Reactive infiltration instability (RII) drives the development of many natural and engineered flow systems. These are encountered e.g. in hydraulic fracturing, geologic carbon storage and well stimulation in enhanced oil recovery. The surface area of the rocks changes as the pore structure evolves. We combined a reactor network model with grey scale tomography to seek the morphological interpretation for differences among geometric, reactive and apparent surface areas of dissolving natural porous materials. The approach allowed us to delineate the experimentally convoluted variables and study independently the effects of initial geometry and macroscopic flowrate. Simulations based on North Sea chalk microstructure showed that geometric surface not only serves as the interface for water-rock interactions but also represents the regional transport heterogeneities that can be amplified indefinitely by dissolutive percolation. Hence, RII leads to channelization of the solid matrix, which results in fluid focusing and an increase in geometric surface area. Fluid focusing reduces the reactive surface area and the residence time of reactants, both of which amplify the differences in question, i.e. they are self-supporting. Our results also suggested that the growing and merging of microchannels near the fluid entrance leads to the macroscopic fast initial dissolution of chemically homogeneous materials.