Steam Cracking: Kinetics and Feed Characterisation

João Pedro Vilhena de Freitas Moreira

Thesis to obtain the Master of Science Degree in Chemical Engineering

Supervisors: Professor Doctor Henrique Aníbal Santos de Matos Doctor Štepánˇ Špatenka

Examination Committee Chairperson: Professor Doctor Carlos Manuel Faria de Barros Henriques Supervisor: Professor Doctor Henrique Aníbal Santos de Matos Member of the Committee: Specialist Engineer André Alexandre Bravo Ferreira Vilelas

November 2015 ii The roots of education are bitter, but the fruit is sweet. – Aristotle

All I am I owe to my mother. – George Washington

iii iv Acknowledgments

To begin with, my deepest thanks to Professor Carla Pinheiro, Professor Henrique Matos and Pro- fessor Costas Pantelides for allowing me to take this internship at Process Systems Enterprise Ltd., London, a seven-month truly worthy experience for both my professional and personal life which I will certainly never forget. I would also like to thank my PSE and IST supervisors, who help me to go through this final journey as a Chemical Engineering student. To Stˇ epˇ an´ and Sreekumar from PSE, thank you so much for your patience, for helping and encouraging me to always keep a positive attitude, even when harder problems arose. To Prof. Henrique who always showed availability to answer my questions and to meet in person whenever possible. Gostaria tambem´ de agradecer aos meus colegas de casa e de curso Andre,´ Frederico, Joana e Miguel, com quem partilhei casa. Foi uma experienciaˆ inesquec´ıvel que atravessamos´ juntos e cer- tamente que a vossa presenc¸a diaria´ apos´ cada dia de trabalho ajudou imenso a aliviar as saudades de casa. As` minhas amigas Helena e Mariana da FEUP, um sentido obrigado pela vossa amizade e companhia. Espero voltar a ver-vos em breve! Giovanni e Gabriele, devo anche dire che sono orgoglioso di voi avere come amici e sono sicuro che rimarremo in contatto. Grazie mille per tutto! 병길, 재흠 과 예라, 여러분을 만나서 정말 반가웠고 여러분과 친구가 될수 있어서 영광이었습니다. 영국, 포르투갈, 혹은 한국에서 우리가 꼭 다시만날 수 있었으면 좋겠습니다. 감사합니다! To all my other friends Artur, Francisco, Maria, Mariana, Ometha, Pierre, Renato and Tomasz, it was a pleasure to share some of the best moments I had in London with you. Nao˜ poderia deixar tambem´ de agradecer a` minha fam´ılia que sempre me apoiou e continua a apoiar. Aos meus avos,´ que tenho a certeza que continuarao˜ a olhar por mim. Ao meu pai, pelos bons momentos que passamos´ e que continuaremos a ter enquanto pai e filho. Por fim, a` minha querida mae,˜ pelo amor incondicional e por fazer de mim nao˜ so´ o aluno e o homem que sou mas certamente o engenheiro que serei amanha.˜ Por ultimo´ mas definitivamente nao˜ menos importante, a` Mariana, minha namorada, pelos quatro maravilhosos anos que passamos´ juntos e pela persistenciaˆ em manter vivo a nossa relac¸ao˜ nos sete meses em que estivemos separados.

v vi Resumo

A produc¸ao˜ de etileno e propileno a partir de nafta e alimentac¸oes˜ gasosas como etano, propano e outros alcanos leves atraves´ do craqueamento termico´ e´ um pilar da industria´ qu´ımica. No presente trabalho, modelou-se uma fornalha de craqueamento termico´ e foram implementados e validados varios´ esquemas cineticos´ da literatura, moleculares e radicalares, usando dados de fornalhas industriais al- imentadas a etano, propano e nafta. Para as alimentac¸oes˜ gasosas, os resultados parecem sugerir que as cineticas´ implementadas sao˜ capazes de prever com exatidao˜ a distribuic¸ao˜ dos produtos a` sa´ıda da fornalha, com especial foco na cinetica´ radicalar. Relativamente a` alimentac¸ao˜ de nafta, as cineticas´ radicalares implementadas foram incapazes de produzir resultados proximos´ dos industriais. A substituic¸ao˜ do vapor de agua´ por outros diluentes foi estudada em estado estacionario,´ tendo-se con- clu´ıdo que se a temperatura de sa´ıda das serpentinas nao˜ puder ser aumentada, nenhuma diferenc¸a podera´ advir da utilizac¸ao˜ de diferentes diluentes. Contudo, se tal constrangimento puder ser alargado, o helio´ parece impor-se como a melhor alternativa. Por fim, tendo em conta que a implementac¸ao˜ de esquemas cineticos´ requer uma composic¸ao˜ molecular da alimentac¸ao˜ e que estas ultimas´ sao˜ normal- mente caracterizadas por outros ´ındices, foi desenvolvido um modelo de caracterisac¸ao˜ de alimentac¸ao˜ l´ıquida. Deste modo, poder-se-iam obter composic¸oes˜ moleculares recebendo como dados de entrada os ´ındices comerciais que habitualmente caracterizam estas frac¸oes˜ petrol´ıferas. Contudo, o modelo mostrou-se insuficiente para prever corretamente tais composic¸oes,˜ tendo-se conclu´ıdo que se teria de incluir a priori alguma informac¸ao˜ por forma a melhorar as previsoes˜ do modelo.

Palavras-chave: Craqueamento termico,´ Etano, Propano, Nafta, Cinetica,´ Caracterizac¸ao˜ de alimentac¸oes˜ l´ıquidas

vii viii Abstract

The production of ethylene and propylene from naphtha and gaseous feedstocks such as ethane, propane and other light alkanes via thermal cracking is a cornerstone of the chemical industry. In the present work a mathematical steam cracking furnace model is presented and several kinetic schemes from literature, both molecular and radical, were implemented and validated against data from industrial ethane, propane and naphtha feedstocks processing furnaces. The results showed that, for gaseous feedstocks, the implemented kinetics were able to accurately predict product yields, with the radical scheme superseding the molecular one. Regarding naphtha cracking, however, the implemented rad- ical kinetics from literature seemed to fail at predicting plant data. A steady-state study on alternative diluents relatively to steam was also carried out and it was concluded that there may actually be no difference between diluents if one is not willing to further increase the coil outlet temperature, although helium posed the best alternative if no constraints on temperature exist. At last, since the implementa- tion of kinetic schemes requires the molecular composition of the feed and because liquid feedstocks are usually characterised by other indices rather than a detailed hydrocarbon analysis, a feed charac- terisation model was developed. This model had the objective to determine the molecular composition of naphtha feedstocks given the commercial indices that usually characterise such petroleum fractions. The results, however, showed that the model is not able to accurately determine such compositions, having been concluded that a priori knowledge had to be included to improve its predictions.

Keywords: Steam cracking, Ethane, Propane, Naphtha, Kinetics, Feed characterisation

ix x Contents

Acknowledgments...... v Resumo...... vii Abstract...... ix List of Tables...... xvi List of Figures...... xix Nomenclature...... xxvi Glossary...... xxviii

1 Introduction 1 1.1 Motivation...... 1 1.2 Scope...... 2 1.3 State-of-the-art...... 2 1.4 Outline...... 2

2 Background 5 2.1 Ethylene market...... 5 2.2 Steam cracking process...... 9 2.2.1 Process description...... 9 2.2.2 Furnace...... 10 2.2.3 Recovery section...... 14 2.2.4 Hydrocarbon fractionation section...... 15 2.3 Steam cracking reactions...... 19 2.3.1 Thermodynamics...... 19 2.3.2 Mechanisms...... 20 2.3.3 Kinetic models...... 23

3 Implementation 31 3.1 The gPROMS® platform...... 31 3.1.1 gPROMS ProcessBuilder® ...... 31 3.2 Foreign Objects...... 32 3.3 Other gPROMS® tools...... 32 3.3.1 Optimisation...... 32

xi 3.3.2 Parameter estimation...... 32 3.4 Physical properties...... 33 3.4.1 Infochem MultiflashTM ...... 33 3.4.2 gSAFT® ...... 34 3.5 Implementation of Large Scale Kinetic Mechanisms...... 34 3.5.1 Sparse matrix compression scheme...... 35 3.5.2 Application of the LSKM foreign object...... 35

4 Steam cracking furnace 39 4.1 Model equations...... 39 4.1.1 Tube model...... 39 4.1.2 Energy input model...... 43 4.1.3 Cooling jacket model...... 48 4.1.4 Furnace and coil model...... 48 4.2 Ethane cracking...... 50 4.2.1 Kinetics...... 50 4.2.2 Industrial case...... 50 4.3 Propane cracking...... 54 4.3.1 Kinetics...... 54 4.3.2 Industrial case...... 54 4.4 Naphtha cracking...... 58 4.4.1 Kinetics...... 58 4.4.2 Industrial case...... 59 4.5 Case studies...... 65 4.5.1 Furnace heat flux correlations...... 65 4.5.2 Alternative diluents...... 67 4.6 Sensitivity analysis...... 71 4.6.1 Fluid properties...... 73 4.6.2 Operating conditions...... 73 4.6.3 Adiabatic section...... 82 4.6.4 Kinetic parameters...... 83

5 Feed characterisation 87 5.1 Introduction...... 87 5.2 Model equations...... 88 5.2.1 ASTM D86 standard test method...... 88 5.3 Model considerations...... 89 5.3.1 Component library...... 89 5.3.2 Thermodynamic models...... 90 5.4 Results...... 90

xii 5.4.1 Selection of thermodynamic model...... 91 5.4.2 Model validation...... 92

6 Conclusions 95 6.1 Achievements...... 96 6.2 Future work...... 97

Bibliography 106

A Thermodynamic properties 107 A.1 Thermodynamic models comparison...... 107

B Kinetics 109 B.1 Molecular kinetics...... 109 B.2 Radical models...... 110 B.2.1 Sundaram and Froment (1978)...... 110 B.2.2 Radical kinetics comparison...... 110 B.2.3 Extended reaction sets...... 112

C gSAFT® 113 C.1 Vapour-liquid equilibria...... 113 C.1.1 Vapour pressure of pure components...... 113 C.1.2 Binary systems...... 114 C.2 Dispersion energies adjustment...... 117

D Naphtha analytical data 119

xiii xiv List of Tables

2.1 Steam crackers projects...... 7 + 2.2 Number of sequential systems (C5 ) to be solved for alkane decomposition...... 26

3.1 Parameter estimation objective function symbol definitions...... 33 3.2 Arrays generated by the LSKM FO for the stoichiometric matrix...... 36 3.3 Arrays generated by the LSKM FO for the reaction order matrix...... 36

4.1 Ethane cracking furnace configuration...... 51 4.2 Operating conditions for ethane cracking...... 51 4.3 Comparison between literature and simulation results...... 52 4.4 Propane cracking furnace configuration...... 54 4.5 Operating conditions for propane cracking...... 55 4.6 Comparison between literature and simulation results...... 55 4.7 Naphtha cracking furnace configuration...... 60 4.8 Operating conditions for naphtha cracking...... 60 4.9 Naphtha feed composition...... 60 4.10 Comparison between literature and simulation results...... 61 4.11 Comparison between literature and simulation results with extended kinetic schemes... 63 4.12 Optimised values of the activation energies performed by Joo (2001)...... 63 4.13 Floor plus wall firing parameters...... 65 4.14 Product distribution results and comparison with the base case...... 66 4.15 Molecular weights of diluting agents being studied...... 67 4.16 Sensitivity analysis on physical properties: density, viscosity and thermal conductivity... 74 4.18 Sensitivity analysis on flowrates...... 77 4.19 Sensitivity analysis on pressures: coil inlet pressure and coil outlet pressure...... 79 4.20 Sensitivity analysis on temperatures: coil inlet...... 82 4.21 Sensitivity analysis on adiabatic section length...... 83 4.22 Sensitivity analysis on activation energies...... 85

5.1 Components included in the library of molecules for naphtha feedstock characterisation.. 90 5.2 Comparison between results from different thermodynamic models and experimental data. 91 5.3 Reduced component list used in the parameter estimation...... 92

xv 5.4 Comparison between parameter estimation results and experimental data: commercial indices...... 93 5.5 Comparison between parameter estimation results and experimental data: molecular compositions...... 93

A.1 Comparison of standard heats of formation and specific heat capacities amongst different sources...... 108

B.1 Molecular kinetic scheme from Sundaram and Froment...... 109 B.2 Single-component cracking reactions from the radical scheme published by Sundaram and Froment...... 110 B.3 Reactions compared between different kinetic models...... 111 B.4 Cyclopentane and cyclohexane cracking reactions added to the studied kinetic schemes. 112

C.1 Adjusted gSAFT® γ-Mie dispersion energies...... 118

xvi List of Figures

2.1 Ethylene product structure...... 6 2.2 Ethylene CFR NE Asia prices...... 6 2.3 World ethylene production distribution...... 7 2.4 Types of feedstocks for the steam cracking process...... 8 2.5 Feedstock percentage in ethylene production...... 8 2.6 Ethylene production cost based on feedstock...... 8 2.7 Simplified flowsheet of the steam cracking process; elements in blue only exist inliquid feedstocks cracking plants...... 9 2.8 Schematic diagram of a thermal cracking furnace in a typical olefin plant...... 11 2.9 Steam cracking coils...... 12 2.10 Pyrolytic and catalytic coke...... 13 2.11 Transfer-line exchangers...... 14 2.12 Front-end demethaniser with tail-end hydrogenation...... 16 2.13 Front-end deethaniser with front-end hydrogenation...... 18 2.14 Repsol Petrochemical Complex at Sines, Portugal...... 18 2.15 Front-end depropaniser with front-end hydrogenation...... 19 2.16 Gibbs free energy of formation of hydrocarbons as a measure of thermodynamic stability. 20 2.17 Internal radical addition on double bond leading to a six membered radical...... 22 2.18 Concerted path molecular reactions...... 22 2.19 n-Pentane decomposition via radical scheme...... 25 2.20 Structure and reaction families in the single-event microkinetic (SEMK) model...... 28

4.1 Schematic of the tube cross sectional area and differential control volume...... 40 4.2 Bend parameters for the bend friction factor coefficient calculation...... 42 4.3 Schematic of the analogy from jet theory...... 45 4.4 Normalised heat flux distribution for floor-only, wall-only and floor plus wall firingcases.. 47 4.5 Schematic of the addition of furnace heat flux correlations to the energy input model.... 48 4.6 Furnace model architecture...... 49 4.7 Pressure and process gas temperature profiles along reactor length...... 53 4.8 Variation of the yield along reactor length of some key components...... 53 4.9 Pressure and process gas temperature profiles along reactor length...... 57

xvii 4.10 Variation of the yield along reactor length of some key components...... 57 4.11 Naphtha cracking coils arrangement...... 59 4.12 Cyclopentane and cyclohexane yield profiles obtained using the implemented kinetics... 62 4.13 Cyclopentane and cyclohexane yield profiles obtained using the extended kinetics..... 62 4.14 Pressure and process gas temperature profiles along reactor length using the extended scheme from Joo...... 64 4.15 Component yields along the reactor length using the extended scheme from Joo...... 64 4.16 Comparison of simulation results obtained using the furnace heat flux correlations with the base case: heat flux and temperature profiles...... 66 4.17 Schematic of the alternative diluents study...... 68 4.18 Optimisation results obtained with upper bound in pressure drop and coil outlet tempera- ture of 1.1 bar and 845 ◦C, respectively, using the radical kinetics proposed by Sundaram and Froment (1978)...... 69 4.19 Optimisation results obtained with upper bound in pressure drop and coil outlet temper- ature of 1.1 bar and 875 ◦C, respectively, using the molecular kinetics proposed by Sun- daram and Froment (1977)...... 72 4.20 Analysis on the influence of hydrocarbon (ethane) flowrate in some key process variables. 76 4.21 Analysis on the influence of coil inlet pressure (CIP) in some key process variables.... 78 4.22 Analysis on the influence of coil inlet temperature (CIT) in some key process variables... 80 4.23 Analysis on the influence of coil outlet temperature (COT) in some key process variables. 81

5.1 Properties of a naphtha feedstock...... 88 5.2 ASTM D86 experiment schematic...... 89 5.3 ASTM D86 boiling curve using different thermodynamic models...... 91 5.4 ASTM D86 boiling curve: experimental data [1] and parameter estimation results...... 92

C.1 Vapour pressure of methylcyclohexane: gSAFT® predictions and experimental data.... 114 C.2 Vapour pressure of trans-dimethylcyclohexanes: gSAFT® prediction (DMCH) and experi- mental data...... 114 C.3 Isothermal vapour-liquid equilibria involving n-pentane (NP), n-octane (NO) and n-decane (ND)...... 115 C.4 Isothermal vapour-liquid equilibria involving n-hexane (NH), 2-methylpentane (2MP) and 2,4-dimethylpentane (24DMP)...... 115 C.5 Isobaric vapour-liquid equilibria involving cyclohexane (CH), methylcyclohexane (MCH) and n-hexane (NH)...... 115 C.6 Isobaric vapour-liquid equilibria involving benzene(B), cyclohexane (CH) and n-hexane (NH)...... 116 C.7 Isobaric vapour-liquid equilibria involving benzene (B), p-xylene (PX) and n-hexane (NH). 116 C.8 Isobaric vapour-liquid equilibria involving toluene (T), p-xylene (PX), cyclohexane (CH) and methylcyclohexane (MCH)...... 116

xviii C.9 Experimental data used for ’cCH2’ interaction parameters estimation...... 117 C.10 Experimental data used for ’CH’ and ’CH3’ interaction parameters estimation...... 118

D.1 Analytical data from a sweetened petroleum naphtha used to validate de feed characteri- sation model...... 120 D.2 Analytical data from a sweetened petroleum naphtha used to validate de feed characteri- sation model (cont.)...... 121 D.3 Analytical data from a sweetened petroleum naphtha used to validate de feed characteri- sation model (cont.)...... 122

xix xx Nomenclature

Acronyms

AAD Average absolute deviation.

AGO Atmospheric gas oil.

ASEM Analytical semi-empirical model.

BTX Benzene, toluene and xylenes.

CIP Coil inlet pressure.

CIT Coil inlet temperature.

COP Coil outlet pressure1.

COT Coil outlet temperature.

EA Ethyl acetate.

EBZ Ethylbenzene.

EDC Ethylene dichloride.

EO Ethylene oxide.

EoS Equation of state.

FCC Fluid catalytic cracking.

GC Gas-chromatography.

GO Gas oil.

HC Hydrocarbon.

HCR Hydrocracking.

HCVD Hydrocracked vacuum distillate.

HDT Hydrotreating/hydroprocessing.

1Although its name refers to the coil it is usually measured after the TLE.

xxi HPLC High-performance liquid chromatography.

HPS High pressure steam.

HPSS High pressure superheated steam.

KAIST Korea Advanced Institute of Science and Technology.

KPIC Korean Petrochemical Industry Co.

LAO Linear alpha olefins.

LPG Liquified petroleum gas.

LPS Low pressure steam.

MA Methylacetylene.

MAPD Methylacetylene and propadiene.

MS Mass spectroscopy.

PAH Polycyclic aromatic hydrocarbons.

PD Propadiene.

PE Polyethylene.

PFR Plug flow reactor.

PS Polystyrene.

PSA Pressure-swing adsorption.

PSSA Pseudo-steady state assumption.

PVC Polyvinyl chloride.

Q8 Kuwait Petroleum International.

QAPCO Qatar Petrochemical Company.

TLE Transfer-line exchanger.

TST Tube skin temperature.

VAM Vinyl acetate monomer.

VCM Vinyl chloride monomer.

VGO Vacuum gas oil.

Greek symbols

α Angle(°).

xxii 0 ∆f H Standard-state heat of formation.

0 ∆Gform Standard-state Gibbs free energy of formation.

∆P Pressure drop (bar).

∆z Infinitesimal length of the control volume (m).

ϵ Wall roughness (m), dispersion energy (J) or emissivity.

γ Ratio of the floor burner-related dimension to the furnace height.

λ Thermal conductivity (kWm-1K-1).

µ Viscosity (Pa · s).

ν Stoichiometric coefficient.

ω Furnace inverse aspect ratio (width/height).

ρ Process gas density (kgm-3).

σ Stefan-Boltzmann constant (kWm-2K-4).

θR Residence time.

ζ Relative power of burners relatively to each other.

Roman symbols

A Cross-sectional area (m2). a Empirical parameter or constant of proportionality. b Empirical parameter or constant normalised heat loss.

C Molar concentration (kmolm-3). c Empirical parameter.

Cp Process gas heat capacity. d Empirical parameter. e Empirical parameter. fbend Friction factor of bends. fFanning Fanning friction factor. h Specific enthalpy (kJkg-1) or heat transfer coefficient (kWm-2K-1).

ID Inner diameter. k Reaction constant (kmoln-1m-3n+3s-1).

xxiii n-1 -3n+3 -1 k0 Pre-exponential factor (kmol m s ).

2 -1 kB Boltzmann constant (m kgs-2K ).

L Reactor/coil length (m).

MW Molecular weight (kgkmol-1).

N Mass flux (kgm-2s-1) or number (integer). n Reaction order. nB Number of bends in the coil.

Nwb Number of wall burner rows.

Nu Nusselt number.

OD Outer diameter.

P Pressure (Pa).

Pr Prandtl number. q Heat flux (kJm-2s-1).

R Radius (m) or ideal gas constant (Jkmol-1K-1). r Rate of reaction/formation (kmolm-3s-1).

Ri General radical or group i.

Re Reynolds number.

T Temperature (K).

T* Reduced flue gas temperature.

T0 Absolute flue gas temperature at the floor (K).

Tflame Effective flame temperature (K).

Tflue Absolute flue gas temperature (K).

max Tmax Absolute flue gas temperature atz (K).

TMT Tube metal temperature (K). v Process gas linear velocity (ms-1). x Distance in number of nozzle diameters, taken from the nozzle exit. x’ Distance in number of nozzle diameters, taken from a virtual origin one diameter upstream of the nozzle exit.

xxiv Y Product yield. y Normalised furnace heat flux. y* Reduced furnace heat flux. y0 Normalised furnace heat flux at the floor. yh Normalised furnace heat flux released from burners. yk Normalised furnace heat flux produced by a row of wall burners.

sum Ymax Maximum value of Y . ymax Maximum normalised furnace heat flux, i.e., one. yp Normalised furnace heat flux absorbed by the coils or otherwise removed from the furnace.

Ysum Sum of all burners normalised heat flux contributions. z Coil axial dimension (m) or furnace normalised elevation. z* Reduced furnace elevation. zk Normalised furnace elevation of a row of wall burners. zmax Normalised furnace elevation at which ymax is observed.

Subscripts avg Stands for average. b Refers to backward reaction constant. bend Refers to coil bends. coke Refers to deposited coke. cool Refers to cooling jacket model or coolant. ext Stands for external. f Refers to forward reaction constant. floor Refers to floor-mounted burners. form Stands for formation. i Refers to chemical species. int Stands for internal. j Refers to chemical reactions. k Refers to a row of wall-mounted burners.

xxv process Refers to the process stream. total Refers to the whole process stream. w Refers to a row of wall-mounted burners.

Superscripts

0 Refers to standard-state.

xxvi Glossary

CFD Computational Fluid Dynamics is a branch of fluid mechanics that uses numerical methods and algorithms to solve problems that involve fluid flows. Gas condensates A low-density mixture of hydrocarbons that are present as gaseous components in raw natural gas and are extracted therefrom by condensa- tion. Group additivity method A group additivity method is a technique that al- lows to predict properties from molecular struc- tures. Incipient cracking temperature Temperature just below the cracking reaction temperature, normally achieved at the radiant coil inlet. Induced draft Slight negative pressure that is produced by a fan at the stack inlet to pull the gases out of the furnace and discharge them to the stack. Lumping Grouping of species which are generally iso- mers or homologous species with similar re- activity in order to reduce the total number of species in a kinetic model. PIONA An analysis method that divides crude oil com- ponents according to their groups, namely paraffins, isoparaffins, olefins, naphthenes and aromatics. PNA An analysis method that divides crude oil com- ponents according to their groups, namely paraffins, naphthenes and aromatics.

xxvii PSSA Pseudo-steady state assumption that states the time rate of change of the concentration of all species covered by this assumption can be considered as zero.

Pygas Pyrolysis gasoline is a C5 to C12 product with a high aromatics content produced as a co- product of high temperature naphtha cracking during ethylene and propylene production. SEMK Single-event microkinetic model is a kinetic model consisting of elementary reactions and accounts for all energetically equivalent reac- tion paths, i.e., single-event, to determine each reaction rate. Steam ratio Key operating parameter in steam crackers de- fined as the mass ratio between dilution steam and pure hydrocarbon feed. Other common names are dilution steam ratio, steam/oil ratio or steam-to-oil ratio. Stiffness (equation) Characteristic of a differential equation whose terms lead to rapid variation in the solution, therefore making the numerical methods for solving the equation unstable, unless the step size is taken to be extremely small.

Straight-run naphthas Petroleum cuts composed by C5−C10 hydro- carbons obtained directly from the crude atmo- spheric distillation unit. TLE Transfer-line exchangers are the exchangers that immediately follow the radiant coil, per- forming an indirect quenching of the cracked gas to prevent further cracking of valuable re- action products.

xxviii Chapter 1

Introduction

Hydrocarbon steam cracking is one of the most important processes in the petrochemical industry as it generates highly valuable olefins – from which ethylene, propylene and butadiene are the most important ones – from lower value feedstocks. Feedstocks for this process usually have fossil origin and range from gaseous feedstocks, like ethane and propane, to liquid, heavier feedstocks, such as naphtha, gas oil and gas condensates [2]. With a world production of around 1.48 million tonnes/year in 2014 [3], ethylene is the major product of a steam cracking unit and it is almost exclusively produced by this process. Being the largest vol- ume building block, it is mainly used in the manufacture of polyethylene, ethylene oxide, vinyl acetate, ethylbenzene and ethylene dichloride [4]. Propylene, on the other hand, is considered a co-product of an olefins plant with nearly 60% of its production – 109 million tonnes in 2014 – being associated with ethylene’s manufacture [5,6]. Nevertheless, propylene is a valuable olefin – in fact, the most rele- vant cracker co-product – being responsible for the production of polypropylene, acrylonitrile, propylene oxide, cumene and isopropanol [7]. Hydrocarbon cracking reactions occur in the presence of steam inside the furnace in the radiant coil at temperatures ranging from 700◦Cat the coil inlet up to 900◦Cat the coil outlet. It is generally accepted that these reactions take place via free-radical mechanisms, with ethylene and propylene yields between 25-50% and 14-17%, respectively [2]. Along with ethylene, propylene and several other co-products, the high temperatures experienced within the coil give rise to coke formation which tends to accumulate on the inside surface of the coil, leading to increased pressure drop, lower heat transfer and ultimately to furnace shutdown. Therefore, a model capable of accurately predicting the product distribution would be of great interest from a whole olefins plant optimisation point of view.

1.1 Motivation

The production of ethylene and propylene from ethane, propane and other light alkanes via thermal cracking is a cornerstone of the chemical industry. It has become even more prominent following the recent advances in the exploitation of shale gas in the United States and elsewhere.

1 On the other hand, the fact that refineries have been processing increasingly heavier crude oilshas brought much attention to liquid feedstocks, with heavier cuts such as atmospheric and vacuum gas oils being considered as possible hydrocarbon sources. Amongst the liquid feedstocks, naphtha has historically been by far the most widely used, playing a major role in the world petrochemical industry as Europe and Asia still considerably rely on it to feed their crackers. In this regard, the need arises for the development of high-fidelity mathematical models, able to fully describe an olefins plant operation and whose application in whole-plant optimisation is of theutmost interest of the petrochemical industry.

1.2 Scope

The current work was intended to bring a much better understanding on literature kinetic schemes for steam cracking, namely on how well do these suffice in accurately predicting product distribution for different feedstocks: ethane, propane and naphtha. To accomplish this, a furnace mathematical model would have to be used in order to implement different kinetics and compare simulation results against industrial data. Having the kinetics been studied, it was also intended to perform a study on different diluents which could pose a beneficial alternative relatively to steam. Finally, since a detailed molecular composition is required in these kind of models, this work was also expected to involve the development and validation of a naphtha feed characterisation model which could provide such information based on easily-obtainable average properties of the mixture.

1.3 State-of-the-art

Steam cracking is a key process for the petrochemical industry and it is well described in chemical engineering encyclopaedias [2,8] and books [9, 10], apart from additional publications. Several kinetic models describing thermal cracking phenomena are available in literature, ranging from empirical models [11, 12] to molecular [13, 14] and mechanistic/radical ones [15, 16, 17, 18, 19]. Regarding cracking feeds characterisation and molecular reconstruction, several recent papers have been published and made available publicly [20, 21, 22]. Finally, various PhD and Master Thesis have been dedicated to steam cracking and its modellling [23, 24, 25, 26, 27, 28, 29].

1.4 Outline

Firstly, a review of existing literature on the steam cracking process and corresponding kinetic mod- elling is shown in chapter2. Chapter3 describes the software platform in which all the modelling presented in the current work was based on, as well as important tools and entities used in the models’ implementation and results’

2 acquisition. In chapter4, the mathematical modelling of a steam cracking furnace is described. Molecular and radical kinetics are implemented and simulation results compared against plant data from industrial ethane, propane and naphtha cracking furnaces. Further in that chapter, two case studies are presented: one involving the use of furnace heat flux correlations and the other regarding the usage of alternative diluents relatively to steam. A sensitivity analysis on some process variables and parameters concludes the chapter. Chapter5 presents the development of a feed characterisation model and its ability to accurately predict molecular compositions of naphtha feeds based on commercial indices is evaluated. Finally, chapter6 summarises the conclusions of this work, referring what was achieved and dis- cussing possible future work.

3 4 Chapter 2

Background

Since the first refinery built in Romania in 1856, crude oil has been fractionated in order toobtain lighter, more valuable cuts. However, the hydrocarbons that usually are found in these lighter fractions are mainly of paraffinic and/or naphthenic nature and thus lack the chemical reactivity needed forthe development of several other petrochemicals of varying complexity. Therefore, industrial processes have been developed in order to convert these saturated compounds into unsaturated, more reactive hydrocarbons, such as olefins and aromatics [9, 30]. In spite of thermal cracking having been first patented in 1913 by a Standard Oil’s scientist, the world’s first steam cracker was only erected in 1941 at Baton Rouge by ExxonMobil’s predecessor, Standard Jersey. At the time, U.S. oil and chemical companies began producing ethylene from ethane obtained from refinery byproduct streams and from natural gas. Since then, ethylene has almost completely replaced acetylene as the most widely used basic hydrocarbon in many synthesis [2,9, 31].

2.1 Ethylene market

Ethylene is mainly used to make polyethylene (PE), which accounts for about 60% of world de- mand. Other major uses include ethylene oxide (EO), ethylene glycol (EG), polyvinyl chloride (PVC) and polystyrene (PS). In addition, linear alpha olefins (LAO), detergent alcohols and plasticiser alcohols, vinyl acetate monomer (VAM) and intermediates such as ethyl acetate (EA) and ethyl acrylate are also produced from ethylene [3]. On the past few years the product structure from ethylene has remained practically unchanged and it is predicted that it will follow the same structure in the coming years (Figure 2.1). Whilst propylene is produced 60% by steam cracking along with ethylene, 31% by refinery operation and 9% by other processes, ethylene is almost exclusively produced (ca. 98%) by steam cracking [31], as none of the alternative technologies has the economics to be a challenge for this so well-established process [2]. Ethylene prices were at multi-year highs of $1,560-1,570/tonne CFR NE Asia in August 2014 and had stayed above $1,400/tonne throughout the first three quarters of 2014 (Figure 2.2). However, prices

5 100% 90% 80% 70% 60% 50% 40%

30% % Ethylene % Demand 20% 10% 0% 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2022

PE EBZ EDC (VCM) EO Others

Figure 2.1: Ethylene product structure [32].

