Barbara Browning
email: barbara.browning@univ-lyon1.fr

Françoise Couenne

Tim Jansen

Maxime Lacroix

Pedro Alvarez

Mélaz Tayakout-Fayolle

Francoise Couenne

Kinetic modeling of deep vacuum residue hydroconversion in a pilot scale continuous slurry reactor with recycle

Keywords: kinetic modeling, slurry phase hydroconversion, distributed lumped model, vacuum residue, continuous reactor, recycle

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

As part of the energy transition, oil product demand is shifting towards the lighter cuts required for petrochemical feedstocks, aviation and shipping [1]. This challenge is amplified by the fact that crude sources are becoming heavier [START_REF] Marafi | Hydroprocessing of heavy residual oil: Opportunities and challenges[END_REF]. Slurry phase hydroconversion processes have the potential to help bridge the gap by upgrading very heavy residues, with high asphaltenes and impurities content, to near total conversion [START_REF] Angeles | A review of experimental procedures for heavy oil hydrocracking with dispersed catalyst[END_REF].

Vacuum Residue (VR) is the heaviest crude oil distillation product and includes everything with an atmospheric boiling point above 525 °C. This material has high viscosity and low hydrogen to carbon ratio. There are two main VR upgrading routes: carbon rejection and hydrogen addition [START_REF] Sahu | A review of recent advances in catalytic hydrocracking of heavy residues[END_REF]. Carbon rejection processes are the simplest and least expensive option, as no catalyst or H2 supply is needed, but higher conversions are achieved with hydrogen addition methods. These processes have the benefit of avoiding coke production but are traditionally dependent on supported catalysts. With very heavy residues, this leads to high reactor pressure drop, fouling and feed diffusion and mass transfer problems [START_REF] Sahu | A review of recent advances in catalytic hydrocracking of heavy residues[END_REF]. Slurry phase hydroconversion adopts unsupported dispersed catalysts, sometimes formed in-situ, to overcome these difficulties [START_REF] Zhang | A Review of Slurry-Phase Hydrocracking Heavy Oil Technology[END_REF]. It is an active area of research with numerous recent studies on catalyst improvements and innovations [START_REF] Alawad | Advances in Upgrading Process of Petroleum Residue: A Review[END_REF][START_REF] Sánchez | Bifunctional MoS 2 -Silica-Alumina Catalysts for Slurry Phase Phenanthrene-Decalin Hydroconversion[END_REF][START_REF] Kim | Active phase of dispersed MoS2 catalysts for slurry phase hydrocracking of vacuum residue[END_REF][START_REF] Kh | Ex-Situ Synthesis and Study of Nanosized Mo-Containing Catalyst for Petroleum Residue Hydro-Conversion[END_REF].

Several reviews [START_REF] Sahu | A review of recent advances in catalytic hydrocracking of heavy residues[END_REF][START_REF] Zhang | A Review of Slurry-Phase Hydrocracking Heavy Oil Technology[END_REF][START_REF] Castañeda | Current situation of emerging technologies for upgrading of heavy oils[END_REF][START_REF] Al-Attas | Recent Advances in Heavy Oil Upgrading Using Dispersed Catalysts[END_REF] follow the recent evolution in slurry phase VR hydroconversion technologies, the most well-known of which are listed in Table 1. Operating conditions are above 400°C and 100 bar with reported conversions of at least 90%. The historical Veba-Combi-Cracking (VCC) process, along with the Eni Slurry Technology (EST) process, is a licensed technology [START_REF] Bellussi | Hydroconversion of heavy residues in slurry reactors: Developments and perspectives[END_REF][START_REF] Kang | A review on the Moprecursors for catalytic hydroconversion of heavy oil[END_REF]. Slurry processes can be classified into two groups by catalyst type: low cost / high concentration (Ex: Fe based) or high cost / low concentration (Ex: Mo based). Of those in Table 1 only VCC falls into the first category.

A refinery scale slurry phase reactor is similar to a bubble column and contains dispersed catalyst suspended in the liquid phase with co-or counter-current gas flow [START_REF] Calderón | Modeling of CSTR and SPR small-scale isothermal reactors for heavy oil hydrocracking and hydrotreating[END_REF]. The molecular complexity of VR means that its components comprise a wide range of activities and, to achieve deep conversion, the processes tend to include a strategy to increase concentration and residence time of the most refractory compounds. Coming back to the processes listed in Table 1, the VCC process valorises unreacted residue through combustion or coking [START_REF] Niemann | The VEBA-COMBI-CRACKING-Technology: An update[END_REF] and the Chevron LC-Slurry process concentrates refractory components through sequential multi-stage reactors and an inter-stage separator. Recycle of unconverted residue is an option with the added benefit of conserving active catalyst within the reactor system [START_REF] Bellussi | Hydroconversion of heavy residues in slurry reactors: Developments and perspectives[END_REF][START_REF] Ramírez-Corredores | The science and technology of unconventional oils: finding refining opportunities[END_REF], but a potential drawback is the accumulation of large agglomerated catalyst crystallites [START_REF] Ramírez-Corredores | The science and technology of unconventional oils: finding refining opportunities[END_REF]. The UOP Uniflex process is reported both with and without a Heavy Vacuum Gas Oil (HVGO) recycle [START_REF] Castañeda | Current situation of emerging technologies for upgrading of heavy oils[END_REF][START_REF] Ramírez-Corredores | The science and technology of unconventional oils: finding refining opportunities[END_REF]. The PVDSA intevep HDH plus process has an optional recycle stream, reported to increase conversion from 91 to 97%. Headwaters Technology Innovation HCAT/(HC)3 and the EST processes both recycle unconverted residue back to the reactor [START_REF] Castañeda | Current situation of emerging technologies for upgrading of heavy oils[END_REF][START_REF] Bellussi | Hydroconversion of heavy residues in slurry reactors: Developments and perspectives[END_REF]. Laboratory and pilot scale studies of continuous VR slurry phase deep hydroconversion are rare [START_REF] Angeles | A review of experimental procedures for heavy oil hydrocracking with dispersed catalyst[END_REF]. Continuous reactors have been used with VR to test slurry phase hydroconversion catalysts [START_REF] Matsumura | Hydrocracking Marlim vacuum residue with natural limonite. Part 2: experimental cracking in a slurry-type continuous reactor[END_REF][START_REF] Noguera | A comparative activity study of a new ultra-dispersed catalyst system for a hydrocracking/hydrotreating technology using vacuum residue oil: Merey/Mesa[END_REF][START_REF] Kh | Formation of Polycondensation Products in Heavy Oil Feedstock Hydroconversion in the Presence of Ultrafine Catalyst:Physicochemical Study[END_REF], alternative catalyst systems [START_REF] Kim | Efficient conversion of extra-heavy oil into distillates using tetralin/activated carbon in a continuous reactor at elevated temperatures[END_REF][START_REF] Morawski | Effects of parameters in Ni-Mo catalysed hydrocracking of vacuum residue on composition and quality of obtained products[END_REF] and catalytic steam cracking [START_REF] Fathi | Catalytic Aquaprocessing of Arab Light Vacuum Residue via Short Space Times[END_REF][START_REF] Cabrales-Navarro | Catalytic Steam Cracking of a Deasphalted Vacuum Residue Using a Ni/K Ultradispersed Catalyst[END_REF][START_REF] Kukushkin | Studying the Steam Cracking of Heavy Oil over Iron-and Molybdenum-Containing Dispersed Catalysts in a Flow-Type Reactor[END_REF].

