# Evaluation of Machine Learning Assisted Phase Behavior Modelling of Surfactant-Oil-Water Systems
## 1 Introduction  
Despite extraction efforts during the primary and secondary recovery phases, substantial volumes of crude oil often remain within reservoirs. Enhanced oil recovery (EOR) methods are implemented to increase the efficiency of oil extraction. Among these methods, chemical flooding has gained prominence as an effective strategy for mobilizing residual oil and improving overall recovery factor [1, 2, 3, 4] through four primary mechanisms: reducing interfacial tension, altering wettability, foam generation, and emulsification [5, 6, 7, 8]. Surfactants are complex organic compounds characterized by two distinct features: a water-attracting (hydrophilic) head and a water-repelling (hydrophobic) tail. This duality allows surfactants to orient themselves at oil-water interfaces forming micelles at a certain concentration [9, 10], known as the critical micelle concentration (CMC). A key parameter indicating the surfactant's solubilization in either oil or water and ability to form microemulsions is the hydrophilic-lipophile balance (HLB) [11]. [PERSON] (1948) [12] first classified microemulsions into Type II\(-\) (dispersed oil in water microemulsion), Type II+ (dispersed water in continuous oil), Type III (middle-phase microemulsion), and Type IV (single-phase microemulsion). [PERSON]'s ratio, introduced in 1954 [13], was used as a tool for analyzing the phase behavior in surfactant-oil-water systems, defined as the ratio of the interactions between the surfactant at the interface and the surrounding oil and water molecules. Considering that microemulsion phase behavior is a function of several features, including oil composition, surfactant structure, cosolvent, salinity, pressure, and temperature [14; 15; 16], HLB and [PERSON]'s ratio approach have limitations in surfactant formulation optimization [17; 18], requiring the understanding and prediction of complex microemulsion phase behavior. The quantitative prediction of microemulsion phase behavior is inherently complex and has been explored through various approaches, including empirical fitting models, lattice-based statistical thermodynamics, and free energy interaction frameworks. The earliest attempt to describe solute partitioning between two phases was proposed by [PERSON] (1930) [19]. This model was later modified and widely adopted for numerical simulations of enhanced oil recovery processes [2]. However, while these models effectively describe two-phase zones, predictions at the three-phase invariant point remain heavily dependent on empirical data, thus limiting their accuracy. [PERSON] et al. (1979) [20] introduced a correlation to optimize three-phase systems for oil recovery, considering variables such as salinity, temperature, oil composition, alcohol type and concentration, and surfactant type. This correlation was later defined as the hydrophilic-lipophilic difference (HLD) concept, which quantifies the chemical potential difference between oil and water to characterize surfactant affinity [21]. The HLD framework has been instrumental in quantifying interfacial tension (IFT) minimization [22]. Nevertheless, the application of the HLD model in phase behavior predictions is constrained by the limited degrees of freedom in its formulation. [PERSON] (2003) [23] expanded on the HLD concept by integrating it with the net-average curvature (NAC) model, creating an equation of state that incorporates the HLD database to predict microemulsion phase behavior. Despite its utility, this model relies on the assumptions of a constant characteristic length, as the optimum solubilization ratio is insensitive to temperature and pressure. Addressing these limitations, [PERSON] and [PERSON] (2016) [24] introduced a novel predictive phase-behavior model that incorporates a pressure-dependent factor into the HLD equation.