A study was conducted on the effects of higher order autocatalysis in vertical slabs modelled with Brinkman's equation. As such, the results for higher order auto-catalysis for flows described with the Navier-Stokes equations and with Darcy's law were compared. This paper not only focuses on the transition to convection, but also studies the nonlinear regime near the onset of convection by solving numerically the reaction-diffusion equations, thus obtaining the increase of speed of the fronts as convection sets in.