In this work we focus on further understanding reactive transport in carbonate rocks, in particular limestones characterized by a bimodal pore size distribution. To this end, we performed injection experiments with CO2-saturated water on a sample of Euville limestone and monitored the experiments with a medical CT scanner. Microscanner imaging was performed before and after alteration. Experiments showed that permeability increased by nearly two decades due to the alteration process. This increase could be attributed to the formation of a preferential dissolution path visualized on the CT images. Microscanner images show that preferential dissolution areas are characterized by the presence of numerous enlarged macropores. The preferential dissolution path created therefore retains a porous structure and does not correspond to a wormhole-type channel. To provide further knowledge of the small-scale physics of reactive transport, we performed Lattice-Boltzmann simulations of flow in a numerically generated model 2D porous medium having geometrical and topological features designed to approach Euville limestone. We showed that the fluid velocity increased in nearly percolating paths of macropores. Considering the experiments, this means that the CO2-saturated water starts to enter high-velocity zones earlier than low-velocity zones, inducing an earlier onset of the alteration process and a more pronounced local dissolution. However, numerical results showed that the alteration of non-connected macropores leads to an increase of permeability much smaller than the experimentally observed one. To explain this fact we used effective medium modelling that permits predicting the variation in permeability as a function of the fraction of macropores and consequently as a function of alteration. It proved that as long as there is no alteration-induced percolating path consisting of macropores, the increase in permeability is relatively low as shown by the Lattice-Boltzmann simulations. An increase in permeability of several orders of magnitude is only observed when the macroporosity is close to the percolation threshold. This fact is in accordance with the experimentally observed results.