# Evaluation of Machine Learning Assisted Phase Behavior Modelling of Surfactant-Oil-Water Systems
## 1 Introduction
By integrating this enhanced HLD equation with the NAC model, they successfully predicted critical parameters, including phase volumes, solubilization ratios, and transitions between microemulsion phases, with validation against experimental data. However, challenges remain in addressing non-physical two-phase regions in the model. [PERSON] and [PERSON] (2016) [25] presented the first flash calculation algorithm, which is non-iterative and robust for three- and two-phase zones, based on the hydrophilic-lipophilic difference net-average curvature (HLD-NAC) framework, capable of modeling all Winsor regions. This algorithm introduced new correlations for the solubilization ratio at optimum formulation, allowing for flexibility with variations in any formulation parameter(s). However, the characteristic length is assumed to remain constant across the three-phase region. [PERSON] and [PERSON] (2022) [26] resolved this limitation by introducing a variable characteristic length in their improved microemulsion flash calculation method. The modification ensures thermodynamic consistency and better replicates phase behavior, particularly in the three-phase and adjacent two-phase regions. However, the improved method requires additional equation-of-state parameters, including coefficients for the HLD equation, characteristic length correlations, and critical tie-line parameterization coefficients, all of which must be calibrated against experimental data. In recent studies, phase behavior calculations have been accelerated by applying ML algorithms [27; 28; 29], further integrated with fundamental physics to accurately address the complexities of multiphase systems while avoiding non-physical behavior [30; 31; 32; 33]. [PERSON] et al. (2024) [34] introduced a hybrid ML model that combines physics-based flash calculations with ML-predicted equilibrium constants for CO\({}_{2}\)-oil systems, achieving high accuracy in compositional space predictions. Several recent studies have focused on employing ML to accelerate microemulsion phase behavior predictions and to estimate surfactant properties based on models or experimental data. [PERSON] et al. (2024) [35] proposed an ML-based workflow for predicting the equivalent alkane carbon number (EACN), a critical parameter in the HLD framework that describes oil phase hydrophobicity but typically requires labor-intensive experimental determination. Similarly, [PERSON] (2016) [36] utilized decision tree methods to predict missing data points in the temperature-composition plane for non-ionic surfactant partitioning. [PERSON] et al. (2023) [37] explored the use of ML to generate surfactant phase diagrams based on known phase behavior. While these studies provided valuable insights, their effectiveness was constrained by limited datasets, resulting in insufficient chemical space coverage. Despite these limitations, the comparative evaluation of different ML techniques identified support vector machines (SVMs) and neural networks as the most effective for such applications. The prediction of surfactant system properties, such as interfacial tension (IFT), presents another empirically challenging area that has been addressed by [PERSON] et al. (2022) [38] and [PERSON] et al. (2023) [39]. Their studies demonstrated the capability of ML algorithms to analyze surfactant sample datasets and achieve accurate predictions, with R\({}^{2}\) values ranging from 0.69 to 0.87. By circumventing the need for empirical tuning across diverse surfactant types, these approaches highlight the utility of ML; however, the relatively small datasets (e.g., 390 experimental IFT data points) increase the risk of overfitting, underscoring the need for dataset expansion to improve generalizability. [PERSON] et al. (2024) [40] extended this application by introducing ML regression models to estimate microemulsion viscosity.