Pore-size controlled solubility (PCS) is incorporated into continuum equations for fluid transport and porosity evolution. The physical properties of a porous domain, in particular pore-size, can modify the effective solubility of minerals, allowing highly supersaturated fluids to exist within submicron-scale pores of rocks; when fluid flows from small pores into larger ones, or vice versa, precipitation or dissolution may occur. Using numerical simulations, we demonstrate that the PCS mechanism can account for the filling of large pore spaces during transport though a heterogeneous rock matrix. Furthermore, depending on flow and initial conditions, the steady state porosity patterns that develop may be heterogeneous. The mechanism is expected to be of significance during diagenesis and fracture mineralization.