A 3D computational fluid dynamics (CFD) model with bioelectrochemical reactions of a microbial fuel cell (MFC) has been developed and applied to the anode-cathode arrangement of a MFC. Results show, that the dominating mass transfer mechanism is pure diffusion. Several geometrical modifications in order to enhance flow and mass transfer to the anode didn't show a large effect due to the very low flow velocity. On the other hand reducing the distance between anode and cathode seems promising to increase the electrical current per volume of the MFC.