Reversible Reaction Networks Research Articles

2P457 Hysteresis phenomena of discrete, reversible reaction networks(50. Non-equilibrium and complex system,Poster Session,Abstract,Meeting Program of EABS & BSJ 2006)

2P457 Hysteresis phenomena of discrete, reversible reaction networks(50. Non-equilibrium and complex system,Poster Session,Abstract,Meeting Program of EABS & BSJ 2006)

Singular perturbation analysis for the reduction of complex chemistry in gaseous mixtures using the entropic structure

We investigate the reduction of complex chemistry in gaseous mixtures. Weconsider an arbitrarily complex network of reversible reactions. We assume that their ratesof progress are given by the law of mass action and that their equilibrium constants arecompatible with thermodynamics; it thus provides an entropic structure [14] [23]. We studya homogeneous reactor at constant density and internal energy where the temperature canencounter strong variations. The entropic structure brings in a global convex Lyapounovfunction and the well-posedness of the associated finite dimensional dynamical system. Wethen assume that a subset of the reactions is constituted of 'Fast' reactions. The partialequilibrium constraint is linear in the entropic variable and thus identifies the 'Slow' and'Fast' variables uniquely in the concentration space through constant orthogonal projections.It is proved that there exists a convex compact polyhedron invariant by the dynamicalsystem which contains an affine foliation associated with a Tikhonov normal form. The reductionstep is then identified using the orthogonal projection onto the partial equilibriummanifold and proved to be compatible with the entropy production. We prove the globalexistence of a smooth solution and of an asymptotically stable equilibrium state for boththe reduced system and the complete one. A global in time singular perturbation analysisproves that the reduced system on the partial equilibrium manifold approximates the fullchemistry system. Asymptotic expansions are obtained.

Singular perturbation analysis for the reduction of complex chemistry in gaseous mixtures using the entropic structure

In this Note, we investigate the reduction of complex chemistry in gaseous mixtures. We consider an arbitrarily complex network of reversible reactions, the equilibrium constant of which are compatible with thermodynamics, thus providing an entropic structure. We assume that a subset of the reactions is consituted of fast reactions and define a constant and linear projection onto the partial equilibrium manifold compatible with the entropy production. This reduction step is used for the study of a homogeneous reactor at constant density and internal energy where the temperature can encounter strong variations. We prove the global existence of a smooth solution and of an asymptotically stable equilibrium state for both the reduced system and the complete one. A global in time singular perturbation analysis proves that the reduced system on the partial equilibrium manifold approximates the full chemistry system. To cite this article: M. Massot, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 93–98.

The Use of Delay Differential Equations in Chemical Kinetics

The concept of a chemically acceptable model is developed. Chemically acceptable models are causal and maintain the nonnegativity of concentrations. An extension of the law of mass action allowing delayed effects is described and shown to lead to chemically acceptable models. Delayed variable enzyme catalysis and Oregonator models are studied and shown to be equivalent to their classical mass-action counterparts from a number of perspectives. This equivalence is shown to be a consequence of an exact correspondence between certain ordinary and distributed-delay differential equations. For sufficiently small delays, this correspondence extends to discrete-delay systems. However, reversible chemical reaction networks cannot be adequately modeled with discrete-delay equations.

Mathematical modelling of diffusion and reaction for gas-solid catalytic systems with complex reaction networks. Negative effectiveness factors

The concept of effectiveness factor (η) as a measure of diffusional limitations for gas-solid catalytic reactions has gone a long way since the time of Thiele. Multiple steady states giving rise to multiple values of (η) for the same bulk conditions, and η values greater than unity have been widely reported in the literature in the last three decades. In this paper an interesting phenomenon associated with the effectiveness factors (η) for industrial gas-solid catalytic reactions is reported, that is the possible occurrence of negative values of η for certain intermediate components. This physically means that diffusional resistance can also reverse the direction of the net production or consumption of intermediate components in consecutive and/or reversible reaction networks. It is shown both numerically and analytically that the results represent real physical phenomenon and not artefacts resulting from numerical problems or model simplifications. Two industrially important reactions are considered, namely, the steam reforming of natural gas which is a highly endothermic reaction and the partial oxidation of O-xylene to phthalic anhydride which is a highly exothermic reaction.

Contributions to the Theory of Mass Action Kinetics. I. Enumeration of Second Order Mass Action Kinetics

By investigating the reaction diagram in its own right, it is possible to solve the problem of enumerating all the different types of mass action kinetics up to second order. The amount of non isomorphic complex sets for a given number of species and of non isomorphic reaction networks and reversible reaction networks which can be derived from a given number of complexes is given.