Extracting qualitative dynamics from experimental data

https://www.engr.colostate.edu/~marchese/combustion10/4.pdf

A Comprehensive Modeling Study of n-Heptane Oxidation

Numerical Initial Value Problems in Ordinary Differential Equations

Chemical kinetic modeling of hydrocarbon combustion

https://www.engr.colostate.edu/~marchese/combustion10/3.pdf

A Comprehensive Modeling Study of iso-Octane Oxidation

A detailed chemical mechanism for the cerium catalyzed bromination and oxidation of malonic acid by bromate has been developed, and complete numerical solutions have been obtained for the temporal behavior of the concentrations of the intermediate species. The many points of similarity with the experimentally observed initial decay, long quiescence, and abrupt transition to sustained oscillation establish confidence in the essential validity of the proposed mechanism. Close examination of the time dependence of these species concentrations as well as the magnitude of the several reaction channels permits the clarification of the switching mechanism causing theoscillatory behavior of this system. The results appear to exhibit limit cycle behavior, in accordance with theoretical predictions.

Mechanistic details of the Belousov–Zhabotinskii oscillations

The mechanisms of the pyrolyses of the n-alkanes C3H8, n-C4H10, and n-C5H12 at temperatures between 390 and 560°C have been studied by the construction and evaluation of sets of several hundred reactions. Rate parameter values were assigned using literature data and calculated estimates. Time-dependent numerical solutions were computed for the experimental conditions of several rate and product studies reported in the literature. The comparisons of these a priori computations with experiment show excellent agreement for propane and agreement for butane and pentane within the estimated error limits of the assigned rate parameters. These results demonstrate that the general “state of knowledge” of the mechanism of alkane pyrolysis, namely, the reactions and their rate parameters, is such that reasonable a priori predictions of experimental results can be made. Discussions of the major stepwise processes in the pyrolyses are presented, and the importance of allyl radicals in termination is demonstrated.

A computational modeling study of the low-temperature pyrolysis of n-alkanes; mechanisms of propane, n-butane, and n-pentane pyrolyses

The previously reported extensive mechanism for the pyrolysis of propane and n-butane around 800 K is reexamined in the light of a recent reevaluation of the rate constant data base, and the sensitivity of model simulations to variations in the rate parameters is studied. The pyrolysis rates of butane and the product distribution of propane remain in good agreement with the available experiments, while the rate of propane and the product distribution of butane now show significant differences. The linear sensitivity analysis of the reaction matrix demonstrates an intimate coupling between initiation, hydrogen abstraction, radical decomposition, and recombination reactions as primarily responsible for the overall behavior of the mechanism. The role of unsaturated radicals in the self-inhibition of the pyrolysis process is quantitatively established. The study of the sensitivity coefficients for butane product formation has permitted pinpointing those specific reaction steps in the mechanism which are most likely responsible for the remaining discrepancies between model and experiment. This particular example demonstrates the usefulness of sensitivity calculations for the isolation of reactions for which improvements in rate parameter values are needed.

A computational analysis of the alkane pyrolysis mechanism: Sensitivity analysis of individual reaction steps

Our previous mechanistic model for the Belousov–Zhabotinsky reaction has been revised to include a more realistic set of reactions for the oxidation pathways of the organic intermediates. A few other rate constants have also been modified to include new information. The revised mechanism reproduces the essential experimental observations, although the periods of oscillation are somewhat too long and oscillations cease at malonic acid concentrations about ten times greater than the observed lower limit. However, the essential features of the mechanism are clearly understood.

Mechanistic details of the Belousov–Zhabotinsky oscillations. II. The organic reaction subset

The kinetic equations for an 81-reaction model of a photochemical smog chamber have been solved using a complete numerical integration as well as a quasi-steady-state approximation (QSSA) procedure. The two sets of results differ markedly in their prediction of experimentally significant factors such as the hydrocarbon depletion rate and the ozone and (NO)x peaking times. The sources of the discrepancy are traced to the fact that the assumed steady-state conditions were not satisfied, leading to errors in the concentrations of intermediate radicals which in turn affect critical rates in the reaction model.



The occurrence of such discrepancies in various types of reaction models, and with different QSSA strategies, is discussed, and it is concluded that the extent of such errors in QSSA calculations cannot be reliably predicted. Their impact on conclusions regarding reaction mechanisms and rate constants can surpass uncertainties in experimental data; conversely the credibility of predictions derived through QSSA calculations becomes highly suspect. Since recently devloped methods for complete numerical integration of systems of kinetic equations are now available, it is recommended that these be adopted in future work, and that the use of QSSA be abandoned.

D. Edelson

Papers

Mechanistic details of the Belousov–Zhabotinskii oscillations

A computational modeling study of the low-temperature pyrolysis of n-alkanes; mechanisms of propane, n-butane, and n-pentane pyrolyses

A computational analysis of the alkane pyrolysis mechanism: Sensitivity analysis of individual reaction steps

Mechanistic details of the Belousov–Zhabotinsky oscillations. II. The organic reaction subset

The steady‐state approximation: Fact or fiction?