1750

1500

1250

1000

750

$/tonne CFR Asia NE 500

Figure 2.2: Ethylene CFR NE Asia prices [3]. fell during the October-December period as a result of a dramatic decline in upstream crude futures. Crude has fallen not just on increased supply, but also on weaker global demand growth [3]. Ethylene production, which reached 1.48 million tonnes in 2014 [3], is somewhat evenly distributed all over the world, being North America and North Eastern Asia the regions of higher preponderance, totalling together almost 50% of world’s production (Figure 2.3). Ethylene plants, which before the 1970s hardly reached 300,000 tons/year, have long passed the 1 million mark and the growing ethylene demand has led olefin producers to install huge-capacity plants, being 1.5 million tons per year a common value (Table 2.1)[8]. These can be designed for a wide range of feedstocks, from the gaseous feedstocks, such as ethane, propane and butane, to liquid feedstocks, such as naphtha, gas oils (AGO, VGO) and gas condensates (Figure 2.4). Working at operating rates of 80-90%, ethylene plants have two major feedstocks: ethane and naphtha (Figure 2.5). Historically, naphtha has always dominated the olefins plant feedstock market but the recent ad- vances in the exploitation of shale gas in the United States and elsewhere have brought higher attention

6 10% North America 23% Latin America 26% 3% Europe ex-USSR 16% Africa 2% 19% 1% Middle East NE Asia Rest of APAC

Figure 2.3: World ethylene production distribution [33].

Table 2.1: Steam crackers projects [3].

Company Capacity(t/a) Location Start-up Q8/Sinopec 800,000 Guandong, China 2018 Indial Oil Corp 850,000 Paradip, India 2015 KPIC 800,000 Onsan, South Korea 2017 QAPCO 1.4m Ras Laffan, Qatar On Hold Sibur 1.5m Tobolsk, Russia 2020 Sadara 1.5m Jubail, Saudi Arabia 2015 Borouge 1.5m Abu Dhabi, UAE 2015 Shell 1.5m Pennsylvania, USA 2018 Axiall/Lotte 1.0m Louisiana, USA 2017 Formosa Plastics 1.2m Louisiana, USA NA Shintech 500,000 Louisiana, USA NA Williams 1.5m Louisiana, USA NA CP Chem 1.5m Texas, USA 2017 ExxonMobil 1.5m Texas, USA 2017 Dow Chemical 1.5m Texas, USA 2017 Formosa Plastics 1.59m Texas, USA 2017 OxyChem/MexiChem 544,000 Texas, USA 2017 Sasol 1.5m Texas, USA 2018 Odebrecht World-scale West Virginia, USA NA

to gaseous feedstocks. In addition, since 2000 a huge amount of new capacities have been installed in the Middle East based on ethane as feedstock [2]. In such regions, one has been witnessing a ”gasifica- tion” of the petrochemical industry due to favourable production costs for ethane-based crackers (Figure 2.6).

Nevertheless, in some other regions such as Europe and Northeast Asia – whose petrochemical industry heavily relies on naphtha – naphtha has had a competitive price in comparison to gaseous feedstocks and even more so with crude oil’s falling prices [3]. Naphtha is therefore expected to continue to play a crucial role in the coming years in world’s petrochemical industry.

7 Methane Methane

Gaseous Ethylene Natural gas feedstocks Raw Propylene natural gas processing Steam Butadiene Liquid

feedstocks cracking Byproducts

Ethane

Butanes

Propane

Naphtha Gas Oil Crude oil Petroleum refinery

Benzene, Toluene and Xylenes Petrochemical intermediate feedstocks

Figure 2.4: Types of feedstocks for the steam cracking process (adapt. [34]).

100% 90% 80% 70% 60% 50% 40%

30% % Ethylene % Demand 20% 10% 0% 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2022

Ethane Propane Butane Naphtha Gas Oil Others Operating Rate

Figure 2.5: Feedstock percentage in ethylene production [32].

Naphtha

1600 Naphtha 1400 Imported 1200 ethane

1000 Imported ethane 800

600

400

200 Ethyleneproduction cost ($/tonne) 0 2014 2014 2020 2020

Figure 2.6: Ethylene production cost based on feedstock [3].

8 2.2 Steam cracking process

2.2.1 Process description

As it has been stated in the previous section, about 98% of world’s ethylene is produced by thermally cracking petroleum hydrocarbons in the presence of steam, a process known as steam cracking or pyrolysis, whose simplified flowsheet is shown in Figure 2.7.

Ethane/propane recycle Ethylene Gas/liquid Hydrocarbon Propylene feed Cracking Oil Water Gas Compression fractionation & Crude C furnace quench quench drying 4 hydrogenation Byproducts Liquid drying Primary Light distillate fractionation Acid-gas removal

Dilution steam Gasoline Pyrolysis gasoline generation stripping Pyrolysis fuel oil

Figure 2.7: Simplified flowsheet of the steam cracking process; elements in blue only exist inliquid feedstocks cracking plants (adapt. [2]).

First, the hydrocarbon feedstock enters the furnace in the convection section (Figure 2.8), where, by heat exchange against flue gases, it is pre-heated, mixed with steam (dilution steam), and the resulting mixture further heated in this section to incipient cracking temperatures of 500-680 ◦C. The gaseous feed immediately heads to the radiant section of the furnace, where fuel burners heat up the firebox to temperatures ranging between 1000-1200 ◦C. Inside the firebox, vertical radiant coils act as fired tubular reactors where the hydrocarbon feedstock is submitted to cracking conditions for 0.1-0.5 s. Due to the endothermicity of the reactions involved, high heat fluxes are required [2]. Depending on the feedstock composition and reaction conditions, the product stream contains typ- ically 10-35 wt% of ethylene, 5-20 wt% of propylene, 1-15 wt% of C4 fraction (mostly butenes and butadiene), 1-10wt% of aromatics (mostly BTX) and 0-15wt% of heavy hydrocarbons called pyrolysis oil [35]. The cracked gas then leaves the radiant coil at 800-850 ◦Cand is cooled within 0.02-0.1s to 550-650 ◦Cin order to prevent further cracking of valuable reaction products and coke formation. The cooling of the reactor effluent is achieved by indirect quenching in the so-called transfer-line exchangers (TLEs)by vaporisation of high-pressure boiler feedwater (BFW) whose high-pressure steam (6-12 MPa) is subse- quently superheated in the convection section [2]. After being cooled in the TLEs, the radiant coil effluent enters the recovery front-end section where it is first submitted to further cooling. In the case of liquid feedstocks, for process reasons, the crackedgas leaves the TLEs at higher temperatures and thus require an oil quench in order to reduce temperature down to 230 ◦C. A primary fractionator (gasoline fractionator) then follows in order to separate the

9 pyrolysis fuel oil from the main stream. Part of the pyrolysis fuel oil is cooled and recycled back to perform cracked gas quenching. Gaseous feedstocks, on the other hand, do not require any of these operations being thus cooled from about 300 ◦Cto about 200 ◦Cin secondary TLEs [2,8]. Then the hydrocarbon product stream, in order to be subjected to further processing, needs to be cooled to near ambient temperature by contacting with a large descending water stream in a water quench tower. Besides from the overhead gas, both quench water and pyrolysis gasoline (pygas) are collected at the bottom of the column [2]. Next, a series of 4 to 6 compression stages with interstage coolers are followed to compress the cracked gas to about 35 bar whilst maintaining its temperature below 100 ◦C. After each interstage cooler, separators collect the condensates, mainly water and pygas. Usually between the 3rd and 4th or the 4th and 5th stage, the hydrocarbon stream is submitted to acid gas removal, namely hydrogen sulphide, H2S, and carbon dioxide, CO2, in a wash tower by contacting with a alkaline solution, usually sodium hydroxide, NaOH [2,8]. The now purified gas is then dried in molecular sieve beds in order to remove practically allthewater (<1 ppm), whose presence is strictly forbidden from this point forward since the hydrocarbon stream will be submitted to cryogenic conditions in downstream equipment [2,8]. Finally the gas is then chilled and separated into its product streams by means of a fractionation train composed by the following distillation columns: demethaniser, deethaniser, depropaniser, debutaniser, ethylene fractionator and propylene fractionator. In order to further increase light olefins yield, acety- lene and methylacetylene (MA) and propadiene (PD) are usually converted to ethylene and propylene, respectively, in catalytic hydrogenation beds [2,8]. Whilst the recovery front-end section is essentially independent from licensors but mostly depending on the feedstock, the hydrocarbon fractionation section has a large variety of process routes, playing the licensor’s technology the major role [2].

2.2.2 Furnace

With capacities ranging from 20,000 to 300,000 tethylene/yr and capital costs representing ca. 20% of total cost of an ethylene plant, thermal cracking furnaces are the heart and the largest energy consumer of the whole process, being a key factor in both economical and smooth running of olefin plants [8]. Thermal cracking furnaces are divided into three main sections: radiant section or firebox, convection section, and stack as shown in Figure 2.8.

2.2.2.1 Convection section

The hydrocarbon feed and steam are pre-heated in the convection section of the furnace by convec- tive heat transfer against the hot flue gases coming out of the radiant section. This section is responsible for recovering more than 50% of the heat from flue gases through both process heat duty (35.5%) –the energy required to preheat feedstock and dilution steam to incipient cracking temperature – and utility heating duty (16%) – the amount of energy necessary to heat BFW from 110 to 180 ◦Cbefore being fed to the TLEs and to superheat the saturated HPS generated in the TLEs. Preheating combustion air for

10 Figure 2.8: Schematic diagram of a thermal cracking furnace in a typical olefin plant [36]. firebox burners is another possibility to increase thermal efficiency. Thanks to waste heat recovery, the flue gases, which in old furnaces left the stack at or above 400 ◦C, are leaving modern furnace’s stack at temperatures even below 100 ◦C. Furnace draft is normally accomplished by using an induced-draft fan instead of a forced-draft one [2, 37].

Dilution steam ratios from 0.25-0.40 (for gaseous feeds) to 0.5-1.0 (for liquid feeds) kgsteam/kghydrocarbon [9], are used in order to heat the feedstock but mainly to reduce hydrocarbon partial pressure inside the cracking coils. Otherwise, the high temperatures experienced would lead to higher rates of coke for- mation, whose deposition on the inside wall of the tube would not only increase pressure drop, thus increasing hydrocarbon partial pressure further raising coke formation, but also hamper heat transfer, which may increase tube skin temperature above the tube maximum allowable temperature (typically 1040-1150 ◦C). In either case, a premature furnace shutdown due to coke build-up would rapidly follow [2,8, 37].

2.2.2.2 Radiant section

The pre-heated gases at incipient cracking temperatures of 500-650 ◦Care then fed into the radiant section of the furnace where 40 to 200 floor- and/or wall-mounted burners – depending on the design and capacity – keep the firebox at temperatures as high as 1000-1200 ◦C. Nearly 90% of the heat transfer in this section is accomplished by radiation mechanisms, namely between hot flue gases/coil

11 and between refractory walls/coil. Overall fuel (oil or gas) efficiencies of 92-95% of lower heating value are typical in steam cracking furnaces [2,8, 37]. The cracking process occurs in fired tubular reactors hanged vertically at the center line of the firebox, called radiant or cracking coils (Figure 2.9a), at low pressure, typically 1.50-2.75 bar, and high temper- atures, from 700 ◦Cto 900 ◦C. Typical conversions on commercial furnaces are 60-70% for ethane, 90-93% for propane and 94-96% for butane [2,8, 37]. Cracking coils dimensions usually are 40-90 m in length and 30-200 mm internal diameter. While the number of coils may vary between 16 and 128 coils, mainly depending on the furnace design and capacity, the coils geometry is also dependent on the feedstock. For instance, gaseous feeds are normally cracked in fixed diameter tubes (Figure 2.9b A), whilst liquid hydrocarbons, such as naphtha and gas oil, due to higher coke formation and higher pressure drop along the reactor, usually react in multi-diameter coils (Figure 2.9b B, C) [2,8, 37].

Since the reactions involved are extremely endothermic (1.6-2.8 MJ/kgHC converted) very high heat 2 fluxes, typically 75-85 kW/m coil, are needed. In fact, of the nearly 42% of the fired duty absorbed in the radiant section, ca. 30% is consumed by cracking reactions [2,8].

(a) Industrial radiant coils [38]. (b) Schematic representation of steam cracking reactors [39].

Figure 2.9: Steam cracking coils.

2.2.2.3 Coking and decoking

Coke, whose precursors are believed to be of acetylenic, diolefinic and aromatic nature, forms onthe inner surface of the radiant coils due to the high temperatures experienced by the hydrocarbon stream. Coke formation is enhanced by high hydrocarbon partial pressures, hence the usage of dilution steam and low pressures to keep these partial pressures as low as possible [2,8]. Although coke formation mechanisms are not fully understood, it is generally well accepted that there are two types of coke being formed in the radiant coils: pyrolytic or thermal coke, which is generated by a fractional population of the free radicals in the process stream, and catalytic, whose formation is primarily due to Fe and Ni active sites on tube metal surfaces (Figure 2.10)[2, 40]. Coke deposits of a few millimetres to centimetres in thickness lead to poor heat transfer and so, in order to retain the same process temperature and hence the same conversion, plant operators have to raise the skin temperature continuously, which often leads to more rapid coke formation. The coke build- up also increases the pressure drop, which increases hydrocarbon partial pressure and thus favours

12 Figure 2.10: Pyrolytic and catalytic coke [2]. even more coke formation, resulting in lower ethylene yield. This coke accumulation forces the operator to shut down the unit either by unreasonable pressure drop or excessive tube skin temperature [40]. After typical run lengths of 40-100 days, a decoking period (12-48 hrs) is followed. Since mechanical techniques are not feasible, coke must be burned out with a mixture of steam and air. After the shutdown, the hydrocarbons are purged with steam and then an air-steam mixture is fed to the coils to remove coke at about 800 ◦C. Air is initially kept at low concentrations, due to hydrogen contained in the coil and within the coke whose fast combustion would otherwise lead to a temperature overshoot, being gradually increased as decoking operation proceeds. Steam-only decoking (950-1000 ◦C) is also possible but because of its endothermic nature, coke is less likely to be burnt out [2,8]. Frequent decoke means lost ethylene production, high operating and maintenance costs and short- ened life of the coil because of the constant thermal cycling of the coil [40].

2.2.2.4 Transfer-line exchangers

After being submitted to cracking reactions, the reaction mixture needs to be almost instantaneously cooled in order to preserve product distribution and prevent further cracking of major olefinic products. This rapid cooling is accomplished through indirect quenching in the so-called transfer-line exchangers (TLEs). Whilst cooling the cracked gas, TLEs allow heat recovery (ca. 29% of fired duty) at temperatures high enough to generate valuable high-pressure steam which, after being superheated in the convection section, is used in the compression section downstream of the process in turbine-driven compressors (Figure 2.11a). The transfer-line exchangers working principle is rather similar to that of fire-tube boilers since the hot gases coming out of the radiant coil flow through the TLE tubes, thus vaporising the BFW surrounding the tubes (Figure 2.11b) [2, 37]. Although the temperature virtually stops cracking reactions, coke can still build-up in this equipments either mechanically dragged by the cracked gas or formed by droplet condensation of heavy compo- nents. As process stream exits the coils, the substantial temperature drop in the TLE generates tar mists, which partially adheres to the surfaces of the equipment. The deposited mists are then readily converted to coke-like material through dehydrogenation reactions [40]. However, this mechanism is only relevant when liquid feedstocks are cracked. Coke formation

13 (a) TLEs and steam generation. (b) Details of the Borsig TLE [2].

Figure 2.11: Transfer-line exchangers. through droplet condensation is, therefore, the reason why TLE outlet temperatures for heavy liquid feedstocks (550-650 ◦C) are significantly higher that those for gaseous and light naphtha feeds (300- 400◦C), thus affecting the downstream processing configuration [2]. When gaseous hydrocarbons are cracked, the primary quenching to ca. 200 ◦Cis achieved in a single or, more commonly, two TLEs arranged in series, contrasting with heavier feedstocks whose further cooling to 230 ◦Cis only achieved in the recovery front-end section, downstream of the furnace section [2].

2.2.3 Recovery section

After being rapidly cooled down, the cracked gas coming out of the furnace section is fed to the recovery front-end section where, after the heavier components are condensed and separated, the effluent is compressed, depleted from acid-gases and dried in order to be further separated initsmain components in the hydrocarbon fractionation section.

2.2.3.1 Quench

For liquid feedstocks, since the outlet temperature of the TLE is substantially higher than 200 ◦C, in order to cool down the effluent to this temperature, the next step to be taken after the indirect quenching is a direct oil quench, which allows cooling to about 230 ◦C. Then a primary fractionator, also called gasoline fractionator, is followed to separate pyrolysis fuel oil, tar and other oily materials from the main stream. A pyrolysis gasoline (pygas) stream coming from the water quench tower located downstream of the process, is fed to the top of the fractionator to promote further cooling. The hot pyrolysis fuel oil is collected at the bottom of the column and its waste heat used to produce dilution steam. A fraction of this quench oil is then recirculated to the quench nozzles downstream of the TLE and the remaining part is fed to a fuel oil stripper before usage or storage. For gaseous feedstocks, however, this step is not required since the slight amount of heavies can easily be removed by downstream processing and TLE outlet temperature is low enough to be fed to the following equipment [2,8, 10]. The main hydrocarbon stream then heads to a water quench tower where the gas stream is cooled

14 to near ambient temperature. The large amounts of circulating water employed condense most of the dilution steam and pygas, being these collected as two separate streams at the column’s bottom. A fraction of water collected is subsequently stripped and sent to recover quench oil waste heat thereby producing dilution steam, and the remaining is cooled and recirculated to the top of the column. Pygas, on the other hand, heads to a pygas collector followed by a stripper and a HDT unit before usage or storage, or a fraction of it is sent back to the top of the primary fractionator if the olefins plant uses liquid feedstocks [2,8, 10].

2.2.3.2 Compression, acid gases and water removal

Cooled cracked gas coming out of the water quench tower undergoes compression to about 35 bar in a series of 4 to 6 turbine-driven centrifugal compression stages with interstage coolers. The number of stages is dictated by the process stream temperature, which must be kept below 100 ◦Cin order to prevent diolefin polymerisation and subsequent equipment fouling. Condensates formed after each interstage cooler are collected in separators [2,8]. Usually between the 3rd and 4th or the 4th and 5th stage, once the the gas volume to be processed has been significantly reduced, the hydrocarbon stream is fed to a once-through caustic washand regenerative scrubbing tower to remove (<0.2 ppm) acid gases, namely hydrogen sulphide, H2S, and carbon dioxide, CO2. Generally, the most economical acid gas removal technique is caustic soda (4- 12% NaOH) scrubbing but at high sulphur contents, an amine system followed by a caustic wash is typically used instead. This unit must be always located upstream of the drying unit to avoid ice and hydrates formation [2,8]. Being the compressed hydrocarbon stream eventually subjected to cryogenic conditions in the frac- tionation section, water must be completely removed in order to prevent ice formation. This is accom- plished in a drying unit composed typically by two molecular sieve dryers, being one on-line (24-48 hrs) and the other being regenerated (usually under high-pressure methane and steam at 225 ◦C. Before being fed to the dryer, the main stream is cooled by a water cooler followed by a propylene refrigerant to further reduce dryer load. However, temperature must be kept above 10-15 ◦Cto prevent hydrate formation [2,8].

2.2.4 Hydrocarbon fractionation section

Gas separation processes like adsorption or membrane technology have made remarkable progress in the recent past but none of them has superseded cryogenic separation as the main method for cracked-gas separation [2]. Unlike the recovery section, the fractionation section of an ethylene plant is mainly dependent on the licensor’s technology, with the feedstock playing solely a minor role. The fractionation sequence is usually defined by the first separation step and the position of the acetylene hydrogenation step.Today there are three predominant routes of commercial importance:

1. Front-end demethaniser with tail-end hydrogenation.

15 2. Front-end deethaniser with front-end hydrogenation.

3. Front-end depropaniser with front-end hydrogenation.

2.2.4.1 Front-end demethaniser with tail-end hydrogenation

With this processing route for hydrocarbon fractionation (Figure 2.12), which was traditionally used by American contractors, after being compressed and dried, the cracked gas is chilled to temperatures as low as -140 to -160 ◦C, thereby condensing practically all the hydrocarbons and leaving hydrogen,

H2 (80-96%), and some uncondensed methane, CH4, in the gaseous state. Hydrogen is typically a desired product, specially due to its use in hydrogenation units not only present in olefins plants but also in refineries, which are often integrated with the former. Carbon monoxide, CO, however, is a poison to all hydrogenation processes, and therefore must be removed. Its removal is usually accomplished through pressure-swing adsorption (PSA), thereby producing fuel gas composed mainly by CH4 and CO, which is used throughout the facility [2,8, 10].

Figure 2.12: Front-end demethaniser with tail-end hydrogenation (adapt. [2]).

After being depleted from non-condensibles, the chilled cracked gas is fed to a demethaniser (dC1), which operates between 1000 (low-pressure demethaniser) and 3800 (high-pressure demethaniser) kPa. This column, which consumes the greatest proportion of net energy from the refrigeration system, + separates methane (95 mol%) from C2 components. This column is integrated with both ethylene and propylene refrigerant cycles, being the condenser cooled by ethylene at ca. -100 ◦Cand the reboiler heated by propylene at ca. 10 ◦C[2, 10, 27]. + The C2 hydrocarbon stream then enters a deethaniser (dC2), the third largest user of refrigeration energy (with the condenser being cooled by a -20 ◦Clevel propylene refrigerant), which allows separating + the C2 from the C3 hydrocarbons. This column usually operates at 2000-2800 kPa and overhead temperatures of ca. 0 to -50 ◦C[8, 10, 27]. The deethaniser top stream is then usually submitted to a hydrogenation step in order to convert acetylene into ethylene, although, whenever justified and appropriate, acetylene may be recovered and sold. The acetylene converter operates at gaseous phase, pressures from 20 to 35 bar, temperatures ◦ from 25 to 100 Cand H2 to acetylene ratios of 1.5-2. The outlet acetylene concentration must be as low as 0.5 ppm due to the 1 ppm specification in ethylene product. Since the hydrogenation stepis

16 highly exothermic, a multiple Pd-based catalyst beds (usually two or three) with intermediate coolers arrangement is employed. Thanks to the selectivity of the catalysts used, the amount of acetylene converted to ethylene surpasses the amount of ethylene hydrogenated to ethane, thus ensuring a net gain of ethylene (40% of the inlet acetylene) [2,8, 10].

This stream then enters the ethylene fractionator, or C2 splitter, to separate ethylene product (>99.9%) from ethane which will be recycled back to the furnaces. Having between 90 and 125 stages, this col- umn operates between 800 (Heat-pumped C2 splitter) and 1700-2800 (High-pressure C2 splitter) kPa and reflux ratios of about 4. High-pressure ethylene fractionators are integrated into the propylene re- frigeration cycles being the condenser (-35 ◦C) cooled by low-pressure propylene vaporisation and the reboiler heated by compressed propylene vapours. On the other hand, heat-pumped C2 splitters use compressed ethylene refrigerant to heat their reboilers. The latter offer a few advantages over the former such as less equipment involved and better relative volatility of ethylene and ethane at lower pressure, thus reducing reflux ratio, power consumption and number of trays [2,8,9].

In the mean time, the deethaniser bottom stream is fed to the depropaniser (dC3), which allows sep- + arating the C3 from the C4 hydrocarbons. Since there are many acetylenic and diolefinic contaminants, in order to prevent fouling, both pressure (1000-1800 kPa) and temperature are kept low [2, 10]. + The dC3 bottoms heads to a debutaniser (dC4), thus recovering at the bottom a pygas fraction (C5 ) and at the top the C4 cut, which contains 1,3-butadiene, whose application in the production of rubber (e.g. SBR and PBR) and elastomers (e.g. ABS) makes it the third most valuable product of an olefins plant.

The dC3 overhead stream is hydrogenated in a methylacetylene/propadiene (MAPD) converter in order to further increase propylene yield from the MAPD (2-6%) still present in the C3 cut. Unlike the acetylene hydrogenation, the MAPD hydrogenation reactions occur most often in liquid phase, in trickle- bed reactors at 50-90 ◦C, where the heat of reaction is removed by partial vaporisation on the processed liquid, thus avoiding the use of multistage adiabatic beds with intercooling steps. Nevertheless, this converter ensures a net gain of propylene, with typical values of 60% of the MAPD in the feedstream. The outlet concentration of methylacetylene and propadiene is dictated by the propylene product grade, being 500-1000 ppm for chemical grade propylene and 20 ppm for polymer grade propylene [2,8, 10].

Finally, the hydrogenated C3 stream is processed in the propylene fractionator, or C3 splitter, to pro- duce propylene product. According to the grade and purity required for propylene (93-95% for chemical grade and >99.5% for polymer grade), the column may operate at high-pressure (1800 kPa) or as a heat- pumped fractionator (800-1100 kPa). Due to the very low relative volatility of propylene and propane, although high-pressures are employed, the polymer grade C3 splitter involves a very high number of trays, between 150-230, and operates at high reflux ratios, ca. 20. As a matter of fact, these columns achieve such dimensions that for mechanical stability purposes the column must be divided in two.

2.2.4.2 Front-end deethaniser with front-end hydrogenation

This configuration (Figure 2.13), which has long been used by Linde and some American licensors, + has a dC2 column as the first separation step, obtaining aC3 cut in the bottom, which then undergoes

17 Figure 2.13: Front-end deethaniser with front-end hydrogenation (adapt. [2]).

– the same fractionation path as in the previous sequence (front-end demethaniser), and a C2 stream, which similarly to the front-end demethaniser route, is also hydrogenated to convert acetylene. The – converted C2 hydrocarbon stream is further chilled and fed to the demethaniser, obtaining hydrogen and methane as top products and ethylene and ethane mixture as the bottom stream, which is then fractionated in a C2 splitter. The hydrogen (85-95%) is separated from methane by Joule-Thompson expansion of the overhead stream [2,9].

Of the three commercially available, this fractionation sequence is the most advantageous one as it has the best energy efficiency and requires lower energy consumption – since onlyH2,C1 and C2 hydrocarbons, and not the entire cracked gas, are chilled to the dC1 inlet temperature. Furthermore, – since the C2 deethaniser overhead stream is H2-rich, there is no need for additional H2 to be supplied for the acetylenes hydrogenation step [2]. As a matter of curiosity, the only olefins plant in Portugal, located at Repsol Petrochemical Complex, Sines (Figure 2.14), uses this processing route.

Figure 2.14: Repsol Petrochemical Complex at Sines, Portugal. Both columns, the highest of the entire complex, are part of the propylene fractionator [41].

2.2.4.3 Front-end depropaniser with front-end hydrogenation

In the front-end depropaniser configuration (Figure 2.15), the same logic previously outlined applies, with the remark that, as the depropaniser is the first separation step, further compression of the overhead stream is needed in order to be processed in downstream fractionators.

18 Figure 2.15: Front-end depropaniser with front-end hydrogenation (adapt. [2]).

2.3 Steam cracking reactions

Generally cracking refers to those reactions in which large molecule hydrocarbons are cracked, thus yielding smaller hydrocarbon compounds. These reactions can be divided into two classes:

• Thermal cracking, in which large hydrocarbon breakdown is induced by high temperatures.

• Catalytic cracking, in which a selective catalyst plays the major role in hydrocarbon cracking.

In modern refineries both these cracking processes are used. Visbreaking and coking units,for instance, are thermal cracking-based whilst fluid catalytic cracking (FCC) and hydrocracking (HCR) units are based on catalytic cracking. Olefins plants, often integrated in a refinery environment, solely rely on thermal cracking toconvert their feedstocks into valuable products. However, steam, hence steam cracking, has to be used in order to prevent excessive coke formation and early furnace shutdown.

2.3.1 Thermodynamics

As in all reactions, thermodynamics determine whether or not a specific reaction path is favourable. At relatively low temperatures, unsaturated hydrocarbons are more unstable than those saturated com- pounds from which they have been formed. At high temperatures, however, the opposite is verified. This not only explains why such high temperatures (700-900 ◦C) are employed in steam cracking coils but also justifies the high reactivity of olefins at relatively low temperatures, which is responsible forthe outstanding flexibility of olefins for organic synthesis [9].

0 Gibbs free energy of formation (∆Gform) of several hydrocarbons is shown in Figure 2.16. It can 0 be seen that, as temperature rises, ∆Gform of saturated hydrocarbons (paraffins and naphthenes) sur- passes that of olefinic components, therefore evidencing that the former become more unstable thanthe latter. Since paraffins are of extremely simple chemical structure, thermal activation can solely causethe scission of a C-C bond or a C-H bond. The breakage of a paraffin C-C bond effectively leads to its

19 Figure 2.16: Gibbs free energy of formation of hydrocarbons as a measure of thermodynamic stability [9]. cracking, thus yielding a smaller paraffin and an olefin (Eq. 2.1a), whilst a C-H bond rupture leads to olefin formation by dehydrogenation (Eq. 2.1b)[9].

Cm+nH2(m+n)+2 → CmH2m + CnH2n (2.1a)

CpH2p+2 → CpH2p + H2 (2.1b)

Moreover, since C-C bond is relatively weaker than the C-H bond – 345 kJ/kmol versus 413 kJ/kmol, respectively – one may also infer that saturated hydrocarbon pyrolysis mainly relies in C-C bond scission [9]. Given both conversions are not only endothermic but also lead to an increase of number of molecules, in order to favour such reactions, steam cracking coils operate at high temperatures and relatively low pressures (1.50-2.75 bar).

2.3.2 Mechanisms

Since the pioneer work of F.O. Rice in the 1930s [42, 43], it is well known that the largest part of gas phase hydrocarbon pyrolysis proceeds through a free radical mechanism which is inherently characterised by a vast number of species and reactions, which in turn tends to grow as the molar mass of the feed molecules increases [15, 17, 19, 23, 44, 45]. Although specific reactions taking place in a free-radical scheme depend on the feed employed, the

20 mechanism is simply summarised with the following reaction classes [39, 46, 47]:

1. Initiation and termination reactions

· · R1−R2 −−→ R1 + R2 (2.2a) · · R3 + R4 −−→ R3−R4 (2.2b)

These unimolecular reactions involve either the C-C bond scission (initiation reactions), thus form- ing two smaller radicals (Eq. 2.2a), or the formation of a new bond (termination reactions) as two radicals come together and produce a single molecule (Eq. 2.2b). It is noteworthy the fact that when two radicals are formed, they fly apart from each other and the odds they will meet again and react, therefore terminating the chain reaction, is so small that termination reactions may be neglected [42]

2. Propagation reactions Once initiation occurs, radicals undergo a series of propagation reactions in which a radical reacts with a molecule and produces a smaller molecule and a new radical, which in turn keeps the reaction chain going.

