Inhibition Kinetics of Hydrogenation of Phenanthrene

IN DEGREE PROJECT CHEMICAL SCIENCE AND ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2020

Inhibition Kinetics of Hydrogenation of Phenanthrene

JOHANNES JOHANSSON

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ENGINEERING SCIENCES IN CHEMISTRY, BIOTECHNOLOGY AND HEALTH

www.kth.se

Inhibition Kinetics of Hydrogenation ofPhenanthrene

Final report

Master Thesis at Nynas ABBy: Johannes Johansson

Supervisor: Jacob Venuti BjorkmanExaminer: Lars J. Pettersson

Submitted June 11th, 2020

Abstract

In this thesis work the hydrogenation kinetics of phenanthrene inhibited by the basic nitro-gen compound acridine and the non-basic carbazole was investigated. Based on a transient reactormodel a steady state plug flow model was developed and kinetic parameters were estimated throughnonlinear regression to experimental data. The experimental data was previously collected from hy-drotreating of phenanthrene in a bench-scale reactor packed with a commercial NiMo catalyst mixedwith SiC. As a first two-step solution, the yields of the hydrogenation products of phenanthrenewere predicted as a function of conversion, which subsequently was used to calculate concentrationprofiles as a function of position in reactor. As a second improved solution, the concentrationprofiles were calculated directly as a function of residence time, and these results were then usedfor further analysis.

Reaction network 2 in figure 7 was considered sufficient to describe the product distributionof phenanthrene, with a pseudo-first-order rate law for the nitrogen compounds. Both solutionmethods provided similar results which gave good predictions of the experimental data, with a fewexceptions. These cases could be improved by gathering more experimental data or by investigatingthe effect of some model assumptions. The two-step method thus proved useful in evaluating thephenanthrene reaction network and providing an initial estimate of the parameters, while the one-step method then could give a more precise solution by calculating all parameters simultaneously.

As expected, acridine was shown to be more inhibiting than carbazole, both in the producedconcentration profiles and estimated parameters. A possible saturation effect was also seen in theinhibition behavior, where adding more nitrogen compounds only had a small additional effecton the phenanthrene conversion. The Mears and Weisz-Prater criteria were found to be inverselyproportional to the concentrations of the nitrogen compounds and otherwise only depend on rateconstants, with values well below limits for diffusion controlled processes. Sensitivity analyses alsosupported that the global minimum had been found in the nonlinear regression solution.

3

Table 1: Nomenclature used throughout the paper.

A Subscript to denote HDA compoundsAb Denotes bulk conditionsads Denotes adsorptioncat Subscript to denote catalystci Concentration of component i [mol/m3]CM Mears criterionCWP Weisz-Prater criterioncal Subscript to denote calculated valuedpe Equivalent particle diameter [m]dt Inner reactor diameter [m]DAB Diffusion coefficient [m2/s]Deff Effective diffusion coefficient [m2/s]des Denotes desorptione Euler’s numberexp Subscript to denote experimental valuef Subscript to denote feed conditionsF Objective function [mol/m3] and [ppm]ki Rate constant of reaction i [s−1] or [min−1]kc Mass transfer coefficient [m/s]kadsi Rate of adsorption of compound i [s−1]kdesi Rate of desorption of compound i [s−1]Kads

i Adsorption equilibrium constant of compound i [m3/mol]L Reactor length [m]m Denotes number of inhibiting speciesmj Catalyst weight used in experiment j [g]Mi Molecular weight of compound i [g/mol]n Reaction orderN Subscript to denote HDN compoundsobs Subscript to denote observed conditionsp Total number of experimental data pointsqi Surface concentration of compound i [g/gcat]qm Catalyst maximum site capacity [g/gcat]qv Concentration of vacant sites on catalyst [g/gcat]Q Volumetric flow rate [m3/s]ri Rate of reaction i [s−1]rp Catalyst particle radius [m]R2 Determination coefficientRe Reynold numberSp Catalyst particle external surface area [m2]Sc Schmidt numberSh Sherwood numberT Temperature [K]tj Reactor residence time of experiment j [min]v Superficial velocity [m/s]Vr Reactor bed volume [m3]

4

Table 2: Nomenclature used throughout the paper, continued.

xj Nitrogen distribution parameter of experiment jX Phenanthrene conversionyi Yield of HDA product iz Distance from top of catalyst bed [cm]ε Bed void spaceµ Viscosity [Pa · s]ρ Solvent density [g/m3]ρbed Catalyst bed density [g/m3]ωi Weight fraction of compound i [ppm]

Table 3: Abbreviations used throughout the paper.

Acr Acridine asym 1,2,3,4,4a,9,10,10a-octahydrophenanthreneCbz Carbazole DiH 9,10-dihydrophenanthreneDMDS Dimethyl disulfide FBR Fixed bed reactorEBR Ebulated bed reactor FID Flame ionization detectorFT-IR Fourier transform infrared spectroscopy GC Gas chromatographyHDA Hydrodearomatization HDN HydrodenitrogenationHDT Hydrotreating HDS HydrodesulfurizationHVGO Heavy vacuum gas oil LHSV Liquid hourly space velocityMB Mass balance MBR Moving bed reactorMS Mass spectroscopy ODE Ordinary differential equationPhe Phenanthrene PHP PerhydrophenanthreneSBR Slurry bed reactor SSITKA Steady state isotopic transient kineticssym 1,2,3,4,5,6,7,8-octahydrophenanthrene TEOM Tapered element oscillating microbalanceTet 1,2,3,4-tetrahydrophenanthrene TBR Trickle-bed reactor

CONTENTS 5

Contents

1 Introduction 6

2 Catalytic hydrotreating 62.1 Hydrotreating reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Model compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Catalysts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.4 Reactor design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.5 Operational parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Dynamic systems 113.1 Dynamic experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Liquid-phase systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3 Experimental criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4 Model development 134.1 Mass balances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.2 Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.3 Additional correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.4 steady state model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5 Model implementation 185.1 Two-step optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205.2 Direct optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215.3 Additional analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

6 Results 236.1 Two-step optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246.2 Direct optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

7 Discussion 367.1 Two-step optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367.2 Direct optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377.3 Method evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387.4 Pitfalls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397.5 Further development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

8 Conclusion 40

9 Appendix 419.1 HDA product distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419.2 Nitrogen distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419.3 Reactor residence times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429.4 Additional results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

1 INTRODUCTION 6

1 Introduction

Petroleum plays a large role in today’s society. Apart from the typical fuel application, it is also usedin production of e.g. plastics, paint, fertilizers or specialty oils. Depending on where the petroleumor crude oil originates from it can vary largely in composition and properties, and this introduces theneed for processing in refineries [1]. Since the aim of the refining process most often is to producefuel, certain fuel standards such as low sulfur content have to be met, and this can be achievedwith catalytic hydrotreating (HDT). HDT is performed after the distillation processes on some ofthe distillates, where the distillates are mixed with hydrogen gas over a catalyst in a reactor. As aresult, impurities such as sulfur and nitrogen or polynuclear aromatics can be converted and removed,improving the quality of the product. As the feed composition can vary, the process conditions haveto be adapted accordingly to ensure the desired product quality is achieved [1].

Nynas AB differs from many refining companies as it focuses on producing naphthenic specialty oils,mainly using the heavy vacuum gas oil (HVGO) from vacuum distillation. For this purpose, the goalof the HDT is to convert polyaromatic compounds such as phenanthrene in hydrodearomatization(HDA) reactions, as this is required to obtain the desired product properties and to comply withlegislation regarding the level of polyaromatic compounds.

The heavier fractions of the oil, e.g. the HVGO, generally contains most of the nitrogen and sulfurcontent from the crude oil [1], and among organic nitrogen species the non-basic carbazoles havebeen reported as highly potent inhibitors in the HDT process [2]. While some recent studies havefocused on the inhibition effect of organic nitrogen compounds on the HDT process for removing sulfur(hydrodesulfurization, HDS), e.g. by comparing the effect of basic and non-basic nitrogen commonlypresent in the feed [3], the effect on the kinetics of the HDA process has only been studied sparsely.

In order to gain insight on this effect, e.g. how it is influenced by operating conditions and how itaffects the reactor performance, a reactor model can serve as a powerful tool. A common assumptionfor the model is steady state, as the majority of chemical processes are performed at steady stateconditions. Start-up conditions and transient regimes, i.e. nonstationary conditions, are commonlyencountered in HDT though due to frequent changes in feed composition and relatively long relaxationtimes [4], which cannot be predicted by a steady state model, and this warrants the development of atransient model applicable to both steady state and transient conditions.

Using phenanthrene as a model compound, the goal of this thesis work was to investigate thehydrogenation kinetics of phenanthrene when inhibited by the organic nitrogen compounds carbazoleand acridine, both during steady state conditions and, if possible, transient conditions. A transientand steady state model was also to be developed for previous hydrogenation experiments.

Some background from an initial literature review will first be presented to give an understanding ofthe reaction process studied. Development of the general transient model will then be shown followedby simplifications made for steady state conditions. Next, the implementation of the model throughadaptation to experimental data will be explained along with numerical methods and some additionalevaluations performed on the results. The results will then be listed in chronological order with respectto the solution process, with brief explanations, followed by a deeper discussion first focused on detailedresults and then general aspects of the work and a conclusion. Lastly, the appendix contains somecomplementary derivations, information used in the numerical methods and some additional results.

