Reaction and flow variants/invariants in chemical reaction systems with inlet and outlet streams

Abstract

The concept of reaction invariants is extended to include flow invariants of chemical reaction systems with inlet and outlet streams. A transformation to normal form is introduced that allows the separation of: (i) the evolution of the reactions, (ii) the influence of inlet streams, and (iii) the behavior of the reaction and flow invariants. Resulting from this transformation to normal form, model reduction, construction of the linearizing feedback and properties such as state accessibility, state reconstruction, and feedback linearizability are analyzed.

Variant and invariant states for chemical reaction systems

“…The idea is to work with the reduced model that does not include the inaccessible invariant part. 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).…”

Optimal feed rate policy for systems with two reactions

“…Consider a homogeneous, constant-density, isothermal, semi-batch chemical reaction system comprising S species and R independent reactions (independent reactions being those which have both independent stoichiometries and independent kinetics (Srinivasan et al, 1998)). The material balance equations and the continuity equation are described by:…”

“…where the superscript + denotes the MoorePenrose pseudo inverse, takes the system (4) to the normal form (Srinivasan et al, 1998):…”

Variant and Invariant States for Reaction Systems

“…He then used them to describe the dynamics of flow through porous media accompanied by chemical reactions [7]. For open homogeneous reaction systems, Srinivasan et al [8] developed a nonlinear transformation of the numbers of moles to reaction variants, flow variants, and reaction and flow invariants, thereby separating the effects of reactions and flows. Later, Amrhein et al [9] refined that transformation to make it linear and therefore simpler (at the price of losing the one-to-one property).…”