Temperature wave‐trains of periodically forced networks of catalytic reactors

Abstract

Networks of N identical catalytic reactors with periodically switched inlet and outlet sections are studied for first-order irreversible exothermic reactions. Switching strategies with inlet and outlet sections periodically jumping a fixed number n s of reactors are considered and the mechanisms governing the formation of traveling temperature wave-trains are analyzed as n s and N are varied. To this aim, a geometric approach to the analysis of the network energy balance is developed. Based on this approach, infinite domains of traveling temperature wave-trains are predicted for any n s and N. Analytical approximations are derived for the stability limits and the spatiotemporal patterns of these regimes. Stability boundaries predicted analytically include for any solution the largest part of the stability region computed by numerical simulation. Moreover, good agreement is found between the structure of the spatiotemporal patterns computed numerically and that predicted based on the proposed approach.

Control of Rotating Wave Trains in a Loop Reactor

“…In accordance with the analysis presented in ref 43 and reviewed in the preceding section, ensuring the stability of T*-periodic wave-train regimes requires that inequalities 5 be satisfied. Once n s , N, and p are fixed, this objective can be achieved by varying the velocities of the temperature fronts or the switching time τ.…”

“…This is of practical importance, as the achievement of low switching times would require frequent modification of the feeding sequence and, thus, cause damage to the external valve system. Altimari et al 43 later demonstrated the possibility of controlling the structure of thermal wave trains. Infinitely many domains of thermal wave trains were demonstrated to exist for any value of n s and any number of reactors composing the network, and analytical approximations were derived for the stability boundaries of the predicted solutions based on geometric analysis of the spatiotemporal temperature pattern.…”

“…The implemented control was adaptive as the set point was updated during each cycle based on the estimated value of the reactionfront velocity. Analytical relationships previously determined for the stability limits of wave-train solutions 43 were used for this purpose.…”

Dynamics and control of loop reactors - a review

“…Analysis by Altimari et al [4], based on a geometrical approach of systems, showed infinitely many domains of T -periodic regimes corresponding to thermal wave trains with various number of waves. Analytical approximations to the stability limits and the spatiotemporal pattern of these solutions were derived for the case of a fast irreversible exothermic reaction.…”

Mapping resonance regions in loop networks with spatio-temporal symmetry

“…Indeed, the rotation of inlet and outlet sections enables to trap an exothermic reaction front within the bed ensuring the possibility to operate at high conversion regimes even with streams characterized by very low adiabatic temperature rise. Moreover, the rotation of inlet and outlet sections interacts with spontaneously forming temperature fronts and might determine temperature patterns enhancing yield of prescribed products in equilibrium limited processes [4][5][6][7][8][9].…”