Parametric Sensitivity in Fitting Nonlinear Kinetic Models

Mezaki, Reiji; Kittrell, J. R.

doi:10.1021/ie50689a007

Cited by 57 publications

(22 citation statements)

References 8 publications

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“…(2) gives the traditional kinetic model. Studies of changes in the form of parameters to the Arrhenius equation can be found in Mezak and Kittrell [15]. Draper and Smith [16] analyzed aspects of reparameterization and also made reference to an equation of this type.…”

Section: Kinetic Modelmentioning

confidence: 99%

“…Draper and Smith [16] analyzed aspects of reparameterization and also made reference to an equation of this type. The reparameterization performed in this work [15] was based on the following transformations of Eq. (3)…”

Section: Kinetic Modelmentioning

confidence: 99%

“…The mathematical structure of the Arrhenius equation, involving the exponentiation of the reciprocal of the absolute temperature, introduces a high correlation between the two parameter estimates. Reparameterizations of the Arrhenius equation have been found in some studies [15,16] due to these difficulties.…”

Section: Introductionmentioning

confidence: 99%

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The Use of Nonlinearity Measures in the Estimation of Kinetic Parameters of Sugarcane Bagasse Pyrolysis

et al. 2010

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The majority of the pyrolysis kinetics models presented in the literature is nonlinear. In these models, the influence of temperature is normally described by the Arrhenius equation. In some studies related to parameter estimation of nonlinear models suggestions can be found for reparameterization of the Arrhenius-type equation due to inadequate results on the parameter estimation. In this work, kinetic modeling is proposed in order to predict the primary biomass decomposition behavior under a dynamic regime. This model is based on the traditional model of parallel reactions and uses the Arrhenius-type equation in the reparameterized form. Some nonlinearity measures are used as a tool to correctly estimate the kinetic parameters of the pyrolysis of sugarcane bagasse. The predictions from the proposed model properly reproduced the experimental DTG curves. The reparametrized model showed non-significance for bias and nonlinearity measures.

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Section: Kinetic Modelmentioning

confidence: 99%

Section: Kinetic Modelmentioning

confidence: 99%

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The Use of Nonlinearity Measures in the Estimation of Kinetic Parameters of Sugarcane Bagasse Pyrolysis

et al. 2010

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“…3͒, it is informative to know the level of confidence of the estimates. A confidence region of the estimates, 26,29 in which the true parameter values are expected to reside, can be shown as a contour of the value ͑S͑k͒͒ given in Eq. 4.…”

Section: Numerical Detailsmentioning

confidence: 99%

Numerical Procedure to Extract Physical Properties from Raman Scattering Data in a Flow Reactor

Hwang

Park

Huang

et al. 2005

J. Electrochem. Soc.

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A parameter estimation procedure was established to extract physical parameters related to chemical vapor deposition ͑CVD͒ processes, which consists of in situ experimental data collection and computational analysis. Specifically, mass-transport behavior in an up-flow cold-wall CVD reactor was monitored using in situ Raman spectroscopy. A two-dimensional axisymmetric model of the reactor was developed and combined with genetic and simplex algorithms for property estimation. The numerical procedure was unambiguously able to extract binary mass diffusivities and Raman cross sections from the same data set for the methane/ nitrogen and ammonia/nitrogen cases. The procedure developed in this study is general and expected to be particularly useful in extracting diffusivities and cross sections for reaction intermediate species and kinetic parameters for complex reacting systems.Metallorganic chemical vapor deposition ͑MOCVD͒ is widely used to deposit thin semiconductor films with good crystalline quality and electrical properties. 1 However, MOCVD processes are influenced by several factors such as the choice of carrier gas, 2 substrate material and its surface preparation, 3 and the gas dynamics inside the reactor including the thermal boundary conditions. 4 Obtaining a realistic reactor model based on a fundamental understanding of the process would be useful, e.g., for optimizing an existing process or designing a new reactor.Accurate reaction kinetic information about homogeneous and heterogeneous chemical reactions in the reactor and the thermophysical properties of the gas and solid phases are required in developing a realistic model. Previously reported kinetic data on the decomposition of metallorganic sources have most often been obtained from simple flow cell or flow tube experiments. 5-7 In those analyses, homogeneous conditions are usually assumed to be established in the cell, which simplifies the subsequent data analysis, although conditions in a real MOCVD process are not truly homogeneous. The kinetic data inferred from flow cell or flow tube experiments could be confounded with other process-specific influences such as flow instability in the reactor and memory effects. 8 As an example, the pyrolysis of trimethylindium, first studied by Jacko and Price, 9 has since been examined in a flow cell experiment by several investigators. 10-13 The reported activation energy for the first-order decomposition reaction ranges from 35.9 to 54.0 kcal/mol, while frequency factors range from 10 12.0 to 10 17.9 s −1 . This wide range of values reflects the uncertainties associated with the determination of decomposition rate constants of metallorganic sources, even though some of the variation could be interpreted by the chemical effects of carrier gas on the decomposition reactions. Accurate transport properties of the gas mixture in an MOCVD reactor are also required for developing a realistic process model, but they are not well reported and usually have been estimated using the Chapman-Enskog equation. 14,15 A we...

