NH3 adsorption/desorption modeling in a fixed bed reactor
Ana Rita Morgado Prates
Thesis to obtain the master degree in
Chemical Engineering
Supervisors: Professor Maria Filipa Ribeiro
David Berthout (IFPEN)
Examination Committee
Chairperson: Professor José Manuel Madeira Lopes
Supervisors: Professor Maria Filipa Ribeiro
Member of the committee: Doctor Ana Isabel Borralho Neto
26th November, 2014
ii
Acknowledgements
I would like to express my deep gratitude to those, friends and colleagues whose support made this project
much easier to accomplish.
Professors Filipa Ribeiro and David Berthout provided me this internship and were always present with their
academic support. Thank you both.
To all the staff of Jade’s department for their daily friendliness and from whom I learned most of my knowledge
of the French language. Special thanks to Eric Jeudy, Laetitia Chaine-Bonnet who I worked with daily and
always answered me with a smile on their faces.
Thanks also to all my friends that took part on this endeavor for acting like a family to me: Ana Silva, Leonor
Catita, Bernardo Barros, Ruben Franco, Ana Rita and Eliana Sobral. To Matthieu Lagauche, for all help, support
and last minute rides. To Marisa Duarte and Mafalda Lancinha a very special “thank you”. I really miss your
friendship, our laughs, and our scientific discussions. Your companionship gave me so much strength…
To Catarina Braz, Claudia Paiva e Cunha e David Faria. For all the laughs, support, friendship, last time batteries
and countless episodes.
I want to extend my thanks to my lifelong friends and colleagues for their companionship and support.
Finally, to my parents: you have always been my inspiration, my support, my strength. Always. I devote this
work to you.
iii
iv
Abstract
The Selective Catalytic Reduction of NOx with ammonia is one of the most promising deNOx technologies for
diesel vehicles. Metal exchanged zeolites are gaining increasing attention due to their high deNO x performance
over a broad range of operation conditions, namely narrow pore zeolites as ZMS-5 and others. The storage of
NH3 is a key step of the overall process, and compromises the SCR performance. The present work presents an
improved model to describe NH3 adsorption and desorption on H-ZMS-5. The objective is to find the most
appropriate approach to describe diffusion and chemical kinetics phenomena within a catalyst, porous media.
A model developed in IFP Energies nouvelles was used for simulate given NH3 TPD experiments in fixed bed.
The model results are compared with experimental data and moreover, some model improvements are
suggested, concerning the analysis of the results. The experimental data evidence intraparticle mass transfer
resistance due to certain parameter variation such as heating rate and inlet flow rate. It is already known from
the literature the importance of this phenomenon on narrow sized pore zeolite. The linear driving force
approximation is suggested as modeling approach to describe internal diffusion resistance within the zeolite.
Experimental data also show a big influence of the amount of Al in the NH3 storage capacity, as well as acid
strength. Some mathematical relation between Si/Al ratio and storage capacity is suggested as model
computation, but results are not accurate enough. To complement these conclusions and optimize the model,
more experimental data are required, and also a study of the zeolite’s acidity.
Keywords: NH3 SCR, NH3 TPD, Mass transfer, mathematical modeling, zeolites
v
Resumo
A redução catalítica selectiva de NOx com amónia apresenta-se como das tecnologias deNOx mais promissoras
para veículos a diesel. Para este processo, o uso de zeólitos com iões metálicos e com diâmetro de poro
pequeno (ZMS-5 por exemplo) tem ganho crescente atenção devido á sua eficiência e performance em
variadas condições operacionais. A adsorção de NH3 no zeólito é uma etapa chave de todo o processo,
comprometendo a sua eficiência. O presente trabalho centrou-se no estudo dos efeitos de difusão e transporte
de massa em zeólitos, meio poroso, nomeadamente a construção/optimização de um modelo para simulação
de experiencias de dessorçao a temperatura programada de NH3 em H-ZMS-5, em rector leito fixo. Como
ponto de partida foi utilizado um modelo já desenvolvido pelo IFP Energies Nouvelles, o qual foi adaptado às
condições experimentais em questão. Os resultados experimentais e as respectivas simulações foram
comparados para consequentemente analisar a capacidade de reprodução do modelo. Os resultados
experimentais e a literatura sugerem a existência de limitações difusionais dentro do zeólito. Como primeira
abordagem sugere-se a implementação no modelo da aproximação pela força linear motriz para descrição do
fenómeno. Os resultados experimentais parecem evidenciar uma relação matemática entre parâmetro Si/Al e a
capacidade de armazenamento do zeólito, no entanto a respectiva expressão não consegue apresentar
resultados satisfatórios para ser implementada no modelo. O rácio de Si/Al tem também implicações na força
ácida nos centros activos, no entanto sem nenhum padrão aparente. Para complementar estas conclusões e
optimizar o modelo são necessários mais dados experimentais e um estudo da acidez do zeólito.
Keywords: NH3 redução catalítica selectiva NH3, dessorção a temperatura programada NH3, transferência de
massa, modelização matemática, zeólitos
vi
Conteúdo
List of Figures........................................................................................................................................... ix
List of tables .............................................................................................................................................x
Nomenclature list .................................................................................................................................... xi
1.
Introduction..................................................................................................................................... 1
1.1. Context ......................................................................................................................................... 1
2.
1.2.
Objectives ................................................................................................................................ 2
1.3.
Thesis outline .......................................................................................................................... 3
State of Art ...................................................................................................................................... 4
2.1. Overview of ammonia SCR ........................................................................................................... 4
2.2.
SCR catalysts substrates .......................................................................................................... 5
2.2.1. SCR on filter ........................................................................................................................... 6
2.3.
SCR catalysts ............................................................................................................................ 7
2.3.1.
Zeolite catalysis ............................................................................................................... 7
2.3.2. Zeolites hydrothermal aging ................................................................................................. 9
2.3.3.
2.4.
NH3 Temperature programed desorption .................................................................... 10
SCR Models ............................................................................................................................ 10
2.4.1.
Kinetic Models ............................................................................................................... 12
2.5. Modeling SCR systems................................................................................................................ 14
2.5.1. Fixed Bed Reactor ................................................................................................................ 14
2.5.2. Mass and Heat Transfer in Catalytic Reactor ...................................................................... 15
Continuity equation for specie A........................................................................................................... 16
2.5.3. Flow through Porous Media ................................................................................................ 17
2.5.4. Complexities in modeling of heterogeneous catalytic reactions ........................................ 18
3. Experimental Material ....................................................................................................................... 22
3.1. Experimental procedure ............................................................................................................. 22
3.2. Study 1: inlet conditions effect- experimental parameters ....................................................... 24
3.3. Study 2: Si/Al ratio effect – experimental parameters............................................................... 25
4. Model Description ............................................................................................................................. 27
4.1. Reactor model ............................................................................................................................ 27
4.2. Kinetic Model – Double-site approach ....................................................................................... 28
4.3. Adaptation of a previous IFP Energies Nouvelles model to the case study ............................... 30
vii
4.4. Model Input Parameters ............................................................................................................ 35
4.5. Simulation................................................................................................................................... 36
5. Results ............................................................................................................................................... 37
5.1. Study 1 – inlet condition effects................................................................................................. 37
5.1.1. NH3 Concentration .............................................................................................................. 37
5.1.2. Temperature Profile ............................................................................................................ 41
5.1.3. Pressure Profile ................................................................................................................... 43
5.2. Study 2 – Si/Al impact ................................................................................................................ 44
5.2.1. NH3 Concentration ............................................................................................................. 45
5.2.2. Temperature profile ............................................................................................................ 47
5.2.3. Pressure Drop Profile .......................................................................................................... 48
5.3. Model improvements ................................................................................................................. 50
6. Conclusion and Perspectives ............................................................................................................. 57
7. References ......................................................................................................................................... 58
8. Annexes ............................................................................................................................................. 61
viii
List of Figures
Figure 1 – Scheme of the gas or bulk phase, the washcoat or catalytic material and the substrate (9) 5
Figure 2 - example of a deNOx catalyst substrate .................................................................................. 6
Figure 3-Example of HC-SCR device, which is a monolithic catalytic converter (10) .............................. 6
Figure 4 – SCR on filter device (13) ......................................................................................................... 7
Figure 5 – Zeolite’s framework (14) ........................................................................................................ 8
Figure 6 - Bronsted and Lewis acid sites (14) .......................................................................................... 8
Figure 7 – Possible reaction mechanism of the SCR process over metal-exchanged zeolites with two
adjacent Bronsted acid sites (1) .............................................................................................................. 9
Figure 8 – Classical 1D catalyst model with lumpted treatment of the surface (left) and 1+1D catayst
modeling including reaction profile in the washcoat (17) .................................................................... 11
Figure 9 – Total mass balance in a generic volume ΔxΔyΔz .................................................................. 16
Figure 10 – stages of the catalytic process (37) .................................................................................... 19
Figure 11 – Concentration profile at the surface and inside the catalyst grain (15)............................. 19
Figure 12 - Fixed bed reactor sketch ..................................................................................................... 23
Figure 13 - TPD stages on temperature profile ..................................................................................... 24
Figure 14 - TPD stages on NH3 concentration ....................................................................................... 24
Figure 15- Pressure drop profile for E11-99: simulation results using model 1 and model 2 .............. 31
Figure 16 - Pressure drop profile for E11-99: simulation results from model 2 and experimental data
............................................................................................................................................................... 32
Figure 17 - Temperature profile for E11-99: simulation results using model 1 and model 2 ............... 32
Figure 18 - - NH3 molar fraction profile for E11-99: simulation results using model 1 and model 2 .... 33
Figure 19 - Pressure drop profile using different void fraction, ɛ, values ............................................. 33
Figure 20 – NH3 %vol, temperature and pressure profile for E11-101, concerning the experimental
data, 1 Fixed bed model (CSTR approach) and 5 Fixed bed model (plug-flow approach) .................... 34
Figure 21- AMESim sketch ..................................................................................................................... 36
Figure 22 - test 1 NH3 molar fraction profiles: experimental data and simulation results .................. 38
Figure 23 - test 2 NH3 molar fraction profiles: experimental data and simulation results .................. 39
Figure 24 -test 3 NH3 molar fraction profiles: experimental data and simulation results ................... 40
Figure 25 – test 1 temperature profies (K) ............................................................................................ 42
Figure 26 test 2 temperature profies (K) ............................................................................................... 42
Figure 27 - test 3 temperature profies (K)............................................................................................. 43
Figure 28 – Pressure profiles for test 1, test 2 and test 3 (bar) ............................................................ 44
Figure 29 – Study 2, NH3 molar fraction profiles: experimental data ................................................... 45
Figure 30 – study 2 NH3 molar fraction: simulation restults ................................................................. 47
Figure 31 – Temperature profile for E11-99 (K) .................................................................................... 48
Figure 32 – Pressure drop profiles for E11-101 and E11-99 (bar) ......................................................... 49
Figure 33 – Variation of NH3 storage, Ω1 and Ω2 with Si/Al. ............................................................... 53
Figure 34 – study 2 temperature profiles (K) ........................................................................................ 67
Figure 35 – Study 2 pressure drop profiles ........................................................................................... 68
Figure 36 – AMESim sketch for the plug flow approach, N=5............................................................... 69
ix
List of tables
Table 1 - Euro 5 and Euro 6 emission limits for Diesel passengers vehicles ........................................... 1
Table 2 – Reactions from the kinetic model of (18) .............................................................................. 12
Table 3 – Different diffusion coefficients .............................................................................................. 21
Table 4 – Tests performed for study 1 .................................................................................................. 25
Table 5 - Operation condition for test 1, adsorption temperature effect, test 2, heating rate effect
and test 3, flow rate effect .................................................................................................................... 25
Table 6 – Some operation parameters for study 2 experiments .......................................................... 26
Table 7 - Average grain diameter for each Si/Al H-ZMS-5 zeolite ......................................................... 26
Table 8 – Reactions for NH3 adsorption and desorption in each site S1 and S2 ................................... 29
Table 9 – Rate expressions for NH3 adsorption and desorption on each acid site S1 and S2 ............... 29
Table 10 – Variation of occupied acid sites fraction ............................................................................. 30
Table 11 - Model input parameters ...................................................................................................... 35
Table 12 – Test 1 : TPD curve area (K) ................................................................................................... 38
Table 13- test 1 temperature of maximum desorption: experimental data and simulation results .... 39
Table 14 – Test 2 : temperature of maximum desorption : experimental data and simulation results 40
Table 15 – Test 3 : TPD curve area (K) ................................................................................................... 40
Table 16- test 3 maximum desorption molar fraction of NH3: experimental data and simulation
results .................................................................................................................................................... 41
Table 17 – difference between the maximum desorption amount of NH3 for E11-87 and E11-89 :
experimental data and simulation results............................................................................................. 41
Table 18 - test 3 temperature of maximum desorption: experimental data and simulation results ... 41
Table 19 – Total pressure drop for experiments E11-87, E11-89, E11-90, E11-92 and E11-93 ............ 44
Table 20 – study 2: experimental maximum desorption tempertures (K) ............................................ 45
Table 21 – Experimental values for NH3 storage capacity .................................................................... 45
Table 22 – Study2 : TPD curve area (s) .................................................................................................. 47
Table 23 – Experimental and simulated pressure drop and particle diameter for study 2 experiments
............................................................................................................................................................... 49
Table 24 – NH3 storage capacity for S1: experimental and calculated value ........................................ 53
Table 25 - – NH3 storage capacity for S2: experimental and calculated value ...................................... 53
x
Nomenclature list
Aj
C
Cs
Ca
CpCC
Cv
D
DAB
Deff
Dinert
Dm
DK
Dp
Dv
Dzeolite
Eaj
Eaj0
F
Fin
Fout
FBmass
Ga
Gca
h
hi
K
k
kg
kj
L
MA
MB
Mcat
Mmol
mg
mi
NA
Ncati
P
Pg
Pout
Qconv
Qexchanged
Qwall
R
RA
Pre-exponential factor for reaction j (m3mol-1s-1)
Concentration of the gas phase (mol m-3 )
Concentration on the surface of the catalyst (mol m-3)
Concentration of the component A in the gas phase (m2 s-1 )
Reactor heat capacity (J kg-1K-1)
Heat capacity of the gas (J kg-1K-1)
Fixed bed diameter (m)
Molecular diffusion coefficient of A for binary mixture (m2 s-1 or cm2 s-1)
Effective diffusion coefficient (m2 s-1 or cm2 s-1)
Inert average grain diameter (m)
Molecular diffusion coefficient (m2 s-1 or cm2 s-1)
Knudsen diffusion coefficient (m2 s-1 or cm2 s-1)
Particle diameter (m)
Characteristic length (m)
Zeolite average grain diameter (m)
Activation energy for reaction j (J mol-1)
Activation energy for reaction j for zero coverage (J mol-1)
Forchheimer coefficient (dimensionless)
Inlet flow rate (kg s-1)
Outlet flow rate (kg s-1)
Reactor mass (kg)
Geometric surface area per unit volume (m2m-3)
Catalytic surface area per unit volume (m2m-3)
Specific enthalpy (J kg-1 )
Specific enthalpy for the ith species (J kg-1)
Fixed Bed permeability (m2 )
Thermal conductivity (W m-2 K-1 )
Mass transfer coefficient (m s-1)
Rate constant for reaction j (mol s-1 kgcatalyst-1)
Reactor length (m)
Molar mass of A (g mol-1)
Molar mass of B (g mol-1)
Catalyst mass (kg)
Molar mass of NH3 (g mol-1)
Gas mixture mass (kg)
Mass for the ith species (kg)
Flux of the component A, (mol m-2 s-1 )
Number of ative sites I per mass washcoat (mol.Kg-1washcoat)
Pressure (Pa or atm)
Gas mixture volume (Pa or atm)
Outlet Pressure (Pa or atm)
Heat transfer due to convection between gas and solid phase (J)
Heat exchanged between the gas and solid phase (J)
Heat exchanged between the reactor and the surroundings (J)
Gas constant (J mol-1 K-1)
Production of A (mol m-3 s-1 )
xi
Re
Reynolds number (dimensionless)
rA
Rate of reaction of A (mol mcat-3 s-1)
rp
pore radius (m)
S1
Weak adsorption site
S2
Strong adsorption site
Sh
Energy generation per unit of volume (J m-3 )
T
Temperature (K)
Tg
Temperature in the gas phase (K)
Ts
Temperature in the solid phase (K)
ui
Internal energy for the ith species (J kg-1)
V
Volume of catalyst (m3)
Vfree
Free volume of the catalyst bed (m3)
Vg
Gas mixture volume (m3)
Vtotal
Fixed Bed volume (m3)
v
Fluid velocity (m s-1 )
xA
Molar fraction for the component A (dimensionless)
xi
Mass fraction for the ith species (dimensionless)
xiin
Inlet mass fraction for the ith species (dimensionless)
xiout
Outlet mass fraction for the ith species (dimensionless)
Greek letters
αj
Coverage dependence in reaction j
Ɛ
Void fraction (dimensionless)
θj
Coverage of site j
µ
Viscosity (kg m-1 s-1 )
ρ
Density of the gas phase (kg m-3 )
σ
Average collision diameter (A)
τ
Tortuosity
Ω
Integral of collision (dimensionless)
Ωj
NH3 storage capacity for site j (molsites kgcat-1 )
ωi
Variation of ith species amount (kg s-1)
xii
xiii
1. Introduction
This report describes the development of a IFP Energies nouvelles model for the NH3 adsorption and
desorption on a H-ZMS-5 zeolite (MFI) in a fixed bed reactor. The model considers mass, heat and pressure
balances as well as a kinetic model. The results provided by this model are compared with experimental data
on NH3 temperature programed desorption on H-ZMS-5. Moreover, some model improvements are proposed.
