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In this work a detailed model to simulate the transient behavior of catalytic converters is presented. The model is able to predict the unsteady and reacting flows in the exhaust ducts, by solving the system of conservation equations of mass, momentum, energy and transport of reacting chemical species. The en-gine and the intake system have not been included in the simulation, imposing the measured values of mass flow, gas temperature and chemical composition as a boundary condition at the inlet of the exhaust system. A detailed analysis of the diffusion stage triggering is proposed along with simplifications of the physics, finalized to the reduction of the calculation time. Submodels for water condensation and its following evaporation on the monolith surface have been taken into account as well as oxygen storage promoted by ceria oxides.