2 Catalytic hydrotreating

The initial refining processes are illustrated in figure 1. As the crude oil enters the refinery it is firstdesalted before being sent to atmospheric distillation. After the initial distillation, the heavier material,

2 CATALYTIC HYDROTREATING 7

i.e. the atmospheric residue oil, is withdrawn from the bottom and sent to vacuum distillation [1].HVGO is one of the heavier fractions from the vacuum distillation, and can in turn be sent to a HDTreactor.

Figure 1: Simplified illustration of the initial refining processes, adapted from J. Ancheyta [1]. Recir-culation and water/steam flows have been omitted for simplicity.

2.1 Hydrotreating reactions

The main reactions to occur in hydrotreating are hydrogenolysis and hydrogenation. In hydrogenation,which is the main reaction in HDA, hydrogen is added to the molecule without any bond cleavage [1].Depending on the amount of aromatic rings in the compound, this happens in several equilibriumsteps in a ring-by-ring fashion [5], which can be presented in the following general form [1]:

Polyaromatics (PA) + H2 −−⇀↽−− Diaromatics (DA) (1)

Diaromatics (DA) + 2 H2 −−⇀↽−− Monoaromatics (MA) (2)

Monoaromatics (MA) + 3 H2 −−⇀↽−− Naphthenes (naph) (3)

In hydrogenolysis on the other hand, a bond between a carbon and a heteroatom other than hydrogenis broken. With the presence of organic nitrogen compounds in the distillate feed, this happens ina so-called hydrodenitrogenation (HDN) process, which can be be treated in the following generalmanner [1]:

R−N + 2 H2 −−→ R−H + NH3 (4)

where R is an arbitrary hydrocarbon molecule. Since the organic nitrogen in petroleum typicallyis classified as basic or non-basic, the HDN process can also be presented as a consecutive reactionscheme [6]:

non−basic nitrogen −−→ basic nitrogen −−→ HC + NH3 (5)

where HC is the remaining hydrocarbon compound.


2.2 Model compounds

Heavy oils contain many polyaromatic compounds, and one typical compound that has been studiedextensively is phenanthrene [7], which here is chosen as a model polyaromatic hydrocarbon compoundfor the HVGO feed. Figure 2 shows in more detail the HDA reaction pathways of phenanthreneadapted from Schachtl et al. [8] and Korre et al. [9].

Figure 2: Detailed HDA reaction network for phenanthrene (Phe) adapted from Schachtl et al. [8]and Korre et al. [9]. DiH: 9,10-dihydrophenanthrene, Tet: 1,2,3,4-tetrahydrophenanthrene, sym:1,2,3,4,5,6,7,8-octahydrophenanthrene, asym: 1,2,3,4,4a,9,10,10a-octahydrophenanthrene, PHP: Per-hydrophenanthrene.

Schachtl et al. showed in their study that the hydrogenation reactions are irreversible at lowphenanthrene conversions. They also showed that the rates of the isomerization reaction DiH −−→ Tetand the conversion Tet −−→ asym are negligible at these conversions [8]. To test these conclusions,three reaction networks for the hydrogenation were suggested in this study, shown in figure 3.

Acridine (Acr) and carbazole (Cbz) are chosen as model organic nitrogen compounds as both canbe found in heavy oil feedstocks [10]. Since the non-basic carbazole has been reported as a highlypotent inhibitor in HDS, it is relevant to investigate if there is a similar effect on the HDA process. Dueto the consecutive reaction scheme (5) it is also important to investigate the simultaneous influenceof basic and non-basic compounds and their relative rates [6] as the compounds might be presentsimultaneously in an HVGO feed.

Lewandowski proposed a reaction scheme for HDN of carbazole by using a NiB alloy, shown infigure 4 [11]. Similarly, the HDN reaction pathway for acridine suggested by Nagai et al. is shown infigure 5 [10].

2.3 Catalysts

In hydrotreating processes γ-Al2O3 is a commonly used support material for the catalyst, and theactive metal is typically molybdenum (Mo) and tungsten (W) sulfides with either cobalt (Co) ornickel (Ni) as a promoter to increase the activity. The composition of the catalyst varies depending onapplication, but CoMo and NiMo/γ-Al2O3 catalysts are usually preferred due to being highly selective,cheap, easy to regenerate and resistant to poisons [1]. Out of these two, the Ni-promoted catalyst hasa better aromatic hydrogenation performance, and may be preferred for an HDA process [12].

The main sources of catalyst deactivation are coking and metal deposition, both of which are


Figure 3: HDA reaction networks used in this thesis work, with corresponding rate constant nomen-clature, adapted from Schachtl et al. [8].

Figure 4: HDN reaction pathway of carbazole over a NiB alloy suggested by Lewandowski [11].

common for heavy oil feeds and result in reduced yields and product quality. The activity loss due tocoking can be counteracted by gradually increasing the reaction temperature, but this will eventuallybe limited by material constraints or possibly sintering issues [13]. Metal deposition can also beproblematic as it is an irreversible process, so the catalyst periodically needs to be replaced [1].


Figure 5: HDN reaction pathway of acridine over an MoO3 on γ-Al2O3 catalyst suggested by Nagaiet al. [10].

2.4 Reactor design

In HDT, some general reactor designs are fixed bed reactors (FBR), moving bed reactors (MBR),ebulated bed reactors (EBR) and slurry bed reactors (SBR). FBR is most often used in commercialhydrotreating.

Three phases are present when processing heavier feeds: a gas-phase with hydrogen and vaporizedliquid, a liquid-phase with the feed liquid, and a solid phase of catalyst. The flow through the packedbed can then create regimes of trickle flow and pulse flow, respectively [14]. If the FBR is operated inthe trickle regime it is usually referred to as a trickle-bed reactor (TBR), and the liquid and gas arecommonly flowing co-currently down the reactor. The liquid becomes the dispersed phase as it formsa thin laminar film with rivulets and droplets around the catalyst, while the gas makes the continuousphase, filling the remaining void surrounding the catalyst [15]. For higher gas and liquid throughputsthe pulse flow regime can be reached, though this does typically not happen with realistic liquid flowrates [14].

The main drawback of FBR is short catalyst cycle life, which could become problematic withheavier feeds due to higher coking and metal deposition risks. In these cases, using MBR, EBR orSBR might be more viable as the catalyst is added and/or withdrawn continuously, while reducingthe risk for bed plugging and minimizing pressure drops [1]. As issues of this kind are outside thescope of this thesis work, only the FBR will be considered further.

2.5 Operational parameters

Conversion, selectivity, catalyst activity and catalyst stability are greatly affected by process param-eters such as total pressure, hydrogen partial pressure, temperature, H2/oil ratio, space velocity andfresh feed rate [1]. The hydrogen partial pressure should generally be as high as possible as this reducescoke formation, and in turn reduces catalyst deactivation. It also increases the conversion, which canbe seen by reactions (1)-(4), and throughput capability. The applied pressure is mainly limited bymaterial constraints and cost considerations, depending on the desired quality of the product [1].

While increasing the temperature yields higher reaction rates, a too high temperature will causethermal cracking, i.e. the heavier hydrocarbons will decompose into lighter hydrocarbons, which alsocan cause hot spots due to further exothermal reactions [1]. Most hydrotreating reactions are alsoexothermal, and Jimenez et al. showed in their modelling of an industrial TBR that the conversionof poly- di- and monoaromatics in HDT goes through a maximum at roughly 370°C, above whichthermodynamic equilibrium constraints are met [16]. Thus, a too high temperature will also result in

3 DYNAMIC SYSTEMS 11

a loss in yield.The space velocity can be measured as a liquid hourly space velocity (LHSV) defined as the ratio of

total volumetric feed flow rate to total catalyst volume, for a catalytic reactor. A higher LHSV meansa lower residence time in the reactor, and thus a lower conversion if equilibrium is not reached [1].

Lastly, the H2/oil ratio is correlated to the hydrogen partial pressure. As a high partial pressuremust be maintained to minimize coke formation and maximize conversion, an excess of hydrogenis used. This excess is recycled to maintain the H2/oil ratio and for economic reasons, though italso serves to strip volatile products from the reactor liquids. If too high ratios are applied a limitwill eventually be reached where the hydrogen partial pressure cannot be increased further, and thedemand on heating and cooling rates outweigh the benefit [1].

For HDT with gas oil as feed, the temperature is typically in the interval 340-425°C, the pressurebetween 800 and 1600 psig (55 and 110 bar) and the LHSV between 0.5 and 1.5 h−1 [1]. Usingdemetalized and deasphalted vacuum gas oil as feed, Jimenez et al. reported a typical operationalpressure of 1500 psig (103 bar), a maximum temperature of 400°C and a LHSV of 1.1 h−1 [16].

