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Group Contribution Based Graph Convolution Network: Predicting Vapor–Liquid Equilibrium with COSMO-SAC-ML

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Abstract

The conductor-like screening model with the segment activity coefficient (COSMO-SAC) model enables us to predict the liquid phase behavior based on quantum chemical calculations when experimental information is unavailable. However, the quantum chemical COSMO calculations require significant computational resources (software, hardware, experience, and time) for successful results. In this work, we suggest machine learning models for replacing COSMO calculations to alleviate the computational burden. The machine learning (ML) models include graph convolutional neural networks. The ML models were constructed based on the molecular level structural information and previous COSMO calculation databases. Additional COSMO calculations were generated to train several missing functional groups, which are not included in the existing databases. The ML prediction abilities were shown by comparison of generated cavity volume and sigma profile with the original COSMO-SAC. The vapor–liquid equilibrium (VLE) prediction results were also compared with the original COSMO-SAC and the UNIQUAC functional-group activity coefficients (UNIFAC) model. It is shown that the suggested ML models can predict VLE with reasonable accuracy comparable with the original COSMO-SAC and UNIFAC. The new ML models can effectively replace the time-consuming COSMO-SAC calculations and experimental data-dependent UNIFAC models.

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Abbreviations

\({A}_{i}\) :

Cavity area of component \(i\) [Å2]

\({a}_{eff}\) :

Effective area parameter [Å2]

\({A}_{ES}\) :

Electrostatic interaction parameter A [kcal Å2·mol−1·e−2]

\({B}_{ES}\) :

Electrostatic interaction parameter B [kcal Å4 K2 mol−1·e−2]

\({c}_{hb}\) :

Hydrogen bonding interaction parameter [kcal Å4·mol−1·e−2]

\({c}_{OH}\) :

OH interaction parameter [kcal Å4·mol−1·e−2]

\({c}_{OH-OT}\) :

OH-OT interaction parameter [kcal Å4·mol−1·e−2]

\({c}_{OT}\) :

OT interaction parameter [kcal Å4·mol−1·e−2]

\({\widehat{f}}_{i}\) :

Partial fugacity of component \(i\) [–]

\(N\) :

Number of learned molecules [–], number of total experimental data points [–]

\(n\) :

Number of grids of screening charge [–]

\(P\) :

Pressure [\({\text{kPa}}\)]

\({P}_{i}^{sat}\) :

Saturation pressure of component i [\({\text{kPa}}\)]

\(p\left(\sigma \right)\) :

Sigma profile [–]

\({q}_{0}\) :

Area normalization parameter [Å2]

\({r}_{0}\) :

Volume normalization parameter [Å3]

R2 :

R-squared score [–]

\({V}_{i}\) :

Cavity volume of component \(i\) [Å3]

\({x}_{i}\) :

Liquid mole fraction of component \(i\) [–]

\({y}_{i}\) :

Vapor mole fraction of component \(i\) [–]

\(z\) :

Coordination number [–]

\(\Delta P\) :

Relative root mean error of pressure [%]

\(\Delta W\) :

Exchange energy [kcal Å4·mol−1]

\(\Delta y\) :

Root mean error of vapor mole fraction [–]

\(\Gamma \left(\sigma \right)\) :

Segment activity coefficient [–]

\({\gamma }_{i}\) :

Activity coefficient of component \(i\) [–]

\(\widehat{{\phi }_{i}}\) :

Partial fugacity coefficient of component \(i\) [–]

\(\sigma\) :

Charge density [e Å2]

COSMO:

Conductor-like screening MOdel

COSMO-RS:

Conductor-like screening MOdel with real solvent

COSMO-SAC:

Conductor-like screening MOdel with segment activity coefficient

GC:

Group contribution

GCM:

Group contribution model

GC-GCN:

Group contribution graph convolution neural network

HDNN:

High-dimensional neural network

LLE:

Liquid–liquid equilibrium

LSTM:

Long short-term memory

M-GCN:

Molecular graph convolution neural network

ML:

Machine learning

RMSE:

Root mean square error

RRMSE:

Relative root mean square error

SLE:

Solid–liquid equilibrium

UNIFAC:

UNIQUAC functional-group activity coefficients

VLE:

Vapor–liquid equilibrium

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Acknowledgements

This work was supported by National Research Foundation of Korea (NRF) grants funded by the Korean government (MSIT) [Grant Numbers NRF- 2021R1A5A6002853 and NRF-2019M3E6A1064876]. This work was also supported by Korea Environment Industry & Technology Institute (KEITI) through Technology Development Project for Safety Management of Household Chemical Products Program, funded by Korea Ministry of Environment (MOE) (ARQ202201483001).

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Authors and Affiliations

  1. Department of Chemical and Biological Engineering, Korea University, 145, Anam-Ro, Seongbuk-Gu, Seoul, Republic of Korea

    Beom Chan Ryu, Seon Yoo Hwang, Sung Sin Kang, Jeong Won Kang & Dongsoo Yang

  2. Graduate School of Energy and Environment, Korea University, 145, Anam-Ro, Seongbuk-Gu, Seoul, Republic of Korea

    Jeong Won Kang

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CREdiT authorship contribution statement. BCR: Conceptualization, Methodology, Investigation, Writing—original draft. SSK: Methodology. SYH: Methodology. JWK: Supervision, Writing—review & editing.

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Ryu, B.C., Hwang, S.Y., Kang, S.S. et al. Group Contribution Based Graph Convolution Network: Predicting Vapor–Liquid Equilibrium with COSMO-SAC-ML. Int J Thermophys 44, 49 (2023). https://doi.org/10.1007/s10765-022-03141-7

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