Hydrogen production by autothermal reforming of
ethanol over monolith reactors: multi-channel approach
Maria Galiano Tavares Casaca Braga
Dissertação para obtenção do Grau de Mestre em
Engenharia Química
Júri
Presidente: Prof. Doutor José Madeira Lopes
Orientadores: Prof. Doutor Carlos Henriques (Instituto Superior Técnico)
Doutor Didier Pavone (IFP Energies nouvelles)
Doutor Nuno Pacheco Magalhães (IFP Energies nouvelles)
Vogais: Profª Doutora Ana Paula Dias
Doutor Victor Costa
Setembro 2010
I
ACKNOWLEDGEMENTS
This document reflects six months of work at IFP Energies nouvelles, but more than that, it is a
set of experiences that I will never forget, and I would like to thank to all that were involved in it.
I start by expressing my gratitude to Professor Fernando Ramôa Ribeiro for giving me the
opportunity of realize this formal training at IFP Energies nouvelles. To IFP Energies nouvelles that
received me and gave me the opportunity of discover the research world.
To my two internship coordinators, Didier Pavone and Nuno Pacheco. To Didier, for all the
kindness, teaching and support and, an above all, for have taught me to see the world from another
point of view. To Nuno, for all the support, patience and for being always so enthusiastic when there
was "no convergence".
To Victor Costa, my sincere gratitude for all kindness and support, since the first moment.
To Portuguese family at Lyon, without you everything would be much more difficult.
To all others interns, for all the support and for sharing this adventure.
I also express my gratitude to all my professors at IST for giving me the tools to develop this
work.
To my friends, for making my world so wonderful.
To Tiago, for being you and always have a smile when it is necessary.
And to my family, for all your love and support, and for making the distance so short.
Thank you. Merci. Obrigado.
All things are difficult before they are easy. (Thomas Fuller)
II
RESUMO
O objectivo desta Dissertação de Mestrado é desenvolver a abordagem multi-canal para
descrever o comportamento do reactor monólito para produção de hidrogénio por reforming auto
térmico (ATR) de etanol. Uma vez que os resultados experimentais evidenciaram perdas de calor no
reactor, a abordagem clássica de modelização de monólitos, por um único canal, não é adequada.
O conceito da abordagem multi-canal consiste em dividir o monólito em três coroas
concêntricas de temperatura homogénea e modelizar um canal representativo de cada zona. O modelo
foi desenvolvido com uma geometria 2-D axisimétrica, contemplando escoamento laminar de gás,
transferência de massa incluindo as reacções químicas na superfície do catalisador e transferência de
calor considerando a transferência de energia entre as coroas. As fugas de calor para o exterior foram
representadas por um modelo térmico desenvolvido num estudo anterior. No modelo totalizam-se 31
variáveis desconhecidas.
As simulações mostraram que o modelo desenvolvido representa com precisão o reactor
monólito ATR, evidenciando-se um perfil radial de temperatura como consequência das fugas de calor
presentes no reactor. A comparação entre os resultados de simulação e experimentais mostram uma
boa concordância entre estes, o que comprova a precisão do modelo e a sua aplicabilidade.
Concluindo, a abordagem multi-canal foi aplicada com sucesso para a modelização detalhada de
reactores monólitos aplicada à produção de hidrogénio por ATR do etanol, podendo este modelo ser
aplicado no futuro.
Palavras-chave: Modelo multi-canal, Monólito, Hidrogénio, Reforming auto-térmico, Etanol,
Modelização, Reactor não-adiabático, Fugas de calor
III
ABSTRACT
Nowadays, the most applied modelling approach to describe the monolith reactors is the single
channel model. In such a model only one channel of the monolith is numerically described and it is
accepted as representative of all. However, experimental results have shown that there are heat losses
in the monolith reactor for hydrogen production by ATR of ethanol. Heat losses lead to radial
temperature profiles and, consequently, different behaviours for the monolith channels. Therefore, the
research goal of this formal training is to develop a new mathematical model of ATR monolith reactor
by a multi-channel approach, which considers the entire reactor as well as the significant effects of the
heat losses. The concept of the multi-channel model is to devise the monolith reactor into three zones
of homogeneous temperature and model a representative channel of each zone (by a standard single
channel modelling approach).
The ATR monolith reactor multi-channel model was developed on a 2-D axisymmetric
geometry considering Navier-Stokes gas flow, mass transfer including surface chemical reactions, and
heat transfer between zones of homogeneous temperature. To represent the reactor heat losses towards
the exterior a thermal model is applied, which was developed on a previous work. From mathematical
point of view, the simulator should solve 2 unknowns for hydrodynamics (u andp ), 7 mass balance
variables, one for each compound (igY ) and the energy balance with 1 unknown (T ), which sums up
to 10 coupled unknowns per channel. Since there are three channels plus the external thermal model,
which accounts with one more unknown (Text), the model developed in this work solves 31 unknowns
that are intrinsically coupled.
Simulation results have shown that the developed model accurately represents the behaviour of
the monolith reactor for hydrogen production by ATR of ethanol, showing a radial temperature
gradient, as a consequence of the heat losses present on the reactor. Comparing the simulated
temperature axial profile with the experimental it can be concluded that the two profiles present
similar trend lines. A comparison between the simulated results and experimental data has been also
made, which shows that the model fits to experimental data, and represents the monolith reactor
behaviour.
Summarizing, it can be said that a new model to represent the monolith reactor for hydrogen
production by ATR of ethanol has been successfully developed and is now available and can be
applied in the future.
Keywords: Multi-channel model, Monolith, Hydrogen, Autothermal reforming, Modelling, Non-
-adiabatic reactor, Heat losses
IV
CONTENTS
INTRODUCTION 1
1 CONTEXT OF THE STAGE 1
2 MOTIVATION AND RESEARCH GOALS : HEAT LOSSES OBSERVATION LEAD TO A NEW MONOLITH
MODELLING APPROACH 2
3 STARTING POINT 5
REVIEW OF MATHEMATICAL MODELLING OF MONOLITH REACTO RS 7
1 OVERVIEW OF MONOLITH REACTORS 7
2 MONOLITH REACTORS MODELLING APPROACHES 10
2.1 CLASSICAL MONOLITH MODELLING: SINGLE CHANNEL APPROACH 11
2.1.1 Geometry: 1-D, 2-D axisymmetric and 3-D approaches 12 2.1.2 Governing equations for the single channel approach 15
2.2 MODELLING APPROACHES CONSIDERING THE ENTIRE REACTOR 19
2.2.1 3-D models 19
2.2.2 2-D axisymmetric models 20
2.2.3 1-D models 21
3 SUMMARY OF THE REVIEW 21
MONOLITH REACTOR MODELLING: NEW APPROACH 23
1 MULTI -CHANNEL APPROACH : MATHEMATICAL MODEL DESCRIPTION 23
1.1 HYDRODYNAMICS OF GAS IN ATR MONOLITH CHANNEL 25
1.2 MASS TRANSFER CONSIDERING MULTI-COMPONENT MAXWELL -STEPHAN DIFFUSION 26
1.3 HEAT TRANSFER INSIDE A MONOLITH CHANNEL 28
1.4 MECHANISM OF HEAT TRANSFER BETWEEN ZONES OF HOMOGENEOUS TEMPERATURE 30
1.5 MULTI -CHANNEL MODEL UNKNOWN VARIABLES 33
2 MULTI -CHANNEL MODELLING APPROACH ON COMSOL MULTIPHYSICS 34
2.1 MESH SIZE FOR ACCURATE SIMULATIONS 35
2.2 CHANNELS COUPLING BY HEAT TRANSFER TERMS 36
RESULTS AND DISCUSSION 38
1.1 TEMPERATURE PROFILES 39
1.2 VELOCITY PROFILES 42
V
1.3 PRODUCT PROFILES AND COMPARISON WITH CHEMICAL DATA 44
CONCLUSIONS AND PERSPECTIVES 48
REFERENCES 49
VI
L IST OF FIGURES
Figure 1. Unit U862 - monolith reactor for hydrogen production by ATR of ethanol. .......................... 3
Figure 2. Axial temperature profile for experiments at 300ºC and 400ºC of injection temperature. ..... 3
Figure 3. Monolith reactor for hydrogen production: components and representation on 2-D
axisymmetric geometry. ................................................................................................................. 5
Figure 4. Number of publications with the word "monolith" or "honeycomb" in the title. The patent
category includes patent applications (Pangarkar et al, 2008). ....................................................... 8
Figure 5. Schematic representation of a monolith structure and a washcoated channel. ........................ 8
Figure 6. Monolith channel densities (CPSI) .......................................................................................... 8
Figure 7. Schematic representation of a square monolith channel (geometry 3-D). ............................... 9
Figure 8. Different types of monolith structures: a)square, circular and hexagonal cordierite monoliths
(Pangarkar et al, 2008); b)metal monolith (Burch);c) copper monolith (Boger et al, 2005). ...... 10
Figure 9.Three zones of a monolith channel: gas phase, washcoat and channel wall. .......................... 11
Figure 10. 1-D model of the monolith channel. .................................................................................... 12
Figure 11. 2-D axisymmetric model of the monolith channel. .............................................................. 13
Figure 12. 3-D model: 1/8 of the monolith channel. ............................................................................. 14
Figure 13. The computational domains of the two washcoat models, where: a) no washcoat volume is
considered (2 computational domains), and b) the washcoat volume is considered (3
computational domains). .............................................................................................................. 15
Figure 14. Hydrodynamics for each zone of the monolith channel. ...................................................... 16
Figure 15. Mechanisms of mass transfer for each zone of the monolith channel. ................................ 17
Figure 16. Heat transfer mechanisms for each zone of the monolith channel. ...................................... 18
Figure 17. 2-D axisymmetric model: homogeneous approach. ............................................................. 20
Figure 18. Multi-channel approach schema: monolith reactor divided into three zones of homogeneous
temperature, with a 2D-axisymetric model for each monolith channel. ....................................... 23
Figure 19. 2-D axisymmetric geometry of a monolith channel, composed by the three sections: gas
phase, washcoat and channel wall. ............................................................................................... 24
Figure 20. Hydrodynamics boundary conditions. ................................................................................. 25
Figure 21. Mass transfer boundary conditions. ..................................................................................... 27
Figure 22. Heat transfer boundary conditions. ...................................................................................... 28
Figure 23. Schematic representation of the transversal cross-section of a monolith reactor................. 31
Figure 24. Radial temperature profile for a 1/8 of monolith. The blue arrows represent the radial heat
transfer direction between zones of homogeneous temperature (from top to bottom): zone 1 to
zone 2; zone 2 to zone 3; zone 3 to exterior. ................................................................................ 32
VII
Figure 25. COMSOL interface. Each tab contain each channel geometry and the first tab concerns to
the thermal model. ........................................................................................................................ 34
Figure 26. Element distribution for the monolith channel. The mesh contains 490 elements............... 35
Figure 27. Representative schema that shows the variables that each channel depends on. ................. 36
Figure 28. COMSOL interface to transfer the boundary information to the adjacent channels: a)to
indentify the variables to transport; b)to choose the destination. ................................................. 37
Figure 29. Temperature profile inside the three representative monolith channels: the right channel
corresponds to the outer channel and the left channel corresponds to the inner channel. ............ 39
Figure 30. Radial temperature profile of each channel. ........................................................................ 40
Figure 31. Comparison between the temperature axial profile: a) simulated for each channel;
b)experimental. ............................................................................................................................. 41
Figure 32. Velocity profile inside the three representative monolith channels: the right channel
corresponds to the outer channel and the left channel corresponds to the inner channel. ............ 42
Figure 33. Radial velocity where a laminar gas flow can be seen. ........................................................ 43
Figure 34. Axial velocity for each monolith channel. ........................................................................... 43
Figure 35. H2 concentration profile (%mol/mol) inside the three representative monolith channels: the
right channel corresponds to the outer channel and the left channel corresponds to the inner
channel. ......................................................................................................................................... 44
Figure 36. Conversion profile for EtOH and O2 along the reactor, for each channel, and comparison
with experimental data. ................................................................................................................. 45
Figure 37. H2,CO, CO2, , CH4, O2 and N2 composition profiles, along the ATR reactor, for each
channel, and comparison with experimental data. ........................................................................ 46
VIII
L IST OF TABLES
Table 1. Experimental injection conditions. .......................................................................................... 38
IX
NOTATION
SR steam reforming
ATR autothermal reforming
POX partial oxidation
CPSI cell density ( )21 inch
u velocity ( )sm
p pressure ( )Pa
iC components concentration ( )3mmol
T temperature ( )K
ρ fluid density ( )3mkg
η fluid viscosity ( )sPa⋅
iY component mass fraction
ijD multi-component thermal diffusion coefficient ( )( )smkg ⋅
n outward convective mass flux ( )( )smkg ⋅2
k thermal conductivity ( )( )KmW ⋅
pC heat capacity ( )( )KkgJ ⋅
Q transferred heat ( )W
U overall heat transfer coefficient ( KmW ⋅2 )
A area ( )2m
N number of channels
F heat flux ( )2mW
k thermal conductivity ( )KmW ⋅
ε porosity
X
Subscripts
i component i
g gas
mono monolith
ap apparent (gas + monolith)
1 exterior zone/channel
2 middle zone/channel
3 interior zone/channel
1
Introduction
1 Context of the stage
Hydrogen has an important role to play in the future as an energy carrier for a clean energy
future in the world, as well as wide applications in areas such as the production of chemicals,
metallurgy and mostly at crude oil refining (Akpan et al, 2007). Therefore, the demand of hydrogen
has increased in recent times: currently about 630 billion Nm3/year of hydrogen is consumed all over
the world (AF H2) and it is expected that its consumption in 2050 represents 12 600 billions Nm3/year
(an increase of 20 times the actual capacity).
