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A Thesis Submitted To The

Department of Chemical Engineering of the University of Technology in a Partial Fulfillment of the Requirements for the

Degree of Master of Science in Chemical Engineering

By Ali Adel Nader

B.Sc. in Chemical Engineering 2004

Supervised by

Dr. Khalid A. Sukkar

November / 2008

Ministry of Higher Education & Scientific Research

University of Technology Chemical Engineering Department

Simulation of Gas-to-Liquid (GTL) Process in Slurry Bubble Column Reactor

مقدمة الى اطروحة جزء من متطلبات وهي الجامعة التكنولوجية /قسم الهندسة الكيمياوية

نيل درجة الماجستير في علوم الهندسة الكيمياوية

من قبل نادر عادلعلي

) 2004الوريوس بك( الدكتور بإشراف

خالد عجمي سكر

2008/ تشرين الثاني

العالي و البحث لعلمي وزارة التعليم الجامعة التكنولوجية

يةقسم الهندسة الكيمياو

التمثيل الرياضي لعملية تحويل الغاز الى سائل في التمثيل الرياضي لعملية تحويل الغاز الى سائل في المفاعل الفقاعي ذو العوالق المفاعل الفقاعي ذو العوالق

حيم حمن الر بسم هللا الر

قالوا سبحانك ال علم لنا إال ما علمتناك أنت العليم الحكيم إن

العلي العظيم هللا ق د ص

سورة البقرة

)32(االية

CERTIFICATION OF THE SUPERVISOR

I certify that this thesis was prepared under my supervision in

a partial fulfillment of the requirements for the degree of Master of

Science in Chemical Engineering at the Department of Chemical

Engineering of the University of Technology

In view of the available recommendation, I forward this thesis

for debate by the Examining Committee.

Signature:

Dr. Khalid A. Sukkar

Supervisor

Date: / / 2008

Signature: Dr. Khalid A. Sukkar

Head of Post Graduate Committee

Chemical Engineering Department

Date: / / 2008

CERTIFICATION

We certify that we have read this thesis and as an Examining

Committee examined the student (Ali Adel Nader) in its content and

that in our opinion, it meets the standard of a thesis for the degree of

Master of Science in Chemical Engineering.

Signature: Name: Dr. Khalid A. Sukkar (Supervisor) Date: / / 2008

Signature: Signature: Name: Dr. Jamal Manee Ali Name: Dr. Wadood T. Mohamed

(Member) (Member)

Date: / / 2008 Date: / / 2008

Signature: Name:. Dr. Balasim Ahmed Abid

(Chairman) Date: / / 2008 Approved by the Head of the Chemical Engineering Department

Signature: Name: Dr. Jamal Manee Ali Head of Chemical Engineering Department Date: / / 2008

CERTIFICATION

I certify that this thesis entitled (Simulation of Gas to Liquid

(GTL) Process in Slurry Bubble Column Reactor) was prepared

under my linguistic supervision. It was amended to meet the style of

English Language.

Signature: Asst Prof. Eyad Shamseldeen University of Technology Date: / / 2008

Dedication

To My Family With Love And Appreciation

Ali

ACKNOWLEDGMENTS

Praise be to Allah Who gave me ability to achieve this research.

I wish to express my sincere gratitude, and appreciation to my supervisor Dr. Khalid A. Sukkar for his kind supervision and useful advice during the work on the research.

My deep thanks go Dr. Jamal Manee Ali the Head of Chemical Engineering Department, for his encouragement and providing facilities throughout this work.

I would also like to express my acknowledgment to the

staff of Chemical Engineering Department of the University of Technology. Also great thanks are due, to the staff of the Central Library in the University.

To all who helped me in one way or another, I wish to

express my thanks. And finally my special thanks go to my family for their

support and encouragement.

Ali

I

Abstract

II

ABSTRACT

Gas-to-liquid (GTL) is one of the new processes that are becoming

increasingly important in petroleum industry. This process enables conversion of the

natural gas into very low sulfur content quality middle distillate. The heart of this

process is the slurry bubble column reactor. In the present study a simulation is

developed to describe mass transfer, heat transfer and reaction kinetics in this

reactor.

The model is simulated through derivation of three differential equations to

describe the transport processes that are present in slurry bubble column reactor:

-Mass balance in gas phase

0 ( θ1

1 1 2

2 ) X - Y - Std

Yd)Yα*(

α*)( - dYd

B

gOG

=++

ξξ

-Mass balance in liquid phase

0exp1θ)2

2=−−+ Xγ/θ) ( CDa η) X - Y (St

dXd

B

P (Z)P(L OL ξ

-Heat balance

0exp1- θ1)(2

2 X Cγ/θ) η( Be Da ) ( - St

dθd Pe PpH =−+ θξ

The differential equations are solved numerically using finite difference

method. The solution is carried out by designing a numerical simulation program in

Fortran language. The simulator is systematically used to predict the effects of

reactor geometry, superficial gas velocity, catalyst concentration, operation pressure

and inlet HR2R/CO ratio on the performance of an industrial scale slurry bubble column

reactor. Two types of catalysts were tested in present model, Cobalt and Iron

Abstract

III

catalysts. The results indicate that, the Cobalt catalyst shows higher conversion rate

of (90%) than that of Iron catalyst (78%). Therefore, the Cobalt catalyst is better for

the Fischer-Tropsch synthesis than Iron catalyst. For both types of catalysts, the

model results show high distribution of solid catalyst along the reactor height. Also,

it was found that the favorable HR2R/CO ratio for Cobalt catalyst is about 2, while, for

Iron catalyst it is in the range of 1.5 to 1.7.

On the other hand, the relation between superficial gas velocity and heat

transfer coefficient in slurry bubble column reactor was studied in model

formulation. The results indicate that the heat transfer coefficient increases with

increasing superficial gas velocity and catalyst concentration.

The predictions of the derived model agree well with the experimental and

theoretical data of the literature with an error of 6 % - 9 %.

Contents

IV

UCONTENTS

UPage No.

Acknowledgment .......................................................................................... I

Abstract ........................................................................................................ II

Contents ...................................................................................................... IV

Nomenclature ............................................................................................ VIII

Greek Symbols ............................................................................................ XI

Chapter One: Introduction

1.1 Introduction ............................................................................................. 1

1.2 The Aims of this Work ............................................................................ 5

Chapter Two: Literature Survey

2.1 Scope ........................................................................................................ 6

2.2 History of Fischer Tropsch Synthesis FTS .............................................. 7

2.3 Gas to Liquid (GTL) Technology ............................................................ 9

2.3.1 Synthesis Gas Manufacturing ....................................................... 11

2.3.2 Fischer-Tropsch Synthesis (FTS) ................................................. 13

2.3.3 Product Upgrading and Separation ............................................. 16

2.4 Fischer-Tropsch Reactors ...................................................................... 18

2.5 Slurry Bubble Column Reactor ............................................................. 22

2.6 Fischer-Tropsch Catalysts ..................................................................... 25

2.7 Hydrodynamic of Slurry Bubble Columns ............................................ 29

Contents

V

2.7.1 Flow Regime Analysis ................................................................ 29

2.7.2 Gas Hold-Up (ERgR) ........................................................................ 31

2.7.3 Operation Pressure ...................................................................... 34

2.7.4 Solid Suspension ......................................................................... 35

2.8 Transport Processes in SBCR ................................................................ 35

2.8.1 Mass Transfer .............................................................................. 35

2.8.2 Heat Transfer ............................................................................... 39

2.9 Fischer Tropsch Mechanism .................................................................. 44

2.9.1 Carbene Mechanism .................................................................... 44

2.9.2 CO-insertion mechanism ............................................................. 45

2.9.3 Parallel mechanism ..................................................................... 46

2.10 Modeling and Simulations ................................................................... 47

Chapter Three: Mathematical Model

3.1 Introduction ........................................................................................... 51

3.2 Reactor Model and Assumptions ........................................................... 52

3.3 Formation of Model Equation ............................................................... 54

3.3.1 Mass Balance for Hydrogen in Gas Phase ................................... 54

3.3.2 Mass Balance for Hydrogen in Liquid Phase ............................... 55

3.3.3 Energy Balance for Hydrogen ....................................................... 57

3.4 Development of Model Equation .......................................................... 58

3.5: Numerical Formulation using (Finite Difference Method) .................. 68

3.5.1 Solution of Mass Balance Equation .............................................. 68

3.5.2 Solution of Energy Balance ........................................................... 71

Contents

VI

3.5.3 Boundary Condition Solution ........................................................ 73

3.6 Parameter Estimation ............................................................................. 74

Chapter Four: Results and Discussion

4.1 Introduction ........................................................................................... 78

4.2 Hydrogen Profile in Liquid and Gas Phase ........................................... 79

4.3 Catalyst Distribution Along the SBCR ................................................. 81

4.4 Temperature Distribution Along the SBCR .......................................... 83

4.5 Superficial Gas Velocity Profile Along The SBCR .............................. 85

4.6 Heat Transfer Coefficient ...................................................................... 87

4.6.1 Effect of Superficial Gas Velocity ............................................... 88

4.6.2 Effect of Catalyst Concentration .................................................. 88

4.7 Syntheses Gas Conversion .................................................................... 91

4.7.1 Effect of Superficial Gas Velocity and Catalyst Concentration .. 91

4.7.2 Effect of Reactor Height .............................................................. 94

4.7.3 Effect of Operating Pressure ....................................................... 95

4.7.4 Effect of Reactor Diameter .......................................................... 97

4.7.5 Effect of inlet ratio ...................................................................... 99

4.8 The Validity of the Present Model ...................................................... 102

4.8.1 Synthesis Gas Conversion .......................................................... 103

4.8.2 Heat Transfer Coefficient .......................................................... 104

4.8.3 Hydrogen Profile in the Gas Phase ............................................ 105

4.8.4 Hydrogen Profile in the Liquid Phase ........................................ 106

Contents

VII

Chapter Five: Conclusions and Recommendations

5.1 Conclusions ......................................................................................... 107

5.2 Recommendations .............................................................................. 109

References .............................................................................................. 110

Appendix A .......................................................................................... A-1

Appendix B ........................................................................................... B-1

Nomenclature

VIII

UNOMENCLATURE

Symbol Definition Units A Across section area of reactor (mP

2P)

ARP Liquid- solid cross section area

a gas–liquid specific interfacial area per unit expanded bed volume (mP

2P/ mP

3P)

aRH specific heat transfer area referred to the total reactor volume (mP

2P/ mP

3P)

aRP Liquid- solid specific interfacial area (mP

2P/ mP

3P)

Be Dimension less group defined by eq

T Hey P

) Cp ρ

ΔH- ( Be

w

oR=

(-)

BROC Bodenstein number of catalyst particles

C

CSOC E

LUB =

(-)

BROG Bodenstein number for gas phase

gg

go

E D

L uB

OG=

(-)

BROL Bodenstein number for liquid phase

LL

goE DL u

BOL

=

(-)

CRg Concentration in gas phase (mol/mP

3P)

CRHR /CRH.L Concentration of hydrogen in the liquid phase (mol/ mP

3P)

CRH* Equilibrium concentration of hydrogen in the liquid phase (mol /mP

3P)

CRH.P Hydrogen concentration at catalyst surface (mol/ mP

3P)

CRP Particles concentration (mol /mP

3P)

Cp Heat capacity of the liquid-solid suspension (J/ kg K)

LCp Heat capacity of liquid (J/ kg K)

PCp Heat capacity of catalyst (J/ kg K)

Da Damkohler number

go

Lfu

L EKDa =

(-)

gD Gas phase dispersion coefficient (mP

2P/ s)

L D Liquid phase dispersion coefficient (mP

2P /s)

HL D . Diffusivity of hydrogen (mP

2P/s)

Pd Catalyst particle diameter (m)

Dr Reactor diameter (m)

Nomenclature

IX

E Specific energy dissipation rate. mP

2P/ s P

3

AE Activation energy (J/ mol) CE Axial dispersion coefficient of the catalyst Particles (mP

2P /s)

gE Gas holdup (-)

LE Liquid holdup (-)

Fr Froude number g Dr/uFr g= (-)

g Gravitation constant (m/ s P

2P)

He Henry coefficient (Kpa/mP

3

PMol) h Heat transfer coefficient (W/mP

2P K )

RΔH− Heat of reaction for the overall conversion of synthesis gas to hydrocarbons

(J/ mol)

I Molar ratio of hydrogen to carbon Monoxide at the reactor inlet

(-)

K Reaction rate constant for hydrogen consumption rate referred to wt % (Fe or Co) in slurry (1/ s)

axK Effective heat conductivity of suspension (W/m K)

fK Frequency factor for hydrogen consumption rate referred to wt % (Fe or Co) in slurry (1/s)

0K f Frequency factor for

fK (1/s)

HK Reaction rate constant for hydrogen consumption rate (1/s)

LK Liquid side mass transfer coefficient (m/ s)

P K Liquid - solid mass transfer coefficient (m/ s)

L Reactor length (m) N Mole flow rate (mole/ s) P Total pressure (Pa)

Pe Peclet number for heat ax L

goKE

LCp ρ uPe= (-)

R Universal gas constant (J /mol K)

2HCOR +

Synthesis gas consumption rate (-)

2H R

Hydrogen reaction rate (-)

Nomenclature

X

HSt Stanton number for heat transferCp ρ u Lh a

Stgo

HH =

(-)

gSt Stanton number in gas phasego

wHLg uHe

LTRa) (KSt

=

(-)

LSt Stanton number in liquid phase go

HLL uLa)(K St =

(-)

T Temperature K TRw Cooling wall temperature K

gu gas velocity (m/ s)

gU Superficial gas velocity (-)

gou Inlet gas velocity (m / s)

CSU Settling velocity of catalyst particle in swarm (m/ s)

U Usage ratio of hydrogen to carbon monoxide (-) V Volume of reactor (mP

3P)

gV Volumetric gas flow rate (mP

3P/ s)

PV Volume fraction of catalyst in suspension (-)

PW Concentration of catalyst in suspension wt% (-)

x Axial coordinate (-)

X Dimensionless hydrogen concentration in liquid phase (-)

HX Conversion of hydrogen (-)

2HCO X +

Conversion of synthesis gas (-)

y Hydrogen mole fraction in gas phase (-)

Y Dimensionless hydrogen concentration y / oy (-)

oy Inlet hydrogen mole fraction (-)

Nomenclature

XI

UGREEK SYMBOLS

Symbol Definition Units ξ Dimensionless axial coordinate (-) α Contraction factor eq. (3.137) (-)

α* Modified contraction factor eq.(3.47) (-)

γ Arrhenius number (-) ηP Liquid – solid mass transfer effectiveness factor (-)

λ Heat conductivity of suspension ( W/m K )

Lλ Heat conductivity of liquid ( W / m K )

Pλ Heat conductivity of catalyst ( W/ m K )

μ Viscosity of suspension (kg /m s)

Lμ Viscosity of liquid (kg /m s)

ρ Density of suspension (kg/ mP

3P)

L ρ Density of liquid (kg /mP

3P)

P ρ Density of particle (kg /mP

3P)

Ө Dimensionless temperature T/TRw (-)

Symbol Definition CFB Circulation fluidized bed FFB Fixed fluidized bed FTS Fischer-Tropsch Synthesis GTL Gas To Liquid LAS Linear Alkyl Benzene Sulphonate

SMDS Shell Middle DistillateSynthesis SMR Steam Methane Reforming TFB Tubular fixed bed

Chapter One Introduction

1

CHAPTER ONE

INTRODUCTION

1.1 GTL is the technology using natural gas to make a clean, versatile

liquid fuel. This is a complementary rather than competitive technology for

the exploitation of stranded natural gas. In the present world of energy

scenario, the supply of oil and other natural resources is limited and not

uniformly distributed [ Dry, 2002; Tiefeng et al.2007].

Introduction

Natural gas is available in large quantities and the reserve is not used

to the same extent as crude oil. Although it does have some drawbacks

compared to other fuels, mainly issues dealing with its volume, it promises to

be an increasingly important energy source in the years to come. It is

important to mention here that methane is the principal component of natural

gas currently being used for home and industrial heating as well as for

generation of electrical power. Also, natural gas burns cleaner and produces

fewer pollutants than other fossil fuels. It has the largest heat of combustion

relative to the amount of CO2 formed. It produces 45% less CO2

than coal for

a comparable amount of energy, and also emits considerably less NOx and

SOx [De smet, 2000; Laurent et al. 2008].

During the last ten years, there has been a renewed interest in Gas-to-

Liquids (GTL) technology, in which natural gas is converted to liquids useful

as fuels and chemicals feedstock through the Fischer-Tropsch-Synthesis

(FTS). In the gas-to-liquid (GTL) technology, natural gas is converted into a

liquid product containing hydrocarbons and oxygenates. In general, the GTL


2

technology consists of the following three main processes: synthesis gas

manufacturing, Fischer-Tropsch synthesis and product upgrading as shown in

Figure (1.1). In this figure, the first unit (reactor) represents the synthetic gas

production process (H2

Synthesis gas is a mixture of carbon monoxide (CO) and hydrogen

(H

and CO), while, the second reactor (slurry bubble

column reactor) represents the Fischer-Tropsch process and then, the final

process includes products separation [Godley et al. 2000; Tiefeng et al.2007].

2

The basic reaction is:

), which can be obtained from any carbon containing feedstock, such as

natural gas. On the other hand, the Fischer-Tropsch reaction represents the

heart of process, because it determines the product types and distributions in

GTL technology.

nCO+(2n+1) H2↔CnH2n+2+nH2O ∆HR

The highly exothermic Fischer-Tropsch reaction converts synthesis

gas into a large range of linear hydrocarbons including gasoline, diesel and

wax [Hindermann et al. 1993; Van der Laan and Beenackers, 1999;

Chowdhury et al.2006].

= -39.4 kcal/mol

Fig. (1.1) : Gas-to-liquid process steps and reactors.


3

The Fischer-Tropsch reaction can be carried out in different kinds of

reactor vessels such as [Jager et al., 1990; Sie, 1998]:

-Slurry bubble column reactors with internal cooling tubes.

-Multi-tubular fixed bed reactor with internal cooling.

-Circulating fluidized bed reactor with circulating solids, gas recycle and

cooling in the gas/solid recirculation loop.

-Fluidized bed reactors with internal cooling.

Currently, there is much interest in using slurry bubble column reactors for this

process because they have the following advantages in comparison with other

multiphase contactors:-

1. They are cheap to run.

2. They are inexpensive to build.

3. They need little maintenance due to simple construction and operation and

cause no problems with sealing due to the absence of moving parts.

4. They have excellent heat transfer properties and, hence, easy temperature

control.

A slurry reactor is a vessel containing the catalyst suspended in a liquid

hydrocarbon. The syngas is brought in at the bottom of the vessel and

bubbled up through the reactor. As the bubbles contact the catalyst, the

Fischer-Tropsch reaction takes place. On the other hand, the hydrodynamics

parameters in the reactor such as: gas holdup, bubble rise velocity, particles

size (catalyst size), pressure drop, and liquid circulation, are complicated and

interact in slurry bubble column and determine the overall transport processes

in such type of reactors. Therefore, the understanding of them is important to

achieve the high reaction rate needed for commercial GTL conversion.

Figure (1.2) shows a schematic representation of interrelations of liquid and

apparatus properties with flow regimes and bubble size in bubble columns.

Additionally, it shows how these factors influence holdup and liquid flow


4

patterns and therefore mass and heat transfer [Jager, 1997; Calemma et al.

2005; Alvare´a and Al-Dahhan, 2006].

Fig. (1.2): Variables that affect SBCR performance [Alvare´a and Al-

Dahhan, 2006].

