The interaction between mineral reaction and mass transport in a rock can lead to reaction front instability and the development of channel-like voids. This phenomenon is studied with a two-dimensional model accounting for the nonlinear feedback between flow, reaction, and matrix porosity-permeability evolution. In our model we calculate the flow field in both the porous medium and the reaction-induced voids, using the Brinkman equation. While a linear analysis cannot determine the length scale of the channels which can develop in a typical geological system, our simulations indicate that the channel size is actually unique and well characterized. While the onset of instability is favored at a preexisting heterogeneity, the channel growth and orientation is governed by the global flow pattern, even in an initially heterogeneous system.