Thermodynamic Properties of Supercritical CO₂/CH₄ Mixtures from the Virial Equation of State

Mixture virial coefficients to seventh order are presented for the system CO₂/CH₄ at four supercritical temperatures: 323.15, 373.15, 473.15, and 573.15 K. Values are evaluated via the Mayer sampling Monte Carlo method using a three-site TraPPE model for CO₂ and a one-site model for CH₄. The coefficients are used to compute seven thermodynamic properties (viz., compressibility factor, isothermal compressibility, volume expansivity, isochoric and isobaric heat capacities, Joule-Thomson coefficient, and speed of sound) as a function of mole fraction and density for these temperatures. Comparison is made with corresponding data in the literature as obtained by molecular dynamics simulation, covering densities up to about twice the critical density. Key conclusions are as follows, noting that some exceptions are observed in each case: (a) The virial equation of state (VEOS) to fourth or fifth order describes all properties to within the simulation uncertainty for densities up to at least the critical density, and the addition of terms up to seventh order extends this range considerably. (b) The accuracy of the VEOS is severely diminished for conditions approaching the critical point (the present work extends down to a reduced temperature of 1.06 for CO₂), and the study of the pure component behavior suggests the critical singularity blocks convergence for conditions at considerably higher temperatures, albeit at correspondingly higher pressures. (c) Comparison of the VEOS at different orders provides a reliable guide to its accuracy at a given order, so the VEOS can provide a self-assessment of its accuracy when independent data for comparison are unavailable. (d) The VEOS provides a good description of the Joule-Thomson coefficient, including the inversion point in particular. The third-order series is needed to obtain behavior that is qualitatively correct, and the addition of higher-order terms steadily improves the accuracy quantitatively. (e) Under conditions where the seventh-order series is converged, properties can be computed to a given precision with VEOS using much less computational effort in comparison to molecular simulation. (Figure Presented).