Reaction flux versus reaction force: easy to stabilize?

Chemical reaction rate, also known as the reaction flux involved in chemical reactors, plays a central role as the source generating the abnormal dynamics characteristics. This paper proposes a structural approach for the stabilization of such systems through the control of the reaction flux by considering the Lyapunov stability theory within a standard thermodynamic framework. More precisely, the reaction flux is structurally considered as a nonlinear function of conjugated reaction force. The thermodynamic constraint of such a relationship is that the inherent non-negative definiteness property of the irreversible entropy production due to chemical reaction has to be fulfilled. Consequently, it allows to reexpress a large class of reaction rates described by the mass-action-law and more interestingly, the operation of the reaction system at a desired set-point consists in controlling the reaction force on the basis of an affinity-related storage function. Numerical simulations for a non isothermal continuous stirred tank reactor (CSTR) involving one reversible reaction operated with multiple steady states illustrate the application of the theoretical developments.