Britt Eeckhaudt isomerization of light alkanes of hydrocarbon-related reactions

Britt Eeckhaudt

isomerization of light alkanesof hydrocarbon-related reactions: application toA generalized methodology for microkinetic modeling

Academiejaar 2008-2009Faculteit IngenieurswetenschappenVoorzitter: prof. dr. ir. Guy MarinVakgroep Chemische proceskunde en technische chemie

Master in de ingenieurswetenschappen: chemische technologieMasterproef ingediend tot het behalen van de academische graad van

Begeleider: Gisela Lozano BlancoPromotoren: prof. dr. ir. Joris Thybaut, prof. dr. ir. Guy Marin

When you look at yourself from a universal standpoint, something inside always reminds or informs you

that there are bigger and better things to worry about

(Albert Einstein, The World as I See It. (1879 - 1955))

a

Dankwoord

Als je aan het begin staat van de opleiding burgerlijk ingenieur lijkt de weg die je moet

afleggen oneindig lang. Nu, bijna vijf jaar later, merk je dat de tijd echt vliegt. Aan het einde

van de rit kan ik terugkijken op vijf fantastische jaren. Niet alleen heb ik ontzettend veel

bijgeleerd, ook heb ik op mijn weg veel interessante mensen ontmoet. Aan het einde van mijn

masterproef neem ik even een moment om hen te bedanken.

Vooreerst wil ik prof. dr. ir. Guy. B. Marin bedanken voor de opportuniteit die we krijgen om

deel te mogen nemen aan het onderzoek binnen de vakgroep ‘Chemische Proceskunde en

Technische Chemie’. Verder bedank ik hem ook voor het ter beschikking stellen van het

materiaal nodig voor de masterproef.

Ook naar mijn promotor prof. Joris Thybaut gaat een woord van dank voor de grote hulp bij

de verwezenlijking van deze thesis. Zelfs in zeer drukke tijden wist je altijd een moment voor

ons vrij te maken en geen enkele vraag was je teveel.

Verder wil ik Andy en Marcel bedanken voor de technische ondersteuning bij de Berty. Dank

u om altijd zeer snel tijd vrij te maken en voor de vele reanimatiepogingen van de opstelling.

A special thank you goes out to my coach Gisela. Without your help I would have not been

able to realize this master project. The experience you had with the computer code was a

blessing to me. I wish you all the best with Andrew and hope you have a nice time in

America.

Een groot woordje van dank gaat ook uit naar ‘coach’ Bart. Alhoewel hij niet mijn officiële

begeleider is, zou de verwezenlijking van deze masterproef niet mogelijk geweest zijn zonder

zijn hulp. Dank u Bart, om altijd te springen als ik vast zat met mijn code, voor de hulp

zonder dat ik er echt om moest vragen, voor de interesse in de vorderingen van mijn

masterproef. Veel succes verder met je doctoraat!

Michaël, Kenneth en Aäron, een speciaal woordje van dank gaat ook uit naar jullie. Zelf op

dagen dat het minder vlot ging, zorgden jullie steeds voor de opgewekte noot. Zonder jullie

zouden de dagen veel langer geduurd hebben. De ontspannende en sportieve middagen waren

ideaal om mijn hoofd te legen en met frisse moed te starten na de middag. Kenneth en Aäron,

b

ik wens jullie veel succes met je doctoraat, en houd de sfeer er in hé! Michaël veel succes in

je loopbaan bij de overheid. Ik hoop dat je al je dromen kan verwezenlijken.

Christof, we hebben elkaar leren kennen tijdens onze studies. Op een mysterieuze manier

waren we ineens de beste vrienden. Dank je voor alle gesprekken de afgelopen jaren en voor

de steun die je voor me was. Ik heb aan de voorbije vijf jaar niet enkel kennis, maar ook

vrienden voor het leven over gehouden.

Tenslotte wil ik ook een speciaal dankjewel richten naar mijn familie. Ik ben niet steeds de

gemakkelijkste dochter geweest, maar ik wil jullie oprecht danken voor de kans die jullie me

hebben gegeven om mijn droom te verwezenlijken. Jullie zijn mijn steun en toeverlaat. Mijn

zussen, Shari en Tess, jullie ook bedankt. Onrechtstreeks hebben jullie ook bijgedragen aan

dit resultaat. Jullie hebben me mee gemaakt tot wie ik geworden ben. Jullie hebben ook mee

gezorgd dat ik me de voorbije 5 jaar niet teveel zorgen hoefde te maken, behalve over mijn

studies.

Een laatste zeer welgemeend dankjewel is voor Koen. Jou wil ik bedanken voor het geduld

dat je met me hebt gehad het afgelopen jaar. Ook voor het begrip en de steun die ik van jou

heb gehad kan ik je niet genoeg bedanken.

Britt

Krijgslaan 281 S5, B -9000 Gent (Belgium)

tel. +32 (0)9 264 45 16 • fax +32 (0)9 264 49 99 • GSM +32 (0)475 83 91 11 • e-mail: Petra.Vereecken@UGent

http://www.lct.ugent.be/start/pages/1/en

3

Laboratorium voor Chemische Technologie

Verklaring in verband met de toegankelijkheid van de scriptie

Ondergetekende, Eeckhaudt Britt,

afgestudeerd aan de UGent in het academiejaar 2008-2009 en auteur van de scriptie met als

titel: A generalized methodology for single-event microkinetic modeling of hydrocarbon-

related reactions: application to isomerization of light alkanes

verklaart hierbij: 1. dat hij/zij geopteerd heeft voor de hierna aangestipte mogelijkheid in verband

met de consultatie van zijn/haar scriptie:

� de scriptie mag steeds ter beschikking gesteld worden van elke aanvrager

� de scriptie mag enkel ter beschikking gesteld worden met uitdrukkelijke, schriftelijke goedkeuring van de auteur

� de scriptie mag ter beschikking gesteld worden van een aanvrager na een wachttijd van…………jaar

� de scriptie mag nooit ter beschikking gesteld worden van een aanvrager 2. dat elke gebruiker te allen tijde gehouden is aan een correcte en volledige

bronverwijzing

Gent,

FACULTEIT TOEGEPASTE WETENSCHAPPEN

Vakgroep Chemische Proceskunde & Technische Chemie Laboratorium voor Chemische Technologie

Directeur: Prof. Dr. Ir. Guy B. Marin

B. Eeckhaudt is associated with the Chemical Engineering Department, Ghent University (UGent), Gent, Belgium. E-mail: [email protected] .

A generalized methodology for microkinetic modeling of hydrocarbon-related reactions: application to isomerization of light alkanes

Britt Eeckhaudt

Supervisor: dr. ir. Gisela Lozano Blanco

Promoters: Prof. dr. ir. Guy B. Marin, Prof. dr. ir. Joris W. Thybaut

Abstract: A fundamental kinetic model for the hydroisomerization of n-pentane on a bifunctional catalyst has been refined. Hydrogenolysis, and formation and reaction of primary carbenium ions considering ideal and non-ideal hydrocracking, i.e., de(hydrogenation) reactions quasi- and non-quasi equilibrated, have been included into the classical reaction network. The single-event concept is used to describe the reaction kinetics. Experimental data obtained on a Pt/H-BEA 0,6 wt% catalyst is used for the regression and estimation of the kinetic parameters. Since experimental data under non-ideal hydrocracking conditions were present in the data set, the non-quasi-equilibration of the (de)hydrogenation reactions were implemented in the computer code.

Keywords: n-pentane hydroisomerization, bifunctional catalyst, kinetic model, single-event, non-ideal hydrocracking

I. INTRODUCTION

Gasoline as produced today contains aromatic components such as toluene or benzene to increase the octane number to a satisfying level [1]. Aromatics are well-known carcinogenic agents [2]. In many countries the maximum allowed amount of aromatics present in gasoline is being tightened [2]. Branched paraffinic compounds are an alternative to aromatics for their high octane number [3]. In particular in the present work, the hydroisomerization of light alkanes is studied. Hydroisomerization is a bifunctional process requiring metal as well as acid sites. The metallic sites provide the hydrogenation-dehydrogenation function, while the acid sites provide the protonation-deprotonation, cracking and isomerization reactions [4]. Saturated hydrocarbons are dehydrogenated on the metal sites. Subsequently, the unsaturated species migrate to the acid sites where they are protonated yielding carbenium ions. Such carbenium ions undergo further isomerization and cracking reactions. The product carbenium ions desorb as alkenes that are hydrogenated into the observable saturated species. Prior to these chemical steps, physisorption occurs in the micropores of the catalyst[5].

II. FUNDAMENTAL KINETIC MODELING OF N-PENTANE

HYDROISOMERIZATION

A. Experimental data

Experimental data was provided by the University of Munich. The experiments were performed on a Pt/H-BEA 0.6 wt%

catalyst. Zeolite BEA 25 (Si/Al=12.5) from Süd-Chemie AG was loaded with Pt by ion-exchange with an aqueous Pt(NH3)4(OH)2 solution A solution containing the appropriate amount of Pt(NH3)4(OH)2 and an amount of NH4OH corresponding to the theoretical concentration of protons (competitive adsorption) in the sample was added dropwise to the slurry at 40°C in order to exchange the cations of the zeolite to obtain the metal loaded H+-form of the zeolite. After the ion exchange the solid was centrifuged, washed and freeze dried. The samples were calcined in air at 350°C for 16 h (heating rate 0.5°C/min) and finally reduced at 300°C in H2 for 4 h. Analysis of the data set pointed out that some experiments are performed under non-ideal hydrocracking conditions. The latter are used for the regression of the kinetic parameters in case of ideal hydrocracking. The non-ideal hydrocracking experiments caused the implementation of non-ideal hydrocracking in the regression computer code. The latter experiments will be used for regression in this extended code.

B. Procedure

Using a computerized algorithm the reaction network comprising every elementary step of hydroisomerization of n-pentane was generated. The reactor is modeled based on a pseudo-homogenous one-dimensional reactor model:

A

A

A R

FWd

dX =)(

0,

(1)

W being the catalyst mass, XA the conversion of component A, FA,0 the inlet flow of component A and RA the net rate of formation of component A. Concentration and temperature gradients are neglected in the reactor, so only mass balances for the alkanes have to be considered.

C. Parameter estimation

Parameter estimation is performed by a combination of a Rosenbrock algorithm and a Levenberg-Marquardt algorithm. The Rosenbrock method is applied first to find an appropriate direction leading to a possible optimum. The Levenberg-Marquardt method is used afterwards to further optimize the parameters [5]. The objective function during the estimation is the weighted sum of the square differences (SSQ) between the experimental and the model calculated responses (R).

∑∑= =

→−=expn

k

nresp

j

b

kikii MinRRw1 1

2,, )(SSQ⌣

(2)

This is performed by adjusting the model parameter vector b, in such a way that it approaches the real parameter vector β [5].

D. Reaction networks

The classical reaction network consists of 6 reaction families: (de)hydrogenation reactions, (de)protonation reactions, alkyl shift, hydride shift, PCP-branching and β-scission. The (de)hydrogenation reactions and (de)protonation reactions are assumed as quasi-equilibrated. In the classical reaction network only secondary and tertiary carbenium ions are considered. When n-pentane is used as feed component, no β-scission reactions considering only secondary and tertiary carbenium ions can occur. According to the experimental data, cracking does occur. Therefore, the reaction network has to be extended. Initially the classical reaction network is extended considering the formation of primary carbenium ions. This approach assumes that carbenium ions can act as reactant and product. Primary carbenium ions have been considered in this work in an ideal and in a non-ideal hydrocracking model as explained in the next section. Another approach is to consider metal-catalyzed cracking reactions, i.e. hydrogenolysis, instead of acid-catalyzed reactions. In this type of reactions methane and ethane is separated from the alkane. In this case it has been assumed that only n-pentane and iso-pentane can undergo hydrogenolysis reactions. Both modifications are performed separately.

III. RESULTS AND DISCUSSION

A. Ideal hydrocracking: Hydrogenolysis and presence of primary carbenium ions

The molar outlet flows of the responses are calculated based on the estimated model parameters and subsequently compared with the experimental outlet flows. The model including hydrogenolysis describes better the experimental data than the model considering primary carbenium ions. The fit for propane, ethane, iso-pentane and n-butane is reasonably good. For both models the fit for methane and iso-butane failed however. This is due to the experimental molar outlet flows of these responses, which are for most of the experiments equal to zero. The conversion as a function of pressure and space-time is slightly underestimated for both models which causes the overestimation of the selectivity.

B. Non-ideal hydrocracking

The balance between the number and the activity or strength of the metal and the acid sites plays a key role in the product selectivities observed in hydrocracking. Compared to acid catalysts used in catalytic cracking, the presence of a metal phase on hydrocracking catalysts enhances isomer formation The term ideal hydrocracking is introduced because of the high isomer yield obtained using hydrocracking catalysts with a high (de)hydrogenation activity.

Non-ideal hydrocracking implies the non-quasi-equilibrium of the (de)hydrogenation reactions. Initially only one rate coefficient is considered for all (de)hydrogenation reactions. For the ideal case, the computer code calculates the concentration of the olefins and the carbenium ions from the equilibrium coefficient. Now the quasi-equilibrium of (de)hydrogenation reactions is no longer valid and hence, the concentration of the olefins appears as variables in the set of equations. On top of the 6 differential equations from the classical reaction network, 10 additional equations have to be solved. Due to the pseudo-steady-state approximation applied for the olefins, these 10 equations are non linear algebraic equations. The equations are solved simultaneously using the DASPK subroutine. DASPK uses variable-step size backward differentiation formulas (BDF) applying either direct linear system methods or a preconditioned Krylov iterative method. In the present work, the direct method was applied and therefore a dense matrix solver is chosen. In order to solve these equations by DASPK, consistent initial values for the solution vector have to be given. Initial values for the paraffin concentrations are known, but those for the olefins are not known a priori. Since the algebraic equations for the olefins are nonlinear, reasonable initial guesses must be provided as input to the solver in order to reach convergence. Therefore the subroutine DNSQE is applied first to calculate initial olefins concentrations. The solution of the solver DNSQE is used as input in the DASPK subroutine. As a result, preliminary parameter estimation results have been obtained. Parities are still to be refined but the code is now available for a further work.

IV. CONCLUSION

A fundamental kinetic model applied to the classical reaction network for hydroisomerization of n-pentane is unable to describe the formation of lighter molecules. The model and reaction network has been modified by including on the one hand hydrogenolysis on the metal sites and on the other hand formation of primary carbenium ions on the acid sites under ideal hydrocracking conditions and also under non-ideal hydrocracking conditions. The best fit between experimental and model calculated values at this moment is obtained for the reaction network including hydrogenolysis, although a further study must be performed for non-ideal hydrocracking conditions.

V. REFERENCES

[1] Courty, P. and J.F. Gruson, Refining clean fuels for the future. Oil & Gas Science and Technology-Revue De L Institut Francais Du Petrole, 2001. 56(5): p. 515-524.

[2] http:// eur-lex.europa.eu/ [3] http://chemed.chem.purdue.edu/ [4] Feng, W., E. Vynckier, and G.F. Froment, Single-Event

Kinetics of Catalytic Cracking. Industrial & Engineering Chemistry Research, 1993. 32(12): p. 2997-3005.

[5] Thybaut, J.W., Production of low-aromatic fuels: kinetics and industrial application of hydrocracking, PhD thesis, 2005,Ghent University

[6] Govaerts, S., Ondersteuning van de ontwikkeling en optimalisering van katalysatoren met behulp van fundamenteel kinetisch modellen, Master Project, 2007,Ghent University

d

Table of contents

DANKWOORD A

VERKLARING IN VERBAND MET DE TOEGANKELIJKHEID

VAN DE SCRIPTIE C

TABLE OF CONTENTS D

LIST OF FIGURES J

LIST OF TABLES N

NOTATION P

ROMAN SYMBOLS P

GREEK SYMBOLS R

SUPERSCRIPTS R

SUBSCRIPTS R

NEDERLANDSE SAMENVATTING I

GESCHIEDENIS VAN DE RAFFINADERIJ : BELANG VAN HYDROCONVERSIEPROCESSEN I

HYDROKRAKEN EN HYDROISOMERISATIE II

MICROKINETISCH MODELLEREN III

DOEL VAN DIT WERK III

HYDROISOMERISATIE VAN N -PENTAAN : TOEPASSING VAN SINGLE-EVENT CONCEPT IV

REACTIEMECHANISME IV

REACTIENETWERK IV

e

REACTORMODEL V

SINGLE-EVENT MICROKINETISCH MODELLEREN V

SNELHEIDSVERGELIJKINGEN VI

MODELLERING VII

EXPERIMENTEEL PROGRAMMA VII

HYDROISOMERISATIE VAN N-PENTAAN OP PT/H-BEA 0,6 WT% KATALYSATOR VII

HYDROISOMERISATIE VAN N-HEXAAN OP MC-301 KATALYSATOR VIII

HYDROISOMERISATIE VAN N -PENTAAN : HET KLASSIEKE REACTIENETWERK UITGEBREID

MET PRIMAIRE CARBENIUM IONEN X

IDEAAL VS NIET-IDEAAL GEDRAG X

REACTIENETWERK X

SNELHEIDSVERGELIJKINGEN XI

MODELPARAMETERS XI

RESULTATEN XI

HYDROISOMERISATIE VAN N -PENTAAN : HET KLASSIEKE REACTIENETWERK UITGEBREID

MET HYDROGENOLYSE XII

REACTIENETWERK XII

SNELHEIDSVERGELIJKINGEN XIII

MODELPARAMETERS XIII

RESULTATEN XIV

HYDROISOMERISATIE ONDER NIET -IDEALE HYDROKRAKINGSCONDITIES XV

REACTIEMECHANISME XV

INVLOED VAN DE WERKINGSVOORWAARDEN OP IDEALITEIT VAN HYDROKRAKEN XVI

TOEPASSING VAN SINGLE-EVENT MICROKINETISCH MODELLEREN OP DE (DE)HYDROGENATIEREACTIES

XVI

IMPLEMENTATIE IN HET COMPUTERPROGRAMMA XVII

BELANG VAN IMPLEMENTATIE XVII

CHAPTER 1 INTRODUCTION 1

1.1 GENERAL BACKGROUND 1

1.2 THE ROLE OF HYDROCRACKING 5

1.3 HYDROISOMERIZATION 6

1.4 M ICROKINETIC MODELING 7

1.5 SCOPE OF THE MASTER PROJECT 8

1.6 REFERENCES 10

f

CHAPTER 2 HYDROISOMERIZATION OF N-PENTANE:

SINGLE-EVENT APPROACH 11

2.1 REACTION MECHANISM 11

2.1.1 DESCRIPTION 11

2.1.2 ISOMERIZATION REACTIONS 13

2.1.3 HYDROCRACKING REACTIONS 14

2.2 REACTION NETWORK 15

2.2.1 REACTION NETWORK GENERATION ALGORITHM 15

2.2.2 REACTOR MODEL 18

2.2.3 SINGLE-EVENT MICROKINETIC MODELING 19

2.2.4 RATE EQUATIONS 22

2.2.5 REGRESSION 26

2.3 REFERENCES 30

CHAPTER 3 EXPERIMENTAL PROGRAM 32

3.1 20-FOLD PARALLEL PLUG FLOW REACTOR 32

3.1.1 EXPERIMENTAL SET UP 32

3.1.2 CATALYST 33

3.1.3 EXPERIMENTAL RESULTS 35

3.2 VAPOUR PHASE CONTINUOUS STIRRED TANK REACTOR 41

3.2.1 EXPERIMENTAL SET UP 41

3.2.2 CATALYST 45

3.2.3 EXPERIMENTAL RESULTS 46

3.3 REFERENCES 50

CHAPTER 4 IDEAL HYDROCRACKING OF N-PENTANE:

REACTION NETWORK INCLUDING PRIMARY CARBENIUM

IONS 51

4.1 IDEAL VERSUS NON-IDEAL BEHAVIOR 51


4.3 NET FORMATION RATES 57

4.4 MODEL PARAMETERS 58

4.5 RESULTS 60

g

4.5.1 ESTIMATED PARAMETERS AND DISCUSSION 60

4.5.2 STATISTICAL ANALYSIS 65

4.5.3 INFLUENCE OF PRESSURE ON CONVERSION AND SELECTIVITY 66

4.5.4 INFLUENCE OF THE SPACE-TIME ON THE CONVERSION AND SELECTIVITY 68

4.6 CONCLUSION 69

4.7 REFERENCES 70

CHAPTER 5 IDEAL HYDROCRACKING OF N-PENTANE:

REACTION NETWORK INCLUDING HYDROGENOLYSIS71


5.2 K INETIC MODEL FOR HYDROGENOLYSIS 74

5.2.1 SELECTED MODEL FOR HYDROGENOLYSIS (ES5B) 74

5.3 NET FORMATION RATES 75

5.4 MODEL PARAMETERS 77

5.5 RESULTS 78

5.5.1 ESTIMATED PARAMETERS AND DISCUSSION 78

5.5.2 STATISTICAL ANALYSIS 81

5.6 INFLUENCE OF PRESSURE ON CONVERSION AND SELECTIVITY 85

5.7 INFLUENCE OF SPACE-TIME ON CONVERSION AND SELECTIVITY 86

5.8 HYDROGENOLYSIS VS PRIMARY CARBENIUM IONS 86

5.9 CONCLUSION 87

5.10 REFERENCES 89

CHAPTER 6 HYDROISOMERIZATION OF N-PENTANE IN

NON-IDEAL HYDROCRACKING CONDITIONS 90

6.1 REACTION MECHANISM FOR NON -IDEAL HYDROCRACKING 91

6.2 INFLUENCE OF THE OPERATING CONDITIONS ON IDEALITY IN

HYDROCRACKING 93

6.3 APPLICATION OF SINGLE -EVENT MICROKINETIC MODELING ON THE

(DE)HYDROGENATION REACTIONS 95

6.4 IMPLEMENTATION IN THE COMPUTER CODE . 96

6.5 PRELIMINARY RESULTS 98

6.6 CONCLUSIONS 100

h

6.7 REFERENCES 102

CHAPTER 7 CONCLUSIONS 104

APPENDIX A : EXPERIMENTAL RESULTS FOR THE

HYDROISOMERIZATION EXPERIMENTS ON THE 20-FOLD

PARALLEL PLUG FLOW REACTOR 106

A.1 INITIAL CONDITIONS ON THE PT/H-BEA 0.6 WT% CATALYST 106

A.2 EXPERIMENTAL MOLAR INLET AND OUTLET FLOWS OF THE COMPONENTS

FOR A PT/H-BEA 0.6 WT% CATALYST 112

APPENDIX B: EXPERIMENTAL RESULTS FOR THE

HYDROISOMERIZATION OF N-HEXANE ON MC-301 119

B.1 INITIAL CONDITIONS 119

B.2 EXPERIMENTAL MOLAR INLET AND OUTLET FLOWS OF THE COMPONENTS

FOR A /H-BEA 0.6 WT% CATALYST 121

APPENDIX C: IDEAL HYDROCRACKING OF N-PENTANE:

PRIMARY CARBENIUM IONS CONSIDERED 123

C.1 INITIAL CONDITIONS OF THE EXPERIMENTS USED FOR THE PARAMETER

ESTIMATION FOR THE CLASSICAL REACTION NETWORK EXTENDED WITH

PRIMARY CARBENIUM IONS 123

C.2 EXPERIMENTAL MOLAR INLET AND OUTLET FLOWS FOR THE

EXPERIMENTS USED FOR THE PARAMETER ESTIMATION 125

C.3 CORRELATION COEFFICIENT MATRIX 126

APPENDIX D: IDEAL HYDROCRACKING OF N-PENTANE:

HYDROGENOLYSIS CONSIDERED 127

i

D.1 INITIAL CONDITIONS OF THE EXPERIMENTS USED FOR THE PARAMETER

ESTIMATION FOR THE CLASSICAL REACTION NETWORK EXTENDED WITH

HYDROGENOLYSIS 127

D.2 EXPERIMENTAL MOLAR INLET AND OUTLET FLOWS FOR THE

EXPERIMENTS USED FOR THE PARAMETER ESTIMATION 129

D.3 CORRELATION COEFFICIENT MATRIX 130

APPENDIX E: OVERZICHTSTABEL VAN ONTWIKKELDE

PROGRAMMATUUR EN UITGEVOERDE

PARAMETERSCHATTINGEN 131

j

List of Figures

FIGURE 1-1: WORLD OIL SUPPLY EVOLUTION [3] .................................................................................... 2

FIGURE 1-2: WORLD OIL DEMAND EVOLUTION [4].................................................................................. 3

FIGURE 1-3: EXAMPLE OF AN INTEGRATED PETROLEUM REFINERY ........................................................ 3

FIGURE 1-4: SHELL HYSOMER PROCESS; A) PROCESS HEATER; B) ISOMERIZATION REACTOR; C)

REACTOR PRODUCT SEPARATOR; D) STABILIZER COLUMN; E) RECYCLE GAS COMPRESSOR [11] .......... 7

FIGURE 2-1: REACTION MECHANISM FOR HYDROISOMERIZATION ON A BIFUNCTIONAL CATALYST [2] 12

FIGURE 2-2: HYDROISOMERIZATION REACTION SCHEME [4] ................................................................ 12

FIGURE 2-3: UPPER FIGURE: HYDRIDE SHIFT; LOWER FIGURE: ALKYLSHIFT (METHYLSHIFT) [5] ......... 13

FIGURE 2-4: MECHANISM FOR PCP BRANCHING OF 2-HEXYL CATION [5] ............................................ 14

FIGURE 2-5: Β-SCISSION REACTION OF 2-PENTYL KATION .................................................................... 15

FIGURE 2-6: WORK-FLOW OF THE REACTION NETWORK GENERATION ALGORITHM ............................. 16

FIGURE 2-7: NUMBERING OF ISO-PENTANE [7] ...................................................................................... 17

FIGURE 2-8: BOOLEAN MATRIX REPRESENTATION OF ISO-PENTANE [7] ............................................... 17

FIGURE 2-9: THERMODYNAMIC CYCLE FOR ALKENE PROTONATION AND ISOMERIZATION WITH A

REFERENCE OLEFIN ................................................................................................................................ 21

FIGURE 2-10: EXPERIMENTAL MOLAR FLOW FOR METHANE ( ), ETHANE ( ), PROPANE ( ), N-

BUTANE ( ), ISO-BUTANE ( ), ISO-PENTANE ( )AS A FUNCTION OF TEMPERATURE FOR PT/H-BEA

0.6 WT% (VMB26: P=4 BAR; MOLAR H/C RATIO= 47.4; W/F0=9.3 103 GCAT S MOL

-1) .......................... 25

FIGURE 2-11: EXPERIMENTAL MOLAR FLOW FOR ISO-PENTANE ( ) AND N-PENTANE( ) AS A

FUNCTION OF TEMPERATURE FOR PT/H-BEA 0.6 WT% AT THE EXIT OF THE REACTOR. (VMB26: P=4

BAR; MOLAR H/C RATIO= 47.4; W/F0=9.3 103 GCAT S MOL

-1)................................................................. 25

FIGURE 3-1: SCHEMATIC REPRESENTATION OF THE 20-FOLD PARALLEL PLUG FLOW REACTOR [1] ..... 33

FIGURE 3-2: SELECTIVITY OF THE ISO-PRODUCTS WITH RESPECT TO THE CONVERSION OF N-PENTANE

(LEFT) AND N-HEXANE (RIGHT) ON DIFFERENT TYPES OF CATALYSTS. ................................................. 35

FIGURE 3-3: EXPERIMENTAL N-PENTANE CONVERSION AND ISO-PENTANE SELECTIVITY ON PT/H-BEA

0.6 WT% (P=4 BAR;H2/HC=38.6;W/F0=25.9 10³ GCAT S MOL-1). ............................................................. 37

FIGURE 3-4: EXPERIMENTAL N-PENTANE CONVERSION AND ISO-PENTANE SELECTIVITY ON PT/H-BEA

0.6 WT% ................................................................................................................................................. 37

k

FIGURE 3-5: CONVERSION OF N-PENTANE AS A FUNCTION OF THE TOTAL PRESSURE FOR THE

HYDROISOMERIZATION OF N-PENTANE ON PT/H-BEA 0.6 WT% ZEOLITE. LEFT: EXP 25&26 VMB02,

EXP 5&6 VMB04. RIGHT: EXP 9&10 VMB04, EXP 11&12 VMB03 AND EXP 17 & 18 VMB03 ........... 38

FIGURE 3-6: ISOMERIZATION ACTIVITY OF PT/H-BEA (104 KJ/MOL) (X), PT/BEA S350 (110 KJ/MOL)

(◊), PT/BEA S450 (109 KJ/MOL) (□) AND PT/BEA S550 (102 KJ/MOL) (∆) [2]. .................................... 40

FIGURE 3-7: SCHEMATICAL REPRESENTATION OF THE BERTY SET UP................................................... 42

FIGURE 3-8: SYMBOLS USED IN THE SCHEMATIC REPRESENTATION OF THE BERTY REACTOR SHOWN IN

FIGURE 3-7. ............................................................................................................................................ 43

FIGURE 3-9: EXPERIMENTAL N-HEXANE CONVERSION ON MC-301 AT P=5 BAR;H2/HC=50;W/F0= 261

103 GCAT S MOL

-1. ..................................................................................................................................... 47

FIGURE 3-10: CONCENTRATION OF THE FEED COMPONENT CA AND CONVERSION OF THE FEED

COMPONENT XA FOR A PLUG FLOW REACTOR (A) AND A CSTR REACTOR (B) FOR IRREVERSIBLE FIRST

ORDER KINETICS[6]................................................................................................................................ 48

FIGURE 3-11: EXPERIMENTAL SELECTIVITY FOR 2-METHYL-PENTANE (RIGHT) AND 3-METHYL-

PENTANE (LEFT) AS A FUNCTION OF TEMPERATURE ON MC-301 AT P=5 BAR;H2/HC=50;W/F0= 261 103

GCAT S MOL-1. ........................................................................................................................................... 48

FIGURE 3-12: EXPERIMENTAL CONVERSION OF N-HEXANE AS A FUNCTION OF TOTAL PRESSURE ON

MC-301 AT T=323°C, H2/HC=50;W/F0= 261 103 GCAT S MOL

-1. ............................................................ 49

FIGURE 3-13: EXPERIMENTAL N-HEXANE CONVERSION AS FUNCTION OF SPACE-TIME AT P=6BAR,

T=312 °C, H2/HC=75 ............................................................................................................................ 49

FIGURE 3-14: EXPERIMENTAL SELECTIVITY TO 2-METHYL-PENTANE (RIGHT) AND 3-METHYL-PENTANE

(LEFT) AS FUNCTION OF SPACE-TIME AT P=6BAR, T=312 °C, H2/HC=75 .............................................. 50

FIGURE 4-1: REACTION PATHWAYS FOR NON-IDEAL HYDROCRACKING ON BIFUNCTIONAL ZEOLITES [3]

............................................................................................................................................................... 52

FIGURE 4-2: INITIAL ACTIVITY (A0) OF PT/HY CATALYSTS AS A FUNCTION OF THE RATIO OF PLATINUM

SITES/ACID SITES [4]. ............................................................................................................................. 53

FIGURE 4-3: CONVERSION OF N-PENTANE AS A FUNCTION OF THE TOTAL PRESSURE FOR THE

HYDROISOMERIZATION OF N-PENTANE ON PT/H-BEA 0.6 WT% ZEOLITE. ........................................... 54

FIGURE 4-4: REACTION NETWORK STARTING FROM N-PENTANE (PART 1 OF THE COMPLETE REACTION

NETWORK) ............................................................................................................................................. 56

FIGURE 4-5: REACTION NETWORK STARTING FROM N-BUTANE (PART 2 OF THE COMPLETE REACTION

NETWORK) ............................................................................................................................................. 56

FIGURE 4-6: SCHEME OF THE ACTIVATION ENERGY FOR THE REACTION FROM A PRIMARY TO A

SECONDARY CARBENIUM ION ................................................................................................................ 60

FIGURE 4-7: ISOMERIZATION REACTION OF 2-METHYL-HEXANE CARBENIUM ION (LEFT) AND

BRANCHING REACTION OF 3-METHYL-HEXANE CARBENIUM ION (RIGHT) [6] ....................................... 61

l

FIGURE 4-8: PARITY DIAGRAMS FOR THE MOLAR EXIT FLOWS OF THE HYDROISOMERIZATION

PRODUCTS OF N-PENTANE ON A PT/H-BEA 0.6 WT% CATALYST. (A) ETHANE, (B) PROPANE, (C) ISO-

PENTANE, (D) N-BUTANE, (E) METHANE AND (F) ISO-BUTANE. ............................................................. 64

FIGURE 4-9: EXPERIMENTAL (▲) AND MODEL CALCULATED VALUES (■) FOR THE CONVERSION OF N-

PENTANE AS A FUNCTION OF PRESSURE FOR HYDROISOMERIZATION OF N-PENTANE. THE EXPERIMENTS

USED FOR THIS GRAPHIC IS REFERRED TO APPENDIX C. ........................................................................ 67

FIGURE 4-10: EXPERIMENTAL (■) AND MODEL CALCULATED VALUES (▲) FOR THE SELECTIVITY TO

ISO-PENTANE AS A FUNCTION OF PRESSURE FOR THE HYDROISOMERIZATION OF N-PENTANE. FOR THE

EXPERIMENTS USED FOR THIS GRAPHIC IS REFERRED TO APPENDIX C. ................................................. 67

FIGURE 4-11: EXPERIMENTAL (■) AND MODEL CALCULATED (▲) RESULTS FOR THE CONVERSION OF

N-PENTANE (LEFT) AND THE SELECTIVITY TO ISO-PENTANE (RIGHT) AS A FUNCTION OF SPACE-TIME AT

A TEMPERATURE OF 280 °C. FOR THE EXPERIMENTS USED IN THIS GRAPHIC IS REFERRED TO APPENDIX

C. ........................................................................................................................................................... 68

FIGURE 5-1: HYDROGENOLYSIS ON METAL SITES ASSUMING THAT CONSECUTIVE CRACKING REACTION

CANNOT OCCUR [2]. ............................................................................................................................... 72

FIGURE 5-2: REACTION NETWORK FOR THE HYDROISOMERIZATION OF N-PENTANE, EXTENDED WITH

HYDROGENOLYSIS ON THE METAL SITES (DEM= DEMETHYLATION; DEET=DEETHYLATION) [2] .......... 73

FIGURE 5-3: REACTION MECHANISM FOR HYDROGENOLYSIS OF N-BUTANE ON A CATALYST

CONTAINING RH [10] ............................................................................................................................. 79

FIGURE 5-4: EQUILIBRIUM BETWEEN THE METALLACYCLOBUTANE COMPLEX AND THE METAL-ALKENE

CARBENIUM COMPLEX.[10] ................................................................................................................... 80

FIGURE 5-5: PARITY DIAGRAMS FOR THE MOLAR EXIT FLOWS OF (A) N-BUTANE, (B) METHANE, (C)

ETHANE, (D) PROPANE, (E) ISO-PENTANE AND (F) ISO-BUTANE IN THE HYDROISOMERIZATION OF N-

PENTANE ON A PT/H-BEA 0.6 WT% CATALYST.. .................................................................................. 81

FIGURE 5-6: N*V MATRIX OF THE EXPERIMENTAL ERRORS [11] ........................................................... 82

FIGURE 5-7: EXPERIMENTAL (▲) AND MODEL CALCULATED VALUES (■) FOR THE CONVERSION OF N-

PENTANE (LEFT) AND FOR THE SELECTIVITY TO ISO-PENTANE (RIGHT) AS A FUNCTION OF PRESSURE

FOR HYDROISOMERIZATION OF N-PENTANE AT A TEMPERATURE OF 280 °C. EXPERIMENTAL DATA

GIVEN IN APPENDIX D ............................................................................................................................ 85

FIGURE 5-8: EXPERIMENTAL (■) AND MODEL CALCULATED (▲) RESULTS FOR THE CONVERSION OF N-

PENTANE (LEFT) AND THE SELECTIVITY TO ISO-PENTANE (RIGHT) AS A FUNCTION OF SPACE-TIME AT A

TEMPERATURE OF 280 °C. EXPERIMENTAL DATA GIVEN IN APPENDIX D ............................................. 86

FIGURE 6-1: SIMULATED ISOMERIZATION CONVERSION OF N-ALKANE ON PT/USY AS A FUNCTION OF

THE TOTAL CONVERSION OF N-ALKANE UNDER IDEAL AND NON-IDEAL HYDROCRACKING CONDITIONS:

AT 520 K (DIAMONDS), 540 K (CIRCLES), 560 K (TRIANGLES), AND 580 K (SQUARES) AND AT 0.1 MPA

(OPEN SYMBOLS), 0.35 MPA (LIGHT SHADED SYMBOLS), 1 MPA (DARK SHADED SYMBOLS), AND 10

MPA (CLOSED SYMBOLS) [2]. ................................................................................................................ 94

m

FIGURE 6-2: PARITY DIAGRAMS FOR THE MOLAR EXIT FLOWS OF THE HYDROISOMERIZATION

PRODUCTS OF N-PENTANE ON A PT/H-BEA 0.6 WT% CATALYST FOR NON-IDEAL HYDROCRACKING. (A)

ETHANE, (B) PROPANE, (C) ISO-PENTANE, (D) N-BUTANE, (E) METHANE AND (F) ISO-BUTANE (VMB 26).

