A process-oriented thermodynamic framework for gas–solid equilibrium under alternative expansion constraints in supersonic separation systems

Carbon capture and storage (CCS) processes are of utmost importance in the hard-to-abate industry sector; therefore, supersonic separators are increasingly investigated as compact process units for gas treatment, where rapid expansion can induce solid CO₂ formation. In such systems, temperature is not an independent variable but results from the imposed expansion constraint. In this work, a unified thermodynamic framework for gas–solid equilibrium is proposed, integrating PT, PH, and PS flash formulations. This work aims to ensure numerical robustness and thermodynamic consistency under alternative process constraints representative of supersonic expansion. The framework is applied to multicomponent mixtures representative of turbine exhaust gases, allowing the determination of CO₂ solid formation envelopes relevant to separator design. The proposed framework enables rapid evaluation of operating conditions associated with effective separation regions, supporting preliminary design, process screening, and operational analysis of compact supersonic separation systems. Results demonstrate that thermodynamics are consistent across alternative flash specifications, supporting the use of the proposed methodology as a reliable thermodynamic module for process-oriented modeling and future optimization of separation and purification technologies for offshore and energy-intensive applications.