Nowadays, hydrogen world production is mainly based on fossil fuels (Ahmed et al, 2001).
Hydrocarbons1, present in natural gas (C1) until naphtha (~C8), are the main source for the
commercial production of hydrogen. However, if a global cycle of clean and sustainable production of
energy is envisaged, a new-eco friendly reservoir of hydrogen is needed (Akpan et al, 2007). In this
context, ethanol (a form of biomass) satisfies most of these requirements since it is easy to produce
and is safe to handle, store and transport. It is also biodegradable, free of sulphur, low in toxicity and
can be easily steam reformed to generate a hydrogen-rich mixture (Rabenstein et al, 2008; Casanovas
et al, 2008; Frusteri et al, 2007).
Three main technologies are used to produce hydrogen from hydrocarbons: steam reforming
(SR), partial oxidation (POX) and autothermal reforming (ATR). The steam reforming is the process
most applied in the industry due to its higher hydrogen yield (Ahmed et al, 2001). The SR reaction of
ethanol is strongly endothermic, Eq. 1:
22252 623 HCOOHOHHC H + →+ ∆+ Eq. 1
molkJH K /174298 +=∆
The ethanol partial oxidation can be described as Eq. 2. Although POX reaction leads to heat
generation, the H2 yield per carbon in the fuel is lower (Krumpelt et al, 2002).
OHCOOOHHC 2252 322 +↔+ Eq. 2
1 Organic substance composed by carbon, hydrogen and oxygen atoms: CnHmOp.
2
molkJH K /3.517298 −=∆
Carbon monoxide can be converted in carbon dioxide by water gas shift reaction (WGS),
completing the hydrogen production (Eq. 3).
222 COHOHCO +↔+ Eq. 3
molkJH K /41298 −=∆
Autothermal reforming combines the effects of both exothermic POX and endothermic SR by
feeding the fuel, oxidant, and water together into the reactor to lead the reactor auto sufficient on
energy. Therefore, a new generation of fuel processors based on ATR is emerging because they can be
more energy-efficient and the equipment can be smaller and lighter (Krumpelt et al, 2002; Ahmed et
al, 2001).
The catalysts are also the key for clean and/or sustainable development in the chemical process
industry. They help to synthesize products in a resource protective way, with less consumption of
energy and, in some cases, without formation of by-products and waste (Tomasic et al, 2006).
According to Tomasic (Tomasic, 2006), monolithic catalysts and/or reactors appear to be one of the
most significant and promising developments in the field of heterogeneous catalysis and chemical
engineering of recent years and will play an important role in the integrated approach to environmental
protection.
An economically viable way of obtaining hydrogen can thus provide an alternative to the
present world-wide reliance on fossil fuels with their attendant high pollution and release of
greenhouse gases to atmosphere. There are, however, a number of significant scientific, technological
and economic obstacles to be overcome before this option can be developed. IFP Energies nouvelles is
contributing to the emergence of this new field (IFP – Hydrogen Production and Transportation) by
developing new technologies, supported by experimentation and mathematical models, that help better
understand the complex phenomena that occur in the autothermal monolith reactors for hydrogen
production.
2 Motivation and research goals: heat losses observation lead to a
new monolith modelling approach
The IFP Energies nouvelles embraces this project with the main goal of understanding the
phenomena that occur in a monolith reactor for hydrogen production by ATR of ethanol. To achieve
this objective it is necessary to carry
reactor model that describes accurately the ATR monolith reactor.
The ATR of ethanol for hydrogen production is
pilot unit U862 (Figure 1). Experiments can be up to
Figure 1. Unit U862 -
Among the several variables that
important. Figure 2 represents the axial temperature profile for two tests, at
400ºC (red line).
Figure 2. Axial temperature profile for
As can be seen, within the first
due to the heat released by the exothermic
3
it is necessary to carry out experimental studies on a monolith reactor and develop a
accurately the ATR monolith reactor.
ol for hydrogen production is studied on the IFP Energies
. Experiments can be up to 20 bar and 1000°C.
- monolith reactor for hydrogen production by ATR of ethanol.
the several variables that are tested in the U862 unit, temperature is one of the most
represents the axial temperature profile for two tests, at 300ºC
Axial temperature profile for experiments at 300ºC and 400ºC of injection temperature
within the first 0.05 meters of the reactor the temperature increases about 200°C
exothermic reactions. Further, until the outlet of the reactor, there is a
out experimental studies on a monolith reactor and develop a
Energies nouvelles ATR
reactor for hydrogen production by ATR of ethanol.
temperature is one of the most
300ºC (blue line) and
300ºC and 400ºC of injection temperature.
ture increases about 200°C
Further, until the outlet of the reactor, there is a
4
temperature decrease to the initial value. Since endothermic reactions occur in the ATR reactor, this
decrease of temperature could be assumed to be due to these reactions. However, if this decrease of
temperature would only due to endothermic reactions and the reactor had an adiabatic behaviour, the
expected temperature at the outlet should be 626°C and 660°C (thermodynamic equilibrium calculated
by PRO II), respectively for each test, instead of the 300°C and 400°C that are measured. Therefore,
the experimental results show that there are heat losses in the monolith reactor. The presence of these
heat losses implies a radial temperature profile inside the monolith reactor, which invalidates the
classical modelling approach. Hence, the aim of this work is to develop a new monolith reactor
modelling approach.
3 Starting point
According to the study of Pacheco (Pacheco, 20
reactor for hydrogen production can be
four reactor components can be defined:
Figure 3. Monolith reactor for hydrogen production: components and representation on 2
As illustrated on Figure 3
hydrogen production: the thermometer stick,
catalyst, where the reactions take place, the metallic reactor wall and the thermal insulation
The thermometer stick is not modelled because
expected.
The reactor wall and the thermal insulation
represent the heat losses of the ATR pilot reactor
developed and validated by Pacheco et al (Pacheco et al, 2010)
thermal model was simplified to scheme presented on
reaction zone is insulated from the top and bottom of the reactor. This simplified geometry is therefore
applied on the new modelling approach
Pacheco (Pacheco, 2010) modelled the m
media, named “homogenized approach”. For that model the kinetic mechanism was also developed
and validated, which was adapted to the new modelling approach developed on this work.
problem is that this homogenous approach does not take into account the structure of a monolith.
5
of Pacheco (Pacheco, 2010), in terms of modelling
reactor for hydrogen production can be accurately represented on a 2-D axisymmetric ge
four reactor components can be defined:
h reactor for hydrogen production: components and representation on 2
geometry.
3 four components can be identified on the ATR
hydrogen production: the thermometer stick, where the central temperature is measured,
catalyst, where the reactions take place, the metallic reactor wall and the thermal insulation
s not modelled because it is along the axis where no gradients are
eactor wall and the thermal insulation compose the thermal model and are modelled
represent the heat losses of the ATR pilot reactor toward to the exterior. This thermal model
y Pacheco et al (Pacheco et al, 2010). Issue of this work, the complete
thermal model was simplified to scheme presented on Figure 3, since it was concluded that the
reaction zone is insulated from the top and bottom of the reactor. This simplified geometry is therefore
the new modelling approach that we developed.
Pacheco (Pacheco, 2010) modelled the monolith considering the entire reactor as a porous
media, named “homogenized approach”. For that model the kinetic mechanism was also developed
pted to the new modelling approach developed on this work.
problem is that this homogenous approach does not take into account the structure of a monolith.
modelling, the pilot monolith
D axisymmetric geometry and
h reactor for hydrogen production: components and representation on 2-D axisymmetric
he ATR monolith reactor for
ere the central temperature is measured, the monolith
catalyst, where the reactions take place, the metallic reactor wall and the thermal insulation.
it is along the axis where no gradients are
compose the thermal model and are modelled to
. This thermal model was
this work, the complete
, since it was concluded that the
reaction zone is insulated from the top and bottom of the reactor. This simplified geometry is therefore
considering the entire reactor as a porous
media, named “homogenized approach”. For that model the kinetic mechanism was also developed
pted to the new modelling approach developed on this work. The
problem is that this homogenous approach does not take into account the structure of a monolith.
6
The present work aims modelling the monolith zone according to the “multi-channel approach”
using the previous (Pacheco, 2010) thermal model and chemical reaction model.
7
Review of mathematical modelling of
monolith reactors
This study is divided into two main parts. The first part, Overview of monolith reactors, gives
the definition and classification of monolith reactors, including these properties and pointing out there
advantages that have led to the development and application of the monolith structures. In the second
part of this chapter, Monolith reactors modelling approaches, the several monolith modelling
approaches are presented and discussed.
1 Overview of monolith reactors
The monolith reactors were initially developed and applied to the automobile industry in
abatement of pollution from non-stationary sources (treatment of exhaust gases from cars and other
vehicles). However, in the last two decades, the success of monoliths as engine emission converters
has encouraged researchers to improve other gas-phase reactions by using monolith catalytic catalysts
and reactors (Tomasic et al, 2006; Chen et al, 2008). Nowadays, monolith reactors are studied to be
employed in other fields, like hydrogen production from ethanol (Casanovas et al, 2008).
According to expectations, monoliths are going to have increasing applications in chemical and
biochemical processes (Tomasic et al, 2006). Obviously, materialization of these expectations requires
further research. Simulations and development of mathematical models allow an adequate knowledge
of the hydrodynamics, mass transfer, and heat transfer, which are the key to an efficient design of the
structured catalytic reactors.
Process intensification draws a lot of attention and has become clear that structured reactors will
play an important role on the future (Pangakar et al, 2008). A structured reactor can be seen as an
intensified form of a randomly packed bed reactor. A monolith reactor is a type of structured reactor.
According to Pangarkar et al (Pangarkar et al, 2008), monolith reactors appear to be one of the most
significant and promising developments in the field of heterogeneous catalysis and chemical
engineering of recent years. The increasing interest in this type of reactor is reflected in literature:
Figure 4. Number of publications with the word "monolith" or "honeycomb"
includes patent applications (
Figure 4 shows that the number of publications on monoliths is
applications in new fields.
A monolith reactor is a
through which the fluid flows (gas or/and liquids). A monolith catalyst is most commonly made by
applying a layer of catalyst in the walls of the structure. This process is known as
(Heiszwolf; Tomasic, 2006; Tomasic et al
channels and a transversal section of a
Figure 5. Schematic representation of a monolith structure and a washcoated channel.
Cell density is often used to characterize the
The cell density is usually represented by channels per square inch, CPSI
Figure
8
. Number of publications with the word "monolith" or "honeycomb" in the title. The patent category
includes patent applications (Pangarkar et al, 2008).
shows that the number of publications on monoliths is increasing
A monolith reactor is a structure with long, parallel and usually straight channels or cells
through which the fluid flows (gas or/and liquids). A monolith catalyst is most commonly made by
applying a layer of catalyst in the walls of the structure. This process is known as
Tomasic et al, 2006). Figure 5 presents a monolith structure with square
channels and a transversal section of a channel with its washcoat layer.
. Schematic representation of a monolith structure and a washcoated channel.