(a) Hydrogen abstraction reactions

· · R1 + R2 −−→ R1 + R2 (2.3)

According to these reactions, smaller reactive radicals, such as hydrogen, methyl, ethyl, propyl and vinyl radicals abstract a hydrogen atom from a molecule, thus forming both a new molecule and a new radical. Kinetic parameters of these reactions are mainly a function of the H abstracting radical and the site from which the H-atom is abstracted.

(b) Radical addition/decomposition

· − −−⇀ · R1 + R2−R3 ↽−− R1−R2−R3 (2.4)

Radicals may react with olefins, thus forming larger, less saturated, radicals and/or the oppo- site may occur, i.e. the C-C bond of large molecules at the β position relatively to the radical is ruptured (β scission), thereby producing an olefin and a new radical. Radical addition re- actions explain the presence in cracked gases of heavier products than those initially present in the feed.

(c) Radical isomerisation reactions

· −−⇀ · R1 −R2−R3−R4−R5−R6 ↽−− R1−R2−R3−R4 −R5−R6 (2.5a)

21 · −−⇀ · R1 −R2−R3−R4−R5−R6 ↽−− R1−R2−R3−R4−R5 −R6 (2.5b)

· −−⇀ · R1 −R2−R3−R4−R5−R6 ↽−− R1−R2−R3−R4−R5−R6 (2.5c)

· − −−⇀ − · R1 −R2−R3 ↽−− R1−R2−R3 (2.6)

Isomerisation reactions of radicals are in competition with the decomposition processes and are responsible for the transfer of the active radical position to another position. This can be accomplished whether by intramolecular H-abstractions (Eq. 2.5) or by an internal addition of the radical position on unsaturated bonds (Eq. 2.6). In the former case, large radicals may isomerise whether through a 5-membered ring, thus performing a 1-4 H-transfer (Eq. 2.5a), a 6-membered ring, resulting in a 1-5 H-transfer (Eq. 2.5b), or 7-membered ring, leading to a 1-6 H-transfer (Eq. 2.5c). Internal radical addition on double bonds, typical for olefinic and aromatic radicals, favours the formation of five orsix membered cyclic components, precursors of aromatic compounds (Figure 2.17).

Figure 2.17: Internal radical addition on double bond leading to a six membered radical.

3. Concerted path molecular reactions

Molecular reactions such as Diels-Alder, electrocyclisation (Fig. 2.18a), cyclo-alkane/olefin iso- merisation, hydrogenation/dehydrogenation, and ene/retro-ene reactions (Fig. 2.18b) play a minor role in steam cracking coils, although they are not to be neglected.

(a) Electrocyclisation. (b) Ene and retro-ene reactions

Figure 2.18: Concerted path molecular reactions.

4. Sucessive condensation reactions

From the moment significant amounts of ethylene and propylene are formed, vinyl, allyl and benzyl radicals, between others, are somewhat abundant and therefore undergo sucessive addition and condensation reactions, which are responsible for the formation of even heavier compounds.

22 2.3.3 Kinetic models

Hydrocarbon steam pyrolysis has been studied for many years and its importance to the petrochem- ical industry has justified the interest involving its kinetic modelling and a major effort has been madein order to develop such reaction models, capable of predicting the products obtained from several feed- stocks under different operating conditions. There are three major types of kinetic models:

• Empirical or regression models

• Molecular models

• Mechanistic models

Empirical models are based on historical or calculated data sets and are mainly used by operators. Since they require a much lower computer performance, these models can be run on small computers and are, therefore, appropriate for process computer control and optimisation. However, rarely regres- sion models give accurate results when falling out of the range of the empirical data field and are always feedstock-specific, thus being inappropriate when it comes to simulate the furnace behaviour with differ- ent operating conditions and several feedstocks. Zarinabadi et al. [11], for instance, obtained empirical correlations for the yields of ethylene and propylene in naphtha cracking furnaces depending on the coil outlet temperature (COT). Sadrameli and Green [12] developed an empirical model based on industrial data for naphtha cracking from which the temperature dependence of several product yields is derived. On the other hand, molecular models pose a more advanced approach to hydrocarbon pyrolysis, since global molecular reactions, whose main products are described as a function of feedstock con- sumption, are applied. Again, although these models have been implemented with some success to sim- ple hydrocarbon thermal cracking, namely gaseous feedstocks, and, to a smaller extent, more complex mixtures, such as naphthas, molecular models give a still rather poor prediction of product distribution. Sundaram and Froment [13] initially published molecular reaction models and their kinetic param- eters for ethane, propane and their mixtures, with each model totalling less than 10 reactions. The same authors [48] then reported kinetic models of the same kind for i-butane, n-butane and for ethane- propane-n-butane mixtures, again with the number of reactions per model rounding 11-23, thus covering practically all the gaseous feedstocks for steam cracking. However, the authors realised the limitations inherent to the use of molecular reactions and disclosed in a posterior paper a kinetic model based on free-radical mechanisms [17]. Kumar and Kunzru [14], on the other hand, disclosed a set of 22 molecular reactions for naphtha pyrolysis. The authors assume naphtha could be represented as a pseudo-pure compound and the primary decomposition of naphtha could be defined by a single reaction with the initial selectivity deter- mined experimentally, thus giving the model a rather empirical nature as well. The only models fully able to accurately simulate pyrolysis phenomena and predict product yields are, therefore, the mechanistic models. These models, which are not surprisingly free-radical scheme- based, require less experimental data and can be easily extrapolated, covering a wide range of operating

23 conditions and multiple feedstocks. Mechanistic models, although much more complex, are specially appropriate for modern olefins plants design, optimisation and operation, thus justifying the interest in developing such models. Barazandeh et al. [49] published a rather simple yet curious kinetic model for naphtha cracking which, in some way, incorporates both empirical, molecular and mechanistic philosophies. This model comprises a set of 22 molecular reactions, 8 radical reactions, 7 coke formation reactions and one single empirical equation for the naphtha cracking itself, yielding smaller products which will then react according to the previous reactions. Promoted by the availability of more accurate thermochemical kinetic and pyrolysis data and of high- speed computers and by the fierce competition between ethylene plant licensors, the development of mechanistic models for steam cracking phenomena over the years has been truly remarkable, with some kinetic schemes involving thousands of reactions and hundreds of chemical species. In this regard, four commercial softwares for hydrocarbon pyrolysis emerge: SPYRO® , CRACKSIM, CRACKER and SHAHAB.

2.3.3.1 SPYRO®

SPYRO® is Technip’s proprietary yield prediction software for the steam cracking process and it has become a well established tool - by 1985 it was used by more than 75% of ethylene producers in the Western Hemisphere - for feedstock selection, optimal ethylene furnace operation and is, for Technip, one of the key instruments for designing and revamping cracking coils [15, 46, 50]. Having been developed in the late 1960s, by 1979 it handled a kinetic scheme of about 2000 re- actions, involving 86 molecular species and 18 chain propagating radicals [15], by 2001 it comprised already 3288 reactions, including 128 components – varying from methane to hydrocarbons up to C42 – and 20 radicals [50], and in 2002 its kinetic scheme was 6,600 reactions and 240 components large [51]. SPYRO® was the first model able to describe with the same mechanistic kinetic scheme all feedstocks from ethane through gas oils. Many kinetic parameters and other useful information are not disclosed for proprietary reasons, in spite of several articles from Prof. Dente and Prof. Ranzi, the main authors of SPYRO® from Polytechnic University of Milan, and from van Goethem have been published over the years [15, 46, 47, 50, 52, 53, 54]. However, some information on how SPYRO® works may be retrieved from these published articles. Detailed mechanistic models involve a huge number of reactions and chemical species, whose sto- ichiometric matrices (reactions × species) size dramatically increase with the molecular weight of the feed molecules. For heavier fractions stoichiometric matrices could have several hundred thousands of positions in size – according to the update on SPYRO® published in 2002 [51], the matrix would have over 1.5 million positions. To overcome this issue, SPYRO® employs two strategies: the first one con- sists of reducing the number of reactions and the second the contraction of the number of components involved. If all intermediate molecular and radical species are included in the model, the resulting kinetic scheme would become too large for practical applications. In this regard, since monomolecular reac-

24 tions of large radicals are much faster than the bimolecular ones, SPYRO® assumes that heavy radicals are almost instantaneously converted directly to the smaller radicals and stable intermediate or final compounds (µ radical hypothesis). Then, a reaction path can be formulated using only these chemical species, thus reducing incredibly the kinetic scheme by heavy radicals and intermediates elimination [46, 47]. The absence of interactions between heavy radicals and the remaining part of the cracking mix- ture allows the substitution of these radicals directly by their isomerisation and decomposition products without any loss of accuracy of the model itself. This can be easily demonstrated with the decomposition of n-pentane, shown in Figure 2.19. First, n- pentane reacts with a free radical, which abstracts an hydrogen atom, and yields three different radicals, depending on the removed H-atom position. Focusing on radical 1, it can be formed either by n-pentane reaction with a free radical or by a 5-membered ring isomerisation of radical 2. On the other hand, it can either isomerise back to radical 2 (1-4 H-transfer) or decompose through β scission. Since radicals are more reactive than molecules and thus rapidly build up their concentrations and stabilise at a certain level, a pseudo-steady-state assumption (PSSA), which states the rate of formation of a radical must equal its rate of disappearance, is used [55]. Therefore, one may write the continuity equation for radical 1 as follows:

Figure 2.19: n-Pentane decomposition via radical scheme.

µ1 + k21 · R2 = kD1 · R1 + k12 · R1 (2.7)

Similar logic may be applied to radicals 2 and 3 (please note that there is no possible isomerisation between radical 1 and 3, according to what was stated in the previous subsection 2.3.2):

µ2 + k12 · R1 = kD2 · R2 + k21 · R2 (2.8)

µ3 = kD3 · R3 (2.9)

25 Generally, for a given radical i the continuity equation can be written as follows:

N N Xiso Xiso µi + kji · Rj = kDi · Ri + kij · Ri (2.10) j j

Having been published values for kinetic parameters for the elementary reactions taking place in these kinetic schemes, namely H-abstraction, isomerisation and decomposition [46, 53, 52], then the whole linear system of 3 equations and 3 variables (R1,R2 and R3) may easily be solved.

It is noteworthy the fact that differential equations (mass, energy and momentum) arising from the reactor model have a characteristic termed as stiffness. The physical origin of stiffness is that concen- trations of molecules vary in rates which differ by orders of magnitude from those of radicals, which are more reactive. Assuming the PSSA implies that radicals concentration is fairly constant and thus their derivatives approach zero, thereby reducing differential equations to simple algebraic equations [55].

When heavier alkane decomposition is concerned, say for instance n-dodecane, C12, then several sequential subsystems of linear equations are originated. After the n-dodecyl C12 radical system has been solved, the next subsystem, for n-decyl radical, follows, which then allows the next one, n-nonyl, to be solved, and so on, until small radicals, which can engage in bimolecular reactions, are formed.

The boundary between the radicals which are large enough to solely undergo monomolecular re- actions and those who can participate in both mono- and bimolecular reactions is not easy to define. SPYRO® assumes only radicals containing less than and including 4 carbon atoms are able to partici- pate also in bimolecular processes [53]. The number of sequential subsystems to be solved for some alkanes is given in Table 2.2.

+ Table 2.2: Number of sequential systems (C5 ) to be solved for alkane decomposition (µ radical hypothesis and PSSA).

Alkane No. of sequential subsystems n-Pentane 1 n-Hexane 1 n-Heptane 2 n-Octane 3 n-Nonane 4 n-Decane 5 n-Undecane 6 n-Dodecane 7

SPYRO® ’s kinetic generator, MAMA programme, manages all these calculations and produces equivalent stoichiometries that compress and lump several reactions into a single equivalent reaction whose apparent stoichiometry is only a relatively weak function of cracking temperature. This approach of lumping reactions is know as single event micro kinetics (SEMK). As an example, for n-decane de- composition, evaluated at 1040 K, the MAMA program is able to produce the following single equivalent reaction [47]:

26 · · · · R + nC10H22 → RH + .0205 H + .0803 CH3 + .2593 C2H5 + .406 nC3H7 + .234 1 -C4H9 + .3785 C2H4 + .3127 C3H6 + .2114 1 -C4H8 + .1870 1 -C5H10 + .1815 1 -C6H12 + .1461 1 -C7H14 + .1284 1 -C8H16 + .0540 1 -C9H18 + .0025 1 -C10H20 + .0006 2 -C5H10 + .0012 C6H12s + 0.0013 C7H14s + .0005 C8H16s + .0100 C10H20s (2.11)

Once these stable olefins and smaller radicals have been computed, they can engage in several radical/molecular reactions, for which kinetic parameters are available – Dente and Ranzi published a set of 109 radical and molecular reactions applicable to radicals up to C4 [15]. Owing to the huge amount of possible isomers for large hydrocarbons – for instance, C14H30 has more than 1800 possible isomers [56] – SPYRO® introduces the concept of lumping components into equivalent or pseudo components as an additional methodology to further diminish kinetic scheme size

(note the C6H12s, C7H14s, C8H16s, C10H20s in the previous Eq 2.11). As an example, the number of species in naphtha cracking is large enough to take the number of elementary steps to about 105 [47]. It is known the distribution of structural isomers is largely independent of the origin of the feedstock. For instance, mono-methyl-alkanes dominate whilst di-methyl and ethyl-alkanes are of lesser predom- inance. Tri-methyl-alkanes are less abundant and quaternary C atoms are of very limited importance. Therefore, its is possible to empirically determine the relative fractions of all isomers belonging to the same lumped class. One lumped component is assumed for each number of C-atoms above 5 and per class of components, i.e., branched alkanes, cycloalkanes and alkyl-aromatics [47]. Lumped species react in a similar way and their internal distribution remains almost unchanged along the reaction process. The equivalent reactions of the different pseudo-components,Cns, are obtained simply by averaging the products of all the elementary reactions of the pure isomers [47] (Eq. 2.12). However, if one finds oneself interested in the pyrolysis of a specific isomer, it is always bothpossible and easy to enlarge the kinetic scheme explicitly to include that component [53].

Np Nj · X X R + Cns → RH + wj · νp,j · P (2.12) p j

Summarising, SPYRO® overcomes the excessive kinetic scheme by drastically reducing both the number of reactions and the number of components through lumping methods, without compromising the model’s accuracy. Once the small radicals(with carbon number less or equal to 4) and stable olefins + (lumped for C5 ) have been generated by the MAMA program, a set of 109 radical and molecular equations is used to model the reactions occurring between the former and the latter.

2.3.3.2 CRACKSIM

CRACKSIM is a SEMK model developed at the Laboratory for Chemical Technology of the University of Ghent. In order to avoid producing unimportant elementary reactions and species and to keep the kinetic scheme to a manageable size, CRACKSIM assumes the same µ radical hypothesis, i.e., the assumption that bimolecular reactions can be neglected for radicals with more than 5 carbon atoms. This allows distinguishing between two types of networks: the monomolecular µ network (based on the PSSA) and the β network, which contains both mono- and bimolecular reactions [23] (Figure 2.20).

27 Figure 2.20: Structure and reaction families in the single-event microkinetic (SEMK) model – µ network and β network [23].

As mentioned before, the separation of radicals into µ and β radicals based on the number of carbon atoms is very rough but CRACKSIM takes into account several exceptions on this rule of thumb. For instance, the benzyl and indenyl radicals, which should belong to the mu network according to their number of carbon atoms, in truth undergo bimolecular reactions. CRACKSIM introduces an additional category for these exception radicals, the β(µ) radicals. Being based on Prof. Froment’s early work [44, 45], in order to keep the number of parameters down to a minimum, a systematic approach is followed for the calculation of kinetic parameters. An extension of Benson’s group additivity concept [57] to transition-state theory is used to compute both pre-exponential factors and activation energies [23]. The β network used in CRACKSIM is taken from the work developed by Pyl [25] and contains 1324 re- versible elementary reactions, 114 recombination/bond scission reactions, 73 intermolecular addition/β scission reactions, 1128 intermolecular hydrogen abstraction reactions, 6 intermolecular hydrogen ab- straction reactions, 2 intramolecular addition/β scission reactions and 1 (retro-)ene reaction between 51 molecules and 43 β(µ) radicals [23]. Facing a large number of components when processing heavier feedstocks, CRACKSIM, similarly to SPYRO® , uses lumping procedures for components, grouping them into pseudo-components [23]. In sum, both SPYRO® and CRACKSIM, two of the most used mechanistic models for hydrocarbon pyrolysis, are based on the same pillar assumption: the µ radical hypothesis for large radicals associ- ated with the pseudo-steady state assumption (PSSA). Moreover, in order to further reduce the kinetic scheme size, both models employ lumping concepts to components in addition to reactions.

2.3.3.3 Other mechanistic models

SPYRO® and CRACKSIM pose highly accurate mechanistic models for hydrocarbon steam crack- ing, with thousands of reactions occurring between tens of components. Nevertheless, there are other

28 publicly available kinetic models mainly relying on free-radical kinetics. Although it is not as well known as SPYRO® and CRACKSIM, PYROL, the model developed in the Institute of Chemical Technology, Czech Republic [35, 39, 58, 59], is based on exactly the same logic – as stated above, i.e., the construction of a separate network regarding the species (C5 ) undergoing solely monomolecular reactions [59] and of a network constituted by the species involved in both mono- and bimolecular reactions. Karaba et al. [58] published kinetic parameters for the elementary reactions taking place in the former network. Belohlav et al. [39] first disclosed a set of 64 molecular reactions involving several species up to C4 for a wide range of feedstocks, mainly focusing on naphtha. However, a novel set of 64 molecular reactions have been recently published from the same authors [35] with the particularity that kinetic parameters are feedstock-specific, namely ethane, LPG, Naphtha and HCVD. Sundaram and Froment, although being somewhat associated to early CRACKSIM work and having realised the limitations of molecular reactions reported in their previous work [13, 48], published in 1978 a kinetic scheme consisting of 133 reactions and including 42 chemical species with number of carbon atoms up to C4 [17]. It is said this reaction scheme is probably one of the best of its kind [15]. Joo and Park, from KAIST, South Korea, developed a PC-based software, CRACKER, which includes a reaction scheme for naphtha cracking comprising a total of 231 reactions between 79 chemical species up to C8 [19, 26]. Towfighi and his coworkers [18, 60], from Olefin Research Group of Tarbiat Modares Univeristy, Iran, developed a simulation software for the prediction of product yields and run lengths of ethane and naph- tha cracking furnaces. The detailed mechanistic kinetic scheme is said to involve 1230 reactions and 122 molecular and radical species [61], although references account for only 133 reactions of Sundaram and Froment’s work for gaseous feedstocks cracking [17, 18] and 150 reactions between species up to

C6 for naphtha cracking [60]. Although it is not explicitly mentioned as being part of the SHAHAB project, Towfighi et al.[62] pub- lished a kinetic model for LPG cracking comprising 108 reactions involving molecules and radicals with number of carbon atoms up to C4, thereby making way for substituting Sundaram and Froment’s scheme for lighter feedstocks. Likewise, Sedighi et al. [63], also from Tarbiat Modares University, apparently re- duced the kinetic scheme for heavy liquid hydrocarbon thermal cracking to 148 reactions and improved its extensiveness to species up to C9. On the other hand, Keyvanloo et al. [64] further reduced the kinetic scheme to only 96 reactions including the same range of components, i.e., up to C6, by lumping some heavier components, thus avoiding complexity in the reaction network.

29 30 Chapter 3

Implementation

3.1 The gPROMS® platform

gPROMS® is the proprietary modelling platform of Process Systems Enterprise Limited (PSE). It is the infrastructure on top of which all PSE’s gPROMS® family products are built. This fast, robust and feature-rich environment brings several major advantages over other comparable modelling software thus claiming itself as a leading modelling product for process industries [65].

gPROMS® family products benefit from: support for multiscale modelling, allowing one to account simultaneously for micro and macro phenomena within the same model; custom modelling of high-fidelity unit models and their subsequent utilisation in a flowsheeting environment along with other models and steady-state and dynamic modelling within the same environment [65].

Finally, one of the most important specificities of the gPROMS® platform, which will be extensively used throughout the present work, is its simultaneous solving of all model equations rather than a se- quential resolution method. This allows one to easily replace assigned variables – keeping the overall degrees of freedom – without the need to conduct a complete model reorganisation.

3.1.1 gPROMS ProcessBuilder®

gPROMS ProcessBuilder® is the brand new product in the gPROMS® family, having been released recently. In addition to the impressive process flowsheeting capabilities and a rather extensive setof model libraries, a custom modelling option is also available, thus allowing an easy drag-and-drop flow- sheeting integration with custom models.

This gPROMS® software was thoroughly used for both model development and flowsheeting in the present work, from the kinetic schemes implementation in existing custom models and furnace simula- tion to the development and validation of the naphtha feed characterisation model.

31 3.2 Foreign Objects

Foreign Objects are external software components that provide certain computational services to gPROMS® Models. These include physical property packages, external unit operation modules, or even complete computational fluid dynamics (CFD) software packages [66]. Five different FOs were used in the present work:

• MultiflashTM – as a physical property package, covered in the following section 3.4.

• gSAFT® – as a physical property package, covered in the following section 3.4.

• LSKM – as the foreign object responsible for the implementation of Large Scale Kinetic Mecha- nisms, further covered in section 3.5.

• ReadDataFO – as the foreign object used to supply external data to gPROMS® , namely the molecular weight of all chemical species;

• LookupTableFO – as the foreign object used to provide interconnected sets of data by means of a table to gPROMS® ; specifically this FO was used to impose an axial temperature profile taken from literature in the gPROMS® reactor model.

3.3 Other gPROMS® tools

Apart from the flowsheeting and custom modelling environment of gPROMS ProcessBuilder® , the Optimisation and Parameter Estimation entities were also used in the current work.

3.3.1 Optimisation

gPROMS® ’ Optimisation tool was used in the alternative diluents study, in which several optimisa- tions at different hydrocarbon conversions were conducted. The objective was to maximise ethylene selectivity by varying the ratio of each diluents relatively to the hydrocarbon feed. The optimisations were subjected to pressure drop and coil outlet temperature constraints.

3.3.2 Parameter estimation

The process of fitting model parameters to a given set of data is called Parameter Estimation. Pa- rameter Estimation in gPROMS® is based on the Maximum Likelihood formulation which provides simul- taneous estimation of parameters in both the physical model of the process and the variance model of the measuring instruments - the Sensor [67]. When solving a Maximum Likelihood Parameter Estimation problem, gPROMS® attempts to deter- mine values for the uncertain physical and variance model parameters, θ, that maximise the probabil- ity that the mathematical model will predict the measurement values obtained from the experiments.

Assuming independent, normally distributed measurement errors, ϵijk, with zero means and standard

32 deviations, σijk, this maximum likelihood goal is achieved through minimisation of the following objective function (Eq. 3.1)[67]:

  NE NVi NMij " 2 # N 1 X X X (˜zijk − zijk) Φ = ln(2π) + min ln(σ2 ) + (3.1) 2 2 θ  ijk σ2  i=1 j=1 k=1 ijk

being the symbols’ definitions summarised in the following Table 3.1:

Table 3.1: Parameter estimation objective symbol definitions [67].

N Total number of measurements taken during all the experiments. Set of model parameters to be estimated. The acceptable values θ may be subject to given lower and upper bounds, i.e., θl ≤ θ ≤ θu. NE Number of experiments performed. th NVi Number of variables measured in the i experiment. th th NMij Number of measurements of the j variable in the i experiment. Variance of the kth measurement of variable j in experiment i. This is σ2 ijk determined by the measured variable’s variance model. th z˜ijk k measured value of variable j in experiment i. th zijk k (model-)predicted value of variable j in experiment i.

The Parameter Estimation entity was used in the Feed Characterisation chapter to adjust the naphtha molecular composition to the provided commercial indices.

3.4 Physical properties

In the present work, two physical properties packages were considered: MultiflashTM and gSAFT® .

3.4.1 Infochem MultiflashTM

Infochem MultiflashTM is a powerful and versatile PVT and EOS modelling software package mainly dedicated to evaluation of fluids’ physical properties for design and process simulation. Being supplied by KBC Advanced Technologies, this software is provided along with gPROMS® as the standard physical property package.

This package was used in both steam cracking furnace and feed characterisation chapters. In the first, the Redlich-Kwong-Soave (RKS) cubic equation of state was used as the thermodynamic model since it is simple, robust and efficient and specially appropriate for petrochemical applications [68]. The SuperTRAPP model was used to provide the transport properties, namely viscosity and thermal conductivity.

On the other hand, in feed characterisation chapter the Redlich-Kwong-Soave(RKS), Redlich-Kwong- Soave Advanced (RKSA) and Peng-Robinson Advanced(PR78A) cubic equations of state and activity models NRTL-RK and UNIQUAC-RK were taken into account.

33 3.4.2 gSAFT®

On the other hand, gSAFT® is a gPROMS® product strictly dedicated to thermodynamic property estimation. It is based on the Statistical Associating Fluid Theory, or SAFT, an advanced thermodynamic molecular method based on physically-realistic models of molecules and their interactions with other molecules. This predictive thermodynamic method was taken into consideration in the feed characterisation chapter.

3.5 Implementation of Large Scale Kinetic Mechanisms

One of the greatest challenges of mechanistic kinetic models implementation is to keep the problem within a manageable size, which is not always straightforward as it tends to grow exponentially with the number of reactions and chemical species considered. Stoichiometric matrices, matrices (reactions × species) in which stoichiometric coefficients are stored, make a good example of this. Two common approaches are used to shorten the number of reactions and to reduce the number of components. In fact, this is easily achieved through lumping as discussed in the previous chapter. However, another alternative was explored in the present work. Although stoichiometric matrices can become quite vast, one frequently observes that most of their content carries no information at all. As a matter of fact, the majority of the stoichiometric matrices are usually sparse, i.e, most of their positions are zero elements – since hardly a reaction involves more than 4/5 species – and this tends to aggravate with the size of the kinetic scheme. If for instance, an average of 3-4 chemical species per reaction is assumed, a kinetic scheme in- volving 150 reactions and 40 chemical species would have a stoichiometric matrix with 6,000 positions, whilst only 7.5-10% (450-600 positions) would actually contain relevant information. The LSKM gPROMS® foreign object is used to pack stoichiometric matrices by eliminating their zero elements, which significantly reduces computation time [69]. This FO is based on the work developed by Tewardson [70], who reported a sparse matrix compression scheme which allows one to store solely its non-zero elements alongside with the necessary indexing information (see section 3.5.1). There are several advantages in using this approach [70]:

• The internal storage of the computer no longer has to deal with enormous matrices.

• Since only the non-zero elements are stored, retrieving data from the compressed form of the matrix becomes significantly faster.

• Only the non-trivial operations are executed – since there is no transmission of zeros – thus saving a sizeable amount of computation time.

• The usage of the compressed form of the matrix can prove itself worthwhile in multiplying several row and column arrays. This is particularly advantageous when linear programming is concerned.

34 3.5.1 Sparse matrix compression scheme

The LSKM FO is based on the second compression scheme reported by Tewardson[70] which stores the information of a sparse matrix in three arrays:

• VE(value of elements), of length equal to the no. of non-zero elements which stores solely the non-zero values of the matrix.

• RI(row indices), of length equal to VE which stores the row index of the ith element of VE in its ith position.

• CIP (column index pointer), of length equal to the no. of columns and whose jth element stores the first non-zero element of the jth row.

  0 x1 x2 0 x3     x4 x5 0 0 0      M =  0 0 0 0 x6 (3.2)      0 0 x7 0 0    0 0 0 x8 0

h i VE = x4 x1 x5 x2 x7 x8 x3 x6 (3.3a) h i RI = 2 1 2 1 4 5 1 3 (3.3b) h i CIP = 1 2 4 6 7 (3.3c)

Considering the sparse matrix M (eq. 3.2), the three array produced using the above logic are present in eqs. 3.3. If for instance, the value in the (2,2) element of the original matrix M is to be obtained, since RI(i) = 2, fori = 1, 3 one concludes that it was stored whether in the 1st or in the 3rd position of VE. However, since CIP (2) = 2 but CIP (3) = 4, the 2nd and 3rd elements of VE had their values in the second column. Therefore the element pointed by both RI and CIP is the 3rd, and consequently

M(2, 2) = VE(3) = x5. It is noteworthy that through this short example it is not easily noticeable the substantial benefit this approach brings in terms of amount of information stored – since the original matrix had 25 elements and the three arrays combined totalled 21 elements. However, when larger sparse matrices are concerned – with hundreds or thousands of elements – this compression scheme rapidly proves itself extremely useful [69].

3.5.2 Application of the LSKM foreign object

The LSKM foreign object (FO) compresses, for a given reaction set, not only the stoichiometric matrix but also the reaction order matrix, using the above-mentioned approach. Along with the arrays in which

35 the information is stored, the following integer scalars are also generated to represent the problem size and define the arrays’ dimensions:

• NoSpecies - returns the total number of species;

• NoReactions - returns the total number of reactions;

• NoStoichCoeffs - returns the total number of non-zero stoichiometric coefficients;

• NoReactants - returns the total number of species acting as reactants in forward reactions (dupli- cated values are allowed);

• NoProducts - returns the total number of species acting as products in forward reactions, hence reactants in backward reactions(duplicated values are allowed).

Whilst for the stoichiometric matrix three arrays are generated (Table 3.2), for the reaction order matrix six are produced instead (Table 3.3), in order to account for forward and backward reactions.

Table 3.2: Arrays generated by the LSKM FO for the stoichiometric matrix.

Array Dimension Description Stores the non-zero stoichiometric coefficients of ReactionSC() NoReactions the sparse matrix, being sorted by species and then by reactions. Returns the reaction id number corresponding to the ReactionID() NoReactions kth element of ReactionSC(). Returns the position of the first non-zero stoichio- SpecStartAddress() NoSpecies metric coefficient of each species i in ReactionSC().

Table 3.3: Arrays generated by the LSKM FO for the reaction order matrix.

Array Dimension Description Stores the non-zero reaction orders of the forward ForwardReactionOrder() NoReactants reactions, being sorted by species and then by re- actions. Returns the species id number corresponding to the ReactionID reactant() NoReactants kth element of ForwardReactionOrder(). Returns the position of the first reaction order for ReactantStartAddress() NoReactions each reaction i in ForwardReactionOrder(). Stores the non-zero reaction orders of the backward BackwardReactionOrder() NoProducts reactions, being sorted by species and then by re- actions. Returns the species id number corresponding to the ReactionID product() NoReactants kth element of BackwardReactionOrder(). Returns the position of the first reaction order for ProductStartAddress() NoReactions each reaction i in BackwardReactionOrder().

36 Since no longer a stoichiometric matrix is used, the equation responsible for calculating reaction rates (see Eq. 4.16 in the following section 4.1.1.4) must be modified to be compatible with the array- compressed form, as in equation 3.4:

ReactantStartAddress(j+1)−1 P roductStartAddress(j+1)−1 Y F orwardReactionOrder(k) Y BackwardReactionOrder(k) rj = kf,j· CReactionID reactant(k)−kb,j· CReactionID product(k) k=ReactantStartAddress(j) k=P roductStartAddress(j) (3.4) Similarly, the equation involving rate of formation calculation (Eq. 4.17 in the following section 4.1.1.4) must also be adapted in order to account for the performed changes, as in equation 3.5.

k=SpecStartAddress(i+1)−1 X rform = ReactionSC(k) · rReactionID(k) (3.5) k=SpecStartAddress(i)

37 38 Chapter 4

Steam cracking furnace

In the current chapter, one will focus on the steam cracking furnace – the reactor and the heart of an olefins plant – where high temperatures favour feedstock thermal cracking, responsible for generating light, high-value olefins such as ethylene and propylene. With increasing capacities of such industrial facilities, the need arises for mathematical models able to accurately predict product distribution in the furnace section, with kinetics playing the major role. In this regard, different kinetic schemes for ethane, propane and naphtha cracking will be imple- mented, and their ability to predict product yields in each case evaluated.

