Modeling of vacuum residue hydrotreatment Engenharia Química

Transcription

Modeling of vacuum residue hydrotreatment
Impact of the feedstock description on model output
Pedro Manuel Mendes Rivotti
Dissertação para obtenção do Grau de Mestre em
Engenharia Química
Júri
Presidente:
Prof. João Carlos Moura Bordado
Orientadores:
Prof. Fernando Manuel Ramôa Cardoso Ribeiro
Dr. Vitor Raul Lameiras Franco da Costa
Vogal:
Prof. Francisco Manuel da Silva Lemos
Setembro de 2009
Resumo
Neste trabalho é apresentado o estudo de um modelo de hidrotratamento de resíduos de vácuo
desenvolvido no IFP.
O modelo em estudo simula a operação de um reactor de hidrodesmetalização e de uma unidade
completa, envolvendo as secções de hidrodesmetalização e hidrodessulfuração. A difusão no interior
do catalisador é descrita pelas equações de Stefan-Maxwell adaptadas a um sistema com moléculas
com grande diferença de dimensões. O elevado número de compostos considerados e as equações
utilizadas para descrever a difusão no interior do catalisador levam a que uma rotina de estimação de
parâmetros possa convergir para um mínimo local sem significado físico, se os parâmetros iniciais
forem introduzidos aleatoriamente.
Neste estudo é apresentada a metologia utilizada para obter estimativas iniciais dos parâmetros
do modelo, nomeadamente das constantes cinéticas e de adsorção. A obtenção das estimativas
iniciais foi feita utilizando como base um resíduo do Médio Oriente (Buzurgan). Com os parâmetros
obtidos, a resposta do modelo foi simulada para outros resíduos, com diferentes origens geográficas
(Arabian Light, Djeno e Oural). O estudo consistiu igualmente numa análise de sensibilidade aos
diferentes valores a introduzir no modelo.
A resposta do modelo a variações nos seus parâmetros e valores de entrada pôde ser explicada,
na maioria dos casos, utilizando argumentos baseados nos fenómenos físicos e químicos envolvidos
no processo catalítico. As simulações efectuadas para resíduos com diferentes origens geográficas
apenas evidenciaram pequenos desvios em relação aos dados experimentais.
Palavras-chave: resíduos, hidrotratamento, modelização, difusão, Stefan-Maxwell
i
Abstract
This work comprises the study of a vacuum residue hydrotreatment model developed in IFP.
The model in study simulates the operation of a hydrodemetallization reactor and of a complete
unit, including the hydrodemetallization and hydrodesulfurization sections. The diffusion inside the
catalyst is described by the Stefan-Maxwell equations extended for starkly different sized molecules.
The large number of compounds considered and the equations used to describe the diffusion inside
the catalyst may cause a parameter estimation routine to converge to a local minimum without
physical significance, if randomly chosen parameters are used as initial estimates.
This study presents the methodology used to obtain initial estimates for the model parameters,
namely for the kinetic and adsorption constants. The initial estimates for the model parameters were
obtained using a Middle East residue (Buzurgan) as a reference. With the obtained parameters, the
model output was simulated for other residues, with different geographical origins (Arabian Light,
Djeno and Oural). The study also included a sensitivity analysis to the required model inputs.
The model sensitivity to variations in its parameters and inputs could be explained, in most cases,
using arguments based on the physical and chemical phenomena involved in a catalytic process. The
simulations for residues with different geographical origins only evidenced slight deviations to the
experimental data.
Keywords: residues, hydrotreatment, modeling, diffusion, Stefan-Maxwell
ii
Acknowledgments
The first acknowledgment must go to Prof. Ramôa Ribeiro, without whom this journey at IFP
would not be possible. I express my deepest appreciation for the friendship and support over the last
years.
I am also thankful to Cristina and Victor for the support and guidance during the internship and for
their precious help with the thesis writing.
I feel lucky to be given the opportunity of sharing a six months adventure with some of my best
friends. For this, I should thank my fellow Portuguese comrades: Akira, Alberto, Bela, Boubou, Clara,
Inês, Leonor, Luís and Susana.
My experience at IFP was certainly improved by the constant mutual aid and cultural exchange
with the best “bureau” mates: Caio, Mathhias, Sebastien and Tarek. I’ll surely miss you all.
I also express my gratitude to the family and friends in Portugal, for the long distance support and
for constantly asking me when I would return home.
iii
Table of contents
1
Introduction ................................................................................................................................... 1
2
Bibliographic study ...................................................................................................................... 2
2.1
Introduction .......................................................................................................................... 2
2.2
Residue feedstocks ............................................................................................................. 2
2.2.1
Introduction.................................................................................................................. 2
2.2.2
Fractioning methods ................................................................................................... 3
2.2.3
Asphaltenes ................................................................................................................. 4
2.2.4
Resins ........................................................................................................................... 5
2.2.5
Metals ........................................................................................................................... 5
2.2.6
Sulfur and nitrogen ..................................................................................................... 6
2.3
Residue hydrotreatment units ............................................................................................ 7
2.3.1
Introduction.................................................................................................................. 7
2.3.2
Hydrotreatment applications...................................................................................... 7
2.3.3
Hydrotreatment catalysts ........................................................................................... 8
2.3.4
Hydrotreatment reactions ........................................................................................... 9
2.3.4.1
HDS ......................................................................................................................... 10
2.3.4.2
HDM ........................................................................................................................ 10
2.3.4.3
HDN......................................................................................................................... 11
2.3.4.4
Cracking reactions .................................................................................................. 11
2.3.4.5
Condensation reactions and coke formation........................................................... 12
2.3.5
Hydrotreatment technology ..................................................................................... 12
2.3.5.1
Fix-bed reactor ........................................................................................................ 13
2.3.5.2
Other types of reactors............................................................................................ 14
2.3.5.3
Operating conditions ............................................................................................... 15
2.4
Conclusions ........................................................................................................................ 15
2.5
Modeling.............................................................................................................................. 16
2.5.1
Introduction................................................................................................................ 16
2.5.2
Hydrodynamics.......................................................................................................... 17
2.5.3
Intragranular diffusion .............................................................................................. 17
2.5.3.1
Fick's first law .......................................................................................................... 19
2.5.3.2
Stefan-Maxwell equations ....................................................................................... 19
2.5.4
Adsorption ................................................................................................................. 21
2.5.5
Deactivation ............................................................................................................... 22
2.5.6
Kinetics and feedstock description ......................................................................... 23
2.5.7
IFP models ................................................................................................................. 24
2.5.7.1
THERMIDOR .......................................................................................................... 24
2.5.7.2
Model for the HDM section ..................................................................................... 24
iv
2.5.7.3
2.6
3
Conclusions ........................................................................................................................ 25
Model description ....................................................................................................................... 26
3.1
Introduction ........................................................................................................................ 26
3.2
Model Description .............................................................................................................. 26
3.2.1
Model hypothesis ...................................................................................................... 27
3.2.2
Feedstock description .............................................................................................. 27
3.2.3
Kinetic network .......................................................................................................... 28
3.2.4
Extragranular phenomena ........................................................................................ 29
3.2.4.1
Hydrodynamic model .............................................................................................. 29
3.2.4.2
Mass balances ........................................................................................................ 30
3.2.5
Intragranular phenomena ......................................................................................... 30
3.2.5.1
Mass balances ........................................................................................................ 30
3.2.5.2
Diffusion .................................................................................................................. 32
3.2.5.3
Adsorption ............................................................................................................... 33
3.2.5.4
Deactivation by decrease of active sites and porosity ............................................ 34
3.2.6
Model entries from experimental data..................................................................... 35
3.2.7
Reactor sequencing .................................................................................................. 37
3.2.8
Summary of the model parameters ......................................................................... 38
3.3
Differential equations solving and parameter optimization .......................................... 39
3.3.1.1
Differential equations .............................................................................................. 39
3.3.1.2
Parameter estimation .............................................................................................. 40
3.4
4
Model for the HDS section ...................................................................................... 25
Conclusion .......................................................................................................................... 40
Results ......................................................................................................................................... 42
4.1
Experimental data .............................................................................................................. 42
4.2
HDM model.......................................................................................................................... 44
4.2.1
Optimization and sensitivity analysis methodology.............................................. 44
4.2.2
Parameter optimization ............................................................................................. 46
4.2.2.1
Adsorption constants............................................................................................... 46
4.2.2.2
Kinetic constants ..................................................................................................... 47
4.2.2.3
Estimation routine results ........................................................................................ 49
4.2.2.4
Optimized results .................................................................................................... 49
4.2.3
Simulations for different residues ........................................................................... 51
4.2.4
Sensitivity analysis ................................................................................................... 53
4.2.4.1
Repartition coefficients ............................................................................................ 53
4.2.4.2
ns numbers .............................................................................................................. 54
4.2.4.3
Distribution coefficients ........................................................................................... 56
4.3
HDM + HDS model .............................................................................................................. 57
4.3.1
Optimization strategy ................................................................................................ 57
4.3.2
Parameter optimization ............................................................................................. 57
v
4.3.2.1
HDM section parameters ........................................................................................ 57
4.3.2.2
HDS section parameters ......................................................................................... 59
4.3.2.3
Optimized results .................................................................................................... 60
4.3.3
4.4
Simulations for different feedstocks ....................................................................... 62
Results summary ............................................................................................................... 64
5
Conclusion and perspectives .................................................................................................... 66
6
Appendices .................................................................................................................................. 67
6.1
Detailed analysis for the different residue feedstocks .............................................. 67
6.1.1
Buzurgan ................................................................................................................ 67
6.1.2
Arabian Light ......................................................................................................... 68
6.1.3
Djeno ...................................................................................................................... 68
6.1.4
Oural ....................................................................................................................... 69
6.2
GPC curves..................................................................................................................... 71
6.2.1
Buzurgan ................................................................................................................ 71
6.2.2
Arabian Light ......................................................................................................... 71
6.2.3
Djeno ...................................................................................................................... 72
6.2.4
Oural ....................................................................................................................... 72
6.3
Simulation results for different residues .................................................................... 73
6.3.1
Arabian Light ......................................................................................................... 73
6.3.2
Djeno ...................................................................................................................... 74
6.3.3
Oural ....................................................................................................................... 76
vi
List of tables
Table 1 – Typical performances of residue hydrotreatment reactions. (Leprince, 2001) ........................ 9
Table 2 – Comparison of different hydrotreating technologies. (Leprince, 2001) ................................. 14
Table 3 – Typical operating conditions of hydrotreating units. (Le Page et al., 1992) .......................... 15
Table 4 – Kinetic network describing all the possible reactions considered in the model. ................... 29
Table 5 – Adsorption constants considered in the model. .................................................................... 34
Table 6 – Summary of the model parameters. ...................................................................................... 39
Table 7 - Operating conditions used in pilot unit scale experiments. .................................................... 42
Table 8 – Available analysis for the 4 vacuum residues used. ............................................................. 42
Table 9 – Adsorption constants optimized for Buzurgan residue feedstock. ........................................ 47
Table 10 – Kinetic constants affecting each of the heteroatom removal and lump fraction curves. ..... 47
Table 11 – Kinetic constants optimized for Buzurgan residue feedstock.............................................. 48
Table 12 – Adsorption constants optimized for the HDM section, using Buzurgan residue as reference.
............................................................................................................................................................... 57
Table 13 – Kinetic constants optimized for the HDM section, using Buzurgan residue as reference... 58
Table 14 - Adsorption constants optimized for the HDS section, using Buzurgan residue as reference.
............................................................................................................................................................... 59
Table 15 - Kinetic constants optimized for the HDS section, using Buzurgan residue as reference. ... 59
Table 16 – Density of Buzurgan residue for different residence times in the HDM and HDS reactor. . 67
Table 17 – Percentage of each SARA fraction in Buzurgan residue, for different residence times in the
HDM and HDS reactor........................................................................................................................... 67
Table 18 – Heteroatoms composition of Buzurgan residue for different residence times in the HDM
and HDS reactor. ................................................................................................................................... 67
Table 19 – Density of Arabian Light residue for different residence times in the HDM and HDS reactor.
............................................................................................................................................................... 68
Table 20 – Percentage of each SARA fraction in Arabian Light residue, for different residence times in
the HDM and HDS reactor..................................................................................................................... 68
Table 21 – Heteroatoms composition of Arabian Light residue for different residence times in the HDM
and HDS reactor. ................................................................................................................................... 68
Table 22 – Density of Djeno residue for different residence times in the HDM and HDS reactor. ....... 68
Table 23 – Percentage of each SARA fraction in Djeno residue, for different residence times in the
Table 24 – Heteroatoms composition of Djeno residue for different residence times in the HDM and
HDS reactor. .......................................................................................................................................... 69
Table 25 – Density of Oural residue for different residence times in the HDM and HDS reactor. ........ 69
Table 26 – Percentage of each SARA fraction in Oural residue, for different residence times in the
vii
Table 27 – Heteroatoms composition of Oural residue for different residence times in the HDM and
HDS reactor. .......................................................................................................................................... 70
List of figures
Figure 1 – Micelle representation of the residues. (Pfeiffer & Saal, 1940).............................................. 3
Figure 2 – Possible structures for asphaltenes molecules: 1 – "continental" type ; 2 – "archipelago"
