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Research activities in the development of reliable computational models for aftertreatment systems are constantly increasing in the automotive field. These investigations are essential in order to get a complete understanding of the main catalytic processes which clearly have a great impact on tailpipe emissions. In this work, a 1D chemical reaction model to simulate the catalytic activity of a Pd/Rh Three-Way Catalyst (TWC) for a Natural Gas heavy-duty engine is presented. An extensive database of tests carried out with the use of a Synthetic Gas Bench (SGB) has been collected to investigate the methane abatement pathways, linked to the lambda variation and oxide formation on palladium surface. Specific steady-state tests have shown a dynamics of the methane conversion even at fixed λ and temperature conditions, essentially due to the Pd/PdO ratio.