The problem of solute transport in interacting ordered porous media is addressed by numerically solving the 2D Fokker-Planck equation using 4-step operator splitting. The subtle interplay between drift and diffusion is shown to result in a nontrivial dependence of solute transport kinetics on pore size. Depending on the strength of attraction to pore walls distinct regimes of pore size dependence of transport kinetics are found. The results suggest a decoupling of local dynamics from large-scale transport.