............................................................................................................................................................... 99

n

List of Tables

TABLE 1-1: PETROLEUM FRACTIONS [4] ................................................................................................. 2

TABLE 1-2: HYDROCARBON OCTANE NUMBERS [5] ................................................................................ 4

TABLE 2-1: PRE-EXPONENTIAL FACTOR AND PHYSISORPTION ENTHALPY FOR N-PENTANE ON SEVERAL

CATALYSTS.[12] .................................................................................................................................... 22

TABLE 2-2: TOTAL AMOUNT OF BRØNSTED ACID SITES FOR DIFFERENT TYPES OF CATALYSTS. .......... 23

TABLE 3-1: CHARACTERISTICS OF PT/H-BEA 0.6 WT%, PT/H-BEA S350 0.6 WT% AND PT/H-BEA

S450 0.6 WT% [2] .................................................................................................................................. 34

TABLE 3-2: INLET CONDITIONS FOR THE HYDROISOMERIZATION OF N-PENTANE OVER PT/H-BEA 0.6

WT% ...................................................................................................................................................... 36

TABLE 3-3: INLET CONDITIONS FOR THE HYDROISOMERIZATION OF N-PENTANE OVER PT/H-BEA S350

0.6 WT% ................................................................................................................................................. 38

TABLE 3-4: INLET CONDITIONS FOR THE HYDROISOMERIZATION OF N-PENTANE OVER PT/H-BEA S450

0.6 WT% ................................................................................................................................................. 39

TABLE 3-5: SPECIFICATIONS OF MC-301 [3] ......................................................................................... 46

TABLE 3-6: INLET CONDITIONS FOR THE HYDROISOMERIZATION OF N-HEXANE OVER MC-301 .......... 46

TABLE 4-1: ACID-CATALYZED REACTIONS OCCURING WHEN CONSIDERING PRIMARY CARBENIUM IONS

............................................................................................................................................................... 55

TABLE 4-2: OVERVIEW OF THE MODEL PARAMETERS TO BE ESTIMATED FOR THE CLASSICAL NETWORK

INCLUDING PRIMARY CARBENIUM IONS. .............................................................................................. 58

TABLE 4-3: CALCULATED VALUES FOR THE PRE-EXPONENTIAL FACTORS OF THE ACID CATALYZED

REACTIONS USING STATISTICAL THERMODYNAMICS.. .......................................................................... 61

TABLE 4-4: ESTIMATED VALUES FOR THE MODEL PARAMETERS IN CASE THAT PRIMARY CARBENIUM

IONS ARE CONSIDERED .......................................................................................................................... 62

TABLE 4-5: ACTIVATION ENERGIES FOR Β-SCISSION REACTIONS FOR DIFFERENT TYPES OF ................ 63

TABLE 4-6: CALCULATED T-VALUES FOR THE MODEL PARAMETERS IN THE CASE THAT PRIMARY

CARBENIUM IONS ARE CONSIDERED ...................................................................................................... 65

TABLE 5-1: OVERVIEW OF THE PARAMETERS THAT HAVE TO BE ESTIMATED IN THE CASE THAT THE

CLASSICAL REACTION NETWORK IS EXTENDED WITH HYDROGENOLYSIS ............................................. 77

TABLE 5-2: ESTIMATED VALUES FOR THE MODEL PARAMETERS IN CASE THAT HYDROGENOLYSIS IS

CONSIDERED .......................................................................................................................................... 78

o

TABLE 5-3: T-VALUES FOR THE ESTIMATION OF THE MODEL PARAMETERS WHERE THE CLASSICAL

REACTION NETWORK IS EXTENDED WITH HYDROGENOLYSIS................................................................ 82

TABLE 5-4: SUMMARY OF THE NUMBER OF REACTIONS PRESENT IN THE DIFFERENT REACTION

NETWORKS. ............................................................................................................................................ 87

TABLE 5-5: NUMBER OF MODEL PARAMETERS AND RESIDUAL SUM OF SQUARES FOR THE DIFFERENT

CASES CONSIDERED IN THIS PROJECT. ................................................................................................... 87

TABLE 6-1: ESTIMATED VALUES FOR THE MODEL PARAMETERS IN CASE THAT PRIMARY CARBENIUM

IONS ARE CONSIDERED UNDER NON-IDEAL HYDROCRACKING CONDITIONS. ........................................ 98

TABLE A–1: INLET CONDITIONS FOR THE HYDROISOMERIZATION EXPERIMENTS OF N-PENTANE ON A

PT/H-BEA 0.6 WT% CATALYST………………………………………………………………………106

TABLE A–2: EXPERIMENTAL INLET AND OUTLET CONDITIONS FOR HYDROISOMERIZATION OF N-

PENTANE ON A PT/H-BEA 0.6 WT% CATALYST …………………………… ………………………..112

TABLE B–1: INITIAL CONDITIONS FOR THE HYDROISOMERIZATION OF N-HEXANE ON A PT/USY

ZEOLITE (MC-301) …………………………… ..………………………….………………………..119

TABLE B–2: EXPERIMENTAL INLET AND OUTLET CONDITIONS FOR HYDROISOMERIZATION OF N-

HEXANE ON MC-301…………………………… ………………………….………………………..121

TABLE C–1: INITIAL CONDITIONS OF THE EXPERIMENTS USED FOR THE REGRESSION OF THE KINETIC

PARAMETERS OF THE MODEL CONSIDERING THE REACTIONS NETWORK INCLUDING PRIMARY

CARBENIUM IONS …………………………… ....………………………….………………………..123

TABLE C–2: EXPERIMENTAL MOLAR INLET AND OUTLET FLOWS FOR THE EXPERIMENTS USED FOR THE

REGRESSION OF THE KINETIC PARAMETERS IN THE MODEL CONSIDERING THE REACTION NETWORK

INCLUDING PRIMARY CARBENIUM IONS ………………………………….………………….……….125

TABLE C–3: BINARY CORRELATION COEFFICIENT MATRIX FOR THE MODEL PARAMETERS OF THE

CLASSICAL REACTION NETWORK EXTENDED WITH PRIMARY CARBENIUM IONS …….……………....126

TABLE D–1: INITIAL CONDITIONS OF THE EXPERIMENTS USED FOR THE REGRESSION OF THE MODEL

PARAMETERS OF THE REACTION NETWORK EXTENDED WITH HYDROGENOLYSIS.………...……..…..127

TABLE D–2: MOLAR INLET AND OUTLET FLOWS OF THE EXPERIMENTS USED FOR THE REGRESSION OF

THE MODEL PARAMETERS FOR THE CLASSICAL REACTION NETWORK EXTENDED WITH

HYDROGENOLYSIS…………………….………………………………….……………………..…..129

TABLE D–3: BINARY CORRELATION COEFFICIENT MATRIX OF THE MODEL PARAMETERS OF THE

CLASSICAL REACTION NETWORK INCLUDING HYDROGENOLYSIS …………………...…………..…..130

Notation

Roman Symbols

A pre-exponential factor

A’ single-event pre-exponential factor

AL pre-exponential factor for the Langmuir coefficient

AS Alkyl shift

b model parameter

bj estimated value for parameter j

C concentration

C5 alkanes consisting of 5 carbenium ions

Ct total concentration of Brønsted acid sites

Ea activation energy

FA Molar flow of alkane A [mol/s]

FC tabulated F-value for statistical tests

Fi,j Exit flow of component j during experiment i

Fj,ik experimental value of response j during experiment I under conditions k

∆H enthalpy difference [J/mol]

∆Hfys enthalpy difference for physisorption of an alkane on the catalyst surface [J/mol]

∆Hpr protonation enthalpy [J/mol]

h Planck’s constant

J jacobian matrix

k rate coefficient

K equilibrium constant

k’ single-event rate coefficient

KL Langmuir equilibrium coefficient

kB Boltzmann constant

lo Row/column of the Boolean matrix to indicate an olefin

Notation Roman Symbols

q

lc Row/column of the Boolean matrix to indicate a carbenium ion

mi,j Element on row I, column j of the Boolean matrix

n-x number of hydrogen atoms removed during adsorption of an alkane on the catalyst

surface

na number of acid sites

ne number of single-events

ni,k type of carbenium ion k

nkr number of replica experiments

nPt number of metal sites

ns number of identical transformations

nobs number of observations

npar number of parameters

nresp number of responses

Oy Olefin consisting of y carbon atoms

Oi,j Olefin j corresponding to alkane i

p primary carbenium ion

P Representation of an alkane

pi partial pressure of component i

PCP Protonated cyclopropane

r reaction rate

r number of different inlet conditions

R universal gas constant

RPA Net rate of formation of alkane A

Rx+ Carbenium ion consisting of x carbon atoms

s secondary carbenium ion

∆S Entropy difference [J/mol K]

t tertiary carbenium ion

tc tabulates t-value

T Temperature [K]

V Variance/covariance matrix

Vm Molar volume

Vp Pore volume

wi weighting factor

Notation Greek symbols

r

Wcat Catalyst weight [kg]

X conversion

yi,j experimental value for response i during experiment j

Greek symbols

1-α probability level

β β-scission

βj real value for parameter j

ρi,j binary correlation coefficient between parameters i and j

σ symmetry number

Superscripts

* composite dehydrogenation, isomerization or cracking rate coefficient

_ mean value

^ intrinsic

^ estimated

0 inlet

0 Standard state

A adsorbed on an acid site

M adsorbed on a metal site

Subscripts

≠ activated complex

0 initial

chem chemisorbed

deh dehydrogenation

dehyd dehydrogenation

dem demethylation

deet deethylation

f-P formation of alkane P

Notation Subscripts

s

fys physisorption

H+ free acid sites

H2 hydrogen

i alkane i

iso isomerization

O olefin

P paraffin

pr protonation

r reactant

R+ carbenium ions

ref reference

Rot rotation

Sat saturation

Tot total

Trans translation

Vib vibration

Nederlandse samenvatting

Geschiedenis van de raffinaderij: belang van

hydroconversieprocessen

Het gebruik van petroleum gaat reeds meer dan 5000 jaar terug. De eerste methoden voor de

destillatie van petroleum werden ongeveer 2000 jaar geleden ontwikkeld door Arabische

wetenschappers. De hedendaagse raffinage startte in 1859 met de ontdekking van petroleum

in Pennsylvania. Na de tweede Wereldoorlog steeg het belang van de landen in het Midden-

Oosten sterk door de ontdekking van nieuwe oliereserves. De stimulans voor de ontwikkeling

van de petroleumraffinaderijen ontstond door de groeiende vraag naar lichtbronnen,

brandstoffen voor de fabrieken, benzine voor de auto-industrie, vliegtuigindustrie, en zo meer.

Ruwe aardolie is een mengsel van componenten met een verschillend kookpunt. Dit mengsel

kan worden gescheiden in verschillende fracties, vaak met een overlappend kookpunt. De

verhoudingen van deze fractie aanwezig in de ruwe stroom hangt af van de oorsprong van de

aardolie. Raffinage kan opgesplitst worden in twee grote delen. Vooreerst wordt de ruwe

aardolie gescheiden door destillatie in de verschillende koolwaterstoffracties. De gevraagde

producten van de raffinage is sterk veranderd door de jaren heen. De vraag naar

middendestillaten is gegroeid, terwijl de vraag naar zware componenten sterk is afgenomen.

Daardoor bestaat het tweede deel van de raffinaderij uit omzettingsprocessen. Zware

componenten worden omgezet in lichtere componenten met een hogere toegevoegde waarde.

De benzine rechtstreeks afkomstig uit de raffinage voldoet niet aan de nodige specificaties

vereist voor het verbranden in een benzinemotor. Deze benzine zal schokgolven veroorzaken

in de motor door onregelmatige verbranding, waardoor de motor zal kloppen. Het octaangetal

is een indicatie voor de bekwaamheid van de benzine om te branden in de motor zonder

kloppen. Om het octaangetal te verhogen wordt de benzine bewerkt.

Het verband tussen het octaangetal en de structuren aanwezig in de benzine wordt gegeven

door bepaalde regels. Zo hebben vertakte alkanen een hoger octaangetal dan lineaire en zorgt

de aanwezigheid van aromatische structuren voor een verhoging van het octaangetal.

Nederlandse samenvatting Geschiedenis van de raffinaderij: belang van hydroconversieprocessen

II

Door de jaren heen zijn verschillende manieren toegepast om het octaangetal te verhogen. De

laatste jaren werd vooral gebruik gemaakt van toevoeging van aromatische structuren.

Nadelen van deze techniek zijn verhoogde NOx-, koolwaterstof- en CO-emissies. Sinds 2005

is de wetgeving omtrent de maximaal toelaatbare concentratie van aromaten in benzine

strenger geworden tot 2,5 vol% voor benzeen en 35 vol% voor andere aromatische structuren.

Een alternatieve manier om het octaangetal te verhogen ligt in het vertakken van lineaire

ketens, wat gebeurt door hydroisomerisatie.

Hydrokraken en hydroisomerisatie

Het hydrokraakproces werd voor het eerst toegepast in 1927 voor de omzetting van lignine in

benzeen. Door hoge operationele kosten bleven de toepassingen van hydrokraken echter

beperkt. De ontwikkeling van katalytische reforming, dat waterstof produceert als bijproduct,

leidde tot nieuwe interesse in het hydrokrakingsprocédé. Deze interesse werd versterkt door

de ontdekking van zeolieten en de toenemende vraag naar middendestillaten.

Bij hydrokraken zijn grote variaties in voeding mogelijk. In tegenstelling tot katalytisch

kraken leidt hydrokraken tot een grotere fractie aan middendestillaten met een goede

kwaliteit. Tevens ligt in de verminderde cokesvorming door de grote partieeldruk van

waterstof een bijkomend voordeel van .

De bifunctionele katalysator, gebruikt bij hydrokraken, bestaat uit een zure functie,

verantwoordelijk voor de isomerisatie- en krakingsreacties, en een metallische functie, die een

hydrogenerende functie heeft. Als zure functie wordt de voorkeur gegeven aan een zeoliet.

Deze bevatten een specifieke poriestructuur en poriedimensies. Ze hebben een hogere

activiteit bij lagere procescondities dan amorfe structuren, maar vertonen ook een lagere

selectiviteit naar middendestillaten. Het gebruik van zeolieten heeft als bijkomend voordeel

dat zijreacties zoals corrosie kunnen vermeden worden door vormselectiviteit.

Ook voor hydroisomerisatie zijn bifunctionele katalysatoren het meest effectief. De lineaire

alkanen diffunderen van de gasfase in de poriën van het zeoliet en adsorberen op de

metallische centra. Daar worden ze gedehydrogeneerd met vorming van alkenen die

diffunderen naar de zure centra. Hier worden ze geprotoneerd tot carbenium ion die dan

verder isomerisatie en krakingsreacties ondergaan. Na deprotonatie op de zure centra en

hydrogenatie op de metallische centra zal het product desorberen.

Nederlandse samenvatting Geschiedenis van de raffinaderij: belang van hydroconversieprocessen

III

Microkinetisch modelleren

In de industrie drukt men snelheidsvergelijkingen doorgaans uit met behulp van eenvoudige

machtswetten. De constanten in deze vergelijkingen worden bepaald door regressie met

experimentele data. Deze werkwijze zorgt ervoor dat de wetten slechts gelden in het smalle

interval van werkingscondities waarbij de regressie uitgevoerd is.

In dit werk zal gebruik gemaakt worden van single-event microkinetisch modelleren, waarbij

elke elementaire reactiestap apart beschouwd wordt in het model. Hiertoe wordt eerst een

reactienetwerk opgesteld. De kinetische parameters in dit model worden opnieuw bepaald

door regressie. Deze methode geeft aanleiding tot een kinetisch model dat geldt over een

breed bereik in werkingscondities.

Doel van dit werk

Onderzoek naar een fundamenteel kinetisch model voor hydroisomerisatie van n-pentaan is

reeds gestart aan het LCT. Het doel van dit werk is de verfijning van het kinetisch model door

middel van het beschouwen van hydrogenolyse, primaire carbenium ionen en niet-ideaal

hydrokraken.

Een experimentele data set is verkregen aan de universiteit van München. Daar werden

experimenten uitgevoerd op een Pt/H-BEA katalysator met 0,6 wt% platina. Tevens zijn

testen volbracht als de katalysator behandeld was met zwavel, bij verschillende temperaturen.

Bij gebruik van deze ingezwavelde katalysatoren werd een selectiviteitsverhoging tot 100%

vastgesteld.

Analyse van de data set wijst uit dat sommige experimenten verkregen werden onder niet

ideale hydrokrakingsvoorwaarden. Naast onderzoek op experimenten onder ideale

omstandigheden zal de bestaande computercode voor hydrokraken van lichte alkanen met

behulp van single-event kinetisch modelleren ook uitgebreid worden met niet ideaal

hydrokraken.

In de experimenten gebruikt voor de regressie van hydroisomerisatie onder ideale

hydrokrakingsvoorwaarden, zijn vele uitlaatstromen voor methaan en ethaan gelijk aan nul.

Dit geeft problemen bij de regressie van het model waarbij deze responsen in beschouwing

genomen worden. Er zou een eigen data set ontwikkeld moeten worden op de Berty reactor

opstelling van de universiteit Gent. Hiertoe worden de eerste stappen gezet voor de

hydroisomerisatie van n-hexaan.

Nederlandse samenvatting Hydroisomerisatie van n-pentaan: toepassing van single-event concept

IV

In een later stadium, als het fundamenteel kinetisch model voor n-pentaan ontwikkeld is, zal

getracht worden de selectiviteitsverhoging bij inzwavelen van de katalysator te verklaren.

Hydroisomerisatie van n-pentaan: toepassing van single-

event concept

Reactiemechanisme

De alkanen geadsorbeerd op de metallische centra worden gedehydrogeneerd tot olefienen.

Deze worden op hun beurt geprotoneerd op de zure centra met vorming van primaire

carbenium ionen. Vervolgens vinden op de zure centra isomerisatie- of krakingsreacties

plaats.

De productdistributie wordt enerzijds bepaald door de relatieve verhouding tussen metallische

en zure functie en anderzijds door de relatieve stabiliteit van de carbenium ionen. De

stabiliteit stijgt met het aantal substituten. Elke substituut werkt stabiliserend, door hun

elektronendonerend effect.

Twee types isomerisatiereacties kunnen optreden: met (PCP-vertakking) of zonder een

verandering van de vertakkingsgraad (alkyl shift, hydride shift). PCP-branching verloopt via

een geprotoneerd cyclopropaan. Dit is een cyclisch alkylcarbenium ion dat bestaat uit een

vijfwaardig gecoördineerd koolstofatoom. De selectiviteit naar de isomeren kan dalen op twee

manieren: hydrogenolyse of krakingsreacties. Hydrogenolyse is een niet-selectieve

krakingsreactie op de metallische centra waarbij methaan of ethaan afgesplitst wordt.

Als krakingsreactie op de zure centra treed β-scissie op. Deze reactie verloopt door het kraken

van de C-C binding in β-positie ten opzichte van het positief geladen koolstofatoom.

Verschillende β-scissie reacties kunnen optreden: (t;t), (s;t), (t;s), (s;s). Primaire carbenium

ionen worden buiten beschouwing gelaten vermits deze energetisch ongunstig zijn.

Aangezien carbenium ionen optreden als intermediairen kunnen ook oligomerisatie en

hydride transfer optreden in competitie met isomerisatie- en krakingsreacties. Echter voor dit

werk worden deze reactiefamilies niet in aanmerking genomen.

Reactienetwerk

Zoals eerder vermeld steunt single-event kinetisch modelleren op de reactiesnelheid van elke

elementaire stap afzonderlijk. De eerste stap is daarbij het opstellen van een reactienetwerk

bestaande uit alle elementaire reacties die op het oppervlak van de katalysator kunnen

optreden. Aangezien de omvang van dit netwerk snel stijgt met het aantal koolstofatomen,


V

wordt het reactienetwerk opgesteld met behulp van een computergestuurd algoritme. Hierin

wordt elke molecule voorgesteld door een Booleanse matrix. Reacties die optreden in het

netwerk worden gerepresenteerd door matrixbewerkingen.

Het klassieke reactienetwerk voor hydroisomerisatie van lichte alkanen bestaat uit 6

reactiefamilies: (de)hydrogenatie, (de)protonatie, hydride shift, alkyl shift, PCP-vertakking en

β-scissie. Zoals reeds besproken worden oligomerisatie en hydride transfer buiten

beschouwing gelaten.

Reactormodel

De reactor wordt beschreven door een eendimensionaal pseudohomogeen model. Dit betekent

dat concentratie- en temperatuursgradiënten in de katalysator verwaarloosd worden.

De modelvergelijkingen voor de reactor volgen uit massabalansen voor de componenten over

de reactor. In het geval van een propstroomreactor leiden dergelijke balansen tot een stelsel

differentiaalvergelijkingen, terwijl voor een volkomen vermengde reactor een stelsel

algebraïsche vergelijkingen verkregen wordt. In beide vergelijkingen is een uitdrukking voor

de reactiesnelheden vereist. Deze wordt afgeleid met de temperatuur, de totaaldruk en de

samenstelling van de voedingsstroom als onafhankelijke variabelen.

Single-event microkinetisch modelleren

Wanneer elke elementaire reactiestap, aanwezig in het reactienetwerk, zou worden

opgenomen zonder verdere aannames, zou dit leiden tot een ontelbaar aantal kinetische

parameters die moeten geschat worden.

Daartoe gaat single-event microkinetisch modelleren ervan uit dat elke snelheidscoëfficiënt

kan geschreven worden als het product van het aantal single-events (ne) en een single-event

snelheidscoëfficiënt (k~

), die enkel afhankelijk is van de reactiefamilie en het type carbenium

ionen betrokken bij de reactie.

De pre-exponentiële factor van deze single-event snelheidscoëfficiënt kan berekend worden

met behulp van statistische thermodynamica. De activeringsenergie is dan nog de enige

parameter die geschat moet worden.

Een tweede manier om het aantal snelheidscoëfficiënten te reduceren betreft de

(de)protonatiereacties waarvoor quasi-evenwicht is verondersteld. Het single-event concept

wordt hiervoor toegepast op de evenwichtscoëfficiënt voor (de)protonatie. Een referentie-

alkeen wordt gebruikt voor de berekening van de single-event evenwichtscoëfficiënt voor

(de)protonatie.


VI

Snelheidsvergelijkingen

De concentratie van het geadsorbeerde alkaan in de microporiën van het zeoliet wordt

beschreven met behulp van een Langmuir isotherm. De Langmuir coëfficiënt voor fysisorptie

wordt berekend met behulp van een Arrhenius verband.

Het gefysisorbeerde alkaan wordt vervolgens gedehydrogeneerd op de metallische sites.

Aangezien onder ideale hydrokrakingscondities de (de)hydrogeneringsreacties in quasi-

evenwicht verondersteld worden, zal dit evenwicht gebruikt worden om de concentratie aan

olefienen te bepalen uitgaande van de concentratie aan gefysisorbeerde alkanen. De

evenwichtscoëfficiënt wordt berekend met behulp van thermodynamica. De nodige

thermodynamische gegevens worden bepaald aan de hand van de Benson

groepscontributiemethode.

De (de)protoneringsreacties worden eveneens in quasi-evenwicht verondersteld. Dezelfde

benadering als voor de olefienen wordt hier toegepast. De concentratie aan carbenium ionen

wordt bepaald uitgaande van de concentratie van het corresponderende olefien. Bij deze

berekening wordt verder vereenvoudigd verondersteld gesteld dat het aantal vrije actieve zure

centra op het oppervlak gelijk is aan het totaal aantal actieve zure centra.

De isomerisatie- en krakingsreacties zijn snelheidsbepalend verondersteld. Bovendien wordt

aangenomen dat de kinetiek beschreven kan worden door een eerste-orde afhankelijkheid in

de concentratie van de carbenium ionen. Door alle bovenstaande vergelijkingen te

combineren kan men de reactiesnelheid schrijven als functie van de concentratie van alkanen

in de gasfase.

De netto-vormingssnelheid van de alkanen bestaat verder uit twee bijdragen. De eerste

bijdrage is de som van de snelheden van de elementaire stappen waarbij carbenium ion i,

corresponderend bij alkaan j, gevormd wordt verminderd met de som van de snelheden van de

elementaire stappen waarbij carbenium ion i wegreageert. De tweede bijdrage bestaat uit de

rechtstreekse vorming van olefien k, corresponderend bij alkane j, door β-scissie.

In het klassieke reactienetwerk voor hydroisomerisatie van lichte alkanen worden enkel

secundaire en tertiaire carbenium ionen verondersteld. Wanneer n-pentaan gebruikt wordt als

voeding betekent dit dat β-scissie niet kan optreden. Uit de experimentele productdistributie

blijkt dat lichtere componenten (C1-C4) gevormd worden. Dit impliceert dat het klassieke

reactienetwerk zal moeten uitgebreid worden. Dit kan enerzijds met de beschouwing van

primaire carbenium ionen, en anderzijds door het beschouwen van hydrogenolyse.

Nederlandse samenvatting Experimenteel programma

VII

Modellering

Parameterschattingen worden uitgevoerd via minimalisatie van de kwadratensom van de

residuelen tussen de experimentele en de modelberekende responsen. De minimalisatie

gebeurt door de waarden van de modelparameters aan te passen. Deze waarden worden

verondersteld de echte parameterwaarden te benaderen in het optimum. Bij de minimalisatie

van de residuele kwadratensom worden de responsen gewogen om responsen met hoge en

lage numerieke waarden eenzelfde relatief belang toe te kennen. Parameterschattingen worden

uitgevoerd aan de hand van een combinatie van een Rosenbrock- en een Marquardtalgoritme.

De methode van Rosenbrock heeft neigt minder naar divergentie wanneer de

parameterwaarden nog ver van het optimum verwijderd zijn, terwijl de methode van

Marquardt superieur is in het bepalen van het ‘exacte’ optimum. Derhalve wordt bij

parameterschattingen initieel een Rosenbrockroutine gebruikt en nadien overgeschakeld op

het Marquardtalgoritme via de ‘gewone kleinste kwadraten’-optie in het vrij beschikbare

pakket ODRPACK.

Ook een statistische analyse wordt via het programma verkregen. De gebruikte statistische

toetsen omvatten de zogenaamde F-toets voor de significantie van de regressie en de t-toets

voor de individuele betrouwbaarheid van de parameters. Bij deze toetsen worden steeds 95%

betrouwbaarheidsintervallen gebruikt. Daarnaast worden ook de binaire

correlatiecoëfficiënten tussen de modelparameters berekend. Een absolute waarde van deze

coëfficiënt die 1 benadert, wijst op een uitgesproken lineair of invers lineair verband en is

ongewenst.

Experimenteel programma

Hydroisomerisatie van n-pentaan op Pt/H-BEA 0,6 wt% katalysator

De kinetische experimenten aan de universiteit van München zijn uitgevoerd op een 20-fold

parallel propstroomreactor. Deze opstelling laat instelwaarden toe voor druk tussen 1 en 50

bar, voor debieten tussen 5 en 100 ml/min en een temperatuur tot 450 °C.

De katalysator is bereid uitgaande van een BEA 25 zeoliet (Si/Al= 12,5). Een oplossing van

Pt(NH3)4(OH)2 en NH4OH werd vervolgens druppelsgewijze toegevoegd aan de slurry om de

kationen van het zeoliet uit te wisselen en zo de metallische centra in het zeoliet te verkrijgen.


VIII

Hetzelfde type katalysator onderging een inzwavelingsprocedure bij 350 en 450°C. Deze

katalysatoren worden aangeduid met respectievelijk Pt/H-BEA S350 0,6 wt% en Pt/H-BEA

S450 0,6 wt%.

Het aantal Pt-atomen aan het oppervlak van de katalysator is bepaald door chemisorptie van

waterstof. De bepaling van het porievolume vond plaats door middel van fysisorptie van

stikstof, met behulp van de t-methode.

Een grafische representatie van de resultaten toont aan dat de selectiviteit voor isopentaan

daalt als de concentratie aan metallische fase in het zeoliet stijgt. Bovendien daalt de

selectiviteit als functie van de conversie. Hoe hoger de conversie, hoe lager de concentratie

aan n-pentaan en hoe groter de kans dat isopentaan zal gekraakt worden.

De conversie zal stijgen als functie van de temperatuur en ruimtetijd, terwijl de selectiviteit

zal dalen. De stijgende conversie als functie van de temperatuur kan verklaard worden door

het Arrheniusverband geldig voor de snelheidscoëfficiënt. De invloed van de ruimtetijd heeft

als logische verklaring dat wanneer de componenten langer in de reactor verblijven, de kans

dat ze reageren groter zal worden. De dalende selectiviteit is een gevolg van de stijgende

conversie.

De conversie als functie van de druk zal bij experimenten uitgevoerd onder lage druk stijgen,

terwijl ze daalt bij experimenten uitgevoerd onder hoge druk. Dit wijst op niet-ideale

hydrokrakingsvoorwaarden bij lage druk.

Hydroisomerisatie van n-hexaan op MC-301 katalysator

De experimenten voor hydroisomerisatie van n-hexaan werden aan de universiteit van Gent

uitgevoerd in een volkomen vermengde gasfasereactor van het Berty-type. Deze opstelling

omvat een voedings-, reactie-, uitlaat- en analysesectie. De vloeibare reagentia worden

gevoed met behulp van een HPLC-pomp. In de voedingssectie van de opstelling bevindt zich

een verdamper om de onder omgevingsomstandigheden vloeibare reagentia te verdampen. De

reactiesectie bevat een volkomen vermengde reactor, wat wordt verwezenlijkt door een

magnetisch aangedreven roerder. Een magnetische aandrijving voorkomt problemen met de

afdichtingen ter hoogte van de lagers van de roerder. De temperatuurregeling van de reactor

wordt uitgevoerd met behulp van een PID-regelaar en een thermokoppel dat zich ter hoogte

van het katalysatorbed in de reactor bevindt. Afzonderlijke thermokoppels zijn steeds

aanwezig om ook een onafhankelijke meting van de reactortemperatuur te kunnen uitvoeren.

De uitlaat- en analysesectie bestaat uit een zeswegkraan waarmee “on-line” een monster kan

genomen worden om te analyseren op een gaschromatograaf uitgerust met een


IX

vlamionisatiedetector (FID). Het gebruik van een interne standaard - in dit geval methaan -

laat toe de atomaire koolstof- en waterstofbalans alsook de totale massabalans over de reactor

te controleren.

De katalysator, MC-301, is een pure USY zeoliet, zonder aanwezigheid van een binder. Deze

katalysator is aanwezig in poedervorm, maar vooraleer hij gebruikt kan worden in de reactor

moet deze omgezet worden in pellets. Het katalysatorbed van de reactor bestaat uit een

gelaagde structuur van katalysatorkorrels afgewisseld met korrels van een inert materiaal van

dezelfde grootte. Bovenaan en onderaan het katalysatorbed bevindt zich een laag inert

materiaal met een grotere diameter.

Analyse van de experimentele resultaten toont aan dat de conversie van n-hexaan stijgt met de

temperatuur. De conversie van n-hexaan ligt veel lager dan de conversie van n-pentaan op een

Pt/H-BEA 0,6 wt% katalysator. De verklaring hiervoor is tweeledig. Enerzijds kan verwacht

worden dat de conversie lager ligt bij n-hexaan, aangezien deze molecule zwaarder is dan n-

pentaan. De hoofdreden echter ligt in het type reactor waarin de experimenten uitgevoerd zijn.

Hydroisomerisatie van n-hexaan is uitgevoerd in een volkomen vermengde reactor, terwijl de

omzetting van n-pentaan gebeurde in een propstroomreactor. Algemeen bekomt men voor

reacties met dezelfde kinetiek een hogere conversie in een propstroomreactor dan in een

volkomen vermengde reactor.

De stijgende conversie als functie van temperatuur impliceert een daling van de selectiviteit

naar 2-methyl-pentaan en 3-methyl-pentaan. De selectiviteit naar 2-methylpentaan ligt

significant hoger dan 3-methylpentaan. Dit kan verklaard worden door het aantal

mogelijkheden waarop de moleculen gevormd kunnen worden. Voor 2-methylpentaan is dit

op twee manieren, terwijl dit voor 3-methyl-pentaan slechts op één manier kan.

De conversie van n-hexaan stijgt als functie van de totaaldruk. Dit wijst erop dat de

experimenten verkregen zijn onder niet-ideale hydrokrakingsvoorwaarden. Opdat

experimenten gebruikt zouden kunnen worden voor de regressie van de modelparameters

onder ideale omstandigheden, zouden experimenten moeten uitgevoerd worden onder hogere

druk. Onder ideale omstandigheden zal de conversie dalen als functie van de totaaldruk.

De conversie van n-hexaan als functie van de ruimtetijd zal stijgen. Dit kan zoals voorheen

verklaard worden doordat de moleculen langer in de reactor zullen verblijven. Als gevolg van

de stijgende conversie zal de selectiviteit dalen. In dit geval wordt dit niet uitgesproken

waargenomen. De oorzaak hiervan ligt in de lage waarden voor de conversie.

Nederlandse samenvattingHydroisomerisatie van n-pentaan: het klassieke reactienetwerk uitgebreid met primaire carbenium ionen

X

Hydroisomerisatie van n-pentaan: het klassieke

reactienetwerk uitgebreid met primaire carbenium ionen

Ideaal vs niet-ideaal gedrag

Hydrokraken is een combinatie van metaal- en zuurgekatalyseerde reacties. De verhouding

van het aantal zure centra tot het aantal metallische centra bepaalt in belangrijke mate de

productselectiviteiten die experimenteel worden waargenomen. In vergelijking met de zure

katalyse in katalytisch kraken geeft de aanwezigheid van een metallische fase bij hydrokraken

aanleiding tot een hogere opbrengst aan isomeren. Hoe hoger de activiteit voor

dehydrogenatie, hoe hoger de opbrengst voor isomeren.

Doorgaans worden krakingsreacties beschouwd als secundaire reacties die volgen op

isomerisatiereacties. Hoe hoger de activiteit voor dehydrogenatie, hoe meer waarschijnlijk het

is dat de ongesatureerde producten zullen gehydrogeneerd worden, in plaats van verder te

reageren tot krakingsproducten.

Wanneer primaire carbenium ionen beschouwd worden is het daarenboven mogelijk dat

krakingsreacties van het lineaire alkaan optreden. Echter wanneer de (de)hydrogenatiereacties

in quasi-evenwicht verondersteld worden, is de vorming van gekraakte producten via deze

weg minimaal. Als quasi-evenwicht kan beschouwd worden voor de (de)hydrogenatiereacties,

spreekt men van ideaal hydrokraken.

Ideaal hydrokraken hangt niet enkel af van het type katalysator, maar eveneens van de

werkingsvoorwaarden. In dit opzicht zullen lage drukken, hoge temperaturen, hoge molaire

waterstof tot koolwaterstofverhoudingen en lange koolstofketens leiden tot niet-ideaal

hydrokraken.

Reactienetwerk

In dit deel wordt het klassieke reactienetwerk, bestaande uit 6 reactiefamilies, uitgebreid met

de beschouwing van primaire carbenium ionen. Dit betekent dat we enkel krakingsreacties

beschouwen op de zure centra.

De veronderstellingen gemaakt voor het klassieke netwerk blijven gelden. Dit houdt in dat

voor (de)hydrogenatie en (de)protonatie quasi-evenwicht verondersteld wordt. Verder worden

oligomerisatie en hydride transfer niet in rekening gebracht. Als bijkomende veronderstelling

geldt nu dat primaire carbenium ionen kunnen optreden als product en als reactant.

Nederlandse samenvattingHydroisomerisatie van n-pentaan: het klassieke reactienetwerk uitgebreid met primaire carbenium ionen

XI

Deze veronderstellingen leiden tot een reactienetwerk bestaande uit 7 alkanen, 10 alkenen en

15 carbenium ionen die optreden als product of reactant in 10 (de)hydrogenaties, 18

(de)protonaties, 8 alkyl shift reacties, 12 pcp-vertakkingen en 12 β-scissie reacties.


De isomerisatie- en krakingsreacties worden nog steeds als snelheidsbepalend verondersteld.

Verder wordt opnieuw gebruik gemaakt van het evenwicht van de (de)hydrogenatie en de

(de)protonatie reactie voor de bepaling van de concentraties aan olefienen en carbenium

ionen. De netto-vormingsnelheid van de alkanen heeft dezelfde uitdrukking als in het

klassieke geval. Het enige verschil bevindt zich in het type van carbenium ionen betrokken bij

de reacties.

Modelparameters

De pre-exponentiële factoren van de single-event snelheidscoëfficiënten worden berekend met

behulp van statistische thermodynamica. De enige factor die geschat wordt voor elke

snelheidscoëfficiënt is de activeringsenergie.

Er zijn elf modelparameters die moeten geschat worden. Hiervan zijn drie

protoneringsenthalpieën voor de vorming van de carbenium ionen. Verder is er één

activeringsenergie voor alkylshift (Ea,AS(p;s)), drie voor PCP-vertakking (Ea,PCP(p;p),

Ea,PCP(p;s), Ea,PCP(s;s)) en vier voor β-scissies (Ea,β (p;p), Ea, β (p;s), Ea, β (s;s), Ea, β (s;p)). De

activeringsenergie voor secundaire naar primaire PCP-vertakking Ea,PCP(s;p) wordt berekend

met behulp van Ea,PCP(p;s) en het verschil tussen de protoneringsenthalpieën voor secundaire

en primaire carbenium ionen.

Resultaten

Het verschil tussen de protoneringsenthalpie voor de vorming van een tertiair en een

secundair carbenium ion bedraagt 42,7 kJ/mol en komt overeen met waarden gevonden in de

literatuur. Het verschil tussen de protoneringsenthalpie voor de vorming van een secundair en

een primair carbenium ion bedraagt 54,7 k/mol en is te klein in vergelijking met waarden

gevonden in de literatuur. Hierin worden waarden rond 100 kJ/mol voorgesteld.

De waarde voor de activeringsenergie voor secundaire naar secundaire PCP-vertakking die in

de literatuur wordt voorgesteld, bedraagt 108,7 kJ/mol. De waarde geschat voor dit

reactienetwerk bedraagt slechts 53,4 kJ/mol.

Nederlandse samenvatting Hydroisomerisatie van n-pentaan: het klassieke reactienetwerk uitgebreid met hydrogenolyse

XII

De activeringsenergie voor β-scissie is lager naarmate een meer stabiel carbenium ion

gevormd wordt. De geschatte waarden voor de vorming van een primair carbenium ion

voldoen enkel aan deze vaststelling indien vertrokken wordt van een tertiair carbenium ion,

niet wanneer vertrokken is van een secundair. Ingeval uitgegaan wordt van een minder stabiel

ion voor β-scissie zal de activeringsenergie eveneens lager zijn.

De pariteitdiagrammen voor de molaire uitlaatstromen voor n-butaan, ethaan en propaan zijn

aanvaardbaar. Deze voor isopentaan is iets minder goed, maar de plots voor methaan en

isobutaan zijn onaanvaardbaar. Het is moeilijk de responsen van methaan en isobutaan

degelijk te beschrijven aangezien de molaire uitlaatstroom van deze responsen voor de meeste

experimenten gelijk zijn aan nul.

Uit de statistische analyse volgt dat zowel de regressie als de schatting van de individuele

parameters significant is. De berekende F- en t-waarden zijn steeds groter dan de

getabelleerde waarde. Uit de matrix met de binaire correlatiecoëfficiënten volgt dat de

activeringsenergie voor PCP-vertakking van een secundair carbenium ion met vorming van

een secundair carbenium ion negatief gecorreleerd is met de protoneringsenthalpie voor een

secundair carbenium ion. Dit kan verklaard worden aan de hand van het reactiemechanisme.

Zowel bij het beschrijven van de invloed van de ruimtetijd als van de druk wordt de conversie

licht onderschat. Dit heeft als gevolg dat de selectiviteit overschat wordt. Desondanks wordt

de trend in de curve wordt steeds goed beschreven.

Hydroisomerisatie van n-pentaan: het klassieke

reactienetwerk uitgebreid met hydrogenolyse

Reactienetwerk

In dit deel van het project wordt het klassieke reactienetwerk bestaande uit de 6

reactiefamilies uitgebreid met krakingsreacties op de metallische centra (hydrogenolyse).

Aangezien primaire carbenium ionen buiten beschouwing worden gelaten, zal voor

hydroisomerisatie van n-pentaan geen β-scissie kunnen optreden.

Bij hydrogenolyse zal ofwel methaan, ofwel ethaan afgesplitst worden. Naargelang het deel

dat afgesplitst wordt, refereren we naar demethylering, respectievelijk deëthylering.

De veronderstellingen gemaakt voor het klassieke reactienetwerk blijven gelden.

Oligomerisatie en hydride transfer worden niet in aanmerking genomen. Quasi-evenwicht is

nog steeds verondersteld voor de (de)hydrogenatie en (de)protonatiereacties.


XIII

Een bijkomende veronderstelling is dat hydrogenolyse enkel in rekening gebracht wordt voor

n-pentaan en isopentaan. Deze veronderstelling is gerechtvaardigd doordat de concentratie

van de C5-alkanen het grootst zal zijn, alsook doordat C5-alkanen de grootste affiniteit zullen

vertonen om te reageren met de metallische centra. De veronderstelling is voornamelijk

ingevoerd om het aantal modelparameters te beperken. Voor elke reactie van een kleiner

alkaan dan C5 die beschouwd wordt, moeten twee extra parameters geschat worden, namelijk

een pre-exponentiële factor en een adsorptie-enthalpie.

Dit reactienetwerk bestaat uit 7 alkanen, 10 alkenen en 7 carbenium ionen die optreden als

product of reactant in 10 (de)hydrogenaties, 11 (de)protonaties, 2 pcp-vertakkingen, 3

demethyleringen en 2 deëthyleringen.

Door de jaren heen is reeds veel onderzoek verricht naar hydrogenolyse. Het model dat de

beste resultaten gaf in het eerder werk, dat verondersteld dat een geadsorbeerd waterstofatoom

betrokken is bij de krakingsreactie; wordt gebruikt voor de beschrijving van hydrogenolyse in

dit werk.


In tegenstelling tot het vorige geval waarbij het klassieke reactienetwerk uitgebreid wordt met

primaire carbenium, veranderen de vergelijkingen van het klassieke reactienetwerk wel

wanneer hydrogenolyse in rekening gebracht wordt. De methode waarmee de vergelijkingen

afgeleid worden, blijft echter wel dezelfde.

Het verschil tussen het klassieke reactienetwerk en dit netwerk ligt in de berekening van de

netto-vormingssnelheid van de alkanen. Naast de bijdrage van de reacties waarbij het

carbenium ion, corresponderend bij het beschouwde alkaan, gevormd wordt of verdwijnt, en

de bijdrage van de rechtstreekse vorming van olefienen door β-scissie, moeten hier ook de

hydrogenolysereacties in rekening gebracht worden. Rechtstreekse vorming van olefienen

door β-scissie geldt enkel voor het algemene geval. Bij hydroisomerisatie van n-pentaan kan

β-scissie immers niet optreden.

Modelparameters

In totaal zijn er 14 modelparameters die geschat moeten worden. Voor de zuurgekatalyseerde

reacties wordt opnieuw het single-event principe toegepast, waarbij enkel de

activeringsenergie overblijft als parameter die geschat moet worden. Voor de

metaalgekatalyseerde hydrogenolysereacties echter wordt het single-event principe ook

toegepast, maar wordt de pre-exponentiële factor eveneens geschat. Literatuurstudie zou


XIV

moeten gebeuren alvorens de pre-exponentiële factor bepaald kan worden door middel van

statistische thermodynamica.

Er zijn twee protoneringsenthalpieën te schatten, namelijk voor de vorming van secundaire en

tertiaire carbenium ionen. Enkel PCP-vertakking van secundaire naar secundaire carbenium

ionen treedt op als zuurgekatalyseerde reactie, wat aanleiding geeft tot één activeringsenergie.

Zowel voor de dissociatieve adsorptie van waterstof als voor de adsorptie van het alkaan moet

een pre-exponentiële factor als een adsorptie-enthalpie geschat worden.

Voor de hydrogenolysereacties, demethylering en deëthylering, moet telkens een pre-

exponentiële factor als een activeringsenergie bepaald worden. Twee verschillende

snelheidscoëfficiënten worden gebruikt daar de experimentele productdistributie aantoont dat

het molaire uitlaatdebiet van ethaan significant hoger is dan dit van methaan.

Als laatste modelparameter wordt tevens het aantal waterstofatomen geschat die verwijderd

worden van het alkaan tijdens chemisorptie op een metallisch centrum.

Resultaten

Het geschatte verschil in protoneringsenthalpie voor de vorming van een secundair en een

tertiair carbenium ion bedraagt 44 kJ/mol. Deze waarde komt overeen met waarden

gepostuleerd in literatuur.

De waarde voor PCP-vertakking van een secundair naar een secundair carbenium ion is

geschat op 92,7 kJ/mol welke iets lager ligt dan waarden gevonden in literatuur.

De enthalpieverandering bij adsorptie van een alkaan op een metallisch centrum is positief.

Dit endotherme karakter wordt eveneens teruggevonden in literatuurgegevens voor lichte

alkanen zoals butaan en propaan. Het endotherme karakter is te wijten aan het optreden van

hydrogenatie tijdens de adsorptie.

De activeringsenergieën voor demethylering en deëthylering zijn overeenkomstig met

waarden uit de literatuur. De activeringsenergie voor demethylering is hoger dan deze voor

deëthylering, welke kan verklaard worden door het reactiemechanisme.

Pariteitdiagrammen voor ethaan, propaan, isopentaan en n-butaan zijn aanvaardbaar. Deze

voor methaan en isobutaan zijn het - zoals in het vorige geval - niet. Dit is opnieuw te wijten

aan de experimentele uitlaatdebieten voor methaan en isobutaan die doorgaans gelijk zijn aan

nul.

Uit de F-test in de statistische analyse blijkt dat de regressie op zich significant is, maar de t-

test wijst uit dat 9 van de 14 modelparameters niet significant geschat worden. Er zijn redenen

om aan te nemen dat de geschatte waarden voor de modelparameters toch significant zouden

Nederlandse samenvatting Hydroisomerisatie onder niet-ideale hydrokrakingscondities

XV

zijn, maar dat er problemen zijn met de manier waarop de t-waarde berekend wordt. De t-

waarde wordt berekend uitgaande van de variantie/covariantiematrix. Deze is op zijn beurt

afhankelijk van het verschil tussen de modelberekende en de experimentele waarden.

