We consider a coupled system of parabolic variational inequalities for a model of biofilm growth and nutrient consumption in porous media at \the pore-scale. The problem involves constraints on the concentration of the biofilm, and possibly on the nonnegativity of the nutrient. In the talk, we first discuss the well-posedness of the problem. Then, we approximate the system by using finite element method in space, and backward Euler in time. We use semi-smooth Newton method to solve the constrained problem with a nonlinear complementarity condition. We show a proof of convergence and simulations in 2D and 3D. Furthermore, we discuss a mixed finite element approach of the system.