1.1. Context
Nitrogen oxides (NOx, x=1,2) are a major source of air pollution, being responsible for acid rain
(deforestation), photochemical smog (health disease), and intensification of ground-level ozone. Most of NOx
produced comes from transportation (combustion processes in diesel engines - thermal NOx). Diesel engines
emissions represent about 75% of total NOx emissions of road traffic. (1)
During combustion process in engines, nitrogen oxides are produced by the oxidation of atmospheric
nitrogen at very high temperatures
𝑁2 + 𝑂2 → 2𝑁𝑂x
1
Consequently, many efforts have been made to minimize NO x produced in particular from Diesel-equipped
vehicles, either by combustion control or by post-combustion control, being the last one the most effective.
Combustion control has been proven to be insufficient due to legislated emission limits, hence the
development of post-treatment technologies is mandatory. (1)
Table 1 - Euro 5 and Euro 6 emission limits for Diesel passengers vehicles
Source: Official Journal of the European
Union
Carbon Monoxide (mg/km)
NOx (mg/km)
Total hydrocarbons + NOx (mg/km)
Particulate matter (mg/km)
Euro 5
September 2009
500
180
230
5
Euro 6
September 2014
500
80
170
5
Concerning techniques to treat exhaust gas (post-combustion control), catalytic technologies seem to
be the most suitable option because of their relative low cost and high efficiency. The three way catalyst
converters for instance, converts carbon monoxide (CO) and unburned hydrocarbons (HC) to produce carbon
dioxide (CO2) and water (H2O) and and also reduce nitrogen oxides (NO x). (2) Three way catalyst converters is
an efficient technology for catalytic reduction of NOx in gasoline engines, operating at stoichiometry, however,
this technology cannot be applied in a diesel engine or other lean burn engines due to oxygen excess in the
exhaust gas. (3)
The following approaches have been investigated for NO x reduction: selective catalytic reduction (SCR)
of NOx by hydrogen (H2), SCR by hydrocarbons (HC), SCR with ammonia or urea among other techniques. SCR
1
processes have been used and developed for stationary applications for several decades to reduce NO x, and
has already been applied to heavy duty diesel vehicles. Since 1990 NOx emissions from diesel engines have
come down because of selective catalytic reduction (SCR) aftertreatment. Urea SCR or ammonia (NH3) was
developed as the most efficient method of reducing NOx emissions, meeting the later emission legislation Euro
V, Table 1. Serial applications that meet the Euro V standard were introduced in commercial vehicles at the
beginning of 2005. These systems are based on non-exhaust gas recirculation (EGR) engines and consequently
expose the catalyst to high NOx and urea concentrations. (1), (3), (4).
Among SCR catalysts already proposed and explored, metal exchanged zeolites seem to be a promising
candidate due to their high deNOx performance in a wide range of operating conditions (5). Narrow pore
zeolites such as MOR, FER, BEA and MFI, exchanged with a transition metal such as Fe, Cu, Cr and Ag have
proven to be very suited for SCR applications (1). Recently, it was proven that Cu-SSZ-13, a zeolite with the
Chabazite structure and containing small pore diameter (~3.8 A) eight-membered ring pores, is more active and
selective for NH3 –SCR than other copper exchanged species. Moreover, Cu-SSZ-13 was found to be less prone
to deactivation by hydrocarbon inhibition and thermal degradation. (6)
In order to meet the emission standards (EURO VI) it is necessary to study the performance of these
catalysts and its limitations.
Although narrow pore zeolites have proven to be very suited for SCR applications, this kind of zeolites
may present internal diffusional limitations in some exhaust operations conditions. Some studies suggest a
significant effect of internal diffusion limitations, that cannot be neglected (7). It should be noted that the
reaction between NH3 and NOx occurs continuously on the surface of a catalyst and NH3 adsorption on the
active centers is a key step that compromises the efficiency of the process. Therefore, the development of a
rigorous model describing the NH3 adsorption on a zeolite is necessary to accurately describe the adsorption
process and understand the possibilities and limitations of the given zeolite. H-ZMS-5 is one of the most suited
zeolites for SCR application. Furthermore, studying this zeolite represents an approach for studying small pore
zeolites.
1.2.
Objectives
Concerning the necessity to minimize NOx emissions and achieve the future legal requirements of
transport emissions, post-combustion treatment technologies must be extensively studied, in order to find the
most efficient system
Models are developed in order to represent the actual behavior of a system, hence the use of models
helps understanding and optimizing the process.
This work aims to find the most appropriate approach to describe diffusion and chemical kinetics
phenomena within a catalyst, porous media. For this purpose, this report comprises the development and
optimization of a given model from IFP Energies nouvelles for adsorption and desorption of NH3 on H-ZMS-5 on
fixed bed reactor. Ammonia adsorption and desorption is the key step of the SCR technology and compromises
the efficiency of the whole process. Since recently small pore size zeolites were found to be the best SCR
catalyst, adsorption and desorption on H-ZMS-5 (MFI) in an approach to study the effects and possibilities with
this kind of catalyst. To this end, a given IFPEN model simulates NH 3 TPD on H-ZMS-5 experiments. The model
considers mass, heat and pressure balances. Both results are compared to understand the accuracy of the
model. Moreover, some improvements to the model are suggested.
2
1.3.
Thesis outline
This work is presented in four distinct sections: state of art, experimental material, model description and
finally results.
The first section concerns the State of the Art, where is given a more detailed overview of the context of
this work and the literature analysis that was required. A brief introduction about zeolite catalysis is given, as
also some considerations about complexities in modeling of heterogeneous catalytic reactions. SCR substrates
and models are presented and the use of a fixed bed reactor is justified. The last part deals with modeling this
kind of reactor.
The second part briefly presents the experimental data that were available for the current study. It should
be noted that these experiments were previously performed by IFP Energies Nouvelles and that experimental
results were posteriorly provided for the present work.
The model description presents the main assumptions of the model developed in IFP Energies nouvelles,
which will be used for simulating the experimental data. Moreover this chapter presents the interface used in
the simulator used for this work, AMESim, and how the model was adapted to the case study.
The results are then presented in a fourth section by the means of NH3 molar fraction, temperature and
pressure profiles, allowing to understand, analyze and criticize the data provided by the model comparing to
the experimental data. Finally it is presented a discussion concerning the results and possible improvements
that should be integrated in the model.
This report ends with a final conclusion about the main remarks of this study.
3
2. State of Art
2.1. Overview of ammonia SCR
Nitrogen oxides can be removed by direct decomposition to nitrogen and oxygen. However this
-1
reactions is kinetically unfavorable (Ea = 362 kJ mol ), requiring a catalyst and a reduction aging to increase its
performance. Selective catalytic reduction of NOx using ammonia (ammonia SCR) was introduced in the 1980s
and developed into a mature technology for reducing NOx emissions from power stations and industrial
facilities (4).
The main feature of the SCR process is the use of reducing agent to react specifically with nitrogen
oxides but not with the excess oxygen in the exhaust gas (1). Ammonia is the only known chemical compound
able to reduce NOx on reactant and product-selective catalysts (SCR catalysts) in the presence of oxygen (a
stronger oxidation agent than NO) to form nitrogen (4). However, pressurized ammonia containers represent a
safety risk when carried onboard a vehicle. Alternatively, aqueous solution of urea is used in diesel vehicles as
an ammonia storage compound (4).
SCR processes using urea as reducing agent in mobile applications have undergone continuous
development since 1989. As early as 1992, this technology was able to successfully reduce NO x emissions to the
later Euro V limit in a steady-state cycle. The SCR process proved to be very effective in reducing NO x emissions,
which has made it the preferred method among European commercial vehicle manufacturers (4).
Before the SCR device, urea is injected into the gas exhaust then is thermolysed into isocyanic acid
which is hydrolysed into ammonia (1), following the two reactions:
𝑁𝐻2 − 𝐶𝑂−𝑁𝐻2 → 𝑁𝐻3 + 𝐻𝑁𝐶𝑂
2
𝐻𝑁𝐶𝑂 + 𝐻2 𝑂 → 𝑁𝐻3 + 𝐶𝑂2
3
Therefore, the ammonia is adsorbed in the active sites of the catalyst. The adsorbed ammonia reacts
with the nitrogen oxides leading to the reduction of NOx to nitrogen and water. There are several reactions that
can occur during reduction of NOx with NH3 depending on the exhaust gas temperature and species
concentrations. Exhaust diesel engines contain nitrogen oxides mainly in the form of nitrogen monoxide (NO).
Therefore, the basic reaction also known as “standard SCR” is:
4𝑁𝐻3 + 4𝑁𝑂 + 𝑂2 → 4𝑁2 + 6𝐻2 𝑂
4
The SCR activity increases with the NO2/NO ratio, occurring the “fast SCR reaction”, for NO2:NO of 1:1
4𝑁𝐻3 + 2𝑁𝑂 + 2𝑁𝑂2 → 4𝑁2 + 6𝐻2 𝑂
5
If NO2/NO fraction is greater than 50%, NO2 reaction takes also place:
4𝑁𝐻3 + 3𝑁𝑂2 → 3.5𝑁2 + 6𝐻2 𝑂
6
4
These are the main SCR reactions, which depend on the stoichiometry of the inlet exhaust gas. There are also
several side reactions that may produce secondary emissions as NO2 or oxide ammonia unproductively (8).
The process has been improved and explored in the last decade, achieving efficiencies greater than
90% (1).
2.2.
SCR catalysts substrates
The ammonia SCR reactions take place within the called washcoat, the catalytic material, where
NH3 is firstly adsorbed.
Figure 1 – Scheme of the gas or bulk phase, the washcoat or catalytic material and the substrate (9)
The effective reaction rate on catalysts will depend on the following steps (4):
 Mass transfer or the reactants from the bulk flow and film diffusion through the stagnant
thin layer of gas to the external catalyst surface (external mass transfer),
 Mass transfer of the reactants into the pore system of the washcoat, onto the internal
surface (“pore diffusion”),
 Chemical reaction on the active centers, i.e. the actual catalyst (“reaction kinetics),
 Mass transfer of the reaction products from the pore system to the external surface,
 Mass transfer of the reaction products from the catalyst surface, and film diffusion
through the stagnant thin layer of gad into the gaseous phase of the catalyst channel.
Under the typical conditions of a vehicle catalyst, reaction kinetics has a limiting effect only at low
exhaust gas temperatures, hence the process performance is determined over a wide load range by the
internal mass transfer in the pores and the external mass transfer through the boundary layer. It should be
noted that exhaust gas aftertreatment operates at high temperatures (above 600°C). Moreover the efficiency
of the catalyst is function of the residence time and the active surface area. Increasing residence time within
the catalyst allows more time for the kinetics to proceed, as increasing the surface area increases the contact
area between the exhaust gas and the catalyst. Some catalyst structures may improve the process performance
due their special geometry, namely honeycomb channels shape (4).
5
Figure 2 - example of a deNOx catalyst substrate
Typically, the ammonia SCR process in vehicles is performed in the exhaust gas aftertreatment area in
a called monolithic catalytic converter. This technology has already been exhaustively studied and
implemented for the past decades.
A monolithic catalytic reactor consists of a monolith encased in a metal can design to distribute the
exhaust gas uniformly. Inside this structure, a honeycomb type ceramic substrate forms hundreds of parallel
channels. The catalytic material used to convert the NOx emissions is distributed over a large surface area. This
distribution of catalytic material is done through impregnation into a washcoat that is directly applied in the
catalyst walls. The channels of the monolith are small, of order of 1 mm, which allows a big number of channels
increases the surface area and leads to a laminar regime within the channels, increasing residence time and
conversion rate. (9)
In the washcoated microchannel, convection and diffusion phenomena describe the mass transfer in
the gas phase, coupled with reaction and internal diffusion within the washcoat, where occur adsorption and
desorption of NH3 as NOx oxidation.
Figure 3-Example of HC-SCR device, which is a monolithic catalytic converter (10)
2.2.1. SCR on filter
In order to reduce packaging volume and costs, there is an increasing interest in combining after treatment
systems in the same device. Typically, deNOx and particulate matter removal are controlled in separated device
systems, SCR monolithic catalytic converted and diesel particulate filter (DPF) respectively. However, one
possibility consists of a NH3 Selective Catalytic Reduction (SCR) on a diesel particulate filter (DPF). (11) This
combination can be a promising alternative to the monolith catalytic converter, due its higher efficiency of
emissions reduction especially considering that, the monolith catalytic converter efficiency seems to be not
enough to achieve future legal emissions requirements, namely Euro 6 (12).
SCR on Filter controls NOx and PM (particulate matter or soot) emissions from diesel engines, on a
single substrate. This device is basically a “wall-flow” ceramic monolith with a catalyst coating. The gases react
as they flow through the system as PM is filtered by SCR on filter. Nitrogen oxides react with ammonia in the
6
active sites of the washcoat, producing nitrogen and water. The soot gets stuck in the SCR on filter, where is
oxidized by NO2 into CO2 and NO (13).
As the SCR monolithic catalytic converter, the catalyst carrier has a pillar shape and is made of a
porous ceramic, leading to a large number of cells placed in parallel with one another each extending in a
longitudinal direction. However, each channel has a cell wall interposed there between in a way that soot is
trapped. The cell wall supports a zeolite as a NOx conversion catalyst. (13).
Figure 4 – SCR on filter device (13)
2.3.
SCR catalysts
For industrial SCR usage, catalysts are based mainly on vanadium supported in titanium (TiO 2 supported
V2O5). This kind of catalyst has also been applied for heavy duty diesel vehicles in Europe, presenting some
problems like high activity for oxidation of SO2 to SO3, decrease of activity and selectivity from 550°C and also
because vanadium volatizes above 650°C, implying toxicity and modification of the catalyst performance (1).
As mentioned before, narrow pore zeolites such as MOR, FER, BEA and MFI exchanged with a
transition metal such as Fe, Cu, Cr and Ag have proven to be very suited for SCR applications (1). It was found
that SCR activity increases as the oxidation activity of the exchanged ion increases. Fe-ZSM-5 was one of the
first studied and presenting high stability and activity in NH 3 – SCR, exceeding V2O5-WO3-TiO2. Significant
2+
research efforts have concentrated on Cu ion exchanged ZMS-5 (Cu-ZMS-5) zeolites to study both its NO
2+
decomposition and SCR activity. Early development efforts have also focused on Cu exchanged beta zeolie
(Cu-beta) for its excellent activity over a wide range of temperatures. However, all these catalyst suffer high
deactivation during high temperatures. Recently, Cu-SSZ-13 with the Chabazite structure and small pore radios
(~3,8 A) has been found as very active and selective for the ammonia SCR process, and less prone to
deactivation thermal degradation (6). In any case, although small pore zeolites assume to be most suited
zeolites for this technology, this kind of zeolites may present some internal diffusional limitations, which would
compromise the process performance.
2.3.1.
Zeolite catalysis
Zeolites are one of the main components of catalysts used in refining and petrochemical industry, and
play an increasingly role in organic synthesis and pollution control. Zeolites have been subject of great interest,
due to their shape selectivity, acidity (both Bronsted protonic acid site and Lewis electrons acceptors acid
sites), framework and acid sites stability, confinement effects within porous, and ion-exchange capacity.
