Carbon capture and storage (CCS) technologies are an important step to mitigate CO₂ emissions. This study focuses on CO₂ capture from biomass combustion in fluidized bed boilers using a vacuum pressure swing adsorption (VPSA) process. A pilot-scale VPSA unit was used to evaluate the dynamic adsorption behavior of zeolite 13X and clinoptilolite under realistic operating conditions. Moreover, a simplified one-dimensional isothermal mathematical model of a fixed-bed adsorption column was developed to simulate breakthrough curves to validate whether the model reproduces the observed experimental trends. Experimental results confirmed that fresh zeolite 13X exhibited the highest CO₂ adsorption capacity, while clinoptilolite showed moderate uptake. For both sorbents, a decrease in derived adsorption capacity was observed after prior use. The developed mathematical model successfully reproduced the experimental breakthrough curves, achieving coefficients of determination (R²) up to 0.99 and percentage fit (%Fit) values close to 94% for fresh sorbents, while lower correlations were observed for used sorbents. The model reliably captured the breakthrough curves, validating its applicability for process prediction. These results highlight the effectiveness of combining experimental measurements with modeling to assess sorbent performance and guide further optimization of VPSA processes under realistic flue gas conditions.