Development of a new optimized dimensional and technological approach to LPG fractionation columns through a hydrodynamic study by the CFD.

REPUBLIQUE TUNISIENNE

MINISTERE DE L’ENSEIGNEMENT SUPERIEUR

ET DE LA RECHERCHE SCIENTIFIQUE

UNIVERSITE DE SOUSSE

THÈSE

Présentée en vue de l’obtention du

Diplôme de DOCTORAT

Spécialité : Génie Mécanique

Par

Hajer TROUDI

Ingénieur mécatronique, Ecole Nationale d’Ingénieurs de Sousse

Intitulée :

Développement d’une nouvelle approche dimensionnelle et

technologique optimisée des colonnes de fractionnement de GPL à

travers une étude hydrodynamique par le CFD

Soutenue publiquement, le 17, décembre 2019, devant le jury composé de :

Président :

Prof. Chokri BOURAOUI

ENISo

Rapporteur :

Prof. Zied DRISS

ENIS

Rapporteur :

Prof. Abdel Majid JEMNI

ENIM

Examinateur : Dr. Borhen LOUHICHI

ISSATSo

Directeur :

Prof. Zoubeir TOURKI

ENISo

Co-Directeur : Ing. Mohamed ELLEJMI

AEI

i

Acknowledgements

First I would like to express my deepest gratitude to who have helped and supported me. Sincere thanks to my supervisors Pr. Zoubeir TOURKI, Mr. Mohamed ELLEJMI and Dr. Moncef GHISS for their valuable support, encouragement, review of this thesis and joint supervision of this work between the “Laboratoire de Mécanique de Sousse” (LMS) at the University of Sousse and the “Alpha Engineering International” (AEI). My discussions with them have been interesting and inspiring.

I also want to thank my committee members. I am grateful to Pr. Zied DRISS and Pr. Abdelmajid JEMNI to have accepted to review this thesis. I am also grateful to Pr. Borhene LOUHICHI for accepting to be part of the jury as examiners and Pr. Chokri BOURAOUI to have presided the jury.

I would also thank Pr. Abdelfattah MLIKA for accepting me at the Mechanical Laboratory of Sousse (LMS) and the National Engineering School of Sousse (ENISo) for giving me the opportunity to work in a collaborative environment, a great rewarding working atmosphere and cheerfulness.

I would like to thank the Numerical Simulation team for all the fruitful meetings we had together and for sharing useful feedback and interesting comments and discussions. I would like also to thank Pr. Mouldi CHRIGUI for giving me the great pleasure of collaborating with its laboratory “Modélisation Mécanique, Energie et Matériaux” (M2EM) at the National Engineering School of of Gabes and for supplying me all necessary equipment to carry out my work.

I would also like to express special thanks to my thesis co-adviser Dr. Moncef GHISS for having welcomed me on several occasions and taking the time to answer all my questions and for being helpful. Sepical thanks to Dr. Najeh Guedria who have helped me during the implementation of my optimisation code.

Thanks to the collegues who have provided me the opportunity to teach during the last four years (Dr. Farhat ZEMEZMI, Dr. Sami BENNOUR and Dr. Ali HLELI).

Special thanks to all the Ph.D. candidates, doctors and engineers with whom I have spent most of the time. Special thanks to Ameni ELLTAEIF, Olfa JEMAA, Mouna FRADI, Sabrine

ii KOUISSI for her help with the administrative stuff.

I would like to thank also Farid CHEDLY EJMILI for his good humor and kindness. Finally, I would like to infinitely thank all my family and particularly my father for his tremendous help and support.

iii

Abstract

Gas flaring poses loss of an important natural resource which is the Liquid Petroleum Gas (LPG) and evidently environmental impacts at the same time. At present, the only technology which is in operation to recover the LPG is the Packed Bed Reactors (PBR). The main aim of this study is to identify the LPG and Condensate Gas (CG) as the primary and secondary fuels and to investigate their hydrodynamic characteristics under different working parameters. In the following, the secondary aim of this study is to modify the typical PBR involving a novel and effective gas-liquid contact mode. The goal is to produce a dense droplet dispersion in contact to the turbulent gaseous crossflow.

To fulfill this goal, several promising configurations are designed and analyzed. These configurations were carried out using two commercial simulators: Aspen Hysys and Ansys Fluent. An Eulerian-Lagrangian approach is implemented for modeling spray and atomization of LPG fuel. The Standard k-ε turbulence model is applied to estimate the turbulent viscosity in the gas phase. The discrete random walk model is employed to trace the droplets in the turbulent gas flow. The effects of propane C3H8 (or C3) and n-butane n-C4H10 (or n-C4) amounts were numerically investigated on fuel spray evaporation and fuel droplets characteristics.

Results were indicated that the droplet temperature evolution can be characterized in three distinct stages namely, the pre-heating, heating and equilibrium stage. The new gas-liquid contact mode was found to enhance spray dispersion for a wide range of crossflow angle. The mean droplet diameter was decreased with an increase in the cross gas velocity. The spray was dispersed more widely and its angle was largely affected by the gas-liquid ratio regardless of the ambient pressure. Observations of the spray morphology made between the spray and the crossflow were presented. Finally, a numerical correlations for normalized droplet diameter and interfacial area are proposed. These correlations were well predicted all measured conditions. Keywords:

iv

Résumé

Le torchage des rejets de gaz fossile à différents étapes entraîne la perte cette ressource naturelle importante qui est le Gaz de Pétrole Liquéfié (GPL) et affecte l’environnement. Jusqu’à présent, la principale technologie permettant de récupérer le GPL est celle des réacteurs à lit à garnissages (PBR).

Le premier objectif de cette thèse est d'identifier les deux mélanges le GPL et le gaz de condensé (GC) comme combustibles primaires et secondaires ainsi d'étudier leurs caractéristiques hydrodynamiques. Le deuxième objectif est de modifier le PBR en utilisant un nouveau mode de contact entre les phases gaz-liquide. Le but de cette modification consiste à produire une large dispersion des gouttelettes en contact avec le courant croisé du flux gazeux.

Pour atteindre ces deux objectives, plusieurs configurations ont été élaborées et analysées. Ces configurations ont été réalisées à l'aide de deux logiciels commerciaux : Aspen Hysysys et Ansys Fluent. Une approche Eulérienne-Lagrangienne (E-L) a été implémenté pour la modélisation de la pulvérisation et de l'atomisation des gouttes de carburant GPL. Un modèle de turbulence de type Standard k-ε a été appliqué pour estimer la viscosité turbulente en phase gazeuse. La phase discrète a été utilisé pour tracer la dispersion des gouttelettes dans le flux turbulent du gaz. L’effet du propane C3H8 (ou C3) et de n-butane n-C4H10 (ou n-C4) sur l'évaporation des gouttes et sur les caractéristiques du spray ont été examinés numériquement. Les résultats montrent que l'évolution de la température à la surface des gouttes pour les mélanges GPL et GC peut être décomposé en trois étapes distinctes, le préchauffage, le chauffage et l'étape d'équilibre. Le nouveau mode de contact gaz-liquide montre une amélioration de la dispersion de la pulvérisation pour une large plage d'angles d'écoulement croisé. Le jet a été largement diffusé dans le lit à garnissage et son angle d’ouverture a été influencé par le rapport gaz-liquide indépendamment de la pression ambiante.