Wanneer de experimentele uitlaatdebieten voor bepaalde responsen gelijk zijn aan nul

resulteert dit in grote afwijkingen tussen modelberekende en experimentele waarden. Om een

betrouwbare statistische analyse te kunnen doen, zou een nieuwe regressie moeten uitgevoerd

worden waarbij de responsen van methaan en isobutaan niet in beschouwing worden

genomen.

Uit de matrix met binaire correlatiecoëfficiënten blijkt opnieuw dat de protonatie-enthalpie

voor de vorming van secundaire carbenium ionen negatief gecorreleerd is met de

activeringsenergie voor PCP vertakking van een secundair carbenium ion met vorming van

een secundair carbenium ion. Dit kan op dezelfde manier verklaard worden als in het geval

waarbij primaire carbenium ionen beschouwd worden.

Verder blijkt ook een negatieve correlatie tussen de adsorptie-enthalpie en beide

activeringsenergieën voor de hydrogenolysereacties. De activeringsenergieën zijn onderling

positief gecorreleerd. Deze afhankelijkheden kunnen verklaard worden op basis van het

reactiemechanisme.

Zowel als functie van de ruimtetijd als van de druk wordt de conversie licht overschat.

Daardoor wordt de selectiviteit naar isopentaan onderschat.

Hydroisomerisatie onder niet-ideale

hydrokrakingscondities

De testen uitgevoerd aan de universiteit van München bevatten enkele experimenten

verkregen onder niet-ideale hydrokrakingsvoorwaarden. Deze laatste vertonen een afwijkend

gedrag. Om deze resultaten nauwkeurig te kunnen beschrijven, moet dit afwijkend gedrag

beschreven worden in de computercode waarmee de regressie gebeurt.

Reactiemechanisme

Single-event benadering is tot dusver hoofdzakelijk toegepast voor zuurgekatalyseerde

reacties. Het klassieke reactienetwerk wordt opnieuw uitgebreid met de beschouwing van

primaire carbenium ionen.

De veronderstellingen gemaakt bij het klassieke reactienetwerk blijven gelden, behalve het

quasi-evenwicht van de (de)hydrogenatiereacties. Aangezien dit evenwicht gebruikt werd


XVI

voor de bepaling van de concentratie aan olefienen, zullen deze concentraties optreden als

variabelen. Dit leidt tot een set van 17 vergelijkingen, in plaats van 7, die opgelost moeten

worden. De residuele n-pentaan stroom wordt bepaald uit de koolstofbalans, wat leidt tot 16

vergelijkingen die opgelost worden.

Voor de olefienen wordt pseudo-stationaire toestand verondersteld, wat ertoe leidt dat de tien

vergelijkingen voor de olefienen niet-lineaire algebraïsche vergelijkingen zullen zijn.

Invloed van de werkingsvoorwaarden op idealiteit van hydrokraken

Zoals eerder vermeld wordt de idealiteit van het hydrokraken niet uitsluitend bepaald door het

type katalysator, maar ook door de werkingsvoorwaarden. Katalysatoren die aanleiding geven

tot ideaal hydrokraken onder een bepaalde set van voorwaarden, kunnen aanleiding geven tot

niet-ideaal hydrokraken onder een andere set.

Een hoge temperatuur en lage druk leiden tot niet-ideaal hydrokraken. Onder deze

omstandigheden zal bij stijgende druk evenzeer de conversie stijgen.

Hoge molaire waterstof tot koolwaterstofverhoudingen leiden eveneens tot niet-ideaal

hydrokraken. De verklaring voor dit effect ligt in de grote invloed van de ratio op de

partieeldruk van de koolwaterstoffen en de kleine invloed van de ratio op de partieeldruk van

waterstof.

Toepassing van Single-event microkinetisch modelleren op de

(de)hydrogenatiereacties

Omdat het evenwicht van de (de)hydrogenatiereacties niet meer geldt, moeten al deze reacties

afzonderlijk in rekening gebracht worden. Ondanks veelvuldig onderzoek is het

reactiemechanisme voor (de)hydrogenatiereacties nog niet bekend. Daardoor wordt single-

event toegepast op de globale reactie, in plaats van op het gehele reactiemechanisme. De

single-event snelheidscoëfficiënt voor dehydrogenatie behoort tot de snelheidsbepalende stap.

Verondersteld is dat de oppervlaktereactie de snelheidsbepalende stap is.

Verstraete stelt in zijn werk voor om een snelheidscoëfficiënt in te voeren afhankelijk van het

type koolstofatoom betrokken bij de dehydrogenatiereactie. Vereenvoudigd wordt in dit

project slechts één snelheidscoëfficiënt verondersteld voor alle dehydrogenatie reacties. Aan

de pre-exponentiële factor wordt een vaste waarde toegekend. Deze waarde is niet gebaseerd

op de transitietoestandstheorie. De activeringsenergie wordt geschat.

Zoals het aantal single-events te gebruiken bij zuurgekatalyseerde reacties, gebruikt

Verstraete een aantal identieke transformaties voor metaalgekatalyseerde reacties.


XVII

Vereenvoudigd wordt in dit werk gesteld dat dit aantal identieke transformaties gelijk is aan

één voor elke reactie.

Implementatie in het computerprogramma

Zoals reeds vermeld, moet een set van 16 vergelijkingen simultaan opgelost worden. Deze set

bestaat uit 6 differentiaalvergelijkingen en 10 niet-lineaire algebraïsche vergelijkingen. Om

deze set simultaan op te lossen, wordt gebruik gemaakt van de DASPK subroutine. Deze

solver gebruikt achterwaartse differentiaalformules.

Opdat de solver een oplossing kan geven voor de set van vergelijkingen moet een consistente

beginschatting gemaakt worden van concentraties van olefienen en paraffines, alsook voor de

eerste afgeleide van deze oplossingsvector. Voor de paraffines is de beginconcentratie

gekend, maar voor de olefienen niet.

Omdat de vergelijkingen van de olefienen niet-lineaire algebraïsche vergelijkingen zijn, moet

de beginschatting nauwkeurig genoeg zijn om de optimale oplossing te vinden. Daartoe wordt

eerst de subroutine DNSQE gebruikt voor de set van 10 algebraïsche vergelijkingen. Deze

routine gebruikt de Powell hybride methode om de vergelijkingen op te lossen. De oplossing

van deze set wordt gebruikt als initiële schatting voor de concentraties van de olefienen voor

de DASPK subroutine.

Belang van implementatie

Onderzoek naar single-event toepassingen op metaalgekatalyseerde reacties is reeds verricht

door Verstraete en Thybaut. In geen van beide werken is de niet-idealiteit van hydrokraken

reeds geïmplementeerd in een computercode voor regressie.

Een sterk vereenvoudigde versie is nu voor de eerste keer ooit geïmplementeerd in een

computercode voor de regressie van hydrokraken van lichte alkanen waarbij single-event

kinetisch modelleren toegepast wordt. Nu deze code werkt, is de stap tot een meer uitgebreide

versie, waarbij de snelheidscoëfficiënten afhangen van het type koolstofatoom betrokken bij

de reactie, verkleind.

1

Chapter 1

Introduction

1.1 General background

The use of petroleum or derived materials, such as asphalt, and the heavier nonvolatile crude

oils is an old art [1]. In fact, petroleum utilization has been documented for more than five

thousand years. The earliest documented uses occurred in Mesopotamia (ancient Iraq) when it

was recognized that the nonvolatile derivatives (bitumen or natural asphalt and manufactured

asphalt) could be used for caulking and as an adhesive for jewelry or as a mastic for

construction purposes. There is also documented use of bitumen for medicinal use [1].

Approximately two thousand years ago, Arabian scientists developed methods for the

distillation of petroleum, which were introduced into Europe by way of the Arabian

incursions into Spain. Petroleum, used in China since it was encountered when drilling for

salt, appears in documents of the third century. The Baku region of northern Persia was also

reported by Marco Polo in 1271-1273 as having a commercial petroleum industry [1].

Interest in naphtha (nafta) began with the discovery that petroleum could be used as an

illuminant and as a supplement to bituminous incendiaries, which were becoming increasingly

common in warfare. Greek fire was a naphtha-bitumen (or naphtha-asphalt) mix; the naphtha

provided the flame and the bitumen (or asphalt) provided the adhesive properties that

prolonged the incendiary effect [1].

Modern refining began in 1859 with the discovery of petroleum in Pennsylvania. After

completion of the first well, the surrounding areas were immediately leased and extensive

drilling took place. In the post-1945 era, Middle Eastern countries continued to rise in

importance because of new discoveries of vast reserves. The United States, though continuing

to be the biggest producer, was also the principal consumer and thus was not an exporter of

oil. At this time, oil companies began to roam much farther in the search for oil, which has

resulted in significant discoveries in Europe, Africa, and Canada.

Introduction

The impetus to develop the petroleum refining industry came from several changes in life

styles. The increased needs for illuminants, for fuel to drive the factories of the industrial

revolution, for gasoline to power the automobiles, as well as the demand for aviation fuel, all

contributed to the increased use of petroleum

Nowadays the supply for oil is still increasing as shown in

Crude oil is a mixture of compounds boiling at different temperatures that can be separated

into a variety of different generic but often overlapping fractions (

these fractions produced by distillation depend on the origin and properties of crude

petroleum [1].

The first step in refining crude oil involves separating the oil into dif

fractions by distillation. A typical set of petroleum fractions is given in the table.

these broad cuts can be marketed directly, while others require further processing in

downstream units to make them saleable.

Fraction

natural gas

petroleum ether

gasoline

kerosene

fuel oils

lubricants

asphalt or coke

76

78

80

82

84

86

88

2003

mb

/d

The impetus to develop the petroleum refining industry came from several changes in life

increased needs for illuminants, for fuel to drive the factories of the industrial


contributed to the increased use of petroleum [2].

l is still increasing as shown in Figure 1-1.

Figure 1-1: World oil supply evolution [3]

compounds boiling at different temperatures that can be separated

into a variety of different generic but often overlapping fractions (Table 1-


The first step in refining crude oil involves separating the oil into dif

A typical set of petroleum fractions is given in the table.

cuts can be marketed directly, while others require further processing in

downstream units to make them saleable.

Table 1-1: Petroleum Fractions [4]

Boiling range (oC) Number of Carbon Atoms

< 20 C1 to C4

20 - 60 C5 to C6

40 - 200 C5 to C12, but mostly C

150 - 260 mostly C12 to C

> 260 C14 and higher

> 400 C20 and above

residue polycyclic

2003 2004 2005 2006 2007 2008 2009

1.1: General background

2

The impetus to develop the petroleum refining industry came from several changes in life-

increased needs for illuminants, for fuel to drive the factories of the industrial


compounds boiling at different temperatures that can be separated

-1). The amounts of


The first step in refining crude oil involves separating the oil into different hydrocarbon

A typical set of petroleum fractions is given in the table. Some of

cuts can be marketed directly, while others require further processing in refinery

Number of Carbon Atoms

4

6

, but mostly C6 to C8

to C13

and higher

and above

polycyclic

Introduction 1.1: General background

3

The composition of the refinery effluent stream has changed during the years. As shown on

Figure 1-2 the demand for heavy products has decreased as the demand for middle distillates

and light products increased. Nowadays almost 50% of the oil demand consists of gasoline.

Figure 1-2: World oil demand evolution [4]

This, in turn, brought about changes in the way crude oil was refined and led to innovations

and developments in the refining industry, thereby giving birth to the integrated petroleum

refinery.

Figure 1-3: Example of an integrated petroleum refinery

Introduction 1.1: General background

4

In these integrated petroleum refineries, heavy products are converted to lighter products by

hydrocracking and catalytic reforming. About 10% of the product of the distillation of crude

oil is a fraction known as straight-run gasoline. This gasoline burns unevenly in high

compression engines, producing a shockwave that causes the engine to “knock”. The most

commonly used measure of a gasoline's ability to burn without knocking is its octane number.

Octane numbers compare a gasoline's tendency to knock against the tendency of a blend of

two hydrocarbons (heptane and 2,2,4-trimethylpentane, or isooctane). Heptane (C7H16) is a

long, straight-chain alkane, which burns unevenly and produces a great deal of knocking.

Highly branched alkanes such as 2,2,4-trimethylpentane are more resistant to knocking.

The relationship between knocking and the structure of the hydrocarbons in gasoline is

summarized in the following general rules [5].

• Branched alkanes and cycloalkanes burn more evenly than straight-chain alkanes. • Short alkanes (C4H10) burn more evenly than long alkanes (C7H16). • Alkenes burn more evenly than alkanes. • Aromatic hydrocarbons burn more evenly than cycloalkanes.

Table 1-2: Hydrocarbon octane numbers [5]

Hydrocarbon Octane Number

Heptane 0

2-Methylheptane 23

Hexane 25

2-Methylhexane 44

1-Heptene 60

Pentane 62

1-Pentene 84

Butane 91

Cyclohexane 97

2,2,4-Trimethylpentane (iso-octane) 100

Benzene 101

Toluene 112

During the years there have been lots of different ways to enhance the octane number of

gasoline. The first change came after the prohibition on the use of leaded gasoline in the mid

nineties. After this they started using methyl tertiary-butyl ether and ethyl tertiary-butyl ether

as octane boosters to a content up to 10 vol% [6]. Recent studies have shown that these

tertiary butyl ethers diffuse through the walls of the gasoline tanks and that they resolve very

Introduction 1.2: The role of hydrocracking

5

good in the underground water. Also have they been suspected to emit toxic formaldehyde

(from methanol) or peroxyacetyl nitrate (from ethanol). Therefore there is a prohibition on the

use of these products too.

The most commercially used octane boosters since then were aromatic hydrocarbons. Their

disadvantages of increasing NOX, hydrocarbons and CO emissions lead also to a legislative

limitation on the maximum amount. Since January 1st 2005 the maximal content of benzene is

2.7 vol% and for aromatic hydrocarbons 35 vol% (2003/17/EG) [7].

Decreasing the amount of aromatic hydrocarbons present in the fuel has a negative impact on

the octane number. Branched hydrocarbons are now considered to be the most environmental

friendly and most promising alternative to aromatics.

1.2 The role of hydrocracking

The hydrocracking process was applied for the first time by I.G. Farben in 1927 for the

conversion of lignin into benzene [8]. Due to the high operation costs, which can be ascribed

to the high consumption of hydrogen, the applications for hydrocracking slowed down. The

development of catalytic reforming in the fifties, producing benzene with a high octane

number, produces also large amounts of hydrogen as a by-product, gave new interest to the

hydrocracking process. The introduction of zeolites in the seventies and the constantly

growing demand for middle distillates enhanced this interest.

Hydrocracking has a large flexibility, a large range of feedstock can be used (100 to 500

kg/kmol) [8]. Due to this the demand to middle distillates can be met. Contrary to catalytic

cracking, hydrocracking has a higher yield for middle distillates (kerosene, gasoline and

aviation fuel) of good quality. The cetane number of diesel obtained through hydrocracking is

higher than when obtained through catalytic cracking. This can be explained by the absence of

olefins and polycyclic aromatics in the product stream. A second advantage for hydrocracking

is found in the fact that the high partial pressure of hydrogen and relative low temperatures

decrease the formation of cokes.

The hydrocracking process uses bifunctional catalysts. These consists of an acid function

originated from the carrier and responsible for isomerization and cracking reactions and of a

metal function, dispersed in the acid phase, which has a hydrogenating function.

As for the acid function there are two types: amorphous silica/alumina and zeolites

(crystalline silica/alumina). The amorphous catalysts appear to have a larger selectivity

Introduction 1.3: Hydroisomerization

6

towards middle distillates, but their activity for cracking is limited so that high temperatures

are necessary. Zeolite hydrocracking catalysts possess a specific pore structure and pore

dimensions. They show a higher activity at lower process conditions, but their selectivity

towards middle distillates is lower [8]. The use of zeolites has the advantage that because of

shape selectivity side reactions such as corrosion can be avoided [9].

1.3 Hydroisomerization

This process is used to raise the octane number of gasoline by increasing the concentration of

branched hydrocarbons. The octane number is proportional to the amount of branched isomers

present in the gasoline stream.

Also for hydroisomerization bifunctional catalysts are the most effective. Zeolites are used for

the acid function of the catalyst, because of their high activity at low process conditions. That

way they have the advantage of the chemical equilibrium which is situated at the side of the

branched products at low temperatures.

The linear alkane diffuses from the bulkphase to the internal surface of the catalyst where it is

physisorbed in the micropores. Once diffused to the metallic sites, the alkane is

dehydrogenated, after which the olefin formed migrates further to the acid sites. Here the

olefin is first converted to a carbenium ion by hydride transfer or protonation on a Brönsted

acid site and hydride abstraction on Lewis sites [10]. The carbenium ions is converted into a

isomerised or cracked olefin and is then hydrogenated on the metal sites of the catalyst. C5, C6

and C7 cannot be hydroisomerised optimal all together. The optimal conditions for the

hydroisomerization of C6 are the same as the optimal conditions for cracking of C7.

An example of an hydroisomerization process is the Shell Hysomer Process. This is a ‘once-

through’ gasphase operation working at pressures of 20-50 bar and temperatures between

240°C and 280°C. Using this process an enhancement of 10 units of the octane number can be

reached [8]. The C5/C

6-rich light gasoline feed is heated up together with hydrogen in the

furnace (a) and isomerized in the reactor (b) containing a noble metal catalyst. The reaction

product is separated, and the stabilized isomerate run down as blending component for motor

gasoline [11].

Because the Shell Hysomer Process is a once through process the effluent can still contain a

high concentration of n-paraffins. To produce effluent stream with a higher octane number the

n-paraffins in the effluent stream can be recycled to the catalytic reactor. An example of this

Introduction 1.4: Microkinetic modeling

7

technology is the Total Isomerization Process (TIP), which provides an iso/normal paraffin

separation in a molecular sieve unit and a subsequent isomerization of the fraction containing

the n-paraffins [11].

Figure 1-4: Shell Hysomer process; a) Process heater; b) Isomerization reactor; c) Reactor product separator; d) Stabilizer column; e) Recycle gas compressor [11]

1.4 Microkinetic modeling

In industry, simple power law rate equations are traditionally used to desctribe catalytic

processes. Power law kinetics are determined by regression with experimental data and are

normally valid in narrow ranges of operating conditions, especially for complex reactions [6].

The description of detailed reactant and product outlet compositions over a wide range of

operating conditions can be achieved by using microkinetic models. If the particular reaction

network includes homologous series of hydrocarbons, a Single-Event MicroKinetic (SEMK)

model is an excellent alternative to model the reaction [6].

In microkinetic models the rate of every elementary step is calculated. Hence, the first step

should be the identification of the elementary steps capturing the essential chemistry involved

in the particular reaction mechanism. Ideally, the model parameters could be obtained from

surface science and/or computational calculations. However, up to date, the lack of accuracy

or availability of the latter requires the parameter adjustment by comparison with

experimental data. The strategy is to establish physically realistic limits for the parameter

values. The comparison of the estimates with experimentally determined values serves as

verification of the adequacy of the reaction mechanism used. The parameters include sticking

Introduction 1.5: Scope of the Master project

8

coefficients, surface bond energies, activation energies and pre-exponential factors of

elementary steps…etc. Once the parameters are estimated, they can be extrapolated to other

experimental regions. Eventually, for the microkinetic model to be valid it should capture the

general experimental trends over a broad range of operating conditions [4].

Generally the microkinetic models applied in literature assume rate-limiting and quasi-

equilibrated reactions. However, initially every elementary reaction should be considered

kinetically relevant and only an a posteriori analysis should determine which parameters are

kinetically significant and which elementary reactions are quasi-equilibrated.

As a consequence, the microkinetic model is valid over a wide range of operating conditions,

since the relative kinetic significance of the elementary steps may change with the operating

conditions. In fact, the microkinetic model enables the identification of the critical elementary

steps for process optimization. Traditionally, kinetic coefficients related to reactivity indexes

such as chemisorptions enthalpies through linear free energy relationships have been used for

describing similar elementary steps.

1.5 Scope of the Master project

The implementation of hydrogenolysis on the metal sites in a fundamental kinetic model was

starts at LCT [12]. The aim in the present work is to further refine the microkinetic model by

considering hydrogenolysis, primary carbenium ions and non-quasi-equilibrated

(de)hydrogenation reactions.

The first step in the development of the fundamental kinetic model is the construction of the

reaction network including the formation and reaction of primary carbenium ions. The

reaction network when considering hydrogenolysis is used as constructed in a previous work

[12].

The hydroisomerization of n-pentane has been studied on different Pt-Beta zeolite by the

university of Munich [6]. The developed data set was for a clean catalyst and for two sulfated

catalysts. On this sulfated catalysts, the isomerization selectivity was close to 100.

From an analysis of the experimental data set obtained in Munich is found that most of the

data are obtained under non-ideal hydrocracking conditions as shown in Chapter 3. Therefore

these experiments will show aberrant behaviour. This behaviour has to be described in the

parameter estimation program in order to describe the experiments correctly.

Introduction 1.5: Scope of the Master project

9

The scope of this project will be first to describe the data set from Munich. Also, some

additional experiments will be done on a Berty reactor at the University of Ghent using a

USY zeolite.

Once the kinetic model and reaction network have been developed, the enhancement of the

selectivity of the isomerization reaction will be explained by estimation the kinetic parameters

in the model.

Developing this fundamental kinetic model to predict the behaviour of hydroisomerization is

of a great use, because they can be used to optimize the reactor design and catalyst

development. Development and optimization of catalysts is an important working area

because catalytic processes represent 83% of the crude oil distillation processes [3].

Introduction 1.6: References

10

1.6 References

[1] Speight, J.G., The Chemistry & technology of petroleum. 2nd ed, I. Marcel Dekker,

New York. 1991.

[2] Kirk-Otthmer, Refinery processes, survey, Encyclodepia of chemical technology, 4th Edition

[3] Silvy, R.P., Future trends in the refining catalyst market. Applied Catalysis a-

General, 2004. 261(2): p. 247-252.

[4] Courty, P. and J.F. Gruson, Refining clean fuels for the future. Oil & Gas Science and Technology-Revue De L Institut Francais Du Petrole, 2001. 56(5): p. 515-524.

[5] http://chemed.chem.purdue.edu/

[6] Woltz, C., Kinetic Studies on alkane hydroisomerization over bifunctional catalysts,

PhD thesis, 2005, Technischen Universität Munchen

[7] Eur-Lex: De toegang tot het recht van de Europese unie: Richtlijn 2003/17/EG van 3 maart 2003 tot wijziging van Richtlijn 98/70/EG betreffende de kwaliteit van benzine en dieselbrandstof. [Available from: eur-lex.europa.eu/].

[8] Becker, A., Kinetische modellering van hydroisomerisatie en hydrokraken van

koolwaterstoffen op een Pt/US-Y zeoliet, PhD Thesis, 1997,Ghent university [9] de Lucas, A., et al., Influence of the Si/Al ratio in the hydroisomerization of n-octane

over platinum and palladium beta zeolite-based catalysts with or without binder. Applied Catalysis a-General, 2005. 289(2): p. 205-213.

[10] Feng, W., E. Vynckier, and G.F. Froment, Single-Event Kinetics of Catalytic

Cracking. Industrial & Engineering Chemistry Research, 1993. 32(12): p. 2997-3005.

[11] Neuwirth, O.S., Oil refining processes, Ullman's encyclopedia of industrial chemistry,

Walther W. Irion [12] Govaerts, S., Ondersteuning van de ontwikkeling en optimalisering van katalysatoren

met behulp van fundamenteel kinetisch modelleren, Master thesis, 2007, Ghent University

11

Chapter 2

Hydroisomerization of n-

pentane: Single-event approach

Abstract: In this chapter, a detailed description of the reaction mechanism for

hydroisomerization of n-pentane is given. The classical reaction network is generated through

a computer algorithm. The rate equations necessary for the reactor models are developed

using single-event approach. Finally the procedure for regression of the model parameters is

described and the statistical analysis is explained.

2.1 Reaction Mechanism

2.1.1 Description

As mentioned before hydrocracking and hydroisomerization processes are catalyzed by

bifunctional catalysts. All possible reactions during hydroisomerization are shown in Figure

2-1.

The linear alkane diffuses from the bulkphase to the internal surface of the catalyst where it is

physisorbed in the micropores. Once diffused to the metallic sites, the alkane is

dehydrogenated, after which the olefin formed migrates further to the acid sites. Here the

olefin is first converted to a carbenium ion by protonation on a Brønsted acid site [1]. The

latter can either isomerize to a more stable carbenium ion or crack with formation of a smaller

carbenium ion and an olefin. The reaction mechanism for isomerization is shown in Figure

2-2.

Hydroisomerization of n-pentane: Single-event approach 2.1: Reaction Mechanism

12

Figure 2-1: Reaction mechanism for hydroisomerization on a bifunctional catalyst [2]

The quick hydrogenation reaction of unsaturated hydrocarbons (and by that means also cokes

precursors) prevent the deactivation of the catalyst [3]. The relative strength of the metal and

acid functions determine the product distribution of isomerization and cracking products.

Also the stability of the carbenium ions plays an important role in the explanation of the

product distribution. The relative stability of a carbenium ion in a saturated structure follows

from the inductive effect of his substituents, because alkyl groups act like electron-donors in

relation to the positive charged carbenium ion. The stability of carbenium ions increases thus

in following order:

3CH primary C secondary C tertiary C+ + + +< < <

Figure 2-2: Hydroisomerization reaction scheme [4]


13

2.1.2 Isomerization reactions

The isomerization of carbenium ions can be divided in two types: isomerization without a

change in degree of branching and isomerization with a changing degree of branching [5].

Isomerization without a change in degree of branching consist of hydride shift and alkyl shift.

These reactions are fast in comparison with the isomerization reaction with changing degree

of branching.

Figure 2-3: Upper figure: Hydride shift; lower figure: alkylshift (methylshift) [5]

Isomerization through protonated cyclopropane intermediates (pcp-branching) is an example

of isomerization with a change in the degree of branching. The mechanism is shown in Figure

2-4 [5]. The first step is the cyclisation of the cation (A) with formation of the protonated

cyclopropane (B). A protonated cyclopropane is a cyclic alkyl carbenium ion which consist of

a carbon atom with a penta-coordination. Afterwards the protonated cyclopropane (B) is

shifted to a new protonated cyclopropane(D) by which the positive charge is located on the

carbon atom without substituents. Opening the ring structure leads to the branched chain. This

secondary carbenium ion can be converted into a more stable tertiary carbenium ion by

hydride transfer.

Due to the formation of strong covalent bonds the enthalpy of protonation and the activation

energy of the isomerization step is expected to be high since this involves the lengthening of

the C-O bond [6]. Also was observed that the rate of isomerization strongly depends on the

chain length of the involved alkanes. The longer the chain, the more stabilized the associated

carbenium ion and the faster the isomerization reaction. However the longer the chain, the

harder it is to achieve high isomerization selectivity. Two reactions can decrease the

selectivity for isomerization. On the one hand hydrocracking can occur consecutively with

isomerization on an ideal catalyst. This behaviour depends on the balance between the acid

and the hydrogenation functions and will be discussed in section 4.1


14

Figure 2-4: Mechanism for PCP branching of 2-hexyl cation [5]

A secondary reaction that can decrease the selectivity for isomerization is hydrogenolysis.

This is a non-selective cracking reaction on the metal sites where mainly methane and ethane

are formed [6].

Because the reaction occurs by carbenium ions as intermediates, oligomerisation and hydride

transfer can compete with isomerization and cracking as well. However, for this project

oligomerisation and hydride transfer is not considered either.

2.1.3 Hydrocracking reactions

Hydrocracking of alkyl carbenium ions occurs through breaking the carbon atoms bond of the

carbon atom in β-position towards the positively charged carbon atom. This type of reactions

is called β-scission. [5]

Two electrons of the carbon-carbon bond in β-position is transferred to the carbon-carbon

bond in α-position. Cracking of the carbon-carbon bond in β-position then occurs leading to a

olefin and a carbenium ion. The structure containing the original α-carbon-carbon bond will

be the olefin. In the other part, the carbon atom originally in γ-position will be electron

deficient, leading to a carbenium ion. The β-scission of 2-pentylkation with formation of

propylene and an ethylkation is shown in Figure 2-5 [5].

Hydroisomerization of n-pentane: Single-event approach 2.2: Reaction Network

15

Figure 2-5: β-scission reaction of 2-pentyl kation

Different β-scission reactions are possible: (t;t), (s;t), (t;s), (s;s). The difference between these

mechanisms lies in the number and positions of the side branches necessary in relation to the

positively charged carbon atom. Only these four reaction types are considered mostly. The use

of primary carbenium ions (p;p); (s;p), (p;s) is energetically unfavorable. Although in order

for pentane to be able to be converted in smaller products using an acid-catalyzed reaction,

primary carbenium ions have to be considered. Therefore the classical reaction network has to

be extended with the possibility for primary carbenium ions to occur. The other possibility for

pentane to be converted in smaller products is considering metal catalyzed reactions like

hydrogenolysis.

2.2 Reaction Network

2.2.1 Reaction Network generation algorithm

The single-event kinetic modelling is, in comparison with the lumped kinetic modelling, a

fundamental approach. This means that the kinetics of each reaction is written in fundamental

elementary steps that occur during the reaction. This way, the kinetic parameters are

independent of the feed composition and chain length of the hydrocarbons.

The first step in the development of the fundamental kinetic model is the generation of a

reaction network consisting of elementary reactions, which take place at the surface of the

catalyst. The size of the reaction networks involved increases rapidly with the carbon number.

Therefore, the generation of the reaction network requires a computerized algorithm. This

algorithm was developed by E. Vynckier [7]. A schematic function of the algorithm is shown

in Figure 2-6.

In this computer program, the structure of the hydrocarbons are represented by a Boolean

matrix. The carbon atoms are numbered, starting with the head chain, followed by the longest

side chain, …etc [7]. Figure 2-7 shows the numbering of iso-pentane.


16

The element mi,j of the Boolean matrix is defined according to next rules:

• mi,j=0 if no bond exist between carbon atom i and j

• mi,j=1 if a bond exist between carbon atom i and j

The Boolean matrix is symmetric and has an order equal to the number of carbon atoms in the

considered structure. The Boolean matrix of iso-pentane is given in Figure 2-8.

The total number of non-zero elements in each row or column of the matrix determine the

type of carbon atom (primary, secondary, tertiary). Two additional parameters are used to

determine whether the hydrocarbon structure represents an olefin (lo=1) or carbenium ion

(lc=1) [7].

The reactions occurring in the network are represented by some matrix manipulations causing

the reactant matrix to be transformed into the product matrix [7].

Figure 2-6: Work-flow of the reaction network generation algorithm


17

5

1

2

34

Figure 2-7: Numbering of iso-pentane [7]

1 2 3 4 5

1 0 1 0 0 0

2 1 0 1 0 1

3 0 1 0 1 0

4 0 0 1 0 0

5 0 1 0 0 0

Figure 2-8: Boolean matrix representation of iso-pentane [7]

In order to determine which elementary steps should be taken into account in the generation

of the reaction network the bifunctional mechanism for hydroisomerization is considered.

Dehydrogenation on the metal sites converts the physisorbed alkane into the corresponding

alkene. After protonation of this alkene on a Brønsted acid site some branching (alkyl shift

and PCP) and cracking reactions (β-scission) occur. The carbenium ions formed are

deprotonated and hydrogenated to form the corresponding alkane [8, 9].

Since carbenium ions are involved in the reactions on the acid sites, two additional reactions

can occur: oligomerisation and hydride transfer. During oligomerisation ,eq. (2-1), a

carbenium ion with x carbon atoms is bound to an olefin with y carbon atoms forming a

carbenium ion with x+y carbon atoms. The second reaction, hydride transfer, eq. (2-2), is a

reaction in which a carbenium ion +2R reacts with an alkane 1P to the formation of another

carbenium ion +1R and an alkane 2P .

x y x y

R O R+++ ←→

(2-1)

1 2 1 2

P R R P+ ++ ←→ + (2-2)

Since the reaction rate for oligomerisation is much smaller than the slowest reaction in the

hydroisomerization process and also because of the absence of heavier components than

pentane in the effluent stream of the reactor, oligomerisation is not considered in the present

work.


18

Under ideal hydrocracking considerations the (de)-hydrogenation reactions are in quasi-

equilibrium and the acid-catalyzed reactions (isomerization and β-scission) are rate

determining, hydride transfer is not considered either.

The classical reaction network is summarized in 6 reaction families: (de)-hydrogenation, (de)-

protonation, alkyl shift, hydride shift, PCP-branching and β-scission reactions.

2.2.2 Reactor Model

A pseudo-homogeneous one dimensional reactor model is applied [6]. Temperature and

concentration gradients in the catalyst are neglected.

A reactor model is developed by mass balances, an energy balance and a momentum balance.

In this case temperature and pressure are considered to be constant. Therefore only the mass

balances has to be taken into account. A mass balance has to be developed for each

independent component. The amounts of the dependent components is then calculated from

the mass conservation law for each atom in the feed.

The experiments at the University of Munich are performed on a plug flow reactor. The

experiments at the University of Ghent will be done on the Berty reactor, which is a

continuous stirred tank reactor. Because a reactor model is dependent of the type of reactor

and the type of flow (plug flow or perfectly mixed flow), a different reactor model has to be

used in each case.

a Plug Flow

Plug flow is a simplified and idealized picture of the motion of a fluid, whereby all the fluid

elements move with a uniform velocity along parallel streamlines. This perfectly ordered flow

is the only transport mechanism accounted for in the plug flow reactor model. No upstream

and downstream mixing is assumed. In this type of reactor, the changing reaction rate creates

a gradient with respect to distance traversed. At the inlet to the PFR the rate is very high, but

as the concentrations of the reagents decrease and the concentration of the product(s)

increases the reaction rate slows down.

Because of the uniformity of conditions in a cross section the steady-state continuity equation

is a very simple ordinary differential equation [10].


19

),,( FpTR

dW

dFtP

cat

AA

=

(2-3)

In which APR is the rate of formation of alkane A per unit volume.

b CSTR

This reactor type is the opposite extreme from the plug flow reactor. The essential feature is

the assumption of complete uniformity of concentration and temperature throughout the

reactor. Therefore, in the perfectly mixed flow reactor, the conversion takes place at a unique

concentration (and temperature) level which, of course, is also the concentration of the

effluent. In order to approach this ideal mixing pattern, it is necessary that the feed be

intimately mixed with the contents of the reactor in a time interval that is very small

compared to the mean residence time of the fluid flowing through the vessel. Therefore an

impeller is present in the reactor.

Since the reactor contents are completely uniform with perfect mixing, the reactor integrated

balances are used for the continuity equation:

catPAA WRFFA

=− 0

(2-4)

In this equation, AF is the flow in the reactor, 0AF is the initial flow what is coming into the

reactor, APR is the rate of reaction of alkane A and catW is the catalyst weight.

2.2.3 Single-event microkinetic modeling

In order to be able to solve the reactor model equations, an expression for the net rate of

production of the alkanes has to be developed first. This is derived by means of a kinetic

model describing the kinetics of the elementary steps as a function of temperature, total

pressure and molar flows of the different components. This means that values for the reaction

rate coefficients have to be determined.

Deriving the kinetic equations corresponding with the generated network without further

assumptions on the kinetic coefficients involved would lead to an insurmountable number of

parameters to be determined.


20

A first step in the reduction of the number of kinetic parameters is the introduction of the

single-event concept. According to the single-event method, the rate coefficient k of the

elementary step can be expressed as the product of a single-event rate coefficient k~

and the

number of single-events ne.

(2-5)

The single-event rate coefficient k~

is only dependent on the reaction family and on the type

of carbenium ions involved. This implies for example:

• The activity for isomerization is only dependent of the type (primary, secondary,

tertiary) and not of the chain length of the carbenium ion

• The single-event rate coefficient k~

for protonation is only dependent of the type of

carbenium and not of the type of olefin.

According to the transition state theory, the reaction from the reactant to product goes through

a intermediate activated complex, and the rate coefficient k can be determined by [9]:

0 0

exp expBk T S H

kH R RT

≠ ≠ ∆ ∆

= −

(2-6)

The entropy at reference temperature S0 can be divided in three contributions:

0 0 0 0

trans vib rotS S S S= + +

(2-7)

The contribution of the rotation consist of an intrinsic term and a term resulting from the

symmetry of the molecule, for which σr and σ≠ are the symmetric numbers of the reactant and

the intermediate activated complex respectively.

σlnˆ 00 RSS rotrot −= (2-8)

This means that the change in entropy can be written as

0 0ˆ ln rS S Rσσ≠ ≠

≠

∆ = ∆ +

(2-9)

With

0,

0,

0,

0 ˆˆrotvibtrans SSSS ≠≠≠≠ ∆+∆+∆=∆

(2-10)

Combination of equation (2-6) and (2-9) leads to the following expression for the rate

coefficient:

enkk~=


21

0 0ˆ

exp expr Bk T S H

kH R RT

σσ

≠ ≠

≠

∆ ∆= −

(2-11)

The number of single-events is the ratio of the symmetry number of the reactant and the

intermediate activated complex.

The single-event pre-exponential factor A~

can be defined as being:

∆= ≠

R

S

h

TkA B

0ˆexp

~ (2-12)

Using thermodynamic data, the pre-exponential factor can be calculated. This implies that

only the activation energies from the elementary steps have to be estimated. The single-event

rate coefficient can be written as:

−=RT

EAk aexp~~

(2-13)

A second type of reduction of the number of kinetic parameters concerns the (de)-protonation

reactions for which quasi-equilibrium is considered. The single-event concept can be applied

on the equilibrium constant for protonation Kpr(Oi,j;ni,k) of an alkene j originating from alkane

i, with the formation of carbenium ion k of type ni,k.

);(~

);( ,,,, kijiprekijipr nOKnnOK = (2-14)

The number of single-event equilibrium constants can be reduced by means of a reference

alkene.

Oref

O i,j C+i,j

Figure 2-9: Thermodynamic cycle for alkene protonation and isomerization with a reference olefin

The isomerization reaction between the alkene Oi,j and the reference alkene Oref is an

equilibrium reaction with equilibrium constant Kiso(Oi,j;Oref). From Figure 2-9 it can be

derived:

);(~

);(~

);(~

,,,, kirefprrefjiisokijipr nOKOOKnOK = (2-15)

In addition to this, the single-event equilibrium constant for (de)-protonation of the reference

alkene Oref is assumed to be independent of the reference alkene considered. Therefore the


22

single-event equilibrium constant for (de)-protonation of Oi,j with respect to the corresponding

carbenium ion ni,k can be expressed as

)(~

);(~

);(~

,,,, kiprrefjiisokijipr nKOOKnOK = (2-16)

2.2.4 Rate equations

The first step of the reaction mechanism is the adsorption of the alkane i from the gas phase in

the pores of the catalyst. The relation between the partial pressure pi of alkane i in the gas

phase and the corresponding concentration Cp(i) in the catalyst pores is described using a

Langmuir isotherm KL [11].

,

,

,1i

L i i

p sat i

L i ii

K pC C

K p=

+∑ (2-17)

The saturation concentration of alkane i is the ratio of the pore volume Vp of the catalyst and

the molar volume Vm of the alkane i.

,

,

p

sat i

m i

VC

V= (2-18)

The molar volume Vm of the alkane is determined by means of the Hankinson-Thomson

model [11]. The Langmuir coefficient for physisorpion of an alkane i is calculated as follows:

, ,exp

fys

L i L i

HK A

RT

∆= −

(2-19)

The pre-exponential factor and the physisorption enthalpy for n-pentane are given for

different catalysts in Table 2-1 [12].

Table 2-1: Pre-exponential factor and physisorption enthalpy for n-pentane on several catalysts.[12]

Catalyst AL

[mol gcat-1 bar-1]

∆Hphys

[kJ mol-1]

BEA 3.88 10-8 -53,0

USY 3.9 10-7 -35.1


23

The physisorbed alkane i is dehydrogenated on the metal sites with formation of the

corresponding alkene j. The concentration of CO(i,j) of the alkene j is determined by means of

the (de)-hydrogenation equilibrium constant Kdehyd(Pi;Oi,j). This is possible because of the

ideal hydrocracking assumption. The (de)-hydrogenation step and the (de)-protonation step is

considered quasi-equilibrated.

( )

,

2

,;

i

i j

dehyd i i j P

O

H

K P O CC

p= (2-20)

The equilibrium coefficient ,

( ; )dehyd i i j

K P O is calculated using thermodynamical data obtained

by means of the Benson group contribution method.

As mentioned before, the (de)-protonation reactions are also assumed to be in quasi-

equilibrium. Therefore the concentration of the carbenium ion k corresponding to alkane i,

+),( kiR

C , can be calculated using the equilibrium coefficient );( ,, kijipr nOK .

++ =HOkijiprR

CCnOKCjiki ,),(

);( ,, (2-21)

A balance is applied to the Brønsted acid sites in order to determine the amount of free acid

sites +HC .

∑ ++ +=k

RHtotki

CCC,

(2-22)

Since the maximum concentration of carbenium ions is negligible [13], a low coverage of acid

sites by carbenium ions is assumed. Consequently the concentration of free acid sites can be

considered equal to the total amount of Brønsted acid sites. The experimental defined total

concentration of Brønsted acid site for different types of catalyst is shown in Table 2-2.

Table 2-2: Total amount of Brønsted acid sites for different types of catalysts.

Catalyst Ctot

[mmol gkat-1]

Pt/H-BEA 0.27

Pt/H-BEA S350 0.37

Pt/H-BEA S450 0.32

The expression for the concentration of carbenium ion k corresponding to alkane i can then be

written as:


24

ji

ki

ji

kiOprrefjiiso

R

O

RCnKOOKC

,

,

,

,)();( , ′′=

++ σ

σ (2-23)

Using equation (2-20) the concentration of the carbenium ions can also be expressed as a

function of the partial pressure of the alkane i and hydrogen.

The rate determining steps are the acid-catalyzed branching and cracking reactions, i.e. alkyl

shift, PCP-branching and β-scission. The rate of these steps is considered as being first order

in the carbenium ion concentration +kiR

C,

.