Jansen et al. performed slurry phase hydroconversion experiments with an atmospheric residue in a continuous micro-pilot with recycle and simulated the results [START_REF] Jansen | Characterization of a continuous micro-scale pilot unit for petroleum residue hydroconversion with dispersed catalysts: Hydrodynamics and performances in once-through and recycling mode[END_REF][START_REF] Jansen | Simulation of Petroleum Residue Hydroconversion in a Continuous Pilot Unit Using Batch Reactor Experiments and a Cold Mock-Up[END_REF] and Alvarez et al. extended this to VR for a range of operating temperatures, residence times and recycle ratios [START_REF] Alvarez | Impact of Unconverted Residue Recycling on Slurry-Phase Hydroconversion Performance in a Continuous Microscale Pilot Unit[END_REF]. The impact of the recycle stream has been simulated with batch and semi-batch reactors by returning some [START_REF] Japanwala | Quality of Distillates from Repeated Recycle of Residue[END_REF] or all [START_REF] Del Bianco | Upgrading Activity of Recycled Mo-Based Dispersed Catalysts[END_REF][START_REF] Zhou | Effect of vacuum bottom recycling on slurry bed hydrocracking of residue[END_REF] of the reaction products to the reactor and reprocessing them several times. Also, hydroconversion products have been combined with fresh feed and then reprocessed [START_REF] Tailleur | Effect of recycling the unconverted residue on a hydrocracking catalyst operating in an ebullated bed reactor[END_REF][START_REF] Kadiev | Structural transformations of asphaltenes during hydroconversion of vacuum residue with recycling the hydroconversion product distillation residue[END_REF][START_REF] Shi | Chemical structure change of recycling vacuum bottom residue from slurry-bed hydrocracking of Karamay atmospheric residue in the pilot plant p[END_REF]. Bellussi et al. [START_REF] Bellussi | The role of MoS 2 nano-slabs in the protection of solid cracking catalysts for the total conversion of heavy oils to good quality distillates[END_REF] describe a pilot scale 7.5 L ebullated bed slurry reactor with a continuous recycle and fractionation system. In general, as residue is recycled, it becomes more refractory to processing. The molecular weight, hydrogen content and reactivity of the residue are reduced and the aromaticity increases.

Asphaltenes content degrades in two stages. Firstly, branches detach, resulting in very stable polyaromatic hydrocarbons with high boiling points. Then, under sufficiently severe operating conditions these, more resistant, components break down [START_REF] Kadiev | Structural transformations of asphaltenes during hydroconversion of vacuum residue with recycling the hydroconversion product distillation residue[END_REF] and complete conversion of the residue is possible [START_REF] Japanwala | Quality of Distillates from Repeated Recycle of Residue[END_REF].

Quitian and Ancheyta discuss kinetic models for slurry phase hydrocracking of residue feedstocks [START_REF] Quitian | Experimental Methods for Developing Kinetic Models for Hydrocracking Reactions with Slurry-Phase Catalyst Using Batch Reactors[END_REF] and Al-Attas et al. list some models proposed in the literature [START_REF] Al-Attas | Recent Advances in Heavy Oil Upgrading Using Dispersed Catalysts[END_REF]. There are few kinetic models for slurry phase hydroconversion [START_REF] Alvarez | Impact of Unconverted Residue Recycling on Slurry-Phase Hydroconversion Performance in a Continuous Microscale Pilot Unit[END_REF][START_REF] Browning | Distributed lump kinetic modeling for slurry phase vacuum residue hydroconversion[END_REF][START_REF] Nguyen | Hydroconversion of an atmospheric residue with a dispersed catalyst in a batch reactor: Kinetic modeling including vapor-liquid equilibrium[END_REF] but many for hydrocracking, with good reviews by Acheyta [START_REF] Ancheyta | Kinetic modeling of hydrocracking of heavy oil fractions: A review[END_REF] and Thybaut and Marin [START_REF] Thybaut | Multiscale Aspects in Hydrocracking[END_REF]. Strategies to represent reaction components range from simple traditional lumping, through microkinetics to complex molecular reconstruction with the level of detail dependent on the available data and time for computation. Single-Event MicroKinetics (SEMK) models for hydrocracking build large kinetic networks up from the elementary reaction steps and control the number of parameters by relumping rate coefficients for similar steps or species [START_REF] Thybaut | Multiscale Aspects in Hydrocracking[END_REF]. Molecular-level kinetic models, such as those developed by Klein's research group, liken residue to a crosslinked polymer with cores, inter-core linkages and side chains. Reaction rates are determined from probability density functions of these structural attributes [START_REF] Horton | Molecule-based modeling of heavy oil[END_REF][41][START_REF] Horton | Molecular-Level Kinetic Modeling of Resid Pyrolysis[END_REF]. Rueda-Velasquez and Gray [START_REF] Rueda-Velásquez | Monte Carlo Simulation of Asphaltenes and Products from Thermal Cracking[END_REF] and Oliveira et al. [START_REF] De Oliveira | Simulating vacuum residue hydroconversion by means of Monte-Carlo techniques[END_REF] developed similar methods and molecular-level kinetic models have also been applied to other refinery processes with good results [START_REF] Nguyen | Development of a Structure-Based Lumping Kinetic Model for Light Gas Oil Hydrodesulfurization[END_REF][START_REF] Chen | Molecular-level kinetic modelling of fluid catalytic cracking slurry oil hydrotreating[END_REF]. These models have intensive analysis requirements. For example, Chen et al. [START_REF] Chen | Molecular-level kinetic modelling of fluid catalytic cracking slurry oil hydrotreating[END_REF] used data from six types of analysis method: density, number average molecular weight, Conrandson carbon residue, elemental, mass spectrometry and simulated distillation.

At the other end of the spectrum are traditional lumped models, with five or six pseudocomponents. These are useful for catalyst screening and process optimization [START_REF] Thybaut | Multiscale Aspects in Hydrocracking[END_REF] or testing new reactor models [START_REF] Calderón | Modeling, simulation, and parametric sensitivity analysis of a commercial slurry-phase reactor for heavy oil hydrocracking[END_REF]. Reaction rate parameters are estimated for each lump and, generally, valid for one feedstock and set of operating conditions [START_REF] Thybaut | Multiscale Aspects in Hydrocracking[END_REF]. It is difficult to extend traditional lumped models because every additional lump requires an accompanying set of parameters. Another limitation is that the heaviest lump has no upper boiling point limit and includes a very wide range of different components, so that it cannot be assumed to have constant physical properties. To overcome this, the lump can be represented as a series of pseudo-components [START_REF] Browning | Distributed lump kinetic modeling for slurry phase vacuum residue hydroconversion[END_REF][START_REF] Rueda-Velásquez | A viscosity-conversion model for thermal cracking of heavy oils[END_REF]. Distributed and continuous lumped models, such as those of Stangeland [START_REF] Stangeland | A Kinetic Model for the Prediction of Hydrocracker Yields[END_REF] and Laxaminarasimhan et al. [START_REF] Laxminarasimhan | Continuous lumping model for simulation of hydrocracking[END_REF], were developed to add detail whilst containing the number of parameters. In particular, Stangeland's model [START_REF] Stangeland | A Kinetic Model for the Prediction of Hydrocracker Yields[END_REF], which combines 22 distributed lumps, four parameters, a cracking rate function and product distribution, has been extended to include the effect of H2 partial pressure on reaction rates [START_REF] Pacheco | Hydrocracking: An improved Kinetic Model and Reactor Modeling[END_REF] and has proven useful to represent hydrocracking kinetics in industrial scale reactors [START_REF] Mohanty | Modeling of a hydrocracking reactor[END_REF][START_REF] Li | Kinetic mechanism research of an industrial hydrocracker based on strict calculation of stoichiometric coefficients[END_REF][START_REF] Harode | Axial dispersion modeling of industrial hydrocracking unit and its multiobjective optimization[END_REF].

Browning et al. [START_REF] Browning | Distributed lump kinetic modeling for slurry phase vacuum residue hydroconversion[END_REF] previously developed a distributed lump kinetic model for slurry phase VR hydroconversion with vapour liquid mass transfer resistances and equilibrium taken into account. This was validated against results from experiments performed in a laboratory scale semi-batch reactor and was a stepping stone towards a model which could include the very high conversions achieved with a recycle stream. The experimental results used in this work come from a continuous hydroconversion slurry pilot operating in recycle mode. Conditions are more severe than could be generated in the previously used laboratory scale semi-batch reactor and are close to those found in a refinery scale slurry phase hydroconversion reactor.

Furthermore, the scale of the pilot plant allowed analysis of the small quantity of sediment found in the product stream. The objective of this work is to improve the model of Browning et al. [START_REF] Browning | Distributed lump kinetic modeling for slurry phase vacuum residue hydroconversion[END_REF] by extending it to include Hydrodesulfurisation (HDS) as an integral part of the model, as opposed to its previous representation as a side reaction, and also extending the model to the pilot operating conditions and quantifying the sediment production rate.