Enfin, des corrélations numériques ont été proposées pour le diamètre normalisé des gouttes et l’aire interfaciale entre les phases. Ces corrélations ont été bien prédites pour toutes les conditions de mesure.

Mots-clés :

CFD, Courant- Croisé, Approche Eulérienne-Lagrangienne, Transfert de chaleur et de masse, GPL, MAPSO.

v

Notations

List of symbols

A interfacial area (m-1)

Ap packed bed area (m2)

1, 2, 3, 4, 5, 6, 7

a a a a a a a unknown coefficients used for the correlations (-)

BM Spalding mass number (–)

bNozzle width of gas nozzle (m)

C Carbon

C2 inertial loss coefficient (1/m)

Cin, Cout inlet and outlet droplets concentrations (kg/s)

cp liquid specific heat (J/kg.°C)

CD drag coefficient

c1’, c2’ and cμ constants of turbulence (-) Cb, CF, Ck and Cd constants in breakage model (-)

dequ equivalent-volume diameter (m)

D diameter of the packed bed (m)

DH hydraulic diameter (m)

,

m T

i i

D D molecular and thermal diffusion coefficient of

the vaporized component in the gas phase (m2.s)

Deq equivalent diameter (m)

dp average size of particles (mm)

dd diameter of individual droplet (mm)

ddo initial droplet diameter (mm)

d32 Sauter mean diameter (mm)

E total energy

exp Exponential

F interphase body forces between phases (N)

ext

F momentum transfer between the gas phase and

each individual droplet (N) L

i

f

liquid activity coefficient of component i

V i

f vapor activity coefficient of component i

g gravitational acceleration (m/s2₎

G Gas flow rate (kg/s)

H column height (m)

Hp packed bed height (m)

h convective heat transfer coefficient (W/m2 °C)

hNozzle height of gas nozzle (mm)

s i

h convection heat transfer coefficient of

component i in the surface of the droplets (W/m2 °C)

i

h convection heat transfer coefficient of

component i in the gas (W/m2 _°C)

I turbulence intensity

i

vi

K specific permeability (m)

k’ turbulent kinetic energy

k thermal conductivity (W/m.°C)

keff effective thermal conductivity (W/m.°C)

L Liquid flow rate (kg/s)

L length scale ( l=0.07 DH) (m)

lNozzle length of gas nozzle (m)

i

m

• _{rate of evaporation (kg/s)}

N number (-)

Nd total number of droplets (-)

i d d

N total number of droplets of diameter di (-)

Nsp total number of chemical species (-)

Ntests total number of numerical tests (-)

Nu Nusselt number (-)

P pressure (bar)

P∞ ambient gas pressure (bar)

sat i

P saturated vapor pressure of component i (bar)

Pcr critical pressure for individual species (bar)

Pr Prandlt number (-)

Δp drop pressure (bar)

Q heat flux (W/m2)

uq velocity of the continuous phase (m/s)

ud velocity of the dispersed phase (m/s)

usg superficial gas velocity (m/s)

usl superficial liquid velocity (m/s)

u∞ gas stream velocity (m/s)

R radius of the packed bed (m)

R universal gas constant (= 8,314 j/mol/K)

r radial distance

r32 Sauter mean radius (m)

r32,child Sauter mean radius of the child droplets (m)

Reg Reynolds number of the gas phase (-)

Rel Reynolds number of the liquid phase (-)

R2 coefficient of determination

S generalized source terms

Sc schmidt number (-)

Tb boiling temperature for individual components

(°C)

Td droplet surface temperature (°C)

Tq temperature of the continuous phase (°C)

T∞ ambient gas temperature (°C)

T time (s)

T

 packed bed volume (m3₎

p

 packings or particles volume (m3)

cell



cell volume (m3)

vii

i

 molecular weight (kg/mol)

X, x component’s mass and mole fraction in liquid phase (Droplet)

xd position of the droplets (m)

2, 3, 4, 5

x x x x normalized input data (-)

Y, y component’s mass and mole fraction in the vapor phase

, i q

Y component’s mass fraction in the continuous

phase (-)

Corr

y extracted results from correlation

CFD or Exp

y extracted results from CFD or Experiment

yd deformation of the droplets (m)

2, 3, 4, 5

y y y y normalized output data (-) Greek letter

ε porosity (-)

’ turbulent energy dissipation rate (m2 /s3)

Φ particle sphericity (-)

μl or μd liquid phase shear viscosity (Pa.s)

μg or μq gas phase shear viscosity (Pa.s)

μt turbulent viscosity

μT viscosity rate of the droplet and gas

l density of liquid phase (kg/m3 )

g density of gas phase (kg/m3 )

Τ stress strain tensor



volume, (m3)

 spray cone angle (°)

Α inlet gas orientation (°)

α' Liquid volume fraction (-)

viii

Σ interfacial (liquid-gas) surface tension (N/m)

σcr critical interfacial (liquid-gas) surface

tension

k’, ’ turbulence constants (-)

 collection efficiency (-)

Superscripts and Subscripts

Cr critical Corr Correlation Child children Cell Cell ∞ stationary point Eff effective Eq equivalent Evp evaporation Exp experiment Ext exterior G gas phase In inlet L liquid phase D droplet/dispersed phase Q continuous phase V vapor O initial out outlet Abbreviation

AEI Alpha Engineering International

CFD Computational Fluid Dynamics

DDPM Dense Discrete Phase Modelling

E-L Eulerian-Lagrangian

EOS Equation Of State

LPG Liquefied Petroleum Gas

MAPE Mean Absolute Percentage Error

NGL Natural Gas Liquefied

PR-EOS Peng–Robinson Equation Of State

MAPSO Modified Accelerated Particle Swarm

Optimization

TAB Taylor analogy breakup

RG Refinery Gas

RE Residu

SIMPLEC Semi-Implicit Method for Pressure Linked

Equations Consistent

VOF Volume Of Fluid

VLE Vapor-Liquid Equilibrium

ix

List of contents

Acknowledgements ... i Abstract ... iii Résumé ... iv Notations ... v List of contents ... ix List of figures ... iv List of tables ... 1 General Introduction ... 2

Aim & Objectives ... 6

Thesis Outline ... 6

Chapter 1: State of the art in CFD simulation of Natural Gas ... 9

1.1. Introduction ... 9

1.2. State of the art ... 9

1.2.1. Separation of oil-water-gas ... 9

1.2.2. Crude oil distillation ... 10

1.2.3. Distillation column ... 12

1.2.4. Flow modes ... 13

1.3. Natural gas NG ... 14

1.3.1. Process description ... 14

1.3.2. Pilot plant ... 15

1.3.3. De-methanizer and de-ethanizer ... 15

1.3.4. De-propanizer ... 16

1.3.5. De-butanizer ... 16

1.4. CFD simulation in natural of Natural Gas ... 18

1.5. Eulerian-Lagrangian approach ... 18

1.5.1. Basic equations ... 19

1.5.2. Heat and mass transfer ... 23

1.5.3. Porous media approach ... 24

1.6. Conclusion ... 25

Chapter 2 : CFD modeling of Deethanizer Column with multicomponent mixture ... 27

