The combination of the lattice Boltzmann Shan-Chen pseudo-potential method for multiphase fluids (Shan & Chen, Phys. Rev. E 47, 1993, 1815 and a grey or partial bounce back lattice Boltzmann algorithm for effective media (Walsh et al, Comp. & Geosci. 35, 2009, 1186, is demonstrated for application to liquid-vapour fluid dynamics in porous media with porosity spanning a very wide range of length scales. Liquid / vapour distributions in cellular like structures with cell walls of reduced permeability are seen to follow expectation.