Thermodynamics and chemical systems stability: The CSTR case study revisited

Variant and invariant states for chemical reaction systems

“…With the inlet flows or the heat input as manipulated variables, the resulting models are typically input-affine and lend themselves well to control via feedback linearization, for which certain conditions are necessary (Fliess et al, 1995;Srinivasan et al, 1998). Applications of such control approaches are available in the literature (Farschman et al, 1998;Favache and Dochain, 2009;Hoang et al, 2014).…”

“…For example, Srinivasan et al (1998) discussed the implications of reaction and flow variants/invariants for control-related tasks such as model reduction, state accessibility, state reconstruction and feedback linearizability. On the one hand, control laws using reaction variants have been proposed for continuous stirred-tank reactors (Hammarstrom, 1979;Waller and Mäkilä, 1981;Dochain et al, 2009;Favache and Dochain, 2009). The concept of extent of reaction is very useful to describe the dynamic behavior of a chemical reaction since a reaction rate is simply the derivative of the corresponding extent of reaction.…”

Passivity Based Control of Irreversible Port Hamiltonian Systems

“…, F em ) ⊤ ), r i =ν i r where r (n, T ) is the reaction rate which is the difference of the forward reaction rate r f and the backward reaction rate r b : r = (r f − r b ) and depends on the temperature and on the reactant mole number,ν i is the signed stoichiometric coefficient: ν i = −ν i if it appears on the left hand side of the reaction scheme,ν i = ν i in the other case. Following the usual assumptions (Aris, 1989;Favache and Dochain, 2009), V the volume in the reactor is assumed to be constant as well as the pressure. We shall assume a reaction in gas phase, but the developments may be applied identically to a reactor with a reaction in liquid phase.…”

“…Assuming constant volume and pressure the reference molar enthalpy h 0i = u 0i (Sandler, 2006), and the balance equation of the internal energy is (Couenne et al, 2006;Favache and Dochain, 2009)…”

Monitoring of Chemical Processes Using Model-Based Approach

“…Application of approaches based on Luenberger and/or Kalman observers to chemical reactors diagnosis are usually designed by resorting to linearized models of the reactor. However, the adoption of linearized models has been proven to work properly for the Continuous Stirred Tank Reactors (CSTRs), mainly operating at steady state, due to their intrinsic unsteady behavior (Rajaraman S. & al., 2006), (Favache A. & al., 2009), (Hsoumi A.…”