2.1. Introduction ... 27

2.2. Multicomponent mixtures: the NGL and CG ... 27

x

2.3.1. Vapor-Liquid Equilibrium (VLE) ... 28

2.3.2. Comparison between Ergun and Peng Robinson ... 29

2.3.3. Initial and boundary conditions ... 30

2.3.4. Computational model setup ... 32

2.4. Results and discussion ... 33

2.4.1. Test mesh independency ... 33

2.4.2. Model validation ... 34

2.4.3. Mole fraction history ... 38

2.4.4. Effect of C1, C2, C3 and C4 on the deformation behavior of multi-component droplet 41 2.4.5. Profiles of component concentrations ... 44

2.4.6. Effect of droplet diameter ... 49

2.4.7. Effect of ambient temperature ... 51

2.4.8. Effect of porosity on pressure drop ... 53

2.5. Conclusion ... 55

Chapter 3: An innovative gas-liquid contact mode in PBRs: The Cross-current flow ... 57

3.1. Introduction ... 57

3.2. Cross-current flow ... 57

3.3. Taylor Analogy Breakup (TAB) ... 58

3.4. Description of the physical model development ... 60

3.4.1. Physical models ... 60

3.4.2. Boundary conditions ... 61

3.5. Results and discussion ... 64

3.5.1. Analysis of single-phase ... 64

3.5.2. Analysis of two-phase ... 66

3.5.2.1. Test grid independency and validation ...66

3.5.2.2. Gas velocity study...69

3.5.2.3. Liquid volume fraction and spray morphology...71

3.5.2.4. Interfacial area identification...75

3.5.2.5. Spray cone angle...77

3.5.2.6. Collection efficiency...79

3.5.2.7. Particle diameter sensibility...80

3.6. Conclusion ... 82

Chaptre 4 : Correlations of hydrodynamic parameters of PBR ... 84

xi

4.2. General form ... 84

4.3. Sauter mean droplet diameter ... 86

4.3.1. Parameter sensitivity analysis ... 87

4.3.2. Simple linear fit ... 91

4.3.3. Multiple linear fit ... 93

4.3.4. Comparison between CFD and correlation results ... 96

4.3.5. Comparison between experimental and correlation results ... 96

4.3.6. A new correlation for d32 ... 98

4.3.7. Main steps of the numerical algorithm ... 99

4.3.8. Comparison of the newly developed correlation with existing correlations .... 101

4.4. Interfacial area correlation ... 102

4.4.1. Multiple lineair fit ... 102

4.4.2. Comparison of new interfacial area model with CFD results ... 105

4.4.3. Comparison of new interfaciale area model with traditional co-current and counter-current model ... 106

4.5. Conclusion ... 108

Conclusions and Future research ... 110

iv

List of figures

Figure 1. 1 Overview of the different steps in the oil and gas processing. ... 10

Figure 1. 2 Structure and operating principle of a crude distillation unit. ... 12

Figure 1. 3 Illustration of packing geometries of a spherical particles and corrugated sheets [44]. ... 13

Figure 1. 4 Overview of the different steps in the oil and gas processing. ... 15

Figure 1. 5 Pilot plant. ... 15

Figure 1. 6 De-propanizer. ... 16

Figure 1. 7 De-butanizer. ... 17

Figure 1. 8 General Distillation Process. ... 17

Figure 1. 9 Flow chart of Eulerian-Lagrangian approach. ... 19

Figure 2. 1 Droplet radius history for a 70% n-heptane/ 30% n-decane bi-component droplet. ... 30

Figure 2. 2 Model of a single droplet evaporation. ... 31

Figure 2. 3 Computational domain and hexahedral grid. ... 33

Figure 2. 4 Meshes performed using ICEM CFD. ... 34

Figure 2. 5 (a) Gas-velocity profile in meridian plane of DC and droplet tracks (right), Effect of mesh size on CFD results in (b) and (c) radial and (d) axial directions. ... 35

Figure 2. 6 History of averaged droplets diameter predicted in present study and compared with experimental data for different systems (pure n-heptane, mixture of 50%, 50% and pure n-decane). ... 37

Figure 2. 7 History of average diameter and surface temperature of droplets predicted in present multicomponent study and compared with experimental data. ... 38

Figure 2. 8 History of average mole fraction on droplets surface predicted in CGM. Operating parameters: P∞= 23.5 bar, T∞ = 272 °C, Td = 69 °C, do = 87 μm. ... 40

Figure 2. 9 History of average mole fraction on the droplets surface predicted in the NGL mixture. Operating parameters: P∞= 23.5 bar, T∞ = 272 °C, Td = 69 °C, do = 87 μm. ... 40

Figure 2. 10 Surface droplet temperature (a) in the first part and (b) in the second and third parts for NGL, CG, MEP mixture and Su and Chen [60] over time at same conditions of P∞= 23.5 bar, T∞ = 272 °C, Td = 69 °C, ddo = 10 μm. ... 42

Figure 2. 11 Average concentration of CH4 and C2H6 over time for NGL, CG and MEP mixture at P∞= 23.5 bar, T∞ = 272 °C, Td = 69 °C, ddo = 10 μm. ... 43

Figure 2. 12 Average concentration of C3H8 and n-C4H10 over time for NGL, CG and MEP mixture at P∞= 23.5 bar, T∞ = 272 °C, Td = 69 °C, ddo = 10 μm. ... 44

Figure 2. 13 Temperature distribution in meridian plane of DC. ... 45

Figure 2. 14 Contour plots of mole fraction of (a) methane CH4, (b) ethane C2H6, (c) propane C3H8, (d) n-butane n-C4H10 and (e) the remaining components C5+ in gas phase at t = 10.2 s. 47 Figure 2. 15 Contour plots of mole fraction of (a) methane CH4, (b) ethane C2H6, (c) propane C3H8 ,(d) n-butane n-C4H10 and (e) the remaining components C5+ in gas phase at t = 46s. .... 48

Figure 2. 16 (a) Droplets diameter and (b) surface temperature histories at 23 bar, u = 0.05 m.s-1 _{and ambient temperature T∞= 272 °C. ... 50}

Figure 2. 17 Variation in evaporation rate with each component i of the NGL for varied ambient temperature T∞ at P∞=23 bar and V = 0.05 m.s-1_{... 52}

v Figure 2. 18 Variation in evaporation rate with each component i of the CG for different

ambient temperature T∞ at P∞=23 bar and V = 0.05 m.s-1... 52

Figure 2. 19 (a) Static pressure and (b) Pressure drop P versus relative gas velocity uq for varied porosity  = 0.90,  = 0.94,  = 0.97 and  = 0.98. Symbols: present work. Dotted lines: Analytical solution of Ergun. ... 54

Figure 3. 1 Schematic diagrams of three-dimensional calculation domain with the boundary conditions: (a) macro- (b) meso- and (c) micro-scales... 62

Figure 3. 2 Geometric drawings of Inlet/Outlet nozzles: (a) top view and (b) side view including α = 0° and α = 45°. ... 63

Figure 3. 3 (a) Two vertical layers of spherical packing (c) gas velocity distribution in m/s, (d) Simulation results for gas velocity in different interval size (horizontal cross-sectional at height of 0.8 m). ... 65

Figure 3. 4 (a) Generated meshes for the geometry, (b) comparison of the predicted volume fraction by CFD against the experimental value of Nemec et al. [24] and (c) computational time. ... 68