Cell density is often used to characterize the monolith reactor configuration (
The cell density is usually represented by channels per square inch, CPSI:
Figure 6. Monolith channel densities (CPSI)
in the title. The patent category
increasing due to its several
structure with long, parallel and usually straight channels or cells
through which the fluid flows (gas or/and liquids). A monolith catalyst is most commonly made by
applying a layer of catalyst in the walls of the structure. This process is known as washcoating
presents a monolith structure with square
. Schematic representation of a monolith structure and a washcoated channel.
monolith reactor configuration (Chen et al, 2008).
Figure 6 shows that the channels size decreases when the CPSI increases. The cell density can
be calculated by Eq. 4:
Assuming that the washcoat distribution on the channel
monolith is defined by the geometry of a channel. A schematic representation of a single square
monolith channel with the channel geometric parameters is illustrated on
Figure 7. Schematic representation of a square monolith channel (geometry 3
The configuration of the monoli
height (Lmonolith), wall thickness (d
modelling zones can be defined: the gas phase that
washcoat and the channel wall.
The physical properties of the monoliths depend on specif
(Tomasic, 2006). For an efficient ATR purpose,
requirements (Tomasic et al, 2006)
stability, high resistance to high
efficiency in the presence of fast changes of composition.
allow rapid heating of the catalyst to the operating temperature and it is important to find a washcoat
that has a thermal expansion of the same order of magnitude as
washcoat layer and support.
A number of different monolith reactors have been developed, as presented on
9
shows that the channels size decreases when the CPSI increases. The cell density can
( )inchdCPSI
channel2
1=
washcoat distribution on the channel is uniform, the geometry of the
monolith is defined by the geometry of a channel. A schematic representation of a single square
el with the channel geometric parameters is illustrated on Figure 7
. Schematic representation of a square monolith channel (geometry 3
The configuration of the monolith channel is represented by the channel size (d
), wall thickness (dwall) and washcoat thickness (dwashcoat). In a monolith channel
can be defined: the gas phase that corresponds to the interior of t
The physical properties of the monoliths depend on specific requirements of the process
For an efficient ATR purpose, the monolith catalyst must present
06) such as low heat capacity, high mechanical strength and chemica
high temperatures, temperature shocks and vibrations, as well as
of fast changes of composition. They must have good heat con
allow rapid heating of the catalyst to the operating temperature and it is important to find a washcoat
that has a thermal expansion of the same order of magnitude as the support to prevent rupture between
r of different monolith reactors have been developed, as presented on
shows that the channels size decreases when the CPSI increases. The cell density can
Eq. 4
is uniform, the geometry of the
monolith is defined by the geometry of a channel. A schematic representation of a single square
7.
. Schematic representation of a square monolith channel (geometry 3-D).
th channel is represented by the channel size (dchannel), channel
). In a monolith channel three
corresponds to the interior of the channel, the
ic requirements of the process
he monolith catalyst must present several
such as low heat capacity, high mechanical strength and chemical
temperature shocks and vibrations, as well as high
They must have good heat conductivity, to
allow rapid heating of the catalyst to the operating temperature and it is important to find a washcoat
the support to prevent rupture between
r of different monolith reactors have been developed, as presented on Figure 8:
10
a) b) c)
Figure 8. Different types of monolith structures: a) square, circular and hexagonal cordierite monoliths
(Pangarkar et al, 2008); b) metal monolith (Burch); c) copper monolith (Boger et al, 2005).
Figure 8 illustrates different types of monolith structures. The monolith channels or cells can be
hexagonal, rectangular or of other shapes. Its materials vary between cordierite, ceramic and metal,
among others. On this work, cordierite monolith structures are used because very high temperature
(1000°C) might be achieved under corrosive conditions.
Monolith reactors present low pressure drop, good mass transfer interphase, good thermal and
mechanical properties and simpler scale-up than conventional particle catalyst reactors such as trickle-
bed and slurry reactors, due to its specific geometric, physical and chemical properties (Chen et al,
2008). In addition, from a research point of view, the well defined monolith geometry allows to
develop detailed and accurate numerical models, which helps on intensification of industrial processes.
However, monolithic reactors may present a lower specific surface when compared with
random packing reactors, which may lead to a lower reaction rate for certain reactions systems.
2 Monolith reactors modelling approaches
The development of mathematical models to describe monolith reactors helps to understand the
interactions between various physical and chemical processes within the channel, on channel walls and
between channels.
There are two different modelling approaches: the single channel approach and the approaches
that consider the entire monolith reactor. At a single channel modelling approach, it is assumed that
every channel behaves exactly the same and, therefore, one channel can represent the entire reactor.
However, when the monolith channels do not behave identically, the single channel model is not
adequate to represent the entire monolith. In such case, it is necessary to model the entire reactor, and
so two main different approaches are possible (Kumar et al, 2010). The first one is based on the
classical modelling of packed-bed reactors, called "homogenized monolith model". The second one is
based on the single channel approach and it is called "multi-channel approach".
In the present work, the monolith reactor is model
single channel approach is inadequate
Among the two possible approaches, the "homogenized monolith model" has already been study by
Pacheco (Pacheco, 2010) but the gas/solid
simplified. In this work, we will develop the "multi
transfers. This point is devised in two parts. First, the single channel approach is presented and
analysed because its concept is employed on the multi
that have been developed to represent the entire monolith reactor are
2.1 Classical monolith modelling
The concept of the single channel
monolith have the same behavio
the entire reactor (Chen et al, 2008)
Figure 9 schematizes a monolith channel where
Figure 9.Three zones of a monolith channel: gas phase, washcoat and channel wall.
Inside the channel, where the gas phase flows, the reactant molecules
the interior of the channel to the was
flow and/or diffuse in the opposite direction. Inside the ATR reactor, the partial oxidation, steam
reforming and water gas shift reactions generate
mass and heat transfers with chemical reactions shall be model
11
In the present work, the monolith reactor is modelled as a full reactor approach because the
single channel approach is inadequate due to the heat losses that cause a radial temperature profile
Among the two possible approaches, the "homogenized monolith model" has already been study by
Pacheco (Pacheco, 2010) but the gas/solid mass and energy transfer were found out to be over
is work, we will develop the "multi-channel approach" to be able to focus on these
This point is devised in two parts. First, the single channel approach is presented and
analysed because its concept is employed on the multi-channel approach. Second,
that have been developed to represent the entire monolith reactor are presented.
modelling: Single channel approach
he single channel modelling approach is to assume that all the channels in the
lith have the same behaviour, so only one channel is mathematically described and it represents
, 2008).
schematizes a monolith channel where the three zones are distinguished:
.Three zones of a monolith channel: gas phase, washcoat and channel wall.
Inside the channel, where the gas phase flows, the reactant molecules flow and/or
the interior of the channel to the washcoat to undergo catalytic reactions. Then, the product molecules
diffuse in the opposite direction. Inside the ATR reactor, the partial oxidation, steam
er gas shift reactions generate heat. Therefore, on the gas phase, hydrod
with chemical reactions shall be modelled on realist geometry.
a full reactor approach because the
a radial temperature profile.
Among the two possible approaches, the "homogenized monolith model" has already been study by
mass and energy transfer were found out to be over
channel approach" to be able to focus on these
This point is devised in two parts. First, the single channel approach is presented and
cond, some approaches
is to assume that all the channels in the
r, so only one channel is mathematically described and it represents
three zones are distinguished:
.Three zones of a monolith channel: gas phase, washcoat and channel wall.
flow and/or diffuse from
he product molecules
diffuse in the opposite direction. Inside the ATR reactor, the partial oxidation, steam
n the gas phase, hydrodynamics,
realist geometry.
2.1.1 Geometry: 1-D, 2-D axisymmetric and 3
Depending on the requirements and objectives of the model
heat transfers that occur in a mono
geometry (Chen et al, 2008).
2.1.1.1 1-D approach
The 1-D model geometry simplifies the complexity of the rad
mass transfer and heat transfer
monolith channel.
Figure
On one hand, Figure 10 shows that the g
other hand, the simplicity of the
result, 1-D models are adequate to predict monolith behaviour and especially the kinetic models
(Tomasic, 2006). However, several studies have shown that 1
precise simulation results once compared to 2
Groppi et al (Groppi et al, 1995)
D for a catalytic combustor. The study had been performed at
and circular channel shape. The results showed that, using proper correlations, 1
profitably used to predict the gas
utilization of one-dimensional models has to be critically evaluated due to the inaccuracy in prediction
of wall temperature profiles.
As a conclusion, this approach is numerically efficient fo
highly detailed reaction models. However,
concentration, velocity field or temperature might be observ
2.1.1.2 2-D axisymmetric approach
The 2-D axisymmetric simul
effects require more computing resources, which sometimes turns into a limiting step
2008).
12
D axisymmetric and 3-D approaches
Depending on the requirements and objectives of the modelling, the hydrodynamics, mass and
n a monolith channel can be simulated in 1-D, 2-D axisymmetric or 3
D model geometry simplifies the complexity of the radial effects on the hydrodynamic
(Chen et al, 2008). The Figure 10 describes the 1
Figure 10. 1-D model of the monolith channel.
shows that the geometric features are not taken into account. On the
of the model geometry allows simulating chemical reactions in detail. As a
D models are adequate to predict monolith behaviour and especially the kinetic models
. However, several studies have shown that 1-D models are insufficient
results once compared to 2-D axisymmetric and 3-D models (Chen et al
, 1995) analyzed the adequacy of 1-D models when compared with 2
The study had been performed at steady-state conditions, laminar flow
and circular channel shape. The results showed that, using proper correlations, 1
profitably used to predict the gas exit temperature. However, simulation results pointed out that
dimensional models has to be critically evaluated due to the inaccuracy in prediction
conclusion, this approach is numerically efficient for simulation of monolith reactors with
detailed reaction models. However, it is not accurate when significant radial profiles of gas
elocity field or temperature might be observed.
D axisymmetric approach
D axisymmetric simulations take into account the radial profiles. However, the radial
effects require more computing resources, which sometimes turns into a limiting step
ing, the hydrodynamics, mass and
D axisymmetric or 3-D
ial effects on the hydrodynamic,
describes the 1-D model of the
eometric features are not taken into account. On the
allows simulating chemical reactions in detail. As a
D models are adequate to predict monolith behaviour and especially the kinetic models
D models are insufficient to generate
Chen et al, 2008).
ls when compared with 2-
state conditions, laminar flow
and circular channel shape. The results showed that, using proper correlations, 1-D models can be
exit temperature. However, simulation results pointed out that
dimensional models has to be critically evaluated due to the inaccuracy in prediction
n of monolith reactors with
is not accurate when significant radial profiles of gas
ations take into account the radial profiles. However, the radial
effects require more computing resources, which sometimes turns into a limiting step (Chen et al,
To transform the three-dimension channel into a two
cross section of each zone (gas phase, washcoat and channel wall) of the square channels. Hence, the
dimensions of the 2-D axisymmetric symmetry are calculated from the dimensions of the squared
channel dimensions as shown on
Surf
This geometrical conversion
washcoat layer the square channel geometry becomes
elsewhere between square and circle
Figure 11 describes the 2-D axisymmetric mode
Figure 11
By applying the 2-D dimensions
temperature radial profiles, which allow
than the 1-D approach. However
than 2-D models, but 3-D models require
Koltsakis et al (Koltsakis et al
model of the catalytic converter featuring
developed model could be conveniently employed for 3
Perdana et al (Perdana et al
single channel models describing transport of NO
forming nitrate species. The kinetic and transport parameters used in the 3
for the 2-D axisymmetric models. Results had revealed no significant d
despite the slight concentration gradient differences in the channel corners that were not included in
the 2-D model. The comparison of results showed that the use of a 2
adequate to study the transport and kinetics of NO
Contrary to 1-D approach, 2
Therefore, this model is more accurate. Nevertheless, the 2
13
dimension channel into a two-dimension it is required
cross section of each zone (gas phase, washcoat and channel wall) of the square channels. Hence, the
D axisymmetric symmetry are calculated from the dimensions of the squared
channel dimensions as shown on Eq. 5:
22 rLSurfSurf circlesquare π=⇔=
This geometrical conversion from squares to circles can be justified since
washcoat layer the square channel geometry becomes a rounded square, therefore, its sh
circle (Stutz et al, 2008).
D axisymmetric modelling approach:
11. 2-D axisymmetric model of the monolith channel.
D dimensions it is possible to analyze the velocity, concentration, and
temperature radial profiles, which allows to evaluate the reactor performances with more accuracy
However, CFD simulations have shown that 3-D models ar
D models require even higher computation resources (Chen et al
Koltsakis et al, 1997) presented a complete 2-D axisymmetric mathematical
model of the catalytic converter featuring an extended reaction scheme. The results showed that the
developed model could be conveniently employed for 3-way catalytic converters optimization.
