The method of quasi-stationary sensitivity analysis

Turányi, Tamás; Bérces, T.; Tóth, János

doi:10.1007/bf01166303

Cited by 56 publications

(92 citation statements)

References 9 publications

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“…Although very simple to implement, this method gives results which are rather difficult to interpret in a correct way and sometimes leads to misleading conclusions. Thus, the combination of species reduction and rate sensitivity analysis 25 seems to be a more effective way for this purpose, the rate of production analysis is a classic method for the identification of important reaction pathways. This methodology requires the calculation of the Pij matrix elements 40,41 , which show the contribution of reaction j to the rate of production of species i.…”

Section: Methodsmentioning

confidence: 99%

“…For complex systems a numerical solution is required. The available methods to solve the differential equations and to investigate the main features of the mechanism are fully discussed in the literature 19,24,25,[36][37][38] .…”

Section: Methodsmentioning

confidence: 99%

“…Reaction rate analysis for complex kinetic systems includes the solution of a mathematical model, i. e., a set of coupled kinetic ordinary differential equations, the study of the effects of parameter changes on the results and the exploration of important reaction pathways [19][20][21][22][23][24][25] . This information is important to decide which reactions should be included in a atmospheric photochemical mechanism and, also, which reactions should be experimentally studied.…”

Section: Introductionmentioning

confidence: 99%

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Kinetic analysis of the gas-phase reactions of methacrolein with the OH radical in the presence of NOx

Pimentel¹,

Arbilla²

1999

J. Braz. Chem. Soc.

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Um mecanismo explícito para a reação da metacroleína (MTA) com radicais OH, numa mistura NOx -ar, foi simulado resolvendo as equações diferenciais ordinárias usando o método RungeKutta-4-semi-implícito. Os resultados simulados são consistentes com os dados experimentais publicados e o modelo explica as principais vias de reação para a oxidação da MTA com radicais OH na presença de NOx -ar. Usando uma análise dos autovetores e autovalores dos coeficientes de sensibilidade, para todas as espécies químicas envolvidas em diferentes tempos de reação, foi extraída informação cinética do sistema. Este método foi utilizado para reduzir o modelo cinético de forma objetiva. Foi utilizado, também, o método tradicional de análise de velocidade de produção (ROPA) para estudar a importância relativa das reações individuais. Usando a informação da análise de componente principal e da análise de velocidade de produção, foram identificadas as principais reações individuais.An explicit chemical mechanism for the reaction of methacrolein (MTA) with OH radicals in NOx-air systems, was simulated by solving the corresponding ordinary differential equations using Runge-Kutta-4-semi-implicit method. The simulated results are consistent with the published experimental data and the model accounts for all the major pathways by which MTA reacts in NOx-air systems. An eigenvalue-eigenvector analysis is used to extract meaningful kinetic information from linear sensitivity coefficients computed for all species of the chemical mechanism at several time points. This method is used to get an objective condition for constructing a minimal reaction set. Also, a classic method called rate of production analysis (ROPA) was used for the study of the reactions relevance. Using the principal component information as well as the rate of production analysis the main paths of reaction are identified and discussed.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Kinetic analysis of the gas-phase reactions of methacrolein with the OH radical in the presence of NOx

Pimentel¹,

Arbilla²

1999

J. Braz. Chem. Soc.

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“…Most modern model reduction methods are based on one of the following three general strategies: lumping 3 , sensitivity analysis [4][5][6] and time scale analysis. Model reduction techniques based on time scale analysis range from the quasi-steady-state assumption (QSSA) 7,8 and the partial equilibrium approximation (PEA) 9 to modern computational methods as computational singular perturbation (CSP) methods 10,11 , inertial manifold approaches 12 , intrinsic low-dimensional manifolds (ILDM) [13][14][15] and ideas from integer optimization 16,17 to eliminate "unnecessary" species and reactions.…”