Figure 3. 5 Comparison of liquid phase volume fraction under different meshs at (y-z) plane and stopped at t = 0.33 s. ... 69

Figure 3. 6 vorticity distribution at (y-z) plane. ... 70

Figure 3. 7 Liquid volume fraction (α’) iso-surfaces and contours for (α’ = 50%) shown in the cross-sectional plane (a) Model 1: α = 0°, (b) Model 2: α = 0°, (c) Model 3: α = 0°. ... 74

Figure 3. 8 Liquid volume fraction (α’) iso-surfaces and contours for (α’ = 50%) shown in the cross-sectional plane (a) Model 1: α = 45° (b) Model 2: α = 45° and (c) Model 3: α = 45°. ... 74

Figure 3. 9 Temporal interfacial area profile between phases at a superficial gas velocity of 0.02 m/s. ... 76

Figure 3. 10 Instantaneous iso-surface of the liquid volume fraction for Model 2. ... 77

Figure 3. 11 schematic diagram of different cone spray angles. ... 78

Figure 3. 12 The changes of atomizing angle as a function of Reynolds numbers. ... 78

Figure 3. 13 Collection efficiency as a function of d32. ... 80

Figure 3. 14 Liquid volume fraction for two types of packed bed (a) dp = 3 mm,  = 0.4 and (b) dp = 6 mm,  = 0.38. ... 81

Figure 4. 1 Probability Density Function PDF for the droplets based on Sauter mean diameter (G = 0.14 Kg/s). ... 88

Figure 4. 2 droplet diameter vs radial spray velocity. ... 89

Figure 4. 3 Droplet size distribution under various superficial gas velocity. ... 90

Figure 4. 4 Scatter plot of correlation between d32 vs usl... 91

Figure 4. 5 Scatter plot of correlation between d32 vs usg. ... 92

Figure 4. 6 Scatter plot of correlation between d32 vs L/G. ... 92

Figure 4. 7 Scatter plot of correlation between d32 vs α. ... 93

Figure 4. 8 Linear functions between yCorr=Log(d32/D) vs (x2, x3, x4, x5). ... 95

Figure 4. 9 Comparison between d32/D predictions calculated by Eq 4.8 with CFD simulations. ... 96

Figure 4. 10 Comparison between d32 predictions calculated by Eq 4.8 with experimental and CFD simulations. ... 98

Figure 4. 11 Relationship between “d32” and “α”. ... 100

Figure 4. 12 Comparison of d32/D calculated by the new correlation Eq 4. 14 and CFD simulations. ... 101

vi Figure 4. 13 Effect of liquid mass flow on interfacial area. ... 103 Figure 4. 14 Linear functions between yCorr=Log(A/Ap) vs (x2, x3, x4, x5). ... 105 Figure 4. 15 Comparison of normalized interfacial area predicted from CFD with computed one form correlation presented in Eq 4.17. ... 106 Figure 4. 16 The scatter of experimental data and Eq. 4.17. ... 108

1

List of tables

Table 2. 1 Fuel mixture ... 36

Table 2. 2 Thermophysical properties of four primary hydrocarbons. ... 39

Table 3. 1 Boundary conditions. ... 63

Table 3. 2 Physical properties used for the simulation. ... 64

Table 3. 3 Geometric parameters. ... 64

Table 4. 1 Sauter mean diameter “d32” calculated for different gas and liquid superficial velocity. ... 87

Table 4. 2 Simple linear fit for Sauter mean diameter ... 93

Table 4. 3 Multiple linear fit for Sauter mean diameter ... 94

Table 4. 4 Regression Statistics. ... 94

Table 4. 5 Multiple linear fit for interfacial area ... 103

Table 4. 6 Regression Statistics. ... 104

2

General Introduction

Nowadays and almost in all over the world, major of oil and gas production sites are commonly surrounded with the so-called gas flaring. This is identified as a persistent problem due to the emission of CO2 which impacts the earth's climate, causes an elevation of global warming and hence intensifies the natural greenhouse effect on atmosphere. According to the 2009 annual data, 139 billions of cubic meters (bcm) of gases are traditionally emitted to the atmosphere and burned as waste [1]. These data varied significantly from city to another in which Russia has surpassed world statistics in flaring (21.2 bcm). In tunisia, according to the 2014 Carbon Limits company report [2], over than 0.55 bcm is wasted in flare installations. The main reasons are reportedly due to the lack of required transportation or refinery infrastructure or economical inefficiency. Also, this practice is suggested as a safety practice. Although gas flaring is known as a natural and economic capital waste, it is noteworthy that this gas presents an attractive marketable fuel, as well. It consists of products such as Natural Gas (NG) (methane and ethane), Liquified Petroleum Gas (LPG) (propane and n-butane) and other fuels (toluene, benzene and n-hexane), etc which they could be all used as a source of energy. These products play an important role in the industrial and especially in the household sector owing to their high flame speeds and wide ignition limits. Therefore, firstly it is needed to reduce those emissions by improving process conditions and then looking for recovery methods. Friendly technologies, such as Packed Bed Reactors (PBRs) having the inherent capacity to promote this recovery or this separation.

PBRs unfold a vast scope for multi-phase chemical processes related applications. They are widely implemented in refineries and used for the separation of high-quality multicomponent fuels (e.g., LPG, Liquified Naturel Gas NGL),…). In particular, PBRs have been increasingly attracted to perform two-phase reactions for many processes, e.g. distillation, gas treatment processes, hydrogen production and gasification processes [3]. They result the high interaction of the gas-liquid, liquid-liquid and gas-solid two phases as well as, gas-liquid-solid three phases in the packing scales [4]. On one hand, available PBRs are operated at the mode of counter-current (i.e. the gas flows upwards and the liquid flows downwards) and co-current flow (i.e. the gas-liquid two-phase flows in the same direction upwards or downwards) [5]. Currently, the counter-current flow has been proved to enhance mass transfer between gas and liquid in diverse processes such as distillation. On the other hand, various designs of PBR are discussed in the literature and comprehensive reviews are presented by [6]–[8]. The aim is

3 to obtain the best trade-offs between capacity and cost-efficiency. In summary, the packing is played an important role in PBRs which composed of porous pellets of mixed complex shapes in order to govern the flow dynamics and to obtain lower pressure drop along the bed. In most applications, there are the spherical and the structured packings arranged in regular and irregular manner. All these packings feature a high interfacial area between the gas and liquid phases where the liquid flowed in the form of a film with a mixing of the adjacent gas flow. Numerous studies have demonstrated that the regular packing is superior to irregular one in performance [9]–[11]. But, in practice, it is rare to find regular packing in industry. So far, irregular packing is widely used because of its simpler installation and blocking resistance [12].

