Miloš Marek

Current status of modeling lean exhaust gas aftertreatment catalysts

Decreasing emission limits lead to the development of combined aftertreatment systems, consisting of combinations of different catalyst technologies and particulate filters. Modeling such systems can contribute considerably in reducing development time and cost. The methodology for developing catalyst models is reviewed and models for the diesel oxidation catalyst (DOC) with hydrocarbon (HC) adsorption, the NOx storage and reduction catalyst (NSRC) and the urea–selective catalytic reduction system (urea–SCR) are developed. Applications for exhaust aftertreatment system modeling are shown.

Strange attractors in coupled reaction-diffusion cells

Abstract A numerical study of two identical reaction cells with diffusion coupling has shown that the structure of motion in the system in principle agrees with results reported for variety of dynamic systems. When the characteristic parameter is varied, alternating sub-intervals of stable periodic ( P k ) and stable aperiodic ( A l ) solutions appear. The sub-intervals are connected by intervals, where tangent bifurcations and infinite sequences of subharmonic bifurcations occur. Feigenbaum relation holds for the studied sequence of subharmonic bifurcations. Aperiodic (chaotic) states are characterized by a complete set of one-dimensional Lyapunov exponents, by power spectra, and by corresponding Poincare maps. The spectra of Lyapunov exponents are of the type (+.0.-.-), and show that the topological dimension of the chaotic attractor is two. The power spectra are of two different types (a) the spectra with sharp peaks located above the broad-band noise, showing statistical phase coherence of the attractor, (b) the flat spectra showing only broad-band noise, corresponding to phase incoherent attractor. The phase coherence is present close after every point of accumulation. Phase incoherence arises when the strange attractors contain unstable periodic orbits with different topology. The relations of bifurcated stable and unstable periodic solutions (computed by means of continuation techniques) to the structure of the strange attractor is discussed and Poincare maps are used to illustrate the dependence of the structure of the attractors on the value of the characteristic parameter.

Dissipative structures in coupled cells: Experiments

A system of coupled cells with mutual mass exchange and reaction is widely used as a model of heterogeneous catalytic reactors, catalytic reactions at the surface of a solid catalyst, in models of cell growth in morphogenesis, modeling of physiological systems, etc. A model hexagonal structure of seven thermostatted, flow‐through, well‐stirred reaction cells with mutual mass exchange between the cells was constructed and tested experimentally. The Belousov–Zhabotinsky reaction of oxidation of malonic acid by acidic bromate with ceric–cerous ion catalyst was used in experiments. Two stable stationary states can exist in a single flow‐through cell in a well‐defined range of inlet concentrations of malonic acid. When a string of up to seven cells is coupled by mutual mass exchange between neighboring cells, various combinations of ’’upper’’ and ’’lower’’ stable stationary states in individual cells—dissapative structures—can exist. The stability of dissipative structures to perturbations in Ce4+ and Br− ion ...

The Reversal and Splitting of Waves in an Excitable Medium Caused by an Electrical Field

The reversal and splitting of traveling concentration waves was observed in a one-dimensional Belousov-Zhabotinski reaction medium under the influence of low-intensity electric field gradients (∼10 V per centimeter). The wave reversal and splitting were strongly correlated with a characteristic transformation of the shape of both the wave front and the refractory tail of a wave in the local field gradient. The secondary role of generated hydrodynamic flow on wave transformation was also investigated.

Modelling of chemical reactors — X Multiple solutions of enthalpy and mass balances for a catalytic reaction within a porous catalyst particle

As was already shown, equations describing mass and enthalpy balances for an exothermic reaction taking place inside a porous catalyst particle can have more than one stationary solution. In this paper, two conditions for the existence of multiple solutions were stated: (1) the value of parameter γβ has to be greater than a certain critical value, (γβ)*, (2) Thieles modulus has to be simultaneously in the definite range φ1 ⩽ φ ⩽ φ2 on the basis of the model, where the state of the particle is described by means of mean values of concentration and temperature. Values of (γβ)* and the critical limits of Thieles modulus φ1 and φ2 for reactions of power and of adsorption type of kinetics were then calculated. Values thus obtained, are in good agreement with correct values, obtained from numerical integration of conservation equations. In the last part of the paper a general procedure was described, which enables one to determine, whether for a given set of values of physical parameters more than one stationary profile of concentration in the catalyst particle can exist.

