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


Bekri S., Ozmen D., ÖZMEN A.

BRAZILIAN JOURNAL OF CHEMICAL ENGINEERING, vol.41, no.1, pp.613-629, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.1007/s43153-023-00377-0
  • Journal Name: BRAZILIAN JOURNAL OF CHEMICAL ENGINEERING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, CAB Abstracts, Compendex, Veterinary Science Database
  • Page Numbers: pp.613-629
  • Keywords: Deep neural network (DNN), Peng–Robinson equation of state (PR-EoS), Refrigerant mixtures, Van der Waals mixing and combining rule, Vapor–liquid equilibrium (VLE)
  • Istanbul University Affiliated: Yes

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.