7
Zeolites are crystalline aluminosilicates with a nanosized pore structure and can be classified into
three pore size categories, small, medium and large pore zeolites, having free diameters of 0.3-0.45nm, 0.450.6nm and 0.6-0.8nm respectively. This well-defined structure, with pores of about the size of molecules, works
as a molecular sieve, providing great shape selectivity in the diffusion process through the zeolite crystals (3).
-
Zeolites are based on a three-dimensional framework of TO4 tetrahedra (SiO4 ou AlO4 ) connected
through their oxygen atoms constituting subunits and finally, forming large lattices of identical blocks
connected with each other. Zeolites structural formula can be described by Mx/n+(Al2O2 )x (SiO2 )y , where n is the
valence of cation M, x+y the total number of tetrahedra per unit cell and y/x the atomic Si/Al ratio from a
minimum of 1 to infinite. (3)
The silicon building block in Zeolite is electrically neutral, but the aluminum building block carries a
negative charge, that can be compensated by a proton Figure 5. Zeolite’s protonic acidity comes essentially
from hydroxyl groups bridging alumina and silica. The strong interaction of O with Al weakens OH bond,
increasing the acid strength (Bronsted sites) Figure 5.
Figure 5 – Zeolite’s framework (14)
Lewis acid sites are electrons acceptor and are generally a metal as a coordinately unsaturated sites,
3+
(ex: Al ) usually represented by an empty square Figure 6. Lewis sites acidity is less strong than Bronsted sites
acidity. These weaker acid sites are usually formed after dehydration, and dehydroxilation, considered as
defects in the crystal lattice.
Figure 6 - Bronsted and Lewis acid sites (14)
Acid sites proximity, Al-OH-Si angle, Si/Al ratio, the presence of trivalent elements in the framework
other than Al, etc, are some of the parameters determining the acid strength of the zeolite protonic sites. (3)
Moreover, extraframework aluminum species also increase catalytic activity of zeolites (Lewis acid species)
showing enhanced acidity through interaction of bridging hydroxyl groups.
The acidity of the zeolite is one of the most important parameter for SCR activity, since ammonia
+
(base) is adsorbed and activated in the form of NH4 ions in the protonic acid sites.
8
Figure 7 – Possible reaction mechanism of the SCR process over metal-exchanged zeolites with two adjacent Bronsted acid
sites (1)
2.3.2. Zeolites hydrothermal aging
When a zeolite is exposed to high temperatures it suffers a process called hydrothermal aging. Typically,
the acidity of zeolites decreases after hydrothermal aging due to dealumination and the loss of surface area.
The dealumination is caused by the loss of alumina from the framework (hydrolysis of Si-O-Al bonds). This
process is more severe for high alumina content zeolites (lower Si/Al). A major problem leading to deactivation
is the tendency of the metal species to cluster into metal oxide aggregates, which leads to inactive metal-oxide
particles (1)
A typical Diesel exhaust aftertreatment system consists of a diesel oxidation catalyst, DOC, a SCR
system and a diesel particulate filter DPF. Since the soot is removed from the DPF at high temperatures
(>650°C), the SCR catalyst will work as these same high temperatures. Hydrothermal aging will lead to the loss
of alumina in the framework, which means that will cause a decrease on the number of Bronsted acid sites,
hence, loss of NH3 storage capacity. Therefore, the zeolite must have high thermal resistance, otherwise will
lose active surface, and the process efficiency decreases (6).
Although metal-exchanged have showed to be a promising alternative, its hydrothermal aging In SCR
catalysis is still a challenge. Among the various zeolites developed for NH 3-SCR, Cu-SSZ-13 (already referred
above) was found to be less prone to deactivation by hydrocarbon inhibition and thermal degradation. (6)
9
2.3.3. NH3 Temperature programed desorption
Temperature programmed desorption (TPD) is a well-known technique for characterization of
heterogeneous catalysts acidity. Basically, after the basis adsorption in the catalyst, the sample temperature
increases constantly forcing desorption at continuously higher temperature. (15)
The TPD procedure comprises different stages. As preparation phase, samples are degassed generally at
100 °C for one hour in flowing helium or azote in order to remove water vapor and to avoid pore damage
programmed to high temperatures, (about 500°C, depending on the sample). This increase of temperature
occurs at a ramp rate of about 10 °C/min and held at that temperature for two hours to remove strongly bound
species and activate the sample. Finally the sample is cooled to 120 °C in a stream of flowing inert gas, helium
or azote. At the adsorption step the catalyst sample is saturated with the basic probe at lower temperature
(120°C-150°C). This temperature is used to minimize physisorption of the ammonia or organic amines. The
temperature-programmed desorption is easily performed by ramping the sample temperature at generally
10°C/minute to high temperature (500°C-700°C, depending on the adsorbed molecule) (16)
Ammonia is the most used basis in TPD essentially for two reasons: NH 3 is a small molecule that more
easily reaches all protonic sites, it is also a strong basis, which guaranties its desorption in all kind of acid sites,
even the weak ones. Pyridine is also a strong basis used in TPD analysis, but its big molar volume compromises
its accessibility to the active sites. (15)
The amount of desorbed NH3 is measured as a function of temperature or time, which representation is
usually referred as TPD curve, allowing an analysis of the range of temperatures desorption occurs. Assuming
that each molecule is adsorbed by a unique acid site, calculating the area under TPD curve gives the total
number of active sites. (15) Each experimental curve areas are equal to the sum of every sub curves areas, each
one representing different acid sites. The sub curves area corresponds to the quantity of the respective acid
site. The stronger the chemical connection is between the adsorbed molecule and the acid site, the more
energy it takes to “broke” it, thus the desorption occurs at higher temperatures (15).
For the present work, ammonia TPD experiments were performed in order to study adsorption and
desorption of NH3 over H-ZMS-5, considering operational condition effects, Al amount effects, etc. and validate
a model for ammonia adsorption and desorption over the same zeolite.
2.4.
SCR Models
Modeling a monolithic catalythic converter leads inherently to a three dimensional (3D) model, with a
different conversion rate and temperature for each channel. This 3D simulation would require a significant
amount of overhead in order to model the system, and also a long time run. As a result of the complexity of
trying a 3D model, most researchers use one-dimensional (1D) models which are computationally efficient and
relatively easy to calibrate (9).
The 1D catalyst modeling has started since the late 1960s with Vardi and Biller’s work, presenting a
pipe wall model approach examining only the effects of heat transfer on the warm-up of the catalyst. Since
then, several expansions have been developed concerning specially the catalyst surface chemistry. Basically
these models assume only an axial gradient and reaction occurs at the surface of the washcoat. These classical
models have been in widespread use and proven their effectiveness in designing catalyst systems for lower
10
emissions levels. However, to meet future emissions standards, the prediction capability within the catalyst
systems needs to be improved. In the literature (9) it is presented a review of classical and future approaches
for modeling 1D catalyst
More recently, some studies such as (17), propose one + one-dimensional modeling of monolithic
converters, introducing a concentration profile within the washcoat, and stressing out the importance of
internal diffusion within catalyst.
Figure 8 – Classical 1D catalyst model with lumpted treatment of the surface (left) and 1+1D catayst modeling including
reaction profile in the washcoat (17)
For both models, bulk gas species equation considers the propagation of species through the channel (x
direction) and the mass transfer of species from the bulk gas to the surface under the laminar conditions in the
channel, equation 7.
𝑘𝑔 𝐺𝐴
𝜕𝐶𝐴
𝜕𝐶𝐴
+𝑣
=(
) (𝐶𝑠 − 𝐶)
𝜕𝑡
𝜕𝑥
ɛ
𝜕𝐶𝑠
𝜕𝑡
=(
𝑘𝑔 𝐺𝐴
ɛ
) (𝐶𝑠 − 𝐶) −
𝑅𝑠 𝐺𝑐𝑎
1−ɛ
7
8
11
𝜕𝐶𝑠
𝜕 2 𝐶𝑠
= 𝐷𝑒𝑓𝑓
− 𝑅𝑠 𝐺𝑐𝑎
𝜕𝑡
𝜕𝑦 2
9
1D model considers mass transfer between the bulk gas to the surface, and the last term on the right that
includes the reactions in the washcoat, equation 8, and while for 1+1D, there is also a concentration profile
within the washcoat (direction y) including a diffusion term, equation 9.
These two models present an example of the different approaches when modeling aftertreatment
systems. As said before, the future demanding emissions levels will need an more rigorous look over the
washcoat phenomena, requiring models with more rigorous treatments of the gas dynamics within catalyst
systems.
Concerning the new promising technology of SCR on filter, the available literature (11) presents a 1D
model for this kind of device, combining kinetics for a Cu-zeolite or an Fe-zeolite SCR catalyst. The model was
originally developed for a flowthrough monolith, with a physical model for a coated DPF. This model is capable
of predicting NOX conversion and NH3 slip from an SCR system in a real diesel exhaust. This model can be
further used to explore a wide range of catalyst and system scenarios, which allow us to efficiently optimize
systems for varied applications and rapidly investigate many parameters with the aftertreatment system.
2.4.1. Kinetic Models
Kinetic models have been used to help to understand all the phenomena occurring in the SCR system.
Several models can be found in literature applied to the different referred catalysts that show different
reaction pathways and mass and energy balances.
Olsson et all (18) presents a model using Cu-ZMS-5 catalyst, which considers each channel of the
monolith a one dimension plug flow reactor (PFR) and no internal diffusion resistance. This model reports a
single-surface site approach. The reaction rates expressions follow the Arrhenius law, a coverage dependent
activation energy was used for ammonia desorption. The film model is used to describe the mass-transfer
between the gas and the catalyst surface. The model includes seven reactions, Table 2
Table 2 – Reactions from the kinetic model of (18)
NH3 adsorption/desorption equilibrium
NH3 oxidation
NO oxidation
Standard SCR
Fast SCR
NO2 SCR
N2O formation
A multi-site approach was also described by Sjovall et al (19) for Cu-ZMS-5 as an improvement from
the single-site model. The model describes each channel of the monolith as a series of continuously stirred tank
reactor, namely 15 elements, as a one dimension plug flow reactor (PFR). The assumptions made for the
12
reactor model are: (i) no gas phase accumulation, ii) no diffusion resistance in the washcoat and iii) no radial
concentration gradients. The mathematical formulation of the reaction rate expressions is the same as that
established for the single site approach., however, the model presents four different surface sites: a metal site
called S1a, where a single molecule of NH3 can be absorbed, a second metal site (S1b), where up to three
molecules of ammonia can be stored, a Bronsted site (S2), and in order to account for the large amount stored
at ambient temperature, sites for weakly bound species (S3), were included as well.
Comparing both models with experimental results (5), the single site model can produce sufficient but
quite rough results, while the multi-site model constitutes a more precise phenomenological approach.
However the last one requires a careful calibration of the countless parameters, thus it is suggested that the
latter model should be applied only when its calibration can be performed by experimental results.
Further improvements have been developed from the existing kinetic models. Olsson et all (20) presents a
model using Cu-ZMS-5, which includes the four active sites referred previously, and based on two sub-models
developed on the same catalysts: ammonia adsorption, desorption and oxidation from (19), and a submodel
that accounts for NOx adsorption and NO oxidation. The two subsystems were combined and additional
reactions were added to account for the selective catalytic reduction of NOx. The initial reaction in the SCR is
assumed to occur between adsorbed NO2 and NH3 followed by reactions forming either HNO2 and HNO3, which
will react with NH3 to produce N2 or N2O and water.
Regarding ammonia adsorption/desorption as one of the key steps of the NH 3-SCR chemistry, Colombo et
al (21) presents a developed model for the ammonia adsorption/desorption process over a commercial Fezeolite SCR catalyst in the 50-550ºC temperature range. For the experiments the authors used a flow micro
reactor consisting of a quartz tube, were the catalyst powder was loaded. The experimental data were
simulated as a heterogeneous one-dimensional plug-flow dynamic reactor. As the models referred previously,
ammonia adsorption/desorption kinetics consists of a non-activated adsorption step with a Temkin-type
desorption kinetics. A dual site approach is proposed, namely Bronsted acids sites, where ammonia is strongly
adsorbed, and Lewis acid sites, where ammonia is weakly adsorbed.
According to the literature, (19) (22) ammonia TPD curve on H-ZMS-5 typically presents two main
desorption peaks: the peak at low temperature and higher temperature peak. Olsson et al (19) suggests that
the peak at low temperature may be related to ammonia desorption from sites for weakly bound ammonia,
and the peak at the higher temperature, is likely desorption from Bronsted acid sites. As reported in studies of
NH3 TPD on H-ZMS-5, (22), the presence of protonic sites, leading to the high temperature peak, has been
assigned to the density of framework aluminum ions (Bronsted acid sites), while concerning the low
temperature peak its origins remain ambiguous. This weaker adsorption site has been correlated mainly to the
presence of Lewis acid sites due to extra-framework aluminum species, or Al-O bonds that have been
transformed by hydrolysis. Moreover, it is also inferred of weakly-bound associations of ammonia to
ammonium ions.
It is known the importance of intraparticle mass transfer resistance over small size pore zeolites (15),
as ZMS-5. Kouva et al (22) presents a model of NH3 adsorption and desorption over H-ZMS-5 concerning two
acid sites and including intraparticle diffusion resistance, described by an effective diffusion model with the
driving force being the concentration gradient in the radial direction of a spherical particle. The intrinsic kinetic
models used are first order non-activated adsorption and activated desorption kinetics with Langmuir
assumptions, as the previous models presented. The study also reports an evidence of a strong dependence of
ammonia self-diffusivity on its loading in H-ZMS-5 and temperature. Inspired by these evidences, the model
presents different diffusion coefficients function on the coverage and temperature, D eff(θ,T), presenting a good
fitting of the experimental data.
13
2.5. Modeling SCR systems
2.5.1. Fixed Bed Reactor
The catalytic exhaust aftertreatment field needs both a monolithic and a packed-bed reactor model
for chemical kinetic studies and parameter calibration (23). Pragmatically, modeling fixed bed reactors leads to
a concrete study of the diffusion and kinetic process within the washcoat, which is the main challenge as a
catalyst modeler and for SCR modeling. Hence, researchers still employ packed-bed reactors in the laboratory
in order to help determine the chemical kinetic mechanisms used within monolithic models. (23) Both for SCR
or SCR on filter, performance relies on the diffusion of the exhaust gas through the catalyst porous media (or
the washcoat) and on the NH3 adsorption, requiring a model that well describes the intrinsic phenomena. For
SCR on filter, exhaust gas travels between the different channels, traveling through the porous wall between
them, which is a determinant domain not only for kinetics modeling but also for mass transport within a porous
media.
Moreover, a fixed bed model can be used as an approach to describe SCR on filter technology. Available
studies of diesel particulate filters show that classic filtration theory can give a good estimate of the sizespecific collection efficiency of “clean” Diesel particulate filter with respect to solid particles. The first study
provided validated design equations for sizing wall-flow filters based on fundamental principles of fluid
mechanics and flow through porous media as Darcy’s law. (24) Moreover, DFP models presented in the
literature use one-dimension model for a coated DPF, which treat the solid (filter wall, catalytic coating and
soot) and gas phases separately and includes equations for the mass, momentum and energy balances of the
gas in the inlet and outlet channels, and the pressure drop across the soot cake and filter wall assuming Darcy’s
Law. Some studies include a Forchheimer term in their pressure drop equation. However, it is reported that
this term can be neglected for the low wall-flow velocities obtained in wall-flow filters under normal
conditions. (11) Since flow through packed bed reactor is based in the same flow laws and also with as gas
phase and a solid phase, hence it seems natural to assume packed bed reactor as an initial approach to
describe diesel particulate filter wall, which is one of the promising technologies for aftertreatment systems.
Concerning the previous arguments, fixed bed model suggests being an accurate approach to study SCR
technologies, namely the phenomena occurring within the washcoat. For the reasons presented, the model
presented and developed in this work describes transport and kinetic on a fixed-bed reactor, in order to better
understand phenomena of diffusion, and kinetics within the zeolite. The main basis and assumptions of the
model used are described in the following chapters. This chapter presents the entire basis behind the
construction and development of any catalytic reactor model.
2.5.1.1. Fixed Bed Models
There are several modeling approaches to describe a fixed reactor. Usually, this kind of reactors are
modeled on the basis of the description of the packed bed as a continuum. Annexe 1 lists the main fixed bed
models that can be used. The pseudo-homogeneous model is the most commonly employed version due to the
simplifying assumptions, and one-dimensional representation regarding to dimensionality. Moreover it
comprises a historical perspective of the available correlations that leads to the choice of a final model for
14
packed-bed reactor studies. Martinez et al (25) presents the four types of approaches, one dimensional and
two-dimensional homogeneous or heterogeneous model comparisons each type of model. It follows that onedimensional model is recommended for a reactor operating under low thermal sensitivity conditions. If axial
dispersion is negligible, pseudo-homogenous models can be applied to a ratio of D/Dp bigger than 10.
