Thermodynamics based stability analysis and its use for nonlinear stabilization of the CSTR

• A tutorial description of the thermodynamic availability concept.
• Its use for open loop dynamic analysis of the non-isothermal CSTR.
• Its use for Lyapunov based control laws derivation of the non-isothermal CSTR.
• Illustration of the performances of the controller by simulations.
• Comparison of the controller with a proportional one.

We show how the availability function as defined from the entropy function concavity can be used for the stability analysis and derivation of control strategies for non-isothermal Continuous Stirred Tank Reactors (CSTRs). We first propose an overview of the required thermodynamic concepts. Then, we show how the availability function restricted to the thermal domain can be used as a Lyapunov function. The derivation of the control law and the way the strict entropy concavity is insured are discussed. Numerical simulations illustrate the application of the theory to the open loop stability analysis and the closed loop control of liquid-phase non-isothermal CSTRs. The proposed approach is compared with the classical proportional control strategy. Two chemical reactions are studied: the acid-catalyzed hydration of 2-3-epoxy-1-propanol to glycerol subject to steady state multiplicity and the production of cyclopentenol from cyclopentadiene by acid-catalyzed electrophilic addition of water in dilute solution exhibiting a non-minimum phase behavior.