Dynamic behaviour of simple thermokinetic chemical reaction schemes in batch, semi-batch, and continuously-stirred tank reactors

Background and motivation

Different types of dynamic behaviour have been reported experimentally in continuously stirred tank reactors: simple oscillatory ignition, multi-stage ignition, complex ignitions, oscillatory cool flames, steady glow etc. The aim of this work is to identify the bifurcation behaviour of simple chemical reaction schemes and to relate it to the experimental observations. To this end we are working with simple thermokinetic schemes.

A goal of this work is to explore the use of continuously-stirred tank reactors in investigating the flammability of gases produced by the decomposition of polymers. A long-term goal is to investigate the interaction between heterogeneously catalysed and homogeneous combustion reactions.

Much of my work in the areas of

can be classified as thermokinetic in nature. You are encouraged to read these pages details of work in these areas.

Thermokinetic schemes to model hydrocarbon oxidation

Combustion scientists and engineers require mathematical descriptions of the combustion of hydrocarbons in order to design and predict the performance of practical combustion processes such as automotive engines. The combustion of hydrocarbons is a complex process. Detailed kinetic models for the low-temperature oxidation of simple hydrocarbon fuels, at the level of elementary chemical reactions, may contain many thousands of elementary steps among hundreds of chemical species (Griffiths, 1995). Although such schemes have many uses, there is still an on-going interest in the use of reduced kinetic schemes (Griffiths, 1995). For example, reduced kinetic schemes may be used in the simulation of combustion systems where the complexities of the complex fluid dynamic flow precludes the use of very detailed mechanisms. Reduced kinetic schemes may also be used for simulations of fuels, or fuel blends, where knowledge of the fundamental chemistry is not detailed enough for developing a comprehensive mechanism. Finally, there is an interest in knowing how far simple mechanisms can predict generic behaviour observed during experimental studies.

The oxidation of hydrocarbons in batch reactors has been extensively studied; thermokinetic features of such studies are described by Griffiths (1985). 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 (Yang & Gray; 1969a, 1969b). This scheme contains two chemical species, representing the fuel and a radical species, undergoing four reactions, an initiation reaction, a branching reaction and two termination reactions, and contains both chemical and thermal feedback mechanisms. It describes many of the qualitative features observed during the oxidation of hydrocarbons (Griffiths, 1985). Note that the chemical `reactions' in reduced schemed do not typically represent specific steps in the oxidation mechanism. Rather, by limiting the number of chemical variables, it is hoped that the scheme will provide insights into experimental observations.

Since the work of Yang and Gray (Yang & Gray; 1969a, 1969b) a number of reduced kinetic models have been proposed, of increasing degrees of chemical complexity (Griffiths, 1995). In this work we plan to analyse a number of these models to see if they simulate closed-vessel experiments.

Griffiths et al (1992) presented an extension of the Gray-Yang scheme that was used to examine ideas relating to the onset of autoignition and knock in engines. This scheme contains four chemical species undergoing six reactions. The chemical species comprise: a fuel, two reactive intermediate species an a non-reactive species. One of the two termination steps is removed from the Gray-Yang scheme and three new reactions are added, One reaction introduces a second autocatalytic branch step. The additional two reactions are included to force chain branching in the second stage of ignition. In (Nelson & Balakrishnan, 2008) we analysed the steady-state behaviour of this scheme in a well-stirred batch reactor, which was the experimental configuration investigated by Yang & Gray (1969a).

We showed that this kinetic scheme has the defect that any steady-state temperature with a temperature greater than Tcr≈ 420 (K) is unphysical as the corresponding chemical concentrations are negative. Thus we conclude that this development of the Gray and Yang model is defective.

  1. J.F. Griffiths. (1985). Thermokinetic oscillations in homogeneous gas-phase oxidations. In, R.J. Field, M. Burger (editors), Oscillations and Travelling Waves in Chemical Systems, John Wiley & Sons, pp 529-564.
  2. J.F. Griffiths. (1995) Reduced kinetic models and their applications to predict practical combustion systems. Prog. Energy. Combustion. Sci, 21, 25-107.
  3. J.F. Griffiths, Q. Jiao, M. Schreiber, J. Meyer, K.F. Knoche. (1992). Development of thermokinetic models for autoignition in a cfd code: Experimental validation and application of the results to rapid compression studies, in 24th Symposium (International) On Combustion, The Combustion Institute, Pittsburgh, 1809-1815.
  4. C.H. Yang, B.F. Gray. (1969a). Unified theory of explosions, cool flames and two stage ignitions, part 2. Trans. Faraday Society 65, 1614--1622.
  5. C.H. Yang, B.F. Gray. (1969b). On the slow oxidation of hydrocarbons and cool flames. The J. Physical Chem 73(10), 3395-3406.

