The success of in situ bioremediation projects depends on the mixing of contaminants and nutrients in the presence of microbes. In this work, a pore-scale model is developed to simulate biomass growth that is controlled by the mixing of an electron donor and acceptor. A homogeneous packing of cylinders representing solid grains is used as the model two-dimensional porous medium. The system is initially seeded with microbes in computational cells located at grain-water interfaces. The solutes enter the system completely unmixed; each solute is input over one half of the inlet boundary. Solute mixing is controlled by molecular diffusion transverse to the flow direction, and solutes are biotransformed according to dual Monod kinetics only where biomass is present. Simulation of biomass growth requires calculation of the water flow field as well as transport and reaction of solutes. The lattice Boltzmann method is used to obtain the flow field. Transport and reaction of the solutes is modeled by a finite volume discretization of the advection-diffusion-reaction equation. Biomass is allowed to grow and spread by means of a cellular automata algorithm. Model parameters are systematically varied to understand their effects on biomass development. Base case parameter values are obtained from batch experiments reported in the literature and are modified to achieve agreement between simulation results and previously reported micromodel experimental results. The most significant mechanisms that control biomass development are shear strength of new biomass and solute degradation rates. The biomass growth model achieves good qualitative agreement with experimental results.