Parameter estimation is carried out and the results are discussed and compared to the experimental data from the hydroconversion slurry pilot. The benefits of a kinetic model validated for refinery conditions will be greater ability to predict plant outputs and to simulate and optimise real operating conditions.

Material and methods

Experimental set-up

Slurry phase hydroconversion experiments were performed in a pilot with 2 x 2.2L continuous reactors and a downstream separation and recycle section. Sediment quantities were measured by precipitation in tetrahydrofurane and the amount of H2 consumed was determined by analysis of the reaction products. In once-through mode, density measurement was by pycnometer and steady state was confirmed by processing until the same result was obtained for two successive samples. For recycle operation, the residue density and outlet flow rate were measured by a Coriolis meter which allowed steady state operation to be verified.

Mass balance data was accurate to ± 5%.

Experimental results

134 experiments were carried out in 12 campaigns in both once-through and recycle mode and with one and two reactors in operation as listed in Table 2. Figure 2 gives HTSD results for the feedstock and typical liquid products at 49% and 94% conversion. HTSD allows analysis of heavy oils up to an atmospheric equivalent boiling point of 749°C [START_REF] Vickers | Higher-Temperature Simulated Distillation with DB-HT Sim Dis Columns: Application, Hydrocarbon Processing[END_REF]. The composition above this was estimated by the extrapolation method described in Riazi [START_REF] Riazi | Characterization and properties of petroleum fractions[END_REF]. This uses Eq. ( 1) to complete the HTSD data for the whole boiling range, with the boiling point and initial boiling points, and in Kelvin,

A and B constant and the distilled fraction. The composition of the residue and condensate liquid products is similar for both conversions shown. However, at 49% conversion, 81% of the liquid product is residue whereas at 94% conversion this drops to 12% with 88% recovered as condensate.

- = 1 1 - (1)

Model Construction

Figure 3 gives the flow diagram used to simulate the slurry phase hydroconversion pilot plant. Physical properties are calculated at the temperatures shown. The reactors were represented as two CSTRs (CSTR 1 and CSTR 2) with the following assumptions:

• Isothermal operation

• All reactions occur in the liquid phase,

• Mass transfer between liquid and vapour phases,

• Perfect mixing in the reactor liquid and vapour phases,

• The vapour phase is considered an ideal gas and the liquid as an ideal solution

The rest of the system was represented using simple standard units. The choice to use a splitter and plug flow reactors was for simplicity and because it was adapted to the data available. The real pilot plant separation system between the reactors and the reservoir comprised a stripper and several other pieces of equipment, operating at different temperatures and pressures (see Figure 1). No equilibrium data was available but the outlet residue, gas and condensate stream compositions were measured. Since the overall experimental separation was known, we used this data to estimate the split for each lump over a range of operating conditions.

Having estimated the overall split we added the two plug flow reactors to take account of the volumes in the system. PFR 1 represents the delay due to the separation system residence time and PFR2 that of the recycle pipeline.

The reservoir was modelled as a continuous stirred tank.

Reactor model

Overall and component mole balances were calculated for the liquid and vapour phases according to Eq.s ( 2) to [START_REF] Alawad | Advances in Upgrading Process of Petroleum Residue: A Review[END_REF], where the subscripts in and out relate to the reactor inlet and outlet streams. Concentrations, C, are in mol.m -3 , Volumes, V, in m 3 , volumetric flowrates, Q, in m 3 .s -1 and vapour liquid mass transfer rates, , are in mol.s -1 . Finally reaction rates, r, are in mol.s -1 .m -3 and , is the molar volume of the lump, i , in m 3 .mol -1 . L and g refer to liquid and gas phases and i and T indicate individual lumps and total quantity.

Component liquid phase:

! = , " # $, " -# $, %& ! ' ! , (2)
Overall liquid phase:

( ! ( = (, " # $, " -( # $, %& ! ' ( ! ,( (3)
Component gas phase:

) ) ! ) ) = , " ) # $, " ) - ) # $, %& ) - , (4)
Overall liquid and gas phases:

( ! ( ! ( ) ) ! ) ( ) = (, " ) # $, " ) -( ) # $, %& ) ! (, " # $, " -( # $, %& ! ' ( (5)
: = ∑ , +1 -∑ , , (6)
The reactor liquid volumes are controlled by overflow into the outlet pipe and the gas volume fraction, -) , is related to the volumetric gas flow rate, # $ ) , in m 3 .s -1 , through the reactor by an in-house correlation in the form of Eq. ( 7) with a and b constant. Vapour liquid mass transfer rates, , , in mol.s -1 , are found from Eq. ( 8) with and * , in mol.m -3 , the liquid concentrations in the reactor and at equilibrium. ,in m 3 , is the liquid volume and / 0, in s - 1 , the vapour liquid mass transfer coefficient.

-) = 0. +# $ ) , (7)
, = / 02 * -3

Kinetic model

The kinetic model is based on our previous work [START_REF] Browning | Distributed lump kinetic modeling for slurry phase vacuum residue hydroconversion[END_REF]. True boiling points were used to define traditional lumps as GAS (Tb < 36°C), NAPH (36°C < Tb < 160°C), DIST (160°C < Tb < 350°C), VGO (350°C < Tb < 525°C) and RES (525°C +). The VGO and RES lumps were then subdivided into distributed lumps of boiling range 35°C: VGOi with i = 1 to 5, LRESi with i = 6 to 11 and HRESi with i = 12 to 16. The Heavy Iran VR feedstock is composed of distributed lumps VGO4 to HRES16. LRESi and HRESi are considered separately based on our observations of their disappearance rates. Note also that the cut point between LRESi and HRESi is 735°C which is very close to the maximum boiling point for HTSD. So, LRESi quantities are measured whereas HRESi are mostly estimated using the Riazi method [START_REF] Riazi | Characterization and properties of petroleum fractions[END_REF].

Figure 4 gives the feedstock mass distribution after lumping as well as typical pilot plant liquid products in once-through and recycle mode without extrapolation of the HTSD analysis results.

To incorporate HDS into the distributed lumped model a second similar set of reduced sulphur distributed lumps with the same boiling ranges was also defined:

VGO_low_Si, LRES_low_Si and HRES_low_Si. Molar masses and volumes are required for each component, including the distributed lumps, and these were estimated using ProSimPlus 3.3 [START_REF] Browning | Distributed lump kinetic modeling for slurry phase vacuum residue hydroconversion[END_REF]. To calculate the molar masses and volumes of the reduced sulphur lumps it was assumed that the sulphur mass distribution is uniform across the feedstock and that the atomic sulphur volume is additive with the volume of the sulphur free distributed lump. Figure 5 gives the results for all the lumps. Figure 6 compares H2S production against residue conversion for slurry phase hydroconversion in a semi-batch reactor [START_REF] Browning | Distributed lump kinetic modeling for slurry phase vacuum residue hydroconversion[END_REF]. The relation appears almost linear and this is used later in the development of the kinetic model. The reaction scheme, shown in Figure 7, is based on our previous work [START_REF] Browning | Distributed lump kinetic modeling for slurry phase vacuum residue hydroconversion[END_REF]. It comprises five sets of hydrocracking reactions, where each step is considered individually, and incorporates HDS. The reactions are listed in Eq.s [START_REF] Castañeda | Current situation of emerging technologies for upgrading of heavy oils[END_REF] to [START_REF] Kh | Formation of Polycondensation Products in Heavy Oil Feedstock Hydroconversion in the Presence of Ultrafine Catalyst:Physicochemical Study[END_REF]. The cracking reactions all consume H2 and produce lighter gas oil products.

Reactions 1 to 4 are thermally activated and reaction 5 is a catalytic cascade. HDS releases sulphur in the form of H2S and transfers material from the sulphur-containing, distributed lumps used to represent the feedstock to the reduced-sulphur lumps. Both the sulphur containing and sulphur reduced lumps undergo the same hydrocracking reactions. The parameter, 4 5 , is introduced to represent the fraction of sulphur content removed from the sulphur containing lumps. Their products, 67_ 9:_; , <=>;_ 9:_; and ?=>;_ 9:_; , contain the residual sulphur.