type (Merdrignac and Espinat, 2007). ..................................................................................................... 5
Figure 3 – Representation of a porphyrin complex with nickel. (Leprince, 2001) ................................... 6
Figure 4 – Hydrotreatment units in the context of a refinery. (Egorova, 2003) ....................................... 8
Figure 5 – Possible shapes for a hydrotreatment catalyst. (Ancheyta and Speight, 2007) .................... 9
Figure 6 – Reaction of sulfur removal from sulfide molecules. (Leprince, 2001) .................................. 10
Figure 7 – Reaction of sulfur removal from thiophenic molecules. (Leprince, 2001) ............................ 10
Figure 8 – Reaction of metal removal from porphyrinic molecules. (Leprince, 2001) ........................... 11
Figure 9 – Reaction of nitrogen removal from aromatic structures. (Leprince, 2001) ........................... 11
Figure 10 – Formation of coke caused by condensation of heavy radicals. (Furimsky and Massoth,
1999)...................................................................................................................................................... 12
Figure 11 – Different types of hydrotreating reactors. (Leprince, 2001) ............................................... 13
Figure 12 – HYVAHL-S hydrotreatment process, with two swing reactors. (ENSPM, 2005) ............... 14
Figure 13 – Different steps of a catalytic process: 1) diffusion of reactants from bulk solution; 2)
reactants internal diffusion; 3) reactants adsorption; 4) reaction; 5) products desorption; 6) products
internal diffusion; 7) products diffusion into bulk solution. ..................................................................... 16
Figure 14 – Diffusion regimes : 1) molecular ; 2) Knudsen and 3) surface (Leinekugel-le-Cocq, 2004).
............................................................................................................................................................... 17
Figure 15 – Collision between molecules with different sizes, as described by Fornasiero (Fornasiero
et al., 2005). ........................................................................................................................................... 20
Figure 16 – Schematic representation of the different lumps considered in the model. ....................... 27
Figure 17 – Discretization adopted for the spherical catalyst and the plug flow reactor. ...................... 39
Figure 18 – Possible method of dividing asphaltenes in 4 fractions for an Oural residue feedstock. ... 43
Figure 19 - Possible method of dividing asphaltenes in 4 fractions for a Buzurgan residue feedstock,
based on the overlap of 4 Lorentz distributions. ................................................................................... 44
Figure 20 – Effect of variations in the adsorption constant ka1 in the model simulated nitrogen removal
from: (a) resins; (b) asphaltenes. .......................................................................................................... 46
Figure 21 - Effect of variations in the kinetic constant k1 on the model simulated nickel removal from
asphaltenes. .......................................................................................................................................... 48
Figure 22 – Optimized model output vs. experimental data (Buzurgan) for: (a) nickel removal; (b)
vanadium removal. ................................................................................................................................ 50
Figure 23 - Optimized model output vs. experimental data (Buzurgan) for: (a) sulfur removal; (b)
nitrogen removal. ................................................................................................................................... 50
Figure 24 - Optimized model output vs. experimental data (Buzurgan) for: (a) total lump fractions; (b)
overall heteroatom removal. .................................................................................................................. 51
viii
Figure 25 – Model output vs. experimental data for Arabian Light residue, using the parameters
optimized for Buzurgan residue. (1) Lump fractions; (2) Overall heteroatom removal. ........................ 52
Figure 26 - Model output vs. experimental data for Djeno residue, using the parameters optimized for
Buzurgan residue. (1) Lump fractions; (2) Overall heteroatom removal. .............................................. 52
Figure 27 - Model output vs. experimental data for Oural residue, using the parameters optimized for
Buzurgan residue. (1) Lump fractions; (2) Overall heteroatom removal. .............................................. 53
Figure 26 – Effect of variations in the total asphaltenes repartition coefficients on the model simulated
asphaltenes fraction. (b) corresponds to a zoom of (a). ........................................................................ 54
Figure 27 – Effect of variations in the ns numbers on the model simulated vanadium removal from
asphaltenes. (b) corresponds to a zoom of (a)...................................................................................... 55
Figure 28 - Effect of variations in the ns numbers on the model simulated sulfur removal from
asphaltenes. (b) corresponds to a zoom of (a)...................................................................................... 55
Figure 29 – Effect of variations in the 4 distribution coefficients for sulfur in resins on the model
-2
-1
simulated total resins fraction using the kinetic constants: (a) k11 = 4.6x10 (b) k11 = 5x10 . ............. 56
Figure 30 – HDM +HDS model: optimized model output vs. experimental data (Buzurgan) for: (a)
nickel removal; (b) vanadium removal. .................................................................................................. 61
Figure 31 – HDM +HDS model: optimized model output vs. experimental data (Buzurgan) for: (a)
sulfur removal; (b) nitrogen removal. ..................................................................................................... 61
Figure 32 - HDM +HDS model: optimized model output vs. experimental data (Buzurgan) for: (a) total
lump fractions; (b) overall heteroatom removal. .................................................................................... 62
Figure 33 – HDM + HDS model: Model output vs. experimental data for Arabian Light residue, using
the parameters optimized for Buzurgan residue. (1) Lump fractions; (2) Overall heteroatom removal. 63
Figure 34 – HDM + HDS model: Model output vs. experimental data for Djeno residue, using the
parameters optimized for Buzurgan residue. (1) Lump fractions; (2) Overall heteroatom removal. ..... 63
Figure 35 – HDM + HDS model: Model output vs. experimental data for Oural residue, using the
parameters optimized for Buzurgan residue. (1) Lump fractions; (2) Overall heteroatom removal. ..... 64
Figure 36 – GPC curves for Buzurgan residue: (a) Asphaltenes ; (b) Resins. ..................................... 71
Figure 37 - GPC curves for Arabian Light residue: (a) Asphaltenes ; (b) Resins. ................................ 71
Figure 38 - GPC curves for Djeno residue: (a) Asphaltenes ; (b) Resins. ............................................ 72
Figure 39 - GPC curves for Buzurgan residue: (a) Asphaltenes ; (b) Resins. ...................................... 72
Figure 40 – HDM +HDS model: optimized model output vs. experimental data (Arabian Light) for: (a)
nickel removal; (b) vanadium removal. .................................................................................................. 73
Figure 41 - HDM +HDS model: optimized model output vs. experimental data (Arabian Light) for: (a)
sulfur removal; (b) nitrogen removal. ..................................................................................................... 73
total lump fractions; (b) overall heteroatom removal. ............................................................................ 74
Figure 43 – HDM +HDS model: optimized model output vs. experimental data (Djeno) for: (a) nickel
removal; (b) vanadium removal. ............................................................................................................ 74
Figure 44 – HDM +HDS model: optimized model output vs. experimental data (Djeno) for: (a) sulfur
removal; (b) nitrogen removal. .............................................................................................................. 75
ix
Figure 45 - HDM +HDS model: optimized model output vs. experimental data (Djeno) for: (a) total
Figure 46 – HDM +HDS model: optimized model output vs. experimental data (Oural) for: (a) nickel
removal; (b) vanadium removal. ............................................................................................................ 76
Figure 47 – HDM +HDS model: optimized model output vs. experimental data (Oural) for: (a) sulfur
removal; (b) nitrogen removal. .............................................................................................................. 76
Figure 48 - HDM +HDS model: optimized model output vs. experimental data (Djeno) for: (a) total
x
Nomenclature and abbreviations
Abbreviations
ABAN – Acid, basic, amphoteric, neutral
ASTM – American Society for Testing and Materials
CCR – Conradson carbon
CSTR – Continuous stirred tank reactor
FCC – Fluid catalytic cracking
GPC – Gel phase chromatography
HDAs – Asphaltenes deaggregation
HDCCR – Reduction of Conradson carbon level
HDM – Hydrodemetallization
HDN – Hydrodentirogenation
HDS – Hydrodesulfurization
HDT – Hydrotreatment
HPLC – High performance liquid chromatography
LHSV – Liquid hourly space velocity
LSFO – Low sulfur fuel oil
RFCC – Residue fluid catalytic cracking
SARA – Saturates, aromatics, resins, asphaltenes
SOL – Structure-Oriented Lumping
TBP – True boiling point
TLC - Thin layer chromatography
VGO – Vacuum gas oil
Nomenclature
-1
as – Specific surface [m ]
bk – Adsorption constant for the group k [m³/mol]
C i f – Molar concentration of lump i in the fluid phase [mol/m³]
C ip – Molar concentration of lump i in the solid phase (catalyst pellet) [mol/m³]
CT – Total molar concentration [mol/m³]
2
De ij – Effective diffusion coefficient between the lump i and j [m /s]
xi
2
Dij – Diffusion coefficient between the lump i and j [m /s]
Dp – Pore diameter
εi – Porosity of the extragranular phase
εp – Porosity of the intragranular phase
φi f
– Volume fraction of lump i in the fluid phase
φip
– Volume fraction of lump i in the solid phase (catalyst pellet)
γi
- Distribution coefficient of lump i
Ka – Adsorption constant of species a
k im – Mass transfer coefficient for the lump i in the fluid phase [m/s]
kB – Boltzmann constant
λ – Ratio between the molecules hydrodynamic radius and the pore radius
Λ - Knudsen number
Lc – Catalyst length
Mw i – Molecular weight of the molecule i
nc – Number of lumps considered in the model
nd – Number of lumps that deposit on the catalyst
N i – Molar flux of the lump i [mol / (m² s)]
N i0 – Molar flux of the unitary molecule [mol / (m² s)]
ns,i – Number of unitary segments in the molecule i
n s ,i – Average number of unitary segments for the group i
ρM – Density of the residue mixture [kg/m³]
qi – Concentration of the lump i in the adsorbed phase [mol/m³]
q mqx - Saturation concentration for the adsorbed phase [mol/m³]
Rc - Catalyst radius [m]
rp j – Repartition coefficient for the family j
2
ri – Reaction rate of the lump i [mol / (m s)]
r – Radial coordinate on the catalyst grain [m]
R – Ideal gas constant [J/(K.mol)]
Rh – Hydrodynamic radius of the molecule [m]
rp – Pore radius of the grain [m]
2
Sc – Catalyst surface area [m ]
τ
- Tortuosity
t – Time coordinate [s]
T – Absolute temperature [K]
θA – Occupied fraction of the surface with species A
ui – Linear velocity of species I [m/s]
µi – Chemical potential of the species i
xii
3
Vc – Volume of the catalyst grain [m ]
v0f - Axial velocity of the fluid inside a plug flow reactor [m/s]
Vm0 - Molecular volume of the reference molecule (H2) [m3/mol]
z – Axial coordinate on a plug flow reactor [m]
xiii
1
Introduction
th
In the end of the 20
century, concerns began to arise due to the depletion of the world's
petroleum reserves and increase of the price of crude oil. The refining trends those years were
focused on the recovery of valuable products from every single drop of petroleum to assure the
profitability of the process and to meet the world's demand on its most important energy source.
Nowadays, despite the ever growing number of proven petroleum reserves and the relative pricing
stability, the tendency remains in taking maximum advantage of the available resources. However, the
reasons for that rely now, on the one hand, on the continuous increase of demand in rapidly
developing countries like India or China. On the other hand, environmental regulations on petroleum
are becoming continuously stricter, particularly in the maximum allowed content of heteroatoms like
sulfur or metals. This way, the removal of these impurities is one of the main challenges in refining
nowadays.
In this context, hydrotreating (HDT) units are achieving ever growing relevance nowadays, and are
likely to play a major role in the refineries in a near future. Residue hydrotreatment units are of special
importance, since residues are the petroleum fractions with higher concentrations of impurities. The
removal of impurities in these units is governed by the properties of the initial feedstock and is carried
out according to the specifications set for the products. For example, in the case of petroleum residue
hydrotreatment, the production of a low sulfur fuel oil (LSFO) requires high HDS activity while the
production of a residue fluid catalytic cracking (RFCC) feedstock requires high HDM activity.
Developing valid kinetic models for residue HDT units that account for the reactivity of residues
from different origins will allow understanding and predicting the behavior of these feedstocks during a
hydrotreatment process. With this knowledge, it will be possible to develop models for a specific
residue hydrotreatment process and use them in the optimization of the operating conditions or in the
design of catalysts.
1
2
Bibliographic study
2.1
Introduction
As the subject of this study is focused on the hydrotreatment of petroleum residues, this chapter
describes the characteristics of residue feedstocks and products, as well as the state of the art on this
refining operation and the approaches used to develop mathematical models for the phenomena
involved.
The first topic of the chapter concerns the definition of a petroleum residue. Given its complexity,
one way of describing a residue mixture consists in separating it into fractions. Examples of available
fractioning methods are given in section 2.2.2. This topic also describes two residue fractions,
asphaltenes and resins, which were emphasized since these are the fractions containing the most
heteroatoms. Also, as presented in chapter 3, these are the two most relevant fractions used for the
feedstock description in the kinetic model. The types of compounds in which metals, sulfur and
nitrogen occur are also presented in this topic.
Afterwards, a topic is dedicated to describe the residue hydrotreatment processes. The most
commonly used catalysts are presented, as well as the main reactions occurring in the unit. The
available hydrotreatment technology is presented, with special emphasis on the fixed-bed reactor
operation since it was the one considered in this study and the most common worldwide.
Finally, the mathematical approaches used to model the phenomena involved on a catalytic
process like residue hydrotreatment are presented. This chapter also identifies the residue
hydrotreatment models developed in IFP.
2.2
Residue feedstocks
2.2.1
Introduction
Petroleum residues are a complex mixture resulting from atmospheric or vacuum distillation of
petroleum. Depending on the distillation cut point and the nature of the crude oil, residues can be
liquid or solid at room temperature. The chemical composition of a residue feedstock varies with the
geological origin of the crude oil. For example, an Oural residue feedstock has a greater concentration
of vanadium than a Djeno residue feedstock (Appendix 6.1).
Although their constituents occur naturally, residues are a product that results from petroleum
refining operations. When compared to the crude oil from which they were obtained, they have a
greater concentration in large molecules and in elements like sulfur, nitrogen and metals.
Contrary to lighter fractions of petroleum, in which the hydrocarbon structures are mainly aliphatic
(paraffins with some mono and di-naphtenes) or monoaromatics, heavy fractions include naphtenic
and aromatic structures with several alkylated cycles.
2
Pfeiffer (Pfeiffer & Saal, 1940) developed a residue representation based on the four SARA
fractions: asphaltenes, resins, aromatics and saturates (chapter 2.2.2), as depicted in Figure 1. In this
model, asphaltenes are represented in solution as having a colloidal structure. The solution
constituents are asphaltene micelles surrounded by resins, aromatics and saturates. It is a continuum
from the most aromatic, to the most aliphatic. In this model asphaltenes are the solute, resins the
dispersant, aromatics the solvent, and finally, saturates are the non-solvent.
Figure 1 – Micelle representation of the residues. (Pfeiffer & Saal, 1940)
2.2.2
Fractioning methods
Owing to the complexity of residues, it would not be feasible to describe all the molecules and
chemical functions present in the mixture. One method commonly used for this description consists of
fractioning the residue into lumps, whose composition varies according to the method used.
Examples of available methods for residue fractioning include distillation cut points, deasphalting,
SAR (saturates, aromatics, resins) or ABAN (acid, basic, amphoteric, neutral) fractioning and solubility
separation. Some of the techniques used are subject to international technical standards, certified by
associations like ASTM (American Society for Testing and Materials).
For distillation cut points, several methods are available, as the TBP (true boiling point, ASTM
D2892) and vacuum Poststill (ASTM D5236), or more recently, simulated distillation (ASTM D5887,
D6352). The boiling point can be directly related to the viscosity and density of the feedstock but not to
its molecular weight, since polar molecules can form colloidal structures that have boiling points higher
than non polar molecules with the same molecular weight.
Deasphalting (ASTM D893, D2006, D2007, D3279) is a method through which asphaltenes are
removed from the residue mixture by contacting it with a paraffin (asphaltenes non-solvent).
Deasphalting is required prior to applying the SAR fractioning method. The other fractions (saturates,
aromatics and resins) are generally separated using techniques like flash chromatography, HPLC
(high performance liquid chromatography) or TLC (thin layer chromatography) (Merdrignac and
Espinat, 2007). The combined method, including deasphalting and SAR fractioning, is referred to as
3
SARA (saturates, aromatics, resins and asphaltenes) method and served as a base for the feedstock
description in the model, as explained in chapter 3.2.2.
The ABAN method separates the residue mixture into acid, basic, amphoteric and neutral
(aromatics and saturates) fractions by means of a cationic resin and treatment with FeCl3 and silica.
Although several methods were developed based on the ABAN fractioning, their use is considered
long and laborious. (Merdrignac and Espinat, 2007)
2.2.3
Asphaltenes
Asphaltenes are the heaviest fraction of a residue and are concentrated in chemical functions
such as polycyclic aromatics, carboxylic acids, sulphides, sulphoxydes, etc, and elements like sulfur,
oxygen, nitrogen and metals .Although their definition remains ambiguous, they are usually defined as
the residue fraction that precipitates in a paraffinic liquid hydrocarbon like n-heptane or n-pentane, but
is soluble in benzene or aromatic naphtas. (Speight, 1999)
Asphaltene molecules are usually bonded by Van der Waals forces (Yen, 1972), leading to the
formation of aggregate structures. The occurrence of these aggregated structures makes it difficult to
correctly determine the asphaltenes molecular weight. Since the aggregation structure depends on the
environment conditions, the measured molecular weight depends on the analytical techniques used.
Molecular weight values published in the literature range from 500 g/mol for dissociated species to
100 000 g/mol for large aggregate molecules (Merdrignac et al., 2004).
Asphaltenes size is also difficult to determine, since some techniques measure the molecular size,
while others measure aggregates size. Recent works (Sheu, 2006) suggest a size as small as 5 to
6 nm.
Concerning the structure of asphaltenes, the two conformations in Figure 2 (Merdrignac et al.,
2004) are generally accepted. The continental type (Figure 2–1) considers a big aromatic core
surrounded by several paraffinic branches, while the archipelago type (Figure 2–2) considers small
aromatic regions linked by paraffinic branches. The adopted conformation is important, since it
determines the stability of the formed aggregates. For example, Murgich (Murgich, 2003) showed that
continental-type asphaltenes, with the big aromatic cores, aggregate more easily with each other.
4
Figure 2 – Possible structures for asphaltenes molecules: 1 – "continental" type ; 2 – "archipelago" type
(Merdrignac and Espinat, 2007).
2.2.4
Resins
The structure of resins is considered to be similar to that of asphaltenes (Gonzalez et al., 2006),
although resins are more aliphatic and less aromatic then asphaltenes. They can also be
distinguished, since resin molecules do not form aggregates and do not associate with asphaltenes
(Zhao and Shaw, 2007).
Concerning their chemical composition, resins are less concentrated in atoms like sulfur, nitrogen