4.1 Model equations

4.1.1 Tube model

This model constitutes the very core of the furnace model by playing the role of the reactor. It is constituted by several other sub-models, with each one performing different and separate calculations to bring the whole tube model together:

• Fluid properties model

• Friction factor coefficient model

• Heat transfer coefficient model

• Kinetic model

These completely-independent sub-models are not restricted to the tube model but can instead be used in other top-level models to perform the same tasks. The tube model is therefore responsible for modelling all the phenomena occurring in a tube, from heat transfer to cracking reactions. Nevertheless, the tube model itself contains specific equations that are not present in any ofthe remaining sub-models, namely the mass, momentum and energy balances and heat transfer equations.

39 Δz N A i z+Δz z N A i z

TMT R Rint Twall-coke Tcoke-process Rext Tprocess

hprocess

λcoke

λwall

Figure 4.1: Schematic of the tube cross sectional area and differential control volume.

Considering a differential control volume located in the process side of the tube (Figure 4.1) and since one can surely neglect the radial contribution of the flux 1, the mass balance is traduced by the following equation :

(Ni · A)|z+A|z·∆z · MWi · rform,i|z= (Ni · A)|z+∆z (4.1) where Ni stands for the component mass flux, A is the cross-sectional area of the tube, MWi is the com- ponent molecular weight and rform,i the component rate of formation (or disappearance, if negative). Rearranging the previous equation and dividing it by the infinitesimal length of the control volume, ∆z, if ∆z → 0, one obtains the differential equation describing the component mass balance in a plug-flow reactor (PFR) (Eq. 4.2):

d [N (z)A(z)] = MW A(z)r (z) (4.2) dz i i form,i

Is it noteworthy that according to this equation the cross sectional area, A, can vary along the z axis, A(z) = πR(z)2, being R the inner radius – for instance if there is a non-uniform coke deposition along the reactor length, thereby decreasing the available cross sectional area. The momentum equation, which determines the pressure P variation with z, is similarly obtained. Apart from the pressure drop in the straight sections of the tube, expressed by the Fanning friction factor, fF anning, an additional term for the bends is taken into account – with the length of the bends being added to the tube length, L – as in equation 4.3:

d dv(z) v(z)2A(z)ρ(z) 2f (z) n f (z) [P (z)A(z)] = −N (z)A(z) − F anning + B bend (4.3) dz total dz 2 R(z) L

1due to high Reynolds numbers experienced inside the coils

40 where Ntotal is the total mass flux, v is the process gas linear velocity, ρ is the process gas density and nB and fbend are the number and friction factor of bends, respectively. Likewise, an energy balance to the differential control volume results in the following differential equation 4.4:

d [q(z)A(z)] = q (z)2πR (4.4) dz ext ext where Rext is the external radius of the tube and q the heat flux defined by equation 4.5:

q(z) = Ntotal(z) · htotal(z) (4.5) where htotal is the specific enthalpy of the process stream. On the other hand, by combining the equations describing the heat transfer in the process side of the tube, through an eventually-deposited coke layer and through the tube wall, one is able to obtain the equation for the external heat flux supplied to the tube, qext (Eq. 4.6):

TMT − Tprocess qext(z) = (4.6)  R R  1 ln( int/R(z)) ln( ext/Rint) Rext · + + hprocess(z)R(z) λcoke λwall with TMT standing for the outer wall temperature of the tube (commonly known as tube metal temper- ature), Tprocess being the process stream temperature, Rint the internal radius of the tube and hprocess,

λcoke and λwall being the process heat transfer film coefficient, the coke thermal conductivity and the tube wall thermal conductivity, respectively.

4.1.1.1 Fluid properties model

This sub-model is responsible for calculating all required physical properties, namely component and total concentration, average molecular weight, specific enthalpy, density, heat capacity, viscosity and thermal conductivity. Whilst the majority of the properties are obtained from an external physical property package, con- centrations and process gas density are derived from the ideal gas law, as in equations 4.7 and 4.8:

P (z) Ctotal(z) = (4.7) R · Tprocess(z)

ρ(z) = Ctotal(z) · MWavg (4.8) being Ctotal, ρ and MWavg the process stream total concentration, density and average molecular weight, respectively, and R the ideal gas constant. Note that the ideal gas law usage is valid since the process gases are subjected to relatively high temperatures and low pressures, conditions under which gas phase behaviour approaches that of an ideal gas.

41 4.1.1.2 Friction factor coefficient model

This sub-model contains all the correlations involving friction factor calculations. Amongst these, the Churchill equation [71] (Eq. 4.9) was used to obtain the Fanning friction factor:

! 0.27ϵ  7.0 0.9 1 = −4 · f (z)1/2log + , Re(z) > 4000 (4.9) F anning 10 2R(z) Re(z) where ϵ is the roughness of the inner surface of the tube contacting with the process stream and Re is the Reynolds number (Eq. 4.10): ρ(z)v(z)2R(z) Re(z) = (4.10) µprocess(z) being µprocess the process stream viscosity. The high velocities and low viscosities, ensure the validity of equation 4.9. The friction factor that accounts for the pressure drop experienced in the tube bends is calculated using the Nekraskov equation [72] (Eq. 4.11):

  αbend 0.19 · 2 · R(z) fbend(z) = (0.7 + 0.35 · ) 0.051 + (4.11) 90 Rbend where αbend and Rbend stand for the angle and radius of the bend (Figure 4.2).

Rbend

αbend

Figure 4.2: Bend parameters for the bend friction factor coefficient calculation.

4.1.1.3 Heat transfer coefficient model

Similarly to the friction factor coefficient model, this model contemplates all the heat transfer correla- tions that allow the calculation of film coefficients. In this regard, the well-known Dittus-Boelter correlation [73] (Eq. 4.12) was used:

Nu(z) = 2.43 × 10−2 · Re(z)0.8 · P r(z)0.4 (4.12) where Nu and P r are the Nusselt and Prandtl number defined by equations 4.13 and 4.14, respectively:

h (z)2R(z) Nu(z) = process (4.13) λprocess(z)

Cp (z)µ (z) P r(z) = process process (4.14) λprocess(z) being Cpprocess the process stream heat capacity and λprocess the thermal conductivity.

42 4.1.1.4 Kinetic model

This sub-model is responsible for selecting the kinetic scheme to be employed in the furnace model.

Once this is done, it calculates the forward and backward reaction constants for each reaction j, kf,j and kb,j, respectively, using Arrhenius equation (Eq. 4.15):

Eaf/b,j − RT (z) kf/b,j(z) = k0,f/b,j · e process (4.15) where k0,j is the pre-exponential factor and Eaj the activation energy.

The reaction rate, rj, is then obtained through equation 4.16:

NReactants NP roducts Y nj,k Y nj,l rj(z) = kf,j(z) · (Ck (z)) − kb,j(z) · (Cl (z)) (4.16) k l where nj,k is the individual component reaction order and C the component molar concentration.

Finally, the component rate of formation, rform,j, used in equation 4.2, is computed using the follow- ing equation 4.17:

N ReactionsX rform,i(z) = (rj · νi,j) (4.17) j where νi,j stands for the stoichiometric coefficient of component i in reaction j.

4.1.2 Energy input model

As it was previously noted, the tube model relates the external heat fluxq ( ext) with both tube metal temperature (TMT ) and process gas temperature (Tprocess), through equation 4.6. However, an addi- tional relation must be added in order to allow for the process gas temperature calculation. The energy input model effectively accomplishes this by:

• Specifying the heat flux profile or its shape.

• Imposing the process gas temperature profile.

• Predicting the heat flux profile.

If the heat flux profile is to be predicted, equation 4.18, derived from the Stefan-Boltzmann law, is used to relate the external heat flux with the tube metal temperature and the effective temperature ofthe flames produced by the furnace burners:

4 4 qext(z) = ϵ · σ(Tflame − TMT ) (4.18) being ϵ the emissivity, σ the Stefan-Boltzmann constant and Tflame the effective flame temperature. Regarding the specification of the heat flux profile shape, a novel approach was explored inorderto predict the relative heat flux profile, i.e. the heat flux normalised by the maximum heat flux, according

43 to the furnace firing type and burners position. This approach is thoroughly explained in the following subsection 4.1.2.1.

4.1.2.1 Furnace heat flux correlations

The heat flux profile plays a major role in the performance of ethylene-cracking units. In thissection the mathematical heat flux model for ethylene furnaces reported by Colannino [74] is presented. This model covers all the three basic varieties of furnace firing: floor-only, wall-only and floor plus wall firing. The contributions to heat flux by floor burners will be deducted from jet theory and a global energy balance on the furnace, whilst the contributions by wall burners will be given assuming these as point sources of heat.

4.1.2.1.1 Floor-only firing

Assuming a normalised heat flux (0 < y < 1) and a normalised elevation (0 < z < 1), a simple energy balance on a two-dimensional control volume inside the furnace results in the following differential equation 4.19:

dy = y (z) − y (z) (4.19) dz h p in which yh stands for the normalised heat released from floor burners and yp stands for the normalised heat loss (absorbed by coils or otherwise removed from the furnace). In order to solve this differential equation, one must be able to explicitly express yh and yp in terms of the normalised elevation, z. Jet theory (Figure 4.3) gives the centreline concentration of a jet along an axial centreline as C(x′) = 1/x′, where C stands for the centreline concentration normalised by the initial concentration (0 < C < 1) and x′ is the number of nozzle diameters downstream a virtual origin located one diameter upstream the nozzle exit. Shifting the origin to the nozzle exit instead,i.e., x′ = x + 1 , one obtains C(x) = 1/(1 + x). If one presumes the heat release to be somewhat proportional to the fuel concentration, its dependency with the normalised elevation is given by equation 4.20:

a y (z) = (4.20) h 1 + γz where a is a constant of proportionality and γ is the ratio of the burner-related dimension to the furnace height.

Assuming a constant heat loss along furnace height, thus yp(z) = b, equation 4.4 becomes equation 4.21a which, after integration, results in equation 4.21b:

dy a = − b (4.21a) dz 1 + γz

y = aln(1 + γz) − bz + y0 (4.21b)

being the integration constant y0 the normalised heat flux at the floorz ( = 0).

44 x x C 7 8 6 7 5 6 4 5 3 4 2 3 1 2

0 1 Dnozzle 0

Dnozzle

Figure 4.3: Schematic of the analogy from jet theory.

By setting equation 4.21a to zero, one obtains the relation between the normalised elevation (zmax =

1) corresponding to the maximum normalised heat fluxy ( max = 1) and the remaining constants (Eq. 4.22):

a = γz + 1 (4.22) b max

Concerning the normalised heat flux difference, given by y − y0, the ratio of this flux difference to the maximum flux difference ymax − y0 = 1 − y0, is given by equation 4.23:

y − y aln(1 + γz) − bz 0 = (4.23) 1 − y0 aln(1 + γzmax) − bzmax

Dividing the previous equation by b and using equation 4.22 to substitute for a/b, one easily gets to equation 4.24:

y − y (1 + γz )ln(1 + γz) − z 0 = max (4.24) 1 − y0 (1 + γzmax)ln(1 + γzmax) − zmax

As a matter of fact, γ is the constant used to ensure that for 0 < z < 1 the maximum value of y will always equal one. This constant is completely independent from y0 and zmax and its value is roughly close to unity (γ = 1.015 ≈ 1), which means that the heat flux distribution correlates with the furnace elevation rather then it scales with a burner-related dimension [74].

If for the sake of convenience one defines the reduced heat flux, y∗, and reduced elevation, z∗, as in equations 4.25a and 4.25b, respectively, equation 4.24 then reduces to the simple equation 4.26.

y − y y∗ = 0 (4.25a) 1 − y0

45 (1 + γz )ln(1 + γz) − z z∗ = max (4.25b) (1 + γzmax)ln(1 + γzmax) − zmax

y∗ = z∗ (4.26)

Equation 4.26 is thereby capable of determining the entire heat flux profile shape inside the floor- fired furnace, as long as both parameters y0 and zmax are provided or if y is provided at any particular elevation. Moreover, if the gas radiation is presumed to prevail beyond the vicinity of the floor, heat flux becomes proportional to flue gas temperature to the fourth power, thus allowing the addition of the reducedflue gas temperature to equation 4.27:

y∗ = z∗ = T ∗ (4.27)

with the reduced flue gas temperature, T ∗, being given by (Eq. 4.28):

4 4 ∗ Tflue − T0 T = 4 4 (4.28) Tmax − T0 where Tflue, T0 and Tmax stand for the absolute flue gas temperature at any given elevation, at thefloor and at zmax, respectively.

4.1.2.2 Wall-only firing

Most wall firing is achieved using premixed burners and this type of burners tends to producerapid combustion and short flames, therefore allowing one to treat them as a point source. Bearing thisis mind, the normalised heat flux from a row of wall burners, yw,k, located at a given normalised elevation, zw,k, will be given by equation 4.29:

ω yw,k = (4.29) p 2 2 ω + (zw,k − z) where ω is the inverse aspect ratio of the furnace, i.e., width/height. However, when multiple rows of wall burners are concerned, one must take into account the heat flux contributions from all the existing rows (Eq. 4.30):

Y (z) y(z) = sum (4.30) Ymax being Ysum(z) and Ymax given by the subsequent equations 4.31a and 4.31b, respectively:

Nwb X ωζw,k Ysum(z) = (4.31a) p 2 2 k ω + (zw,k − z)

Ymax = max Ysum(z) (4.31b) 0≤z≤1

where ζw,k is the relative power of a row of burners in comparison to another – for instance, if a twice-

46 as-powerful new row is installed (ζw,k = 2) in comparison to the one already installed (ζw,k = 1) – and

Nwb the total number of wall burner rows.

4.1.2.3 Floor plus wall firing

When both floor and wall burners are employed, all the previously noted equations are still valid,with the floor-only firing equations remaining true only for the floor burners’ contribution toheatflux, yfloor. In this regard, only equation 4.31a suffers a slight modification into the following equation 4.32:

Nwb X ωζw,k Ysum(z) = + yfloor(z)ζfloor (4.32) p 2 2 k ω + (zw,kz) where ζfloor is the relative power of the floor-mounted burners, which usually is considered as being the reference (ζfloor = 1) of the wall burners. Figure 4.4 shows the normalised heat flux distribution in terms of furnace normalised elevation for floor-only, wall-only and floor plus wall firing cases.

1

0.9

0.8

0.7

0.6

0.5

0.4 Normalisedelevation 0.3

0.2

0.1

0 0 0.2 0.4 0.6 0.8 1 Normalised heat flux

Floor-only firing Wall-only firing Floor plus wall firing

Figure 4.4: Normalised heat flux distribution for floor-only (with y0 = 0.60 and zmax = 0.36), wall-only (with ω = 0.183, Nwb = 1 and zw,1 = 0.8) and floor plus wall firing cases (previous parameters plus ζfloor = 1.0 and ζw,1 = 0.5).

In conclusion, in order to predict the heat flux distribution generated by floor-plus-wall-mounted burn- ers, five parameters are necessary: y0, zmax, ω, zw,k and ζw,k. Although most of these are easily determinable, that is often not the case for the floor-related ones, since neither y0 nor zmax (or T0 and

Tmax) are known prior to measurement of the heat flux curve. Colannino claims to have correlated y0 and zmax from more than 65 floor-fired heat flux tests as a function of several operating, furnaceand burner factors but no further information was disclosed.

47 4.1.2.4 Addition to energy input model

Once having been determined the normalised heat flux distribution inside the furnace, the relative heat flux profile to the coils, derived from the latter, was added to the energy inputmodel. To successfully accomplish this, since the coils do not cover the full height of the furnace and, there- fore, are not exposed to the entirety of its heat flux, two additional parameters were added, namely the floor top coil normalised distances from the floor and top inside the furnace, dcoil and dcoil, respectively. In this sense, the heat flux profile obtained through the heat flux correlations is somewhat ”cropped” using these parameters before imposing it to the coil sections (Figure 4.5). Moreover, it was necessary to account for the flow direction in each straight section of the coil, since a downflow section will experience a reverse heat flux distribution to that of an upflow section(Figure 4.5) – for instance, in a floor-only firing situation, a downflow section will experience a much higherheat flux near the end due to the burners located at the floor.

1 Relative heat flux Relative heat

Dimensionless tube section length

Normalised furnace elevation Normalisedfurnace 1 Relative heat Relative flux heat

Dimensionless tube section length

Normalised furnace heat flux

Figure 4.5: Schematic of the addition of furnace heat flux correlations to the energy input model.

4.1.3 Cooling jacket model

The cooling jacket model, instead of supplying heat (qext > 0), withdraws energy from the tube model (qext < 0), contrasting with the energy input model. The external heat flux is thus computed by the following equation 4.33:

qext(z) = hcool · (Tcool − Tprocess(z)) (4.33) where hcool is the heat transfer coefficient and Tcool is the coolant temperature.

4.1.4 Furnace and coil model

The coil model can be composed by one tube model and one energy input model or can be alter- natively modelled as an association of several tube models in series, representing each one a section

48 of the tube, with the same number of energy input models. Being the simulation results equivalent, the decision on how the coil should be modelled depends on the available information on the individual sections of the coil and on how the energy input model will provide the thermal specification to the coil – for instance, if the heat flux correlations are to be used, one must have each straight portion oftube specified in order to impose the correct relative heat flux distribution. The furnace model, on the other hand, includes the coil model, an adiabatic section model and a transfer line exchanger (TLE) model. The adiabatic section is the section of tube which connects the radiant coils to the TLE and in which reactions still proceed significantly. Since the process gas hydrocarbon sampling for analysis is usually performed after the TLE – once the process gas has been drastically cooled – a typical length of 1-2 m of adiabatic section will always be considered in the furnace model, even if no information is provided. Figure 4.6 depicts how the furnace model is organised in terms of sub-models. The adiabatic section is modelled simply by a tube model coupled with an energy input model with no heat flux suppliedq ( ext = 0). In turn, since the TLE is basically a multi-tubular reactor with a rapid cool- ing (reactions proceed to very little extent but are not completely absent), its modelling is successfully accomplished by coupling a tube model with a cooling jacket model.

Furnace model

Coil model Adiabatic section model

feed Energyinput model

Tube model(s) Tube model Energyinput model

Hydrocarbon Hydrocarbon

(

q ext

Friction factor Friction factor Kinetic model Kinetic model = coefficient model coefficient model const

Fluid properties Heat transfer Fluid properties Heat transfer = . 0

model coefficient model model coefficient model )

(

s )

Dilution steam Dilution Transfer-line exchanger model

Tube model Coolingjacket model Friction factor Kinetic model coefficient model

Cracked gas Cracked Fluid properties Heat transfer model coefficient model

Figure 4.6: Furnace model architecture: material connections (black) imply transmission of main stream characteristics (flowrate, mass fractions, pressure, temperature, etc.) whilst thermal connections (red) entail the transmission of thermal characteristics of the process (process and tube metal temperatures, heat fluxes, etc.).

As one has already seen, the described ethylene furnace model is derived essentially from first- principles equations and, therefore, it constitutes a generic model which can be used to simulate barely any industrial furnace reactor. Throughout the following sections, the models above-described will be used to model different industrial furnaces processing different feedstocks. Each specific case, however, will certainly involve a different furnace configuration, component list and reaction set (with correspond- ing kinetic parameters).

49 4.2 Ethane cracking

Ethane is the most widely used gaseous feedstock for steam cracking and, in the recent years, a higher attention has been brought to these kind of feedstocks due to recent advances in the exploitation of shale gas in the United States and elsewhere. In the present section, an industrial case of an ethane cracking furnace will be used to evaluate both molecular and radical kinetic schemes’ ability to predict product distribution, a key factor to the operation of an olefins plant. As a matter of fact, in spite of the increasing trend in using radical kinetic schemes over molecular ones in steam cracking mathematical models, molecular kinetics are still used for gaseous feedstocks cracking. In truth, apart from still being able to predict main product yields, they allow one to avoid the mathematical difficulties encountered with the integration of systems involving stiff differential equations associated with radical reactions [13].

4.2.1 Kinetics

Sundaram and Froment published in 1977 [13] a molecular kinetic model for the cracking of ethane, propane and their mixtures, possessing each case a set of five, nine and ten reactions, respectively (Table B.1 in Appendix). It is noteworthy that although radical reactions were, in fact, used to develop these schemes, they were not considered because of the numerical problems they carry. However, the same authors must have realised of the limitations coming from the implementation of these simplified kinetic schemes and published in 1978 [17] a radical kinetic scheme for the pyrolysis of light C2-C4 paraffins and olefins, thus covering the entirety of gaseous feedstocks. The entire scheme consists of 133 reactions and involves 20 molecular and 16 radical species. An interesting feature of this kinetic scheme is that depending on the paraffin or olefin being cracked, a different subset of reactions is selected from the entire published reaction set (see Table B.2 in Ap- pendix). When mixtures of these paraffins and olefins are concerned, however, the authors suggest that the final set of reactions is to be obtained by superposition of all the subsets corresponding totheeach individual component cracking. In the following ethane cracking industrial case both molecular and radical kinetic schemes published by Sundaram and Froment will be used not only to evaluate their ability to predict product yields but also to verify whether or not radical schemes pose a serious alternative relatively to molecular ones.

4.2.2 Industrial case

The industrial case to be used in this section for ethane cracking was recently published by Yanchesh- meh et al. [75], in which the usage of CO2 as alternative diluent (relatively to steam) was studied. The author used plant data to validate his mathematical model before using it in his study. The configuration of the industrial furnace is summarised in Table 4.1, will then be used to validate Sundaram and Froment’s both molecular and radical kinetics as well as the reactor model itself. Inter-

50 esting to note that the industrial reactor is a fixed diameter coil, something that would be expected for gaseous feeds. The operating conditions are present in Table 4.2.

Table 4.1: Ethane cracking furnace configuration.

Reactor configuration [75] Total length (m) 78 ID (mm) 100 Thickness (mm) 8

Adiabatic section characteristics Lengtha (m) 1 ID/ODb (mm) 100/116 a assumed by author b estimated by author

Table 4.2: Operating conditions for ethane cracking [75].

Ethane molar flux per coil (mol/m2/s) 15.84 CIT (◦C) 695 COT (◦C) 845 CIP (bara) 3.09 COP (bara)a 2.12 S/O ratio (kg/kg) 0.3 a not used as simulation input

As mentioned before, Sundaram and Froment also published, along with the ethane cracking molec- ular kinetics, a molecular reaction set covering the pyrolysis of ethane-propane mixtures and it has been deemed interesting to verify to what extent does this scheme predict industrial results. Furthermore, it would also be of interest to evaluate how would the entire set of Sundaram and Froment’s radical scheme perform relatively to predicted product yields. Therefore, once the furnace model has been set and inputs provided, the above mentioned four different kinetics were implemented and simulation results compared against plant data reported by Yancheshmeh (Table 4.3). Interesting conclusions may be withdrawn from Table 4.3. Firstly, it is observed that both molecu- lar and radicals kinetics specific for ethane-only cracking seem to more accurately predict plant data relatively to the more comprehensive ones with substantially lower main product yields AADs. However, the molecular kinetics covering the cracking of ethane-propane mixtures, although having a higher average absolute deviation, seem to better predict not only conversion and selectivity but also hydrogen and ethylene yields relatively to the molecular ethane-specific scheme. On the other hand, methane and propylene yields are significantly more poorly met, thus justifying the higher AAD observed. Between the ethane-specific schemes, the radical kinetics seem to clearly supersede the molecular ones as conversion, selectivity and every product yield are much more accurately predicted, with an

AADmain of 8.8% against the 19.9% of the molecular scheme. These results thus support the statement

51 Table 4.3: Comparison between literature and simulation results.

Molecular Molecular Radical Radical Industrial kinetics kinetics kinetics kinetics data [75] Ethane [13] Mix E+P [13] Ethane [17] All [17] Results Dev. Results Dev. Results Dev. Results Dev. COP (bar) 2.12 2.15 1% 2.15 1% 2.16 2% 2.20 4% Conversion (%) 65.8 69.4 5% 68.5 4% 65.2 -1% 57.5 -13% Selectivity (%) 87.1 76.8 -12% 85.5 -2% 82.9 -5% 78.2 -10% Yields (dry mol%) Hydrogen 37.36 38.49 3% 38.14 2% 37.92 1% 34.28 -8% Methane 5.81 6.60 14% 4.65 -20% 4.34 -25% 5.54 -5% Acetylene 0.27 0.25 -6% 0.02 -92% 0.03 -88% 0.06 -77% Ethylene 34.56 32.56 -6% 35.81 4% 33.85 -2% 29.71 -14% Ethane 20.6 18.74 -9% 19.25 -7% 21.82 6% 28.23 37% Propylene 0.51 0.22 -57% 1.43 181% 0.48 -6% 0.37 -28% Propane 0.08 0.41 408% 0.06 -26% 0.00 -97% 0.00 -99% 1,3-Butadiene 0.44 2.73 521% 0.15 -66% 0.62 40% 0.59 34% a AADmain - 19.9% 51.7% 8.8% 13.7% a Average absolute deviation of the main product yields: ethylene, propylene, hydrogen and methane

that radical schemes are more predictive than the molecular ones and thus the increasing trend there has been in developing and implementing such schemes. Nevertheless, the radical scheme for ethane cracking still fails at predicting some product yields such as methane, acetylene, propane and butadiene. Although it would be interesting to tune some key kinetic parameters to better match these individual yields and verify the extensiveness of the tuned reaction set to other industrial cases, that work would fall out of the scope of the current work and consequently will not be considered. The results summarised in Table 4.3 therefore validate not only the implemented radical kinetics from Sundaram and Froment [17] but also the first-principles furnace model itself. Finally, it is interesting to note the high ethylene selectivities involved in ethane cracking, roughly rounding 85%. These somewhat justify the widespread use of ethane as a feedstock of ethylene plants. The conversion, ca. 65%, is also within the typical conversion range for ethane cracking, 60-70% [2]. It is now possible to analyse the variation of some relevant variables along the reactor length, namely the pressure and process gas temperature and the yields of ethane and key products, whose profiles are plotted in Figures 4.7 and 4.8, respectively. Pressure-wise, it is easily observed in Figure 4.7 that pressure decreases slightly faster towards the reactor outlet in comparison to what would be expected for the pressure drop in a regular tube section. The reason for this observation is the fact that as cracking reactions proceed, the average molecular weight of the mixture is lowered, thus leading to a decrease in process gas density and an increase in velocity, which generates a higher pressure drop according to Equation 4.3. Relatively to the process gas temperature profile, one observes a rapid increase in temperature in the first few metres of the coil whilst a much more steady increase is noted for the remaining length.This

52 860 3.2 840 C)

° 3 820 800 2.8 780 2.6 760 740 2.4 Pressure (bara) Pressure 720 2.2 Process Process gas temperature ( 700 680 2 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Reactor length (m) Process gas temperature Pressure

Figure 4.7: Pressure and process gas temperature profiles along reactor length. is verified because in the initial section of the coil cracking reactions do not occur significantly. Oncethe cracking reaction temperature is achieved (around 740 ◦C), reactions become meaningful with most of the heat supplied to the coils being consumed by these.

100 4.0 90 3.5 80 3.0 70 60 2.5 50 2.0 40 1.5

Yields (dry wt%) (dry Yields 30 wt%) (dry Yields 1.0 20 10 0.5 0 0.0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Reactor length (m) Reactor length (m) Ethane Ethylene Propylene Hydrogen Methane Butadiene

(a) Ethane and ethylene yields. (b) Propylene, hydrogen, methane and 1,3-butadiene yields.

Figure 4.8: Variation of the yield along reactor length of some key components.

In terms of product yield profiles, the most interesting observations are the steep increase in methane that is verified towards the reactor outlet and the invariable butadiene yield. In fact, although ethylene and hydrogen yields seem to have a somewhat steady increase throughout the coil, methane formation sees to increase in an exponential-like fashion. This shows a significant dependence of residence time in ethylene (and propylene) selectivity. Butadiene, on the other hand, seems not to be significantly formed as its yield remains unchanged throughout the entire reactor length. As a matter of fact, butadiene is not expected to be significantly produced in gaseous feedstocks cracking and even less when solely ethane is concerned. Although bu- tadiene is mainly produced as a co-product of the steam cracking process, its production only becomes meaningful when liquid feedstocks are used instead. Finally, propylene formation seems to cease towards the coil outlet as its yield stabilises. In truth, as process gas flows through the coils, propylene, which is being produced as a side product ofethane cracking, is also being subjected to pyrolytic reactions and eventually propylene cracking reactions will

53 start to take over the propylene forming ones.

4.3 Propane cracking

Ethane cracking leads, as one has observed in the previous section, to high ethylene selectivities and these somewhat justify ethane’s preponderance over other gaseous feedstocks. Nevertheless, propane still constitutes a commercially attractive feedstock for the steam cracking process, being both easy to ship an store, and therefore its cracking will be studied and used, once again, to evaluate implemented kinetics’ ability to predict product distribution.

4.3.1 Kinetics

In this section, the molecular and radical kinetics for propane cracking published along with the ethane-only cracking ones by Sundaram and Froment in 1977 [13] and 1978 [17], respectively, were used. Once again, an industrial case, now involving propane-only cracking, will be used to evaluate each of these kinetics’ ability to predict product yields but also to verify whether or not radical schemes pose a serious alternative relatively to molecular ones.

4.3.2 Industrial case

The industrial case to be used in this section for propane cracking was published by Van Damme et al. [76], in which the thermal cracking of propane and propane-propylene mixtures was studied through industrial and pilot plant data comparison. The industrial furnace, whose configuration is summarised in Table 4.4, will then be used to vali- date Sundaram and Froment’s both molecular and radical kinetics as well as the reactor model itself. It is noteworthy that the industrial reactor is a fixed diameter coil, as one would expect from gaseous feedstocks cracking. The operating conditions are present in Table 4.5.

Table 4.4: Propane cracking furnace configuration.

Reactor configuration [76] Total length (m) 95 Length of straight portions (m) 8.85 ID/OD (mm) 108/124 Length of bends (m) 0.554 Radius of bends (m) 0.178

Adiabatic section characteristics Lengtha (m) 2 ID/ODb (mm) 108/124 a assumed by author b estimated by author

54 Table 4.5: Operating conditions for propane cracking [76].

Industrial data Total mass flux per coil (kg/m2/s ) 86.35 Feed composition (mol%) Propane 100 CIT (◦C) 600 COT (◦C) 838 CIP (atm abs.) 3 COP (atm abs.)a 2 S/O ratio (kg/kg) 0.4 Temperature at 20% coil length (◦C) a 740 Temperature at 80% coil length (◦C) a 812 a not used as simulation inputs

Similarly to the ethane cracking case, the molecular kinetic scheme published by Sundaram and Froment covering the pyrolysis of ethane-propane mixtures will also be used, along with the already discussed propane-specific one. Likewise, the entire set of Sundaram and Froment’s radical scheme will also be taken into account to evaluate the accuracy of its predictions. Once the furnace model has been set and inputs provided, the above mentioned four different kinetics were implemented and simulation results compared against plant data reported by Van Damme (Table 4.6).

