Dissipative pseudo-Hamiltonian realization of chemical systems using irreversible thermodynamics

Hoang, N. Ha;Dochain, Denis;Couenne, Françoise;Le Gorrec, Yann
(2017) Mathematical and Computer Modelling of Dynamical Systems : methods, tools and applications in engineering and related sciences — Vol. 23, n° 2, p. 135-155 (2017)

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  • Hoang, N. HaUniversity of Technology, HCM City, Vietnam
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  • Dochain, DenisUCLouvain
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  • Couenne, FrançoiseLAGEP, Université de Lyon, Villeurbanne, France
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  • Le Gorrec, YannUniversité de Bourgogne Franche-Comté, Besançon, France
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Abstract
As motivated by the use of physical variables as Hamiltonian storage functions, this article focuses on dissipative pseudo-Hamiltonian realizations of chemical reaction systems, but with a particular emphasis on the continuous stirred tank reactor (CSTR) in order to further explore the structural differences. More precisely, two different dissipative pseudoHamiltonian representations are proposed to a given non-isothermal CSTR dynamics thanks to a unified potential function that verifies a thermodynamic evolution criterion. The first one with the singularity of the structure matrix F (where F ¼JR) resulting from thermodynamically inherent properties of the process, is obtained on the basis of functional separability. Even though the amount of dissipation is explicitly derived and exactly exhibits the process irreversibility, the main disadvantage of such a result is that the derivation of alternative pseudo-Hamiltonian models is impossible. One way to circumvent this inherent difficulty is to consider the Brayton–Moser form of the original dynamics. On this basis, a solution required for the Brayton–Moser formulation is first proposed. Interestingly, the proposed solution is based on thermodynamic information only.
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Hoang, N. H., Dochain, D., Couenne, F., & Le Gorrec, Y. (2017). Dissipative pseudo-Hamiltonian realization of chemical systems using irreversible thermodynamics. Mathematical and Computer Modelling of Dynamical Systems : methods, tools and applications in engineering and related sciences, 23(2), 135-155. https://doi.org/10.1080/13873954.2016.1237973 (Original work published 2017)