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Abstract: This work reports the application of thermodynamic models, including equations of state, to binary (salt-free) CH4–H2O fluid inclusions. A general method is presented to calculate the compositions of CH4–H2O inclusions using the phase volume fractions and dissolution temperatures of CH4 hydrate. To calculate the homogenization pressures and isolines of the CH4–H2O inclusions, an improved activity–fugacity model is developed to predict the vapor–liquid phase equilibrium. The phase equilibrium model can predict methane solubility in the liquid phase and water content in the vapor phase from 273 to 623K and from 1 to 1000bar (up to 2000bar for the liquid phase), within or close to experimental uncertainties. Compared to reliable experimental phase equilibrium data, the average deviation of the water content in the vapor phase and methane solubility in the liquid phase is 4.29% and 3.63%, respectively. In the near-critical region, the predicted composition deviations increase to over 10%. The vapor–liquid phase equilibrium model together with the updated volumetric model of homogenous (single-phase) CH4–H2O fluid mixtures (Mao S., Duan Z., Hu J. and Zhang D. (2010) A model for single-phase PVTx properties of CO2–CH4–C2H6–N2–H2O–NaCl fluid mixtures from 273 to 1273K and from 1 to 5000bar. Chem. Geol. 275, 148–160), is applied to calculate the isolines, homogenization pressures, homogenization volumes, and isochores at specified homogenization temperatures and compositions. Online calculation is on the website: http://www.geochem-model.org/. [Copyright &y& Elsevier]