Product stoichiometric coefficients, @ A B , for VGO and DIST from reaction 1 and 2 are estimated for the heaviest reacting lump. The lighter distributed lumps produce less VGO and DIST proportionally to their reacting lump molar mass. GAS and NAPH stoichiometric coefficients are calculated to complete the mass balance. Reactions 3 and 4 compete to convert HRESi distributed lumps respectively into DIST and sediment with no secondary products. Reaction 5 is a cascade through LRESi, VGOi and DIST. Reaction 1 VGO product repartition coefficient, P Q , gives a linear distribution since there are up to 5 potential products.

P Q is calculated by Eqn. ( 9) for lumps, i, VGO1 to VGON receiving reaction 1 product where NVGO is the number of VGO product lumps and R is the estimated parameter. So, if R = 0 the product is equally distributed between the VGO lumps.

P Q = 1 T $UV ! W 2T $UV ! 13 2 -YZ R (9)

Reaction 1:

<=>; ! [ 1 ? \ → @ B P 67 Q ! @ ^_`6 ; with i from 6 to 11 and j from 1 to 5 [START_REF] Castañeda | Current situation of emerging technologies for upgrading of heavy oils[END_REF] 67 ! [ 1 ? \ → @ B P 67 Q ! @ ^_`6 ; with i from 2 to 5 and j from 1 to 4 [START_REF] Al-Attas | Recent Advances in Heavy Oil Upgrading Using Dispersed Catalysts[END_REF] 67 ! [ 1 ? \ → @ a^bc de; ! @ ^_`6 ;

(12) Reaction 2:

<=>; ! [ 1 ? \ → @ \ B de; ! @ \ f_gh T i?

67 ! [ 1 ? \ → @ \ B de; ! @ \ f_gh T i?

(13) (14)
Reaction 3: Temperature dependent cracking rates, ' A, , in mol.m -3 .s -1 , are given by Eq.s ( 20) to [START_REF] Fathi | Catalytic Aquaprocessing of Arab Light Vacuum Residue via Short Space Times[END_REF] with thermal reactions 1 to 4 represented by Eq. ( 20) and catalytic reaction 5 by Eq. ( 21). The symbols, / , and, / A , represent the reaction rate constant at the reference and reaction temperatures respectively. >0 A , in J.mol -1 , is the activation energy, R the ideal gas constant and T the temperature in Kelvin.

?=>; ! [ 1 ? \ → @ j B de; (15
' A, = 4 A, / A " B with r = 1 to 4 ( 20
)
' A, = 4 A, / A q r with r = 5 ( 21)

2/ A 3 = +/ ,A , - >0 A = (22)
Catalytic cascade reaction 5 is first order with respect to the concentration of the distributed lump and H2. Thermal reactions 3 and 4 are also first order with respect to the distributed lump concentrations. For thermal reactions 1 and 2, reaction orders, n, are calculated as shown in Eq. [START_REF] Cabrales-Navarro | Catalytic Steam Cracking of a Deasphalted Vacuum Residue Using a Ni/K Ultradispersed Catalyst[END_REF], where i corresponds to the distributed lump number for VGO1 to LRES11.

A reactivity parameter, s, is incorporated into the pre-exponential reaction constant as shown in Eq. ( 24). This gives a distribution of reaction rates increasing with boiling point as observed in the literature [START_REF] Weitkamp | The Influence of Chain Length in Hydrocracking and Hydroisomerization of n -Alkanes[END_REF].

n = n m ! n \ (23)
/ ,A, = / ,A exp 2s. m3

The HDS reaction rate is coupled to the hydroconversion rate as shown in Eq.s [START_REF] Jansen | Characterization of a continuous micro-scale pilot unit for petroleum residue hydroconversion with dispersed catalysts: Hydrodynamics and performances in once-through and recycling mode[END_REF] and [START_REF] Jansen | Simulation of Petroleum Residue Hydroconversion in a Continuous Pilot Unit Using Batch Reactor Experiments and a Cold Mock-Up[END_REF].

Based on Figure 6, the relationship between hydroconversion and H2S is approximately linear and it is assumed that this can be extrapolated to all the distributed lumps and to the continuous reactor operating conditions.

Finally, the H2 consumption rate depends on reaction type with one general consumption rate parameter, [ , for thermal reactions (r = 1 to 4) and another, [ \ , for the cascade reaction, (r = 5).

Parameter estimation

Table 3 lists the 19 estimated parameters for the slurry phase hydroconversion kinetic model with recycle. The VGO product repartition parameter applies only to reaction set 1 and stoichiometric coefficients are only for reactions 1 and 2. Parameter estimation was carried out against the 1324 data points from the 74 experiments comprising the six later campaigns numbered, 7 to 12, because these include measurement of the produced sediment quantities and H2 consumed. Campaigns 7 to 12 were all performed in recycle mode with both reactors in operation. The temperature range covered is 420 -435°C. The data points are the total outlet mass flow rates of all the measured components, the NAPH and DIST boiling ranges and the distributed lumps. The sediment, H2 and H2S data was weighted to compensate for low mass flow rates. MATLAB non-linear least squares solver function, lsqnonlin, was used with the trust-region-reflective algorithm which minimises an objective function based on an input vector of differences between the measured and calculated data.

Parameter significance levels and confidence limits were determined from Eq.s ( 27) to (29) [START_REF] Rasmuson | Mathematical Modeling in Chemical Engineering[END_REF]. J is the Jacobian matrix and zl+{ | , is the standard error found for each parameter. SSE, nd and p are the sum of the errors squared and the numbers of data points and parameters respectively. { | is the parameter value, t ~ is the observed student t-value and R • /2 is the significance level.

Reactions

Reaction specific parameters:

1 2 3 4 5
Pre-exponential constants (mol -1 .m 3 ) n-1 .s -1 ln2k13 ln2k23 ln2k33 ln2k43 ln2k53* Activation energies (kJ.mol -1 )

Ea1 Ea2 Ea3 Ea4 Ea5 Stoichiometric coefficients (-) 4 4
*(mol -1 .m 3 ) n .s -1 zl+{ | , = ‰ ;;> 22Š ( Š3 p 3 || 2 ‹ -OE3 (27)
t ~= { | zl+{ | , (28)
{ | ± zl+{ | ,t2 ‹ -OE; R • /23 (29)

Results and Discussion

Table 4 gives the estimated parameters and corresponding 95% confidence limits. The reaction constants are in the form of their natural logs at the reference temperature ln(k0,r).

All the parameters are significant to 95% except for [ \ , the stoichiometric coefficient for H2 consumption applied to reaction set 5, the catalytic cascade. The activation energy confidence limits are quite wide for reactions 4 and 5, perhaps because the temperature range of the data selected for parameter estimation is quite narrow and also, catalytic reaction 5 is not very temperature sensitive. It is interesting to compare the new parameter values with those from our previous work at lower conversions with a Safaniya VR in a semi-batch reactor [START_REF] Browning | Distributed lump kinetic modeling for slurry phase vacuum residue hydroconversion[END_REF]. The value of the VGO product repartition parameter, α, is unchanged and indicates that reaction 1 produces 2.13 times more VGO1 than VGO5. The estimated reaction 1 and 2 order parameters, n1 and n2, correspond to reaction orders decreasing from 3.60 to 2.45 as the distributed lumps, VGO1 through RES6 get heavier. This agrees with our previous work [START_REF] Browning | Distributed lump kinetic modeling for slurry phase vacuum residue hydroconversion[END_REF] and is coherent with the increased value of the reactivity parameter, f, to 1.22 from 0.845 and the idea that lighter distributed lumps become more heterogeneous by receiving more hydroconversion products with a wide range of structures. The estimated activation energies at deep hydroconversion for reactions 1 to 3 are all high relative to our previous results at moderate conversions, respectively 289, 334 and 306 kJ.mol -1 for the same reactions in a semi-batch reactor [START_REF] Browning | Distributed lump kinetic modeling for slurry phase vacuum residue hydroconversion[END_REF]. Finally, the stoichiometric coefficient for reaction 1 is unchanged, but that of reaction 2 has adjusted to account for the inclusion of reaction 4, HRES to sediment.