or oxygen (Castex, 1985).
In the residue mixture, resins enable a single phase (chapter 2.2.1) and make asphaltenes soluble
(Andersen and Speight, 2001).
2.2.5
Metals
The removal of metals from residues is important for several reasons. Firstly, the catalysts used in
hydrotreating and other subsequent refining operations (ex. FCC) resist only to a low amount of
metals. Also, when the treated residue is used as LSFO, residual metals cause corrosion in furnaces
and promote dust formation in combustion gases (Leprince, 2001).
Residues are the petroleum fractions with the larger concentration of metals. The most abundant
are nickel and vanadium, with concentrations that may vary from 5 to 1500 ppm. They occur in
organometallic complexes that can be classified as porphyrins or non porphyrins. Amongst these
complexes, the most well known are the porphyrin type, in which the metals are bounded to four
nitrogen atoms, as shown in Figure 3 (Leprince, 2001).
5
Figure 3 – Representation of a porphyrin complex with nickel. (Leprince, 2001)
In general, the quantity of vanadium in the residues is higher than that of nickel. Also, according to
experimental results obtained for the hydrotreatment of a Maya crude oil (Ancheyta et al., 2003),
vanadium shows superior reactivity in demetallization than nickel. This occurs since, contrary to nickel
(Figure 3), vanadium in porphyrin structures is perpendicularly linked to oxygen atoms that strongly
interact with the catalyst surface.
2.2.6
Sulfur and nitrogen
Sulfur and nitrogen are the most abundant heteroatoms found in residues and their removal is
essential to both carry out refining operations like FCC and to meet environmental specifications.
Sulfur compounds in crude oil result from the presence, in the reservoir, of elemental sulfur that
slowly reacts with petroleum during its maturation stage (Speight, 1999). In petroleum residues, it is
the heteroatom found in higher quantities and its removal remains one of the main objectives of
hydrotreatment owing to the polluting potential of this element. In fact, sulfur is a poison for catalysts
used in vehicles and refining operations and there are strict laws limiting its content in fuels (10 wtppm
in 2009 for diesel and gasoline in the European Union (Web Article, 2009)), it.
Sulfur compounds present in petroleum residues have two chemical forms that determine their
reactivity: sulfide and thiophenic. For example, sulfides can be removed through thermal reactions,
whereas thiophenes need a catalytic reaction (Callejas and Martinez, 1999).
Nitrogen contents are also subject to strict environmental regulations, due to the risk of NOx
formation. Also, nitrogen compounds strongly adsorb in catalyst active sites, thus causing inhibition in
operations such as FCC.
Nitrogen is present in residues in two principal forms: non-basic heterocyclic structures (pyrrole
family) and basic heterocyclic compounds (pyridine family). The majority of nitrogen molecules have
very stable aromatic structures, thus being difficult to remove. For most molecules, it is necessary to
hydrogenate the aromatic structure before removing the nitrogen (Leprince, 2001).
6
2.3
Residue hydrotreatment units
2.3.1
Introduction
Residue hydrotreatment units are used in refineries to obtain low sulfur heavy oils or to pretreat
the feedstocks of other refining units like catalytic reforming, hydrocracking or FCC. These units aim to
remove impurities like sulfur, nitrogen and metals and also to reduce asphaltenes and other coke
precursors (Conradson carbon – CCR) content. The feedstocks to be treated are usually the residues
issued from atmospheric or vacuum distillation or mixtures of them.
Several technologies are available to carry out residue hydrotreatment as described in section
2.3.5. These vary according to the operation mode and can be classified as processes in fixed bed,
mobile bed, ebullated bed and slurry bed.
A fixed-bed hydrotreatment unit comprises two different sections optimized to perform
hydrodemetallization and hydrodesulfurization, respectively. These sections use different types of
catalyst, as explained in section 2.3.3. Industrially, the different reactors operate at temperatures
-1
between 360 and 420ºC, global space velocities (LHSV) of 0.15 to 0.30 h
and high hydrogen
pressures (100 to 200 bar), depending on the nature of feedstock, deactivation degree of the catalysts
and product specifications.
2.3.2
Hydrotreatment applications
Originally, in the 1950s, hydrotreatment units were used to remove sulfur from catalytic reformer
feedstocks. Nowadays, their use is extended to treat several streams in a refinery (kerosene, gas oil,
vacuum gas oil and residues), as depicted in Figure 4. These units allow to remove about 90% of
impurities such as sulfur, nitrogen, oxygen and metals, thus avoiding their detrimental effects on the
equipment, process catalysts and quality of the finished products. For example, a hydrotreatment unit
processing catalytic cracking feedstocks can prevent catalyst deactivation by nitrogen and metals and
allows to obtain lower sulfur contents in the cracked products.
Although the removal of sulfur, nitrogen and metals is the main goal of hydrotreatment, other
improvements can be obtained. Hydrogenation of unsaturated hydrocarbons also occurs and gives a
lighter product, with less tendency to form coke in downstream operations. Also, with the removal of
feedstock impurities, hydrotreatment allows enhancing the odor, color and oxidation stability of the
products.
7
Figure 4 – Hydrotreatment units in the context of a refinery. (Egorova, 2003)
2.3.3
Hydrotreatment catalysts
Hydrotreatment catalysts present an active phase finely dispersed on a support that should have a
large surface area to allow the deposit of a considerable amount of active phase precursors. Owing to
its importance, the support's study and development is a matter of great research effort. Currently, the
most widely used support is alumina-γ.
The size, shape, porosity and type of active phase of the catalyst vary according to the
hydrotreatment objective and the specific feedstock to be processed.
For residue hydrotreatment catalysts, catalysts with a CoMo active phase are generally more
effective for HDS, while NiMo catalysts are good for hydrogenation and HDN. (Ancheyta and Speight,
2007)
The acidity of residue hydrotreatment catalysts results on the presence of cracking reactions that
may occur directly or as a consequence of heteroatom removal reactions. A very high catalyst acidity
is not desired, due to the extensive coke formation.
8
The shape and size of the catalyst have to be chosen according to the properties of the feedstock,
the process technology and the type of reactor. For heavy feedstocks, special attention should be
given to the size and shape, due to the diffusional limitations of the large molecules, such as
asphaltenes. Figure 5 presents possible shapes for the hydrotreatment catalysts.
Figure 5 – Possible shapes for a hydrotreatment catalyst. (Ancheyta and Speight, 2007)
Usually the use of multilobe shaped catalyst, with big pores, small diameter and large external
area is preferred. Cooper et al. (Cooper et al., 1986) also showed that three-lobed catalysts show less
pressure drop than cylinder shaped catalyst.
2.3.4
Hydrotreatment reactions
The main reactions occurring in residue hydrotreatment units are hydrodemetallization (HDM),
hydrodesulfurization (HDS), hydrodenitrogenation (HDN), asphaltenes deaggregation (HDAs),
hydrodecarbonization (HDCCR, reduction of Conradson carbon level) and partial or total
hydrogenation of aromatic rings (Le Page et al., 1992). Typical performance ranges for these
reactions are listed in Table 1. The ranges presented are general and concern the performance of
different residue hydrotreatment units.
Table 1 – Typical performances of residue hydrotreatment reactions. (Leprince, 2001)
Reaction
Typical performance
HDM
80 – 99%
HDS
80 – 95%
HDN
20 – 60%
HDAs
50 – 90%
HDCCR
50 – 80%
9
2.3.4.1
HDS
As referred in section 2.2.6, sulfur compounds can be found in residues as sulfide and thiophenic
compounds.
Sulfides are partly found in the asphaltenes in the form of condensed naphtheno-aromatic rings
connected by sulfur bridges (Leprince, 2001). These compounds can be dissociated thermally or
catalytically, according to the reaction presented in Figure 6.
Figure 6 – Reaction of sulfur removal from sulfide molecules. (Leprince, 2001)
Thiophenic compounds are only decomposed catalytically. As depicted in Figure 7, the
hydrogenolysis of the C-S bond can be or not preceded by an intermediate hydrogenation step.
Figure 7 – Reaction of sulfur removal from thiophenic molecules. (Leprince, 2001)
2.3.4.2
HDM
Hydrodemetallization reactions in porphyrins (section 2.2.5) occur with an intermediate
hydrogenation step as shown in Figure 8. Metals are removed in the form of metallic sulphides that
deposit on the catalyst pores.
10
Figure 8 – Reaction of metal removal from porphyrinic molecules. (Leprince, 2001)
The sulphide deposits (Ni and V) have two distinct effects on the catalyst activity. On the one
hand, they have a catalytic effect themselves but they also have a deactivation effect, since they
gradually plug the catalyst pores and make them less accessible to reactants.
The types of hydrodemetallization reactions occurring in non porphyrinic compounds are
unknown.
2.3.4.3
HDN
As referred in section 2.2.6, the nitrogen containing compounds present in residues have very
stable aromatic structures. Therefore, the hydrogenolysis of the C-N bond is preceded by an aromatic
ring hydrogenation step, as shown in Figure 9.
Figure 9 – Reaction of nitrogen removal from aromatic structures. (Leprince, 2001)
2.3.4.4
Cracking reactions
In residue feedstocks processing, cracking reactions are important since they produce light and
valuable products (gases, gasoline, gas oils and vacuum distillates). Although cracking reactions are
11
not the main objective of hydrotreatment, they also occur to some extent (directly or as byproduct of a
heteroatom removal reaction).
Conversion into lighter fractions can occur in two ways. If only hydrogenation and hydrogenolysis
occurs, the obtained products have a molecular weight only slightly modified but their boiling
temperature is substantially lower. The lighter fractions can also be obtained by splitting C-C bonds by
catalytic hydrocracking or thermal cracking.
2.3.4.5
Condensation reactions and coke formation
Coke formation occurs with all hydroprocessing feedstocks employed and increases with the
molecular weight and boiling range of the feedstock.
The mechanism for coke formation is not yet completely understood but it is common to consider
that it originates from the condensation of heavy radicals formed during cracking (Furimsky and
Massoth, 1999), as shown in Figure 10.
Figure 10 – Formation of coke caused by condensation of heavy radicals. (Furimsky and Massoth, 1999)
2.3.5
Hydrotreatment technology
Hydrotreatment processes vary according to the method of feedstock introduction, the
arrangement of the catalytic beds and the mode of operation of the reactors.
Commercially available hydrotreatment reactors can be classified in four main groups (Figure 11):
1) fixed-bed, 2) moving-bed, 3) ebullating-bed and 4) slurry-bed.
For residue hydrotreatment, the major licensors are AXENS, Chevron, Exxon and UOP/Unocal.
(Leprince, 2001)
12
Figure 11 – Different types of hydrotreating reactors. (Leprince, 2001)
Since the hydrotreatment model considered in this study was developed for a fixed-bed reactor
and since it is the dominant technology for the residues hydrotreatment, only this type will be
described in greater detail below.
2.3.5.1
Fix-bed reactor
The fixed-bed hydrotreating reactor is schematically depicted in Figure 11-1. As it can be seen in
this representation, the feedstock previously mixed with the H2 stream, enters the top of the reactor,
trickles through a catalytic bed, where chemical transformations take place, and leaves at the bottom.
The downflow operation limits the formation of small particles resulting from the catalyst mechanical
degradation. However, this type of flow may lead to liquid preferential pathways and dead volumes.
Industrially, the reactor is optimized to operate as close as possible to a plug flow reactor.
Owing to the low space velocities and high flow rates observed, catalyst volumes are large, forcing
the use of the largest reactor diameter possible (up to 5m), to minimize pressure drop. As a
consequence, small linear velocities are observed (0.2 to 0.5 cm/s (Leprince, 2001)), thus requiring an
efficient distribution system, to avoid poorly irrigated zones that can quick plug, leading to an increase
in pressure drop.
Since the reactions occurring inside the reactor are exothermic, a temperature profile rises from
the top to the bottom. Temperature in the process is controlled by gas injections (quenches) on flow
lines between reactors or between two catalyst beds
One of the problems associated with the conventional fix-bed operation is that after a certain
period, the catalyst at the top of the bed will have its pores completely plugged, resulting in a loss of
catalytic activity. As a consequence, the entire reactor would have to be shut down, in order to replace
the catalyst.
Some technologies have been proposed to avoid the above mentioned problems, such as the
HYVAHL-S process developed by IFP. This process uses a swing reactor system, consisting of two
reactors that can be switched alternatively in operation. The swing reactors are followed by a series of
13
fixed-bed reactors, as shown in Figure 12. The HYVAHL-S process allows to remove up to 80% of the
metals of a crude oil containing up to 250-400 ppm of vanadium and nickel, operating continuously for
a minimum of one year (Kressmann et al., 1998).
Figure 12 – HYVAHL-S hydrotreatment process, with two swing reactors. (ENSPM, 2005)
2.3.5.2
Other types of reactors
The main difference between the fixed-bed and other types of hydrotreatment reactors is that the
latter present an inlet of fresh catalyst at the top of the reactor, except for the slurry-bed reactor, in
which fresh catalyst is introduced through the bottom, mixed with the reactor feedstock (Figure 11).
The choice of the type of reactor to be used is based on the characteristics of the feedstock (for
example the total metal content) and the product quality required. Table 2 gives examples of product
yields and quality from the different processes applied to a heavy Safaniya vacuum residue (Leprince,
2001).
Table 2 – Comparison of different hydrotreating technologies. (Leprince, 2001)
Fixed bed
Moving bed
Ebullating bed
Number of units (1993)
34
2
6
Maximum Ni + V content in feed (wppm)
120-500*
500-700
> 700
Tolerance for impurities
Low
Low
Average
Max. conversion of 550ºC (wt%)
60-70
60-70
80
Distillate quality
Good
Good
Good
Fuel oil stability
Yes
Yes
Borderline
Unit operability
Good
Difficult
Difficult
* Swing reactor
14
2.3.5.3
Operating conditions
The severity of the operating conditions is determined by the boiling point and the impurities
content of the feedstock. Higher boiling points and elevated impurities contents require the use of
higher temperatures and pressures.
Temperature in hydrotreatment units may rise up to 420ºC. Higher temperatures are avoided,
since above these values aromatics polymerization and condensation become more significant,
resulting in a greater tendency to form coke. This effect is more important for feedstocks with high
asphaltene contents. High temperatures also result in increased pressure drops, catalyst deactivation
and product instability.
High hydrogen pressures are required to hydrogenate the radicals formed during cracking
reactions (section 2.3.4.4) and thus avoid polycondensation and coke formation. The operation
pressure does not affect thermal cracking reactions significantly (Leprince, 2001).
Table 3 presents typical values for the operating conditions of hydrotreating units.
Table 3 – Typical operating conditions of hydrotreating units. (Le Page et al., 1992)
2.4
-1
Space velocity
0.2 to 0.5 h
Pressure
100 to 200 bar
Hydrogen recycle rate
500 to 1200 m³ (STP) / m³ feed
Temperature
360 to 420 ºC
Conclusions
The state of the art presented in this chapter illustrates that residues are object of continuous
study and many publications exist on this subject. However, publications that try to explain the
different reactivity of residues from different origins are very rare if not inexistent. Instead, reactivity is
studied for a specific oil and most works are just an analysis of how reactivity changes with different
operating conditions.
As seen in this chapter, many technologies are available to carry out residue hydrotreatment but
the operating conditions depend on the specific residue used. Experimentally optimizing these
operating conditions is not feasible, since it would be a time-consuming task, limited by economic
constraints and subject to the availability of the different feedstocks. Thus, developing a model for a
specific process accounting for the reactivity of residues with different origins could be of great value.
If the model correctly accounted for the catalyst description, it could also be used as a tool for catalyst
design.
15
2.5
Modeling
2.5.1
Introduction
In the following chapters, a description is made of the approaches commonly used to model the
phenomena occurring in a catalytic process like hydrotreatment.
A first chapter (chapter 2.5.2) concerns the reactor hydrodynamics and presents the different
models used to determine the fluid velocity and flow profiles inside the reactor. The subsequent
chapters relate to the processes occurring near or inside the catalyst. A catalytic process results from
the coupling of several physical and chemical processes (Figure 13): 1) diffusion of the reactants to
the catalyst surface; 2) internal diffusion in the catalyst; 3) reactants adsorption in active sites; 4)
reaction; 5) product desorption; 6) internal diffusion of the products and 7) their external diffusion into
the fluid phase. The global reaction rate depends on all of these steps and the model is more or less
detailed depending on how many of these phenomena are considered. The main phenomena
reviewed in this chapter are those occurring inside the catalyst (steps 2, 3, 4, 5 and 6 in Figure 13)
and are described in chapters 2.5.3 to 2.5.6.
Figure 13 – Different steps of a catalytic process: 1) diffusion of reactants from bulk solution; 2) reactants
internal diffusion; 3) reactants adsorption; 4) reaction; 5) products desorption; 6) products internal
diffusion; 7) products diffusion into bulk solution.
In a final chapter (chapter 2.5.7), the residue hydrotreatment models previously developed in IFP
are presented.
The approaches used to account for the energy balances are not in this bibliographic study, since
the studied model comprises an isothermal reactor (hypothesis H10, chapter 3.2.1).
16
2.5.2
Hydrodynamics
Heterogeneous catalysis reactors can be of several types, although the most commonly used are
of the plug flow type, consisting of one or several tubes (Lemos et al., 2002). The flow in these
reactors is generally described through convective movements and axial dispersion. A plug flow
reactor with dispersion can be approximately described as a series of CSTR (continuous stirred tank
reactor) reactors (Froment and Bischoff, 1990).
The models commonly used to describe the hydrodynamics of these reactors vary according to
the phases considered. Since residue hydrotreatment involves the presence of the residue (liquid
phase), hydrogen (gas phase) and the catalyst (solid phase), a triphasic heterogeneous model, where
the resistances in the solid/liquid and liquid/gas interfaces are considered, would be more rigorous.
However, simplifications are generally made and different pseudo-homogeneous models can be used:
•
Single phase models that consider equilibrium between all the phases, thus corresponding
to a homogeneous model;
•
Two phase models, considering a single fluid phase where gas and liquid are in
equilibrium. These models consider the resistance between the single fluid phase and the
solid phase.
The flow profile of a fixed bed reactor is normally described as a plug flow with dispersion (Iliuta et
al., 2006). The dispersion represents the deviation to the ideal plug flow.
2.5.3
Intragranular diffusion
The diffusion regime observed inside the catalyst depends on the pore size and the mean free
path of the molecules. Figure 14 depicts the different types of diffusion that can be observed in a
catalytic process: 1) molecular diffusion; 2) Knudsen diffusion and 3) surface diffusion. Depending on
the diffusion regime, different expressions are used to determine the diffusion coefficients.
Figure 14 – Diffusion regimes : 1) molecular ; 2) Knudsen and 3) surface (Leinekugel-le-Cocq, 2004).
17
The diffusion regime observed can be determined by means of the Knudsen number,
relates the mean free path of the molecules,
Λ=
λ
dp
λ,
Λ , which
and the pore diameter:
(1) with
λ=
M
ρ 2πσ 2
(2)
Molecular diffusion (Figure 14-1) occurs when collisions between molecules take place, rather
than collisions between molecules and pore walls. This situation occurs when the mean free path of
the molecules is small (Knudsen number less than 1), compared to the pore diameter. In this case, the
diffusion coefficients are obtained using the Stokes-Einstein correlation:
D0 =
k B .T
6.π .υ .r
(3)
When the mean free path of the molecules is approximately the same as the size of pores
(Knudsen number close to 1), collisions between molecules and the pore walls become important and
the diffusion regime is referred to as Knudsen diffusion (Figure 14-2). In this case, for gas, the
diffusion constant can be calculated according to the kinetic theory of gases (Froment and Bischoff,
1990):
4  2.R.T 
D0 = R g 

