Dissipative pseudo-Hamiltonian realization of chemical systems using irreversible thermodynamics

N. Ha Hoang, Denis Dochain, Françoise Couenne and Yann Le Gorrec

Mathematical and Computer Modelling of Dynamical Systems, 2017, vol. 23, issue 2, 135-155

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 pseudo-Hamiltonian 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 $$F = J - R$$F=J−R ) 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.

Date: 2017
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DOI: 10.1080/13873954.2016.1237973

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