However, the design of bubble columns is very difficult, principally because

the complex hydrodynamic behavior of such units, so that, numerous

investigators have studied the slurry bubble column experimentally and

prepared a wide range of hydrocarbons by using different types of catalysts

through GTL process [Joan et al. 1999; Krishna and van Baten, 2003; Ahmad

et al. 2008; Guillou et al. 2008]. On the other hand, few theoretical works

were developed in literature to predict the design parameters, mass transfer,

heat transfer, reaction kinetics and catalyst performance in slurry bubble

column under industrial operating conditions. Therefore, there is a real need


5

to develop a comprehensive theoretical simulation to describe the transport

processes in slurry bubble column.

1.2 The aims of the present study are: -

The Aims of this Work

1- To develop a comprehensive theoretical simulation by deriving mathematical

models, which are capable of predicting the main parameters of hydrodynamic,

reactor geometry, superficial gas velocity, catalyst concentration, operation

pressure, inlet H2

2- To study the catalyst performance (the general types are Co and Fe catalysts) in

Fischer-Tropsch reaction under different operating conditions.

/CO ratio, mass, heat and reaction in slurry bubble column that

are conducted in GTL process.

3- To compare the theoretical results with experimental and theoretical results in

literature over a wide range of operating conditions in order to test the validity

of the present models.

Chapter Two Literature Survey

6

CHAPTER TWO

LITERATURE SURVEY

2.1Gas to Liquid (GTL) process is an umbrella term for the process that

can create liquid hydrocarbon fuels from a variety of feed stocks. The

conversion of natural gas into liquid fuels is an attractive option to

commercialize abundant gas reserves. GTL, with virtually unlimited markets,

offers a new way to unlock large gas reserves, complementary to other

traditional technologies such as Liquefied-Natural-Gas and pipelines. GTL

has the potential to convert a significant percentage of the world estimated

and potential gas reserves which today holds little or no economic value

[Heng and Idrus, 2004; Levenspeil, 2005; Tiefeng et al., 2007].

Scope

In essence, GTL uses catalytic reactions to synthesize complex

hydrocarbons from carbon monoxide and hydrogen. There has been

significant improvement in reactor design and technology over the last

decade. However, many reactors have been used in GTL process such as:

fixed bed reactor, fluidized bed reactor, circulating fluidized bed reactor, and

slurry bubble column. In recent years, the slurry bubble column reactor is

regarded as the main reactor type that is used in GTL technology. Therefore,

the design and construction of such reactor depends on the transport

processes that occur in it. The main transport processes that determine the

performance of slurry bubble column reactor are: hydrodynamic, mass

transfer, heat transfer, and reaction kinetics [Sie, 1998; Saib et al. 2006].

Therefore, in this chapter, the literature review on GTL technology,

reactor types, catalyst types, operating conditions, hydrodynamic

characterizes, mass transfer, and heat transfer are presented.


7

2.2

The FT process had a lively history of about eight decades since its

discovery in Germany by Franz Fischer and Hans Tropsch in the 1920.

During world war-II, two processes for converting coal to liquid transport

fuels were tried in Germany. The first, direct liquefaction (Bergius process)

involves the direct catalytic hydrogenation of coal to liquids which are

further refined. In contrast, indirect liquefaction involves conversion of coal

by partial oxidation in the presence of steam to yield syngas, which after

purification reacts catalytically to form liquid hydrocarbon fuels. Both

Bergius and FT were discontinued after the war because of easy availability

of petroleum. However, FTS was started on a big scale at Sasol Company in

South Africa in the 1950 [Xing et al. 2006]. Sasol, a world-leader in the

commercial production of liquid fuels and chemicals from coal and crude oil,

started up its first FT plant (Sasol I) in Sasolburg, South Africa. The plant’s

capacity is 6 million tonnes /yr of FT products from coal [Dry, 1982].

History of Fischer-Tropsch Synthesis (FTS)

Sasol Company submitted three plants to produce hydrocarbons

successfully based on FTS (Sasol I, Sasol II and III) which came on line in

1980 and 1982, respectively. These plants are located in Secunda, South

Africa. Sasol II and III all have circulating fluid bed (CFB) reactors. From

1995 to 1999, these second generation CFB reactors were replaced with eight

fixed fluid bed (FFB) reactors [Van Nierop et al. 2000].

In the early 1990, two other FT plants came on line. Then, in 1992 the

Mossgas plant, which converts natural gas to FT products using high

temperature process and Iron catalyst, started up in South Africa [Dry, 2002].

This plant produces 1 million tonnes /yr of FT products including motor


8

gasoline, distillates, kerosene, alcohols and LPG. Additionally, Shell

commissioned a plant in 1993 in Bintuli, Malaysia, using the Shell Middle

Distillate Synthesis process, which is essentially enhanced FT synthesis. This

plant produces 500,000 tonnes /yr (12,000 BPD) of FT products from natural

gas using a Cobalt catalyst [Senden, et al. 1992; Haid, et al. 2000].

In early 2000, Sasol studied the feasibility of replacing coal with

natural gas. Therefore, they were built a network of natural gas pipelines in

2004. Sasol plans to use the natural gas as a supplementary feedstock at

Secunda and as a replacement feedstock for the coal in Sasolburg. A brief

history of FTS and the related events during the last century are given in

Table (2.1) [Dry, 2002; Jager, 2003].

Table (2.1): Brief history of commercial Fischer-Tropsch synthesis [Dry, 2002].

1902 Methanation reaction with Syngas over Ni catalyst.

1923 Franz Fischer & Hans Tropsch reported hydrocarbon synthesis at higher pressure using Co, Fe Ru catalysts.

1936 4 FT Plants commissioned in Germany

1950 Hydrocol plant operated for sometime based on Fixed Fluidized Bed rector with Fe-K catalyst, Cap. 5000 bpd at Brownsville, Texas.

1950-1953

In Germany, Koelbel set up 1.5 m dia. slurry phase reactor at Rheinpreussen and operated it successfully

1955 German plants were shut down after brief operation using petroleum residue. Interest in FTS declined worldwide, when oil deposits were discovered in abundance in the Middle East.

1970-1980

Renewed interest in FTS due to increased oil prices and fear of oil shortage

1990s Further revival of FTS or GTL due to discoveries of huge stranded natural gas reserves and requirement for clean fuels.

1992 First natural gas based plant (Mossgas) set up in S.Africa, based on Sasol’s Synthol reactor.

1993 Shell Middle Distillate Synthesis (SMDS) plant (12,500 bpd) was set up in Malaysia (natural gas based) using TFB reactor and Co catalyst


9

2.3The Fischer–Tropsch synthesis (FTS) is an important industry process

for the conversion of syngas (CO and H

Gas to Liquid (GTL) Technology

2

) derived from coal or natural gas

into hydrocarbons and oxygenates. As an important type of FTS reactors,

slurry bubble column reactor (SBCR) attracts more and more interest because

of its advantages relative to other types of reactors. These advantages mainly

include: (1) nearly isothermal operation, (2) small solids particle size that

results in good productivity, (3) good interface contacting, (4) low pressure

drop, and (5) low construction and operation costs [Godley et al. 2000; Ding

et al. 2004; Xing et al. 2006].

The strategy for GTL depends on the location of methane, demand for

products, construction costs, the economic and geopolitical stability etc.

Where natural gas is extracted along with crude oil, there may not be buyers

for the gas along with the crude in which case it becomes a liability and the

gas may be available at cheap cost. There is the other case where the gas

extracted is in abundance and the utilization is poor. In such cases

transportation through pipeline or conversion to LNG is expensive

alternatives. At present in many fields, the excess gas is re-injected into the

well and as the oil reserve gets depleted, an increasing amount of gas will be

recycled per barrel of oil produced. In a free market economy, the

profitability of these facilities will depend on the selling price of the product

and the cost of alternative technologies, both of which may fluctuate

significantly over a short period.

From an economic view point, Fischer-Tropsch derived fuels are easily

transported in standard vessels or pipelines relative to natural gas and LNG.


10

Therefore, the FT process of converting natural gas to marketable

liquid hydrocarbons comprises three main steps as shown in Figure (2.1):

a) Synthesis gas, a mixture of CO and H2

b) Fischer Tropsch Synthesis (FTS) .

(syngas) production .

c) Product Upgrading and Separation

Fig. (2.1): The main three processes present in Fischer-Tropsch synthesis

[Tiefeng et al. 2007].


11

In FTS, the feed gas will be treated initially to remove the sulphur

compounds which otherwise poison the catalyst, in addition to causing

corrosion and environmental problems.

Many authors [Rostrup, 2000; Vosloo, 2001; Abbott and Crewdson,

2002] have recommended autothermal reforming or autothermal reforming in

combination with steam reforming as the best option for syngas generation.

This is primarily attributed to the resulting H2/CO ratio and the fact that there

is a more favorable economy of scale for air separation units than for tubular

reactors (steam methane reforming - SMR). If the feedstock is coal, the

syngas is produced via high temperature gasification in the presence of

oxygen and steam. Depending on the types and quantities of FT products

desired, either low temperature (200–240°C) or high temperature (300–

350°C) synthesis is used with either an Iron or Cobalt catalyst. Fischer-

Tropsch Synthesis temperatures are usually kept below 400°C to minimize

CH4

production. If maximizing the diesel product fraction, a slurry reactor

with a cobalt catalyst is the best choice. The FT reactors are operated at

pressures ranging from 10-40 bar (145–580 psi).

2.3.1 Synthesis Gas Manufacturing In GTL technology, FT conversion process is employed which requires

a specific molar ratio of hydrogen depending upon the product. One or more

of several processes, working in parallel, in a combined mode or with the

addition or extraction of hydrogen, can achieve the appropriate syngas

composition ratio. In an FT complex the syngas generation accounts for 60-

70% of the capital and running costs of the total plant. Reduction of the

synthesis gas costs could also be accomplished by a decrease in steam/carbon

and oxygen/carbon ratios in the feedstock [Basini, and Piovesan, 1998].


12

Xing et al. (2006) and Chowdhury et al. (2006) compared economical

evaluations of steam-CO2 reforming, autothermal reforming, and combined

reforming processes. They concluded that combined reforming has the lowest

production and investment costs at a H2

Synthesis gas can be obtained by steam reforming or (catalytic) partial

oxidation of fossil fuels: coal, natural gas, refinery residues, biomass or

industrial off-gases. The composition of syngas from the various feedstocks

and processes is given in Table (2.2)

/CO ratio of 2.

Table( 2.2): Synthesis gas composition of different feedstock [De smet, 2000].

Feedstock Process Component (vol%)

H2 CO CO2 Other

Natural gas, steam SR 73.8 15.5 6-6 4-1

Natural gas, steam, CO CO2 2 52.3 26.1 8-5 13-1 – SR

Natural gas, O2, steam, CO ATR 2 60.2 30.2 7-5 2-0

Coal/heavy oil, steam Gasification 67.8 28.7 2-9 0-6

Coal, steam, oxygen Texaco gasifier 35.1 51.8 10-6 2-5

Coal, steam, oxygen Shell/Koppers

gasifier 30.1 66.1 2-5 1-3

Coal, steam, oxygen Lurgi gasifier 39.1 18.9 29-7 12-3

In reforming, the feed stream is passed over a Ni-based catalyst

together with H2O and/or CO2

CHR4R + HR2RO → CO + 3HR2R ∆H= 226 kJ /mole


13

In general, large furnaces are used, inflicting large capital investments.

The endothermicity of the steam reforming process is compensated by the

addition of oxygen in the autothermal reforming process. The synthesis gas

from industrial steam reformers has a high H

at high temperatures (1073-1173 K) and

medium pressures (10-30 bar). Steam reforming and oxy-steam reforming (or

so-called autothermal reforming) hold the leading positions among the

commercial processes of synthesis gas production in the synthesis of

methanol and ammonia. Steam reforming of methane is highly endothermic:

2/CO ratio (H2/CO=3-7 and

CO/CO2

In partial oxidation, the feed stream is mixed with oxygen and steam

and fed to a high temperature flame (1573-1773 K). The feed is partially

combusted followed by endothermic reforming steps and the water-gas shift

reaction. The synthesis gas from industrial partial oxidation has a low H

=0.3-1.5).

2/CO

ratio (H2/CO=0.5-2 and CO/CO2

In the catalytic partial oxidation a catalyst takes over the function of

the flame in the partial oxidation. The advantages of the catalytic partial

oxidation of methane over steam reforming of methane are the low

exothermicity of the process and the high reaction rates, leading to significant

smaller reactors [De smet, 2000]:

=5-15).

CH4 + 1/2 O2 → CO + 2H2

∆H= -22 kJ

/mole

2.3.2 Fischer-Tropsch Synthesis (FTS) In the second step of the GTL process, syngas is converted into

paraffinic and olefinic hydrocarbons of varying chain length. The reaction

occurs in the slurry bubble column reactor (SBCR). GTL can also produce

methanol and DME. FTS typically uses Iron or Cobalt based catalysts. The

process takes place at moderate temperature (200-300o

C) and moderate

pressure (10 – 40 bar). [de Swart et al. 1997; Song et al. 2003; Fernandes and

Fabiano, 2005; and Fernandes, 2006].


14

The basic reaction is:

nCO+(2n+1) H2↔CnH2n+2+nH2O ∆HR

= -39.4 kcal/mol

(Paraffin's)

Other reactions also take place in the process, resulting in the formation of

olefins and alcohols; besides, there are some side reactions.

n CO + 2nH2 → CnH2n + nH2

n CO + 2nH

O

(Olefins)

2 → CnH2n+1OH + (n-1)H2

O

(Alcohols)

Much attention is focused on developing catalysts with appropriate

selectivity and physical properties. Catalyst selectivity, syngas composition

and process conditions (principally temperature) govern the product

distribution and the limit of the paraffinic chain length. The temperature,

pressure and catalyst determine whether light or heavy hydrocarbons are

produced. For example, high temperature process using Iron catalyst at about

340oC mainly produces gasoline and chemicals like alpha olefins. On the

other hand, the low temperature process using either Iron or Cobalt based

catalyst at about 230o

C mainly produces waxes. Cobalt based catalyst is

preferred over Iron based due to its high activity and long life [Vosloo,

2001].

The exothermic nature of the Fischer-Tropsch reaction combined with

the high activity of the Cobalt catalyst makes the removal of heat from the

reactor of critical importance. The wax and hydrocarbon mixture produced


15

by the low temperature FT process consists of linear paraffins with a small

fraction of olefins and oxygenates. The hydrogenation of olefins and

oxygenates and the hydrocracking of wax to naphtha and diesel is done under

relatively mild conditions [Zhou et al. 2003; and wan et al. 2006].

The exact FT mechanism is complex and it can be described in a simplified

manner in the following steps:

1) Initiation or C1

2) Hydrocarbon chain growth by successive insertion of the C

compound formation.

1

3) Chain termination by: (a) desorption of unsaturated surface species, and

(b) hydrogenation and desorption of saturated species.

.

The types of catalysts employed in syngas conversion are shown in

Table (2.3). FT process typically involves the recycle of unconverted gases to

the reactor, CO2 removal from the recycle loop and dehydration of the

recycle gas. In some cases, the process separates H2 for using in the product-

upgrading unit. The recycle gas may be used as fuel gas. In addition to

distillates, Fischer-Tropsch GTL plants can also produce a range of specialty

products, such as n-paraffins (C10-C13

range), a feedstock used in the

detergent industry for the production of linear alkyl benzene sulphonate

(LAS), one of the world’s most widely used surfactants. Some plants

however, may not produce paraffin's suitable for LAS and suitability will

depend on GTL catalyst selection and process conditions.

Table (2.3): Potential FT catalysts.

Source of carbon Catalyst Property

Any source Ni Methanation


16

Carbon rich (coal) Fe WGS with CO2 production

Hydrogen rich (natural gas) Co Highly active and gives linear

hydrocarbons

Different carbon sources Ru Very active but expensive

2.3.3 Products Upgrading (Separation) Conventional refinery processes can be used for upgrading of Fischer-

Tropsch liquid and wax products. A number of possible processes for FT

products are: wax hydrocracking, distillate hydrotreating, catalytic reforming,

naphta hydrotreating, alkylation and isomerization [Choi et al. 1996; Zhou et

al. 2003].

GTL-Fischer-Tropsch plants produce many of products that are

significantly different from that produced from a typical crude oil refinery as

shown in Figure (2.2). GTL plants are capable of producing many of

products with highly desirable properties, including LPG, gasoline, diesel

fuel, jet fuel, petrochemical naphtha and waxes. It is important to mention

here that the diesel fuel represents the main product of GTL products. On the

other hand, all GTL products are sulfur free with very low aromatic. These

products meet the environmental requirements for clean fuels.


17

Fig. (2.2): Comparison of the GTL barrel vs. conventional refined barrel

[Godley et al. 2000].

In GTL process, the final product stream usually consists of various

fuel types. The definitions and conventions for the composition and names of

the different fuel types are obtained from crude oil refinery processes and are

given in Table (2.4).

Table (2.4): Conventions of fuel names and composition [Kroschwitz,

and Howe, 1996].

Name Synonyms Components

Fuel gas C1 - C2

LPG C3 - C4

Gasoline C5 - C12

Naphtha C8-C12

Kerosene Jet fuel C11-C13

Diesel Fuel oil C13-C17

Middle Distillates Light gas oil C10-C20

Soft Wax C19-C23

Medium Wax C24-C35


18

Hard Wax C35+

The produced diesel fraction by GTL process has a high cetane number

resulting in superior combustion properties and reduced emissions as shown

in Table (2.5). New and stringent regulations may promote replacement or

blending of conventional fuels with sulfur and aromatic free FT products

[Fox, 1993 and Gregor, 1990].

On the other hand, many products besides fuels can be manufactured

with Fischer-Tropsch in combination with upgrading processes, for example,

ethene, propene, olefins, alcohols, ketones, solvents, specialty waxes, and so

forth. These valuable by-products of the Fischer-Tropsch process have higher

added values, resulting in an economically more attractive process economy.

According to Table (2.5) the value of Fischer-Tropsch products used as

blending stocks for transportation fuels (diesel) is higher than that of crude

oil derived fuels due to their excellent properties. These superior properties of

GTL fuels are attracted to the clean feedstock which is the natural gas [Saib

et al. 2006; Tiefeng et al. 2007].

Table (2.5): The comparison between conventional and GTL diesel [Sie, 1998].

Diesel Property Conventional GTL

Cetane number 45 74

Sulfur, ppm 330 >10

Specific Gravity 0.84 0.78

Flash Point, °C 71 81

Cloud Point, °C -17 -12


19

2.4The Fischer Tropsch synthesis section consists of: FT reactors, recycle

and compression of unconverted synthesis gas, removal of hydrogen and

carbon dioxide, reforming of methane produced and separation of the FT

products. The most important aspects for development of commercial

Fischer-Tropsch reactors are the high reaction heats and the large number of

products with varying vapor pressures (gas, liquid, and solid hydrocarbons).

The main reactor types which have been proposed and developed after 1950

are [Jager, et al. 1990; Jager, 1997; and Sie, 1998; Tiefeng et al. 2007]:

Fischer-Tropsch Reactors

1. Three-phase slurry bubble column reactors with internal cooling tubes

Sasol; Energy International, Exxon, see Figure (2.3a).

2. Multitubular fixed bed reactor with internal cooling (Sasol; SMDS: Shell,

see Figure (2.3b).

3. Circulating fluidized bed reactor with circulating solids, gas recycle and

cooling in the gas/solid recirculation loop (Sasol), Figure (2.3c).