Modelling of catalytic monolith converters with low- and high-temperature NOx storage compounds and differentiated washcoat

Two types of catalytic washcoats with different properties can be present simultaneously in a monolith channel, e.g. the flat foils and the corrugated ones in metallic monolith can be individually coated with specific type of the washcoat. The model of such multiphase, differentiated NOx storage and reduction (NSR) catalytic monolith converter has been developed. The important reactions as are the oxidation of carbon monoxide, hydrocarbons and hydrogen, the reduction of nitrogen oxides (NOx), the water gas shift and the steam reforming reactions, the NO/NO2 transformation, and the oxygen and NOx storage are considered. Unknown kinetic parameters of the NSR are evaluated from transient experiments with the samples of two different types of NSR catalysts. The first catalyst is of the Pt–γ-Al2O3–CeO2 type with alkali earth metals (e.g. barium) as NOx storage components (active at lower temperature). The second one is of the PtRh–γ-Al2O3–CeO2 type with both alkali earth metals and alkali metals (e.g. potassium) as NOx storage components (active at higher temperature). Simulations of periodic lean/rich operation of the low-temperature, the high-temperature and the differentiated (combined) NSR converters are performed. The results of the computations agree well with the experimental data. The dependences of integral NOx conversion on the lengths of the lean and rich phases and on the temperature of the inlet gas are discussed. The efficiencies of the low-temperature, the high-temperature and the differentiated NSR converters are compared at different operating conditions.

Packed bed axial thermal conductivity

Abstract Packed bed axial thermal conductivity has been evaluated from steady state packed bed axial temperature profiles. Solid particles of different sizes, shapes and thermal conductivities have been used for measurements, which covered large interval of Reynolds numbers, Re ϵ 3 >. Empirical relation for estimation of Peclet number for axial heat transport, which includes effects of all significant heat transport mechanisms, has been obtained in the form

Modeling of Transport and Transformation Processes in Porous and Multiphase Bodies

Abstract A methodology for computer representation of the structure of spatially complex multiphase media and for the modeling of reaction, transport, and structure-transformation processes in those media, is reviewed. The methodology is demonstrated via several examples including phase transition and structure evolution in porous and granular media, the morphogenesis of polymer particles, and heterogeneous catalysis. Several future potential applications of the methodology are identified.

Mathematical modelling of catalytic monolithic reactors with storage of reaction components on the catalyst surface

Abstract Effects of periodic switching between lean and rich combustion conditions on CO, HC and NO x conversion on a monolithic catalyst with NO x storage were simulated by mathematical model. The model includes description of oxygen and NO x storage on the washcoat. Parametric study showed possibility to reach much improved time-averaged NO x conversion on a single monolith in comparison with steady-state operation, but lower CO and HCs conversions under reducing (rich) conditions. Sequence of monoliths, the first one with NO x storage catalyst and the second one with oxidizing catalyst, then enables to obtain satisfactory conversions of all pollutants.

Dynamics of particle growth and overheating in gas-phase polymerization reactors

The particle overheating is an important problem in the industrial catalytic gas-phase olefin polymerization reactors. It has been first investigated with a pseudo-stationary model of a single polymer particle by Hutchinson and Ray (J. Appl. Poly. Sci. 34 (1987) 657). A systematic study of overheating of polymer particle with models based on Ficks and dusty gas model (DGM) transport described below is conducted by tools of continuation (steady-state) analysis and by dynamic simulations. The consideration of convective flow of species in particle pores driven by pressure gradient due to the change in the number of moles in the course of the polymerization reaction makes the polymer particle in the reaction environment containing only monomer more susceptible to overheating. It is found that an intraparticle mass transport resistance has an important effect on particle overheating. The prediction and discussion of a time-scale of particle overheating under industrial process conditions is coupled with the discussion of the dynamics of particle growth and dynamic changes of catalyst activity.