Perdana et al, 2007) developed transient two-dimensional and three
el models describing transport of NOx into a NaZSM-5 film and kinetics for reactions
forming nitrate species. The kinetic and transport parameters used in the 3-D were the same as those
D axisymmetric models. Results had revealed no significant difference between the models,
despite the slight concentration gradient differences in the channel corners that were not included in
D model. The comparison of results showed that the use of a 2-D axisymmetric model is
and kinetics of NOx adsorption.
D approach, 2-D axisymmetric approach allows estimating the radial profile.
Therefore, this model is more accurate. Nevertheless, the 2-D axisymmetric approach is more
it is required to conserve the
cross section of each zone (gas phase, washcoat and channel wall) of the square channels. Hence, the
D axisymmetric symmetry are calculated from the dimensions of the squared
Eq. 5
to circles can be justified since after applying the
a rounded square, therefore, its shape is
is possible to analyze the velocity, concentration, and
to evaluate the reactor performances with more accuracy
D models are more accurate
Chen et al, 2008).
D axisymmetric mathematical
an extended reaction scheme. The results showed that the
way catalytic converters optimization.
dimensional and three-dimensional
5 film and kinetics for reactions
D were the same as those
ifference between the models,
despite the slight concentration gradient differences in the channel corners that were not included in
D axisymmetric model is
D axisymmetric approach allows estimating the radial profile.
D axisymmetric approach is more
computational exigent than the 1
the radial effects are significant, which is the ca
channels during ATR process, namely when the gas flow is laminar, which impacts the mass and hea
transfer.
2.1.1.3 3-D approach
The 3-D model is becoming the greatest choice for reactor design, which permits to simulate
with more accuracy the monolith channel
and for symmetry reasons, only one
Figure
However, this approach presents
justified in terms of accuracy, leading to the use of two
(Perdana et al, 2007). Therefore, the 2
monolith channel, since it is a goo
14
computational exigent than the 1-D approach. As a consequence, this approach shall be chosen when
the radial effects are significant, which is the case of the phenomena that happen
cess, namely when the gas flow is laminar, which impacts the mass and hea
D model is becoming the greatest choice for reactor design, which permits to simulate
with more accuracy the monolith channel behaviour (Chen et al, 2008). In case of squared channels
and for symmetry reasons, only one-eighth of the channel is modelled, as demonstrated on
Figure 12. 3-D model: 1/8 of the monolith channel.
ver, this approach presents greater needs of computer resources,
justified in terms of accuracy, leading to the use of two-dimension models in the most of the cases
. Therefore, the 2-D axisymmetric approach is generally chosen for modelling a
monolith channel, since it is a good compromise between accuracy and computational efficiency.
consequence, this approach shall be chosen when
se of the phenomena that happen inside the monolith
cess, namely when the gas flow is laminar, which impacts the mass and heat
D model is becoming the greatest choice for reactor design, which permits to simulate
. In case of squared channels,
ed, as demonstrated on Figure 12:
and is probably not
dimension models in the most of the cases
D axisymmetric approach is generally chosen for modelling a
d compromise between accuracy and computational efficiency.
2.1.2 Governing equations for the single channel approach
In all three zones of the monolith channel, the gas phase, the
(Figure 9) a set of generalized partial differential equations describing the mass, heat and momentum
balance can be established:
• hydrodynamics
• mass transfer, including chemical reaction
the several elements of the gas,
• heat transfer, including heat of reaction, which invo
T;
At the channel interior, the gas phase, all the phenomena are considered:
transfer, and heat transfer.
According to the thickness of the washcoat, this zone can be considered
media (Chen et al, 2008). Stutz et al
methane through a numerical model of an adiabatic monolith reformer (e.g. for a micro fuel cell
system). Two different 2-D axisymmetric models were investigated in this study. The first completely
neglected the physical thickness of the washcoat (
domains. The second model accounted for the physical presence and finite thickn
(Figure 13b) and consisted of three computational domains.
two models is that on the first one the
wall and interior, and on the second one the
a)
Figure 13. The computational domains of the
(2 computational domains), and b)
Simulation results have shown that
considered) is powerful in determining trends and performing optimization with respect to washcoat
parameters. However, the other model can be also applied in estimations of re
its computational cost is significantly lower and less
15
Governing equations for the single channel approach
In all three zones of the monolith channel, the gas phase, the washcoat, and the channel wall
ized partial differential equations describing the mass, heat and momentum
dynamics, which involves the fluid velocity u and pressure
mass transfer, including chemical reactions, which involves the concentration of
the several elements of the gas, iC ;
heat transfer, including heat of reaction, which involves the channel temperature,
the gas phase, all the phenomena are considered: hydrodynamics, mass
According to the thickness of the washcoat, this zone can be considered as a surface or a porous
. Stutz et al (Stutz et al, 2008) investigated the syngas production by POX of
through a numerical model of an adiabatic monolith reformer (e.g. for a micro fuel cell
D axisymmetric models were investigated in this study. The first completely
neglected the physical thickness of the washcoat (Figure 13a) and contained only two computational
The second model accounted for the physical presence and finite thickn
and consisted of three computational domains. Therefore, the differ
two models is that on the first one the catalytic reaction take place at the interface between
, and on the second one the catalytic reaction undergo in the washcoat volume.
b)
. The computational domains of the two washcoat models, where: a) no washcoat volume is considered
and b) the washcoat volume is considered (3 computational domains)
mulation results have shown that the second model (where the washcoat volume is
is powerful in determining trends and performing optimization with respect to washcoat
model can be also applied in estimations of reactor performance, and
its computational cost is significantly lower and less model parameters are needed, resulting as a
washcoat, and the channel wall
ized partial differential equations describing the mass, heat and momentum
and pressure p ;
ch involves the concentration of
lves the channel temperature,
hydrodynamics, mass
as a surface or a porous
investigated the syngas production by POX of
through a numerical model of an adiabatic monolith reformer (e.g. for a micro fuel cell
D axisymmetric models were investigated in this study. The first completely
) and contained only two computational
The second model accounted for the physical presence and finite thickness of the washcoat
Therefore, the differences between the
place at the interface between the channel
in the washcoat volume.
o washcoat volume is considered
(3 computational domains).
(where the washcoat volume is
is powerful in determining trends and performing optimization with respect to washcoat
actor performance, and
parameters are needed, resulting as a
viable approach. For the model developed in the present formal training
a catalytic surface, where the he
the catalytic chemical reactions.
On the channel wall the phenomena that take place is the mass transfer. Here, no catalytic
activity or fluid flow are considered
2.1.2.1 Hydrodynamics in a monolit
For the different zones of the monolith channel, the hydrodynamics can be characterized as:
Figure 14. Hydrodynamics for each zone of the monolith channel.
Before establishing the mathematical
channel it is important to analyze and establish the flow conditions.
Many flows of great practical importance, those in pipes and channels, are treated as one
dimensional, incompressible, and laminar f
equations is the most accurate model for the description of the laminar flow of a chemically reacting
fluid (Tischer et al, 2001).
In Chen et al (Chen et al, 2008)
reactions is proposed and discussed for various
is described by Navier-Stokes equations for a one
which means Poiseuille profile. Ch
channels as uncompressible fluid although there are slight changes in its density and viscosity along
the reactor. When the fluid density is highly affected by temperature and composition cha
happens in ATR reactor, an incompressible fluid
Mladenov et al (Mladenov et al
catalytic converters using four different formulations of momentum equations for steady
16
developed in the present formal training the washcoat was mode
heat and mass transfers phenomena are considered
On the channel wall the phenomena that take place is the mass transfer. Here, no catalytic
are considered.
in a monolith channel
For the different zones of the monolith channel, the hydrodynamics can be characterized as:
. Hydrodynamics for each zone of the monolith channel.
the mathematical equations that describe the fluid flow in a monolith
to analyze and establish the flow conditions.
Many flows of great practical importance, those in pipes and channels, are treated as one
dimensional, incompressible, and laminar flows (Perry et al, 1999). The set of Navier
equations is the most accurate model for the description of the laminar flow of a chemically reacting
, 2008) review, a general monolith single channel
reactions is proposed and discussed for various modelling applications, where the fluid hydrodynamics
Stokes equations for a one-directional, laminar and fully dev
lle profile. Chen et al (Chen et al, 2008) also treated the gas in the monolith
channels as uncompressible fluid although there are slight changes in its density and viscosity along
When the fluid density is highly affected by temperature and composition cha
an incompressible fluid cannot be assumed.
Mladenov et al, 2010) evaluated the role of mass transport in automotive
catalytic converters using four different formulations of momentum equations for steady
the washcoat was modelled as
s phenomena are considered, as consequence of
On the channel wall the phenomena that take place is the mass transfer. Here, no catalytic
For the different zones of the monolith channel, the hydrodynamics can be characterized as:
s that describe the fluid flow in a monolith
Many flows of great practical importance, those in pipes and channels, are treated as one-
. The set of Navier-Stokes
equations is the most accurate model for the description of the laminar flow of a chemically reacting
l model for gas phase
the fluid hydrodynamics
minar and fully developed fluid,
also treated the gas in the monolith
channels as uncompressible fluid although there are slight changes in its density and viscosity along
When the fluid density is highly affected by temperature and composition changes, as
evaluated the role of mass transport in automotive
catalytic converters using four different formulations of momentum equations for steady-state
isothermal flows. Simulation results had shown that although Navier
computationally expensive, they provide the most accurate solution.
Like Mladenov, in the present work the fluid flow i
conditions. It is also considered a
and viscosity are taken in to account.
2.1.2.2 Mass transfer with chemical reactions on monolith surface
For a monolith channel, the mass transfer mechanisms for ea
Figure 15. Mechanisms of mass transfer for each zone of the monolith channel.
The mass balance equation
term, the source term that corresponds to the catalytic chemical reaction and the accumulation term. If
steady-state conditions are assumed for the system the
The most common approach f
species is to use the Fick's law
system, use of Fick's law results in violation of overall mass conservation (
If the mass fraction of a certain species is large everywhere in the mixture and this species is
also non-reacting, it can be deemed as "buffer" or "diluent". It is generally believed that the use of
dilute approximation for multi-component systems is valid wh
large (Bird et al, 2001). Nevertheless, Kumar et al (
errors incurred by using the dilute approximation specifically for catalytic combustion applications,
indicate that the dilute approximation may not always be accurate, and its validity depends on the used
operating conditions. Therefore, in a multi
Maxwell-Stephan equations (Bird et al
rigorous and guarantees mass conservation, that accuracy leve
which, in some cases, may also require more computer time (
17
isothermal flows. Simulation results had shown that although Navier-Stokes models are more
computationally expensive, they provide the most accurate solution.
e present work the fluid flow is considered laminar and
s also considered as a weakly compressible fluid since the changes at the gas
re taken in to account.
ransfer with chemical reactions on monolith surface
For a monolith channel, the mass transfer mechanisms for each zone are presented on
. Mechanisms of mass transfer for each zone of the monolith channel.
The mass balance equation includes four terms: the mass diffusion term, the mass convection
corresponds to the catalytic chemical reaction and the accumulation term. If
state conditions are assumed for the system the accumulation term is not taken
The most common approach for modelling diffusive transport in systems comprising two
aw for diffusion (Kumar et al, 2010). However, in a multicomponent
system, use of Fick's law results in violation of overall mass conservation (Bird et al
he mass fraction of a certain species is large everywhere in the mixture and this species is
reacting, it can be deemed as "buffer" or "diluent". It is generally believed that the use of
component systems is valid when the mass fraction of the diluent is
). Nevertheless, Kumar et al (Kumar et al, 2008), in their study to quantify the
errors incurred by using the dilute approximation specifically for catalytic combustion applications,
at the dilute approximation may not always be accurate, and its validity depends on the used
operating conditions. Therefore, in a multi-component system, diffusion is best described by the
Bird et al, 2001). However, while the Maxwell-Stephan equations are
rigorous and guarantees mass conservation, that accuracy level requires solving advanced algorithms,
which, in some cases, may also require more computer time (Kumar et al, 2008).