Table 4.6: Comparison between literature and simulation results.

Molecular Molecular Radical Radical Industrial kinetics kinetics kinetics kinetics data [76] Propane [13] Mix E+P [13] Propane [17] All [17] Results Dev. Results Dev. Results Dev. Results Dev. COP (bar) 2 1.94 -3% 1.94 -3% 2.00 0% 1.99 0% Conversion (%) 90.6 97.7 8% 97.7 8% 83.20 -8% 87.97 -3% Selectivity (%) 59.8 21.8 -64% 21.9 -63% 64.6 8% 60.9 2% Yields (dry wt%) Hydrogen 1.2 4.23 252% 4.23 252% 0.81 -32% 0.71 -40% Methane 24.0 8.62 -64% 8.57 -64% 24.71 3% 27.10 13% Acetylene 0.4 1.41 252% 1.41 253% 1.24 210% 1.59 298% Ethylene 34.5 13.55 -61% 13.57 -61% 34.15 -1% 34.07 -1% Ethane 5.8 1.06 -82% 1.16 -80% 3.13 -46% 4.67 -19% Propylene 14.7 57.23 289% 57.35 290% 15.28 4% 13.76 -6% Propane 9.3 2.34 -75% 2.35 -75% 16.87 81% 12.08 30% 1,3-Butadiene 1.5 1.03 -31% 1.04 -31% 2.80 86% 3.63 142% Butenes 1.0 0.27 -73% 0.05 -95% 0.00 -100% 0.17 -83% Butanes 0.1 0.00 -100% 0.00 -100% 0.01 -88% 0.00 -98% + C5 7.0 10.26 47% 10.27 47% 1.01 -86% 2.18 -69% a AADmain - 166.6% 166.8% 10.1% 15.3% a Average absolute deviation of the main product yields: ethylene, propylene, hydrogen and methane

Surprisingly, Table 4.6 shows an enormous discrepancy between results predicted by molecular

55 kinetics and by radical kinetics, with the molecular ones being completely unable to predict any entry of industrial data. Although one could foresee a higher struggle of these schemes to predict propane cracking results – due to the higher complexity relatively to ethane cracking – one could not have anticipated such disparity between plant data and simulation results using molecular kinetics, even more so when it is shown in the paper that this scheme is able to accurately predict industrial data. A likely explanation therefore lies in the fact that the published kinetic parameters were tuned using a rather narrow set of experimental/plant data and, therefore, are not able to predict results outside a given range of operating conditions. Still regarding the molecular kinetics, a close similarity between the molecular scheme for propane- only cracking and the one for ethane-propane cracking is observed. This is verified because, since no ethane is being cracked, both reaction sets will only differ in the activation energy of reaction 2 (Table B.1 in Appendix), whose value in the ethane-propane cracking set is 18% lower relatively to the propane- specific one. Radical kinetics-wise, it is noted that the propane subset of reactions is able to produce results with an acceptable agreement with industrial data, with and AADmain of 10.1%. Nevertheless, although ethylene, propylene and methane yields are rather well met, ethane conversion, in spite of being within 10% deviation, is still being significantly underpredicted. This means if one was to meet the same conversion, one would not probably get the same rea- sonable agreement in terms of product yields. Moreover, ethylene selectivity, which is already being overpredicted, would further increase its deviation relatively to the industrial value. Apart from the above observations, the predictions of other product yields are quite unsatisfactory, with most of deviations relatively to plant data surpassing 80%. Once again, although falling out of the scope of the current work, it would be of one’s interest to optimise some key kinetic parameters to match industrial data and evaluate the extensiveness of the optimised reaction set to other industrial cases. Finally, and as one could foresee based on the previous results from the ethane industrial case, the entire radical kinetic scheme published by Sundaram and Froment predicts industrial data more poorly than the propane-specific subset of reactions. The results from Table 4.3 thus somewhat validate the implemented radical kinetics from Sundaram and Froment [17]. The first-principles furnace model is once again validated. Regarding some product yields, it is noticeable that propane cracking presents much lower ethylene selectivities, ca. 60%, in comparison to ones found in ethane cracking (roughly 85%). Consequently, + higher yields of heavier components such as butadiene, butenes and C5 are observed. It interesting as well to note that conversion, around 90%, is within the typical range for propane cracking, 90-93% [2]. Similarly to the ethane industrial case, the variation of some relevant variables along the reactor length have been investigated, namely the pressure, process gas temperature and the yields of propane and key products. These results are shown in Figures 4.9 and 4.10, respectively.

56 3.2 840

C) 810 ° 3 780 750 2.8 720 2.6 690 2.4 660 (bara) Pressure 630 2.2 Process Process gas temperature ( 600 570 2 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 Reactor length (m) Process gas temperature Pressure

Figure 4.9: Pressure and process gas temperature profiles along reactor length.

Relatively to pressure, the same slightly more pronounced decrease towards the end of the reactor is observed, owing to the decreasing average molecular weight which raises process gas velocity, hence increasing the pressure drop. On the other hand, temperature-wise, although one perceives the same initial rapid increase in pro- cess gas temperature – due to the somewhat inactive cracking reactions – this increase is not as distinct as the one observed in the ethane cracking case. Furthermore, the cracking reaction temperature, which in the ethane cracking case rounded 740 ◦C, appears to be much lower, roughly rounding 690 ◦C. As a matter of fact, the longer the hydrocarbon chain, the easier will be for the molecule to un- dergo cracking in comparison to smaller ones. The results perfectly support this statement as propane requires lower temperatures in order to cracking reactions to become meaningful (thus explaining the lower operating CIT from the industrial case). Also, as propane is more easily cracked than ethane, pyrolysis reactions will more gradually become significant, justifying the smoother increase in temperature in the first few metres ofthecoil.

100 3.0 90 2.5 80 70 2.0 60 50 1.5 40 1.0 Yields (dry wt%) (dry Yields 30 wt%) (dry Yields 20 0.5 10 0 0.0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 Reactor length (m) Reactor length (m) Propane Methane Ethylene Propylene Hydrogen Butadiene

(a) Propane, ethylene, propylene and methane yields. (b) Hydrogen and 1,3-butadiene yields.

Figure 4.10: Variation of the yield along reactor length of some key components.

In terms of product yield profiles, one not only observes that there is a more pronounced decreasein propane yield along the reactor length but also higher yields of propylene, butadiene and methane over lighter products, such as ethylene and hydrogen, are noted.

57 The former consideration is easily explained based on what has just been mentioned, i.e., the higher tendency for propane to be cracked relatively to ethane. Also, because propane is heavier than ethane, its propensity to form heavier products is also higher, thus justifying the latter observation. Finally, it is noteworthy that there is a maximum in propylene yield at 97% of total coil length, although barely noticeable. This supports the statement that at some point propylene-decomposing reactions will take over the propylene-forming ones, thus leading to a decrease in propylene production. Nevertheless, the operating conditions are well specified as only 0.3% of propylene (mass) is lost due to excessive cracking.

4.4 Naphtha cracking

Liquid feedstocks have been historically predominant in the steam cracking process in spite of the higher ethylene selectivities being achieved through gaseous feedstocks cracking. As a matter of fact, a large portion of Europe and Asia’s petrochemical industry still relies on naphtha feedstocks to feed their crackers, although in some other geographical regions (e.g. United States or Saudi Arabia) a ”gasification” of the petrochemical industry has been taking place. On the other hand, higher attention has been brought to liquid feedstocks as refineries have been dealing with increasingly heavier crude oils, being light fractions scarcer and scarcer. In truth, efforts have been made in order to allow one to use heavier petroleum cuts, such as atmospheric and vacuum gas oils, as feedstocks for the steam cracking process, thus showing the importance liquid feedstocks have and possibly may have in the future. In this regard, the development of mathematical models able to predict product yields whenever these complex mixtures cracking is concerned is of the utmost interest for the petrochemical industry, with the deep understanding of the complex kinetics involved being a key factor. As a result, in the section to follow two different radical kinetic schemes for naphtha cracking will have their ability to accurately predict product distribution evaluated by comparison against published indus- trial data. Note that molecular schemes, although published, do not accurately represent the complex cracking phenomena occurring in liquid feedstocks pyrolysis and, therefore, will not be considered.

4.4.1 Kinetics

Towfighi and Karimzadeh published in 1993 [18] a naphtha cracking radical scheme comprising 150 reactions and involving 22 molecular and 18 radical species, covering the pyrolysis of species up to C6. Furthermore, Joo published in 2000 [26] a seemingly more complex kinetic set describing the free- radical mechanisms occurring in naphtha pyrolysis, totalling 233 reactions. This radical scheme covers the thermal cracking of species up to C8, involving 31 molecular and 48 radical species. These schemes were found to have reactions in common with the radical scheme from Sundaram and Froment, used in the previous sections 4.2 and 4.3. A comparison in terms of kinetic parameters is presented in the Appendix section B.2.2.

58 Both kinetic schemes, although diverging significantly in number of reactions and chemical species taken into account, are said to accurately predict pyrolysis phenomena and thus product yields. In order to validate these kinetic models, the following industrial case is concerned.

4.4.2 Industrial case

The plant data for an industrial naphtha cracker published by Niaei et al. [77] was used in the current section in order to evaluate the performance of both naphtha cracking radical schemes proposed by Towfighi and Karimzadeh and Joo. The industrial furnace configuration is summarised in Table 4.7, being the coil depicted in Figure 4.11. Note that contrary to what has been observed in the ethane and propane cracking furnaces (fixed diameter coils), in this case a multi-diameter split coil arrangement is observed, with smaller inlet coils combining into larger outlet coils. This allows shorter residence times and the higher process gas temperatures required for liquid feedstocks cracking.

Figure 4.11: Naphtha cracking coils arrangement. (adapt. [77])

The operating conditions and the detailed hydrocarbon analysis of the naphtha feedstock, which were used as inputs to the furnace model, are presented in Table 4.8 and Table 4.9, respectively. The above described industrial reactor was modelled using both kinetic schemes published by Tow- fighi and Karimzadeh [18] and Joo [26] and corresponding results compared with reported industrial data by Niaei (Table 4.10). Apparently neither of the kinetic schemes seems to accurately predict the product distribution. In fact, the published scheme by Towfighi and Karimzadeh remarkably fails to predict most of the yields, + with the exception of methane and ethylene. From all the yields, the one corresponding to the C5 non-aromatic fraction, noted by ”Others”, has the largest deviation, being greatly overpredicted. On the other hand, the reported scheme from Joo – which takes into account 81 more reactions and almost twice the chemical species than the one from Towfighi and Karimzadeh – seems to show a better agreement with plant data reported by Niaei et al. [77], with an AADmain of 52.3% against 68.7% from Towfighi and Karimzadeh’s scheme, even though methane and ethylene yields are worsened. Once + again, the C5 non-aromatic fraction yield is being considerably overpredicted.

59 Table 4.7: Naphtha cracking furnace configuration.

Reactor configuration [61, 77] Total length (m) 45 Length coil 1 (m) 22.5 ID/OD coil 1 (mm) 85/92 Length coil 2 (m) 22.5 ID/OD coil 2 (mm) 121/130

Adiabatic section characteristics Lengtha (m) 1 ID/ODb (mm) 170/181

Transfer line exchanger arrangement [61] No. of TLE 1 No. of tubes in TLE 152 Tube length (m) 4.96 Tube ID/OD (mm) 24/32 a assumed by author b estimated by author

Table 4.8: Operating conditions for naphtha cracking [77].

Industrial data Simulation results Total feed flowrate (kg/h) 11600 11600 CIT (◦C) 600 600 COT (◦C) 860 860 CIP (bara) 2.2 2.2 COP (bara)a 1.55 1.6 S/O ratio (kg/kg) 0.7 0.7 Residence time (s)a 0.4 0.4 Temperature at TLE outlet (◦C) 371 367 a not used as simulation inputs

Table 4.9: Naphtha feed composition [77].

n-Butane 4.53 2,2,3-Trimethylbutane 7.20 i-Butane 0.12 Benzene 2.17 n-Pentane 22.52 Toluene 0.37 i-Pentane 16.48 p,m-Xylene 0.44 2,2-Dimethylbutane 0.30 Cyclohexane 7.13 2,3-Dimethylbutane 1.18 n-Heptane 1.69 Cyclopentane 7.38 2,3-Dimethylpentane 1.10 2-Methylpentane 12.17 n-Octane 0.63 n-Hexane 12.02 i-Octane 0.20 2,4-Dimethylpentane 2.30 n-Nonane 0.07

It is also noteworthy that in the reference paper the authors used the same industrial case to vali- date their own mathematical model, achieving a quite reasonable agreement with plant data (AADmain = 4.4%). It is stated that the detailed mechanistic kinetic model used by the authors involved 1230 reac-

60 Table 4.10: Comparison between literature and simulation results.

Towfighi and Karimzadeh’s scheme Joo’s scheme Industrial data[77] Results Dev. Results Dev. Residence time (s) 0.4 0.42 5% 0.42 6% COP (bara) 1.55 1.75 13% 1.76 13%

Yields (dry wt%): Hydrogen 1.2 0.35 -70% 0.35 -71% Methane 17.7 16.61 -6% 13.92 -21% Acetylene 0.93 1.34 44% - - Ethylene 35.42 37.20 5% 32.59 -8% Ethane 6.04 0.10 -98% 3.24 -46% Propylene 12.05 7.99 -34% 13.59 13% Propane 0.48 0.01 -99% 0.00 -100% 1,3-Butadiene 4.23 10.09 139% 7.35 74% Butenes 1.8 0.01 -99% 5.56 209% Butanes 0.24 0.12 -49% 0.23 -3% Aromatics 10.82 4.48 -59% 2.99 -72% Others 9.09 21.70 139% 19.36 113% a AADmain - 68.7% 52.3% a Average absolute deviation of the main yields: hydrogen, methane, ethylene, ethane, propy- lene, 1,3-butadiene, aromatics and ”others”.

tions and 122 chemical species. However, the references of the used kinetic model point to the radical scheme of Towfighi and Karimzadeh [18] and to the one reported by Sundaram and Froment, whose total number of reactions combined does not exceed 300. This observation supports the suspicion that all information regarding the complete kinetic models may not have been entirely disclosed. As a matter of fact, many kinetic models are often proprietary and confidential and, in this sense, may not be of the authors’ interest to publicly disclose information sothat others can exactly reproduce their results. The fact that the cracking of meaningful naphtha components is not taken into account by neither of the implemented kinetic schemes supports this idea that not all information may be available. In truth, cyclopentane cracking is not considered in neither of them and even cyclohexane pyrolysis is solely considered in Towfighi’s scheme, as depicted in Figure 4.12. Because neither of the kinetics schemes is able to describe the cracking of all heavier components, lower yields for the main products are observed. One may verify that most of the products are being underpredicted. In order to demonstrate this, the above kinetic schemes were extended with the addition of cracking reactions involving cyclopentane and cyclohexane (see the Appendix section B.2.3), which, from the unconverted components, are the ones present in highest amounts (Table 4.9). The yield profiles for cyclopentane and cyclohexane obtained using the extended kinetic schemes are plotted in Figure 4.13 and the main results summarised in Table 4.11. By observing Figure 4.13 and Table 4.11 one is able to verify that cyclopentane and cyclohexane + conversion increased, thus leading to an appreciable decrease in the yield of the C5 non-aromatic

61 9.0 8.5 8.0 7.5 7.0 6.5 6.0

Yields (dry wt%) (dry Yields 5.5 5.0 4.5 4.0 0 5 10 15 20 25 30 35 40 45 Reactor length (m) Cyclopentane - Towfighi and Karimzadeh Cyclohexane - Towfighi and Karimzadeh

Cyclopentane - Joo Cyclohexane - Joo

Figure 4.12: Cyclopentane and cyclohexane yield profiles obtained using the implemented kinetics.

10 9 8 7 6 5 4

Yields (dry wt%) (dry Yields 3 2 1 0 0 5 10 15 20 25 30 35 40 45 Reactor length (m) Cyclopentane - Towfighi and Karimzadeh ext. Cyclohexane - Towfighi and Karimzadeh ext. Cyclopentane - Joo ext. Cyclohexane - Joo ext.

Figure 4.13: Cyclopentane and cyclohexane yield profiles obtained using the extended kinetics. fraction – in the case of Joo’s kinetics, this has been more than halved. Because more components are undergoing pyrolysis, higher product yields are globally observed.

However, although the AADmain decreases significantly from the original results, these are still in profound disagreement with plant data, being the most satisfying result the ethylene yield predicted using Joo’s radical scheme, which almost matches the industrial value. In order to be able to predict product yields, not only more reactions would probably have to be added but also a kinetic parameter tuning process would have to be carried out. Once again, although interesting, this would fall out of the scope of the current work and, therefore, will not be implemented. Joo, however, co-published a posterior paper in 2001 [19] in which an optimisation of a selected set of activation energies was performed in order to better fit the reported pilot plant data. One may therefore suspect of the extensiveness of the published scheme to other industrial cases rather than the ones used for its tuning. Although it is said the customised kinetic values are useful and valid solely for the studied pilot plant, one sees oneself still tempted to implement such changes. The considered reactions and the corresponding kinetic parameters before and after the optimisation are summarised in Table 4.12. The naphtha industrial case was quickly simulated using the original scheme with the optimised acti- vation energies, having the simulation results shown an increase of 3.8% in both ethylene and propylene

62 Table 4.11: Comparison between literature and simulation results with extended kinetic schemes.

Towfighi and Karimzadeh’s scheme Joo’s scheme extended extended Industrial data[77] Results Dev. Results Dev. Residence time (s) 0.4 0.42 4% 0.42 5% COP (bara) 1.55 1.75 13% 1.7 13%

Yields (dry wt%): Hydrogen 1.2 0.35 -62% 0.35 -71% Methane 17.7 16.66 -6% 13.58 -23% Acetylene 0.93 1.53 65% - - Ethylene 35.42 39.06 10% 35.29 0% Ethane 6.04 0.10 -98% 3.74 -38% Propylene 12.05 9.52 -21% 16.25 35% Propane 0.48 0.01 -99% 0.00 -100% 1,3-Butadiene 4.23 11.83 180% 7.21 70% Butenes 1.8 0.01 -99% 8.77 387% Butanes 0.24 0.12 -49% 0.24 2% Aromatics 10.82 5.12 -53% 2.99 -72% Others 9.09 15.58 71% 10.62 17% a AADmain - 62.6% 40.8% a Average absolute deviation of the main yields: hydrogen, methane, ethylene, ethane, propy- lene, 1,3-butadiene, aromatics and ”others”.

Table 4.12: Optimised values of the activation energies performed by Joo (2001) [19].

Activation energy (J/mol) Reaction Initial value Optimised value Variation · · C2H5 → C2H4 + H 191207.9 187065.0 -2.1% · · C3H7 → C2H4 + CH3 142262.5 141431.1 -0.6% · · · C2H5 → C3H7 + H 163183.9 156527.7 -4.1%

yields with little changes to the remaining product yields. This illustrates the meaningful influence the tuning of some parameters may have upon simulation results. The main conclusions one may take from these results is that both kinetics greatly fail at reproducing plant data, owing to an insufficient number of reactions and to possibly non-optimised kinetic parameters. It is also important to bear in mind that many of these kinetic schemes are proprietary and confidential and, in this sense, one may not have access to all or even completely correct information in publicly- available literature. Finally, similarly to the ethane and propane industrial cases, the pressure and process gas temper- ature profiles and the yields of key components along the reactor length were obtained. These results, produced using the extended scheme from Joo, are presented in Figures 4.14 and 4.15, respectively. Regarding the process gas temperature profile, the rapid temperature increase in the first fewsec- tions of the coil is no longer observed but a much gradual increase is verified instead, thus contrasting with the ethane and propane cases. The explanation behind this observation lies in the multiplicity of

63 900 2.3

2.2 850 C) ° 2.1 800 2.0

750 1.9

1.8

700 (bara) Pressure 1.7

Process Process gas temperature ( 650 1.6

600 1.5 0 5 10 15 20 25 30 35 40 45 Reactor length (m)

Temperature - Niaei et al. (2004) Temperature Pressure

Figure 4.14: Pressure and process gas temperature profiles along reactor length using the extended scheme from Joo. components that constitute the naphtha feed, with heavier components undergoing pyrolysis much faster than the lightest ones. It is also interesting to note that at 22.5 m there is a slight decrease in temperature, owing to the coil arrangement. In fact, at 22.5 m of coil length, the process gas from two split coils merges to a single, larger coil section, thus decreasing the amount of heat supplied to the gas by the furnace and, ultimately, leading to a decrease in temperature due to highly endothermic cracking reactions. When compared to the simulation profile reported by Niaei, one may note that between 2.5 and 15 m of reactor length, the obtained profile predicts significantly lower temperatures. The most likely explanation is that the model developed by Niaei uses a much more rigourous approach (multizonal heat transfer) to model the heat exchange inside the furnace. In fact, in the simulation profile from literature, a much higher temperature increase is observed in the initial sections of the coil, something that would be expected because of the split coil arrangement.

40 35 30 25 20 15 Yields (dry wt%) (dry Yields 10 5 0 0 5 10 15 20 25 30 35 40 45 Reactor length (m) n-Pentane i-Pentane n-Hexane i-Hexane i-Heptane Hydrogen Methane Ethylene Propylene Butadiene Aromatics

Figure 4.15: Component yields along the reactor length using the extended scheme from Joo.

Relatively to component yields, one may clearly observe the high molecular weight hydrocarbons being cracked whilst lower molecular weight products are formed. Note that, as expected, higher molec-

64 ular weight hydrocarbons, such as iso-heptane, more rapidly undergo cracking reactions than lower molecular weight ones, such as n-pentane. Finally, significantly higher yields of secondary products such as propylene, methane, butadiene and aromatics are observed in comparison to ethane and propane. This was also expected in the sense that the heavier the feed, more secondary products will be formed.

4.5 Case studies

4.5.1 Furnace heat flux correlations

In this section the novel approach regarding the thermal specification of the coils, described inthe previous section 4.1.2, is to be applied to an already studied industrial case. As it was mentioned before, the several parameters needed for the three types of furnace firing are not usually disclosed or are not easily obtainable. A case study will be performed, assuming a given set of parameters, in order to solely assess the influence of the heat flux profile on simulation results and also if the furnace heat flux correlations pose a serious alternative to the existing thermal specification options of the model. Since this approach requires information regarding the individual, straight sections of the coil, the industrial case to be considered as the base case will be the one used in propane cracking, whose configuration and operating conditions are presented in Table 4.4 and 4.5, respectively. The heat flux distribution, which was being predicted by the model, will now be imposed to thecoils via a relative heat flux profile which is to be calculated using the heat flux correlations. The furnace firing arrangement which has been assumed for this study is summarised inTable 4.13.

Table 4.13: Floor plus wall firing parameters.

Coils Floor burners Wall burners floor dcoil 0.05 y0 0.6 ω 0.183 top dcoil 0.05 zmax 0.36 Nwb 2 ζfloor 1.0 zw,1 0.7 zw,2 0.9 ζw,1 0.25 ζw,2 0.50

Although hypothetical, the furnace arrangement in Table 4.13 is not completely random. A reason- able value of 5% of furnace height was considered as the distance between the coils and the floor and top of the furnace. Since each straight section of coil has 9.4 m, this assumption is equivalent to say that there is a 0.5 m slack between the coils and the furnace top and floor.

As for the floor burner parameters, y0 and zmax were taken from the typical heat flux profile distribu- tion disclosed by Colannino [74] and the floor burners were taken as a reference in terms of power, i.e.,

ζfloor = 1.

65 Regarding the wall burner parameters, the inverse aspect ratio of the furnace, ω=0.183, was taken from the furnace specifications provided by Niaei [77] for the naphtha cracking furnace presented in the previous section 4.1. Finally, the elevations of each row of wall burners, which are positioned in order to compensate the lower heat fluxes experienced by the coils near the top, were assumed based on literature schematics [2, 74], which show two rows of wall burners at approximate heights of 70 and 90% of the total furnace height. However, their relative powers were completely arbitrary except for the fact that these are usually less powerful than the floor-mounted onesζ ( w <ζfloor). The simulation results obtained using such firing configuration for the furnace are summarised in Figures 4.16a and 4.16b and Table 4.14.

920

880

840

800

760

720 Temperature(K) 680

640

600 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 Coil length (m)

(a) External heat flux distribution: base case (dashed) and with (b) Tube metal temperature (black and gray) and process gas the addition of furnace heat flux correlations (full). temperature (coloured) profiles: base case (dashed) and with the addition of furnace heat flux correlations (full).

Figure 4.16: Comparison of simulation results obtained using the furnace heat flux correlations with the base case: heat flux and temperature profiles.

Table 4.14: Product distribution results and comparison with the base case.

Yield (dry wt%) Base case Results Dev. H2 0.81 0.81 0.1% CH4 24.71 24.70 0.1% C2H2 1.24 1.24 0.1% C2H4 34.15 34.13 0.0% C2H6 3.13 3.13 0.1% C3H6 15.28 15.28 0.0% C3H8 16.87 16.90 0.2% C4H6 2.80 2.79 0.2% C5+ 1.01 1.00 0.2%

As it is readily observed in Figure 4.16, although the heat flux profile shape is completely different due to the inclusion of the heat flux correlations, the difference between the base case and the current one greatly decreases from the heat flux distribution to the tube metal temperature profile. This isalso verified when passing from the latter to the process gas temperature profile, where little tonoinfluence of the heat flux correlations is observed. In fact, because the temperature profile remains unchanged, the several product yields shown in

66 Table 4.14 also seem indifferent to the inclusion of the heat flux correlations. The conclusion one may make from these results is that the presented addition to the ethylene furnace model, although it consists of a more realistic approach in terms of heat flux distribution, does not meaningfully affect simulation results when compared with the already existing option of letting the model itself predict the heat flux profile.

4.5.2 Alternative diluents

As it is already known, steam plays a crucial role in the furnace as it lowers hydrocarbon partial pressure thus favouring cracking reactions over secondary and coke-forming ones. However, the usage of steam is costly since water is completely removed from the cracked gas by condensation, part of it being vaporised once again before the generated steam can be fed back into the furnace. In this regard, there has been an increasing trend in studying other diluents which may pose an alternative to steam, with increased ethylene selectivity and lower energy consumption. The usage of carbon dioxide in the steam cracking process diluent has already been studied by Choudhary [78], Yancheshmeh et al. [75] and Alselaa et al. [79], with the main conclusions being that carbon dioxide is beneficial to the overall process due to higher yields of ethylene and propylene and less coke accumulation, thus increasing furnace run length. However, in the present case a steady-state study will be carried out in order to solely analyse the influence of the physical properties of the diluent in the furnace performance. Please note that thisstudy applies to start-of-run conditions and therefore coke is not being considered, and neither is the diluent’s ability to react with it. Moreover, the downstream processing cost of each of these diluents, although certainly relevant in a whole-plant scenario, was also not taken into consideration. Apart from carbon dioxide, several other diluting agents will be taken into account so that the effects of two main physical properties can be studied: molecular weight, which influences gas phase density (Eq. 4.8) – hence weighing on velocity and residence time – and heat capacity, which affects temperature and energy consumption. These alternative diluents and corresponding properties are summarised in Table 4.15.

Table 4.15: Molecular weights of diluting agents being studied.

Diluent MW (g/mol) Cp1000K (J/mol/K)

H2 2.02 30.3 He 4.00 20.8 CH4 16.04 71.8 Steam 18.02 41.2 N2 28.01 32.7 CO2 44.01 54.3

It is important to mention that hydrogen and methane were chosen not only because they are side- products of ethylene’s production, and therefore can influence reversible reactions, but also because it

67 would be interesting to see the effects of their molecular weights and heat capacity, comparing to steam. On the other hand, nitrogen and helium’s selection was merely based on different molecular weights and heat capacities, since these are rather expensive inert gases (specially helium). This study will be based on the ethane industrial case reported by Yancheshmeh [75], presented in the previous section 4.2.2, and on the radical kinetics published by Sundaram and Froment [17]. From all the industrial cases and implemented kinetics, these proved to have the best agreement between simulation results and plant data, hence seeming the most appropriate choice for this type of analysis. The study consisted of several optimisations, each one corresponding to a different fixed valued for (ethane) conversion (replacing COT), in which the hydrocarbon (ethane) feed flowrate, coil inlet pressure (CIP) and inlet temperature (CIT) were kept constant (Figure 4.17). The objective was to maximise ethylene selectivity by allowing the model to vary each diluent ratio (relatively to hydrocarbon), being the optimisation subjected to both pressure drop and coil outlet temperature constraints.

Fixed conversion

Fixed hydrocarbon Maximise ethylene Pressure drop feed flowrate selectivity constraints

Fixed coil inlet Optimisation pressure

Fixed coil inlet Coil outlet temperature temperature Varying diluent ratio constraints

Figure 4.17: Schematic of the alternative diluents study.

In the first case, since typical pressure drops for a steam cracking coil are around 1 bar, inorderto allow some slack, the upper bound for the pressure drop was set to 1.1 bar. The maximum coil outlet temperature, on the other hand, was set to its base case value, 845 ◦C, in order to verify whether the process can operate at lower temperatures or not. The corresponding results are summarised in Figure 4.18. Interesting observations can be made from Figure 4.18. From the plots regarding pressure drop (a) and COT (b), one is able to verify that at low conversions pressure drop hits the upper bound whilst at high conversions COT is the one to hit its maximum allowable value. It is also noticeable that at low conversions, the mass diluent ratio (c) follows the molecular weights of the diluents, whilst the molar diluent ratio (d) follows the inverse order. The same also seems to happen with residence time (e) and ethylene selectivity (f), respectively. At high conversions, however, the diluent ratios (mass and molar), residence time, ethylene selectivity and production (g) for each diluent seem to decrease and become coincident towards higher conversion values. Whilst diluent ratios and selectivity abruptly decrease towards high conversions, residence time

68 1.40 1.30 870 1.20 860 1.10 Steam Steam 850 C)

1.00 CO2 ° CO2 0.90 N2 840 N2 COT( 0.80 He 830 He

Pressure (bar) drop Pressure 0.70 H2 820 H2 0.60 CH4 CH4 0.50 810 55 57.5 60 62.5 65 67.5 70 55 57.5 60 62.5 65 67.5 70 Conversion (%) Conversion (%)

(a) Pressure drop in the coils at different ethane conversions. (b) Coil outlet temperature at different ethane conversions.

0.80

) 1.20

) 0.70

ethane 1.00

ethane 0.60 Steam Steam 0.50 0.80 CO2 CO2 0.40 N2 0.60 N2 0.30 He 0.40 He 0.20 H2 H2 Dulient ratio (kg/kg 0.10 0.20 Dulient (mol/mol ratio Dulient CH4 CH4 0.00 0.00 55 57.5 60 62.5 65 67.5 70 55 57.5 60 62.5 65 67.5 70 Conversion (%) Conversion (%)

(c) Mass diluent ratios at different ethane conversions. (d) Molar diluent ratios at different ethane conversions.

1.00 89 0.90 87 0.80 Steam 85 Steam CO2 CO2 0.70 83 N2 N2

selectivity (%) selectivity 81

0.60 4 He H He 2 79 Residence time (s) time Residence C H2 H2 0.50 77 CH4 CH4 0.40 75 55 57.5 60 62.5 65 67.5 70 55 57.5 60 62.5 65 67.5 70 Conversion (%) Conversion (%)

(e) Residence time at different ethane conversions. (f) Ethylene selectivity at different ethane conversions.