4. Fluidized bed reactors with internal cooling (Sasol), Figure (2.3d).

Table (2.6) summarizes the general types of multiphase reactors that

are used in Fischer Tropsch synthesis. The same table shows the historical

development of such type of reactor besides the catalyst type and operation

mode. On the other hand, Figure (2.3) shows the main reactors types of FTS.


20

Fig. (2.3) Possible reactors for Fischer-Tropsch synthesis: a- Slurry

bubble column reactor; b- Multitubular trickle bed reactor;

c- Circulating fluidized bed reactor; d- Fluidized bed reactor

[Jager, 1990; Sie et al., 1998].

Many authors studied different types of FT reactors. De swart, (1996)

modeled a Cobalt-based FT process both in trickle bed reactors and in slurry

bubble column reactors. The major conclusion was that 10 multitubular

trickle bed reactors (6 m diameter, 20 m height) or 4 slurry reactors (7.5 m

diameter, 30 m height) can produce 5000 tonnes of middle distillates (C5) per

day. Mainly due to the high heat transfer rates occurring in the slurry system,

the capital costs of this system reportedly can be 60 % lower than that of the

multitubular system. Jager, (2003) stated that the costs of a single 10,000

bbl/day slurry reactor system is about 25 % of that of a tubular fixed bed

reactor.


21

Table (2.6): GTL reactors in commercial practice.

Reactor Advantages/Disadvantages Features

Tubular Fixed Bed (TFB)

Relatively simple design, expensive construction due to large No. of tubes. Temp. gradient causes sintering. Gives high pressure drop. Catalyst replacement a major undertaking. Fe catalysts, which are inherently unstable, have to be replaced periodically. Co catalysts can be regenerated

TFB was used in Sasol I and in Shell plant catalyst pellets are packed in the tubes and the cooling medium flows around the outside of the tubes, similar to a shell & tube exchanger.


22

Fluidized Bed i) Circulating Fluidized Bed (CFB)

Better heat removal and temperature control. Less pressure drop problems. Physically complex and suspended in a complex structure. Circulation of large tonnage of catalyst results in considerable recycle gas compression with added costs. Operates normally at higher temperature

Used in Sasol I & II (Synthol Reactor). Fused Iron catalyst is circulated with syngas through a complex reactor / hopper / standpipe system and heat is removed as steam through coils. The reactor needs a complex support system to cope with the circulating catalyst loads and temperature differences.

ii)Fixed Fluidized Bed (FFB)

Improved stability and less catalyst consumption. Less erosion than CFB reactor Product must be volatile at the reaction conditions since non-volatile hc. may decrease bed fluidization.

Used in Sasol II & III (SAS Reactor) Basically a vessel with a gas distributor at the bottom and heat exchange tubes suspended in the F.B Catalyst inventory and product selectivity (low M.W) is same as Synthol reactor.

Slurry Phase Bubble Column Reactor (SBCR)

Simple design and construction. Ease of addition and removal of catalyst. Good heat transfer and temperature control. Good selectivity, Low pressure drop. Ideal for high boiling products Potentially high capacity (10,000-20,000 BPD). Improved catalyst economy and low turn down ratio. Slurry - phase reactor is about 45% cheaper in construction TFB.

Most accepted future reactor for GTL. Syngas is bubbled up through a slurry, made of paraffinic high boiling liquid with the catalyst suspended in 50-80 µm.

2.5In general, Fischer Tropsch reactors for large-scale conversion of

natural gas to liquid hydrocarbons can be divided into three classes:

(a) fluidized bed reactor, (b) tubular fixed bed reactor (TFBR), and (c) slurry

bubble column reactor (SBCR). SBCR has been found to be the most suitable

Fischer-Tropsch reactor. Figure (2.4) shows the general arrangement of

slurry bubble column. In this reactor preheated synthesis gas is fed to the

Slurry Bubble Column Reactor


23

bottom of the reactor and bubbled up through the reactor. As the bubbles

contact the catalyst, the Fischer-Tropsch reaction takes place.

The hydrodynamics in the reactor are complicated but understanding

them is important to achieving the high reaction rate needed for commercial

GTL conversion. To achieve a high mass transfer rate, the goal is to have

good gas bubble distribution throughout the reactor with a large interfacial

surface area between bubbles and the liquid hydrocarbon media.

The Fischer-Tropsch reactions are exothermic, therefore, the heat

generated is removed through the reactor's cooling coils where steam is

generated for use in the process. Heat transfer coefficients up to 1000 W/m2

De Swart et al. (1996) compared the multitubular fixed bed reactor

with the slurry reactor operating in either the homogeneous or heterogeneous

regime. With a maximum weight of 900 ton/reactor as a limiting criterion,

the number of reactors needed for a plant capacity of 5000 ton/day was found

to be 10 for the multitubular fixed bed reactor, 17 for the slurry reactor

operating in the homogeneous regime, and 4 for the slurry reactor operating

in the heterogeneous regime. Krishna and Sie, (2000) compared the several

reactor types for the Fischer-Tropsch synthesis process and concluded that

the slurry reactor is the best reactor type for large-scale plants. For the

K

can be obtained in this type of reactor [Tiefeng et al. 2007]. Heat transfer

coefficient increases with increasing gas velocity and with increasing solids.

Because of the churning nature of the slurry-gas bubble interaction, the slurry

phase is well mixed and tends to be isothermal. This gives better and more

flexible temperature control [Jager and Espinoza, 1995]. Online catalyst

removal and additions can also be done without difficulty in SBCR whereas

in TFBR catalyst has to be replaced from time to time.


24

specific case of conversion of syngas into a relatively heavy Fischer-Tropsch

synthesis product Deckwer (1993) mentioned that under specific conditions,

such as important heat removal, BCRs and SBCRs could be used for fast-

reaction processes. Thus, BCRs and SBCRs appear also to be suitable for

conducting highly exothermic fast reaction processes, which are widely used

in the chemical, biochemical, petrochemical applications.

Therefore, the advantages of SBCR type over both the fixed – and fluidized-

bed reactors are summarized as follows [Dziallas et al. 2000; Fleisch et al.

2002; Wang et al. 2006; Alvarea and Al-Dahhan, 2006]:

1- The capability for processing gas of a low H2

2- High conversion can be achieved in a single pass.

/CO ratio. CFBR and FBR

require hydrogen upgrading to avoid carbon deposition.

3- Formation of nonvolatile waxy hydrocarbons does not impair SBCR

performance, whereas the production of waxy hydrocarbons causes

catalyst agglomeration in a CFBR and pore filling in a FBR.

4- The catalyst in a SBCR does not require high crush strength, but, catalysts

in a FBR require high crush strength, and those in a FBR require high

resistance to attrition.

5- A spatially uniform temperature profile can be achieved in the SBCR

because the liquid carrier provides excellent heat transfer. This prevents

the hot spots which accelerate carbon deposition in fixed bed reactors.


25

Fig. (2.4): Fischer-Tropsch slurry bubble column reactor [Tiefeng et al. 2007]. 2.6

The most common Fischer-Tropsch catalysts are group VIII metals

(Co, Ru, and Fe). Iron catalysts are commonly used, because of their low

costs in comparison to other active metals. Most early FT catalysts were

prepared with precipitation techniques. Novel catalyst preparation methods

are sintering and fusing metal oxides with desired promoters. Alkali-

promoted Iron catalysts have been applied industrially for the Fischer-

Fischer-Tropsch Catalysts


26

Tropsch synthesis during many years [Rao et al. 1995; Zhou et al. 2003; and

Brumby et al. 2005].

These catalysts have a high water gas shift activity; this high water-gas

shift activity causes these catalysts to be flexible towards the H2/CO feed

ratio of the synthesis gas. This allows the utilization of a large variety of

feedstocks, while every syngas manufacturing technology can be applied.

Because coal results in a syngas with a low H2

The application of Fe-based catalysts in the production of heavy wax is

limited. This is mainly due to its tendency to form elemental carbon, causing

deactivation of the catalyst. Moreover, water, which is produced in large

quantities as side product, has an inhibiting effect on the activity, resulting in

low conversions per pass. The latter effect results in large recycle streams

after water removal.

/CO ratio, this feedstock can

only be used in combination with a Fe-based catalyst. However, the water-

gas-shift activity of the catalyst also results in a low carbon efficiency of the

gas-to-liquid process. [Kolbel and Ralek, 1980; Jager et al.1995].

On the other hand Cobalt catalysts give the highest yields and longest

life-time and produce predominantly linear alkanes. The water-gas shift

activity of Co-based catalysts is low. The Cobalt is generally poorly

dispersed on metal oxide supports and Ru, Re, or Pt promoters are applied to

prevent catalyst deactivation by carbon formation or oxidation. Compared to

Fe-based catalysts, olefins tend to reenter the chain growth process by

readsorption on Co-based catalysts, increasing the selectivity towards heavy

hydrocarbons. Disadvantages are the high costs of Cobalt and low water gas

shift activity. Therefore, Cobalt catalysts are viable for natural-gas based

Fischer-Tropsch processes for the production of middle distillates and high-

molecular weight products. Cobalt catalysts are not inhibited by water,

resulting in a higher productivity at a high synthesis gas conversion


27

[Tavasoli, 2005; Bartholomew et al. 2006]. Table (2.8) shows the comparison

between the two types of catalysts that are used in GTL plant.

Table (2.8): General Fischer-Tropsch catalyst characteristics.

Iron (Fe) Cobalt (Co)

Short life (limited to eight weeks) Higher conversion rate and a longer

life (over five years)

Low cost Expensive (exotic promoters )

Generally preferred for coal-based

syngas

Generally preferred for natural gas-

based syngas

Precipitated / fused Support (Al2O3, SiO2, TiO2)

Syngas ratio H2 Syngas ratio H /CO =1.5 2/CO =2

By product H2 By product H /CO / steam 2O / steam

Inhibited by water Not inhibited by water

High water gas shift activity Low water gas shift activity

Selectivity to olefins Produce paraffin's in the diesel range

Higher molecular weight products

(higher alpha)

Lower molecular weight products

(lower alpha)

On the other hand Ruthenium is a very active but expensive catalyst

for the Fischer-Tropsch synthesis relative to Co and Fe. At relatively low

pressures (P < 100 bar) ruthenium produces much methane, while, at low

temperatures and high pressures, it is selective towards high molecular

waxes. The catalyst is active in its metallic form and no promoters are

required to stabilize its activity. However, the high price of ruthenium

excludes its application on industrial scale and the use of Ru-based catalysts


28

for the Fischer-Tropsch synthesis is limited to academic studies [Ding et al.

2004].

Cobalt catalysts are usually supported on metal oxides due to the

higher Cobalt price and better catalyst stability. These catalysts consist of

12–20 wt% Cobalt, a second metal promoter (Ru or Re), an oxide promoter

(such as lanthana, zirconia, or alkali oxide), and a support (alumina, silica, or

titania). These three support materials were selected on the basis for most of

the patents assigned to many companies: Gulf/Chevron (alumina), Exxon

(titania), Shell (silica), and Statoil (alumina). [Pedrick, 1993; Tavasoli, 2005;

Sadaghiani et al. 2007]. The activity varied in the following order Al2O3 >

SiO2 >TiO2

as shown in Figure (2.5).

Higher porosity modified titania supports were obtained and used to

produce Co Fischer-Tropsch catalysts. While the production of high surface

area supports may have been successful, these catalysts are probably only

good for fixed-bed reactor applications. The binders are combined with

titania in an extrusion process suitable for making large catalyst pellets not

suitable for slurry bubble column application. Grinding these pellets in order

to produce a catalyst with a suitable particle size distribution for slurry

bubble column application would result in a catalyst with low attrition

resistance.[ Saib et al. 2006]

Jothimurugesan et al. (2000) showed that, the type binder or binder-

and-precipitated, and the content of SiO2 incorporated into Iron catalysts

have significant effects on catalyst attrition property. They reported that the

catalyst with 12–14 wt. % binder SiO2


29

In general Cobalt catalysts may be regenerated by calcinations at high

temperatures (burning off of the carbon residues) followed by reduction.

[Soled et al.1995].

exhibited good attrition resistances.

Pham et al. (2000) reported that the addition of silica as the binder improved

the attrition resistance of the Iron catalyst.

Fig. (2.5) Support effect on FTS over Cobalt–based catalysts in FBR and

SBCR [Yang et al. 2004].

Compared with SiO2, the addition of Al2O3 facilitates the

adsorption of H2, but significantly suppresses the CO adsorption. It is well

known that strong surface basicity can promote CO adsorption and

suppress H2 adsorption. [Yang et al. 2004; Wan et al. 2006]. Dry, (2002)

reported that more K was required when acidic compounds, e.g., SiO2 or

Al2O3 were present. In other words, the acidic SiO2 or Al2O3 can

combine with the basic K promoter, forming the strong K-SiO2 or K-

Al2O3

2.7

interaction. This interaction could decrease the effective potassium

content and further weaken the surface basicity.

The performance of multiphase reactors (i.e SBCR) is determined by

their hydrodynamic characteristics. It is well known that the transport

processes and reaction kinetic are function to the hydrodynamic parameters

such as: superficial gas velocity, gas holdup, flow pattern, pressure drop,

height / diameter ratio, sparger design, solid holdup and solid distribution in

Hydrodynamic of Slurry Bubble Columns


30

the reactor. Therefore the present section will focus on the most important

hydrodynamic parameter that affects the performance of SBCR directly.

2.7.1 Flow Regime Analysis When a column filled with a liquid is sparged with gas the bed of

liquid begins to expand as soon as gas is introduced. As the gas velocity is

increased the bed height increases almost linearly with the superficial gas

velocity Ug, provided the value of Ug stays below a certain value Utrans

When the U

. This

regime of operation of a bubble column is called the homogeneous bubbly

flow regime. The bubble size distribution is narrow and a roughly uniform

bubble size, generally in the range 1-7 mm, is found. These small bubbles all

have approximately the same diameter and rise velocity and are modeled

with a plug flow equation. Figure (2.6) shows the flow regime in bubble

column. Liquid products and catalyst are withdrawn from the reactor at the

top. Concentrated fresh catalyst enters the reactor at the bottom, so the

reactor operates in a co-current mode with respect to slurry and gas. Due to

the high degree of back mixing in the slurry phase countercurrent operation

does not offer much advantage. Co-current operation however avoids catalyst

settling tendencies, which could result in serious heat transfer problems (hot

spots). Heat removal is by means of cooling tubes installed in the reactor

[Krishna and Van Baten, 2003; Vandu et al. 2004; Wang et al. 2005].

g reaches the value Utrans, coalescence of the bubbles takes

place to produce the first fast-rising “large” bubble. The appearance of the

first large bubble changes the hydrodynamic picture dramatically. The

velocity that exceeds Utrans is referred to as the heterogeneous or churn-

turbulent flow regime. In the heterogeneous regime, small bubbles combine

in clusters to form large bubbles in the size range 20- 70 mm [Ellenberger et

al. 1994; De swart, 1996; Shaikh et al. 2005; Sardeing et al. 2006].


31

Fig. (2.6) : Homogeneous and churn-turbulent regimes in a gas-liquid

bubble column [Krishna and Van Baten, 2003].

The large bubbles travel up through the column at high velocities (in the

range 1-2 m/s), in a more or less plug flow manner. These large bubbles have

the effect of churning up the liquid phase. The large bubbles are mainly

responsible for the throughput of gas through the reactor. Small bubbles,

which co-exist with large bubbles in the churn-turbulent regime, are

“entrained” in the liquid phase and as a good approximation have the same

backmixing characteristics of the liquid phase. The two regimes are portrayed

in Figure (2.6) which shows also in a qualitative way the variation in the gas

holdup ε as a function of the superficial gas velocity Ug

. When the gas

distribution is very good, the regime transition region is often characterized

by a maximum in the gas holdup. The transition between homogeneous and

churn-turbulent regimes is often difficult to characterize [Hoefsloot et al.

1993; Wang et al. 2006]


32

2.7.2 Gas Hold-Up (εg

Gas hold-up is dimensionless key parameter for phenomena purposes

of bubble column systems. All studies examine gas hold up because it plays

an important role in design and analysis of bubble columns. The variation in

gas hold-up, i.e. gas hold up profile is an important factor which gives rise to

pressure variation and thus liquid recirculation. Since liquid recirculation

plays an important role in mixing and heat and mass transfer predictions of

radial gas hold up, profiles would lead to better understanding of this

phenomenon and thus more reliable bubble column scale-up [Krishna and

Van Baten, 2003].

)

In slurry bubble column reactor Deckwer et al. (1980) is calculate gas

holdup from the following empirical equation. 1.1

053.0 gg U=ε ………. (2.1)

Equation (2.1) presents a good compromise at low gas velocities (ug

≤

4 cm/ sec) and obviously also applies to larger diameter columns and higher

gas velocities

Abdul-Rahman, (1989) studied the gas hold-up in three phase systems

and correlated the results with the general empirical equations:

smUForCU gvLgg /07.032.1 06.0028.0 <= −−µε …… (2.2)

smUForCU gvLgg /07.0445.0 6.0028.06.0 >= −−µε …… (2.3)


33

Koide et al. (1984) used the electro resistively probe to measure the

gas hold-up locally in large cylindrical vessel at diameter of (550cm) and of

(900cm) height. The value of gas hold-up is measured between (0.145-0.065)

using the following equation:

dtEE

TtT

g )0()(

0

1∫=ε …… (2.4)

where,

T: the integration time equals (1.5-3) minutes.

)t(E : output voltage at time

sE : longitudinal dispersion coefficient for solid

Auroba, (1993) studied the effect of solid particles on hydrodynamics of SBC

with different liquid-phase (alcohols and electrolytes). The dimensional

analysis was used to correlate the gas hold-up with gas velocity and liquid

properties. The correlations which were used to measure the gas hold-up are:

Without adding solid particles:

22.0

3

492.0.

)1( 4

−

∗

∗∗=−LL

L

L

Lg gUA

g

g

σρµ

σµ

εε …… (2.5)

With adding solid particles:

08.0885.073.04 ..25.11

...

)1(

22.0

3

492.0

−

∗

−+

=−

−

L

Lgc

L

Ls

s

s

LL

L

L

Lg

UDC

gUA

g

g

µρ

ρρρ

ρ

σρµ

σµ

εε …… (2.6)


34

Koide and Shibata, (1992) found that the gas hold-up in air-water-glass

spheres system; and that the larger solid particles showed a somewhat smaller

gas hold-up. Based on visual observations, they suggested that this is caused

by the larger rising velocity of coalesced bubbles in the presence of solid

particles.

Naseer, (1994) studied the effect of solid particles and column

dimensions on the gas hold-up and liquid phase mass transfer coefficient in

solid suspended bubble column with draught tube. The author found that the

gas hold-up is not affected by column diameter and the effect of (Cs) on (εg

)

becomes less pronounced. The gas hold-up and the volumetric liquid phase

mass transfer coefficient are correlated by the two correlations:

2978.09891.1429.0101005915.2 aorg GBF ∗∗∗∗= −ε …… (2.7)

210*47811.010*73.1769.110*92

686.4 −−∗== −−

graoca FGBSDDKl

L

c ε …… (2.8)

Li and Prakash, (2000) reported that the static height in three phase

SBCRs can be expressed as:

HgP ssLLgg ∆++=∆ )( ερερερ …… (2.9)

By proper substitutions, starting with the equation (2.9), one can factor out

the εg

∆∆

+=

HP

g ss

g )(1

11 φρφρε

as:

…… (2.10)


35

Equation (2.10) can be directly applied for estimation of gas hold up in a

SBCRs.

van Baten et al (2003) studied the effect of column diameter and slurry

concentration on the gas hold up slurry bubble column reactors the major

conclusion of this work is that with increasing slurry concentrations. The

total gas holdup decreases, and gas holdup in the dense phase is practically

independent of the column diameter.

