Abstract: In order to accurately apply the state equation to confined spaces, the thermophysical properties and phase behavior of CO₂ and its mixtures in confined spaces have been systematically investigated by extending the Peng-Robinson state equation. The traditional PT equation of state is modified by introducing the interaction between molecules and walls and the capillary effect. Combining the experimental data and molecular simulation results, a critical migration model based on the size of nano-aperture and molecular size is developed to describe the migration phenomenon of critical characteristics. Based on the established equation of state model combined with the critical shifting model, the variation of interfacial tension with temperature, pressure, and nanochannel size in CO₂-nC₁₀ and CO₂-CH₄ binary hybrid systems was studied. It is found that the predicted value of the modified PT equation of state is in good agreement with the experimental data. The expanded equation of state shows high accuracy in predicting the thermophysical properties and phase behavior of CO₂ and hydrocarbon binary mixed systems in nanochannels. The new model provides a reliable theoretical tool for understanding the phase behavior of the fluid at the nanoscale, and contributes to a deeper understanding of the thermophysical properties and phase behavior of CO₂ and its mixtures in confined space.