The mathematical theory of a countercurrent catalytic reactor

Abstract

The steady-state behaviour of a countercurrent catalytic reactor has been analysed mathematically for a reversible reaction─adsorption system A ⇌ A* ⇌ B* ⇌ B occurring, in the first instance, under the ideal chromatographic conditions in which negligible axial dispersion and instantaneous local adsorption equilibrium are assumed. The system is considered to be one-dimensional and isothermal. The internal discontinuity of the steady-state model was analysed in connection with the transient model, while the boundary behaviour was investigated in relation to the non-equilibrium-adsorption model. Two of the most influential parameters on the system behaviour were found to be the relative adsorptivity of the two chemical species A and B, and the relative carrying capacity of the two moving streams. It has been shown by heuristic examples how the chemical reaction process and the adsorption process interact to break the local thermodynamic equilibrium limitation by the formation of a stationary shock front inside the reactor. The physical meaning of this internal shock appears to be that it is the interface between two different regions; on one side the process is controlled by the reaction rate, and on the other side by the adsorption rate. The effect of non-ideality has also been investigated, and the performance characteristics have been discussed in comparison with those of the conventional fixed-bed reactor.