＇Amorphous＇ porous catalysts and catalyst supports have a rough internal surface. Small-angle and wide-angle X-ray scattering results confirm the original but inconclusive suggestion from adsorption experiments that this surface is often fractal on molecular scales. Not only does this imply that the accessible surface area depends on the size of the molecules moving through the pores, but there also exists an accessibility distribution along the surface. Transport and reaction processes may therefore depend on surface roughness, in a way that can be quantified using fractal geometry. The effect of fractal surface roughness on Knudsen diffusion is discussed. An analytical expression for the Knudsen diffusivity is derived and the residence time distribution of the molecules is obtained from Monte-Carlo simulations. The equations for diffusion and reaction in fractal pores and in porous catalysts with a fractal internal surface are given. Practical examples -vinyl acetate production and the catalytic reforming of naphtha - illustrate the significant influence of fractal roughness on product yields and distributions of industrial processes, from the microscale up to the observable reactor scale. This indicates how conversions and selectivities may be increased by modifying the catalyst surface morphology. (C)1999 Elsevier Science B.V. All rights reserved.