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. The generic model is further used to describe a diesel particulate filter coated with functionalities for selective catalytic reduction of nitrogen oxide emissions (SDPF). This dedicated model, as a part of a full diesel exhaust line, is combined with a passenger car vehicle and thermodynamic engine model. The whole system model is assessed in office PC simulation regarding result plausibility and computational performance during the New European Drive Cycle and a randomly assembled drive cycle. The real-time capability of the full model is demonstrated by running it on the NI VeriStand real-time simulation environment. The presented type of system model contributes to answer upcoming questions in the context of real driving emissions (RDE) by means of simulation.