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The present work introduces an extended particulate filter model focusing on capabilities to cover catalytic and surface storage reactions and to serve as a virtual multi-functional reactor/separator. The model can be classified as a transient, non-isothermal 1D+1D two-channel model. The applied modeling framework offers the required modeling depth to investigate arbitrary catalytic reaction schemes and it follows the computational requirement of running in real-time. The trade-off between model complexity and computational speed is scalable. The model is validated with the help of an analytically solved reference and the model parametrization is demonstrated by simulating experimentally given temperatures of a heat-up measurement. The detailed 1D+1D model is demonstrated in a concept study comparing the impact of different spatial washcoat distributions.