INSTITUTE OF CHEMICAL TECHNOLOGY, PRAGUE
Department of Chemical Engineering
Matyáš Schejbal
Dynamic Behaviour of Complex Catalytic Systems
PhD Thesis Annotation
Thesis supervisors:
Prof. Ing. Miloš Marek, DrSc.
Prof. RNDr. Milan Kubı́ček, CSc.
Prague, 2009
Annotation
This PhD thesis is devoted to mathematical modelling of diesel particulate filters
(DPF) and the application of such models in the software tool for simulation of
complete aftertreatment systems.
The first chapter of the thesis deals with the introduction of diesel engines,
their advantages and disadvantages. One of their properties is lean character
of emissions, containing high concentrations of oxygen and nitrogen oxides, and
production of solid particulates. Formation, properties, health issues and environmental impact of emitted gases and particulate matter are discussed.
The second chapter describes current technologies used for purification of diesel
exhaust gas. These technologies introduced here are diesel oxidation catalyst
(DOC), NOx storage and reduction catalyst (NSRC), selective reduction catalyst
(SCR) and the above mentioned DPF. Proper combinations of these monolithic
converters forms interconnected systems that remove harmful gaseous components and particulate matter from the exhaust. Function of individual converters
and their contribution to emission control is described in detail: The DPF, often called wall-flow monolith, serves for the removal of diesel particulate matter
while the flow-through converters–diesel oxidation catalyst or NOx storage and
reduction catalyst–are used for the abatement of hydrocarbons, carbon monoxide
and nitrogen oxides.
The third chapter covers chemical reactions occurring within the DPF or its
catalytic version (CDPF). Main attention is paid to soot oxidation reactions and
their kinetics. Reaction mechanisms are also mentioned as well as the influence
of moisture. Soot combustion section can be divided into three parts: soot oxidation by O2 , by NOx +N2 O and by NO2 –O2 mixture. Pt-doped catalytic coating
of the CDPF is also able to convert gaseous components, hence, the following
reactions are involved: First, NO2 /NO transformation, which plays a major role
in passive filtration systems, where NO2 is the only soot oxidizing agent. Second,
hydrocarbons, carbon monoxide and hydrogen oxidation reactions, which form
the basic reaction set for every catalyzed converter. Third, different reactions
of NOx reductions, which can occur in the case of lack of oxygen and, finally,
reactions producing hydrogen (water gas shift and steam reforming reactions).
The fourth chapter introduces two general models of the DPF. First section
covers geometrical and design terminology necessary for the understanding of
DPF issues. Next sections include developed models: the simple one–lumped
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model, based on the approach of Bissett and Shadman. This model is presented
both in dimensionless and dimensional form. Enhanced version of the model,
contains beyond the enthalpy and soot balances also reactions of NO2 (Bissett
assumed the reaction soot–O2 as the only occurring reaction), ash balance, and
continuous soot collection. Second model is a spatial two-dimensional model of
channel pair with plug flow. This model allows to compute concentration, pressure, velocity and temperature profiles in the inlet and outlet channels. Reaction–
diffusion–convection equation representing component balance is solved to obtain
concentration profiles within the porous wall, catalytic coating layer and soot
cake. The model also includes enthalpy and mass balances of soot. Operational
indicator of the soot loading inside the DPF is pressure drop and thus one section
of the fourth chapter is devoted to models and estimation problems of the overall
pressure loss of the filter. Pressure drop of porous parts of the filter and soot
cake are presented as well as pressure drops caused by inlet and outlet conical
tube or gas expansion and contraction at the inlet resp. outlet of the channels.
Wall pressure drop computations strongly depend on permeability, which can
be influenced by deep-filtration of solid particles inside the pores. This is the
topic of the last section of the chapter. Deep-filtration model is employed to
describe changes in the structure of filtration barrier. Spatial distribution of
porosity, permeability or, for example, particle concentration is computed by this
submodel.