+=kiRtskiASPCPtskiASPCP Cnnknnr

,);();( ,,/,,/ (2-24)

+=kiRtskiyxtski CnnkOnnr

,);();;( ,,,,, ββ (2-25)

The net rate of formation iPR of an alkane i is determined based on two contributions. The

first contribution is the sum of the rates of the elementary steps in which the carbenium ion k

corresponding with alkane i is formed, minus the sum of rates in which the carbenium ion k is

consumed. The other contribution is the rate by which alkene j, corresponding with alkane i,

is directly formed from β-scission.

∑ ∑+= +k j

ORP jikiiRRR

,, (2-26)

With

∑∑∑∑

∑∑∑∑

∑∑∑∑

−

+−

+−=+

s tyxkits

s tyxkits

s tkitsAS

s tkitsAS

s tkitsPCP

s tkitsPCPR

OnnrOnnr

nnrnnr

nnrnnrRki

);;();;(

);();(

);();(

,,,,,,

,,,,

,,,,,

ββ

(2-27)

And

∑∑=s t

jiedtsO OnnrRji

);;( ,,,, β (2-28)

A remark that has to be made is that in the classical network the formation of primary

carbenium ions is not considered. This is because of their much lower compared to that of the

secondary and tertiary carbenium ions. The stability of the carbenium ions is reduced as the

number of substituents different from a hydrogen atom is lower: R3C+ >> R2CH+ >> RCH2

+.

The difference in stability between a tertiary and a secondary carbenium ion amounts to 54

kJ/mol. As for the difference between a secondary carbenium ion and a primary carbenium

ion is equal to 105 kJ/mol [14]. When only secondary and tertiary carbenium ions are


25

considered a β-scission reaction of a pentane carbenium ion cannot occur. Because of this, the

classical reaction network will only consist of n-pentane and iso-pentane.

Figure 2-10: Experimental molar flow for methane ( ), ethane ( ), propane ( ), n-butane ( ), iso-butane ( ), iso-pentane ( )as a function of temperature for Pt/H-BEA 0.6 wt% (VMB26: p=4 bar; molar H/C ratio= 47.4; W/F0=9.3

103 gcat s mol-1)

Figure 2-11: Experimental molar flow for iso-pentane ( ) and n-pentane( ) as a function of temperature for Pt/H-BEA 0.6 wt% at the exit of the reactor. (VMB26: p=4 bar; molar H/C ratio= 47.4; W/F0=9.3 103 gcat s mol-1)

As can be seen from Figure 2-10 and Figure 2-11, the effluent stream of the reactor also

consists of light alkane components (< C5). This means that the classical reaction network

cannot fully describe the process of hydroisomerization. Therefore in the next chapter, the

formation and reaction of primary carbenium ions is considered. The other possibility for the

formation of these lighter products can be found in the occurrence of a cracking reaction on

the metal sites, e.g. by hydrogenolysis. During these reaction methane or ethane can be

obtained [15].

0,0E+00

1,0E-07

2,0E-07

3,0E-07

4,0E-07

5,0E-07

260 280 300 320 340 360

Mo

lar

flo

w (

mo

l/s)

Temperature (°C)

0,0E+00

2,0E-07

4,0E-07

6,0E-07

8,0E-07

1,0E-06

1,2E-06

260 280 300 320 340 360

Mo

lar

flo

w (

mo

l/s)

Temperature (°C)


26

2.2.5 Regression

a Parameter Estimation Method

Once the microkinetic model has been developed, the parameters have to be estimated. A

commonly used technique for parameter estimation consists in minimizing the weighted sum

of squares of the residuals between the experimental and the model calculated outlet flow

rates. The minimization occurs by adjusting the model parameter b, which is expected to

approach the real parameter β vector when the optimum is reached. The sum of squares is

given by the equation [2]:

∑ ∑ →−== =

nobs

k

nresp

i

b

kikiiMinFFwSSQ

1 1

2

,,)ˆ(

(2-29)

In which jiF , stands for the experimentally observed outlet flow rate of response j in

experiment i. jiF ,ˆ represents the model calculated values. The outlet flow rates are used as

responses and not the net production rates in order to eliminate correlation between the

independent variables and the responses. Such a correlation is encountered when the net

production rates are used as responses because the outlet flow rates are then used to calculate

both the experimentally observed net production rates and the partial pressures used in the

model calculated net production rates [2].

In case of a normal distribution with zero mean of the experimental errors the weighting

factors iw are obtained as the diagonal elements of the inverse of the covariance matrix of the

experimental errors [2]. In general this matrix is not readily available and has to be estimated.

This is possible when at r different inlet conditions krn replicate experiments are available.

The weighting factor can then be obtained from:

( )

−−

= ∑∑

∑= =

=

r

k

n

i

kj

kijr

kk

j

k

FF

rn

w1 1

2,

1

1

(2-30)

With kijF , the experimental value of response j in experiment i under conditions k and with

kjF the mean value for response j under conditions k. If no replicate experiments are available


27

the weighting factor iw can be calculated as i-th diagonal element of the inverse matrix Σ-1 of

the error covariance matrix Σ [16]:

=Σ

nrespnresp

nresp

nresp

σσσ

σσσσσσ

⋯

⋮⋱⋮⋮

⋯

⋯

3231

22221

11211

(2-31)

For the statistical analysis performed by the program, only the diagonal elements of the error

covariance matrix are considered different from zero. The elements of the error covariance

matrix are estimated from [16]:

( )nparnrespnobs

yyyy jjiiij −×

−−=

)ˆ)(ˆ(σ (2-32)

Parameter estimation was performed using a combination of a Rosenbrock and a Marquardt

algorithm. Since the Rosenbrock method has a smaller chance to diverge when the parameter

values are far from the optimum, this method is applied first to find an appropriate direction

leading to a possible optimum. In order to prevent the combined Rosenbrock Marquardt

search from arriving in a local optimum a cycle of a few Rosenbrock Marquardt searches is

performed until the residual sum of squares obtained from both methods is identical and does

not improve significantly with variations in the parameters [2, 16].

For the Rosenbrock method an in-house written code was used, while for the Marquardt

algorithm the ‘ordinary least squares’ (OLS) option of the ODRPACK-package version 2.01

was used. Some additional source code was added to ODRPACK in order to retrieve

additional statistical information.

b Statistical analysis

Once the regression is performed, several statistical tests are performed in order to investigate

the significance of the regression and parameter estimates [17, 18].

The significance of the regression is verified by the F-test, which compares the regression

sum of squares and the residual sum of squares [18]:


28

1 1 1

1 1 1

ˆ ˆ

ˆ ˆ( )( )

nresp nresp nobjk

ij ikj k i

C nresp nresp nobjk

ij ij ik ikj k i

y y

nparF

y y y y

nob nresp npar

σ

σ

= = =

= = =

=− −

∗ −

∑ ∑ ∑

∑ ∑ ∑

(2-33)

The regression is considered meaningful if the ratio is larger than the tabulated α-percentage

point of the F distribution with npar and (nobs x nresp - npar) degrees of freedom [2]. α is

taken as 0.05, meaning 95% probability level.

The t-test is applied to verify the significance of the parameters with respect to a reference

value, which is usually zero, when the rest of the parameters are kept at their optimal value

[18]:

( )

j j

c

jj

bt

V b

β−=

(2-34)

Where j

b is the estimate, j

β is the reference parameter value, and ( )jj

V b the j-th diagonal

element of the variance-covariance matrix of the parameter estimates defined by [18]:

( )1

1 1

nresp nrespjk T

j kj k

V b J Jσ−

= =

= ∑ ∑

(2-35)

With i

J the Jacobian matrix of the response j

y with respect to the parameter b:

( )j

j

y bJ

b

∂ =

∂

(2-36)

The confidence interval is defined as the limits at the probability level 1-α on which the

estimates do not significantly differ from the optimal value j

b [18]:

( ) ( ),1 ,12 2j j jjj jj

b t nob nresp npar V b b t nob nresp npar V bα αβ

− × − − ≤ ≤ + × − −

(2-37)

With α taken again as 0.05, namely 95% confidence interval.

Finally, binary correlation coefficients are used to investigate possible correlations between

the parameter values:


29

( )

( ) ( )jk

jk

jj kk

V b

V b V bρ =

(2-38)

Absolute values for the correlation coefficients close to unity imply strong linear relationship

between the estimated values of the corresponding parameter j and k. The value of the

parameter i determines the value of parameter j to a proportional, 1≈ρ or inverse

proportional 1−≈ρ , extent without changing the calculated responses and, hence, the

residual sum of squares in a significant way [2].

Hydroisomerization of n-pentane: Single-event approach 2.3: References

30

2.3 References

[1] Feng, W., E. Vynckier, and G.F. Froment, Single-Event Kinetics of Catalytic Cracking. Industrial & Engineering Chemistry Research, 1993. 32(12): p. 2997-3005.

[2] Thybaut, J.W., Production of low-aromatic fuels: kinetics and industrial application of

hydrocracking, PhD thesis, 2005,Ghent University

[3] Langlois, G.E. and R.F. Sullivan, Chemistry of Hydrocracking. Advances in Chemistry Series, 1970(97): p. 38-&

[4] Keller, V., F. Garin, and G. Maire, Study of the isomerization of C-13 labelled

methylpentanes on oxygen modified bulk tungsten carbides. Physical Chemistry Chemical Physics, 2000. 2(13): p. 2893-2902

[5] Becker, A., Gasfase hydroïsomerisatie en hydrokraking van koolwaterstoffen in een

Berty-reactor, 1995,Ghent University [6] Woltz, C., A. Jentys, and J.A. Lercher, Improving bifunctional zeolite catalysts for

alkane hydroisomerization via gas phase sulfation. Journal of Catalysis, 2006. 237(2): p. 337-348

[7] Vynckier, E., Kinetische modellering van de katalytische hydrokraking, 1997,Ghent

University [8] Narasimhan, C.S.L., et al., Kinetic modeling of pore mouth catalysis in the

hydroconversion of n-octane on Pt-H-ZSM-22. Journal of Catalysis, 2003. 220(2): p. 399-413.

[9] Winzor, D.J. and C.M. Jackson, Interpretation of the temperature dependence of rate

constants in biosensor studies. Analytical Biochemistry, 2005. 337(2): p. 289-293 [10] Martens, G.G., J.W. Thybaut, and G.B. Marin, Single-event rate parameters for the

hydrocracking of cycloalkanes on Pt/US-Y zeolites. Industrial & Engineering Chemistry Research, 2001. 40(8): p. 1832-1844

[11] Aalto, M., et al., An improved correlation for compressed liquid densities of

hydrocarbons .1. Pure compounds. Fluid Phase Equilibria, 1996. 114(1-2): p. 1-19. [12] Denayer, J., Adsorption and reaction on zeolites: an integrated approach, PhD

Thesis, 1998,Vrije Universiteit Brussel [13] Thybaut, J.W., et al., Alkene protonation enthalpy determination from fundamental

kinetic modeling of alkane hydroconversion on Pt/H-(US)Y-zeolite. Journal of Catalysis, 2001. 202(2): p. 324-339

Hydroisomerization of n-pentane: Single-event approach 2.3: References

31

[14] Baltanas, M.A., et al., Fundamental Kinetic Modeling of Hydroisomerization and Hydrocracking on Noble-Metal-Loaded Faujasites .1. Rate Parameters for Hydroisomerization. Industrial & Engineering Chemistry Research, 1989. 28(7): p. 899-910

[15] Govaerts, S., Ondersteuning van de ontwikkeling en optimalisering van katalysatoren

met behulp van fundamenteel kinetisch modellen, Master Project, 2007,Ghent University

[16] Lozano, G., Single-Event Microkinetics for Metal Catalysis: Fischer-Tropsch

Synthesis, 2007,Ghent University [17] Froment, G.F. and K.B. Bischoff, Chemical reactor analysis and design. 2nd ed.

1990, Wiley: New York [18] Thybaut, J.W., Chemometrie en ontwerp van Experimenten. 2008: Universiteit Gent

32

Chapter 3

Experimental Program

Abstract: This chapter gives an overview of the different experimental reactor set ups. The

preparation and the properties of the catalysts used for performing the experiments are

described in detail. Experimental results are given and analyzed.

3.1 20-fold parallel plug flow reactor

3.1.1 Experimental set up

The kinetic investigations on alkane hydroisomerization at the University of Munich were

carried out using a 20-fold parallel flow reactor system, schematically shown in Figure 3-1.

The setup allows to investigate the catalytic activity and selectivity in a pressure range

between 1 and 50 bar, flow rates between 5 and 100 ml/min and a temperature range up to

450°C [1].

For hydroisomerization, liquid hydrocarbons are mixed with the hydrogen in an digital

controlled mixer-evaporator which is operated at a temperature of 120°C. Flow and pressure

are controlled for each reactor individually by using electronic mass flow (MFC) and back

pressure regulators (BPR) . The analysis of the bypass and product stream is carried out using

a HP-micro gaschromatograph. A more detailed description of this reactor system is given

elsewhere [1].

Experimental Program 3.1: 20-fold parallel plug flow reactor

33

Figure 3-1: Schematic representation of the 20-fold parallel plug flow reactor [1]

3.1.2 Catalyst

Typical hydrocracking catalysts consist of a metal function deposited on an acidic support. In

this project platinum was selected as metal function because of its excellent (de)-

hydrogenation performance [2].

a Catalyst Preparation

Zeolite BEA 25 (Si/Al=12.5) from Süd-Chemie AG was loaded with Pt at concentrations

between 0.2 and 2.3 wt % by ion-exchange with aqueous Pt(NH3)4(OH)2 solution [1]. A

solution containing the appropriate amount of Pt(NH3)4(OH)2 and an amount of NH4OH

corresponding to the theoretical concentration of protons (competitive adsorption) in the

sample was added drop wise to the slurry at 40°C in order to exchange the cations of the

MF

C 2

MF

C 4

MF

C 3

MF

C 6

MF

C 5

MF

C 8

MF

C 7

MF

C10

MF

C 9

MF

C 3

MF

C 12

MF

C 14

MF

C 13

MF

C 16

MF

C 15

MF

C 18

MF

C 17

MF

C 20

MF

C 19

MF

C 11

MF

C 2

MF

C 4

MF

C 3

MF

C 6

MF

C 5

MF

C 8

MF

C 7

MF

C10

MF

C 9

BP

R1

BP

R2

BP

R3

BP

R4

BP

R5

BP

R6

BP

R7

BP

R8

BP

R9

BP

R10

BP

R11

BP

R12

BP

R13

BP

R14

BP

R15

BP

R16

BP

R17

BP

R18

BP

R19

BP

R20

Micro GC

Helium

Hydrogen

Hydrogen

FeedC

5

MFC 1

FeedC5

Mixer

Evaporator

MFC [1..20]PR [1..20]Valve PVTemp.Konz Feed C5

4PV14PV2

10PV1

10PV2

4PV3

H2 Konz [C1..C6]

MF

C 2

MF

C 4

MF

C 3

MF

C 6

MF

C 5

MF

C 8

MF

C 7

MF

C10

MF

C 9

MF

C 3

MF

C 12

MF

C 14

MF

C 13

MF

C 16

MF

C 15

MF

C 18

MF

C 17

MF

C 20

MF

C 19

MF

C 11

MF

C 2

MF

C 4

MF

C 3

MF

C 6

MF

C 5

MF

C 8

MF

C 7

MF

C10

MF

C 9

BP

R1

BP

R2

BP

R3

BP

R4

BP

R5

BP

R6

BP

R7

BP

R8

BP

R9

BP

R10

BP

R11

BP

R12

BP

R13

BP

R14

BP

R15

BP

R16

BP

R17

BP

R18

BP

R19

BP

R20

Micro GC

Helium

Hydrogen

Hydrogen

FeedC

5

MFC 1

FeedC5

Mixer

Evaporator

MFC [1..20]PR [1..20]Valve PVTemp.Konz Feed C5

4PV14PV2

10PV1

10PV2

4PV3

H2 Konz [C1..C6]


34

zeolite to obtain the metal loaded H+-form of the zeolite. After the ion exchange the solid was

centrifuged, washed and freeze dried. The samples were calcined in air at 350°C for 16 h

(heating rate 0.5°C/min) and finally reduced at 300°C in H2 for 4 h. The samples are referred

to as Pt/H-BEA.

The effect of sulfation of the catalyst was analyzed for two different sulfation temperatures

(350 and 450 °C). These catalyst are called respectively Pt/H-BEA S350 0.6 wt% and Pt/H-

BEA S450 0.6 wt% [1].

b Properties

The number of platinum atoms at the surface is determined by hydrogen chemisorption. For

the calculation of this fraction the assumption was made that only one hydrogen atom adsorbs

on each platinum atom.

The determination of the pore volume was carried out by the physisorption of nitrogen, using

the t-plot method. A detailed description of the methods used for characterization of the

different catalysts can be found elsewhere [1].

The characteristics of the different catalysts used are given in Table 3-1.

Table 3-1: Characteristics of Pt/H-BEA 0.6 wt%, Pt/H-BEA S350 0.6 wt% and Pt/H-BEA S450 0.6 wt% [2]

Pt

[wt%]

Brønsted

acid sites

[mmol/gcat]

Lewis

acid sites

[mmol/gcat]

Surface

Pt atoms[a]

[mol/mol]

Pore

volume[b]

[cm³/gcat]

Pt/H-BEA 0.6 0.27 0.27 0.63 110

Pt/H-BEA S350 0.6 0.37 0.27 0.10 102

Pt/H-BEA S450 0.6 0.32 0.27 0.06 105 [a] Determined by hydrogen chemisorption [b] Determined by the t-plot method by nitrogen adsorption

Experimental Program

3.1.3 Experimental results

Figure 3-2: Selectivity of the iso-products with respect

Figure 3-2 gives a graphical representation of the pentane and hexane isomerization results

obtained by the university of Munich. From the pentane isomerization

selectivity for iso-pentane decreases as the concentration of metal phase in the zeolite

increases.

The selectivity decreases as the conversion increases. This is because the concentration of

normal pentane decreases with increasing

iso-pentane to be cracked in smaller products.

When comparing the results for pentane and hexane, the selectivity for the same amount of

metal phase is larger for hexane then for pentane. This can be expla

reaction network between the two hydrocarbons. The reaction mechanism for hexane is more

extensive than for pentane. Hexane has two different types of isomers (2

3-methylpentane), while pentane has only one (2

As mentioned above, three catalysts will be considered further on in

BEA 0.6 wt%, Pt/H-BEA S350 0.6 wt% and Pt/H

pentane and the selectivity to iso

analyzing the molar content of the outlet stream

conditions are summarized in

Table 3-4 for each of the considered catalysts. The specific inlet

more detail in appendix A.

3.1: 20-fold parallel plu

results

products with respect to the conversion of n-pentane (left) and ndifferent types of catalysts.

gives a graphical representation of the pentane and hexane isomerization results

obtained by the university of Munich. From the pentane isomerization it can be seen that the

pentane decreases as the concentration of metal phase in the zeolite


with increasing conversion, therefore enhancing the possibility for

pentane to be cracked in smaller products.


metal phase is larger for hexane then for pentane. This can be explained by the difference in


extensive than for pentane. Hexane has two different types of isomers (2-

methylpentane), while pentane has only one (2-methylbutane).

As mentioned above, three catalysts will be considered further on in the present work

BEA S350 0.6 wt% and Pt/H-BEA S450 0.6 wt%. The conversion of n

pentane and the selectivity to iso-pentane were determined for each of these catalysts by

analyzing the molar content of the outlet stream at different reaction conditions. The inlet

Table 3-2, Table 3-3 and

for each of the considered catalysts. The specific inlet conditions are describe

fold parallel plug flow reactor

35

pentane (left) and n-hexane (right) on

gives a graphical representation of the pentane and hexane isomerization results

can be seen that the

pentane decreases as the concentration of metal phase in the zeolite


onversion, therefore enhancing the possibility for


ined by the difference in


-methylpentane and

the present work: Pt/H-

BEA S450 0.6 wt%. The conversion of n-

f these catalysts by

reaction conditions. The inlet

conditions are described in


36

Table 3-2: Inlet conditions for the hydroisomerization of n-pentane over Pt/H-BEA 0.6 wt%

Experiment Series

Catalyst weight [mg]

Temp [°C]

Total pressure

[bar]

Molar ratio H2/HC

[-]

Space-time W/F0 [10³

gcats/mol]

VMB01 30 260-351 4 38.6 25.9

VMB02 30 30 30

280 280 280

5 7.5 10

11.7-33.9 18-50.3 24-66.9

38.8-73.4 34.1-58.2 30.3-48.5

VMB03 30

30 30 30 30 30

280 280 280 280 280 280

12.5 15

17.5 20

22.5 25

24.3-41.6 28.9-51.2 33.7-58.1 38.4-66.2 43.3-74.9 47.2-82.7

24.4-32.3 22.4-29.3 20.7-26.4 19.3-24.2 18.1-22.4 16.9-20.7

VMB04 30

30 30 30 30 30 30 30 30 30 30 30 30

280 280 280 280 280 280 280 280 280 280 280 280 280

5 7 9 11 13 15 17 19 21 23 25 27 29

53.9 52.4 51.7 51.7 49.2 48.6 48.3 47.9 47.5 47.6 47.3 47.1 47.3

88.8 62.8 48.6 39.8 33

28.4 25

22.3 20.1 18.4 16.9 15.6 14.5

VMB17 19.8 320 4 39.7 25.8

VMB26 19.8 260-338 4 47.7 9.3

VMB27 19.8

19.8 19.8

280 300 320

4 4 4

39.2 39.2 39.2

8.4-52.4 8.5-26.5 8.4-25.8

In the first set of experiments (VMB01), the influence of the temperature on the conversion of

n-pentane and on the selectivity towards iso-pentane is shown in Figure 3-3. The other inlet

conditions remain constant. At increasing temperatures the conversion of n-pentane increases.

This is a logical consequence of the Arrhenius equation for the rate coefficient:


37

1

exp( )kT

−∼ (3-1)

As the temperature increases, the rate coefficient will increase as well.

The isomerization yield also increases slightly in the beginning, but decreases however from

300°C onwards. This can be explained by the large conversion at high temperatures. The

possibility that isomers act as reactants gets larger, thereby decreasing the isomer yield.

Figure 3-3: Experimental n-pentane conversion and iso-pentane selectivity on Pt/H-BEA 0.6 wt% (p=4 bar;H 2/HC=38.6;W/F0=25.9 10³ gcat s mol-1).

In the last set of experiments (VMB27), the influence of the space-time on the conversion of

n-pentane and on the isomerization yield is examined at three different temperatures, i.e.

280°C, 300°C and 320 °C, while the other inlet conditions remain constant.

Figure 3-4: Experimental n-pentane conversion and iso-pentane selectivity on Pt/H-BEA 0.6 wt%

(p=4 bar; H2/HC =39 and T=280°C).

The conversion of n-pentane increases with increasing space-time. High space-times

correspond to high average residence times of the molecules in the catalyst pores. This

0,0

20,0

40,0

60,0

80,0

100,0

260 310

Co

nv

ers

ion

n-p

en

tan

e (

%)

Temperature (°C)

0

20

40

60

80

260 280 300 320 340

Se

lect

ivit

y i

so-p

en

tan

e (

%)

Temperature (°C)

0,0

20,0

40,0

60,0

80,0

0 20 40 60Co

nv

ers

ion

n-p

en

tan

e

(%)

Space-time W/F0 (10³ gcats/mol)

0

10

20

30

40

50

60

0 20 40 60

Se

lect

ivit

y i

so-p

en

tan

e

(%)

Space-time W/F0 (10³ gcats/mol)


38

implies that n-pentane molecules are more likely to react, which ultimately results in high

conversions. However, the probability for iso-pentane to be cracked into smaller products

increases as well under the same circumstances. Therefore, the isomerization yield will be

influenced in an opposite way with increasing space-times.

Figure 3-5: Conversion of n-pentane as a function of the total pressure for the hydroisomerization of n-pentane on Pt/H-BEA 0.6 wt% zeolite. Left: exp 25&26 VMB02, exp 5&6 VMB04. Right: exp 9&10 VMB04, exp 11&12 VMB03

and exp 17 & 18 VMB03

The conversion of n-pentane increases at low pressure, but decreases at high pressure when

inlet flows and temperature remains constant, as shown in Figure 3-5. This phenomenon will

be further investigated in section 6.2. It is difficult to investigate the influence of the pressure

using the experiments obtained at TUM because of the lack of experiments with equal inlet

flows. In order to properly investigate the influence of the pressure, a new data set has to be

developed in which only the pressure is varied. This is considered to be future work.

Table 3-3: Inlet conditions for the hydroisomerization of n-pentane over Pt/H-BEA S350 0.6 wt%

Experiment Series


Temp [°C]

Total pressure

[bar]

Molar ratio H2/HC

[-]

Space-time W/F0

[10³ gcats/mol]

VMB17 19.8 19.8

320 320

4 4

39.7 41.0

25.8 52.4

VMB26 19.8 260-344 4 46.9-48.7 9.3

VMB27 19.8 19.8 19.8

280 300 320

4 4 4

39.5 39.4 39.5

8.4-52.4 8.5-51.7 8.4-52.4

20,0

25,0

30,0

35,0

7 8 9 10

Co

nv

ers

ion

n-p

en

tan

e (

%)

Total pressure (bar)

0,0

5,0

10,0

15,0

20,0

25,0

11 13 15 17

Co

nv

ers

ion

n-p

en

tan

e (

%)



39

Table 3-4: Inlet conditions for the hydroisomerization of n-pentane over Pt/H-BEA S450 0.6 wt%

Experiment Series


Temp [°C]

Total pressure

[bar]

Molar ratio H2/HC

[-]

Space-time W/F0 [10³

gcats/mol] VMB01 30 260-351 4 38.6 26.0

VMB02 30 30 30

280 280 280

5 7.5 10

11.7-33.9 18-37.1 24-66.9

39.1-73.4 34.4-51.1 30.7-48.5

VMB03

30 30 30 30 30

280 280 280 280 280

12.5 17.5 20

22.5 25

41.6 42.7

38-66.2 43.3-74.9 47.2-82.7

32.3 23.3

19.5-24.2 18.3-22.4 17.0-20.7

VMB04

30 30 30 30 30 30 30 30 30 30 30 30 30

280 280 280 280 280 280 280 280 280 280 280 280 280

5 7 9 11 13 15 17 19 21 23 25 27 29

53.9 52.4 51.7 51.7 49.2 48.6 48.3 47.9 47.5 47.6 47.3 47.1 47.3

89.7 63.4 49.1 40.1 33.3 28.7 25.3 22.6 20.3 18.6 17.0 15.8 14.7

In Figure 3-2 the selectivity obtained on different types of catalysts are compared. When

comparing the selectivity to isopentane for hydroisomerization on a PT/H-BEA 0.6 wt%

catalyst and on the sulfated version, a increasement of the selectivity to almost 100 % is

noticed. Investigation was performed by Woltz [1] on the effect of sulfur on the catalyst. A

brief summary of his findings are given now.

Figure 3-6 shows an Arrhenius plot of the catalytic activity of the parent Pt/BEA and the

sulfidated samples at a total pressure of 4 bar, a WHSV of 30 hr-1 and at temperatures

between 260 and 350°C. In general, a higher isomerization rate was observed with decreasing

sulfation temperature. Increasing the sulfation temperature to 550°C even leads to a reduction

of the isomerization rate compared with that of the parent material. The apparent activation


40

energies vary between 102 and 110 kJ/mol. The subtle variations in the apparent energy of

activation and the larger variations in the composed pre-exponential factors suggest that the

sulfate treatment mainly resulted in a change in the concentration of the (Brønsted) acid sites.

Treatment with H2S and subsequent oxidation results in a significantly decreased amount of

metal surface atoms able to chemisorb H2. Therefore, it can be concluded that sulfation leads

to poisoning of a large fraction of the surface atoms with sulfur [2]. In addition, the Pt

particles sinter to an increasing extent as the treatment temperature rises to 450 and 550°C.

Figure 3-6: Isomerization activity of Pt/H-BEA (104 kJ/mol) (x), Pt/BEA S350 (110 kJ/mol) (◊), Pt/BEA S450 (109 kJ/mol) (□) and Pt/BEA S550 (102 kJ/mol) (∆) [2].

The influence of the sulfur treatment on the acid sites consists of a reduction of the

concentration of the strongest acid sites, because these will bond with sulfur, and in an

increase of the amount of sites of weak and moderate acid strength. The increase of the

concentration of Brønsted acid sites is caused by one or two effects: the formation of new

Brønsted-acid OH groups originating from sulfate groups, or the removal of cationic alumina

species from proton exchange sites making zeolite Si-OH-Al groups accessible [2].

The enhancement of the iso-pentane selectivity can be explained by two possible routes:

bifunctional hydrocracking or metal-catalyzed hydrogenolysis. As mentioned before, the

metal sites take care of the dehydrogenation of alkanes to alkenes, while isomerization and

cracking reactions occur on the acid sites. The increase in isomerization yield after sulfation is

then caused by the reduced strength of the Brønsted acid sites as proved by TPD experiments

with ammonia. These acid sites retain less alkenes, leading to a lower fraction of cracked

molecules. Because the changes in the distribution of acid sites are rather subtle, it is however

Experimental Program 3.2: Vapour phase continuous stirred tank reactor

41

difficult to accept that such a small change leads to such a pronounced modification of the

catalytic properties [2].

Hydrogenolysis, the second possible reaction pathway to light alkanes, occurs only on the

metal sites. A reduction in available metal surface atoms would lead to a severely reduced rate

of this structure-sensitive reaction. It has been argued that hydrogenolysis requires larger

ensembles of metal atoms, or the presence of highly uncoordinated metal atoms, because the

reaction involves dehydrogenated intermediates with multiple bonds to the metal particles.

Both free ensembles of Pt atoms and highly reactive and exposed metal atoms would be

dramatically reduced by the presence of sulfur on the metal.

In contrast, hydrogenation/dehydrogenation is less demanding with respect to the number,

arrangement, and reactivity of metal surface atoms. It is therefore more likely that sulfur

treatment reduces the amount of active metal sites in such a way that the arrangement

necessary for hydrogenolysis is disturbed, while on the other hand the concentration is still

sufficiently high to maintain the hydrogenation/dehydrogenation equilibrium. However, on

Pt/H-BEA S550 0.6 wt% the concentration of metal sites is too low for

hydrogenation/dehydrogenation equilibrium which results in a lower isomerization yield as

shown on Figure 1-7.

3.2 Vapour phase continuous stirred tank reactor

3.2.1 Experimental set up

A schematic representation of the Berty set up is given in Figure 3-7. The symbols used in the

latter are given in Figure 3-8. Four different sections can be distinguished: the feed section,

the reaction section, the effluent section and the analysis section.


42

Figure 3-7: Schematical representation of the berty set up

TI

PI

PI

TI

FI

PIC

PI

PIC

AIR

PI

PIC

PS

VP

SV

TC

TC

TI

TC

FI

PIC

12

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

212

2

TI

H

2

PI

PIC

FIC

3

bala

nce

FIC

N

2

PI

PIC

C

H4

PI

PIC

FIC

H

2

PI

PIC N

2

PI

PIC

N

2


43

Figure 3-8: Symbols used in the schematic representation of the Berty reactor shown in Figure 3-7.

a Feed Section

The liquid hydrocarbon feed (1) is pumped to the reaction section using an HPLC pump (High

Pressure Liquid Chromatography) (2). Liquid flow rates can be adjusted between 10 µmol s-1

and 500 µmol s-1. The viscosity of the feed determines the upper flow rate. In order to avoid

too low maximum flow rates for heavy components, the feed line can be heated to reduce the

viscosity of the feed. The hydrogen and nitrogen flow rates are controlled using Brooks

thermal mass flow controllers in the range of 5 to 100 µmol s-1 for hydrogen (3) and of 50

µmol s-1 to 1 mmol s-1 for nitrogen (4). Both gas flows are mixed and the majority of the

mixture is sent to the reaction section via a mixer/evaporator/preheater (6) where it is mixed

with the evaporating hydrocarbons and preheated to a typical temperature of 473 K. The

remaining part of the hydrogen/nitrogen mixture enters the reaction section via the shaft of the

magnetic drive assembly to cool it and to prevent hydrocarbon condensation in that shaft.

b Reaction Section

The high pressure reactor (8) is of the Berty type constructed by Autoclave Engineers. A

magnetic driven impeller (11) induces an internal recycle flow pattern in the reactor going

TC

PI Pressure Indicator

TI Temperature Indicator

FI Flow Indicator

Valve

PSV Pressure Safety Valve Heated line

Check valve

Filter

Thermocouple Control line

BP Backpressure RegulatorPIC Membrane Backpressure

Controller


44

upward between the catalyst basket (9) and the reactor wall and going down through the

catalyst basket (10). The gaseous hydrogen/nitrogen/hydrocarbon mixture enters the reactor

just above the blades of the impeller, while the effluent leaves the reactor at the bottom under

the impeller. If a uniform flow through the catalyst bed is established and a recycle ratio of at

least 20 is obtained, the Berty reactor can be modeled as a continuous stirred tank or a mixed

flow reactor. Typically the impeller is set to revolve at a speed of 1500 rpm. The temperature

in the reactor is maintained by a heating cap (12) containing three heating elements of 500 W

each controlled by two PID controllers (13) and (14) connected to two thermocouples

measuring the temperature just on top of and below the catalyst basket. A third thermocouple

is used as a safety control to measure the external wall temperature of the reactor. It is

connected to an on-off switch ensuring that the temperature will not rise above a certain safety

level. The sealing between the reactor body and cover is ensured by the use of a ductile

aluminum gasket. Due to its high ductility, the gasket needs to be replaced after tightening the

reactor screws a few times.

c Effluent and Analysis Section

The reactor effluent passes through a filter (15) before being mixed with the internal standard

methane. The molar methane (99,95 vol% L’Air Liquide) flow rate is controlled with a

Brooks thermal mass flow controller (5) in the range 5 to 100 µmol s-1 and is taken equal to

the molar hydrocarbon feed flow rate. The mixture of the reactor effluent and the internal

standard is split into two flows. The major flow is directly sent to a condenser (17), while a

minor flow passes through a six-way sampling valve (16) before being sent to the condenser.

In the condenser the major part of the hydrocarbons condenses and is kept in a collector. The

uncondensed part of the reactor effluent flows through the back pressure regulator (18) which

is used to keep the installation under the desired pressure and is sent to the vent afterwards

(20) [3].

A 20 µl sample of the reactor effluent is sent on-line to a gas chromatograph (GC Hewlett

Packard 5890 series II) (21) by changing the position of the six-way valve. A capillary

column of 60 m and internal diameter 0.25 mm with a 1 µm thick polydimethylsiloxane film

is used to separate the various hydrocarbons in the mixture. With a cryogenic cooling

equipment (22) it is possible to work at temperatures lower than room temperature improving

the separation of light components. An FID-detector is used in the GC-analysis. The signal


45

generated by the detector is sent to a local PC where the XChrom package performs the

integration of the chromatogram [3].

3.2.2 Catalyst

a Catalyst Preparation

MC-301 is available in powdered form and has to be converted to granulates before it can be

used in the reactor. This is done by first pressing the powder forming a pellet. This pellet is

then converted to granulates by a set of sieves. A sieve with a grid of 0.7 mm is located on top

of a sieve with a grid of 0.4 mm. The pellet starts at the top. The granulates between the first

and the second sieve have the right size and can be used to construct the catalyst bed.

Once the catalyst is pelletized, the dry weight has to be determined. Therefore, the catalyst is

introduced in the oven to remove all the water present.

Once the preparation of the catalyst is finished the catalyst bed can be made [3, 4]. The

catalyst bed consists of the catalyst granulates and inert granulates and has a layered structure.

Onto the carrying net of the catalyst basket a layer of inert granulates of intermediate size is

introduced. On top of this layers of inert granulates with the same size as the catalyst

granulates are alternated with layers of catalyst granulates. At the end another layer of

intermediate sized inert granulates is introduced.

The last step in the preparation is the reduction of the catalyst. This is performed in the reactor

at a slightly high pressure and at a temperature of 400 °C.

b Properties

The experiments on the Berty reactor are performed using a commercial hydrocracking

catalyst, denoted as MC-301. This catalyst is derived from Lind LZ-Y20, a H-USY zeolite

with a total Si/Al ratio of 2.6, a framework Si/Al ratio of 28, a unit cell constant of 2.431 nm

and a pore volume of 0.31 x 10-³ m³/kg. Platinum was introduced via ion exchange with

Pt(NH3)4Cl2. MC-301 is a pure zeolite in which no binder is present. The total concentration

of Bronsted acid sites Ct, is approximated by the concentration of framework aluminium

atoms [5]. The specifications for MC-301 are given in Table 3-5.


46

Table 3-5: Specifications of MC-301 [3]

Catalyst MC-301

Pt content (%wt) 0.5

α activity 53

Total Brønsted acid sites (mol/kgcat) 0.425

3.2.3 Experimental results

As mentioned above the experiments on the Berty reactor set up were performed using MC-

301, a Pt/USY zeolite. The experiments are performed with n-hexane as feed component.

The inlet conditions for the experiments are summarized in Table 3-6. The specific inlet

conditions and outlet flows are given in appendix B.

Table 3-6: Inlet conditions for the hydroisomerization of n-hexane over MC-301

Catalyst weight

[g]

Temperature [°C]

Total pressure

[bar]

Molar ratio H2/HC

[-]

Space-time [gcat s/ mol]

6.67 319.85 5 50 260.748 6.67 319.85 5 75 260.748 6.67 319.85 5 100 260.748 6.67 319.85 5 50 260.748 6.67 310 5 50 173.808 6.67 314 11 50 173.808 6.67 314 10 75 173.808 6.67 313 6 75 173.808 6.67 313 6.5 100 173.808 6.67 313 12 100 173.808 6.67 312 4.5 50 260.748 6.67 312 6 75 260.748 6.67 312 10.5 75 260.748 6.67 314 11 100 260.748 6.67 326 10 50 260.748 6.67 323 5 50 260.748 6.67 323 5 75 260.748 6.67 322 11 75 260.748 6.67 323 11 100 260.748 6.67 322 5 100 260.748


47

6.67 321 10.5 25 130.356 6.67 324 5 25 130.356 6.67 323 6 50 130.356 6.67 323 11 50 130.356 6.67 323 12 75 130.356 6.67 323 6 75 130.356 6.67 322 4 25 173.808 6.67 356 10 25 173.808 6.67 362 10 50 173.808 6.67 360 10.5 50 173.808 6.67 359.85 10 50 260.748 6.67 359.85 10 75 260.748 6.67 359.85 10 100 260.748 6.67 359.85 15 50 260.748

Figure 3-9 shows the conversion as a function of temperature. The conversion increases with

temperature as can be expected according to Figure 3-5 (see section 3.1.3). When comparing

this graphic to Figure 3-3 for n-pentane on a plug flow reactor the conversion in this case is

much lower and higher temperatures are necessary to obtain small conversions for n-hexane.

This can be on the one hand explained by the fact that n-hexane is a heavier component than

n-pentane, but the main reason lies on the reactor used for performing the experiments.

Figure 3-9: Experimental n-hexane conversion on MC-301 at p=5 bar;H2/HC=50;W/F0= 261 103 gcat s mol-1.

Figure 3-10 compares the conversion obtained in a stationary CSTR with the conversion

obtained in a stationary plug flow reactor for the same first order kinetics. The higher

conversion in the case of the plug flow accounts for each positive reaction order. This

explains the lower conversion of n-hexane in comparison with n-pentane at the same reaction

conditions.


48

Figure 3-10: Concentration of the feed component CA and conversion of the feed component XA for a plug flow

reactor (a) and a CSTR reactor (b) for irreversible first order kinetics[6].

The selectivity to 2-methyl-pentane and 3-methyl-pentane as a function of temperature is

shown in Figure 3-11. The selectivity is slightly decreasing with increasing temperature as a

consequence of the increasing conversion.

Figure 3-11: Experimental selectivity for 2-methyl-pentane (right) and 3-methyl-pentane (left) as a function of

temperature on MC-301 at p=5 bar;H2/HC=50;W/F0= 261 103 gcat s mol-1.

The selectivity to 2-methyl-pentane is much higher than to 3-methyl-pentane. The explanation

here lies on the number of reaction pathways in which the component can be formed. 2-

methyl-pentane can be formed by the addition of a methyl branch on the second or the fourth

carbon atom of pentane. 3-methyl-pentane can only be formed by the addition of a methyl

chain on the third carbon atom of pentane.

55

57

59

61

63

65

310 315 320 325

Se

lect

ivit

y f

or

2-m

eth

yl-

pe

nta

ne

(%

)

Temperature (°C)

35

36

37

38

39

40

310 315 320 325

Se

lect

ivit

y f

or

3-m

eth

yl-

pe

nta

ne

(%

)

Temperature (°C)


49

Figure 3-12: Experimental conversion of n-hexane as a function of total pressure on MC-301 at T=323°C,

H2/HC=50;W/F0= 261 103 gcat s mol-1.

Figure 3-12 shows the n-hexane conversion as a function of total pressure. The conversion

increases with the pressure, which indicates that the experiments are performed under non-

ideal hydrocracking conditions. In order to obtain a data set useful for the estimation of the

model parameters, experiments still have to be performed at higher pressures.

Figure 3-13: Experimental n-hexane conversion as function of space-time at p=6bar, T=312 °C, H2/HC=75

As shown in Figure 3-13,the conversion increases with increasing the space-time as can be

explained in section 3.1.3. The longer the components stay in the reactor, the higher reactivity

for this components. The increasing conversion with increasing space-time leads to the

decreasing selectivity towards the isomerization products as can be seen in Figure 3-14.