3  π .M 
0.5
(4)
Another possible diffusion regime is referred as configurational or surface diffusion (Figure 14-3).
This type of diffusion occurs when molecules adsorb on the pore surface and hop from one site to
another through interactions between the surface and molecules (Leinekugel-le-Cocq, 2004).
The diffusion coefficients in equations (3) and (4) are not effective coefficients, since they do not
consider the geometry of the catalyst pore. To obtain the effective diffusion coefficients, the porosity
and tortuosity of the pore have to be taken into account by using the following relation (Froment and
Bischoff, 1990):
De = D0
ε
τ
(5)
.
As described in chapter 2.3.3, the two sections of a hydrotreatment unit (HDM and HDS) differ in
the type of catalyst used. The large pored catalyst of the HDM section favors a molecular type of
diffusion, while the smaller pores of the HDS catalyst favor a Knudsen type of diffusion (LeLannic,
2006). Nevertheless, owing to the large size of the molecules (asphaltenes), diffusion limitations
should not be neglected even for the HDM section where molecular diffusion occurs preferentially
(Tayakout, 2006).
18
2.5.3.1
Fick's first law
In 1855, Adolf Fick proposed an empirical relation between the diffusive flux and the concentration
gradient by postulating that the flux goes from regions of high concentration to regions of low
concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative).
This relation is known as Fick's first law and can be written as follows (Froment and Bischoff, 1990):
N A = −D AB
dC A
dz
(6)
Fick’s law was later demonstrated by Einstein, who used his Brownian motion work to prove it as
an exact law.
Equation (6) is the most simple way to explicit the intragranular diffusion and can be used
rigorously for binary mixtures. For mixtures of more components, with low concentrations in an inert, it
is not an exact law but serves as a good approximation.
Fick's first law does not take into account the phenomena caused by electrostatic or centrifuge
forces. It is also not appropriate for concentrated environments (like crude oils) where friction between
all species exists and is not taken into account. Owing to this limitation, more elaborate models are
required, considering the collisions between all the different molecules present in the feedstocks.
2.5.3.2
Stefan-Maxwell equations
When compared to Fick's first law, the Stefan-Maxwell equations are considered as a more
general and convenient way of describing diffusion (Krishna and Wesselingh, 1997), since they take
into account thermodynamic non idealities and the influence of external forces.
The Stefan-Maxwell equations are derived from heat balances of molecules collisions and can be
written as follows:
n
− ∇T µ i = R.T ∑
j =1
j ≠1
x j (u i − u j )
Dij
Ni =u i Ci
⇔
−
n x N − x N
xi
j
i
i
j
∇T µ i = ∑
, i = 1,...., n
R.T
c t Dij
j =1
(7)
j ≠1
Recently, Fornasiero (Fornasiero et al., 2005) adapted the above equations to a system where
molecules have very different sizes.
Fornasiero's formalism thus corresponds to an adaptation of equation (7), in which the collisions
between molecules are supposed to occur between equivalent volumes. This situation is depicted in
Figure 15, where a molecule B is divided into segment of the same of the unit molecule, Molecule A. As
19
seen in this figure, 18 molecules of A would be needed to collide with B. This number is called the
number of segments (ns) of molecule B.
Figure 15 – Collision between molecules with different sizes, as described by Fornasiero (Fornasiero et
al., 2005).
To mathematically account for the collision occurring by volume equivalence, Fornasiero
introduces the relation between volume fraction and molar concentration, equation (8), and between
the flux Ni of a molecule and the flux of the unitary molecule, equation (9). In Figure 15, the molecule A,
with only one fragment, corresponds to the unitary molecule.
φi = Ci ns ,iVm0
Ni0 = ns ,i Ni
(8)
(9)
Replacing equations (8) and (9) in (7), relation (10) is obtained.
−
φi
∇T µ i =
0
R.T .ns ,i .Vm
1
CT
nc
∑
j =1
j ≠1
φ j Ni 0 − φi N j 0
Dij
0
, i = 1,.nc
(10)
This formulation of the diffusion law is particularly useful when molecules of greatly different sizes
are present, as in the case of petroleum residue feedstocks and products (Fornasiero et al., 2005).
Equation (10) may be rewritten in terms of measurable variables by introducing the equation for
the chemical potential gradient, in which the fluid is considered as ideal (hypothesis H1, chapter 3.2.1)
and the total concentration CT is considered to be constant:
20
µ i = µ iref + RT ln
CiP
∇φ p
⇔ ∇µ i = RT ln CiP = RT . pi
CT
φi
(11)
By replacing equation (11) in (10), the flux equation (12) is obtained. This equation may also be
written in the matrix form (13).
∇φi
1
=
0
ns ,i .Vm CT
1