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“…Dieses Kriterium wurde in analoger Weise auch von HanEil, Mitschka und Beranek [27], von H a j e k , D u c h e t und K o c h l o e f l [42] und von Mezaki und Kittrell [29] benutzt. Es mussen alle Modelle als gultig betrachtet werden, deren Fehlerquadratsumme kleiner Qkril ist.…”

Section: Mathematische Behandlung Der Datenunclassified

Dehydratisierung von Alkoholen an Al₂O₃XV. Kinetik der Dehydratisierung von tertiärem Butanol

Kochloefl

Knözinger

1971

Ber Bunsenges Phys Chem

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Es werden die kinetischen Daten der Dehydratisierung von tertiärem Butanol an Aluminiumoxid, die in einer früheren Arbeit [13] beschrieben sind, mit Hilfe der nicht‐linearen Regression hinsichtlich ihrer Beschreibbarkeit durch Langmuir‐Hinshelwood‐Modelle untersucht. Die Anfangsgeschwindigkeiten bei verschwindendem Wasserpartialdruck lassen in dem begrenzten Meßbereich keine eindeutige Entscheidung zu; zusammen mit Messungen bei verschiedenen Temperaturen und bei erhöhten Wasserpartialdrücken wird aber ein reaktionskinetisches Modell, das dissoziative Adsorption des Alkohols und molekulare Adsorption des kommenden Wassers postuliert, wahrscheinlich gemacht. Es wird dieses Ergebnis mit anderen experimentellen Ergebnissen zum Mechanismus der Olefinbildung verglichen und die Diskrepanzen werden diskutiert.

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Parametric Sensitivity in Fitting Nonlinear Kinetic Models

Cited by 57 publications

References 8 publications

The Use of Nonlinearity Measures in the Estimation of Kinetic Parameters of Sugarcane Bagasse Pyrolysis

The Use of Nonlinearity Measures in the Estimation of Kinetic Parameters of Sugarcane Bagasse Pyrolysis

Numerical Procedure to Extract Physical Properties from Raman Scattering Data in a Flow Reactor

Dehydratisierung von Alkoholen an Al₂O₃XV. Kinetik der Dehydratisierung von tertiärem Butanol

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Parametric Sensitivity in Fitting Nonlinear Kinetic Models

Cited by 57 publications

References 8 publications

The Use of Nonlinearity Measures in the Estimation of Kinetic Parameters of Sugarcane Bagasse Pyrolysis

The Use of Nonlinearity Measures in the Estimation of Kinetic Parameters of Sugarcane Bagasse Pyrolysis

Numerical Procedure to Extract Physical Properties from Raman Scattering Data in a Flow Reactor

Dehydratisierung von Alkoholen an Al2O3XV. Kinetik der Dehydratisierung von tertiärem Butanol

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Dehydratisierung von Alkoholen an Al₂O₃XV. Kinetik der Dehydratisierung von tertiärem Butanol