Reaction invariants and their importance in the analysis of eigenvectors, state observability and controllability of the continuous stirred tank reactor

Fjeld, Magne; Asbjørnsen, O.A.; Åström, Karl Johan

doi:10.1016/0009-2509(74)85009-8

Cited by 64 publications

(24 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, the evolution of n is no longer restricted to an R-dimensional space as previously; it evolves in a larger space. A similar conclusion has been drawn by Fjeld et al (1974).…”

Section: Reaction Invariants In the Presence Of Inlets And Outletssupporting

confidence: 87%

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

1998

View full text Add to dashboard Cite

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.

show abstract

“…Thus, the evolution of n is no longer restricted to an R-dimensional space as previously; it evolves in a larger space. A similar conclusion has been drawn by Fjeld et al (1974).…”

Section: Reaction Invariants In the Presence Of Inlets And Outletssupporting

confidence: 87%

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

1998

View full text Add to dashboard Cite

show abstract

“…In addition, it is possible to express the invariant states as P + n(t) = 0 q , which is useful in many applications (Waller and Mäkilä, 1981;Fjeld et al, 1974;Gadewar et al, 2002). We develop next a similar transformation applicable to distributed reaction systems.…”

Section: Distributed Reaction Systemsmentioning

confidence: 99%

“…The concept of reaction variants/invariants as introduced by Asbjornsen and Fjeld (1970), Asbjornsen (1972), Fjeld et al (1974) is briefly reviewed next. The idea is to use the stoichiometric matrix to construct a linear transformation of the states n to the reaction-variant states y r and the reaction-invariant states y iv .…”

Section: Reaction Variants/invariants In the Literaturementioning

confidence: 99%

“…For example, reaction invariants have been used to study the state controllability and observability of continuous stirred-tank reactors (Fjeld et al, 1974;Bastin and Lévine, 1993). Reaction invariants have also been used to automate the task of formulating mole balance equations for the non-reacting part (such as mixing and splitting operations) of complex processes, thereby helping determine the number of degrees of freedom for process synthesis (Gadewar et al, 2002).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Variant and invariant states for chemical reaction systems

Rodrigues

Srinivasan

Billeter

et al. 2015

Computers & Chemical Engineering

View full text Add to dashboard Cite

a b s t r a c tModels of chemical reaction systems can be quite complex as they typically include information regarding the reactions, the inlet and outlet flows, the transfer of species between phases and the transfer of heat. This paper builds on the concept of reaction variants/invariants and proposes a linear transformation that allows viewing a complex nonlinear chemical reaction system via decoupled dynamic variables, each one associated with a particular phenomenon such as a single chemical reaction, a specific mass transfer or heat transfer. Three aspects are discussed, namely, (i) the decoupling of reactions and transport phenomena in open non-isothermal both homogeneous and heterogeneous reactors, (ii) the decoupling of spatially distributed reaction systems such as tubular reactors, and (iii) the potential use of the decoupling transformation for the analysis of complex reaction systems, in particular in the absence of a kinetic model.

show abstract

“…Asbjørnsen and co-workers [2], [3], [4] introduced the concept of reaction variants and invariants and used it for reactor modeling and control. However, for open reactors, the reaction variants proposed in the literature are also affected by the inlet and outlet flows and therefore represent more than the reaction contributions.…”

Section: Introductionmentioning

confidence: 99%

Variant and Invariant States for Reaction Systems

Srinivasan

Billeter

Bonvin

2013

IFAC Proceedings Volumes

View full text Add to dashboard Cite

Abstract-Models of chemical reactors can be quite complex as they include information regarding the reactions, the transfer of species between phases, the transfer of energy, and the inlet and outlet flows. Furthermore, the effects of the various phenomena are quite intertwined and thus difficult to quantify from measured data. This paper proposes a mathematical transformation of the balance equations that allows viewing a complex reaction system via decoupled dynamic variables, each one associated with a particular phenomenon such as a single chemical reaction, a specific mass transfer or heat transfer between the reactor and the jacket. Three aspects are investigated, namely, (i) the decoupling of mole balance equations, (ii) the decoupling of mole and heat balance equations, and (iii) the applicability of the decoupling transformation for model reduction, static state reconstruction and incremental kinetic identification.

show abstract

Reaction invariants and their importance in the analysis of eigenvectors, state observability and controllability of the continuous stirred tank reactor

Cited by 64 publications

References 3 publications

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

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

Variant and invariant states for chemical reaction systems

Variant and Invariant States for Reaction Systems

Contact Info

Product

Resources

About