13,4

13,6

13,8

14,0

14,2

14,4

4 6 8 10 12Co

nv

ers

ion

of

n-h

ex

ane

(%)


0,00

2,00

4,00

6,00

8,00

10,00

12,00

150 200 250 300Co

nve

rsio

n o

f n

-he

xan

e (

%)

Space time (gcat s mol-1)

Experimental Program 3.3: References

50

Figure 3-14: Experimental selectivity to 2-methyl-pentane (right) and 3-methyl-pentane (left) as function of space-

time at p=6bar, T=312 °C, H2/HC=75

3.3 References

[1] Woltz, C., Kinetic studies on alkane hydroisomerization over bifunctional catalysts, PhD Thesis, 2005,Technischen Universität München

[2] Woltz, C., A. Jentys, and J.A. Lercher, Improving bifunctional zeolite catalysts for

alkane hydroisomerization via gas phase sulfation. Journal of Catalysis, 2006. 237(2): p. 337-348

[3] Thybaut, J.W., Production of low-aromatic fuels: kinetics and industrial application

of hydrocracking, PhD thesis, 2005,Ghent University [4] Becker, A., Kinetische modellering van hydroisomerisatie en hydrokraken van

koolwaterstoffen op een Pt/US-Y zeoliet, PhD Thesis, 1997,Ghent university [5] Martens, G.G., J.W. Thybaut, and G.B. Marin, Single-event rate parameters for the

hydrocracking of cycloalkanes on Pt/US-Y zeolites. Industrial & Engineering Chemistry Research, 2001. 40(8): p. 1832-1844.

[6] Froment, G.F. and K.B. Bisschoff, Chemical reactor analysis and design. 2nd ed.

1990: Wiley: New York.

59,28

59,30

59,32

59,34

59,36

59,38

59,40

59,42

150 200 250 300

Se

lect

ivit

y t

o 2

-me

thy

l-

pe

nta

ne

(%

)


38,50

39,00

39,50

40,00

40,50

41,00

150 200 250 300

Sele

ctiv

ity

to 3

-me

thyl

-

pe

nta

ne

(%)


51

Chapter 4

Ideal hydrocracking of

n-pentane: reaction network

including primary carbenium

ions

Abstract: First the influence of the composition of the catalyst on the hydrocracking

behaviour is investigated. In this chapter the reaction network is extended with primary

carbenium ions. The net formation rate is determined, regression of the model parameters is

performed and the results are discussed.

4.1 Ideal versus non-ideal behavior

Hydrocracking is a combination of metal- and acid-catalyzed reaction steps. Therefore, both

metallic and acidic sites are necessary on the catalyst. Conversion over such a bifunctional

catalyst exceeds the summation of both conversions of the individual types of sites [1]. These

catalysts are typically zeolites on which framework alumina usually takes care of the acid

sites. The metallic function, for example Pt, Pd or sulfidated NiMo or NiW, is deposited on

the catalyst afterwards.

The combination of the number and the activity or strength of the metal and acid sites plays a

key role in the product selectivities observed during experiments. Compared to acid catalysts

used in catalytic cracking, the presence of a metal phase on hydrocracking catalysts enhances

isomer formation. The higher the dehydrogenation activity of the metal compared to the acid


n-pentane: reaction network including primary carbenium ions 4.1: Ideal versus non-ideal behavior

52

strength of the catalyst, the higher the isomer yield [2, 4]. This can be concluded from Figure

4-1. The cracking reaction of the carbenium ions on the acid sites is mostly seen as a

secondary reaction following to the isomerization reaction. The higher the (de)-hydrogenation

activity of the metal sites, the more likely it is that the unsaturated products are hydrogenated,

rather than being converted through a secondary reaction to cracked products. When the

catalytic strength of the metal is sufficiently high in order to establish quasi-equilibrium, the

isomer yield does not increase any further.

When working with light alkanes such as pentane, and considering the formation of primary

carbenium ions, β-scission reactions might also occur directly on the ion of the linear alkane.

When the (de)-hydrogenation reaction is in quasi-equilibrium, the formation of cracked

products through consecutive reactions is minimal. The rate of these reactions will be very

low because of the instability of the primary carbenium ions in comparison with secondary

and tertiary ions.

As mentioned before, high activity of the metal sites enhances isomer formation. If quasi-

equilibrium can be assumed, the term ‘ideal hydrocracking’ is introduced. However, ideal

hydrocracking circumstances are not determined by the catalyst properties only, but are also

depending on the operating conditions.

Figure 4-1: Reaction pathways for non-ideal hydrocracking on bifunctional zeolites [3]

The catalyst dependence is characterized by the type of metal present in the catalyst and by

the ratio of the number of hydrogenation sites to the number of acid sites. The ideal situation


n-pentane: reaction network including primary carbenium ions 4.1: Ideal versus non-ideal behavior

53

occurs for large values of this ratio [4]. When this is rather low, the amount of metallic sites is

not sufficiently high in order to provide enough olefins for the acid sites. This implies that the

dehydrogenation of the reactant becomes the limiting step in the alkane transformation

process. As shown in Figure 4-2, the activity increases as the amount of metallic sites (nPt)

becomes higher for samples with the same number of acid sites (na).

Figure 4-2: Initial activity (A 0) of Pt/HY catalysts as a function of the ratio of platinum sites/acid sites [4].

From a certain value on, this ratio starts losing its effect on the activity, which eventually

reaches its maximum value. This means that the amount of metallic sites is sufficiently high

in order to produce enough olefins to occupy the acid sites. It follows that the acid-catalyzed

reactions now become the rate-limiting steps in the hydrocracking process [4].

The effect of the operating conditions on the ideality of the hydrocracking behavior was

extensively investigated by Debrabandere et al.[5]. In the investigated range of operating

conditions, low pressures, high temperatures, high molar hydrogen-to-hydrocarbon inlet

ratios, and high reactant carbon numbers tend to favor non-ideality. This is further explained

in section 6.2.

For the analysis of the data set, only the effect of the total pressure will be considered. In

practice, the ideality of the hydrocracking behavior is assessed by investigating the

relationship between the pressure and the conversion. Decreasing conversion with increasing

pressure characterizes ideality, while the opposite applies for non-ideal behavior.


n-pentane: reaction network including primary carbenium ions 4.2: Reaction network

54

The experiments at low pressure obtained by TUM Munich were carried out under non-ideal

operating conditions as shown in Figure 4-3 (left). Considering Figure 4-3 (right), ideal

hydrocracking is assumed for experiments at higher pressures.

Figure 4-3: Conversion of n-pentane as a function of the total pressure for the hydroisomerization of n-pentane on Pt/H-BEA 0.6 wt% zeolite.

Ideal or non-ideal hydrocracking behavior is strongly reflected in the isomer yield. Under

ideal hydrocracking conditions, the isomer yield is maximized [2].

4.2 Reaction network

In this chapter the cracking reactions are considered to occur only in the acid sites. This

means that hydrogenolysis is assumed not to occur, and only β-scission leads to cracked

products.

The assumptions made in the generation of the reaction network for the classical case remain

(see section 2.2.1). This means that hydride transfer, oligomerisation and hydride shift on the

acid sites are not taken into account, and (de)hydrogenation and (de)protonation reactions are

considered at quasi-equilibrium.

For the generation of the reaction network all possible types of carbenium ions are

considered: primary, secondary and tertiary ions.

The reactions occurring in the classical hydroisomerization process extended with the

assumption of primary carbenium ions are summarized in Table 4-1. In this table,

methylcarbenium ions are considered as being primary carbenium ions.

20,0

25,0

30,0

35,0

7 8 9 10

Co

nv

ers

ion

n-p

en

tan

e (

%)


0,0

5,0

10,0

15,0

20,0

25,0

11 13 15 17

Co

nv

ers

ion

n-p

en

tan

e (

%)



n-pentane: reaction network including primary carbenium ions 4.2: Reaction network

55

Table 4-1: Acid-catalyzed reactions occuring when considering primary carbenium ions

Reaction Type of carbenium ions involved

Alkylshift secondary – primary

primary – secondary

PCP-branching

primary – primary

secondary – secondary

secondary – primary

primary – primary

β-scission

primary – primary

secondary – primary

primary – secondary

tertiary – primary

The classical reaction network extended with the consideration of primary carbenium ions

contains: 7 alkanes, 10 olefins and 15 carbenium ions.

The number of reactions occurring in this network are:

• 10 (de)hydrogenations

• 18 (de)protonations

• 8 alkyl shift reactions

• 12 pcp-branching reactions

• 12 β-scission reactions

Because of the complexity, the complete reaction network is divided in two parts (starting

from n-pentane and n-butane) and is shown in Figure 4-4 and Figure 4-5.


n-pentane: reaction network including primary carbenium ions

Figure 4-4: Reaction network starting from n

Figure 4-5: Reaction network starting from n

pentane: reaction network including primary carbenium ions

: Reaction network starting from n-pentane (part 1 of the complete reaction network)

: Reaction network starting from n-butane (part 2 of the complete reaction network)

4.2: Reaction network

56

1 of the complete reaction network)

butane (part 2 of the complete reaction network)


n-pentane: reaction network including primary carbenium ions 4.3: Net formation rates

57

4.3 Net formation rates

The method and equations for the calculation of the net rate of formation Rp for this extended

reaction network are identical than those for the classical network. The detailed description

for the derivation of the rate equations was given in section 2.2.4.

Under ideal hydrocracking conditions the acid-catalyzed reactions, i.e. alkyl shift, PCP-

branching and β-scission are the rate determining steps. The reaction rate of these rate

determining steps is assumed to be first order in the carbenium ion concentration.


,);();( ,,/,,/ (4-39)


,);();;( ,,,,, ββ (4-40)

The concentration of carbenium ion k corresponding to alkane i can be related to the partial

pressure of the considered alkane and hydrogen using equations (4-41) to (4-43).

ji

ki

ji

kiOprrefjiiso

R

O

RCnKOOKC

,

,

,

,)();( , ′′=

++ σ

σ (4-41)

( )

,

2

,;

i

i j

dehyd i i j P

O

H

K P O CC

p= (4-42)

,

,

,1i

L i i

p sat i

L i ii

K pC C

K p=

+∑ (4-43)

The net rate of formation of the different alkanes in the reaction network can be divided into two contributions: ∑ ∑+= +

k jORP jikii

RRR,,

(4-44)

With

∑∑∑∑

∑∑∑∑

∑∑∑∑

−

+−

+−=+

s tyxkits

s tyxkits

s tkitsAS

s tkitsAS

s tkitsPCP

s tkitsPCPR

OnnrOnnr

nnrnnr

nnrnnrRki

);;();;(

);();(

);();(

,,,,,,

,,,,

,,,,,

ββ

(4-45)


n-pentane: reaction network including primary carbenium ions 4.4: Model parameters

58

And

∑∑=s t

jiedtsO OnnrRji

);;( ,,,, β (4-46)

The only difference between equations (4-44) – (4-46) and equations (2-26) – (2-28) lies on

the type of carbenium ions involved in the rate determining steps.

4.4 Model parameters

The single-event concept describes the rate coefficient by the product of a number of single-

events and a single-event rate coefficient, which is only dependent on the reaction family and

on the type of carbenium ions involved, as explained in section 2.2.3. By using statistical

thermodynamics the single-event pre-exponential factor A~

of the acid-catalyzed reactions can

be calculated. Consequently only the activation energies for these reactions have to be

estimated. All the parameters that have to be estimated are given in Table 4-2.

Table 4-2: Overview of the model parameters to be estimated for the classical network including primary carbenium ions.

Parameter Description

∆Hpr(p) Protonation enthalpy for formation of primary carbenium ions

∆Hpr(s) Protonation enthalpy for formation of secondary carbenium

ions

∆Hpr(t) Protonation enthalpy for formation of tertiary carbenium ions

Ea,AS(p,s) Activation energy for alkyl shift from a primary carbenium ion

to a secondary carbenium ion

Ea,PCP(p,p) Activation energy for PCP-branching from a primary to a

primary carbenium ion


n-pentane: reaction network including primary carbenium ions 4.4: Model parameters

59

Ea,PCP(p,s) Activation energy for PCP-branching from a primary to a

secondary carbenium ion

Ea,PCP(s,s) Activation energy for PCP-branching from a secondary to a


Ea,β(p,p) Activation energy for β-scission from a primary to a primary

carbenium ion

Ea,β(p,s) Activation energy for β-scission from a primary to a secondary

carbenium ion

Ea,β(s,p) Activation energy for β-scission from a secondary to a primary

carbenium ion

Ea,β(t,p) Activation energy for β-scission from a tertiary carbenium ion

to a primary carbenium ion

The activation energy for PCP-branching from a secondary to primary carbenium ion

(Ea,PCP(s,p)) and the activation energy for alkyl shift from a secondary to a primary carbenium

ion (Ea,β(s,p)) are calculated from the protonation enthalpies for the formation of primary and

secondary carbenium ions (∆Hpr(p) and ∆Hpr(s)) and from the activation energies for the

reaction from a primary to a secondary carbenium ion (Ea,PCP(p,s) or Ea,β(p,s)).

According to Figure 4-6 the following expression can be derived for the relationship between

),( psEa and ),( spEa :

( ))()(),(),( pHsHspEpsE prpraa ∆−∆−= (4-47)


n-pentane: reaction network including primary carbenium ions 4.5: Results

60

Figure 4-6: Scheme of the activation energy for the reaction from a primary to a secondary carbenium ion

4.5 Results

4.5.1 Estimated parameters and discussion

The experiments used for the parameter estimation on a Pt/H-BEA 0.6wt% catalyst are given

in appendix C. In order to explain the formation of lighter components as methane and ethane

primary carbenium ions are considered. Cracking reactions on the metal sites, such as

hydrogenolysis are not taken into account.

The pre-exponential factors are calculated using statistical thermodynamics. The general

equation is given in section 2.2.3, equation (2-12). The change in entropy, used in the

exponential term, is different for isomerization and cracking reactions. For isomerization,

reactant, transition state and product have a similar entropy, which implies a standard

activation entropy equal to zero [6]. In this case the equation for the calculation of the pre-

exponential factor is simplified to:

h

TkA B=~

(4-48)

Gas phase

Secondary C+

Ea(p,s)

Ea(s,p)

∆Hpr(s) ∆Hpr(p)

Primary C+



61

Figure 4-7: Isomerization reaction of 2-methyl-hexane carbenium ion (left) and branching reaction of 3-methyl-hexane carbenium ion (right) [6]

For the cracking reactions the transition state has one translational degree of freedom more

than the reactant. Therefore the standard activation entropy will be equal to one third of the

translational entropy [6]. The pre-exponential factor for the β-scission reactions are calculated

according to:

=R

S

h

kBTA trans

3exp

~ (4-49)

In which:

( )

Rh

TkNM

N

VRS BAw

A

mtrans 2

5/2ln

2/3

2+

=π

(4-50)

The resulting values for the pre-exponential factors for the acid catalyzed reactions are given

in Table 4-3.

Table 4-3: Calculated values for the pre-exponential factors of the acid catalyzed reactions using statistical thermodynamics.

Reaction A~

[mol/(gcat s)]

Alkyl shift 3.11 109

PCP-branching 3.11 109

β-scission 4.07 1012

The estimated values for the parameters, together with the 95% confidence interval are given

in Table 4-4. The absolute difference between the enthalpy change for the formation of a

secondary carbenium ion and the enthalpy change for the formation of a tertiary carbenium

ion 1 ion 2

G

ion 1

ion 2 + olefin

G



62

ion is equal to 42.7 kJ/mol. From the literature it is known that the difference in stability

between a secondary and a tertiary carbenium ions amounts to 40-50 kJ/mol [7]. Hence, the

estimated difference shows a good correspondence with the literature. The absolute

difference between the enthalpy change for the formation of a primary carbenium ion and the

enthalpy change for the formation of a secondary carbenium ion is equal to 54.7 kJ/mol.

According to literature, the difference in enthalpy change should amount to about 100 kJ/mol

[8]. The estimated difference is thus much smaller.

Table 4-4: Estimated values for the model parameters in case that primary carbenium ions are considered

Parameter Value

[kJ/mol]

)( pH pr∆ -12.61 (±1.04)

)(sH pr∆ -67.29 (±6.21)

)(tH pr∆ -109.99 (±4.26)

),(, spE ASa 44.55 (±6.75)

),(, ppE PCPa 53.40 (±8.76)

),(, spE PCPa 102.62 (±21.35)

),(, ssE PCPa 94.29 (±8.49)

),(, ppEa β 77.78 (±4.51)

),(, spEa β 104.54 (±15.8)

),(, psEa β 131.17 (±7.57)

),(, ptEa β 193.64 (±43.7)

The estimated activation energy for secondary to secondary PCP-branching equals 53.40

kJ/mol, while literature review proposes a value of 108.7 kJ/mol [9].

The activation energy for the β-scission reaction starting from primary carbenium ion to form

a secondary carbenium ion is lower than the activation energy when started from a secondary

carbenium ion. This is due to the stability of the ion formed during the reaction.



63

The activation energy for the β-scission reaction starting from primary carbenium ion to form

another primary carbenium ion is rather low. This is because the primary carbenium ion is

unstable. On the other hand, a tertiary carbenium ion is very stable, which leads to the high

activation energy for the β-scission reaction starting from a tertiary carbenium ion. Literature

values for β-scission reactions are given in Table 4-5.

Table 4-5: Activation energies for β-scission reactions for different types of

carbenium ions involved as reactants and products [5].

Reaction Value [kJ/mol]

),(, ssEa β 142.7 (±0.1)

),(, stEa β 148.6 (±1.0)

),(, tsEa β 127.9 (±4.9)

),(, ttEa β 125.1 (±3.8)

When a secondary carbenium ion is formed through a the β-scission reaction the activation

energy is higher than the case in which a tertiary carbenium ion is formed. If we would

extrapolate this conclusion, the formation of a primary carbenium ion should have an even

higher activation energy than for formation of a secondary. As can be seen from Table 4-4

this is indeed the fact when starting from a tertiary carbenium ion, but not when a secondary

carbenium ion is used as a reactant.

Figure 4-8 shows the parity diagrams for the molar exit flows of the hydroisomerization

products of n-pentane on a Pt/H-BEA 0.6 wt% catalyst. The experiments used for these

graphics are the same as for the parameter estimation and are given in appendix C.

The model regression for ethane, propane and n-butane are reasonable. The fitting for iso-

pentane is a bit worse and for methane and iso-butane is not good.

For methane and iso-butane it is difficult to describe the experimental results because less

experiments used for the parameter estimation have an outlet flow for methane and iso-butane

different from zero. This is also reflected on the results of the other components.



64

a) b)

c) d)

e) f)

Figure 4-8: Parity diagrams for the molar exit flows of the hydroisomerization products of n-pentane on a Pt/H-BEA 0.6 wt% catalyst. (a) ethane, (b) propane, (c) iso-pentane, (d) n-butane, (e) methane and (f) iso-butane.

0E+00

2E-08

4E-08

6E-08

8E-08

1E-07

0E+00 5E-08 1E-07

Fb

er(m

ol/

s)

Fexp (mol/s)

0E+00

2E-08

4E-08

6E-08

8E-08

1E-07

1E-07

0E+00 5E-08 1E-07 2E-07

Fb

er(m

ol/

s)

Fexp (mol/s)

0E+00

1E-07

2E-07

3E-07

4E-07

5E-07

6E-07

7E-07

0E+00 2E-07 4E-07 6E-07 8E-07

Fb

er(m

ol/

s)

Fexp (mol/s)

0E+00

5E-09

1E-08

2E-08

2E-08

3E-08

3E-08

4E-08

4E-08

5E-08

0E+00 2E-08 4E-08 6E-08

Fb

er(m

ol/

s)

Fexp (mol/s)

0E+00

5E-05

1E-04

2E-04

2E-04

3E-04

0E+00 1E-04 2E-04 3E-04

Fb

er(m

ol/

s)

Fexp (mol/s)

0E+00

5E-10

1E-09

2E-09

2E-09

3E-09

3E-09

4E-09

0E+00 1E-09 2E-09 3E-09 4E-09

Fb

er(m

ol/

s)

Fexp (mol/s)



65

4.5.2 Statistical analysis

Testing the significance of the regression is equal to testing the hypothesis that all parameters

are equal to zero at the same time. This hypothesis is tested by the F-test (see section 2.2.5).

The calculated F-value equals 415, and exceeds the tabulated F-value for a 95% probability

level which is equal to 2.79. This means that the regression is significant.

The next step is a test for the significance of the individual parameters. The calculated t-

values are given in Table 4-6. The tabulated t-value for a 95% probability level and 217

degrees of freedom is equal to 1.971. The absolute calculated t-value is larger than the

tabulated one for each model parameter, which implies that every parameter is significantly

different from zero.

Table 4-6: Calculated t-values for the model parameters in the case that primary carbenium ions are considered

Parameter t-value

)( pH pr∆ -8.868

)(sH pr∆ -25.33

)(tH pr∆ -25.59

),(, spE ASa 18.23

),(, ppE PCPa 7.45

),(, spE PCPa 12.66

),(, ssE PCPa 26.41

),(, ppEa β 31.79

),(, spEa β 19.17

),(, psEa β 31.05

),(, ptEa β 21.02

The binary correlation coefficient matrix is shown in appendix C. The change in enthalpy

when forming a primary carbenium ion is negatively correlated with the changes in enthalpy

when forming a secondary or tertiary carbenium ion.



66

The binary correlation coefficient between the activation energy for secondary to secondary

PCP-branching and the protonation enthalpy to a secondary carbenium ion is quite high (-

0.8963). This can be explained by the hydroisomerization reaction mechanism. A more

negative value for the protonation enthalpy to a secondary carbenium ion results in a higher

concentration of secondary carbenium ions on the Brønsted acid sites. These secondary

carbenium ions can be isomerized through PCP-branching. To retain the same reaction rate

for PCP-branching with a higher concentration of secondary carbenium ions the rate

coefficient for PCP-branching will have to be decreased. This decrease can be performed by

enhancing the activation energy. Thus the smaller the value for the protonation enthalpy of a

secondary carbenium ion, the larger the value for the activation energy for secondary to

secondary PCP-branching has to be. This explains the large and negative correlation.

The residual sum of squares in this case is 1.149 104.

4.5.3 Influence of pressure on conversion and selectivity

Figure 4-9 compares the experimental conversion of n-pentane as a function of pressure with

the model calculated conversion of n-pentane. From this figure can be seen that the

conversion is slightly underestimated. Figure 4-10 gives the selectivity to iso-pentane as a

function of pressure. When comparing the experimental and the model calculated values, the

calculated selectivity is slightly overestimated. The overestimation of the selectivity can be

seen as a consequence of the underestimation of the conversion. Because of the latter, the

concentration of iso-pentane will be lower, which makes the probability for a consecutive

reaction less plausible.



67

Figure 4-9: Experimental (▲) and model calculated values (■) for the conversion of n-pentane as a function of pressure for hydroisomerization of n-pentane. The experiments used for this graphic is referred to appendix C.

The experiments used in the following Figure 4-9 and Figure 4-10 are the same as for the

parameter estimation (section 4.5.1) when considering the classical reaction network extended

with primary carbenium ions.

Figure 4-10: Experimental (■) and model calculated values (▲) for the selectivity to iso-pentane as a function of pressure for the hydroisomerization of n-pentane. For the experiments used for this graphic is referred to appendix C.

2

4

6

8

10

12

14

16

10 15 20 25 30Co

nv

ers

ion

of

n-p

en

tan

e

(%)

Pressure (bar)

0

20

40

60

80

100

10 15 20 25 30Se

lect

ivit

y f

or

iso

-pe

nta

ne

(%)

Pressure (bar)



68

4.5.4 Influence of the space-time on the conversion and selectivity

The conversion and the selectivity are investigated as a function of the space-time at 280°C. For

the complete set of experiments used in this paragraph, the reader is referred to appendix C. Both

experimental and model calculated values are shown in Figure 4-11.

Figure 4-11: Experimental (■) and model calculated (▲) results for the conversion of n-pentane (left) and the selectivity to iso-pentane (right) as a function of space-time at a temperature of 280 °C. For the experiments used in

this graphic is referred to appendix C.

The model calculated conversion and selectivity describe well the experimental trend. The

conversion of n-pentane is only slightly underestimated compared to the experimental values.

The selectivity on the other hand is overestimated. This can be seen again as a consequence of

the underestimated conversion.

The conversion of n-pentane increases as the space-time increases. This is a trend that was

already found in section 3.1.3. The selectivity to iso-pentane shows a small decrease as the

space-time increases. Again this can be expected as explained in section 3.1.3. The more n-

pentane is converted into iso-pentane, the more probable it will be that iso-pentane will be

converted to cracked products by a consecutive reaction.

0

5

10

15

20

0 5 10 15

Co

nv

ers

ion

of

n-p

en

tan

e

(%)

Space-time (103 gcat s mol-1)

0

20

40

60

80

100

120

0 5 10 15

Se

lect

ivit

y t

o i

so-p

en

tan

e

(%)

Space-time (103 gcat s mol-1)


n-pentane: reaction network including primary carbenium ions 4.6: Conclusion

69

4.6 Conclusion

In this chapter the classical reaction network is extended by including primary carbenium ions

that can be formed and react. Cracking reactions on the metal sites are not taken into account.

This reaction network consist of: 10 (de)hydrogenations, 8 (de)protonations, 8 alkyl shift

reactions, 12 pcp-branching reactions and 12 β-scission reactions. For these reactions it is

assumed that the (de)hydrogenation and (de)protonation reactions are at quasi-equilibrium.

For the experiments performed on a 20-fold parallel plug flow reactor, ideal plug flow is

assumed. A one-dimensional pseudo-homogeneous model was used as the reactor model. The

development of the net rate of formation of the paraffins, was determined by applying the

single-event concept. It is assumed that the acid-catalyzed reactions are rate determining. The

pre-exponential factor of the single-event rate coefficients is calculated using statistical

thermodynamics.

In this reaction network 11 model parameters are determined. By comparison to the

experimental data given in appendix C. The estimation is performed using a combination of

Rosenbrock algorithm and a Levenberg-Marquardt algorithm. The model developed for this

extended reaction network is acceptable to describe ethane, propane and iso-pentane flow, but

fails in describing methane and iso-butane. This can be the consequence of the lack of

experiments used for the estimation, i.e. almost no data is available for methane and iso-

butane.

On the other hand, the influence of the pressure and of the space-time can be described

properly by the model. The conversion is only slightly underestimated, while the selectivity is

slightly overestimated. The error on the selectivity can be a consequence of the

underestimated conversion.

The influence of the temperature on the conversion of n-pentane and the selectivity to iso-

pentane for hydroisomerization of n-pentane could not be investigated. The experiments used

for the parameter estimation are all obtained at the same temperature.


n-pentane: reaction network including primary carbenium ions 4.7: References

70

4.7 References

[1] Froment, G.F. and K.B. Bischoff, Chemical reactor analysis and design. 2nd ed. 1990, Wiley: New York.

[2] Woltz, C., Kinetic studies on alkane hydroisomerization over bifunctional catalysts,

PhD Thesis, 2005,Technischen Universität München [3] Martens, G.G., J.W. Thybaut, and G.B. Marin, Single-event rate parameters for the

hydrocracking of cycloalkanes on Pt/US-Y zeolites. Industrial & Engineering Chemistry Research, 2001. 40(8): p. 1832-1844.

[4] Thybaut, J.W., et al., Acid-metal balance of a hydrocracking catalyst: Ideal versus

non-ideal behavior. Industrial & Engineering Chemistry Research, 2005. 44(14): p. 5159-5169.

[5] Thybaut, J.W., et al., Alkylcarbenium ion concentrations in zeolite pores during

octane hydrocracking on Pt/H-USY zeolite. Catalysis Letters, 2004. 94(1-2): p. 81-88. [6] Marin, G.B., Catalytic reaction engineering: bridging the gap between fundamentals

and industrial application. Presentation Nanocat IDECAT, Lyon, October 26, 2005. [7] Govaerts, S., Ondersteuning van de ontwikkeling en optimalisering van katalysatoren

met behulp van fundamenteel kinetisch modellen, Master Project, 2007,Ghent University

[8] Bond, G.C., Kinetic modeling of metal-catalyzed reactions of alkanes. Industrial &

Engineering Chemistry Research, 1997. 36(8): p. 3173-3179. [9] Brown, P.N., A.C. Hindmarsh, and L.R. Petzold, Consistent initial condition

calculation for differential-algebraic systems. Siam Journal on Scientific Computing, 1998. 19(5): p. 1495-1512.

71

Chapter 5


n-pentane: reaction network

including hydrogenolysis

Abstract: The second possibility for explaining the formation of lighter alkanes (<C5) consists

in considering hydrogenolysis on the metal sites. In this case primary carbenium ions are not

considered, which implies that β-scission cannot occur on the acid sites. The net formation

rate and the model parameters that have to be estimated are determined. The estimated values

for the model parameters are given and discussed. A statistical analysis is performed.

5.1 Reaction Network

During hydrogenolysis a carbon-carbon bond is cracked in an alkane chemisorbed on the

metal surface of the catalyst, thereby forming either methane or ethane [1]. The reactions

whereby methane and ethane are separated, are called demethylation and deethylation

respectively.

For this reaction network the same assumptions as in the classical network are applied. This

means that oligomerisation, hydride transfer and hydride shift are not taken into account, and

the (de)hydrogenation and (de)protonation reactions are considered at quasi-equilibrium.

For the hydrogenolysis reactions it is assumed that only n-pentane and iso-pentane can be

cracked on the metallic sites, forming methane/ethane and an alkane with one or two carbon

atoms less than the original one. This assumption is justified because on the one hand C5-


n-pentane: reaction network including hydrogenolysis 5.1: Reaction Network

72

alkanes (n-pentane and iso-pentane) will have the largest affinity to interact with the metal

sites and on the other than the concentration of C5 alkanes will be much larger than the

concentrations of smaller chains. The assumption is also introduced to reduce the number of

model parameters to be estimated. Figure 5-1 shows the reaction network considering

hydrogenolysis assuming that consecutive cracking reactions cannot occur.

Figure 5-1: Hydrogenolysis on metal sites assuming that consecutive cracking reaction cannot occur [2].

The classical reaction network extended to hydrogenolysis on the metal sites consists of 7

alkanes, 10 alkenes and 7 carbenium ions.

The number of reactions present in this reaction network are:

• 10 (de)hydrogenations

• 11 (de)protonations

• 2 pcp-branching reactions

• 3 demethylations

• 2 deethylations

Figure 5-2 shows the classical reaction network extended to hydrogenolysis on the metal sites.

For the sake of clarity of the scheme, the dehydrogenation and deprotonation reactions of the

formed products through hydrogenolysis is not shown in Figure 5-2. For the development of

the fundamental kinetic model, the complete extended reaction network was used.


n-pentane: reaction network including hydrogenolysis 5.1: Reaction Network

73

Figure 5-2: Reaction network for the hydroisomerization of n-pentane, extended with hydrogenolysis on the metal sites (dem= demethylation; deet=deethylation) [2]


n-pentane: reaction network including hydrogenolysis 5.2: Kinetic model for hydrogenolysis

74

5.2 Kinetic model for hydrogenolysis

Kinetic models for hydrogenolysis have been developed for light alkanes (ethane, propane,

butane) [3, 4]. From the models, an appropriate model was selected. The model selection was

based on the following criteria [3, 4]:

• The rate equation must describe adequately the experimental data.

• The rate equation must be derived from a physical possible model.

• The estimated value for the model parameters must be physically meaningful, i.e., the

magnitude value must be reasonable and must show a correct temperature dependence.

• The number of parameters to be estimated has to be limited.

A detailed description of the different models found in literature is given in a previous work

[5]. In the following section the selected model (ES5B) is explained [5].

5.2.1 Selected model for hydrogenolysis (ES5B)

This model assumes that an adsorbed hydrogen atom is involved in the cracking reaction of

the carbon-carbon bond instead of an active metal site. The elementary steps of the reaction

mechanism is shown below [6, 7]:

Adsorption

-.(/) 0 21 3456 2-1 (5-1)

78-9(/) 0 (: 0 1 ; <)1 3456 78-=

1 0 (: ; <)-1 (5-2)

Cracking of C-C bond

78-=1 0 -1

>? 7@-A

1 0 78B@-=BA1 (5-3)

m-p=1 for demethylation

m-p=2 for deethylation

Desorption

7@-A1 0 (2C 0 2 ; D)-1

EFGH5I6 7@-.@J. 0 (2C 0 3 ; D)1 (5-4)


n-pentane: reaction network including hydrogenolysis 5.3: Net formation rates

75

The reaction rate for hydrogenolysis according to this mechanism is:

( ) ( )2

2

1

2

)2

1(

22

)(

++

=

−+

−

−−

xn

HH

xn

HHAA

xn

HHAAysishydrogenol

pKpKpK

pKpkKr (5-5)

5.3 Net formation rates

The derived equations for the calculation of the net rate of formation of the paraffins Rp for

the classical reaction network, extended with hydrogenolysis, are slightly different from those

for the classical reaction network. The method for deriving the equations remains the same.

The detailed description of this method is given in section 2.2.4.

Under ideal hydrocracking conditions the acid catalyzed reactions, i.e. alkyl shift, PCP-

branching and β-scission are the rate determining steps. The reaction rate of these rate

determining steps is assumed to be first order in the carbenium ion concentration:


,);();( ,,/,,/ (5-6)


,);();;( ,,,,, ββ (5-7)

The concentration of carbenium ion k corresponding to alkane i can be related to the partial

pressure of the considered alkane and hydrogen using equations (4-41) to (4-43).

ji

ki

ji

kiOprrefjiiso

R

O

RCnKOOKC

,

,

,

,)();( , ′′=

++ σ

σ (5-8)

( )

,

2

,;

i

i j

dehyd i i j P

O

H

K P O CC

p= (5-9)

,

,

,1i

L i i

p sat i

L i ii

K pC C

K p=

+∑ (5-10)


n-pentane: reaction network including hydrogenolysis 5.3: Net formation rates

76

The net rate of formation of the different alkanes iPR in the classical reaction network can be

divided into two contributions:

∑ ∑+= +k j

ORP jikiiRRR

,, (5-11)

With

∑∑∑∑

∑∑∑∑

∑∑∑∑

−

+−

+−=+

s tyxkits

s tyxkits

s tkitsAS

s tkitsAS

s tkitsPCP

s tkitsPCPR

OnnrOnnr

nnrnnr

nnrnnrRki

);;();;(

);();(

);();(

,,,,,,

,,,,

,,,,,

ββ

(5-12)

And

∑∑=s t

jiedtsO OnnrRji

);;( ,,,, β (5-13)

When extending the classical reaction network with hydrogenolysis, methane or ethane can be

separated: The net rate of formation iPR in equation (5-11) has to be corrected for the

occurrence of hydrogenolysis.

ii Pysehydrogenol

s s ttskiPCP

tkitsPCPP RnnrnnrR ,,,,, );();( ++= ∑ ∑∑∑

(5-14)

iPysehydrogenolR , is the rate at which alkane i is formed through hydrogenolysis minus the rate

at which it is cracked into lighter products through hydrogenolysis. When the alkane

considered has 3 or more carbon atoms iPysehydrogenolR , can be expressed as:

∑∑

∑∑

−

+−=

kkideet

kikdeet

kkidem

kikdemPysehydrogenol

PPrPPr

PPrPPrRi

);();(

);();(,

(5-15)

For methane and ethane the expression will be slightly different.

);();( 462, 4CHHCrPPrR dem

k llkdemCHysehydrogenol ∑∑ += (5-16)

);();( 62104, 62HCHCrPPrR deet

k llkdemHCysehydrogenol ∑∑ += (5-17)

The reaction rate of demethylation and deethylation have been determined in section 5.1.


n-pentane: reaction network including hydrogenolysis 5.4: Model Parameters

77

5.4 Model Parameters

For describing the hydrogenolysis reaction two possible fundamental kinetic models are

determined. For each of those models the set of parameters that has to be estimated are the

same. All the parameters to be estimated are summarized in Table 5-1.

Table 5-1: Overview of the parameters that have to be estimated in the case that the classical reaction network is extended with hydrogenolysis

Parameter Description )(sH pr∆

Protonation enthalpy for formation of a secondary carbenium ion

)(tH pr∆

Protonation enthalpy for formation of a tertiary carbenium ion

),(, ssE PCPa Activation energy for PCP-branching from a secondary to


2,HchemA

Pre-exponential factor for the equilibrium coefficient KH for chemisorption of H2 on the metal site

2,HchemH∆

Change in enthalpy for chemisorption of H2 on a metal site

alkanechemA , Pre-exponential factor for the equilibrium coefficient KH for

chemisorption of a C5 alkane on the metal site

alkanechemH ,∆

Change in enthalpy for chemisorption of a C5 alkane on a metal site

demA' Pre-exponential factor for demethylation

demaE , Activation energy for demethylation

deetA' Pre-exponential factor for deethylation

deetaE , Activation energy for deethylation

xn− Number of hydrogen atoms removed during alkane chemisorption for

hydrogenolysis Since primary carbenium ions are not considered in the reaction network β-scission reactions

and alkyl shift reactions do not occur. As for PCP-branching, only secondary to secondary

reaction takes place.

The single-event concept explained in section 2.2.3 is applied to PCP-branching,

demethylation and deethylation. The pre-exponential factors for the acid-catalyzed reactions


n-pentane: reaction network including hydrogenolysis 5.5: Results

78

such as PCP-branching will be calculated using statistical thermodynamics (see section 2.2.3).

The pre-exponential factors of demethylation and deethylation on the other hand are

estimated. In theory statistical thermodynamics can be applied to calculate these pre-

exponential factors as well, but for simplicity these values are firstly estimated.

Two different rate coefficients are used for demethylation and deethylation respectively. This

is justified by the experimental observed data (Figure 2-10). The molar exit flow of ethane is

significantly higher than the exit flow of methane.

5.5 Results

5.5.1 Estimated Parameters and discussion

The experiments used for the parameter estimation on a Pt/H-BEA 0.6wt% catalyst are given

in appendix D. The estimated values for the parameters, together with the 95% confidence

interval, are given in Table 5-2.

Table 5-2: Estimated values for the model parameters in case that hydrogenolysis is considered

Parameter Value Unit )(sH pr∆ -69.3 (±14.6) kJ/mol

)(tH pr∆ -113.0 (±23) kJ/mol

),(, ssE PCPa 92.7 (±18.3) kJ/mol

2,HchemA 16.0 (±187) 1/bar

2,HchemH∆ -12.5 (±9.3) kJ/mol

alkanechemA , 4.5 (±37.5) 108 1/bar

alkanechemH ,∆ 79.6 (±1140) kJ/mol

demA' 4.87 (±74) 1014 mol/(gcat s)

demaE , 149.0 (±1151) kJ/mol

deetA' 1.65 (±297) 1014 mol/(gcat s)

deetaE , 140.0 (±1160) kJ/mol

xn− 1.3 (±0.715) kJ/mol

The difference in protonation enthalpy between a secondary and a tertiary carbenium ion

according to literature review is between 40 and 50 kJ/mol [8]. According to the regression of



79

the model parameters for the classical reaction network extended with hydrogenolysis the

difference in protonation enthalpy is 44 kJ/mol, which thus corresponds with the literature.

Thybaut et al. [9] determined an activation energy for PCP-branching from secondary to

secondary carbenium ions on a PT/USY zeolite equal to 108.7 (±0.7) kJ/mol. The value

estimated in this regression is a little lower than this value.

The estimated change in enthalpy for the chemisorption of the C5 alkane is a positive value.

This endothermic character is due to the occurrence of dehydrogenation during adsorption.

According to literature, the equilibrium coefficient of this dehydrogenative chemisorption

increases as a function of temperature [3]. This confirms the endothermic character found in

the regression. Bond and Cunningham [3] investigated the dehydrogenative chemisorption of

light alkanes, propane and butane, on a Pt-catalyst. For the dehydrogenative chemisorption of

propane, respectively butane, values of 88.1 and 76.6 kJ/mol were reported. The estimated

enthalpy change for chemisorption of a C5 alkane on a metal site is equal to 79.6 kJ/mol,

which is higher than would be expected according to literature.

The activation energy for demethylation and deethylation are slightly underestimated

compared with literature values. According to Bond [4][6], the values for the activation

energies should range between100 and 170 kJ/mol.

Figure 5-3: Reaction mechanism for hydrogenolysis of n-butane on a catalyst containing Rh [10]

The activation energy for demethylation is higher than the activation energy for deethylation.

This can be explained by the reaction mechanism for hydrogenolysis. According to the

reaction mechanism the alkane is dehydrogenatively chemisorbed on the metal site with

formation of a metallacyclobutane complex. This is a ring structure consisting of three carbon

atoms and a metal atom. In Figure 5-3 is assumed that 2 hydrogens are removed during the



80

adsorption of the alkane. Figure 5-4 shows that the metallacyclobutane complex is in

equilibrium with two metal-alkene carbenium complexes [10].

Figure 5-4: Equilibrium between the metallacyclobutane complex and the metal-alkene carbenium complex.[10]

Due to the electron-donating character of the methyl group the formation of the alkene

carbenium complex consisting the C2 alkene (Figure 5-4, right) is favored. Hence,

deethylation will occur more easily than demethylation [10] which results in the higher

activation energy for demethylation.

The parity diagrams for the different responses of the hydroisomerization of n-pentane are

shown in Figure 5-5. The responses for isopentane, ethane, propane and n-butane are

adequately described. The description of the experimental data failed completely for methane

and iso-butane. This is caused by the observed molar exit flow for methane and iso-butane

which is zero for most experiments.



81

a) b)

c) d)

e) f)

Figure 5-5: Parity diagrams for the molar exit flows of (a) n-butane, (b) methane, (c) ethane, (d) propane, (e) iso-pentane and (f) iso-butane in the hydroisomerization of n-pentane on a Pt/H-BEA 0.6 wt% catalyst..

5.5.2 Statistical Analysis

The t-values for the model parameters are given in Table 5-3. The tabulated t-value for 133

degrees of freedom is 1.978. As shown in Table 5-3, 9 out of the 14 model parameters have a

t-value lower than the tabulated value, which means that these parameters are not significantly

estimated and zero lies in the 95% confidence interval.