The magnitude of gas hold up radial gradients depends on superficial

gas velocity, column diameter, physical properties of the system and

operating conditions

2.7.3 Operation Pressure Operation pressure has a significant influence on the Fischer-Tropsch

Synthesis and product distribution. The goal products are gasoline, kerosene,

and diesel. Gasoline forms in the highest quantity at low pressures and high

H2/CO mass ratios or at moderate pressures and low H2/CO mass ratios.

Kerosene is also formed in the highest quantities at low pressures and high

H2 mass fraction or at moderate pressures and high H2 mass fractions.

Finally diesel is synthesized best at low and moderate pressures, with little

influence from mass ratio, or at relatively high pressures and low H2

2.7.4 Solid Suspension

/CO

ratios. [Fernandes and Fabiano, 2005; Calemma et al., 2005].

The solid concentration is defined as the volume fraction, (εs), of

solids in the gas-free slurry. To design a column of this type as a slurry

reactor, the behavior of the suspended solid particles, that is, the values of the

critical gas velocity required for complete suspension of solid particles and


36

the concentration distribution of the solid particles, should be known [Letzel

et al. 1999].

2.8 UTransport Processes in SBCR 2.8.1 Mass Transfer

In SBCR, the gas-phase is conventionally sparged through the slurry at

the bottom of the reactor through a specially designed distributor, leading to

different flow regimes, and complex hydrodynamic as well as mass transfer

behavior. Due to the small size of catalyst particles in slurry reactors (particle

diameter typically of the order of 50 μm), intra particle diffusion is not a

limiting factor. With catalysts of relatively low activity present in low

concentration in bubble columns operated in the homogeneous regime, gas-

liquid mass transfer is unlikely to be a limiting factor either in view of the

large surface area of the small bubbles or their long residence time in the

liquid. However, for reactors of increased productivity, because of the use of

more active catalysts in high concentrations and operation in the

heterogeneous regime, gas-liquid mass transfer becomes a factor that needs

serious consideration. Conventional calculation of mass transfer rates based

on the application of the surface renewal theory with the holdup and size of

the large bubbles (which represent the major part of the gas throughput) as

input yields relatively low rates which would considerably detract from the

attractiveness of bubble columns as Fischer-Tropsch reactors.

Letzel et al. (1999) measured the volumetric mass transfer coefficient

kRLRa for the air-water system at various system pressures. Their experimental

data showed that the whole data set could be approximated by the simple

relation:


37

5.0≈ε

aKL ……………… (2.11)

De Swart et al. (1996) also determined that the exchange of gas

between various bubble classes occurs at a very high rate, at least 4 s–1

The influence of bubble-bubble exchanges is illustrated by simulations

carried out for conditions relevant for the Fischer-Tropsch synthesis.

Hydrogen absorption from synthesis gas into paraffin oil at a pressure of 40

bar and a temperature of 513 K is considered. Hydrogen and carbon

monoxide are present in the syngas feed at a ratio of 2. The superficial gas

velocity through the total large bubble population, of 0.079 m/s, is assumed

to be constant over the reactor height of 30 m. Figure (2.7) shows the

dimensionless hydrogen concentration C

, which

is higher than the characteristic renewal rate for mass transfer.

g.H2/Cg0.H2

profile along the column

height obtained for each of three bubble size classes: 0.01, 0.04 and 0.1 m in

diameter. The three profiles coincide with one another because of very

frequent exchange rates between the bubble classes and the conversion at the

reactor outlet which is 68%. The conversion behaviour of the three-bubble

class system, with 0.01, 0.04 and 0.1 m diameter bubbles is found equivalent

to that of a single bubble class system of diameter 0.021 m.


38

Fig 2.7: Effect of bubble-bubble interaction on axial concentration profiles

of hydrogen concentration in the bubbles as determined by computer

modeling [De Swart et al.1996].

In another way, due to frequent bubble-bubble interchanges the

effective bubble diameters for the 0.04 and 0.1 m diameter classes are

reduced to about 0.02. This implies an enhancement for the 0.1 m bubble

class of a factor equal to 5. In order to further demonstrate the significance of

the bubble-bubble interchange, simulations were also carried out assuming

no exchanges between the three bubble classes. The results of this model are

shown as dashed line in Figure (2.7). The overall conversion achieved by the

non-exchanging bubble ensemble is only 43%, significantly lower than that

obtained taking interactions into account.

For a bubble column reactor operating with concentrated slurry in the

heterogeneous flow regime at elevated pressures, the relation (2.1) can be

applied after applying two corrections. Firstly, the total gas holdup is

predominantly made up of large bubbles and so ε ≈ ε b. Secondly, the mass


39

transfer coefficient needs to be corrected for the liquid phase diffusivity

under the actual conditions prevailing in the Fischer-Tropsch reactor:

refL

L

b

L

DDaK

.

5.0≈ε ……………….(2.12)

where DL is the diffusion coefficient in the liquid phase, while DL. ref is equal

to 2 × 10–9 m2/s (valid for the measurement systems in Vermeer and

Krishna,(1981)). The diffusivities DL of the H2 and CO species at a reaction

temperature of 240°C are 45.5 × 10–9 and 17.2 × 10–9 m2

/s respectively.

For most gas liquid reactions that occur in present of suspended solid

catalyst. It is usually assumed that the catalyst particle diameter is large in

comparison with the thickness of the liquid film found at the phase interface

and that the catalytic reaction does not accelerate the absorption process, then

the well-known series arrangement of transport resistance can be applied

before the gas reactant can react at the catalyst surface, transport resistances

must be overcome, as shown in Figure (2.8) the following restrictions may

arise:

1- Mass transfer across the gas-liquid interface, i.e. transport between

bulk gas phase and liquid phase, may be impeded, in which case the

absorption rate

2- Passage of the dissolved gas reactant from the bulk of the liquid phase

to the external catalyst surface may be hindered.

3- Simultaneous pore diffusion and a first order reaction in a may arise

with in the catalyst.


40

Fig 2.8: Schematic representation of possible transport resistance in

catalytic reactions in suspension phase [Deckwer,.1991].

2.8.2 Heat Transfer Bubble column and slurry bubble column reactors are widely

employed in petrochemical, chemical, and biochemical processes due to their

easy installation, easy operation, and high heat and mass transfer rates caused

by strong gas–liquid interactions. These reactors are operated under high

pressure in many industrial applications, such as heavy oil upgrading,

Fischer–Tropsch synthesis, and methanol synthesis. A number of studies

have been performed on the heat transfer coefficient in bubble columns

[Saxena et al.1990; Li and Prakash 2002; Kantarci et al. 2005].


41

Table (2.9) summarizes recent reported studies in both bubble and

slurry bubble columns. Generally there are two ways of obtaining the heat

transfer coefficient. One of them is calculating the heat transfer coefficient

based on measurement of the energy input from the heated source to the bulk

media and the temperature difference between them [Hikita et al. 1981;

Saxena, 1989; Cho et al. 2002]. In this case, the following equation is used

[Deckwer et al. 1980]:

TAiUh∆

= ……………….. (2.13)

where, h is the heat transfer coefficient (kw/(m2 K)), i is electric current (A),

U is voltage (V), A is the heat transfer area (m2

In applying this methodology, error in the calculation of heat flux based on

the energy input is inevitable, because the heat loss in heating up all the

surrounding materials, including the connecting fittings and/or column wall,

was also counted into the heat transferred from the heat source to the bulk

flow.

) and ∆T the temperature

difference between the heat source and the bulk media (K).

In recent years, heat flux measurement technology has progressed, and

led to a second method. In this method the heat flux from the heat source to

the bulk media is directly measured, and taken together with the

measurement of the temperature difference between them, the heat transfer

coefficient can be acquired in a more accurate way [Yang et al. 2000; Li and

Prakash, 2002; Kantarci et al. 2005]. For this method, the following equation

is used [Li and Prakash, 2002]:

∑= ∆

=∆

=n

i Tqi

nTqih

1ave ,1h , ………………….. (2.14)


42

where:

hi = the instantaneous local heat transfer coefficient (kw/m2

q

K),

i= the heat flux across the sensor (kw/m2

∆T

),

i= the instantaneous temperature difference between the heat source and

the bulk (K), which is the time averaged heat transfer coefficient (kw/

m2

In the reported studies [Yang et al. 2000; Li and Prakash, 2002;

Khalid, 2004], many parameters can affect the heat transfer in bubble/slurry

bubble columns. It has been reported that the heat transfer coefficient

increases with superficial gas velocity, heat capacity, and thermal

conductivity of the liquid. However, it decreases with an increase in the

viscosity of the liquid in gas–liquid or gas–liquid–solid systems [Deckwer et

al. 1980; Saxena et al. 1990; Li and Prakash, 1997; Yang et al. 2000].

Pressure has a significant effect on the hydrodynamics and bubble dynamics

(especially the bubble size) in bubble/slurry bubble columns. There are only a

few studies about heat transfer coefficient in high-pressure reactors [Deckwer

et al. 1980; Luo et al. 1997; Yang et al. 2000], an area that needs further

evaluation. Deckwer et al. (1980) investigated the heat transfer coefficient

from an immersed heat source to the surrounding media in a system

prevailing in the Fischer–Tropsch slurry process (P = 0.1–1.6MPa, T = 143–

270 ◦C), and they found increasing heat transfer coefficient with increasing

superficial gas velocity and catalyst concentration.

K) and n is the total number of the samples.

Yang et al. (2000) investigated the effect of pressure on the local heat

transfer coefficient in the center of a slurry bubble column. They found that

the heat transfer coefficient decreases with an increase in pressure. The

effective heat transfer and the good temperature equalisation in a slurry

bubble column, particularly when operated in the heterogeneous regime, are

important advantages of this type of reactor.


43

Table (2.9): Parameters in the literatures on heat transfer coefficients in bubble columns and slurry bubble columns

Researcher System

Solids diamet

er (µm)

Column diameter/height

(m)

Ug (m/s)

Pressure

(MPa) Sparger Correlation

Fair et al. (1962) Air–water No

solid 0.46/3.2, 1.07/3.04

0.006–0.045

0.1 Sparger

ring 22.0 gw UNh = where N=8850 J/m3 K

Hart (1976) Air–water, air–ethylene

No solid 0.1/1.07 0.003–

0.2 0.1 Single nozzle

25.036.0

125.0−

=

g

UK

CUC

h

L

Lg

L

LP

gPL

w

µρµ

ρ

Deckwer et al. (1980)

Nitrogen–xylene,

kogasin, decalin, nitrogen–paraffin–

powdered Al2O3

5 0.1/0.6 0.003–0.04

0.4–1.1

Sintered plate

( )[ ]25.02PrRe1.0 −= mm FrSt

Hikita et al. (1981)

Air–water, air–1–butanol,

air–sucrose Methanol

No solid 0.29/1.5 0.050–

0.34 0.1 Single nozzle

308.0851.03/2

411.0

=

−

L

LLg

L

LP

gPL

w gUK

CUC

hσρµ

σµµ

ρ

Lewis et al. (1982)

Air–water, N2–cumene, N2–glycol

No solid

0.1/1.62, 0.19/2.4

0.02–0.165 0.1 Perforated

plate -


44

Verma (1989) Air–water No

solid 0.11/1.7 0.1–0.4 0.1 Perforated plate

851.035.0

)1(121.0

−=

−

gKCE

UCh

L

LL

L

LPg

gPL

w

µρµµ

ρ

Saxena

(1989)

Air–water, air–water– magnetite

35.7–

137.5 0.11/2.25

0.015–

0.333 0.1 Porous

plate )(12.03/16/12

max. Pmmmm

gm

m

mw CKgh ρ

ρρρ

µρ

−

=

Schlüter et al. (1995)

Air–water, air–propylene

No

solid 0.29/4.27

0.01–

0.65 0.1 Sieve tray –

Li and Prakash

(1997, 2002)

Air–water– glass beads 35 0.28/2.4

0.05–

0.35 0.1

Six-arm

distributor –

Yang et al. (2000)

Nitrogen–Paratherm NF heat transfer

fluid–glass beads

53 0.10/1.37 0.01–

0.20

0.1–

4.2

Perforated

plate ( )

22.0

87.1

1PrRe037.0

−

−=

g

gmm E

EFrSt

Cho et al. (2002)

Air–viscous liquid

No

solid 0.152/2.5

0.02–

0.12

0.1–

0.6

Perforated plate

–

Kantarci et al. (2005)

Air–water–yeast, air–water–cell

10,

0.2–0.7 0.17/0.6

0.03–

0.20 0.1

Six-arm

distributor ( )

EDCB

Rr

HXFrASt

= PrRe


44

2.9Although the product distribution demonstrates the polymerization

character of the Fischer- Tropsch synthesis, a great deal of controversy still

exists on the chemical identity of the monomeric building block and, in

relation to this, of the growing hydrocarbon chain. This result from the vast

product spectrum of alkanes, alkenes, alcohols, and acids, observed during

the Fischer-Tropsch synthesis. From literature, the three major reaction

mechanisms for the Fischer-Tropsch synthesis are [Hindermann et al. 1993]:

Fischer Tropsch Mechanisms

1. The carbene mechanism;

2. The hydroxy-carbene mechanism;

3. The CO-insertion mechanism.

Figure (2.9) shows the main three mechanisms for the FT reaction

2.9.1 Carbene Mechanism In the carbene mechanism, oxygen free C1,ads intermediates are formed

from the hydrogenation of surface carbon following the dissociation of

adsorbed CO. Chain growth proceeds via the insertion of a CHx,ads species

into the metal-carbon bond of a CxHy,ads

There are a vast number of studies that support the carbene mechanism

and it is often referred to as the most probable Fischer-Tropsch mechanism.

These studies include the analysis of surface species, C-tracer techniques, the

addition of probe molecules, and olefin cofeeding studies [Dry, 2002; Yi-

Ning et al. 2003].

species. As shown in Figure (2.9)

the mechanism was first proposed by Fischer and Tropsch in 1926 and in

their proposal the synthesis proceeds via hydrogenation of surface carbides to

methylene groups. These methylene groups polymerize to surface alkyl

species that terminate in the reaction products.


45

Fig (2.9): Schematic of basic Fischer Tropsch reaction mechanisms, i.e.

the carbine mechanism, the hydroxycarbene mechanism, and

the CO-insertion mechanism [Yi-Ning et al. 2003].

2.9.2 CO-Insertion Mechanism In the CO-insertion mechanism, chain growth proceeds via the

insertion of a carbonyl intermediate (COads

) into the metal-alkyl bond. For

the C-C coupling reaction to take place, the resulting species is first

hydrogenated to an alkyl chain. This mechanism explains the formation of

alcohols, aldehydes, and hydrocarbons. It is shown in Figure (2.9) where the

carbonyl species is the key intermediate.


46

Pichler and Schulz first proposed the CO-insertion mechanism in 1970,

it is based on the work on organometallic complexes. Assuming that the

active surface during heterogeneous catalysis should be considered to consist

of individual active sites possessing a specific coordination, organometallic

complexes represent chain growth sites during the Fischer- Tropsch

synthesis. Indeed, CO-insertion into a metal-alkyl complex is frequently

observed with Fe complexes and Ru-complexes. However, methylene

insertion according to the carbene mechanism is also reported for

organometallic systems [Hindermann et al. 1993; Anfray et al. 2007].

There is still no exclusive experimental evidence for the CO-insertion

as the key mechanism for the hydrocarbon formation during the Fischer-

Tropsch synthesis.

2.9.3 Parallel Mechanism All three mechanisms mentioned above share one important common

feature: the presence of a single key intermediate. None of the mechanisms is

capable of predicting the whole product spectrum observed for the four

Fischer-Tropsch metals of interest, i.e. Iron, Cobalt, Ruthenium, and Nickel.

Moreover, the Fischer-Tropsch reaction over these catalysts produces

comparable product spectra, while a carbidic surface is active for Fe-based

catalysts and a metallic surface for Co- and Ru-based catalysts. In addition,

the water-gas shift reaction on Fe-oxides is important on Fe-based catalysts,

whereas this reaction is absent on Co- and Ru-based catalysts.

This has led researchers to assume that the Fischer-Tropsch

mechanism likely involves more than only one key intermediate [Dry, 2002;

Anfray et al. 2007]. In this respect, they proposed that a CO-insertion

mechanism is responsible for the formation of oxygenates, while


47

hydrocarbons are formed via the O-free carbene mechanism. Acids are

formed via the insertion of CO2

. It is emphasized that a large variety of O-,

H-, and C-containing species are present on the catalyst surface that all may

be involved in the Fischer-Tropsch mechanism.

2.10For engineering purposes, many researchers have carried out

theoretical work in direction of modeling and simulation on gas-liquid and

gas-liquid-solid reactors.

Modeling and Simulations

Dragomir and Bukur, (1983) showed the estimation of kinetic

parameter (e.g. the effective rate constant and the activation energy). They

concluded that the degree of axial mixing in the liquid phase has such

profound effect on the reactor performance at high values of reactant

conversion. This model is based on the assumption that the liquid phase is

completely mixed by rising bubbles. Mass balance equations for hydrogen in

gas and liquid phase are:

Gas phase:

)()( * HHgb CCKLaCudxd

−=− ................................ (2.15)

Liquid phase:

HLHL

L

HHLC CEKVdxCCaKA =−∫0

* )( .......................... (2.16)


48

David et al. (1985) derived a mathematical model to describe the

performance of SBCR used for Fischer-Tropsch synthesis. The model

accounts for axial dispersion in both the gas and liquid phases. The authors

concluded that the finite resistance to gas – liquid mass transfer decreases the

conversion of syngas that can be a achieved for affixed set of operating

conditions.

Gerard et al. (1999) developed a mathematical design model for

Fischer -Tropsch SBCR. The model takes into account the water gas shift and

Fischer-Tropsch reactions as well as individual hydrocarbon product

formation rates. Under the operating conditions investigated the Fischer-

Tropsch SBCR is mainly reaction controlled. The model predicts the

composition of the gaseous and liquid streams operating in the churn-

turbulent regime as a function of the operating parameters. The gas-phase

mass balance for component i in the large bubbles, rising in plug flow is

0)()()(

.

argarg

=−+−

LiHGL

elig

iL

eligdfb C

mC

aKdL

Cuud ......................... (2.17)

The gas-phase mass balance for component i in the small bubbles

(completely mixed) is

)()()( ., LiHGL

smalligsmall

iLsmalliggi

df Cm

CaKCC

Lu

−=− ........................ (2.18)


49

The mass balance for component i in the completely mixed liquid phase can

be written as

0

)()()()(1

.1

..

arg

0

arg

=−+

−+−

∑

∫

= LiHn

js

jPPL

LiHGL

smalligsmall

iLLiHGL

elig

Lel

iL

CLu

REE

Cm

CaKdLC

mC

aKL

ρ

........................... (2.19)

The same author developed energy balance for the slurry phase reads,

assuming that catalyst and the liquid temperature are equal

0))(

)(()( )(1

=−

+−−∆−∑ =

outpP

in

n

j pPs

WHjRPPL

TC

TCLu

TTahRHEE

ρ

ρρ

.......................... (2.20)

Krishna and De Swart (2002) develops a model to simulate the

dynamic and steady-state behaviour of Fischer–Tropsch bubble column

slurry reactor operating in the churn-turbulent regime. A distinction is made

between ‘large’ and ‘small’ bubble classes and the axial dispersion model is

used to simulate their mixing behaviour. The results of the dynamic

simulations indicate that no thermal runaways are to be expected and that

steady-state is achieved within about 7 min from start-up. Analysis of the

steady-state behaviour shows that the hydrogen conversion in the reactor is

mainly dictated by the ‘large’ bubbles, which account for a major fraction of

the gas throughput.