Figure 8 (a) shows the experimental conversions for all the experiments compared against those calculated with the estimated parameters. There is a good fit for the experiments used to estimate the parameters, campaigns 7 to 12. Campaigns 1 to 3 were performed with a single reactor in once-through mode. The recycle was introduced from campaign 4 and the second reactor from campaign 5. The first experiment of each campaign was performed in once-through mode at these experiments stand out because of their low conversion rates. The results validate the estimated parameters but the conversion is consistently underestimated for the pilot in once-through mode. It is well known that the small amount of residue remaining at the very high conversions obtained in recycle mode is less reactive than that found in VR feedstock. The rate equations for reaction sets 1 and 2 are designed to take this into account by inclusion of a reaction order distribution but reactions 3, 4 and 5 are all first order. Figure 8 (b) and (c) compare the calculated and experimental yields for VGO, GAS and NAPH and DIST. Figure 9 (a) gives the calculated reaction rates for all the campaigns. It shows that at very high conversions it is the catalytic cascade reaction which dominates. Unlike reaction sets 1 and 2, the catalytic cascade is a first order reaction and therefore does not take any heterogeneity within the distributed lumps into account. So this could be the cause of the discrepancy observed between the measured and calculated conversions in once-through mode. This result corresponds well with the knowledge that it is the catalytic slurry phase hydroconversion processes that achieve very high conversions; once all the material that can be consumed by the thermal reactions is gone, catalytic reactions continue to erode the remaining refractory molecules. Figure 9 (b) and (c) show the calculated concentrations. Figure 10 shows the yields parity plot for GAS, NAPH and DIST and the overall VGO and residue lumps. The yields fit well except for the VGO which is slightly overestimated. At deep conversion, the VGO product is more reactive than the model predicts. This is probably due to ageing and, as for the discrepancy in the once-through mode conversions, could be a consequence of representing reaction 5 as first order. stoichiometric coefficient across all the reactions but more detail is needed to observe the mechanisms at play. Also, the H2 consumption rate is much lower than in our previous work with a Safaniya VR [START_REF] Browning | Distributed lump kinetic modeling for slurry phase vacuum residue hydroconversion[END_REF]. H2 consumption depends on the molecular structures undergoing hydroconversion, whereas our distributed lumps are defined by true boiling point only. If we compare the two VRs, the Iran Heavy has lower total hydrogen content than the Safaniya, more aromatics and less resins, with reported atomic H/C ratios of 1.44 [START_REF] Zhao | Feedstock characteristic index and critical properties of heavy crudes and petroleum residua[END_REF] and 1.5 [START_REF] Thomas | Visbreaking of Safaniya vacuum residue in the presence of additives[END_REF] respectively. So, the Safaniya does not seem to lack hydrogen. However, Saturates, Aromatics, Resins and Asphaltenes (SARA) analysis results from the literature, given in main conclusion that can be drawn is that H2 consumption is highly dependent on feedstock composition. To consider the impact of this on the model, the cascade reaction rate depends on H2 concentration whilst thermal reaction rates are independent of it. However, reactor H2 concentrations are more likely to be controlled by the reactor operating pressure than the reaction rates. So, the likely outcome of modeling with the reported parameters would be a misrepresentation of H2 requirements, and the best option would be to adjust the H2 consumption parameters for the new feedstock. If the H2 partial pressure in the reactor was reduced, the catalytic cascade reaction rate would decrease and the reaction profile would shift towards more thermal reactions. The model results are of correct order although there is some scatter. According to our model, sediment production from heavy residue does not have time to stabilise under recycle operation and sediment accumulates in the reactors. Figure 13 shows the H2S yield parity plot with good results in both once-through and recycle modes. This validates the linear approach to modelling the relation between hydroconversion and HDS.

Conclusions

The

  Figure 1 gives a simplified flow diagram of the equipment. Operation is possible with one or two reactors online and in once-through or recycle mode. Campaigns of experimentswere carried out where the first set of operating conditions were always in once-through mode and recycle rates could be specified from the second experiment to the end of the campaign. The separation section includes a high pressure separator and a stripper operating at atmospheric pressure. Gases and condensate streams pass through a scrubber and low pressure separator before analysis. Liquids are collected in a reservoir before recycle back to the reactors. The feedstock was an Iran Heavy VR with 4.2 wt % sulphur content and density of 1053 kg.m -3 at 15°C and atmospheric pressure. This was mixed with a catalyst precursor and H2 at 150 bar upstream of the reactor. Operating temperatures ranged from 420 to 452°C with feed flow rates from 0.27 kg.h -1 to 1.23 kg.h -1 in once through mode. Recycle rates are up to 3.2 times the feed mass flow rate. Outlet gases were analysed online by gas chromatography. All condensate and residue liquid products were analysed by High Temperature Simulated Distillation (HTSD) using an Agilent series 6890 chromatography column and according to the standard ASTM guideline D7169[START_REF]ASTM D7169-16[END_REF].

Figure 1 .

 1 Figure 1. Simplified Process Flow Diagram of slurry phase hydroconversion pilot plant.

Figure 2 .

 2 Figure 2. Typical HTSD results at (a) 49% (b) 94% conversion. Feedstock, residue and condensate represented by solid, dashed and dotted lines respectively.

Figure 3 .

 3 Figure 3. Flow diagram for slurry phase hydroconversion pilot plant simulation.

Figure 4 .

 4 Figure 4. Distributed lump mass fractions for (a) feedstock and typical liquid products in (b) once-through and (c) recycle modes.

Figure 5 .Figure 6 .

 56 Figure 5. Calculated molar masses and molar volumes of hydrocarbon lumps with and without sulphur content.

Figure 7 .

 7 Figure 7. Reaction scheme showing all reaction sets .

i = 1 to 5 i

 5

Figure 8 .Figure 9 .

 89 Figure 8. Calculated and experimental (a) conversions (b) VGO and GAS yields (c) NAPH and DIST yields for all the campaigns.

Figure 10 .

 10 Figure 10. Yields parity plot for GAS, NAPH and DIST and the overall VGO and residue lumps.

Figure 11 shows

 11 Figure11shows the experimental and calculated H2 consumption against conversion. The

Figure 11 .

 11 Figure 11. Experimental and calculated H2 consumption against conversion.

1 )Figure 12 (

 112 Figure 12 (a) gives the parity plot between the calculated and experimental values for

Figure 12 .Figure 13 .

 1213 Figure 12. Sediment (a) yield parity plot (b) reactor calculated concentration

Fexα

  distributed lump model of VGO and RES for slurry phase VR hydroconversion has been extended to include sediment production and give a more physical representation of HDS. The new version of the model has been tested against deep hydroconversion data from a continuous pilot plant with recycle. The linear approach to integrating the HDS reaction has been validated against the experimental data and the sediment production results indicate an accumulation in the reactor in recycle operating mode. The reaction regime under the deep hydroconversion conditions found in recycle operating mode shifts away from thermal reactions and towards the catalytic cascade. This reaction should be the focus in adapting this kinetic model to represent the full operating range of an industrial slurry phase hydroconversion unit. Vapour liquid mass transfer rates (mol.s -1 ) k Reaction rate constant kla Vapour -liquid mass transfer coefficient(s -1 ) n Reaction order (-), reaction order parameter (-) NVGO Number of VGO product lumps Qv Volumetric flow rate (m 3 .s -1 ) r Reaction rate (mol.s -1 .m -3 ) R Ideal gas constant (kJ.mol -1 .K -1 ) Parameter for repartition coefficient for reaction 1VGO product (-) ɛg Volumetric gas fraction β Repartition coefficient for reaction 1VGO product (-) η1, η2 H2 consumption rate parameters (-), (-)

Table 1 . VR Slurry phase hydroconversion upgrading processes

 1

	Process name	Reactor conditions	Conversion Type of process
		Temperature	Pressure
		(°C)	(bar)
	Veba-Combi-Cracker	440-485	220-250 >90	Once-through with 5
	(VCC)				wt% iron based catalyst
	[12,14]				[13].
	UOP Uniflex	450-460	160-180 97	Once-through or recycle
	(CANMET)
	[13,15]
	Eni Slurry Technology	410-450	150	95-99	Recycle
	(EST)
	[12]
	PVDSA-Intevep HDH	430-460	170-210 92	Optional recycle
	plus				increases conversion to
	[12,15]				97%
	Chevron LC-Slurry	400-440	100-200 97	Sequential multi-stage
	[13,15]				reactors with inter-stage
					separator and possible
					recycle
	Headwaters Technology	430-450	140	95	Recycle
	Innovation HCAT/(HC)3
	[10,13,15]

Table 2 . Campaigns performed with hydroconversion pilot plant.