Stokes models are more
laminar and at steady-state
weakly compressible fluid since the changes at the gas density
ch zone are presented on Figure 15:
. Mechanisms of mass transfer for each zone of the monolith channel.
term, the mass convection
corresponds to the catalytic chemical reaction and the accumulation term. If
accumulation term is not taken into account.
diffusive transport in systems comprising two
). However, in a multicomponent
Bird et al, 2001).
he mass fraction of a certain species is large everywhere in the mixture and this species is
reacting, it can be deemed as "buffer" or "diluent". It is generally believed that the use of
en the mass fraction of the diluent is
), in their study to quantify the
errors incurred by using the dilute approximation specifically for catalytic combustion applications,
at the dilute approximation may not always be accurate, and its validity depends on the used
component system, diffusion is best described by the
Stephan equations are
solving advanced algorithms,
In the present work the mass transfer
dealing with a multi-component system, without a major fluid compo
modelled by the Maxwell-Stephan equations, despite a
Concerning to chemical reactions
phase (Pacheco, 2010), but chemical reactions
washcoat layer (Stutz et al, 2008).
2.1.2.3 Heat transfer in a monolith channel
The heat balance equatio
radiation, heat source terms and
in the gas phase, the source terms are zero. In addition,
several applications, present in literature consider heat transfer by radiation negligible (
2008).
Hayes et al (Hayes et al, 1992
for the simulation of a single channel o
small effect on the monolith temperature. Hence, Hayes et al (
related with aspects of heat and mass transfer in a circular channel of a honeycomb monolith r
ignored radiation on the 2-D axisymmetric model development.
Kumar et al (Kumar et al
converters with complex heterogeneous chemistry. To simplify
was neglected. For the model that we
neglected.
Thus, for the different zones of the monolith channel the heat transfer mechanisms are:
Figure 16. Heat transfer mechanisms for each zone of the monolith channel.
18
mass transfer is considered at steady-state conditions
component system, without a major fluid component, the diffusive transport i
Stephan equations, despite a greater computer demands.
Concerning to chemical reactions or mass source terms, no reactions are considered
phase (Pacheco, 2010), but chemical reactions are considered as surface reactions that occur on the
, 2008).
in a monolith channel
ion covers five terms: thermal conduction, thermal c
and accumulation term. Because no homogeneous reactions are assumed
in the gas phase, the source terms are zero. In addition, several studies on monolith react
several applications, present in literature consider heat transfer by radiation negligible (
1992), on their study over the development of a finite
for the simulation of a single channel of a catalytic monolith reactor, considered that radiation has a
small effect on the monolith temperature. Hence, Hayes et al (Hayes et al, 1999
related with aspects of heat and mass transfer in a circular channel of a honeycomb monolith r
D axisymmetric model development.
Kumar et al, 2010) developed a new implicit coupled solver for catalytic
lex heterogeneous chemistry. To simplify the model heat transfer by radiation
that we develop in this work the radiation contribution has been
or the different zones of the monolith channel the heat transfer mechanisms are:
. Heat transfer mechanisms for each zone of the monolith channel.
state conditions. Since we are
nent, the diffusive transport is
greater computer demands.
, no reactions are considered in the gas
are considered as surface reactions that occur on the
rmal convection, heat
Because no homogeneous reactions are assumed
several studies on monolith reactors, for
several applications, present in literature consider heat transfer by radiation negligible (Chen et al,
), on their study over the development of a finite-element model
f a catalytic monolith reactor, considered that radiation has a
1999), on later study,
related with aspects of heat and mass transfer in a circular channel of a honeycomb monolith reactor,
) developed a new implicit coupled solver for catalytic
the model heat transfer by radiation
in this work the radiation contribution has been also
or the different zones of the monolith channel the heat transfer mechanisms are:
. Heat transfer mechanisms for each zone of the monolith channel.
19
As it can be seen on Figure 16, for a monolith channel only convection and conduction
mechanism are considered.
In the washcoat, the heat source is generated by surface catalytic reactions, like Mladevov et al
(Mladenov et al, 2010) and Koop et al (Koop et al, 2009).
2.2 Modelling approaches considering the entire reactor
When the "single channel approach" is not adapted for monolith reactor modelling, the entire
reactor is modelled, including the same physical and chemical phenomena that occur in one channel,
plus the interaction between channels, or even between the reactor and its surrounding.
The principal issue on developing a model considering the entire reactor is to decide if a one-,
two- or three-dimensional modelling geometry is necessary. A great number of models have been
presented until today, varying from fast approximated models to very detailed and computationally
intensive models, depending on the objectives and application range (Pontikakis et al, 2004).
However, the modelling of catalytic monolith reactors in a full reactor approach has received little
attention compared with a single channel model.
Along this chapter, there will be presented some of the entire reactor models that have been
developed and its applications, advantages and disadvantages.
2.2.1 3-D models
The 3-D model is the ideal choice for reactor design, which permits to simulate with the greatest
accuracy the monolith reactor behaviour.
Jahn et al (Jahn et al, 2007) constructed experimental monolith reactor to measure the
temperature profiles along 24 chosen channels for the CO ignition phenomena over a Pt-Rh
commercial catalyst. It was developed a two-phase 3-D model, considering heat conduction in the
solid phase and mass and heat balances on the surface of the catalyst and in the gas phase. However,
this model was not tested because its numerical solution was extremely computer time expensive.
Therefore, a well founded simplification was introduced: 3-D in the solid phase and 1-D in the gas
phase in individual channels.
The example shows that despite 3-D models simulate with a great detail the reactor behaviour
they require high computing resources and simulation, which may turn the model impracticable. The
2-D axisymmetric models can be seen as a better alternative.
2.2.2 2-D axisymmetric models
For 2-D axisymmetric models there are two approaches that can be considered: homogeneous
approach and multi-channel approach
The concept of the homogeneous model is to consider the whole monolith as porous bed
reactor, where no details of the several channels
homogeneous phase.
Figure 17. 2
Pacheco (Pacheco, 2010)
production by ATR of methane and ethanol, when reactor heat losses were observed at experiments.
Simulations have shown that this model represent the experimental data
compared with the single channel model, however
Alternatively to the “homogenized approach
developed on this work. The concept of the multi
zones of homogeneous characteristics (temperature, reagent distribution, etc...) and to model a
representative channel of each zone. The channels are m
modelling approach. With this model
gas and solid phase. Nevertheless, every radial profile of the whole reactor is discontinuous.
work we develop a multi-channel model considering zones of homogeneous temperature.
Kolaczkowski et al (Kolaczkowski
that accounts channels interactions in a monolith reactor with square shaped channels, resu
maldistribution in fuel supply into a catalytic monolith combusto
divided into rings of elements which were model
rings affects the temperature of
temperature, which means no heat flux across the channels walls of the same ring. Models simulations
provided mathematical data which will aid
20
D axisymmetric models there are two approaches that can be considered: homogeneous
channel approach (Kumar et al, 2010).
oncept of the homogeneous model is to consider the whole monolith as porous bed
o details of the several channels can be obtained, i.e., the reactor is mode
. 2-D axisymmetric model: homogeneous approach.
Pacheco (Pacheco, 2010) has developed this model for a monolith reactor for hydrogen
production by ATR of methane and ethanol, when reactor heat losses were observed at experiments.
hown that this model represent the experimental data with more accura
d with the single channel model, however details of channel interior are neglected.
homogenized approach” there is the “multi-channel approach
The concept of the multi-channel model is to devise the monolith reactor into
zones of homogeneous characteristics (temperature, reagent distribution, etc...) and to model a
representative channel of each zone. The channels are modelled as described before at
this model it is possible to obtain details of the phenomena that occur at the
Nevertheless, every radial profile of the whole reactor is discontinuous.
channel model considering zones of homogeneous temperature.
Kolaczkowski et al, 1995) develop a multi-channel mathematical model
that accounts channels interactions in a monolith reactor with square shaped channels, resu
maldistribution in fuel supply into a catalytic monolith combustor. In this model the channels a
divided into rings of elements which were modelled as heat losses, i.e., the heat
rings affects the temperature of each section. Inside the rings all the channels have the same
no heat flux across the channels walls of the same ring. Models simulations
ed mathematical data which will aid the system design.
D axisymmetric models there are two approaches that can be considered: homogeneous
oncept of the homogeneous model is to consider the whole monolith as porous bed
reactor is modelled as a
has developed this model for a monolith reactor for hydrogen
production by ATR of methane and ethanol, when reactor heat losses were observed at experiments.
with more accuracy, when
neglected.
channel approach” that is
channel model is to devise the monolith reactor into
zones of homogeneous characteristics (temperature, reagent distribution, etc...) and to model a
ed as described before at Classical
is possible to obtain details of the phenomena that occur at the
Nevertheless, every radial profile of the whole reactor is discontinuous. In this
channel model considering zones of homogeneous temperature.
channel mathematical model
that accounts channels interactions in a monolith reactor with square shaped channels, resulting from a
r. In this model the channels are
ed as heat losses, i.e., the heat exchanged by this
n. Inside the rings all the channels have the same
no heat flux across the channels walls of the same ring. Models simulations
21
2.2.3 1-D models
Papadias et al (Papadias et al, 1999) pointed out that 1-D model can only be used for evaluation
of experimental simple power law kinetics and in quantification of the effects of some design variables
on reactor performance. However, when more complex kinetic parameters were tested was no possible
to get the computer program to converge. Furthermore, 1-D full reactor models cannot predict some
physical effects that occur in monolith reactors (Koltsakis et al, 1997). However, this approach
integrated with model with others dimensions can obtain accurate results.
3 Summary of the review
Until this point of the report it has been made a review of the mathematical modelling of
monolith reactor, as well as some references of what was applied to the model developed on the
present work. Thus, is exposed that most monolith reactor models concentrate on modelling a single
channel of the monolith in isolation. However, under certain conditions, it is possible that the adjacent
channels of the monolith reactor interact with one another and with the exterior, which leads to the
development of full reactor modelling approaches. Several experiences made on a monolith channel
for hydrogen production by ATR of ethanol have shown that this reactor presents significant heat
losses. Therefore, the entire monolith reactor must be modelled. Broadly, there are two main
approaches for full reactor modelling that can be considered. The first approach is called the
homogenized approach, where the monolith is modelled as a porous medium, as is done traditionally
for packed-bed reactors. The second one, the multi-channel approach, is one where a representative
channel of a zone homogeneous temperature is modelled, and the results are coupled through heat
transfer terms.
It was also shown that to develop an appropriate model, some decisions must be made
concerning the number of space dimensions to consider. 1-D models are very efficient when model
quick solutions are demanded. However, in order to design a monolith reactor it is critical to fully
understand the chemical and physical phenomena that happen in a monolith reactor, such as mass
transfer effects, reaction kinetics effect, and monolith geometry effect. Therefore, 2-D axisymmetric or
even 3-D models are more desired to get the insight of the monolith performance. Despite the 3-D
models are more realistic, these may be computationally prohibitive and is probably not justified in
terms of accuracy. A good compromise for the monolith reactor modelling is a 2-D axisymmetric
model.
In terms of establish de model governing equations it was revealed that the Navier-Stokes
equation, for a laminar and fully developed flow, is the equation most applied to describe
hydrodynamics on a monolith reactor, and here it is employed for a weakly compressible fluid. For
22
mass transfer mechanism diffusion and convection are taken into account. Usually, mass diffusion is
calculated by Fick's law. However, in the presence of multicomponent systems diffusion must be
determined by Maxwell-Stephan equations. For heat transfer mechanism, generally only conduction,
convection and the heat generated by reactions are considered. Therefore, the radiation effects are
neglected. Particularly for this work, the heat losses are also integrated.
On the next sections it is described the modelling strategy adopted to model the ATR monolith
reactor for hydrogen production by a multi-channel approach.
Monolith reactor
The multi-channel modellin
hydrogen production by ATR of e
1 Multi- channel approach:
The concept of the multi-
zones of identical characteristics and to model a representative channel
case, the monolith is divided into zones of homogeneous temperature, once a radial temperature
profile was observed by Pacheco (Pacheco, 2010).
The monolith applied on hydrogen production has approximately five rows of channel
inside to the outside, so we have considered
homogeneous temperature. In case of this approach be wrong, one, two or may more zones could be
added Based on the concept of the model, a representat
temperature has been developed:
Figure 18. Multi-channel approach schema: monolith reactor divided into three zones of h
temperature, with a
The model presented on Figure
each one containing a number of monolith channels. These rings
temperature and are coupled by heat transfer
23
Monolith reactor modelling: new approach
channel modelling approach developed to characterize the monolith reactor for
ATR of ethanol is described on this chapter.
channel approach: mathematical model description
-channel modelling approach is to divide the monolith into several
zones of identical characteristics and to model a representative channel for each zone.
s divided into zones of homogeneous temperature, once a radial temperature
profile was observed by Pacheco (Pacheco, 2010).
