The spatial structure present in particulate and porous environments is implicated in the maintenance of the high levels of microbial diversity that are often observed in these habitats. However, the issue of how preferential flow in porous media might influence microbial growth, how microbial growth alters flow, and the effect these might have on creating physical and chemical heterogeneity that promotes high levels of microbial diversity have not been studied extensively. Here we present a spatially structured metapopulation model on a square lattice that simulates flow, growth, and nutrient depletion phenomena that occur in fluid-saturated particulate environments. This model uses an innovative application of an electromagnetic resistor manifold analogy to calculate flow perpendicular to the main flow path through the lattice. The approach used in this model provides a novel way to explore the effect of fine-scale heterogeneity in nutrient levels, fluid flow, and competitive dynamics in particulate environments. The model allowed us to explore competitive outcomes as model parameters were varied. The development of preferential flow paths due to biomass-mediated resistance, microhabitats with different nutrient levels, and surface area for attachment provide the setting for extended coexistence. The results from the model demonstrated that strains that compete for the same growth limiting nutrients but differ in terms of their Monod growth parameters can coexist for extended periods of time due to spatial heterogeneity. Differences in nutrient concentration and surface area for biofilm attachment were found to be equally important in permitting coexistence.