The behaviour of a reacting, viscous flow inside the complex geometry of a fixed-bed reactor has been studied by means of a lattice Boltzmann automata (LBA). In particular, two tasks have been investigated in detail. The geometrical structures of the fixed bed have been generated with a Monte-Carlo method. This allows to simulate very efficiently the placement of randomly packed spheres in a cylinder and to obtain detailed information of statistical properties, such as the voidage distribution. This geometrical information is the base for the subsequent numerical flow simulation using a lattice Boltzmann automata. This approach allows to predict the local fluid velocity distribution in the bed as well as the transport and reactions of chemical species taking into account the effect of heterogeneous catalysis. Thus, detailed information can be provided for the diffusion/dispersion effects around catalytic particles and ensembles of spheres. It is shown that this approach allows to improve the understanding of the underlying transport and reaction phenomena in these reactors and to obtain a reliable database for their operating behaviour and design.