ± 0.3 | 27.6 ± 0.2 | 1.55 ± 0.28 | 0.30 ± 0.04 |
2 | 120.00 | 72.50 | 3.50 | 8.7 ± 0.2 | 26.4 ± 0.7 | 2.50 ± 0.49 | 0.20 ± 0.01 |
3 | 5.00 | 72.50 | 3.50 | 7.8 ± 0.2 | 27.5 ± 0.5 | 1.25 ± 0.35 | 0.30 ± 0.03 |
4 | 91.25 | 95.00 | 3.50 | 9.8 ± 0.2 | 25.0 ± 0.5 | 1.60 ± 0.14 | 0.20 ± 0.04 |
5 | 33.75 | 50.00 | 3.50 | 12.5 ± 0.4 | 26.1 ± 0.7 | 1.38 ± 0.17 | 0.10 ± 0.01 |
6 | 91.25 | 91.25 | 3.50 | 10.1 ± 0.5 | 26.4 ± 0.4 | 1.13 ± 0.18 | 0.30 ± 0.07 |
7 | 33.75 | 95.00 | 3.50 | 7.3 ± 0.6 | 26.1 ± 0.4 | 2.03 ± 0.25 | 0.20 ± 0.02 |
8 | 91.25 | 80.00 | 6.00 | 12.4 ± 0.4 | 25.0 ± 0. 6 | 1.08 ± 0.11 | 0.10 ± 0.01 |
9 | 33.75 | 65.00 | 1.00 | 6.7 ± 0.2 | 23.7 ± 0.1 | 2.30 ± 0.35 | 0.30 ± 0.06 |
10 | 91.25 | 65.00 | 1.00 | 5.3 ± 0.6 | 25.2 ± 0.3 | 2.00 ± 0.21 | 0.30 ± 0.03 |
11 | 62.50 | 87.50 | 1.00 | 7.2 ± 0.6 | 24.9 ± 0.1 | 2.13 ± 0.18 | 0.30 ± 0.04 |
12 | 33.75 | 80.00 | 6.00 | 10.3 ± 0.5 | 23.7 ± 0.4 | 1.38 ± 0.17 | 0.10 ± 0.02 |
13 | 62.50 | 57.50 | 6.00 | 11.9 ± 0.5 | 25.1 ± 0.5 | 1.25 ± 0.35 | 0.10 ± 0.01 |
X1: contact time (min), X2: decolourisation temperature (˚C), X3: adsorbent dose (mass %), Yloss: Oil loss (%), YAv : acid value (mg KOH/g), YPv: peroxide value (meq O2/Kg), YColour: Lovibond red colour.
Coefficient | Oil loss (%) | Acid value | Peroxide value | Colour |
---|---|---|---|---|
b0 | 10.370 | 27.500*** | 1.500* | 0.300 |
b1 | 0.361 | 0.000 | 0.156 | 0.00 |
b2 | −1.089 | −0.303 | 0.189 | 0.00 |
b3 | 3.125** | 0.000 | −5.110 | −0.12* |
b12 | 2.870 | -0.808 | 0.000 | −0.12 |
b13 | 1.067 | 0.280 | −0.153 | 0.05 |
b23 | −0.376 | −1.461 | −0.265 | −0.02 |
b11 | −2.135 | −0.500 | 0.375 | −0.05 |
b22 | 0.142 | −2.033 | −0.125 | −0.12 |
b33 | −1.568 | −3.771* | 0.063 | −0.11 |
R2 | 0.96 | 0.87 | 0.60 | 0.85 |
AAD | 4.65 | 1.51 | 14.72 | 3.73 |
b1 = contact time, b2 = decolourisation temperature, b3 = adsorbent dose (mass %). *Significant at 0.05; **Significant at 0.01; ***Significant at 0.001.
From data in
As shown in
The data in
For lovibond colour index, both the linear and quadratic terms of adsorbent dosage showed a positive effect on the colour of yellow shea butter (
The statistical analyses indicated that the proposed models were adequate with satisfactory values of R2 and AAD. The closer the value of R2 to the unity, the better the empirical model fits the actual data. The smaller the value of R2 the less relevant the dependent variables in the model have to explain the behaviour variation [
By analysing the influence of decolourisation conditions on oil loss, colour, acid value and peroxide value of shea butter, all the responses were found to vary substantially with decolourisation temperature and adsorbent dose (mass %) for decolourisation of yellow shea butter. Using the predicted polynomial models (Equations (3)-(6)), contour plots for the independent variables as a function of decolourisation temperature and adsorbent mass percentage were generated and the limits of acceptance were set for each attribute.
The contour plot for oil loss indicated that a high decolourisation temperature and little adsorbent mass % were necessary to obtain a low oil loss. But, moderate decolourisation temperature (60-70˚C) and high adsorbent dose (mass %) gave low colour intensity. It is also observed that a high decolourisation temperature gave a high acid value, whereas low decolourisation temperature and a more adsorbent dose (mass %) produced shea butter with low peroxide value.
Numerical OptimisationA numerical optimisation was carried out to identify the overall optimal conditions for oil loss, colour, acid value and peroxide value of shea butter. Mathcad numerical analysis was used to do this part of the work. The criteria applied for numerical optimisation included minimum oil loss (<7.0%), Lovibond colour (<3.0), acid value (<12.0%) and peroxide value (<3.0%).
Using Mathcad software and the model equation 2, the optimum conditions of decolourisation of yellow shea butter were found to be:
1) Oil loss (2.8%): contact time 15 min, decolourisation temperature 95˚C, adsorbent dosage 1.3 mass %.
2) Colour index (0.05): contact time 35 min, decolourisation temperature 95˚C, and adsorbent dosage 4.7 mass %.
3) Acid value (22.6): contact time 20 min, decolourisation temperature 95˚C and adsorbent dosage 6 mass %.
4) Peroxide value (1 meq/kg): contact time 40 min, decolourisation temperature 55˚C, and adsorbent dosage 6 mass %. See Figures 1-4.
Since the optimum independent parameters for each response did not fall exactly in the same region, the superimposition of the entire contour plot obtained was done.
The optimum zone (black shaded area) as shown in the
Response surface methodology using Doehlert experimental design was successfully applied in the optimisation of decolourisation parameters of crude yellow shea butter. Second order polynomial models with satisfactory validation in terms of coefficient of determination (R2) and absolute average deviation (AAD), were generated and described the decolourisation process. The optimum decolourisation conditions were found to be: 30 min contact time, 72˚C - 95˚C decolourisation temperature and 1.5 - 2.5 mass % adsorbent dosage.
This work is supported by the French Government through EGIDE program and University of N’djamena, Chad.
A. M.Mohagir,C. F.Abi,N. D.Bup,R.Kamga,C.Kapseu, (2015) Optimisation of Decolourisation Conditions of Crude Shea (Vitellaria paradoxa Gaertner F) Butter: Yellow Type. Advances in Chemical Engineering and Science,05,505-514. doi: 10.4236/aces.2015.54053
R2 Coefficient of determination
AAD Absolute Average Deviation
Yi response function
YAv acid value (mg KOH/g oil)
YPv peroxide value (meq O2/kg oil)
YColour lovibond colour index
yi.exp experimental response
yi.cal calculated response
y yield (g/g)
t time (min)
a; b constants.
Z number of experimental run
Xi ; Xj independent variables
xi coded value
X1 contact time (min)
X2 decolourisation temperature (˚C)
X3 adsorbent dose (mass %)
b0 constant term
bi inear effect
bii quadratic effect
bij interaction effect
P probability (0.001, 0.01 and 0.05)