0.95 7.50 ) 7.40 C2H4 0.90 7.30 Steam 7.20 Steam 0.85 CO2 7.10 CO2 7.00 N2 N2 0.80 6.90

production(ton/h) He 6.80 He 4 H 2 0.75 6.70 C H2 H2 6.60

CH4 consumption(MJ/kg Energy CH4 0.70 6.50 55 57.5 60 62.5 65 67.5 70 55 57.5 60 62.5 65 67.5 70 Conversion (%) Conversion (%)

(g) Ethylene production at different ethane conversions. (h) Specific energy consumption (relatively to ethylene pro- duced) at different ethane conversions.

Figure 4.18: Optimisation results obtained with upper bound in pressure drop and coil outlet temperature of 1.1 bar and 845 ◦C, respectively, using the radical kinetics proposed by Sundaram and Froment (1978).

69 and ethylene production seem to increase with conversion. Finally, regarding the specific energy consumption (h), one does not observe any order in particular, being methane and nitrogen/helium (low/high conversions) the diluents leading to the highest and lowest energy consumption, respectively. For the sake of discussion, two distinct sections will be outlined: low conversions and high conver- sions. First, at low conversions one observed that pressure drop was hitting the upper bound. This happens because, since the objective is to maximise selectivity, the model will try to minimise not only the hydrocarbon partial pressure but also the residence time by increasing the diluent ratio as much as possible. Hence, the denser the diluent (higher molecular weight), the higher will be the mass ratio and lower will be the molar ratio for the same pressure drop. Because the molar diluent ratio is lower, the velocity will also be lower, consequently leading to higher residence times which are then responsible for lowering selectivity and thus production (conversion fixed). Furthermore, because denser diluents lead to higher residence times, a lower COT is required to achieve a given conversion, which contributes to lower energy consumption. Energy consumption, however, must also take into account the heat capacity of the diluent. One is now able to understand why methane is the one leading to the highest energy consumption – it has low density (high molar diluent ratio) and the highest heat capacity (molar) – and why nitrogen is the one with the lowest energy consumption - it is relatively dense and has a relatively low heat capacity. Finally, at high conversions one observed that coil outlet temperature was the variable hitting the upper bound. This can easily be explained because of the strong relation between temperature and conversion. Since temperature is being constrained, the only existing solution to meet the fixed conversions is to increase residence time and the model accomplishes this by abruptly lowering diluent ratios. With decreasing diluent ratios, comes lower pressure drop, lower selectivities and lower energy consumption. Moreover, since COT hits its upper bound at high conversions, heat capacity effect on energy con- sumption will become predominant over density and this is the reason behind the helium becoming the least energy demanding diluent at high conversions. At last, because residence time has to increase to meet the high conversions being specified, the higher the conversion, the less slack there will be for the diluent ratio to change between diluents. As a matter of fact, at the limit, to meet maximum conversion, all the diluent ratios would have to be zero and this justifies why variables were becoming coincident towards very high conversion values. The main conclusion one may draw from these results is that, at high conversions, if one is not willing to let COT increase above a certain value, there may actually be no difference between diluents. On the other hand, if COT is allowed to increase, helium seems the best alternative to steam as it leads to significantly higher ethylene selectivities and lower specific energy consumption. Nevertheless, hydrogen and methane results seem to suggest that these have absolutely no influ- ence on ethylene selectivity due to reversible reactions. Methane-wise, these results were expected since no reversible reactions involving it are considered

70 in the used radical kinetics. Hydrogen, on the other hand, was expected to greatly influence ethylene selectivity as ethylene’s hydrogenation to ethane (reaction 132 in [17]) is taken into account in the kinetic scheme. The most likely explanation lies in the fact that the corresponding kinetic parameters probably haven’t been tuned for such hydrogenating conditions and therefore, are not able to accurately describe reality. In this sense, in order to evaluate hydrogen’s role in ethylene selectivity, the molecular kinetics from Sundaram and Froment [13], previously introduced in section 4.2.1 (see also section B.1 in Appendix), were used. This kinetic scheme, which also takes into account ethylene’s hydrogenation to ethane, is then expected to produce more realistic results in the presence of high hydrogen concentrations. It is noteworthy that although the scheme considers a reversible reaction involving methane, it does not affect ethylene selectivity and therefore, methane results are not expected to change significantly. The upper bound on pressure drop was kept at its previous value of 1.1 bar, whilst the coil outlet temperature constraint was loosen up to its highest typical value, 875 ◦C, taken from literature [2]. The results are present in Figure 4.19. As it is visible in Figure 4.19, although the diluent ratios and residence time follow the ascend- ing/descending molecular weights’ order, hydrogen which had the highest ethylene selectivities and production, because it was the lightest diluent, now has one of the lowest due to ethylene’s hydrogena- tion. In addition, because less ethane is being converted due to ethylene’s reaction with hydrogen, higher coil outlet temperatures are required to maintain the same conversion. It is interesting to see that hydrogen, which required the highest COTs because of the lowest molecular weight, now demands an even higher COT due to reversible reactions. Because the coil outlet temperature drastically increases, the energy consumption also profoundly increases, thus becoming the diluent leading to the highest energy consumption. Finally, it is also interesting to note that helium is the lowest energy demanding diluent and not nitrogen as one has observed with the radical kinetics. This happens because with these molecular kinetics, the impact of residence time on product distribution is much more marked, and since more ethylene is being produced when helium is used, the specific energy consumption is much lower.

4.6 Sensitivity analysis

Having the main results been presented and discussed, it is now important to understand and study the role of specific key variables/parameters in simulation results. In this regard, a sensitivity analysis will be conducted on physical properties, operating conditions and kinetic parameters. In addition, the influence of the adiabatic section length, which has been assumed in all studied cases, willalsobe considered. Similarly to the case study on alternative diluents (section 4.5.2), this analysis will be conducted based on the ethane industrial case reported by Yancheshmeh [75], presented in the previous section 4.2.2, and on the radical kinetics published by Sundaram and Froment [17].

71 1.40 880 1.30 870

1.20 Steam 860 Steam

1.10 CO2 C) 850 CO2 °

1.00 N2 840 N2 COT(

0.90 He 830 He Pressure(bar)drop 0.80 H2 820 H2 CH4 CH4 0.70 810 55 57.5 60 62.5 65 67.5 70 55 57.5 60 62.5 65 67.5 70 Conversion (%) Conversion (%)

(a) Pressure drop in the coils at different ethane conversions. (b) Coil outlet temperature at different ethane conversions.

0.80 1.30

) 1.20 ) 0.70

1.10 ethane

ethane 0.60 Steam 1.00 Steam 0.50 CO2 0.90 CO2 0.40 0.80 N2 N2 0.30 0.70 He 0.60 He 0.20 H2 0.50 H2 Dulient ratio (kg/kg 0.10 Dulient Dulient (mol/molratio 0.40 CH4 CH4 0.00 0.30 55 57.5 60 62.5 65 67.5 70 55 57.5 60 62.5 65 67.5 70 Conversion (%) Conversion (%)

(c) Mass diluent ratios at different ethane conversions. (d) Molar diluent ratios at different ethane conversions.

0.80 89 0.75 87 0.70 Steam 85 Steam 0.65 CO2 CO2 0.60 83 N2 N2

0.55 selectivity (%) 81 4

He H He

2 79 Residencetime (s)

0.50 C H2 H2 0.45 77 CH4 CH4 0.40 75 55 57.5 60 62.5 65 67.5 70 55 57.5 60 62.5 65 67.5 70 Conversion (%) Conversion (%)

(e) Residence time at different ethane conversions. (f) Ethylene selectivity at different ethane conversions.

0.95

) 7.90 C2H4 0.90 7.70 Steam 7.50 Steam 0.85 CO2 7.30 CO2 N2 N2 0.80 7.10

production(ton/h) He He

4 6.90 H 2 0.75

C H2 H2 6.70

CH4 Energy consumption(MJ/kg CH4 0.70 6.50 55 57.5 60 62.5 65 67.5 70 55 57.5 60 62.5 65 67.5 70 Conversion (%) Conversion (%)

(g) Ethylene production at different ethane conversions. (h) Specific energy consumption (relatively to ethylene pro- duced) at different ethane conversions.

Figure 4.19: Optimisation results obtained with upper bound in pressure drop and coil outlet temperature of 1.1 bar and 875 ◦C, respectively, using the molecular kinetics proposed by Sundaram and Froment (1977).

72 4.6.1 Fluid properties

In mathematical models of chemical processes the physical properties employed may differ depend- ing on assumptions and/or the package supplying them. Although they may provide similar predictions, there are always some discrepancies which can leave one tempted to blame the physical properties for differences observed in simulation results. In this sense, a sensitivity analysis was performed to the majority of the physical properties of the process gas. These include the gas density, calculated based on the ideal gas law (Eq. 4.8), viscosity and thermal conductivity. These will be varied +10% and -10% since predictions of physical properties from different packages and methods usually do not differ more than 10% from each other. It is noteworthy the fact that heat capacity and standard heat of formation, although known to play a key role in the process, are not directly used in the model, having been included in the specific enthalpy TM htotal calculation by the external physical properties package, Multiflash . Nevertheless, a brief comparison of heat capacity and standard heat of formation from NIST Chemi- cal WebBook database and the ones obtained from MultiflashTM and from CHEMKIN (software tool used worldwide in chemical processing), is presented in the Appendix section A.1. The sensitivity analysis to process gas density, viscosity and thermal conductivity of the process stream is summarised in Table 4.16. From the results presented in Table 4.16, one can easily conclude that density is the only physical property with a meaningful impact on simulation results, with viscosity and thermal conductivity having a completely negligible effect, even for viscosity whose a 10% variation leads to a maximum absolute deviation relatively to the base case of 0.3% From the analysis on density one may observe a higher impact on residence time and on the coil outlet pressure. The explanation to these observations lies on the inverse dependency of gas velocity in respect to density. Residence time is then inversely affected by velocity. Pressure drop, on the other hand, depends on density and on squared velocity, thus ultimately depending on the inverse of density. Additionally, a significant influence of density on conversion and product yields is also observed. Since these roughly follow residence time, the same trend will be noted in respect to process gas density. Furthermore, an increase in density seems to favour the formation of methane and propylene and + C5 over ethylene, thus leading to lower ethylene selectivity. This happens due to the increase in the residence time which tends to decrease ethylene selectivity by favouring other products’ production.

4.6.2 Operating conditions

Operating conditions, as their name indicates, are the ones responsible for defining the furnace operation and, in that sense, play a major role in simulation results. A sensitivity analysis to key operating conditions will then be carried out in order to evaluate the impact of each individual condition on the model’s predictions. The studied operating conditions can be arranged into three classes: flowrates, pressures and temperatures.

73 Table 4.16: Sensitivity analysis on physical properties: density, viscosity and thermal conductivity.

Density Viscosity Thermal conductivity +10% -10% +10% -10% +10% -10% Base case Result Dev. Result Dev. Result Dev. Result Dev. Result Dev. Result Dev. Residence time (s) 0.68 0.76 11.4% 0.60 -11.4% 0.68 -0.1% 0.68 0.1% 0.68 0.000% 0.68 0.000% COP (bara) 2.16 2.27 4.8% 2.03 -6.2% 2.16 -0.3% 2.17 0.3% 2.16 0.000% 2.16 0.000% Conversion (%) 65.24 65.78 0.8% 64.51 -1.1% 65.21 -0.1% 65.28 0.1% 65.24 -0.004% 65.25 0.004% Selectivity (%) 82.85 82.51 -0.4% 83.30 0.5% 82.87 0.03% 82.83 -0.03% 82.85 0.001% 82.85 -0.001% 74 Yields (dry wt%): Hydrogen 4.05 4.08 0.6% 4.01 -0.9% 4.05 0.0% 4.05 0.0% 4.05 -0.004% 4.05 0.000% Methane 3.69 3.79 2.9% 3.55 -3.7% 3.68 -0.2% 3.70 0.2% 3.69 -0.010% 3.69 0.000% Ethylene 50.31 50.50 0.4% 50.02 -0.6% 50.29 -0.03% 50.32 0.0% 50.30 -0.003% 50.31 0.000% Ethane 34.76 34.22 -1.5% 35.49 2.1% 34.79 0.1% 34.72 -0.1% 34.76 0.008% 34.75 0.000% Propylene 1.07 1.11 3.9% 1.01 -4.9% 1.06 -0.2% 1.07 0.3% 1.07 -0.006% 1.07 0.000% 1,3-Butadiene 1.76 1.79 1.6% 1.73 -2.1% 1.76 -0.1% 1.77 0.1% 1.76 -0.011% 1.77 0.000% + C5 4.18 4.31 3.3% 4.00 -4.3% 4.17 -0.2% 4.19 0.2% 4.18 -0.011% 4.18 0.010% a AADmain - 1.9% 2.5% 0.1% 0.1% 0.01% 0.01%

a Average absolute deviation of the main product yields: ethylene, propylene, hydrogen and methane 4.6.2.1 Flowrates

Hydrocarbon and steam flowrates are two important process variables since they will play amajor role in velocity, hence in pressure drop and residence time, and in hydrocarbon partial pressure, re- spectively. The steam flowrate itself, however, is not usually considered a process variable, beingthe steam-to-oil ratio specified instead. First, in order to study the influence of hydrocarbon flowrate, the profiles of some key process vari- ables along the reactor length were obtained at different values of this variable. These results are plotted in Figure 4.20. As one could foresee, the hydrocarbon flowrate plays a major role in pressure (Fig. 4.20a) as a higher flowrates result in higher velocities and, consequently, higher pressure drops. The temperature profile (Fig. 4.20b) shape, on the other hand, practically remains unchanged as both CIT and COT are being specified. It is also verified that higher heat fluxes (Fig. 4.20c) are required for higher hydrocarbon flowrates. Since the temperature profile barely changes, the higher the flowrate the higher will be theenergy requirements, thus the heat flux. Relatively to the product yield profiles (Fig. 4.20d-g), as the hydrocarbon flowrate increases, the lower will be the residence time and conversion (Fig. 4.20h), thus justifying the decreasing yields with increasing hydrocarbon flowrate. Finally, although ethane conversion decreases with increasing hydrocarbon flowrate (due to lower residence times), ethylene selectivity (Fig. 4.20h), on the other hand, seems to increase as residence time decreases. This was already expected as it is well known that low residence times tend to favour the formation of ethylene (and propylene) over secondary products. However, it is just as acknowledged that higher hydrocarbon partial pressures lead to lower ethylene (and propylene) selectivities. The results then seem to suggest a higher influence of the residence time than the partial pressure. Similar profiles are obtained concerning steam-to-oil ratio (SOR) and barely the same conclusions are drawn, i.e., the higher the SOR, the higher will be the total flowrate and higher will be the velocity and lower the residence time. Furthermore, although selectivity also increases with increasing SOR mainly due to lower residence time, it is also expected a certain contribution owing to lower hydrocarbon partial pressures. Quantitatively, both hydrocarbon flowrate and steam-to-oil ratio were varied by +10% and -10%and the main simulation results compared with the base simulation results from the ethane industrial case. These results are summarised in Table 4.18. The conclusion of the sensitivity analysis on hydrocarbon flowrate and SOR is that both significantly affect simulation results, having a direct impact on pressure and residence time and an indirect influence on conversion, selectivity and product yields. Of all products, methane and propylene are the most sensitive to flowrates, and ethylene and hydrogen the least. Finally, SOR has a lower impact on results because the total flowrate is obviously less sensitive toit

75 900 3.4 3.2 850

3.0 C) ° 2.8 HC = 2.2 ton/h 800 HC = 2.2 ton/h 2.6 HC = 2.1 ton/h HC = 2.1 ton/h 2.4 2.2 HC = 1.9 ton/h 750 HC = 1.9 ton/h 2.0 HC = 1.7 ton/h HC = 1.7 ton/h Pressure (bara) Pressure 1.8 HC = 1.5 ton/h 700 HC = 1.5 ton/h 1.6 HC = 1.4 ton/h HC = 1.4 ton/h Process gas temperature ( 1.4 650 HC = 1.2 ton/h HC = 1.2 ton/h 1.2 1.0 600 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Reactor length (m) Reactor length (m)

(a) Pressure profile along the reactor length at different hydro- (b) Process gas temperature profile along the reactor length at carbon (ethane) flowrates. different hydrocarbon (ethane) flowrates.

80 60

75 55 50 70 45 65 HC = 2.2 ton/h 40 HC = 2.2 ton/h 60 HC = 2.1 ton/h 35 HC = 2.1 ton/h 55 HC = 1.9 ton/h 30 HC = 1.9 ton/h

50 HC = 1.7 ton/h 25 HC = 1.7 ton/h 20 45 HC = 1.5 ton/h HC = 1.5 ton/h External heat flux (kW) HC = 1.4 ton/h wt%) (dry yield Ethylene 15 HC = 1.4 ton/h 40 10 HC = 1.2 ton/h HC = 1.2 ton/h 35 5 30 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Reactor length (m) Reactor length (m)

(c) External heat flux profile along the reactor length at different (d) Ethylene yield profile along the reactor length at different hydrocarbon (ethane) flowrates. hydrocarbon (ethane) flowrates.

5.0 2.4 2.2 4.5 2.0 4.0 1.8 HC = 2.2 ton/h 3.5 HC = 2.2 ton/h 1.6 HC = 2.1 ton/h 3.0 HC = 2.1 ton/h 1.4 1.2 HC = 1.9 ton/h 2.5 HC = 1.9 ton/h 1.0 HC = 1.7 ton/h 2.0 HC = 1.7 ton/h

0.8 HC = 1.5 ton/h 1.5 HC = 1.5 ton/h Hydrogen yield (dry wt%) (dry yield Hydrogen Propylene yield (dry wt%) (dry yield Propylene 0.6 HC = 1.4 ton/h HC = 1.4 ton/h 1.0 0.4 HC = 1.2 ton/h HC = 1.2 ton/h 0.2 0.5 0.0 0.0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Reactor length (m) Reactor length (m)

(e) Propylene yield profile along the reactor length at different (f) Hydrogen yield profile along the reactor length at different hydrocarbon (ethane) flowrates. hydrocarbon (ethane) flowrates.

6.5 Conversion Selectivity 6.0 80.0 90.0 5.5 5.0 88.0 75.0 4.5 HC = 2.2 ton/h 86.0 4.0 84.0 HC = 2.1 ton/h 70.0 3.5 82.0 HC = 1.9 ton/h 3.0 65.0 80.0 HC = 1.7 ton/h 2.5 78.0 HC = 1.5 ton/h

2.0 Selectivity (%) Conversion (%) 60.0 76.0 Methane yield (dry wt%) (dry yield Methane 1.5 HC = 1.4 ton/h 74.0 1.0 HC = 1.2 ton/h 55.0 0.5 72.0 0.0 50.0 70.0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 Reactor length (m) Hydrocarbon flowrate (ton/h)

(g) Methane yield profile along the reactor length at different (h) Conversion (ethane) and ethylene selectivity dependency hydrocarbon (ethane) flowrates. on hydrocarbon (ethane) flowrate.

Figure 4.20: Analysis on the influence of hydrocarbon (ethane) flowrate in some key process variables.

than to the hydrocarbon flowrate.

76 Table 4.18: Sensitivity analysis on flowrates: hydrocarbon flowrate and steam-to-oil ratio.

Hydrocarbon flowrate Steam-to-oil ratio +10% -10% +10% -10% Base case Result Dev. Result Dev. Result Dev. Result Dev. Residence time (s) 0.68 0.60 -11.5% 0.77 13.7% 0.66 -3.5% 0.70 3.6% COP (bara) 2.16 1.91 -11.6% 2.37 9.3% 2.11 -2.7% 2.37 9.3% Conversion (%) 65.24 62.57 -4.1% 67.65 3.7% 64.58 -1.0% 65.89 1.0% Selectivity (%) 82.85 84.26 1.7% 81.49 -1.6% 83.35 0.6% 82.35 -0.6% Yields (dry wt%): Hydrogen 4.05 3.91 -3.4% 4.17 3.0% 4.02 -0.7% 4.08 0.7% Methane 3.69 3.24 -12.1% 4.13 12.1% 3.54 -4.0% 3.84 4.2% Ethylene 50.31 49.08 -2.4% 51.28 1.9% 50.10 -0.4% 50.49 0.4% Ethane 34.76 37.43 7.7% 32.35 -6.9% 35.42 1.9% 34.11 -1.9% Propylene 1.07 0.93 -12.5% 1.19 11.7% 1.01 -5.3% 1.12 5.5% 1,3-Butadiene 1.76 1.61 -8.8% 1.92 8.7% 1.73 -1.8% 1.80 1.7% + C5 4.18 3.60 -13.8% 4.75 13.8% 3.99 -4.4% 4.36 4.5% a AADmain - 7.6% 7.2% 2.6% 2.7% a Average absolute deviation of the main product yields: ethylene, propylene, hydrogen and methane

4.6.2.2 Pressures

In the steam cracking process, pressure plays a key role since it directly influences hydrocarbon partial pressure. Although in the simulated cases the coil inlet pressure (CIP) has always been used as an input, with the outlet pressure (COP) being an output of the model, it is common in industrial facilities to operate based on on the COP rather than the CIP. In this sense, a sensitivity analysis was performed on both CIP and COP. Note that to study COP’s effect in simulation results, CIP had to be removed as an input, having been changed to model output instead. First, in order to study the influence of the CIP, the profiles of some key process variables alongthe reactor length were obtained at different values of this variable. These results are plotted in Figure 4.21 and show that the coil inlet pressure, although has no influence on the process gas temperature, still significantly influences heat flux and, to some extent, product yields. The explanation to these observations lies on the fact that pressure increases gas density, thus decreasing velocity and leading to higher residence times. These are then responsible for higher con- versions and, consequently, higher product yields and higher heat fluxes. Also, because residence time increases, the higher the CIP the lower will be ethylene selectivity. Similar results are verified when COP is concerned and the same goes for the drawn conclusions, i.e, the higher the pressure the higher will be the residence time, being then responsible for increasing ethane conversion whilst diminishing ethylene selectivity. A quantitative analysis on these two parameters was carried out, having both CIP and COP been varied by +10% and -10% and the main simulation results compared with the base simulation results from the ethane industrial case. These results are summarised in Table 4.19. The conclusions of the sensitivity analysis on CIP and COP are that these also significantly affect simulation results, having a direct impact on residence time and, consequently, on conversion, selectivity

77 5.0 900 4.8 4.5 850 C)

CIP = 5.00 bara ° CIP = 5.00 bara 4.3 4.0 CIP = 4.75 bara 800 CIP = 4.75 bara 3.8 CIP = 4.50 bara CIP = 4.50 bara 3.5 CIP = 4.25 bara 750 CIP = 4.25 bara 3.3 CIP = 4.00 bara CIP = 4.00 bara

Pressure (bara) Pressure 3.0 CIP = 3.75 bara 700 CIP = 3.75 bara 2.8 CIP = 3.50 bara CIP = 3.50 bara 2.5 Process gas temperature ( 650 CIP = 3.25 bara CIP = 3.25 bara 2.3 CIP = 3.09 bara CIP = 3.09 bara 2.0 600 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Reactor length (m) Reactor length (m)

(a) Pressure profile along the reactor length at different coil inlet (b) Process gas temperature profile along the reactor length at pressures. different coil inlet pressures.

70.0 60 55 67.5 50 CIP = 5.00 bara CIP = 5.00 bara 65.0 45 CIP = 4.75 bara 40 CIP = 4.75 bara 62.5 CIP = 4.50 bara 35 CIP = 4.50 bara 60.0 CIP = 4.25 bara 30 CIP = 4.25 bara CIP = 4.00 bara 25 CIP = 4.00 bara 57.5 CIP = 3.75 bara 20 CIP = 3.75 bara External heat flux (kW) 55.0 CIP = 3.50 bara wt%) (dry yield Ethylene 15 CIP = 3.50 bara 10 52.5 CIP = 3.25 bara CIP = 3.25 bara 5 CIP = 3.05 bara CIP = 3.09 bara 50.0 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Reactor length (m) Reactor length (m)

(c) External heat flux profile along the reactor length at different (d) Ethylene yield profile along the reactor length at different coil inlet pressures. coil inlet pressures.

2.4 5.0

2.2 4.5 2.0 4.0 CIP = 5.00 bara CIP = 5.00 bara 1.8 3.5 1.6 CIP = 4.75 bara CIP = 4.75 bara 1.4 CIP = 4.50 bara 3.0 CIP = 4.50 bara 1.2 CIP = 4.25 bara 2.5 CIP = 4.25 bara

1.0 CIP = 4.00 bara 2.0 CIP = 4.00 bara 0.8 CIP = 3.75 bara 1.5 CIP = 3.75 bara

0.6 wt%) (dry yield Hydrogen Propylene yield (dry wt%) (dry yield Propylene CIP = 3.50 bara CIP = 3.50 bara 1.0 0.4 CIP = 3.25 bara CIP = 3.25 bara 0.2 0.5 CIP = 3.09 bara CIP = 3.09 bara 0.0 0.0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Reactor length (m) Reactor length (m)

(e) Propylene yield profile along the reactor length at different (f) Hydrogen yield profile along the reactor length at different coil inlet pressures. coil inlet pressures.

6.5 Conversion Selectivity 6.0 80.0 90.0 5.5 5.0 CIP = 5.00 bara 88.0 75.0 4.5 CIP = 4.75 bara 86.0 4.0 84.0 CIP = 4.50 bara 70.0 3.5 82.0 CIP = 4.25 bara 3.0 65.0 80.0 CIP = 4.00 bara 2.5 78.0 CIP = 3.75 bara

2.0 Selectivity (%) Conversion (%) 60.0 76.0 Methane yield (dry wt%) (dry yield Methane 1.5 CIP = 3.50 bara 74.0 1.0 CIP = 3.25 bara 55.0 0.5 72.0 CIP = 3.09 bara 0.0 50.0 70.0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 Reactor length (m) Coil inlet pressure (bara)

(g) Methane yield profile along the reactor length at different (h) Conversion (ethane) and ethylene selectivity dependency coil inlet pressures. on coil inlet pressure.

Figure 4.21: Analysis on the influence of coil inlet pressure (CIP) in some key process variables.

and product yields. Once again, propylene and methane yields are the most sensitive to pressure whilst ethylene and hydrogen are the least sensitive.

78 Table 4.19: Sensitivity analysis on pressures: coil inlet pressure and coil outlet pressure.

CIP COP +10% -10% +10% -10% Base case Result Dev. Result Dev. Result Dev. Result Dev. Residence time (s) 0.68 0.76 12.4% 0.59 -12.9% 0.72 5.7% 0.64 -6.5% COP/CIP (bara) 2.16/3.09 2.59 19.7% 1.68 -22.2% 3.23 4.6% 2.93 -5.1% Conversion (%) 65.24 67.56 3.6% 62.07 -4.9% 66.38 1.7% 63.77 -2.3% Selectivity (%) 82.85 81.02 -2.2% 84.97 2.6% 81.99 -1.0% 83.89 1.3% Yields (dry wt%): Hydrogen 4.05 4.15 2.4% 3.90 -3.8% 4.10 1.2% 3.98 -1.7% Methane 3.69 4.26 15.4% 3.06 -17.0% 3.95 7.2% 3.38 -8.4% Ethylene 50.3 50.92 1.2% 49.1 -2.4% 50.63 0.7% 49.80 -1.0% Ethane 34.76 32.44 -6.7% 37.93 9.1% 33.63 -3.3% 36.23 4.2% Propylene 1.07 1.29 20.7% 0.83 -22.1% 1.17 9.6% 0.95 -11.1% 1,3-Butadiene 1.76 1.88 6.4% 1.61 -8.6% 1.82 3.1% 1.69 -4.0% + C5 4.18 4.87 16.6% 3.38 -19.1% 4.50 7.8% 3.78 -9.4% a AADmain - 9.9% 11.3% 4.7% 5.5% a Average absolute deviation of the main product yields: ethylene, propylene, hydrogen and methane

However, contrary to what one would expect, the CIP has a much higher influence on results than COP does. This happens because of the influence of pressure in cracking reactions. In fact, pressure influences hydrocarbon concentrations and, therefore, reaction rates and, ultimately, product yields, although its effect is not as pronounced as the one of residence time. This not also just explains why a variation of just +-10% in CIP leads to a variation of +-20% in COP (and a variation of +-10% in COP leads to a variation of just +-5% in CIP) but also why simulation results are significantly more sensitive to pressure (namely CIP) than to flowrates, even thought the variation in residence time is of the same order of magnitude (around 11-12%).

4.6.2.3 Temperatures

Temperature, above all process variables, undoubtedly plays the most relevant role in generating the product distribution since it commands all reaction rates. In steam cracking furnaces, both inlet and outlet coil temperatures (CIT and COT, respectively), are specified, being the most important operating conditions for its operation. In this regard, a sensitivity analysis will be performed on both CIT and COT. First, in order to study the influence of the CIT, the profiles of some key process variables alongthe reactor length were obtained at different values of this variable. These results are plotted in Figure 4.22. Interesting conclusions may be withdrawn from the analysis on Figure 4.22. The first one, is that the process gas temperature profile is only affected in the first few metres of the reactor whilst theremaining length is kept unchanged. This was already expected in the sense that COT is being specified and in this initial section the heat supplied to the coils is solely used to heat the feed up to the cracking reaction temperature, above which the heat of consumed by reactions takes over. One may clearly observe this in the heat flux profile, where the initial heat flux is much lower for higher inlet temperatures. Relatively to product yields, conversion and selectivity, one does not observe a great impact of CIT

79 3.1 850 3.0 2.9

C) 800 ° 2.8 CIT = 725°C CIT = 725°C 2.7 CIT = 715°C 750 CIT = 715°C 2.6 CIT = 705°C CIT = 705°C 2.5 CIT = 695°C 700 CIT = 695°C 2.4 Pressure (bara) Pressure CIT = 685°C CIT = 685°C 2.3 CIT = 675°C CIT = 675°C 2.2 Process gas temperature ( 650 CIT = 665°C CIT = 665°C 2.1 2.0 600 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Reactor length (m) Reactor length (m)

(a) Pressure profile along the reactor length at different coil inlet (b) Process gas temperature profile along the reactor length at temperatures. different coil inlet temperatures.

80 50

45 75 40 70 CIT = 725°C 35 CIT = 725°C 65 CIT = 715°C 30 CIT = 715°C 60 CIT = 705°C 25 CIT = 705°C

CIT = 695°C 20 CIT = 695°C 55 CIT = 685°C 15 CIT = 685°C External heat flux (kW) 50 CIT = 675°C wt%) (dry yield Ethylene CIT = 675°C 10 45 CIT = 665°C CIT = 665°C 5

40 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Reactor length (m) Reactor length (m)

(c) External heat flux profile along the reactor length at different (d) Ethylene yield profile along the reactor length at different coil inlet temperatures. coil inlet temperatures.

5.0 1.4 4.5

1.2 4.0

3.5 1.0 CIT = 725°C CIT = 725°C CIT = 715°C 3.0 CIT = 715°C 0.8 CIT = 705°C 2.5 CIT = 705°C

0.6 CIT = 695°C 2.0 CIT = 695°C

CIT = 685°C 1.5 CIT = 685°C 0.4 Hydrogen yield (dry wt%) (dry yield Hydrogen Propylene yield (dry wt%) (dry yield Propylene CIT = 675°C CIT = 675°C 1.0 0.2 CIT = 665°C CIT = 665°C 0.5

0.0 0.0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Reactor length (m) Reactor length (m)

(e) Propylene yield profile along the reactor length at different (f) Hydrogen yield profile along the reactor length at different coil inlet temperatures. coil inlet temperatures.