Over the past decades, the hydrodynamic and heat and mass transfer through PBR have been studied using experimental and numerical approaches [13]–[15].Besides experiment, the numerical simulation has been another effective method to study the flow characteristics in PBRs with development of CFD (Computational Fluid Dynamic) technology [16]. Essentially two main models have been used: the “Eulerian– Eulerian” approach (E-E), in which the gas and liquid phases are treated as interpenetrating continua, and the “Eulerian–Lagrangien” approach (E-L), in which the gas phase is treated as continuous and the liquid phase as discrete. Among current available models, “E-L” approach was the most commonly applied one for many numerical studies [17]. In E-L, the liquid can be tracked by a dense number of droplets pulverized from a spray mode for a very high gas flow. Most importantly, this approach can generate detailed information of the liquid phase, such as spray breakup and atomization; droplet drag, collisions, and coalescence. PBR involving spray injection technique is appeared to be advantageous in terms of mixing, dispersion and controlled penetration [18]. For example, Deshpande et al. [19] applied the spherical packed bed with three-phase E-L model for their studies. They have yielded a liquid-continuous packing with dispersed gas bubbles where the spray zone is defined in the bottom. They especially studied the effect of bubble size over the bed with different particle to diameter ratios and reported that significant huge bubbles coalescence only occurred where the particle diameter was very small. Velo et al. [20] reviewed the main liquid holdup characteristic of random packing.

Also, the performance of such packed bed depends heavily on models describing the pressure drop of the two phases through the bed. To save computational cost, the packed bed was considered as porous media [21]. The available porous media models in the CFD simulations are the Ergun et al. [22], Stichlmair et [23], which was expressed on the basis of 640 experiments on spherical particles of different diameters, sand and coke particles in the

4 range 0.4<Re<1000. However, the area of particles in such real-world packed bed were not all equally effective and non-uniformly sized. The presence of different particle shapes or sphericities (for spheres to non-spherical particles) was taken early in the pressure drop calculation by correcting the Ergun’s equation [24], [25]. Several modeling efforts have been devoted to accommodate the distribution of particle sizes. Feng et al. [26] have made a new correlation based on the relationship between the modified Ergun’s equation and the effective area of each particle. This correlation has invoked the use of a so-called sphericity, defined as the ratio of the surface area of the volume-equivalent sphere to the actual particle surface area. Kruggel-Emden et al. [27] and Vollmari et al. [28] have conducted their research on a number of irregularly shaped particles using CFD model coupling with Discrete Element Methods (DEM). They have systematically evaluated the different contact orientation. Meanwhile, all these correlations have been proven to be more appropriate if irregularly shaped particles have to be resolved. However, in our study, we carried out only the spherical particles with uniform size. So, Ergun’s equation may be applicable by reference to its advantages in several works and especially when Reynolds number is Re < 500 and particle to diameter ratios of at least 20.

A wide variety of fuels that are distilled and used in the chemical and power industries. One such fuels attracting commercial interest over the years are the LPG which is a byproduct of the petroleum refining mainly consists of propane and butane. LPG presents a prospective alternative in vehicules, since it is renewable and has the advantages of low boiling point and low price. To extract the LPG from PBRs, at least two fuels mixtures need to be addressed: the NGL and CG. These fuels are a kind of multicomponent mixture. They composed of a large gamme of hydrocarbons in which methane CH4 (or C1), ethane C2H6 (or C2), propane C3H8 (or C3) and n-butane n-C4H10 (or n-C4) present the main ones. In PBR, those hydrocarbons can be either as gases or vapours or as spray injections. The main problems arises from the physical barrier between phases that can alter the typical evaporation process. Moreover, the thermo-transport properties of these hydrocarbons are different from those of gasoline. To our knowledge, the two fuels have not been fully understood in CFD nother in experimental studies. Consequently, those hydrocarbon are attempted as conscientiously as possible in this research.

Nowadays, majority of the studies were focused on the evaporation of the diesel and gazoline [17]. They investigated the spray characteristics of diesel and gazoline in a constant volume chamber under both conventional diesel combustion and low temperature combustion conditions. Furthermore, many researchers studied extensively the phenomenon of a single droplet immersed in hot air. Mono-, bi- and multi-component droplet evaporations were

5 investigated via both experiment and simulation. As an example, Daif et al. [29] have experimentally studied the evaporation process of bi-component heptane–decane droplet, under three typical modes: natural, forced and mixed convective modes. They have examined a single evaporating droplet composing of different initial blend compositions, at temperatures up to 350 K and at atmospheric pressures. The droplet size varied in the range of 0.5 to 0.756 mm and their experiments have proved that the vaporization in a forced convection would lead to an increase in the evaporation rate than that in natural convection. However, Gavhane et al. [30] numerically have investigated the evaporation performance of n-heptane-n-dodecane and methanol-ethanol droplets in a non-convective medium of fuel vapors. They have concluded that the presence of fuel vapors in a free stream would raise the droplet lifetime due to the condensation of the vapors at the droplet surface. Furthermore, several studies have analyzed the influence of the turbulence on the vaporization rate. They have concluded that the turbulence had a great impact on the evaporation of all components in the droplets, even the less volatile one ([11-12]). Extensive investigations of a three-component gasoline surrogate were made by Elwardany et al. [33] to predict the influence of a carbon portion and the different surrogates on both droplet diameter and temperature’s evolution.

On the other hand, papers published on the multi-component systems are comparatively rare. They have used commercial gasoline fuels with a smaller number of hydrocarbon (between 2 to 7) compared to the real gasoline fuels. Furthermore, different complex structures have been replaced with single components as reviewed by [34]. Chen et al. [35] have studied the evaporation of multicomponent fuels in laminar flows and at low ambient temperatures. Ra and Reitz [36] have developed a discrete multi-component model to track the evaporation of each component in the fuel mixture separately at various ambient and droplet temperatures. They have concluded that the regression of the droplet life time of a multicomponent single droplet significantly differed from that of a single component droplet. The evaporation became better in the early stages of the drop temperature. In other study, in order to incorporate the gravity dependence on the droplet heating period and lifetime, Huang and Chen [37] have assumed that the gravity causes the forced convection in the droplet surface which leads to an increase in the vaporization and a decrease on the droplet lifetime. Padoin et al. [38] have applied a Eulerian-Eulerian approach in a pseudo 1D geometry to investigate the coupled heat and the mass transfer. A multicomponent mixture composed of four hydrocarbons has been studied to predict the equilibrium concentration in the steady state condition.

6

Aim & Objectives

The general objective of this thesis is to develop a new small-scale of PBR and to numerically understand the evaporation of LPG. This thesis represents a significant progress from the previous studies and the main objectives are:

• to investigate how CFD or Ansys FLUENT can be used to model heat and mass transfer phenomena in PBR,

• to construct a novel column with uniform spherical particles which is the industrially preferred configuration due to high surface-to-volume ratio and to propose a new flow mode between phases,

• to work with real feed mixtures of NGL and CG using Aspen Hysys for their process and Raoult’s law for their physical parameters,

• to thoroughly investigate and discuss the effect of initial conditions e.g. species concentration and temperature profiles on the droplets surface, droplet diameter, as well as pressure drop across the packed bed. Furthermore, transient variations of interfacial area between phases and spray angle are included for the analysis.

• and finally to develop empirical expressions derived from numerical results.

Thesis Outline

The thesis is organized as follows:

The first chapter, an extensive literature survey of natural gas is necessary. Besides, an overview of the various distillation column is presented. The physical description of the multicomponent mixture is revisited. This chapter also contains a brief description of E-L approach with the governing equations solved. The evaporation model is also carried out in this chapter.

