Carbon dioxide (CO
2
) sequestration in subsurface reservoirs is important for limiting atmospheric CO
2
concentrations. However, a complete physical picture able to predict the structure developing within the porous medium is lacking. We investigate theoretically reactive transport in the long-time evolution of carbon in the brine–rock environment. As CO
2
is injected into a brine–rock environment, a carbonate-rich region is created amid brine. Within the carbonate-rich region minerals dissolve and migrate from regions of high-to-low concentration, along with other dissolved carbonate species. This causes mineral precipitation at the interface between the two regions. We argue that precipitation in a small layer reduces diffusivity, and eventually causes mechanical trapping of the CO
2
. Consequently, only a small fraction of the CO
2
is converted to solid mineral; the remainder either dissolves in water or is trapped in its original form. We also study the case of a pure CO
2
bubble surrounded by brine and suggest a mechanism that may lead to a carbonate-encrusted bubble owing to structural diffusion.