production of liquid fuels from natural gas: by saiedeh

Production of Liquid Fuels from Natural Gas:

Simulation of Synthesis Gas and Fischer-Tropsch Reactors

by

SAIEDEH ARABI

Presented to the Faculty of the Graduate School of

The University of Texas at Arlington in Partial Fulfillment

of the Requirements

for the Degree of

DOCTOR OF PHILOSOPHY

Department of Mechanical and Aerospace Engineering

THE UNIVERSITY OF TEXAS AT ARLINGTON

MAY 2019

ii

Copyright © by Saiedeh Arabi Bolaghi 2019

All Rights Reserved

iii

Dedication

To my lovely parents, Pari & Vali and my love, Taha

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ACKNOWLEDGEMENTS

First and foremost, I would like to thank my advisor, Prof. Brian H. Dennis, for his

guidance throughout my studies as a graduate student at the University of Texas at

Arlington. It was a great fortune to have been given the opportunity to join his research

group. This work would not have been possible without his invaluable insights and his

commitment to excellence in research. Thanks are also due to Prof. Frederick

MacDonnell, for providing us with such great research project.

Next, I would like to give thanks to my committee members for their valuable time

and comments regarding this thesis.

I offer my regards to all Mechanical & Aerospace Engineering department faculty

and staff at University of Texas at Arlington, and all CREST members specially Dr.

Wilaiwan Chanmanee who supported me in any respect during the completion of my

experimental studies.

Most importantly, I would like to thank my love, Taha for his invaluable support,

love and caring and to my parents, Pari and Vali, and to my sister, Vahideh. I would not

be where I am today without their love and support.

December 6th, 2018

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ABSTRACT

Production of Liquid Fuels from Natural Gas:

Simulation of Synthesis Gas and Fischer-Tropsch Reactors

Saiedeh Arabi, Ph.D.

The University of Texas at Arlington, 2018

Supervising Professor: Brian Dennis

ABSTRACT

Gas to Liquid (GTL) processes chemically convert natural gas to valuable liquid

hydrocarbon products. The GTL process considered in this research is comprised of

three phases: 1) syngas production, 2) Fischer-Tropsch synthesis (FTS), and 3) product

separation. This study focuses on the simulation and optimization of a GTL process to

convert natural gas to more valuable liquid fuels.

In syngas production, steam methane reforming (SMR) is typically used although

it requires an external heat source due to the endothermic nature of the reaction. In

addition, the SMR approach produces syngas with a hydrogen to carbon monoxide ratio

that is not ideal for the FTS reaction. An alternative approach that combines partial

oxidation of methane (POX) and SMR in series is considered in this work. The heat

released in the exothermic POX stage drives the endothermic SMR stage resulting in an

auto-thermal reforming reaction (ATR) that is net exothermic. The resulting syngas

product has the ideal hydrogen to carbon monoxide ratio for FTS.

6

The aim of this work is to establish numerical models for the ATR and FTS

reactor components of a GTL plant and study the impact of various input parameters on

the output of the overall system. Kinetic models were developed based on laboratory

data collected from a GTL pilot plant operating at UTA. A multiphysics finite element

model was developed to simulate a multi tubular packed bed reactor for FTS. The impact

of coolant flow rate and syngas space velocity on oil productivity and syngas conversion

was studied.

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Table of Contents

ACKNOWLEDGEMENTS ................................................................................................... 4

ABSTRACT ......................................................................................................................... 5

GAS TO LIQUID TECHNOLOGY .................................................................... 14 Chapter 1

Synthesis Gas Production ............................................................................................. 14

Catalytic Fischer-Tropsch Synthesis ............................................................................. 16

Product Workup ............................................................................................................. 16

Fischer-Tropsch Reactors ............................................................................................. 16

GTL MECHANISM ........................................................................................... 18 Chapter 2

Reforming Mechanism................................................................................................... 18

Reforming Technical Problems ..................................................................................... 20

CFD Modeling Background ........................................................................................... 20

Research Objectives ..................................................................................................... 21

PROCESS DESCRIPTION .............................................................................. 23 Chapter 3

Pilot Plant Process Description ..................................................................................... 23

Pilot Plant Demonstration .............................................................................................. 24

ASPEN HYSYS SIMULATION ......................................................................... 29 Chapter 4

GTL Process Simulation ................................................................................................ 29

Pilot Plant Simulation ..................................................................................................... 29

Kinetic Model ................................................................................................................. 33

CFD SIMULATION OF FISCHER-TROPSCH ................................................. 34 Chapter 5

Fixed Bed Reactor Modeling ......................................................................................... 34

Mathematical Model ...................................................................................................... 35

FT Plant Description ...................................................................................................... 36

Kinetics of Fischer–Tropsch Reactor ............................................................................ 39

RESULTS AND DISCUSSION......................................................................... 43 Chapter 6

Experimental Results ..................................................................................................... 43

Effect of Steam/NG Molar Ratio ................................................................................ 46

Simulation of Syngas and Oil Production ...................................................................... 56

CFD Simulation of Fischer-Tropsch Reactor................................................................. 63

Simulation Setup ........................................................................................................ 64

Parametric Study ....................................................................................................... 66

Conclusion and Summary ............................................................................................. 80

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ABBREVIATIONS ............................................................................................................. 81

APPENDIX A ..................................................................................................................... 82

REFERENCES .................................................................................................................. 84

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LIST OF FIGURES

Figure ‎3-1 Process Flow Diagram of The GTL Process Used in This Research Study ... 26

Figure ‎3-2 ATR Pilot Plant Used in This Research Study ................................................ 27

Figure ‎3-3 Burner Designed Used in This Research Study .............................................. 27

Figure ‎3-4 Vertical Single Tube FTR Used in This Research Study ................................ 28

Figure ‎3-5 Catalyst Type Used in Secondary Reformer ................................................... 28

Figure ‎4-1 Block Flow Diagram of GTL Process .............................................................. 31

Figure ‎5-1 Diagram of Multi Tubular Fixed Bed Reactor .................................................. 35

Figure ‎5-2 Schematic Design of Two-Step FT Reactor .................................................... 36

Figure ‎6-1 Structure of the Burner .................................................................................... 43

Figure ‎6-2 Schematic of proposed ATR ............................................................................ 44

Figure ‎6-3 Schematic Reformer Design ............................................................................ 46

Figure ‎6-4 Schematic Design of Primary and Secondary Reformer ................................. 46

Figure ‎6-5 H2/CO Experiment Ratio in Primary Reformer ................................................ 51

Figure ‎6-6 %CO Experiment in Primary Reformer ........................................................... 52

Figure ‎6-7 %H2 Experiment in Primary Reformer ............................................................. 52

Figure ‎6-8 %CO2 Experiment in Primary Reformer .......................................................... 53

Figure ‎6-9 H2/CO Experiment Ratio in Secondary Reformer ........................................... 53

Figure ‎6-10 % Unconverted CH4 In Secondary Reformer ................................................ 54

Figure ‎6-11 %CO Experiment in Secondary Reformer ..................................................... 54

Figure ‎6-12 %H2 Experiment in Secondary Reformer ...................................................... 55

Figure ‎6-13 %CO2 Experiment in Secondary Reformer ................................................... 55

Figure ‎6-14 Comparison of H2/CO Ratio in Experimental and ATR Simulation ............... 59

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Figure ‎6-15 %CO Simulation in ATR ................................................................................ 59

Figure ‎6-16 %H2 Simulation in ATR .................................................................................. 60

Figure ‎6-17 % Unconverted CH4 Simulation in ATR......................................................... 60

Figure ‎6-18 %H2O Simulation in ATR ............................................................................... 61

Figure ‎6-19 Simulation Study of CH4 Conversion in ATR ................................................. 61

Figure ‎6-20 GTL Process Flow Diagram in This Study to Get 50% Syngas Conversion . 62

Figure ‎6-21 Geometry of Fischer-Tropsch Reactor Used in This Research Study .......... 65

Figure ‎6-22 Mesh Layout Used in This Research Study .................................................. 65

Figure ‎6-23 Syngas Conversion Profiles of FT Reactor, Tinitial: 518.15 K ......................... 70

Figure ‎6-24 The Rate of C5+ Production In FT Reactor .................................................... 71

Figure ‎6-25 The Rate of C5+ Production in FT Reactor (Detailed View of Figure 6-17) ... 71

Figure ‎6-26 Oil Productivity for Different Amounts of Product Species ............................ 72

Figure ‎6-27 Syngas Conversion for Different Amounts of Product Species ..................... 72

Figure ‎6-28 3D Profiles of (a) Bulk Temperature, (b) CO Mass Fraction, (c) H2 Mass

Fraction, (d) C5+ Mass Fraction, (e ) H2O Mass Fraction, (f) CH4 Mass Fraction, (g) Bulk

Temperature at The Centerline of Tube (to get 50% syngas conversion, Tinitial: 518.15 K)

.......................................................................................................................................... 74

Figure ‎6-29 3D Profiles of (a) Coolant Temperature, (b) Bulk Temperature, (c) CO Mass

Fraction, (d) H2 Mass Fraction, (e ) H2O Mass Fraction, (f) C5+ Mass Fraction, (g) CH4

Mass Fraction and (h) Syngas Conversion (ucoolant/ufeed=5, Tinitial: 518.15 K) .................... 75

Figure ‎6-30 3D Profiles of (a) coolant Temperature, (b) bulk Temperature, (c) CO Mass

Fraction, (d) H2 Mass Fraction, (e ) H2O Mass Fraction, (f) C5+ Mass Fraction, (g) CH4

Mass Fraction and (h) Syngas Conversion (ucoolant/ufeed=1, Tinitial: 518.15 K) .................... 76

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Figure ‎6-31 Multi Tubular 3D Profiles of (a) Coolant Temperature, (b) Bulk Temperature,

(c) CO Mass Fraction, (d) H2 Mass Fraction, (e ) H2O Mass Fraction, (f) C5+ Mass

Fraction, (g) CH4 Mass Fraction and (h) Syngas Conversion (ucoolant/ufeed=15, Tinitial:

518.15 K) ........................................................................................................................... 78

Figure ‎6-32 3D Profiles of (a) Coolant Temperature Plane, (b) Coolant Temperature, (c)

Syngas Conversion (ucoolant/ufeed=2, Initial Temperature: 518.15 K) ................................. 78

Figure ‎6-33 Mass Fraction Rate of Reactants and Products in FT Tube ......................... 79

Figure ‎6-34 Bulk Temperature Profile in Different Volume Bed Fraction ......................... 79

Figure ‎6-35 Syngas conversion at the center tube in different feed temperature ............ 80

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LIST OF TABLES

Table ‎2-1 Reforming Technologies of Syngas .................................................................. 19

Table ‎4-1 Streams Conditions .......................................................................................... 31

Table ‎5-1 Lumped Kinetic Rate Expressions for Overall Syngas ..................................... 37

Table ‎5-2 The List of Kinetic Model Used in Sadeqzadeh et al. ....................................... 40

Table ‎5-3 Optimized Parameters for n Components Used in This Research Study ........ 42

Table ‎5-4 Optimized Parameters Considering C12 as A Product Used in This Study ...... 42

Table ‎6-1 Multi Channel Burner ........................................................................................ 44

Table ‎6-2 Mole Fraction of Feed Stream in Different Steam Flow Rates ......................... 44

Table ‎6-3 Feed Stream Used in Experimental Setup ....................................................... 46

Table ‎6-4 Primary Reformer Results of Selected Runs (Run 1-6) ................................... 48

Table ‎6-5 Primary reformer results of selected runs (Run 7-12) ...................................... 49