3 Dynamic systems

In a heterogeneous catalytic reaction, the process can be divided into four general steps for a reactant:

• External diffusion from bulk fluid to external catalyst surface

• Internal diffusion from pore mouth to internal catalyst surface

• Adsorption on the catalyst surface

• Reaction on the catalyst surface

The three first steps are then reversed for the formed product, i.e. the product is desorbed and diffusesto the bulk fluid [17].

In steady state systems, the overall rate will be governed by the slowest step in the process, alsocalled the rate-limiting step [17]. While steady state experiments can show the overall rates, they oftendo not show the true nature of the underlying reaction mechanism, which can be crucial in dynamicsystems. Under these nonstationary conditions the concept of a rate-limiting step cannot be used sincethe slowest step not necessarily is the same step as under steady state conditions. Understanding andquantifying this dynamic behavior is important for reactor optimization and control, and it can beinvestigated through dynamic experiments [4].

3.1 Dynamic experiments

Dynamic experiments are generally performed by changing a state variable in a system at steady stateand then measuring the response. The change causes the system to be under nonstationary conditionsuntil a relaxation time has passed, after which a steady state is reached again. Measurements takenover time before the steady state is reached allow the dynamic behavior to be investigated [4].

The dynamic experiments can differ depending on which equipment is used, which parameter ischanged, how it is changed and how the response is measured. The reactors used for these experimentsare generally (semi-)batch reactors with a suspended slurry catalyst or continuous reactors with packedcatalyst beds. The (semi-)batch reactor is used for most liquid-solid and gas-liquid-solid reactions, butdue to reactor characteristics such as relatively large volume it has a low time resolution and cannotbe used to study fast processes. The continuous fixed bed reactor on the other hand has a higher time

3 DYNAMIC SYSTEMS 12

resolution and is mainly used for gas-phase reactions, but it has recently been applied more to liquid-and gas-liquid systems as well. Compared to the (semi-)batch reactor the continuous reactor is easierto operate and construct, and is typically run at atmospheric pressure [18].

The most useful parameters to change in chemical relaxation methods are reactant concentrationsand temperature. The system can either be made to reach a new thermodynamic state or return to theoriginal state. The methods can also be divided into single-cycle transient analysis, where the systemsimply relaxes to a new steady state, or multiple-cycle transient analysis, where e.g. the reactantconcentration is changed periodically to allow the system to switch between two steady states [4].

There are several transient techniques available, and some examples are the step-response, pulse,isotope exchange and temperature-programmed experiments. These techniques are summarized withrespective analysis instruments in table 4.

Table 4: Summary of some transient techniques, adapted from Murzin and Salmi [4]. MS: massspectrometry, GC: gas chromatography, FT-IR: fourier transform infrared spectroscopy.

Transient technique Instrument Characteristic features

Step-response experiment MS/rapid GC Inlet parameters aresuddenly changed

Pulse experiment MS/GC Inlet is subject to severalgroups of pulse inputs withthe same time interval

Temperature-programmeddesorption

MS Desorption is performedafter adsorption at roomtemperature

Temperature-programmedsurface reaction

MS The temperature ischanged after each steadystate is reached

Isotope exchangeexperiments

MS A molecule is replaced byits isotope

Transient infrared studies FT-IR Gas composition in bulkphase and on catalystsurface is analyzed

The pulse experiments can be varied by pulsing different reactants simultaneously or at differenttime intervals, and the technique has shown to be useful in mechanistic studies, kinetic studies andstudies of adsorption and diffusion in microporous materials, and is still under further development [18].Since the pulse method starts and ends with the same steady state, it is in general less informativethan the step-response method, where the steady state is changed. The step change is also easier toperform, with the exception of highly exo- or endothermic reactions, where the enthalpy changes canmake it difficult to keep the system isothermal [4].

For isotope experiments, one typical method is the isotope tracer technique, where labeling par-ticular molecules by isotopes allows them to be traced through the reaction system. As a moleculeis exchanged with its isotope both reaction rates and equilibriums change, which can be used to gaininformation about reaction pathways and mechanisms. This is particularly useful in catalyst surfaceanalysis since it can show whether species present on the catalyst surface during the reaction areby-products or intermediates [4].

Another isotope experiment method is the steady state isotopic transient kinetics analysis (SSITKA)in which a reactant is replaced by its isotope as a step or pulse input. The total concentration of la-

4 MODEL DEVELOPMENT 13

beled and nonlabeled reactants, adsorbates and products are kept at steady state conditions while theisotopic transient response is monitored [4].

An emerging technology also suitable for catalysis is the tapered element oscillating microbalance(TEOM) reactor. At the lower end of the reactor the catalyst sample is constrained as a test bed ina tapered glass element. The tapered element is oscillated at a constant amplitude, allowing changesin frequency to be measured. At the top end of the reactor the reactants are injected as pulse orstep inputs, and the resulting variation in frequency can be used to calculate changes in mass veryaccurately. This can also be combined with gas chromatography (GC) and mass spectrometry (MS)to study changes in gas composition. The technique has mainly been applied to study coke deposition,but has also found use for some catalyst applications such as adsorption and diffusion in zeolites, gasstorage, reforming of natural gas and synthesis of carbon fibers [18].

3.2 Liquid-phase systems

Many dynamic studies focus on gas-phase reactions, though liquid-phase systems are becoming moreand more important. Studies of dynamic liquid-phase systems, or the even more challenging gas-liquid systems, are somewhat limited by poor time resolution of the equipment. As a comparison, the(semi-)batch reactors commonly applied to liquid and gas-liquid systems have a time resolution in theorder of minutes, while the continuous fixed-bed reactors have a time resolution between 0.1 and 1 sfor gas-phase systems, and at least 10 s for liquid-phase systems. This has motivated development ofmicroreactors where various analysis methods are integrated on the same reactor chip, such as fastGC methods [18], which could be especially useful for hydrotreating.

3.3 Experimental criteria

An important part of the experiments is to maintain representative conditions so that the resultsonly reflect the phenomena desired for the study. For instance, if the reaction kinetics are to bestudied in a packed bed reactor, an ideal plug-flow should be maintained and there should be nomass transport limitations in the system (in most cases). This can be ensured by calculating certaindefined dimensionless parameters and confirming that the values are below or above empirical criteriaavailable in literature. Some processes can be much faster under transient conditions compared tosteady state, which means that some of the criteria are stricter under these conditions. The criteriacan vary with experimental setup and chosen technique, and would thus have to be investigated foreach case [18].

After the dynamic experiments, the derived kinetic models and parameters can be applied to bothtransient- and steady state reactor simulations with the use of reactor models [18].

4 Model development

Depending on factors such as operating conditions, feedstock and aim of the model, there are manyoptions in modelling HDT, due to the complex nature of the trickle-bed flow [15]. While many modelshave focused on HDS with an oil feedstock, some have also included simplified HDN and/or HDAreactions to investigate the simultaneous reaction processes [16] [19]. There are models which havefocused on describing hydrodynamic phenomena using computational fluid dynamics, though a morecommon approach is the plug flow model illustrated in figure 6, where the gas and liquid flows aretreated as a two-phase flow, and the interfacial mass transfer rates are estimated through overalltransfer coefficients. These estimations could also include concentration gradients inside the catalystparticles [16].


Figure 6: Illustration of a two-phase plug flow model, adapted from Jimenez et al. [16].

Most of the models found in literature thus focus on steady state conditions and predicting trans-port phenomena, but the goal of this thesis work was to develop a model based on transient conditions,with the focus on inhibition reaction kinetics. A model with a similar purpose was previously devel-oped by Ho and Nguyen [20] [2] and White and Ho [21], and this model could be adapted and modifiedto predict HDA instead of HDS by applying similar assumptions and derivations. To assure that themodel developed here achieves the right goal, the main assumptions applied are thus:

• Negligible coke formation

• Isothermal and isobaric system

• Fully wetted and uniformly shaped catalyst

• No wall effects or backmixing

• Liquid and hydrogen feed is in equilibrium before entering the reactor

• Hydrogen partial pressure is approximately constant and not rate limiting

• No mass transfer resistances

Some general mass balance (MB) equations applicable for transient conditions will be presentedbefore further simplifications are made for the steady state model.

4.1 Mass balances

With close analogy to the work of White and Ho [21], mass balances can be set up for compoundsA related to the HDA reactions and compounds N related to the HDN reactions, in an attempt todescribe the transient response of the system after introducing the nitrogen compounds. Time t ishere defined as the time after introducing the inhibiting compounds, i.e. t = 0 when no nitrogen isadded and t > 0 after nitrogen has been added. An MB over compound A in the liquid phase yields:

v∂cA∂z

+ ε∂cA∂t

+(1− ε)ρbed

MA

kadsA cA

qm − m∑j=1

qj

− kdesA qA

= 0 (6)


and in the solid phase:

∂qA∂t

= kadsA cA

qm − m∑j=1

qj

− kdesA qA + rA (7)

Similarly, an MB over compound N in the liquid phase yields:

v∂cN∂z

+ ε∂cN∂t

+(1− ε)ρbed

MN

kadsN cN

qm − m∑j=1

qj

− kdesN qN

= 0 (8)

and in the solid phase:

∂qN∂t

= kadsN cN

qm − m∑j=1

qj

− kdesN qN + rN (9)

where z is the vertical distance from the top of the catalyst bed, v the superficial fluid velocity,ε the bed void fraction, ρbed the catalyst bed density. cA and cN are the liquid concentrations ofcompounds A and N, respectively, MA and MN the corresponding molecular weights, kadsA and kadsN

the corresponding adsorption rate constants, kdesA and kdesN the desorption rate constants and qA andqN the surface concentrations. rA and rN are the rates of formation of A and N through HDA andHDN, respectively, qj the surface concentration of any adsorbed compound j, and qm the total sitecapacity on the catalyst.

