## 2 Materials and Methods
### Static Adsorption Experiments  
In order to investigate the effect of the polymer on the surfactant adsorption, static experiments were carried out for both the eutectic mixture and the surfactant alone. To that end, 1 g of crushed sandstone was added to 9 g of solution with concentrations of the eutectic ranging from 500 ppm to 10,000 ppm, or to the same mass of solution with surfactant concentrations ranging from 165.5 ppm to 3310 ppm (equalizing the concentrations of surfactant in the eutectic solutions). The salinity of all solutions was fixed at 0.5 wt% NaCl. All the samples were agitated for 24 h at 298.15 K and left for another 24 h to reach equilibrium. After this time, solutions were centrifuged at 1000 rpm for 30 min and then filtered. The final concentration of AOT was determined by UV-Vis spectrophotometry. Two of the most common models used to fit the adsorption isotherms of surfactants are the Langmuir and Freundlich isotherms, which describe the phenomena of adsorption with non-linear curves [24]. According to the Langmuir model, the adsorption occurs in a monolayer fashion and there is no interaction between molecules [26]. The isotherm is given by the following equation:  
\[q_{e}=q_{m}K_{L}\cdot\frac{C_{e}}{1+K_{1}C_{e}} \tag{5}\]in which \(q_{m}\) is the maximum amount of adsorbed surfactant (mg/g), \(K_{L}\) is the Langmuir equilibrium constant (L/mg), and \(C_{e}\) is the concentration of surfactant at equilibrium (mg/L). On the other hand, the Freundlich model describes multilayer adsorption [26] with the following equation:  
\[q_{e}=K_{F}C_{e}^{\frac{1}{2}} \tag{6}\]  
where \(K_{F}\) is the constant of Freundlich adsorption (L/g) and \(n\) is an empirical constant related to adsorption intensity: If 0.1 < 1/\(n\) < 0.5, adsorption will be favorable; if 0.5 < 1/\(n\) < 1, adsorption will be easily attainable; if 1/\(n\) > 1, adsorption will be almost impossible [25]. Oil Recovery  
Core-flooding experiments are definitive tests in order to check the efficacy of a formulation for EOR [12; 13; 22; 27; 28]. The core-flooding system used in this work consisted of a Hassler H00 021 0 core holder and two floXlab BTSP 500-5 piston pumps (equipped with an accurate pressure sensor), one for aqueous solutions and another for crude oil. Core holder and pumps were purchased from Vinci Technologies. Given the anionic character of the surfactant, a sandstone core of 3.84 cm diameter and 7.62 cm length was used for the test. A confining pressure of 50 bar was established using an Enerpac P142 manual hydraulic pump, and it was maintained at a value at least 35 bar higher than the flooding pressure in order to prevent hydraulic side flow. Experiments were performed at room temperature. The core was subjected to a vacuum for 24 h, and then it was flooded with brine (0.5 wt% NaCl). After 24 h, the rock was characterized by determining the pore volume (PV), using its dry and wet weights. To determine the absolute permeability (\(k_{w}\)) of the rock, the injection flow rate was varied between 1 mL/min and 10 mL/min, recording for each value the pressure difference between the inlet and outlet points (\(\Delta P\),Pa). The plot of the injection flow rate versus the pressure drop yields a straight line with a slope that enables the calculation of the absolute permeability of the brine using [PERSON]'s law [29]:  
\[q=\frac{\Delta P}{\eta}\cdot\frac{A}{L}\cdot k_{w} \tag{7}\]  
where \(q\) is the injection rate (m\({}^{3}\)/s), \(\eta\) is the dynamic viscosity of the brine (Pa-s), \(A\) is the cross-sectional area (m\({}^{2}\)), and \(L\) is the length of the core (m). After this characterization, the core was flooded with crude oil at an increasing injection rate, from 2 mL/min to 10 mL/min, until the effluent was free of water (oil cut > 99%). OOIP was determined as the difference between crude oil injected and crude oil recovered.