This study reports the high pressure phase transition data for both methane and carbon dioxide and two large protic ionic liquids: N-methyl-2-hydroxyethylammonium propanoate [m-2HEA] [Pr] and bis(2-hydroxyethyl) ammonium butanoate [BHEA] [Bu]. The experimental data were obtained using the static-synthetic visual method by a variable-volume cell unit. The apparatus and experimental methodology were validated by methane + N-methyl-2-hydroxyethylammonium propanoate equilibrium data. The low deviation between the data indicates the experimental data is consistent with previous literature. Structure and purity of ILs were confirmed by FT-ER spectroscopy, H-1 and C-13 NMR studies. Water contents were measured by Karl Fischer volumetric measurements. NMRs and water contents analyses were performed on samples collected before and after the experiments. The phase transitions were classified as bubble points and studied at five temperatures from 313.1 to 353.1 K and pressures up to 20 MPa. Experimental data were correlated using the three-parametric Redlich Kwong - Peng Robinson equation of state (RKPR-EoS) coupled to mixing rules van der Waals type, cubic regarding the composition, and temperature dependence for the interaction energy parameter (CMR-T). Henry's law constants and ideal CO2/CH4 selectivities were calculated from this model and compared to other as ones.