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The paper presents a mathematical model for the simulation of the operational characteristics of the trap during transient operation, based on trap inlet conditions of the exhaust gas and trap history. The model incorporates (a) the formulation of flow conditions in the trap (b) the fundamental mass and energy balance of the system (c) the formulation of the oxidation process through chemical kinetics and (d) the description of mass and heat transfer conditions, including the possibility for calculation of trap operation during both particulate accumulation and regeneration phases. The major output of the model comprises ceramic wall and exhaust gas temperature fields in the trap, as functions of time, as well as the loading level of the trap. The application of the simulation model clarifies the critical importance of the wall temperature at trap outlet and forecasts the failure probability of the ceramic material due to overheating, under specific conditions at trap inlet.