 2

	Campaign	Number of reactors	Sediment	Operating mode
	number	in operation	measurement	Experiment 1	Subsequent experiments
	1-3	1	N	Once-through	Once-through
	4	1	N	Once-through	Recycle
	5	2	N	Once-through	Recycle
	6	2	N	Once-through	Recycle
	7-12	2	Y	Once-through	Recycle

  Reactor liquid volume is calculated using the molar volumes and based on the assumption that the liquid is an ideal solution

					Gases and condensate
					330/350°C
	RSV + H 2	350°C	8	8
					330/350°C
			CSTR 1	CSTR 2	Splitter	PFR 1
					8
					230°C
					230°C
					Residue
				PFR 2	Reservoir

Table 3 . Parameters estimated for slurry phase hydroconversion kinetic model with recycle.

 3

Table 4 .

 4 Estimated parameter values for slurry phase hydroconversion kinetic model with recycle

			Reaction specific parameters
	Reaction	ln(k0)	Ea	ν	α	[ \
		(mol -1 .m 3 ) n-1 .s -1	(kJ.mol -1 )	(-)	(-)	(-)
	1	-28.4 ± 0.5	410 ± 13	5.07 ± 0.09 0.036 ± 0.012
	2	-29.3 ± 0.5	376 ± 13	4.37 ± 0.46
	3	-8.43 ± 0.09	366 ± 5
	4	-12.6 ± 0.5	299 ± 29
	5	-16.70 ± 0.04*	79 ± 10			0.4 ± 0.7
						*(mol -1 .m 3 ) n .s -1
	General parameters
	n1	-0.115 ± 0.040
	n2	3.717 ± 0.198
	f	1.220 ± 0.143
	[	5.992 ± 1.287
	νHDS	0.859 ± 0.039

Table 5 ,

 5 indicate that Safaniya VR is richer in Resins and Asphaltenes and, therefore, it may be the cracking reactions associated with these species which consume more hydrogen. The

	0.6
	0.5
	0.4
	0.3
	0.2
							GAS
							NAPH
	0.1						DIST
							VGO
							RES
	0	0	0.1	0.2	0.3	0.4	0.5	0.6
				Experimental yield g.g effluent -1

Table 5 . SARA fractions of Iran Heavy and Safaniya VRs

 5

		Saturates	Aromatics	Resins	Asphaltenes
	Iran Heavy [60] 12.6	46.7	29.9	10.8
	Safaniya [62]	11	39	34	14

Acknowledgements

The authors would like thank TOTAL for financial support.


Estelle Moulis

Stéphane Barthélemi
email: steph.barthelemi@wanadoo.fr

Laurent Delsol

with severe MIH involving first permanent molars extractions: A case report

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Class II division 1 is a very frequent malocclusion in Europe with an increased overjet [START_REF] Booij | Class II treatment by extraction of maxillary first molars or Herbst appliance: dentoskeletal and soft tissue effects in comparison[END_REF] and mainly due to a retrognathic mandible. The risk of such overjet in young patients is anterior dental trauma [START_REF] Koroluk | Incisor trauma and early treatment for Class II Division 1 malocclusion[END_REF] as well as being bullying at school which is particularly important in class II division 1 patients [START_REF] Seehra | Bullying in orthodontic patients and its relationship to malocclusion, self-esteem and oral health-related quality of life[END_REF]. The Molar-Incisor Hypomineralisation (MIH) is also relatively frequent in young patients, around 15% of children with many country variations [START_REF] Zhao | The Prevalence of Molar Incisor Hypomineralization: Evidence From 70 Studies[END_REF] and with many difficulties of restorative treatments. In these cases when the prognosis of the four first permanent molars is poor, the extractions followed by an orthodontic treatment with extraction space closure is a good issue when the third molars germs are present offering the patient a definitive solution to this problem. When the MIH is combined with the class II division 1 malocclusion, the orthodontic mechanics should be adequate to avoid side-effects of the extraction space closure. When the skeletal pattern is adequate, temporary bone anchorage devices (TADS) are helpful for anchorage control, but in young patients the loss rate is increased due to the quality of bone, and in some cases the orthodontist must deal with the dental anchorage only.

Molar-Incisor Hypomineralisation (MIH)

In 2001 Molar-Incisor Hypomineralisation (MIH) was suggested by Weerheijm et al. [START_REF] Weerheijm | Molar-incisor hypomineralisation[END_REF] to describe an enamel developmental defect defined as a hypomineralisation of systemic origin of one to four first permanent molars (FPM), sometimes associated with similarly affected permanent incisors. This structural qualitative enamel defect is caused by reduced mineralisation and inorganic components and leads to demarcated opacities, from whitecreamy, yellow, yellowish brown to brown. Opacities are usually localized to the occlusal or buccal third of the crown, rarely involving the cervical third [START_REF] Weerheijm | Molar-incisor hypomineralisation[END_REF][START_REF] Weerheijm | Judgement criteria for molar incisor hypomineralisation (MIH) in epidemiologic studies: a summary of the European meeting on MIH held in Athens, 2003[END_REF]. Hypomineralised enamel, more porous and less hard than normal enamel, has less distinct prism edges and crystals. This may contribute to the development of tooth decay; thus, a systematic review showed a significant association between MIH and tooth decay [START_REF] Americano | A systematic review on the association between molar incisorhypomineralization and dental caries[END_REF][START_REF] Almuallem | Molar incisor hypomineralisation (MIH) -an overview[END_REF]. Affected teeth are more sensitive to thermal stimuli and children frequently report pain when brushing teeth, poor dental brushing facilitates plaque accumulation and decay development [START_REF] Americano | A systematic review on the association between molar incisorhypomineralization and dental caries[END_REF][START_REF] Almuallem | Molar incisor hypomineralisation (MIH) -an overview[END_REF][START_REF] Lygidakis | Best Clinical Practice Guidance for Clinicians Dealing With Children Presenting With Molar-Incisor-Hypomineralisation (MIH): An EAPD Policy Document[END_REF][START_REF] Hernandez | Do We Really Know the Prevalence of MIH?[END_REF].

Prevalence of MIH

Prevalence of MIH worldwide has been reported from 2,8 to 40%. A lack of standardization of criteria for diagnosing MIH could explain these variations but a recent meta-analysis including 70 studies showed a high overall prevalence of MIH (14,2%) (4). Globally, in the studies, no statistical difference between genders were identified [START_REF] Hernandez | Do We Really Know the Prevalence of MIH?[END_REF][START_REF] Chawla | Clinical studies on molar-incisor-hypomineralisation part 2: development of a severity index[END_REF].

Aetiology of MIH

Etiological mechanisms are still unclear but seem to be multifactorial. Disruption to ameloblast function during the late stage of amelogenesis is thought to be involved. Prenatal, perinatal and post-natal factors have been explored and showed that acute or chronic illness or exposure to environmental pollution such as dioxins or bisphenol A during the last gestational trimester or the first three years of life may contribute to MIH occurrence. A combination of factors and their action in synergism have been suggested; perinatal complications, premature birth, oxygen starvation, low birth weight, respiratory tracts infections, fevers, childhood diseases, use of antibiotics or prolonged breast feeding [START_REF] Almuallem | Molar incisor hypomineralisation (MIH) -an overview[END_REF][START_REF] Lygidakis | Best Clinical Practice Guidance for Clinicians Dealing With Children Presenting With Molar-Incisor-Hypomineralisation (MIH): An EAPD Policy Document[END_REF][START_REF] Elhennawy | Managing molar-incisor hypomineralization: A systematic review[END_REF][START_REF] Silva | Etiology of Molar Incisor Hypomineralization -A Systematic Review[END_REF][START_REF] Jedeon | Enamel hypomineralization due to endocrine disruptors[END_REF][START_REF] Sapir | Clinical Solutions for Developmental Defects of Enamel and Dentin in Children[END_REF].