Moreover, (25) presents as well correlations for the model parameters involved. Papageorgiou et al (26)
developed a two-dimensional homogeneous and heterogeneous models with porosity and velocity profiles.
The fluid flow in packed beds was simulated by incorporating the structural nonuniformities of the bed into the
Navier-Stokes equations for flow thrugh porous media, hence the velocity field is characterized by a significant
nonuniformity. The heterogeneous model provides better insight in term of reactor behavior, its accuracy of
the model predictions relies to a great extent upon the validity of the available correlations for the estimation
of the effective mass and heat parameters. In paper (23) for example, a one-dimensional pseudo-homogeneous
packed-bed reactor model is presented, described as being useful for calibration of chemical kinetics in the
catalytic exhaust aftertreatment field.
In some publications, the packing is regarded as a discrete structure (cell modes). As an example,
Schnitzlein et al (27), presents a model based on the discrete structure of a randomly packed bed of particles,
in which the elementary units consist of two minireactors as ideally mixed tan reactor followed by an onedimensional ideal plug-flow reactor in series.
2.5.2. Mass and Heat Transfer in Catalytic Reactor
For the simulation of a catalytic reactor, it is necessary to establish the model that better represents
the reactor behavior. The complexity of the model will depend on the simulation objectives. The compromise
between the simulation objectives, precision of the results and computing time must generally be analyzed.
Simplified models are often a less complex alternative to describe the system, giving enough accurate results
for the simulation objectives. (9) (17)
In order to simulate fluid flow or heat transfer, it is necessary to describe the associated physics in
mathematical terms. Nearly all the physical phenomena of interest to this subject are governed by principles of
conservation and are expressed in terms of partial differential equations. For instance, the continuity equations
allow solving problems of mass and heat transfer, describing the transport of a conserved quantity in a generic
volume (28) (29).
Considering a control volume of size ΔxΔyΔz, the conservation equations can be expressed as the variation
of a specific quantity in the control volume over time. The conservation principle states that accumulation of a
specific quantity is equal to the net influx of the given quantity and its generation inside the control volume.
Bellow it is presented the balances describing for the energy and mass conservative equations (28) (29).

Energy equation
Assuming low-speed flow and negligible viscous dissipation, the general conservation equation may be
written in terms of the specific enthalpy, h, as in equation 10
(𝜕𝜌ℎ)
+ ∇(𝜌𝑉ℎ) = ∇(𝑘∇𝑇) + 𝑆ℎ
𝜕𝑡
10
where k is the thermal conductivity, T is the temperature, V the velocity field and Sv the generation per unit of
volume.
15

Species equation
The continuity equations express the mass conservation within a controlled volume.
Figure 9 – Total mass balance in a generic volume ΔxΔyΔz
Considering the balance of the mass flux, ρv, dividing by ΔxΔyΔz and taking the limit ΔxΔyΔz→0, leads to
the continuity equations. (29)
Continuity equation for specie A
Rectangular coordenates
𝜕𝐶𝐴
𝜕𝑁𝐴𝑥 𝜕𝑁𝐴𝑦 𝜕𝑁𝐴𝑧
+(
+
+
) = 𝑅𝐴
𝜕𝑡
𝜕𝑥
𝜕𝑦
𝜕𝑧
11
The flux of a generic component, NA, it is given by the convective flux, (CA v), and diffusional or molecular
flux usually given by Fick’s Law
⃗⃗𝑥𝐴
𝑁𝐴 = 𝐶𝐴 𝑣⃗ − 𝐶𝐷𝐴𝐵 ∇
12
resulting in the continuity equation function of the concentration of A, C A. (29)
13
This 3D description for both mass and energy balance would require significant amount of overhead in
order to model the system, taking too much time to run. Most of times, simplifications of the previous
equations present a satisfactory behavior of the system, avoiding long time simulations as a large amount of
experimental data, boundary conditions, sensors, analyzers and data acquisition hardware to capture this
information. For instance, generally a one-dimensional representation is sufficient for laboratory analysis since
the packed-bed reactor is often only a small core of material with negligible distance in the radial direction.
(23)
16
It should be noted that in a fixed-bed reactor the catalyst pellets are held in place and do not move with
respect to a fixed reference frame. Material and energy balances might be required for both the fluid, which
occupies the interstitial region between catalyst particles, and the catalyst particles, in which the reactions
occur. Several phenomena as external or internal diffusional limitations due to the solid catalyst compromises
mass and heat transport, hence, the reactor model. (30) Some fixed bed models are presented in Annexe 1.
2.5.3. Flow through Porous Media
As a fluid passes through the packed bed it experiences pressure loss due to factors such as friction. For
flow through porous media it is desirable to be able to predict the pressure drop necessary to obtain a specific
flow rate, as it influences directly convection heat and mass transfer.
The complexity of the flow pattern rules suggests an empirical or quasiempirical correlation. Moreover,
various models published in literature present different approaches as phenomenological models, model based
on conduit flow (geometrical models, statistical models, models utilizing complete Navier-Stokes equation) or
models based in submerged objects. (31)
The pressure drop behavior in porous media will depend on the flow rate. There are three main controlling
regimes, Darcy, Post-Darcy and turbulent flow.
Darcy regime is characterized by creeping flows (Re<1) in which viscous forces are predominant. Darcy law
describes this regime, equation 14, in which pressure drop depends linearly with flow rate.
−∆𝑃 µ
= 𝑣
𝐿
𝐾
14
As the flow rate increases, the inertial effects get significant, marking the beginning of the new regime
usually referred to as inertial, Forchheimer or simply non-Darcy regime. Pressure drop presents a non-linear
behavior with flow rate at this higher flow rates. Forchheimer equation is also known as the Forchheimerextended Darcy equation, is presented in equation 15.
−∆𝑃 µ
𝜌𝐹 2
= 𝑣+
𝑣
𝐿
𝐾
√𝐾
15
where F is the Forchheimer coefficient that accounts for inertia/form drag. (32)
Possibly, the best known equation describing pressure drop in porous media is the Ergun equation, which
describes the behavior of pressure drop including the two regimes described above. This equation is actually an
equivalent expression for Forchheimer equation.
−∆𝑃
µ 𝑣 (1 − 𝜀)2
𝜌 𝑣 2 (1 − 𝜀)
= 150
+ 1.75
2
3
𝐿
𝐷𝑝 𝜀
𝐷𝑝 𝜀 3
16
The Ergun equation, 16, combines both the laminar and turbulent components of the pressure loss
across a packed bed, although it does not describe Darcy flow. In laminar flow conditions, the first component
of the equation dominates, with the Ergun equation essentially reducing to the Carman-Kozeny equation,
although with a slight variation in the constants used due to variations in the experimental data with which the
17
correlations was developed. In the laminar region the pressure drop through the packed bed is independent of
fluid density and has a linear relationship with superficial velocity. Under turbulent flow conditions the second
component of the Ergun equation dominates. Here the pressure drop increases with the square of the
superficial velocity and has a linear dependence on the density of the fluid passing through the bed (32), (31),
(33), (34).
For randomly non-spherical particles, it is used the spherical equivalent particle diameter De (the
diameter of a sphere having the same surface area to volume ratio as the non-spherical particle) instead of Dp.
If the packed bed are not mono-sized the surface-volume mean diameter, <De> should be used in place of the
spherical equivalent particle diameter De.
Ergun proposed a well-known correlation of Darcy-Forchheimer drag, with two constant coefficients
(A=150 and B=1.75). However, the literature presents other values and expansions for these constants, as
Macdonalds et al (31) suggested A=180 and B=(1.8 – 4) depending on surface roughness of the particles. Lee et
Yang (33) describe several pressure drop models presented in the literature, as for Ward model authors
-0.5 1.5
suggest a similar correlation to Ergun equation with a dimensionless constant (c= B*A ε ), or Coulaud who
uses a numerical method to model the Darcy-Forchheimer drag. Comitri and Renaud (35) present a capillary
model for non-linear laminar type.
2.5.4. Complexities in modeling of heterogeneous catalytic reactions
2.5.4.1. Adsorption
The attractive interactions between the reactants and the catalyst surface are the adsorption
phenomena, leading to a decrease in entropy and free energy of the adsorbed fluids compared to the bulk
phase gases. It is also an exothermic process. There are two types of adsorption: i) physisorption, resulting
from van der Waals forces or ii) chemisorption, a far stronger interaction. As reactants are absorbed within the
pore, they diffuse into the pore towards to the active centers. (36)
Adsorption isotherms represent the amount of reactant adsorbed in equilibrium, as a function of
concentration or partial pressure in the bulk phase. Various empirical adsorption isotherms have been
developed such as: Langmuir, Temkin etc (36)
2.5.4.2. External and Internal Diffusion Limitations
Zeolite’s catalytic active sites are inside the pore network. Within the zeolite’s pore network, mass and
energy transport phenomena are different from the bulk phase. Moreover, diffusion controls the local
concentration of the reactants at the active sites, which will have a determinant role in catalyst activity. (15)
The catalytic cycle may be described with seven stages as shown in Figure 10: 1) external diffusion, 2)
internal diffusion, 3) adsorption, 4) chemical reaction at the surface, 5) desorption, 6) internal diffusion and
finally 7) external diffusion. (15)
18
Figure 10 – stages of the catalytic process (37)
Each stage velocity will compromise the global reaction rate. For instance, around the catalyst grain, the
interface is responsible for the main mass transfer resistance, hence the concentration on the bulk phase
outside the catalyst, C, is bigger than the concentration at catalyst surface, C s, being this difference the driving
force for mass transfer. In this case, the global reaction rate will rely on mass transfer coefficient and reaction
constant rate. In extreme situations, external diffusion may be faster than reaction rate, so C s ≃ C in the bulk
phase. On the contrary, if reaction rate is faster than mass transfer coefficient, reactant is readily consumed
and Cs ≃ 0. (15)
Between reaction and internal diffusion, one of these mechanisms may be relatively slow comparatively to
the other, leading to a regime with well-defined characteristics and, in limit situations, leading to the classic
internal regimes of kinetic or mass transfer control. If diffusion within catalyst porous media is efficient
comparing to the reaction rate, the internal surface of catalyst (pore wall) is easily available as the external
surface of the catalyst hence there is no internal diffusion limitations. In the case of relatively large grains, with
narrow pore diameter and a high reaction rate, internal diffusion rate will be small, leading to a concentration
profile within the catalyst, in which concentration decreases as it gets further the catalyst surface. (15)
Figure 11 – Concentration profile at the surface and inside the catalyst grain (15)
Internal diffusion limitations effects also increase at high temperatures, once the reaction activation
energy is higher than internal diffusion activation energy. (15)
19
2.5.4.3. Diffusion within porous media
The total flux in a porous media, results from the combination of the surface flux and the flux within
the pores. This last one, couples diffusive and viscous flux within the porous media. (38)
Diffusive flux within porous media can be described by 3 main phenomena: i) Knudsen diffusion
(collisions with the pore walls), ii) molecular diffusion (molecule-molecule scattering), iii) transition regime, in
which both mechanisms are assumed. Each mechanism is predominant depending on pressure conditions, pore
diameter etc. Sometimes pore entrance effects can also be important (36).
The combination of Knudsen and Molecular diffusion as a transition regime can be done according to
three distinct models: Fick’s Law, Fickian diffusion/convection model and the dusty-gas model (39).
For Fick’s Law model, the driving force for mass transport is the species concentration gradient, having
as characteristic parameter the effective diffusion coefficient, Deff, which is itself function of Knudsen and
molecular diffusion coefficient. Fick’s Law is the simplest and well-known diffusion model of the intraparticle
mass transport, and it is given by equation 17:
𝑁𝐴 = −𝐷𝑒𝑓𝑓
𝑑𝐶𝐴
𝑑𝑧
17
If the intraparticle viscous flow is considered important, the Fickian model can be complemented by
Darcy’s Law, as taking part for the convection within porous media, resulting in the Fickian diffusion/convection
model. However, convection within porous media it is usually neglected.
The Dusty-gas model comes from the application of the Stefan-Maxwell relations to the diffusive
transport in the pores. It considers a pseudo species in the mixture, the pore wall, which is considered as a
giant static molecule of infinite molecular weight, and whose concentration is homogeneously distributed. (38)
-
Diffusion coeficients
The diffusion coefficient measures how fast does a component travel. Some properties as porosity, pore
size and tortuosity influence the rate at which gas molecules migrate in response to chemical potential
gradients. This parameter is applied in Fickian model and Dusty-gas model. Depending on the assumed
diffusion mechanism, this parameter will be given by different models or empirical observations.
20
Table 3 – Different diffusion coefficients
Regime’s
name
Molecular
Diffusion
coeficciente
Mechanism
Conditions
collisions between gas molecules
- high pressures;
DAB / Dm
-relatively large diameter pores;
collisions with pore walls
Knudsen
Dk
-low concentrations;
-low pressure;
-small diameter pores;
Transition
regime
Deff
Transition between Knudsen and
molecular diffusion
-intermediate pressures;
There are several equations present in the literature to calculate molecular diffusion coefficient.
Simplified equations are listed in a book by Poling et al. (40). As an example, Chapman and Cowling (1970)
equation present an equation for molecular diffusion coefficient in binary mixture, DAB , assuming ideal gas of
hard-particles. Further expansions from this equation were also developed, as Chapman-Enskog for instance,
adding a temperature dependent prefactor. (38) Holman (1997) gives a semiempirical equation by Giliard et al
(1974), although the author cautions that the expression is useful for various mixtures, but should not be used
in place of experimental values of DAB. (40)
As for Knudsen diffusion coefficient, DK, it may be given by several formulations as by the treatment of
Knudsen (1909) (41) and other expressions that may be found in the present literature (39) (36) (38).
Effective diffusion coefficient, Deff, subsumes all effects of gas molecule collisions with pore walls and
other gas molecules and is function of Knudsen and molecular diffusion coefficient. Typically, Deff,, is described
by Bonsaquet relation (38):
1
1
1
=
+
𝐷𝑒𝑓𝑓 𝐷𝐾 𝐷𝑚
18
21
3. Experimental Material
In order to study NH3 diffusion and chemical kinetics phenomena within a zeolite, porous media,
several NH3 TPD experiments were conducted in fixed bed reactor.
Two sets of experiments were performed, study 1 and study 2. For the study 1, a series of experiments
were conducted using H-ZMS-5 with silica alumina ratio of 15, while some operation conditions were changed.
For the experiences carried out for study 2, experimental parameters were kept constant, while silica alumina
ratio of the zeolite changes in each experience (between 11.5 and 500).
It should be noted that these experiments were performed before the present study. I and the results
(experimental data) were after given afterwards. This chapter presents mainly the operational conditions and
other basic information.
3.1. Experimental procedure
The NH3 TPD tests were conducted using a Micromeritics, Autochem II 2920 in a fixed bed reactor,
with a zeolite bed of H-ZMS-5 (MFI).
The AutoChem II 2920 permits the user select any number of ramp rates to 1100°C, gas flow rates, and
data measurement intervals in desired time. Highly sensitive linear thermal conductivity detector (TCD) reads
conductivity variations of the outlet and inlet flow of the sample reactor, which allows calculating
concentration. It assures the calibration volume remains constant over the full range of peak amplitudes so the
area under the peak is directly proportional to the volume of gas reacted. This change in the gas concentration
is recorded by the Thermal Conductivity Detector downstream as in Figure 12. Moreover, an RMN analysis is
performed to the out let flow, in order to verify if the variation of concentration is due to NH3 or due to other
components like water that may be resident in the reactor or that may appear from leaks. The AutoChem II
2920 includes an “U” form fixed bed reactor as the one presented in Figure 12, where “c” corresponds to the
zeolite bed, L the characteristic length, D the fixed bed diameter and D p the catalyst grain diameter.
22
Figure 12 - Fixed bed reactor sketch
The catalysts were prepared using H-ZMS-5 powder with different silica alumina ratios. Each type Si/Al
ratio zeolite was pelletized into grains with different diameter (on order of µm). Using zeolite grains as small as
the pelletized ones, would lead to a very compact fixed bed, which would increase significantly the pressure
drop. In order to normalize the pressure drop, the fixed bed is composed not only by the small grains of zeolite,
but also by grains of SiC, which diameter is on order of mm. Introducing these bigger grains, reasonable
pressure drop is achieved. SiC is an inert hence does not interfere with NH3 adsorption/desorption.
