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When an engine is operated at a lean air-fuel (A/F) ratio, a lean NOx trap (LNT) (or lean NOx catalyst) is needed to increase the NOx conversion efficiency. The presence of sulfur in the fuel degrades the LNT NOx storage capacity and significantly reduces its NOx conversion efficiency. The sulfur degradation is reversible and requires maintaining a temperature of 650 °C at a rich A/F ratio condition (λ < 1.00) for a period of approximately 5 minutes to purge the trap. The desulfation method used here produces an exotherm in an LNT by sequential A/F modulation of the cylinders, resulting in exhaust flows of rich and lean mixtures and creating an exotherm in the LNT (Reference (18). SIMULINK/MATLAB software is used for modeling the temperature and the oxidant-reductant concentrations. The TWC and the LNT are divided into cells. The function of each cell is described using mass and energy balance equations for the gas and solid phases.