Approximate characteristics of a moving temperature front in a fixed-bed catalytic reactor

The study deals with a nonstationary process of mass and heat transfer accompanied by a chemical reaction occurring in a catalytic reactor. Based on the assumptions of the ‘ideal thermal front’ in the reactor, approximate solutions are obtained for the equations that describe the process. Thus, relations are derived which define the principal properties of the thermal front, namely its propagation velocity in the bed and the maximum temperature of the front. The above relations express these properties in terms of dimensionless numbers that characterise the chemical reaction taking place in the reactor and the operating parameters of the vessel. Good agreement is found between the front properties as calculated using the approximate formulae and those yielded by the integration of the complete model equations, i.e. the exact values. A method is proposed for determining approximate temperature profiles in the bed, which is by far simpler and less time-consuming than the integration of a complete set of partial differential equations. Both the formulae derived and the method proposed for calculating the temperature profiles along the bed may be useful in the design of reactors with the periodic reversal of the feed mixture. They enable the effect to be analysed of the various operating parameters upon the propagation velocity of the thermal front and its maximum temperature, without resorting to tedious and time-consuming trial and error methods that require repeated integration of the model equations.