For the actual tests, the feed mixture contained 10%(v/v) of NH3 in N2 as a vector gas. The adsorption
step occurs at 150°C and desorption step increases temperature until 600°C. Each test is composed in four
main steps. The first step corresponds to NH3 adsorption until the saturation of the zeolite, performed with a
feed mixture containing 10%(v/v) NH3. In the second step the temperature is kept constant and equal to the
adsorption temperature, the NH3 feed is truncated and the inlet flow is composed solely by the vector gas, N 2
in this case. The pure N2 flow rate will clean the reactor removing non absorbed NH3. In the desorption step,
the inlet flow rate is composed by pure N2 that is heated at a constant heating rate until temperature reaches
600°C. In the fourth step the inlet flow rate is kept at 600°C. These TPD profiles are represented in Figure 13
and Figure 14, which show a general temperature profile and NH3 outlet concentration profile during a TPD
experiment, describing the inlet and outlet flow rate composition at each stage.
23
Tiemperature (K)
TPD stages - Temperature profile
Tdes
max
Step 1
(Adorption)
Inlet: NH3/N2
1:9 vol
Step 2
Inlet: N2
Step 3
(Desorption)
Inlet: N2
Step 4
Inlet: N2
Tad
Time
NH3 Concentration
Figure 13 - TPD stages on temperature profile
Step 1
(Adorption)
Inlet:
NH3/N2 1:9
vol
Step 2
Inlet: N2
Step 3
(Desorption)
Inlet: N2
Step 4
Inlet:
N2
Time
Figure 14 - TPD stages on NH3 concentration
For a proper modeling methodology, one must analyze heat and mass transport, kinetics and pressure
drop in the fixed bed. From each experiment there are available as experimental data TPD curves (only the
desorption step), and also outlet temperature (measured with a temperature sensor) and pressure profiles. It
should be noted that the outlet pressure of the fixed bed was at atmospheric pressure, thus, the pressure
profiles presented on this work are the absolute pressure at the fixed bed entry, which reveals the pressure
drop suffered from the reactor
3.2. Study 1: inlet conditions effect- experimental parameters
24
Study 1 aims to evaluate adsorption temperature, heating rate and flow rate effects on TPD curves
separately. Hence, three different tests were conducted, as shown in Table 4. Each test comprises one single
parameter variation, as the other condition parameters remain approximately constant for a proper analysis.
The zeolite used in the listed experiments was H-ZMS-5 Si/Al 15, with an average particle size of 0.2824 µm.
Table 4 – Tests performed for study 1
Test
Test 1
Test 2
Test 3
Data File
E11-092
E11-093
E11-089
E11-093
E11-087
E11-089
Variation Parameter
Adsorption temperature
Desorption heating rate
Flow rate
The operation conditions of the run experiments are listed in Table 5. It should be noted that in each
test the fixed operation conditions are approximately constant, hence little deviations are not significant.
Table 5 - Operation condition for test 1, adsorption temperature effect, test 2, heating rate effect and test 3, flow rate
effect
Zeolite sample(g)
Flow rate
(mL/min)
Tad
(°C)
Desorption heating rate
(°C/min)
SiC
(g)
Bed depth
(cm)
Pression
Max (Pa)
0,20
20
150
10
1,50
1,92
E11-089
0,20
50
150
10
1,50
2,15
101973,5
108523,5
E11-090
E11-092
0,25
50
150
5
1,50
2,00
107696,1
0,30
50
100
10
1,50
2,31
106868,7
E11-093
0,30
50
250
10
1,50
2,23
107696,1
Data File
T3
T1
E11-087
3.3. Study 2: Si/Al ratio effect – experimental parameters
Additional experiments were carried out to investigate the impact of Si/Al ratio of the zeolite. Six
experiments were performed at different Si/Al ratio, while all the other operation parameters were kept
approximately constant, as shown in Table 6.
25
T2
Table 6 – Some operation parameters for study 2 experiments
Zeolite
Si/Al ratio
Data File
Zeolite sample
weight (g)
11.5
15
25
40
140
500
E11-099
E11-100
E11-101
E11-102
E11-104
E11-106
0,20
0,20
0,19
0,19
0,21
0,20
SiC
weight
(g)
1,50
1,50
1,50
1,50
1,50
1,50
Bed depth
(cm)
pressure (Pa)
Flow rate (g/s)
1,98
1,96
2,33
1,89
1,60
1,81
106000
106000
108000
106000
106000
106000
0,001
0,001
0,001
0,001
0,001
0,001
The adsorption was conducted at 150°C, with an adsorption heating rate of 10°C/min till 600°C.
It should be noted that each zeolite Si/Al has a different average grain diameter, as listed in Table 7.
Table 7 - Average grain diameter for each Si/Al H-ZMS-5 zeolite
Dzeolite
(µm)
1,29
0,43
0,28
0,19
Si/Al
ratio
11,5
40
15
25
26
4. Model Description
This work aims to find an appropriate approach to describe diffusion and chemical kinetics phenomena
within a zeolite (MFI), porous media.
An given IFP Energies nouvelles was used for simulate given experimental data from the previous chapter.
This chapter describes all assumptions considered in the model developed by IFP Energies nouvelles, which
can be divided in two sections: i)the reactor model, which is a set of balance equations that described the
reactor, ii) kinetic model and also the correlation for the model parameters involved.
LMS Imagine.Lab AMESim was used as simulation software. The following model equations (or model
computations) were written/programmed in C language with AMESet.
It was performed a sensibility analysis to the presented model and to all the improvements and studies
described in 4.3., in order to well understand the behavior of each model. However, the sensibility analysis
results are not presented in the present document.
4.1. Reactor model
In the present model, the fixed bed reactor is described as heterogeneous CSTR model, in a way that
all properties and variables are constant in the whole reactor. Hence, it is not considered thermal and mass
dispersion in axial direction or radial gradient.
Further, the main assumptions made for the reactor model are: no gas phase accumulation and no
diffusion resistance, which means all adsorption acid sites are immediately available and there is no radial
concentration gradients inside the zeolite grains. Deviations from the ideal state were not considered. The
model does not take into account the presence of impurities existing in the zeolite. For the thermal description
of the system it was considered that there are no heat exchanges with external systems, so it is considered
adiabatic.
Before presenting the model equations, fixed bed characterized lengths are shown below In Figure 12,
namely fixed bed length, L, reactor diameter, D, and catalyst diameter Dp. The previous parameters are
measured experimentally.
Material and energy balances are required for both the fluid, which occupies the interstitial region
between catalyst particles, and the catalyst particles, in which the reactions occur. The bed porosity, Ɛ, is a
parameter that measures the “free space” within the bed and it is generally defined as ratio between the free
volume available for the fluid, and the total volume of the fixed bed. In this case, Ɛ is also an input parameter
for the model and is generally obtained experimentally.
As for the heat balance, the following equations describe temperature in the gas and solid (fixed bed)
phase
27
𝑑𝑇𝑔 ∑ 𝑚𝑖 ℎ𝑖 +
=
𝑑𝑡
𝑑𝑉𝑔
𝑑𝑚𝑔
𝑑𝑄𝑐𝑜𝑛𝑣
𝑑𝑥
− 𝑃𝑔
− 𝑚𝑔 ∑ 𝑖 𝑢𝑖 −
𝐶 𝑑𝑇
𝑑𝑡
𝑑𝑡
𝑑𝑡
𝑑𝑡 ∫ 𝑣
𝑚𝑔 𝐶𝑣
𝑑𝑇𝑠 −𝑄𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒𝑑 + 𝑄𝑤𝑎𝑙𝑙
=
𝑑𝑡
𝐹𝐵𝑚𝑎𝑠𝑠 ∗ 𝐶𝑝𝐶𝐶
19
20
where
𝑄𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒𝑑 = −2.89
𝑉𝑡𝑜𝑡𝑎𝑙 − 𝑉𝑓𝑟𝑒𝑒
𝑘
∗6
(𝑇𝑔 − 𝑇𝑠 )
𝐷𝑝
𝐷𝑝
21
st
The balance heat in the gas phase is based on the 1 law of thermodynamics, of conservation of
energy, where is considered convection between gas and solid phase (Q conv in J).
The heat balance in the solid phase, takes into consideration the exchanged heat between the gas and
solid phase (Qexchanged ). Heat exchange between the reactor and the surroundings, (Qwall) which is neglected so
Qwall ≃0. Further, reaction heat is neglected and the fixed bed heat capacity, CpCC, is considered constant.
The mass balance for each gas component (i) is presented by the following equation.
𝑑𝐹𝑖
= −𝑥𝑖𝑜𝑢𝑡 ∗ 𝐹𝑜𝑢𝑡 + 𝑥𝑖𝑖𝑛 ∗ 𝐹𝑖𝑛 + 𝜔𝑖
𝑑𝑡
22
In the present study, ωi is only formation and disappearing of NH3, which corresponds to the
adsorption and desorption of NH3 in the catalyst, as it is defined in the following kinetic model.
The gas velocity is computed according to laminar Ergun’s equation:
𝑣=
(𝑃𝑔 − 𝑃𝑜𝑢𝑡 )𝐷𝑝2 𝜀 3
𝐿 ∗ 150 ∗ µ (1 − 𝜀)2
23
Being gas pressure, Pg computed from the following equation:
𝑑𝑃𝑔
𝑑𝑇𝑔
𝑑𝑟
𝑑𝜌
= 𝜌 ( 𝑇𝑔 + 𝑟
) + 𝑟𝑇 ∑
𝑑𝑡
𝑑𝑡
𝑑𝑡
𝑑𝑡
24
4.2. Kinetic Model – Double-site approach
The double site approach is reported in several studies like (19)and (22) where ammonia storage is
modeled over two kinds of active sites, S1 for lower adsorption temperature site of ammonia on the zeolite
28
(weak site) and S2 for higher adsorption temperature (strong site) as it is referred in (22). The reaction steps
are shown in Table 8.
Table 8 – Reactions for NH3 adsorption and desorption in each site S1 and S2
Site (j)
Reaction
1
𝑁𝐻3 + 𝑆1 ⇔ 𝑁𝐻3 − 𝑆1
2
𝑁𝐻3 + 𝑆2 ⇔ 𝑁𝐻3 − 𝑆2
The given kinetic model is a first-order non-activated adsorption and an activated desorption kinetics.
The rate constants are described by the Arrhenius expression, for each site (j)
𝑘𝑗 = 𝐴𝑗 𝑒 −𝐸𝑎𝑗 /𝑅𝑇
25
Aj accounts for the adsorption or desorption pre-exponential factor, Eaj for the respective activation
energy, R as the ideal gas constant, and T the solid phase temperature.
Previous studies, (19), suggest desorption activation energy defined as a coverage dependent, α, by a
Temkin approach. Also (42) demonstrates a coverage dependent heat of adsorption for ammonia for H-ZMS-5
from calorimetric results. The peaks broadness is due to the set of different strength sites in the same peak.
This parameter, α, describes the broad nature of the ammonia desorption peak . Low coverage dependences,
α, present a narrow peak, smaller range of temperature, hence a smaller set of different acid sites. A high α
describes the opposite. Adsorption is considered non-activated.
For activated desorption kinetics, activation energy is given by:
𝐸𝑎𝑗 = 𝐸𝑎𝑗0 (1 − 𝛼𝑗 𝜃𝑗 )
26
Eaj0 stands for the activation energy of desorption when the surface coverage equals zero, α j as surface
coverage dependent and θj as the fraction of occupied active sites for S1 and S2.
The reaction rates are given for both sites, S1 and S2, in the following equations.
Table 9 – Rate expressions for NH3 adsorption and desorption on each acid site S1 and S2
Adsorption Rate of S1
mol/(molsites1.s)
Desorption Rate of S1
mol/(molsites2.s)
Adsorption Rate of S2
mol/(molsites1.s)
Desorption Rate of S2
mol/(molsites2.s)
rdes1
rdes2
𝑟𝑎𝑑1 = 𝐴𝑎𝑑1 ∗ 𝐶𝑁𝐻3 ∗ (1 − 𝜃1 )
−Ea01des
(1 − 𝛼1 θ1 )) ∗ 𝜃1
= A0des1 ∗ exp(
R∗T
𝑟𝑎𝑑2 = 𝐴𝑎𝑑2 ∗ 𝐶𝑁𝐻3 ∗ (1 − 𝜃2 )
−Ea02des
(1 − 𝛼2 θ2 )) ∗ 𝜃2
= A0des2 ∗ exp(
R∗T
Langmuir kinetics is assumed, where kad and kdes are the rate constants for adsorption and desorption,
respectively, for each acid site S1 and S2.
29
𝑑𝜃𝑗 = 𝑟𝑎𝑑𝑗 − 𝑟𝑑𝑒𝑠𝑗
27
Table 10 – Variation of occupied acid sites fraction
Variation of fraction
sites1 occupied
Variation of fraction
sites2 occupied
𝑑𝜃1 = 𝑟𝑎𝑑1 − rdes1
𝑑𝜃2 = 𝑟𝑎𝑑2 − rdes2
Assuming this kinetic approach, formation or consumption of NH 3, ωNH3, will be given by the following
equation
𝜔𝑁𝐻3 = 𝑀𝑚𝑜𝑙 ∗ (−𝑑𝜃1 (𝛺1 ∗ 𝑀𝑐𝑎𝑡 ) − 𝑑𝜃2 (𝛺2 ∗ 𝑀𝑐𝑎𝑡 ))
28
where Ωj is the storage capacity for each (j) site, Mcat and Mmol stands for the catalyst’s mass and NH3’s molar
mass.
4.3. Adaptation of a previous IFP Energies Nouvelles model to the case
study
In order to adequate the IFP model to this study, it was added a Dp computation to take into account
the granulometry of the fixed bed of the performed experiments. Hence, two model parameters were
included: Dinert, Dzeolite.
The previously presented model computes pressure drop from Ergun equation, which is function of
several variables such as particle diameter, bed void fraction, reactor length, and intrinsic fluid characteristics
such as density and viscosity. The model considers only laminar term of Ergun equation, because normally TPD
tests are carried out at low flow rates and consequently at Re laminar regime. Moreover, the equation assumes
an average particle diameter, Dp which corresponds to the catalyst diameter. However, in the present study the
fixed bed presents two different types of grains with different average diameter, for the zeolite and for the SiC
respectively. In fact, the model computes pressure drop using the catalyst diameter (on order of µm) but does
not take into account the presence of SiC grains that were used for normalize pressure drop in the actual
experiments, and have a bigger grain diameter (on order of mm).
Ergun equation may be used for fixed bed with different granulometries using an equivalent diameter.
In order to adapt Ergun’s equation to the actual experiment, D p is defined as an average equivalent diameter
concerning the average of the the zeolite and SiC average grain diameter, as can be seen in equation 29.
𝐷𝑝 =
𝑀𝑐𝑎𝑡
𝐹𝐵𝑚𝑎𝑠𝑠 − 𝑀𝑐𝑎𝑡
𝐷
+
𝐷𝑖𝑛𝑒𝑟𝑡
𝐹𝐵𝑚𝑎𝑠𝑠 𝑧𝑒𝑜𝑙𝑖𝑡𝑒
𝐹𝐵𝑚𝑎𝑠𝑠
29
30
Inert diameter, Dinert, and zeolite diameter, Dzeolite, were introduced as reactor parameters. It is
assumed that the total fixed bed mass, FBmass, is the amount of zeolite and inert mass and that the mean
particle diameter Dp is therefore an average between the zeolite and inert diameter.
Introducing this Dp computation in the previous model will allow a better description of the fixed bed
used in the current case study. The modifications presented showed an extraordinary improvement in the
pressure drop profile. As an example, simulation results of the experiment E11-099 are presented in Figure 15
showing the great improvement in the pressure drop resulting from the different computation of Dp. The
previous model and the improved model with a different Dp computation are referred as model 1 and model 2
respectively. As it is referred before, it should be noted that the outlet pressure of the fixed bed was at
atmospheric pressure, thus, the pressure profiles presented on this work are the absolute pressure at the fixed
bed entry, which reveals the pressure drop suffered from the reactor.
