# Evaluation of Machine Learning Assisted Phase Behavior Modelling of Surfactant-Oil-Water Systems
## 3 Results and Discussion
### Graphical Equation-of-State Model vs Experimental and Physical Model Results  
The final step in this analysis involves comparing the graphical equation-of-state model (based on the compositional space generated by the SVM machine learning model) with both experimental data and the physical model (modified HLD-NAC). Figure 11 presents the solubilization ratios of oil (\(\sigma_{\rm o}\)) and water (\(\sigma_{\rm w}\)) as functions of salinity, where the experimental data are shown alongside the predictions from the graphical model and the physical model.  
The results demonstrate that the graphical equation-of-state model captures the key trends observed in the experimental data, particularly in reproducing the transitions between Winsor Type I, III, and II+ microemulsions. Both the oil and water solubilization ratios show a strong alignment with experimental data across the salinity range. The graphical model's ability to follow these trends closely underscores its robustness and accuracy in modeling surfactant-oil-water systems.  
When compared to the physical model, the graphical equation-of-state model (driven by the compositional space mapped by the SVM ML model) performs exceptionally well. This consistency across different methods demonstrates the power of combining machine learning-generated compositional mapping with traditional physical models. The graphical model reproduces not only the equilibrium solubilization ratios but also the critical transitions between single-phase, two-phase, and three-phase regions.  
Figure 11: Graphical equation-of-state model performance compared to experimental data and physical model, salinity scan. Data from [PERSON] et al. (2015) [41].  
Figure 10: Illustration of less accuracy with sparse data available for SVM training.  
We note here that although the graphical method is powerful, it heavily relies on the quality and abundance of compositional data. Large sets of experimental compositional data are often difficult to measure and acquire. In situations where only sparse experimental data are available, feeding such data into machine learning models to define the compositional space for the graphical model may limit its effectiveness. As such, we suggest employing a hybrid approach, where experimental data are used in conjunction with physical models to generate a broader and more reliable compositional space of interest. This space can then be used to train machine learning models effectively. The graphical method can subsequently be applied using either ML-generated compositional spaces or physical model-based spaces, offering flexibility in different modeling scenarios.  
Overall, we have shown that machine learning algorithms can capture complex multiphase behavior and phase transitions in a controlled environment with synthetic physical model data. However, machine learning algorithms alone cannot capture all physical limitations such as mass balance across combined single-, two-, and three-phase regions and the thermodynamic constraints of tie lines and tie triangles. Therefore, in this paper, machine learning was combined with a physically constrained graphical equation-of-state model that incorporates physical constraints and mass balance. Thus, physics-based machine learning and hybrid modeling can be viable solutions for complex systems such as multiphase surfactant-oil-water phase behavior.