Table ‎6-6 Primary reformer results of selected runs (Run 13-18) .................................... 49

Table ‎6-7 Primary Reformer Results of Selected Runs (Run 19-21) ............................... 49

Table ‎6-8 Secondary Reformer Results of Selected Runs (Run 1-6) ............................... 50

Table ‎6-9 Secondary Reformer Results of Selected Runs (Run 7-12) ............................. 50

Table ‎6-10 Secondary Reformer Results of Selected Runs (Run 13-18) ......................... 50

Table ‎6-11 Secondary Reformer Results of Selected Runs (Run 19-21) ......................... 51

Table ‎6-12 Syngas Composition Result ............................................................................ 57

Table ‎6-13 Final Amount and Process Conditions for The Feed Flow Properties............ 57

Table ‎6-14 FT Products to Get 50% And 70% Conversion, Aspen Results ..................... 63

Table ‎6-15 Selectivity of Products, Aspen Results ........................................................... 63

Table ‎6-16 Physical Parameters in Single Tube Reactor ................................................. 66

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Table ‎6-17 Physical Parameters in Multi Tubular Reactor ............................................... 66

Table ‎6-18 Product Results in FT Reactor, 5 Species ...................................................... 68

Table ‎6-19 Product Results in FT Reactor, 9 Species ...................................................... 70

Table ‎6-20 The Effect of Coolant Velocity on Productivity ................................................ 78

14

GAS TO LIQUID TECHNOLOGY Chapter 1

Gas-To-Liquids (GTL) technology was developed to account for limited crude oil

resources. The process of converting coal gasification to synthesis gas was developed by

Franz Fischer and Hans in effort to produce a high value of liquid hydrocarbons that later

became known as Fischer-Tropsch (F-T) synthesis. F-T synthesis was an experimental

success [1]. The syngas that is utilized in F-T synthesis can be produced from various

feed stocks like coal, natural gas, and biomass [2].

The GTL technologies can convert methane from the natural gas reserves to

liquid fuels and other valuable hydrocarbons that can then be easily and efficiently

transported [2, 3]. It is also noted that high quality diesel with a high cetane number

(close to 70), low aromatics (less than 1%), and low Sulphur (less than 5 ppm) can be

produced from GTL technologies [4].

The GTL process is comprised of three fundamental steps as given below:

The production of synthesis gas

Catalytic F-T synthesis

Product workup

A brief discussion of each of the above steps is given in the sections below.

Synthesis Gas Production

Synthesis gas is a mixture of hydrogen (H2) and carbon monoxide (CO)

commonly obtained from a variety of feed stocks, like natural gas, naphtha, coal,

biomass, waste, catalytic and non-catalytic partial oxidation, steam reforming, and Auto-

Thermal Reforming (ATR). ATR is the main method for producing synthesis gas. In non-

catalytic partial oxidation, the feed stream is mixed with oxygen in a combustion chamber

15

operated at high temperatures (1200- 1500 ºC). The following reactions take place during

combustion:

𝐶𝐻4 + 0.5𝑂2 → 𝐶𝑂 + 2𝐻2 + 𝑞 Eq. 1-1

𝐶𝐻4 + 2𝑂2 → 𝐶𝑂2 + 2𝐻2𝑂 + 𝑞 𝑂𝑡ℎ𝑒𝑟 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛𝑠 Eq. 1-2

2𝐶𝑂 → 𝐶 + 𝐶𝑂2 𝐵𝑜𝑢𝑑𝑎𝑟𝑑 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛, 𝑐𝑎𝑟𝑏𝑜𝑛 𝑏𝑙𝑎𝑐𝑘 Eq. 1-3

The main problem with this method is the formation of carbon black in the

combustion chamber which requires a carbon black removal section, and thus increases

the plant cost. In industry, partial oxidation yields synthesis gas with a low H2/CO ratio

(range of 0.5-2, depending on the feed) [5].

Catalysts partial oxidation are used to produce synthesis gas at temperatures in

the range of 673-1273 K. The advantages of catalytic partial oxidation over the non-

catalytic process are the low exothermic nature of the reaction and high reaction rates

leading to better conversion [10]. The main concern of this process is the commercial

aspect of the catalysts.

The steam reforming method is the most widely used process to produce

synthesis gas. In this method, the feed steam is passed over the catalyst (endothermic

reaction of the steam reforming method) and depends on the exothermic reaction of

partial oxidation. The reaction temperature is maintained by the heat of reaction. Lurgi

and Haldor-Topsoe detail the ATR process.

The reactions involved in steam reforming are given below:

𝑞 + 𝐶𝐻4 + 𝐻2𝑂 ↔ 𝐶𝑂2 + 𝐻2 Eq. 1-4

The water-gas shift reaction is the competing reaction and is responsible in

increasing the H2/CO ratio. The industrial steam reformers produce synthesis gas with

high H2/CO ratio (H2/CO = 3-7) [11].

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Catalytic Fischer-Tropsch Synthesis

The catalytic F-T synthesis is the most important step of the GTL process, as it is

in this step that high value products are produced. The syngas (H2+CO) undergoes a

polymerization reaction in the presence of a catalyst (Fe/Co/Ru-based) to produce a wide

range of products, like paraffins, olefins and oxygenates, often known as Syncrude. The

water-gas shift (WGS) reaction takes place only on iron (Fe) based catalysts. Rao et al.,

claim that the WGS reaction occurs on the catalytic sites with irreducible magnetite. On

the other hand, cobalt (Co) based catalysts are not WGS active. Iron, cobalt, ruthenium,

and nickel have the highest capacity to dissociate CO in the presence of H2, hence

making them excellent Fischer-Tropsch catalysts [9, 10]. The reaction conditions play a

crucial role in defining the product distribution. It is desirable to have heavier

hydrocarbons (C5+) as a major fraction due to their commercial value in the products.

Low temperatures (220-250 C), high pressure, and low a H2/CO ratio are the process

conditions favorable to heavy hydrocarbon production [14].

Product Workup

Syncrude from F-T synthesis mainly consists of high carbon number linear

hydrocarbons over a large boiling range. Hydrocracking of high carbon number paraffins

will give high quality gasoil (C4-C12 range). Hydrocracking has a low selectivity towards

C1-C3 hydrocarbons. Other processes, like isomerization, catalytic reforming, alkylation,

and oligomerization are used to increase the octane number of F-T wax [9, 11].

Fischer-Tropsch Reactors

High-Temperature-Fischer-Tropsch (HTFT) and Low-Temperature-Fischer-

Tropsch (LTFT) are the two main types of Fischer-Tropsch process technologies. In

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HTFT, as the operating temperature is high (320- 350 C), the major fraction of products

are short chain hydrocarbons, mainly comprised of propane, butane, and olefins [5]. The

operating pressure is about 2.5 MPa, and the conversion is more than 85% [17].

Fluidized bed reactors are used for the HTFT process. In LTFT, the low temperature

conditions (220- 240 C) lead to the formation of heavy hydrocarbons. In this process, the

Fischer-Tropsch reaction is preferred to a methanation reaction. The operating pressure

is in the range of 2-2.5 MPa, and the conversion is about 60% [8]. LTFT produces a

synthetic fraction of diesel, which is free of Sulphur and aromatics. Fixed-bed reactors

and slurry phase reactors are generally used for the LTFT process.

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GTL MECHANISM Chapter 2

Reforming Mechanism

The major component in a fuel processing system is the conversion of

hydrocarbon fuel to synthesis gas, which occur due to three main mechanisms in the

reforming reactor:

Steam reforming (SR), partial oxidation (POX), and auto-thermal reforming (ATR) [16].

The three fuel reforming reactions are expressed in Equations 2-1 through 2-3.

Steam Reforming:

𝐶𝑚𝐻𝑛 + 𝑚𝐻2𝑂 ↔ 𝑚𝐶𝑂 + (𝑚 +1

2𝑛)𝐻2, ∆𝐻 > 0, 𝑒𝑛𝑑𝑜𝑡ℎ𝑒𝑟𝑚𝑖𝑐 Eq. 2-1

Partial Oxidation:

𝐶𝑚𝐻𝑛 +1

2𝑂2 ↔ 𝑚𝐶𝑂 + (

1

2𝑛)𝐻2, ∆𝐻 < 0, 𝑒𝑥𝑜𝑡ℎ𝑒𝑟𝑚𝑖𝑐 Eq. 2-2

Auto thermal Reforming:

𝐶𝑚𝐻𝑛 +1

2𝑚𝐻2𝑂 +

1

4𝑚𝑂2 ↔ 𝑚𝐶𝑂 + (

1

2𝑚 +

1

2𝑛)𝐻2, ∆𝐻 < 0, 𝑒𝑥𝑜𝑡ℎ𝑒𝑟𝑚𝑖𝑐 Eq. 2-3

The approach with high hydrogen concentrations is steam reforming (SR), which

is a high endothermic reaction, which as is shown in Equation 2-3, requires a lot of heat

from some sources [15]. Hydrocarbon fuels like methane are converted to syngas by

partially oxidizing in POX, which is a highly exothermic reaction process according to

Equation 2-2, and the operating temperature range is from 1,100 ºC to 1,200 ºC to avoid

any coking in the chamber. POX has a fast start-up time compared to reforming and also

has a more rapid response [2,15]. POX includes two types of reactors: homogeneous

POX (NCPOX) and heterogeneous catalytic POX (CPOX). NCPOX is the reaction of

fuels with the oxygen at high temperature and pressure in the absence of any catalyst to

produce syngas [12].

19

The NCPOX process needs temperatures in excess of 1000 ºC. However, the

presence of catalyst in POX might decrease the operating temperature to 800-900 ºC,

which enhances system efficiency. Moreover, the catalyst can only be used if the sulfur

content is below 50ppm in the fuel feed to avoid catalyst poisoning [23].

The combination of partial oxidation and steam reforming, which are exothermic

and endothermic reactions respectively, is called Auto-thermal reforming (ATR). The heat

released by POX can keep steam methane reformer, making the overall ATR reaction

gradually exothermic. The operating temperature in ATR is usually in the range of 900 ºC

to 1150 ºC, and the pressure is lower than partial oxidation [12]. In the outlet of ATR, the

H2/CO molar ratio is about 2 and is more attractive compared to the POX outlet. Table 2-

1 describes three advantages and disadvantages of syngas production through SR, POX,

and ATR [15].

Table 2-1 Reforming Technologies of Syngas [4]

Technologies Advantages Disadvantages

Steam Reforming

Most industrial experience

Oxygen not required

Lowest temperature

Highest H2/CO ratio

Slow startup

Highest air emissions

Heavy system

Heat source required

Partial Oxidation

Higher sulfur tolerance

No heat source required

Compact system

Fast startup

Low H2/CO ratio

Highest temperature

Coke formation

Oxygen or air required

Too much heat produced

Autothermal Reforming

Medium temperature

No heat source required

Favorable H2/CO ratio

Least coke formation

Relatively compact

Limited experience

Oxygen or air required

20

Reforming Technical Problems

Several concerns for the performance and design of ATR for heavy hydrocarbon

fuels are described below:

One concern is that because there is no uniform distribution of temperature, local

hot-spots can be observed in the reforming, which causes local catalyst deactivation by

the local high temperature. Another concern is that coking may be produced because of

large carbon contents in the reforming system decreasing the effectiveness of the

catalyst [26]. Finally, the mixture of reactants, air, fuel, and steam could lead to coke

formation on the surface of the catalyst and also local hot spots.

Some efforts are done to minimize hot-spots like employing suitable materials for

reactors that have more effective heat transfer and improved uniform temperature

distribution. Stainless steel has suitable properties like thermal conductivity and high

temperature tolerance and can be used to solve the above-mentioned problem [32]. Flow

with high turbulence is the other approach to minimize the hot-spots by increasing the

heat transfer coefficient between the flow and solid works.