The monolith applied on hydrogen production has approximately five rows of channel
we have considered that three zones are enough to represent areas of
In case of this approach be wrong, one, two or may more zones could be
Based on the concept of the model, a representative channel of each zone of homogeneous
temperature has been developed:
channel approach schema: monolith reactor divided into three zones of h
temperature, with a 2D-axisymetric model for each monolith channel.
Figure 18 can be viewed as a series of equidistant
each one containing a number of monolith channels. These rings represent zones of homogeneous
are coupled by heat transfer terms to simulate the heat losses of the whole reactor.
: new approach
the monolith reactor for
model description
approach is to divide the monolith into several
for each zone. In the present
s divided into zones of homogeneous temperature, once a radial temperature
The monolith applied on hydrogen production has approximately five rows of channels from the
that three zones are enough to represent areas of
In case of this approach be wrong, one, two or may more zones could be
ive channel of each zone of homogeneous
channel approach schema: monolith reactor divided into three zones of homogeneous
tric model for each monolith channel.
equidistant concentric rings,
represent zones of homogeneous
to simulate the heat losses of the whole reactor.
Thus, one of the challenges to overcome during the development of the model is how to couple the
zones of homogeneous temperature through heat transfer terms.
To develop the multi-channel model
temperature was modelled based on the single channel
described on section Classical monolith
According to the Review of mathematical modelling of monolith reactors
is modelled as a 2-D axisymmetric geometry, where three phases can be indentified: gas phase (yellow
zone), channel wall (white zone), and washcoat (orange zone), whic
Figure 19. 2-D axisymmetric geometry of a monolith channel, composed by the three sections: gas phase,
It has been assumed that the washcoat has a negligible thickness when compared with the other
two zones, gas phase and monoli
condition.
Besides the washcoat thickness
model:
• steady-state conditions;
• uniform distribution of catalyst activity;
• the contribution of the homogeneous reactions have been neglected;
Based on the physical and chemical phenomena study that was c
mathematical modelling of monolith reactors
equations that define each phenomena that o
boundary conditions. It is also
accurate simulation results.
24
Thus, one of the challenges to overcome during the development of the model is how to couple the
zones of homogeneous temperature through heat transfer terms.
channel model each channel corresponding to each zone of homogeneous
temperature was modelled based on the single channel modelling approach, which concepts are
Classical monolith modelling: Single channel approach.
Review of mathematical modelling of monolith reactors, the monolith channel
D axisymmetric geometry, where three phases can be indentified: gas phase (yellow
zone), channel wall (white zone), and washcoat (orange zone), which are shown on
D axisymmetric geometry of a monolith channel, composed by the three sections: gas phase,
washcoat and channel wall.
the washcoat has a negligible thickness when compared with the other
two zones, gas phase and monolith wall, and for that reason has been modelled
Besides the washcoat thickness, other modelling assumptions have been established
state conditions;
uniform distribution of catalyst activity;
the contribution of the homogeneous reactions have been neglected;
Based on the physical and chemical phenomena study that was carry out on the
ing of monolith reactors, is now important to establish the mathematical
equations that define each phenomena that occurs in each monolith channel, as well as, the model
necessary to establish the appropriate mesh size in or
Thus, one of the challenges to overcome during the development of the model is how to couple the
each channel corresponding to each zone of homogeneous
approach, which concepts are
, the monolith channel
D axisymmetric geometry, where three phases can be indentified: gas phase (yellow
h are shown on Figure 19:
D axisymmetric geometry of a monolith channel, composed by the three sections: gas phase,
the washcoat has a negligible thickness when compared with the other
modelled as a boundary
assumptions have been established for the
the contribution of the homogeneous reactions have been neglected;
arry out on the Review of
, is now important to establish the mathematical
ccurs in each monolith channel, as well as, the model
necessary to establish the appropriate mesh size in order to obtain
1.1 Hydrodynamics of gas in ATR monolith channel
The fluid flow occurs in the interior of the channel,
The gas is treated as weakly compressible fluid
taken in to account. The fluid flow i
the order of 10, therefore far less than 2000.
7):
( ) [ug ∇=∇⋅ρ
The unknown variables of the Navier
The equations also utilize the fluid density (
composition and temperature. Therefore, th
transfers.
The mixture viscosity is calculated by the
components from the software
available on Poling et al (Poling et al, 2004).
To solve the Navier-Stokes equations, boundary conditions need to be established.
shows the trivial boundary conditions for a monolith channel.
Figure
On the yellow domain, the gas enters with
(blue boundary), 0
→v . At the channel outlet, the gas leaves the mon
25
of gas in ATR monolith channel
in the interior of the channel, i.e., the gas phase.
s treated as weakly compressible fluid since the changes at the gas properties were
flow is also considered to be laminar since the Reynolds number is
the order of 10, therefore far less than 2000. Navier-Stokes equations are established as (
( )( ) ( )( )[ ]IuuupI gT
g ⋅∇−∇+∇+− 32ηη
( ) 0=⋅∇ uρ
The unknown variables of the Navier-Stokes equations are the velocity (u
the fluid density (ρ ) and viscosity (η ), that are dependent on the gas
composition and temperature. Therefore, the fluid hydrodynamics is coupled w
s calculated by the Method of Wilke, using the viscosity of pure
components from the software Component Plus. These method equations and assumptions are
available on Poling et al (Poling et al, 2004).
Stokes equations, boundary conditions need to be established.
shows the trivial boundary conditions for a monolith channel.
Figure 20. Hydrodynamics boundary conditions.
, the gas enters with a parabolic profile with a well defined initial velocity
. At the channel outlet, the gas leaves the monolith channel with a set
since the changes at the gas properties were
since the Reynolds number is of
re established as (Eq. 6 and Eq.
Eq. 6
Eq. 7
u ) and pressure (p ).
), that are dependent on the gas
e fluid hydrodynamics is coupled with heat and mass
, using the viscosity of pure
equations and assumptions are
Stokes equations, boundary conditions need to be established. Figure 20
a well defined initial velocity
olith channel with a set pressure
26
(pink boundary), P . The green boundary was defined as the axis of symmetry, since we are in a 2-D
axisymmetric geometry. The boundary that corresponds to the washcoat layer, orange boundary, is
defined as a wall with no slip condition, which means velocity equal to zero.
1.2 Mass transfer considering multi-component Maxwell-Stephan diffusion
The mass transfer is an important phenomenon since it deals with the chemical reaction and
fluid diffusion. In the developed model the mass transport by convection and diffusion only occurs in
the interior of the channel, the gas phase.
The mass balance for each component present on the monolith channel can be established as
follows:
( )( )( ) igkkkkkg RuYppwxxDY =+∇−+∇Σ−∇ 111 ρρ Eq. 8
According to the Review of mathematical modelling of monolith reactors, the diffusion term is
calculated by the Maxwell-Stefan equation, since we are in the presence of a multicomponent mixture.
Altogether 8 components can be counted on the monolith channel: hydrogen (H2), water (H2O), carbon
monoxide (CO), carbon dioxide (CO2), methane (CH4), ethanol (C2H5OH), oxygen (O2) and nitrogen
(N2), which means seven mass balance equations with the eighth compound calculated by difference.
Hence, the unknown variables of the mass balance are the components mass fractions (iY ).
The mass convection term depends on the hydrodynamics (u andp ). The diffusion coefficients
are estimated by the kinetic theory of gases, and depend on the gas temperature ( )T . Therefore, the
mass transfer is intrinsically coupled to the hydrodynamics and heat transfer.
The gas phase chemical reactions are neglected, according to previous work (Pacheco, 2010).
Only surface reactions are taken into account, and they are simulated as boundary conditions. Figure
21 shows the boundary conditions for mass balance equations on the monolith channel.
Figure
On the yellow domain, the
mass fraction (Yi). On the outlet, the gas leaves the channel by convective flux, which transport can be
expressed by Eq. 9:
( 1Σ− DYn kkigρ
As stated before, the orange boundary corresponds to the washcoat, where the surface catalytic
chemical reactions occur. Therefore, this boundary contains the sum of terms of reaction that take
place in the monolith channel, which are (Pacheco, 2010):
Ethanol decomposition:
Partial oxidation:
Methane incomplete steam reforming:
Water gas shift:
Finally, as established for hydrodynamics, since we are at a 2
green boundary is considered as axis of symmetry.
27
Figure 21. Mass transfer boundary conditions.
the gas phase, the gas enters in the monolith channel with a well defined
On the outlet, the gas leaves the channel by convective flux, which transport can be
( )( ) ) 0=∇+∇−+∇ TTDppwxx Tkkkk
As stated before, the orange boundary corresponds to the washcoat, where the surface catalytic
chemical reactions occur. Therefore, this boundary contains the sum of terms of reaction that take
the monolith channel, which are (Pacheco, 2010):
Ethanol decomposition: COCHHOHHC ++→ 4256
Partial oxidation: COOHOOHHC 232 2252 +→+
Methane incomplete steam reforming: COHOHCH +↔+ 224 3
Water gas shift: 222 COHCOOH +↔+
Finally, as established for hydrodynamics, since we are at a 2-D axisymmetri
s considered as axis of symmetry.
gas phase, the gas enters in the monolith channel with a well defined
On the outlet, the gas leaves the channel by convective flux, which transport can be
Eq. 9
As stated before, the orange boundary corresponds to the washcoat, where the surface catalytic
chemical reactions occur. Therefore, this boundary contains the sum of terms of reaction that take
Eq. 10
Eq. 11
Eq. 12
Eq. 13
D axisymmetric geometry the
1.3 Heat transfer inside a monolith channel
The applied heat balance (
convective term and thermal conductive
∇
In the present model the
interior of the channel, the gas phase.
there is no gas flow.
On Eq. 14 it can be seen that the unk
The heat transfer depends on the hydrodynamics (
composition and therefore the parameters
The thermal conductivity of the mixture is calculated by the
thermal conductivities of pure components
equation and assumptions are available on reference Poling et al (Poling et al, 2004).
According to the Review of mathematical modelling of monolith reactors
radiation is considered negligible.
monolith structure are constant and independent of the monolith temperature.
The heat generated by reactions and the heat losses are simulated as a boundary condition.
Figure 22 illustrates the boundary conditions for h
Figure
28
inside a monolith channel
heat balance (Eq. 14) shows that the developed model depends
thermal conductive term:
( ) TuCTkipgg ∇=∇− ρ
odel the heat transport, by convection and conduction,
interior of the channel, the gas phase. On the channel wall occurs heat transfer by conduction since
it can be seen that the unknown variable of the heat balance is the temperature (
The heat transfer depends on the hydrodynamics (u ) and mass transfer, which affects the gas
the parametersreactionQ , ipC andk .
The thermal conductivity of the mixture is calculated by the Wassilijewa Equation
components obtained by the software Component Plus
ssumptions are available on reference Poling et al (Poling et al, 2004).
Review of mathematical modelling of monolith reactors
s considered negligible. In addition, it is also assumed that the physical prop
monolith structure are constant and independent of the monolith temperature.
The heat generated by reactions and the heat losses are simulated as a boundary condition.
illustrates the boundary conditions for heat balance equations on the monolith channel.
Figure 22. Heat transfer boundary conditions.
depends on the thermal
Eq. 14
heat transport, by convection and conduction, only occurs in the
On the channel wall occurs heat transfer by conduction since
is the temperature (T ).
) and mass transfer, which affects the gas
Wassilijewa Equation, using the
Component Plus. The method
ssumptions are available on reference Poling et al (Poling et al, 2004).
Review of mathematical modelling of monolith reactors, the heat transfer by
s also assumed that the physical properties of the
The heat generated by reactions and the heat losses are simulated as a boundary condition.
eat balance equations on the monolith channel.
29
On the yellow domain, the gas phase, the gas enters in the monolith channel with a well defined
injection temperature (injT ). It is established, on the pink boundary, that the gas leaves the channel by
convective flux, which transport is represented by Eq. 15:
( ) 0=∇− Tkn Eq. 15
As established for hydrodynamics and mass transfer, since we are at a 2-D axisymmetric
geometry the green boundary is considered as axis of symmetry.
Like stated before, the orange boundary corresponds to the washcoat, where the surface
catalytic chemical reactions occur. Therefore, this boundary corresponds to the heat generated by
reactions that take place ( )reactionQ .
On the blue domain, the channel wall, only occurs heat transfer by conduction. According to the
Review of mathematical modelling of monolith reactors, the single channel approach assumes that the
monolith external wall in insulated once all channels are similar and therefore no heat exchanges
occur. However, previous studies (Pacheco, 2010) have shown that only the top and the bottom of the
monolith channel can be considered insulated, which correspond the black boundaries. For the lateral
monolith wall, red boundary, this boundary condition was changed to heat flux, to simulate the heat
losses of the monolith reactor. The simulations of heat losses, however, are not trivial. The deduction
is explained below (Section 1.4).