Highlights of research in simple thermokinetic reaction schemes

  1. Showed how the parameter regions in which oscillatory behaviour occurs in a well-stirred semi-batch reactor can be estimated by applying the Hopf bifurcation theorem. (abstract)
  2. Modelling of the open vat fermentation process used for making red wine. This was a MISG 2002 problem originating with Beringer-Blass Wine Estates (Nuriootpa, South Australia). A new reactor configuration was designed with the potential for significantly decreasing the processing time. (Submitted)

    I particularly enjoyed this problem because I've had a long standing interest in the end product of the open vat fermentation process.

  3. Analysed a reduced kinetic scheme, consisting of four chemical species undergoing six chemical reactions, that has been proposed as an extension of the Gray-Yang scheme. Showed that any steady-state solution of this model having a steady-state temperature greater than 420K 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. (Nelson & Balakrishnan, 2008).

Other `highlights' that can also be considered to be in the area of chemical reactor engineering can be found in

My collaborators in modelling simple thermokinetic reaction schemes

Dr E. Balakrishnan 2004-present
Dr. G.N. Mercer 1999-Present
Dr. J. Sexton 1999-Present
Dr. H.S. Sidhu 1999-Present
Dr. A.G. Tate 2002-Present
Dr. R.O. Weber 1999-Present.


    Referred papers

  1. H.S. Sidhu, M.I. Nelson, G.N. Mercer and R.O. Weber. Dynamical analysis of an elementary X+Y-->P reaction in a continuously stirred tank reactor Journal of Mathematical Chemistry, 28(4):353-375, 2000.
  2. M.I. Nelson and H.S. Sidhu. Bifurcation phenomena for an oxidation reaction in a continuously stirred tank reactor. I Adiabatic operation. Journal of Mathematical Chemistry, 31(2): 155-186, February 2002.
  3. M.J. Sexton, H.S. Sidhu, and M.I. Nelson. Numerical Investigation of a Reaction in a Batch Reactor: Flammability Limits. The Anziam Journal, 44(E): C687-C704, 2003.

    The full text of this article is available from http://anziamj.austms.org.au/V44/CTAC2001/Sext/home.html.

  4. M.I. Nelson and H.S. Sidhu. Bifurcation phenomena for an oxidation reaction in a continuously stirred tank reactor. II Diabatic operation. The Anziam Journal, 45, 303-326, 2004.
  5. M.I. Nelson and H.S. Sidhu. Flammability limits of an oxidation reaction in a batch reactor. II The Rychlý mechanism. Journal of Mathematical Chemistry, 35(2), 119-129, February 2004.

    The DOI (Digital Object Identifier) link for this article is http://dx.doi.org/10.1023/B:JOMC.0000014308.66514.e7.

  6. M.I. Nelson. Bifurcation phenomena for an oxidation reaction in a continuously stirred tank reactor. III The inhibiting effect of an inert species. The ANZIAM Journal, 46(3), 399-416, March 2005.
  7. H.S. Sidhu and M.I. Nelson. Behaviour of an elementary oxidation reaction in a semi-batch reactor. Chemical Engineering Journal, 110(1-3), 31-39, 2005.
  8. The DOI (Digital Object Identifier) link for this article is http://dx.doi.org/10.1016/j.cej.2005.04.012.

  9. H.S. Sidhu, S.D. Watt, M.I. Nelson and A.K. Ray. Performance improvement and dynamical behaviour analysis of a cascade of two CSTRs. International Journal of Chemical Reactor Engineering, 5: A13, 2007.

    This paper is available at http://www.bepress.com/ijcre/vol5/A13.

  10. M.I. Nelson and E. Balakrishnan. Autoignition of hydrocarbons in a batch reactor. Analysis of a reduced model. Applied Mathematics Letters, 21(8), 866-871, 2008.
  11. The DOI (Digital Object Identifier) link for this article is http://dx.doi.org/10.1016/j.aml.2007.08.014.

    Refereed conference proceedings

  12. H.S. Sidhu, M.J. Sexton, M.I. Nelson, G.N. Mercer, and R.O. Weber. A simple combustion process in a semibatch reactor. In R.L. May, G.F. Fitz-Gerald, and I.H. Grundy, editors, EMAC 2000 Proceedings, pages 251--254. The Institution of Engineers, Australia, 2000. ISBN 085825 705X.

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Page Created: 18th April 2002.
Last Updated: 20th June 2008.