CFD Modeling Background

Computer design methodology is used to design the pilot and commercial plant

to achieve a high quality of fuels in the chambers. Some of the work focuses on

microchannel reactor computational fluid dynamics (CFD) simulation for different kinds of

reactors. The effect of buoyancy on reactor temperature and the determinants of partial

boiling coolant was studied by Arzmendi et al. using CFD [2]. Kshetrimayum et al. [16]

used the CFD model for a multichannel reactor to design FT reaction and analyze heat

transfer phenomena while studying the reaction to runaway situations. In addition, the

effect of coolant type and wall boiling condition were investigated with reactor

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temperature profile in 2D dimension. The effect of cannel geometry on the performance

of thermal microchannel reactor was studied by Na and Lee. Park et al. [19,20]. They

also investigated the reactor’s performance with different kinds of flow and coolant

channels. Recently, Jung et al. [21] proposed a strategy to optimize the size of the

reactor block in a pilot plant scale. Deshmukh et al. [11] simulated the reactor using 276

process channels and 132 coolant channels in cross-flow configuration.

Research Objectives

The optimal design of GTL process is presented in this paper. The developed

ATR and FT reactor is designed and described using nickel and cobalt catalysts,

respectively. GTL process was designed to obtain the desired molar ratio of H2/CO to

produce liquid hydrocarbon. This research is presented as follows:

In Chapter 3, a detailed description of GTL pilot plant is presented, and the effect

of steam flow rate on H2/CO molar ratio, CO, H2, CO2, and unreacted CH4 mole fraction is

studied. In Chapter 4, the simulation of pilot plant using Aspen Hysys (V.10) is described.

In addition, this Chapter explains the effect of various operation conditions of fuel feed,

and different amounts of H2O/CH4 on producing the desired molar ratio of H2/CO in the

outlet of POX and SMR. Also, the effect of different kinetic models is studied on both ATR

and FTR to achieve the higher efficiency of fuel. Finally, the whole energy required to

convert natural gas to liquid hydrocarbons by optimization of proper required of O2/CH4 is

minimized and calculated. In Chapter 5, two-dimensional and three-dimensional CFD

simulations of multi tubular Fischer-Tropsch reactor are studied to investigate the effect

of inlet syngas temperature, space velocity, and coolant temperature on selectivity of C5+

over a Co/Al2O3 catalyst. The distribution of bulk temperature, the pressure gradient

through a packed bed, and the composition of liquid hydrocarbons in the reactor outlet





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22

were determined by transport equations in porous media. The final section summarizes

results and finishes with how GTL technology can be progressed in the future.

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PROCESS DESCRIPTION Chapter 3

The GTL pilot plant examined in this research consists of three main process

units; a reforming unit that is split into primary and secondary reforming units where

syngas (CO + H2) is derived from natural gas, the FTR unit where jet fuel is converted

into liquid hydrocarbons, and a separation of products. This plant is capable of producing

1 LPD per reactor unit of jet fuel.

Pilot Plant Process Description

Figure 3-1 presents the process flow diagram of GTL pilot plant. This process is

split into three sections: 1) the methane reforming 2) the FT reaction, and 3) the product

separation unit. Boiler feed water, natural gas, and pure oxygen are fed to the reforming

and converted to syngas in the reforming section and then passed to the FT reaction

section as feed. Before entering the FT section, the water should be removed from

syngas. The reforming section consists of pre-processing, using primary and secondary

reforming units to heat up the steam, mixing natural gas and steam, and pressurizing the

natural gas to derive syngas. Boiler feed water (BFW) is received by a storage tank and

then pumped to the steam generator where it is produced. After mixing natural gas and

steam in the burner, pure oxygen which is supplied to the primary reformer section

passes through the burner before entering the secondary reformer.

The steam reforming and partial oxidation of methane are illustrated in Equation

3-1 and 3-2, respectively:

𝐶𝐻4 + 𝐻2𝑂 ↔ 3𝐻2 + 𝐶𝑂 ∆𝐻298° = 206.3 𝑘𝐽 𝑚𝑜𝑙⁄ Eq. 3-1

𝐶𝐻4 + 0.5𝑂2 ↔ 2𝐻2 + 𝐶𝑂 ∆𝐻298° = −35.6 𝑘𝐽 𝑚𝑜𝑙⁄ Eq. 3-2

The secondary reformer of methane controls the syngas ratio (H2/CO) in the

product stream. The H2/CO ratio is the key factor to produce high quality jet fuel. The

24

reformer system including burner dimension, catalyst packed bed distance from flame,

and required steam flow rate has been successfully developed in this pilot plant. Besides

steam methane reformer and partial oxidation of methane reactions, complete

combustion of methane takes place at a high reactor temperature, which increases the

generation of CO2 in the product stream.

𝐶𝐻4 + 2𝑂2 ↔ 2𝐻2𝑂 + 𝐶𝑂2 ∆𝐻298° = −880 𝑘𝐽 𝑚𝑜𝑙⁄ Eq. 3-3

Pilot Plant Demonstration

The overview GTL pilot plant is shown in Figure 3-2 to Figure 3-5. The GTL pilot

plant process includes three operating sections 1) the reformer 2) FT synthesis 3) and

the separator. In the pre-reformer section, oxygen and natural gas at room temperature

are passed through two annular tubes and after sparking, ignition occurs between 1000-

1100 °C. The flow then passes through the packed catalyst bed. In the secondary

reformer, Ni over Al2O3 catalysts are packed into the reactor. Two thermocouples are set

in the inlet and outlet catalyst bed. Also, the temperature and pressure are set to 1000–

500 °C and 1.5 bar, respectively. The total operation time of the reformer section to run

the entire range of variables, including ignition start-up time, takes approximately 8 days,

and after each run the process is repeated. The mass flow rate of steam, oxygen volume

flow rate, and volume ratio flow rate of oxygen to natural gas (O2/NG) are 0-3 lb/h, 18

LPM, and 0.6, respectively. Both the primary and secondary reformers are made of

stainless steel and are cooled by liquid water on the shell side. The pressure drop was

0.1-0.2 bar through the reformer section. The high temperature of the produced syngas

was reduced (∼30 °C) by a multi tubular heat exchanger and then chilled water was used

to trap saturated water in the syngas by cooling it down.

25

FT reactor is kept in the operating conditions of 300 psig, 245 °C. Syngas is fed

to the top of FT reactor as shown in Figure 3-4. The reactor catalyst bed is kept under

250 °C using a PID controller. After that, hydrogen is applied at a flow rate of 20 LPM for

one day. The loaded supported catalyst is filled in the FT reactor with a total volume of

800 ml. A multiple thermocouple (10 positions) is put in the reactor to measure

temperature during FT synthesis, which allows for effective temperature control inside the

packed bed reactor. According to the exothermic reactions inside the reactor, to control

the temperature, an air blower is used to adjust the profile temperature inside the reactor

to prevent coking of the catalysts. Cobalt-based catalyst with a silica support (20 wt%

Co/SiO2) is used for the FT reaction. The products of the FT reaction are split into oil,

water, wax, and light hydrocarbons. The unconverted synthesis gas and FT tail gas

leaves the stream and is routed to the tail flare unit.

26

Figure 3-1 Process Flow Diagram of The GTL Process Used in This Research Study

During FT synthesis, the syngas from ATR in the pilot plant and gas product from

FTR are analyzed by gas chromatography (GC) (Shimadzu 2014). The GC is fitted with a

flame ionization detector (FID) and thermal conductivity detector (TCD) using helium and

argon as carrier gas, and has Molsieve 5A 80/100 mesh, HayeSep Q 80/100 mesh, and

Alumina PLOT #CP7568 capillary columns. The period time for the gaseous sample

analysis is 15 min. The unconverted synthesis gas and FT tail gas leaves the stream and

is routed to the tail flare unit. FT fixed bed reactor is maintained at operating conditions of

20 bar, 220 °C- 240 °C, and flow rate of 10 g/min.

https://www.sciencedirect.com/topics/chemical-engineering/thermal-conductivity

27

Figure 3-2 ATR Pilot Plant Used in This Research Study

Figure 3-3 Burner Designed Used in This Research Study

Mix

CH4 & H2O

Pure O2

This Figure has been redacted


28

Figure 3-4 Vertical Single Tube FTR Used in This Research Study

Figure 3-5 Catalyst Type Used in Secondary Reformer


29

ASPEN HYSYS SIMULATION Chapter 4

GTL Process Simulation

The simulation of GTL process for natural gas conversion to high efficiency of

liquid hydrocarbons such as gasoline and diesel is considered in this study. The flow

sheet of the GTL pilot plant process is diagramed in Figure 4-1. The main problems that

are investigated in this study are how to reduce the high energy consumption and how to

increase the efficiency of the GTL process [27].

To optimize and simulate the entire pilot plant study the Aspen HYSYS is used,

which leads to a better understanding of the effect of the main parameters on producing

jet fuel. In this study O2/CH4, steam/CH4, and a proper kinetic model using both ATR and

FTR are selected as variables for optimization of all whole plants. Also, for study of ATR

and FTR simulations in Aspen HYSYS simulator, two types of reactors, conversion and

equilibrium reactors, are utilized.

Pilot Plant Simulation

The model is developed to simulate the reactions and the product formation

under various conditions and to determine the optimum operating conditions for the GTL

to maximize the formation of liquid hydrocarbon from methane combustion. Experiments

are also carried out to test the validity of the model proposed. The model is used to study

the product compositions under different operating conditions and different steam flow

rate. The product gases in the outlet of ATR and FT are optimized to produce the

required ratio of H2/CO and maximum liquid hydrocarbon using the equilibrium model.

The equilibrium conversion of the methane with oxygen and steam is calculated under

1.5 barg.

30

As explained previously, the ATR involves complex chemical reactions: 1) total

oxidation, 2) partial oxidation, 3) steam reforming, and 4) methanation and CO2 reforming

[25]. The ATR efficiency could be increased with simultaneous reactions in SR and POX

chambers. The appropriate choice of O2/CH4 and H2O/CH4 helps promote the process

without any extra heating [6]. Important parameter study in ATR simulation is H2O/CH4

molar ratio. The reactions set for the ATR simulations and FT reactor are listed in

Equation 4-1 through Equation 4-10.

ATR kinetics:

𝐶𝐻4 + 0.5𝑂2 ↔ 2𝐻2 + 𝐶𝑂 Eq. 4-1

𝐶𝐻4 + 2𝑂2 → 2𝐻2𝑂 + 𝐶𝑂2 Eq. 4-2

𝐶𝑂 + 𝐻2𝑂 ↔ 𝐻2 + 𝐶𝑂2 Eq. 4-3

𝐶𝐻4 + 𝐻2𝑂 ↔ 3𝐻2 + 𝐶𝑂 Eq. 4-4

𝐶𝐻4 + 2𝐻2𝑂 ↔ 4𝐻2 + 𝐶𝑂2 Eq. 4-5

𝐶𝐻4 + 𝐶𝑂2 ↔ 2𝐻2 + 2𝐶𝑂 Eq. 4-6

FT Kinetics:

𝐶𝑂 + 3𝐻2 → 𝐻2𝑂 + 𝐶𝐻4 Eq. 4-7

2𝐶𝑂 + 5𝐻2 → 2𝐻2𝑂 + 𝐶2𝐻6 Eq. 4-8

3𝐶𝑂 + 7𝐻2 → 3𝐻2𝑂 + 𝐶3𝐻8 Eq. 4-9

𝑛𝐶𝑂 + (2𝑛 + 1)𝐻2 → 𝑛𝐻2𝑂 + 𝐶𝑛𝐻2𝑛+2 Eq. 4-10

Paying attention to role of oxygen in ATR is important as it provides the heat

required for the secondary reformer and is powerful enough to cut down fuel into smaller

compounds. At a high ratio of oxygen to natural gas, the energy of fuel is converted to

heat rather than H2 production [18]. Simulations are done by varying the amount of the

H2O/CH4 ratio by the constant O2/CH4 ratio. The conditions of feed streams are described

in Table 4-1 for the simulation used in this study.

