Phase equilibria for the mixtures of the deep eutectic solvent L-menthol + thymol plus CO2 at high pressure

•The menthol + thymol DES can be dissolved in supercritical CO2 up to ca. yDES = 0.05 at 35–60 °C and 200 bar.•CO2 can also be dissolved in this DES in appreciable quantities and the solubility decreases with temperature.•The mutual solubility of DES and CO2 is lower than that of the components separately.•The phase behaviour of the DES + CO2 system is determined by the hydrogen bonds between menthol and thymol.•The Peng-Robinson Equation of State can describe the main features of the binary and ternary systems.