4.2 Kinetics

During the hydrotreating process the hydrogen partial pressure is close to constant and can thereforebe included in lumped rate constants [8]. Following the simplified reaction networks for phenanthreneshown in figure 3 and applying the same notation, the following rate expressions can be set up fornetwork 1:

rPhe = −(k1 + k2)qPhe (10)

rDiH = k1qPhe − k3qDiH (11)

rTet = k2qPhe − k4qTet (12)

rasym = k3qDiH − k5qasym (13)

rsym = k4qTet − k6qsym (14)

rPHP = k5qasym + k6qsym (15)

For reaction network 2, equations (12) and (13) are replaced by:

rTet = k2qPhe − (k23 + k4)qTet (16)

rasym = k3qDiH + k23qTet − k5qasym (17)

Similarly, for network 3:

rDiH = k1qPhe − (k12 + k3)qDiH (18)

rTet = k2qPhe + k12qDiH − (k23 + k4)qTet (19)

rasym = k3qDiH + k23qTet − k5qasym (20)


Different power laws have been reported for the HDN reactions, though most studies have con-cluded that pseudo-first-order kinetics apply [3] [22]. As the nitrogen compounds are difficult tomeasure and are often present in small amounts, the distribution of HDN products will not be consid-ered, but only the consumed amounts of carbazole and acridine. The following rate expressions willbe used:

rCbz = −kN1qCbz (21)

rAcr = −kN2qAcr (22)

4.3 Additional correlations

The catalyst particles in this work are assumed to be shaped as spheres. The bed void fraction canbe estimated through the correlation:

ε = 0.38 + 0.0073

[1 +

( dtdpe− 2)2

( dtdpe

)2

](23)

where dt is the reactor inner diameter and dpe the equivalent particle diameter. dpe is calculated bythe particle volume Vp and external area Sp for a sphere with radius rp as follows [1]:

Vp =4

3πr3p (24)

Sp = 4πr2p (25)

dpe =VpSp

=rp3

(26)

4.4 steady state model

Assuming the surface reaction is the rate limiting step, the surface concentration of compound j canbe expressed in terms of an adsorption equilibrium constant Kads

j :

Kadsj =

kadsj

kdesj

=qjcjqv

(27)

⇔ qj = Kadsj cjqv (28)

where qv is the concentration of vacant sites on the catalyst. The total concentration of sites on thecatalyst is the sum of vacant and occupied sites. This can be combined with equation (28):

qm = qv +m∑j=1

qj = qv +m∑j=1

Kadsj cjqv = qv

1 +

m∑j=1

Kadsj cj

(29)

The nitrogen compounds have shown to have a strong inhibiting effect compared to self-inhibitionof sulfur in HDS [20], and although Beltramone et al. [12] showed that three-ring aromatic compoundsconsiderably inhibit the hydrogenation of two- and one-ring compounds, this inhibition is assumed tobe negligible compared to the strong inhibition of nitrogen. Thus, only the nitrogen compounds areincluded in equation (29), which is rearranged to:

qv =qm

1 +KadsCbzcCbz +Kads

AcrcAcr(30)


Next, the surface reaction is assumed to be the rate-limiting step of the catalytic process. Forsteady state conditions, surface concentrations do not change over time, i.e. ∂qA

∂t = ∂qN∂t = 0, and

equation (30) is equivalent to the term in the parenthesis of equation (7) and (9). Thus, equations (7)and (9) can be simplified to the following expressions, also known as Langmuir isotherms in competitiveenvironments [20]:

qA =Kads

A cAqm


AcrcAcr(31)

qN =Kads

N cNqm


AcrcAcr(32)

Equations (7) and (9) can also be rewritten as:

−rA = kadsA cA (qm − qCbz − qAcr)− kdesA qA (33)

−rN = kadsN cN (qm − qCbz − qAcr)− kdesN qN (34)

Furthermore, equations (6) and (8) are simplified by setting ∂cA∂t = ∂cN

∂t = 0 and by inserting equations(33) and (34):

dcAdz

=(1− ε)ρbedMAv

rA (35)

dcNdz

=(1− ε)ρbedMNv

rN (36)

Finally, combining equations (10)-(15) with equation (31) and (35), and similarly, equations (21) and(22) with (32) and (36) yields the final set of ordinary differential equations (ODEs) for network 1. Fornetworks 2 and 3, the corresponding expressions (16)-(20) are used. The resulting ODEs for network2 are shown in equations (37)-(44).

dcPhe

dz= −(1− ε)ρbedqm

MPhev

[(k1 + k2)K

adsPhecPhe


AcrcAcr

](37)

dcDiH

dz=

(1− ε)ρbedqmMDiHv

[k1K

adsPhecPhe − k3Kads

DiHcDiH


AcrcAcr

](38)

dcTet

dz=

(1− ε)ρbedqmMTetv

[k2K

adsPhecPhe − (k23 + k4)K

adsTetcTet


AcrcAcr

](39)

dcasymdz

=(1− ε)ρbedMasymv

[k3K

adsDiHcDiH + k23K

adsTetcTet − k5Kads

asymcasym


AcrcAcr

](40)

dcsymdz

=(1− ε)ρbedqm

Msymv

[k4K


symcsym


AcrcAcr

](41)

dcPHP

dz=

(1− ε)ρbedqmMPHP v

[k5K

adsasymcasym + k6K

adssym


AcrcAcr

](42)

dωCbz


MCbzv

[kN1K

adsCbzωCbz


AcrcAcr

](43)

dωAcr


MAcrv

[kN2K

adsAcrωAcr


AcrcAcr

](44)

5 MODEL IMPLEMENTATION 18

ωi denotes the weight fraction of compound i, here expressed in ppm, while the concentration of ci isexpressed in mol/m3. These units are chosen to avoid numerical issues due to large differences in orderof magnitude, as the concetrations of the HDN compounds are much lower than the concentrations ofHDA compounds. For the expression in the denominators, the concentrations are converted as follows:

ci =ωiρ

Mi× 10−6 [mol/m3] (45)

where ρ is the solvent density and Mi the molecular weight of compound i.Using f as a subscript to denote feed, the boundary conditions are as follows:

cPhe = cPhe,f cCbz = cCbz,f cAcr = cAcr,f (46)

cDiH,f = cTet,f = casym,f = csym,f = 0 (47)

5 Model implementation

Having developed an initial steady state model, the next step is to implement the model by fittingit to experimental data, and this can be done through nonlinear regression. The set of differentialequations consist of a number of variables independent of the reaction progress. If an initial guessof the parameters to be estimated yields a calculated outlet concentration cij,cal for compound i andexperiment j, the objective function F is defined as:

F =

p∑ij=1

(cij,cal − cij,exp)2 (48)

where cij,exp is the experimentally measured outlet concentration of compound i in experiment j andp the total number of experimental data points. For the parameters to be as accurate and precise aspossible, the calculated points should be as close to the experimental data as possible, i.e. the valueof the objective function should be as low as possible. This optimization process was carried out inPython using the least squares module in the SciPy library.

The experimental data used was previously gathered from hydrotreating of phenanthrene in abench-scale reactor packed with a commercial NiMo catalyst mixed with SiC. Certain reaction condi-tions and concentrations were not changed in between experiments and these are summarized in table5. The catalyst particle diameter was chosen as 0.2 mm. The feed concentrations of carbazole andacridine as well as the catalyst weight were varied between experiments, as shown in table 6. TheHDA product distribution and total nitrogen content of the outlet measured after each experiment arelisted in table 7. The HDA products were measured using gas chromatography with a flame ionizationdetector (GC-FID). Due to the low concentrations of the nitrogen compounds, only the total nitrogencontent could be measured indirectly through combustion combined with chemiluminescence.

Note that the measured outlet nitrogen content in experiment N14 was higher than the totalnitrogen in the feed. As this might be due to a random measurement error, the outlet content wasassumed to be the same as the inlet content in that case.


Table 5: Reaction conditions and concentrations not varied between experiments. n-tetradecane wasused as an internal standard and DMDS was used to keep the catalyst sulfided.

Temperature 300°C Solvent DecalinPressure 120 bar Phenanthrene concentration 0.05 mmol/cm3

Volumetric flow 0.1 cm3/min n-tetradecane concentration 0.08 mmol/cm3

Catalyst bed length 7 cm DMDS concentration 1500 ppmReactor inner diameter 10 mm Catalyst particle size 0.16-0.25 mm

Average particle size SiC in bed 0.12 mm

Table 6: Catalyst weight and inlet concentrations of carbazole and acridine (weight basis) for eachexperiment.

