Reactive transport calculations simulating the interaction between hyperalkaline solutions derived from the degradation of cement and potential host rocks for repositories for low- and intermediate-level radioactive waste have been performed. Two different cases are shown: (a) The example of the planned repository at Wellenberg and (b) the modeling of the GTS-HPF experiment at the Grimsel Test Site. The GIMRT code has been used for the simulations. Mineral reactions are described by kinetic rate laws. The reaction rates for the primary minerals are based on experimentally determined rates published in the literature and geometric considerations combined with measurements regarding mineral surface areas. Relatively fast rates for the secondary minerals have been used, so the results resemble the local equilibrium solution for these minerals. In both cases, the alteration of the rock and the precipitation of secondary phases cause a reduction in the permeability of the system, which would actually be beneficial for the performance of a repository. Mineral surface area controls, to a large extent, the amount of mineral alteration and the change in permeability.