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A numerical model describing the ammonia based SCR process of NOX on zeolite catalysts is presented. The model is able to simulate coated and extruded monoliths. The development of the reaction kinetics is based on a study which compares the activity of zeolite and vanadium based catalysts. This study was conducted in a microreactor loaded with washcoat powder and with crushed coated monoliths. A model for the SCR reaction kinetics on zeolite catalysts is presented. After the parameterization of the reaction mechanism the reaction kinetics were coupled with models for heat and mass transport. The model is validated with laboratory data and engine test bench measurement data over washcoated monolith catalysts. A numerical simulation study is presented, aiming to reveal the differences between zeolite and vanadium based SCR catalysts.