Figure 15- Pressure drop profile for E11-99: simulation results using model 1 and model 2
The expected pressure profile behavior is according with the simulated results for both models (Figure
15): the pressure increases as the adsorption set starts, and in kept constant until is finishes. When the
desorption step starts the increase of flow rate and increase of temperature consequently increases the
pressure drop. Finally, when desorption step finishes the flow rate is again constant, however, since the
temperature is higher the pressure will be higher. Figure 15 however evidences a drastic difference between
31
the two models. It is immediately noticeable that using Dp as an average of Dzeol and Dinert (model 2) decreases
the pressure profile for more reasonable values, now on order of 1 bar. Using Dp as Dzeol (model 1) the
1
respective pressure drop presents values on order of 10 bar, which are extremely high comparing to the
experimental data.
Figure 16 - Pressure drop profile for E11-99: simulation results from model 2 and experimental data
As can be observed, Figure 16 model 2 still can’t fit the experimental curve correctly. The available
experimental data reveal a pressure drop of 0,006075 barA during desorption, with a final pressure of 1,06036
barA. Regarding the pressure profile from model 2, the total pressure drop is around 0,0007518 barA, the
pressure drop during desorption is 0,0005362 barA and the final pressure is 1,01375 barA.
Concerning the temperature profiles, the same models present approximately the same results as
expected, Figure 17. Regarding the mass balance, Figure 18, the models present different results, since
different pressures will create different fluid velocities (taking into account Ergun’s equation) compromising
the mass balance consequently.
Figure 17 - Temperature profile for E11-99: simulation results using model 1 and model 2
32
Figure 18 - - NH3 molar fraction profile for E11-99: simulation results using model 1 and model 2
Pressure (barA)
In order to make a detailed analysis of the new model behavior, several bed void fraction were tested,
as showed in Figure 19.
Desorption step
Figure 19 - Pressure drop profile using different void fraction, ɛ, values
As expected, for lower void fractions the pressure is higher and the peaks on desorption step increase.
The two peaks presented during the desorption step correspond to the two desorption peaks of NH3, in which
flow rate increases and consequently pressure. These results suggest that bed void fraction shall be small.
However, even with small values, the behavior does not fit the experimental results. Moreover, modified Ergun
33
equations were tested, (31) but the results did not improved significantly. It also should e noted the the grain
porosity, ɛgrain was not taken into account.
Pressure (barA)
Temperature (K)
[NH3]%vol
Furthermore, in order to find better results a different reactor model approach was tested, namely a
plug flow type approach. To this end, instead of having a single device with a heterogeneous CSTR model in
AMESim sketch, N fixed bed subunits were placed in series as an heterogeneous plug-flow approach.
Simulation were performed for N=3 and 5. As an example, Figure 20, presents one of the studies performed to
evaluate the impact of the plug flow approach, with N=5 fixed bed. Annexe 4 presents the AMESim sketch used
for this approach.
Figure 20 – NH3 %vol, temperature and pressure profile for E11-101, concerning the experimental data, 1 Fixed bed model
(CSTR approach) and 5 Fixed bed model (plug-flow approach)
The higher is N, the more precise results should be obtained, from all the studies performed results
using N=3 and N=5 did not present significant improvements comparing to the original N=1. Regarding these
results, and taking into account the greater complexity of working with more than 1 fixed bed unit and
exporting more data from the software, the plug flow approach was a discarded hypothesis.
Modeling flow through porous media is in a fact a difficult task. The void space with porous solids
consists of labyrinths of contorted interconnected paths with irregular cross-sections. For instance, the void
fraction parameter is not truly constant in the fixed bed due to the confining effect of the wall of the bed.
Consequently there will be preferential pathways for the flow. Moreover, the inert and zeolite diameters
themselves are an average of the geometrical diameter of the grains of zeolite and SiC.
Several studies present detailed modeling accounting for radial voidage profiles. According to (26).in a
randomly packed bed, the layer of spheres nearest to the wall tends to be highly ordered, and the subsequent
layers are less and less ordered, until a fully randomized arrangement is attained in regions far away from the
wall. This study approaches the fixed bed as a series of cylindrical concentric layers with a different void
fraction, calculating the voidage distribution in a fixed bed. Other studies suggest presents modified Ergun’s
equation, as referred previously (31).
In fact, to take into account all randomness of the porous fixed bed in order to find more accurate
results, a much more complex model would be needed, which is not necessary in the context of this work.
Regarding the previous results and simulation, laminar Ergun equation with the new computation of D p is
considered to well describe the pressure drop for the case study, considering the relative similarity of
experimental pressure drop values.
34
More accurate results may be obtained using computational fluid dynamics; CFD modeling in a fixed
bed (43). This tool is used for obtaining the detailed velocity temperature and concentration fields, presenting
a much more complex calculations and consequently more accurate results.
The simulated results presented in the following chapters use IFPEN given model with this small
modification (referred as model 2). This model is the starting point for an improved model of NH 3 desorption
on H-ZMS-5 in fixed bed reactor, which is the main objective of this work.
4.4. Model Input Parameters
In the Table 11 are listed the model input parameters for any simulation. It should be noted that some
parameters are already known from the experimental data. For the unknown parameters, the selection of
initial guesses was guided by the available literature, being therefore modified according to the pretended
fitting.
Table 11 - Model input parameters
Inlet conditions
Kinetic Parameters
(for both acid sites 1
and 2)
Reactor Parameters
Inlet temperatures [K] and pressures [barA]
Mass flow [g/s] - Qm
NH3 mass fraction
Adsorption preexponential factor - Ao ad
Desorption preexponential factor- Ao des
Desorption activation energy [J/mol]- Ea des
Coverage dependence - α
NH3 coverage capacity [mol/gzeolite] - Ω
bed lenght [mm]- L
reactor diameter [mm] - D
zeolite diameter [mm] – Dzeolite
inert diameter [mm] – Dinert
Bed void fraction - ε
fixed bed mass [mg] – FBmass
Parameters
given
from
experimental procedure
the
Parameters given by the available
literature on sorption and diffusion of
NH3 in H-ZMS-5 (19)
Parameters
given
from
the
experimental procedure.
Void fraction, ε, is not available from
the experimental data, however, the
simulations were performed varying
0,2≤ε≤0,8 and choosing the value that
most fitted to the experimental
results.
Zeolite mass [mg]
Heat Transfer
-1
-1
Fixed bed heat capacity [J.kg .K ] - HC
This parameter is not given from the
experimental data, and was not found
in literature. However, the simulations
were performed varying fixed bed
heat capacity and choosing the value
that most fitted to the experimental
temperature profile results.
The model input parameters for the simulations presented in this work are listed on Annexe 2.
35
4.5. Simulation
Taking into consideration the previous conditions and models, the following sketch was created in
simulation environment LMS.Imagine.Lab AMESim using IFPEN-Exhaust Library. Figure 21 illustrates the used
sketch.
Figure 21- AMESim sketch
The model input parameters are inserted in each subunit respectively. The inlet conditions are divided
by the temperature subunits at the top, mass flow unit, and inlet flow rate composition. In the inlet conditions
subunits, “k” subunits are used for constant parameters, such as mass flow, the conversion of °C to K, and the
mass fraction of the different components 1, 3, 4, 5, 6, 7, 8, 9, 10 and 12, which is zero All the other subunits
are used for non-constant parameters, such as temperature and inlet NH3 and N2 mass fraction, which depends
in of the TPD stage. The reactor subunit receives all the reactor, kinetic and heat transfer parameters. The
analyzers subunits (before and after the reactor) give information about the properties of the respective flow.
Although in the present work it is only studied NH 3 adsorption and desorption, the inlet conditions are
ready to simulate a complete exhaust gas flow rate, for possible future studies, namely: 1-fuel, 2 – N2, 3 – O2, 4
– H2, 5 – H2O, 6 – CO, 7 – CO2, 8 – NO, 9 – NO2, 10 – CaHb (hidrocarbonatos), 11- NH3, 12 – C (Soot). For the
present work, inlet flow was only composed by NH3 and N2.
36
5. Results
For each simulation, mass, heat and pressure profiles were obtained and compared to the
experimental data. In order to achieve the best fitting, kinetic and heat parameters were manipulated taking
into account available kinetic parameters in the literature.
The main objective for an acceptable model is considered to be its ability to reasonably explain the
observed qualitative characteristics of mass transport, temperature and pressure profile. The case study is NH 3
adsorption and desorption on H-ZMS-5 (MFI) in a fixed bed reactor, namely temperature programmed
desorption (TPD) experiments.
In order to better evaluate the model response between the experimental data, the TPD curves areas
were calculated for both experimental and simulated results. It shoud be noted these area values do not have
any physical meaning besides from a tool to compare experimental data and simulated results, in a way that
the closest the area value, the better fitting was obtained. The available mass data units were given in NH3
molar fraction. To calculate the amount of NH 3 desorbed directly from the TPD curved integration, the flow
rate profiles should have been given previously by AMESim.
5.1. Study 1 – inlet condition effects
As it is referred before, there were three tests performed for study 1, in order to evaluate the effects
of different adsorption temperature, heating rate and flow rate respectively. In each test, all parameters were
kept constant besides from the operational parameter tested.
5.1.1. NH3 Concentration
The obtained TPD curves are shown in Figure 22, where the effects of adsorption temperature, heating
rate and flow rate are shown clearly. As expected, the double site hypothesis is according with NH3 TPD
experimental results. The experimental data and simulation results are both presented and compared.
37
Figure 22 - test 1 NH3 molar fraction profiles: experimental data and simulation results
For test 1, the adsorption was conducted at either 100°C (E11-092) and 250°C (E11-093). While having
NH3 adsorption at 150°C presents the expected two desorption peaks, having adsorption temperature of 250°C
provides enough energy to cause NH3 immediate desorption on the weakly bounded sites. As a result,
adsorption at 250°C (E11-093) shows only the strong bounded Bronsted site peak.
In Table 12 are listed the TPD curves area for each experiment, showing that the model presents a
similar response to the experimental data. Moreover, the simulated TPD curve with Tad= 250°C also shows a
small weakly bounded desorption peak, which suggest that desorption activation energy for S1 is higher
comparing to the real value.
Table 13 collects the temperatures of maximum adsorption for experimental data and for the
simulated results. Is it noticeable a difference of temperature peaks between experimental and simulated data.
It has to be stressed out that this simulation is not fitting the experimental data perfectly, although the results
are quite accurate. A more rigorous fitting would allow finding better values.
Table 12 – Test 1 : TPD curve area (K)
Data File
Exp data
Area (K)
Simulation results
Area (K)
E11-92
E11-93
1,82
1,07
1,61
0,74
38
Table 13- test 1 temperature of maximum desorption: experimental data and simulation results
Data File
E11-92
E11-93
Acid
Sites
S1
S2
S2
Exp data
T max (K)
524,5
759,0
750,1
Simulation results
T max (K)
513,1
747,6
747,6
Figure 23 - test 2 NH3 molar fraction profiles: experimental data and simulation results
Concerning heating rate effects, for higher heating rate, 10°C/min, the amount of desorbed NH3
increases comparing to 5°C/min , since the system receives more energy allowing a more effective desorption
as expected These results are consistent with the available literature (22).. Moreover, at higher heating rates
the desorption maximum is slighted shift to a higher temperature, especially for the lower temperature acid
site, in which the maximum temperature adsorption difference is 20 ºC. This behavior is often attributed to
intraparticle mass transfer limitations, (22), although the difference is not very predominant
The model seems to well describe experimental data, though a better calibration of the parameters
should give a better fitting.
39
Table 14 – Test 2 : temperature of maximum desorption : experimental data and simulation results
E11-89
E11-90
Acid sites
S1
S2
S1
S2
Exp data max
temp of
desorption(K)
Simulated results
max temp of
desorption(K)
526
732
505
726
538
724
528
711
Figure 24 -test 3 NH3 molar fraction profiles: experimental data and simulation results
Regarding flow rate effects, test 3, although the NH3 storage capacity is the same for both E11-087 and
E11-089, it is expected that the corresponding TPD do not show the same coverage area, since the flow rates
are different and TPD curves are presented in molar fraction of NH3 . The NH3 ideally is always the same so for
higher flow rates, the molar fraction is smaller
However, experimental results show that the desorbed amount of NH3 at 50L/min is substantially
smaller than the desorbed NH3 from simulated results. For simulated results, the difference of maximum molar
fraction is 0,0046 for S1 and 0,0033 for S2, while that for experimental results this differences are about 0,0056
and 0,0023 respectively, Table 17.
Table 15 – Test 3 : TPD curve area (K)
Data File
Exp data
Area (K)
Simulation results
Area (K)
E11-87
E11-89
1,93
0,81
1,95
0,84
40
Table 16- test 3 maximum desorption molar fraction of NH3: experimental data and simulation results
Data Files
E11-87
E11-89
Exp data
Max desorption
molar fraction
0,0085
0,0053
0,0029
0,0023
Acid sites
S1
S2
S1
S2
Simulated results
Max desorption
molar fraction
0,0085
0,0057
0,0039
0,0025
Table 17 – difference between the maximum desorption amount of NH3 for E11-87 and E11-89 : experimental data and
simulation results
exp results
simul resutls
0,0056
0,0046
0,0030
0,0033
∆S1 (max
molar fraction)
∆S2 (max
molar fraction)
This incoherency is a clearly evidence of intraparticle mass transfer, once at higher flow rates the
amount of NH3 per unit of time is higher and consequently the internal diffusion resistance is bigger, as the
concentration at the surface. Hence the amount of NH3 is lower, and the TPD area is smaller.
In Table 18 are listed the maximum desorption temperatures for both experimental and simulated data.
Table 18 - test 3 temperature of maximum desorption: experimental data and simulation results
Data Files
E11-87
E11-89
Acid Sites
S1
S2
S1
S2
Exp data
Simulated results
Max Temp (K)
547,5
764,1
525,9
732,2
Max temp (K)
548,5
755,5
531,4
732,2
5.1.2. Temperature Profile
For study 1, experimental temperature profiles were not available. However simulated results are
presented and compared with the inlet temperature of the fixed bed reactor.
As can be seen in the following Figure 25, the temperature profiles correspond approximately to the
flow rate inlet temperatures.
41
Figure 25 – test 1 temperature profies (K)
Regarding test 1, the reactor immediately increases upon the adsorption temperature, 100ºC for E1192 and 250ºC for E11-93 and temperature is constant till for step 1 (adsorption) and step 2 (step 1 = 4000sec
and step 2 = 1500s). Both simulations present the same heating rate, 10ºC/min and temperature increases till
600ºC.
Figure 26 test 2 temperature profies (K)
For test 2, both reactor increase to 150ºC during adsorption step. Since heating rates are different,
desorption slopes are different. For E11-089, the heating rate is higher, 10ºC/min, so the inlet gas achieves
600ºC faster, in 2700sec. For E11-90, the heating rate is 5ªC/min so it achieves 600ºC after 5400sec of
desorption.
42
Figure 27 - test 3 temperature profies (K)
Regarding test 3, the results show that for lower flow rates the reactor takes more time to heat. In
fact, at higher flow rates the heat transfer coefficient is bigger and the heat exchange increases.
Already mentioned, it is considered that the reactor works adiabatically.
5.1.3. Pressure Profile
There were no available data for pressure profiles in this study, however, simulated results are
presented in Figure 28.
43
Figure 28 – Pressure profiles for test 1, test 2 and test 3 (bar)
Regarding the simulated pressure drop profiles, Figure 28 show a drastic increase as the adsorption
step starts and is kept constant until it finishes. When desorption step starts, the increase of flow rate
consequently increases the pressure drop, due to NH3 desorption will
Table 19 – Total pressure drop for experiments E11-87, E11-89, E11-90, E11-92 and E11-93
dP (barA)
Test 1
E11-92
E11-93
Tad=100°C
Tad=250°C
0,001
0,001
Test 2
E11-89
10°C/min
0,0003
E11-90
5°C/min
-4
2,66x10
Test 3
E11-87
E11-89
20L/min
50L/min
-5
-4
8,25x10
8,25x10
Concerning test 1, pressure during adsorption step is higher for E11-93, Tad=250°C, since the weak
adsorption site adsorbs and desorbs immediately, increasing the outlet flow rate.
Analyzing test 2 results, the Figure 28 shows a higher pressure drop slope for E11-89 during the
desorption step, once that at higher heating rate NH3 desorption is faster increasing which increases the flow
rate.
As for test 3, pressure drop is higher for E11-87, which flow rate is 50L/min.
5.2. Study 2 – Si/Al impact
For this study, seven experiments were carried out with the same operational parameters. However,
each experiment used a zeolite H-ZMS-5 with a different Si/Al ratio.
