Prediciton 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 CO 2 -ester binaries (CO 2 -ethyl caprate, CO 2 -ethyl caproate, CO 2 -ethyl caprylate, CO 2 -diethyl carbonate, CO 2 -ethyl butyrate and CO 2 -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 CO 2 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.

Vapor-Liquid equilibria modeling using gray-box neural networks as binary interaction parameters predictor

“…The training process corresponds to the determination of the ANNs internal parameters (weights and Figure 2. Procedure for PR-EOS GNM modeling Source: Adapted from [23] bias of each neuron) by performing sensitivity analyses on an objective function, which is optimized by different methods. After calculation of the new weights, the fixed GNM weights were restored to their values by using a modified version of the Matlab algorithm (trainlm).…”

“…Si-Maussa et al [23] focused in the VLE prediction of carbon dioxideesters mixtures and reported Absolute Relative Deviations in the order of 4.95% and 0.19% for pressure and mole fraction estimations, respectively. Similarly, Karimi and Yousefi [25] studied a VLE of four binary refrigerant systems.…”

Preliminary Modeling of an Industrial Recombinant Human Erythropoietin Purification Process by Artificial Neural Networks

“…Since ANN have the ability to extract from experimental data the highly non-linear and complex relationships between the variables of the problem without any detailed knowledge of the system (Si-Moussa et al, 2008;Khaouane et al, 2013) and, given the great amount of available experimental data in the study, it was decided to apply this approach. In this way, it was possible to extract useful information for making decisions without the need to have a theoretical model of process behaviour.…”

Prediction the Vapor-Liquid Equilibria of CO2-Containing Binary Refrigerant Mixtures Using Artificial Neural Networks

“…Direct measurement of precise experimental data is often difficult and expensive, while the second method, which includes a large number of equations of states and excess Gibbs free energy models, is tedious and involves a certain amount of empiricism to determine mixture constants, through fitting experimental data and using various arbitrary mixing rules, making it difficult to select the appropriate model for a particular case [9]. Thus due to the difficulties of experimental measurements and also their time-consuming and costly nature, it is desirable to develop predictive methods for estimating the phase behavior of these kinds of systems.…”

“…This method provides nonlinear function mapping of a set of input variables into the corresponding network output. ANNs can be applied for accurate VLE determination of polar and nonpolar components [9,[34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]. Basic theory and application to chemical problems of ANN with the back-propagation algorithm have been previously discussed in [48].…”