Graph Neural Networks embedded into Margules model for vapor-liquid equilibria prediction

TL;DR

The paper investigates embedding a Graph Neural Network (GH-GNN) within the extended Margules model to predict vapor–liquid equilibria by extrapolating finite-concentration activity coefficients from infinite-dilution data. Using the GH-GNN to infer $\gamma_i^\infty$ and embedding it in a thermodynamically consistent Margules head, the approach is benchmarked against UNIFAC-Dortmund across extensive binary and limited ternary VLE data. Results show UNIFAC-Dortmund generally delivers higher accuracy, but GH-GNN–Margules offers a meaningful baseline and niche advantages, particularly when expansion data are scarce or certain mixtures lack applicable UNIFAC parameters. The study underscores the value of combining data-driven models with thermodynamic constraints, and highlights data curation and broader VLE training data as key pathways to improve predictive performance in early-stage design.

Abstract

Predictive thermodynamic models are crucial for the early stages of product and process design. In this paper the performance of Graph Neural Networks (GNNs) embedded into a relatively simple excess Gibbs energy model, the extended Margules model, for predicting vapor-liquid equilibrium is analyzed. By comparing its performance against the established UNIFAC-Dortmund model it has been shown that GNNs embedded in Margules achieves an overall lower accuracy. However, higher accuracy is observed in the case of various types of binary mixtures. Moreover, since group contribution methods, like UNIFAC, are limited due to feasibility of molecular fragmentation or availability of parameters, the GNN in Margules model offers an alternative for VLE estimation. The findings establish a baseline for the predictive accuracy that simple excess Gibbs energy models combined with GNNs trained solely on infinite dilution data can achieve.

Figures (7)

• Figure 1: Heatmap of the mean absolute error achieved by the GH-GNN model embedded into the Margules model for different types of binary mixtures at isothermal conditions. The error is measured with respect to the vapor phase molar fraction. The number in each cell represents the number of data points included in the corresponding binary category.
• Figure 2: Isothermal vapor-liquid equilibria (VLE) diagram for two systems that are unfeasible to predict with UNIFAC-Dortmund.
• Figure 3: Heatmap of the mean absolute error achieved by the GH-GNN model embedded into the Margules model for different types of binary mixtures at isobaric conditions. The error is measured with respect to the vapor phase molar fraction. The number in each cell represents the number of data points included in the corresponding binary category.
• Figure 4: Isobaric vapor-liquid equilibria (VLE) diagram comparing experimental data with the predictions of UNIFAC-Dortmund and the GH-GNN model embedded into the Margules model. The system is pyridine/1,2,3,4-tetrahydronaphthalene at 26.66 kPa.
• Figure 5: Isobaric vapor-liquid equilibria (VLE) diagram comparing experimental data with the predictions of UNIFAC-Dortmund and the GH-GNN model embedded into the Margules model. The system is tetrahydrofuran/ethanol at 25 kPa.