A new reactor concept is studied for highly endothermic heterogeneously catalysed gas phase reactions at high temperatures with rapid but reversible catalyst deactivation. The reactor concept aims to achieve an indirect coupling of energy necessary for endothermic reactions and energy released by exothermic reactions, without mixing of the endothermic and exothermic reactants, in closed-loop reverse flow operation, Periodic gas flow reversal incorporates regenerative heat exchange inside the reactor. The reactor concept is studied for the coupling between the non-oxidative propane dehydrogenation and methane combustion over a monolithic catalyst. Two different reactor configurations are considered: the sequential reactor configuration, where the endothermic and exothermic reactants are fed sequentially to the same catalyst bed acting as an energy repository and the simultaneous reactor configuration, where the endothermic and exothermic reactants are fed continuously to two different compartments directly exchanging energy. The dynamic reactor behaviour is studied by detailed simulation for both reactor configurations. Energy constraints, relating the endothermic and exothermic operating conditions, to achieve a cyclic steady state are discussed. Furthermore, it is indicated how the operating conditions should be matched in order to control the maximum temperature. Also, it is shown that for a single first order exothermic reaction the maximum dimensionless temperature in reverse flow reactors depends on a single dimensionless number. Finally, both reactor configurations are compared based on their operating conditions. It is shown that only in the sequential reactor configuration the endothermic inlet concentration can be optimised independently of the gas velocities at high throughput and maximum reaction coupling energy efficiency, by the choice of a proper switching scheme with inherently zero differential creep velocity and using the ratio of the cycle times. In this first part, both the propane dehydrogenation and the methane combustion have been considered as first order irreversible reactions. However, the propane dehydrogenation is an equilibrium reaction and the low exit temperatures resulting from the reverse flow concept entail considerable propane conversion losses. How this 'back-conversion' can be counteracted is discussed in part II Chemical Engineering Science, 57, (2002), 855-872.