Hydrogen production by autothermal reforming of · PDF fileHydrogen production by autothermal reforming of ... for all your love and support, ... Schematic representation of the transversal

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


the new modelling approach that we developed.

Pacheco (Pacheco, 2010) modelled the monolith considering the entire reactor as a porous


pted to the new modelling approach developed on this work.


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


considering the entire reactor as a porous


pted to the new modelling approach developed on this work. The


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


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


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


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


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


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


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


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.


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


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,


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


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,


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


are considered.

in a monolith channel


. 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


, 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


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



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


l model for gas phase

the fluid hydrodynamics

minar and fully developed fluid,

also treated the gas in the monolith


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


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


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


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


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


with more accuracy, when

neglected.

channel approach” that is

channel model is to devise the monolith reactor into


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


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


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



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



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.


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


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


other hand, the monolith channels are connected by their walls throughout the entire diameter, which


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


section of a monolith reactor.

, a monolith is represented by a number of channels

o radial exchange of gas between


nnected by their walls throughout the entire diameter, which


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


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


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


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


w model that characterize the reactor behaviour. Hence, it can be said that the temperature


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



w model that characterize the reactor behaviour. Hence, it can be said that the temperature


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


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


, 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


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


(radial coordinate) and z

), for each representative channel.

concentration profile (%mol/mol) inside the three representative monolith channels: the right


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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