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Publication# Concept and Applications of Extents in Chemical Reaction Systems

Michael Amrhein, Julien Léo Billeter, Dominique Bonvin, Diogo Filipe Mateus Rodrigues, Sriniketh Srinivasan

2017

Conference paper

2017

Conference paper

Abstract

Models of chemical reaction systems can be quite complex as they typically include information regarding the reactions, the various transfers of heat and mass, as well as the effects of the inlet and outlet flows. It is well known that a linear transformation involving the reaction stoichiometry allows artitioning the state space into a reaction invariant subspace and its complement. Alternative transformations have been proposed to partition the state space into various subspaces that are linked to the reactions, the heat and mass transfers, the inlets, and the initial conditions. This paper analyzes this partitioning of the state space, which helps isolate the effects of the various rate processes. The implications of this partitioning are discussed with respect to several modeling and estimation applications.

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Chemical reaction

A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the posit

Mass transfer

Mass transfer is the net movement of mass from one location (usually meaning stream, phase, fraction or component) to another. Mass transfer occurs in many processes, such as absorption, evaporation,

Chemical reaction engineering

Chemical reaction engineering (reaction engineering or reactor engineering) is a specialty in chemical engineering or industrial chemistry dealing with chemical reactors. Frequently the term relates

Michael Amrhein, Julien Léo Billeter, Dominique Bonvin, Diogo Filipe Mateus Rodrigues

Models of chemical reaction systems can be complex as they need to include information regarding the reactions and the mass and heat transfers. The commonly used state variables, namely, concentrations and temperatures, express the interplay between many phenomena. As a consequence, each state variable is affected by several rate processes. On the other hand, it is well known that it is possible to partition the state space into a reaction invariant subspace and its orthogonal complement using a linear transformation involving the reaction stoichiometry. This paper uses a more sophisticated linear transformation to partition the state space into various subspaces, each one linked to a single rate process such as a particular reaction, mass transfer or heat transfer. The implications of this partitioning are discussed with respect to several applications related to data reconciliation, state and rate estimation, modeling, identification, control and optimization of reaction systems.

2018Michael Amrhein, Julien Léo Billeter, Dominique Bonvin, Diogo Filipe Mateus Rodrigues, Sriniketh Srinivasan

Models of chemical reaction systems can be complex as they need to include information regarding the reactions and the mass and heat transfers. The commonly used state variables, namely, concentrations and temperatures, express the interplay between many phenomena. As a consequence, each state variable is affected by several rate processes. On the other hand, it is well known that it is possible to partition the state space into a reaction invariant subspace and its orthogonal complement using a linear transformation involving the reaction stoichiometry. This paper uses a more sophisticated linear transformation to partition the state space into various subspaces, each one linked to a single rate process such as a particular reaction, mass transfer or heat transfer. The implications of this partitioning are discussed with respect to several applications related to data reconciliation, state and rate estimation, modeling, identification, control and optimization of reaction systems.

Julien Léo Billeter, Dominique Bonvin, Diogo Filipe Mateus Rodrigues

Abstract of the conference paper The kinetic identification of chemical reaction systems often represents a time-consuming and complex task. This contribution presents an approach that uses rate estimation and feedback linearization to implement effective control without a kinetic model. The reaction rates are estimated by numerical differentiation of reaction variants. The approach is illustrated in simulation through the temperature control of a continuous stirred-tank reactor. Extended abstract Model identification and controller design are often seen as closely related tasks, since the control law is calculated using the plant model. Previous control approaches based on extensive variables or inventories are examples of this strong dependence on the model [1, 2]. Since the identification of chemical reaction systems can be a time-consuming and complex task, one would ideally like to avoid it as much as possible. The concept of variant and invariant states allows isolating the different rates in chemical reaction systems, thereby facilitating analysis, monitoring and control [3-5]. Using this concept, one can estimate dynamic effects without the need of identifying the corresponding kinetic models. This contribution presents a feedback linearization approach that is based on the estimation of unknown rates, such as the rates of reaction and mass transfer, thus allowing efficient control without the use of kinetic models. Rate estimation uses the numerical differentiation of appropriately transformed extensive variables called rate variants that are invariant with respect to the manipulated variables. A rate variant contains all the information about the corresponding rate and, as such, is decoupled from the other unknown rates. Since it is possible to estimate the unknown rates this way, the controller does not require kinetic information. However, because of the differentiation step, the controller is most effective with frequent and precise measurements of several output variables. Feedback linearization sets a rate of variation for the controlled variables, thereby guaranteeing quick convergence of these variables to their set points. For open chemical reactors, the parameters of the feedback linearization controller are determined by readily available information, such as the reaction stoichiometry, the heats of reaction, the inlet composition or the inlet and outlet flow rates. This novel control strategy is illustrated in simulation for the control of both concentration and temperature in a continuous stirred-tank reactor. [1] Georgakis, Chem. Eng. Sci., 1986, 41, 1471 [2] Farschman et al., AIChE J., 1998, 44, 1841 [3] Asbjørnsen and Fjeld, Chem. Eng. Sci., 1970, 25, 1627 [4] Bhatt et al., Ind. Eng. Chem. Res., 2011, 50, 12960 [5] Srinivasan et al., IFAC Workshop on Thermodynamic Foundations of Mathematical Systems Theory, Lyon, 2013.