  1 nc 1 p
p
 ϑ 0n ∇φ1  
∑ φk
si

  CT kk =≠11 D1k
M

 
M

 

=
M
M

 
M

 
M

  1 p
1
− φnc −1
 1
p 
Dnc −11
∇φnc −1   CT
ϑ 0n


snc
−
1


nc
∑
−
φ j N i 0 − φi N j 0
Dij
j =1
j ≠1
0
, i = 1,.nc
(12)

0
  N1 
 M 


M


O
M
 M 


O
M



M


1 nc 1
L L
φ jp   0 
∑
CT k =1 Dnc −1 j  Nnc −1 

k ≠nc
1 p 1
φ1
L L
CT
D12
O
L
−
1 p 1
φ1
CT
D1nc −1
(13)
These equations must take into account the volume constraint:
nc
∑φ
i
p
=1
(14)
i =1
The use of Stefan-Maxwell equation to describe intragranular diffusion in a residue hydrotreatment
kinetic model is described in literature by C. Ferreira (Ferreira et al., 2009).
2.5.4
Adsorption
Chemical adsorption and desorption were first described by Langmuir, who built a model based on
simple assumptions:
•
The adsorbed species are bounded to the active sites and have no mobility;
•
Each active site is occupied by only one specie;
•
The heat of adsorption does not depend on the adsorbed quantity.
Taking into account these assumptions, the adsorption equilibrium is represented by the following
relation for the occupied fraction of the surface, θA:
21
θA =
K a PA
1 + K a PA
(15)
Equation (15) can be generalized for the case of competitive adsorption between i species, when
each specie occupies only one active site:
θA =
K a PA
1 + ∑ K i Pi
(16)
i
Owing to the simplicity of the Langmuir formulation, it is the law most commonly used to describe
adsorption in kinetic models.
2.5.5
Deactivation
Several different approaches are suggested in literature to model the deactivation of
hydrotreatment catalysts. In this chapter some of these models are presented.
The Shell RESIDS model (Oelderik et al., 1989) was developed to predict the deactivation in
CoMo/AL2O3 and NiMo/Al2O3 residue hydrotreatment HDM and HDS catalysts. The deactivation
phenomena are assumed to be due to pore plugging by metal deposition and the model does not take
into account the initial coke build-up in the operation. Since the model assumes that coke formation
reaches a stationary level, it cannot be used to simulate the operation when low hydrogen pressures
are present.
Another pore plugging model considering plugging by metal deposition was developed by
Oyekunle (Oyekunle and Hughes, 1987). The model intended to show that the catalyst life can be
improved by choosing an appropriate pore structure.
Takatsuka
(Takatsuka
et
al.,
1996)
developed
a
deactivation
model
for
residue
hydrodesulfurization considering that the deactivation occurs by coke deposition on active sites, in the
initial stages of the operation. Pore plugging by metal deposition is also taken into account. Metal and
coke deposition are considered to affect the catalyst surface area and the effective diffusivity of the
feedstock molecules in the catalyst pores.
Corella (Corella et al., 1988) developed a different model in which deactivation is considered to
occur only due to coke formation.
All the approaches presented successfully describe the catalyst deactivation phenomena, in
agreement with experimental data. However, this might be due to the many parameters used in these
models, which can be changed to correctly fit experimental data.
22
2.5.6
Kinetics and feedstock description
As referred in chapter 2.2, residues are a complex mixture with a chemical composition that is not
accurately determined by analytical techniques. For that reason, it is not possible to incorporate a
description of all the compounds in a model. Therefore, the development of a kinetic model for residue
hydrotreatment involves the choice of a method to describe the feedstock and the obtained model
depends on that option. Several alternatives for the residue feedstock description are presented in the
literature and their choice depends on the objective of the model.
One possible method used to represent the feedstock involves grouping the compounds into
lumps that represent a vast number of compounds sharing a common property. For example, the
model can be developed with a feedstock description based on the 4 SARA fractions (Haulle and
Kressmann, 2002; LeLannic and Guibard, 2005). Rodriguez (Rodriguez and Ancheyta, 2004)
developed a kinetic model for vacuum gas oil hydrotreatment where the reaction rates are based on
the concentration of the heteroatoms. In this case, the lumping consists on grouping all the molecules
that contain each heteroatom.
Kinetic models can also be developed by using correlations based on experimental tendencies
(Oyekunle and Kalejaiye, 2003). In this case, the physical phenomena are not incorporated in the
model, thus resulting in a limited applicability. The model output can only be considered valid if the
same experimental conditions are used and it is not possible to extrapolate the results for other
operating condition and different feedstocks.
Another approach for the feedstock description is based on stochastic reconstruction. For
example, Verstraete (Verstraete et al., 2008) recently used these methods to describe an Arabian light
vacuum residue. The obtained properties for the resins, saturates and aromatics were in good
agreement with experimental data but for the asphaltenes, the reconstruction underestimated the
heaviest ones. Another project involving stochastic reconstruction (Neurock et al., 1989) considered a
distribution of 10.000 different asphaltene structures. The kinetic model resulting from this distribution
is obtained by using random sampling algorithms (Monte Carlo method) and considering 3 possible
reactions, alkylation and hydrogenation of naphtenes and aromatics.
Jaffe (Jaffe et al., 2005) proposed another feedstock description method, based on a concept
called SOL (Structure-Oriented Lumping). In this method, the molecules are reconstructed using a
limited number of elementary structures. The simulated assembly of molecules is considered
satisfactory if it has the same physical and chemical properties as those experimentally measured for
the residue.
Another method to develop kinetic models is by using artificial neural networks. Bellos (Bellos et
al., 2005) showed that good agreement between experimental data and model output can be obtained
for a HDS unit using little experimental input. The obtained results can be improved by updating the
model with steady-state operation data of the industrial unit.
23
2.5.7
IFP models
2.5.7.1
THERMIDOR
THERMIDOR (Thermal Monitoring for Isoperformance Desulfurization of Residua) is a residue
hydrotreatment deactivation model developed in IFP that aims to simulate the HYVAHL process
(chapter 2.3.5.1) operation along time, taking into account the associations of guard bed materials and
catalysts including particle size, activity, pore size and shape grading effects (Toulhoat et al., 2005).
The model considers a plug flow reactor with two phases, a pseudo homogeneous fluid (hydrogen
gas and crude oil) and the catalyst, in non stationary state. Heat balances are considered in a pseudo
steady state, with thermal equilibrium between solid, liquid and gas phases at any position and time,
and heat transfer occurring only by convection through the liquid. The reactor can be chosen to
operate at constant temperature (isothermal operation) or constant performance (adiabatic operation,
with temperature variation) as in industrial operation mode.
The intragranular diffusion phenomena are described by Fick's first law (chapter 2.5.3.1). Catalyst
deactivation by pore plugging is considered through two different mechanisms: coke formation and
metal deposition.
The feedstock representation is based on a set of lumped components, with a certain reactivity
and different chemical properties. The reaction kinetics is described by a pseudo LangmuirHinshelwood formalism, with first order reactions inhibited by the adsorption of asphaltenes.
2.5.7.2
Model for the HDM section
Haulle (Haulle, 2002) developed a kinetic model for the HDM section of the hydrotreatment
process.
In the model, the flow pattern is assumed to be that of a plug flow reactor and the operating
conditions are fixed at a temperature of 380ºC and a pressure of 150 bar. The model is homogenous,
considering a single phase that includes the hydrogen gas, the residue and the solid catalyst. Since
only one phase is considered, intragranular diffusion was not considered.
The feedstock description is based on the four SARA fractions (chapter 2.2.2), and a temperature
cut at 520°C, that splits aromatics in two fraction s.
Based on the feedstock description, the kinetic model considers 12 reactions, including
hydrocracking, hydrodesulfurization and hydrodemetallization. The reaction rates are described
according to the Langmuir-Hinshelwood formalism and the reactions are considered to be irreversible,
of first order. In this model, the deactivation caused by coke is considered negligible.
The model predictions for the HDM section performance are considered acceptable for a Middle
East residue. However, for other types of residues, the obtained predictions are not so satisfactory.
24
2.5.7.3
Model for the HDS section
LeLannic (LeLannic, 2006) developed a kinetic model for the HDS section of the hydrotreatment
process, based on the THERMIDOR model (chapter 2.5.7.1).
The model considers two phases, a pseudo homogeneous fluid (hydrogen gas and residue) and
the catalyst. Intragranular diffusion effects are taken into account.
The feedstock description method is the same used by Haulle for the HDM section but also
includes a deposits lump and considers the 520ºC temperature cut for both aromatics and resins.
The performances of this section are simulated with the kinetic model implemented in
THERMIDOR. The obtained results were only validated for Middle East residue feedstocks.
2.6
Conclusions
The state of the art presented in this chapter illustrates that residues are object of continuous
study and many publications exist on this subject. However, there are no publications that
demonstrate the characteristics explaining the different hydrotreatment reactivity of residues from
different origins. Instead, reactivity is studied for a specific oil and most works are just an analysis of
how reactivity changes with different operating conditions.
As seen in this chapter, many technologies are available to carry out residue hydrotreatment but
the operating conditions depend on the specific residue used. Experimentally optimizing these
operating conditions is a time-taking task that has to be carried out for all the feedstocks treated in a
refinery. Thus, developing a model accounting for the reactivity of residues with different origins could
be of great value.
The objective being set to study the differences in reactivity for residues with different origins, the
kinetic model should be based on the mathematical description of the phenomena involved and not in
the extrapolation of experimental results. Otherwise, the model could only be applied to a specific
feedstock, processed at specific operating conditions.
The use of Stefan-Maxwell equation to describe intragranular diffusion in a residue hydrotreatment
is the most adequate method of describing the diffusion for a complex mixture like residues. Its
incorporation on a kinetic model can provide new insights on the reactivity of residues with different
origins.
25
3
3.1
Model description
Introduction
In this chapter, the model development is described. Firstly, the main assumptions in which the
model is based are presented. Then, a chapter is dedicated to explain the methodology used to
describe the residue feedstock and products, followed by a chapter containing the kinetic network
description along with its inherent assumptions. In this topic, all possible reactions considered in the
model are listed, as well as the corresponding kinetic constants.
Subsequently, the phenomena occurring in the catalyst extragranular phase are described. This
involves the choice of the hydrodynamic model for the reactor and corresponding mass balances. The
mass balances inside the catalyst are described in the next chapter, "Intragranular phenomena”. This
chapter also contains topics on adsorption and diffusion, as well as deactivation phenomena.
Afterwards, since the model is presented only for the HDM reactor, an outline is given on the
modifications to introduce when considering both the HDM and HDS sections.
Finally, an overview of the algorithms used to solve differential equations and to estimate the
model parameters is presented.
3.2
Model Description
The model presented in this chapter was developed in the context of the PhD thesis of C. Ferreira.
It aimed to simulate the performances of a petroleum residue hydrotreating unit. More precisely, the
thesis objective was to develop a model for both catalytic sections of an industrial unit (HDM+HDS)
using vacuum residue feedstocks from different geographic and geochemical origin. Ultimately, the
developed model may provide insights upon residue feedstock reactivity.
The model was developed by coupling two simplified models, each highlighting the description of
a specific phenomenon. In a first model, the intragranular diffusion was emphasized, using the StefanMaxwell equations coupled with Fornasiero’s formalism. In the other model, the intragranular diffusion
phenomena were not considered and emphasis was given to the feedstock description, with a larger
set of lumps being considered, resulting in a more complex kinetic network.
These two models were coupled, resulting on a model that highlights both the intragranular
diffusion phenomena and the kinetic network.
26
3.2.1
Model hypothesis
The model was developed under the following hypothesis:
•
H1 – The liquid mixture has ideal behavior;
•
H2 – The molar volumes are equal in the liquid phase and in the adsorbed phase;
•
H3 – The heat of adsorption is equal for all lumps;
•
H4 – Adsorption equilibrium is represented by the generalized Langmuir model and local
equilibrium is assumed along the whole radius;
•
H5 – Chemical reactions only occur in the adsorbed phase;
•
H6 – Diffusion in the catalyst is described by the Stefan-Maxwell equations, coupled with
Fornasiero’s formalism (Fornasiero et al., 2005);
•
H7 – The external film resistance in the catalyst is described as a linear driving force;
•
H8 – The kinetic rates do not depend on the hydrogen concentration, since it is in large
excess in the reactor;
3.2.2
•
H9 – The catalyst particles are considered to be spherical;
•
H10 – The system is considered to be isothermal.
Feedstock description
Since the residue feedstocks are mixtures with complex chemical composition containing
thousands of species, the different compounds are usually lumped into families that share a certain
property. The lumps considered in this model are based on four families (Saturates, Asphaltenes,
Resins and Aromatics) obtained by liquid chromatography (chapter 2.2.2). This distribution is known
as SARA.
Figure 16 illustrates the different lumps used to represent the residue feedstock and the reaction
products, as well as NH3, H2S and coke.
Asp
Res
AspNi
ResNi
AspV
ResV
AspN
ResN
AspS
ResS
AspNiN
ResNiN
AspNiS
ResNiS
AspVN
ResVN
a2s1
a2s2
aromaticity
x4
a1s1
a2s2
aliphaticity
Aro
AroS
Sat
NH3
H2S
coke
Figure 16 – Schematic representation of the different lumps considered in the model.
27
As depicted in Figure 16, 9 lumps are considered to describe the asphaltenes and the resins: the
simple ones, the ones containing metals, the ones containing nitrogen or sulfur and the ones that have
combinations of a metal and nitrogen or sulfur. Each of these lumps (9 for the resins and 9 for the
asphaltenes) is further subdivided into 4 fractions, which consider different levels of aliphaticity and
aromaticity.
For the aromatics, experimental data evidences that only sulfur atoms are present in significant
quantities. Therefore, the model only takes into account 2 lumps: the simple aromatics and the
aromatics containing sulfur. On the other hand, for the saturates, only the simple ones are considered.
The other lumps considered in the model are the reaction products: hydrogen sulfur (H2S),
ammonia (NH3) and coke.
Even though hydrogen has a major role in the hydrotreating process, this compound was not
considered in the model, since it is in large excess in the reactor (hypothesis H8, chapter 3.2.1). Thus,
the concentration of hydrogen is incorporated in the hydrotreating kinetic constants.
In total, the considered lumping scheme contains 77 lumps.
3.2.3
Kinetic network
Based on the lumping scheme presented in chapter 3.2.2, the model considers demetallization,
desulfurization, denitrogenation and cracking reactions, as well as coke formation.
The establishment of the kinetic network was based on the following assumptions:
•
For the demetallization reactions, the aliphaticity and aromaticity level, as well as the amount
of sulfur and nitrogen, is not affected by the metal removal;
•
Two types of desulfurization reactions are considered: with and without the removal of a
saturate. For the desulfurization with saturate removal, the aliphaticity level of the compound
decreases;
•
Denitrogenation reactions only occur in compounds without metals;
•
Cracking reactions lead to a decrease in the level of aliphaticity or aromaticity of the
compound. Asphaltenes of the type a1s1 (Figure 16) may also be cracked, leading to the
formation of a2s2 resins. Besides this, a cracking reaction in which resins are transformed in
aromatics and saturates is also considered;
•
Asphaltenes cracking reactions only occur for simple asphaltenes and the ones with metals;
•
Coke is formed through asphaltenes and resins both without metals.
The resulting kinetic network considers 148 reactions (Table 4). Therefore, considering a different
kinetic constant for each reaction would lead to a very large amount of model parameters. To avoid
this, only 17 kinetic constants are considered and each of them represents a group of reactions, as
shown in Table 4. For example, the kinetic constant 5 represents the denitrogenation reactions of
asphaltenes with nitrogen of the four fractions (table of Figure 16).
28
Table 4 – Kinetic network describing all the possible reactions considered in the model.
Kinetic constant
Reaction
Number of reactions
1
AspNi Asp + Ni
3 x 4 = 12
2
AspV Asp + V
3 x 4 = 12
3
AspS ansm Asp ansm + H2S n = 1,2 ; m = 1,2
3 x 4 = 12
4
AspS ans2 Asp ans1 + H2S + Sat n = 1,2
3x2=6
5
AspN Asp + NH3
4
6
Asp ans2 –> Asp ans1 + Sat n = 1,2
3x2=6
7
Asp a2sm Asp a1sm + Aro m = 1 , 2
3 x 4 = 12
Asp a1sm Res a2s2 + Aro m = 1 , 2
3.2.4
3.2.4.1
8
ResNi Res + Ni
3 x 4 = 12
9
ResV Res + V
3 x 4 = 12
10
ResS ansm Res ansm + H2S n = 1,2 ; m = 1,2
3 x 4 = 12
11
ResS ans2 Res ans1 + H2S + Sat n = 1,2
3x2=6
12
ResN Res + NH3
4
13
Res ans2 –> Res ans1 + Sat n = 1,2
3x2=6
14
Res a2sm Res a1sm + Aro m = 1 , 2
3x2=6
15
Res Aro + Sat
1
16
AroS Aro + H2S
1
17
Asp / Res coke
6 x 4 = 24
Extragranular phenomena
Hydrodynamic model
As referred in chapter 2.5.2, there are different ways to model the hydrodynamics of an
hydrotreating reactor. In this model, as a simplification, the reactor is considered to be biphasic. The
hydrogen and the residue feedstock are considered as a single fluid phase that exchanges mass with
the solid phase, the catalyst.
The hydrotreating reactor is considered as a plug flow reactor, in which the single phase moves
across its length with a speed
v0f uniform along the whole radius.
29
3.2.4.2
Mass balances
According to the chosen hydrodynamic model, the mass balances in the extragranular phase are
established for a plug flow reactor. The mass balance is established in steady state and may be
written as follows:
∂C if
3 m f
ε iν
= (1 − ε i )ε p
k i (C i − C ip ) i = 1, nc - 1
∂z
Rc
f
o
(17)
This equation may be written in terms of volume by introducing the relation between volume
fraction and molar concentration, given by:
φi = Ci ns ,iVm0
(18)
Equation (17) then becomes:
ε iν of
∂φif
3 m f
= (1 − ε i )ε p
k i (φi − φip ) i = 1, nc - 1 (19)
∂z
Rc
As indicated in equation (17), the mass balances in the extragranular phase are established for all
the lumps except one. This equation is replaced by the following constraint:
nc
∑φ
f
i
=1
(20)
i =1
3.2.5
3.2.5.1
Intragranular phenomena
Mass balances
The mass balances inside the catalyst are established in transient state for a spherical particle
(hypothesis H9, chapter 3.2.1), as follows:
∂Cip
1 ∂ 2
εp
= εp 2
r .N i + (1 − ε p )as ri i = 1, nc
∂t
r ∂r
(
)
(21)
30
The flux Ni may be replaced by the flux of the unitary molecule, by introducing the relation:
Ni0 = ns ,i Ni
(22)
Introducing also (18), equation (21) becomes:
∂φ i p
1 ∂ 2 0
εp
= Vm0ε p 2
r .N i + (1 − ε p )as ri
∂t
r ∂r
(
)
i = 1, nc - 1
(23)
Equation (23) is linked to the constraints:
•
One constraint corresponding to the volume balance:
nc
∑φ
p
i
=1
(24)
i =1
•
One constraint corresponding to the diffusion law:
nc
∑N
0
i
=0
(25)
i =1
And to the boundary conditions:
∀t
at r = R p ,
∀t
N i0 =
at r = 0,
(
)
k im f
φi − φip i = 1, nc
Vm0
Ni0 = 0 i = 1, nc
(26)
(27)
In equation (23), the specific surface, aS, varies with the coke deposits according to:
as =
Sc initially
available
Vc
− Sc occupied ,coke
(28)
int ragranular phase
The surface occupied by coke is related to its volume fraction inside the catalyst, by assuming that
the molecule is a sphere and its surface is equivalent to the section area. Taking also into account
hypothesis H9 (chapter 0), equation (28) may be rewritten as follows:
as =
Sc initially available
φcoke
−
3
4 πRc
4 Rmcoke
3
3
(29)
31
Since the reactions only occur in the adsorbed phase (hypothesis H5, chapter 0), the reaction
rates in equation (23) are expressed in terms of the lump's adsorbed quantity, qi, thus requiring the
use of the relation:
∂qij nc ∂qij ∂Ckj , p
=∑
j ,p
∂t
∂t
k =1 ∂Ck
(30)
To express the reaction rates, first order laws are considered for the reactions that do not involve
a deposit in the catalyst:
r = k .q
(31)
When a deposit is involved, second order reactions are considered and the maximum adsorbed
quantity is included in the reaction rate law:
r = k .q.q max
3.2.5.2
(32)
Diffusion
The fluxes inside the catalyst which appear in equation (23), are determined by the StefanMaxwell equations, extended with Fornasiero's formalism (Fornasiero et al., 2005). The StefanMaxwell equations coupled with Fornasiero’s formalism are given by equation (13) (chapter 2.5.3.2)
The diffusion coefficients in equation (13) are effective diffusion coefficients, that take into account
the variations in the pore radius and porosity that occur due to deposition of metals and coke. The
effective diffusion, Deff, may be determined by the following relation (Jost et al., 1985):
Deff =
ε
KK D
τ r r p i, j
(33)
The coefficients Di,j in equation (34) are determined by correlations presented in the literature. The
model considers the Scheibel correlation, valid for liquids (Li and Carr, 1997):