0,E+00

2,E-08

4,E-08

6,E-08

2,E-08 3,E-08 4,E-08 5,E-08

Fb

er

(mo

l/s)

Fexp (mol/s)

0,E+00

5,E-05

1,E-04

2,E-04

2,E-04

3,E-04

0,E+00 1,E-04 2,E-04 3,E-04

Fb

er

(mo

l/s)

Fexp (mol/s)

0,E+00

5,E-08

1,E-07

2,E-07

4,E-08 6,E-08 8,E-08 1,E-07 1,E-07

Fb

er

(mo

l/s)

Fexp (mol/s)

0,E+00

5,E-08

1,E-07

2,E-07

4,E-08 6,E-08 8,E-08 1,E-07 1,E-07

Fb

er

(mo

l/s)

Fexp (mol/s)

0,E+00

2,E-07

4,E-07

6,E-07

8,E-07

2,E-07 4,E-07 6,E-07 8,E-07

Fb

er

(mo

l/s)

Fexp (mol/s)

0,E+00

1,E-09

2,E-09

3,E-09

4,E-09

0,E+00 1,E-09 2,E-09 3,E-09 4,E-09

Fb

er

(mo

l/s)

Fexp (mol/s)



82

The statistical analysis is performed based on multiresponse regression analysis. This means

that more than one response is important. Supposing n experiments were performed

considering v dependent variables the vn* experimental errors can be ordered in a vn*

matrix as shown in Figure 5-6.

Table 5-3: T-values for the estimation of the model parameters where the classical reaction network is extended with hydrogenolysis.

Parameter t-value )(sH pr∆ -9.241

)(tH pr∆ -9.625

),(, ssE PCPa 10.14

2,HchemA 0.1677

2,HchemH∆ -2.658

alkanechemA , 0.2137

alkanechemH ,∆ 0.1364

demA' 1.288

demaE , 0.2541

deetA' 0.1147

deetaE , 0.2371 xn− 3.554

Figure 5-6: n*v matrix of the experimental errors [11]

The v errors belonging to the v responses for the same experiment have a

variance/covariance matrix which can represented by:



83

=∑

ivvvivi

viii

viii

i

σσσ

σσσσσσ

…

⋮⋱⋮⋮

…

…

21

22212

11211

(5-18)

For each experiment a different variance/variance matrix can be determined. In the case that

these variance/covariance matrices are unknown, the matrices are assumed equal for all

experiments. The case in which the unknown variance/covariance matrices are varying with

the experiments, is impossible to implement in the program. Too many variables would be

unknown [11].

The objective function that is minimized on this way, demands that all vn* responses have to

be known. In the experiments obtained under non-ideal hydrocracking conditions the exit

molar flows for methane and isobutene are most of the experiments zero. This complicates the

minimization of the objective function and the statistical analysis.

This can be explained by the explicit form of the variance/covariance matrix [11]:

−

−

−

=

∑

∑

∑

∑

=

=

=

n

iii

n

iii

n

iii

y

y

y

1

211

1

211

1

211

)(00

0)(0

00)(

η

η

η

⋯

⋮⋱⋮⋮

⋯

⋯

(5-19)

This variance/covariance matrix is thus dependent on the difference between the experimental

and model calculated value of the molar exit stream of all the responses. Therefore it is

necessary that for all the responses the experimental outlet flow is known and different from

zero [11]. The experimental values for methane and isobutane which are for most of the

experiments zero will exhibit a strong influence on this variance/covariance matrix and thus

on the statistical analysis.



84

The absolute t-values of the estimated model parameters are not reliable due to the responses

for methane and iso-butane. On the other hand, the relative ratio of the t-values between the

parameters is reliable.

In order to obtain a reliable statistical analysis, the computer code should be adapted so that

the responses for methane and iso-butane are neglected for the calculation of the

variance/covariance matrix.

The regression itself can be considered significant, because the calculated F-value equals 67

and exceeds the tabulated F-value for a 95% probability level which is equal to 2.79.

The binary correlation coefficient matrix is given in appendix D. The protonation enthalpy to

a secondary carbenium ion is strongly and negatively correlated with the activation energy for

secondary to secondary PCP-branching. This was explained in section 0 in the previous

chapter.

The enthalpy change for the dehydrogenative chemisorption of a C5 alkane is negatively

correlated with the activation energies for demethylation and deethylation, while the

activation energies for demethylation and deethylation are positively correlated with each

other. This is a result of the hydrogenolysis reaction mechanism considered. When the

enthalpy change for the dehydrogenative chemisorption for the alkane becomes less positive,

the concentration of adsorbed C5-alkanes on the surface increases. A larger concentration of

reactants will increase the reaction rate of the cracking reaction of the C-C bond. In order to

maintain the same reaction rate, the activation energy for demethylation and deethylation has

to increase, which explains the negative correlation.

The strong correlation between the activation energies for demethylation and deethylation is

due to the fact that these reactions are competitive. If the activation energy for demethylation

decreases, the reaction rate of demethylation will increase, which causes the demethylation

reaction to become more dominant with respect to deethylation reation. In order to maintain

the same reaction rates for demethylation and deethylation, the activation energy for

deethylation has to decrease as well.

The residual sum of squares in this case is 65.3.


n-pentane: reaction network including hydrogenolysis 5.6: Influence of pressure on conversion and selectivity

85

5.6 Influence of pressure on conversion and selectivity

Figure 5-7: Experimental (▲) and model calculated values (■) for the conversion of n-pentane (left) and for the selectivity to iso-pentane (right) as a function of pressure for hydroisomerization of n-pentane at a temperature of 280

°C. Experimental data given in appendix D

Figure 5-7 shows the experimental and model calculated values for the conversion of n-

pentane (left plot) and the selectivity to iso-pentane (right plot) as function of pressure when

hydrogenolysis is considered. The experiments used for the calculation of these values are the

same as for the regression of the kinetic model. These experiments are given in appendix D.

The conversion of n-pentane is slightly overestimated, while the selectivity to iso-pentane is

underestimated. The latter is a consequence of the underestimation of the conversion. A lower

conversion results in a lower concentration of adsorbed iso-pentane on the metal sites, which

results in a lower consecutive cracking reaction rate.

0

5

10

15

20

25

30

10 15 20 25 30

Co

nv

ers

ion

of

n-p

en

tan

e

[%]

Pressure [bar]

60

70

80

90

100

10 15 20 25 30

Se

lect

ivit

y t

o i

so-p

en

tan

e

[%]

Pressure [bar]


n-pentane: reaction network including hydrogenolysis 5.7: Influence of space-time on conversion and selectivity

86

5.7 Influence of space-time on conversion and

selectivity

Figure 5-8: Experimental (■) and model calculated (▲) results for the conversion of n-pentane (left) and the selectivity to iso-pentane (right) as a function of space-time at a temperature of 280 °C. Experimental data given in

appendix D

Figure 5-8 shows the experimental and model calculated values for the conversion of n-

pentane (left plot) and the selectivity to iso-pentane (right plot) as function of space-time. The

experiments used for the calculation of these values are the same as for the regression of this

kinetic model and are given in appendix D.

The conversion of n-pentane is slightly overestimated, while the selectivity is underestimated.

The latter is again caused by the overestimation of the conversion. The conversion is

increasing with temperature, which can be explained by the reaction mechanism. The

selectivity remains roughly the same which is due to the low total conversion of n-pentane.

5.8 Hydrogenolysis vs primary carbenium ions

Table 5-4 compares the reactions considered in each reaction network. The number of model

parameters and the residual sum of squares which is an indication of the difference between

the experimental and model calculated values are given in Table 5-5. Considering

hydrogenolysis leads to 14 model parameters to be estimated, while the reaction network

including primary carbenium ions leads to only 11 model parameters.

0

5

10

15

20

25

30

0 5 10 15

Co

nv

ers

ion

of

n-p

en

tan

e

[%]

Space-time [gcat s/mol]

60

70

80

90

100

0 5 10 15

Se

lect

ivit

y t

o i

so-p

en

tan

e

[%]

Space-time [gcat s/mol]


n-pentane: reaction network including hydrogenolysis 5.9: Conclusion

87

Table 5-4: Summary of the number of reactions present in the different reaction networks.

Hydrogenolysis Primary Carbenium ions

Metal sites (de)hydrogenation 10 10 demethylation 3 Not considered deethylation 2 Not considered

Acid sites (de)protonation 11 18 alkyl shift 0 8

PCP-branching 2 12 β-scission 0 12

Table 5-5: Number of model parameters and residual sum of squares for the different cases considered in this project.

Classical reaction network

extended with

# model parameters Residual sum of squares

Primary carbenium ions 11 11490

Hydrogenolysis 14 65

The residual sum of squares are still quite large. This is because the calculation of this value is

dependent on the weighting factors used. These factors are calculated based on difference

between the experimental and the model calculated value for the molar exit flows of the

different alkanes. The experimental values for the molar exit flows for methane and isobutene

are most of the time zero, leading to large deviations for these values.

Although the values of the residual sum of squares are high, the value for the classical

reaction network extended with hydrogenolysis on the metal sites is much less than when

primary carbenium ions are considered. This implies that the consideration of hydrogenolysis

is the best of these two to describe the experimental data.

5.9 Conclusion

In this chapter the classical reaction network for the hydroisomerization of n-pentane is

extended with hydrogenolysis, which is a metal-catalyzed reaction producing methane or

ethane from a longer paraffin. The formation of methane and ethane, is called demethylation

and deethylation respectively. This reaction network consist of 7 paraffins, 10 olefins and 7

carbenium ions which react in 10 (de)hydrogenations, 11 (de)protonations, 2 PCP-branching


n-pentane: reaction network including hydrogenolysis 5.9: Conclusion

88

reactions, 3 demethylation reactions and 2 deethylation reactions. The (de)hydrogenation and

(de)protonation reactions are assumed to be in quasi-equilibrium. Since primary carbenium

ions are not considered, β-scission does not occur.

The reactor model is the same than explained in section. The single-event concept is again

applied to determine the net rate of formation of the paraffins. The pre-exponential factors of

the acid catalyzed reaction (PCP-branching) is calculated using statistical thermodynamics.

The pre-exponential factors of the metal-catalyzed reactions on the other hand are estimated.

Future work is to implement pre-exponential factors of the metal-catalyzed reactions

calculated with statistical thermodynamics and hence reduce the number of kinetic

parameters. Two different rate coefficients are used for demethylation and deethylation. Due

to the clear difference shown in the experimental product distributions for the ethane and

methane.

The model considering hydrogenolysis can describe reasonable well the responses of ethane,

propane, n-butane and iso-pentane. The model description for methane and iso-butane

however failed completely. This is due to the lack of experimental responses of these two

components.

The influence of the pressure and the space-time on the conversion of n-pentane and on the

selectivity to iso-pentane can be adequately described. The conversion is slightly

overestimated, which causes the selectivity to be underestimated. The influence of

temperature could not be investigated. Because all experiments under ideal hydrocracking

conditions are performed at the same temperature.

The statistical analysis shows that 9 model parameters are individually not significantly

estimated. This can be due to the way the statistical parameters are calculated. The

variance/covariance matrix depends on the difference between the experimental and the

model calculated value. The lack of experimental responses for methane and iso-butane may

be one of the main reasons for the poor statistical analysis obtained.


n-pentane: reaction network including hydrogenolysis 5.10: References

89

5.10 References

[1] Menon, P.G. and Z. Paal, Some aspects of the mechanisms of catalytic reforming reactions. Industrial & Engineering Chemistry Research, 1997. 36(8): p. 3282-3291.

[2] Govaerts, S., Ondersteuning van de ontwikkeling en optimalisering van katalysatoren

met behulp van fundamenteel kinetisch modellen, Master Project, 2007, Ghent University

[3] Bond, G.C. and R.H. Cunningham, Alkane transformations on supported platinum

catalysts .4. Kinetics of hydrogenolysis of ethane, propane, and n-butane on Pt/Al2O3 (EUROPT-3) and PtRe/Al2O3 (EUROPT-4). Journal of Catalysis, 1997. 166(2): p. 172-185.

[4] Bond, G.C., Kinetic modeling of metal-catalyzed reactions of alkanes. Industrial &

Engineering Chemistry Research, 1997. 36(8): p. 3173-3179. [5] Shang, S.B. and C.N. Kenney, Steady-State and Transient Kinetic-Studies of Ethane

Hydrogenolysis over Ru/Al2o3. Journal of Catalysis, 1992. 134(1): p. 134-150. [6] Kristyan, S. and J. Szamosi, Hydrogenolysis of Ethane .2. Initial Rate Measurements

over Ni and Pd Catalysts. Journal of the Chemical Society-Faraday Transactions I , 1988. 84: p. 917-921.

[7] Kristyan, S. and J. Szamosi, Mechanistic Study of the Catalytic Hydrogenolysis of

Ethane. Journal of the Chemical Society-Faraday Transactions I, 1984. 80: p. 1645-1650.

[8] Martens, G.G., et al., A fundamental kinetic model for hydrocracking of C-8 to C-12

alkanes on Pt/US-Y zeolites. Journal of Catalysis, 2000. 195(2): p. 253-267. [9] Thybaut, J.W., et al., Alkylcarbenium ion concentrations in zeolite pores during

octane hydrocracking on Pt/H-USY zeolite. Catalysis Letters, 2004. 94(1-2): p. 81-88.

[10] Dhepe, P.L., A. Fukuoka, and M. Ichikawa, Catalyst preparation using supercritical

carbon dioxide: preparation of Rh/FSM-16 catalysts and their catalytic performances in butane hydrogenolysis reaction. Catalysis Letters, 2002. 81(1-2): p. 69-75.

[11] Thybaut, J.W., Chemometrie en Ontwerp van experimenten. 2007-2008, Ghent

University.

90

Chapter 6

Hydroisomerization of n-pentane

in non-ideal hydrocracking

conditions

Abstract: In this chapter the implementation of non-ideal hydrocracking of light alkanes in the

computer code is described in detail. This implementation is done for the first time in a

hydrocracking computer code applying single-event concept. Some preliminary experiments

are performed as well.

As mentioned in Chapter 4, the relative strength of the metallic sites in comparison with the

acid sites controls the product distribution of the isomerization and cracking products. Under

ideal hydrocracking conditions, the (de)hydrogenation reactions on the metal sites can be

considered in quasi-equilibrium which implies that the reactions of the carbenium ions are rate

determining. Under non-ideal hydrocracking conditions, secondary cracking and isomerization

reactions can occur, as explained in section 4.1. High temperature and low pressure lead to

non-ideal hydrocracking.

Experiments obtained under non-ideal hydrocracking conditions show an aberrant behavior.

Our aim is to develop a microkinetic model able to describe this abnormal behavior.

The development of the reaction rates for ideal hydrocracking accounts with the quasi-

equilibrium of the (de)hydrogenation reaction. In non-ideal hydrocracking the concentration of

the olefin cannot be calculated from the concentration of the corresponding paraffin. It is

assumed that (de)protonation reactions are in quasi-equilibrium. Therefore the equilibrium

coefficient of this reaction family can be used to calculate the concentration of the carbenium


in non-ideal hydrocracking conditions 6.1: Reaction mechanism for non-ideal hydrocracking

91

ions from the corresponding olefin. Mass balances are applied to each paraffin and olefin of the

reaction network.

6.1 Reaction mechanism for non-ideal hydrocracking

The single-event methodology based upon elementary steps has been developed and applied so

far mainly for acid catalyzed reaction steps such as isomerization, cracking and alkylation of

hydrocarbons. An analogous methodology for (de)hydrogenation has been suggested by Van

engelandt [1].

In the development of the rate equations for non-ideal hydrocracking, it is assumed that

(de)hydrogenation reactions occur molecularly through an Eley-Rideal mechanism.

The reaction network when primary carbenium ions are considered consist of:

• 7 paraffins

• 10 olefins

• 15 carbenium ions

Assuming quasi-equilibrium for the (de)protonation reactions, this reaction network leads to 17

equations that need to be solved. This can be reduced to 16 when the residual amount of n-

pentane present in the product stream is calculated from the carbon balance. An alternative is to

solve all 17 equations and then perform a carbon balance for verification.

The net rate of formation of the alkane then becomes:

−−=

Mdeh

HMOM

PdehP K

pCCkR 2 (6-1)

Accounting for the chemisorptions on the metal surface, equation (6-1) can be rewritten using

the concentrations of physisorbed in the pores:

∑ ∑∑ ++ −−−−−− +++

−−

=

g jCj

M

Cji

OiM

OiPgM

Pg

deh

HOP

Mt

MPdeh

P CKCKCK

K

pCCCKk

R1

2

(6-2)

With:

MO

MPM

dehdeh K

KKK = (6-3)


in non-ideal hydrocracking conditions 6.1: Reaction mechanism for non-ideal hydrocracking

92

The alkene component surface concentration on the metal sites can be assumed to be very low

compared to the alkane surface concentrations under the experimental conditions used in this

work. Because of a more favorable interaction with a metal surface at equal partial pressures,

the concentration of unsaturated species on the metal surface is calculated to be a factor 10 to

100 higher than the saturated species surface concentration. However, under typical

equilibrium conditions, the ratio between saturated and unsaturated species in the vapor phase

amounts to 107, which means that 106 times more saturated than unsaturated species are

expected on the metal surface. If the (de)hydrogenation reactions are not quasi-equilibrated and

assuming 103 times more unsaturated species than under quasi-equilibrium conditions, still the

ratio of saturated to unsaturated species on the metal surface amounts to 102 to 103, which is

considered high enough to neglect the concentration of the unsaturated species on the metal

surface [2].

According to the assumption made previously about the (de)protonation reactions, a quasi-

equilibrium relationship is used between the alkene concentration and the corresponding

carbenium ion concentration

∑ −−−

=+

gOg

MOg

OAO

At

C CK

CKCC

1

(6-4)

For the alkenes pseudo steady-state hypothesis is applied [2]. This leads to the following

expression for the net rate of formation of a physisorbed n-alkene:

0*

,

*,

2 =

−−

−= −

−−−

−−−iso

OisoOn

AOniso

ndeh

HOnPn

MPnndehOn K

CCKk

K

pCCKkR (6-5)

With:

∑ −−+

=

gPg

MPg

Mtdeh

dehCK

Ckk

1* (6-6)

Atisoiso Ckk =* (6-7)

The alkene component concentrations are the only unknowns in equation (6-5). Development

of similar equations for the isomer and cracked alkene components lead to:


in non-ideal hydrocracking conditions 6.2: Influence of the operating conditions on ideality in hydrocracking

93

0**

,

*,

2 =−

−−

−= −−

−−−

−−−− Oiso

AOisocr

iso

OisoOn

AOniso

isodeh

HOisoPiso

MPisoisodehOiso CKk

K

CCKk

K

pCCKkR

(6-8)

02 *

,

*,

2 =+

−= −−

−−−− Oiso

AOisocr

crdeh

HOcrPcr

MPcrcrdehOcr CKk

K

pCCKkR (6-9)

The net production rate of the carbenium ions remain the same as for ideal hydrocracking.

∑∑∑∑

∑∑∑∑

−+

−=+

l ovukiol

l ovukiol

l oolki

PCPAS

l okiol

PCPASPCPAS

R

OmmrOmmr

mmrmmrRki

),;(),;(

);();(

,,,,,,

,,/

,,///

,

ββ

β

(6-10)

6.2 Influence of the operating conditions on ideality in

hydrocracking

The occurrence of ideal hydrocracking is dependent both on the type of catalyst and on the

operating conditions. Catalysts exhibiting ideal hydrocracking under one set of operating

conditions may exhibit non-ideal hydrocracking under another set of operating conditions. The

effect of the operating conditions on the ideality of the hydrocracking behavior on a given

catalyst is illustrated in Figure 6-1. The upper curve represents the isomerization conversion as

a function of the total conversion under ideal hydrocracking conditions. The lower the

maximum in the other curves, the stronger the deviation from ideal hydrocracking. Under ideal

hydrocracking conditions, an apparently unique relationship exist between product yields and

total conversion.


in non-ideal hydrocracking conditions 6.2: Influence of the operating conditions on ideality in hydrocracking

94

Figure 6-1: Simulated isomerization conversion of n-alkane on Pt/USY as a function of the total conversion of n-alkane under ideal and non-ideal hydrocracking conditions: at 520 K (diamonds), 540 K (circles), 560 K (triangles), and 580 K (squares) and at 0.1 MPa (open symbols), 0.35 MPa (light shaded symbols), 1 MPa (dark shaded symbols), and 10 MPa

(closed symbols) [2].

Increasing the temperature favors non-ideal hydrocracking. The same effect was noticed when

the total pressure is reduced. A detailed explanation is given elsewhere [3, 4]. In non-ideal

hydrocracking, the rates increase with pressure, as for ideal hydrocracking the rates decrease

with increasing pressure. This is also shown in Figure 3-5. This effect is related to the effect of

total pressure on the alkene and hence carbenium ion formation [2]. In non-ideal

hydrocracking, i.e. when (de)hydrogenation reactions are not quasi-equilibrated, a kinetic effect

of an increasing dehydrogenation rate leading to higher alkene and carbenium concentrations is

observed. These higher carbenium ion concentrations will increase the rate of the acid-

catalyzed isomerization and cracking reactions, leading to higher hydrocracking rates with the

total pressure because the number of moles increases upon dehydrogenation. The lower

carbenium ion concentration lead to lower reaction rates for the acid-catalyzed isomerization

and cracking, leading to lower hydrocracking rates with increasing total pressure [4].

A third observation that was made by Thybaut et al. [4] with respect to the effect of the

operating conditions on the ideal hydrocracking behavior was that higher molar hydrogen-to-

hydrocarbon ratios favor non-ideal hydrocracking. This effect seems less evident than the

temperature or pressure effect. One could expect that the reaction rate would increase as the

amount of hydrogen present increases. However, an increase of the hydrogen-to-hydrocarbon

ratio will hardly affect the hydrogen partial pressure. The influence of the increased hydrogen-


in non-ideal hydrocracking conditions 6.3: Application of single-event microkinetic modeling on the (de)hydrogenation

reactions

95

to-hydrocarbon ratio on the partial pressure of the hydrocarbons will be much stronger. This

partial pressure effect is invoked to explain the observed effect of the molar hydrogen-to-

hydrocarbon ration on the non-ideal character of the hydrocracking experiments [4, 5].

6.3 Application of single-event microkinetic modeling on

the (de)hydrogenation reactions

In contrast to the mechanism for the acid-catalyzed reactions no literature agreement exists for

the mechanism of the metal catalyzed hydrogenation reactions. In some models a rate-

determining step in the hydrogenation sequence is assumed [6, 8], while in others no rate

determining step is assumed [9]. Because of this lack of agreement the single-event

methodology for (de)hydrogenation is related to the global (de)hydrogenation reaction. This is

in fact not in line with the original single-event philosophy which considers elementary steps.

The single-event rate coefficient for (de)hydrogenation corresponds to a rate-determining

elementary step, which is assumed to be the surface reaction step.

Verstraete [10] assumed that the dehydrogenation rate coefficients for saturated hydrocarbons

are assumed to depend only on the structure of the double bond which is formed, i.e., whether

the carbon atoms involved in the dehydrogenation are primary, secondary or tertiary carbon

atoms. This assumption was based on an increasing steric hindrance in hydrogen abstraction

and an increasing alkene stability with the degree of substitution of the carbon atoms involved

in the double bond formation. However, for the present work, initially it is assumed one rate

coefficient exist for all the dehydrogenation reactions. In a future work the extension can be

done towards rate coefficients depending on the types of carbon atoms involved.

Verstraete [10] used statistical factors instead of symmetry numbers [11, 12]. The numbers of

single-events, ne, for an acid-catalyzed elementary step being defined as the ratio of the

symmetry numbers of reactant and activated complex, is replaced by the numbers of identical

transformations, ns, for a metal-catalyzed reaction which is calculated as the ratio of the

statistical factors of reactant and product molecules. In the present work the number of

identical transformations is set equal to one.


in non-ideal hydrocracking conditions 6.4: Implementation in the computer code.

96

6.4 Implementation in the computer code.

Non-ideal hydrocracking implies the non-quasi-equilibration of the (de)hydrogenation

reactions. Apart from the 7 paraffins, the olefins will also be variables of the system. For 6

paraffins mass balances, which are differential equations, have to be solved. The outlet molar

flow of n-pentane is calculated using a carbon balance. In order to calculate the concentrations

of the olefins, the pseudo steady-state approximation is applied, which states that the net rate of

formation is equal to zero. The mass balances for the olefins are thereby simplified to nonlinear

algebraic equations. Since the (de)protonation reactions are assumed at quasi-equilibrium, the

concentration of the carbenium ions is calculated by the (de)protonation equilibrium coefficient

and the concentration from the olefins. This results in a set of 16 equations, from which 6 are

differential and 10 are algebraic, that have to be solved by a computer program.

This set of equations is solved simultaneously with the numerical subroutine DASPK from

Netlib software library [13]. DASPK uses variable-step size backward differentiation formulas

(BDF) applying either direct linear system methods or a preconditioned Krylov iterative

method. In the present work, the direct method was applied and therefore a dense matrix solver

is chosen. This means that the matrix of partial derivatives of the system of differential

equations is approximated by numerical differences.

BDF is a popular multistep method for stiff problems. The problem is referred to as being stiff

if the absolute stability requirement dictates a much smaller step size than is needed to satisfy

approximation requirements alone. BDF methods are implicit and are usually implements

together with a modified Newton method to solve the nonlinear system at each time step [14,

15].

For one-step methods, e.g. Runge-Kutta methods, 0)0( yy = is the only initial value necessary

for the system:

0),,( =′yytG (6-11)

to start up the iteration.

With a multistep method like BDF, e.g. a k-step method, k initial values 110 ,...,, −kyyy are

needed to start the iterative cycle. These additional initial values 121 ,...,, −kyyy must be )( phO

accurate for a method of order p, if the full convergence order is to be realized. If error control

is used, these additional starting values must be accurate to a given error tolerance. This means


in non-ideal hydrocracking conditions 6.4: Implementation in the computer code.

97

that in order to be able to apply DASPK the integration must start with a consistent set of initial

conditions 0y and 0y′ . Consistency requires in particular that 0),,( 000 =′yytG . The initial

concentration of the gas-phase components is known, but the initial concentration of the

intermediate species is not known however.

Because the algebraic equations for the olefins are nonlinear, reasonable initial guesses must be

provided as input to the solver in order to reach convergence. Hence the numerical subroutine

DNSQE also available at Netlib library, is used to solve the set of nonlinear algebraic equations

by implementation of a hybrid Powell method. This subroutine will provide the reasonable

initial values of the variables associated with the algebraic equations required by DASPK to

converge efficiently for different parameter values.

The subroutine DASPK provides optional strategy for solving the initialization problem when

some of the variables are unknown in the initial point [16]. In this case the unknown variables

are the variables associates with the algebraic equations.

DASPK has an integer array argument INFO which is used to specify a variety of options [7].

In order to have DASPK solve the initialization problem for which the differential variables Yd

are specified and the algebraic variable (Ya) are unknown, INFO(11), has to be put to 1. In this

case, the user must identify the differential and algebraic components of Y, by setting an array

ID as part of the integer work array INTWORKM:

• ID(I) = +1 if Y(I) is a differential variable

• ID(I) = -1 if Y(I) is an algebraic variable.

Control can be returned back to the calling program immediately after the initial condition

calculation, before proceeding to the integration of the system (e.g. to examine the computed

0y and 0y′ ) by setting INFO(14) equal to 1. If this is done, and if the initialization succeeded,

INFO(11) is reset to 0 for the next call, to prevent the solver from repeating the initialization

and to avoid an infinite loop.

A maximum step size can be specified, so that the code will avoid passing over very large

regions. Also differential/algebraic problems may occasionally suffer from severe scaling

difficulties on the first step. To alleviate this problem it can help to specify an initial step size

h0. These specifications are also applied through the integer INFO array. The specific values

can be given in an input file.

When the consistent initial values of the concentrations for olefins and carbenium ions are

calculated, also the derivatives of the initial solution components have to be determined.


in non-ideal hydrocracking conditions 6.5: Preliminary results

98

Therefore the subroutine FCN_DDASPK will be called once before the main subroutine

DDASPK is called.

6.5 Preliminary results

In order to prove the computer code is running some preliminary estimation is performed. The

experimental set VMB26 is used for the regression of the kinetic parameters.

Regression have been performed as explained in section 2.2.5

The values for the kinetic parameters according to this preliminary regression are given in

Table 6-1.

Table 6-1: Estimated values for the model parameters in case that primary carbenium ions are considered under non-ideal hydrocracking conditions.

Parameter Value

[kJ/mol]

)( pH pr∆ -13.663 (± 0.001)

)(sH pr∆ -68.953 (± 0.004)

)(tH pr∆ -105.94

dehaE , 50.0032 (±0.0002)

),(, spE ASa 124.32 (± 0.18)

),(, ppE PCPa Not significantly estimated

),(, spE PCPa Not significantly estimated

),(, ssE PCPa 106.705 (± 0.06)

),(, ppEa β 90.467 (± 0.01)

),(, spEa β 116.182 (± 0.01)

),(, psEa β 142.965 (± 0.01)

),(, ptEa β 150.517 (± 0.008)


in non-ideal hydrocracking conditions 6.5: Preliminary results

99

The estimated values for the activation energies for PCP-branching starting from a primary

carbenium ion are not significantly different than zero. This is because the influence of the

activation energy for PCP-branching from a secondary carbenium ion is much higher. The

initial parameter values for the regression have to improve in order to estimate the other

activation energies for PCP-branching significantly. The parity diagrams with these

preliminary results are shown in Figure 6-2.

a) b)

c) d)

e) f)

Figure 6-2: Parity diagrams for the molar exit flows of the hydroisomerization products of n-pentane on a Pt/H-BEA 0.6 wt% catalyst for non-ideal hydrocracking. (a) ethane, (b) propane, (c) iso-pentane, (d) n-butane, (e) methane and (f)

iso-butane (VMB 26).

0E+00

1E-07

2E-07

3E-07

4E-07

0E+00 1E-07 2E-07 3E-07

F be

r(m

ol/

s)

Fexp (mol/s)

0E+00

1E-07

2E-07

3E-07

4E-07

0E+00 1E-07 2E-07 3E-07

Fb

er(m

ol/

s)

Fexp (mol/s)

0E+00

1E-07

2E-07

3E-07

4E-07

5E-07

0E+00 1E-07 2E-07 3E-07 4E-07 5E-07

Fb

er(m

ol/

s)

Fexp (mol/s)

0E+00

1E-07

2E-07

3E-07

0E+00 5E-08 1E-07 2E-07

Fb

er(m

ol/

s)

Fexp (mol/s)

0E+00

1E-07

2E-07

0E+00 5E-08 1E-07 2E-07 2E-07

Fb

er(m

ol/

s)

Fexp (mol/s)

0E+00

1E-07

0E+00 1E-08 2E-08 3E-08 4E-08

Fb

er(m

ol/

s)

Fexp (mol/s)


in non-ideal hydrocracking conditions 6.6: Conclusions

100

The regression of the model is still to be improved but these preliminary results are

encouraging to continue working on this direction. For these results, only one rate coefficient is

assumed for all dehydrogenation reactions. A further improvement of the model, for instance,

will probably be achieved by considering different kinetic coefficients for different

(de)hydrogenation reactions

6.6 Conclusions

A single-event methodology to metal catalyzed reactions in general and to the

(de)hydrogenation of (un)-saturated cyclic components in particular has been proposed by

Verstraete [5, 10]. However this methodology has not been applied as such so far.

The computer code developed in this chapter for the single-event microkinetic modeling of the

non-quasi-equilibrium of the (de)hydrogenation reactions was the first application in a

hydrocracking computer code at the single-event molecular scale.

Non-ideal hydrocracking implies that the (de)hydrogenation reactions are not in quasi-

equilibrium. However, it is assumed that the (de)protonation reactions are still at quasi-

equilibrium. At the first step, a single rate coefficient is assumed for all the dehydrogenation

reactions.

The classical reaction network including primary carbenium ions consists of 7 paraffins, 10

olefins and 15 carbenium ions. The mass balances for the paraffins lead to ordinary differential

equations. Because the residual stream for n-pentane will be calculated from the carbon

balance, only 6 differential equations will be solved. For the net rates of formation of the

olefins, the pseudo-steady state approximation is applied. Therefore the mass balances of these

components will be simplified to nonlinear algebraic equations.

In the objective function defined in equation (2-29) the calculated values follow from the

solution of the set of the ordinary differential equations and nonlinear algebraic equations. This

set of equations is solved simultaneously with the numerical subroutine DASPK from the

Netlib software library. When using DASPK, the integration must start with a consistent set of

initial conditions 0y and 0y′ . In this case, the variables associated with the algebraic

equations will be unknown. Because this algebraic equations will be nonlinear, reasonable

initial guesses must be provided as input to the solver in order to reach convergence. Hence, the


in non-ideal hydrocracking conditions 6.6: Conclusions

101

numerical subroutine DNSQE, also available at Netlib software library, is used to first solve the

set of 10 nonlinear algebraic equations. The solution of this system will then be used as initial

values for the olefin concentrations.

In order to calculate the first derivatives of the initial guesses the subroutine FCN_DDASPK is

applied first before DASPK. DASPK itself provides also an optional strategy for solving the

initialization problem when some of the variables are unknown in the initial point.

Immediately after the initial calculation, before proceeding to the integration of the system,

control is returned to the calling program to examine the computed 0y and 0y′ . Afterwards

DASPK is called again to complete the algorithm.

Some preliminary results are shown as well. Although the regression of the model is not

reasonable yet, these results shown here are encouraging to continue working on this direction.

An improvement of the model will be achieved by considering different rate coefficients,

dependent on the type of carbon atom involved in the dehydrogenation reaction.


in non-ideal hydrocracking conditions 6.7: References

102

6.7 References

[1] Vanengelandt, W., Reformuleren van Nafta door selectieve hydrokraking, PhD Thesis, 1998,Ghent University

[2] Ward, J.W., Hydrocracking Processes and Catalysts. Fuel Processing Technology,

1993. 35(1-2): p. 55-85. [3] Debrabandere, B. and G.F. Froment, Influence of the hydrocarbon chain length on the

kinetics of the hydroisomerization and hydrocracking of n-paraffins. Hydrotreatment and Hydrocracking of Oil Fractions, 1997. 106: p. 379-389.

[4] Thybaut, J.W., et al., Acid-metal balance of a hydrocracking catalyst: Ideal versus non-

ideal behavior. Industrial & Engineering Chemistry Research, 2005. 44(14): p. 5159-5169.

[5] Thybaut, J.W., Production of low-aromatic fuels: kinetics and industrial application of

hydrocracking, PhD thesis, 2005,Ghent University [6] Rahaman, M.V. and M.A. Vannice, The Hydrogenation of Toluene and Ortho-Xylene,

Meta-Xylene, and Para-Xylene over Palladium .2. Reaction Model. Journal of Catalysis, 1991. 127(1): p. 267-275.

[7] Lin, S.D. and M.A. Vannice, Hydrogenation of Aromatic-Hydrocarbons over

Supported Pt Catalysts .1. Benzene Hydrogenation. Journal of Catalysis, 1993. 143(2): p. 539-553.

[8] Kehoe, J.P.G. and J.B. Butt, Kinetics of Benzene Hydrogenation by Supported Nickel at

Low-Temperature. Journal of Applied Chemistry and Biotechnology, 1972. 22(1): p. 23-&.

[9] Chou, P. and M.A. Vannice, Benzene Hydrogenation over Supported and Unsupported

Palladium .2. Reaction Model. Journal of Catalysis, 1987. 107(1): p. 140-153. [10] Verstraete, J., Kinetische studie van de katalytische reforming van nafta over een Pt-

Sn/Al2O3 Katalysator, PhD thesis, 1997,Ghent University [11] Bishop, D.M. and K.J. Laidler, Symmetry Numbers and Statistical Factors in Rate

Theory. Journal of Chemical Physics, 1965. 42(5): p. 1688-&. [12] Bishop, D.M. and K.J. Laidler, Statistical Factors for Chemical Reactions. Transactions

of the Faraday Society, 1970. 66(571): p. 1685-&. [13] www.netlib.org.


in non-ideal hydrocracking conditions 6.7: References

103

[14] Ascher, U.M. and L.R. Petzold, Computer methods for ordinary differential equations and differential-algebraic equations. 1998: Society for Industrial and Applied Mathematics: Philadelphia.

[15] Ascher, U.M. and R.J. Spiteri, Collocation Software for Boundary-Value Differential-

Algebraic Equations. Siam Journal on Scientific Computing, 1994. 15(4): p. 938-952. [16] Brown, P.N., A.C. Hindmarsh, and L.R. Petzold, Consistent initial condition

calculation for differential-algebraic systems. Siam Journal on Scientific Computing, 1998. 19(5): p. 1495-1512.

104

Chapter 7

Conclusions

At the University of Munich hydroisomerization of n-pentane on a Pt/H-BEA 0.6 wt%

bifunctional catalyst was investigated. The conversion of n-pentane and the selectivity to iso-

pentane was analyzed. After a sulfur treatment of the catalyst at different temperatures a

remarkable increase in selectivity was observed. In order to explain this phenomenon and to

optimize the catalysts used in industrial hydroisomerization of light alkanes a better insight in

the reaction mechanism for hydroisomerization of light alkanes by microkinetic modeling has

been performed in this work.

The laboratory reactor is modeled based on a pseudo-homogenous one-dimensional reactor

model. The experiments on the hydroisomerization of n-pentane were performed at the

University of Munich on 20-fold parallel fixed bed reactors (plug flow), leading to ordinary

differential equations, while the experiments for the hydroisomerization of n-hexane were

performed at LPT on a Berty reactor (CSTR) leading to algebraic equations. The latter

experiments were obtained as part of the present work.

A single-event microkinetic model was applied. This fundamental model considers the kinetics

of all the elementary steps of the reaction network. The classical reaction network consists of 6

reaction families, i.e., (de)hydrogenation, (de)protonation, alkyl shifts, hydride shifts, PCP

branching and β-scission reactions. It is assumed that (de)hydrogenation and (de)protonation

reactions are quasi-equilibrated. Moreover only secondary and tertiary carbenium ions are

considered. When n-pentane is used as feed component, no β-scission reactions considering

only secondary and tertiary carbenium ions can occur. According to the experimental data,

cracking does occur. Therefore, the reaction network had to be extended.

Initially, the classical reaction network is extended considering the formation of primary

carbenium ions. This approach assumes that carbenium ions can act as reactant and product.

Another approach is to consider metal-catalyzed cracking reactions, i.e., hydrogenolysis,

instead of acid-catalyzed reactions. In this type of reactions methane and ethane are separated

Fout! Gebruik het tabblad Start om Heading 1 toe te passen op de tekst die u hier wilt weergeven.

105

from the alkane. In this case, it has been assumed that only n-pentane and iso-pentane can

undergo hydrogenolysis reactions. Both modifications are performed separately.

Based on the residual sum of squares and on the parity diagrams, the reaction network

including hydrogenolysis gives a better result describing the experimental data. For both

models the fit for methane and iso-butane failed however. This is because for most of the

experimental conditions the concentration of these species was zero.

Considering hydrogenolysis and as a further work, the pre-exponential factors should be

calculated using statistical thermodynamics in order to have a consistent approach for all the

pre-exponential factors. The parity diagrams can also be improved by considering secondary

hydrogenolysis reactions. If these modifications do not significantly improve the parity

diagrams, both primary carbenium ions and hydrogenolysis should be taken into account in the

reaction network. The presence of experiments obtained under non-ideal hydrocracking

conditions obliged the implementation of the non-quasi-equilibration of the (de)hydrogenation

reactions in the computer code. In this case, the concentration of the olefins are variables as

well as the concentration of the paraffins. The (de)hydrogenation kinetic coefficients have to be

estimated now instead of using the equilibrium coefficients as previously in the ideal

hydrocracking case. For simplicity, only one rate coefficient is assumed for all

dehydrogenation reactions as a first step.

For the non-ideal hydrocracking, apart from the 6 differential equations resulting from the

reactor model applied to the paraffins, the pseudo-steady state approximation is assumed for

the olefins, leading to 10 additional nonlinear algebraic equations. This set of algebraic and

differential equations is solved simultaneously with the numerical subroutine DASPK. Proper

initial guesses for the concentrations of the olefins are obtained by solving only the algebraic

equations with the DNSQE-subroutine. The computer code developed in this work is the first

implementation in a hydrocracking code of the non-quasi equilibrium of the (de)hydrogenation

reactions at a single-event molecular scale. The regression of the model is still to be improved

but preliminary results shown here are encouraging to continue working on this direction. A

further improvement of the model, for instance, can be achieved by considering different

kinetic coefficients for different (de)hydrogenation reactions.

Under ideal hydrocracking conditions the reaction network extended with hydrogenolysis

presented the best results. The implementation of hydrogenolysis under non-ideal

hydrocracking conditions could be a future reaction network to investigate.

:

Experimental results for the hydroisomerization experiments on the 20-fold parallel plug flow reactor

106

Appendix A : Experimental results for the hydroisomerization

experiments on the 20-fold parallel plug flow

reactor

A.1 Initial conditions on the Pt/H-BEA 0.6 wt% catalyst

Table A-1: Inlet conditions for the hydroisomerization experiments of n-pentane on a Pt/H-BEA 0.6 wt% catalyst

nr EXP Pressure [bar]

catalyst weight [10-3 gcat]

Temperature [° C]

Space time [gcat s mol-1]

F n-C5 / [mol/s]

F iso-C5 [mol/s]

F H2 (mol/s)

Ratio H2/C5

1 VMB01 3 30 260 26.13 1.14E-06 7.67E-09 4.43E-05 38.56 2 VMB01 3 30 260 26.39 1.14E-06 7.67E-09 4.43E-05 38.56 3 VMB01 3 30 267 26.51 1.12E-06 7.57E-09 4.37E-05 38.62 4 VMB01 3 30 267 26.78 1.12E-06 7.57E-09 4.37E-05 38.62 5 VMB01 3 30 274 26.85 1.11E-06 7.47E-09 4.31E-05 38.62 6 VMB01 3 30 274 27.12 1.11E-06 7.47E-09 4.31E-05 38.62 7 VMB01 3 30 281 27.19 1.10E-06 7.81E-09 4.26E-05 38.62 8 VMB01 3 30 281 27.46 1.10E-06 7.81E-09 4.26E-05 38.62 9 VMB01 3 30 288 27.34 1.09E-06 7.72E-09 4.21E-05 38.34 10 VMB01 3 30 288 27.61 1.09E-06 7.72E-09 4.21E-05 38.34 11 VMB01 3 30 295 27.84 1.07E-06 7.62E-09 4.16E-05 38.57

:


107

12 VMB01 3 30 295 28.12 1.07E-06 7.62E-09 4.16E-05 38.57 13 VMB01 3 30 302 28.10 1.06E-06 7.95E-09 4.11E-05 38.46 14 VMB01 3 30 302 28.38 1.06E-06 7.95E-09 4.11E-05 38.46 15 VMB01 3 30 309 28.46 1.05E-06 7.85E-09 4.06E-05 38.49 16 VMB01 3 30 309 28.75 1.05E-06 7.85E-09 4.06E-05 38.49 17 VMB01 3 30 316 28.85 1.03E-06 7.76E-09 4.01E-05 38.56 18 VMB01 3 30 316 29.14 1.03E-06 7.76E-09 4.01E-05 38.56 19 VMB01 3 30 323 29.18 1.02E-06 7.67E-09 3.96E-05 38.54 20 VMB01 3 30 323 29.47 1.02E-06 7.67E-09 3.96E-05 38.54 21 VMB01 3 30 330 29.24 1.02E-06 7.98E-09 3.92E-05 38.17 22 VMB01 3 30 330 29.53 1.02E-06 7.98E-09 3.92E-05 38.17 23 VMB01 3 30 337 29.81 9.99E-07 7.49E-09 3.87E-05 38.46 24 VMB01 3 30 337 30.10 9.99E-07 7.49E-09 3.87E-05 38.46 25 VMB01 3 30 344 30.15 9.88E-07 7.41E-09 3.83E-05 38.46 26 VMB01 3 30 344 30.45 9.88E-07 7.41E-09 3.83E-05 38.46 27 VMB01 3 30 351 30.67 9.71E-07 7.32E-09 3.79E-05 38.70 28 VMB01 3 30 351 30.98 9.71E-07 7.32E-09 3.79E-05 38.70 1 VMB02 4 30 280 57.37 5.19E-07 3.81E-09 1.77E-05 33.90 2 VMB02 4 30 280 57.94 5.19E-07 3.81E-09 1.77E-05 33.90 3 VMB02 4 30 280 42.62 6.99E-07 5.07E-09 1.75E-05 24.93 4 VMB02 4 30 280 43.04 6.99E-07 5.07E-09 1.75E-05 24.93 5 VMB02 4 30 280 34.26 8.70E-07 6.16E-09 1.74E-05 19.84 6 VMB02 4 30 280 34.60 8.70E-07 6.16E-09 1.74E-05 19.84 7 VMB02 4 30 280 28.49 1.05E-06 7.43E-09 1.72E-05 16.33 8 VMB02 4 30 280 28.77 1.05E-06 7.43E-09 1.72E-05 16.33 9 VMB02 4 30 280 24.19 1.23E-06 8.70E-09 1.70E-05 13.71 10 VMB02 4 30 280 24.43 1.23E-06 8.70E-09 1.70E-05 13.71 11 VMB02 4 30 280 20.89 1.43E-06 9.97E-09 1.68E-05 11.71 12 VMB02 4 30 280 21.10 1.43E-06 9.97E-09 1.68E-05 11.71 13 VMB02 6.5 30 280 37.47 7.95E-07 6.12E-09 4.03E-05 50.31 14 VMB02 6.5 30 280 37.84 7.95E-07 6.12E-09 4.03E-05 50.31 15 VMB02 6.5 30 280 27.82 1.07E-06 7.75E-09 4.00E-05 37.08

:


108

16 VMB02 6.5 30 280 28.10 1.07E-06 7.75E-09 4.00E-05 37.08 17 VMB02 6.5 30 280 22.40 1.33E-06 9.38E-09 3.97E-05 29.66 18 VMB02 6.5 30 280 22.62 1.33E-06 9.38E-09 3.97E-05 29.66 19 VMB02 6.5 30 280 18.35 1.62E-06 1.14E-08 3.94E-05 24.11 20 VMB02 6.5 30 280 18.53 1.62E-06 1.14E-08 3.94E-05 24.11 21 VMB02 6.5 30 280 15.84 1.88E-06 1.35E-08 3.92E-05 20.68 22 VMB02 6.5 30 280 16.00 1.88E-06 1.35E-08 3.92E-05 20.68 23 VMB02 6.5 30 280 13.85 2.15E-06 1.51E-08 3.89E-05 17.95 24 VMB02 6.5 30 280 13.99 2.15E-06 1.51E-08 3.89E-05 17.95 25 VMB02 9 30 280 27.89 1.07E-06 7.97E-09 7.19E-05 66.89 26 VMB02 9 30 280 28.17 1.07E-06 7.97E-09 7.19E-05 66.89 27 VMB02 9 30 280 20.51 1.45E-06 1.01E-08 7.15E-05 48.90 28 VMB02 9 30 280 20.72 1.45E-06 1.01E-08 7.15E-05 48.90 29 VMB02 9 30 280 16.52 1.80E-06 1.30E-08 7.12E-05 39.19 30 VMB02 9 30 280 16.68 1.80E-06 1.30E-08 7.12E-05 39.19 31 VMB02 9 30 280 13.66 2.18E-06 1.52E-08 7.08E-05 32.23 32 VMB02 9 30 280 13.80 2.18E-06 1.52E-08 7.08E-05 32.23 33 VMB02 9 30 280 11.76 2.53E-06 1.74E-08 7.04E-05 27.60 34 VMB02 9 30 280 11.87 2.53E-06 1.74E-08 7.04E-05 27.60 35 VMB02 9 30 280 10.29 2.89E-06 2.03E-08 7.01E-05 24.04 36 VMB02 9 30 280 10.40 2.89E-06 2.03E-08 7.01E-05 24.04 1 VMB03 11.5 30 280 6.71 4.48E-06 3.06E-08 1.10E-04 24.27 2 VMB03 11.5 30 280 6.65 4.48E-06 3.06E-08 1.10E-04 24.27 3 VMB03 11.5 30 280 8.40 3.58E-06 2.49E-08 1.10E-04 30.60 4 VMB03 11.5 30 280 8.31 3.58E-06 2.49E-08 1.10E-04 30.60 5 VMB03 11.5 30 280 11.33 2.66E-06 1.81E-08 1.11E-04 41.63 6 VMB03 11.5 30 280 11.22 2.66E-06 1.81E-08 1.11E-04 41.63 7 VMB03 14 30 280 5.52 5.45E-06 3.75E-08 1.59E-04 28.91 8 VMB03 14 30 280 5.47 5.45E-06 3.75E-08 1.59E-04 28.91 9 VMB03 14 30 280 6.95 4.33E-06 2.94E-08 1.60E-04 36.65 10 VMB03 14 30 280 6.88 4.33E-06 2.94E-08 1.60E-04 36.65 11 VMB03 14 30 280 9.64 3.12E-06 2.12E-08 1.61E-04 51.25

:


109

12 VMB03 14 30 280 9.55 3.12E-06 2.12E-08 1.61E-04 51.25 13 VMB03 16.5 30 280 4.71 6.39E-06 4.44E-08 2.17E-04 33.71 14 VMB03 16.5 30 280 4.66 6.39E-06 4.44E-08 2.17E-04 33.71 15 VMB03 16.5 30 280 5.92 5.08E-06 3.55E-08 2.18E-04 42.71 16 VMB03 16.5 30 280 5.87 5.08E-06 3.55E-08 2.18E-04 42.71 17 VMB03 16.5 30 280 8.02 3.75E-06 2.66E-08 2.20E-04 58.14 18 VMB03 16.5 30 280 7.94 3.75E-06 2.66E-08 2.20E-04 58.14 19 VMB03 19 30 280 4.09 7.36E-06 4.93E-08 2.84E-04 38.42 20 VMB03 19 30 280 4.05 7.36E-06 4.93E-08 2.84E-04 38.42 21 VMB03 19 30 280 5.18 5.81E-06 4.06E-08 2.86E-04 48.88 22 VMB03 19 30 280 5.13 5.81E-06 4.06E-08 2.86E-04 48.88 23 VMB03 19 30 280 6.98 4.31E-06 2.90E-08 2.88E-04 66.25 24 VMB03 19 30 280 6.91 4.31E-06 2.90E-08 2.88E-04 66.25 25 VMB03 21.5 30 280 6.23 4.83E-06 3.30E-08 3.65E-04 74.93 26 VMB03 21.5 30 280 3.60 8.28E-06 5.50E-08 3.61E-04 43.33 27 VMB03 21.5 30 280 3.64 8.28E-06 5.50E-08 3.61E-04 43.33 28 VMB03 21.5 30 280 4.54 6.56E-06 4.40E-08 3.63E-04 54.90 29 VMB03 21.5 30 280 4.59 6.56E-06 4.40E-08 3.63E-04 54.90 30 VMB03 21.5 30 280 6.17 4.83E-06 3.30E-08 3.65E-04 74.93 31 VMB03 24 30 280 4.96 6.07E-06 4.08E-08 4.50E-04 73.68 32 VMB03 24 30 280 5.51 5.41E-06 3.62E-08 4.51E-04 82.68 33 VMB03 24 30 280 5.56 5.41E-06 3.62E-08 4.51E-04 82.68 34 VMB03 24 30 280 4.91 6.07E-06 4.08E-08 4.50E-04 73.68 35 VMB03 24 30 280 4.12 7.31E-06 4.98E-08 4.49E-04 60.96 36 VMB03 24 30 280 4.08 7.31E-06 4.98E-08 4.49E-04 60.96 37 VMB03 24 30 280 3.20 9.39E-06 6.34E-08 4.47E-04 47.22 38 VMB03 24 30 280 3.17 9.39E-06 6.34E-08 4.47E-04 47.22 1 VMB04 4 30 280 90.18 3.30E-07 2.36E-09 1.79E-05 53.85 2 VMB04 4 30 280 91.08 3.30E-07 2.36E-09 1.79E-05 53.85 3 VMB04 6 30 280 44.79 6.65E-07 4.62E-09 3.51E-05 52.39 4 VMB04 6 30 280 45.24 6.65E-07 4.62E-09 3.51E-05 52.39 5 VMB04 8 30 280 26.73 1.11E-06 7.63E-09 5.80E-05 51.66

:


110

6 VMB04 8 30 280 26.99 1.11E-06 7.63E-09 5.80E-05 51.66 7 VMB04 10 30 280 17.91 1.66E-06 1.14E-08 8.66E-05 51.71 8 VMB04 10 30 280 18.09 1.66E-06 1.14E-08 8.66E-05 51.71 9 VMB04 12 30 280 12.21 2.44E-06 1.71E-08 1.21E-04 49.20 10 VMB04 12 30 280 12.33 2.44E-06 1.71E-08 1.21E-04 49.20 11 VMB04 14 30 280 9.07 3.29E-06 2.28E-08 1.61E-04 48.63 12 VMB04 14 30 280 9.16 3.29E-06 2.28E-08 1.61E-04 48.63 13 VMB04 16 30 280 7.01 4.25E-06 2.93E-08 2.07E-04 48.31 14 VMB04 16 30 280 7.08 4.25E-06 2.93E-08 2.07E-04 48.31 15 VMB04 18 30 280 5.57 5.35E-06 3.66E-08 2.58E-04 47.95 16 VMB04 18 30 280 5.63 5.35E-06 3.66E-08 2.58E-04 47.95 17 VMB04 20 30 280 4.52 6.59E-06 4.47E-08 3.15E-04 47.52 18 VMB04 20 30 280 4.57 6.59E-06 4.47E-08 3.15E-04 47.52 19 VMB04 22 30 280 3.78 7.88E-06 5.37E-08 3.78E-04 47.64 20 VMB04 22 30 280 3.82 7.88E-06 5.37E-08 3.78E-04 47.64 21 VMB04 24 30 280 3.17 9.39E-06 6.34E-08 4.47E-04 47.26 22 VMB04 24 30 280 3.21 9.39E-06 6.34E-08 4.47E-04 47.26 23 VMB04 26 30 280 2.71 1.10E-05 7.40E-08 5.21E-04 47.12 24 VMB04 26 30 280 2.74 1.10E-05 7.40E-08 5.21E-04 47.12 25 VMB04 28 30 280 2.36 1.26E-05 8.53E-08 6.01E-04 47.31 26 VMB04 28 30 280 2.39 1.26E-05 8.53E-08 6.01E-04 47.31 1 VMB17 3 20 320 29.60 6.64E-07 5.14E-09 2.66E-05 39.73 1 VMB26 3 20 260 10.47 1.88E-06 1.35E-08 8.90E-05 47.08 2 VMB26 3 20 266 10.60 1.85E-06 1.34E-08 8.80E-05 47.12 3 VMB26 3 20 272 10.68 1.84E-06 1.32E-08 8.70E-05 46.94 4 VMB26 3 20 278 10.84 1.81E-06 1.31E-08 8.61E-05 47.12 5 VMB26 3 20 280 10.99 1.79E-06 1.30E-08 8.58E-05 47.61 6 VMB26 3 20 280 10.89 1.80E-06 1.30E-08 8.58E-05 47.19 7 VMB26 3 20 284 10.98 1.79E-06 1.30E-08 8.52E-05 47.22 8 VMB26 3 20 290 11.04 1.78E-06 1.28E-08 8.42E-05 46.96 9 VMB26 3 20 296 11.40 1.72E-06 1.27E-08 8.34E-05 48.04 10 VMB26 3 20 314 11.51 1.71E-06 1.31E-08 8.08E-05 47.01

:


111

11 VMB26 3 20 320 11.65 1.69E-06 1.30E-08 8.00E-05 47.08 12 VMB26 3 20 302 11.50 1.71E-06 1.25E-08 8.25E-05 47.92 13 VMB26 3 20 308 11.76 1.67E-06 1.24E-08 8.17E-05 48.53 14 VMB26 3 20 344 12.18 1.61E-06 1.33E-08 7.70E-05 47.36 15 VMB26 3 20 326 12.17 1.61E-06 1.28E-08 7.93E-05 48.73 16 VMB26 3 20 332 11.84 1.66E-06 1.35E-08 7.85E-05 46.92 17 VMB26 3 20 338 11.98 1.64E-06 1.34E-08 7.77E-05 47.03 1 VMB27 3 20 280 56.87 3.46E-07 2.61E-09 1.43E-05 40.95 2 VMB27 3 20 280 27.28 7.21E-07 5.22E-09 2.85E-05 39.23 3 VMB27 3 20 280 17.74 1.11E-06 7.83E-09 4.27E-05 38.25 4 VMB27 3 20 280 13.19 1.49E-06 1.04E-08 5.69E-05 37.90 5 VMB27 3 20 280 10.70 1.84E-06 1.30E-08 7.11E-05 38.46 6 VMB27 3 20 280 8.75 2.25E-06 1.57E-08 8.53E-05 37.70 7 VMB27 3 20 280 56.87 3.46E-07 2.61E-09 1.43E-05 40.95 8 VMB27 3 20 280 27.28 7.21E-07 5.22E-09 2.85E-05 39.23 9 VMB27 3 20 280 17.74 1.11E-06 7.83E-09 4.27E-05 38.25 10 VMB27 3 20 280 13.19 1.49E-06 1.04E-08 5.69E-05 37.90 11 VMB27 3 20 280 10.70 1.84E-06 1.30E-08 7.11E-05 38.46 12 VMB27 3 20 280 8.75 2.25E-06 1.57E-08 8.53E-05 37.70 13 VMB27 3 20 300 30.29 6.49E-07 4.76E-09 2.75E-05 42.12 14 VMB27 3 20 300 19.31 1.02E-06 7.55E-09 4.13E-05 40.24 15 VMB27 3 20 300 14.22 1.38E-06 1.01E-08 5.50E-05 39.47 16 VMB27 3 20 300 11.21 1.75E-06 1.26E-08 6.87E-05 38.89 17 VMB27 3 20 300 9.20 2.14E-06 1.51E-08 8.24E-05 38.26 18 VMB27 3 20 300 30.29 6.49E-07 4.76E-09 2.75E-05 42.12 19 VMB27 3 20 300 19.31 1.02E-06 7.55E-09 4.13E-05 40.24 20 VMB27 3 20 300 14.22 1.38E-06 1.01E-08 5.50E-05 39.47 21 VMB27 3 20 300 11.21 1.75E-06 1.26E-08 6.87E-05 38.89 22 VMB27 3 20 300 9.20 2.14E-06 1.51E-08 8.24E-05 38.26 23 VMB27 3 20 320 19.47 1.01E-06 7.71E-09 3.98E-05 39.18 24 VMB27 3 20 320 14.86 1.32E-06 1.03E-08 5.32E-05 39.88 25 VMB27 3 20 320 11.68 1.68E-06 1.28E-08 6.64E-05 39.19

:


112

26 VMB27 3 20 320 9.41 2.09E-06 1.54E-08 7.96E-05 37.83 27 VMB27 3 20 320 29.60 6.64E-07 5.14E-09 2.66E-05 39.73 28 VMB27 3 20 320 19.47 1.01E-06 7.71E-09 3.98E-05 39.18 29 VMB27 3 20 320 14.86 1.32E-06 1.03E-08 5.32E-05 39.88 30 VMB27 3 20 320 11.68 1.68E-06 1.28E-08 6.64E-05 39.19 31 VMB27 3 20 320 9.41 2.09E-06 1.54E-08 7.96E-05 37.83

A.2 Experimental molar inlet and outlet flows of the components for a Pt/H-BEA 0.6

wt% catalyst

Table A-2: Experimental inlet and outlet conditions for hydroisomerization of n-pentane on a Pt/H-BEA 0.6 wt% catalyst

Inlet conditions Exit flows Conversion

Selectivity

nr n-C5 (mol/s)

iso-C5 (mol/s)

H2 (mol/s)

C1 (mol/s)

C2 (mol/s)

C3 (mol/s)

iso-C4 (mol/s)

n-C4 (mol/s)

iso-C5 (mol/s)

n-C5 (mol/s)

n-C5 (%)

iso-C5 (%)

1 1.14E-06 7.67E-09 4.43E-05 3.27E-05 1.64E-08 1.73E-08 0 5E-09 5.36E-08 1.07E-06 6.4 61.96319 2 1.14E-06 7.67E-09 4.43E-05 4.36E-05 2.27E-08 2.41E-08 0 7.27E-09 7.27E-08 1.04E-06 9.2 61.63793 3 1.12E-06 7.57E-09 4.37E-05 4.3E-05 2.29E-08 2.42E-08 0 7.17E-09 7.62E-08 1.02E-06 9.5 63.48548 4 1.12E-06 7.57E-09 4.37E-05 6.46E-05 3.14E-08 3.36E-08 4.48E-10 1.03E-08 1.04E-07 9.83E-07 13.1 64.95468 5 1.11E-06 7.47E-09 4.31E-05 6.37E-05 3.19E-08 3.36E-08 4.43E-10 1.02E-08 1.08E-07 9.64E-07 13.7 65.31792 6 1.11E-06 7.47E-09 4.31E-05 9.03E-05 4.25E-08 4.51E-08 8.85E-10 1.42E-08 1.45E-07 9.11E-07 18.4 66.66667 7 1.10E-06 7.81E-09 4.26E-05 8.92E-05 4.28E-08 4.5E-08 8.74E-10 1.36E-08 1.48E-07 8.95E-07 18.9 67.08595 8 1.10E-06 7.81E-09 4.26E-05 1.21E-04 5.6E-08 5.73E-08 1.31E-09 1.88E-08 1.95E-07 8.27E-07 25.0 67.72152 9 1.09E-06 7.72E-09 4.21E-05 1.19E-04 5.61E-08 5.7E-08 1.3E-09 1.81E-08 1.99E-07 8.15E-07 25.8 67.63359

:


113

10 1.09E-06 7.72E-09 4.21E-05 1.63E-04 7.17E-08 7.08E-08 2.16E-09 2.46E-08 2.53E-07 7.32E-07 33.3 67.02128 11 1.07E-06 7.62E-09 4.16E-05 1.64E-04 7.16E-08 7.08E-08 2.13E-09 2.39E-08 2.55E-07 7.19E-07 33.2 69.16667 12 1.07E-06 7.62E-09 4.16E-05 2.20E-04 9.04E-08 8.74E-08 3.84E-09 3.2E-08 3.17E-07 6.28E-07 41.7 68.72038 13 1.06E-06 7.95E-09 4.11E-05 2.15E-04 8.93E-08 8.64E-08 3.79E-09 3.08E-08 3.14E-07 6.2E-07 41.9 68.39135 14 1.06E-06 7.95E-09 4.11E-05 2.88E-04 1.1E-07 1.05E-07 6.32E-09 4.09E-08 3.73E-07 5.23E-07 51.0 67.10526 15 1.05E-06 7.85E-09 4.06E-05 2.85E-04 1.09E-07 1.04E-07 6.24E-09 3.95E-08 3.7E-07 5.18E-07 50.8 67.52137 16 1.05E-06 7.85E-09 4.06E-05 3.72E-04 1.32E-07 1.24E-07 9.57E-09 5.08E-08 4.2E-07 4.3E-07 59.2 66.08812 17 1.03E-06 7.76E-09 4.01E-05 3.63E-04 1.29E-07 1.22E-07 9.46E-09 4.85E-08 4.12E-07 4.29E-07 58.7 66.12795 18 1.03E-06 7.76E-09 4.01E-05 4.81E-04 1.55E-07 1.45E-07 1.4E-08 6.21E-08 4.44E-07 3.46E-07 66.7 62.89271 19 1.02E-06 7.67E-09 3.96E-05 4.66E-04 1.53E-07 1.43E-07 1.38E-08 6.02E-08 4.38E-07 3.47E-07 66.3 63.12649 20 1.02E-06 7.67E-09 3.96E-05 6.02E-04 1.8E-07 1.67E-07 1.99E-08 7.52E-08 4.49E-07 2.82E-07 72.6 59.12807 21 1.02E-06 7.98E-09 3.92E-05 5.86E-04 1.78E-07 1.65E-07 1.97E-08 7.28E-08 4.41E-07 2.83E-07 72.4 58.33333 22 1.02E-06 7.98E-09 3.92E-05 7.48E-04 2.07E-07 1.92E-07 2.65E-08 8.96E-08 4.34E-07 2.36E-07 77.0 53.91658 23 9.99E-07 7.49E-09 3.87E-05 7.22E-04 2.04E-07 1.88E-07 2.58E-08 8.66E-08 4.28E-07 2.38E-07 76.4 54.64876 24 9.99E-07 7.49E-09 3.87E-05 9.06E-04 2.38E-07 2.19E-07 3.42E-08 1.05E-07 4.01E-07 2E-07 80.1 48.7937 25 9.88E-07 7.41E-09 3.83E-05 8.69E-04 2.32E-07 2.14E-07 3.3E-08 1.01E-07 3.97E-07 2.02E-07 79.7 49.15842 26 9.88E-07 7.41E-09 3.83E-05 1.08E-03 2.71E-07 2.48E-07 3.49E-08 1.21E-07 3.58E-07 1.71E-07 82.8 42.49643 27 9.71E-07 7.32E-09 3.79E-05 1.05E-03 2.65E-07 2.43E-07 4.12E-08 1.17E-07 3.55E-07 1.72E-07 82.5 43.13914 28 9.71E-07 7.32E-09 3.79E-05 1.26E-03 3.03E-07 2.77E-07 5.01E-08 1.37E-07 3.11E-07 1.46E-07 85.0 36.50794 1 5.19E-07 3.81E-09 1.77E-05 0 3.78E-08 3.67E-08 1.83E-09 1.48E-08 1.38E-07 3.27E-07 37.5 68.62197 2 5.19E-07 3.81E-09 1.77E-05 0 4.91E-08 4.67E-08 3.1E-09 2.01E-08 1.61E-07 2.84E-07 45.7 65.82569 3 6.99E-07 5.07E-09 1.75E-05 0 4.07E-08 3.92E-08 2.01E-09 1.64E-08 1.89E-07 4.43E-07 37.0 70.70778 4 6.99E-07 5.07E-09 1.75E-05 0 5.26E-08 4.98E-08 3.47E-09 2.21E-08 2.22E-07 3.87E-07 45.0 68.45135 5 8.70E-07 6.16E-09 1.74E-05 0 4.38E-08 4.2E-08 2.37E-09 1.79E-08 2.4E-07 5.54E-07 36.7 72.62919 6 8.70E-07 6.16E-09 1.74E-05 0 5.6E-08 5.29E-08 3.83E-09 2.41E-08 2.84E-07 4.9E-07 44.1 72.13813 7 1.05E-06 7.43E-09 1.72E-05 0 4.65E-08 4.45E-08 2.55E-09 1.93E-08 2.91E-07 6.71E-07 36.3 74.27208 8 1.05E-06 7.43E-09 1.72E-05 0 5.89E-08 5.55E-08 4.2E-09 2.55E-08 3.48E-07 5.95E-07 43.5 74.24363 9 1.23E-06 8.70E-09 1.70E-05 0 4.91E-08 4.67E-08 2.74E-09 2.04E-08 3.44E-07 7.89E-07 36.4 74.3019 10 1.23E-06 8.70E-09 1.70E-05 0 6.2E-08 5.84E-08 4.56E-09 2.74E-08 4.13E-07 6.98E-07 43.7 74.70529 11 1.43E-06 9.97E-09 1.68E-05 0 5.18E-08 4.93E-08 2.92E-09 2.19E-08 3.98E-07 9E-07 37.3 72.48893 12 1.43E-06 9.97E-09 1.68E-05 0 6.51E-08 6.11E-08 4.93E-09 2.9E-08 4.79E-07 7.96E-07 44.6 73.31813 13 7.95E-07 6.12E-09 4.03E-05 0 4.97E-08 5.09E-08 1.64E-09 1.89E-08 1.52E-07 5.71E-07 28.6 63.62007

:


114

14 7.95E-07 6.12E-09 4.03E-05 0 6.9E-08 6.82E-08 2.88E-09 2.71E-08 1.88E-07 4.97E-07 37.9 59.94587 15 1.07E-06 7.75E-09 4.00E-05 0 5.38E-08 5.46E-08 1.64E-09 2.09E-08 2.08E-07 7.78E-07 27.9 66.53005 16 1.07E-06 7.75E-09 4.00E-05 0 7.43E-08 7.27E-08 3.29E-09 3E-08 2.59E-07 6.91E-07 35.9 64.89926 17 1.33E-06 9.38E-09 3.97E-05 0 5.75E-08 5.79E-08 2.05E-09 2.26E-08 2.59E-07 9.88E-07 26.2 71.11111 18 1.33E-06 9.38E-09 3.97E-05 0 7.92E-08 7.72E-08 3.7E-09 3.24E-08 3.28E-07 8.87E-07 33.8 70.50817 19 1.62E-06 1.14E-08 3.94E-05 0 6.12E-08 6.12E-08 2.05E-09 2.46E-08 3.13E-07 1.2E-06 26.3 69.9714 20 1.62E-06 1.14E-08 3.94E-05 0 8.38E-08 8.13E-08 4.11E-09 3.49E-08 3.98E-07 1.08E-06 34.1 69.29308 21 1.88E-06 1.35E-08 3.92E-05 0 6.45E-08 6.41E-08 2.05E-09 2.59E-08 3.63E-07 1.42E-06 25.0 73.76623 22 1.88E-06 1.35E-08 3.92E-05 0 8.87E-08 8.54E-08 4.11E-09 3.74E-08 4.7E-07 1.27E-06 32.7 73.72263 23 2.15E-06 1.51E-08 3.89E-05 0 6.77E-08 6.69E-08 2.46E-09 2.75E-08 4.15E-07 1.63E-06 24.9 74.14449 24 2.15E-06 1.51E-08 3.89E-05 0 9.28E-08 8.91E-08 4.52E-09 3.94E-08 5.39E-07 1.46E-06 32.5 74.44574 25 1.07E-06 7.97E-09 7.19E-05 0 5.26E-08 5.62E-08 1.46E-09 2.04E-08 1.62E-07 8.27E-07 23.1 62.05882 26 1.07E-06 7.97E-09 7.19E-05 0 7.59E-08 7.96E-08 2.92E-09 2.99E-08 2.07E-07 7.36E-07 31.6 58.70968 27 1.45E-06 1.01E-08 7.15E-05 0 5.69E-08 6.06E-08 1.46E-09 2.26E-08 2.17E-07 1.12E-06 23.5 60.21277 28 1.45E-06 1.01E-08 7.15E-05 0 8.25E-08 8.54E-08 2.92E-09 3.36E-08 2.82E-07 1.02E-06 30.5 61.04746 29 1.80E-06 1.30E-08 7.12E-05 0 6.13E-08 6.5E-08 1.46E-09 2.41E-08 2.69E-07 1.44E-06 20.5 68.95874 30 1.80E-06 1.30E-08 7.12E-05 0 8.83E-08 9.05E-08 2.92E-09 3.65E-08 3.56E-07 1.32E-06 27.3 68.97059 31 2.18E-06 1.52E-08 7.08E-05 0 6.5E-08 6.93E-08 1.46E-09 2.63E-08 3.21E-07 1.75E-06 20.1 69.14191 32 2.18E-06 1.52E-08 7.08E-05 0 9.41E-08 9.56E-08 3.65E-09 3.94E-08 4.25E-07 1.6E-06 27.1 68.75 33 2.53E-06 1.74E-08 7.04E-05 0 6.86E-08 7.3E-08 1.46E-09 2.77E-08 3.71E-07 2.07E-06 18.8 73.93293 34 2.53E-06 1.74E-08 7.04E-05 0 9.92E-08 1E-07 3.65E-09 4.16E-08 4.96E-07 1.89E-06 25.8 72.61641 35 2.89E-06 2.03E-08 7.01E-05 0 7.15E-08 7.59E-08 2.19E-09 2.92E-08 4.18E-07 2.38E-06 18.4 74.04891 36 2.89E-06 2.03E-08 7.01E-05 0 1.04E-07 1.04E-07 3.65E-09 4.38E-08 5.63E-07 2.18E-06 25.1 74.32567 1 4.48E-06 3.06E-08 1.10E-04 0 9.35E-08 9.92E-08 2.28E-09 4.1E-08 6.08E-07 3.74E-06 17.1 74.74151 2 4.48E-06 3.06E-08 1.10E-04 0 6.5E-08 6.84E-08 1.14E-09 2.74E-08 4.69E-07 3.92E-06 13.1 74.27466 3 3.58E-06 2.49E-08 1.10E-04 0 8.55E-08 9.01E-08 2.28E-09 3.65E-08 4.97E-07 2.96E-06 18.0 72.75923 4 3.58E-06 2.49E-08 1.10E-04 0 5.82E-08 6.16E-08 1.14E-09 2.51E-08 3.85E-07 3.12E-06 13.4 74.35294 5 2.66E-06 1.81E-08 1.11E-04 0 7.53E-08 7.98E-08 2.28E-09 3.19E-08 3.75E-07 2.18E-06 18.5 71.95402 6 2.66E-06 1.81E-08 1.11E-04 0 5.13E-08 5.47E-08 1.14E-09 2.17E-08 2.94E-07 2.3E-06 14.0 73.78049 7 5.45E-06 3.75E-08 1.59E-04 0 9.36E-08 1E-07 1.64E-09 4.1E-08 6.19E-07 4.71E-06 14.1 74.84144 8 5.45E-06 3.75E-08 1.59E-04 0 6.24E-08 6.73E-08 1.64E-09 2.79E-08 4.7E-07 4.91E-06 10.6 74.50425 9 4.33E-06 2.94E-08 1.60E-04 0 8.54E-08 9.03E-08 1.64E-09 3.78E-08 5.06E-07 3.73E-06 14.5 75.32468

:


115

10 4.33E-06 2.94E-08 1.60E-04 0 5.58E-08 6.07E-08 1.64E-09 2.46E-08 3.84E-07 3.88E-06 10.9 74.48276 11 3.12E-06 2.12E-08 1.61E-04 2.07E-04 7.39E-08 7.88E-08 1.64E-09 3.28E-08 3.74E-07 2.67E-06 15.0 74.91289 12 3.12E-06 2.12E-08 1.61E-04 1.38E-04 4.93E-08 5.25E-08 1.64E-09 2.13E-08 2.87E-07 2.79E-06 11.3 74.65438 13 6.39E-06 4.44E-08 2.17E-04 0 8.94E-08 9.61E-08 2.24E-09 4.02E-08 6.28E-07 5.67E-06 12.0 75.65217 14 6.39E-06 4.44E-08 2.17E-04 0 5.81E-08 6.26E-08 0 2.68E-08 4.67E-07 5.88E-06 8.7 75 15 5.08E-06 3.55E-08 2.18E-04 0 8.05E-08 8.72E-08 2.24E-09 3.58E-08 5.1E-07 4.47E-06 12.6 73.3564 16 5.08E-06 3.55E-08 2.18E-04 0 5.36E-08 5.59E-08 0 2.46E-08 3.84E-07 4.64E-06 9.3 73.23944 17 3.75E-06 2.66E-08 2.20E-04 0 7.15E-08 7.6E-08 2.24E-09 3.13E-08 3.89E-07 3.3E-06 12.7 75.70093 18 3.75E-06 2.66E-08 2.20E-04 0 4.69E-08 4.92E-08 0 2.01E-08 2.95E-07 3.44E-06 9.1 77.92208 19 7.36E-06 4.93E-08 2.84E-04 0 8.46E-08 8.76E-08 2.92E-09 3.79E-08 6.3E-07 6.68E-06 9.8 79.91968 20 7.36E-06 4.93E-08 2.84E-04 0 5.25E-08 5.84E-08 0 2.33E-08 4.67E-07 6.86E-06 7.3 76.88172 21 5.81E-06 4.06E-08 2.86E-04 0 7.59E-08 8.17E-08 2.92E-09 3.5E-08 5.17E-07 5.28E-06 9.9 82.32323 22 5.81E-06 4.06E-08 2.86E-04 0 4.96E-08 5.25E-08 0 2.34E-08 3.85E-07 5.43E-06 7.2 81.94444 23 4.31E-06 2.90E-08 2.88E-04 0 6.71E-08 7E-08 0 2.92E-08 3.94E-07 3.87E-06 10.8 77.63975 24 4.31E-06 2.90E-08 2.88E-04 0 4.38E-08 4.67E-08 0 2.04E-08 2.95E-07 3.99E-06 8.1 75.83333 25 4.83E-06 3.30E-08 3.65E-04 0 5.91E-08 6.65E-08 0 2.96E-08 3.95E-07 4.39E-06 9.9 75.38462 26 8.28E-06 5.50E-08 3.61E-04 0 4.8E-08 5.17E-08 0 2.22E-08 4.65E-07 7.8E-06 6.3 77.62238 27 8.28E-06 5.50E-08 3.61E-04 0 7.76E-08 8.13E-08 0 3.69E-08 6.28E-07 7.6E-06 8.8 78.28283 28 6.56E-06 4.40E-08 3.63E-04 0 4.43E-08 4.8E-08 0 2.22E-08 3.84E-07 6.18E-06 6.5 79.31034 29 6.56E-06 4.40E-08 3.63E-04 0 7.02E-08 7.39E-08 0 3.32E-08 5.17E-07 6.02E-06 8.9 80.50314 30 4.83E-06 3.30E-08 3.65E-04 0 3.69E-08 4.06E-08 0 1.85E-08 2.99E-07 4.53E-06 6.8 80 31 6.07E-06 4.08E-08 4.50E-04 0 4.56E-08 5.02E-08 0 2.28E-08 4.24E-07 5.59E-06 8.5 73.68421 32 5.41E-06 3.62E-08 4.51E-04 0 3.19E-08 3.65E-08 0 1.82E-08 3.01E-07 5.09E-06 6.5 74.35897 33 5.41E-06 3.62E-08 4.51E-04 0 5.47E-08 5.93E-08 0 2.74E-08 3.97E-07 4.95E-06 9.2 71.81818 34 6.07E-06 4.08E-08 4.50E-04 0 2.74E-08 3.19E-08 0 1.37E-08 3.24E-07 5.74E-06 6.0 77.5 35 7.31E-06 4.98E-08 4.49E-04 0 6.39E-08 6.84E-08 0 3.19E-08 5.2E-07 6.75E-06 8.2 77.44361 36 7.31E-06 4.98E-08 4.49E-04 0 3.65E-08 4.1E-08 0 1.82E-08 3.88E-07 6.93E-06 5.9 77.89474 37 9.39E-06 6.34E-08 4.47E-04 0 6.84E-08 7.3E-08 0 3.65E-08 6.43E-07 8.82E-06 6.8 90.71429 38 9.39E-06 6.34E-08 4.47E-04 0 4.1E-08 4.56E-08 0 2.28E-08 4.7E-07 9.04E-06 4.4 97.8022 1 3.30E-07 2.36E-09 1.79E-05 0 2.66E-08 2.66E-08 1.28E-09 9.67E-09 8.6E-08 2.03E-07 39.1 64.32584 2 3.30E-07 2.36E-09 1.79E-05 0 3.45E-08 3.38E-08 2.01E-09 1.3E-08 1.02E-07 1.75E-07 47.5 63.0485 3 6.65E-07 4.62E-09 3.51E-05 0 3.65E-08 3.83E-08 1.43E-09 1.36E-08 1.38E-07 4.71E-07 29.6 67.20721

:


116

4 6.65E-07 4.62E-09 3.51E-05 0 4.93E-08 4.97E-08 2.15E-09 1.9E-08 1.71E-07 4.15E-07 38.0 65.44944 5 1.11E-06 7.63E-09 5.80E-05 1.13E-04 4.31E-08 4.55E-08 1.18E-09 1.66E-08 1.87E-07 8.74E-07 22.2 72.20903 6 1.11E-06 7.63E-09 5.80E-05 1.63E-04 6.03E-08 6.32E-08 2.36E-09 2.36E-08 2.38E-07 7.77E-07 30.8 66.66667 7 1.66E-06 1.14E-08 8.66E-05 1.22E-04 4.68E-08 4.94E-08 8.83E-10 1.85E-08 2.3E-07 1.36E-06 18.7 69.77401 8 1.66E-06 1.14E-08 8.66E-05 1.85E-04 6.89E-08 7.24E-08 2.65E-09 2.74E-08 3.12E-07 1.3E-06 22.7 79.06977 9 2.44E-06 1.71E-08 1.21E-04 1.33E-04 4.93E-08 5.3E-08 1.23E-09 2.1E-08 2.84E-07 2.1E-06 14.6 74.48276 10 2.44E-06 1.71E-08 1.21E-04 2.07E-04 7.4E-08 7.89E-08 2.47E-09 3.08E-08 3.81E-07 1.95E-06 20.6 71.95122 11 3.29E-06 2.28E-08 1.61E-04 0 5.09E-08 5.25E-08 1.64E-09 2.13E-08 3.23E-07 2.9E-06 12.4 73.2 12 3.29E-06 2.28E-08 1.61E-04 0 7.72E-08 8.21E-08 1.64E-09 3.28E-08 4.43E-07 2.73E-06 17.5 72.52125 13 4.25E-06 2.93E-08 2.07E-04 0 5.06E-08 5.27E-08 0 2.11E-08 3.63E-07 3.85E-06 10.0 77.83251 14 4.25E-06 2.93E-08 2.07E-04 0 7.8E-08 8.23E-08 2.11E-09 3.37E-08 5.06E-07 3.66E-06 14.4 77.39726 15 5.35E-06 3.66E-08 2.58E-04 0 5.01E-08 5.27E-08 0 2.11E-08 4E-07 4.89E-06 9.2 73.40426 16 5.35E-06 3.66E-08 2.58E-04 0 7.64E-08 8.17E-08 2.63E-09 3.42E-08 5.58E-07 4.69E-06 12.9 75.28517 17 6.59E-06 4.47E-08 3.15E-04 0 4.83E-08 5.15E-08 0 2.25E-08 4.38E-07 6.11E-06 7.8 75.7764 18 6.59E-06 4.47E-08 3.15E-04 0 7.4E-08 8.04E-08 0 3.54E-08 6.15E-07 5.89E-06 11.3 76.2931 19 7.88E-06 5.37E-08 3.78E-04 0 4.63E-08 5.02E-08 0 2.32E-08 4.75E-07 7.44E-06 6.2 85.15625 20 7.88E-06 5.37E-08 3.78E-04 0 7.33E-08 7.72E-08 0 3.47E-08 6.68E-07 7.22E-06 9.0 85.48387 21 9.39E-06 6.34E-08 4.47E-04 0 4.56E-08 4.56E-08 0 2.28E-08 5.02E-07 8.87E-06 6.1 75.59055 22 9.39E-06 6.34E-08 4.47E-04 0 7.3E-08 7.75E-08 0 3.65E-08 7.11E-07 8.63E-06 8.7 78.88889 23 1.10E-05 7.40E-08 5.21E-04 0 4.26E-08 4.26E-08 0 2.13E-08 5.32E-07 1.04E-05 5.6 73.50427 24 1.10E-05 7.40E-08 5.21E-04 0 6.91E-08 7.45E-08 0 3.19E-08 7.55E-07 1.02E-05 7.7 80 25 1.26E-05 8.53E-08 6.01E-04 0 3.68E-08 4.3E-08 0 1.84E-08 5.65E-07 1.21E-05 5.0 75.72816 26 1.26E-05 8.53E-08 6.01E-04 0 6.75E-08 6.75E-08 0 3.07E-08 7.98E-07 1.18E-05 7.1 78.91156 1 6.64E-07 5.14E-09 2.66E-05 1.61E-03 4.65E-07 4.39E-07 5.18E-08 1.23E-07 7.55E-08 1.88E-08 97.2 10.81308 1 1.88E-06 1.35E-08 8.90E-05 1.85E-04 1.06E-07 1.06E-07 0 2.64E-08 5.91E-08 1.7E-06 10.3 23.36449 2 1.85E-06 1.34E-08 8.80E-05 2.43E-04 1.4E-07 1.37E-07 8.99E-10 3.42E-08 7.64E-08 1.64E-06 12.3 27.45098 3 1.84E-06 1.32E-08 8.70E-05 3.15E-04 1.83E-07 1.73E-07 8.89E-10 4.53E-08 9.87E-08 1.55E-06 16.6 27.66571 4 1.81E-06 1.31E-08 8.61E-05 4.06E-04 2.34E-07 2.17E-07 1.76E-09 5.71E-08 1.28E-07 1.45E-06 20.6 30.53613 5 1.79E-06 1.30E-08 8.58E-05 4.47E-04 2.54E-07 2.34E-07 0 6.13E-08 1.37E-07 1.4E-06 22.5 30.51948 6 1.80E-06 1.30E-08 8.58E-05 4.42E-04 2.56E-07 2.37E-07 1.75E-09 6.22E-08 1.38E-07 1.39E-06 23.3 29.33884 7 1.79E-06 1.30E-08 8.52E-05 5.27E-04 2.95E-07 2.7E-07 2.61E-09 7.31E-08 1.63E-07 1.32E-06 26.9 30.82437 8 1.78E-06 1.28E-08 8.42E-05 6.56E-04 3.64E-07 3.3E-07 4.3E-09 9.03E-08 2.03E-07 1.19E-06 33.7 31.48148

:


117

9 1.72E-06 1.27E-08 8.34E-05 8.28E-04 4.42E-07 3.98E-07 6.81E-09 1.12E-07 2.49E-07 1.05E-06 39.3 34.70662 10 1.71E-06 1.31E-08 8.08E-05 1.54E-03 7.14E-07 6.32E-07 2.48E-08 1.88E-07 3.76E-07 5.75E-07 66.6 31.65105 11 1.69E-06 1.30E-08 8.00E-05 1.87E-03 8.1E-07 4.69E-07 3.76E-08 2.18E-07 3.93E-07 4.21E-07 75.2 29.71246 12 1.71E-06 1.25E-08 8.25E-05 1.03E-03 5.3E-07 4.74E-07 1.1E-08 1.35E-07 2.97E-07 8.9E-07 48.3 34.10931 13 1.67E-06 1.24E-08 8.17E-05 1.26E-03 6.2E-07 5.51E-07 1.67E-08 1.6E-07 3.38E-07 7.23E-07 57.1 33.85417 14 1.61E-06 1.33E-08 7.70E-05 0 1.11E-06 1.01E-06 1.2E-07 2.99E-07 2.52E-07 7.07E-08 95.6 15.36906 15 1.61E-06 1.28E-08 7.93E-05 2.23E-03 8.94E-07 7.87E-07 5.26E-08 2.45E-07 3.93E-07 3E-07 81.6 28.59756 16 1.66E-06 1.35E-08 7.85E-05 2.64E-03 9.73E-07 8.66E-07 7.29E-08 2.69E-07 3.57E-07 1.91E-07 88.6 23.20173 17 1.64E-06 1.34E-08 7.77E-05 3.15E-03 1.05E-06 9.49E-07 9.68E-08 2.9E-07 3.12E-07 1.17E-07 92.9 19.44157 1 3.46E-07 2.61E-09 1.43E-05 3.44E-04 1.43E-07 1.27E-07 6.43E-09 4.12E-08 6.72E-08 1.05E-07 69.8 26.5625 2 7.21E-07 5.22E-09 2.85E-05 3.33E-04 1.53E-07 1.38E-07 3.8E-09 4.44E-08 1.22E-07 4.28E-07 41.0 39.11765 3 1.11E-06 7.83E-09 4.27E-05 3.28E-04 1.55E-07 1.42E-07 2.63E-09 4.47E-08 1.45E-07 7.87E-07 29.5 41.67776 4 1.49E-06 1.04E-08 5.69E-05 3.26E-04 1.55E-07 1.45E-07 2.34E-09 4.5E-08 1.58E-07 1.14E-06 23.8 41.24386 5 1.84E-06 1.30E-08 7.11E-05 3.24E-04 1.56E-07 1.48E-07 2.19E-09 4.53E-08 1.7E-07 1.54E-06 16.9 50.23364 6 2.25E-06 1.57E-08 8.53E-05 3.21E-04 1.55E-07 1.49E-07 1.75E-09 4.47E-08 1.77E-07 1.92E-06 15.4 46.34761 7 3.46E-07 2.61E-09 1.43E-05 3.44E-04 1.43E-07 1.27E-07 6.43E-09 4.12E-08 6.72E-08 1.05E-07 69.8 26.5625 8 7.21E-07 5.22E-09 2.85E-05 3.33E-04 1.53E-07 1.38E-07 3.8E-09 4.44E-08 1.22E-07 4.28E-07 41.0 39.11765 9 1.11E-06 7.83E-09 4.27E-05 3.28E-04 1.55E-07 1.42E-07 2.63E-09 4.47E-08 1.45E-07 7.87E-07 29.5 41.67776 10 1.49E-06 1.04E-08 5.69E-05 3.26E-04 1.55E-07 1.45E-07 2.34E-09 4.5E-08 1.58E-07 1.14E-06 23.8 41.24386 11 1.84E-06 1.30E-08 7.11E-05 3.24E-04 1.56E-07 1.48E-07 2.19E-09 4.53E-08 1.7E-07 1.54E-06 16.9 50.23364 12 2.25E-06 1.57E-08 8.53E-05 3.21E-04 1.55E-07 1.49E-07 1.75E-09 4.47E-08 1.77E-07 1.92E-06 15.4 46.34761 13 6.49E-07 4.76E-09 2.75E-05 7.61E-04 2.98E-07 2.64E-07 1.72E-08 8.74E-08 1.68E-07 1.88E-07 71.2 35.06965 14 1.02E-06 7.55E-09 4.13E-05 7.43E-04 3.07E-07 2.74E-07 1.27E-08 9.09E-08 2.55E-07 4.66E-07 54.5 44.25113 15 1.38E-06 1.01E-08 5.50E-05 7.14E-04 3.1E-07 2.78E-07 1.01E-08 9.08E-08 3.08E-07 7.83E-07 43.7 48.93617 16 1.75E-06 1.26E-08 6.87E-05 6.97E-04 3.11E-07 2.82E-07 8.45E-09 9.16E-08 3.47E-07 1.12E-06 36.3 52.03074 17 2.14E-06 1.51E-08 8.24E-05 7.00E-04 3.14E-07 2.87E-07 7.61E-09 9.21E-08 3.77E-07 1.46E-06 32.2 52.25885 18 6.49E-07 4.76E-09 2.75E-05 7.61E-04 2.98E-07 2.64E-07 1.72E-08 8.74E-08 1.68E-07 1.88E-07 71.2 35.06965 19 1.02E-06 7.55E-09 4.13E-05 7.43E-04 3.07E-07 2.74E-07 1.27E-08 9.09E-08 2.55E-07 4.66E-07 54.5 44.25113 20 1.38E-06 1.01E-08 5.50E-05 7.14E-04 3.1E-07 2.78E-07 1.01E-08 9.08E-08 3.08E-07 7.83E-07 43.7 48.93617 21 1.75E-06 1.26E-08 6.87E-05 6.97E-04 3.11E-07 2.82E-07 8.45E-09 9.16E-08 3.47E-07 1.12E-06 36.3 52.03074 22 2.14E-06 1.51E-08 8.24E-05 7.00E-04 3.14E-07 2.87E-07 7.61E-09 9.21E-08 3.77E-07 1.46E-06 32.2 52.25885 23 1.01E-06 7.71E-09 3.98E-05 1.51E-03 5.05E-07 4.54E-07 4.29E-08 1.5E-07 2.48E-07 1.73E-07 83.0 28.46079

:


118

24 1.32E-06 1.03E-08 5.32E-05 1.43E-03 5.15E-07 4.57E-07 3.65E-08 1.57E-07 3.9E-07 3.86E-07 71.0 40.06908 25 1.68E-06 1.28E-08 6.64E-05 1.37E-03 5.17E-07 4.6E-07 3.13E-08 1.58E-07 4.98E-07 6.4E-07 62.3 45.96514 26 2.09E-06 1.54E-08 7.96E-05 1.34E-03 5.18E-07 4.64E-07 2.78E-08 1.59E-07 5.83E-07 9.13E-07 56.6 47.66804 27 6.64E-07 5.14E-09 2.66E-05 1.61E-03 4.65E-07 4.39E-07 5.18E-08 1.23E-07 7.55E-08 1.88E-08 97.2 10.81308 28 1.01E-06 7.71E-09 3.98E-05 1.51E-03 5.05E-07 4.54E-07 4.29E-08 1.5E-07 2.48E-07 1.73E-07 83.0 28.46079 29 1.32E-06 1.03E-08 5.32E-05 1.43E-03 5.15E-07 4.57E-07 3.65E-08 1.57E-07 3.9E-07 3.86E-07 71.0 40.06908 30 1.68E-06 1.28E-08 6.64E-05 1.37E-03 5.17E-07 4.6E-07 3.13E-08 1.58E-07 4.98E-07 6.4E-07 62.3 45.96514 31 2.09E-06 1.54E-08 7.96E-05 1.34E-03 5.18E-07 4.64E-07 2.78E-08 1.59E-07 5.83E-07 9.13E-07 56.6 47.66804

:

Experimental Results for the hydroisomerization of n-hexane on MC-301

119

Appendix B : Experimental Results for the hydroisomerization of

n-hexane on MC-301

B.1 Initial conditions

Table B-1: Initial conditions for the hydroisomerization of n-hexane on a Pt/USY zeolite (MC-301)

Nr Catalyst weight

[g]

Total pressure [bar]

Temperature [°C]


n-C6 H2 Molar ratio H2/HC

1 6.67 5 319.85 260.748 2.56E-05 1.42E-03 50 2 6.67 5 319.85 260.748 2.56E-05 1.97E-03 75 3 6.67 5 319.85 260.748 2.56E-05 2.53E-03 100 4 6.67 5 319.85 260.748 2.56E-05 1.42E-03 50 5 6.67 5 310 173.808 3.84E-05 1.89E-03 50 6 6.67 11 314 173.808 3.84E-05 1.89E-03 50 7 6.67 10 314 173.808 3.84E-05 2.84E-03 75 8 6.67 6 313 173.808 3.84E-05 2.84E-03 75 9 6.67 6.5 313 173.808 3.84E-05 3.78E-03 100 10 6.67 12 313 173.808 3.84E-05 3.78E-03 100 11 6.67 4.5 312 260.748 2.56E-05 1.42E-03 50 12 6.67 6 312 260.748 2.56E-05 1.97E-03 75

:


120

13 6.67 10.5 312 260.748 2.56E-05 1.97E-03 75 14 6.67 11 314 260.748 2.56E-05 2.53E-03 100 15 6.67 10 326 260.748 2.56E-05 1.46E-03 50 16 6.67 5 323 260.748 2.56E-05 1.46E-03 50 17 6.67 5 323 260.748 2.56E-05 1.97E-03 75 18 6.67 11 322 260.748 2.56E-05 1.97E-03 75 19 6.67 11 323 260.748 2.56E-05 2.53E-03 100 20 6.67 5 322 260.748 2.56E-05 2.53E-03 100 21 6.67 10.5 321 130.356 5.12E-05 1.42E-03 25 22 6.67 5 324 130.356 5.12E-05 1.42E-03 25 23 6.67 6 323 130.356 5.12E-05 2.53E-03 50 24 6.67 11 323 130.356 5.12E-05 2.53E-03 50 25 6.67 12 323 130.356 5.12E-05 3.64E-03 75 26 6.67 6 323 130.356 5.12E-05 3.64E-03 75 27 6.67 4 322 173.808 3.84E-05 1.15E-03 25 28 6.67 10 356 173.808 3.84E-05 1.14E-03 25 29 6.67 10 362 173.808 3.84E-05 1.96E-03 50 30 6.67 10.5 360 173.808 3.84E-05 1.97E-03 50 31 6.67 10 359.85 260.748 2.56E-05 1.42E-03 50 32 6.67 10 359.85 260.748 2.56E-05 1.97E-03 75 33 6.67 10 359.85 260.748 2.56E-05 2.53E-03 100 34 6.67 15 359.85 260.748 2.56E-05 1.42E-03 50

:


121

B.2 Experimental molar inlet and outlet flows of the components for a /H-BEA 0.6 wt%

catalyst

Table B-2: Experimental inlet and outlet conditions for hydroisomerization of n-hexane on MC-301

Inlet flows Outlet flows Conversion

Selectivity

Nr n-C6 [mol/s]

H2 [mol/s]

C3 [mol/s]

ic4 [mol/s]

2,2-dimethyl-pentane [mol/s]

2,3-dimethyl-pentane [mol/s]

2-methyl-pentane [mol/s]

3-methyl-pentane [mol/s]

n-C6 [mol/s]

n-C6 [%]

2-methyl-pentane

[%]

3-methyl-pentane

[%]

1 2.56E-05 1.42E-03 0 0 6.29333E-08 0 1.8509E-06 1.1651E-06 1.96E-05 13.58 60.12 37.84 2 2.56E-05 1.97E-03 0 0 0 0 1.4011E-06 9.0611E-07 1.91E-05 10.76 60.73 39.27 3 2.56E-05 2.53E-03 0 0 0 0 1.202E-06 8.0904E-07 2.16E-05 8.52 59.77 40.23 4 2.56E-05 1.42E-03 0 0 6.55461E-08 0 1.9403E-06 1.2333E-06 1.87E-05 14.79 59.90 38.08 5 3.84E-05 1.89E-03 0 0 5.21257E-08 0 1.7572E-06 1.1704E-06 2.84E-05 9.49 58.97 39.28 6 3.84E-05 1.89E-03 0 0 0 0 1.5601E-06 1.0735E-06 3.09E-05 7.86 59.24 40.76 7 3.84E-05 2.84E-03 0 0 0 0 1.4863E-06 1.0172E-06 2.88E-05 8.01 59.37 40.63 8 3.84E-05 2.84E-03 0 0 0 0 7.6747E-07 5.2429E-07 1.56E-05 7.64 59.41 40.59 9 3.84E-05 3.78E-03 0 0 0 0 1.2037E-06 8.4996E-07 3.04E-05 6.32 58.61 41.39 10 3.84E-05 3.78E-03 0 0 0 0 1.6956E-06 1.203E-06 4.07E-05 6.65 58.50 41.50 11 2.56E-05 1.42E-03 0 0 4.7821E-08 0 1.5183E-06 9.7243E-07 1.94E-05 11.58 59.81 38.31 12 2.56E-05 1.97E-03 0 0 3.53057E-08 0 1.2656E-06 8.3337E-07 1.94E-05 9.92 59.30 39.05 13 2.56E-05 1.97E-03 1.04E-08 0 3.76207E-08 0 1.4341E-06 9.4617E-07 1.99E-05 10.84 59.18 39.05 14 2.56E-05 2.53E-03 0 0 3.15523E-08 0 1.2804E-06 8.6365E-07 2.14E-05 9.22 58.85 39.70 15 2.56E-05 1.46E-03 3.65E-08 0 1.34334E-07 0 2.9453E-06 1.8171E-06 1.75E-05 21.89 59.92 36.97 16 2.56E-05 1.46E-03 0 0 1.35039E-07 0 2.929E-06 1.8097E-06 2.14E-05 18.53 60.10 37.13 17 2.56E-05 1.97E-03 0 0 8.29897E-08 0 1.9572E-06 1.2159E-06 1.71E-05 16.01 60.11 37.34

:


122

18 2.56E-05 1.97E-03 0 0 8.08798E-08 0 2.1787E-06 1.3635E-06 1.74E-05 17.27 60.13 37.63 19 2.56E-05 2.53E-03 0 0 7.13005E-08 0 2.0296E-06 1.2972E-06 2.02E-05 14.43 59.73 38.17 20 2.56E-05 2.53E-03 0 0 7.34232E-08 0 1.8467E-06 1.1706E-06 2.06E-05 13.07 59.75 37.88 21 5.12E-05 1.42E-03 4.68E-08 0 2.01204E-07 0 5.0422E-06 3.1213E-06 3.61E-05 18.87 60.11 37.21 22 5.12E-05 1.42E-03 6.59E-08 0 2.48109E-07 0 5.3996E-06 3.2848E-06 3.72E-05 19.43 60.22 36.64 23 5.12E-05 2.53E-03 3.75E-08 0 3.58881E-07 0 3.655E-06 2.3134E-06 4.07E-05 13.50 57.59 36.45 24 5.12E-05 2.53E-03 3.6E-08 0 1.34262E-07 0 3.895E-06 2.486E-06 3.94E-05 14.21 59.61 38.05 25 5.12E-05 3.64E-03 2.76E-08 0 9.41748E-08 0 3.0898E-06 2.0251E-06 4.12E-05 11.26 59.15 38.77 26 5.12E-05 3.64E-03 0 0 1.01849E-07 0 2.9665E-06 1.93E-06 4.22E-05 10.58 59.35 38.61 27 3.84E-05 1.15E-03 0 0 2.49656E-07 0 4.8152E-06 2.8988E-06 2.79E-05 22.18 60.46 36.40 28 3.84E-05 1.14E-03 4.81E-07 6.39E-08 8.69031E-07 6.61366E-08 8.9409E-06 5.2417E-06 1.73E-05 47.18 57.99 34.00 29 3.84E-05 1.96E-03 8.91E-07 7.85E-08 9.518E-07 4.89951E-08 9.2891E-06 5.4404E-06 1.85E-05 46.79 57.16 33.47 30 3.84E-05 1.97E-03 5.02E-07 5.14E-08 6.94716E-07 0 7.4137E-06 4.3357E-06 1.68E-05 43.15 58.17 34.02 31 2.56E-05 1.42E-03 1.05E-07 4.88E-08 4.45167E-08 0 1.1999E-06 7.1671E-07 7.48E-06 22.34 55.78 33.32 32 2.56E-05 1.97E-03 1.1E-07 2.97E-08 1.63313E-07 0 3.347E-06 2.0105E-06 1.59E-05 26.08 59.50 35.74 33 2.56E-05 2.53E-03 1.17E-07 0 2.03935E-07 0 3.8032E-06 2.299E-06 1.74E-05 26.81 59.74 36.11 34 2.56E-05 1.42E-03 1.77E-07 2.71E-08 3.10001E-07 1.94345E-08 3.7563E-06 2.1496E-06 8.95E-06 41.57 58.99 33.76

:

Ideal hydrocracking of n-pentane: primary carbenium ions considered

123

Appendix C : Ideal hydrocracking of n-pentane: primary

carbenium ions considered

C.1 Initial conditions of the experiments used for the parameter estimation for the

classical reaction network extended with primary carbenium ions

Table C-1: Initial conditions of the experiments used for the regression of the kinetic parameters of the model considering the reactions network including primary carbenium ions

nr EXP Relative Pressure

[bar]

Catalyst weight [10-3 g]

Temperature [°C]


n-C5 [mol/s]

iso-C5 [mol/s]

H2 [mol/s]

Ratio H2/C5

9 VMB04 12 30 280 12.21 2.44E-06 1.71E-08 1.21E-04 49.20 7 VMB03 14 30 280 5.52 5.45E-06 3.75E-08 1.59E-04 28.91 9 VMB03 14 30 280 6.95 4.33E-06 2.94E-08 1.60E-04 36.65 11 VMB03 14 30 280 9.64 3.12E-06 2.12E-08 1.61E-04 51.25 11 VMB04 14 30 280 9.07 3.29E-06 2.28E-08 1.61E-04 48.63 13 VMB04 16 30 280 7.01 4.25E-06 2.93E-08 2.07E-04 48.31 13 VMB03 16.5 30 280 4.71 6.39E-06 4.44E-08 2.17E-04 33.71 15 VMB03 16.5 30 280 5.92 5.08E-06 3.55E-08 2.18E-04 42.71 17 VMB03 16.5 30 280 8.02 3.75E-06 2.66E-08 2.20E-04 58.14 15 VMB04 18 30 280 5.57 5.35E-06 3.66E-08 2.58E-04 47.95

:


124

19 VMB03 19 30 280 4.09 7.36E-06 4.93E-08 2.84E-04 38.42 21 VMB03 19 30 280 5.18 5.81E-06 4.06E-08 2.86E-04 48.88 23 VMB03 19 30 280 6.98 4.31E-06 2.90E-08 2.88E-04 66.25 17 VMB04 20 30 280 4.52 6.59E-06 4.47E-08 3.15E-04 47.52 25 VMB03 21.5 30 280 6.23 4.83E-06 3.30E-08 3.65E-04 74.93 27 VMB03 21.5 30 280 3.64 8.28E-06 5.50E-08 3.61E-04 43.33 29 VMB03 21.5 30 280 4.59 6.56E-06 4.40E-08 3.63E-04 54.90 19 VMB04 22 30 280 3.78 7.88E-06 5.37E-08 3.78E-04 47.64 31 VMB03 24 30 280 4.96 6.07E-06 4.08E-08 4.50E-04 73.68 33 VMB03 24 30 280 5.56 5.41E-06 3.62E-08 4.51E-04 82.68 35 VMB03 24 30 280 4.12 7.31E-06 4.98E-08 4.49E-04 60.96 37 VMB03 24 30 280 3.20 9.39E-06 6.34E-08 4.47E-04 47.22 23 VMB04 26 30 280 2.71 1.10E-05 7.40E-08 5.21E-04 47.12 25 VMB04 28 30 280 2.36 1.26E-05 8.53E-08 6.01E-04 47.31

:


125

C.2 Experimental molar inlet and outlet flows for the experiments used for the

parameter estimation

Table C-2: Experimental molar inlet and outlet flows for the experiments used for the regression of the kinetic parameters in the model considering the reaction network including primary carbenium ions

Inlet flows Exit flows Conversion Selectivity nr n-C5

[mol/s] iso-C5 [mol/s]

H2 [mol/s]

C1 [mol/s]

C2 [mol/s]

C3 [mol/s]

iso-C4 [mol/s]

n-C4 [mol/s]

i-C5 [mol/s]

n-C5 [mol/s]

n-C5 (%) Iso-C5 (%)

9 2.44E-06 1.71E-08 1.21E-04 1.33E-04 4.93E-08 5.30E-08 1.23E-09 2.10E-08 2.84E-07 2.10E-06 14.6 74.48276 7 5.45E-06 3.75E-08 1.59E-04 0 9.36E-08 1.00E-07 1.64E-09 4.10E-08 6.19E-07 4.71E-06 14.14897 74.84144 9 4.33E-06 2.94E-08 1.60E-04 0 8.54E-08 9.03E-08 1.64E-09 3.78E-08 5.06E-07 3.73E-06 14.5 75.32468 11 3.12E-06 2.12E-08 1.61E-04 2.07E-04 7.39E-08 7.88E-08 1.64E-09 3.28E-08 3.74E-07 2.67E-06 15.0 74.91289 11 3.29E-06 2.28E-08 1.61E-04 0 5.09E-08 5.25E-08 1.64E-09 2.13E-08 3.23E-07 2.90E-06 12.4 73.2 13 4.25E-06 2.93E-08 2.07E-04 0 5.06E-08 5.27E-08 0 2.11E-08 3.63E-07 3.85E-06 10.0 77.83251 13 6.39E-06 4.44E-08 2.17E-04 0 8.94E-08 9.61E-08 2.24E-09 4.02E-08 6.28E-07 5.67E-06 12.0 75.65217 15 5.08E-06 3.55E-08 2.18E-04 0 8.05E-08 8.72E-08 2.24E-09 3.58E-08 5.10E-07 4.47E-06 12.6 73.3564 17 3.75E-06 2.66E-08 2.20E-04 0 7.15E-08 7.60E-08 2.24E-09 3.13E-08 3.89E-07 3.30E-06 12.7 75.70093 15 5.35E-06 3.66E-08 2.58E-04 0 5.01E-08 5.27E-08 0 2.11E-08 4.00E-07 4.89E-06 9.2 73.40426 19 7.36E-06 4.93E-08 2.84E-04 0 8.46E-08 8.76E-08 2.92E-09 3.79E-08 6.30E-07 6.68E-06 9.8 79.91968 21 5.81E-06 4.06E-08 2.86E-04 0 7.59E-08 8.17E-08 2.92E-09 3.50E-08 5.17E-07 5.28E-06 9.9 82.32323 23 4.31E-06 2.90E-08 2.88E-04 0 6.71E-08 7.00E-08 0 2.92E-08 3.94E-07 3.87E-06 10.8 77.63975 17 6.59E-06 4.47E-08 3.15E-04 0 4.83E-08 5.15E-08 0 2.25E-08 4.38E-07 6.11E-06 7.8 75.7764 25 4.83E-06 3.30E-08 3.65E-04 0 5.91E-08 6.65E-08 0 2.96E-08 3.95E-07 4.39E-06 9.9 75.38462 27 8.28E-06 5.50E-08 3.61E-04 0 7.76E-08 8.13E-08 0 3.69E-08 6.28E-07 7.60E-06 8.8 78.28283 29 6.56E-06 4.40E-08 3.63E-04 0 7.02E-08 7.39E-08 0 3.32E-08 5.17E-07 6.02E-06 8.9 80.50314 19 7.88E-06 5.37E-08 3.78E-04 0 4.63E-08 5.02E-08 0 2.32E-08 4.75E-07 7.44E-06 6.2 85.15625 31 6.07E-06 4.08E-08 4.50E-04 0 4.56E-08 5.02E-08 0 2.28E-08 4.24E-07 5.59E-06 8.5 73.68421 33 5.41E-06 3.62E-08 4.51E-04 0 5.47E-08 5.93E-08 0 2.74E-08 3.97E-07 4.95E-06 9.2 71.81818 35 7.31E-06 4.98E-08 4.49E-04 0 6.39E-08 6.84E-08 0 3.19E-08 5.20E-07 6.75E-06 8.2 77.44361 37 9.39E-06 6.34E-08 4.47E-04 0 6.84E-08 7.30E-08 0 3.65E-08 6.43E-07 8.82E-06 6.8 90.71429

:


126

23 1.10E-05 7.40E-08 5.21E-04 0 4.26E-08 4.26E-08 0 2.13E-08 5.32E-07 1.04E-05 5.6 73.50427 25 1.26E-05 8.53E-08 6.01E-04 0 3.68E-08 4.30E-08 0 1.84E-08 5.65E-07 1.21E-05 5.0 75.72816

C.3 Correlation coefficient matrix

Table C-3: Binary correlation coefficient matrix for the model parameters of the classical reaction network extended with primary carbenium ions

1 2 3 4 5 6 7 8 9 10 11 1 1.0000 -0.1744 -0.3059 0.3164 0.0224 0.1375 -0.0780 -0.3555 0.0129 0.1626 -0.0936 2 -0.1744 1.0000 0.5551 0.4457 0.5296 0.1127 -0.8963 0.1304 0.2099 -0.6398 -0.0586 3 -0.3059 0.5551 1.0000 0.1639 0.2582 -0.0362 -0.3933 0.2639 0.1166 -0.4763 -0.1324 4 0.3164 0.4457 0.1639 1.0000 0.7105 0.6412 -0.7834 -0.6373 -0.2281 -0.2663 -0.2794 5 0.0224 0.5296 0.2582 0.7105 1.0000 0.5034 -0.7375 -0.5404 -0.0012 -0.2425 -0.7122 6 0.1375 0.1127 -0.0362 0.6412 0.5034 1.0000 -0.3898 -0.7947 -0.7394 0.0806 -0.2339 7 -0.0780 -0.8963 -0.3933 -0.7834 -0.7375 -0.3898 1.0000 0.2420 -0.0497 0.5495 0.2154 8 -0.3555 0.1304 0.2639 -0.6373 -0.5404 -0.7947 0.2420 1.0000 0.4167 -0.4234 0.3046 9 0.0129 0.2099 0.1166 -0.2281 -0.0012 -0.7394 -0.0497 0.4167 1.0000 -0.2361 -0.0090 10 0.1626 -0.6398 -0.4763 -0.2663 -0.2425 0.0806 0.5495 -0.4234 -0.2361 1.0000 0.0686 11 -0.0936 -0.0586 -0.1324 -0.2794 -0.7122 -0.2339 0.2154 0.3046 -0.0090 0.0686 1.0000

:

Ideal hydrocracking of n-pentane: hydrogenolysis considered

127

Appendix D : Ideal hydrocracking of n-pentane: hydrogenolysis

considered

D.1 Initial conditions of the experiments used for the parameter estimation for the

classical reaction network extended with hydrogenolysis

Table D-1: Initial conditions of the experiments used for the regression of the model parameters of the reaction network extended with hydrogenolysis

nr EXP Relative Pressure

[bar]

Catalyst weight [10-3 g]

Temperature [°C]


n-C5 [mol/s]

iso-C5 [mol/s]

H2 [mol/s]

Ratio H2/C5

9 VMB04 12 30 280 12.21 2.44E-06 1.71E-08 1.21E-04 49.20 7 VMB03 14 30 280 5.52 5.45E-06 3.75E-08 1.59E-04 28.91 9 VMB03 14 30 280 6.95 4.33E-06 2.94E-08 1.60E-04 36.65 11 VMB03 14 30 280 9.64 3.12E-06 2.12E-08 1.61E-04 51.25 11 VMB04 14 30 280 9.07 3.29E-06 2.28E-08 1.61E-04 48.63 13 VMB04 16 30 280 7.01 4.25E-06 2.93E-08 2.07E-04 48.31 13 VMB03 16.5 30 280 4.71 6.39E-06 4.44E-08 2.17E-04 33.71 15 VMB03 16.5 30 280 5.92 5.08E-06 3.55E-08 2.18E-04 42.71 17 VMB03 16.5 30 280 8.02 3.75E-06 2.66E-08 2.20E-04 58.14 15 VMB04 18 30 280 5.57 5.35E-06 3.66E-08 2.58E-04 47.95

:


128

19 VMB03 19 30 280 4.09 7.36E-06 4.93E-08 2.84E-04 38.42 21 VMB03 19 30 280 5.18 5.81E-06 4.06E-08 2.86E-04 48.88 23 VMB03 19 30 280 6.98 4.31E-06 2.90E-08 2.88E-04 66.25 17 VMB04 20 30 280 4.52 6.59E-06 4.47E-08 3.15E-04 47.52 25 VMB03 21.5 30 280 6.23 4.83E-06 3.30E-08 3.65E-04 74.93 27 VMB03 21.5 30 280 3.64 8.28E-06 5.50E-08 3.61E-04 43.33 29 VMB03 21.5 30 280 4.59 6.56E-06 4.40E-08 3.63E-04 54.90 19 VMB04 22 30 280 3.78 7.88E-06 5.37E-08 3.78E-04 47.64 31 VMB03 24 30 280 4.96 6.07E-06 4.08E-08 4.50E-04 73.68 33 VMB03 24 30 280 5.56 5.41E-06 3.62E-08 4.51E-04 82.68 35 VMB03 24 30 280 4.12 7.31E-06 4.98E-08 4.49E-04 60.96 37 VMB03 24 30 280 3.20 9.39E-06 6.34E-08 4.47E-04 47.22 23 VMB04 26 30 280 2.71 1.10E-05 7.40E-08 5.21E-04 47.12 25 VMB04 28 30 280 2.36 1.26E-05 8.53E-08 6.01E-04 47.31

:


129

D.2 Experimental molar inlet and outlet flows for the experiments used for the

parameter estimation

Table D-2: Molar inlet and outlet flows of the experiments used for the regression of the model parameters for the classical reaction network extended with hydrogenolysis

Inlet flows Exit flow Conversion Selectivity nr n-C5

[mol/s] iso-C5 [mol/s]

H2 [mol/s]

C1 [mol/s]

C2 [mol/s]

C3 [mol/s]

iso-C4 [mol/s]

n-C4 [mol/s]

i-C5 [mol/s]

n-C5 [mol/s]

n-C5 (%) Iso-C5 (%)

9 2.44E-06 1.71E-08 1.21E-04 1.33E-04 4.93E-08 5.30E-08 1.23E-09 2.10E-08 2.84E-07 2.10E-06 14.6 74.48276 7 5.45E-06 3.75E-08 1.59E-04 0 9.36E-08 1.00E-07 1.64E-09 4.10E-08 6.19E-07 4.71E-06 14.14897 74.84144 9 4.33E-06 2.94E-08 1.60E-04 0 8.54E-08 9.03E-08 1.64E-09 3.78E-08 5.06E-07 3.73E-06 14.5 75.32468 11 3.12E-06 2.12E-08 1.61E-04 2.07E-04 7.39E-08 7.88E-08 1.64E-09 3.28E-08 3.74E-07 2.67E-06 15.0 74.91289 11 3.29E-06 2.28E-08 1.61E-04 0 5.09E-08 5.25E-08 1.64E-09 2.13E-08 3.23E-07 2.90E-06 12.4 73.2 13 4.25E-06 2.93E-08 2.07E-04 0 5.06E-08 5.27E-08 0 2.11E-08 3.63E-07 3.85E-06 10.0 77.83251 13 6.39E-06 4.44E-08 2.17E-04 0 8.94E-08 9.61E-08 2.24E-09 4.02E-08 6.28E-07 5.67E-06 12.0 75.65217 15 5.08E-06 3.55E-08 2.18E-04 0 8.05E-08 8.72E-08 2.24E-09 3.58E-08 5.10E-07 4.47E-06 12.6 73.3564 17 3.75E-06 2.66E-08 2.20E-04 0 7.15E-08 7.60E-08 2.24E-09 3.13E-08 3.89E-07 3.30E-06 12.7 75.70093 15 5.35E-06 3.66E-08 2.58E-04 0 5.01E-08 5.27E-08 0 2.11E-08 4.00E-07 4.89E-06 9.2 73.40426 19 7.36E-06 4.93E-08 2.84E-04 0 8.46E-08 8.76E-08 2.92E-09 3.79E-08 6.30E-07 6.68E-06 9.8 79.91968 21 5.81E-06 4.06E-08 2.86E-04 0 7.59E-08 8.17E-08 2.92E-09 3.50E-08 5.17E-07 5.28E-06 9.9 82.32323 23 4.31E-06 2.90E-08 2.88E-04 0 6.71E-08 7.00E-08 0 2.92E-08 3.94E-07 3.87E-06 10.8 77.63975 17 6.59E-06 4.47E-08 3.15E-04 0 4.83E-08 5.15E-08 0 2.25E-08 4.38E-07 6.11E-06 7.8 75.7764 25 4.83E-06 3.30E-08 3.65E-04 0 5.91E-08 6.65E-08 0 2.96E-08 3.95E-07 4.39E-06 9.9 75.38462 27 8.28E-06 5.50E-08 3.61E-04 0 7.76E-08 8.13E-08 0 3.69E-08 6.28E-07 7.60E-06 8.8 78.28283 29 6.56E-06 4.40E-08 3.63E-04 0 7.02E-08 7.39E-08 0 3.32E-08 5.17E-07 6.02E-06 8.9 80.50314 19 7.88E-06 5.37E-08 3.78E-04 0 4.63E-08 5.02E-08 0 2.32E-08 4.75E-07 7.44E-06 6.2 85.15625 31 6.07E-06 4.08E-08 4.50E-04 0 4.56E-08 5.02E-08 0 2.28E-08 4.24E-07 5.59E-06 8.5 73.68421 33 5.41E-06 3.62E-08 4.51E-04 0 5.47E-08 5.93E-08 0 2.74E-08 3.97E-07 4.95E-06 9.2 71.81818 35 7.31E-06 4.98E-08 4.49E-04 0 6.39E-08 6.84E-08 0 3.19E-08 5.20E-07 6.75E-06 8.2 77.44361 37 9.39E-06 6.34E-08 4.47E-04 0 6.84E-08 7.30E-08 0 3.65E-08 6.43E-07 8.82E-06 6.8 90.71429

:


130

23 1.10E-05 7.40E-08 5.21E-04 0 4.26E-08 4.26E-08 0 2.13E-08 5.32E-07 1.04E-05 5.6 73.50427 25 1.26E-05 8.53E-08 6.01E-04 0 3.68E-08 4.30E-08 0 1.84E-08 5.65E-07 1.21E-05 5.0 75.72816 23 1.10E-05 7.40E-08 5.21E-04 0 4.26E-08 4.26E-08 0 2.13E-08 5.32E-07 1.04E-05 5.6 73.50427 25 1.26E-05 8.53E-08 6.01E-04 0 3.68E-08 4.30E-08 0 1.84E-08 5.65E-07 1.21E-05 5.0 75.72816

D.3 Correlation coefficient matrix

Table D-3: Binary correlation coefficient matrix of the model parameters of the classical reaction network including hydrogenolysis

1 2 3 6 7 8 9 10 11 12 13 14 1 1 -0.3775 -0.9491 -0.0261 -0.0448 0.0118 -0.0054 0.0062 0.0069 -0.0126 0.0057 0.006 2 -0.3775 1 0.6205 -0.0167 0.0868 0.0464 0.0651 0.1597 -0.0491 -0.0343 -0.0607 -0.1216 3 -0.9491 0.6205 1 0.0215 0.0792 -0.0084 0.0055 0.061 -0.0017 -0.0068 -0.0058 -0.0369 6 -0.0261 -0.0167 0.0215 1 -0.0683 -0.1673 -0.1016 -0.0128 0.0371 -0.3662 0.0127 0.1415 7 -0.0448 0.0868 0.0792 -0.0683 1 0.0605 0.0192 0.2553 0.0108 0.0038 -0.0045 0.0284 8 0.0118 0.0464 -0.0084 -0.1673 0.0605 1 -0.2384 -0.0361 0.2876 -0.3088 0.2666 -0.3996 9 -0.0054 0.0651 0.0055 -0.1016 0.0192 -0.2384 1 0.1345 -0.9947 0.0085 -0.9944 0.2173 10 0.0062 0.1597 0.061 -0.0128 0.2553 -0.0361 0.1345 1 -0.0687 -0.4984 -0.1625 -0.1105 11 0.0069 -0.0491 -0.0017 0.0371 0.0108 0.2876 -0.9947 -0.0687 1 -0.0357 0.9938 -0.266 12 -0.0126 -0.0343 -0.0068 -0.3662 0.0038 -0.3088 0.0085 -0.4984 -0.0357 1 0.0626 0.2794 13 0.0057 -0.0607 -0.0058 0.0127 -0.0045 0.2666 -0.9944 -0.1625 0.9938 0.0626 1 -0.2384 14 0.006 -0.1216 -0.0369 0.1415 0.0284 -0.3996 0.2173 -0.1105 -0.266 0.2794 -0.2384 1

131

Appendix E : Overzichtstabel van ontwikkelde programmatuur

en uitgevoerde parameterschattingen

Ontwikkelde programmatuur + uitgevoerde parameterschattingen Labjournaal (pagina)

Generering reactienetwerk voor hydroisomerisatie van n-pentaan zonder hydride shift, met primaire carbenium ionen en zonder hydrogenolyse. Primaire carbenium ionen treden op als reactant en product.

4

Generering reactienetwerk voor hydroisomerisatie van n-pentaan zonder hydride shift, met primaire carbenium ionen en zonder hydrogenolyse. Primaire carbenium ionen kunnen niet optreden als reactanten.

6

Aanpassen van code voor parameterschattingen die rekening houdt met primaire carbenium ionen: • aanvullen met reacties waarbij primaire carbenium ionen betrokken zijn. • Toevoegen van hydride abstractie en hydride donatie

10-14

Aanpassen code voor parameterschatting die rekening houdt met primaire carbenium ionen: • Toevoegen van hydide transfer door combinatie hydride donatie en hydride abstractie

20-21

Aanpassen code voor parameterschatting die rekening houdt met primaire carbenium ionen: • Aanpassen subroutine sekisom

22-24

:

Overzichtstabel van ontwikkelde programmatuur en uitgevoerde parameterschattingen

132

Generering reactienetwerk voor hydroisomerisatie van n-pentaan zonder hydride shift, met primaire carbenium ionen en zonder hydrogenolyse. Primaire carbenium ionen treden op als reactant en product. Neopentaan mag niet gegenereerd worden

25

Generering reactienetwerk voor hydroisomerisatie van n-pentaan zonder hydride shift, met primaire carbenium ionen en zonder hydrogenolyse. Primaire carbenium ionen kunnen niet optreden als reactanten. Neopentaan mag niet gegenereerd worden

26

Aanpassen code voor parameterschatting die rekening houdt met primaire carbenium ionen: • Aanpassen subroutine sekisom

33

Aanpassen code voor parameterschatting die rekening houdt met hydrogenolyse • Aanpassen subroutine sekisom • Aanpassing correctiefactor pre-exponentiële factoren

43

Generering reactienetwerk voor hydroisomerisatie van n-pentaan zonder hydride shift, met primaire carbenium ionen en zonder hydrogenolyse. Primaire carbenium ionen kunnen optreden als reactanten en producten. (de)hydrogenatiereacties zijn in niet-quasi-evenwicht

45-49

Aanpassen code voor parameterschatting die rekening houdt met primaire carbenium ionen: uitbreiding voor niet-ideaal hydrokraken:

• Metallische sites niet in evenwicht toevoegen aan subroutine FCN • Toevoeging van subroutine FCN_DDASPKM: metallische centra niet in evenwicht • Implementatie van de dehydrogenatie reacties in dubroutine KINETICS

50 52-53 54-55


• Subroutine DASPK implementeren voor ideaal hydrokraken in FCN en FCN_DDASPKI

56-58

Aanpassen code voor parameterschatting die rekening houdt met primaire carbenium ionen: • Toevoegen van fysisorptie-eigenschappen voor propaan en butaan

60

:

Overzichtstabel van ontwikkelde programmatuur en uitgevoerde parameterschattingen

133


• Implementatie van subroutine DNSQE voor metallische centra niet in evenwicht in FCN • Implementatie van subroutine FCN_DNSQEM

63-64 65

Overzicht van de instelwaarden van de experimenten voor hydroisomerisatie van n-hexaan op MC-301 in een Berty reactor

74-75

Overzicht van de resultaten van de experimenten voor hydroisomerisatie van n-hexaan op MC-301 in een Berty reactor

76-77

Britt Eeckhaudt isomerization of light alkanes of hydrocarbon-related reactions

Documents

Transcript of Britt Eeckhaudt isomerization of light alkanes of hydrocarbon-related reactions