Deep learning based combining rule for the estimation of vapor-liquid equilibrium

Abstract

Vapor-liquid equilibrium (VLE) data plays a vital role in the design, modeling and control of process equipment. In this study, to estimate the VLE data of binary systems, a deep neural network (DNN)-based combining rule was proposed based on the cross-term parameter (a(ij)) in the two-parameter Peng-Robinson cubic equation of state (PR-EoS) combined with the one-parameter classical van der Waals mixing and combining rule (1PVDW). Experimental VLE data of alternative binary refrigerant systems selected from the literature were calculated using both the PR + 1PVDW and the DNN-based model. Vapor phase mole fractions (y(i)) and equilibrium pressures (P) obtained from the proposed DNN-based and PR + 1PVDW models were compared in the terms of average percent deviations. For the DNN-based model, the vapor phase mole fractions give at least as good results as the models in the literature, and also it has been shown that a much better estimate of the equilibrium pressure (P) is obtained when compared with that of the literature. Results obtained using the proposed DNN-based model are presented with tables and graphs. For the equilibrium pressure, while the average percent deviation errors (Delta P/P%) calculated in the literature are less than 7.739, the errors obtained with the proposed DNN-based model are smaller than 3.455. And also, for vapor phase mole fractions, while the maximum error (Delta(y1)/(y1) %) in the literature is obtained as 6.142, the largest error calculated with DNN-based model is 3.545. It has been seen that the proposed DNN-based model makes more practical and less error-prone estimations than the methods in the literature.