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A low-temperature process involving the formation of dry ice to separate carbon dioxide (CO2) from a CO2-containing mixture is proved to be energy efficient. An accurate prediction of the phase equilibria of the components is necessary for the development of such a process. The current work extended a model for simultaneous calculation of phase stability and flash computations for a multicomponent and multiphase system to a system involving the formation of dry ice. This study derived composition-independent correlations of solid–vapor and solid–liquid and introduced these correlations into a Gibbs energy minimization algorithm with the stability variable of phase in predicting the phase diagram of pure CO2and the solid–fluid-phase equilibria of a methane (CH4)–CO2binary mixture. A CO2solid-phase equation of state (EoS) based on Gibbs free energy and a fluid-phase EoS based on Helmholtz free energy were used in this study. Experimental data were compiled for a CH4–CO2mixture involving the solid–vapor, solid–liquid, and solid–liquid–vapor equilibria. In general, modeling results agreed with the experimental data, and discrepancies between the modeling and experimental data have been well identified and discussed. The solid–vapor-phase equilibrium region that can be used for low-temperature CO2separation was suggested.