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A mathematical model has been developed in order to support the design, engineering and testing of a membrane based biological air filter, removing and converting gas phase contaminants present within a closed environment, like manned space habitats, before they reach toxic concentrations. The configuration of the system is described by a gas phase, containing the contaminants, and a liquid phase, separated by membrane material, supporting a film of selected innocuous microorganisms in a near resting state, catabolizing the contaminants to inert materials, mainly carbon dioxide, water and salts. The process simulation and its results are discussed, considering the different diffusion and biochemical processes taking place inside the biological system.