In the second chapter, we have made a comparison between the two streams “LPG” and the CG under the same conditions. An alternative PBR model is numerically investigated using CFD. In this chapter, a simplification in design was done in order to decrease the memorial computational demand. The packed bed was considered as porous medium where the packings shape, size and porosity have been assumed constants during the computations. An evaporating fuel sprays were also included. The effect of key parameters, namely, the mass fraction of heavy components in the droplets and the droplet size, on heat and mass transfer was investigated.

7 Nonetheless, further validations will be shown by comparing two-component direct numerical simulation droplet evaporation. This chapter is published as an article by Hajer et al. [39]. In the third chapter, we proposed a new type of gas-liquid contact, named the cross flow. An alternative designs of PBR were presented to handle various gas flow configurations. A set of particles were placed inside the bed in order to form a real geometrical packed structure. First, results of single-phase flow including comparisons with experimental data are briefly outlined and then, modifications in the modelling of packed bed are described. Finally, a conservative design is proposed based on results of the sensitivity analysis.

Chapter 4 is concerned to develop new correlations for sauter mean diameter and interfacial area using two different methods (The LINEST and the MAPSO).

Finally, chapter 5 will summarise the present research study and highlight the conclusions drawn from the work. Suggestions for further research based on the current work will also be made there.

8

Chapter 1:

State of the art in CFD simulation of

Natural Gas

9

Chapter 1: State of the art in CFD simulation of Natural Gas

1.1. Introduction

This chapter is organized as follows. In brief, Section 1.2 provides insight into the state-of-the-art research in the refinery process, as well as into different applications which suits the natural gas treatment to generate LPG and NGL. Section 1.3 provides on overview on the NG traitement unit. The Eulerian-Lagrangian framework is chosen to be used as a basis for all the simulations and discussed in detail in Section 1.4. Expressions of pressure drop are also outlined. Key conclusions from the first chapter are highlighted in the final Section 1.5. 1.2. State of the art

Natural gas is made by processes based on the separation of oil-water-gas towers or distillation columns comprised in a closed unit. The first is a sample technologies as they are easy to install and more flexible. While, the second one is operated based on the phases conversion (from gas to liquid and from liquid to gas). The main roles of the processing plants are to process the oil supplied by various wells, separate the oil, gas and water phases, and purify them into specialized sections, as we shall discuss below. The following subsections provide an overview of the processes present on site, as well as the values of the set temperatures and pressures used for the simulations.

1.2.1. Separation of oil-water-gas

The first step is the three phase separation, in which three processors are highlighted: the gravity separator, hydrocyclone and the gas flotation unit (Figure 1.1). The gravity separator is a stainless-steel tank with internal equipement divided into three groups: the top, middle, and bottom. The mixture stream is fed from the top and splited into three separate phases. The heaviest phase is colleted and departed the vessel from the water outlet, while gas phase, as the lightest phase, leaved the vessel by a butterfly valve in the top gas outlet. The crude oil phase departed the vessel through oil outlet gate. Normally, the gravity separator are set as horizontal or vertical vessel depending on the platform requirements and can simulate gas-liquid two-phase flow, liquid-solid two-two-phase flow or gas-liquid-solid three-two-phase flow. Cyclonic separations are used to remove particulates or sands from wet gas, oil, and water streams, without the use of filters, through vortex separation. In this setup, a swirling gas flow is formed when the particle-gas stream enters the choking nozzle input, which centrifuges the particles toward the wall, allows sufficient gas residence time and enhances separation process. The wet

10 gas is often mixed by a large amount of water vapor. The presence of water vapor in the natural gas poses many difficulties such as corrosion and hydrate formation in the corresponding trunk-lines. So, it is imperative to reduce the water content using the so-called dehydration processes, such as condensation by cooling, chemical adsorption, absorption and membrane technology, as shown in Figure 1.1. To date, absorption is the most attractive one which involves adding a glycol (e.g., TEG, MEG) as a solvent to the wet gas in order to adsorbe the water content which can then be separated. Thus, the glycol and the water accumulate by gravity in the lower part of the separator, while the natural gas gathers in the upper part. The absorption happen in several kinds of porous solid materials. The removed water is circulated into the liquid storage tank while the crude oil is pumped into the crude distillation unit.

Figure 1. 1 Overview of the different steps in the oil and gas processing.

1.2.2. Crude oil distillation

The crude distillation is the major fractionation unit placed in any refinery. Although the actual units are very complex, a schematic of a typical one can be described as shown in Figure 1.2. It consists of a vertical cylindrical column containing a number of inlets and outlets that are located at top, middle and bottom to transport the gas and liquid phase respectively. It composes of some external devices (tanks, special steam pumps, steam reboiler, etc…) and internal ones

Gravity separator Cyclone separator Natural gas Water Crude Oil Three streams + dust particles Sand Handing Gas treatment Condensation Absorption Adsorption Membrane Crude distillation unit Porous structure

11 (the liquid distributor, packing materials, demister, etc…) The crude oil passed through the preaheted section and was then pumped into the reboiler. The reboiler is installed at the downstream of the column and used to heat the oil feed. The heat causes components with lower boiling points to be vaporized, leaving low volatile components as residues. The heated vapor feed stream is then flown up the column. The feed inlet is loaded into the column from its bottom by a peristaltic pump, making direct contact with a counter flowing gas stream. Inside the column, both gas and liquid revolve around the vertical axis. The reflux is flowed into a collector and then sparged from the top through a liquid distributor with pore diameters. The purpose of the distributor is to generate small droplets, and distribute these droplets as evenly as possible among the packed beds. The lower end of the column is immersed in residue (RE). The column is employed either to integrate or remove heat in order to recover the difference in relative volatility. This complicates the separation of close-boiling compounds. Thus, it is necessary to use some appropriate distillation techniques to achieve the desired separation. The gas exiting the top such as the Refinery Gas (RG) and Liquefied Petroleum Gas (LPG) alone are taken off of the column and condensed by the overhead condensers before venting to the fractionnation columns. This technique can provide the so-called the Condensate Gas (CG) which accounts as a significant part of NG. Meanwhile, the GC is a very complex mixture, since a large number of components have already been produced. Another common gas that is gradually appeared during the course of the CG is MEP. This gas is obtained by mixing three ligth components which are Methane (M), Ethane (E), and Propane (P), as described in [39]. Naphtha is produced as a vapour and Kerosene, diesel, and atmospheric gas oil are withdrawn as side streams and further refined using side columns. The residue is formed by some heavy compounds (e.g., lubricant, asphalt and coke).

12

Figure 1. 2 Structure and operating principle of a crude distillation unit.