31

Figure 4-1 Block Flow Diagram of GTL Process

Table 4-1 Streams Conditions

Stream Temperature

[C] Mass Flow

[gm/h]

NG 25 1,180

Oxygen 25 1,545

Steam 350 0-680

The process flow diagram of the GTL pilot plant used in this simulation is

illustrated in Figure 4-1. Aspen HYSYS software is used to optimize the jet fuel

productivity. The Peng-Robinson (Peng) equation of state is considered as a

thermodynamic package in this study. In the GTL process, the first stage is related to

syngas production, which converts natural gas to the hydrogen and carbon monoxide

mixture. Several approaches are considered for synthesis gas generation. Producing

syngas is one of the most important parts of a GTL plant. In addition, in syngas

32

production, about 48% of the GTL cost investment is due to syngas. The H2/CO mole

ratio is the key factor that should be measured at the outlet of secondary reformer.

Operating temperature and pressure, the method of syngas production, and the amount

of steam are the parameters that effect the value of the H2/CO ratio [38]. Under 2.20

MPa, 850 °C , and 3 for steam to carbon ratio conditions, the ratio of H2/CO in the syngas

stream at the outlet of the auto thermal reactor is about 4.8, and it is decreased to 2.1 at

2.6 MPa and 1000 °C (same steam to carbon ratio) [27].

Low temperature is required in the steam methane reformer section. However,

because of endothermic reactions in SMR, large amounts of heat should be supplied.

Moreover, in this chamber a high ratio of H2/CO in the syngas stream is obtained (more

than 2), which is useless for the FT process and therefore needs some additional

treatment to control the high ratio of H2/CO like Pressure Swing Adsorption (PSA),

reverse water gas shift reactor, or adding pure CO2 to reach the proper ratio (around 2)

[28]. The SMR reactions listed in Equation 4-3 to 4-5 are supposed to reach chemical

equilibrium at the outlet of secondary reformer. Based on Chatelier's theory, to reach

higher conversion (Equation 4-3), the steam reforming of the methane reactions must

happen at high temperature, at a high ratio of steam to carbon (like NG), and under low

pressure. The required heat in the SMR section is supplied by generated heat in partial

and complete combustion of methane. Water gas shift (WGS) is the other reaction that

occurs in SMR. The most important ATR reactions because of high temperatures (around

1000 °C) in the chamber outlet are assumed in the equilibrium [23].

The primary reformer reactions are listed in Equation 4-1 and Equation 4-2.

According to Equation 4-7, methanation reactions are assumed to be in equilibrium. In

this study, the inlet operation temperature in the secondary reformer is considered 900

°C. The outlet temperature of the reformer is adjusted by applying a different oxygen

33

flowrate [20]. The hot syngas leaves the multi tubular heat exchanger (including 21 tubes)

and is then cooled down to 30 °C to remove the moisture before entering the FR unit.

Kinetic Model

In the FTR process, the basic estimation for lower syngas conversion (lower than

65%) is the first-order FT kinetics [17]. Linear kinetic models can be used in most FT

reactor simulations. Numerous complex studies have been completed on FT kinetic

models that have little credibility and therefore doubts in their accuracy remain [19]. The

kinetic model used in this study coupled through the Aspen HYSYS reaction set

simulates the plug FT reactor. The kinetic model is applied to simulate the second stage

of the GTL reaction and is used to calculate the syngas conversion. The kinetic model is

expressed in Equation 4-11. The Fischer-Tropsch (FT) reaction includes exothermic

reactions and the hydrocarbon chains are produced according to Equation 4-10.

−𝑟𝐶𝑂,𝐹𝑇 =𝑎𝑃𝐻2𝑃𝐶𝑂

(1+𝑏𝑃𝐶𝑂)2 Eq. 4-11

𝑎 = 1010𝑒𝑥𝑝(−115

𝑅𝑇) 𝑚𝑜𝑙 𝑠. 𝑘𝑔. 𝑏𝑎𝑟2⁄ Eq. 4-12

𝑏 = 3.5 × 10−23𝑒𝑥𝑝(192

𝑅𝑇) 1 𝐾. 𝑏𝑎𝑟⁄ Eq. 4-12

The detailed of kinetic model using in both CFD simulation and Aspen HYSYS

are described in Chapter 5.

34

CFD SIMULATION OF FISCHER-TROPSCH Chapter 5

Fixed Bed Reactor Modeling

Numerous studies have been conducted on the lumped kinetic model, and there

are some problems with their results. One problem is that this kinetic model cannot

estimate the exact amount of heat released by exothermic reactions through the FT

reactor; however, the heat released producing one mole of decane is different than the

heat released producing one mole of methane. In fact, 156 kJ and 206 kJ of heat are

released per CO mole consumed in each case. These complicated FT reactions cannot

be estimated by one single equation like Equation 5-1:

𝐶𝑂 + 2𝐻2 → (−𝐶𝐻2 −) + 𝐻2 ∆𝐻298° = −152

𝑘𝐽

𝑚𝑜𝑙 Eq. 5-1

As discussed above, in the GTL process, syngas converts to liquid hydrocarbons

and the main products are synthetic gasoline and/or diesel. The disadvantage of the fixed

bed reactor is poor control of temperature gradient along the heat transfer phenomena.

However, this type of reactor does have benefits such as being flexible, low cost, and low

maintenance [4]. For this reason fixed bed reactors should be studied in terms of a large

number of parameters to have a better understanding of their behavior. Because the

kinetic model used in the FT reactor is an exponential function of temperature, if the

minimum requirement of coolant flow rate and temperature are not calculated, the

temperature inside the FT reactor rapidly increases and causes hot spots [5]. This

phenomenon leads the destruction of the catalyst bed and the structure of the shell in the

multi tubular FT reactor.

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35

Mathematical Model

To design the multi-tubular reactor, the structure of the shell and tube heat

exchanger is considered. Each tube is packed by catalyst bed. As seen in Figure 5-1, the

coolant works to keep each tube in isothermal conditions. Therefore, it is necessary to

couple the behavior of the fluid in the shell section to the fluid in the tube.

Figure 5-1 Diagram of Multi Tubular Fixed Bed Reactor

The assumption is that each tube is eventually packed. In this model, it is

assumed that saturated liquid water is circulated in the shell section to keep the multi

tubular reactor working in isothermal conditions. The ratio of each tube length to diameter

(L/D) is set for the case study. In addition, to control temperature throughout the packed

bed reactor, the initial syngas temperature, initial coolant flow rate, and temperature are

the other variables that are studied in this research. The assumption is based on steady

state conditions. The FTS reactor is described in Equations 5-2 through 5-4.

𝑛𝐶𝑂 + (2𝑛 + 1)𝐻2 → 𝐶𝑛𝐻2𝑛+2 + 𝑛𝐻2𝑂 Eq. 5-2

𝑛𝐶𝑂 + 2𝑛𝐻2 → 𝐶𝑛𝐻2𝑛 + 𝑛𝐻2𝑂 Eq. 5-3

𝐶𝑂 + 𝐻2𝑂 → 𝐶𝑂2 + 𝐻2 Eq. 5-4

36

Where −(𝐶𝐻2)𝑛 − is the methylene group polymerizing into a hydrocarbon chain.

Table 5-1 shows the lumped kinetic model over cobalt catalyst in FT reactor [8, 14].

Moreover, the detailed stationary equations studied in this chapter are described and the

related boundary conditions are illustrated in Equations 5-5 through 5-12.

FT Plant Description

As seen in Figure 5-2, the FTR in the commercial plant is considered a two stage

multi tubular reactor. In the first stage, 50% syngas conversion on cobalt catalyst is

desired. The FT plant is simulated by computational fluid dynamics in 3D geometry in

single tube and multi-tubular tubes. The syngas gas is fed through the top of the first

stage, and then passes through the packed bed. The FT product from first stage

(unconverted syngas) is removed from the bottom of the reactor tube and subsequently

fed to the top of the second stage of the reactor. The temperature profile is kept constant

by circulation of pressurized water in the shell section or through steam as a coolant.

Figure 5-2 Schematic Design of Two-Step FT Reactor

https://www.sciencedirect.com/science/article/pii/S037838201300307X#bb0040

37

Table 5-1 Lumped Kinetic Rate Expressions for Overall Syngas

Kinetic Expression Reference

a 𝑘𝑃𝐻2 [32, 31, 30]

b 𝑘𝑃𝐻2𝑎 𝑃𝐶𝑂

𝑏 [31]

c 𝑘𝑃𝐻2

𝑃𝐶𝑂

𝑃𝐶𝑂 + 2𝑃𝐻2𝑂

[29, 30]

d 𝑘𝑃𝐻2

2 𝑃𝐶𝑂

𝑃𝐶𝑂𝑃𝐻2+ 𝑎𝑃𝐻2𝑂

[30]

e 𝑘𝑃𝐻2

2 𝑃𝐶𝑂

1 + 𝑎𝑃𝐶𝑂𝑃𝐻2

2 [31]

f 𝑘𝑃𝐻2

𝑃𝐶𝑂

𝑃𝐶𝑂 + 𝑎𝑃𝐶𝑂2

[24]

g 𝑘𝑃𝐻2

𝑃𝐶𝑂

𝑃𝐶𝑂 + 𝑎𝑃𝐻2𝑂 + 𝑏𝑃𝐶𝑂2

[26,24]

h 𝑘𝑃𝐻2

1/2𝑃𝐶𝑂

1/2

(1 + 𝑎𝑃𝐶𝑂1/2

+ 𝑏𝑃𝐻2

1/2)2 [25]

i 𝑘𝑃𝐻2

1/2𝑃𝐶𝑂

(1 + 𝑎𝑃𝐶𝑂 + 𝑏𝑃𝐻2

1/2)2 [30]

j 𝑘𝑃𝐻2

𝑃𝐶𝑂

(1 + 𝑎𝑃𝐶𝑂)2 [26]

Mass transfer of species in tube:

∇. (−𝐷𝑖∇𝑐𝑖) + 𝑢. ∇𝑐𝑖 = 𝑅𝑖 Eq. 5-5

Governing equation for Darcy flow:

∇. (𝜌𝑢) = 𝑄𝑚 Eq. 5-6

The velocity of Darcy flow is defined as:

𝑢 = −𝐾𝑝𝑟

𝜇∇𝑃 Eq. 5-7

The heat energy transport in multi tubular reactor and mixture fluid flow:

