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The aim of the present study is the simulation of the dispersion of natural gas issuing from the silencer of compressor stations during vent operations. The objective is to analyze the dispersion of the gas emitted under different conditions of mass flow rate at the exit and ambient cross-flow velocity. We have considered a silencer with an upper cover to protect it from the rain and the fall of objects. The influence of the upper cover of the silencer on the dispersion of natural gas has also been studied, and non-dimensional approaches of the model have been proposed to simplify the problem. Seven different cases have been solved, using two models: a 3D model based on the commercial code FLUENT, and a simplified quasi-one-dimensional model. The results obtained in both cases have been compared, and the range of validity of the one-dimensional model in non-dimensional form has been discussed.