30
1.4 Mechanism of heat transfer between zones of homogeneous temperature
For the mechanism of heat transfer between zones, it is assumed that these zones exchange
energy according to Eq. 16, in analogy to heat exchangers:
TAUQ ∆⋅⋅= Eq. 16
Where U is the overall heat transfer coefficient ( KmW ⋅2 ), A the surface area of heat
exchange ( 2m ) and T∆ the temperature difference between zones (K ).
Each homogeneous temperature zone is composed by N number of channels. Therefore, the
energy exchanged by each channel is an Nth part of the total energy exchanged between zones, Eq. 17:
NTAUQchannel /∆⋅⋅= Eq. 17
The heat exchanged by each channel needs to be converted in a heat flux to be employed as a
boundary condition. This heat is the integral of the flux along the exchange surface. Therefore, the
following differential equation, Eq. 18, can be established to obtain the heat flux across the lateral
surface of the channel:
channel
ringchannelHL
ringchannelchannel
channelchannel
NR
TRUF
dzRN
TUdzRF
dAN
TUdAF
∆=⇔
⇔∆=⇔
⇔∆=
:
22 ππ Eq. 18
Hence, the heat flux that is employed as a boundary condition on Figure 22 to simulate the heat
loss per channel is calculated by Eq. 18, channelHLF : .
The overall heat transfer U is a measure of the overall ability of a series of conductive and
convective barriers to heat transfer and can be calculated as the reciprocal of the sum of a series of
thermal resistances (Bird et al, 2001). Therefore, several questions arise in calculation of U: which
transfer mechanisms to consider, which media offer thermal resistance, and how to estimate the mean
thermal resistance.
On Figure 23, a schematic representation of the transversal section of a monolith is shown:
Figure 23. Schematic representation of the transversal cross
As can be schematically seen on
that are separated from each other by channel walls.
the channels is feasible and consequently, no convective heat transfer in this direction occurs. On the
other hand, the monolith channels are co
transfer heat by conduction with each other. Therefore, the monolith presents resistance to the heat
transfer by radial conduction.
The thermal resistance is determined by the ratio between the
zones,x , and the thermal conductivity of the two phases of the monolith: solid
to the monolith walls, and gas phase.
conductionR
In order to simplify the determination of
monolith, Borger et al (Borger et al
conductivity apk in monolith structures based on th
monok of the monolith walls, assuming that monolith behaves like a homogeneous media (
(
= monoap kk
Roh et al (Roh et al, 2010)
conductivity of a reactor bed with metal monolith catalyst for the steam reforming of natural gas.
31
. Schematic representation of the transversal cross-section of a monolith reactor.
As can be schematically seen on Figure 23, a monolith is represented by a number
that are separated from each other by channel walls. On one hand, no radial exchange of gas between
the channels is feasible and consequently, no convective heat transfer in this direction occurs. On the
other hand, the monolith channels are connected by their walls throughout the entire diameter, which
transfer heat by conduction with each other. Therefore, the monolith presents resistance to the heat
The thermal resistance is determined by the ratio between the thickness of the heat transfer
, and the thermal conductivity of the two phases of the monolith: solid phase that
to the monolith walls, and gas phase.
( )gmonomonolithconduction kkf
x
,_ =
to simplify the determination of the thermal conductivity of both components of the
Borger et al, 2005) applied a correlation to calculate the effective radial
in monolith structures based on the void fraction, ε, and the thermal conductivity
of the monolith walls, assuming that monolith behaves like a homogeneous media (
( )
1
1
1
−
+−
+−εε
εε
mono
G
k
k
l, 2010) applied the same correlation, Eq. 20, for the estimation
conductivity of a reactor bed with metal monolith catalyst for the steam reforming of natural gas.
section of a monolith reactor.
, a monolith is represented by a number of channels
o radial exchange of gas between
the channels is feasible and consequently, no convective heat transfer in this direction occurs. On the
nnected by their walls throughout the entire diameter, which
transfer heat by conduction with each other. Therefore, the monolith presents resistance to the heat
thickness of the heat transfer
phase that corresponds
Eq. 19
both components of the
applied a correlation to calculate the effective radial
, and the thermal conductivity
of the monolith walls, assuming that monolith behaves like a homogeneous media (Eq. 20):
Eq. 20
estimation of thermal
conductivity of a reactor bed with metal monolith catalyst for the steam reforming of natural gas.
The correlation of Eq. 20
their study of the effective thermal conductivity of monolith honeycomb structures.
To model the heat transfer on the monolith reactor it i
centre of a zone of homogeneous temperature
interface between the two zones (
performed on a 1/8 of monolith channel:
Figure 24. Radial temperature profile for a 1/8 of monolith. The blue arrows represent the r
direction between zones of homogeneous temperatu
Based on Figure 24, knowing which media offers resistance to heat transfer and how to
calculate the monolith thermal conductivity, it is possible to esta
equations, for each zone:
zone 3 to zone 2:
32
was also tested and validated by Hayes et al (Hayes et al
their study of the effective thermal conductivity of monolith honeycomb structures.
er on the monolith reactor it is considered that it occurs between the
homogeneous temperature ( 'iR ) to the centre of the adjacent zone
interface between the two zones (iR ), as schematically shown on Figure
a 1/8 of monolith channel:
Radial temperature profile for a 1/8 of monolith. The blue arrows represent the r
between zones of homogeneous temperature (from top to bottom): zone 1 to zone 2; zone 2 to zone 3;
zone 3 to exterior.
, knowing which media offers resistance to heat transfer and how to
calculate the monolith thermal conductivity, it is possible to establish the overall heat transfer
to zone 2:
'23
3'2
3'3
'33
23
1
→→
→ −+
−=
apap k
RR
k
RRU
Hayes et al, 2009) in
their study of the effective thermal conductivity of monolith honeycomb structures.
s considered that it occurs between the
to the centre of the adjacent zone ( '1+iR ), across the
Figure 24 for a simulation
Radial temperature profile for a 1/8 of monolith. The blue arrows represent the radial heat transfer
re (from top to bottom): zone 1 to zone 2; zone 2 to zone 3;
, knowing which media offers resistance to heat transfer and how to
blish the overall heat transfer
Eq. 21
33
zone 2 to zone 1:
'12
2'1
2'2
'22
12
1
→→
→ −+
−=
apap k
RR
k
RRU Eq. 22
zone 1 to exterior:
1'1
'11
1
1
→
→ −=
ap
ext
k
RRU Eq. 23
Eq. 21, Eq. 22 and Eq. 23, integrated on Eq. 16, allow to couple zones of homogeneous
temperature by heat transfer terms and, consequently, the representative channels of each zone by Eq.
17.
To summarize, the simulation of heat losses using the multi channel approach is not trivial. A
heat flux per channel needs to be established to simulate the global heat loss. Furthermore, the heat
loss per channel depends on the global heat transfer coefficient of each zone that depends on gas
composition and temperature. This strategy allows accurately simulating the heat loss using the multi--
-channel modelling approach.
1.5 Multi-channel model unknown variables
For each channel there are 3 unknowns for hydrodynamics ( zu , ru andp ), 6 mass balance
variables ( igY ), and the energy balance with 1 unknown (T ), which adds up to 10 coupled unknowns
per channel. Since there are three channels plus the external thermal model, which accounts for one
more unknown, the model developed in this work accounts for 31 unknown that are intrinsically
coupled. As a result, to solve the reactor model the software COMSOL Multiphysics3.5a has been
used, which has showed that it is adapted to solve multiphysics problems of this dimension.
34
2 Multi-channel modelling approach on COMSOL Multiphysics
As stated before, the software COMSOL Multiphysics3.5a is adapted to solve a multiphysics
problem as the presented one. To obtain the simulation results it is required to perform the following
simulation steps:
1. geometry draw, where the object dimensions and shape are defined;
2. mesh, where the geometry mesh is established in order to obtain accurate simulation results;
3. domain conditions, where the mathematical equations are defined for each physical and chemical phenomena;
4. boundary conditions, where the defined boundary conditions are introduced;
5. solver, where the adequate solving method is chosen and performed to obtain the numerical solution;
6. post-processing, where the numerical solution results are given and analyzed;
Figure 25 shows the COMSOL Multiphysics interface, where each channel is defined, as well as
the thermal model developed by Pacheco et al (Pacheco et al, 2010):
Figure 25. COMSOL interface. Each tab contains each channel geometry and the first tab concerns to the
thermal model.
Among all the steps that are required to implement the multi-channel model, there are two that
can be pointed out: the mesh size and the boundary condition that lets couple the channels through the
heat transfer terms defined above. These two modelling steps are presented bellow.
35
2.1 Mesh size for accurate simulations
In order to obtain the maximum accuracy of the simulation solution it is necessary to size the
mesh correctly: minimize the computational time, while at the same time have elements small enough
to capture the sharp gradients (Hayes et al, 1992).
For the monolith channels for hydrogen production by ATR of ethanol the mainly chemical
phenomena occur near to the entrance of the channel, as often in tubular reactors. This leads naturally
to the use of a variable mesh size, with small elements near to the monolith entrance and larger
elements elsewhere. Figure 26 shows the mesh used in this work for a monolith channel:
Figure 26. Element distribution for the monolith channel. The mesh contains 490 elements.
Using this mesh, 40-cm-long reactor contains 490 elements. In each finite element mesh, each
unknown, such as temperature or velocity, is quadratic with respect to the independent coordinates, r
and z. In each vertex of the mesh the model need to solve the intrinsically coupling hydrodynamics,
mass transfer and heat transfer mathematical equations, as well as account for the effects of catalytic
chemical reaction and heat transfer between the channels and the exterior.
36
2.2 Channels coupling by heat transfer terms
As stated on the section Mechanism of heat transfer between zones of homogeneous
temperature, the channels are coupled by heat flux terms, as defined on Eq. 24:
channel
ringchannelHL NR
TRUF
∆=:
Eq. 24
Therefore, each channel depends on its own temperature and the temperature of the adjacent
zones, as schematically represented on Figure 27:
Figure 27. Representative schema that shows the variables that each channel depends on.
So, it is required to transfer the information relative to the channel temperature to the
boundaries of the adjacent channels. That can be done using a COMSOL option called Extrusion
variables. In order to simplify the model and reduce the computational resources it is considered that
there is no radial gradient of temperature in the channels. Therefore, it can be made a temperature
boundary extrusion instead of temperature domain extrusion.
( )ii
ringiiiiii RN
RTTUF
−= +→+
+→11
1
( )11
111
−−
−→−→−
−=
ii
ringiiiiii RN
RTTUF
i
( )ii
ringiiiiii RN
RTTUF
−= +→+
+→11
1
( )11
111
−−
−→−→−
−=
ii
ringiiiiii RN
RTTUF
i
37
a)
b)
Figure 28. COMSOL interface to transfer the boundary information to the adjacent channels: a) to indentify the
variables to transport; b) to choose the destination.
As shown on Figure 28a), the first step is to define on geometry i±1 the variable that is going to
be extruded to geometry i. The second step (Figure 28b) is to define the destination of the extruded
variable to geometry i, where the heat fluxes are calculated.
Summarizing, with this COMSOL tool it is possible to transport the information between the
different geometry tabs, as developed on this work.
38
Results and discussion
To study the heat losses of a monolith reactor for hydrogen production by ATR of ethanol, a
new multi-channel modelling approach has been developed. In order to accurately represent the
monolith reactor behaviour, the model consists in dividing the monolith into three zones of
homogeneous temperature, as represented on Figure 18, which exchange energy between them. For
each zone it has been modelled a representative single channel that are coupled to each other by heat
flux terms. Hence, in addition to heat transfer, the representative channels also take into account the
hydrodynamics and the mass transfer phenomena, with chemical reaction, that occur in a monolith
reactor.
After establishing the mathematical equations for each physical and chemical reactions and
model boundary conditions, several computer simulations took place in order to estimate the unknown
variables of the model:
• hydrodynamics: velocity (u ) and pressure (P )
• mass transfer: components concentration (iC )
• heat transfer: temperature (T )
In this point of the report, the simulations results are presented and discussed. In addition, the
calculated gaseous components concentrations (H2, CO, CO2, CH4, O2 and N2) are compared with
experimental data.
