Estimation of the interaction parameters between carbon dioxide and an organic solvent by the Peng–Robinson equation of state via an artificial neural network

The equation of state (EoS) is a tool for estimating the thermodynamic and physical properties of compounds, including mixtures, across a range of temperatures and pressures. When dealing with mixtures, a mixing rule is required to calculate the mixture parameters. Mixing rules may involve interaction parameters, such as k_ij and l_ij, that correct for differences between components. However, obtaining this data requires specialized equipment and techniques and significant measurement time, resulting in limited reported EoS parameters. In this study, we introduce an artificial neural network (ANN) to predict interaction parameters in the van der Waals one-fluid mixing rule. These parameters are used to calculate the physical properties of mixtures using the Peng–Robinson (PR) EoS. The interaction parameters are used in two cases, namely the one-parameter and two-parameter mixing rules (OP and TP, respectively), in which only k_ij and both k_ij and l_ij are employed, respectively. The vapor–liquid equilibrium (VLE) data of CO₂/organic solvent binary systems are collected and correlated by the PR EoS to construct a database of 1286 and 1292 parameters for the OP and TP, respectively. The molecular weight, critical temperature and pressure, acentric factor of the organic solvent, and temperature are used as input parameters for the ANN. In addition, we optimize the structure of the ANN by changing the activation function, number of neurons, and number of hidden layers. The optimized ANN uses a tanh activation function. Hidden layers are used for both the OP and TP, along with 40 and 50 neurons, respectively. The results confirm that the model can determine the interaction parameters of the PR EoS, which can be used to estimate the VLE. These results are useful for incorporation into process simulators for chemical process design.