UK Nonlinear News, February 1999

Analysis, simulation, dynamics of chemical reactors: Introduction to some fundamental techniques

Editors: Gaetano Continillo, Silvestro Crescitelli & Pier Giorgio Lignola

Reviewed by Harvinder S. Sidhu

Publisher: CUEN, Napoli, Italy . 1995.
ISBN: 88 7146 293-9
Price: US $ 35.00

This book is based upon a lecture course organised within the Interdivisional Study Group on Computational Chemistry of the Italian Chemical Society. The main purpose of the course was to highlight the important role that mathematics plays in problems relating to chemical reactor dynamics. The contents do not appear as chapters but as a series of 17 self-contained articles, presumably based upon the lectures. References are given at the end of each article, which I found to be quite useful. The articles are of two types: mathematically-based, providing theory and examples applied to chemical reactions, and chemistry-based, describing the processes involved.

The first two articles provide a good elementary introduction to mathematical models of the batch and continuous flow reactors, and a description of numerical methods for solving ordinary differential equations. Although the latter discussion was somewhat brief, it was of sufficient rigour.

Current issues in modelling diffusion and chemical reactions in porous solids are described in the third article, whereas the next two articles are more mathematically based. At 40+ pages article 4 is one of the longest in the book and provides a general overview of the usefulness of singularity theory in explaining bifurcation behaviour in well stirred flow reactors. The use of statistical analysis in chemical reaction modelling is described in the next article. The 6th article provides an interesting overview of the kinetic analysis of complex reacting systems and provides some intriguing suggestions for future work in this area.

Articles 7, 10, 14 and 16 provide a general description of nonlinear dynamical system analysis of chemical reactions. The discussions in these articles include phase-plane analysis, bifurcation theory, phase transitions, symmetry breaking phenomena, Turing patterns, parameter continuation techniques and chaotic chemical reactions, including chemical turbulence. In my opinion most of these articles are well written and would provide a good starting point for chemists or chemical engineers who are interested in nonlinear dynamical systems. The issues of multiplicity of steady-states, stability of chemical reactors and parameter sensitivity which are addressed in article 11, are extremely important in reactor theory as they have serious safety implications.

The next article provides an overview of gas-liquid reactions. Elementary discussions of reaction-diffusion equations are discussed in article 13. This is followed by a brief description of chemical reaction engineering of multi component mixtures. I found that the final article, which describes the distributed-parameter models of exothermic reactions with heat transfer effects, most stimulated my interest.

In summary I believe that this is a useful book which has achieved its goal of drawing the attention of the mathematical community to the `fertile' field of chemical reactor dynamics. Although the brevity of some articles may be criticised by some, a full description of these may require several volumes. Nevertheless the book provides enough information to ``wet the appetite'' of an interested reader.

Harvinder S. Sidhu
School of Mathematics and Statistics
University College (University of New South Wales)
Australian Defence Force Academy
Northcott Drive
Canberra ACT 2600

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