It is important to refer that the presented results correspond to a simulation realized with the
same injection conditions that the one of the experiments performed by Pacheco (Pacheco, 2010),
which are presented on Table 1:
Table 1. Experimental injection conditions.
Pressure (Pa) Temperature (ºC) FAir (Nm3/s) FH2O (kg/s) FEtOH (kg/s)
7.48x105 350 1.19x10-5 2.27 x10-5 8.21 x10-6
Due to heat losses presented by the monolith reactor for hydrogen production, arose the need to
develop a new model that characterize the reactor behaviour. Hence, it can be said that the temperature
is the most interesting variable to analyse, so it is by this variable that begins this results analysis.
1.1 Temperature profiles
Figure 29 shows the temperature profiles inside the three representative reactor channels, as
function of r (radial coordinate) and
CT º350= ).
Figure 29. Temperature profile inside the three representative monolith channels: the right channel corresponds
to the outer channel and the left channel corresponds to the inner channel.
39
Due to heat losses presented by the monolith reactor for hydrogen production, arose the need to
w model that characterize the reactor behaviour. Hence, it can be said that the temperature
is the most interesting variable to analyse, so it is by this variable that begins this results analysis.
Temperature profiles
the temperature profiles inside the three representative reactor channels, as
(radial coordinate) and z (axial coordinate), for the given injection temperature (
Temperature profile inside the three representative monolith channels: the right channel corresponds
to the outer channel and the left channel corresponds to the inner channel.
Due to heat losses presented by the monolith reactor for hydrogen production, arose the need to
w model that characterize the reactor behaviour. Hence, it can be said that the temperature
is the most interesting variable to analyse, so it is by this variable that begins this results analysis.
the temperature profiles inside the three representative reactor channels, as
(axial coordinate), for the given injection temperature (
Temperature profile inside the three representative monolith channels: the right channel corresponds
to the outer channel and the left channel corresponds to the inner channel.
40
As expected, there is a radial temperature profile inside the monolith reactor, where the inner
channels are hotter than the outer channels, as consequence of the heat losses to the exterior that were
observed experimentally by Pacheco (Pacheco, 2010) on the monolith reactor for hydrogen
production. On each channel the radial temperature profile inside is negligible, as shown on Figure 30:
Figure 30. Radial temperature profile of each channel.
As represented on Figure 29, the temperature raise observed at the entrance of the channels,
particularly at the inner channel, is due to the heat released by the exothermic ethanol partial
oxidation. Hence, the observed temperature decrease derives from two effects: the endothermic
reactions that consume part of the heat, and the reactor heat losses, as expected.
It is also interesting to compare simulated axial temperature profile with the axial profile
obtained experimentally. However, it is very difficult to measure the temperature inside the monolith
reactor and unfortunately those measurements were not made on experiments with the same injection
values. Nevertheless, the temperature trend lines can be compared to other experimental case, as
illustrated on Figure 31, as function of z (axial coordinate) and T (temperature coordinate).
370.70
370.75
370.80
370.85
370.90
370.95
371.00
371.05
371.10
371.15
0.0000 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006
r (m)
T (
°C)
T interior channel
T middle channel
T external channel
41
a)
b)
Figure 31. Comparison between the temperature axial profile: a) simulated for each channel; b) experimental.
Although the represented axial temperature profiles do not correspond to the same injection
conditions, it can be observed similar temperature trend lines along the reactor: the initial peak that
corresponds to the exothermic partial oxidation, and the continuous temperature decrease due to the
endothermic reactions and reactor heat losses.
330
350
370
390
410
430
450
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
z (m)
T (
°C)
T interiorchannel
T middlechannel
T externalchannel
250
300
350
400
450
500
550
600
650
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
z (m)
T (
°C)
T experimental
1.2 Velocity profiles
Figure 32 illustrates the velocity profiles inside the three representative reactor channels, as
function of r (radial coordinate) and
Figure 32. Velocity profile inside the three representative monolith channels: the right channel corresponds to
the outer channel and the left channel corresponds to the inne
As expected, the fluid flows inside the channels with a Poiseulle
is maximum at the channel centre and zero along the
(Figure 33).
42
illustrates the velocity profiles inside the three representative reactor channels, as
(radial coordinate) and z (axial coordinate), for the given injection conditions (
. Velocity profile inside the three representative monolith channels: the right channel corresponds to
the outer channel and the left channel corresponds to the inner channel.
As expected, the fluid flows inside the channels with a Poiseulle-like profile, where the velocity
the channel centre and zero along the wall, as consequence of the laminar gas flow
illustrates the velocity profiles inside the three representative reactor channels, as
(axial coordinate), for the given injection conditions (Table 1).
. Velocity profile inside the three representative monolith channels: the right channel corresponds to
r channel.
profile, where the velocity
wall, as consequence of the laminar gas flow
43
Figure 33. Radial velocity where a laminar gas flow can be seen.
On Figure 34 it can be observed that at the channel entrance, particularly at the inner channel,
there is a significant raise of fluid maximum velocity. According to the perfect gas law, this velocity
increase is the consequence of two effects: the gas thermal expansion due to temperature increase, and
the chemical reactions that cause molar gas expansion.
Figure 34. Axial velocity for each monolith channel.
As stated before, it can be observed an initial velocity peak as consequence of gas thermal and
molar expansion. As expected, once the interior channel reaches higher temperatures, the thermal
expansion is higher in this channel, which corresponds to the highest peak. Therefore the lowest peak
corresponds to the outer channel. Further, it can be observed a velocity increase that is consequence of
the temperature decrease. Then, it can also be observed a new velocity increase, as consequence of the
molar expansion.
0
0,05
0,1
0,15
0,2
0,0E+00 1,0E-04 2,0E-04 3,0E-04 4,0E-04 5,0E-04
velo
city
(m/s
)
r (m)
Velocity radial centre channel
Velocity radial middle channel
Velocity radial exterior channel
0.14
0.15
0.16
0.17
0.18
0.19
0 0.1 0.2 0.3 0.4
z (m)
velo
city
(m
/s)
Velocity interior channel
Velocity middle channel
Velocity exterior channel
1.3 Product profiles and comparison with chemical data
There are 8 different species in the monolith reactor for hydrogen production by ATR of
ethanol: H2, H2O, CO, CO2, CH4, EtOH, O
Figure 35 shows the hydrogen composition profile, as function of
(axial coordinate), for the given injection conditions (
Figure 35. H2 concentration profile (%mol/mol) inside the three representative monolith channels: the right
channel corresponds to the outer channel and the left channel corresponds to the inner channel.
Figure 35 illustrates a fast hydrogen production at the reactor entrance, which is consequence of
the reactions that take place: partial oxidation and ethanol decomposition (
fact can be enhanced by Figure
consumed close to the reactor entrance. Further, until the outlet of the reactor, there is a decrease on
44
Product profiles and comparison with chemical data
There are 8 different species in the monolith reactor for hydrogen production by ATR of
, EtOH, O2 and N2.
shows the hydrogen composition profile, as function of r (radial coordinate) and
(axial coordinate), for the given injection conditions (Table 1), for each representative channel.
concentration profile (%mol/mol) inside the three representative monolith channels: the right
channel corresponds to the outer channel and the left channel corresponds to the inner channel.
t hydrogen production at the reactor entrance, which is consequence of
the reactions that take place: partial oxidation and ethanol decomposition (Eq. 10
Figure 36, where it is shown that the oxygen and ethanol are completely
the reactor entrance. Further, until the outlet of the reactor, there is a decrease on
There are 8 different species in the monolith reactor for hydrogen production by ATR of
(radial coordinate) and z
), for each representative channel.
concentration profile (%mol/mol) inside the three representative monolith channels: the right
channel corresponds to the outer channel and the left channel corresponds to the inner channel.
t hydrogen production at the reactor entrance, which is consequence of
10 and Eq. 11). This
hanol are completely
the reactor entrance. Further, until the outlet of the reactor, there is a decrease on
45
the hydrogen concentration, due to the incomplete steam reforming of methane (or methanation
reaction) and WGS reactions (Eq. 12 and Eq. 13), which are reversible and therefore consume
hydrogen to produce the reaction reagents, whose concentration profiles are presented on Figure 37.
On Figure 35 it can also be observed that there is a greater hydrogen production in the inner
channel, when compared with the two others. In fact at higher temperatures, the methanation reaction
equilibrium favours the hydrogen side because it is endothermic in this reaction direction. However,
the differences that are observed are not very distinct.
In addition, it can be observed that at the reactor outlet all the channels have the same hydrogen
concentration. This fact is due to the thermodynamic equilibrium that is reached.
Figure 36 shows the ethanol and oxygen conversion profiles along the monolith reactor,
comparing the simulated results, for the centre channel and the experimental data, obtained by
Pacheco (Pacheco, 2010).
Figure 36. Conversion profile for EtOH and O2 along the reactor, for each channel, and comparison with
experimental data.
Figure 36 shows that the simulation results for both components match the experimental results,
which mean that the model accurately simulates the experimental results.
The oxygen profile shows that its consumption is very fast, which allows to confirm that the
POX reaction takes place near to the reactor entrance. The same observation can be made for ethanol
profile, which is completely consumed at the reactor inlet, although after the oxygen. Therefore, it can
be said that the two main reactions for hydrogen production occur at the reactor entrance, nevertheless
the POX reaction occurs before the ethanol decomposition reaction.
0
20
40
60
80
100
0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4
Con
vers
ion
(%)
z (m)
EtOH simulation
O2 simulation
EtOH experimental
O2 experimental
46
To understand the behaviour of the monolith reactor it is also interesting to compare all
components concentration profiles, for each channel. In addition, a comparison between the simulated
results and experimental data, obtained by Pacheco (Pacheco, 2010), is also important to analyse.
Therefore, Figure 37 illustrates all component profiles along the monolith reactor, for each channel, as
well as a comparison between the simulated results and experimental data, as function of z (axial
coordinate) and gas composition (%mol/mol).
Figure 37. H2,CO, CO2, , CH4, O2 and N2 composition profiles, along the ATR reactor, for each channel, and
comparison with experimental data.
On Figure 37 it can be observed that methane concentration increases along the reactor, as a
consequence of the inverse reaction of incomplete steam reforming of methane, which consumes
hydrogen (Eq. 12). Therefore, when the methane concentration increases the hydrogen concentration
decreases.
Figure 37 also shows that the carbon monoxide produced by ethanol decomposition and partial
oxidation is then consumed by the reverse reaction of methane incomplete steam reforming.
0.0
0.2
0.4
0.6
0.8
0 0.1 0.2 0.3 0.4
z (m)
Gas
com
posi
tion
(%m
ol/m
ol)
H2 centre channel
H2 middle channel
H2 external channel
CO centre channel
CO middle channel
CO external channel
CO2 centre channel
CO2 middle channel
CO2 external channel
CH4 centre channel
CH4 middle channel
CH4 external channel
O2 centre channel
O2 middle channel
O2 external channel
N2 centre channel
N2 middle channel
N2 external channel
Exp H2
Exp CO
Exp CO2
Exp CH4
Exp O2
Exp N2
47
It can also be observed that the carbon monoxide concentration increases significantly at the
reactor entrance due to the inverse WGS reaction favoured by high temperatures. Further, its
composition stabilizes as consequence of its consumption by the reverse reaction of methane
incomplete steam reforming.
Summarizing, for all gas components, Figure 37 shows that the concentration trend lines are
similar in levels and in shapes. Therefore, it can be stated that the model correctly represents the
monolith reactor behaviour despite some mismatches that are related to the difficulty to get
experimental data.
48
Conclusions and perspectives
The first conclusion of this work is that the new modelling approach, the “multi-channel model”
was successfully developed to describe the monolith reactor for hydrogen production.
Simulations have shown that the developed model accurately represents the behaviour of the
monolith reactor for hydrogen production by ATR of ethanol, showing a radial temperature gradient,
as consequence of the heat losses present on the reactor. Comparing the simulated temperature axial
profile with the experimental one it can be concluded that the two profiles present similar trend lines.
For the gas composition profile, for each compound, the results agree with the expected ones, where
the ethanol and oxygen are completely consumed for producing hydrogen. A comparison between the
simulated results and experimental data was also made, which showed that the model fits to
experimental data, and represent the monolith reactor behaviour.
To improve the multi-channel model several adjustments could be made in the future, namely to
increase the number of zones and try different thickness of the zones. An improved chemical model
can be also introduced in order to get even more similarities between the simulation and the
experimental results.
Hence, a new model to represent the monolith reactor for hydrogen production by ATR of
ethanol is now available and will be able to be applied in the next future.
49
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