The focus of this paper is the derivation of an effective model for biofilm growth in a porous medium and its effect on fluid flow. The starting point is a pore-scale model in which the local geometry of the pore is represented as a thin strip. The model accounts for changes in pore volume due to biomass accumulation. As the ratio of the width of the strip to its length approaches zero, we apply a formal limiting argument to derive a one-dimensional upscaled (effective) model. For a better understanding of the terms and parameters involved in the equations derived here, we compare these equations to a well-known core-scale model from the literature.