Determining interaction parameter for equations of state (EOS) of water – amines systems are crucial to develop accurate models in chemical engineering processes. The binary system of N-methyldiethanolamine (MDEA) and water in biogas purification was evaluated using both φ – φ and γ – φ approaches, classic Peng–Robinson with the empirical “non-random” mixing rule and Peng–Robinson with the Wong-Sandler mixing rule EOS to optimize pure components acentric factor, ω, and binary interaction parameters, 𝑘𝑖𝑗. The interaction parameters 𝑢𝑖𝑗 from EOS that incorporate UNIQUAC model, such as γ – φ approach and Wong-Sandler mixing rule were optimized as well. These parameters were evaluated using a bubble pressure algorithm, MATLAB coding and minimization of objective functions related to absolute average deviation, AAD, between experimental and calculated data at different temperatures. The calculated ω of water, CO2 and MDEA were 0.3275, 0.2039 and 1.0133 respectively with lower AAD than literature values. The 𝜑−𝜑 approach classic Peng–Robinson with Wong – Sandler mixing rule EOS was better suited for the MDEA – H2O binary, resulting in as 𝑢120=−234.2841, 𝑢12𝑇=1.0499, 𝑢210=266.4326, 𝑢21𝑇=0.1966, 𝑘𝑖𝑗=−0.0715, with vapor pressure AAD% = 6.57% and composition AAD% = 17.51%. Due to the highly non-ideal nature of the CO2 – H2O binary system, neither φ – φ or γ – φ approaches using the selected EOS resulted in accurate vapor – liquid equilibrium (VLE) bubble point pressure diagrams.