Mineral precipitation at interfaces between contrasting materials and porewaters decreases the local porosity and consequently reduces transport across the interface. The near-field of waste repositories usually contains reactive interfaces, and the long-term evolution of diffusive transport away from the waste across the near-field is of special interest in this context. Diffusion as well as further mineral reactions significantly slow down when complete porosity clogging is approached, such that any further development is difficult to detect in experiments. But ongoing diffusion, even if very limited, might be significant for relevant times of up to 1 million years. If clogging occurs in clay materials, experimental studies report a much stronger decrease in anion diffusion compared to that of cations or neutral species. Continuum-scale reactive transport codes can predict experimentally observed clogging, but rely on specific implementations based on conceptual assumptions. Typically, the codes calculate porewater-mineral reactions only within a single cell, and they neglect the physical contact of the clogging mineral in one cell with the porewater in an adjacent cell (no inter-cell reactions considered). This can lead to unrealistic model predictions if porosity approaches zero. For instance, neutral pH porewater is permitted to be in contact with clogging cement hydrates in the adjacent cell, and the implied dissolution of the high-pH minerals is not considered anymore. Thus, intrinsically reactive minerals can be converted erroneously into inert, relict phases by such models. We present a new approach that mimics inter-cell reactions. In doing so, clogging is substantially delayed, and no real steady state with the boundary conditions can be attained, in contrast to conventional approaches. Furthermore, we use a dual-porosity reactive transport approach that takes into account the electrostatic effects of charged clay surfaces on diffusion and precipitation, and apply it to concrete-clay interaction. No complete clogging of the pore space occurs, and the predictions well fit experimental data. Modelling studies that predict the separation of a reactive system into two domains by localised full porosity clogging, followed by separate internal equilibration of the domains, are widespread in the literature. This prediction is interpreted as a conceptual artefact of continuum-scale modelling, which should be avoided by allowing for reactions of completely clogged cells with adjacent porewater. For clays, the dual-porosity model may be a viable option in this respect.