The fifth chapter serves as an overview of mathematical models and kinetics
of other converters used in a combination with the filter–DOC and NSRC. Model
equations and their boundary conditions are briefly summarized together with
the lists of corresponding reactions and reaction kinetic rates.
The sixth chapter is devoted to description of numerical solution of filter models. Lumped model is effectively integrated by adaptive Merson method, while
spatial 2D model requires special advanced procedures. The finite volume method
is used to represent derivatives contained in model equations. Property values
are evaluated within the volumes and the flow quantities are balanced on the
border between discretisation volumes. The types and the choice of proper approximation schemes on the boundaries are also discussed. Resulting algebraic
equation systems are solved sequentially and thus model decomposition is employed in the course of the integration time loop. Soot, enthalpy or component
balances of solid parts must be solved in dynamic space in accordance with the
shrinking or expanding soot filtration layer. The method of solution is discussed
together with describing of complex geometric structure of the filter. Numerical solution is implemented in the in-house software (named DPFVM) developed
in Fortran 77 by PhD thesis author. Significance and benefits of the original
solution software are fast computations (e.g., for kinetic parameters evaluation
from laboratory data), feasibility of prompt modifications, problem adaptation
or platform independence.
The seventh chapter of the thesis presents results obtained by the above referred models. The results are divided into several thematic groups as follows:
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Annotation
Lumped model applications and results are subject of the first section (7.1) of
the Results chapter. Several case studies are used to describe basic processes inside the filters. As the computations with the lumped model are
fast, the model can be also used for various parametric studies or analysis.
One example is the investigation of soot ignition temperature. The method
for the observation of such temperature is explained together with the computation of ignition temperature dependence on parameters (e.g., filtration
area, initial soot loading or inlet flow rate).
Comparison of two presented models–the lumped model of Bissett (more correctly, its upgraded version) and the spatial 2D model. The second section
(7.2) is focused on the comparison of simulation results predicted by both
models. It has been shown, that application of the lumped model is limited,
nevertheless, it could be used for very fast estimative tests, for the observation of general trends and dependences. Soot mass evolutions obtained by
models are mutually shifted, but both of them may be used profitably.
Deep-filtration model is tested and its performance is shown in Section 7.3.
Model particle distribution has been chosen to test how particles are collected inside the porous wall of a non-catalyzed filter. This simulation has
shown changes in the wall structure, development of gas velocity in the
channels and velocity in the solid.
Validation of spatial 2D model is shown in Section 7.4. Data obtained from
measurements of catalytically coated and uncoated filters have been fitted.
Laboratory data (temperature, NO, NO2 concentrations, pressure drop) of
standard European driving cycle have been compared with the model prediction as well as soot loading and pressure drop experiments. It could be
seen that the simulated data are in good agreement with real emission data.
Regeneration and kinetics studies form the last part of a section dealing
with the single DPF. Concentration profiles of NOx along the channels and
within the solid (catalytic coating and wall) or soot oxidation in different
gaseous mixtures are presented. Soot combustion, and the consequent filter
regeneration by an increase of temperature have been also studied.
Zoned coating of catalyst can be used to optimize catalytic filter performance.
Zoned coating can be a way how to improve cold start problem or it can
enhance oxidation of carbon monoxide or hydrocarbons by the filter. Several
different set-ups of the filter are introduced and tested in this section (7.7).
Various types of DPF have been discussed in Section 7.8. Engine outlet concentrations of NO2 , which is an efficient soot oxidizing agent, are very low
and must be increased via the conversion of NO. Such filter systems are
often called passive, since they do not need special actions of a control
unit–particulate matter is continuously oxidized by NO2 at standard temperatures of exhaust gases. Four types of DPF in combination with monolithic diesel oxidation catalyst are presented in terms of pressure drop, soot
combustion efficiency during the driving cycle. Parametric studies of these
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passive filtration systems are shown. Special test, where the equilibrium
temperature (for which the mass of the oxidized soot is equal to the mass
of the collected soot), is also demonstrated.
