Display omitted •Solubility of oleic acid in supercritical CO2 was measured.•The solubility of the sunflower oil blend with oleic acid in scCO2 was measured.•The critical properties values was crucial to well correlate the data from the phase equilibrium.•The modeling using Peng-Robinson equation was unable to represent the ternary system. To evaluate the selectivity of supercritical carbon dioxide (scCO2) as a solvent to deacidify vegetable oils, the solubility of oleic acid and of a mixture of oleic acid and refined sunflower oil in scCO2 was measured. Sunflower oil was adopted as a pseudo-pure component and the phase equilibrium of ternary and binary systems were thermodynamically modeled by the Peng-Robinson equation of state with classical mixing rule. The values of the estimated and/or adopted critical properties in modeling thermodynamics were shown to be of great influence on the quality of data correlation. Although correlating data from binary systems is possible, the modeling was incapable of satisfactorily predicting the behavior of the phase equilibrium of the ternary system. The large deviations observed may derive from the presence of specific intermolecular interactions between the components of these systems that were not considered in this type of modeling.