AsT   3V j
Di , j =
1+
1
 
η j Vi 3   Vi




2
3




(34)
The coefficients Kr and Kp in equation (33) take into account the diminution of the diffusion
coefficients with the increase of the hydrodynamic radius of the molecule, Rh. Thus, their calculation
requires the knowledge of Rh, which may be obtained by the Stokes-Einstein equation:
32
D∞ =
kT
kT
⇔ Rh =
6πηR h
6πηD∞
(35)
Equation (35) is only valid for gases but, as an approximation, it is considered valid for the residue
feedstock and the diffusion coefficient
D∞ is considered equal to Di,j given by equation (34).
The coefficients Kr and Kp are then obtained by the following correlations (Jost et al., 1985):
K p = (1 − λ ) 2 ; λ ≤ 0.5
(36)
K p = 1 − 2,104λ + 2,089λ3 − 0,948λ5 ; λ ≤ 0.5
(37)
where λ represents the ratio between the molecules hydrodynamic radius and the pore radius:
λ=
Rh
rp
(38)
The pore radius rp varies in time, due to the deposition of metals and coke. Considering that the
inner channels of the catalyst are cylindrical and the number of channels remains constant during the
operation, a relation may be derived between the pore radius variation and the porosity variation:
r0 (r , t ) = r0 (r ,0) *
ε p (r , t )
ε p (r ,0)
(39)
The method used to describe the evolution of the catalyst porosity with time is described below, in
the topic "Deactivation by decrease of active sites and porosity".
Owing to the variation of the pore radius with time and radial position in the catalyst, the effective
diffusion coefficients in equation (13) will also vary with time and radial position in the catalyst.
3.2.5.3
Adsorption
The adsorption in the model is described by the generalized Langmuir model, given by:
33
qi =
q max bi Cip
i = 1, nc
nc
1 + ∑ bkC
k =1
(40)
p
k
Although equation (40) is written for all lumps, the model only considers adsorption constants, bk,
for 6 groups, according to Table 5.
Table 5 – Adsorption constants considered in the model.
3.2.5.4
Adsorption constant
Group
1
Asp
2
Res
3
Aro
4
Sat
5
NH3
6
H2S
Deactivation by decrease of active sites and porosity
This topic presents the methods used to take into account the catalyst deactivation due to the
deposition of metals and coke, as well as the presence of other adsorbed species at the catalyst
surface. More specifically, deactivation phenomena will impact the maximum number of active sites
and on the catalyst porosity, inducing modifications to them with time and along the radius
coordinates.
For the number of active sites, it was considered that one mol of deposit (metal or coke) would
deactivate only one active site, even for coke formation. This decrease is expressed by the following
equation:
t nd
φkj , p
0 k =1
ns ,kVm0
q max (r , t ) = q max (r , t = 0) − ∫ ∑
dt
(41)
For the decrease on porosity, a similar equation is adopted which accounts for the volume
occupied by the deposits (metals and coke) or other adsorbed species at a given time:
t nd
ε p (r , t ) = ε p (r , t = 0) − ∫ ∑ φkj , p dt
(42)
0 k =1
34
3.2.6
Model entries from experimental data
The model requires an initial set of
φi
values to solve equation (19). Since these cannot be
measured directly, it is necessary to calculate them through the available experimental data.
The relevant available experimental data consists of:
•
the residue mixture density ( ρ M );
•
the density of each SARA family ( ρ i );
•
the mass fraction of each SARA family (wi ) ;
•
the elemental analysis (C, H, N, S, Ni, V) associated to each SARA family.
The first step consists on the calculus of the total volume fraction of each SARA family according
to the following equation:
φfamily , t = w family ×
ρM
ρ fraction
(43)
Equation (43) allows directly determining the volume fraction of the saturate species, since only
one type of lump is considered for this family.
To calculate the volume fractions of the other lumps, some assumptions must be considered:
1. All the lumps inside a SARA family are considered to have the same density,
ρi ;
2. For the aromatics with sulfur, it is considered that each molecule has one atom of sulfur;
3. For the lumps with metals, it is considered that each molecule has one metal;
4. Asphaltenes and resins with metals are divided into the 4 fractions (table of Figure 16) using
repartition coefficients. These coefficients are model inputs that will have to be set having in mind
that the sum of them, for a metal, equals one;
5. To divide simple asphaltenes and resins into the 4 fractions (table of Figure 16), repartition
coefficients are also considered and once again the sum of the 4 equals one;
6. For lumps with both a metal and nitrogen or sulfur, it is considered that the quantity of sulfur is
related to that of the metals, corrected by a distribution coefficient. These coefficients, one for
each fraction, are values required as model input;
7. The only species that describe the feedstock are those presented in Figure 16;
8. Two ns numbers are required as model inputs, one for saturates and one for aromatics. The ns
numbers for asphaltenes and resins are obtained through the relations:
ns ,asphaltene s = n s ,re sin s + n s ,aromatics
(44)
35
ns ,re sin s = n s ,aromatics + n s ,saturates
(45)
The ns numbers of aromatics and saturates are calculated by adjusting its value (equation (46)),
so that the molecular mass of the lump has an acceptable value, in accordance with the values found
in literature.
M asp1S x =
1
ρ asp1
(46)
nsasp1S x1ϑ 0
The volume fraction of the aromatics with sulfur may be directly determined as follows:
φaro S = φaro , t × ρaro × ns aroS ×Vm0 ×
ωS aro
Mw S
(47)
The volume fraction of the other aromatic lump, the simple aromatics, is then calculated by the
difference to the total volume fraction of aromatics:
φaro , simple = φaro , t − φaro S
(48)
For asphaltenes and resins, first the total volume fraction is calculated for the lumps with, nickel
and vanadium, according to (example for the asphaltenes):
φasp Ni = φaspt × ρ asp × ns asp Ni ×Vm0 ×
ωNi asp
Mw Ni
(49)
To determine the total volume fraction of asphaltenes and resins with nitrogen or sulfur, an
equation similar to (49) is used, adding a correction with the relevant distribution coefficient. For
example, for the total volume fraction of asphaltenes with sulfur:
φ asp S = φ aspt × ρ asp × n s asp S × Vm0 ×
ω S asp
Mw S
/ γ S asp
(50)
The next step is to calculate the volume fractions of each lump comprising a metal and nitrogen or
sulfur. The following equation exemplifies this calculus for the volume fraction of asphaltenes with
nickel and sulfur, of the a2s2 fraction (Figure 16):
36
φ asp
a 2S 2
Ni S
= φ asp Ni × rp a Ni a 2 s 2 × ρ asp × n s asp Ni S × Vm0 ×
ω S Ni asp
MwNi
/ γ S a2s 2
(51)
It may be noted in the above equation that the ns value used is not specific to the a2s2 fraction.
Instead, an average value is used, weighted by each of the 4 fractions' (table of Figure 16) repartition
coefficient, as follows:
4
nsasp NiS = ∑ ns j ×rpa NiS ( j )
(52)
j =1
Using the results of equations (50) and (51), it is possible to calculate the volume fraction of
simple asphaltenes or resins with metals, as follows (example for simple asphaltenes with nickel):
φAspNi , simple = φAspNi − φAspNiN − φAspNiS
(53)
Simple asphaltenes and resins may be calculated by the following volume balance (example for
simple asphaltenes):
φAsp , simple = φAsp , t − φAspNi − φAspV
(54)
The remaining lumps, simple asphaltenes or resins with nitrogen or sulfur are calculated using
equation (55) (example for the simple asphaltenes with nitrogen):
φAspS , simple = φAspS − φAspNiS − φAspVS
3.2.7
(55)
Reactor sequencing
While presenting the above equations, only the HDM reactor was considered. To model the
complete process, comprising both the HDM and HDS reactors in sequence, some slight changes
should be introduced.
In terms of model entries, the data required for the HDS section is no longer obtained
experimentally and is now based on the output from the HDM reactor.
Also, differences in the initial porosity, pore radius and shape of the catalyst should be introduced,
owing to the different nature of the HDS catalysts.
37
The catalyst shape, which is considered to be cylindrical in the HDS section, impacts the ratio
used in the extragranular phase mass balance. The value
Sc
Vc
3
in equation (17) is thus replace by the
Rc
ratio:
Sc 2(Rc + Lc ) Lc >>Rc 2
=
=
Vc
Rc Lc
Rc
(56)
The mass balance in the intragranular phase, equation (21) should be replaced by the following:
∂C ip
1 ∂
εp
= εp
r .N i + (1 − ε p )as r i i = 1, nc
∂t
r ∂r
(
)
(57)
Finally, since the active phase is not the same, the kinetic and adsorption parameters optimized
for the HDM section should be readjusted for the HDS section.
3.2.8
Summary of the model parameters
As discussed in chapter 3.2.3, 17 kinetic constants are required to define the kinetic network. For
adsorption (chapter 3.2.5 – Adsorption), 6 different constants are considered.
The model also requires the input of 8 repartition coefficients for the simple asphaltenes and
resins and 16 for asphaltenes and resins with metals (chapter 3.2.6). Since these repartition
coefficients are bounded to 6 constraints (the sum for each of the 6 groups considered equals 1), they
only correspond to 18 inputs in the model.
In chapter 3.2.6, 16 distribution coefficients are also introduced, relative to asphaltenes and resins
with sulfur or nitrogen.
Finally, two ns numbers are required, one for aromatics and one for saturates. The ns values for
asphaltenes and resins are obtained using equations (44) and (45), respectively.
In total, the model considers 23 parameters and 36 required inputs, as listed in Table 6.
38
Table 6 – Summary of the model parameters.
Type of parameter
Number of parameters
Kinetic constants
17
Adsorption constants
6
Repartition coefficients
Simple asphaltenes and resins
6
Asphaltenes and resins with metals
12
Distribution coefficients
16
ns numbers
2
23 parameters
Total:
3.3
36 required inputs
Differential equations solving and parameter optimization
In this chapter, an overview of the algorithms used to solve the differential equations and to
estimate the model parameters is presented.
The model code was developed and implemented in FORTRAN, using routines from the IMSL
Fortran Numerical Library.
3.3.1.1
Differential equations
Solving the set of differential equations of (19) and (23) involves a discretization scheme by the
finite volume technique along the integration variables. Figure 17 shows the discretization adopted for
the spherical catalyst (variable r) and for the plug flow reactor (variable z).
∆r
Rc
∆z
LR
Figure 17 – Discretization adopted for the spherical catalyst and the plug flow reactor.
The equations system is solved using the DASPK integration subroutine, using several backward
differentiation formula (BDF) methods.
39
3.3.1.2
Parameter estimation
As seen in chapter 3.2.8, the model contains a large amount of parameters, thus requiring robust
parameter estimation routines.
The least square method is solved using a routine of the IMSL library based on a LevenbergMarquardt procedure. For a vector θ, containing the model parameters, the routine adjust θ in order to
respect the criterion in equation (58), under the physical constraint that parameters are non negative:
nc N p
[
]
J(θ) = minθ ≥ 0 ∑∑ φl ,fmeas (i ) − φl ,fmod (i )
l =1 i =1
3.4
2
(58)
Conclusion
In this chapter, a model for residue hydrotreating units has been presented. The different
phenomena involved are described, namely the extragranular and intragranular phenomena and the
scheme used to describe the feedstock and products.
The diffusion is described by the Stefan-Maxwell equations coupled with Fornasiero's formalism,
to account for size differences between feedstock's lumps. The adopted feedstock and products
description scheme comprises 77 lumps, leading to a kinetic network with 148 reactions. Catalyst
deactivation is also considered, by taking into account variations in the number of active sites and
porosity resulting from the presence of deposits.
Based on the chosen feedstock description, the model considers 23 parameters (kinetic and
adsorption constants) and 36 required inputs (repartition coefficients, distribution coefficients and ns
numbers).
The model equations were presented for the HDM section but it was shown that the incorporation
of the entire process, with the HDM and HDS reactors in sequence, could be easily carried out with
minor modifications in the code: The different shape of the catalyst implies changes in its surface to
volume ratio and in the intragranular mass balance formulation; The data required for the HDS section
is obtained through the output of the HDM section.
Regardless of the parameter estimation routines implemented, good initial estimates for the model
parameters will be required to obtain satisfactory agreement between experimental data and model
output. This implies a preliminary handmade optimization to insure the convergence and
trustworthiness of the model.
When compared to other existing hydrotreating models (chapter 2.5.7), where diffusion was
usually based on Fick's law, the present model features a more complex description. The use of
Stefan-Maxwell equations coupled with Fornasiero's formalism allows accounting for the collisions
between lumps with different volumes. Indeed, by introducing Fornasiero's formalism, all the mass
40
balances become written in terms of volume, thus leading to a model that takes into account the
volume constraints of the interaction between the catalyst and the residue feedstock.
Also, the present model considers a feedstock description with various parameters to differentiate
asphaltenes and resins, resulting in a scheme with 77 lumps. Although other models exist that
describe the feedstock and products with a comparable level of complexity, these models don't
simultaneously contain a more detailed description of the diffusion phenomena occurring inside the
catalyst.
The more detailed description used in this model intends to better differentiate residues from
different origins and to obtain insights on the reactivity of these residue feedstocks.
41
4
4.1
Results
Experimental data
To simulate the performance of a residue hydrotreatment unit and to validate these simulations,
the kinetic model in study requires the input of experimental data concerning the reactor operating
conditions, the feedstock and the catalyst.
As mentioned in chapter 2.3, industrial residue hydrotreatment units comprise two different
sections usually designated as HDM and HDS sections. In this study, the model aimed to simulate the
operation of a reactor with a single HDM section and afterwards the operation of the unit with both
HDM and HDS sections. However, the available experimental data was obtained in a pilot unit with
only one reactor. Therefore, to reproduce the two sections, the HDM and HDS catalysts were both
introduced in the reactor, in a 1:1 volume proportion, thus resulting in the same residence time for
each catalyst.
Temperature and pressure in the pilot unit were chosen to be coherent with typical industrial
values for vacuum residue hydrotreatment (chapter 2.3.5.3). As for the residence time, although the
values were chosen to be in the industrial ranges, they were subject to specific constraints related to
the pumps used in the unit. The operating conditions used are presented in Table 7.
Table 7 - Operating conditions used in pilot unit scale experiments.
Pressure
150 atm
Temperature
360 ºC
Residence time
1h and 2h in each section
The catalysts used in the pilot unit were stabilized (pre-used) for 1120 hours under residue in
order to prevent the rapid initial catalyst deactivation due to coke formation and to obtain a constant
catalytic activity. The catalyst was also submitted to a sulfidation pretreatment, carried out in-situ using
a vacuum gas oil (VGO).
As for the feedstock used, the choice was made in order to consider residues with characteristics
as different as possible. However, this choice was also subject to the feedstock availability and to
constraints of the pilot unit as the maximum content of metals allowed. Table 8 presents the most
relevant analysis available for the 4 vacuum residue feedstocks used: Buzurgan, Arabian Light, Djeno
and Oural. Complete analysis of these residues can be found in appendix 6.1.
Table 8 – Available analysis for the 4 vacuum residues used.
Buzurgan
Asphaltenes
[wt%]
11.8
Sulfur
[wt%]
6.21
Metals (Ni + V)
[wppm]
241
Density
[g/cm³]
1.0370
Arabian Light
9.5
4.22
125
1.0218
Djeno
3.9
0.45
95
0.9890
Oural
5.2
2.72
220
1.0030
Residue
42
For each of these 4 residues, the available experimental data includes the fraction of each SARA
lump (chapter 2.2.2) and of heteroatoms (S, N, Ni and V) in asphaltenes, resins and aromatics. These
analysis are available for the initial feedstock and for the products obtained after the HDM and HDM +
HDS operation (1h and 2h of residence time in each reactor).
The GPC (gel permeation chromatography) profiles for asphaltenes and resins in each of the 4
feedstocks are also available (appendix 6.2). These profiles allow obtaining an approximate molecular
weight distribution for asphaltenes and resins, relative to polystyrene. However, it should be noted that
the GPC profiles do not depend exclusively on the molecular weight but also on other factors like the
aromaticity of the molecules.
The GPC profiles can be used to determine the repartition coefficients of total asphaltenes and
total resins, required as model inputs (chapter 3.2.6). Two different methods can be used to obtain the
4 repartition coefficients from the GPC curves. A first method (Figure 18) consists in defining relevant
points in the GPC curve and considering them as the boundary between two distinct fractions. The
curve is thus divided into 4 fractions corresponding, in increasing order of molecular weight, to the
asphaltenes or resins of type, a1s1, a1s2, a2s1 and a2s2. As shown in Figure 18, the points used to
delimitate the 4 fractions correspond to the inflection point at Mi = 3550, the curve maximum at Mi =
6330 and the intersection of two slopes at Mi = 15000.
Figure 18 – Possible method of dividing asphaltenes in 4 fractions for an Oural residue feedstock.
Another possible method considers that the GPC profile results from the overlapping of 4 Lorentz
distributions (one for each fraction) described by the following equation:
f (x) = A ⋅
σ2
4
⋅
1
σ
2
4
+ (x − x0 ) 2
(59)
43
The parameters A (amplitude), σ (half-width at half-maximum) and x0 (abscissa of the distribution
peak) in equation (59)
are obtained by minimization of the square difference between the
experimental curve and the sum of the 4 distributions. Afterwards, the 4 fractions can be obtained by
determining the ratio between the area of each distribution and the total area of the curve. This
method is represented in Figure 19 for a Buzurgan feedstock.
Figure 19 - Possible method of dividing asphaltenes in 4 fractions for a Buzurgan residue feedstock, based
on the overlap of 4 Lorentz distributions.
Since the division of asphaltenes in 4 fractions results from a hypothesis assumed in the model
development, there is no possible way of experimentally confirming which of the methods used to
analyze the GPC curve is the most appropriate. However, since the model in study was developed
assuming discrete lumps (for a given molecular weight, only one lump is present), the method in
Figure 18 was the one used to determine the repartition coefficients for total asphaltenes and resins.
To use the method in Figure 19, the model would have to account for the molecular weight
overlapping that occurs when considering the four Lorentz distributions. The sensitivity of the model to
the input of different values of repartition coefficients is analyzed in chapter 4.2.4.
4.2
HDM model
4.2.1
Optimization and sensitivity analysis methodology
A method commonly used to obtain a model’s parameters consists of using an estimation routine
that tests different combinations of parameters and finds the set that leads to the best agreement
between experimental data and model output. However, apart from the large number of parameters in
44
this model, the use of the Stefan-Maxwell equations (chapter 2.5.3.2) to describe the diffusion inside
the catalyst introduces matrixes with large dimensions, significantly increasing the required
computation time. Therefore, it would be unfeasible to run an estimation routine with randomly chosen
initial estimates. The first part of the optimization scheme consisted in finding these initial estimates
using the method described below.
As presented in chapter 3.2, the model under study comprises 17 kinetic constants and 6
adsorption constants. It was assumed that these parameters should be the same for all residue
feedstocks, since the type of reactions occurring and the catalyst used are the same. Therefore, a
reference residue was defined, for which the kinetic and adsorption constants were optimized. In this
