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This study is focused on the detailed examination of the combustion properties and kinetic analysis of a cellulose acetate fibrous bundle (CAFB), separated from used cigarette filters. It was shown that the faster rate of CAFB heating allows a large amount of heat to be supplied to a combustion system in the initial stages, where the increase in heating rate has a positive response to ignition behavior. The best combustion stability of CAFB is achieved at the lowest heating rate. Through the use of different kinetic methods, it was shown that combustion takes place through two series of consecutive reaction steps and one independent single-step reaction. By optimizing the kinetic parameters within the proposed reaction models, it was found that the steps related to the generation of levoglucosenone (LGO) (by catalytic dehydration of levoglucosan (LG)) and acrolein (by breakdown of glycerol during CAFB burning—which was carried out through glycerol adsorption on a TiO2 surface in a the developed dehydration mechanism) represent rate-controlling steps, which are strongly controlled by applied heating rate. Isothermal predictions have shown that CAFB manifests very good long-term stability at 60 °C (which corresponds to storage in a sea shipping container), while at 200 °C, it shows a sudden loss in thermal stability, which is related to the physical properties of the sample. [ABSTRACT FROM AUTHOR]