𝜌𝐶𝑝u. ∇𝑇 = ∇. (𝐾𝑒𝑓𝑓∇𝑇) + 𝑄 Eq. 5-8

𝜌𝐶𝑝u. ∇𝑇 = ∇. (𝐾𝑐∇𝑇) + 𝑄 Eq. 5-9

38

𝜌(𝑢𝑐 . ∇)𝑢𝑐 = ∇. [−𝜌𝐼 + (𝜇 + 𝜇𝑇)(∇𝑢𝑐 + (∇𝑢𝑐)𝑇 ) −

2

3(∇. 𝑢𝑐)𝐼] −

∇. [𝜌𝑐𝑑(1 − 𝑐 𝑑) (𝑢𝑠𝑙𝑖𝑝 −𝐷𝑚𝑑 ∇𝜑𝑑

(1−𝑐𝑑)𝜑𝑑) (𝑢𝑠𝑙𝑖𝑝 −

𝐷𝑚𝑑 ∇𝜑𝑑

(1−𝑐𝑑)𝜑𝑑)𝑇

] + 𝜌𝑔 + 𝐹

Eq. 5-10

(𝜌𝑐 − 𝜌𝑑) {∇. [𝜑𝑑(1 − 𝑐𝑑)𝑢𝑠𝑙𝑖𝑝 − 𝐷𝑚𝑑∇𝜑𝑑] +𝑚𝑑𝑐

𝜌𝑑

} + 𝜌𝑐(∇. 𝑢𝑐) = 0 Eq. 5-11

𝜌(𝑢𝑐 . ∇)𝑘 = ∇. [(𝜇 +𝜇𝑇

𝜎𝑘

)∇𝑘] + 𝑃𝑘 − 𝜌𝜖 Eq. 5-12

𝜌(𝑢𝑐 . ∇)𝜖 = ∇. [(𝜇 +𝜇𝑇

𝜎𝜖

)∇𝜖] + 𝐶𝜖1

𝜖

𝑘𝑃𝑘 − 𝐶𝜖2

𝜖2

𝑘𝑃𝑘 Eq. 5-13

Inlet boundary conditions in porous media:

At 𝑟 = 0 ∶

�⃗� (𝑟, 0) = 𝑢0 ⃗⃗⃗⃗ ⃗ Eq. 5-14

𝑇(𝑟, 0) = 𝑇0 Eq. 5-15

𝐶𝑖(𝑟, 0) = 𝐶𝑖,0 Eq. 5-16

𝑃(𝑟, 𝐿) = 𝑃𝑜𝑢𝑡 Eq. 5-17

∀𝑧, 𝑟 = 0: 𝜕𝐶𝑖

𝜕𝑟=

𝜕𝑇

𝜕𝑟= 0 Eq. 5-18

∀𝑧, 𝑟 = 𝑅: �⃗� (𝑅, 𝑧) = 0 Eq. 5-19

𝜕𝐶𝑖

𝜕𝑟= 0 Eq. 5-20

∀𝑧, 𝑟 = 𝑅: 𝐾𝜕𝑇

𝜕𝑟= ℎ𝑐(𝑇 − 𝑇𝑐) Eq. 5-21

ℎ𝑐 = K(0.023𝑅𝑒0.8𝑃𝑟0.33) Eq. 5-22

(CFD) modeling used the software COMSOL Multiphysics 5.3, which has built-in

multi-physics modules to simulate the mass, energy, and momentum equation packages.

[29, 30]. The major aims in this study are: 1) increasing the efficiency of jet fuel and 2)

defining the kinetic model that can best predict the behavior of an FT reactor.

https://www.sciencedirect.com/science/article/pii/S0016236115006201#b0145

39

Kinetics of Fischer–Tropsch Reactor

The biggest challenge in designing an FT reactor is choosing the proper kinetic

modeling with special attention to the complexity of the reaction’s mechanism. Some

simulations are considered with syngas conversion and do not mention the selectivity of

different hydrocarbon fractions. For FT synthesis, iron and cobalt on various oxide

supports are manipulated. Although cobalt catalysts are more expensive compared to

iron ones, cobalt catalysts have a much higher resistance and are also less sensitive to

water. Only paraffin production is considered in this study (Equation 5-2). Cobalt catalyst

has weak activity versus the WGS reaction, and for simplicity Equations 5-3 and 5-4 are

neglected [40]. Here Arrhenius law is applied for the kinetic model and the parameters of

the kinetic model is detailed in Table 5-2. The monoxide carbon consumption rate and

other species involved in the FT reactor are listed from Equations 5-23 through 5-30:

𝑟𝐶𝑂 = −𝑟𝐹𝑇 Eq. 5-23

With

𝑟𝐹𝑇 =𝑎.𝑒𝑥𝑝

(−𝐸𝑎𝑅𝑇 )

.𝑐𝐶𝑂𝑐𝐻2

(1+𝑏.𝑒𝑥𝑝(−∆𝐻𝑏𝑅𝑇 )

.𝑐𝐶𝑂)

2 Eq. 5-24

According to the stoichiometry of Equation 5-2, the water formation rate is

calculated by:

𝑟𝐻2𝑂 = −𝑟𝐶𝑂 = 𝑟𝐹𝑇 Eq. 5-25

The production rates of light hydrocarbon like methane rC1 and ethane rC2 are

determined by Arrhenius law:

𝑟𝐶1= 𝑑. 𝑒𝑥𝑝(

−𝐸𝑑𝑅𝑇

). 𝑟𝐹𝑇 Eq. 5-26

𝑟𝐶2= 𝑒. 𝑒𝑥𝑝(

−𝐸𝑒𝑅𝑇

). 𝑟𝐹𝑇 Eq. 5-27

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40

For other hydrocarbons higher than methane and ethane, the produced reaction

rates used are based on Anderson–Schultz–Flory theory (Equation 5-28). The constant

chain growth probability (α) is assumed to be 0.9. Therefore, the rate of hydrocarbons

production is given by:

For (n>2)

𝑟𝐶𝑛= 𝛼. 𝑟𝐶𝑛−1

Eq. 5-28

Also, according to Equation 5-2, the consumption rate of hydrogen is given by:

−𝑟𝐻2= ∑ (2𝑖 + 1). 𝑟𝐶𝑖

𝑁𝑖 Eq. 5-29

And also

−𝑟𝐶𝑂 = 1. 𝑟𝐶1+ 2. 𝑟𝐶2

+ 3. 𝑟𝐶3+ ⋯+ 𝑁. 𝑟𝐶𝑛

= ∑ 𝑖. 𝑟𝐶𝑖

𝑁𝑖 Eq. 5-30

The kinetics parameters and activation energy used in this study is reported by

Sadeqzadeh et al. (2012) and shown in Table 5-3.

Table 5-2 The List of Kinetic Model Used in Sadeqzadeh et al.

Parameter Value Unit

a 7.17× 107 m6.kgcat

-1.mol

-1s

-1

b 44.93 m3mol

-1

d 3.08× 107 -

e 2.01× 103 -

Ea 100 kJ.mol-1

Eb 20 kJ.mol-1

Ed 81 kJ.mol-1

Ee 49 kJ.mol-1

As the first step, a simple model using chemical reaction rate equations is made

and a system of differential equations is constructed. For each chemical reaction included

in the system, the chemical equilibrium equation that incorporates reaction rate is written.

The values for some of the reaction rates are the uncertainties of this model and the aim

of this research is to find optimum values. One goal is to match the experimental results

41

as much as possible. For the simple model, a good agreement with the lab experiments

is difficult to achieve. The solution of the system gives a concentration of all the chemical

species as a function of time. The final values of the concentrations are converted to the

appropriate quantities measured in the experiment. Next, an objective function on errors

between measured and simulated values is defined. A low objective function value close

to zero indicates a good fit. An optimization problem with the defined objective function to

find the optimum set of values for the uncertain reaction rates is created. Two reaction

rates for CH4 and all other hydrocarbons are modified so that a new temperature

dependency is created that can be manipulated. Specifically, two extreme experimental

results in the lower and higher bounds of the temperature window where the simulation

and experiment differ are found. Finally, the modified equations are chosen to

compensate for the difference, and the model is fit to the data.

Optimized Parameters and kinetic models:

For n components (case 1):

𝑟𝐹𝑇 =𝐾𝑎.𝑐𝐶𝑂𝑐𝐻2

(1+𝐾𝑏.𝑐𝐶𝑂)2 Eq. 5-31

𝑟𝐶1= 𝐾𝑑 . 𝑟𝐹𝑇 Eq. 5-32

𝑟𝐶𝑖= 𝛼𝑖−2𝐾𝑑 . 𝑟𝐹𝑇 𝑖 = 2, …𝑛 Eq. 5-33

𝐾𝑎 = 𝑎. 𝑒𝑥𝑝(−𝐸𝑎𝑅𝑇

) Eq. 5-34

𝐾𝑏 = 𝑏. 𝑒𝑥𝑝(−𝐸𝑏𝑅𝑇

) Eq. 5-35

𝐾𝑑 = 𝑑. 𝑒𝑥𝑝(

−𝐸𝑑𝑅𝑇𝑓(𝑇)𝛾𝑑

) Eq. 5-36

𝐾𝑒 = 𝑒. 𝑒𝑥𝑝(

−𝐸𝑒𝑅𝑇𝑓(𝑇)

) Eq. 5-37

𝑓(𝑇) =𝑇−470

255−200 Eq. 5-38

42

Table 5-3 Optimized Parameters for n Components Used in This Research Study

Parameter Initial Guess Fitted Value Unit

a 26.77× 103 31.79× 103 m6.kgcat

-1.mol

-1s

-1

b 3.69 2.955 m3mol

-1

d 2.08E8 184460528 -

e 6.65E3 5332 -

𝛼 0.9 0.7559 -

Ee 49 48.142 kJ/mol

Simplified model (Using C12H26 as an average of products, case 2):

𝑟𝐶𝑂 = −𝑟𝐶1− �̅�. 𝑟𝐶𝑜𝑖𝑙

Eq. 5-39

𝑟𝐻2= −3. 𝑟𝐶1

− (2�̅� + 1)𝑟𝐶𝑜𝑖𝑙 Eq. 5-40

𝑟𝐻2𝑂 = 𝑟𝐶1+ �̅�. 𝑟𝐶𝑜𝑖𝑙

Eq. 5-41

𝑟𝐶𝐻4= 𝑟𝐹𝑇 . 𝑑. 𝑒𝑥𝑝

(−𝐸𝑑

𝑅𝑇𝑓(𝑇)𝛾𝑑) Eq. 5-42

𝑟𝐶𝑜𝑖𝑙= 𝑟𝐹𝑇 . 𝑒. 𝑒𝑥𝑝

(−𝐸𝑒

𝑅𝑇𝑓(𝑇)) Eq. 5-43

�̅� = 12

𝐾𝑑 = 𝑑. 𝑒𝑥𝑝(

−𝐸𝑑𝑅𝑇𝑓(𝑇)𝛾𝑑

) Eq. 5-44

𝐾𝑒 = 𝑒. 𝑒𝑥𝑝(

−𝐸𝑒𝑅𝑇𝑓(𝑇)

) Eq. 5-45

𝑓(𝑇) =𝑇−470

255−200 Eq. 5-46

Table 5-4 Optimized Parameters Considering C12 as A Product Used in This Study

Parameter Initial Guess Fitted Value Unit

a 26.77× 103 31.79× 103 m6.kgcat

-1.mol

-1s

-1

b 3.69 3.187 m3mol

-1

d 2.08E08 201465553 -

e 6.65E03 8004.9 -

𝛾𝑑 1 48.142K 1.1989

43

RESULTS AND DISCUSSION Chapter 6

In this chapter results are illustrated in three parts: 1) ATR experiment, 2) Aspen

HYSYS simulation of GTL, and 3) CFD simulation of results. The description of the entire

GTL plant as constructed is explained in Chapter 4. All results are generated based on

50% syngas conversion using suitable and modified kinetic models.

