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The increasingly restrictive legislation on pollutant emissions is involving new homologation procedures driven to be representative of real driving emissions. This context demands an update of the modelling tools leading to an accurate assessment of the engine and aftertreatment systems performance at the same time as these complex systems are understood as a single element. In addition, virtual engine models must retain the accuracy while reducing the computational effort to get closer to real-time computation. It makes them useful for pre-design and calibration but also potentially applicable to on-board diagnostics purposes. This paper responds to these requirements presenting a lumped modelling approach for the simulation of aftertreatment systems.