Krishna and Van Batten (2003) developed a strategy for a bubble

column slurry reactor; the strategy involves development of a proper


50

description for the large bubble swarm velocity in highly concentrated

paraffin-oil slurries in columns of varying diameters. The volume-averaged

mass and momentum conservation equations in the Eulerian framework are

given by

0).()(=∇+

∂∂

kkKkK u

tρερε

...................................... (2.21)

gMPuuuut

ukKLK

TkkKKkkkK

kkK ρεεµρερε++∇−=∇+∇−∇+

∂∂ )))((.()(

.............................. (2.22)

Laurent et al. (2008) developed a mathematical model and showed that

the conversion and liquid hydrocarbon yield increased with increasing reactor

height. On the other hand, the conversion slightly decreased with increasing

reactor diameter.

The major objective of the present work is to develop comprehensive

theoretical simulation to describe the transport processes in slurry bubble

column reactor by deriving mathematical models, which are capable of

predicting the main parameters of hydrodynamic, mass, heat and reaction in

slurry bubble column that was conducted in GTL process, and studied the

catalysts performance (the general types are Co and Fe catalysts) in Fischer-

Tropsch reaction under different operating conditions.

Chapter Three Mathematical Model

51

CHAPTER THREE

MATHEMATICAL MODEL

3.1 In most transfer phenomenon problems, mathematical modeling is

regarded as one of the most important steps in the understanding and solving

these problems. The objective of modeling is to construct from theoretical

and physical knowledge of the process, a mathematical formulation that can

be used to predict the behavior of the process [Drahos et al. 1992; Brakel,

2000, Yu Wang et al. 2008]

Introduction

The slurry bubble column reactor is regarded as the heart of the

industrial GTL to produce hydrocarbons. Therefore, in this work a simulation

model is presented for a (industrial scale) slurry bubble column reactor

operating in the heterogeneous or churn-turbulent flow regime. The model

predicts the mass transfer rate, heat transfer rate and reaction Kinetics in the

Fischer-Tropsch Reactor.

The present model is based on a first order rate expression for

hydrogen consumption and considers all relevant hydrodynamic phenomena.

The parameters involved in the model equations were estimated from

literature correlations [Satterfield and Huff, 1980; Deckwer, 1991; and De

Swart and Krishna, 2002 ]

The basic set of operational conditions was selected in present model

for comparison requirement with practice. The objective of this chapter is to

present a model which can be used to estimate the behavior and performance

of Industrial scale Fischer-Tropsch slurry bubble column reactor.


52

The simulator was systematically used to predict the effects of reactor

geometry (inside diameter and height) as well as superficial gas velocity and

catalyst concentration on the performance of the large scale slurry bubble

column reactors provided with cooling pipes and operating under Fischer-

Tropsch condition with two types of catalyst used, Cobalt and Iron based

catalyst.

3.2 The design model involves numerous quantities which may influence

the performance of the Fischer-Tropsch slurry process. This requires

restriction on a certain set of basic parameter values used in most

computations is given in Table (3.1) in brackets. These dimensions are

representing a real industrial Fischer– Tropsch plant and it was selected in

present model for comparison requirement with practice.

Reactor Model and Assumptions

In the Fischer-Tropsch process, the reactor operates at a pressure of 12

bar. In all the simulations the average reactor temperature equals 268 0C and

the area available for heat transfer is 0.1 cm2 (cm3 reactor) −1, depending on

the operating conditions. A constant coolant temperature TW of 258 0C is

used in the simulations. In the reactor design, the contraction factor α is

assumed to be equal to −0.5 [Deckwer et al.1982]. All computations were

carried out with a CO to H2

In this study, the slurry bubble column reactor of Fischer-Tropsch

synthesis is simulated using an axial dispersion model, the developed model

incorporates the following assumptions:

inlet ratio of I=1.5 for this value of I the usage

ratio U is equal to I, which always desirable.


53

1- The reactor is operating in a steady-state with exothermic reaction.

2- There is axial dispersion in the gas and liquid phase.

3-The Fischer–Tropsch reaction is first order in hydrogen and

hydrogen is considered to be the limiting component in the

reaction.

Table (3.1): Quantities Required in Computation [Deckwer, 1991].

Variable Value Units

Reactor diameter Dr 1.5 m

Reactor length L 8 m

Particle diameter dp 50 µm

Inlet Gas Velocity ugo 0.01-0.12 m / sec

Inlet hydrogen mole fraction Yo 0.4 -

CO / H2 1.5 inlet ratio I -

Pressure P 1.2 Mpa

Wall (cooling ) temperature Tw 531 0K

Specific heat exchange area a 10 H 1/ m

CO / H2 1.5 usage ratio U -

Contraction factor -0.5 -

Concentration of catalyst suspended in slurry phase

wt% 20-25 -

Preexponential factor, Kfo (s% Fe in slurry)-1

1.12 *10

(referred to as synthesis gas conversion ) - 5

Activation energy. E 70 A KJ/mol

Heat of reaction −∆HR 165 KJ/(mole

syngas)


54

3.33.3.1 Mass Balance for Hydrogen in Gas Phase

Formation of Model Equation

Rate of mass transfer in across surface at x by axial diffusion and motion is:

dy dzCudx

dC dy dz DE

xN

HgH

ggH+−= ............................ (3.1)

Rate of mass transfer out across surface at x + Δx by axial diffusion and

motion is:

x dy dz ) d Cudx

dCdy dz D (E

x

dy dz Cudx

dC dy dz DE

ΔxxN

HgH

gg

HgH

ggH

+∂∂

−+−=+

................................ (3.2)

The rate of mass generated by chemical reaction in the gas phase =0

The rate of mass consumption by chemical reaction in the gas phase

) - C* A (CK H.LHL .......................................... (3.3)

Applying the mass balance:

(Mass in – Mass out) + Mass generated by chemical reaction –Mass

consumption by chemical reaction =0

00 =−+−∂∂

+−++−

) - CA (C Kdy dz) dx Cudx

dCdy dz D(E

x

dy dz Cudx

dCdy dz DEdy dz Cu

dx

dC dy dz DE

H.LH*L HgH

gg

HgH

gg HgH

gg

................................... (3.4)


55

Rearranging Eq. (3.4) to get:

0)( =−∂∂−

∂∂

) - C A (C K dx dy dzCu

xdxHdC

)gD dy dz dx g( Ex H.L H*L Hg

...................................... (3.5)

Dividing by volume (dy dz dx) gives

0( ) =−∂∂−

∂∂

) - C (Ca K Cu

xdxHdC

)g Dg (E x H.LH*H

LHg

....... (3.6)

where VAaH = ................................... (3.7)

substitute RTpyy CC gH == ................................... (3.8)

0=−∂∂−

∂∂ ) - C (C a K y ) C ( u

x)

dxdy C D( E

x H.LH*HLggggg ........ (3.9)

3.3.2 Mass Balance for Hydrogen in Liquid Phase Rate of mass transfer in across surface at x by axial dispersion

dx

dC dy dz DE

xN H.L

LLH−= ........................ (3.10)

Rate of mass transfer out across surface at x+Δx by axial

dispersion

)dxdx

dCdy dz DE(

x

dx

dCdy dz DEdxN

xN

ΔxxN

H.LLL

H.L LLAAH

−∂∂+

−=∂∂+=

+

......................... (3.11)


56

The rate of mass generated by chemical reaction in the liquid phase

) - CA (CK H.L H*L ................ (3.12)

The rate of mass consumption by chemical reaction in the liquid phase

) - C (CAK H.PH.Lp p .......... …….. (3.13)

Applying the mass balance:

(Mass in – Mass out) + Mass generated by chemical reaction –Mass

consumption by chemical reaction =0

0 . =

∂∂++−

) - C (CA )- K - CA (C K

)dxdx

dC dy dz D(E

x

dx

dC dy dz DE

dx

dC dy dz DE

PHH.LPPH.LH*L

H.L LLH.L

LLH.L

LL

....................... (3.14)

Rearranging Eq. (3.14) gives:

0=+∂∂ ) - C (CA )- K - C A (C Kdx

dx

dCdy dz DE

x H.PH.LPPH.LH*LH.L L L

.......................... (3.15)

Dividing by volume (dy dz dx) yields

0=+∂∂ ) - C (C a) - K - C (C a K

dx

dC DE

x H.PH.LPPH.LH*HL

H.LLL

............................... (3.16)

02

2

=+ ) - C (C a) - K - C (C a Kdx

Cd ) D(E H.PH.LPPH.LH*HL

H.LLL

………….(3.17)


57

3.3.3 Energy Balance for Hydrogen Rate of heat conduction transfer in across surface at x by axial

conductive is

dxdT dy dz KExQ axL−= ...................... (3.18)

Rate of heat transfer out across surface at x+Δx by axial conductive is

dxdxdT dy dz KE

x

dxdT dy dz KEQdx

xQΔxxQ axLaxL

∂∂−−=

∂∂+=+

......................... (3.19)

The rate of heat generated by chemical reaction is

dx dy dzQVQ o o = ........................... (3.20)

The rate of heat removed by convection is calculated as follows:

)h A (T - Tw ................................ (3.21)

Applying the heat balance gives:

(Heat in – Heat out) + Heat generated by chemical reaction – Heat

removes by convection =0

0

)(

) h A (T - T dx dy dzQ

dxdxdT dy dz KE

x

dxdT dy dz KE

dxdT dy dz KE

w

axLaxLaxL

o =−+

∂∂++−

......................... (3.22)

Rearranging Eq. (3.22) gives:

) h A (T - Tdx dy dz Qdx dxdT dy dz K E

waxL o

x 0=−+

∂∂

……………..(3.23)


58

Dividing by volume (dydzdx) results in

0)( =−+∂∂ ) (T - Th aQ

dxdT KE

x wHaxLo ........... (3.24)

Substitute 2

HR ) RΔH(Qo −= ........................ (3.25)

) (T - Th a)RΔH( dx

Td KE wHHRaxL 02

2

2=−−+ .................... (3.26)

3.4 The rate limiting step is first order in H

Development of Model Equation 2

CKR HHH =2

and zero order in CO as

proposed by [Dry, 2002] and successfully applied by [Krishna and De swart

2002; Novica et al. 2003] therefore, the kinetic law is given by

................................ (3.27)

And the rate of synthesis gas consumption is given by

22HHCO U) R(I R +=+ ..................................... (3.28)

where U is the Co to H 2

2

H

COΔNΔ N

U =

usage ratio

.................................... (3.29)

The gas phase balance is

0 ) - C (Ca) y ) - (K C( udxd) - dx

dy C E ( Ddxd

H.LH*HLggggg =

............................ (3.9)


59

And for the batch liquid phase we have

02

2

) - C (C a ) - K - C (Ca) (K dxCd

DE H.PH.LPPH.LH*HLH.L

LL =+

......................... (3.17)

The heat balance of the suspension phase is

0H2

2

2 ) R(- Δ ) (T - T - h a

dxTd KE HRWHaxL =+ ................... (3.26)

At the catalyst phase liquid – solid mass transfer is followed by reaction,

hence at steady state the balance is given by

2

H.PPLH.PH.LPPH CC K E ) - C (C a K R == ........................ (3.30)

The H2

H.PPLH.PPPH.LPP CC K E C a -K C aK =

concentration on the catalyst surface can be expressed as a function

of the liquid phase concentration from Eq. (3.30), it follows that

......................... (3.31)

)CK E a(K C C aK PLPP H.PH.LPP += ............................ (3.32)

Rearranging Eq. (3.32) yields

] aKCK E

[

C C

PP

PL

H.LH.P

+=

1 .................................... (3.33)

H.LPH.P Cη C = ..................................... (3.34)

where η P

…………..…… (3.35) ] aK

EK C / [ η

PP

LPP += 11


60

Therefore the reaction rate can be expressed by

……………(3.36)

2H.L P pLH CηC K E R =

The variable gas velocity is given by[Krishna and De swart 2002]

…………………. (3.37) )X (uu HCOgog2

α1 ++=

where the synthesis gas conversion is related to the hydrogen conversion by

………… (3.38) HHCO XIU X +

+=+ 11

2

The hydrogen conversion is defined by

…… (3.39) )Y U( yu yu

- yuy-uy u

X gogo

g

ogo

gogoH −=== 1 1

Substitute Eq. (3.39) into Eq. (3.38) to give

)Y U (IU X gHCO −+

+=+ 111

2 ……………….... (3.40)


) )Y U )IUα ( )I

U α (uu ggog ++−+

++= 11

11(1 ….……… (3.41)

)Y Uα* (U gg *α1 −+= ……………………. (3.42)

Where

I

Uα α* ++= 1

1 …………………... (3.43)

Rearrange Eq. (3.42) to give

…………………… (3.44) g Yα*

α* U++=

11

Henry equation is given by

………….(3.45) CHe

oP y)H * (x == 0


61

The liquid phase concentration is due to the saturation value at the reactor

inlet

is the effectiveness factor

/HeP yC

CC

Xo

H.L

)H * (x

H.L === 0

……………… (3.46)

The mean superficial gas velocity is:

………………. (3.47) goggU /uu=

………..… (3.48) T R / PCg = From gas law

And introducing a dimensionless axial coordinate

x / L=ξ …………...……… (3.49)

oy/yY = ………...……… (3.50)

The gas phase balance can be written as

012

2

2 ) CC

-( Ca) -(KL R T P yuU

dYd -

dYd

R T L P y ED

H*

H.LH*HL

ogo gogg =ξξ

......……..… (3.51)


012

2

2 ) P y /HeC

-(HeP y a) - (KL R T

P y uU dYd -

dYd

R T L P y ED

H.LHL

ogogogg =ξξ

…………...……… (3.52)

Dividing Eq. (3.52) by ( P y RO R ugo / L R T ) gives

0 2

2 ) / He P y

CY( Heu

R T L a)) - (KU Y (dd -

dYd L u

ED

o

H.L

goHLg

go

gg =−ξξ …………………... (3.53)


62


0 )X - Y( u He L T Ra)(K - ) Y U (d

d - dYd L u

E D

goHLg

go

gg 2=ξξ

……...……… (3.54)

From Eq. (3.44), it follows that

α* U Yα*U gg +=+ 1 ………...……… (3.55)

Dividing Eq. (3.55) by α* and rearranging gives

)U(α* α*U

α*Y U gg

g −+=−+= 11111 …...……… (3.56)

Derive Eq. (3.56) with respect to ξ

1 dUd

α*)Y U(dd g

g ξξ −= …………...………(3.57)

By using chain rule relation to give

ξξ dYd .

YdUd

dUd gg = ………...………(3.58)

Derive Eq. (3.44) and substitute into Eq. (3.43)

ξξ dYd

)Yα*(α*)α*() * Yα*(

dUd

g21101

++−+= ………...…… (3.59)

ξξ dYd

)Yα*(α*)α*(

dUd g

211++−= ………...…… (3.60)


ξξ dYd

)Yα*(α*)(

dY Ud g

211++= …………...……… (3.61)


63

And the gas phase balance Eq. (3.54) can be written as

0 111

2

2 ) X - Y (He u

R T La) - (KdYd

)Yα*(α*)( - d

YdB

go

HLOG

=++

ξξ

…………… (3.62)

With dimensionless group

gg

goE DL u

BOG

= …………...…… (3.63)

By introducing Eq. (3.46) and (3.49) into Eq. (3.17) and referring to ugo

H.PH.LPPH*

H.LH*HL

H*LL ) - C (C a ) -KCC

- ( Ca) (K d

XdL

C DE012

2

2 =+ξ

the

liquid phase balance is given by:

…………...………(3.64)

0 C ηCEK - ) Hey / PC

- (1Hey Pa)(K

dXd

HeLy P D E

H.LP PLH.L

HLoLL

2

2

2=+

ξ …………...………(3.65)

divided by u go

0

12

2

X Heu P y ηC L K E

) -P y / HeC

- (He uP y La) (K

dXd

L He uP y DE

go

oPPL

H.L

go HL

go

o LL

=

+ξ

/ L

………...…… (3.66)

divided by ( P y O

012

2 X u

ηCL K E ) -/ HeP y

C - ( u

YL a)(K d

XdL u

DE

go

PPL

o

H.L

goHL

go

LL =+ξ

/ He )

…………...………(3.67)


64

Substituting Eq. (3.46) into Eq. (3.67) gives:

0 1 2

2 Xu

LECK η) X - Y(uLa)(K

dXd

B

goLPP

goHL

OL=−+

ξ

…………...…… (3.68)

with dimensionless group

LL

goE DL u

BOL

= …………...……… (3.69)

From the heat balance i.e Eq. (3.26), it follows introducing Eq. (3.30), (3.34)

and by dividing by Cp ρgou gives:

H.LP PLgo

R

wgo

H

go

axL

CηC) K E uCp ρ

-Δ (

) ( T - TCp ρ u h a

- dx

Td Cp ρ u

KE

0H

2

2

=

+

………...…… (3.70)

Substituting Eq. (3.49) into Eq. (3.70) and multiplying by L gives:

0H

2

2

XgouL η E K CHe

oP y )

Cp ρ -Δ

(

) (T - TCp ρ gou

Lh a - d

Td LCp ρ gou

E

PLPR

wHaxKL

=

+ξ

………...……… (3.71)

By referring to the temperature of the wall or cooling coil (T w

wT/Tθ =

),

the dimensionless temperature distribution is:

…………...………(3.72)


65

And introducing the dimensionless numbers yields

ax L

goKE

LCp ρ uPe= …………...………(3.73)

Cp ρ u Lh a

Stgo

HH = …………...………(3.74)

T Hey P

) Cp ρ

ΔH- ( Be

w

oR= …………...………(3.75)

And the Arrhenius law is

exp γ /θ)( KK f −= ………...………(3.76)

And the Arrhenius number is

/ wA R TEγ = ………...………(3.77)

Eq. (3.71) can be written as:

0exp1 (θ12

2 X Cγ/θ) η( K Eu

L Be ) - - Std

θd Pe ppfLgo

H =−+ξ

……...………(3.78)

In this equation the dependency of Cp ρ on temperature and catalyst

concentration has been neglected however the heat balance as well as the

liquid phase balance, i.e., equation (3.68) considers yet the local dependency

of the catalyst concentration. This concentration can be calculated from the

dispersion sedimentation model for batch suspension, this model yields [kato

et al. 1972]

02

2

=+ dxdC

Udx

CdE P

CSP C

…………...………(3.79)

with the boundary condition at x=0 and x=L

Pdx

dC0= …………...………(3.80)


66

The EC presents the dispersion coefficient of catalyst particles and UCS

The solution of Eq. (3.79) and (3.80) and considering the mean catalyst

concentration

is

their settling velocity in the particale swarm .