Experiment name Catalyst weight [mg] Carbazole [ppm] Acridine [ppm]

N1 50.2 0 0N5 50.2 0 35N9 50.2 17.5 17.5N7 50.2 35 35N3 50.2 35 0N18 75.44 0 0N11 75.44 0 17.5N13 75.44 17.5 0N14 75.44 17.5 35N15 75.44 17.5 17.5N12 75.44 35 17.5N2 100.56 0 0N6 100.56 0 35N10 100.56 17.5 17.5N4 100.56 35 0N8 100.56 35 35


Table 7: Product distribution normalized as a percentage of the inlet phenanthrene concentration,along with total liquid nitrogen content for each experiment.

Experiment name Phe DiH Tet sym asym PHP N content [ppm]

N1 3.7 20.2 1.7 36.8 17.5 20.0 0N5 78.5 9.1 9.2 2.6 0.7 0 33N9 74.0 10.7 10.8 3.2 1.3 0 32.6N7 79.0 8.7 9.2 2.3 0.9 0 68.4N3 52.0 19.1 12.6 11.9 4.5 0 19.4N18 3.7 17.0 1.5 31.9 16.1 29.9 0N11 61.1 15.4 13.0 7.3 3.2 0 13.3N13 37.8 23.1 11.5 20.0 7.6 0 6.3N14 74.3 11.0 9.9 3.4 1.4 0 54.2N15 67.2 14.5 12.5 5.8 0 0 30.4N12 67.7 13.5 11.7 5.0 2.1 0 45N2 1.7 14.5 0.9 30.4 15.9 36.6 0N6 62.9 15.2 13.1 6.2 2.6 0 29.2N10 59.5 16.4 13.4 7.5 3.2 0 29.2N4 27.6 25.9 9.5 26.6 10.4 0 7.1N8 68.0 14.5 12.2 5.3 0 0 63.5

The optimization was initially performed in a two-step process as described in the following section.Using the results and conclusions from this solution, the optimization was then performed in a direct,one-step method instead. The accuracy of each solution was evaluated continually by calculating thedetermination coefficient, R2.

5.1 Two-step optimization

Nonlinear regression generally requires a good initial guess to converge to a solution, and while alocal minimum can be found, it is not necessarily the global minimum. In other words, even thougha solution to the system is found, there might still be a more accurate solution if a better startingguess is provided. Another potential problem in the parameter estimation is correlation betweenparameters. An example of this is the strong correlation between the rate constants ki and theadsorption equilibrium constants Kads

i . If the value of a rate constant increases, this increase iscompensated by a decrease in the adsorption constant, resulting in an equally good fit to the dataeven though the individual error of both constants might increase [23]. For this reason, in the numericalsolution, any product or quotient of constants should be treated as a single lumped constant.

In an attempt to avoid correlations and provide a decent initial guess the initial set of ODEs(37)-(44) were rewritten in terms of HDA product yields yi as a function of phenanthrene conversionX, as previously done by Korre et al. [9]. The yield of HDA product i is defined as the concentrationof product i divided by the feed concentration of phenanthrene. A detailed derivation is shown in theappendix, section 9.1, to give the set of ODEs (49)-(53). Reaction network 2 shown in figure 3 wasultimately chosen as it provided the best fit to experimental data, as illustrated later in the resultssection. Initial guesses for the parameters were gathered from the literature.


dyDiH

dX=MPhe

MDiH

[k1

k1 + k2−

k3KadsDiH

(k1 + k2)KadsPhe

yDiH

(1−X)

](49)

dyTet

dX=MPhe

MTet

[k2

k1 + k2−

(k23 + k4)KadsTet

(k1 + k2)KadsPhe

yTet

(1−X)

](50)

dyasymdX

=MPhe

Masym

[k3K

adsDiH

(k1 + k2)KadsPhe

yDiH

(1−X)+

k23KadsTet

(k1 + k2)KadsPhe

yTet

(1−X)−

k5Kadsasym

(k1 + k2)KadsPhe

yasym(1−X)

](51)

dysymdX

=MPhe

Msym

[k4K

adsTet

(k1 + k2)KadsPhe

ysym(1−X)

−k6K

adssym

(k1 + k2)KadsPhe

ysym(1−X)

](52)

dyPHP

dX=

MPhe

MPHP

[k5k

adsasym

(k1 + k2)KadsPhe

yasym(1−X)

+k6K

adssym

(k1 + k2)KadsPhe

ysym(1−X)

](53)

Writing the yields as functions of phenanthrene conversion allowed the HDA reaction network tobe investigated independently of the HDN kinetics. The solution of this system is the relative rateconstants of each reaction, i.e. the apparent rate constant of each reaction divided by the apparentrate constant of the phenanthrene consumption. To determine the rate of each reaction the rate ofthe phenanthrene consumption would thus have to be estimated along with the rate- and adsorptionconstants for the HDN reactions. This was done by inserting the results of this first optimization inthe original set of ODEs, and then performing a second optimization. In this second step the resultsfrom the first optimization were kept constant while the constants of the phenanthrene consumptionand HDN kinetics were set as independent variables. Equation (23) was used to estimate the bed voidfraction.

For the experiments involving a mixture of carbazole and acridine the true product distribution ofthese is unknown since only measurements of the total nitrogen content is available. This distributionwas instead included as a parameter xj for each experiment, defined as the weight percentage carbazoledivided by the total weight percentage nitrogen, for each experiment. This is explained in more detailin the appendix, section 9.2.

5.2 Direct optimization

After the two-step optimization, a direct optimization was performed instead to improve the results.The coordinate z was re-calculated in terms of residence time t, as shown in section 9.3 in the appendix.Similarly to the work of Schachtl et al. [8], the set of ODEs was then expressed with the residence


time as the variable in equations (54)-(60), making it independent of the operating conditions.

dcPhe

dt= −

(k1 + k2)KadsPhecPhe


AcrcAcr(54)

dcDiH

dt=k1K


DiHcDiH


AcrcAcr(55)

dcTet

dt=k2K

adsPhecPhe − (k23 + k4)K

adsTetcTet


AcrcAcr(56)

dcasymdt

=k3K

adsDiHcDiH + k23K


asymcasym


AcrcAcr(57)

dcsymdt

=k4K


symcsym


AcrcAcr(58)

dcPHP

dt=k5K

adsasymcasym + k6K

adssymcsym


AcrcAcr(59)

dωCbz

dt= −

kN1KadsCbzωCbz


AcrcAcr(60)

dωAcr

dt= −

kN2KadsAcrωAcr


AcrcAcr(61)

Note that the concentrations of carbazole and acridine again are calculated in ppm (weight basis) andconverted to mol/m3 through equation (45).

5.3 Additional analyses

Some additional analyses were performed to evaluate the results and some of the initial assumptionsfor the model. Firstly, parity plots were produced from the final results by plotting the concentrationspredicted by the model against the measured experimental concentrations. In the ideal case thepredicted concentrations should be the same as the experimental data at every point, following adiagonal line starting from the origin.

Secondly, with the work of Fu et al. [24] as a reference, the Mears criterion CM was calculated tocontrol that the reaction was not limited by the rate of external diffusion:

CM =(−r′obs)(1− ε)ρbedrpn

kccAb(62)

where r′obs is the observed rate of reaction in mol/(gcats), rp the catalyst particle radius, n the reactionorder, kc the mass transfer coefficient and cAb is the reactant bulk concentration, in this case the bulkconcentration of phenanthrene. As the catalyst particle diameter was chosen as 0.2 mm before, aparticle radius of 0.1 mm was used here. The mass transfer coefficient was calculated using theThoenes-Kramers correlation as previously done by Fu et al. [24]:

Shε

1− ε=

(Re

1− ε

)1/2

Sc1/3 (63)

where Sh, Re and Sc is the Sherwood number, Reynolds number and Schmidt number, respectively,

6 RESULTS 23

defined as:

Sh =kcrpDAB

(64)

Re =ρvrpµ

(65)

Sc =v

DAB(66)

where DAB is the diffusion coefficient, v the superficial velocity, µ the liquid viscosity and ρ the densityof the solvent. The value of the viscosity was gathered from Fu et al. [24] since there is little variationin the viscosity at high temperatures. The effective diffusion coefficient through the catalyst particlesDeff was assumed to be the same as in the bulk liquid and was estimated through the followingexpression [24]:

DAB = 9700 · 5.4× 10−7 ·(T

M

)1/2

(67)

where T is the reaction temperature and M the molecular weight of phenanthrene. Combining equa-tions (63)-(66) allowed the mass transfer coefficient to be estimated:

kc =DAB(1− ε)

rpε

[ρvrp

µ(1− ε)

]1/2 [ µ

ρDAB

]1/3(68)

The observed rate of reaction was calculated by equation (54) after solving the set of ODEs for eachexperimental inlet condition and residence time. If the calculated value of CM is less than 0.15, thereaction is not limited by the rate of external diffusion [24].

To control that the reaction was not limited by the rate of internal diffusion the Weisz-Pratercriterion CWP was calculated:

CWP =(−r′obs)ρbedr2p

Deffcs(69)

where cs is the reactant concentration at the catalyst outer surface. If the reaction is not limited byexternal diffusion this will be the bulk concentration of phenanthrene, and if the calculated value ofCWP is less than 1, the reaction is not limited by the rate of internal diffusion [24].

