In order to fury understand the operation of porous catalyst pellets in a reactor it is necessary to determine the influence of the complex structure of the pore space and void/solid matrix interface on the various chemical and physical processes taking place within the pellet. Recent developments in the formulation of structural representations of porous pellets that are more accurate over a wider range of lengthscales than in previous work have been discussed. A new model of interpretation for deuterium NMR data on the motion of benzene molecules on the surface of amorphous catalyst supports has been developed. The model, based on fractal concepts, has shown that the pre-exponential factor for an activated jump-type motion model correlates quantitatively with the degree of surface structural disorder, as characterised by the surface fractal dimension. This finding suggests a new way of measuring surface fractal dimension. This model has then been used to confirm the supposition that surface diffusing molecules effectively probe larger lengthscales as the temperature is increased. (C)1999 Elsevier Science B.V. All rights reserved.