PC gives

) B( )B(B

CC OC

OC

OCPP (Z)

expexp1 ξ−−−

= .......….(3.81)

where C

CSOC E

LUB = ………...………(3.82)

When calculating effectiveness factor ( p η ) one has to consider that

(aP

p η) depends on the catalyst concentration profile then, from Eq. (3.35) and

(3.76) that effectiveness factor ( ) can be calculated as follows:

1) θ / λ-exp

1)−+= ) aK

( EC K(η

PP

LPfp(θ

……… (3.83)

And by defining

PP

LPfPo aK

ECKη = …………...……… (3.84)

One obtains 1θ))λexp1(θ

- / (- η(η PO)P += …...………(3.85)

Consideration of this equation and the dimensionless number

gives:

goHLL u

La)(K St = …………...………(3.86)

go

wHLg uHe

LTRa) (KSt

= …………...………(3.87)


67

go

Lfu

L EKDa = …………...………(3.88)

From the final form of the balance equation gas phase H2

balance is obtained

0 ( θ1

1 1 2

2 ) X - Y - Std

Yd)Yα*(

α*)( - dYd

B

gOG

=++

ξξ ...……… (3.89)

Liquid phase H 2

0exp1θ)2

2=−−+ Xγ/θ) ( CDa η) X - Y (St

dXd

B

P (Z)P(L OL ξ

balance is

...……… (3.90)

And Heat balance equation is

0exp1- θ1)(2

2=−+ X Cγ/θ) η( Be Da ) ( - St

dθd Pe PpH θξ

.…… (3.91)

Boundary condition

0011110 ==−++== d

θd ;dXd ; d

YdBYα*

Yα*) ( : OG

ξξξξ

…………...………(3.92)

0001 ==== d

θd ;d

Xd ; dYd: ξξξξ

…………...………(3.93)


68

3.5

The finite difference method is used to solve the differential equations

that were derived in present work. An approximate solution of equations

(3.89), (3.90) and (3.91) will be obtained at a finite number of grid points

having coordinates: (

Numerical Formulation Using Finite Difference

Method

ξ =i ξ∆ ) where ( i ) is integer see Fig (4-1),. The grid

spacing in x-directions is denoted by ( ξ∆ ).It is important to mention here,

the values of Y, X, Ө at each grid point are considered as an average value

over small volume of fluid surrounding the point.

Fig (4-1) Grid points of the numerical solution

3.5.1 Solution of Mass Balance Equation Equation (3.89) which represents mass balance in gas phase can be

solved numerically by explicit finite difference method which

will be described for each term as follows:-

0 ( θ1

1 1 2

2 ) X - Y - Std

Yd)Yα*(

α*)( - dYd

B

gOG

=++

ξξ ...……… (3.89)

(i, j ) (i+1,j) (i-1,j)

ξ∆


69

-Diffusion Flux Differencing: second order central differencing

method is used for diffusion of flux differencing term as follows:

211

2

2 211 Δ

YYYB

d

YdB

)(i(i))(i

OGOG

ξξ−+ +−= ……………... (3.94)

-Motion Flux Differencing: first order central differencing

method is used for motion flux differencing term as follows:

ξξ Δ211

11 11

22 *YY

)Yα*(α*)( d

Yd)Yα*(

α*)( )(i)(i

(i) −+ −

++=

++ ...…… (3.95)

Substituting Eq. (3.94) and (3.95) into Eq. (3.89) we obtain:

0

Δξ21

121 11

22

11

=+

−

+

++− −+−+

(i)i)i(i)

)(i)(i

(i)

)(i(i))(i

X θ StY θ- St

*

YY

)Yα*(

α*)( - Δξ

YYY

B

(g)(g

OG

………….… (3.96) Rearranging Eq. (3.96) gives

0ξ2111

2

1122

11

2

=+−

++−+

=+

−+−+

(i)(i)

)(i)(i

(i)

)(i)(i

OG

(i)(i)OG

X θSt

*ΔYY*

)Yα*(α*)(

ΔξYY

B

Y θ StBΔξ

g

g

…………. (3.97)

(i)OG

(i)(i))(i)(i

(i)

)(i)(i

OGi)

θ StBΔξ

X θSt*ΔYY*

)Yα*(α*)(

ΔξYY

B

Yg

g(

+

+−++−+

=

−+−+

2

1122

11

2ξ21

11

……………… (3.98)


70

Eq. (3.98) represents the numerical solution of the

differential equation for H 2 mass balance in the gas phase. And it

is used to calculate the concentration of H 2

Eq. (3.90) which represent, mass balance in liquid phase can

be solved numerically by explicit finite difference method which

will be described for each term as following:-

along the reactor

using Fortran program. The computer program and its algorithm

are shown in appendix A and B respectively.

0exp1θ)2

2=−−+ Xγ/θ) ( CDa η) X - Y (St

dXd

B

P (Z)P(L OL ξ

…………...…… (3.90)

-Diffusion Flux Differencing: second order central differencing

method is used for diffusion flux differencing term as follows:-

211

2

2 211Δξ

XXXB

dξ

XdB

)i(i))(i

OLOL

( −+ +−= ……… (3.99)

Substituting equations (3.99) into equation (3.90) we obtain

0X)γ/θ( exp C η Da

-X St YSt Δ

XX2XB

1

)((i)

(i)21)(i(i)1)(i

)P()( P

L(i) L

=−

−++− −+

i

OL

ξ

ξ

θ

………. (3.100) Rearranging equation (3.100) to give

(i)2

1)(i1)(i

)((i)2

Y St ΔBXX

X)γ/θ( exp C η Da St ΔB

L

)P()( PL2

++=

−++

−+

ξ

ξξ

OL

iOL

θ

………… (3.101)


71

)γ/θ( exp C η Da St ΔB

Y St ΔBXX

X(i))(2

(i)2

1)(i1)(i

)(

P)( PL2

L

−++

++ −+

=

ξOL

OLi

ξ

ξ

θ

...... (3.102)

Equation (3.102) represents the numerical solution of the

differential equation for H 2 mass balance in the liquid phase. And

it is used to calculate the concentration of H 2

along the reactor

using Fortran program. The computer program and its algorithm

are shown in appendix A and B respectively.

3.5.2 Solution of Energy Balance Equation (3.91) in which represents energy balance can be

solved numerically by explicit finite difference method which

will describe each term as follows:-

PpH X C(γ/θ) η( Be Da ) ( - Std

θd Pe 0 θ)exp1- θ12

2=−+

ξ

…………...……… (3.91)

-Conduction Heat Flux Differencing: second order central

differencing method is used for calculating conduction flux

differencing term as follows:

21)(i(i)1)(i

2

2

Δθ2θθ

Pe1

dθd Pe

1ξξ

−+ +−= …….………(3.103)


72

Substituting Eq. (3.103) into Eq. (3.91) we obtain

0exp

21

)(

211

=−

+++− −+

(i)(i)

(i))(i(i))(i

X C )ηγ/θ(

Be Da St θ - StΔξ

θθθ Pe

P P

HH

θ

……….. (3.104) Rearranging Eq.(3.104) to give

(θexp

121 2

11

2

−

+++

=+−+

(i)(i)

)(i)(i

(i)X C)ηγ/θ(

Be Da StΔξ

θθPe θ St

Δξ Pe

P )p

HH

………..……. (3.105)

H

P)p(H(i)

St Δ

2 Pe1

X C )ηγ/θ( exp Da Be StΔ

θθPe1

θ2

(i)(i)21)(i1)(i

+

−+++

=

−+

ξ

ξ θ

………………. (3.106)

Eq. (3.106) represents the numerical solution of the

differential equation heat balance. And it is used to calculate the

temperature distribution along the reactor using Fortran program.

The computer program and its algorithm are shown in appendix A

and B respectively


73

3.5.3 Boundary Condition Solution Equation (3.92) which represents boundary condition at ξ =0

can be solved numerically by explicit finite difference method

which will be described as follows:-

2111 00 XX

ΔξXX

dξXd =⇒=−⇒= ……………. (3.107)

2121 00 θθ Δξ

θθ dξθd =⇒=−⇒= ………………. (3.108)

21

OG)(

)(

OG

YYB

1Y*α1Y α*)(1 1d

YdB

1Y*α1Y α*)(1 1 ξξ i

i

∆−−

++=⇒−

++=

…………………. (3.109)

Equations (3.109) in which represents boundary condition at

ξ =1 can be solved numerically by explicit finite difference

method which will be described as follows:-

mmmm XX Δξ

XXdξXd

11 00 −− =⇒=−⇒=

………. (3.110)

100 1−=⇒=−⇒= −

mm YY ΔξYY dξ

Yd mm …. (3.111)

1mmm1m θθ 0Δ

θθ0 dθd

−− =⇒=−⇒= ξξ …….. (3.112)


74

3.6 In order to solve equations (3.89),(3.90), and (3.91) their coefficients

must be estimated as follows:

Parameter Estimation

-Rate Constant for H2

U

K fof +=

1K

Consumption.

………………. (3.113)

The heat of reaction is obtained by linear interpolation from the following

equation:

515040165 .)/.*(UΔHR −+=− ………………. (3.114)

-Volume Fraction of Catalyst in Slurry:

) -(W- W

VLPPP

PLP ρρρ

ρ= ……..…. (3.115)

-Temperature Dependent Quantities. Density [Deckwer et al.1980]

33 37310 55507580 ) g/cm(T* . - . ρ -L

−= ………………. (3.116)

Viscosity [Deckwer et al.1980a]

sec . /cmg T)) / (3266 6.905- ( exp 0.052 μL += ………... (3.117) Diffusivity [Satterfield and Huff, 1980]

sec T2285/ -exp10 357 23 /) cm ( * . D -L.H

= ………………. (3.118)

Henrys constant [Deckwer, 1991]

)/mol cm/T) ( Kpa(.(*. He 37 583 23261exp 10 2912 +−= …. (3.119)


75

-Properties of Suspension.

The physical properties of the suspensions from the individual date of

solid and the paraffin are estimated. The mean densities are calculated from

3 g/cm ρ1

L ) V( ρVρ

PPP−+= …………………. (3.120)

where, V represents the volume fraction and P, L refer to solid and liquid

paraffin.

The Viscosities are obtained from De Swart and Krishna, (2002) relation.

.sec g/cm541 ) V. (μμPL += …………………. (3.121)

The heat capacity of the suspension is then given by [De Swart and Krishna,

2002]

LPPP )CpW ( CpWCp −+= 1 …………………. (3.122)

where W represents the weight fraction.

For estimating heat conductivities of suspensions [De Swart and Krishna,

2002] proposed the equation.

)λ(λVλλ)λ(λVλ λ

λλPLPPL

PLPPLL −++

−−+=

222

………………. (3.123)

- Mass Transfer Gas / Liquid.

The gas was sparged by a porous plate sparger having a mean pore

diameter of 75µm at temperature above 250 0

1.1 053.0 gg UE =

C the gas holdup is calculated

from the following empirical equation [Deckwer et al, 1980]

…………. (3.124)


76

Interfacial area is [Deckwer et al. 1980]

1 1.1 cmU 4.5a g

−= ………………. (3.125)

Mass transfer coefficient is [Satterfield and Huff, 1980]

/seccm ) T(-4570/ exp μρ 0.1165 K

1/3

L

= ……………. (3.126)

- Mass Transfer Liquid / Catalyst.

Interfacial area

PP

PP ρd

ρ)gE(Wa

−=

1 6 ………………. (3.127)

Mass transfer coefficient [Deckwer,1991]

+=

μρ d E

Dρμ 0.5452d

DK3

341/3

L

LP

LL

L

P

LP ……………. (3.128)

with

sec6 cm/u g if uE gg ≤= ………………. (3.129)

/seccm 6 gu if 3 /sec2cm 5886 constant E ⟩==

- Heat Transfer Coefficient

Heat transfer from walls and inserted coils was analyzed theoretically

by [Deckwer et al., 1980]

.sec.K J/cm 10 2

0.2523 −

= λCp μ

μg ρu

)u Cpρ(.h gg

……………. (3.130)

-Dispersion Coefficients.

Gas phase is [Satterfield and Huff, 1980]

sec 10 5 2513 4 / cm Dr ) /Eu(*D .ggg

−= ………………. (3.131)


77

Liquid phase is [Deckwer, 1991] 3402

832.

OL g Dru

.B g

= ………………. (3.132)

sec 6763 2341320 / cmDr u .D . .gL = ………………. (3.133)

Effective heat conductivity of suspension is

K sec. cm. / J C ρDK pLax = ………………. (3.134)

- Solid Phase Dispersion and Sedimentation [Kato et al. 1972]. Dispersion coefficient

850113

.C

OC Fr Fr

EDr u

B g+

== ………………. (3.135)

with ………………. (3.136)

- Contraction Factor

The variability of the molar gas flow rate in the reactor can be taken

into account by application of a gas phase contraction factor ALPHA,

defined as in [Levenspiel, 1972; De Swart and Krishna, 2002]:

0)(XV

0)(XV1)(XVα

2HCOg

2HCOg2HCOg

=

=−==

+

++ ……………. (3.137)

From experimental results [Deckwer, and Schumpe, 1993] it can be

deduced that α varies between -0.5 and -0.6 in the following computation a

constant value of α =-0.5 will be used throughout.

g Dr/uFr g=

Chapter Four Result and Discussion

78

CHAPTER FOUR

RESULTS AND DISCUSSION

4.1

The present chapter shows the results of the mathematical model that is

derived in chapter three. The model is based on the principles of transport

processes and reaction kinetic in multiphase flow. In this chapter the

influences of the superficial gas velocity, operating pressure and temperature,

solid concentration, column dimensions, heat transfer coefficient and gas

liquid distribution for Cobalt and Iron based catalyst are discussed.

Introduction

In order to get a clear picture of design and simulation of slurry bubble

column reactor (SBCR) in GTL process the results of the present model are

compared with the results of Fischer– Tropsch process that was investigated

in literature [Krishna and de Swart,2002; Novica et al.,2003; Laurent et al.,

2008]. The reactor dimensions selected were 150 cm for diameter, dispersion

height L=800 cm and operating with a superficial gas velocity Ug

=12 cm /s.

These dimensions represent a real industrial Fischer– Tropsch plant and it

was selected in the present model for comparison requirement with practice.


79

4.2

Hydrogen Profile in Liquid and Gas Phase

Figures (4.1) and (4.2) show the hydrogen concentration profiles over

the reactor height in the gas and the liquid phase for both Cobalt and Iron

based catalyst, in this figure Y represents hydrogen concentration in the gas

phase and X represents hydrogen concentration in the liquid phase, and it can

be seen that for Cobalt-based catalyst the hydrogen bubble concentration in

the gas phase decreases from 0.91 at the inlet of the reactor to 0.62 at the

outlet of the reactor and for the Iron-based catalyst the hydrogen bubble

concentration decreases from 0.79 at the inlet of the reactor to an equilibrium

value with the liquid phase of about 0.45 at the outlet of the reactor.

Such behaviour can be explained on the basis that, the rate of mass

transfer for all components is very high, therefore the inlet gas will

instantaneously equilibrate with the liquid, and the dimensionless

concentration for H2 in liquid phase is significantly lower than those in the

gas phase due to the finite mass transfer resistance. These results are in

agreement with those reported by Dragomir (1983), Krishna and De swart

(2002), Laurent et al. (2008).


80

0 0.25 0.5 0.75 1Reactor height

0.5

0.6

0.7

0.8

0.9

1

Hyd

roge

npr

ofile

XY

Gas phase

Liquid phase

Fig. (4.1): Hydrogen profile over the reactor height with Cobalt catalyst.

0 0.25 0.5 0.75 1

Reactor height

0.4

0.5

0.6

0.7

0.8

0.9

1

Hyd

roge

npr

ofile

XY

Gas phaseLiquid phase

Fig. (4.2): Hydrogen profile over the reactor height with Iron catalyst.


81

4.3 Catalyst Distribution Along the SBCRIn three phase reactor the catalyst distribution is an important task

because high dispersion catalyst means higher mass transfer and higher

synthesis gas conversion. Figure (4.3) shows the Cobalt catalyst distribution

along the reactor height. According to this figure the catalyst profile is very

flat, obviously distribution is high enough to suppress settling of catalyst

particles, It is clear that, the catalyst profile is highest at the bottom of the

reactor, this is due to the fact that the settling velocity of the particles in a

swarm is higher than the resistance of the liquid phase. Such explanations are

in agreement with explanation of Wallis. (1969), Van Baten et al. (2003), van

Baten and Krishna (2004).

The same behavior is noted for Iron based catalyst as shown in Figure

(4.4) which gives high distribution of catalyst. It is important to mention

here, that, the partical diameter of catalysts that is used in Fischer Tropsch

reaction is in range of 25 to 200 µm. The more favorable particle diameter is

about 50 µm for such type of reaction [Michael et al. 2005; Fabiano et al.

2007; Laurent et al. 2008].

The present study is concerned with the hydrodynamic effect of

Fischer-Tropsch reactor performance, pore diffusion limitations were not

considered in the model computations. Under all conditions simulated i.e., at

various temperatures, gas velocities, and column diameters, the particle sizes

have no significant influence on the conversion, in model computational if 50

µm particles are applied, the catalyst is uniformly distributed over the reactor

volume even for the lowest gas velocities.


82

Figures (4.3) and (4.4) show the catalyst profile along the reactor

height for Cobalt and Iron catalyst respectively and indicate that the catalyst

sedimentation and liquid – solid mass transfer resistances can be neglected in

the FT slurry process. Therefore, in the model equations (3.90) and (3.91) the

effectiveness factor )( θηP can be set to one , and instead of CCAT

0exp1θ)2

2=−−+ Xγ/θ) ( CDa η) X - Y (St

dXd

B

P (Z)P(LOL

ξ

(z) the

average catalyst concentration can be used .

…..…….. (3.90)

X C(γ/θ) η( Be Da ) ( - Std

θd Pe PpH

0 θ)exp1- θ12

2=−+

ξ ………….. (3.91)

0 0.25 0.5 0.75 1

Reactor height

20

21

22

23

24

25

26

27

28

29

30

cata

lyst

conc

entra

tion

wt%

Fig. (4.3): Cobalt catalyst profile over the reactor height.


83

0 0.2 0.4 0.6 0.8 1

Reactor height

20

21

22

23

24

25

26

27

28

29

30ca

taly

stco

ncen

tratio

nw

t%

Fig. (4.4): Iron catalyst profile over the reactor height.

4.4 Temperature Distribution Along the SBCRTemperature is a basic process variable that has a profound effect on

the overall yield of a Fischer-Tropsch reactor. Temperature is normally used

to control the distribution of products in the reaction, where one product may

predominate at lower temperatures (kinetically controlled) and another

predominates at a higher temperature (thermodynamically controlled). All

reactions that take place in the Fischer-Tropsch process are extremely

exothermic, so temperature control is extremely necessary to ensure the

reaction goes to significant products [Mills et al.,1996; Fernandes and

Fabiano, 2005].Therefore in the design and construction of SBCR the

monitoring of reaction temperature is important.


84

Figure (4.6) shows the temperature profile of Cobalt and Iron catalyst

respectively. The temperature profile is based on the result of model

according to energy balance equation (3.91).

X C(γ/θ) η( Be Da ) ( - Std

θd Pe PpH

0 θ)exp1- θ12

2=−+

ξ …………………. (3.91)

The computations were done either for isothermic condition i.e the

specific heat exchanger area was set to such a high value that the slurry

temperature agreed with the wall temperature or for non-isothermic

conditions i.e, Tw (wall temperature) was set to 258oC and aH 0.1 cm-1. Then

the slurry temperature could rise to higher value than Tw

Figure (4.6) shows that for Cobalt-based catalyst the temperature of

reaction is approximate to be 260

because of heat

generated by reaction, and within the reactor a small temperature profile was

built up.

oC, on the other hand for Iron based catalyst

the temperature rises to 267 o

Due to this little temperature difference in a tall reactor it is permitted

from a more practical viewpoint to assume an approximately constant

temperature along reactor. Nevertheless a heat balance i.e. Eq.(3.91), is

required to calculate the operating temperature under non isothermic

condition .

C from results of this figure it can be concluded

that, for the two types of catalysts the flat temperature profile exists due to

high dispersion in liquid phase and confirms to the well know fact that due to

the good mixing properties slurry bubble column reactor (SBCR) offers

relatively easy heat removal with less cooling area than some other types of

Fischer-Tropsch reactors (e.g. trickle bed ) .


