### Abstract

In the late 1960s Gray and Yang developed the first reduced kinetic model for the oxidation of hydrocarbon fuels that qualitatively described many features observed experimentally. Since then a number of reduced kinetic models have been proposed in the literature. In this contribution we analyse the steady-state behaviour of one such scheme. The chemical component of the model contains four chemical species undergoing six reactions. By making a pool chemical approximation this system is reduced to three coupled non-linear differential equations: a temperature equation and equations for two reactive chemical intermediates. It is shown that any steady-state solution of this model having a steady-state temperature greater than 420 K is non-physical as the steady-state concentrations of the chemical species are negative. Hence this particular scheme does not simulate closed-vessel experiments and is defective as an extension of the Gray-Yang model.

Original language | English |
---|---|

Pages (from-to) | 866-871 |

Number of pages | 6 |

Journal | Applied Mathematics Letters |

Volume | 21 |

Issue number | 8 |

DOIs | |

Publication status | Published - Aug 2008 |

### Fingerprint

### Keywords

- Autoignition
- Batch reactor
- Reduced kinetic model

### ASJC Scopus subject areas

- Computational Mechanics
- Control and Systems Engineering
- Applied Mathematics
- Numerical Analysis

### Cite this

*Applied Mathematics Letters*,

*21*(8), 866-871. https://doi.org/10.1016/j.aml.2007.08.014

**Autoignition of hydrocarbons in a batch reactor : Analysis of a reduced model.** / Nelson, M. I.; Balakrishnan, E.

Research output: Contribution to journal › Article

*Applied Mathematics Letters*, vol. 21, no. 8, pp. 866-871. https://doi.org/10.1016/j.aml.2007.08.014

}

TY - JOUR

T1 - Autoignition of hydrocarbons in a batch reactor

T2 - Analysis of a reduced model

AU - Nelson, M. I.

AU - Balakrishnan, E.

PY - 2008/8

Y1 - 2008/8

N2 - In the late 1960s Gray and Yang developed the first reduced kinetic model for the oxidation of hydrocarbon fuels that qualitatively described many features observed experimentally. Since then a number of reduced kinetic models have been proposed in the literature. In this contribution we analyse the steady-state behaviour of one such scheme. The chemical component of the model contains four chemical species undergoing six reactions. By making a pool chemical approximation this system is reduced to three coupled non-linear differential equations: a temperature equation and equations for two reactive chemical intermediates. It is shown that any steady-state solution of this model having a steady-state temperature greater than 420 K is non-physical as the steady-state concentrations of the chemical species are negative. Hence this particular scheme does not simulate closed-vessel experiments and is defective as an extension of the Gray-Yang model.

AB - In the late 1960s Gray and Yang developed the first reduced kinetic model for the oxidation of hydrocarbon fuels that qualitatively described many features observed experimentally. Since then a number of reduced kinetic models have been proposed in the literature. In this contribution we analyse the steady-state behaviour of one such scheme. The chemical component of the model contains four chemical species undergoing six reactions. By making a pool chemical approximation this system is reduced to three coupled non-linear differential equations: a temperature equation and equations for two reactive chemical intermediates. It is shown that any steady-state solution of this model having a steady-state temperature greater than 420 K is non-physical as the steady-state concentrations of the chemical species are negative. Hence this particular scheme does not simulate closed-vessel experiments and is defective as an extension of the Gray-Yang model.

KW - Autoignition

KW - Batch reactor

KW - Reduced kinetic model

UR - http://www.scopus.com/inward/record.url?scp=44949165595&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=44949165595&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2007.08.014

DO - 10.1016/j.aml.2007.08.014

M3 - Article

VL - 21

SP - 866

EP - 871

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

IS - 8

ER -