Prediction of high-pressure vapor liquid equilibrium of six binary systems, carbon dioxide with six esters, using an artificial neural network model

Abstract

Artificial neural networks are applied to high-pressure vapor liquid equilibrium (VLE) related literature data to develop and validate a model capable of predicting VLE of six CO2-ester binaries (CO 2-ethyl caprate, CO2-ethyl caproate, CO2-ethyl caprylate, CO2-diethyl carbonate, CO2-ethyl butyrate and CO2-isopropyl acetate). A feed forward, back propagation network is used with one hidden layer. The model has five inputs (two intensive state variables and three pure ester properties) and two outputs (two intensive state variables).The network is systematically trained with 112 data points in the temperature and pressure ranges (308.2-328.2 K), (1.665-9.218 MPa) respectively and is validated with 56 data points in the temperature range (308.2-328.2 K). Different combinations of network architecture and training algorithms are studied. The training and validation strategy is focused on the use of a validation agreement vector, determined from linear regression analysis of the plots of the predicted versus experimental outputs, as an indication of the predictive ability of the neural network model. Statistical analyses of the predictability of the optimised neural network model show excellent agreement with experimental data (a coefficient of correlation equal to 0.9995 and 0.9886, and a root mean square error equal to 0.0595 and 0.00032 for the predicted equilibrium pressure and CO2 vapor phase composition respectively). Furthermore, the comparison in terms of average absolute relative deviation between the predicted results for each binary for the whole temperature range and literature results predicted by some cubic equation of state with various mixing rules and excess Gibbs energy models shows that the artificial neural network model gives far better results.