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An equation of state (EOS) explicit in Helmholtz free energy has been improved to calculate the PVTx and vapor–liquid phase equilibrium properties of CH 4 –CO 2 fluid mixture. This EOS, where four mixing parameters are used, is based on highly accurate EOSs recommended by NIST for pure components (CH 4 and CO 2 ) and contains a simple generalized departure function presented by Lemmon and Jacobsen (1999). Comparison with experimental data available indicates that the EOS can calculate both vapor–liquid phase equilibrium and volumetric properties of this binary fluid system with accuracy close to that of experimental data up to high temperature and pressure within full range of composition. The EOS of CH 4 –CO 2 fluid, together with the updated Gibbs free energy model of solid CO 2 (dry ice), is applied to calculate the CH 4 content ( x CH4 ) and molar volume ( V m ) of the CH 4 –CO 2 fluid inclusion based on the assumption that the volume of an inclusion keeps constant during heating and cooling. V m − x CH 4 diagrams are presented, which describe phase transitions involving vapor, liquid and CO 2 solid phases of CH 4 –CO 2 fluid inclusions. Isochores of CH 4 –CO 2 inclusions at given x CH 4 and V m can be easily calculated from the improved EOS. [ABSTRACT FROM AUTHOR]