Lastly, a sensitivity analysis was performed on the calculated parameters to confirm that the globalminimum was found. One by one, each parameter was multiplied with a factor ranging from ±20%,and the objective function value was calculated for each perturbation. For the nitrogen distributionparameters, the factor was adjusted so that the mass balanced were still fulfilled. If the objectivefunction value is lowest when there is no perturbation, this confirms that the global minimum hasbeen found. However, if any parameter shows a new minimum after the perturbation, the estimatedparameters are incorrect [25].

6 Results

In this section the results of the model implementation are summarized and explained briefly, while adeeper discussion is provided in section 7. All the figures shown here were produced in Python andare the final results after various solution iterations.

6 RESULTS 24


Figure 7 shows the predicted yields of each HDA product written above each graph, as functions ofphenanthrene conversion, for HDA network 1 and 2. Table 8 shows all the calculated parameters fornetworks 1-3 along with determination coefficients. It can be seen that the rate of reaction pathwayDiH −−→ Tet was negligibly small, and since network 3 predicted roughly the same yields as network2 it was omitted from the graphs.

Figure 7: HDA product yields predicted using network 1 and 2, respectively, as a function of phenan-threne conversion, along with experimental data points. Each graph represents a compound.

Figure 7 and table 8 were used to draw the conclusion that network 2 gave a better prediction thannetwork 1, and that the influence of the extra parameter added in network 3 was negligible. Thus,network 2 was chosen to describe the HDA reactions throughout the rest of this thesis work.

Figure 8 shows predicted concentration profiles of each HDA compound as a function of positionin the reactor for some representative experiments stated above each graph. These experiments werechosen as they summarize the results at four different degrees of phenanthrene conversion, and wereproduced by solving the original set of ODEs (37)-(44) in combination with the results in table 8, as

6 RESULTS 25

Table 8: Calculated parameters from yield expressions for each of the suggested HDA reaction networksalong with corresponding determination coefficients.

Value [−]Parameter Network 1 Network 2 Network 3

k1k1+k2

0.4663 0.4506 0.4506k12Kads

DiH

(k1+k2)KadsPhe

- - 7.3 ×10−15

k3KadsDiH

(k1+k2)KadsPhe

0.4249 0.3973 0.3974

k23KadsTet

(k1+k2)KadsPhe

- 0.1928 0.1928

k4KadsTet

(k1+k2)KadsPhe

2.130 2.084 2.084

k5Kadsasym

(k1+k2)KadsPhe

0.3947 0.4422 0.4422

k6Kadssym

(k1+k2)KadsPhe

0.1919 0.1654 0.1654

R2 0.9758 0.9771 0.9771

explained in section 5.1. Representative concentration profiles for the HDN compounds from the samesolution are shown in figure 9. For the sake of completion, concentration profiles for the rest of theexperiments are found in the appendix, section 9.4. Table 9 lists the final calculated parameters fromthis second solution step.

Figure 8: Calculated concentration profiles of each HDA compound as a function of distance from thetop of the catalyst bed, along with experimental points, for some representative experiments.

6 RESULTS 26

Figure 9: Calculated concentration profiles of the HDN compounds as a function of distance from thetop of the catalyst bed, along with experimental points, for some representative experiments.

Table 9: Calculated lumped rate constants, adsorption constants, nitrogen distribution parametersand determination coefficient.

Parameter Value Unit

qm(k1 + k2)KadsPhe 1.333× 10−5 [m3/(mol · s)]

qmkN1 5.053× 10−7 [s−1]qmkN2 7.012× 10−8 [s−1]Kads

Cbz 22.86 [m3/mol]Kads

Acr 59.03 [m3/mol]xN9 0.4632 [−]xN7 0.4883 [−]xN15 0.4328 [−]xN12 0.6183 [−]xN10 0.4129 [−]xN8 0.4516 [−]R2 0.9798 [−]

6 RESULTS 27

Figures 7, 8 and 9 show a decent prediction of most data, except for some specific cases. Theseresults indicated that there was room for improvement in the numerical process, which is why a directoptimization carried out instead as a new method, utilizing the results from this two-step optimizationas an initial guess.


Figures 10-12 show the calculated variation in concentration of each compound over residence timefrom solving the set of ODEs (54)-(61). Each graph in figure 10 and 11 shows the HDA compoundsand are separated depending on the amount of carbazole and acridine fed at the inlet of the reactor, aswritten above each graph. Figure 12 similarly shows the corresponding profiles of the HDN compoundsseparated by the inlet composition, though some curves have been put in the same graphs. Table 10summarizes the estimated parameters along with determination coefficient.

Figure 10: Calculated concentration profiles of each HDA compound as a function of residence time,along with experimental points, separated for each inlet composition.

6 RESULTS 28

Figure 11: Calculated concentration profiles of each HDA compound as a function of residence time,along with experimental points, separated for each inlet compositions.

Table 10: Calculated apparent rate constants for the HDA reactions, rate constants for the HDNreactions, adsorption constants, parameters for nitrogen distribution and determination coefficient.

Parameter Value Unit Parameter Value Unit

k1KadsPhe 3.566× 10−2 [m3/(mol ·min)] Kads

Cbz 21.58 [m3/mol]k2K

adsPhe 4.298× 10−2 [m3/(mol ·min)] Kads

Acr 56.42 [m3/mol]k3k

adsDiH 3.192× 10−2 [m3/(mol ·min)] xN9 0.4632 [−]

k23KadsTet 1.780× 10−2 [m3/(mol ·min)] xN7 0.4883 [−]

k4KadsTet 0.1423 [m3/(mol ·min)] xN15 0.4323 [−]

k5Kadsasym 3.483× 10−2 [m3/(mol ·min)] xN12 0.6175 [−]

k6Kadssym 1.224× 10−2 [m3/(mol ·min)] xN10 0.4124 [−]

kN1 3.387× 10−3 [min−1] xN8 0.4511 [−]kN2 4.311× 10−4 [min−1] R2 0.9802 [−]

6 RESULTS 29

Figure 12: Calculated concentration profiles of carbazole and acridine as a function of residence time,along with experimental points, separated for each inlet composition.

Figures 13-18 show the parity plots produced for each HDA compound while the nitrogen com-pounds are represented by the total nitrogen content in figure 19, since the concentrations of Cbz andAcr were not measured directly. The reference lines illustrate the trend that the results would followin the ideal case, if the prediction was perfect. Any points above the reference line indicate that themodel predicted a higher concentration than the experimental data, and vice versa.

6 RESULTS 30

Figure 13: Concentrations of Phe predicted by model plotted against experimentally measured con-centrations. The reference lines show how the trend would look like in the ideal case.

Figure 14: Concentrations of DiH predicted by model plotted against experimentally measured con-centrations. The reference lines show how the trend would look like in the ideal case.

6 RESULTS 31

Figure 15: Concentrations of Tet predicted by model plotted against experimentally measured con-centrations. The reference lines show how the trend would look like in the ideal case.

Figure 16: Concentrations of asym predicted by model plotted against experimentally measured con-centrations. The reference lines show how the trend would look like in the ideal case.

6 RESULTS 32

Figure 17: Concentrations of sym predicted by model plotted against experimentally measured con-centrations. The reference lines show how the trend would look like in the ideal case.

Figure 18: Concentrations of PHP predicted by model plotted against experimentally measured con-centrations. The reference lines show how the trend would look like in the ideal case.

6 RESULTS 33

Figure 19: Total nitrogen content predicted by model plotted against experimentally measured values.The reference lines show how the trend would look like in the ideal case.

Figure 20 shows the calculated values of the Mears criterion using the estimated rate of reactionof phenanthrene at the outlet conditions of each experiment, i.e. at each residence time where ex-perimental data was taken. As the values are well under the limit 0.15 the reaction processes werenot limited by external diffusion. Similarly, figure 21 shows the subsequently calculated values of theWeisz-Prater criterion. These values are also well under the limit 1, confirming that the process wasnot limited by internal diffusion either.

Lastly, figures 22 and 23 show the results of the sensitivity analysis of the rate parameters andthe nitrogen distribution parameters, respectively. A reference line was added to each plot to showthe lowest achieved value of the objective function. The objective function consists of values in bothmol/m3 and ppm for the nitrogen compounds to not be neglected in the minimization process, andshould therefore only be treated as a signal response.

These figures show that for every parameter, the lowest value is found at 0% perturbation, whichconfirms that the global minimum was found. The perturbation values in figure 23 for the nitrogendistribution parameters were chosen as ±20% when possible, and otherwise chosen as maximum andminimum allowed values, respectively, according to the mass balances explained in section 9.2.

6 RESULTS 34

Figure 20: Calculated values of the Mears criterion at outlet conditions of each experiment along withthe limiting value.

Figure 21: Calculated values of the Weisz-Prater criterion at outlet conditions of each experimentalong with the limiting value.

6 RESULTS 35

Figure 22: Calculated objective function values after various perturbations of each rate and adsorptionconstants parameter, one by one. The reference line shows the lowest achieved value of the objectivefunction.

Figure 23: Calculated objective function values after various perturbations of each nitrogen distri-bution parameter, one by one. The reference line shows the lowest achieved value of the objectivefunction.

