Download the paper from http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/702.
This paper was awarded a `John A Brodie Medal: Certificate of Merit' for being one of the top six papers published in the 9th Asia Pacific Confederation of Chemical Engineers Congress (2002) in practical application of chemical engineering. There were over 900 papers provided to the congress. The award is given annually by the Chairman of College of Chemical Engineers, The Institution of Engineers of Australia.
Abstract
We study the spatial behaviour of the hydrogen-chlorine reaction in a
batch reactor. The solutions exhibit regimes of slow and fast
reaction. The main aim of this work is to distinguish between flaming
and non-flaming mixtures from the numerical solutions. After
setting out a practical criterion for flammability, we construct
diagrams in parameter space which display the regions in which the
reaction mixture is flammable.
M.J. Sexton, H.S. Sidhu, and M.I. Nelson. Numerical Investigation of a Reaction in a Batch Reactor: Flammability Limits. ANZIAM Journal, 44(E): C687-C704, 2003.
Download the paper from http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/702.
Introduction
The past four decades have seen extensive research aimed at improving product yields in chemical reactors. Many studies, both experimental and theoretical, have shown that periodic forcing is an appropriate engineering tool to improve the conversion or selectivity of a desired product [Silveston et al, Stankiewicz & Kuczynski]. However, the additional complications and costs associated with implementing external periodic operation have limited the uptake of this technique within industry [Silveston et al, Stankiewicz & Kuczynski].
Recently Ray [Jianqiang & Ray, Ray] and Yang [Balakrishnan & Yang, Yang & Su] have independently investigated the possibility of combining the advantages of periodic operation with the benefits of using two reactors arranged in series through the use of `natural oscillations'. By `natural oscillations' it is meant that the process parameters are chosen so that a steady input of reactants into the first reactor generates self-sustained oscillations in its output. This output then forces the second reactor.
The attraction of this method is that no external energy is required to generate the oscillations. Improvements in reactor performance are therefore achieved without the additional costs associated with external periodic forcing. Consequently, this approach harnesses the advantages of periodic forcing without the expense of implementing such perturbations.
Previous investigations have shown significant increases in product yields for biochemical processes using this approach processes using this approach [Balakrishnan & Yang, Jianqiang & Ray, Ray, Yang & Su]. These results were obtained through extensive computations: the governing equations were integrated for numerous values of the process parameters to find the values giving the best reactor performance. This approach is time consuming. More importantly, regions of parameter space may be easily missed. Balakrishnan and Yang found that such an omission occurred in the work reported in Yang & Su, despite the simplicity of the system investigated. As the system complexity increases (through more detailed chemistry and/or systems with more than two reactors) the likelihood of similar omissions increases when investigation relies upon direct integration. Hence there is need for a more efficient and systematic approach to investigate these systems.
Here we illustrate how the application of techniques from nonlinear dynamical systems theory, in particular bifurcation analysis and singularity theory, provides practical insights into this novel operational strategy. For instance, it is important to identify the regions of parameter space in which natural oscillations occur. On a bifurcation diagram the regions in which a steady input of reactants into reactor 1 may produce a periodic input of reactants into reactor 2 are defined by parameter values that represent degenerate Hopf bifurcations. Within these regions the values of the primary bifurcation parameter over which periodic behaviour occurs are defined by Hopf and/or double-zero bifurcation points. As noted in Balakrishnan & Yang the optimal yield may not be associated with a limit-cycle, but rather may occur at a stable steady-state. Thus it is important to investigate both both the dynamic and static multiplicity of the reactor model. In this paper we report some results along these lines.
References
M.I. Nelson and H.S. Sidhu. Improving the Productivity of Bioreactors using Natural Oscillations. In R.L. May, and W.F. Blyth, editors, EMAC 2003 Proceedings, pages 163--168. Engineering Mathematics Group, Anziam, 2003. ISBN 1-86365-533-6.
Abstract
We investigate the yield of a biological reaction occurring in a reactor system
that consists of two well-stirred reactors arranged in series.
Previous
investigations into this model used numerical integration of the
governing equations to determine operating conditions for maximum
product yield. In this study we show a more efficient
and systematic means of analysing the system through the use of
nonlinear dynamical systems theory and the
software package Auto.
M.I. Nelson and H.S. Sidhu. Efficient Means of Determining Product Yields in Reactors. In Proceedings of the 31st Australasian Chemical Engineering Conference, CHEMECA 2003, 6 pages (on CDROM), 2003. ISBN 0-86396-829-5.
This paper was awarded a `John A Brodie Medal: Certificate of Merit' for being one of the top six papers published in the 9th Asia Pacific Confederation of Chemical Engineers Congress (2002) in practical application of chemical engineering. There were over 900 papers provided to the congress. The award is given annually by the Chairman of College of Chemical Engineers, The Institution of Engineers of Australia.
Abstract
In this paper we model the thermal behaviour of cellulosic
materials in the presence of micro-organisms undergoing exothermic reactions.
For simplicity we consider a spatially uniform model which is based upon
Semenov's theory for thermal explosions.
We use singularity theory to investigate the generic properties of the model.
We consider first the case in which chemical reactions are absent, which
represents heat generation in low-oxygen containing environments. Here we
show that there are two generic steady-state diagrams including one
in which the temperature-response curve is the standard
S-shaped curve familiar from combustion problems. Thus biological
self-heating can cause jumps in the steady temperature. We then
investigate the full model, which is shown to have three generic
steady-state diagrams. If the energy released from the chemical
reaction is sufficiently small then the steady-state
diagram may contain an elevated
temperature branch, which is the feature of practical interest in
facilities such as industrial compost heaps and municipal tips.
If the chemical reaction is too strong the
energy released by biological action increases the local temperature
sufficiently high that spontaneous ignition of the cellulosic material
occurs. For a given degree of chemical activity it is possible to predict
the biological activity at which combustion is initiated.
M.I. Nelson, E. Balakrishnan, and X.D. Chen. A Semenov model of self-heating in compost piles. Transactions of IChemE Part B: Process Safety and Environmental Protection. 81(B), 375-383, 2003.