Kinetic Polynomial: A New Concept of Chemical Kinetics

Lazman, Mark; Yablonskii, G. S.

doi:10.1007/978-1-4612-3206-3_8

Cited by 9 publications

(3 citation statements)

References 16 publications

(10 reference statements)

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“…For the analysis of nonlinear cycles the new concept of kinetic polynomial was developed (Yablonskii, Lazman, & Bykov (1982); Lazman & Yablonskii (1991)). It was proven that the stationary state of the single-route reaction mechanism of catalytic reaction can be described by a single polynomial equation for the reaction rate.…”

Section: Introductionmentioning

confidence: 99%

Chapter 3 Dynamic and Static Limitation in Multiscale Reaction Networks, Revisited

Gorban

Radulescu

2008

Advances in Chemical Engineering - Mathematics in Chemical Kinetics and Engineering

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The concept of the limiting step gives the limit simplification: the whole network behaves as a single step. This is the most popular approach for model simplification in chemical kinetics. However, in its elementary form this idea is applicable only to the simplest linear cycles in steady states. For such simple cycles the nonstationary behaviour is also limited by a single step, but not the same step that limits the stationary rate. In this paper, we develop a general theory of static and dynamic limitation for all linear multiscale networks. Our main mathematical tools are auxiliary discrete dynamical systems on finite sets and specially developed algorithms of "cycles surgery" for reaction graphs. New estimates of eigenvectors for diagonally dominant matrices are used.Multiscale ensembles of reaction networks with well separated constants are introduced and typical properties of such systems are studied. For any given ordering of reaction rate constants the explicit approximation of steady state, relaxation spectrum and related eigenvectors ("modes") is presented. In particular, we prove that for systems with well separated constants eigenvalues are real (damped oscillations are improbable). For systems with modular structure, we propose the selection of such modules that it is possible to solve the kinetic equation for every module in the explicit form. All such "solvable" networks are described. The obtained multiscale approximations, that we call "dominant systems" are computationally cheap and robust. These dominant systems can be used for direct computation of steady states and relaxation dynamics, especially when kinetic information is incomplete, for design of experiments and mining of experimental data, and could serve as a robust first approximation in perturbation theory or for preconditioning.

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Section: Introductionmentioning

confidence: 99%

Chapter 3 Dynamic and Static Limitation in Multiscale Reaction Networks, Revisited

Gorban

Radulescu

2008

Advances in Chemical Engineering - Mathematics in Chemical Kinetics and Engineering

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“…However, later Lazman and Yablonskii in the series of papers in the 1980s and 1990s (Yablonskii et al, 1982(Yablonskii et al, , 1983Lazman and Yablonskii, 1991) theoretically showed that, in the general case of the non-linear catalytic mechanism, the reaction rate of complex reaction is an implicit, not explicit function of concentrations and temperature. It is a single polynomial (so called kinetic polynomial) in terms of reaction rate and concentrations, and of course temperature.…”

Section: Article In Pressmentioning

confidence: 97%

Cycles Across an Equilibrium: A Kinetic Investigation of the Reverse and Forward WGS Reaction over a 2% Pt/CeO2 Catalyst (Experimental Data and Qualitative Interpretation)

Yablonsky

Pilasombat

Breen

et al. 2010

Chemical Engineering Science

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“…It also explains the need to introduce new ideas to anticipate the rate of processes performed in practice. We will try to introduce the concept of polynomial kinetic presented in 1 and 2 into a real‐world process. The authors showed that the kinetic polynomial is the most generalized form of the rate equation and is consistent from a thermodynamic point of view.…”

Section: Introductionmentioning

confidence: 99%

Application of the kinetic polynomial idea to describe catalytic hydrogenation of propene

Szukiewicz,

Chmiel‐Szukiewicz,

Zaręba

2024

Int J of Chemical Kinetics

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The kinetics of heterogeneous catalytic reactions is a topic of theoretical and practical importance that combines theoretical and experimental efforts to achieve a deeper insight into the process. Theoretical aspects are concerned with determination of the process mechanism, whereas in practical applications kinetic experiments are applied to assist reactor design and scaling up of various processes. These approaches overlap; basis of the assumed mechanism that consists of many elementary steps, it is possible to find a kinetic equation for which precision is verified by comparison with experimental data. The method most often applied requires finding a single step that has the strongest influence on the process rate. This “classical approach” fails if the rate of two or more steps has comparable values, the precision of the determined kinetic rate becomes only average or even low. Such accuracy was observed, among others, for the gas‐phase hydrogenation of propene. The reaction is easy to carry out and proceeds under mild conditions; the byproducts are not observed. It suggests that there cannot be a single dominating effect step on the process rate. In this work, the application of the polynomial kinetic idea to the gas‐phase hydrogenation of the propene process realized in practice is tested. An attempt of obtaining a handy and precise relationship, without insignificant parameters was made. To realize this, the theoretical form of the polynomial kinetic was derived, and then, using statistical analysis of estimated polynomial parameters, the kinetic relationship was simplified. The final version of the kinetic polynomial and some selected kinetic equations taken from the literature were compared with respect to precision. The differences were significant: the precision of anticipation of the kinetic rate by the polynomial kinetic was 5% higher than for the power law and 12% higher than for the LHHW kinetic.

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Kinetic Polynomial: A New Concept of Chemical Kinetics

Cited by 9 publications

References 16 publications

Chapter 3 Dynamic and Static Limitation in Multiscale Reaction Networks, Revisited

Chapter 3 Dynamic and Static Limitation in Multiscale Reaction Networks, Revisited

Cycles Across an Equilibrium: A Kinetic Investigation of the Reverse and Forward WGS Reaction over a 2% Pt/CeO2 Catalyst (Experimental Data and Qualitative Interpretation)

Application of the kinetic polynomial idea to describe catalytic hydrogenation of propene

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