44
5.2.1. NH3 Concentration
Figure 29 – Study 2, NH3 molar fraction profiles: experimental data
Table 20 – study 2: experimental maximum desorption tempertures (K)
S1
S2
E11-99
Si/Al 11.5
511,92
719,09
E11-100
Si/Al 15
525,6
725,4
E11-101
Si/Al 25
507,6
716,3
E11-102
Si/Al 40
512,2
719,7
E11-104
Si/Al 140
481,4
677,6
Table 21 – Experimental values for NH3 storage capacity
experimental
File
Site 1 µmol/g
Site 2 µmol/g
E11-099
510
879
E11-100
396
554
E11-101
165
366
E11-102
127
311
E11-104
0
88
The Si/Al ratio drastically influences the amount of available acid sites. As stated above, zeolite’s
protonic acidity comes essentially from hydroxyl groups bridging framework aluminum and silica leading to
Bronsted acid sites. Moreover, Lewis acid sites come from extraframework aluminum species, or defects in the
crystal lattice, so it will depend on the amount of Al species available. Hence, the higher Si/Al the fewer
available Bronsted and Lewis sites for NH3 adsorption, decreasing NH3 storage. The impact of this ammonia
storage decreasing can be clearly seen in Figure 29 and Table 21. It should be stressed out that the weak
adsorption peak has a prevalent decrease as Si/AL ratio increases, comparing to the strong adsorption peak.
45
The behavior suggests that Bronsted sites are rather formed than Lewis sites having a low amount of available
Al. As the Si/Al ratio decreases, (low Si/Al ratios) there is more available Al to form Lewis acid sites. For more
conclusive answers, it would be useful to subject the different zeolite sample to some analysis, in order to have
more accurate information about the type and accessibility of the acid sites.
At higher Si/Al ratio, TPD curves present some noise, such as for Si/Al ratio of 140 and 500. At this high
ratios the adsorbed and desorbed amount of NH 3 is very low and probably near the sensor sensibility limit.
The obtained TPD curves show not only a decrease of storage capacity, as the curve area decrease, but
also a slightly shift of the desorption maximum to a lower or higher temperature, as shown in Table 20.This
phenomena clearly shows a variation of acid strength, which may be related by several aspects. It is well known
that Si/Al ratio effects strength of protonic sites of zeolites, in such a way that the presence of neighbors
(protonic sites in the surroundings) decreases acid strength. Hence, the higher Si/Al, the stronger acid site,
since the chances of having an alumina on the surroundings are lower. (3) This effect increases the acid
strength, which can be reported between E11-99 (Si/AL 11.5) and E11-100 (Si/Al 15) for example. However,
extraframework aluminum species (low Si/Al) increase acidity by interaction of bridging hydroxyl groups
(Bronsted) and Lewis sites. Hence, low Si/Al, increase acid strength, which can be reported for E11-101 and
E11-104. Moreover, it should be noted that each zeolite sample has a different average grain diameter. If
internal diffusion resistance is significant, the respective TPD curves may be being delayed if the grain diameter
is higher than the other. For instance, TPD curve for E11-099, presents the highest maximum desorption
temperatures, and also coincides with the zeolite sample with higher mean grain diameter (≃1.29µm). There is
no available information to clearly understand each effect contribution in each sample.
For simulate the experimental data presented above, firstly, the simulated results were fitted to E11099 experimental data, which zeolite sample has the smallest Si/Al ratio (11.5). The suitable model parameters
found for E11-099 were used for the other experimental data fitting, except from the storage capacity of each
site, Ω1 and Ω2. As said before, the experimental NH3 storage parameter was used as a model input for each
experiment. Results are shown in Figure 30, where experimental simulated data results are presented for E11099, E11-100, E11-101, E11-102 and E11-104 respectively.
46
Figure 30 – study 2 NH3 molar fraction: simulation restults
Table 22 – Study2 : TPD curve area (s)
Exp data area (s)
Model area (s)
E11-99
Si/Al 11.5
8,84
7,13
E11-100
Si/Al 15
6,34
4,83
E11-101
Si/Al 25
3,88
2,52
E11-102
Si/Al 40
3,07
2,16
E11-104
Si/Al 140
1,27
0,50
As expected, the model cannot predict the Si/Al effect on acid sites strength, although the difference is
not very significant. As a result, TPD curves are slighted shifted from the simulated ones, since desorption
activation energy has decreased. However, manipulating these four parameters, storage capacity, Ω1 , Ω2 and
desorption activation energy Eades1, Eades2, the model presents a satisfactory response.
5.2.2. Temperature profile
The temperatures profiles obtained by the model used in this work correctly fit experimental results.
Indeed, the heat changes between the reactor and surroundings can be neglected and the reactor temperature
47
is approximately the inlet flow temperature. All simulations performed for fitting study 2 experiments show the
same behavior. As an example, experimental and simulated results for E11-99 are shown in Figure 31 . The
other results may be analyzed in the Annexe 3.
Figure 31 – Temperature profile for E11-99 (K)
5.2.3. Pressure Drop Profile
As expected, the simulated results present similar profiles as the ones presented for study 1. Since the
pressure profiles are similar for the several experiments, only E11-99 and E11-101 are presented as an
example. Other results are presented in Annexe 3.
48
Figure 32 – Pressure drop profiles for E11-101 and E11-99 (bar)
Regarding the simulated pressure drop profiles, the pressure increases drastically as the adsorption
step starts and is kept constant until it finishes. When desorption step starts, the increase of flow rate will
consequently increase the pressure drop due to NH3 desorption. This type of profile would be expectable
however the pressure values reveal a slight discrepancy between experimental and model results. This model
behavior suggests that pressure drop is not being correctly computed. However for our simulation objectives,
this difference is not significant.
As expected, both experimental and model results also show that the pressure drop is bigger as
smaller is the catalyst diameter.
Table 23 – Experimental and simulated pressure drop and particle diameter for study 2 experiments
file
E11-99
E11-100
E11-101
E11-102
E11-104
Si/Al
11,5
15
25
40
140
diameter (µm)
1,29
0,28
0,19
0,42
0,67
dP exp (bar)
0,00610
0,0097
0,018
0,00230
0,00224
dP model total (bar)
0,00075
0,00075
0,00010
0,00081
0,00064
dP model desorption (bar)
0,00054
0,00054
0,00071
0,00058
0,00046
49
5.3. Model improvements
The results obtained in the previous chapters provide some information about the accuracy of the
model concerning the case study.
From study 1, the model seems to well predict the experimental results for mass and temperature.
However, the small discrepancy shown in test 3 evidences how the model deviations in case of internal
diffusion resistance. Concerning study 2, the model well predicts the experimental data with an appropriate
parameter fitting. Nevertheless, the experimental data show an evident relation between Si/Al ratio and NH3
storage and Eades parameters. If this relation is found to be accurate enough, there might be a possibility to the
given model predict NH3 storage and Eades itself. To understand this kind of relation, it is essential to understand
the type and relative amount of acid sites and quantify the zeolite’s acidity.
Regarding the model specified in the previous chapters, various improvements could be made in order
to expand and improve its use. These improvements are mostly linked to the limitations considered above and
the available literature, and concern mainly these three subjects:



Diffusional Resistance
Influence of Si/Al
Zeolite’s acidity
A) Diffusional resistance
The analysis of the previous results shows a considerable impact of diffusional resistance in kinetics
and mass transfer. Moreover, previous studies reveal significant internal diffusion resistance in the ammoniaTPD system, playing an essential role in the construction of a kinetic model (22) As a matter of fact, H-ZMS-5 is
a medium-small pore sized zeolite, which is a known factor for increasing diffusional resistance within the
zeolite. Based on the previous arguments, it is reasonable to propose the introduction intraparticule mass
transfer resistance.
Including intraparticle mass transfer resistance in the given model, would be the first step of the
modeling procedure. The second step will be to prove the models efficiency with some experimental data.
Further experiments evidencing diffusion resistance should be performed in order to make a proper
comparison:
 Experiments testing zeolite particle size diameters effect: internal diffusion limitations
increase with the zeolite particle size diameter.

Experiments testing desorption heating rate for constant particle size: at higher heating rates,
the TPD curve is slightly deviated to higher temperatures due to intraparticle diffusion
limitations.
Diffusional resistance may be computed in the model as it is presented below.
As first approach, one may use the film model to describe the mass-transfer from the gas to the
catalyst surface as it is described in (20).
The mass transfer coefficient, kg can be calculated using the Sherwood number according to:
50
𝑆ℎ =
𝑘𝑔 𝐷𝑝
𝐷𝑒𝑓𝑓
30
where the effective diffusion coefficient can be obtained from available literature (7) or correlations, Fuller
correlation for instance, as described in (20). Sherwood number is function of Reynolds and Schmitt number,
and may be given by some empiric correlations for fixed bed reactors (29)
As for the mass balance, it is presented by equation 31 instead of equation 22 whose assumptions are
referred previously.
𝑑𝐹𝑖
= −𝑥𝑖𝑜𝑢𝑡 ∗ 𝐹𝑜𝑢𝑡 + 𝑥𝑖𝑖𝑛 ∗ 𝐹𝑖𝑛 − 𝑘𝑔 𝐴(𝐶 − 𝐶𝑠 )
𝑑𝑡
31
For the actual model, gas accumulation is neglected so dFi/dt≃0
The surface balances are given by equations 32, 33 and 34. It is assumed that there is no accumulation
at the catalyst surface, so dCs/dt ≃0
𝑘𝑔 𝐴(𝐶 − 𝐶𝑠 ) + (𝑁𝑐𝑎𝑡1 𝑑𝜃1 + 𝑁𝑐𝑎𝑡2 𝑑𝜃2 )𝑚𝑧𝑒𝑜𝑙 = 0
32
𝑁𝑐𝑎𝑡1
𝑑𝜃1
= 𝑟𝑎𝑑1 − 𝑟𝑑𝑒𝑠1
𝑑𝑡
33
𝑁𝑐𝑎𝑡2
𝑑𝜃2
= 𝑟𝑎𝑑2 − 𝑟𝑑𝑒𝑠2
𝑑𝑡
34
The intraparticle mass transfer can be described by an effective diffusion model with the driving force
being concentration gradient in the radial direction of a spherical particle. (22) As referred before, the
mathematical description of mass transport in a porous media leads to a set of partial differential equations
which may assume some complexity.
As reported in (38)the first and widely used approximation for spherical sorbents, proposed by
Glueckauf and Coates (1947), is the linear driving force (LDF) approximation. For adsorption of a spherical
particle subject to a step change in the surface concentration, the LDF describes the adsorption rate being
proportional to the difference between the surface concentration and the average concentration within the
particle.
The specific LDF expressions can be derived using Fickian diffusion model, Fickian diffusion/convection
model or the dusty-gas model, the adsorption isotherm is linear or nonlinear and the intraparticle partial
pressure profiles can be assumed parabolic or polynomials. In general, these expressions have the form of a
system of ordinary differential equations for the vector of the average concentrations of the species and the
vector os some other average concentrations (auxiliary variables) as it is described in (39). The right-hand side
of the system has the compact form of the product of an LDF matrix and a vector of driving forces (differences)
involving the average concentration in the pellet and the concentrations at the external surface.
Generally, LDF approximations are based on the Fickian diffusion model, which is the simplest of all
mass transport models. This may be first option for including the LDF approximation in the model developed in
51
the current work. At this point, the model should be tested in order to evaluate its accuracy due experimental
data. In the presence of intraparticle total pressure gradients, using the Fickian diffusion model may produce
inaccurate results because Knudsen flow is underestimated and viscous flow is not taken into account.
In that case, LDF approximation should approach Fickian diffusion/convection model, which uses Darcy’s law to
account for the viscous fluxes of the components. If Fickian diffusion/convection model approach does not
show enough improvements, dusty-gas model should be employed.
The effective transport coefficients used in LDF approximation may be computed from the following
equations, as suggested by (38)
Coefficients
Equation
Effective Binary Diffusion
Coefficient for gases
DAB
Chapman-Enskog equation
𝐷𝐴𝐵 = 2.628 ∗ 10−3
Knudsen diffusion
Dk
Effective Diffusion coefficient
√𝑇 3 (𝑀𝐴 + 𝑀𝐵 )/(2𝑀𝐴 𝑀𝐵 )
𝑃𝜎 2 𝛺
𝑟𝑝 𝑇
( )
𝜏 𝑀𝐴
Bonsaquet’s relation
1
1
1
=
+
𝐷𝑒 𝐷𝐾 𝐷𝑚
𝐷𝐾 = 3.068
35
36
37
More correlations are available in the literature (40).
B) Influence of Si/Al
B1) Influence of Si/Al on ammonia storage effect parameter, Ω1 and Ω2
As it is known, and also based on the preliminary experimental results, it is evident that Si/Al has a
significant effect on storage and acid site strength.
Zeolite’s protonic acidity comes essentially from hydroxyl groups bridging alumina and silica. This
strong interaction of O with Al weakens OH bond, increasing the acid strength (Bronsted sites). Moreover,
extraframework aluminum species also increase catalytic activity of zeolites (Lewis acid species) showing
enhanced acidity through interaction of bridging hydroxyl groups. Therefore, the higher alumina amount the
higher number of acid sites, hence higher storage. In fact, it is well noticeable the decrease of S1 and S2 storage
with the increase of Si/Al, as it is shown in Table 21.
The variation of acid site storage with Si/Al ratio seems to reveal a consistent tendency. Using some of
the available data of Ω1 and Ω2 of Si/Al of 11, 15 and 140, a tendency line was built to find a mathematical
description of this behavior.
52
Figure 33 – Variation of NH3 storage, Ω1 and Ω2 with Si/Al.
Regarding Figure 33, two mathematical expressions were found to describe both tendency of Ω1 and
Ω2, with R squared value of approximately 0.8357 and 0.994 respectively.
In order to evaluate the prediction of an eventual mathematical relation, as shown in Figure 33, the
values of Ω1 and Ω2 were obtained for all the experiments (Si/Al ratios) and compared with the experimental
data, Table 24 and Table 25.
Table 24 – NH3 storage capacity for S1: experimental and calculated value
Si/Al
11
15
25
40
140
Ω1 model (µmol/g)
594,2
495
275
20
620
Ω1 exp (µmol/g)
510,14
396
164,51
126,73
126,73
%error
16,48
25
67,16
84,22
389,23
Table 25 - – NH3 storage capacity for S2: experimental and calculated value
Si/Al
Ω2 model (µmol/g)
Ω2 exp (µmol/g)
%error
11
856,25
878,61
2,55
15
573,43
554,00
3,51
25
368,25
366,33
0,52
40
244,99
310,96
21,21
140
82,69
0
0,0083
Concerning Ω1, the expression results are far different from the experimental ones, which conclude
that the results predicted from the expression are not trustful for an accurate prediction of Ω1 with Si/Al. The
achieved expression for Ω2, presents accurate results for low Si/Al, 11, 15 and 25 and high Si/Al of 140.
The previous results suggest that a descriptive model of NH 3 adsorption and desorption on zeolite may
be able to predict each site storage from the input parameter of Si/Al. However, this prediction would be only
reliable for low Si/Al and only for storage capacity of the Bronsted acid sites. In either case, in order to have an
accurate mathematical expression for describe this behavior, more experimental data from different Si/Al
ratios will be needed. If the predicted results well correspond to the experimental ones, the expression can be
implemented in the model, which from the new parameter Si/Al will compute Ω1, Ω2 or both.
B2) Influence of Si/Al on the acid strength
53
Si/Al ratio has effects on the acid strength as shown in Table 20 from the variation of the maximum
desorption temperatures. However, and as it is referred before, the variation of E ades does not have a
preferential tendency with SI/Al ratio, since as the ratio increases, the respective maximum desorption
temperature increases or decreases almost randomly.
As mentioned before, there are three main effects that explain this variation: (i) the presence of
neighbors (protonic sites in the surroundings) decreases acid strength, which means that a higher Si/Al ratios,
increases acid strength, (ii) extra framework aluminum species (low Si/Al) increase acidity by interaction of
bridging hydroxyl groups (Bronsted) and neighboring small extra-framework aluminum species (Lewis sites), so
high Si/Al ratio, decreases the acid strength. (ii) internal diffusion limitations, which play a bigger rule for higher
grain diameter zeolites.
The available data results do not give enough information to know which type of acid site is
predominant in each peak, or which effect is predominant is each case.
Firstly, it should be noted that each MFI Si/Al used in this work (study 2) has a different average grain
diameter. In order to have a proper comparison between the different Si/Al the zeolite particle diameter
should be approximately the same. It has already been proven that internal diffusional are a significant
phenomenon in MFI zeolite internal diffusion, which compromises the maximum desorption temperature (TPD
curves are delayed).