Clinical appearance -diagnosis of MIH

MIH Intra and Inter-patient variability is very large. Defects are asymmetrical for both presence and severity but when a severe defect is found in a tooth it is likely that the contralateral tooth is also affected. Molars are generally more hypomineralised than incisors but when several molars are affected the risk of finding incisor opacities is increased [START_REF] Ghanim | Validity and reproducibility testing of the Molar Incisor Hypomineralisation (MIH) Index[END_REF][START_REF] Mittal | Phenotypes of Enamel Hypomineralization and Molar Incisor Hypomineralization in Permanent Dentition: Identification, Quantification and Proposal for Classification[END_REF]. However, similar enamel hypomineralisation have been reported in other teeth i.e. primary teeth and permanent cuspids, bicuspids and second molars [START_REF] Garot | Are hypomineralised lesions on second primary molars (HSPM) a predictive sign of molar incisor hypomineralisation (MIH)? A systematic review and a meta-analysis[END_REF]. The presence of hypomineralised second primary molars (HSPM) could be a predictive factor for MIH [START_REF] Jedeon | Enamel hypomineralization due to endocrine disruptors[END_REF][START_REF] Mittal | Phenotypes of Enamel Hypomineralization and Molar Incisor Hypomineralization in Permanent Dentition: Identification, Quantification and Proposal for Classification[END_REF][START_REF] Wright | Diagnosis and treatment of molar-incisor hypomineralization. Handbook of Clinical Techniques in Pediatric Dentistry[END_REF]. MIH clinical appearance depends on the severity of the lesions determined by the size (larger than 1 mm for MIH defect [START_REF] Wright | Diagnosis and treatment of molar-incisor hypomineralization. Handbook of Clinical Techniques in Pediatric Dentistry[END_REF] and the depth of hypomineralisation. Hypomineralised brittle enamel can lead to post-eruptive breakdown, plaque deposit and rapid decay. Thus, MIH may be classified as mild, moderate or severe [START_REF] Wright | Diagnosis and treatment of molar-incisor hypomineralization. Handbook of Clinical Techniques in Pediatric Dentistry[END_REF][START_REF] Elhennawy | Outcome and Comparator Choice in Molar Incisor Hypomineralisation (MIH) Intervention Studies: A Systematic Review and Social Network Analysis[END_REF], figure1. In mild MIH, opacities are located in non-stress bearing areas, there are no caries, no hypersensitivity and the incisors are usually mildly affected if concerned. In moderate MIH, limited post-eruptive enamel breakdown on molars are due to important masticatory forces and incisors are frequently involved. In severe MIH, the whole enamel layer is hypomineralised, and large cuspal breakdowns prone to rapid secondary caries due to hypersensitivity, lack of hygiene and dental plaque retention, crown destruction and atypical restorations are likely. In addition, in severe cases of MIH, regular hypersensitivity, pain and re-treatment cycles affect children's quality of life [START_REF] Fütterer | Influence of Customized Therapy for Molar Incisor Hypomineralization on Children's Oral Hygiene and Quality of Life[END_REF][START_REF] Cabral | Reliability and Validity of a New Classification of MIH Based on Severity[END_REF]. Recently, severity systems have been proposed, taking particularly into account the particularly the opacities colours. Indeed, a long-term follow-up showed that yellow and brown opacities are more linked to breakdown than white ones. All these indexes aim to guide clinicians in managing and treatment of MIH [START_REF] Oliver | Distribution and Severity of Molar Hypomineralisation: Trial of a New Severity Index[END_REF][START_REF] Steffen | The Würzburg MIH concept: the MIH treatment need index (MIH TNI) : A new index to assess and plan treatment in patients with molar incisior hypomineralisation (MIH)[END_REF][START_REF] Elhennawy | Managing molar-incisor hypomineralization: A systematic review[END_REF].

Treatment challenge -First Permanent Molar (FPM) extractions and orthodontic treatment of MIH

Treatment of severely affected molars present real challenges for clinicians, and has many negative clinical impacts, teeth sensitivity resulting in poor local hygiene, caries susceptibility increase, chronic pulp inflammation and difficulties in obtaining adequate local analgesia, multiple dental procedures and restorations failures, and dental fear and behavioural management difficulties [START_REF] Oliver | Distribution and Severity of Molar Hypomineralisation: Trial of a New Severity Index[END_REF][START_REF] Steffen | The Würzburg MIH concept: the MIH treatment need index (MIH TNI) : A new index to assess and plan treatment in patients with molar incisior hypomineralisation (MIH)[END_REF]. The first problem in severe MIH is to specify the cavity margins. Glass ionomer cement can be used as an intermediate approach when moisture control is not possible until permanent restoration by resin composite can be done. If composites are the most suitable materials, the enamel-adhesive interface in MIH is more porous and often lead to cohesive failures. Thus, preformed dental crowns can be used with a high success rate [START_REF] Lygidakis | Best Clinical Practice Guidance for Clinicians Dealing With Children Presenting With Molar-Incisor-Hypomineralisation (MIH): An EAPD Policy Document[END_REF][START_REF] Fütterer | Influence of Customized Therapy for Molar Incisor Hypomineralization on Children's Oral Hygiene and Quality of Life[END_REF][START_REF] Mathu-Muju | Loss of Permanent First Molars in the Mixed Dentition: Circumstances Resulting in Extraction and Requiring Orthodontic Management[END_REF]. Finally, tooth removal combined with an orthodontic treatment must be considered as an alternative to avoid the spiral of failure and multiple dental procedures in anxious and fearful children. The first clinical step in severe MIH is to decide whether to restore or to extract these FMPs considering several factors such as child's age, dental crowding, malocclusion, overbite, agenesis, presence of the third molars, status of neighbouring teeth, FPMs restorations long-term prognosis or need for endodontic treatment if pulp is irremediably damaged. Severe MIH treatment is demanding and requires close and early collaboration between the paediatric dentist and the orthodontist to determine the optimal moment to extract such molars. Ideal age should be radiographically indicated by the beginning of the calcification of the lower second molar's bifurcation (maxilla 8,5-10 years, mandible 10,5-11,5 years) [START_REF] Fütterer | Influence of Customized Therapy for Molar Incisor Hypomineralization on Children's Oral Hygiene and Quality of Life[END_REF][START_REF] Mathu-Muju | Loss of Permanent First Molars in the Mixed Dentition: Circumstances Resulting in Extraction and Requiring Orthodontic Management[END_REF][START_REF] Cobourne | National Clinical Guidelines for the Extraction of First Permanent Molars in Children[END_REF] when there is no associated malocclusion. Extraction of the four FMPs may achieve the best long-term prognosis and promotes the establishment of a functional arch by the mesial drift of the second permanent molar and later by the eruption of the third permanent molar [START_REF] Cobourne | National Clinical Guidelines for the Extraction of First Permanent Molars in Children[END_REF]. When the mandibular aetiology is determined and when the skeletal pattern of the patient is deep bite, the extraction of permanent teeth is not suitable. However, when the class II malocclusion is associated with an MIH affecting the first permanent molars, orthodontic treatment involving extractions of the first molars with poor prognosis is sometimes necessary. The aim of this paper is to describe the treatment management of a case of class II division 1 with MIH, involving class II correction and extractions of the four FPM.

Diagnosis of the clinical case report

Anamnesis A 10.3-year-old girl, without any general health problems was referred by her general dentist for orthodontic treatment. The patient did not like the overjet and her facial appearance, and expressed some difficulties with mastication due to the severe MIH on the four first molars. Extraoral examination (figure 2) Face: The face was "respiratory" on Sigaud classification. It was approximatively symmetrical with a slight deviation of the nose to the right side and the chin to the left side. Bi-commissural and bi-pupillary lines were non-parallel with left side convergence. Nasal pyramid was average. The left eye had an anti-mongoloïd orientation. Nostrils were not very visible and did not look completely functional. The upper lip was quite thin, the lower lip was wider, and they were not closed at rest. Profile: The profile was convex with a retrognathic mandible, but the chin was present in the profile. The nasal ensella was well defined; the naso-labial angle was very open. The labial relationship was reversed with retrusion of the lower lip and the labio-mental line was increased. Smile: The smile was quite poor and revealed only the maxillary incisors and the primary cuspids.

