Artificial neural network-based estimation of interaction parameters between carbon dioxide and organic solvents using the Peng–Robinson equation of state with the van der Waals one-fluid mixing rule and quantum chemical data; Part 2, two-parameter mixing rule

The Peng–Robinson (PR)–van der Waals (vdW) model is a combination of the PR equation of state and the vdW mixing rule. In a previous study, we constructed a model that uses an artificial neural network (ANN) to predict the interaction parameters k_ij in the vdW mixing rule, which is necessary for the wide application of this model. The vdW mixing rule includes a two-parameter mixing rule that combines l_ij with k_ij, and by using this rule, the range of application of the PR-vdW model can be expanded. In this study, an ANN model was constructed to predict k_ij and l_ij between CO₂ and organic solvents. The inputs used were the pure-component parameters and molecular information of the organic solvents, and the molecular information was obtained using the general-purpose quantum chemical calculation software Gaussian. In addition, the ANN was optimized by varying the transfer function, number of neurons, and number of hidden layers. The optimized ANN employed a tanh function as the transfer function for the hidden layers, with two hidden layers containing 40 and 20 neurons. This model could predict k_ij effectively, but problems with predicting l_ij remained. The results of the SHapley Addtive exPlanations analysis of the optimized ANN revealed that k_ij was related to the interactions between different molecules and that l_ij was related to the volume of the mixture. Thus, improving the accuracy of l_ij prediction requires the addition of related parameters.