Experimental Results

As discussed in chapter 3, in the auto thermal reforming (ATR) pilot plant, the

natural gas and oxygen passed through two concentric tubes. The experimental tests

were carried out in ATR, which includes a burner, non-catalyst partial oxidation (NCPOX),

and Steam Methane Reforming (SMR). Natural gas and the oxidizer in room temperature

were injected into the chamber through a multi-channel burner (Figure 6-1). In Table 6-1,

the feed stream operating conditions and burner geometric parameters are illustrated. A

different amount of steam flow rate in 1.5 psig was injected into the reformer with natural

gas. Table 6-2 shows the information of feed streams to the reformer chamber. By

controlling the O2/CH4 ratio in the feed stream of the primary reformer, the operating

temperature range was kept between 900–1000 ℃ to produce a lower syngas (H2/CO)

ratio compared to the secondary reformer. The schematic geometry of the burner and

pilot plant ATR is shown in Figure 6-2 and Figure 6-3.

Figure 6-1 Structure of the Burner

44

Table 6-1 Multi Channel Burner

Channel OD Diameter

(in.) Feed stream

Flowrate (LPM-lb/h)

Temperature (K)

1 1/4 Natural Gas/H2O 30/(0-3) 298.15/623.15

2 3/8 O2 18 298.15

Table 6-2 Mole Fraction of Feed Stream in Different Steam Flow Rates

Composition Steam (lb/h)

0 0.5 1 1.5 2 2.5 3

CH4 0.6274 0.5692 0.5209 0.4801 0.4453 0.4152 0.3889

C2H6 0.0139 0.0127 0.0116 0.0107 0.0099 0.0092 0.0086

O2 0.3586 0.3254 0.2977 0.2744 0.2545 0.2373 0.2223

H2O 0 0.0928 0.1698 0.2347 0.2903 0.3383 0.3802

Figure 6-2 Schematic of proposed ATR

As shown in Figure 6-3, the chamber was designed to be 24 ft. in length, have an

internal diameter of 7.5”, and includes insulation and a shell section to promote cooling.

The catalyst packed bed has a length of 12”, dimeter of 7.5”, and weight of 5.3 kg, and it


45

was located 8” away from the flame. Qubic Ni/Al2O3 catalysts were placed in the reactor

in order to achieve a higher H2/CO ratio. As shown in Figure 6-2, the inlet and outlet

temperature was observed through two thermocouples in two different zones in the

chamber (TC-01 and TC-02).

Feed stream (oxygen and natural gas) delivery to the chamber was adjusted by

Brooks and Alicat mass-flow controllers. The water was pumped to a coil heater and

vaporized at the beginning of the tube to the chamber, before being mixing with natural

gas. The steam tubes were covered by insulation. Two pressure indicators connected to

the chamber monitored the pressure upstream and downstream the catalytic bed. Two

K-type thermocouples were used to measure the temperature profile through the packed

bed reactor in the secondary reformer. To cool down the produced syngas in the catalyst

bed, it was passed through a multi-tubular heat exchanger. Temperature (TC-03) and

pressure indicators downstream the chamber were used to observe and record the

changes in the process. Two different experiments, both with and without the catalyst bed

in the chamber, were conducted to study the methane conversion and syngas selectivity

through chamber.

To investigate the CO, H2, CO2, and unconverted CH4 mole percentage, the

analysis of the outlet dry base gas composition was done by GC. The feed stream mole

fractions for the experimental set up in the reformer for both the non-catalyst and catalyst

chambers are specified in Table 6-3. The details of the ATR pilot plant used in this study

are shown in Figure 6-4.

46

Figure 6-3 Schematic Reformer Design

Figure 6-4 Schematic Design of Primary and Secondary Reformer

Table 6-3 Feed Stream Used in Experimental Setup

Parameter Value

Natural gas flow rate [LPM] 18

Oxygen flow rate/Natural gas flow rate [LPM] 0.6

Steam flow rate [Ib/h] 0-3

Effect of Steam/NG Molar Ratio

In the present work, the effect of the Steam/NG molar ratio on composition of

syngas stream was investigated in the porous and non-catalyst zone. Also, the required

steam flow rate to get a value of 2 for the H2/CO ratio in gas stream was studied. The

operating pressure and O2/NG volume ratio were 1.5 barg and 0.6, respectively, through


47

the ATR pilot plant setup. TC-01, TC-02, and TC-03 were observed at 950 ºC, 888 ºC,

and 30 ºC without the catalyst bed, and 950 ºC, 550 ºC, and 30 ºC in the catalyst bed.

Endothermic reactions through porous media, causes decreasing in temperature gradient

in the secondary chamber. The values of the steam/NG mole ratio, 0, 0.16, 0.31, 0.47,

0.63, 0.78 and 0.94, are selected in this research.

It is generally agreed that the methane conversion to syngas in auto thermal

reforming occurs in five steps. The main reactions are given below:

𝐶𝐻4 + 0.5𝑂2 ↔ 2𝐻2 + 𝐶𝑂 Eq. 6-1

𝐶𝐻4 + 2𝑂2 → 2𝐻2𝑂 + 𝐶𝑂2 Eq. 6-2

𝐶𝑂 + 𝐻2𝑂 ↔ 𝐻2 + 𝐶𝑂2 Eq. 6-3

𝐶𝐻4 + 𝐻2𝑂 ↔ 3𝐻2 + 𝐶𝑂 Eq. 6-4

𝐶𝐻4 + 2𝐻2𝑂 ↔ 4𝐻2 + 𝐶𝑂2 Eq. 6-5

To get the steady-state condition, before sampling the gas stream from GC, the

reformer was run for about 12 hours. Then gases were sampled every 5 mins. The

results for primary and secondary reformers are displayed in Tables 6-4 through 6-11 and

reported every 4 hours. No significant changes in gas compositions within 4 h were

observed.

However, the secondary reformer was seen to have lower carbon dioxide

because of water gas shift reaction, higher hydrogen and H2/CO ratio content in gas

product compared with primary reformer, and a decrease in the bed temperature from

980 ºC to 550 ºC. Increasing the steam flow rate is favorable for water-gas shift methane

reforming reactions (Eq. 6-3 and 6-4) and causes a decrease in packed bed temperature.

The effect of the steam/NG ratio on the gas compositions are shown in Figures

6-5 through 6-8 in the primary reformer, and Figures 6-9 through 6-13 in the secondary

reformer. It can be observed that the CO and H2 mole percentage, with the rise of

48

steam/NG ratio, decreases and increases respectively, and the ratio of H2/CO shows the

trend of the increase.

The steam/NG ratio with a value of 0.31 was able to reach the desired H2/CO

ratio of 2, which is favorable as a feed stream for Fischer-Tropsch reactor. However,

when the steam/NG ratio increases, the increasing in CO2 amount is observed which is

not suitable for FT reactor and absorbing CO2 is an important challenge these days.

The effects of the steam/NG mole ratio on the syngas H2/CO mole ratio, CO, H2,

and CO2 compositions in syngas streamline at the outlet of primary chamber are shown

in Figures 6-5 through 6-10, and the results are compared with secondary reformers (see

Figures 6-11 to 6-14). By increasing the steam/NG mole ratio, the increase in H2/CO is

observed in the stream gas product, which confirms the effect of higher steam flow rates

on the H2/CO ratio in the Aspen simulation in the next section. Also, adding the steam is

useful to protect the burner.

Table 6-4 Primary Reformer Results of Selected Runs (Run 1-6)

Run Run 1 Run 2 Run 3 Run 4 Run 5 Run 6

O2 [LPM] 18 18 18 18 18 18

O2/Natural gas [vol/vol] 0.6 0.6 0.6 0.6 0.6 0.6

Steam/NG [mol/mol] 0 0 0 0.16 0.16 0.16

TC-01/TC-02 ( C) 968/890 950/891

H2 (%) 40.8 40.8 40.8 40.3 40.3 40.3

CO (%) 28.9 28.9 28.9 28.0 28.0 28.0

CO2 (%) 6.65 6.63 6.63 7.55 7.55 7.54

CH4 (%) 23.1 23.1 23.1 22.1 22.0 22.1

H2/CO 1.38 1.38 1.38 1.43 1.43 1.43

This Table has been redacted

49

Table 6-5 Primary reformer results of selected runs (Run 7-12)


O2 [LPM] 18 18 18 18 18 18


Steam/NG [mol/mol] 0.31 0.31 0.31 0.47 0.47 0.47

TC-01/TC-02 ( C) 950/890 948/887

H2 (%) 40.2 40.2 40.1 39.7 39.7 39.7

CO (%) 27.7 27.7 27.7 25.9 25.9 25.9

CO2 (%) 8.55 8.55 8.55 9.43 9.45 9.44

CH4 (%) 22.3 22.3 22.3 23.0 23.0 23

H2/CO 1.45 1.45 1.45 1.47 1.47 1.47

Table 6-6 Primary reformer results of selected runs (Run 13-18)


O2 [LPM] 18 18 18 18 18 18


Steam/NG [mol/mol] 0.63 0.63 0.63 0.78 0.78 0.78

TC-01/TC-02 ( C) 950/890 950/888

H2 (%) 36.8 36.8 36.8 35.7 35.8 35.7

CO (%) 24.9 24.9 24.9 24.1 24.1 24.1

CO2 (%) 10.3 10.3 10.3 11.1 11.1 11.1

CH4 (%) 24.3 24.3 24.3 26.5 26.0 26.1

H2/CO 1.48 1.48 1.48 1.48 1.49 1.48

Table 6-7 Primary Reformer Results of Selected Runs (Run 19-21)

Run Run 19 Run 20 Run 21

O2 [LPM] 18 18 18

O2/Natural gas [vol/vol] 0.6 0.6 0.6

Steam/NG [mol/mol] 0.94 0.94 0.94

TC-01/TC-02 ( C) 950/890

H2 (%) 34.5 34.5 34.5

CO (%) 23.0 23.1 23.0

CO2 (%) 11.8 11.8 11.8

CH4 (%) 27.1 26.9 27.0

H2/CO 1.49 1.49 1.49




50

Table 6-8 Secondary Reformer Results of Selected Runs (Run 1-6)


O2 [LPM] 18 18 18 18 18 18


Steam/NG [mol/mol] 0 0 0 0.16 0.16 0.16

TC-01/TC-02 ( C) 950/558 950/555

H2 (%) 54.9 54.9 54.9 55.8 55.7 55.7

CO (%) 31.0 30.9 31 29.4 29.4 29.4

CO2 (%) 6.52 6.52 6.51 7.6 7.62 7.62

CH4 (%) 7.3 7.3 7.31 6.79 6.78 6.78

H2/CO 1.77 1.77 1.77 1.89 1.89 1.89



O2 [LPM] 18 18 18 18 18 18


Steam/NG [mol/mol] 0.31 0.31 0.31 0.47 0.47 0.47

TC-01/TC-02 ( C) 950/550 950/551

H2 (%) 55.1 54.9 55.1 56.7 56.7 56.7

CO (%) 27.5 27.5 27.5 27.9 28 27.9

CO2 (%) 8.75 8.76 8.75 9.25 9.25 9.25

CH4 (%) 6.58 6.57 6.57 6.29 6.29 6.28

H2/CO 1.99 2.03 2.02 2.05 2.04 2.05



O2 [LPM] 18 18 18 18 18 18


Steam/NG [mol/mol] 0.63 0.63 0.63 0.78 0.78 0.78

TC-01/TC-02 ( C) 950/890 950/888

H2 (%) 57.4 57.4 57.4 57.6 57.6 57.6

CO (%) 26.2 26.2 26.1 25 25.1 25.1

CO2 (%) 9.79 9.78 9.79 10.9 10.8 10.9

CH4 (%) 5.93 5.93 5.93 5.01 5.02 5.02

H2/CO 2.19 2.19 2.19 2.28 2.28 2.29




51


Run Run 19 Run 20 Run 21

O2 [LPM] 18 18 18

O2/Natural gas [vol/vol] 0.6 0.6 0.6

Steam/NG [mol/mol] 0.94 0.94 0.94

TC-01/TC-02 ( C) 950/890

H2 (%) 58.8 58.8 58.8

CO (%) 23.4 23.4 23.4

CO2 (%) 13.1 13.1 13.1

CH4 (%) 3.99 3.98 3.99

H2/CO 2.49 2.49 2.49

Figure 6-5 H2/CO Experiment Ratio in Primary Reformer

1.35

1.37

1.39

1.41

1.43

1.45

1.47

1.49

1.51

0 0.2 0.4 0.6 0.8 1

H

2/C

O [

mo

lar

rati

o]

