The aim of this project is the development and optimization of membrane biofilm reactor (MBfR) systems for the anaerobic fermentation of synthesis gas through the use of mathematical modelling and complementary experiments. The focus is on the development of biofilm models that enable reactor optimization and upscaling. Our investigations are based on a co-culture biofilm consisting of Clostridium (C.) autoethanogenum and C. kluyveri. This co-culture is capable of converting the carbon monoxide (CO) contained in synthesis gas into a mixture of _C4 and C6 _fatty acids (butyrate and caproic acid) and their corresponding alcohols (butanol and hexanol). We will develop mathematical models in 1D and 2D that represent this co-culture system and serve as design tools to optimize product yield in MBfRs. Special attention will be paid to the influence of different membrane module configurations and operating strategies. The models will also be designed to be applicable to other mono- or co-culture systems.