© 2014 The Author(s) Published by the Royal Society. All rights reserved. The stability of convection in an anisotropic porous medium, where the solute concentration is assumed to decay via a first-order chemical reaction, is studied. This is a simplified model for the interactions between carbon dioxide and brine in underground aquifers; the instability of which is essential in reducing reservoir mixing times. The key purpose of this paper is to explore the role porous media anisotropy plays in convective instabilities. It is shown that varying the ratio of horizontal to vertical solutal diffusivites does not significantly affect the behaviour of the instability. This is also the case for changes of permeability when the diffusion rate dominates the solute reaction rate. However, interestingly, when the solute reaction rate dominates the diffusion rate a change in the permeability of the porous material does have a substantial effect on the instability of the system. The region of potential subcritical instabilities is shown to be negligible, which further supports the novel instability behaviour.