Comparison the capability of artificial neural network (ANN) and EOS for prediction of solid solubilities in supercritical carbon dioxide

Abstract

The aim of this study is develop a feed-forward multi-layer perceptron neural network (MLPNN) model to predict the solid solubilities of aromatic hydrocarbons, aliphatic carboxylic acids, aromatic acids, heavy aliphatic and aromatic alcohols in the supercritical carbon dioxide. Different networks are considered and trained using 627 data sets; the accuracy of the network is validated by 343 testing data sets. The networks were different regarding to network parameters, such as number of hidden layer, hidden neurons and training algorithm. Using validating data set, the network that is having the lowest absolute average relative deviation percent (AARD%), mean square error (MSE) and the highest regression coefficient ( R 2) is selected as an optimal configuration. To verify the network generalization, 100 different data sets of 23 binary systems have been considered. In the present work, 970 experimental data points of different works (up to now) which covers a wide range of temperatures and pressures have been used. Statistical analyses show that the artificial neural network (ANN) predictions have an excellent agreement (AARD% = 0.98, MSE = 2.8 × 10 −5 and R 2 = 0.99813) with the experimental data set. Also, accuracy of the cubic Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK) equations of state by using six mixing rules, namely, the Wong–Sandler (WS) rule, the Orbey–Sandler (OS) rule, the van der Waals one fluid rule with one (VDW1) and two (VDW2) adjustable parameters, the covolume dependent (CVD) rule and the Esmaeilzadeh–As’adi–Lashkarbolooki (EAL) mixing rule for the prediction of solubility of solids in supercritical carbon dioxide has been compared with a developed neural network model. To base this comparison on a fair basis, same experimental data points of 23 different compounds has been used for both optimization of equations of state parameters and training, validation and testing of neural network. Results show that developed optimal ANN model is more accurate compared to the PR and SRK EOSs with mentioned mixing rules for the same compounds.