Functional examination

Ventilatory function: Mixed. No allergy, no ENT procedure. Tongue examination: Primary deglutition with anterior interposition. The volume was average and the mobility was limited due to lingual fraenulum. The tonicity was good. Labial and facial muscular tonicity: was weak for lips and average for facial muscles. TMJ examination: Rectilinear closure and no joint noises. C0/CR: Identical. Adverse Habits: None.

Intraoral examination (figure 2)

The patient was in mixed dentition, the four second deciduous molars have been extracted due to MIH with mesial version of the four first permanent molars, resulting in a lack of space for the second bicuspids eruption and they present severe MIH. MIH was also visible on the central maxillary incisors. No restorations were visible. The over-bite was severe. The periodontium was average, inflammatory on the anterior area of maxillary arch due to mixed oral/nasal breathing. The upper lip fraenum had a normal insertion. Lateral bridles on the maxillary arch were present. Panoramic radiograph (figure 3) A severe MIH on the first four molars was visible. All permanent dental germs were visible including third molar germs. 55,65,75 and 85 were not present with a lack of space for second bicuspid eruption. There was a severe lack of space for 43 eruption and the risk of impaction of maxillary canines was high . The length of the roots looked good without any root resorption and a good alveolar bone level. The nasal cavities did not look clear and the maxillary sinus was not clear on the right side. The condyles are symmetrical with a normal shape. Lateral X-rays (figure 3) Facial cavities were well developed and clear. The airways were wide and not obstructed by palatal or pharyngeal tonsils. The palatal plane was linear without rotation. Mandible morphology according to Björk signs was normodivergent. The mental symphysis was thick. The soft tissues were thinner on the mental area and the labio-mental line was reduced due to lip closure with effort. The hyoid bone was situated towards C3. The maxillary incisor edge was situated 2mm under the labial junction. The patient presented a skeletal Class II malocclusion with a retrognathic mandible and chin compensation, a normal vertical skeletal pattern, an increased overbite and overjet with correct incisors angulation.

Treatment plan

A two-phase treatment was planned. The first step was to correct the transverse maxilla deficiency by alveolar expansion by Quad Helix, followed by a Lautrou class II activator to stimulate the mandibular growth and a tongue physiotherapy.

The second step was a fixed appliance straight wire technique with extractions of 16, 26, 36 and 46 to solve the severe MIH problem and the discrepancy at the mandible in particular. A class II mechanics was associated to improve the mandibular growth. -Multiband appliance.022x.028 straight wire technique with .020x.028 slot on maxillary incisors to increase the torque control, with 16, 26, 36 and 46 extractions. The third molars were scheduled to be controlled at the end of treatment and eventually placed on the arches. -16, 26, 36 and 46 were extracted two months before the bonding -The maxillary arch was equipped first followed by the mandibular arch 3 months later, waiting for the evolution of the blocked 35 and 46 due to the early extractions of 75 and 85 -After alignment, maxillary space closure was planned only by mesialisation of 16 and 26 to avoid the increase of the naso-labial angle which was already very open. At the mandible level, space closure was done on the right side by retracting the first bicuspids to allow cuspids alignment, and the remaining space closure was achieved by molar mesialisation -Class II mechanics was applied when .019x.025 SS archwires were placed on the two arches with 4.5oz 5/16 e worn 22 hours/day to facilitate the mandibular extractions space closure and stimulate the mandibular growth -Finishing and intercuspation phases were done with TMA arch wires and class II elastics worn 14 hours per day.

-A physiotherapy accompanied the active treatment and the retention phase.

-A bonded retainer cuspid-to-cuspid for the mandible and tongue-repositioning device worn 14 hours per day were done to help stability and wait the third molars eruption.

Treatment follow-up

-At the end of the early treatment (Quad Helix 5 months and Class II activator 7 months), the transverse maxillary dimension was normalized and the overjet was reduced, but there was still a cuspid class II on the left side. On the facial point of view the lip closure was better, but the profile remained retrognathic (figure 4). At this point the discussion was focused on the MIH problem as the first four molars were compromised and the mandibular growth was disappointing despite an excellent cooperation in the activator wearing. The patient and the parents were in favour of the four first molar extractions due to permanent pain of the patient on these teeth and the presence of the four third molar germs, but were against surgery for the mandibular deficiency.

-The fixed appliance was placed at the age of 13.9 as it was necessary to wait for the evolution of the second molars and the mandibular second bicuspids which were impacted under the first molars. The key point was to control the maxillary incisor torque during the space closure of the first molar extractions, as the naso-labial angle was very wide. The use of .020x.022 slots on the maxillary incisors with .019x.025 SS archwire was helpful for this control. The fixed appliance duration was 22 months, which was relatively short for a first molar extraction treatment. The patient was debonded at 15.11 years old and fixed retainers cuspid to cuspid were placed in conjunction with a tongue repositioning device.

-Active treatment evaluation: At the completion of the treatment (figure 5), the profile was still retrognathic but was improved with a better chin projection. The naso-labial angle was still open but did not get worse. This was one of the key points of the treatment as it was necessary to mesialize the first maxillary molars. No bone anchorage was placed in this case, the torque control was done only by the adequate archwires. The smile was wide, revealing the maxillary teeth and up to the second bicuspids. On the intraoral point of view, at the end of active treatment, the overjet and the overbite were normalized with a molar and canine class I, the midlines were centred, and the extraction spaces were closed. On the panoramic X-ray the roots are parallel and the third molars are still in the bone. On the lateral X-ray, the overjet and overbite were normalized (figure 6). The general superimposition shows the limited retroclination of the maxillary incisor and the control of the mandibular incisor as well as the mandibular growth initiated by the early treatment. The local maxillary superimposition reveals a clockwise rotation of the maxilla and a vertical growth. The local mandibular superimposition shows the vertical growth of the ramus and the limited change in the mandibular incisor axis change (figure 7).

-Post retention evaluation: 5.9 years after debonding, at the age of 21.8 years old, the facial and occlusal results are stable and on the panoramic the third molars are erupting with a satisfactory axis. The profile was still retrognathic, but the patient is very satisfied by the results and no breathing disorders are noticeable as the airways are very wide on the lateral Xray with no reduction due to the treatment. If one day the patient was not satisfied by her profile, a double maxillary advancement would be easily feasible as the occlusion is good six years after the active treatment (figure 8).

Conclusion

Young patients suffering from MIH are relatively frequent and first molar extraction and space closure when the third molars are present are often a good solution for the patient, avoiding very difficult endodontic and restorative treatment on these teeth, and most of all a sustainable solution. When the MIH is accompanied by a class II division 1 malocclusion, the orthodontic mechanics must be carefully controlled for the aesthetic preservation of the profile despite of the closure of the extraction spaces, especially when the use of bone anchorage is not easy.

Disclosure of interest:

The authors declare that they have no competing interest. [START_REF] Wright | Diagnosis and treatment of molar-incisor hypomineralization. Handbook of Clinical Techniques in Pediatric Dentistry[END_REF]. Figure 2: Extra-and intra-oral views before treatment. Figure 3: X-rays before treatment. Figure 4: Extra-and intra-oral views at completion of early treatment. Figure 5: Extra-and intra-oral views at completion of active treatment. Figure 6: X-rays at completion of active treatment and cephalometric measurements. Figure 7: Pre-post treatment comparison of lateral X-rays and structural superimpositions (black: before treatment, blue: at completion of early treatment, red at completion of active treatment). Figure 8: Extra-intra-oral views and panoramic 5.9 years after the active treatment.

Legends of figures

Figure 1 :

 1 Severity score of teeth affected by MIH from J. Timothy Wright "Diagnosis and treatment of molar-incisor hypomineralization". Handbook of Clinical Techniques in Pediatric Dentistry. Chapter 12