Section: Introductionmentioning

confidence: 99%

Approximation of Slow Attracting Manifolds in Chemical Kinetics by Trajectory-Based Optimization Approaches

Reinhardt

Winckler

Lebiedz³

2008

J. Phys. Chem. A

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Many common kinetic model reduction approaches are explicitly based on inherent multiple time scales and often assume and directly exploit a clear time scale separation into fast and slow reaction processes. They approximate the system dynamics with a dimension-reduced model after eliminating the fast modes by enslaving them to the slow ones. The corresponding restrictive assumption of full relaxation of fast modes often renders the resulting approximation of slow attracting manifolds inaccurate as a representation of the reduced model and makes the numerical solution of the nonlinear "reduction equations" particularly difficult in many cases where the gap in intrinsic time scales is not large enough. We demonstrate that trajectory optimization approaches can avoid such severe restrictions by computing numerical solutions that correspond to "maximally relaxed" dynamical modes in a suitable sense. We present a framework of trajectory-based optimization for model reduction in chemical kinetics and a general class of reduction criteria characterizing the relaxation of chemical forces along reaction trajectories. These criteria can be motivated geometrically exploiting ideas from differential geometry and fundamental physics and turn out to be highly successful in example applications. Within this framework, we provide results for the computational approximation of slow attracting low-dimensional manifolds in terms of families of optimal trajectories for a six-component hydrogen combustion mechanism.

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“…Since the main goal of this study was the sensitivity and rate of production analysis 21 , only slight modifications were made in the previous proposed models. The model was discussed by Bauerfeldt and Arbilla 19 .…”

Section: Formulation Of the Modelsmentioning

confidence: 99%

Kinetic analysis of the chemical processes in the decomposition of gaseous dielectrics by a non-equilibrium plasma - part 2: SF6 and SF6/O2

Bauerfeldt¹,

Arbilla²

2000

J. Braz. Chem. Soc.

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Neste trabalho é realizada a simulação numérica da decomposição em fase gasosa de SF 6 e misturas de SF 6 /O 2 , na presença de silício. São determinadas as velocidades relativas dos processos individuais, o efeito da incerteza dos parâmetros e os coeficientes de sensibilidade. Os resultados são comparados com dados experimentais encontrados na literatura e resultados calculados previamente para a corrosão do silício, a fim de ajustar os parâmetros do modelo. À semelhança do que acontece com o CF 4 , o principal agente de corrosão é o flúor atômico e a concentração das principais espécies envolvidas depende da composição da mistura. A forma das curvas de sensibilidade segue o formato geral das curvas que representam a velocidade dos processos individuais e a relação entre os coeficientes de sensibilidade calculados para as diferentes etapas de reação é uma medida da contribuição de cada uma ao processo total.In this work, a numerical modelling analysis of the gas-phase decomposition of pure SF 6 and SF 6 /O 2 mixtures, in the presence of silicon was performed. The relative rate of individual processes, the effect of the parameters uncertainties and the sensitivity coefficients were determined. The results were compared with literature experimental data for the plasma etching of silicon and with previous simulated results to adjust the model parameters. As in the CF 4 system, the main etching agent is atomic fluorine and the concentration of the major species depends on the composition of the mixture. The shape of the sensitivity curves follows the general shape of the individual rate curves and the ratio between the calculated sensitivity coefficients is closely related to the contribution of each reaction.

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The method of quasi-stationary sensitivity analysis

Cited by 56 publications

References 9 publications

Kinetic analysis of the gas-phase reactions of methacrolein with the OH radical in the presence of NOx

Kinetic analysis of the gas-phase reactions of methacrolein with the OH radical in the presence of NOx

Approximation of Slow Attracting Manifolds in Chemical Kinetics by Trajectory-Based Optimization Approaches

Kinetic analysis of the chemical processes in the decomposition of gaseous dielectrics by a non-equilibrium plasma - part 2: SF6 and SF6/O2

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