Moreover, further experiments and analysis should be done to help understand the predominant
acidity in different Si/Al ratio (44). It should be noted that determining quantitatively acid sites strength is still a
challenge and in fact, no satisfactory acidity scale for solids has been stablished.

Experiments with different Si/Al ratio, constant particle size: for truly compare Si/Al effects
without zeolite size influence. In order to avoid diffusional resistance effects, one possibility
is to use constant and small diameter zeolite grains.

Calorimetric studies of the adsorption of NH3 : measuring the heat of adsorption and
desorption heat

Ammonia TPD allows the determination of the number of acid sites, and its relative strength,
moreover provides quantitative information on the distribution of acid sited strength in
zeolites.

Temperature-programed desorption of probe molecules such as pyridine: study the type and
accessibility and amount of acid sites

Infrared Spectroscopy: allowing the measurement of relative acidity of Bronsted sites

Infrared Spectroscopy measuring bands by the adsorption of basic probe molecules: giving
information about the nature, amount, strength, density, microenvironment location and
accessibility of acid sites

Solid-State Al MAS NMR: determination of the structure or the localization of alumina.
Aluminum spectrum presents two distinct peaks corresponding to tetrahedral and octahedral
structures, which corresponds to Bronsted and Lewis sites respectively.
54

H MAS NMR technique can also provide information about the acidity of the zeolite, using H
chemical shifts as the basis of an acidity scale. This parameter can be correlated with the
proton donor ability of the corresponding site, in a way that higher acid strength indicates a
proton more positively charged, and less shielded, which means higher chemical shifts. So far
it has been possible to identify six distinct types of proton from the chemical shift value,
refereeing to different types of acid sites, in different types of cavities. (45)

The previous analysis would give information about the amount and type of each acid sites,
Bronsted and Lewis, which would be very useful for understanding Si/Al consequences,
relative storage capacity, etc.
Moreover, the porosity repartition of a given zeolite is important information concerning the
accessibility of the acid sites and the available internal catalyst area. Commonly, textural characterization of
porous solids is carried out by physical adsorption of gases. For instance, typical N2 adsorption isotherm on HZMZ-5 leads to a type I isotherm, suggesting a predominant micro porosity and an internal surface area
relatively small (3).
1
Some studies (45) report the use of NH3 TPD and H MAS NMR to characterize the acid strength of HZMS-5. In this case, acid strength distributions of Bronsted sites have been determined by deconvolution of
1
both spectra. The H MAS NMR spectra is deconvoluted into Gaussian components using Fit2003 software of
Massiot et al., from which results the chemical shift, identification and relative amount. It should be stressed
out that the observations made may not hold for other H-MFI with different Si/Al. The TPD profile is
deconvoluted into several components characterized by the number and strength of the acid sites. It is
assumed that the desorption form the acid sites is irreversible and kinetically first-order, and that there is no
interaction between two acid sites. Each individual components obtained correspond to a family of sites
characterized by the same acid strength, from which it is possible to derive number os acid sites, desorption
1
rate constant and the activation energy, Eades . In this case, for TPD acidity is defined by the Eades, while for H
MAS NMR acidity scale is based on the proton chemical shift.
The authors (45) recall a relationship between the acidity and the H chemical shift, proposing a
1
correlation between NH3 TPD and H MAS NMR results as the basis of an acidity scale for Bronsted acidic sites,
1
namely a linear relationship between the activation energy for ammonia desorption, Eades and the H NMR
chemical shift. As expected, the equations predict that the heat of adsorption of ammonia and the chemical
shift of the acidic proton increase with an increase of the hydroxyl hydrogen positive charge, i.e., acid strength.
These correlations may open a door for an acidity scale for zeolites, helping to predict their catalytic activity.
1
Using the available TPD curves of this work and performing an H MAS NMR, one would be able to predict the
acid strength of a given zeolite, for a given Si/Al, as it is suggested in (45), and define a correlation between ,
Eades and H chemical shift.
Improving the model requires not only a good approach, but also using the most convenient
parameters. When developing kinetic models, the precision of used parameters is very important for the model
reliability. In this case, one can use micro calorimetric results not only determining the adsorption heat, but
also the coverage dependent activation energy parameter, α. In the available literature (42) it is presented a
strategy to calculate the coverage dependent activation energy on H-ZSM-5, conducting an ammonia stepwise
experience. Results show a linear dependence of the heat of adsorption (∆Had) on the coverage. The heat of
adsorption is equal to the activation energy for adsorption, Eaad minus the activation energy for desorption,
Eades. Assuming that the activation barrier for ammonia adsorption in non-activated, Eades is equal to the
55
negative heat of adsorption (-∆Had) brings out that the equation for the linear fitting results as equation 38,
from which one can determine α.
𝐸𝑎𝑗 = 𝐸𝑎𝑗0 (1 − 𝛼𝑗 𝜃𝑗 )
38
This study describes all the experimental procedure and data treatment to determine this parameter. This
procedure would confirm the kinetic assumptions assumed in the present model, and introduce also more
accurate parameters.
56
6. Conclusion and Perspectives
A fixed bed reactor model of ammonia adsorption and desorption has been analyzed and compared to
experimental data.
It has been shown that the model well describes the experimental data although it presents some
limitations due to internal diffusional phenomena. The importance of this phenomenon must not be neglected
in this kind of technology and in this kind of zeolite, H-ZSM-5 (22). In fact, the experimental results evidence
this kind of limitations (test 2 and test3 from study one), which is in accordance with previous studies of NH3
adsorption/desorption on H-ZMS-5, noting the significant effect of the phenomenon.
It is known that internal diffusion limitations are more prevalent in small pore zeolites. Moreover, as
previously mentioned, small pore zeolites are the ones that seem more suitable for SCR technology. Recently it
was reported (6) that a Cu-SSZ-13, a zeolite with the Chabazite structure is more active and selective for this
technology comparing to other zeolites, which suggests that an SCR model should take into account this
phenomenon. The model used in this study should be improved in this way, and later one must prove its
accuracy comparing to experimental data.
Concerning the Si/Al ratio effect on NH3 storage, it seems to be a dependent relation between these
two parameters. Additional experiments are required to eventually find a mathematic model to well describe
this relation, which will allow the storage capacity to be directly computed from Si/Al ratio. The effect of Si/Al
ratio on desorption activation energy is still not clear, further experiments should be repeated using similar
particle sizes, in order to avoid diffusional limitations effects. The analysis of the type of predominant acid sites
for each Si/Al ratio would also help to understand these variations.
The adsorption of NH3 is one of the key steps of the SCR system. As such, it is important to well
understand the acid sites concentration, type, strength and accessibility. Zeolite acidity characterization would
be a valuable tool to understand the different zeolite acidity in different conditions namely the Si/Al ratio
variation and the high temperatures the catalyst undergoes in an exhaust aftertreatment system.
Nevertheless, it would be valuable to test the accuracy of the final model towards other types of
zeolites used in SCR technology, such as metal-exchanged ZSM-5 or Chabazite. It also should be interesting to
improve the kinetic model in order to consider the complete exhaust gas composition and deNOx reactions.
57
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60
8. Annexes
1- Anexxe 1 – Fixed Bed Models
There are basically two kinds of model for describing fixed bed reactors: i) homogeneous, which considers
the fixed bed as a pseudocontinuum media, and ii) heterogeneous, which distinguish temperatures and
concentrations balances in the gas phase, and in the solid phase, (catalyst). Each category may contain
different approaches and assumptions, as the one-dimensional model which assumes thermal and mass
dispersion only in axial direction and two-dimensional model for instance, which assumes thermal and mass
dispersion in axial and radial direction. The model’s choice depends on how detailed or simplified one wants
the model to be. Homogeneous models have been widely used due to their simplicity, although they might be
inaccurate in some conditions like highly exothermic processes or for severe operating conditions for example.
(26)
As for the pseudohomogeneous models, the phenomena occurring at the surface or within the catalyst are
ignored and it is described as a homogeneous reactor. As stated above, pseudohomegeneous model may have
different assumptions. PH1, the simplest model, considers the ideal plug-flow model, in which there is no
concentration or temperature gradient in radial direction, having a constant velocity flow in axial direction.
Moreover, one may admit axial dispersion, having the one-dimensional PH2, or assume also radial dispersion,
leading to the two-dimensional PH3. (30)
61
In the heterogeneous model, the heat and mass balances are made separately for the gas phase and for
the solid catalyst phase. Concerning this heterogeneous reactor approach, there are three main models, HT1,
HT2 and HT3. The first two models, HT1 and HT2, consider a heterogeneous plug-flow model for the fluid,
without thermal and mass dispersion in axial direction or radial gradient. (30)
In HT1 model, external resistance to diffusion is considered, leading to two mass balances to the species in
the gas phase and at the catalyst surface as presented in the following balances.
𝑑𝐶𝐴
= 𝑘𝑔 (𝐶𝐴 − 𝐶𝑆 )
𝑑𝑧
39
𝑘𝑔 (𝐶𝐴 − 𝐶𝑆 ) = −𝑟𝐴 𝑉
40
𝑣
In this case, the flux of A is given by the difference between the concentration in the bulk phase (C A ) and
at the catalyst surface (CS ). The concentration at the surface will be function of the mass transport coefficient,
which measures how fast does the mass transfer occurs, and from the reaction kinetics (r AV).
Resembling to the previous model, HT2 also considers internal diffusional resistance within the particle. In
this case, there’s a nonlinear concentration gradient inside the particle that can be written as follows:
𝐷𝐴𝐵 (
1 𝑑 2 𝑑𝐶𝐴
(𝑟
) − 𝑅𝐴 = 0
𝑟 2 𝑑𝑟
𝑑𝑟
41
This is basically the simplification of the continuity equation in spherical coordinates, assuming exclusively
radial diffusion within the catalyst grain in steady state. The resulting solution leads to an equation with a
dimensionless parameter, the Thiele modulus, which describes the relationship between diffusion and reaction
rate in porous catalyst pellets (30).
Mathematically, describing mass transport in a porous media may assume some complexity and
consequently, high consumption of computational memory and time. Linear driving force approximation (LDF)
is an example of a simplified description of concentration within the porous media. Basically, the
approximation states that the uptake rate of a species is proportional to the difference between the surface
concentration, Cs, and the average concentration inside the particle, replacing the partial differential mass
balance equation in the particle by a simpler ordinary differential equation (38).
2 – Annexe 2 – Simulation parameters
Test 1 – Adsorption Temperature Effect
Parameters
E11-092
S1 – Weak
acid site
S2 Strong acid
site
A0ad1
A0des1
Eades1 (J/mol)
α1
Ω1 (mol/gcat)
A0ad2
A0des2
Eades2 (J/mol)
900
2,5E+13
115000
0,12
0,000697665
700
2,5E+13
170000
E11-093
900
2,5E+13
115000
0,12
4,62335E-05
700
2,5E+13
170000
62
Inlet
conditions
Reactor
parameters
S1 – Weak
Acid site
S2 Strong acid
site
Inlet
conditions
Reactor
parameters
α2
Ω2 (mol/gcat)
Mass sample (zeolite) (mg)
Qm (g/s)
NH3 %massica
T adsorçao (°C)
t step 1 (s)
t step 2 (s)
T dessorçao-max (°C)
t step 3 (s)
t step 4
L (mm)
D (mm)
Dzeolite (µm)
Dinert (µm)
Ɛ
FBmass (g)
-1 -1
HC (J.kg .K )
0,09
0,000504406
300,3
0,001006036
0,063304972
100
4000
1500
600
3000
1780
21,48
9
0,2824
1000
0,5
1,8019
100
Test 2 – Heating Rate Effect
E11-089
Parameters
A0ad1
600
A0des1
2E+13
Eades1 (J/mol)
120000
α1
0,03
Ω1 (mol/gcat)
0,00032
A0ad2
500
A0des2
2E+13
Eades2 (J/mol)
171000
α2
0,1
Ω2 (mol/gcat)
0,000521
Mass sample (zeolite) (mg)
203,8
Qm (g/s)
0,001
NH3 %massica
0,0633
T adsorçao (°C)
150
t step 1 (s)
1500
t step 2 (s)
1500
T dessorçao-max (°C)
600
t step 3 (s)
2700
t step 4
1780
L (mm)
21,48
D (mm)
9
Dzeolite (µm)
0,2824
Dinert (µm)
1000
0,09
0,000507082
300,3
0,001006036
0,063304972
250
4000
1500
600
2100
1780
21,48
9
0,2824
1000
0,5
1,8019
100
E11-090
600
2E+13
120000
0,03
0,00032
500
2E+13
171000
0,1
0,000521
238,446
0,001
0,0633
150
1500
1500
600
5400
1780
21,48
9
0,2824
1000
63
Ɛ
FBmass (g)
-1 -1
HC (J.kg .K )
S1 – Weak
acid site
S2 Strong acid
site
Inlet
conditions
Reactor
parameters
0,5
1,7050
100
Test 3 – Flow Rate Effect
E11-087
Parameters
A0ad1
900
A0des1
2E+13
Eades1 (J/mol)
115000
α1
0,04
Ω1 (mol/gcat)
0,000443
A0ad2
700
A0des2
2E+13
Eades2 (J/mol)
175000
α2
0,13
Ω2 (mol/gcat)
0,000522
Mass sample (zeolite) (mg)
198,6
Qm (g/s)
0,000333
NH3 %massica
0,0633
T adsorçao (°C)
150
t step 1 (s)
1500
t step 2 (s)
1500
T dessorçao-max (°C)
600
t step 3 (s)
2700
t step 4
1780
L (mm)
19,20
D (mm)
9,44
Dzeolite (µm)
0,2824
0,5
1,7391
100
E11-089
900
2E+13
115000
0,04
0,000443
700
2E+13
175000
0,13
0,000522
203,8
0,001
0,0633
150
1500
1500
600
2700
1780
19,20
9,44
0,2824
64
Dinert (µm)
Ɛ
FBmass (g)
-1 -1
HC (J.kg .K )
Inlet
Conditions
S1 – Weak
acid site
(kinetic
parameters)
S2 Strong acid
1000
0,5
1,6992
100
1000
0,5
1,7050
100
Parameters/file
E11-99
E11-100
E11-101
E11-102
E11-104
Si/Al
11,5
15
25
40
140
Mass sample
(zeolite) (mg)
197,4
198,5
186,7
194,1
207,0
Qm (g/s)
0,00100564
0,00100564
0,00100604
0,00100564
0,00100524
NH3 %massica
T adsorçao (°C)
0,06330126
0,06330126
0,06330126
0,06330126
0,06330126
150
150
150
150
150
T dessorçao-max (°C)
600
600
600
600
600
t step 1 (s)
2000
2000
2000
2000
2000
t step 2 (s)
1500
1500
1500
1500
1500
t step 3 (s)
2700
2700
2700
2700
2700
t step 4 (s)
1780
1780
1780
1780
1780
A0ad1
500
500
500
500
500
A0des1
2E+13
2E+13
2E+13
2E+13
2E+13
Eades1 (J/mol)
104000
104000
104000
104000
104000
α1
Ω1 (mol/gcat)
A0ad2
A0des2
0,01
0,01
0,01
0,01
0,01
0,000510136
500
1,5E+14
0,000396
500
1,5E+14
0,000164511
500
1,5E+14
0,00012673
500
1,5E+14
0
500
1,5E+14
65
site (kinetic
parameters)
Reaction
parameters
Eades2 (J/mol)
167000
167000
167000
167000
167000
α2
Ω2 (mol/gcat)
L (mm)
0,09
0,000878609
19,84
0,09
0,000554
19,62
0,09
0,000366325
23,34
0,09
0,000310959
18,9
0,09
8,7992E-05
15,98
D (mm)
9,44
9,4
8,84
8,84
9,2
Dzeolite (µm)
1,28665
0,2824
0,19235
0,4249
0,6653
Dinert (µm)
1000
1000
1000
1000
1000
Ɛ
1,698
1,700
1,682
1,691
1,709
FBmass (g)
-1 -1
HC (J.kg .K )
0,4
0,4
0,4
0,4
0,4
20
20
20
20
20
- Annexes 3 - Study 2 temperature and pressure drop profiles
66
Figure 34 – study 2 temperature profiles (K)
67
Figure 35 – Study 2 pressure drop profiles
Annexe 4 – Model AMESim sketch for the plug flow approach, N=5
68
Figure 36 – AMESim sketch for the plug flow approach, N=5
69