85

Fig. (4.5): Temperature profile over the reactor height (Cobalt and Iron

catalysts).

4.5

According to many investigations [Krishna and van Baten, 2003;

Ahmad et al. 2008; Guillou et al. 2008] when gas is injected into the SBCR

from the bottom, the slurry bed expands, and holdup of each phase will be

formed. Then each phase presents different velocity and recirculation

patterns. Therefore Figure (4.6) shows the gradient of the superficial gas

velocity over the reactor height for two types of catalyst (Cobalt and Iron).

From this figure it is clear that the highest value of superficial gas velocity is

present at the reactor inlet, and it decreases gradually until it arrives to

Superficial Gas Velocity Profile Along the SBCR


86

constant rate at the reactor outlet. The explanation of such conclusion is

regard the gas volume contraction (α), and it is cited in Eq.(3.137).

The same behavior is noted for both types of catalysts because the

same weight and particle size.

It is important to mention here that in the derivation of mathematical

model the gas contraction factor (α) is calculated under the following

simulation condition,Ug0 = 1–12 cm/s , T = 258–267oC, P = 1.2 MPa, H2

/CO

= 1.5. The different product distributions under different conditions result in

the different values of α., the value of α is given in the model equations like

some authors Ahon et al. (2005), Maretto and Krishna (1999).

0.2 0.4 0.6 0.8Reactor height

0.5

0.6

0.7

0.8

0.9

1

Sup

erfic

alga

sve

loci

ty

Cobalt catalystIron catalyst

Fig. (4.6): Superficial gas velocity profile with reactor height.


87

4.6 Heat Transfer CoefficientThermal control in slurry bubble columns is of importance since in

Fischer Tropsch processes, chemical reactions are usually accompanied by

heat removal (exothermic) operation. Many hydrodynamic studies investigate

the heat transfer process between the heating object and the system flow to

understand the effects of hydrodynamic parameters on the heat transfer for

improving the design and operation of bubble column reactors. [Li and

Prakash, 1997; Quiroz et al.2003; Chengtian et al.2007]

Literature studies reported on heat transfer measurements in three

phase systems can be divided into: (1) estimation of bed-to-wall heat transfer

coefficients, and (2) estimation of immersed object-to-bed heat transfer

coefficients. However, measurements of instantaneous heat transfer

coefficients provide more insight into bubble dynamics and mechanism of

heat transfer. The use of average heat transfer coefficient causes the loss of

information related to the effect of instantaneous bubble dynamics on heat

transfer. It is important for us the in instantaneous heat transfer in bubble

columns under wide range of conditions to have a comprehensive

understanding of the heat transfer mechanism and reliable modeling to

improve design and operation.

Many literature correlations exist for estimation of heat transfer

coefficient that can be applied to two-phase bubble columns and three-phase

slurry bubble columns, several of these correlations are presented in chapter

two. The basic parameters affecting the heat transfer are mainly the

superficial gas velocity, particle size and concentration, liquid viscosity, and

column dimensions. Therefore, the present model focuses on studying the

effect of superficial gas velocity, catalyst concentration on heat transfer

coefficient.


88

4.6.1 Effect of Superficial Gas Velocity The superficial gas velocity is a dominant factor that affects the heat

transfer coefficient, generally the heat transfer coefficient increases with an

increase in the superficial gas velocity.

The model result of superficial gas velocity vs. heat transfer coefficient

is shown in Figure (4.7). From this figure it is clear that there is a direct

relationship between gas velocity and heat transfer coefficient. The heat

transfer coefficient increases due to superficial gas velocity increase and this

leads to high degree in liquid mixing and then to higher rate of heat transfer.

Moreover it is important to mention here that, the degree of mixing is also

related to the liquid circulation rate. On the other hand, the heat transfer

coefficient has a direct connection to the bubble size: it increases with an

increase in bubbles size, because large bubbles can create strong vortices and

intense mixing in the wake region. This result is in agreement with those of

Kumar et al. (1992) , Chen et al. (1994) , Luo et al. (1999) , Rados, ( 2002 ),

Ong, ( 2003), Xue, (2004).

4.6.2 Effect of Catalyst Concentration The influence of the catalyst concentration on heat transfer coefficient

is a very important factor to understand the heat transfer behavior. The

influence of the catalyst concentration on heat transfer coefficients is shown

in Figure (4.8). From this figure it is clear that, as the solid contents increase

the heat transfer coefficient increases. It is possible that similar to gas – solid

fluidized beds, the increase in heat transfer coefficient is caused by

independent motion of the particles leading to increased exchange frequency

of fluid elements at the heat surface area. Such explanation is in agreement

with work of Li and Prakash, (1997),Cho et al. (2002), Xue, (2004).


89

0 1 2 3 4Superfical gas velocity m / sec

8400

8600

8800

9000

9200

9400

9600

9800

10000

Hea

ttra

nsfe

rcoe

ffici

ent

W/m

k2

Fig. (4.7): Superficial gas velocity profile with heat transfer coefficients.

The reason given for the heat transfer coefficients increase is the

alteration of thermo-physical properties of the slurry with the introduction of

solids and also enhanced exchange rate of fluid elements on the heated

surface of the exchanger that is inserted inside the reactor is due to motion of

solid particles. Moreover, the alteration of the bubble properties with solid

addition is also needed to be taken into account. Therefore, it can be

concluded that, the increasing the solids concentrations, increases the bubble

coalescence leading to the formation of larger size bubbles with higher rise

velocities, and thus higher heat transfer rates are likely to be obtained. This

result is in full agreement with those of Kolbe et al. (1960), Deckwer et al.

(1980).


90

On the other hand, Li and Prakash (1997) reported an opposite trend to

that of Deckwer. They reported that as solid concentration increases the heat

transfer coefficient decreases. This can be explained by the fact that the

slurry viscosity grows with the increment of main solid concentration and the

convective heat transfer coefficient reduction while the viscosity of the bed

increases .When the slurry viscosity increases, the space between particles

will be reduced, and that affects the fluid dynamics behavior in several ways:

1- The mobility or velocity of particles decreases.

2- The boundary sub layer thickness of laminar flow around the heater grows.

3- The turbulent decreases.

4- The viscous friction loss between phases grows.

10 20 30 40 50

Catalyst concentration wt %

8600

8800

9000

9200

9400

9600

9800

10000

Hea

ttra

nsfe

rcoe

ffici

ent

W/m

k2

Fig. (4.8): The effect of catalyst concentration on heat transfer

coefficients.


91

4.7 The conversion of natural gas to liquid fuel (GTL) via the Fischer–

Tropsch synthesis (FTS) process continues to be an attractive option for

monetising stranded natural gas. Supported Cobalt catalysts are the system of

choice for the Fischer-Tropsch synthesis as compared to Iron due to the high

conversion, low water gas shift activity and paraffinic nature of the resulting

synthetic crude.

Syntheses Gas Conversion

4.7.1 Effect of Superficial Gas Velocity and Catalyst

Concentration The important process variable present in the Fischer-Tropsch process

is the catalyst. The main purpose of a catalyst is to break apart the syngas

molecules and dramatically increase their reactivity. In the kinetic catalyst is

shown splitting the molecules into the very reactive radical atoms, which

stabilize by combining into hydrocarbon radicals, which can combine with

other catalyzed radicals and form stable chains.

Figures (4.9) and (4.10) show the model results of the effect of

superficial gas velocity on synthesis gas conversion at different weights of

catalyst. Figure (4.9) is for Cobalt based catalyst, while Figure (4.10) for Iron

based catalyst. It is noted that, the synthesis gas conversion decreases with

increase in superficial gas velocity and it increases with catalyst

concentration. Therefore for Cobalt and Iron catalysts the reactor

performance could be improved by increasing catalyst concentration these

result are agree with that given by Inga et al. (1996). Then, the reactor would

approach a mass transfer controlled regime, especially at high catalyst

concentration which would markedly increase the bubble size. When mass

transfer is very rapid the conversion of H2 in the reactor depends only on the


92

total mass of catalyst in the reactor and is not influenced by the spatial

distribution of catalyst. The synthesis gas conversion decreases with

increasing superficial gas velocity suggesting small increases of mass transfer

rate compared to the decrease in the residence time of the gaseous reactant

(CO and H2

) which becomes too short for conversion.

2 4 6 8 10 12

Superficial gas velocity cm / sec

0.6

0.65

0.7

0.75

0.8

0.85

0.9

Syn

thes

esga

sco

nver

sion

20 %wt Co12 %wt Co8 %wt Co

Fig.(4.9): The effect of superficial gas velocity on the synthesis gas

conversion at different weights of Cobalt based catalyst.

From the comparison of the results for both types of catalysts, it is

clear that , the Cobalt catalyst shows higher conversion value of about (0.9)

than Iron catalyst (0.78) at different weights of catalyst (8-12-20 wt%), and

it can be seen that for Cobalt based catalyst the synthesis gas conversion


93

decreases from (0.9) at superficial gas velocity 2 cm/s to about (0.6) at

superficial gas velocity 12 cm/s and for the Iron based catalyst the synthesis

gas conversion decreases from (0.78) at superficial gas velocity 2 cm/s to

about (0.45) at superficial gas velocity 12 cm/s.

It is important to mention here the weaker dependence of the

conversion of synthesis gas on superficial gas velocity for the case of finite

mass transfer resistance is due to the increase in mass transfer coefficient

KLa with ugo

. As KLa increases the liquid phase approaches equilibrium with

the gas phase and as a result the reaction rate increases. This conclusion is in

accord with explanation of Deckwer, (1991).

2 4 6 8 10 12

superficial gas velocity cm / sec

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

synt

hese

sga

sco

nver

sion

20 % wt Fe12 % wt Fe8 % wt Fe

Fig.(4.10): The effect of superficial gas velocity on the synthesis gas

conversion at different weights of Iron based catalyst.


94

4.7.2 Effect of Reactor Height The effect of reactor height on the performances of slurry bubble

column reactor operating at initial superficial gas velocity of 9.5 cm /sec is

shown in Figures (4.11) and (4.12). As can be seen in Figure (4.11) for

Cobalt based catalyst the synthesis gas conversion increases from 0.15 at the

inlet of the reactor to 0.9 at the outlet of the reactor. While Figure (4.12) for

Iron based catalyst shows the synthesis gas conversion increases from 0.1 at

the inlet of the reactor to 0.71 at the outlet of the reactor.

For both types of catalyst the synthesis gas conversion increases over

the reactor height, the higher value of synthesis gas conversion is expected at

the reactor outlet, these results on this behavior agrees with the results that

given by de swart (1996).

0 0.2 0.4 0.6 0.8 1Reactor height

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Syn

thes

isga

sco

nver

sion

Fig. (4.11): Syntheses gas conversion profile with reactor height (Cobalt

based catalyst).


95

0 0.2 0.4 0.6 0.8 1Reactor height

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1S

ynth

esis

gas

conv

ersi

on

Fig. (4.12): Syntheses gas conversion profile with reactor height (Iron

based catalyst).

4.7.3 Effect of Operating Pressure In SBCR the operation pressure is regarded one of the most important

parameters. Variation in pressure in Fischer-Tropsch process is important

because of their direct effect on product distribution. It is known that, the two

major products of the Fischer-Tropsch reaction are olefin and paraffin.

Paraffin tends to be synthesized more readily at low pressures (0.5- 1.0 MPa

H2) and at low mass ratios of H2/CO (0.6-1.0). Olefin is produced in higher

concentrations at high pressures (2.0-4.0 MPa H2) and high mass ratios of

H2

/CO (1.5-2.5) [Yu Wang et al.2008].


96

Figures (4.13) and (4.14) show influence of operating pressure in

SBCR on synthesis gas conversion in the case of isothermal and non

isothermal condition. These figures show that, the synthesis gas conversion is

not influenced by changing of the operating pressure under isothermal

condition. On the other hand, if the reactor operates under non-isothermal

condition, the pressure increases due to temperature increase and in this

cause the synthesis gas conversion increases. The linear increase in the

conversion with synthesis pressure is a result of first order rate expression.

Such results are in agreement with work of Hall et al. (1952) and Calemma et

al. (2005).

From the comparison of the results for both types of catalysts, it is

clear that, the Cobalt catalyst shows higher conversion value of about (0.9)

than Iron catalyst (0.8) at non-isothermal reaction condition.

1 2 3 4Pressure MPa

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Syn

thes

isga

sco

nver

sion

Fig. (4.13): Influence of pressure on the synthesis gas conversion (Cobalt

catalyst).


97

1 2 3 4Pressure MPa

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Syn

thes

isga

sco

nver

sion

Fig. (4.14): Influence of pressure on the synthesis gas conversion (Iron

catalyst).

4.7.4 Effect of Reactor Diameter In the slurry bubble column reactor (SBCR) the column diameter is a

very important factor especially with the studies that deal with the

hydrodynamic, dispersion coefficients, heat and mass transfer coefficients,

and synthesis gas conversion.

Therefore, in this section the simulation program was tested with

different column diameter ranging from 2 to 5 m. This treatment aims to

understand the effect of column diameter on the synthesis gas conversion.

Figure (4.15) and (4.16) show the synthesis gas conversion profile with


98

reactor diameter for Iron and Cobalt catalyst respectively, in the case of

isothermal and non isothermal reaction condition.

And it can be seen from these figures under isothermal and non

isothermal reaction conditions the synthesis gas conversion for Cobalt based

catalyst decreases from (0.94) to about (0.5) and for the Iron based catalyst

the synthesis gas conversion decreases from (0.8) to about (0.32).

It is important to mention here that, the main reason for synthesis gas

conversion decreases with increasing reactor diameter, it is that dispersion

increase that present in wider column, and decreased plug flow of the liquid

phase character leads to lower conversion of syntheses gas. However this

consideration is important when scaling up slurry reactors.

2 2.5 3 3.5 4 4.5 5Reactor diameter M

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Syn

thes

isga

sco

nver

sion

Non isothermalIsothermal

Fig. (4.15): Synthesis gas conversion profile with reactor diameter (cobalt

catalyst).


99

2 2.5 3 3.5 4 4.5 5Reactor diameter M

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1S

ynth

esis

gas

conv

ersi

onNon isothermalIsothermal

Fig.(4.16): Synthesis gas conversion profile with reactor diameter (Iron

catalyst).

4.7.5 Effect of Inlet Ratio The (H2/CO) ratio of the synthesis gas is an important designing

variable for maximizing the production of high quality diesel. From the

Figure (4.17) for Cobalt based catalyst, the synthesis gas conversion

increases with increase in inlet ratio (H2

/CO), and it was found that the best

inlet ratio is about (2), which gives the highest value of conversion of about

(0.9).


100

0 0.5 1 1.5 2Inlet ratio H / CO

0.4

0.5

0.6

0.7

0.8

0.9

1

Syn

thes

isga

sco

nver

sion

2

Fig. (4.17): Dependence of synthesis gas conversion on inlet H2

/CO ratio

for (cobalt based catalyst).

On the other hand, Figure (4.18) shows the effect of (H2/CO) ratio on

synthesis gas conversion for Iron catalyst. From Figure (4.18) it is clear that

the synthesis gas conversion also increases with increase in the inlet ratio

(H2/CO), and the best value is about (1.6), which gives the highest value of

conversion of about (0.86). Depending on the water gas shift reaction (WGS)

activity, the water gas shifts reaction is important to change the (H2

CO + H

/CO) ratio

for Iron (high WGS-activity) and Cobalt catalysts (no WGS activity).

2O CO2 + H2 (WGS) -∆ HWGS= 41.3

kJ/mol


101

For Iron catalyst, the (H2/CO) ratio in the reaction media is very high

even when the feed ratio is low (<1.5), because of the production of more H2

An important consequence of the occurrence of water gas shift is that

the consumption ratio is maintained close to the H

by the WGS reaction.

2

/CO ratio in the feed.

This contributes to efficient utilization of the feed. This result is in agreement

with those David et al. (1985).

0 0.5 1 1.5 2Inlet ratio H / CO

0.4

0.5

0.6

0.7

0.8

0.9

1

Syn

thes

isga

sco

nver

sion

2

Fig. (4.18): Dependence of synthesis gas conversion on inlet H2

/CO ratio

for (Iron based catalyst)


102

4.8 In order to test the validity of the present model, this Section is focused

on the comparison of the results of the present model with that of a different

models and experimental work.

The Validity of the Present Model

The comparison with other work must be made under the same

physical properties and operating conditions (i.e., temperature range, column

Geometry, and superficial gas velocity) therefore, the comparison process is

based on applying the real operation conditions and dimensions of different

authors in present model. The present model is based on three differential

equations derived in present work:

Mass balance in gas phase

0 ( θ1

1 1 2

2 ) X - Y - Std

Yd)Yα*(

α*)( - dYd

B

gOG

=++

ξξ ...……… (3.89)

Mass balance in liquid phase

0exp1θ)2

2=−−+ Xγ/θ) ( CDa η) X - Y (St

dXd

B

P (Z)P(L OL ξ

...……… (3.90)

Heat balance

0exp1- θ1)(2


dθd Pe PpH =−+ θξ …… (3.91)

Therefore, the present section focuses on comparison between the

hydrogen profile (Y, X) in gas and liquid phase respectively, heat transfer

coefficient and Synthesis gas conversion with the data of authors.


103

4.8.1 Synthesis Gas Conversion The comparison of synthesis gas conversion that is calculated from

present model with that calculated from the model of David et al. (1985) is

shown in Figure (4.19). The comparison was carried out by substitution of

the values of reactor dimensions and hydrodynamic parameters of this model

David et al. (1985) in present model. It is concluded that the present model is

in accord with model data of the David et al. (1985) with deviation of 8%.

2 4 6 8 10 12Superfical gas velocity cm / sec

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Syn

thes

isga

sco

nver

sion

David et al modelPresent model

Fig. (4.19): The comparison between the present model Synthesis gas

conversions with model of David et al. (1985).


104

4.8.2 Heat Transfer Coefficient Figure (4.20) shows the comparison of heat transfer coefficients of

present model with that of the Fan et al (1999).The comparison was carried

out by substitution of the values of reactor dimensions and hydrodynamic

parameters of this investigator Fan et al (1999) in the present model. It was

concluded that the present model is in accord with experimental data of the

Fan et al (1999) with deviation of 9%.

0 1 2 3 4Superfical gas velocity m / sec

8000

8200

8400

8600

8800

9000

9200

9400

9600

9800

10000

Hea

ttra

nsfe

rcoe

ffici

ent

W/m

k

Present modelFan et al. experimental

2

Fig. (4.20): The comparison between the heat transfer coefficient of

present models with experimental data of Fan et al. (1999).


105

4.8.3 Hydrogen Profile in the Gas Phase Figure (4.21) shows the comparison of hydrogen profile in the gas

phase that is calculated from equation (3.89) with the model of Krishna and

De swart (2002). As can be seen from this figure the present model is in

accord with data of the Krishna and De swart (2002) with deviation of 6%.


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Hyd

roge

npr

ofile

inga

sph

ase

Krishna et al modelPresent model

Fig. (4.21): The comparison between the hydrogen gas profiles of the

present model with the model of Krishna (2002).


106

4.8.4 Hydrogen Profile in the Liquid Phase Figure (4.22) shows the comparison of hydrogen profile in the liquid

phase that is calculated from equation (3.90) with the model of Krishna and

de swart.(2002). As can be seen from this figure the present model is in

accord with model data of the Krishna and de swart.(2002).with deviation of

7%.


