By limiting crystal size, nanometer-scale pores in geological media can control the effective solubility of mineral phases. Since mineralization is determined by solubility, this mechanism, termed pore-size controlled solubility (PCS), is potentially significant for the evolution of porosity and permeability during reactive transport. To demonstrate the potential impact in geological systems, we developed a new one-dimensional numerical model, using a moving boundary condition, to describe the mineralization in the rock matrix adjacent to a pressure solution (stylolite) interface. In the model, the porous domain initially possesses a polymodal pore size distribution, although this is allowed to change in response to mineral precipitation, and the evolution of porosity and pore size distributions was simulated both for systems with constant mineral solubility and for systems in which solubility was pore size controlled. Consistent with field observations, total porosity decreases near the stylolite interface in all the simulations. However, in systems with constant solubility, nanometer-scale pores close rapidly because of their high specific surface area; by contrast, when the PCS mechanism is included in the model, transient bimodal pore size distributions develop, with nano-pores remaining open throughout the simulation. Our simulations suggest that the combination of the PCS mechanism with kinetic models for mineral precipitation can account for the bimodal pore size distributions observed in sedimentary carbonate rocks. Furthermore, while the mechanism is unlikely to affect rocks such as sandstones, PCS can impact carbonate and clay-bearing sediments, which typically possess high levels of submicron porosity.