Biogrout is a new method for soil reinforcement, which is based on microbial-induced carbonate precipitation. Bacteria and reactants are flushed through the soil, resulting in calcium carbonate precipitation and consequent soil reinforcement. Bacteria are crucially important in the Biogrout process since they catalyse the reaction. Hence, to control the process, it is essential to know where the bacteria are located. The bacteria are possibly in suspension but can also be adsorbed or fixated on the matrix of the porous structure. In this article, a model is derived for the placement of bacteria. The model contains three phases of bacteria: bacteria in suspension, adsorbed bacteria and fixed bacteria. An analytical solution is derived for instantaneous reactions between these three phases. The analytical solution is compared to numerical simulations for finite reaction rates. For the numerical simulations the standard Galerkin Finite Element Method is used.