Mathematical treatment of transient kinetic data: Combination of parameter estimation with solving the related partial differential equations

Linde, Simon C. van der; Nijhuis, T.A.; Dekker, F.H.M.; Kapteijn, Freek; Moulijn, Jacob A.

doi:10.1016/s0926-860x(96)00260-8

Cited by 69 publications

(40 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It was found that fairly good agreement could be achieved between the predictions based on these models using literature values and the PET data. For further details concerning the mathematical modeling of this data the reader is referred to the original papers and to the review by Van der Linde et al [30].…”

Section: Non-medical Applications Of Petmentioning

confidence: 99%

Positron emission imaging in catalysis

Anderson

Santen

IJzendoorn

1997

Applied Catalysis A: General

View full text Add to dashboard Cite

Section: Non-medical Applications Of Petmentioning

confidence: 99%

Positron emission imaging in catalysis

Anderson

Santen

IJzendoorn

1997

Applied Catalysis A: General

View full text Add to dashboard Cite

“…Recently, a detailed estimation of the validity of TZTR-model was reported. 139 There are a number of approaches/methodologies in the TAP data analysis which are discussed in detail in the literature, including the moment-based integral approach, 19,106,140,141 differential approach, 142 curve fitting, 31,108,123,124,127,[143][144][145][146][147][148][149] as well as the extraction of kinetic parameters. 19,106 Briefly, the moment-based theory 106 is an integral analysis of each individual pulse in the series of pulses, both reactants and products.…”

Section: Discussionmentioning

confidence: 99%

“…33 Curve fitting is another commonly used approach where the experimental transient responses are fitted to different assumed kinetic models. 31,[143][144][145][146][147][148][149] The most plausible model is selected on the basis of model discrimination tests. The parameter (rate and diffusion coefficients, as well as activation energy) estimation procedure is based on a numerical solution of partial differential equations describing diffusion, adsorption, desorption, and reaction in the TAP microreactor.…”

Section: Discussionmentioning

confidence: 99%

Forty years of temporal analysis of products

Morgan

Maguire

Fushimi

et al. 2017

Catal. Sci. Technol.

131

101

View full text Add to dashboard Cite

A detailed understanding of reaction mechanisms and kinetics is required in order to develop and optimize catalysts and catalytic processes. While steady-state investigations are known to give a global view of the catalytic system, transient studies are invaluable since they can provide more comprehensive insight into elementary steps. For almost forty years temporal analysis of products (TAP) has been successfully utilized for transient studies of gas phase heterogeneous reactions, and there have been a number of advances in instrumentation and numerical modeling methods in that time. Since TAP is a complex methodology it is often viewed as a niche specialty. With the purpose to make TAP more relevant and approachable to a wider segment of the catalytic research community, part of the intention of this work is to highlight the significant contributions TAP has made to elucidating mechanistic and kinetic aspects of complex, multistep heterogeneous reactions. With this in mind, an outlook is also disclosed for the technique in terms of what is needed to revitalize the field and make it more applicable to the recent advances in catalyst characterization (e.g. operando modes).

show abstract

“…It contains two computational operations: the simulation and the NLSQ regression. For TAP, the simulation and regression were carried out numerically as outlined by van der Linde et al (1997), making use of the Livermore solver for ordinary differential equations (LSODE) from ODEPACK (Hindmarsh, 1983) for the simulation and ODRPACK (in ordinary least-squares mode) for the regression (Boggs et al, 1987).…”

Section: Data Preconditioningmentioning

confidence: 99%

Second-order statistical regression and conditioning of replicate transient kinetic data

Roelant¹,

Constales²,

Keer³

et al. 2008

Chemical Engineering Science

View full text Add to dashboard Cite

A new method has been developed to estimate physico-chemical parameters from transient kinetic data: second-order statistical regression (SOSR). It allows to account for heteroskedasticity and nonwhiteness of the noise in the time series measured. SOSR makes use of replicates to estimate the second-order statistics, i.e. the autocovariance pattern of the noise. A sample principal noise component analysis of the experimental time series allows nonlinear least-squares (NLSQ) regression of the latter. The method has been validated by regression of artificially generated experimental data and the results have been compared with those obtained with direct NLSQ regression. The SOSR has also been applied to the irreversible adsorption of oxygen on a reduced vanadia/silica catalyst and the interaction of propane with a copper/ceria catalyst, as studied with a Temporal Analysis of Products (TAP) setup. In general, compared with those obtained with direct NLSQ regression, the parameter estimates and their confidence intervals are more accurate.

show abstract

Mathematical treatment of transient kinetic data: Combination of parameter estimation with solving the related partial differential equations

Cited by 69 publications

References 34 publications

Positron emission imaging in catalysis

Positron emission imaging in catalysis

Forty years of temporal analysis of products

Second-order statistical regression and conditioning of replicate transient kinetic data

Contact Info

Product

Resources

About