Comparison between neural network and mathematical modeling of supercritical CO2 extraction of black pepper essential oil

A feed-forward multi-layer neural network with Levenberg–Marquardt training algorithm was developed to predict yield for supercritical carbon dioxide extraction of black pepper essential oil. Since yield of extraction strongly depends on five independent variables including residence time, supercritical carbon dioxide temperature and pressure, particle size and supercritical carbon dioxide mass flux per unit mass of substratum, these five inputs were devoted to the network. Different networks were trained and tested with different network parameters using training and testing data sets. Using validating data set the network having the highest regression coefficient (r2) and the lowest mean square error was selected. To confirm the network generalization, an independent data set was used and the predictability of the network was statistically assessed. Statistical analyses showed that the neural network predictions had an excellent agreement (r2 = 0.9698) with experimental data. Furthermore, a mass transfer based mathematical model was developed for constant rate period and diffusion-controlled regime of supercritical carbon dioxide extraction. The proposed model was numerically solved using modified Euler's and finite difference methods. Comparing predicted results of the neural network model and the mathematical model to experimental data indicated that the neural network model had better predictability than the mathematical model.