In this paper, we study a Darcy‐scale mathematical model for biofilm formation in porous media. The pores in the core are divided into three phases: water, oil, and biofilm. The water and oil flow are modeled by a generalized version of Darcy's law, and the substrate is transported by mechanical dispersion, diffusion, and convection in the water phase. Initially, there is biofilm on the pore walls. The biofilm consumes substrate for production of biomass and modifies the pore space, which changes the rock permeability. The model includes detachment of biomass caused by water flux and death of bacteria, and it is implemented in the MATLAB Reservoir Simulation Toolbox (MRST). We discuss the capability of the numerical simulator to capture results from laboratory experiments. We perform a novel sensitivity analysis based on sparse‐grid interpolation and multiwavelet expansion to identify the critical model parameters. Numerical experiments using diverse injection strategies are performed to study the impact of different porosity/permeability relationships in a core saturated with water and oil.