Multiplicities of temperature wave trains in periodically forced networks of catalytic reactors for reversible exothermic reactions

Networks of catalytic reactors with periodically switched inlet and outlet sections offer a competitive technological solution to the operation of reversible exothermic reactions. Traditionally, this operation mode is implemented by periodically shifting inlet and outlet sections so as to jump a single reactor unit in the flow direction. Here, a network of four catalytic reactors carrying on the methanol synthesis process is considered and the effect of varying the number (ns) of reactor units jumped by inlet and outlet sections on network stability and performance is investigated. Increasing ns, a greater variety of periodic regimes giving rise to trains of temperature waves characterized by spatial periodicity are detected as the switching velocity varies. These regimes well reproduce the inter-stage cooling effect of multistage fixed bed reactors and, hence, guarantee in general large conversion values. Moreover, an intriguing coexistence between T-periodic and multi-periodic temperature wave trains is revealed, T being the period needed for the system to recover its initial configuration. A T periodic symmetric wave train characterized by k waves always coexists with a number of k-1 stable symmetric kT-periodic regimes, except when symmetry breaking is encountered. The k-1 coexisting regimes correspond to wave trains with a number of waves ranging between 1 and k-1. Bifurcational analysis is performed to characterize the stability range of periodic regimes and to systematically analyze multiplicities and bifurcations as the switching velocity is varied and at different ns.