Interconnected systems simulations form the content of the last section of the
chapter. Several combinations of the entire aftertreatment systems including
DOC, NSRC and (C)DPF are compared under model inlet conditions, as
well as dynamic inlet conditions of the driving cycle. All simulations have
lean/rich alternating character for sufficient operation of NSRC, however,
different timings of lean and rich phase have been examined. The inlet
temperature has been also varied and the resulting conversions of soot and
NOx have been discussed. If NOx storage material is included in catalytic
coating of the filter, soot and NOx should be simultaneously removed. Such
system has been compared with the operation of sequence of three catalytic
converters for soot and NOx conversions.
The last parts of the thesis contains Appendices: Appendix A introduces mathematical derivation of Bissett and Shadman’s model by the method of perturbation expansions of parameters. Appendix B demonstrates derivation of spatial
2D model equations and Appendix C serves as a database for correlations of
physical-chemical properties.
Conclusions
This dissertation has investigated mathematical modelling of diesel particulate
filters and application of such models to the interconnected system of converters
for aftertreatment of diesel emissions. In the course of this work, the developed
spatial two-dimensional model enabling to study complex behaviour of the DPF
has been introduced, validated and applied. Numerical procedures and solution
methodology have been used to develop efficient versatile software for model solution. This software tool can be combined with other software developed in
a similar manner by Monolith research group at the Department of Chemical
Engineering of ICT Prague. It has been shown that this way of mathematical
modelling and investigation is useful, because the performance of chosen individual converter can be evaluated as a part of the complex system.
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Publications
Journal articles
M. Schejbal, M. Marek, M. Kubı́ček & P. Kočı́, Modelling of diesel filters for particulates removal, Chemical Engineering Journal, In press, 2009,
DOI:10.1016/j.cej.2009.04.056.
M. Schejbal, J. Štěpánek, M. Marek, P. Kočı́ & M. Kubı́ček, Modelling of soot oxidation by NO2 in various types of Diesel particulate filters, Submitted to Fuel,
September, 2009.
E. Fıratlıgil–Durmuş, E. Šárka, Z. Bubnı́k, M. Schejbal & P. Kadlec, Size properties of legume seeds of different varieties using image analysis, Journal of Food
Engineering, In press, 2009, DOI:10.1016/j.jfoodeng.2009.08.005.
A. Sýkorová, E. Šárka, Z. Bubnı́k, M. Schejbal & P. Dostálek, Size distribution of
barley kernels, Czech Journal of Food Sciences, In press, 2009.
P. Kočı́, M. Schejbal, J. Trdlička, T. Gregor, M. Kubı́ček & M. Marek, Transient
behaviour of catalytic monolith with NOx storage capacity, Catalysis Today, 119,
64–72, 2007, DOI:10.1016/j.cattod.2006.08.014.
M. Marek, M. Schejbal, P. Kočı́, V. Nevoral, M. Kubı́ček, O. Hadač & I. Schreiber,
Oscillations, Period-Doublings, and Chaos in CO Oxidation and Catalytic Mufflers, Chaos, 16, 037107–1–13, 2006, DOI:10.1063/1.2354429.
Peer-reviewed conference papers
M. Schejbal, P. Kočı́, M. Marek & M. Kubı́ček, Modelling of wall-flow filters for
diesel particulate removal, Computer Aided Chemical Engineering, 26, 803–808,
2009, DOI:10.1016/S1570-7946(09)70134-8.
M. Schejbal, M. Marek, P. Kočı́, M. Kubı́ček & J. Štěpánek, Modelling of catalytic
diesel particulate filter systems with passive and active regeneration, Proceedings
of EuropaCat IX, 30th August–4th September, Salamanca, Spain, 2009.
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