7 DISCUSSION 36

7 Discussion

In this section the results are first discussed in the chronological order by which they were presented,and a more general discussion is provided after.


Calculating the yields of the HDA products independently allowed the HDA reaction network to beevaluated, and as shown in figure 7 network 2 gave a good prediction except for a few cases, such asthe yields of Tet and asym at medium conversions. These deviations were the reason that the pathwayTet −−→ asym was added, and it clearly resulted in a better prediction of both Tet and asym. Similarly,the pathway DiH −−→ Tet was added in network 3 in an attempt to improve the prediction of Tet,but with no effect. Both of these reaction paths have previously been found to become notable above20% conversion of phenanthrene [8], though PHP has generally not been present in these studies asphenanthrene conversions have been kept relatively low.

As all the reaction steps are connected, the systematic underprediction of Tet and asym is probablynot a numerical error, since increasing the yield of Tet at medium conversions of phenanthrene wouldeither result in lower yields of asym and sym or lower yields of DiH, introducing more error. The yieldof PHP is slightly overpredicted at conversions between 0.6 and 0.8 though, while both asym, sym andDiH seem to be underpredicted at these conversions, which could indicate that the formation of PHPis not irreversible. A parameter estimation was also performed by excluding the two points below thecurve for asym, but this did not cause the predicted curve to move up or give a better fit, indicatingthat the points are not outliers.

Looking at the representative experiments in figure 8, the prediction appears to be best for ex-periments N5 and N2, i.e. when the conversion of phenanthrene is low and high, respectively. Whilesome errors are seen in the prediction of experiment N11, the prediction of experiment N13 has somerelatively large errors. This is likely due to the model prediction of PHP, which starts at 60% conver-sion, while experimentally, PHP was only detected above 95% conversions. As seen from experimentN13, the model thus predicts PHP to form when it should not, in turn causing the underpredictionof Phe. To improve the model accuracy, more data points could be taken in the conversion range of0.7-0.9 to see when PHP actually starts forming.

As for the nitrogen kinetics, having the nitrogen distribution parameters allowed the data pointsto be adjusted to the curves, which is what made the fits good, keeping in mind that the numericalvalues of the concentrations were very low. The nitrogen concentrations were initially converted tomol/m3, just as the HDA products, though this gave very small numbers and cancellation errors in thenumerical solution, causing the nitrogen concentrations to be neglected altogether. If anything, theprediction was slightly worse at higher degrees of HDN, and this could be due to increased uncertaintyin the distribution parameter and random errors in the measurement of the nitrogen content. Due tothe good fit of the model, the pseudo-first-order rate law for HDN was concluded as sufficient.

Looking at the rate parameters, k1/(k1+k2) was fairly close to 0.5 which is consistent with the 50%selectivity between formation of DiH and Tet which previously has been reported for the Ni-promotedcatalyst [8]. The conversion from Tet to sym was much quicker than the other reaction steps though,which is why the maximum yield of Tet is achieved at lower phenanthrene conversions than the otherproducts. In addition to this, the rate of consumption of sym is relatively low, resulting in sym beingthe main product at medium conversions. While the rate of the step Tet −−→ asym is not low enoughto be negligible, it does have a relatively small impact on the results as seen on the curves of network1 and 2 in figure 7, which coincide for DiH, sym and PHP.

7 DISCUSSION 37


Sorting the results by inlet conditions in figures 10-12 allowed some experimental points to be showntogether for comparison. As was seen for the two-step optimization, the model succeeds in predictingsome conditions, but not all. Looking at the case of no nitrogen for instance the data points areall fairly close to the curves, with mostly random errors, which indicates that there is no significantnumerical error in the solution. The model seems to overpredict the concentrations of Phe and Tetin that case, though the opposite can be said for some other plots where nitrogen is present. Therandom errors are probably due to random errors in the measurements, and since the determinationcoefficient is relatively close to 1, the accuracy of the model is probably good enough.

As for the general trends, the highest conversion is clearly achieved when no nitrogen is present,which is also when the PHP yield is highest. Comparing the phenanthrene concentrations when 35ppm carbazole is present to when 35 ppm acridine is present, much more phenanthrene is convertedin the former case, indicating that acridine is much more inhibiting than carbazole. This has alsobeen concluded in previous studies [3]. A similar trend can be observed when comparing 17.5 ppmcarbazole to 17.5 ppm acridine, and comparing these separate cases to the case of carbazole andacridine present simultaneously, even lower conversions are seen. Comparing only 35 ppm carbazoleto 35 ppm carbazole and 17.5 ppm acridine simultaneously again shows that even a small amount ofacridine inhibits the HDA reaction a lot, though the difference is small when an additional 17.5 ppmacridine is present. There is also no significant difference between only 35 ppm acridine and 35 ppm ofeach of acridine and carbazole, which could mean that the inhibition kinetics are saturated, i.e. whenhaving at least 35 ppm acridine the maximum degree of inhibition is already achieved.

The concentration profiles of the nitrogen compounds show slightly steeper curves for carbazolethan acridine, which is consistent with the stronger inhibition of acridine, since it might stay adsorbedlonger before reacting, effectively reducing the vacant spots on the catalyst for the HDA compoundsto react on. Similarly to the two-step optimization, only small errors are seen for the HDN reactions.

A systematic error that can be seen is that when only carbazole is present, the model predictsa small yield in PHP, even though no PHP was ever measured with nitrogen present. This error isconnected to the error seen at medium phenanthrene conversion mentioned earlier and is probablydue to one of the assumptions of the model. Beside the assumed reaction network, it could be thatthe self-inhibition of the HDA reactions becomes more prominent when no acridine is present, due tothe relatively weak inhibition of carbazole, but if that was the case the curves for when no nitrogen ispresent would not fit so well.

The rate constants for the HDA reactions show the same trends identified in the two-step opti-mization, since both optimization methods gave roughly similar results illustrated in different ways.To further emphasize the inhibiting effect of acridine, it can be seen that the adsorption constant isthree times larger than for carbazole, giving a higher contribution to the inhibition part of the rateexpressions.

Parity plots were produced to further evaluate the accuracy of the results, as seen in figures 13-19,and the same trends as have been identified for the HDA compounds can be seen there, i.e. a decentprediction of most compounds except for some underpredictions of Tet and overpredictions of PHP.This serves to further validate the model with respect to the experimental data, and it can be seen thatthe deviations are mostly small and random. Since some data for carbazole and acridine were fittedwith the distribution parameters, these are not necessarily the true values, but the values that themodel predict. Hence, it is more relevant to investigate the total nitrogen content which actually wasmeasured, in figure 19. This graph confirms that the predicted values closely follow the experimentaldata, irrespective of how the nitrogen distribution was estimated.

As for the Mears and Weisz-Prater criteria in figure 20 and 21, these confirm that there were no

7 DISCUSSION 38

limitations in diffusion present during the experiments, and that the surface reaction successfully wasthe rate-limiting step, as intended in the experimental design. Combining the definitions (62) and (69)with the rate equation (54) shows that the criteria are independent of the phenanthrene concentrationand inversely proportional to the carbazole and acridine concentrations. Thus, both the criteria arelargest when there is no nitrogen present, and are mainly controlled by the rate constants. This alsomeans that the criteria reach a maximum at the outlet conditions of each experiment, since this iswhen the nitrogen concentrations are the lowest.

Lastly, the sensitivity analysis in figure 22 and 23 confirms that the solution found is the globalminimum of the system, i.e. there is no better solution that can be reached by providing a differentinitial guess. The sensitivity analysis also gives an illustration of the influence of each parameter onthe final results. Both the rate constants for phenanthrene give the most rapid increase in error whenperturbed, excluding the nitrogen distribution parameters, since the yield of each HDA product isdependent on the consumption of phenanthrene, allowing the error to grow larger for each reactionstep. Conversely, the influence of the parameters becomes smaller for the steps closer to the finalproduct. An exception is the parameter k23K

adsTet , confirming that the pathway added in network 2

has a relatively small influence on the solution, which was concluded previously.The sensitivity analysis also shows that both the rate and adsorption parameters of the HDN

reactions have a large influence on the results, and this is partly because the nitrogen concentrationswere kept in ppm. It can be seen again that the adsorption constant of acridine has a higher influencethan carbazole, which is because it is more inhibiting and has a larger impact on all the HDA reactions.

The parameters for the nitrogen distribution differ much in response and seem to have a largeinfluence on the results, except for parameters xN9 and xN7. Both experiment N9 and N7 wereperformed at short residence times, and at these points the rate of reaction will be relatively highindependent of the distribution of the nitrogen. Conversely, experiment N8 was performed with thelongest residence time and maximum nitrogen content, and thus xN8 had the largest influence.

7.3 Method evaluation

As mentioned, a problem with nonlinear regression can be to find an accurate initial guess, whichbecomes more problematic with more parameters and correlations between them. For this reason, thetwo-step optimization served as a valid method to not only produce a decent initial guess, but alsodivide one larger problem into two smaller ones. With less parameters present there are less guessesthat have to be accurate and less computational power is potentially required for each step, althoughthe solutions of the steady state model was not computationally demanding. An important trait of amodel is to be simple, as it will not only be easier to use but also easier to understand. Focusing onthe yields of the HDA products allowed the reaction network to be improved in a way that might nothave been obvious if the direct optimization was applied right away, due to the combined influence ofthe nitrogen kinetics.

