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A novel design for the energy storage by adsorption-absorption for the partial CO2 capture of the energy supply buildings with fixed CO2 emission is proposed. The new design successfully utilizes the attainment of the low energy consumption and implements energy storage through adsorption part, overcoming the deficiencies of poor selectivity through absorption part. Numerical approaches have been developed for modeling the adsorption-absorption procedure, while attaining satisfactory agreement with experimental data. The adsorption process is modeled based on the finite volume method, and the absorption process is simulated based on the double-film theory and the rate-based model. The issue of operating parameters upon system assessments has received considerable critical attention by numerical implementations. The results show that the mass fraction of CO2 in the flue gas has been increased to 39.0%. The comprehensive enhancement effects are instrumental at a height of 20 m in the absorption tower. As the CO2 concentration of the flue gas increases from 5.0% to 20.0%, the absorbent flow, absorber diameter, and reboiler specific load decrease by 13.0%, 42.1%, and 16.6%, in respective. The present analysis and design will provide guidance and gain fresh prominence with advantages in the CO2 capture and purification.