Thermodynamically consistent vapor-liquid equilibrium modelling with artificial neural networks
Andrés Carranza-Abaíd, Hallvard F. Svendsen, Jana P. Jakobsen
Abstract
An integration of Artificial Neural Networks (ANNs) and thermodynamics through the application of Neural Network Programming (NNP) is proposed. Thermodynamic consistency is achieved because the thermodynamic relationships and constraints are transcribed into a specially crafted ANN. Moreover, the developed models allow predicting and extrapolating the model outside the experimental data boundaries. The Wilson and NRTL models are used as case studies. Modifications to these models based on sigmoid functions are rigorously assessed in order to perform the simultaneous modelling of VLE and excess enthalpy. The automatic differentiation together with the ANN optimization algorithms can find sets of parameters that are better than the ones obtained with traditional gradient-based optimizers. The frequently disregarded concepts of thermodynamic modelling with ANNs are discussed in-depth. A mathematical analysis of the impossibility of typical fully connected ANNs to formulate thermodynamically consistent equilibrium models is discussed and their use is discouraged (e.g., VLE, LLE, or adsorption.).