Investigating vapor–liquid equilibria of binary mixtures containing supercritical or near-critical carbon dioxide and a cyclic compound using cascade neural network

Vapor–liquid equilibria (VLE) play an important role in designing and modeling of separation processes, in which containing vapor and liquid in equilibrium. Since it is not always possible to carry out experiments at all temperatures and pressures of interest, especially near the critical region, generally thermodynamic models based on equations of state (EoS) are used for the estimation of VLE. In the present work, an alternate tool, i.e. the cascade-forward back-propagation artificial neural network (ANN) model, has been applied for estimation of bubble- and dew-point pressures of binary mixtures containing carbon dioxide (CO2) + cyclic compounds as function of reduced temperature of the system, critical pressure, acentric factor of the cyclic compound, and CO2 composition. Six binary systems within temperature and pressure ranges of 298.15–473.15 K and 0.89–27.71 MPa were used to examine the feasibility of the proposed ANN model for the binary systems of CO2 + cyclic compounds. The obtained results show that the proposed neural network method is able to predict the phase envelope of binary systems containing supercritical or near-critical CO2 + cyclic compounds with an acceptable average absolute relative deviation percent (AARD%) of 1.51% and the coefficient of determination (R2) value of 0.9989 within their experimental uncertainties.