1.2.3. Distillation column

Frequently, the packed bed design consists mainly of a dense array of spherical packings which also called solid particles (e.g, ceramic Raschig Rings, Ceramic Sponges, Berl and Intalox Saddles, Tellerette and Pall Rings, etc,…), as illustrated in Figure 1.3. The spherical packing designs were previously studied by Lopes et al. [40], But also, there are the packed bed with structured packings made of corrugated sheets arranged in parallel successive layers (e.g, Mellapack 250Y, Mellapack 250X, TSP250X..) [41].The structure achieves great efficiency in heat and mass exchange with low incrustation/retention of dirt [42]. The fluid is circulated in the spacing between the grill-shaped plates and its configuration allows a perfect distribution of air within the contact fill. However, design of a structured packing is restricted to the best knowledge of some specific parameters, e.g. surface area, void fraction. Moreover, the corrugated shape of these packings and their angle have an impact on the uniform distribution of the flow and, consequently, on the heat and mass transfer performances. There are some other technologies consist of cylindrical, hollow cylindrical and angular parallelepipeds particles, which have advantages compared to conventional packings [14], [43]. These

Heavy Bottoms : Lubricants Coke Asphalt Gas Cr u d e oil d istil la tion Kerosene Diesel Heavy Naphtha Light Naphtha Liquefied Petroleum Gas LPG Gasoline Crude storage tank Furnace

Crude oil pump Preheating

13 configurations afford high interface-to-volume ratios necessary for high heat and mass transfer effectiveness not only along the height of the column but also in the cross section. For each particle, the mixing of gas–liquid is floated and a thin liquid film around the particles is generated.

Figure 1. 3 Illustration of packing geometries of a spherical particles and corrugated sheets [44].

1.2.4. Flow modes

Genrally, the design of the PBRs has unchanged for a century. With regard to the industry, the commonly used modes in the PBRs can be classified into two categories, i.e. the co-current and counter-current flow, where the gas moves either upwards or downwards. However, these modes have given rise to some problems such as, liquid flooding, low wetting capacity of the packings and high pressure drop which, in turn, limit their widespread applications. Moreover,

Liquid Feed

Vapor Feed Packing

Interface

14 the gas charging and discharging in PBR can affect the transfer efficiency between phases. In order to solve these problems, it is recommended to change the flow mode. One of the most promising modes in PBR is the cross-flow, where the gas flows tangentially within the bed and circulates around the spray area, as will be discussed in Chapter 3. This one of process creates the so-called centrifugal force which drives the spray to flow toward the radial positions and thus leads to a more effective separation. To the best of our knowledge, this process is often studied either in moving beds (e.g., rotating packed bed) or in diesel engines. Recently, a more general comparison of different modes has been numerically observed by Marek [14]. He investigated and confirmed that the cross-flow mode is an efficient way to achieve the lowest pressure drop and the shortest maldistribution factor. Also, the interest of combined PBRs and cross-flow has been shown by the work of Kaskes et al. [45] and Liu et al. [46]. For a better understanding of this mode, reference is made to Chapter 3.

1.3. Natural gas NG 1.3.1. Process description

In general, NG is converted to liquid in order to allow it transportation from the reserves to the market. Before the liquefaction of NG, toxic components such as carbon dioxide CO2 and carbon monoxide CO must be completely eliminated or, as far as possible, transformed into methane by methanisation. This is done because when liquefying the NG, CO2 will be cooled and thus damage the pipelines. Similarly, the remaining low-boiling impurities, e.g. hydrogen H2 and nitrogen Ni can be removed before, during, or at the last stage of the liquefaction process. After that, NG enters in the liquefaction plant at the pressure of 50 bar and temperature of 25 °C. To date, the cascade process by a heat exchanger is the most operated one in the liquefaction process, in which NG is pressurized and cooled by the water-coolers. As it passes through the heat exchanger, its temperature decreases to approximately 48 °C. Then the cold NG undergoes the first expander to reduce its pressure and temperature. After pre-cooling, NG enters the Laval nozzle and is liquefied at high velocity and low temperature. Next, the remaining gas and the condensate enters the fractionation unit where the two phase are separated. The liquids flow into the NGL storage tank then they enter the farctionation unit, in which C1, C2 and LPG are separated in several stages operated at different temperature and pressure levels. The low temperature natural gas from the gas-liquid separator mixes with the BOG (boil-off gas) produced from the NGL storage tank and then enters into the heat exchanger

15 to heat the inlet natural gas. In short, this process is considered simple and does not take much installation space. Also, it does not require any additional energy, e.g. reboilers, condensers...

Figure 1. 4 Overview of the different steps in the oil and gas processing.

1.3.2. Pilot plant

Figure 1.5 presents a pilot plant of a natural gas fractionation unit, which have provided the experimental data used in this work. The Aspen HYSYS (version 7.3) is used [47]. The system mainly comprises of de-methanizer, de-ethanizer, de-propanizer and de-butanizer reactors where subsequent oxidation and reduction reactions take place respectively. The pilot plant includes a number of distillation columns, reboilers, column condensers (air cooler or water cooler), reflux drums, etc.

Figure 1. 5 Pilot plant.

Fractionation unit NG Liquefaction NGL storage tank NG compressor Mercury removal unit NG dehydration unit NG traitement section LPG C1 C2 Condensate

16 1.3.3. De-methanizer and de-ethanizer

The deethanizer column has 26 stages including condenser and reboiler with tray efficiency of 50 % utilizing valve tray. The top product of the deethanizer column is “ethane” and it is sent to an adjacent petrochemical plant. The bottom product is called “LPG” consisting almost propane, i-butane and n-butane. The required heat input to derive the hydrocarbon separation is supplied by low pressure (LP) steam at the reboiler (steam in tube side). The run specifications for the deethanizer column in terms of condenser and reboiler temperatures are 6 °C and 95 °C, respectively. The demethanizer pressure considered is 3516 kPa, in accordance with industry standards.

1.3.4. De-propanizer

The cut of C3+ from the bottom of the de-ethanizer, feeds the second de-propanizer column. The role of de-propanizer is to separate propane C3 at the top of the column from the rest C4+. As aforementioned, Propane is a component of LPG family and C4+ is thus transported to the third column. De-propanizer operates at a pressure of about 2356 kPa. The temperature at the head is about 63°C and temperature at the bottom is about 118°C. Below, Figure 1.6 is a numerical example of a de-propanizer column made by the Hysys software.

Figure 1. 6 De-propanizer.

1.3.5. De-butanizer

The cut C4+ from the bottom of the de-propanizer, enters the third de-butanizer column. The role of de-butanizer is to separate the butane C4 at the top of the column from the rest C5+ which is placed at the bottom of the head and known as gasoline. De-butanizer has about 40 trays and operates at a pressure of about 2468 kPa. The temperature of the head is about 100°C and the bottom temperature is about 123°C.

17

Figure 1. 7 De-butanizer.

The feed stream containing NGL can be introduced into the distillation column between the packed sections S1 and S2 (Figure 1.8). The reboiler located at the bottom, is used to vaporizer a part of the NGL with the desired operating temperature. The rest is extracted as bottom stream. A total condenser at the top allows condensing the entire overhead vapor stream, which is collected in a reflux drum. Part of the condensed liquid is fed back to the column as reflux, while the remainder leaves the column as distillate. Both liquid and vapor phases flowed through the column counter currently via distributors.

Figure 1. 8 General Distillation Process.

