Reaction and Flow Variants/Invariants

M. Amrhein, B. Srinivasan and D. Bonvin
Completed project (1993-1998)

This project was concerned with the development of a methodology for the kinetic investigation of chemical reaction systems using measured data. The main contribution of this work was the derivation of a nonlinear transformation of the dynamic model that enables the separation of the evolution of the states into variants and invariants.

Transformation of First-Principle Dynamic Models

For the analysis of first-principles models, it is important to distinguish between the states that depend on the reactions and those which do not. That is why the concept of reaction invariants was extended to include the flow invariants of reaction systems with inlet and outlet streams. A nonlinear 3-way transformation of the first-principles dynamic model to normal form was proposed and model reduction, state accessibility, and feedback linearizability were analyzed in the light of this transformation.

Factorization of Concentration Data

This project showed that concentration data could be analyzed in the framework of the 3-way decomposition provided by the transformation to normal form. The resulting factorization of concentration data enabled (i) the separation of the reaction and flow variants/invariants and (ii) the segregation of the dynamics (extents of reaction, integral of flows) from the static information (stoichiometry, initial and inlet concentrations). Using the factorization of concentration data, this work showed how to isolate the unknown reaction variant part, which depends on the kinetic description (typically the main difficulty in modeling chemical reaction systems), by subtracting the known/measured reaction-invariant part from measured concentrations. It was also shown that, in cases where the reaction variants could be computed from the concentrations of a few measured species, the concentrations of the remaining species could be reconstructed using the known reaction-invariant part.

Keywords

Reaction invariant; Flow invariant; Model reduction; State accessibility; State reconstruction; Factorization of concentration data

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