A new methodology has been developed to design non-isothermal, non-adiabatic heterogeneous catalytic fixed bed and tubular reactors with optimal temperature profiles inside a reactor. Catalyst characteristics such as pellet diameter, shape and activity distributions inside a pellet are considered simultaneously for reactor design. Various types of non-uniform activity distributions inside a pellet are modelled and optimised for the maximisation of an objective such as yield or selectivity. Dirac-delta, layered and general non-uniform distribution profiles such as egg-shell, egg-yolk and middle peak distributions are applied for the reactor design. The research demonstrates that different catalyst distribution profiles can approach the optimum performance. Whilst it is known that the Dirac-delta profile (and its step-function equivalent) always gives the best performance for clean catalyst, other profiles can approach this performance and might offer advantages in catalyst manufacture and under degraded conditions. A profile-based synthesis approach is applied to generate various shapes of activity profiles for multiple sections along the reactor during the optimisation of non-uniform catalyst pellets. A case study with the ethylene oxidation process illustrates that the catalyst characteristics, such as activity distribution profiles inside a pellet, sizes and shapes can be manipulated to control the temperature through the reactor very effectively, leading to significant improvements in selectivity or yield. The non-uniform catalyst pellet is further applied to various reactor configurations such as inert mixing and We stream distributions. This work is the first to consider all of these effects simultaneously. (C) 2004 Elsevier Ltd. All rights reserved.