Relux drum Distillate materials Bottoms Feed materials Reboiler Outlet materials

18 1.4. CFD simulation in natural of Natural Gas

To date, it is worth mentioning that works relating to the use of mixture of light and heavy components, i.e. methane CH4, ethane C2H6, propane C3H8 and n-butane n-C4H10, and other components were widely unattended. Mostly, they were only provided by using a process simulation such as Aspen Hysys and not yet been treated by using a fluid dynamics simulation such as CFD [48]. The main reason is that the computational cost for light components is expensive and the complexity of modelling increases considerably as the number of components increases. In addition, the use of CFD also presents a great challenge since the local temperature of the four primary components in the liquid phase is below - 100°C. Likewise, there were few available experimental data for these components in both phases (liquid and gas), due to their extremely high vapour pressure at high temperature. However, these components are indeed widely engineerable at the PBRs, and in particular, in distillation columns. On the contrary, the recent studies have been greatly limited on the separation of reduced pure fuels namely, oil and gas, biodiesel and commercial diesel by such as Magaril et al. [49], Perez et al. [50], Huang et al. [51] and Ren et al.[52]. The reason behind this is that these components were already condensed, immiscible and have a high boiling point, as well they were ease functioning. These fuels were generally studied in constant volume chambers [53] or in simple engines regardless the complexity of the PBR in order to reduce the computational cost and augmenting the mesh resolution.

Similarly, less work has been done on the internal configuration of the PBR, i.e. the shape of inlet/outlet system as well as the two-phase flow mode. According to [54], the co-current mode has suffered from some drawbacks owing to the uniform distribution of the gas and liquid phases along the column. The same thing for counter-current mode as discussed in Section 1.2.4. Using CFD, the counter-current mode was totally ignored. To summarize, this thesis addresses the aforementioned issues.

1.5. Eulerian-Lagrangian approach

With the continuous progress of the computer science, CFD has proven to be a very useful tool in the processe design and simulation involving, e.g. spray flow, heat and mass transfer. As mentionned in the introduction, the E-E approach has proven to be inappropriate to fully describe the interaction between species. Even if the present PBR has been considerably simplified compared to a real device, the complexity of the two-phase flow make the use of E-L method very significant. In this thesis, E-E-L is used for two ways: to describe the coupled external heat and mass transfer from gas to droplet which are important for treating the

19 evaporation of species in the droplets (See Chapter 2), and to track droplet motion around the solid particles which, consequently, change the moment of spray morphology (See Chapter 3). In addition, E-L treats the coupling between phases through their own properties (velocity, temperature,…). It takes into account the phenomena of growth, breakage and coalescence of droplets. For modelling, ANSYS Fluent 14.5 has been performed throughout the thesis in order to tackle the objectives. For better understanding the process, a general scheme which summarizes the necessary conditions for E-L is represented in Figure 1.9. A complex pattern of momentum exchange between droplets and gas phase takes place.

Figure 1. 9 Flow chart of Eulerian-Lagrangian approach.

1.5.1. Basic equations

The Eulerian-Lagrangian method is used to describe the thermo-fluid behavior of the evaporated droplets in the gas. The droplets compositions are modeled as discrete mixture of 12 species. They formed a group of zero-dimensional spherical parcels with identical properties. The parcels are individually tracked, both with respect to their spatial coordinates in the model

Main CFD Framework

Gas phase

12 species : C₁-C₁₂ Standard K-ε

Packed bed: Porous medium

Ergun model Permeability K Inertial loss coefficient C₂

Liquid phase: Spray/ Droplet

Discret phase model 12 liquid species : C₁-C₁₂ Evaporation model

VLE by Raoult’s law

Initialize temperature, velocity and mass fraction of each species, k-ε model

Initialize bed porosity, shape, Initialize temperature, mass flow rate, mean droplet size, mass fraction of each species, coalescence and breakup

20 domain and attributed scalar properties. The gas phase is formulated through a set of conservation equations for mass, momentum, energy and turbulence. The subscripts “q” and “p” respectively define the continuous phase, which is the gas, and the dispersed phase, which is the multicomponent droplets.

(a) The continuity equation for the gas phase is governed by:

( )

₍

₎

1 . u sp N q q q i i m t • =  +  = 



  Eq 1. 1

(b) The momentum equation for the gas phase is governed by:

( ) (

quq . _qu u_q q

)

_q .

(

(

_{q sgs}

)

( )

u_q

)

_q p P p g F t H       _ +  = − +  +  + + −  Eq 1. 2

(c) The energy balance for the gas phase is governed by:

(

)

₍

₍

₎

₎

₍

₎

_{( )}

, 1 . . . . u . sp N q q m T q q q q q eff q q q i q i i q i i q E T V E p k T h D Y D t = T       +  + = −  −  + _{ }−  − __  _



_{ } A _B C     Eq 1. 3

(d) The conservation of species in the gas-phase is governed by:

(

)

₍

₎

, u q q i q m T q i q q i q i i q i q Y T Y D Y D m t T    •     +  = − −_  − _+  _{ } Eq 1. 4

where t represents time,

u

q the instantaneous velocity of the gas phase, q is the ambient gas density, 1 sp N i i m • =



are the inter-phase mass transfer terms from the liquid phase due to surface chemistry at the gas–liquid interface and i is an integer in the range 1 i N_sp. In present simulations, these inter-phase terms are summed over the species in contact with the droplet where Nsp is the total number of chemical species in both phases. pis the pressure,g is the

gravitational force,



qis the dynamic viscosity and the subscript q refers to the liquid phase.

P



is the pressure drop and

H

pis the height of the packed bed. The forceF is the coupling

term with the discrete phase solver, and represents the momentum exchange due to droplets passing through each computational cell.

21 In Eq.1.3, Tq represents the temperature field of the gas phase. The expressions on the right

hand are as follows: A represents the heat transfer by conduction, where the effective conductivity keff is assumed to be the summation of mass fraction Yi of species i in the gas phase

and their conductivity ki. B denotes the heat transfer caused by viscous dissipation. Neglecting

Soret effect, the right side C is the enthalpy source caused by the diffusion of Nsp species in the

gas phase and is obtained by multiplaying with the diffusion flux of species i at the mixture of phase g.



D_im,D_iT



are the mass and thermal diffusion coefficients of i-th vaporized species in the phase (either gas or liquid). hi is their corresponding enthalpy due to species diffusion. For

such multicomponent problems, the transport of enthalpy hi has a significant effect on the

enthalpy field and should not be neglected. The species flux either in the liquid phase or gas phase is expressed using Fick’s law. A and C represent the flux of the heat transfer.

The mass transfer flux rate coefficient (the j vector) is determined by the mass fraction and temperature gradients at the interface. To base on the Stefan–Maxwell, it can be expressed in the form of (Nsp -1) dimensional matrix:

, q m T i q i i q i q

T

j

D

Y

D

T









= −



_



+



_





Eq 1. 5

Finally, the right hand side term C of Eq 1.3 may also be expressed as shown in Eq 1.6:

1 sp N i i i h j =



Eq 1. 6

Notice that in Eq 1.4, species released by reaction rate are neglected. Here, the mixture only undergoes an equilibrium liquid-vapor, as will be presented in the ensuing Chapter 2. Mass transfer source term m_i

•

is not zero at the interface where mass transfer occurs.

For the turbulent models, most researchers were pointed out that the application of large eddy simulations and multiple droplet size simulations help to improve the simulation results. The standard (k-ɛ) model is used to model the turbulence phenomena in the gas phase, whilst the dispersed phase zero equation model was used for the liquid phase, but the influence of the dispersed phase on turbulence of the gas phase was taken into account using Sato and Sekoguchi model. The transport equations for the turbulence kinetic energy (k’) and the rate of dissipation of turbulence kinetic energy (ɛ’) for the liquid phase are thus: