Modelling of the extraction of valuable compounds from Scleocarya birrea

Abstract

Two different modelling techniques were investigated viz. empirical modelling and response surface methodology, by monitoring their performance in predicting the oil yield of Sclerocarya birrea kernel oil via literature data obtained from supercritical CO2 fluid extraction process. The data comprised of 89 experimental runs of which was made up of 9 experimental runs for the determination of the solubility of marula oil in supercritical carbon dioxide in which the temperature was varied between 40, 60 and 75 °C. The pressure was varied between 250, 350 and 450 bar. A fatty acid composition was also conducted to determine palmitic acid, margaric acid, stearic acid, palmitoleic acid, oleic acid, linoleic acid, saturated fat, mono-unsaturated fat and poly-unsaturated fat percentage. The fatty acid composition comprised of 80 experimental runs in which the temperature was varied between 40, 60 and 80 °C and the pressure was varied between 250, 350 and 450 bar. The reaction time, particle size and carbon dioxide flowrate were kept constant for all experimental runs. The accuracy of the empirical models was determined by observing the determination coefficient value (R2) and the average absolute relative deviation (AARD%), whereas the R2 value, adjusted R2 value, p-values and F-values were taken into account in determining the efficiency of the response surface methodology model. Six empirical-density based models of Chrastil, del Valle and Aguilera, Adachi and Lu, Sparks et al., Kumar and Johnston, and Mendez-Santiago and Teja were investigated to fit the experimental data for the solubility of marula oil in supercritical carbon dioxide by utilizing the values obtained from literature for the 9 experimental runs. The R2 value of the models ranged between 0.72 - 0.95, and the AARD percentages ranged between 15.53 -0.049%. The Mendez-Santiago and Teja model provided the best as it has regressed well with the experimental data, yielding an R2 value of 0.95 and AARD% of 0.049%. The findings observed from the empirical density models were then studied to develop a new and novel model that can better predict the solubility of marula oil in supercritical carbon dioxide with greater accuracy and minimal error. Thus, a novel density-based model is proposed by making minor modifications to the Mendez-Santiago and Teja model. The novel model in comparison to the Mendez-Santiago and Teja model reduced the AARD% significantly from 0.049% to 0.00065% thus indicating that the correlated model is more accurate in predicting marula oil solubility. The external mass transfer coefficient, diffusion coefficient and axial dispersion coefficient for marula kernel oil was also determined from the experimental values, together with the Sherwood, Reynolds, and Schmidt dimensionless consortiums. The Reynolds number ranged between 8 to 15, indicating that natural convection occurred. Although the solubility of marula oil decreased as temperature rose, its effective diffusivity and external mass transfer coefficient increased. However, as the pressure increased, the external mass transfer coefficient, diffusion coefficient and axial dispersion coefficient decreased because at higher pressures, there is a decrease in binary diffusivity. Although the solvent’s density increases with pressure, thus increasing the solute's diffusivity in supercritical CO2, the coefficients drop as a result, but the amount of extract is amplified by the increase in solvent power. The optimization of marula kernel oil and the extraction of the fatty acids present in marula was also carried out in this study by using response surface methodology (RSM). The effect of two parameters, viz. temperature and pressure on the yield of marula oil and the fatty acids were considered in this investigation. A correlation was also determined for the density of supercritical carbon dioxide at the various temperatures and pressures. The results of the experiments, along with the factors taken into consideration, were modelled, and analysed using a quadratic model that was achieved by utilising the optimal (custom) design available on Design-Expert version 13. Furthermore, the models were modified based on the observations made during the analytical procedure. Thus, the response surface methodology based on the statistical analysis of the experimental data allowed for the formulation of a mathematical equation in terms of coded and uncoded factors corresponding to the processing parameters that were considered in this investigation. The mathematical equations proved to represent the experimental data extremely well as indicated by the highly significant model p-value of <0.0001, and R2 values ranging between 0.922 to 1 for all of the mathematical models. The predicted models obtained with the aid of Design Expert Version 13 were then further optimized to determine the most suitable operating conditions for maximum yield.