Steam/NG [molar ratio]

Steam/NG=0 Steam/NG=0.16 Steam/NG=0.31Steam/NG=0.47 Steam/NG=0.63 Steam/NG=0.78Steam/NG=0.94


52

Figure 6-6 %CO Experiment in Primary Reformer

Figure 6-7 %H2 Experiment in Primary Reformer

22

23

24

25

26

27

28

29

30

0 0.2 0.4 0.6 0.8 1 %

CO

[m

ole

per

centa

ge

-Dry

bas

e]


Steam/NG=0 Steam/NG=0.16 steam/NG=0.31Steam/NG=0.47 Steam/NG=0.63 Steam/NG=0.78Steam/NG=0.94

30

32

34

36

38

40

42

44

0 0.2 0.4 0.6 0.8 1

%

H2 [

mo

le p

erce

nta

ge

- D

ry b

ase]



53

Figure 6-8 %CO2 Experiment in Primary Reformer

Figure 6-9 H2/CO Experiment Ratio in Secondary Reformer

4

5

6

7

8

9

10

11

12

13

0 0.2 0.4 0.6 0.8 1

%

CO

2 [

mo

le p

erce

nta

ge

- D

ry b

ase]



1.5

1.7

1.9

2.1

2.3

2.5

2.7

0 0.2 0.4 0.6 0.8 1

H

2/C

O [

mo

lar

rati

o]



54

Figure 6-10 % Unconverted CH4 In Secondary Reformer

Figure 6-11 %CO Experiment in Secondary Reformer

3

3.5

4

4.5

5

5.5

6

6.5

7

7.5

8

0 0.2 0.4 0.6 0.8 1

%

unre

acte

d C

H4 [

mo

le p

erce

nta

ge

- D

ry

bas

e]



3.00

8.00

13.00

18.00

23.00

28.00

33.00

0 0.2 0.4 0.6 0.8 1 %

CO

[m

ole

per

centa

ge

- D

ry b

ase]



55

Figure 6-12 %H2 Experiment in Secondary Reformer

Figure 6-13 %CO2 Experiment in Secondary Reformer

40

45

50

55

60

65

0 0.2 0.4 0.6 0.8 1

%

H2

[mo

le p

erce

nta

ge

- D

ry b

ase]



4

5

6

7

8

9

10

11

12

13

14

0 0.2 0.4 0.6 0.8 1

%

CO

2

[mo

le p

erce

nta

ge-

Dry

bas

e]



56

Simulation of Syngas and Oil Production

According to the pilot plant setup discussed in the previous section, the Aspen

HYSYS simulation model was used for the syngas and oil production. The Peng

Robinson equation of state was employed to calculate the physical properties of the

stream lines. The process flow diagram for the GTL plant is shown in Figure 6-20.

Simulation study on the GTL (produced jet fuel from natural gas) process was

done through Aspen simulation to get the H2/CO=2 in syngas stream and maximum

production of jet fuel. By changing the steam flow rate to the primary reformer, the GTL

operating condition of the reformer was controlled. The simulation assumption was based

on steady state conditions. The reaction kinetic models for FTS over cobalt catalyst unit

are described in Equation 4-11.

The water stream leaves the heater at 350ºC and a pressure of 1.5 barg at the

flowrate of 30 mol/hr. After mixing with the methane stream at room temperature, the

methane enters the primary reformer and reacts with oxygen. In this research, a low

steam/methane ratio of 0.38 and oxygen/methane ratio of 0.6 is selected for the first

stage of GTL simulation to obtain the proper H2/CO ratio of 2. The SMR and WGS

reactions are assumed based on equilibrium reactions. All of the reactions occurring in

the primary and secondary reformers are described in Equations 6-1 through 6-5.

The high amount of heat released by complete and partial oxidation of methane

caused hot syngas production to streamline by 800 K in the outlet of ATR. After this, the

hot syngas is cooled to ambient temperature by heat exchanger. Table 6-12 shows the

derived syngas composition result to get the desired H2/CO.

57

Table 6-12 Syngas Composition Result

Temperature [302.15 K] Pressure [1.4 barg]

Component Mole fraction Mole flow rate [mol/h]

CO 0.2099 40.45

H2 0.4208 81.1

H2O 0.2426 46.75

CH4 0.064 12.33

CO2 0.0627 12.1

The first major simulation units were the primary and secondary reformers.

These units convert methane to syngas. More oxidation reactions occur when higher flow

rates of O2 is applied into the reactor. This creates a syngas stream with lower H2/CO

ratios while the temperature out of the reactor increases [42]. However, increasing the

steam flow rate has the opposite effect on H2/CO. This is because more endothermic

reactions are occurring in the reactor. Syngas production should have a H2/CO ratio of

roughly 2 as a feed stream in the FTS unit. Therefore, 540 g/h steam was needed to be

used by the reactor to satisfy this requirement. Table 6-13 shows the feed stream

conditions in syngas to get the desired H2/CO ratio. The final amounts and properties of

the process are presented in Table 6-13. Figures 6-14 to 6-19 show the rate of species in

the outlet of ATR, and the trend has good agreement with experimental data.

Table 6-13 Final Amount and Process Conditions for The Feed Flow Properties

Feed Stream [g/h] Mass Flow Rate [g/h] Temperature [°C] Pressure [barg]

Natural gas 1290 25 1.5

Oxygen 1415 25 1.5

Steam 540 350 1.5

After the hot syngas stream line was cooled by the heat exchanger, the 28%

(%mol) of water was collected by the separator. The cooled syngas with an H2/CO ratio

of 2.005, was compressed to 20 barg and heated to 245 ºC before entering the packed

58

bed FT reactor with a catalyst load of 2000 g. Because FTR exothermic reactions

happen, heat must be removed by a coolant. The hydrocarbon synthesis reaction

through FTR is considered a polymerization reaction [44]. Equations 5-31 through 5-38

were used in the simulation of the FT reactor in Aspen HYSYS. The chain growth

probability α was set to 0.75, and the oil fractions were assumed from CH4 to C15H32 in

this simulation. Figure 6-20 depicts the FT synthesis process flow diagram used in this

simulation and presents the mole and mass balances for the entire GTL plant. The

hydrocarbon products are split by a condenser to separate the light and heavy

hydrocarbons. A three phases condenser is used to separate the water, gas, and final

products.

Table 6-14 shows the FTR mass fraction products with different syngas

conversions. A single pass flow and the volume of the reactor being 4.5 liters are

assumed. As shown in Table 6-15, water is the major product (54%), and the C5H12

fraction has the higher mass fraction in liquid oil product. The results were compared to

the reliability of FTR. Simulation results were also compared by CFD simulation, as

discussed in the next section, to check the agreement between these two simulations.

59

Figure 6-14 Comparison of H2/CO Ratio in Experimental and ATR Simulation

Figure 6-15 %CO Simulation in ATR

1.6

1.8

2

2.2

2.4

2.6

2.8

3

0 0.2 0.4 0.6 0.8 1

%

H2/C

O

[mo

le p

erce

nta

ge]


Aspen Results Experimental Results

14

16

18

20

22

24

0 0.2 0.4 0.6 0.8 1

% C

O [

mo

le p

erce

nta

ge]

Steam/Natural Gas [molar ratio]

60

Figure 6-16 %H2 Simulation in ATR

Figure 6-17 % Unconverted CH4 Simulation in ATR

30

32

34

36

38

40

42

44

46

48

50

0 0.2 0.4 0.6 0.8 1

% H

2 [

mo

le p

erce

nta

ge]


0

1

2

3

4

5

6

7

8

9

10

0 0.2 0.4 0.6 0.8 1

% U

nco

nver

ted

C

H4

[mo

le p

erce

nta

ge]


61

Figure 6-18 %H2O Simulation in ATR

Figure 6-19 Simulation Study of CH4 Conversion in ATR

20

21

22

23

24

25

26

27

28

29

30

0 0.2 0.4 0.6 0.8 1

% H

2O

[m

ole

per

centa

ge]


90

90.5

91

91.5

92

92.5

93

93.5

94

94.5

95

0 0.2 0.4 0.6 0.8 1

% C

H4 C

onver

sio

n


62

Figure 6-20 GTL Process Flow Diagram in This Study to Get 50% Syngas Conversion

63

Table 6-14 FT Products to Get 50% And 70% Conversion, Aspen Results

Component Temperature: 518.15 K

CR: 50% CR: 70%

CH4 0.0898 0.182

C5H12 0.01694 0.02237

C6H14 0.01589 0.02236

C7H16 0.015229 0.02134

C8H18 0.01519 0.02129

C9H20 0.015157 0.02123

C10H22 0.015 0.02116

C11H24 0.01498 0.02102

C12H26 0.01431 0.02

C13H28 0.01415 0.0198

C14H30 0.01331 0.0187

C15H32 0.0073 0.0102

H2O 0.2712 0.369

Table 6-15 Selectivity of Products, Aspen Results

%Selectivity Temperature: 518.15 K

CR: 50% CR: 70%

SC1 14.15 14.13

SH2O 54.76 54.82

SC5+ 29.712 29.85

CFD Simulation of Fischer-Tropsch Reactor

In this section, the Fischer-Tropsch reactor with a 3D geometry is numerically

investigated and coupled with mass, momentum, heat transfer, and kinetic modules. The

operation parameters, bulk temperature distribution, the selectivity, and the productivity of

the products are analyzed using this model.

64

Simulation Setup

The fixed bed single tube and multi tubular Fisher-Tropsch reactor is described in

Figure 6-21, and Table 6-16 and Table 6-17 list the parameters of both reactors that are

used in this study. Coarser mesh was initially used to find a quick solution to the problem,

but later all of the modules were solved using a finer mesh size (see Figure 6-22).

Although a coarser mesh decreases the time to find a solution, the error in mass

conservation was 20% in the FT tube, which could only be corrected using a finer mesh

to fix the problem. The syngas conversion, water, gas, and oil selectivity are defined in

Equations 6-6 through 6-19.

