Reaction and flow variants/invariants for the analysis of chemical reaction data

This dissertation is concerned with the development of a methodology and appropriate tools for the investigation of chemical reaction systems using measured data. More specifically, the determination of reaction stoichiometry and kinetics from concentration or, preferably, spectral measurements is considered. The main contribution of this work is the derivation of a nonlinear transformation of the dynamic model that enables the separation of the evolution of the states into three parts: (i) the reaction-variant part (related to the reactions), (ii) the reaction-invariant and flow-variant part (related to the inlet and outlet streams), and (iii) the reaction- and flow-invariant part (related to the initial conditions). This transformation is very helpful in the analysis of concentration and spectral data. Dynamic model First-principles models of reaction systems are gaining importance in chemical and biotechnological production. They can considerably reduce process development costs and be used for simulation, model-based monitoring, control, and optimization, thus leading to improved product quality, productivity, and process safety. These models include information regarding both the chemical reactions and the operational mode of the reaction system. For the analysis of these models, it is important to distinguish between the states that depend on the reactions and those which do not. The concept of reaction invariants is extended to include the flow invariants of reaction systems with inlet and outlet streams. A nonlinear transformation of the first-principles dynamic model to normal form is proposed. Model reduction, state accessibility, and feedback linearizability are analyzed in the light of this transformation. Concentration data Concentration data collected from reaction systems are highly structured, a result of the underlying reactions and the presence of material exchange terms. It is shown that concentration data can be analyzed in the framework of the three-level decomposition provided by the transformation to normal form. The resulting factorization, termed the factorization of concentration data, enables (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, it is possible to isolate the reaction variant part by subtracting the reaction-invariant part from measured concentrations. The reaction-variant part is often unknown, since it depends on the kinetic description (typically the main difficulty in modeling chemical reaction systems). In contrast, the reaction-invariant part is usually known or measured. It is shown that, in cases where the reaction variants can be computed from the concentrations of a few measured species, the concentrations of the remaining species can be reconstructed using the known reaction-inva