A deep geological repository is considered an appropriate option for disposal of radioactive waste containing long-lived radionuclides. Engineered barriers’ degradation and radionuclide transport strongly depend on the conditions in the repository. This work presents the assessment of the geochemical evolution in a radioactive long-lived intermediate-level waste disposal cell constructed in granite. The considered cell consists of cemented waste packages, cementitious backfill and several meters of host rock. Three abstracted reactive transport models of different complexity were developed: a 1D model and a 2D model considering transport by advection and diffusion and a 2D model with diffusive transfer only. The changes in the pH, the pore water composition and the materials’ mineralogical composition were observed. The modelling results indicate an increase in the pH in the disposal cell due to leaching of alkalis, which is followed by the dissolution of portlandite and the precipitation of calcite at the granite-vault backfill boundary. The obtained changes in the pH indicate that the geochemical alterations in the disposal cell proceed very slowly. Such a slow degradation could be the result of the formation of the higher pH zone upstream from the disposal tunnel. The advection–diffusion models in 1D and 2D geometries produced similar results. However, the 2D model also identified spatial peculiarities in the changes of the geochemical environment. Comparison of the pure diffusive case results with the advection–diffusion cases demonstrated that both processes are relevant in the analysed disposal cell.