study, the Buzurgan residue was used as a reference.
The curves resulting from the model output include the sulfur fraction in asphaltenes, resins and
aromatics; the fraction of nitrogen, nickel and vanadium in asphaltenes and resins; and the total
fraction of asphaltenes, resins, aromatics and saturates, for different residence times. For all of these
curves, experimental points are available with reference to the initial feedstock and the product
obtained using a reactor residence time of 1h and 2h. The goal of this optimization is to find the
parameters that lead to the minimal difference between experimental data and model output.
It should be noted that different sets of kinetic and adsorption constants may serve as a solution
for the parameter optimization problem. For example, if the kinetic constant for the nickel removal from
asphaltenes (chapter 3.2.3) is set to a very high value, the reaction rate will be the main factor
determining the model simulations for this reaction. In this case, several values for the asphaltenes
adsorption constant can be used, since they will only affect the model response if set to sufficiently
high values. However, it should always be assured that the obtained values are physically possible
and coherent with the phenomena involved.
Apart from the above mentioned situation, variations in the adsorption constants are expected to
impact several curves (chapter 4.2.2.1). Therefore, these were the constants firstly optimized, in order
to get a model output as close as possible to experimental data. This optimization was carried out by
choosing different values for the constants and picking the ones that led to the best fit. Afterwards, the
model output was fine-tuned by changing the kinetic constants.
Using the kinetic and adsorption constants optimized for the Buzurgan residue, simulations were
carried out for Arabian Light, Djeno and Oural residues. These simulations intended to analyze how
the model responds to variations in the experimental input and to verify if good adjustments could be
obtained for different residues using the parameters optimized for the Buzurgan residue.
Finally, the model sensitivity to variations in the repartition coefficients, distribution coefficients and
ns numbers was tested (chapter 4.2.4). This analysis was carried out for Buzurgan residue using the
kinetic and adsorption constants previously obtained.
45
4.2.2
4.2.2.1
Parameter optimization
Adsorption constants
As described in chapter 4.2.1, the first step in the strategy to set the initial values for the model
parameters consisted in determining the adsorption constants that gave a good initial fit between
experimental data and model output.
Since the model only considers 6 adsorption constants, variations in a single adsorption constant
are expected to affect several of the curves to be fitted, unless the kinetic constants are set to very
high values (chapter 4.2.1).
As an example, Figure 20 shows the effect of a variation in the asphaltenes adsorption constant
(ka1) in the model simulations for the nitrogen removal from resins and asphaltenes. As seen in this
figure, the nitrogen removal from asphaltenes is higher for higher values of ka1. For resins, although
the effect is less pronounced, the order of the curves is the opposite, with higher nitrogen removal
occurring for smaller values of ka1.
(a)
(b)
Figure 20 – Effect of variations in the adsorption constant ka1 in the model simulated nitrogen removal
from: (a) resins; (b) asphaltenes.
For asphaltenes, the tendency observed in Figure 20 results from the fact that the nitrogen
removal is favored when reactants adsorb easily in the catalyst active sites. This situation occurs for
higher values of the adsorption constant, according to equation (40). This equation also shows that the
reactants adsorption is competitive, i.e., the adsorption rate of a reactant diminishes in the presence of
another reactants competing for the same active site. This explains the opposite behavior observed for
resins, since favoring the adsorption of asphaltene compounds is unfavorable for resin compounds.
-3
In Figure 20, the curve highlighted in orange (ka1=1x10 ) corresponds to the values of the
asphaltenes constant that led to a smaller difference between experimental data and model output.
The same reasoning was used while adjusting the values of the other adsorption constants. The
values optimized for the adsorption constants are listed in Table 9.
46
Table 9 – Adsorption constants optimized for Buzurgan residue feedstock.
Group
Asphaltenes
Resins
Aromatics
Saturates
NH3
H2S
Adsorption constant
-3
1.00x10
-4
5.63x10
-4
3.30x10
-6
8.94x10
-4
9.82x10
-4
3.19 x10
The adsorption constants presented in Table 9 suggest that asphaltenes are the SARA fraction
with the strongest adsorption on the catalyst. Since there is no physical explanation for having such a
difference between the adsorption constant for asphaltenes and resins, the high value observed for
asphaltenes may result from purely mathematical arguments. Also, the adsorption constants for NH3
and H2S would be expected to have higher values, owing to the strong interaction between these
compounds and the catalyst.
4.2.2.2
Kinetic constants
Contrary to the adsorption constants, the kinetic constants implemented in the model are in
sufficient number to allow varying one constant without affecting a large number of curves. For
example, by changing the kinetic constant k1, (chapter 3.2.3) only the curve concerning the nickel
removal from asphaltenes would be affected. Table 10 shows which kinetic constants affect each of
the heteroatom removal and lump fraction curves.
Table 10 – Kinetic constants affecting each of the heteroatom removal and lump fraction curves.
S
N
Ni
V
Lump fraction
Asphaltenes
Resins
Aromatics
Saturates
k3, k4
k5
k1
k2
k4, k6, k7
k10, k11
k12
k8
k9
k7, k11, k13, k14, k15
k16
k7, k14, k15
k13, k15, k4, k11
According to Table 10, variations in the constants k4 and k11 affect both the sulfur removal and the
lump fraction curves of asphaltenes and resins. Therefore, it was chosen to use these constants only
to adjust the sulfur removal curves, while the lump fraction curves were adjusted with the other
relevant constants. It should also be pointed out that constants k3 and k4 for asphaltenes and k10 and
k11 for resins were given the same value, since there is no evidence on how the saturation removal
influences the reaction rate.
The optimization methodology for the kinetic constants is exemplified in Figure 21 for the nickel
removal from asphaltenes curve. In accordance with Table 10, the kinetic constant used to adjust this
curve was k1. It can be seen that higher values of k1 imply higher nickel removal from asphaltenes,
which would be the expected behavior since k1 represents the nickel removal from asphaltenes
reaction rate.
47
The methodology used to adjust the other curves was analogous to the one used for the nickel
removal from asphaltenes. In the case of the lump fraction curves, since cracking reactions always
affect more than one lump, several combinations of these parameters had to be tested in order to find
the ones that led to the minimal difference between experimental data and model output.
Figure 21 - Effect of variations in the kinetic constant k1 on the model simulated nickel removal from
asphaltenes.
As emphasized in chapter 4.2.1, although at this point it was important to obtain a reasonable
adjustment between experimental data and model output, the main goal was to confirm whether the
model was sensitive to variations on these parameters and if the variations could be explained using
arguments based on the phenomena involved.
Table 11 presents the set of kinetic constants resulting from this optimization.
Table 11 – Kinetic constants optimized for Buzurgan residue feedstock.
Kinetic constant
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Reaction
AspNi Asp + Ni
AspV Asp + V
AspN Asp + NH3
ResNi Res + Ni
ResV Res + V
ResN Res + NH3
Res Aro + Sat
AroS Aro + H2S
Asp / Res coke
Value
-2
4.20x10
-2
5.25x10
-4
5.20x10
-4
5.50x10
-2
4.00x10
-2
5.72x10
-2
5.24x10
-2
6.66x10
-2
7.98x10
-2
4.25x10
-2
4.60x10
-2
3.00x10
-2
2.09x10
-2
2.96x10
-2
2.81x10
-2
4.00x10
-4
6.11x10
48
The kinetic constants presented in Table 11 suggest that for asphaltenes, the rate at which the
saturation level is lowered (k6) is higher than the rate for aromaticity lowering (k7). For the resins, the
opposite behavior is observed, according to the values of the kinetic constants k13 and k14. There is no
physical evidence for this difference between asphaltenes and resins and, as shown in chapter
4.3.2.1, other sets of kinetic constants can be used without observing this behavior. As expected, the
kinetic constant for the removal of aromaticity and saturation from asphaltenes (k15) is intermediary
between k13 and k14.
The kinetic constants obtained for desulfurization reactions suggest that this reaction occurs with a
greater rate in resins and aromatics (k10, k11 and k16) than in asphaltenes (k3 and k4). This observation
arises from the fact that sulfur in asphaltenes is present in compounds more refractory than those of
resins and aromatics.
The kinetic constant k17, corresponding to the coke formation reaction, did not have impact in any
of the curves simulated by the model. Therefore, it was not optimized and a wide range of values
could be used for this parameter.
As referred in chapter 4.2.1, different combinations of parameters may serve as a solution.
Therefore, the kinetic constants here presented should be analyzed carefully to avoid drawing false
conclusions on the reactivity of a residue.
4.2.2.3
Estimation routine results
The model parameters obtained for the Buzurgan residue (Table 10 and Table 11) were
afterwards used as initial values for the estimation routine implemented on the model. With the
maximum iterations number set to 250 iterations, the sum of square differences between experimental
data and model output could be decreased by 5%.
For the same number of maximum iterations, two modifications were tested in the estimation
routine. A first attempt consisted in giving more importance to the sulfur in asphaltenes in the sum of
square difference between experimental data and model output, since this was the curve that showed
more deviations (Figure 23). A weight 1000 times higher was given to its square difference. For
another attempt, all the experimental data and model output were normalized (divided by its initial
values) and the routine was set to minimize the square difference between the normalized values.
However, none of these modifications improved the estimation routine results. To further decrease the
sum of square differences experimental data and model output, the computation time would have to
be increased, by increasing the maximum number of iterations.
4.2.2.4
Optimized results
The results from a simulation using the optimized kinetic and adsorption constants of Table 10 and
Table 11 are presented in the following figures (Figure 22 to Figure 24) along with the corresponding
experimental data.
49
As seen in these figures, an optimization based only on the kinetic and adsorption constants
resulted in a good agreement between experimental data and model output for a given residue.
However, a tendency towards high fractions was observed in the sulfur removal from asphaltenes
curve and towards low fractions in the nitrogen removal from resins. Different sets of kinetic and
adsorption constants could have been tested, to obtain a better fit for these curves. However, to test
the performance of the implemented estimation routine (chapter 4.2.2.3), the parameters should not
be set to values that lead to a perfect adjustment, since any possible improvements obtained with the
routine would be imperceptible.
(a)
(b)
Figure 22 – Optimized model output vs. experimental data (Buzurgan) for: (a) nickel removal; (b)
vanadium removal.
(a)
(b)
Figure 23 - Optimized model output vs. experimental data (Buzurgan) for: (a) sulfur removal; (b)
nitrogen removal.
50
(a)
(b)
Figure 24 - Optimized model output vs. experimental data (Buzurgan) for: (a) total lump fractions; (b)
overall heteroatom removal.
4.2.3
Simulations for different residues
Following the optimization scheme presented in chapter 4.2.1, the kinetic and adsorption
constants optimized for Buzurgan residue were used to simulate the other residues: Arabian Light,
Djeno and Oural. The repartition and distribution coefficients were kept at the same values used for
Buzurgan residue, except for the repartition coefficients of total asphaltenes and resins, which are
determined using the GPC curves (chapter 4.1). The values used for the ns numbers of aromatics and
saturates of each residue were based on the value for Buzurgan residue. This value was multiplied by
the ratio of molecular weights of the fraction in the two residues.
The simulations for different residues allow understanding how the model responds to variations in
experimental input. The input to be changed when a new residue is introduced includes the feedstock
density, the fraction of each SARA lump and the analysis of heteroatoms in asphaltenes, resins and
aromatics.
The obtained results (lump fraction and overall heteroatom removal) for Arabian Light are
presented in Figure 25. As shown in this figure, good adjustments were obtained for the overall
heteroatom removal and for the lump fractions, although in the latter slight tendencies towards low
fractions were observed for saturates and aromatics and towards high values for resins.
51
(a)
(b)
Figure 25 – Model output vs. experimental data for Arabian Light residue, using the parameters
optimized for Buzurgan residue. (1) Lump fractions; (2) Overall heteroatom removal.
Figure 26 presents the lump fraction and overall heteroatom removal simulated for Djeno residue.
In this case, the overall sulfur removal is underestimated by the model and slight tendencies towards
high fractions can be observed in the case of resins and towards low values in the case of aromatics.
(a)
(b)
Figure 26 - Model output vs. experimental data for Djeno residue, using the parameters optimized for
Buzurgan residue. (1) Lump fractions; (2) Overall heteroatom removal.
The lump fraction and overall heteroatom removal simulated for Oural residue are presented in
Figure 27. From the observation of this figure it is not clear whether the model simulations are in
agreement with experimental data, since only two experimental points are available for each curve.
However, the curves for sulfur and vanadium removal in Figure 27-b) appear to be deviated from the
corresponding experimental points.
52
(a)
(b)
Figure 27 - Model output vs. experimental data for Oural residue, using the parameters optimized for
Buzurgan residue. (1) Lump fractions; (2) Overall heteroatom removal.
4.2.4
Sensitivity analysis
As referred in chapter 4.2.1, the sensitivity analysis here presented intends to determine how the
model responds to variations in the repartition coefficients, distribution coefficients and ns numbers. It
was carried out for Buzurgan residue using the optimized kinetic and adsorption constants (chapter
4.2.2).
4.2.4.1
Repartition coefficients
The repartition coefficients are model inputs defined for total asphaltenes and resins, for
asphaltenes and resins with vanadium and for asphaltenes and resins with nickel. They represent the
fraction of these compounds that are of types a2s2, a2s1, a1s2 and a1s1.
As an example, Figure 28 presents the model simulated asphaltenes fraction resulting from
variations in the total asphaltenes repartition coefficients. As seen in Figure 28-a), the model did not
show much sensitivity to these variations. This observation was general and no curves showed
significant variations.
Figure 28-b) corresponds to a zoom of Figure 28-a) and intends to show in which order the small
variations observed occur.
53
a2s2 ; a2s1 ; a1s2 ; a1s1
(a)
a2s2 ; a2s1 ; a1s2 ; a1s1
(b)
Figure 28 – Effect of variations in the total asphaltenes repartition coefficients on the model simulated
asphaltenes fraction. (b) corresponds to a zoom of (a).
As expected, the model predicts less conversion for asphaltenes when a bigger weight is given to
the heavier fractions (a2s2). On the other hand, when the lighter fractions (a1s1) are favored, more
conversion for asphaltenes is simulated by the model. It can also be observed that the model predicts
more conversion for compounds with less degree of saturation (compounds of the type axs1).
4.2.4.2
ns numbers
As described in chapter 3.2.6, two ns numbers are required as model inputs, one for aromatics
and one for saturates. These numbers represent the ratio between the molar volume of a molecule
and the molar volume of hydrogen (unitary molecule).
As an example, Figure 29 presents the model simulated vanadium removal from asphaltenes,
resulting from variations in these two ns numbers. The chosen values intended to test the influence of
having bigger molecules (ns Sat = 29; ns Aro = 30), smaller molecules (ns Sat = 9; ns Aro = 10) and the
influence of separately having bigger saturates (ns Sat = 30; ns Aro = 20) or bigger aromatics
(ns Sat = 19; ns Aro = 30). Figure 29-b) corresponds to a zoom of Figure 29-a).
54
(a)
(b)
Figure 29 – Effect of variations in the ns numbers on the model simulated vanadium removal from
asphaltenes. (b) corresponds to a zoom of (a).
The effect observed in Figure 29-b) is in agreement with the expected, with more vanadium
removal occurring when smaller molecules are considered. Also, for bigger molecules, the model
predicts less removal. As for the impact of separately having bigger saturates or bigger aromatics, the
two curves corresponding to this situation only slightly differ. However from the order observed in
Figure 29-b), less removal is predicted when bigger saturates are considered. This tendency is similar
to that observed in chapter 4.2.4.1 where a higher degree of saturation limited the asphaltenes
conversion.
A limitation of the model was also observed while varying the ns numbers, since the simulated
sulfur removal was higher for large molecules and lower for smaller molecules, contrary to the
expected. Figure 30 shows the model simulated sulfur removal from asphaltenes when the previously
mentioned variations were carried out. The order of the curves in this case is inverse to that observed
in Figure 29.
(a)
(b)
Figure 30 - Effect of variations in the ns numbers on the model simulated sulfur removal from
asphaltenes. (b) corresponds to a zoom of (a).
55
4.2.4.3
Distribution coefficients
The distribution coefficients are model inputs defined for the sulfur or nitrogen in asphaltenes and
resins. For each of these lumps, there are 4 distribution coefficients (one for each fraction, a2s2, a2s1,
a1s2 or a1s1) and they represent the total number of sulfur atoms in the lump fraction.
In general, the model output showed little sensitivity to variations in these coefficients. For
example, when the 4 distribution coefficients were changed from 15 to 10 and 50, no significant
changes were observed in any curve (Figure 31-a). However, when the kinetic constant k11 (Table 11)
-2
was set to higher values, from 4.6x10
-1
to 5x10 , and the same variations in the distribution
coefficients were performed, a variation was observed in the total resins fraction curve, as presented
in Figure 31-b). According to the figure below, the resins conversion is favored when less sulfur atoms
are present in this lump, which would be expected since compounds with less sulfur atoms will have
smaller sizes and thus will react more easily.
This example points out that a sensitivity analysis carried out with fixed values for the kinetic and
adsorption constants can lead to false conclusions. For example, in this case, the number of sulfur
atoms in the resins lump only impacts the reactivity if the desulfurization reaction with resins cracking
is given enough importance (high values for the kinetic constant k11). However, analyzing the
combined effect of variations in all parameters and model inputs would not be possible, since it would
involve a large amount of simulations.
(a)
(b)
Figure 31 – Effect of variations in the 4 distribution coefficients for sulfur in resins on the model simulated
-2
total resins fraction using the kinetic constants: (a) k11 = 4.6x10 (b) k11 = 5x10-1.
56
4.3
HDM + HDS model
4.3.1
Optimization strategy
For the complete model, with both HDM and HDS sections, the number of kinetic and adsorption
constants is twice as that of the HDM model. However, the principle of a hydrotreatment unit consists
on having separate sections for HDM and HDS and therefore the parameters for each section can be
optimized separately.
The parameter optimization scheme used is analogous to the one presented for the HDM section