5.5 Conversion Selectivity 5.0 66.0 83.0 4.5 65.8 82.9 4.0 CIT = 725°C 65.6 82.8 3.5 CIT = 715°C 65.4 82.7 3.0 65.2 82.6 CIT = 705°C 2.5 65.0 82.5 CIT = 695°C 2.0 64.8 82.4 CIT = 685°C Selectivity (%) 1.5 Conversion (%) 64.6 82.3 Methane yield (dry wt%) (dry yield Methane CIT = 675°C 1.0 64.4 82.2 CIT = 665°C 0.5 64.2 82.1 0.0 64.0 82.0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 665 675 685 695 705 715 725 Reactor length (m) Coil inlet temperature (°C)

(g) Methane yield profile along the reactor length at different (h) Conversion (ethane) and ethylene selectivity dependency coil inlet temperatures. on coil inlet temperature.

Figure 4.22: Analysis on the influence of coil inlet temperature (CIT) in some key process variables.

on these results. In fact, since the process gas profile is not profoundly affected, reaction rates willnot vary much and therefore the formation of each product is not expect to change significantly.

80 After examining the influence of the CIT, the same study will take place regarding the COT, having the profiles of key process variables been plotted in Figure 4.23.

3.1 900 3.0 2.9 850 C) ° 2.8 COT = 875°C 800 COT = 875°C 2.7 COT = 865°C COT = 865°C 2.6 COT = 855°C 750 COT = 855°C 2.5 COT = 845°C COT = 845°C 2.4 Pressure (bara) Pressure COT = 835°C 700 COT = 835°C 2.3 COT = 825°C COT = 825°C 2.2 Process gas temperature ( 650 COT = 815°C COT = 815°C 2.1 2.0 600 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Reactor length (m) Reactor length (m)

(a) Pressure profile along the reactor length at different coil out- (b) Process gas temperature profile along the reactor length at let temperatures. different coil outlet temperatures.

80 60 55 75 50 70 45 COT = 875°C 40 COT = 875°C 65 COT = 865°C 35 COT = 865°C 60 COT = 855°C 30 COT = 855°C COT = 845°C 25 COT = 845°C 55 COT = 835°C 20 COT = 835°C External heat flux (kW) 50 COT = 825°C wt%) (dry yield Ethylene 15 COT = 825°C 10 45 COT = 815°C COT = 815°C 5 40 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Reactor length (m) Reactor length (m)

(c) External heat flux profile along the reactor length at different (d) Ethylene yield profile along the reactor length at different coil outlet temperatures. coil outlet temperatures.

5.0 1.4 4.5

1.2 4.0

3.5 1.0 COT = 875°C COT = 875°C COT = 865°C 3.0 COT = 865°C 0.8 COT = 855°C 2.5 COT = 855°C

0.6 COT = 845°C 2.0 COT = 845°C

COT = 835°C 1.5 COT = 835°C 0.4 Hydrogen yield (dry wt%) (dry yield Hydrogen Propylene yield (dry wt%) (dry yield Propylene COT = 825°C COT = 825°C 1.0 0.2 COT = 815°C COT = 815°C 0.5

0.0 0.0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Reactor length (m) Reactor length (m)

(e) Propylene yield profile along the reactor length at different (f) Hydrogen yield profile along the reactor length at different coil outlet temperatures. coil outlet temperatures.

5.5 Conversion Selectivity 5.0 80.0 4.5 89.0 4.0 75.0 COT = 875°C 87.0 3.5 COT = 865°C 70.0 85.0 3.0 COT = 855°C 83.0 2.5 65.0 COT = 845°C 2.0 81.0 COT = 835°C Selectivity (%) 1.5 Conversion (%) 60.0 Methane yield (dry wt%) (dry yield Methane COT = 825°C 79.0 1.0 55.0 COT = 815°C 77.0 0.5 0.0 50.0 75.0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 815 825 835 845 855 865 875 Reactor length (m) Coil outlet temperature (°C)

(g) Methane yield profile along the reactor length at different (h) Conversion (ethane) and ethylene selectivity dependency coil outlet temperatures. on coil outlet temperature.

Figure 4.23: Analysis on the influence of coil outlet temperature (COT) in some key process variables.

81 Figure 4.23 shows a much higher influence of COT on results than CIT, being the process gas temperature profile responsible for that. As a matter of fact, changing COT changes the temperature profile in such a way that the feed spends a much longer time at a higher/lower temperatures comparing to the base case. This is then responsible for the higher impact not only on the heat flux – as more heat is required for higher COTs – but also on ethane conversion and product yields – as higher temperatures induce higher reaction rates. Furthermore, higher coil outlet temperatures seem to favour secondary products formation over ethylene since its selectivity decreases with increasing COTs. Also propylene formation seems to be unfavoured by higher temperatures as a maximum in propylene yield is observed at a COT of 875 ◦C. Finally, a quantitative analysis on these two parameters was carried out, having both CIT and COT been varied by +10% and -10% (relatively to the values in degrees Celsius) and the main simulation results compared with the base simulation results from the ethane industrial case. These results are summarised in Table 4.20.

Table 4.20: Sensitivity analysis on temperatures: coil inlet temperature and coil outlet temperature.

CIT COT +10% -10% +10% -10% Base case Result Dev. Result Dev. Result Dev. Result Dev. Residence time (s) 0.68 0.67 -1.5% 0.69 1.5% 0.64 -5.6% 0.73 7.6% COP (bara) 2.2 2.2 -0.4% 2.2 0.4% 2.1 -4.0% 2.3 4.5% Conversion (%) 65.24 65.75 0.8% 64.78 -0.7% 80.92 24.0% 45.41 -30.4% Selectivity (%) 82.85 82.59 -0.3% 83.09 0.3% 77.66 -6.3% 87.75 5.9% Yields (dry wt%): Hydrogen 4.05 4.08 0.6% 4.02 -0.6% 4.91 21.3% 2.88 -28.8% Methane 3.69 3.78 2.4% 3.61 -2.1% 6.16 67.0% 1.74 -52.8% Ethylene 50.3 50.54 0.5% 50.09 -0.4% 58.38 16.0% 37.12 -26.2% Ethane 34.76 34.25 -1.5% 35.22 1.3% 19.08 -45.1% 54.59 57.1% Propylene 1.07 1.08 1.6% 1.05 -1.5% 1.09 2.6% 0.78 -26.6% 1,3-Butadiene 1.76 1.80 2.0% 1.73 -1.8% 3.27 85.2% 0.80 -54.6% + C5 4.18 4.29 2.6% 4.08 -2.3% 6.94 66.1% 1.90 -54.4% a AADmain - 1.3% 1.2% 26.8% 33.6% a Average absolute deviation of the main product yields: ethylene, propylene, hydrogen and methane

As it is clearly seen in Table 4.20, and could have been foreseen at this point, CIT has little influence on simulation results whilst COT has a profound impact on the vast majority of the results owing to reaction rates. Residence time and COP,on the other hand, although dependent on temperature through gas phase density (ideal gas law), are less sensitive to temperature changes. Selectivity also does not seem to be as sensitive to temperature as conversion and, in this sense, some benefits may arise from using higher COTs in spite of higher energy consumption.

4.6.3 Adiabatic section

As mentioned previously in section 4.1.4, it has been assumed a reasonable adiabatic section length of 1-2 m in every simulated case in order to account for the section of tube connecting the radiant coil

82 and the transfer-line exchanger. In order to verify to what extent does the inclusion of this adiabatic section affect simulation results, its length, which in the base case assumed the value of 1 m, will be varied by +50% (1.5 m) and by -50% (0.5 m), having the results been summarised in Table 4.21. The results prove that the adiabatic section only plays a minor role in the product distribution and therefore its presence does not have a significant impact on simulation results. The slight increase observed in conversion is a result of cracking reactions still proceeding inside this tube although no heat is supplied to the mixture.

Table 4.21: Sensitivity analysis on adiabatic section length.

Adiabatic section length +50% -50% Base case Result Dev. Result Dev. COP (bara) 2.16 2.16 -0.3% 2.17 0.3% Conversion (%) 65.24 65.52 0.4% 64.92 -0.5% Selectivity (%) 82.85 82.85 0.0% 82.85 -0.0% Yields (dry wt%): Hydrogen 4.05 4.07 0.4% 4.03 -0.5% Methane 3.69 3.73 1.0% 3.65 -1.1% Ethylene 50.31 50.47 0.3% 50.12 -0.4% Ethane 34.76 34.48 -0.8% 35.08 0.9% Propylene 1.07 1.07 0.3% 1.06 -0.3% 1,3-Butadiene 1.76 1.79 1.1% 1.74 -1.3% + C5 4.18 4.22 1.1% 4.13 -1.2% a AADmain - 0.5% 0.6% a Average absolute deviation of the main product yields: ethylene, propylene, hydrogen and methane

4.6.4 Kinetic parameters

Finally, in order to conclude this sensitivity analysis chapter, the influence of kinetic parameters on simulation results will be studied. In fact, the kinetic schemes used in these kind of mathematical models are usually subjected to a parameter tuning using industrial or experimental data. In particular, activation energy is often chosen over the pre-exponential factor in parameter fitting due to its exponential impact on reaction constants (Eq. 4.15). In this sense, only the activation energies will be considered in the current analysis. However, not all the reactions have the same influence on simulation results and, as a consequence, not all of them are used in the tuning process, being considered only the most relevant ones. As it has been mentioned in the previous section 4.4.2, Joo, Park and Lee [19] conducted a parameter optimisation of Joo’s kinetic scheme in order to better fit plant data of a specific industrial case andthey too had to determine the most relevant reactions. These reactions, which directly affect both ethylene and propylene formation rates, have been presented in Table 4.12. Fortunately, these reactions were also present in Sundaram and Froment’s radical kinetic scheme, corresponding to reaction ID numbers 62, 64 and 65 [17], respectively, and, therefore, will be the ones used in the current analysis.

83 The activation energies of each of these three reactions were varied by +10% and -10%, having simulation results been compared with the base simulation results from the ethane industrial case (Table 4.22). It is visible from Table 4.22 that reaction 62 clearly has a considerable impact on product distribution, in contrast with reactions 64 and 65. As a matter of fact, in the base case, the rate of reaction 62 is more than two orders of magnitude higher relatively to the rates of the other two – hence, any change concerning it will have a much higher influence on results. However, the most surprising result is that although reaction 62 affects directly ethylene yield, a much higher impact is observed in methane and propylene yields. It is believed that this reaction directly competes alongside with other reactions which are responsible for methane and propylene formation, thus any small change in reaction 62 rapidly allows these rival reactions to take over. In fact, this reaction has such an impact on the process that temperature profile and energy consumption are considerably changed. Concerning the other reactions, it seems reactions 64 and 65 have little influence on results, with exception of propylene yield which suffers a considerable impact. It is interesting to note that with increasing activation energy of reaction 64, one should expect a meaningful decrease in ethylene pro- duction but a relevant increase in propylene is observed instead. Once again, it is strongly believed that competing reactions, such as reaction 65, may take advantage of this activation energy increase, affecting other product yields. These results, although specific to the used kinetic scheme, demonstrate the significant impactki- netic parameters of some reactions may have upon the entire furnace performance.

84 Table 4.22: Sensitivity analysis on activation energies: reactions 62, 64 and 65 [17].

Activation energy of reaction 62 Activation energy of reaction 64 Activation energy of reaction 65 +10% -10% +10% -10% +10% -10% Base case Result Dev. Result Dev. Result Dev. Result Dev. Result Dev. Result Dev. Residence time (s) 0.68 0.69 2.2% 0.68 -0.6% 0.68 0.0% 0.68 0.0% 0.68 0.0% 0.68 0.0% COP (bara) 2.16 2.20 1.4% 2.16 -0.4% 2.16 0.0% 2.16 0.0% 2.16 0.0% 2.16 0.0% Conversion (%) 65.24 65.08 -0.3% 65.33 0.1% 65.26 0.0% 65.24 0.0% 65.24 0.0% 65.26 0.0% Selectivity (%) 82.85 67.60 -18.4% 87.01 5.0% 82.76 -0.1% 82.87 0.0% 82.87 0.0% 82.73 -0.1% 85 Yields (dry wt%): Hydrogen 4.05 3.36 -17.0% 4.25 4.8% 4.05 0.1% 4.05 0.0% 4.05 0.0% 4.06 0.1% Methane 3.69 8.47 129.6% 2.30 -37.8% 3.66 -0.8% 3.70 0.2% 3.70 0.2% 3.65 -1.1% Ethylene 50.31 40.91 -18.7% 52.92 5.2% 50.26 -0.1% 50.32 0.0% 50.32 0.0% 50.24 -0.1% Ethane 34.76 34.93 0.5% 34.67 -0.3% 34.75 0.0% 34.76 0.0% 34.76 0.0% 34.74 0.0% Propylene 1.07 4.06 280.5% 0.19 -82.1% 1.15 8.0% 1.05 -1.9% 1.04 -2.1% 1.18 10.9% 1,3-Butadiene 1.76 1.65 -6.7% 1.80 2.2% 1.76 -0.2% 1.77 0.0% 1.77 0.1% 1.76 -0.3% + C5 4.18 4.68 12.0% 3.84 -8.0% 4.18 0.1% 4.18 0.0% 4.18 0.0% 4.18 0.0% a AADmain - 111.5% 32.5% 2.3% 0.5% 0.6% 3.1%

a Average absolute deviation of the main product yields: ethylene, propylene, hydrogen and methane 86 Chapter 5

Feed characterisation

5.1 Introduction

The petrochemical industry is continuously looking for improvements on the performance of its facil- ities and, in this regard, mathematical models play a fundamental role. Once a model is fully designed, simulations can easily take place and results obtained just as easily.

The kinetic schemes used in such models, like the one described in the previous section4, however, require a detailed molecular feedstock composition, something that is not usually straightforward to obtain when heavier, liquid feedstocks, such as naphtha, are concerned.

In fact, although during the past decade several analytical techniques, such as GC-MS and HPLC, have been developed and improved, there are several drawbacks to these methods, namely the fact that these are often error-prone and time-consuming. Furthermore, petroleum fractions are usually characterised by easily-obtainable average properties of the mixture, the so-called commercial indices, instead of the more time-consuming analytical techniques [20].

In this regard, the need arises for mathematical models capable of converting a set of commercial indices into a detailed molecular composition, which then can be integrated and used in furnace models.

Common commercial indices are the average molecular weight, specific density, H/C ratio, carbon and hydrogen content, (n-)paraffin, iso-paraffin, olefin, naphthenes and aromatics (PIONA) weight frac- tions and a set of ASTM boiling points (Figure 5.1).

Literature-wise, in recent years a higher attention has been brought to these composition-predicting models with several papers being published on the matter [20, 21, 22]. Very briefly, the feed charac- terisation method is faced as a non-convex optimisation problem based on Shannon’s entropy criterion and allows one to generate the molecular composition of a naphtha cut that meets all the boundary conditions (or constraints) set by the industrially available commercial indices [20].

Shannon’s entropy theory is widely applied in all sorts of engineering fields, ranging from quantum chemistry over civil engineering to hydrodynamics. Applied to feed characterisation problems, Shan- non’s entropy is described by equation 5.1[20]:

87 Figure 5.1: Properties of a naphtha feedstock [2]

N X S(xi) = − xi · ln xi (5.1) i=1

in which xi represents the molar fractions of the components in the library. Shannon’s entropy is a measure of the homogeneity of the distribution of molar fractions and it is stated that the most informative state is found at its maximum value, thus creating a more uniform distribution. In this chapter, a feed characterisation model will be developed in such a way that in simulation mode can trivially generate commercial indices from given molecular compositions. Then, once the model has been developed, a parameter estimation will take place to determine the molecular composition that is able to reproduce reported commercial indices from analytical data.

5.2 Model equations

In terms of modelling, the vast majority of the most common commercial indices is quite straightfor- ward to obtain, either coming directly from physical properties packages, as specific density, or resulting from extremely simple calculations involving weight fractions and the elemental constitution of hydrocar- bons, as PIONA analysis and H/C ratio. As a matter of fact, the only exceptions are the ASTM D86 boiling points, which require a mathemati- cal model to describe the standard test method. Modelling the ASTM D86 method, briefly outlined in the following section 5.2.1, therefore poses the most challenging part of this feed characterisation model.

5.2.1 ASTM D86 standard test method

Ever since the petroleum industry existed, simple batch distillation has been used as a basic test method to determine the boiling range of petroleum products. The ASTM D86 is one of the oldest standard test methods, consisting of the atmospheric, one-theoretical-plate fractionation of petroleum

88 products using a laboratory batch distillation unit to determine quantitatively their boiling range charac- teristics [80]. The basic components of the distillation unit (Figure 5.2) are the distillation flask, the condenser and associated cooling bath, the heat source and the receiving cylinder to collect the distillate. A sam- ple is then distilled and systematic temperature readings and volume percentages of condensate are performed, depending on one’s needs [80].

Figure 5.2: ASTM D86 experiment schematic [80].

This experiment is accurately modelled by a single component mass balance (Eq. 5.2) to the distilling flask and by two equilibrium relations corresponding to vapour phase compositions and temperature (Eqs. 5.3a and 5.3b), which are provided by the physical properties package.

dM · w 0 = F · w + L,i (5.2) V,i dt

wV,i = f(wL,i) (5.3a)

T = f(wL,i) (5.3b)

The volume percent recovered is calculated based on the volume difference relatively to the initial volume of the mixture in the distilling flask (a given reference temperature is used for this calculation).

5.3 Model considerations

5.3.1 Component library

The selection of a molecular library, although may seem trivial, is of the utmost importance for the success of a feed characterisation model, since a library containing components that are not represen- tative for a given feedstock hardly can result in an accurate characterisation.

89 The molecular library determines the number of possible compositions that satisfy all the boundary conditions, and thus affects the model’s predictions. If an important component is not included in the library, the composition obtained via the method can never be representative of the mixture [20]. In the present work solely naphtha feedstocks were considered and, in this sense, the 37-component library suggested by Van Geem [20] (Table 5.1) was used. It is noteworthy that these components were selected from 30 reference naphthas with widely varying characteristics.

Table 5.1: Components included in the library of molecules for naphtha feedstock characterisation [20].

C3 Propyne, 1,2-propadiene, propene, n-propane C4 n-butane 2,3-Di-methyl butane, 2-methyl pentane, 3-methyl C5 2-methyl butane, n-pentane, cyclo pentane C6 pentane, n-hexane, methyl cyclo pentane, cyclo hexane, benzene 2,3-Di-methyl pentane, 2-methyl hexane, 3-methyl 2-Methyl heptane, 3-methyl heptane, n-octane, C7 hexane, n-heptane, methyl cyclo hexane, di-methyl C8 di-methyl cyclo hexane, tri-methyl cyclo pentane, cyclo pentane, toluene ethylbenzene, xylene 2-Methyl octane, 3-methyl octane, n-nonane, tri- C9 C10 n-Decane methyl cyclohexane, tri-methyl benzene C11 n-Undecane

5.3.2 Thermodynamic models

The ASTM D86 boiling curve is intimately related to its hydrocarbon composition and properties and because of that plays undoubtedly a key role in feed characterisation. As in all unit operations involving vapour-liquid equilibrium, the accurate modelling of the ASTM distillation highly depends on the thermodynamic model in use. In this chapter, two physical properties packages, MultiflashTM and gSAFT® , were considered, hav- ing the corresponding thermodynamic predictions been tested against experimental data. Regarding MultiflashTM, the Redlich-Kwong-Soave (RKS), Redlich-Kwong-Soave Advanced (RKSA) and Peng- Robinson Advanced (PR78A) cubic equations of state were taken into account. The activity models NRTL-RK and UNIQUAC-RK were also considered. The selection of the most appropriate thermody- namic model, however, will be presented in the following results chapter. Finally, it is noteworthy that since some group interaction parameters from gSAFT® were initially missing or were not fully tuned, their estimation/optimisation had to be carried out using vapour-pressure and binary VLE data (see AppendixC).

5.4 Results

Having the model been developed, it is now possible to evaluate its performance using experimental data. Finding analytical data from industrial naphtha feedstocks is not easy due to confidentiality issues that impede the disclosure of such information. Fortunately, a report containing compositional data for test samples included in the category of gasoline blending streams was available [1].

90 Since naphtha feedstocks for steam cracking are usually characterised by having little to no olefins and a low aromatic content, from all the sample reports presented, the one belonging to a sweetened petroleum naphtha (Figs. D.1-D.3 in Appendix) seems the most convenient as all the remaining either apply to catalytic cracked or reformed naphthas. This analytical report possessed not only the commer- cial indices but also the corresponding detailed hydrocarbon analysis, thus all the information required to validate the developed model.

5.4.1 Selection of thermodynamic model

Firstly, the selection of the most appropriate thermodynamic model was carried out. Using the above- mentioned molecular composition, the commercial indices produced by the model using different ther- modynamic models were compared against the experimental ones from the naphtha sample. This comparison is summarised in Figure 5.3 and Table 5.2.

120

110

100

90

C) ° 80

70

Temperature( 60

50

40

30 0 10 20 30 40 50 60 70 80 90 100 Volume percent recovered

Experimental Multiflash - RKS Multiflash - RKSA Multiflash - PR78A Multiflash - NRTL-RK Multilfash - UNIQUAC-RK gSAFT

Figure 5.3: ASTM D86 boiling curve using different thermodynamic models.

Table 5.2: Comparison between results from different thermodynamic models and experimental data.

MultiflashTM gSAFT® Exp. RKS RKSA PR78A NRTL-RK UNIQUAC-RK Density at 15°C (kg/m3) 678.2 622.8 681.8 681.6 680.6 680.6 683.9 Molecular Weight (g/mol) 81 80.6 80.6 80.6 80.6 80.6 80.6 PIONA (vol%) Paraffins 72.1 77.4 77.2 77.2 77.1 77.1 77.5 Olefins 0.1 0.0 0.0 0.0 0.0 0.0 0.0 Naphthenes 20.9 18.2 18.5 18.5 18.4 18.4 18.3 Aromatics 6.9 4.5 4.5 4.5 4.4 4.4 4.5 AAD - 12.0% 11.3% 11.3% 12.3% 11.9% 12.9%

Concerning the results in Table 5.2, one may conclude that MultiflashTM’s RKSA and PR78A cubic EoSs provide the most accurate results. This was already expected in the sense that these are not only simple, robust and efficient but specially appropriate for refinery and petrochemical applications [68]. The thermodynamic model selected was the Redlich-Kwong-Soave Advanced (RKSA) equation of

91 state.

5.4.2 Model validation

As previously mentioned in section 3.3.2 the validation of the feed model was performed using the powerful gPROMS® ’ Parameter Estimation tool. This entity uses a set of measurements (commercial in- dices) and estimates a defined set of parameters (feed component mass fractions) so that the maximum likelihood objective function, described by Equation 3.1, is maximised. However, because there are only 19 commercial indices compared to the entire library of 38 com- ponents, in order to avoid over-parametrising the estimation problem, the component library had to be further reduced to the 19 most meaningful components (Table 5.3).

Table 5.3: Reduced component list used in the parameter estimation.

C4 n-butane C5 2-methyl butane, n-pentane, cyclo pentane 2,3-Di-methyl butane, 2-methyl pentane, 3-methyl 2,3-Di-methyl pentane, 2-methyl hexane, 3-methyl C6 pentane, n-hexane, methyl cyclo pentane, cyclo C7 hexane, n-heptane, methyl cyclo hexane, di-methyl hexane, benzene cyclo pentane, toluene C8 n-octane

In addition to the commercial indices, Shannon’s entropy has also been included in the Parameter Estimation entity so that one can verify whether or not its presence improves results. The parameter estimation results without and with the inclusion of Shannon’s entropy are summarised in Figure 5.4 and Tables 5.4 and 5.5.

130

110

C) ° 90

70 Temperature(

50

30 0 10 20 30 40 50 60 70 80 90 100 Volume percent recovered

Experimental PE w/o Shannon entropy PE w/ Shannon entropy

Figure 5.4: ASTM D86 boiling curve: experimental data and parameter estimation results.

Firstly, regarding the results without taking into account Shannon’s entropy, one may verify that al- though the commercial indices are well met, with an AAD of 2.9%, the resulting feed composition is in profound disagreement with the experimental one, with an AAD of 95%. In fact, many components’ fractions were estimated to be zero, some of them corresponding to meaningful components in the real naphtha sample. On the other hand, with the inclusion of Shannon’s entropy in the parameter estimation, the weight fractions seem to be much better predicted, with an AAD of 38 % even though the agreement with

92 Table 5.4: Comparison between parameter estimation results and experimental data: commercial indices.

w/o Shannon w/ Shannon entropy entropy Commercial index Exp. [1] Result Dev. Result Dev. Density at 15°C (kg/m3) 678.2 681.1 0% 683.2 1% Molecular Weight (g/mol) 81 80.6 0% 80.4 -1% PONA (vol%) Paraffins 72.1 74.1 3% 75.1 4% Olefins 0.1 0.0 - 0.0- Naphthenes 20.9 20.5 -2% 20.1 -4% Aromatics 6.9 5.7 -18% 5.0 -28% AAD - 2.9% 3.6%

Table 5.5: Comparison between parameter estimation results and experimental data: molecular compositions.

w/o Shannon entropy w/Shannon entropy Compositions (wt%) Exp. [1] Result Dev. Result Dev. 2,3-dimethylbutane 1.80 0.00 - 11.41 - 2,3-dimethylpentane 0.76 0.00 - 0.35 - 2-methylbutane 11.04 10.01 9% 10.28 7% 2-methylhexane 1.06 0.00 - 1.60 - 2-methylpentane 11.56 39.20 239% 16.40 42% 3-methylhexane 1.20 0.00 - 0.71 - 3-methylpentane 7.92 0.00 100% 6.33 20% benzene 5.12 3.52 31% 5.40 6% dimethylcyclopentane 2.58 0.00 - 0.96 - cyclohexane 5.04 0.00 100% 1.33 74% cyclopentane 2.63 0.00 - 6.10 - methylcyclohexane 1.06 0.00 - 1.01 - methylcyclopentane 9.33 22.64 143% 12.82 37% n-butane 1.13 5.48 - 5.54 - n-heptane 1.25 0.00 - 0.24 - n-hexane 15.76 0.00 100% 5.80 63% n-octane 0.16 3.14 - 3.36 - n-pentane 19.73 12.24 38% 9.32 53% toluene 0.63 3.77 - 1.02 - AAD - 95% 38% experimental commercial indices is slightly worsened. The explanation to this lies in the fact that, as mentioned in the previous section 5.1, Shannon’s entropy maximisation leads to a more uniform (thus realistic) distribution of the component’s compositions. The estimated compositions, however, are still significantly off in comparison to the experimental ones.

One can therefore conclude that the model, as it is, does not suffice in obtaining reasonable naphtha compositions. As a matter of fact, there may exist several compositions which may lead to the same commercial indices. To overcome such multiplicity of solutions the approach followed in this work would probably have to be supplemented by a considerable amount of a priori knowledge, for instance, typical naphtha compositions which would provide tighter bounds on the estimated parameters.

Furthermore, the estimation could be tailored to a given refinery if historical analytical data from

93 produced naphthas exists. Historical data could be incorporated into the parameter estimation so that a more likely, accurate characterisation could be performed. However, if a refinery changes significantly its crude feedstock, which is often the case, the naphtha compositions would vary considerably and, in this regard, no benefit would exist from adding historical data.

94 Chapter 6

Conclusions

In this work a mathematical model of a steam cracking furnace was used and several literature molecular and radical kinetics were implemented and validated against plant data from industrial ethane, propane and naphtha cracking furnaces. Relatively to gaseous feedstocks, namely ethane and propane, it was concluded that the imple- mented molecular kinetics from Sundaram and Froment failed at predicting the main product yields whilst the radical ones seemed to accurate predict industrial data, thus supporting the statement that radical schemes are more predictive than molecular ones. In addition, the results from the ethane crack- ing case showed a better agreement with plant data relatively to the propane cracking case. Naphtha-wise, the radical kinetics from Towfighi and Karimzadeh and Joo were implemented. How- ever, the simulation results showed a quite profound disagreement with industrial data, with special + emphasis on the C5 non-aromatic fraction yield which was being greatly over-predicted. It was found out that neither of the kinetic schemes took into consideration the cracking of some meaningful heavier components of the naphtha feed, such as cyclopentane and cyclohexane. A few reactions regarding the free-radical pyrolysis of these two components were added to both kinetic schemes, having the simulation results been slightly improved but not to the point at which they be- come reasonable. The conclusion on the implemented kinetics for naphtha cracking was that most probably these are confidential property, therefore not being of the authors’ interest to make all the information regarding these schemes publicly available. The fact that results remained in disagreement with industrial data even more so when cyclopentane and cyclohexane cracking reactions were added, arises the suspicion that kinetic parameters disclosed may not be fully tuned or even correct due to proprietary reasons. The ethane industrial case was used to study alternative diluents which could replace steam in the steam cracking process. Two effects were studied: molecular weight and heat capacity. It was concluded that molecular weight plays the major role as heavier diluents lead to lower molar diluent ratios, lower velocities, hence higher residence times and consequently lower selectivities, COTs and energy consumption. Heat capacity only has a significant impact in energy consumption. Another conclusion was that if one is not willing to further increase the coil outlet temperature, there may actually

95 be no difference between diluents. Helium, however, posed the best alternative if no COT constraints exist, as it leads to high ethylene selectivities and low energy consumption.

Furthermore, a sensitivity analysis was conducted in order to analyse the influence of some key variables/parameters in the model’s predictions. Relatively to the fluid properties, density showed some impact on results whilst viscosity and thermal conductivity’s influence seemed to be rather negligible. Operating conditions-wise, it was found out that COT had the highest impact, since it profoundly changes the temperature profile which severely affects reaction rates, followed by CIP,hydrocarbon flowrate, COP, SOR and CIT. An analysis on the assumed length for the adiabatic section was also conducted and its influence was deemed to be somewhat meaningless. At last, the influence of kinetic parameters was studied through the activation energies of three relevant reactions, having been concluded that some reactions may have quite an impact on simulation results.

Finally, a feed characterisation model was developed in order to overcome the fact that naphtha feeds are not usually characterised by a detailed hydrocarbon analysis, which is required for kinetics imple- mentation and furnace simulation, but instead by easily-obtainable average properties of the mixture, the so-called commercial indices. A parameter estimation was set in order to fit simulated commercial indices to experimental ones by varying the composition of the naphtha feed.

The results showed that the inclusion of Shannon’s entropy criterion in the parameter estimation helps in obtaining a more uniform, realistic composition. Although the commercial indices were met, the estimated compositions were quite unsatisfactory. It has been concluded that most likely there is more than one composition able to match the same commercial indices and, in this sense, the solution to obtain more accurate results would be the inclusion of a priori knowledge in the parameter estimation. For instance, the analysis of several naphtha samples with widely-varying properties would provide tighter bounds for the parameters to be estimated.

At last, the estimation could be tailored to a given refinery if historical analytical data from produced naphthas exists. Historical data could be incorporated into the parameter estimation so that a more likely, accurate characterisation could be performed. However, if a refinery changes significantly its crude feedstock, which is often the case, the naphtha compositions would vary considerably and, in this regard, no benefit would exist from adding historical data.

