Mathematics in Chemical
Kinetics and Engineering

The Laboratory for Petrochemical Technology (LPT) and the Research Group for Numerical functional analysis and Mathematical Modelling (NfaM2) of Ghent University are pleased to invite you to attend the annual seminar on "Mathematics in Chemical Kinetics and Engineering" which will be held on April 25th, 2003 in Ghent, Belgium.

After the successful international Mackie-2002 conference held last year at Ghent University, the local organizers have now invited two world-class experts from the fields of mathematics and chemical engineering, Prof. Gerhart Eigenberger (Stuttgart Univ.) and Prof. Vladimir Gol'dshtein (Ben-Gurion Univ.) to give seminar talks during a one-day mini-symposium.

Participation to the seminar is free, but registration is requested AS SOON AS POSSIBLE. Lunch is available at the venue (15 euro).

Program

• 10:00 Coffee and registration
• 10:45 Introduction
• 11:00 Gerhart Eigenberger on Pattern formation in fixed-bed reaction and separation processes - Analysis and application
• 12:00 Question time and discussion
• 12:30 Lunch
• 14:30 Vladimir Gol'dshtein on Multiscale analysis of multiphase combustion
• 15:30 Question time and discussion
• 16:00 Concluding remarks and closing address

Organizing Committee

• Denis Constales (NfaM2)
• Geraldine Heynderickx (LPT)
• Guy Marin (LPT)
• Roger Van Keer (NfaM2)

Abstracts

• "Pattern formation in fixed-bed reaction and separation processes --- Analysis and application", by Gerhart Eigenberger and Grigorios Kolios, Institut für Chemische Verfahrenstechnik, Universität Stuttgart, Germany.
  Characteristic patterns in fixed-bed processes are self-sharpening or dispersive reaction and/or adsorption fronts. They play an important role in Chemical Engineering processes. In this contribution we will present an overview about the origin and the basic characteristics of the different fronts and discuss the influence on the behavior of the reaction and separation processes in which they occur.
  We will distinguish between simple temperature fronts (heat waves) and reaction fronts of fluid reactions for endothermic reactions and for exothermic with and without deactivation. A second class comprises of reaction fronts in which a part of the solid fixed-bed participates in form of a fluid-solid reaction. Typical examples are coke combustion from catalyst beds or soot combustion from Diesel particulate filters. Compared to exothermic reaction fronts for fluid reactions the behavior is further influenced by the availability and consumption of the solid reactant.
  The third class of fronts are adsorption/desorption fronts which tend to be self-sharpening or dispersive depending upon the curvature of the adsorption isotherm or the volume fraction of adsorbable component in the feed.
  Reaction or sorption fronts have found their most interesting applications in periodi-cally operated fixed-bed processes which cycle between a storage and regeneration phase. If this cycling is combined with a periodic reversal of flow direction, an additional positive feedback is introduced which can substantially influence process dynamics and stability. Examples are fixed-bed reactors with periodic flow reversal and pressure swing adsorption processes for gas phase separations which will be presented in some detail.
  The parametric sensitivity and stability analysis of cyclic, spatially extended systems is so far not very well developed. For high cycling frequency an analogy with co- or countercurrent membrane processes can be used. For larger cycle periods, characteristic of most engineering applications, efficient methods for the direct calculation of the cyclic steady state will be required. We will discuss some novel developments in this area.
• "Multiscale analysis of multiphase combustion", by Igor Goldfarb and Vladimir Gol'dshtein, Department of Mathematics Ben-Gurion University of the Negev, Israel.
  Multiphase combustion is a widespread phenomenon in industry (sprays in Diesel engines, spontaneous insulation fires in chemical plants, flame propagation in porous media, etc). Physico-chemical processes of different nature with sufficiently different time scales are generally involved in multiphase combustion processes. Existence of an essential dispersion of time scales leads to multiscale systems of governing equations (more formally, singularly perturbed systems of differential equations).
  The hierarchical structure of mathematical models allows to apply various asymptotic approaches for analysis of systems dynamics. We suggested to use a geometrical asymptotic method of invariant (integral) manifolds (MIM) adapted to combustion and chemical kinetics problems. MIM permits to conduct an analytical investigation of the multiphase combustion models, allows to describe qualitatively systems dynamics and to gain estimations of key parameters. This geometrical interpretation of multi-scale hierarchy of systems dynamics permits to decompose an original high dimensional problem to a few separate problems of essentially lower dimension on invariant (integral) manifolds.
  We will discuss two main types of problems: thermal runaway and flame propagation in sprays. The obtained results are relevant to modeling of Diesel engines and hazardous flames formation and propagation in insulation materials. One of distinguishing features of the multiphase combustion is existence of comparatively long-time delay before finale blow-up due to competition between the exothermic chemical reaction and heat sink to the liquid and/or solid phase. Typical examples are self-ignition delay in Diesel engines and long-time self-ignition delays in insulation materials.
  Thermal runaway. This phenomenon is modelled using the spatially uniform approach. The typical parametric classification of the dynamical behavior includes conventional (?fast?) thermal runaway and the mainly interesting phenomenon of delayed self-ignition. Estimations for the delay time are derived for the typical sprays and porous media. The relevant estimates for simplified models of Diesel engines have good agreement with appropriate numerical simulations.
  Pressure driven flames. Traditionally the study of the premixed gas flames in an open space ignores the pressure perturbations. It means that pressure disturbances come away from the reaction zone and do not influence on the intensity of the thermal processes. In this research we deal with a gas phase combustion in inert porous media. The distinguishing feature of inert porous media is the well-known fact that under definite conditions the speed of pressure perturbations may be significantly lower than sound velocity in the open space. In these conditions the local elevation of the pressure may lead to a formation of the self-sustaining combustion wave controlled by pressure diffusion (rather than the conventional thermal diffusion) We will discuss an original model proposed for description of the phenomenon and a special asymptotic approach (based on MIM) which allow us to study a fine structure of flame front and the the flame velocity dependence on barodiffusion.

Venue

Tourist Attractions in Ghent

Ghent, founded in the 10th century AD, has today a population of over 200 thousand. The official language is Dutch; knowledge of English is very widespread.

Major touristic attractions include the Gothic Cathedral and other medieval churches, the Van Eyck Altarpiece depicting the Adoration of the Mystic Lamb, the City Museum of Contemporary Art (SMAK), and numerous shops selling Flemish specialities such as local beers, lace and many other renowned products of authentic handicraft.

Weather

You can register by sending e-mail to dcons@world.std.com. Please also state if you want lunch at the venue (cost: 15 euro).

For the latest information, consult the annual seminar's Web site at www.mackie-workshops.com