In this paper we present a methodology for modelling of local reaction-transport processes in a digitally reconstructed, porous heterogeneous catalyst. Microkinetics of the CO oxidation on Pt/gamma-Al2O3 with an explicit consideration of the surface-deposited species has been employed in the model. The reaction takes place on the Pt sites located on the gamma-Al2O3 surface and in the meso-pores, simultaneously with the transport of gaseous reaction components. Several 3D porous structures have been digitally reconstructed from the typical scanning electron microscopy images of Pt/gamma-Al2O3 catalytic washcoats of monoliths. Typical dependences of overall CO reaction rate and the effectiveness factor on the temperature and properties of the porous Pt/gamma-Al2O3 structure (washcoat macro-porosity, characteristic size of the macro-pores, the size of gamma-Al2O3 particles, noble metal loading and distribution) are evaluated. Non-monotonous dependence of the averaged reaction rate on the macroporosity of the washcoat is observed. It is shown that the dependence of the average reaction rate on the amount of Pt in the porous layer is strongly non-linear under certain conditions and the spatial distribution of the catalytically active sites within the porous structure of the support controls the effectiveness factor to a significant extent. In the combination with semi-deterministic methods of the reconstruction (simulation of the catalyst preparation process) the results can be used for the optimisation of the washcoat structure. The methodology presented in this work is also a contribution to the development of multi-scale simulation techniques whereby volume-averaged parameters calculated at one spatial scale are used as input values for simulations at a larger scale. (c) 2006 Elsevier Ltd. All rights reserved.