Reactive flows inside porous media play an important role in a number of geophysical and industrial processes. Here, we present three-dimensional experimental measurements on how precipitation and flow patterns change with the flow rate inside a model porous medium consisting of monodisperse glass beads. The sample is initially filled with an aqueous solution of sodium carbonate into which a solution of barium chloride is injected at a constant flow rate. Upon contact and reaction, the two reactants produce water-insoluble barium carbonate which precipitates onto the glass beads. This precipitate then modifies the flow morphology which in turn changes the spatial distribution of the precipitate. We discuss the influence of the flow rate on the morphology of the flow pattern and demonstrate that neither viscous fingering nor the Rayleigh–Taylor instability have any significant influence in our model system.