TY - JOUR
T1 - Chebyshev expansions and sensitivity analysis for approximating the temperature- and pressure-dependence of chemically-activated reactions
AU - Venkatesh, Prasana K.
AU - Dean, Anthony M.
AU - Cohen, Morrel H.
AU - Carr, Robert W.
N1 - Funding Information:
We are grateful to Professor John P. Boyd for an insightful correspondence on the convergence of Chebyshev expansions. Financial support for this work was provided by the Exxon Research and Engineering Co., Annnandale, NJ, the Department of Chemical Engineering and Material Science at the University of Minnesota, Minneapolis, MN and the National Science Foundation. Computational support was provided by the Minnesota Supercomputing Centre.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 1997
Y1 - 1997
N2 - For some time now, the importance of properly treating the pressure dependence of unimolecular dissociation and bimolecular reactions involving chemical-activation has been clearly recognized. Traditional approaches which germinated from ideas originally due to Lindemann such as Troe's Fcent method work well for single-well, single-product dissociation cases. For chemically-activated reactions multi-well, multi-product cases are typical. There is thus a need to develop accurate representations of the pressure and temperature dependences of those reactions so that the simulation, optimization and control of detailed kinetic models containing chemically-activated reactions can become routine. We argue that direct approximation of the rate coefficients via Chebyshev expansions yields reliable and accurate representations of the pressure-temperature behaviour of these reactions superior to using a Lindemann approach to fit the form factor representing the fall-off-surface. Following up on an earlier study, we review the method in detail and confirm its superiority in a study of sixteen channels corresponding to four different reactions important in combustion chemistry over the ranges 300 K - 3000 K and 0.02 Atm. - 200 Atm. Additionally, rigorous theoretical methods for estimating the interpolation errors are discussed. A variational method of sensitivity analysis is reviewed and a discussion relating the sensitivity of the reaction mechanism to the accuracy of the approximations is provided.
AB - For some time now, the importance of properly treating the pressure dependence of unimolecular dissociation and bimolecular reactions involving chemical-activation has been clearly recognized. Traditional approaches which germinated from ideas originally due to Lindemann such as Troe's Fcent method work well for single-well, single-product dissociation cases. For chemically-activated reactions multi-well, multi-product cases are typical. There is thus a need to develop accurate representations of the pressure and temperature dependences of those reactions so that the simulation, optimization and control of detailed kinetic models containing chemically-activated reactions can become routine. We argue that direct approximation of the rate coefficients via Chebyshev expansions yields reliable and accurate representations of the pressure-temperature behaviour of these reactions superior to using a Lindemann approach to fit the form factor representing the fall-off-surface. Following up on an earlier study, we review the method in detail and confirm its superiority in a study of sixteen channels corresponding to four different reactions important in combustion chemistry over the ranges 300 K - 3000 K and 0.02 Atm. - 200 Atm. Additionally, rigorous theoretical methods for estimating the interpolation errors are discussed. A variational method of sensitivity analysis is reviewed and a discussion relating the sensitivity of the reaction mechanism to the accuracy of the approximations is provided.
UR - http://www.scopus.com/inward/record.url?scp=0002506486&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0002506486&partnerID=8YFLogxK
U2 - 10.1515/REVCE.1997.13.1.1
DO - 10.1515/REVCE.1997.13.1.1
M3 - Article
AN - SCOPUS:0002506486
SN - 0167-8299
VL - 13
SP - 1
EP - 67
JO - Reviews in Chemical Engineering
JF - Reviews in Chemical Engineering
IS - 1
ER -