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Ammonia-selective catalytic reduction (SCR) systems have been introduced commercially in diesel vehicles, however catalyst systems with higher conversion efficiency and better control characteristics are required to know the actual emissions during operation and the emissions in random test cycles. Computational fluid dynamics (CFD) is an effective approach when applied to SCR catalyst development, and many models have been proposed, but these models need experimental verification and are limited in the situations they apply to. Further, taking account of redox cycle is important to have better accuracy in transient operation, however there are few models considering the cycle. Model development considering the redox reactions in a zeolite catalyst, Cu-ZSM-5, is the object of the research here, and the effects of exhaust gas composition on the SCR reaction and NH3 oxidation at high temperatures are investigated.