Magnetic Resonance Imaging (MRI) and PGSE NMR studies have shown that it is necessary to consider heterogeneities in the porous structure over different lengthscales in order to be able to understand the relationship between structure and transport in porous solids. Moreover, the spatial distribution in pore structure is seen to influence strongly mass transfer processes occurring within the porous medium. The MRI studies described here have suggested that a fractal representation might be appropriate in describing heterogeneous porous systems. Numerical simulations have been performed of transport within Cluster-Cluster Aggregate (CCA) structures. A comparison of methods of simulating the diffusion process is presented. The results of the simulations are compared with MRI and PGSE NMR measurements of the tortuosity of commercial catalyst pellets. In the light of complementary nitrogen desorption and mercury porosimetry data, a multifractal description of porous media is also proposed in the form of a Composite CCA structure in which both the macroscopic heterogeneity associated with the pore-size distribution and the fractal characteristics of the microscopic pore structure itself are represented.