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A two-dimensional numerical model describing the ammonia based SCR-process on vanadia-titania catalysts is presented. The model is able to simulate coated and extruded monoliths. For the determination of the intrinsic kinetics of the various NH3-NOx reactions, unsteady microreactor experiments were used. In order to account for the influence of transport effects the kinetics were coupled with a fully transient two-phase 1D+1D monolith channel model. The model has been validated extensively with laboratory data and engine test bench measurements. After validation the model has been applied to calculate catalyst NOx conversion maps, which were used to define catalyst sizes. Additional simulations were conducted studying the influence of cell density and NH3-dosage ratio.