(chapter 4.2.1). The only difference is that, in this case, the initial conditions for the HDS model are
determined by the model simulations in the HDM section for residence times of 1h and 2h. Therefore,
the parameter optimization for the HDM section should be carried out together with the HDS section,
so that an overall minimum is found.
The sensitivity analysis to variations in the repartition coefficients, distribution coefficients and ns
numbers, as the one presented in chapter 4.2.4 for the HDM section, was not carried out for this
model since the results tendency was expected to be similar.
4.3.2
4.3.2.1
Parameter optimization
HDM section parameters
The kinetic and adsorption constants optimized for the HDM section of the model are presented in
Table 12 and Table 13, respectively.
Table 12 – Adsorption constants optimized for the HDM section, using Buzurgan residue as reference.
Group
Adsorption constant
Asphaltenes
1.00x10
Resins
5.63x10
Aromatics
3.30x10
Saturates
8.94x10
NH3
3.00x10
H2S
3.19x10
-3
-4
-4
-6
-2
-2
As referred in chapter 4.3.1, the adsorption constants presented in Table 12 should be similar to
those optimized for the HDM model (Table 9). In fact, the adsorption constants for the four SARA
fractions are the same as those optimized for that model. However, in this case the adsorption
constants optimized for NH3 and H2S have higher values, in accordance with the strong interaction
expected between these compounds and the catalyst.
57
Table 13 – Kinetic constants optimized for the HDM section, using Buzurgan residue as reference.
Kinetic constant
Reaction
Value
-2
1
AspNi Asp + Ni
3.00x10
2
AspV Asp + V
5.00x10
3
7.00x10
4
7.00x10
5
AspN Asp + NH3
8.00x10
6
5.00x10
7
5.00x10
8
ResNi Res + Ni
1.60x10
9
ResV Res + V
2.00x10
10
1.10x10
11
1.10x10
12
ResN Res + NH3
8.00x10
13
4.00x10
14
4.00x10
15
Res Aro + Sat
1.50x10
16
AroS Aro + H2S
7.00x10
17
Asp / Res coke
1.00x10
-2
-3
-3
-2
-2
-2
-1
-1
-1
-1
-2
-2
-2
-1
-2
-4
As expected, the kinetic constants presented in Table 13 are similar to those optimized for the
HDM model (Table 11). The differences between the two sets of kinetic constants may arise from the
inherent uncertainty of the parameters. Also, as referred in chapter 4.3.1, the HDM kinetic constants
had to be readjusted since they have influence on the initial values of the HDS section.
The values obtained for the desulfurization rates in asphaltenes (k3 and k4), resins (k10 and k11)
and aromatics (k16) indicate a lower rate for asphaltenes, in accordance with the observations of
chapter 4.2.2.2.
As mentioned in chapter 4.2.2.2, the kinetic constant k17, corresponding to the coke formation
reaction, did not have impact in any of the curves simulated by the model. Therefore, it was not
optimized and several different values could have been presented in Table 11.
It should be re-emphasized that different combinations of parameters can serve as a solution.
Therefore, the kinetic constants here presented should be analyzed carefully to avoid drawing false
conclusions on the reactivity of a residue.
58
4.3.2.2
HDS section parameters
The kinetic and adsorption constants optimized for the HDS section of the model are presented in
Table 14 and Table 15, respectively.
Table 14 - Adsorption constants optimized for the HDS section, using Buzurgan residue as reference.
Group
Adsorption constant
-4
Asphaltenes
3.00x10
Resins
2.29x10
Aromatics
8.95x10
Saturates
8.94x10
NH3
3.00x10
H2S
3.19x10
-4
-5
-6
-2
-2
As expected, the adsorption constants in Table 14 differ from those optimized for the HDM section
(Table 12), since the two sections use different catalysts. The agreement between the adsorption
constants of saturates, NH3 and H2S in both sections results only from the fact that the values
optimized for the HDM section were used as a starting point for the optimization in the HDS section. It
does not have physical significance. The observations concerning the relative values of the constants
in Table 14 are analogous to those pointed out for the HDM section, with the NH3 and H2S adsorption
constants having the highest values.
Table 15 - Kinetic constants optimized for the HDS section, using Buzurgan residue as reference.
Kinetic constant
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Reaction
AspNi Asp + Ni
AspV Asp + V
AspN Asp + NH3
ResNi Res + Ni
ResV Res + V
ResN Res + NH3
Res Aro + Sat
AroS Aro + H2S
Asp / Res coke
Value
-15
1.00x10
-2
5.00x10
-3
2.00x10
-3
2.00x10
-3
5.00x10
-1
5.00x10
1.00
1.00
2.50
-1
2.50x10
-1
2.50x10
-3
5.00x10
1.00
1.00
2.50
1
1.55 x10
-1
1.00x10
59
The very low value of k1 in Table 15 corresponds to the lower limit that kinetic constants can
assume in the model. A reaction with such low kinetic constant should be considered not to occur in
significant extent. However, this value should not be related to an inferior demetallization catalytic
activity. Instead, it probably reflects the diffusion limitations of asphaltenes that cause small
concentrations of asphaltenes with nickel inside the catalyst, thus lowering the reaction rate. This
effect is not observed for asphaltenes with vanadium (k2), which may be due to the higher
concentrations of vanadium in the Buzurgan residue.
The kinetic constants of desulfurization reactions indicate higher rates in resins (k10 and k11) and
aromatics (k16) than those observed in the HDM section, which would be expected considering the
type of catalyst used.
The values obtained for the asphaltenes cracking (k6 and k7) and resins cracking (k13, k14 and k15)
indicate a higher rate for these reactions in the HDS section. This behavior would be expected since
the catalyst used in this section has a higher acidity.
4.3.2.3
Optimized results
Figure 32 to Figure 34 present the results of a simulation using the kinetic and adsorption
constants optimized for the HDM + HDS model, along with the corresponding experimental data. In
these figures, the solid lines represent the model output for the HDM section while the dashed lines
represent the model output for the HDS section. The experimental data is represented by the filled and
unfilled marks, for the HDM and HDS sections, respectively.
The results presented in these figures reveal that the model output satisfactorily represents the
HDM experimental data. The slight deviations observed in the nitrogen removal curve (Figure 33-b)
could have been readjusted by further tuning the kinetic constants.
As for the HDS section, the results in general are considered satisfactory. However, some of the
experimental data like the nickel fraction in asphaltenes or the sulfur fraction in resins does not appear
to be correctly simulated by the model. In other cases, for example for the vanadium in asphaltenes, it
is difficult to find a set of parameters that gives good predictions, simultaneously for the two residence
times in study.
60
(a)
(b)
Figure 32 – HDM +HDS model: optimized model output vs. experimental data (Buzurgan) for: (a) nickel
removal; (b) vanadium removal.
(a)
(b)
Figure 33 – HDM +HDS model: optimized model output vs. experimental data (Buzurgan) for: (a) sulfur
removal; (b) nitrogen removal.
61
(a)
(b)
Figure 34 - HDM +HDS model: optimized model output vs. experimental data (Buzurgan) for: (a) total
lump fractions; (b) overall heteroatom removal.
4.3.3
Simulations for different feedstocks
The simulations for different residue feedstocks were carried out in the same way as for the HDM
model (chapter 4.2.3), i.e., the kinetic and adsorption constants were set to the optimized values
(chapter 4.3.2) and for each feedstock, the only model inputs changed were the total repartition
coefficients of asphaltenes and resins, and the ns numbers of aromatics and saturates.
The experimental data to be introduced is the same as for the HDM model and corresponds to the
analysis of the feedstock (density, fraction of each SARA lump and analysis of heteroatoms in
asphaltenes, resins and aromatics). Having the HDS section incorporated in the model does not imply
the need of additional experimental data, since the initial conditions for this section are determined by
the output of the HDM section.
The obtained results (lump fraction and overall heteroatom removal) for the Arabian Light vacuum
residue are presented in Figure 35. The results for the HDM section are similar to those obtained for
this feedstock in the HDM model (chapter 4.2.3), which would be expected since similar sets of kinetic
and adsorption constants are used. However, in Figure 35-b), a slight tendency towards low fractions
can be observed for the sulfur removal. Also, Figure 35-a) the conversion of aromatics and resins
simulated by the model slightly differs from the experimentally observed. For the HDS section, no
significant deviations were observed.
62
(a)
(b)
Figure 35 – HDM + HDS model: Model output vs. experimental data for Arabian Light residue, using the
parameters optimized for Buzurgan residue. (1) Lump fractions; (2) Overall heteroatom removal.
Figure 36 presents the results of the simulation carried out for the Djeno residue. For the HDM
section, the model simulated curves have a similar behavior to those presented for the HDM model.
However, some additional deviations towards low fractions can be observed for the nickel and
nitrogen removal curves. As for the HDS section, the results can be considered satisfactory, except for
the nickel removal curve (Figure 36-b), which is dislocated towards low fractions.
(a)
(b)
Figure 36 – HDM + HDS model: Model output vs. experimental data for Djeno residue, using the
The results obtained for Oural residue feedstock are presented in Figure 37. As mentioned in
chapter 4.2.3, it is difficult to compare the HDM model simulations with experimental data for this
63
feedstock, since only two experimental points are available. However, the general tendency of
experimental points in Figure 37 appears to be well simulated by the model.
(a)
(b)
Figure 37 – HDM + HDS model: Model output vs. experimental data for Oural residue, using the
4.4
Results summary
The results presented in the above chapters concern a residue hydrotreatment kinetic model that
simulate the operation of a reactor with a single HDM section and afterwards the operation of the unit
with both HDM and HDS sections.
Based on the parameter optimization carried out for Buzurgan residue, it may be concluded that it
is possible to satisfactorily adjust the model output to experimental data by optimizing the kinetic and
adsorption constants. To improve the slight deviations observed, further simulations with different
parameters would have to be carried out or the obtained set of parameters would have to be
introduced in the estimation routine implemented. However, it was shown that for a maximum of 250
iterations, the sum of square differences between experimental data and model output only decreased
by 5%.
The values obtained for the kinetic and adsorption constants not always could be explained based
on the phenomena involved. However, it should be noted that of values with different physical
meaning can sometimes serve as a solution for the problem, based on purely mathematical
arguments.
The kinetic and adsorption constants optimized for the reference residue can be used to simulate
for other residues. The obtained model simulations only show slight deviations from experimental
data, which could be improved by changing the repartition coefficients, distribution coefficients and ns
numbers.
64
According to the sensitivity analysis carried out, the impact of varying the repartition coefficients,
distribution coefficients and ns numbers may be, in most cases, explained using arguments based on
the phenomena involved. However, an inconsistency was found while varying the ns numbers since
the model simulated a higher sulfur removal for large molecules and lower removal for smaller
molecules, contrary to the expected.
The results presented in the sensitivity analysis also pointed out that the model response to
variations in a certain parameter may depend on the values set for other parameters. Therefore, the
sensitivity analysis results should be analyzed carefully, to avoid drawing false conclusions.
Although many of the results presented are focused on finding a good adjustment between
experimental data and model output, the main goal of this study was to determine the model’s
sensitivity to variations in its parameters and how it responds for feedstocks with different origins.
65
5
Conclusion and perspectives
The main purpose of this study was to analyze the sensitivity of the model output to variations in
its parameters and to verify if these variations were coherent with the phenomena occurring in a
residue hydrotreatment reactor. In most cases, the observed results could be explained based on the
phenomena occurring with some exceptions.
One of the problems perceived during the parameter optimization concerned the lack of
experimental data. To ensure that the optimized parameters correctly describe the experimental
observations, more data should be obtained, especially for the Oural residue in both sections.
The kinetic and adsorption constants optimization was carried out for a chosen reference
feedstock, in this case Buzurgan residue. Using the obtained parameters to simulate for other
residues (Arabian Light, Djeno and Oural), the results are mainly satisfactory although some deviation
were observed between experimental data and model output. For future work, it would be interesting
to optimize these parameters for a different feedstock and see how this would impact the model
simulations for residues with different origins.
It was pointed out that using the implemented estimation routine, significant computation time is
required to decrease the sum of square differences between experimental data and model output by
only 5%. For future work it would be interesting to analyze the results of long estimation run, with a
high number of maximum iterations. The set of kinetic and adsorption constants obtained in this study
could be used as an initial value for this estimation.
Although this model was developed with the purpose of understanding the reactivity of residue
feedstocks with different origins, it could be used as a base for a model describing the full operation of
an industrial residue hydrotreatment unit. This would imply taking into account the series of reactors
used in each section, the intermediary quenching operations and the effect of variations in the
operating conditions of the unit such as the reactor temperature.
66
6
Appendices
6.1
Detailed analysis for the different residue feedstocks
The following tables present the detailed analysis available for the different residue feedstocks
(Buzurgan, Arabian Light, Djeno, Oural). For each residue, the available data includes the feedstock
density, the percentage of each SARA fraction and the composition in heteroatoms (sulfur, nitrogen,
nickel and vanadium). All available data is presented for the different residence times studied in each
reactor (HDM and HDS).
6.1.1
Buzurgan
Table 16 – Density of Buzurgan residue for different residence times in the HDM and HDS reactor.
HDM reactor
Residence time (h)
3
Density (kg/m )
HDS reactor
0
1
2
1
2
1037
1034
1026
1013
998
Table 17 – Percentage of each SARA fraction in Buzurgan residue, for different residence times in the
HDM and HDS reactor.
HDM reactor
HDS reactor
Residence time (h)
0
1
2
1
2
S
9.6
11.1
11.1
13.3
15.4
A
38.5
39.3
40.8
43.7
45.2
R
37
34.7
35.2
30.1
27.4
A
14.9
14.9
12.8
12.9
12
Table 18 – Heteroatoms composition of Buzurgan residue for different residence times in the HDM and
HDS reactor.
HDM reactor
Asphaltenes
Resins
Aromatics
HDS reactor
Residence time
0
1
2
1
2
S (%wt)
8.04
8.33
8.07
8.34
8.03
N (%wt)
Ni (wppm)
V (wppm)
1.09
251
801
1.02
207
626
0.84
207
600
0.99
249
590
0.98
252
630
S (%wt)
7.15
6.09
5.74
5.52
4.6
N (%wt)
Ni (wppm)
V (wppm)
0.78
56
172
0.75
55
163
0.76
45
132
0.8
47
161
0.8
30
77
S (%wt)
4.87
4.53
4.04
2.29
1.98
67
6.1.2
Arabian Light
Table 19 – Density of Arabian Light residue for different residence times in the HDM and HDS reactor.
HDM reactor
Residence time (h)
3
Density (kg/m )
HDS reactor
0
1
2
1
2
1017
996
995
990
989
Table 20 – Percentage of each SARA fraction in Arabian Light residue, for different residence times in the
HDM and HDS reactor.
HDM reactor
HDS reactor
Residence time (h)
0
1
2
1
2
S
10.8
12.3
14.3
14.6
16.6
A
42.5
45
47.1
47.6
47.8
R
37.7
34.5
30.7
30.3
27.7
A
9
8.2
7.9
7.5
7.8
Table 21 – Heteroatoms composition of Arabian Light residue for different residence times in the HDM
and HDS reactor.
HDM reactor
Residence time
0
1
2
1
2
Asphaltenes
S (%wt)
N (%wt)
Ni (wppm)
V (wppm)
6.84
1.16
202
628
7.02
0.92
158
488
6.78
0.88
160
463
6.74
0.96
202
497
5.72
0.89
157
370
Resins
S (%wt)
N (%wt)
Ni (ppm)
V (wppm)
6.05
0.75
25
107
5.42
0.71
33
106
4.99
0.79
33
94
4.69
0.76
27
93
4.12
26
78
0.71
S (%wt)
3.87
3.78
3.66
2.54
1.69
Aromatics
6.1.3
HDS reactor
Djeno
Table 22 – Density of Djeno residue for different residence times in the HDM and HDS reactor.
HDM reactor
Residence time (h)
3
Density (kg/m )
HDS reactor
0
1
2
1
2
989
984
984
984
989
68
Table 23 – Percentage of each SARA fraction in Djeno residue, for different residence times in the HDM
and HDS reactor.
HDM reactor
HDS reactor
Residence time (h)
0
1
2
1
2
S
18.8
20.2
20.7
21.3
21.4
A
28
30.8
31.7
33.7
34.9
R
47.9
44.5
41.1
43.1
39.2
A
5.2
4.5
4.4
3.9
4.4
Table 24 – Heteroatoms composition of Djeno residue for different residence times in the HDM and HDS
reactor.
HDM reactor
Residence time
0
1
2
1
2
Asphaltenes
S (%wt)
N (%wt)
Ni (wppm)
V (wppm)
0.52
1.44
479
47
0.52
1.5
414
50
0.49
1.52
413
55.5
0.48
1.58
500
39
0.45
1.43
374.4
56.5
Resins
S (%wt)
N (%wt)
Ni (wppm)
V (wppm)
0.65
1.25
125
16
0.4
1.2
120
13
0.38
1.21
108
11
0.37
1.27
112
12
0.29
1.16
96
11
S (%wt)
0.52
0.27
0.31
0.19
0.38
Aromatics
6.1.4
HDS reactor
Oural
Table 25 – Density of Oural residue for different residence times in the HDM and HDS reactor.
Residence time (h)
3
Density (kg/m )
HDM reactor
HDS reactor
0
2
1
2
1004
995
990
989
69
Table 26 – Percentage of each SARA fraction in Oural residue, for different residence times in the HDM
and HDS reactor.
HDM reactor
HDS reactor
Residence time (h)
0
2
1
2
S
11.1
13.6
15.5
18.2
A
43.5
46.5
47.7
R
39.8
37.1
33.2
29.6
A
5.7
4.5
4.8
4.5
44.8
Table 27 – Heteroatoms composition of Oural residue for different residence times in the HDM and HDS
reactor.
HDM reactor
HDS reactor
Residence time
0
2
1
2
Asphaltenes
S (%wt)
N (%wt)
Ni (wppm)
V (wppm)
3.24
1.37
336
1006
2.53
1.31
287
765
3.16
1.38
374
886
2.84
1.38
259.9
591.8
Resins
S (%wt)
N (%wt)
Ni (wppm)
V (wppm)
3.17
1.18
77
283
2.55
1.12
52
144
2.52
1.17
52
154
1.9
1.22
41
114
S (%wt)
3.11
3.1
2.11
1.31
Aromatics
70
6.2
GPC curves
The following figures present the GPC curves for the resins and asphaltenes in each residue
feedstock.
6.2.1
Buzurgan
(a)
(b)
Figure 38 – GPC curves for Buzurgan residue: (a) Asphaltenes ; (b) Resins.
6.2.2
Arabian Light
(a)
(b)
Figure 39 - GPC curves for Arabian Light residue: (a) Asphaltenes ; (b) Resins.
71
6.2.3
Djeno
(a)
(b)
Figure 40 - GPC curves for Djeno residue: (a) Asphaltenes ; (b) Resins.
6.2.4
Oural
(a)
(b)
Figure 41 - GPC curves for Buzurgan residue: (a) Asphaltenes ; (b) Resins.
72
6.3
Simulation results for different residues
The following chapters present the results of simulations for different residues using the
parameters optimized for the HDM + HDS model with Buzurgan used residue as a reference. In these
figures, the solid lines represent the model output for the HDM section while the dashed lines
represent the model output for the HDS section. The experimental data is represented by the filled and
unfilled marks, for the HDM and HDS sections, respectively.
6.3.1
Arabian Light
(a)
(b)
Figure 42 – HDM +HDS model: optimized model output vs. experimental data (Arabian Light) for: (a)
nickel removal; (b) vanadium removal.
(a)
(b)
sulfur removal; (b) nitrogen removal.
73
(a)
(b)
total lump fractions; (b) overall heteroatom removal.
6.3.2
Djeno
(a)
(b)
Figure 45 – HDM +HDS model: optimized model output vs. experimental data (Djeno) for: (a) nickel
74
(a)
(b)
Figure 46 – HDM +HDS model: optimized model output vs. experimental data (Djeno) for: (a) sulfur
(a)
(b)
Figure 47 - HDM +HDS model: optimized model output vs. experimental data (Djeno) for: (a) total lump
fractions; (b) overall heteroatom removal.
75
6.3.3
Oural
(a)
(b)
Figure 48 – HDM +HDS model: optimized model output vs. experimental data (Oural) for: (a) nickel
(a)
(b)
Figure 49 – HDM +HDS model: optimized model output vs. experimental data (Oural) for: (a) sulfur
76
(a)
(b)
Figure 50 - HDM +HDS model: optimized model output vs. experimental data (Djeno) for: (a) total lump
fractions; (b) overall heteroatom removal.
77
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Modeling of vacuum residue hydrotreatment Engenharia Química

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