0.2

0.3

0.4

0.5

0.6

0.7

Hyd

roge

npr

ofile

inliq

uid

phas

e

Krishna et al. modelPresent model

Fig. (4.22): The comparison between the hydrogen liquid of the profile

present model with the model of Krishna (2002).

Chapter Five Conclusions & Recommendations

107

CHAPTER FIVE

CONCLUSIONS & RECOMMENDATIONS

5.1The overall aim of this thesis is to get an understanding of the effect of the

design parameters, hydrodynamics parameters, and reaction kinetics on transport

processes in slurry bubble column reactor that is conducted in GTL process to

produce clean fuels of hydrocarbons.

Conclusions

The following major conclusions can be drawn from the present study: -

1- The results obtained in this work clearly point to the direct link between the

hydrodynamics, mass transfer, heat transfer, and reaction kinetics in slurry

bubble column reactor.

2- From the comparison of the results for both types of catalysts (Co and Fe), it is

clearly noted that, the Cobalt catalyst shows higher conversion value of about

(0.9) than that of the Iron catalyst (0.78). Therefore, Cobalt catalyst is the best

choice for the Fischer-Tropsch Synthesis due to the high conversion, and low

water gas shift activity compared with Iron catalyst.

3- The results point to that, both types of catalysts show a flat temperature profile a

long reactor height. This can be explained on the basis of a high dispersion in

liquid phase and confirms the well known fact that due to the good mixing

properties, slurry bubble column reactor offers relatively easy heat removal with

less cooling area than some other types of Fischer-Tropsch reactors.

4- The present model has studied the relation between superficial gas velocity and

heat transfer coefficient. The results indicate that the heat transfer coefficient

increases with superficial gas velocity increase, also the heat transfer coefficient

increases with increasing of the solid concentration.


108

5- Synthesis gas conversion decreases with increasing superficial gas velocity

because decrease in the residence time of the gaseous reactant (CO and H2

6- The effect of reactor geometry on the performances of slurry bubble column

reactor is a very important factor. And it is noted that, the synthesis gas

conversion increases with increase in reactor height and decreases with increase

in reactor diameter.

)

which becomes too short for conversion. On the other hand the synthesis gas

conversion increases with catalyst concentration. Therefore for Cobalt and Iron

catalysts the reactor performance could be improved by increasing the catalyst

concentration.

7- The H2

8- The results of the present model are compared with that of different models and

experimental work. The present model is in accord with model and experimental

data of authors with an error of about (5-10) %.

/CO ratio of the synthesis gas is an important design variable. For Cobalt

catalyst the favorable ratio is about 2, while for Iron catalyst it is in the range of

1.5 to 1.7.


109

5.2Recommendations for future work are: -

Recommendations:

1- Study experimentally the conversion reaction in gas to liquid process

(GTL) by building a pilot plant and investigating different new types of

catalysts.

2- Develop the kinetic model to include the second and third order chemical

reactions for Cobalt and Iron catalysts.

3- An extension of the theoretical work can be done by using Computational

Fluid Dynamic (CFD), which is a new technique used recently for solution

and modeling of the transport phenomenon in bubble columns.

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110

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Appendix A

A -1

APPENDIX A COMPUTER SIMULATION FORTRAN

PROGRAM

PROGRAM ALI IMPLICIT NONE INTEGER,PARAMETER::M=21 REAL,DIMENSION(1:M)::Y,TH,X,Z,Ccat,XH,XH2 REAL,DIMENSION(1:M)::StG,UGd,EG,DG,BOG,a,E,StL,ETA_SO,Pe REAL,DIMENSION(1:M)::aS,KS,ETA_S,Fr,Boc,h,StH,DL,Lmda_ax,BOL REAL::UGO,L REAL::U,I,ALFAS,ALFA,dR REAL::R,T,Tw,He,Wcat,KL REAL::rouL,meuL,DLH,Vcat,roud,meud,rou_cat REAL::EL,Da,Kf,GAMA,EA,Ccatd,dcat,G REAL::Kfod,MKAM INTEGER::IT,J,MJ1 REAL::LZ,DZ,Rel REAL::Be,aH,Cp,Lmda_cat,LmdaL,Lmdad,Cp_cat,CpL REAL::dHR,P,yo REAL::ANS REAL::ERROER,ERMAX,XH2OLD OPEN(1,FILE='Y-X.PLT') OPEN(2,FILE='Ccat.PLT') OPEN(3,FILE='XH2.PLT') OPEN(4,FILE='TEMP.PLT') OPEN(5,FILE='UGd.PLT') OPEN(10,FILE='INT.PLT') OPEN(20,FILE='CONV.PLT') MJ1=M-1 LZ= Rel= DZ=LZ/REAL(MJ1) DO J=1,M Z(J)=DZ*(J-1)

Appendix A

A -2

TH(J)= ENDDO R= !EQUATION1 U= I= L= UGO= dR= ALFA= P= yo= IT=0 DO IT=IT+1 DO J=1,M !EQUATION1 !---BOG----------------------------- ALFAs=ALFA*(1+U)/(1+I) UGd(J)=(1+ALFAs)/(1+ALFAs*Y(J)) EG(J)=0.053*UGd(J)**1.1 DG(J)=5E-4*(UGd(J)/EG(J))**3*dR**1.5 BOG(J)=UGO*L/DG(J)/EG(J) PRINT*,"ALFAs,UGD,EG,DG,BOG" PRINT*,ALFAs,UGD,EG,DG,BOG !---------------------------------- T= rou_cat= Wcat= rouL=0.758-0.555E-3*(T-373) meuL=0.052*EXP(-6.905+3266./T) DLH=7.35E-3*EXP(-2285/T) He=2.291E7*EXP(-1.2326+(583/T)) Vcat=rouL*Wcat/(rou_cat-Wcat*(rou_cat-rouL)) roud=Vcat*rou_cat+(1-Vcat)*rouL meud=meuL*(1+4.5*Vcat)

Appendix A

A -3

!---StG----------------------------- Tw= a(J)=4.5*UGd(J)**1.1 KL=0.1165*(roud/meud*EXP(-4570/T))**(1/3.0) StG(J)=KL*a(J)*L/UGO*R*Tw/He*1000.0 !-------------------------------------- !EQUATION2 !---BOL----------------------------- EA= Ccatd= G= Kfod= EL= IF(UGd(J)<=6)THEN E(J)=UGd(J)*G ELSE E(J)=5886 ENDIF DL(J)=3.676*UGd(J)**0.32*dR**1.34 BOL(J)=2.83*(UGd(J)**2/G/dr) !-Da-------------------------- Kf=Kfod/(1+U) PRINT*,KF,EL,L,UGO Da=Kf*EL*L/UGO !--------------------------- StL(J)=KL*a(J)*L/UGO GAMA=EA/R/TW*1000.0 dcat= aS(J)=6*Wcat*(1-EG(J))*roud/dcat/rou_cat KS(J)=DL(J)/dcat*(2+0.545*(meuL/rouL/DL(J))**(1/3.0)*(E(J)*dcat**4* rouL**3/meuL**3)) !---ETA_S----------------------------- ETA_SO(J)=Kf*Ccatd*EL/KS(J)/aS(J) ETA_S(J)=(1+ETA_SO(J)*EXP(-GAMA/TH(J)))**(-1) !---Ccat----------------------------- Fr(J)=UGd(J)/SQRT(G*dR) Boc(J)=13.*Fr(J)/(1+8*Fr(J)**0.85) Ccat(J)=Ccatd*Boc(J)*EXP(-Boc(J)*Z(J))/(1-EXP(-Boc(J)))

Appendix A

A -4

!EQUATION3 !---StH----------------------------- aH= CpL= Cp_cat= LmdaL= Lmda_cat= Cp=Wcat*Cp_cat+(1-Wcat)*CpL Lmdad=LmdaL*(2.*LmdaL+Lmda_cat-2.*Vcat*(LmdaL-Lmda_cat))/& (2.*LmdaL+Lmda_cat+Vcat*(LmdaL-Lmda_cat)) h(J)=0.1*roud*Cp*UGd(J)*(UGd(J)**3*roud/G/meud*(meud*Cp/Lmdad) **2)**(-0.25) StH(J)=h(J)*aH*L/UGO/roud/Cp Lmda_ax(J)=DL(J)*roud*Cp Pe(J)=UGO*roud*Cp*L/EL/Lmda_ax(J) !--Be--------------------------------- dHR=(165+40*(U-0.5)/1.5) Be=dHR/roud/Cp*P*yo/He/Tw XH(J)=1-UGd(J)*Y(J) XH2(J)=(1+U)/(1+I)*XH(J) ENDDO DO J=2,MJ1 Y(J)=(1-Rel)*Y(J)+Rel*( 1/BOG(J)*(Y(J+1)+Y(J-1))/DZ**2-(1+ALFAs)/(1+ALFAs*Y(J))**2*(Y(J+1)-Y(J-1))/2.0/DZ+& StG(J)*TH(J)*X(J) )/(2/DZ**2/BOG(J)+StG(J)*TH(J)) MKAM=( 2.0/BOL(J)/DZ**2+StL(J)+Da*ETA_S(J)*Ccat(J)*EXP (-GAMA/TH(J)) ) PRINT*,MKAM,STL,GAMA,BOL,Da,ETA_S ,Ccat X(J)=(1-Rel)*X(J)+Rel*( 1/BOL(J)*(X(J+1)+X(J-1))/DZ**2+StL(J)*Y(J) ) /MKAM TH(J)=(1-Rel)*TH(J)+Rel*(1/Pe(J)*(TH(J+1)+TH(J-1))/DZ**2+StH(J)+ Be*Da*ETA_S(J)*& Ccat(J)*EXP(-GAMA/TH(J))*X(J))/(2./Pe(J)/DZ**2+StH(J))

Appendix A

A -5

ENDDO Y(1)=Y(2)+BOG(1)*DZ*( 1-( (1+ALFAS)*Y(1)/(1+ALFAS*Y(1)) ) ) X(1)=X(2) TH(1)=TH(2) Y(M)=Y(MJ1) X(M)=X(MJ1) TH(M)=TH(MJ1) ERMAX=1E-5 XH2OLD=ANS CALL INTG(XH2,DZ,ANS) ERROER=ABS(ANS-XH2OLD) PRINT*,IT,ERROER WRITE(20,*)IT,ERROER,ANS IF(ERROER<ERMAX)EXIT ENDDO !FOR MAIN ITRATION DO J=1,M WRITE(1,"(3F20.15)")Z(J),Y(J),X(J) ENDDO DO J=1,M WRITE(4,"(2F20.15)")Z(J),TH(J)*TW-273 ENDDO DO J=1,M WRITE(2,"(2F20.15)")Z(J),Ccat(J)*100.0 ENDDO DO J=1,M WRITE(3,"(3F20.15)")Z(J),XH2(J),UGd(J) ENDDO DO J=1,M WRITE(5,"(3F20.15)")Z(J),UGd(J),EG(J) ENDDO

Appendix A

A -6

CALL INTG(XH2,DZ,ANS) WRITE(10,"(A,F20.15)")"XH2",ANS CALL INTG(X,DZ,ANS) WRITE(10,"(A,F20.15)")"X",ANS END PROGRAM ALI !000000000000000000000000000000000000000000000000000000000000000 SUBROUTINE INTG(FIA,DZ,I) IMPLICIT NONE INTEGER,PARAMETER::NT=21 REAL,DIMENSION(1:NT)::FIA REAL::SUMOLD,SUMEVEN REAL::DZ,I,LZ INTEGER::N LZ= SUMEVEN=0.0 SUMOLD=0.0 DO N=2,NT-1,2 SUMEVEN=SUMEVEN+4.*FIA(N) ENDDO DO N=3,NT-2,2 SUMOLD=SUMOLD+2.*FIA(N) ENDDO I=DZ/3.*(FIA(1)+SUMOLD+SUMEVEN+FIA(NT))/LZ END SUBROUTINE INTG !----------------------------------------------------------------

Appendix B

B - 1

APPENDIX B ALGORITHM OF FORTRAN PROGRAM

START

MJ1 =M - 1

Read Input Data Ugo , L , dR , P , I , U etc

DZ= L Z / Real (MJ1)

Do J=1, M

Z (J) = DZ * ( J-1 )

TH ( J ) =1 If

J > M

No

Yes

IUα α* +

+= 11

Yα*

α* gU++=

11

IT = 0

IT = IT + 1

Appendix B

B - 2

1.1 053.0 gUgE =

) (T* . - . ρ -L 37310 55507580 3 −=

513 4 10 5 . Dr )g /Egu(*gD −=

gE gDL gou

BOG =

)) T / (3266 6.905- ( exp 0.052 μL +=

) ( * . D -L.H T2285/ -exp 10 357 3=

/T)(.(*. He 583 23261exp 10 2912 7 +−=

) -(W- W

VLPPP

PLP ρρρ

ρ=

L ρ1 ) V( ρVρ PPP −+=

)V. (μμ PL 541+=

1.1

gU 4.5a =

Appendix B

B - 3

1/3

) T(-4570/ exp μρ 0.1165 KL

=

gouHeLTR

a) (KgSt WHL

=

341320 6763 . . Dr gu .DL =

If

6 ≤gU Yes

No

g guE * =

5886 E =

3402 832

.

OLg Drgu

.B

=

UfoK

f +=

1K

gou

L EfKDa

L=

Appendix B

B - 4

WA/ R TEγ =

gouLa)(K St HLL =

PP

PP ρd

ρ)gE(Wa

−=

16

+=

μ

ρ d EDρμ

0.5452dD

K3

341/3

L

LP

LL

L

P

LP

PP

LPPO aK

ECfKη =

1θ))λexp1(θ- / (- η(η PO)P +=

g Dr/uFr g=

850113

.OCFr Fr

E

Dr guB

C +==

) B( )B(

BCC OC OC

OCPP (Z)

ξ−−−

= expexp1

Appendix B

B - 5

LPPP )CpW ( CpWCp −+= 1

)λ(λVλλ)λ(λVλ λ

λλPLPPL

PLPPLL −++

−−+=

222

0.2523

10

−

= λCp μ

μg ρgu

)gu Cpρ(.h

Cp ρ gou Lh a

St HH =

C ρDλ pLax =

OLBKE LCp ρ gou

Peax L

==

515040165 .)/.*(UΔHR

−+=−

T Heoy P

) Cp ρ

RΔH- ( Be

W=

)Y gU( XH −=1

Appendix B

B - 6

)Y gU (IU X HCO −+

+=+ 111

2

(J)OG

(J)(J))(J)(J

(J)

)J)(J

(J)θg St

BΔξ

X θgSt*ΔYY*

)Yα*(α*)(

ΔξYY

B

YOG

+

+−++−+

−+−+

=

2

22

2ξ21

11 111(1

If J > M

No

Yes

Do J=2 , MJ1

Go To Do

Loop

)γ/θ( exp C η Da St ΔB

Y St ΔBXX

X(J))P()( PL

2

(J)L1)(J1)(J

)(2 OL

2 OL

−++

++ −+

=

ξξ

ξJ

θ

St

Δ2

Pe1

(i)X C )ηγ/θ( exp Da Be StΔz

θθPe1

θ

H

P)p((i)H1)(i1)(i

(i)2

2

+

−+++

=

−+

ξ

θ

If J > M

Yes

No

Appendix B

B - 7

Calculate Boundary Condition

1- 21OG)(

)( YYB

1Y*α1Y α*)(1 1 ξi

i∆−−

++=

2- 11 XX =

3- 21 θθ = 4- mm XX 1−= 5- 1−= mm YY 6- 1mm θθ −=

ER Max = 1E-5

XCO+H2 old =Mean XCO+H2

Calculate Mean XCO+H2 by using simsun role program

Error = ABS = ( Mean XCO+H2- XCO+H2 old )

Write IT, Error, XCO+H2 Mean

If Error < ER Mxa

Yes

No

Go To Itration

Loop

Do J = 1 , M

Write Y , X , TH , XCO+H2 , Pe ,STH , h , Fr etc

Appendix B

B - 8

If J > M

Yes

No

Go To Do Loop

End

Appendix B

B - 9

START

Read Input Data FIA ,SUMOLD, SUMEVEN etc

Do J=2, NT-1 ,2

SUMEVEN = SUMEVEN +4 * FIA

If J < M

No

Yes

SUMEVEN = 0 SUMOLD =0

Do J=3, NT-2 ,2

SUMOLD = SUMOLD + 2 * FIA

If J < M

No

Yes

ZZ LNTFIASUMEVENSUMOLDFIADI /)()1(*

3+++=

END

الخالصة

- 1-

U الخالصة

والتي تزداد أهميتها في الصناعات . حديثةواحدة من الطرق العملية تحويل الغاز الى سائل هي

ذات النوعية العالية المقطرات الوسطية ز الطبيعي الى احيث ان هذه العملية تحول الغ. النفطية

يعتبر قلب هذه ية ذات العالق الصلبفقاعال عمدةان مفاعل األ. ائ جدوالمحتوى الكبريتي الواط

ل الكتلة وأنتقال الحرارة وميكانيكيةفي الدراسة الحالية طور تمثيل رياضي ليصف أنتقا، العملية

. التفاعل في هذا النوع من المفاعالت

ثالث معادالت تفاضلية لتصف عمليات األنتقال التي في الموديل الرياضي أشتقاق كما تم

: ت العالق الصلبتظهر في مفاعل األعمدة الفقاعية ذا

:نة الكتلة في الطور الغازيزموا -

0 ( θ1

1 1 2

2 ) X - Y - Std

Yd)Yα*(

α*)( - dYd

B

gOG

=++

ξξ

:سائلنة الكتلة في الطور المواز -

0exp1θ)2

2=−−+ Xγ/θ) ( CDa η) X - Y (St

dXd

B

P (Z)P(L OL ξ

:حرارةنة المواز -

0exp1- θ1)(2


dθd Pe PpH =−+ θξ

وذلك عن طريق ) finite difference method( بأستخدام عدديا المعادالت التفاضلية حلت

بين تأثير أبعاد المفاعل، سرعة يان الموديل الرياضي . برنامج رياضي بلغة الفورتران تصميم

الخالصة

- 2-

نسبة الداخل من الهايدروجين الى أول أوكسيد ، الظغط التشغيلي الغاز، تركيز العامل المساعد،

. الكاربون على أداء المفاعل ذات المقياس الصناعي

عمدة على أداء مفاعل األ) الكوبلت والحديد(كما تم دراسة تأثير نوعين من العوامل المساعدة

أن النتائج أكدت أن الكوبلت يعطي معدل تحول أعلى من الحديد . الفقاعية ذات العالق الصلب

لذا يفضل أستخدام % 78بينما معدل تحول الحديد ، % 90حيث أن معدل تحول الكوبلت تقريبا

لكال نوعين من العوامل المساعدة النتائج بينت . بلت كعامل مساعد في عمليات فشر تروبشزالكو

المفضلة بالنسبة HR2R/COالداخل منوأن نسبة توزيع منتظم للعامل المساعد على طول المفاعل

. 1.7الى 1.5في مدى أما بالنسبة للحديد تكون 2للكوبلت هي

ية فقاعال عمدةالغاز ومعامل أنتقال الحرارة في مفاعل األ ومن ناحية اخرى أن العالقة بين سرعة

ذات العالق الصلب أيضا درست في الموديل الرياضي حيث أن النتائج أكدت أن معامل أنتقال

. الحرارة تزداد مع زيادة سرعة الغاز وتركيز العامل المساعد

%. 9 -6بة خطأ تتراوح بين الموديل المشتق يتوافق مع النتائج العملية والنظرية للباحثين بنس

simulation of gas-to-liquid (gtl) process in slurry bubble ... adel.pdf ·...

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