6.1 Achievements

The present work focused on different areas of the steam cracking process, such as implementation of various molecular and radical kinetics for gaseous feedstocks and naphtha, naphtha feed characteri- sation and optimisation studies on cracking furnace operation.

A much better understanding has been brought on various kinetic schemes and feed characterisation approaches in literature and the challenges involved in applying them for predicting real plant operation. The optimisation studies on alternative diluents have brought lot of insights into the trade-offs associated with the selection of diluents in the operational optimisation of cracking furnaces.

96 6.2 Future work

Relatively to radical kinetics, the implemented kinetics could be further tuned using sets of plant/ experimental data and even extended to account for lacking components. In addition, the approach presented in section 2.3.3, which is followed by steam cracking commercial softwares, such as SPYRO and CRACKSIM, should also be explored. Feed characterisation-wise, the approach should be supplemented using substantial amounts of data regarding naphthas with widely-varying characteristics so that tighter bounds could be provided to the components’ composition. Furthermore, the incorporation of historical data, if available, in the parameter estimation is also recommended.

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106 Appendix A

Thermodynamic properties

A.1 Thermodynamic models comparison

MultiflashTM, gPROMS® ’ standard physical property package, was used to provide the necessary thermodynamic and transport properties for the steam cracking furnace modelling. DIPPR (AIChE) was used as the component databank and the Redlich-Kwong-Soave (RKS) equation of state (EoS) was employed. Thermodynamics play a crucial role in a model’s simulation results and, in that sense, having different properties may produce substantially different outcomes, even if the model equations remain the same. Enthalpic calculations are crucial to steam cracking modelling since they influence temperature which, in turn, directly affects reaction rates. In this regard, the standard heats of formation and specific heat capacities predicted by MultiflashTM for some of the major components are compared against the ones from NIST Chemistry WebBook database [81] and from the thermodynamic database of CHEMKIN [82, 83], a software tool used world- wide in chemical processing to solve complex chemical kinetics problems. The comparison is sum- marised in Table A.1. Table A.1 shows some small differences in the enthalpies of formation between CHEMKIN and MultiflashTM predictions, with the maximum relative deviation (observed for 1,3-Butadiene) being approx- imately 8%. Nevertheless, both predictions show a reasonable agreement and are usually in accordance with or within the bounds withdrawn from NIST. Heat capacity-wise, CHEMKIN and MultiflashTM’s predictions are substantially more similar in com- parison to what has been observed in terms of heats of formation. Moreover, the values obtained using MultiflashTM show an even better agreement with the ones from NIST than CHEMKIN’s predictions do. In conclusion, in spite of the small disparities observed in terms of enthalpy of formation of some minor components, one should expect the mixture properties not to change significantly and, therefore, these should not be blamed for substantial discrepancies in simulation results.

107 Table A.1: Comparison of standard heats of formation and specific heat capacities amongst different sources.

0 -1 1100K -1 -1 ∆f H (kJmol ) Cp (Jmol K ) Species NIST CHEMKIN MultiflashTM NIST CHEMKIN MultiflashTM Water -241.83 -241.84 -241.81 42.52 42.64 42.55 Hydrogen 0.00 0.00 0.00 30.58 30.63 30.61 Methane -74.87 to -73.40 -74.89 -74.52 77.92 75.60 76.83 Ethylene 52.47 52.47 52.51 98.00 97.97 98.84 Ethane -84.67 to -83.80 -83.68 -83.82 128.55 127.86 128.69 Propylene 20.41 20.42 20.23 150.83 150.05 151.48 Propane -104.7 to -103.8 -103.76 -104.68 182.67 181.69 182.74 1,3-Butadiene 108.8 to 111.9 118.53 109.24 179.36 178.04 179.70 n-Butane -127.1 to -125.6 -128.20 -125.79 237.48 242.63 237.37 i-Butane -135.6 to -134.2 -133.97 -134.99 238.49 239.64 238.56 n-Pentane -147.1 to -146.4 -146.44 -146.76 293.72 292.00 294.35 i-Pentane -154.5 to -153.7 – -153.70 299.57 – 300.40

108 Appendix B

Kinetics

B.1 Molecular kinetics

In 1977, Sundaram and Froment [13] published a molecular kinetic model for the cracking of ethane, propane and their mixtures. The reactions for each case and their corresponding kinetic parameters are summarised in Table B.1.

Table B.1: Molecular kinetic scheme from Sundaram and Froment [13].

Ethane Propane Ethane+Propane No. Reaction log(Aa) Eab log(Aa) Eab log(Aa) Eab −−⇀ 1 C3H6 ↽−− C2H2 + CH4 8.99 36.92 11.58 59.39 11.58 59.39 −−⇀ 2 C2H6 ↽−− C2H4 + H2 13.67 65.20 14.74 60.01 13.67 65.20 3 C2H4 + C2H6 −−→ C3H6 + CH4 13.85 60.43 - - 13.85 60.43 4 2 C2H6 −−→ C3H8 + CH4 11.59 65.25 - - - - 5 C2H2 + C2H4 −−→ C4H6 12.01 41.26 - - - -

6 C3H8 −−→ C2H4 + CH4 - - 10.67 50.60 10.67 50.60 −−⇀ 7 C3H8 ↽−− C3H6 + H2 - - 10.77 51.29 10.77 51.29 8 C3H8 + C2H4 −−→ C2H6 + C3H6 - - 13.40 59.06 13.40 59.06 9 C3H6 −−→ 3 C2H4 - - 11.18 55.80 11.18 55.80 10 2 C3H6 −−→ 0.5 C6 + 3 CH4 - 9.15 45.50 9.15 45.50 11 C3H6 + C2H6 −−→ C4H8 + CH4 - - 14.00 60.01 14.00 60.01 12 C2H4 + C2H2 −−→ C4H6 - - 12.01 41.26 12.01 41.26 a units: s-1 or Lmol-1s-1. b units: kcal/mol.

109 B.2 Radical models

B.2.1 Sundaram and Froment (1978)

Sundaram and Froment published in 1978 an extensive reaction scheme for the pyrolysis of paraffins and olefins, involving 133 reactions and 36 chemical species, 16 of which are radicals. The entireset of 133 reactions, however, is not applicable to all gaseous feedstocks compositions, being selected a subset of reactions according to the single-components to be cracked, as Table B.2 summarises. Whenever cracking of mixtures of these components is concerned, the selected subset of reactions should be obtained by superposition of the subsets regarding single-component cracking.

Table B.2: Single-component cracking reactions from the radical scheme published by Sundaram and Froment [17].

Total no. Component Reactions considered (from [17]) of reactions 1, 3, 4, 10, 12, 13, 23, 24, 41, 61-65, 67, 68, 71, 72, 78-82, 84, 86, 90, 95-98, 101-104, Ethane 49 106, 108, 111-114, 117, 119-122, 126, 128, 130, 131 1, 2, 10, 12-17, 23-28, 34-36, 41-44, 50, 51, Propane 80 61-68, 71-74, 78-82, 84-87, 90, 93, 95-106, 108, 109, 111-117, 119-128, 130, 131 1, 3, 4, 10, 12-17, 20, 21, 23-28, 31, 32, 34, 38, 39, 41, 42, 45, 47, 48, 53, 54, 58, 59, 61- n-Butane 86 68, 71-74, 78-82, 84-87, 90, 92, 95-106, 108, 109, 111-117, 119-123, 126-128, 130, 131 5, 10-14, 17-19, 22-25, 28-30, 33, 34, 37, 40, 42, 46, 49, 52, 55-57, 60-64, 66-70, 73-80, i-Butane 86 81-95, 97-99, 101-107, 109-114, 117-120, 125, 127-131 1, 3, 4, 6, 10, 12-14, 23-25, 34, 41, 61-68, Ethylene 66 71-74, 78-82, 84-87, 90, 92, 95-97, 101-106, 108, 109, 111-114, 117, 119-128, 130-133 7-10, 12-14, 23-25, 34, 41, 42, 56, 57, 61- 68, 71-74, 78-82, 84-87, 90, 92, 95-106, 108, Propylene 68 109, 111-117, 119, 120, 123-126, 128, 130, 131

B.2.2 Radical kinetics comparison

The radical kinetics reported by Sundaram and Froment, for gaseous feedstocks, and Towfighi and Karimzadeh, and Joo, for naphtha feedstocks, were found to have a rather extensive set of reactions in common. Table B.3 contains the set of common reactions shared between the three kinetic models pub- lished, having the respective kinetic parameters also been compared against NIST Kinetics Database [84].

110 Table B.3: Reactions compared between different kinetic models.

log10Pre-exponential factor Activation energy Reference: NISTa [17]b [18]c [26]d NISTa [17]b [18]c [26]d · · 1-C3H7 → C2H4 + CH3 12-13 13.6 13.6 13.7 ≈130 32.6 32.6 142.3 · · 1-C3H7 → C3H6 + H ≈13 13.3 13.3 14.3 ≈150 38.4 38.4 163.2 · · 2-C3H7 → C3H6 + H ≈13 13.3 13.3 14.3 ≈160 38.7 38.7 179.9 · · 1-C4H8 · → C3H5 + CH3 16.0 16.9 16.9 15.8 305 74.0 74.0 306.7 · · 1-C4H9 → 1-C4H8 + H 13-14 12.2 12.2 14.1 ≈155 28.0 28.0 163.2 · · 1-C4H9 → C2H5 + C2H4 ≈13 13.0 13.0 14.2 ≈120 36.6 36.6 129.7 · · 2-C4H9 → C2H5 + C2H4 - 13.4 13.4 14.3 123.0 31.9 31.9 142.2 · · i-C4H9 → C3H6 + CH3 12-13 13.9 14.0 14.5 ≈130 33.0 32.8 142.2 · · i-C4H10 → 2-C3H7 + CH3 ≈16 16.3 - 17.7 325 82.0 - 352 · · 1-C5H11 → C3H7 + C2H4 ≈13 13.5 13.5 14.0 ≈125 31.5 31.5 125.5 · · 1-C5H11 → 2-C5H11 ≈11 - 11.0 11.3 ≈80 - 20.0 76.6 · · 2-C5H11 → 1-C5H11 - - 11.1 11.5 - - 23.4 90.4 · · 2-C5H11 → C3H6 + C2H5 13.7 12.6 12.6 14.0 123.0 28.7 28.7 129.7 · · n-C5H12 → 1-C4H9 + CH3 16.5 - 16.8 17.8 331.0 - 85.4 357.7 · · n-C5H12 → 1-C3H7 + C2H5 - - 16.8 17.1 - - 81.9 341.4 · · i-C5H12 → 2-C4H9 + CH3 - - 17.1 17.5 - - 82.9 351.5 · · i-C5H12 → 2-C3H7 + C2H5 - - 16.6 16.9 - - 79.2 335.2 · · i-C5H12 → i-C4H9 + CH3 - - 16.7 17.4 - - 85.0 357.3 · · 1-C6H13 → 2-C6H13 8-10 - 9.2 10.6 ≈50 - 11.1 51.0 · · 2-C6H13 → 1-C6H13 10.4 - 9.3 10.7 88.1 - 14.9 64.9 · · i-C6H13 → 2-C3H7 + C3H6 - - 13.4 14.0 - - 28.2 121.3 · · n-C6H14 → 1-C3H7 + 1-C3H7 - - 16.5 16.5 - - 81.9 342.7 · · n-C6H14 → 1-C4H9 + C2H5 - - 16.8 16.8 - - 81.9 342.7 · · i-C6H14 → 1-C3H7 + 2-C3H7 - - 16.6 16.6 - - 79.2 331.4 · · i-C6H14 → i-C4H9 + CH3 - - 16.8 16.8 - - 81.0 338.9 · · i-C6H14 → 2-C5H11 + CH3 - - 17.1 17.1 - - 82.9 346.9 · · n-C7H16 → 1-C5H11 + C2H5 - - 16.8 16.6 - - 81.9 220.0 · · n-C7H16 → 1-C6H13 + CH3 - - 16.8 16.3 - - 85.4 300.0 · · i-C7H16 → 2-C6H13 + CH3 - - 17.1 16.6 - - 82.9 300.0 · · CH3 + CH3 → C2H6 ≈13 10.1 10.1 13.3 0 0 0 0 · · C2H3 + C2H3 → C4H6 ≈13 10.1 10.1 13.1 0 0 0 0 · · C2H4 + H → C2H5 11-13 10.0 10.0 14.0 3-6 1.5 1.5 8.4 · · C2H4 + CH3 → C2H3 + CH4 ≈12 10.0 10.0 12.8 ≈60 13.0 13.0 62.7 · · C2H5 + CH3 → C3H8 ≈13 9.5 9.5 13.0 0 0 0 0 · · C2H5 + C2H4 → C3H6 + CH3 - 9.5 9.5 12.5 - 19.0 19.0 79.5 · · C2H5 + C2H5 → C4H10 ≈13 8.6 8.6 12.3 0 0 0 0 · · C2H6 + H → C2H5 + H2 13-14 11.0 11.0 13.9 ≈40 9.7 9.7 33.4 · · C2H6 + CH3 → C2H5 + CH4 ≈13 11.6 11.6 13.0 ≈75 16.5 16.5 49.8 · · C3H5 + CH3 → 1-C4H8 12.4 9.5 9.5 12.9 0 0 0 0 · · C3H6 + H → 1-C3H7 12-13 10.0 10.0 13.6 ≈13 2.9 2.9 8.4 · · C3H6 + H → 2-C3H7 ≈13 10.0 10.0 13.6 ≈5 1.5 1.5 8.4 · · C3H6 + C2H5 → C2H6 + C3H5 10.7 8.0 8.0 12.6 21.7 9.2 9.2 58.6 · · 1-C4H8 + H → 1-C4H9 12.2 10.0 10.0 13.9 7.83 1.2 1.2 8.4 · · 2-C4H8 + H → 2-C4H9 ≈13 9.8 - 14.0 ≈8.7 1.2 - 10.5 · · i-C4H8 + H → i-C4H9 12.5 10.0 - 14.0 11.0 1.2 - 8.4 · · n-C4H10 + H → 1-C4H9 + H2 ≈13 11.2 11.2 14.8 ≈40 9.7 9.7 33.5 · · n-C4H10 + H → 2-C4H9 + H2 ≈14 11.0 11.0 14.8 ≈35 8.4 8.4 33.5 · · n-C4H10 + CH3 → 1-C4H9 + CH4 ≈13 10.5 10.5 13.0 56.87 11.6 11.6 49.8 a units: cm3mol-1s-1, kJ/mol; b units: Lmol-1s-1, kcal/mol ; c units: Lmol-1s-1, kcal/mol (deducted); d units: cm3mol-1s-1, kJ/mol;

111 B.2.3 Extended reaction sets

The original kinetic schemes published by Towfighi and Karimzadeh [18] and Joo [26] although involv- ing a large number of reactions they do not account for the cracking of cyclopentane and cyclohexane and in this respect, an extension of these was proposed in order to prove the impact some reactions may have in the final product distribution. In this regard, for each component three H-abstraction reactions were added, corresponding each · · · one to the reaction with H , CH3 and C2H5 , the three most abundant radicals. Finally, the decomposi- tion reactions involving the corresponding radical forms of cyclopentane and cyclohexane were added. The H-abstraction reactions were obtained from NIST Kinetics Database [84] and by Towfighi and Karimzadeh [18] whilst the decomposition reactions were withdrawn from the kinetic scheme proposed by Joo [26] and by Towfighi and Karimzadeh – which surprisingly did not comprise the H-abstraction reactions and therefore was not able to crack neither of these components. The set of added reactions used in the extension of Towfighi and Karimzadeh’s and Joo’s schemes is summarised in Table B.4.

Table B.4: Cyclopentane and cyclohexane cracking reactions added to the studied kinetic schemes.

log10Pre-exponential factor Activation energy Reaction (s-1 or cm3mol-1s-1) (kcal/mol) Source H-abstraction reactions · · a a cC5H10 + H → cC5H9 + H2 14.53 7.78 [84] · · cC5H10 + CH3 → cC5H9 + CH4 11.30 8.60 [84] · · cC5H10 + C2H5 → cC5H9 + C2H6 11.20 9.56 [84] · · cC6H12 + H → cC6H11 + H2 11.00 8.50 [18] · · cC6H12 + CH3 → cC6H11 + CH4 11.00 8.50 [18] · · b cC6H12 + C2H5 → cC6H11 + C2H6 11.00 8.50 [18] Decomposition reactions · · cC5H9 → aC3H5 + C2H4 13.00 19.46 [26] · b b cC5H10 → cC5H9 + H 16.30 82.00 [18] · · cC6H11 → C2H5 + C4H6 13.00 26.59 [26] · · cC6H11 → aC3H5 + C3H6 13.00 20.57 [26] · cC6H12 → cC6H11 + H 16.30 82.00 [18] a calculated by NIST data; b assumed by author;

By extending the kinetic schemes it is expected that cyclopentane and cyclohexane will now be subjected to cracking hence having a direct impact in ethylene, propylene and butadiene yields. It should be noted again that the extension had solely the objective to demonstrate the impact some reactions may have in the final product distribution, not being the author’s intention to include all the cracking- related reactions involving these two components – for instance, there surely are reactions that account for the C-C bond scission of these naphthenes that were not considered.

112 Appendix C gSAFT®

gSAFT® was considered in the feed characterisation model as a possible thermodynamic model and physical properties package. Since some parameters were not fully tuned or even missing, their optimisation and inclusion had to be carried out. gSAFT® ’s γ-Mie method in particular allows one to obtain high-fidelity thermodynamic properties for any given molecule simply by representing it in terms of functional groups. Apart from intramolecular group interactions, which give the compound its properties, such as density, heat capacity, vapour pres- sure, etc., intermolecular group interactions play a substantial role whenever mixtures are concerned. Whilst vapour pressure is a direct measure of the interactions of a pure component, binary mixture vapour-liquid equilibria T-x-y and P-x-y plots are, undoubtedly, a reflex of both pure component and mixture behaviour. In this regard, vapour pressure data was used to adjust group interaction parameters, ® namely the dispersion energy, ϵ/kB [85], and to prove gSAFT ’s predictive nature. Several binary systems were therefore studied in order to demonstrate the accuracy of gSAFT® γ-Mie’s thermodynamic predictions.

C.1 Vapour-liquid equilibria

C.1.1 Vapour pressure of pure components

Some of the main naphthenic constituents of naphtha are the methylated cyclopentane and cyclo- ® hexane. These molecules are represented in gSAFT by ’cCH2’, ’CH’ and ’CH3’ groups, with their multiplicity depending on how many substituents these naphthenes possess. Although most dispersion energies between these groups were somewhat optimised, the dispersion interaction between ’cCH2’ and ’CH’ was not. In order to overcome rather unsatisfactory predictons, vapour pressure data had to be used in order to adjust this parameter, being methylcyclohexane the chosen compound. ® The ϵ/kB was adjusted from 570 to 520 K. gSAFT predictions before and after the parameter adjustment are compared against experimental data in Figure C.1. As it can be observed in Figure C.1, gSAFT® predictions after the parameter having been optimised

113 120

100

80

60

40 Vapourpressure (kPa)

20

0 280 300 320 340 360 380 Temperature (K)

Figure C.1: Vapour pressure of methylcyclohexane: gSAFT® predictions (lines: dashed - before adjustment, full - after adjustment) and experimental data (circles) [86, 87]. are quite satisfactory and show a substantial improvement in comparison with the unoptimised situation.

However the new value for ϵ/kB is only valid for six-membered rings, as a five-membered ring (found, for instance, in cyclopentane), has different chemical bonds and thus different group interactions – the interaction parameter shall remain at its initial value of 570 K. In order to show gSAFT® ’s predictive nature, vapour pressure obtained by gSAFT® for dimethylcy- clohexane (DMCH) is compared against experimental data for trans-isomers of dimethylcyclohexane in Figure C.2.

DMCH 100 t-1,2-DMCH

80 t-1,3-DMCH t-1,4-DMCH

60

40 Vapourpressure (kPa) 20

0 310 320 330 340 350 360 370 380 390 400 Temperature (K)

Figure C.2: Vapour pressure of trans-dimethylcyclohexanes: gSAFT® prediction (DMCH - line) and experimental data (circles) [87].

Once again, after the adjustment having been made using methylcyclohexane vapour pressure data, gSAFT® simulation results for the trans-isomers of dimethylcyclohexane show an quite reason- able agreement with experimental data.

C.1.2 Binary systems

Paraffins are the main constituents of naphtha, being theC5−C7 fraction the most representative. Figures C.3 and C.4 show isothermal VLE plots for some binary systems involving these hydrocarbons. Naphthenes are also commonly found on naphtha feeds and, therefore, interactions amongst these

114 200 NP(1)- NO(2) (303.7 K)

150 NP(1)- NO(2) (308.7 K) NP(1)- NO(2) (313.7 K) 100

NP(1)- ND(2) (317.7 K) Pressure(kPa) NP(1)- ND(2) (333.7 K) 50

0 0 0.2 0.4 0.6 0.8 1 mole fraction of component 1

Figure C.3: Isothermal vapour-liquid equilibria involving n-pentane (NP), n-octane (NO) and n-decane (ND): gSAFT® predictions (lines) and experimental data (circles) [88].

40

35 NH(1) - 2MP(2) (283.15 K)

30 NH(1) - 2MP(2) (293.15 K) 25 NH(1) - 2MP(2) (303.15 K) 20 NH(1) - 24DMP(2) (283.15 K)

Pressure(kPa) 15 NH(1) - 24DMP(2) (293.15 K)

10 NH(1) - 24DMP(2) (303.15 K)

5 0 0.2 0.4 0.6 0.8 1 mole fraction of component 1

Figure C.4: Isothermal vapour-liquid equilibria involving n-hexane (NH), 2-methylpentane (2MP) and 2,4-dimethylpentane (24DMP): gSAFT® predictions (lines) and experimental data (circles) [89]. and with paraffins must be investigated. In this regard, Figure C.5 shows the VLE plots for some binary systems involving naphthenes and paraffins.

375

370 CH(1) - MCH(2) (100.00 kPa) 365

NH(1) - CH(2) (101.33 kPa) 360 NH(1) - MCP(2) (101.33 kPa) 355

350 Temperature(K) 345

340

335 0 0.2 0.4 0.6 0.8 1 mole fraction of component 1

Figure C.5: Isobaric vapour-liquid equilibria involving cyclohexane (CH), methylcyclohexane (MCH) and n-hexane (NH): gSAFT® predictions (lines) and experimental data (circles) [90, 91, 92].

Finally, aromatics are the third most representative hydrocarbon class found on naphthas, with the olefinic fraction being completely meaningless. Hence, VLE plots of binary systems of aromatics, aro-

115 matics with paraffins and with naphthenes were obtained in order to reiterate the usefulness® ofgSAFT for the current model (Figures C.6, C.7 and C.8).

354

352 NH(1) - B(2) (101.33 kPa)

350 NH(1) - B(2) (97.99 kPa)

348 B(1) - CH(2) (101.33 kPa)

346 Temperature(K) 344

342

340 0 0.2 0.4 0.6 0.8 1 mole fraction of component 1

Figure C.6: Isobaric vapour-liquid equilibria involving benzene (B), cyclohexane (CH) and n-hexane (NH): gSAFT® predictions (lines) and experimental data (circles) [93, 94].

420

410 NH(1) - PX(2) (101.33 kPa) 400

NH(1) - PX(2) (95.80 kPa) 390 B(1) - PX(2) (101.33 kPa) 380

370 Temperature(K) 360

350

340 0 0.2 0.4 0.6 0.8 1 mole fraction of component 1

Figure C.7: Isobaric vapour-liquid equilibria involving benzene (B), p-xylene (PX) and n-hexane (NH): gSAFT® predictions (lines) and experimental data (circles) [95, 96].

420

410 CH(1) - T(2) (100.00 kPa)

400 MCH(1) - PX(2) (101.33 kPa)

390

380

Temperature(K) 370

360

350 0 0.2 0.4 0.6 0.8 1 mole fraction of component 1

Figure C.8: Isobaric vapour-liquid equilibria involving toluene (T), p-xylene (PX), cyclohexane (CH) and methylcyclohexane (MCH): gSAFT® predictions (lines) and experimental data (circles) [90, 97].

116 C.2 Dispersion energies adjustment

In order to be able to correctly predict the interactions between the major classes of hydrocarbon commonly present in naphtha, an adjustment of dispersion energies had to be carried out, namely those involved in naphthenes and aromatics. The interactions considered were the following:

1 2 • 1. ’cCH2 ’ and ’aCH ’

• 2. ’cCH2’ and ’aCCH3’

• 3. ’CH’ and ’aCH’

• 4. ’CH’ and ’aCCH3’

• 5. ’CH3’ and ’aCCH3’

In order to adjust the dispersion energies regarding ’cCH2’, vapour-liquid equilibrium data of cyclo- hexane was used, first with benzene (Figure C.9a) to optimise interaction no.1 and then with p-xylene (Figure C.9b) to optimise interaction no.2.

355 40 298.15 K 35 308.15 K 354

30 328.15 K

353 25 20

352 15

Pressure(kPa) Temperature(K) 10 351 5

350 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 benzene(mol%) cyclohexane(mol%)

(a) Isobaric vapour-liquid equilibria of the binary system (b) Isothermal vapour-liquid equilibria of the binary system benzene-cyclohexane at 101.33 kPa [91]. cyclohexane-p-xylene [98].

Figure C.9: Experimental data used for ’cCH2’ interaction parameters estimation.

Subsequently, for the dispersion energies regarding ’CH’ and ’CH3’, found in methylated naphthenic compounds, VLE data of methylcyclohexane was used, having interaction no.3 been obtained using a binary system with benzene (Figure C.10a) whilst interactions no.4 and no.5 were optimised with toluene (Figure C.10b) and p-xylene (Figure C.10c).

The fitted ϵ/kB which were used to obtain the VLE plots and used in the feed characterisation model are summarised in Table C.1.

1’c’ stands for cyclic 2’a’ stands for aromatic

117 100 60

90 55

80 50

70 45 Pressure(kPa)

Temperature(K) 60 40

50 35

40 30 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 methylcyclohexane(mol%) toluene(mol%)

(a) Isothermal vapour-liquid equilibria of the binary system (b) Isothermal vapour-liquid equilibria of the binary system methylcyclohexane-benzene at 348.15 K [99]. toluene-methylcyclohexane at 348.15 K [99].

415 410 405

400 395 390

Temperature(K) 385 380 375 370 0 0.2 0.4 0.6 0.8 1 methylcyclohexane (mol%)

(c) Isobaric vapour-liquid equilibria of the binary system methylcyclohexane-p-xylene at 101.33 kPa [97].

Figure C.10: Experimental data used for ’CH’ and ’CH3’ interaction parameters estimation.

Table C.1: Adjusted gSAFT® γ-Mie group dispersion energies.

No. Groups ϵ/kB (K) 1 cCH2, aCH 418 2 cCH2, aCCH3 505 3 CH, aCH 450 4 CH, aCCH3 600 a 5 CH3, aCCH3 408 a previous value: 368 K

118 Appendix D

Naphtha analytical data

The experimental data used in the feed characterisation chapter was found to be part of an analytical report regarding test samples that fit in the category of gasoline blending streams. The selected analysis of a sweetened petroleum naphtha sample is presented in Figure D.1-D.3.

119 Naphtha Data Presentation

CLI Log # DC-1239 API Description. 81-08

API Gravity D287 @60 76.9 Density D287 @15 C .6782 Molecular Weight D2224 gm/mol 81 Refractive Index RI units @20 C 1.3892

Total Sulfur D3120 ppm/wt 1170 Total Nitrogen Chemil. ppm/wt

Distillation D86 vol/deg F IBP/5 io2/ii5 io/2o 120/124 30/40 i29/i33 50160 138/144 70/80 150/159 90/95 170/188 End Point 238 Received 98.0 Residue 1.0 Loss 1.0

Bvdrocarbon Type Analysis

Saturates D1319 vol % 95.9 W W <0 .i 01efins W W Aromatics Total 100.0

Mass Spectrometer Analysis (D27891

Paraffins D2789/MS vol % 72.1 W N Naphthenes 20.9 N I 01efins <0.1 W W Aromatics 6.9 Indans/Tetralins W U 0.1 Naphthalenes W W Total I00.0

32

Figure D.1: Analytical data from a sweetened petroleum naphtha used to validate de feed characterisation model [1].

120 Naphtha Component Analysis by CaDilliarv GC and GC/MS

CLI Log | DC-1239 API Designation 81-08

Component ID Component ID bv GC/MS bY CaD GC Wt %

Iso-Butane 0.07 n-Butane 1.13 Neopentane 0.01 Iso-Pentane ii.01 l-Pentene <0.01 2-Methyl-l-butene <0.01 n-Pentane 19.67 trans-2-Pentene 0.01 cis-2-Pentene <0.01 2-Methyl-2-butene 0.01 2,2-Dimethylbutane 0.34 Cyclopentane 2.62 2,3-Dimethylbutane 1.45 2-Methylpentane 11.53 3-Methylpentane 7.90 n-Hexane 15.71 Methylcyclopentane 9.30 2,2-Dimethylpentane 0.20 2,4-Dimethylpentane 0.01 Benzene 5.10 3,3-Dimethylpentane 0.01 Cyclohexane 5.02 2-Methylhexane 1.06 2,3-Dlmethylpentane 0.54 1,1-Dimethylcyclopentane 0.28 3-Methylhexane 1.20 cis-l,3-Dimethylcyclopentane e 0.66 trans-l,3-Dimethylcyclopentane 0.51 trans-l,2-Dimethylcyclopentane 1.07 n-Heptane 1.25 cls-l,2-Dlmethylcyclopentane 0.05 Methylcyclohexane fused 1.06 l,l,3-Trlmethylcyclopentane fuged 0.02 Ethylcyclopentane unknown 0.03 2,5-Dimethylhexane unknown 0.01 1,2,4-Trimethylcyclopentane fused 0.02 C8 Naphthene unknown 0.02 Toluene 0.63 2,3,4-Trimethylpentane unknown 0.01

33

Figure D.2: Analytical data from a sweetened petroleum naphtha used to validate de feed characterisation model [1] (cont.).

121 Component ID Component ID by GC/MS bV CaD GC Wt

2-Methylheptane 0.04 4-Methylheptane unknown 0.01 3-Methylheptane 0.02 l,l-Dimethylcyclohexane unknown 0.02 trans-l,4-Dimethylcyclohexane unknown 0.01 C8 Naphthene unknown 0.01 C8 Naphthene unknown 0.01 C8 Naphthene unknown 0.01 1-Methyl-l-ethylcyclopentane unknown 0.01 1,2,3-Trimethylcyclopentane unknown 0.01 n-Octane 0.16 Naphthene unknown 0.01 C9 Paraffin unknown 0.01 C9 Naphthene unknown 0.01 C9 Naphthene unknown 0.01 Ethylbenzene 0.01 C9 Parraffin unknown 0.01 p + m Xylene N.D. 0.01 C9 Paraffin N.D. 0.01 C9 Paraffin N.D. 0.01 C9 Paraffin N.D. 0.01 n-Nonane 0.02 C10 Paraffin N.D. o.ol Total 100.00

NOTE: *Indicates capillary GC ID matches that of GC/MS.

34

Figure D.3: Analytical data from a sweetened petroleum naphtha used to validate de feed characterisation model [1] (cont.).

122