An accurate modelling of bio-electrochemical processes that govern Microbial Fuel Cells (MFCs) and mapping their behaviour according to several parameters will enhance the development of MFC technology and enable their successful implementation in well defined applications. The geometry of the electrodes is among key parameters determining efficiency of MFCs due to the formation of a biofilm of anodophilic bacteria on the anode electrode, which is a decisive factor for the functionality of the device. We simulate the bioelectrochemical processes in an MFC while taking into account the geometry of the electrodes. Namely, lattice Boltzmann methods are used to simulate the fluid dynamics and the advection-diffusion phenomena in the anode compartment. The model is verified on voltage and current outputs of a single MFC derived from laboratory experiments under continuous flow. Conclusions can be obtained from a parametric analysis of the model concerning the design of the geometry of the anode compartment, the positioning and microstructure of the anode electrode, in order to achieve more efficient overall performance of the system. An example of such a parametric analysis is presented here, taking into account the positioning of the electrode in the anode compartment.