Optimal distributor networks in porous catalyst pellets. I. Molecular diffusion

The effect of introducing a network of distributor channels in a nanoporous catalyst pellet was studied. The diffusivity in the distributor channels is orders of magnitude larger than in the nanoporous material itself. Introduction of distributor channels leads to an increasing volume-averaged diffusivity but a decreasing amount of catalytically active material per unit volume. This implies that, to maximize yield, there is an optimal volume fraction occupied by the distributor network and an optimal way to distribute and connect this fractional volume in a catalyst pellet of a given geometry and volume. It was found that a distributor network consisting of a large number of straight channels with a position-dependent channel diameter, and without branches, is the global optimum for all 2D and 3D catalyst pellet geometries without corners (spheres, infinite cylinders, infinite sheets, etc.) when there is pure molecular diffusion in the distributor channels and a first-order reaction in the catalyst. The volume fraction occupied by the distributor channels should always be less than 0.5. Moreover, the difference between the global optimum and a network of channels with constant diameter is negligible with respect to the yield. In practice, the latter is preferred because of easier synthesis and an almost identical yield compared to the former. When only the skin of a catalyst pellet contributes to the yield, these results also apply to geometries with corners (squares, cubes, etc.) because effects of corners are insignificant.