In the same sense, the coordinate system was changed for the direct optimization to make themodel more simplistic and focus on phenomena and trends rather than exact values. Provided a goodenough initial guess is available, the direct optimization will provide a better end result since thereis only one error to be minimized. In the two-step optimization a certain error was found in the firstsolution step, and when performing the second solution step this error was carried on as the relativerates were not adjusted further. Hence, the errors of both the solution steps add up to a larger finalerror, compared to the single error of the direct optimization.

7 DISCUSSION 39

7.4 Pitfalls

There are many time consuming pitfalls in model development and numerical methods which can beavoided with experience. For this reason it is important to reflect over some of the obstacles in thisthesis work and take knowledge from it to avoid repeating some mistakes in the future.

It is easy to be optimistic at the start of a project and assume that everything will go as planned,and so the focus was initially to keep the model advanced and as similar to the target as possible,but this goal was changed gradually as unforeseen problems appeared over the course of the work. Alesson to be taken from this is that a model that can describe general trends and has known limitationsis better than a theoretically more exact model that cannot be solved or cannot be validated byexperimental data. The model in this work was developed based on nonstationary conditions, butthere was a lack of data for these conditions and overall less information available in literature, inaddition to the difficulty in solving partial differential equations. The steady state model that wasdeveloped from this served as a frame of reference instead that might be used to further develop thetransient model in the future.

Early on in the solution of the model an analytical approach was taken since this would be possiblee.g. when no nitrogen is present. While an analytical solution might be more exact, a numericalsolution is more practical in many ways. Not only was the numerical solution easier to develop, it alsoallowed all experimental conditions to be included simultaneously in the nonlinear regression processrather than separating the solution into parts that can be solved analytically, and parts that cannot.Another approach was also to separate the numerical solution into two cases; one where nitrogen ispresent and one where it is not. While the idea was to describe each case better, this only made themodel less robust compared to one solution that consistently can describe both cases.

To avoid pitfalls it is important to make informed decisions and continually evaluate results.Graphical analysis was a good tool for this, partly because it gave insight to which assumptionsshould be tested and partly because it helped finding errors otherwise lost among many lines of code.For instance, the parity plots were used to find some errors that had otherwise been missed, beforeproducing the final solution.

The literature references played an important role in the model development, which is a good wayto gain insight in the ability and applicability of a model, but relying too much on references cancause issues. For instance, rate and adsorption constants were gathered from literature to providethe first guesses of the parameters, but these guesses were very different from the final results. Thiswas especially true for the nitrogen kinetics, where the results converged to a different local minimumbecause the guess was too inaccurate, and providing a new guess simply by looking at the solutionallowed the correct solution to be found. Rate constants can be very dependent on e.g. the catalystpreparation process, which means that deviations from references do not necessarily mean that thesolution is incorrect.

7.5 Further development

The results of the steady state model showed some room for improvement, which as mentioned couldbe by using more experimental data or adjusting some of the assumptions such as the HDA reactionnetwork, the inhibition kinetics or e.g. the influence of vaporization.

Having solved the steady state model, the next step would be to further develop the transientmodel that was used as a starting point. As mentioned earlier, the HDT process is often accompaniedby changes in feed composition and relatively long relaxation times, and the behavior during thesenonstationary conditions are too complex to be described by the steady state model, which onlyprovides limited insight into the mechanism [4]. This limitation was also shown by Ho and Nguyen [20],

8 CONCLUSION 40

as the steady state model failed to predict transient behavior yet accurately matched steady state data.Thus, while the transient model is more complex and has been applied less previously, it will describethe real process better and provide more useful information upon solution. As part of this thesiswork, their transient model was also partly adjusted to hydrotreating of phenanthrene inhibited bycarbazole and acridine, but this was not finished due to time constraints.

8 Conclusion

To conclude, the steady state model developed in this thesis work was able to fit to most of theexperimental data, with the main exception being PHP yields at higher conversions of phenanthrene.If the focus was to improve this aspect of the model, the two-step method developed here could serveas a simple numerical tool to evaluate the results.

The results also showed that acridine is a much stronger inhibitor than carbazole, as expected,but to investigate the inhibition kinetics in more detail the transient model would probably have tobe solved. Since the model would share some assumptions with the steady state model, the steadystate model could still be used as a simpler tool to evaluate these assumptions. For instance, if someassumptions about the inhibition kinetics were to be changed, the one-step method developed herecould be used to analyze the solution of the steady state model before applying this change to thetransient model.

Acknowledgements

Special thanks go to my supervisor Jacob Venuti Bjorkman and examiner Lars J. Pettersson for theircontinued support and interest in my work. I would also like to thank Nynas AB for the providedworkplace and insight on industry.

9 APPENDIX 41

9 Appendix

9.1 HDA product distribution

The yield of product i is expressed with yi:

yi =ci

cPhe,f(70)

where cPhe,f is the feed concentration of phenanthrene. The conversion of phenanthrene, X, is definedas:

X =cPhe,f − cPhe

cPhe,f(71)

yi and X are differentiated and combined:

dci = dyicPhe,f ⇒dcidz

= cPhe,fdyidz

(72)

dcPhe = −cPhe,fdX ⇒dcPhe

dz= −cPhe,f

dX

dz(73)

⇒ dyidz

/dX

dz=dyidX

=1

cPhe,f

dcidz

/− 1

cPhe,f

dcPhe

dz=dcidz

/(−dcPhe

dz

)(74)

Combining equations (70) and (71) gives:

ci = yicPhe,f cPhe = cPhe,f (1−X) (75)

⇒ cicPhe,f

=yi

(1−X)(76)

Applying equations (74) and (76) to equations (37) and (38) gives:

dyDiH

dX=MPhe

MDiH

[k1K


DiHcDiH

(k1 + k2)KadsPhecPhe

]=MPhe

MDiH

[k1

k1 + k2−

k3KadsDiH

(k1 + k2)KadsPhe

cDiH

cPhe

](77)

=MPhe

MDiH

[k1

k1 + k2−

k3KadsDiH

(k1 + k2)KadsPhe

yDiH

(1−X)

](78)

The procedure is repeated for equations (39)-(42) to yield the set of ODEs (49)-(53).

9.2 Nitrogen distribution

For experiment j with both acridine and carbazole in the inlet, a parameter xj is defined as:

xj =ωj,Cbz

ωj,N=

ωj,Cbz

ωj,Cbz + ωj,Acr(79)

where ωj,N is the total outlet nitrogen content measured. xj is combined with the measured value toestimate the carbazole and acridine content in the outlet:

ωj,Cbz = xjωj,N (80)

ωj,Acr = (1− xj)ωj,N (81)

9 APPENDIX 42

A mass balance for carbazole over reactor shows that the maximum allowed value of xj , xj,max

corresponds to the inlet concentration of carbazole, since no carbazole is produced in the reaction:

ωCbz,f = xj,maxωj,N ⇔ xj,max =ωCbz,f

ωj,N(82)

Conversely, the acridine content is highest at the lowest value of xj , xj,min. This is bound by the massbalance of acridine over the reactor:

ωAcr,f = (1− xj,min)ωj,N ⇔ xj,min = 1−ωAcr,f

ωj,N(83)

9.3 Reactor residence times

The maximum catalyst load of the reactor is m3 = 100.56mg. Assuming this fills the given bed sizeof the reactor, it can be used to calculate the bed density ρbed:

Vr =d2tπL

4=

(10× 10−3)2 ·π · 7× 10−2

4= 5.50× 10−6 m3 (84)

ρbed =m3

Vr=

100.56× 10−3

5.50× 10−6= 1.83× 104 g/m3 (85)

where Vr is the bed volume, dt the inner reactor diameter and L the reactor length.If the bed density is used to calculate the bed volume for each catalyst loading, dividing this by

the volumetric flow Q through the reactor yields the residence time for each catalyst loading:

t1 =V1Q

=m1

ρbedQ=

50.2× 10−3

1.83× 104 · 0.1× 10−6= 27.4 min (86)

t2 =75.44× 10−3

1.83× 104 · 0.1× 10−6= 41.2 min (87)

t3 =100.56× 10−3

1.83× 104 · 0.1× 10−6= 55.0 min (88)

9.4 Additional results

Figures 24-26 show the calculated concentration profiles of the HDA compounds for the rest of theexperiments produced with figure 8. Figures 27 and 28 show the corresponding concentration profilesfor the HDN compounds, produced with figure 9.

9 APPENDIX 43

Figure 24: Calculated concentration profiles of each HDA compound as a function of distance fromthe top of the catalyst bed, along with experimental points.


9 APPENDIX 44


Figure 27: Calculated concentration profiles of each HDN compound as a function of distance fromthe top of the catalyst bed, along with experimental points.

9 APPENDIX 45

Figure 28: Calculated concentration profiles of each HDN compound as a function of distance fromthe top of the catalyst bed, along with experimental points.

REFERENCES 46

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Inhibition Kinetics of Hydrogenation of Phenanthrene

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