%𝑋𝑠𝑦𝑛𝑔𝑎𝑠 =𝑚𝑠𝑦𝑛𝑔𝑎𝑠,𝑜𝑢𝑡𝑙𝑒𝑡

°

𝑚𝑡𝑜𝑡𝑎𝑙° × 100 Eq. 6-6

%𝑆𝐶5+=

𝑚𝐶5+°

𝑚𝑤𝑎𝑡𝑒𝑟° +𝑚𝑜𝑖𝑙

° +𝑚𝑔𝑎𝑠° × 100 Eq. 6-7

%𝑆𝑔𝑎𝑠 =𝑚𝑔𝑎𝑠

°


° +𝑚𝑔𝑎𝑠° × 100 Eq. 6-8

%𝑆𝑤𝑎𝑡𝑒𝑟 =𝑚𝑤𝑎𝑡𝑒𝑟

°


° +𝑚𝑔𝑎𝑠° × 100 Eq. 6-9

65

Figure 6-21 Geometry of Fischer-Tropsch Reactor Used in This Research Study

Figure 6-22 Mesh Layout Used in This Research Study

66

Table 6-16 Physical Parameters in Single Tube Reactor

Parameter Value

Tube height 9 [m]

Tube diameter 2.54 [cm]

Pressure 21 [bar]

Bulk density 500.72[kg/m3]

Inlet concentration of H2 66.67 [%mol]

Inlet concentration of CO 33.33 [%mol]

Bed porosity 0.5 [-]

Chain growth possibility 0.79 [-]

Table 6-17 Physical Parameters in Multi Tubular Reactor

Parameter Value

Tube height 15 [cm]

Tube diameter 2.54 [cm]

Pressure 21 [bar]

Bulk density 500.72[kg/m3]

Inlet concentration of H2 66.67 [%mol]

Inlet concentration of CO 33.33 [%mol]

Bed porosity 0.5 [-]

Chain growth possibility 0.79 [-]

Parametric Study

The FTS catalyst with 20wt% cobalt on an SiO2 support was considered in the

kinetic modeled described in Chapter 5. The reaction was conducted at a temperature of

245°C, pressure of 21 bar, and mole ratio of H2/CO=2. The physical properties of the

reactant and coolant streams were considered as a function of composition, pressure,

and temperature. The thermal conductivities, densities, viscosities, specific heat

capacities, and hydrocarbons enthalpies of formation are shown in Appendix A.

In this study, only hydrocarbon species CH4 and C12H26 were used to reduce the

model complexity; in addition, hydrocarbon species CH4, C5H12, C8H16, C10H22, C12H26,

and C15H32 were the products of this research. Methane is a major hydrocarbon product

67

through FTS, explaining why it should be selected in each case [53]. For grid generation,

the free quad method in the software was used, and Galerkin’s method was applied with

the tolerance of the relative errors specified as 10e-3 [58].

The reactor performance of the 3D model is compared in Tables 6-18 and 6-19

with different fraction numbers of hydrocarbons. FT synthesis shows a similar result and

is derived from the Aspen simulation in which water is a major product. Productivity

increased by increasing in the SV for both cases (5 species and 9 species). Figure 6-23

illustrates the trend of syngas conversion at an initial feed temperature of 245 °C and

different amounts of space velocities.

Table 6-18 and Table 6-19 present syngas conversion as a function of the SV. At

the same space velocity, in FT simulation, less syngas conversion is gained for a higher

number of species (9 species) as compared to a lower species (5 species). Also, syngas

conversion decreases with an increase in the SV. As seen in Table 6-20 and Table 6-21,

an increase in the SV from 174 to 774 [Nml/gcat.h] resulted in a decrease in syngas

conversion from 86.29% to 26.6% in simulation of 5 species, and 70.74% to 19%, in

simulation of 9 species. The reason is that a higher SV has a lower residence time, which

causes a decrease in syngas conversion. Furthermore, Figure 6-23 illustrates the syngas

conversion profile results along the tube length for different amounts of SV. The results

showed a higher residence time and syngas conversion is derived in lower space

velocities. Product selectivity and selectivity are shown in Table 6-18 and Table 6-19 at

245 °C and 21 bar. As can be seen, the oil and methane selectivity in simulation of 9

species is lower than 5 species, and the increase in selectivity of C5+ is observed by

increasing the SV. However, for some space velocities, there was a slight increase in

methane, which is not a significant change in different space velocities. Diffusion has a

dominant role in the removal of hydrocarbon fractions from the catalyst surface by

68

increasing the space velocity. Therefore, the selectivity of C5+ was increased by

increasing SV [33]. Another reason could be the presence of higher molecular mass

products inside the pores, which increases residence time and, with that, oil selectivity

[56, 57].

The overall oil productivity in FTS is shown in Figure 6-24 and Figure 6-25. Since

the desired product is liquid hydrocarbon and the undesired product is light

hydrocarbons, the simulation was carried out to reach the higher productivity of C5+. As

seen in Figure 6-24, higher productivity results from increasing the SV; however, it

causes lower syngas conversion. In addition, Figure 6-26 and Figure 6-27 compare

syngas conversion and oil productivity against the SV for the different oil species

considered in model. At an SV of 391.79 [Nml/gcat.h], the productivity of 5 species is

approximately 38% more than 9 species. Also, when the feed temperature was

increased, it was observed that the syngas conversion in the catalytic bed was higher in

lower space velocity.

Figure 6-28 shows the profile contour of the bulk temperature and product

species through the reactor under the conditions of Tfeed,in = 518.15 K. Figure 6-28a and

Figure 6-28g show the slight increase of bulk temperature in the center tube of the FT

reactor. The increase in temperature is carried out in the inlet zone of the tube and it is

approximately 2K. The increase happens abruptly, and the hot spot should be controlled

by the coolant channel. As shown in Figure 6-28g, the hot spot occurs in the first 2m of

the reactor bed. Figures 6-28b to Figure 6-28f show the contour of reactants and

products mass fraction through packed bed reactor. Finally, the rate of mass fraction for

all species is plotted in Figure 6-33 to calculate how to reach 50% syngas conversion.

In Figure 6-29 and Figure 6-30, the 3D contours of the tube shell FT reactor are

shown, and the effect of coolant velocity over feed velocity ratio is considered as a

69

variable. The results show that by decreasing the ratio, a higher syngas conversion is

gained. The initial feed and coolant temperatures were set to 518.15 K and 513.15 K. As

shown in Figure 6-31 and Figure 6-32, the multi tubular FT reactor and coolant

temperature distribution were simulated to show the higher amount of temperature

around the tubes to remove the hot spot. According to Table 6-20, by increasing the

coolant velocity, the syngas conversion and oil productivity decreases. Also, increasing

the volume bed fraction from 40% to 80% flattens the bulk temperature distribution

because of an increase in the effective thermal conductivity in the tube, which causes

improved heat transfer between the reactor body and coolant bodies (see Figure 6-34).

As shown in Figure 6-35, the syngas conversion is investigated at different initial feed

temperatures. By increasing the feed temperature, higher syngas conversion is gained.

However, at the same space velocity, the model with 9 species has a lower conversion,

and the difference for each case is approximately 15%.

Table 6-18 Product Results in FT Reactor, 5 Species

Parameter Run 1 Run 2 Run 3 Run 4 Run 5

SV [Nml/gcat.h] 174.12 261.206 391.8 530.95 774.9

H2O [g/gcat.h] 3.91E-02 4.87E-02 3.80E-02 5.31E-02 5.34E-02

CH4 [g/gcat.h] 5.45E-03 6.84E-03 7.54E-03 7.62E-03 7.70E-03

C12 [g/gcat.h] 2.59E-02 3.23E-02 3.47E-02 3.53E-02 3.56E-02

%Xsyngas 86.29 71.547 51.348 38.504 26.565

%SOil 36.82 36.759 36.722 36.738 36.812

%SH2O 55.46 55.466 5.55E+01 55.51 55.55

%SCH4 7.717 7.8001 7.8984 7.9537 8.0021

70

Table 6-19 Product Results in FT Reactor, 9 Species

Parameter Run 1 Run 2 Run 3 Run 4 Run 5

SV [Nml/gcat.h] 174.12 261.206 391.8 530.95 774.9

H2O [g/gcat.h] 3.12E-02 3.55E-02 2.67E-02 3.73E-02 3.57E-02

CH4 [g/gcat.h] 9.18E-03 1.04E-02 1.09E-02 1.10E-02 1.11E-02

C5+ [g/gcat.h] 1.74E-02 1.95E-02 2.04E-02 2.07E-02 2.09E-02

%Xsyngas 70.74 52.93 36.841 27.55 19.058

%SOil 30.108 30.112 30.113 30.12 30.125

%SH2O 55.167 55.216 55.31 55.265 55.286

%SCH4 15.961 16.146 16.29 16.358 16.419

Figure 6-23 Syngas Conversion Profiles of FT Reactor, Tinitial: 518.15 K

0

10

20

30

40

50

60

70

80

90

100

00.511.522.533.544.555.566.577.588.59

%

Syngas

Co

nver

sio

n

Tube length [m]

SV=391 SV=528 SV=750 SV=220

71

Figure 6-24 The Rate of C5+ Production In FT Reactor

Figure 6-25 The Rate of C5+ Production in FT Reactor (Detailed View of Figure 6-17)

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

00.511.522.533.544.555.566.577.588.59

Pro

duct

ivit

y C

5+

[g/g

cat.

h]

Tube length [m]

SV=774.87 SV=522.4 SV=391.8 SV=261.19 SV=190.97

0.02

0.022

0.024

0.026

0.028

0.03

0.032

0.034

0.036

0.038

00.511.522.533.544.555.566.577.588.59

Pro

duct

ivit

y C

5+

[g/g

cat.

h]

Tube length [m]

SV=774.87 SV=522.4 SV=391.8 SV=261.19 SV=190.97

72

Figure 6-26 Oil Productivity for Different Amounts of Product Species

Figure 6-27 Syngas Conversion for Different Amounts of Product Species

1.00E-021.50E-022.00E-022.50E-023.00E-023.50E-024.00E-024.50E-025.00E-025.50E-026.00E-02

80 280 480

Oil

Pro

duct

ivit

y [

g/g

cat.

h]

Space Velocity [Nml/gcat.h]

SV=174.13, 5 species SV=217.67, 5 species SV=261.21, 5 species




SV=348.27, 10 species SV=530.95, 10 species

0

20

40

60

80

100

80 280 480

%

Syngas

Co

nver

sio

n

Space Velocity [Nml/gcat.h]

SV=174.13, 5 species SV=217.67, 5 species SV=261.21, 5 speciesSV=304.73, 5 species SV=348.27, 5 species SV=391.79, 5 speciesSV=530.95, 5 species SV=174.13, 10 species SV=217.67, 10 speciesSV=261.21, 10 species SV=304.73, 10 species SV=348.27, 10 speciesSV=391.79, 10 species SV=530.95, 10 species

73

c

b a

d

e f

74

Figure 6-28 3D Profiles of (a) Bulk Temperature, (b) CO Mass Fraction, (c) H2 Mass Fraction, (d) C5+ Mass Fraction, (e ) H2O Mass Fraction, (f) CH4 Mass Fraction, (g) Bulk Temperature at The Centerline of Tube (to get 50% syngas conversion, Tinitial: 518.15 K)

518

518.5

519

519.5

520

520.5

521

00.511.522.533.544.555.566.577.588.59

Bulk

Tem

per

ature

[K

]

Tube Length

f

a b

c d

75

Figure 6-29 3D Profiles of (a) Coolant Temperature, (b) Bulk Temperature, (c) CO Mass Fraction, (d) H2 Mass Fraction, (e ) H2O Mass Fraction, (f) C5+ Mass Fraction, (g) CH4

Mass Fraction and (h) Syngas Conversion (ucoolant/ufeed=5, Tinitial: 518.15 K)

e f

g h

a b

76

Figure 6-30 3D Profiles of (a) coolant Temperature, (b) bulk Temperature, (c) CO Mass Fraction, (d) H2 Mass Fraction, (e ) H2O Mass Fraction, (f) C5+ Mass Fraction, (g) CH4

Mass Fraction and (h) Syngas Conversion (ucoolant/ufeed=1, Tinitial: 518.15 K)

c d

e f

g h

77

a b

c d

e f

g h

78

Figure 6-31 Multi Tubular 3D Profiles of (a) Coolant Temperature, (b) Bulk Temperature, (c) CO Mass Fraction, (d) H2 Mass Fraction, (e ) H2O Mass Fraction, (f) C5+ Mass

Fraction, (g) CH4 Mass Fraction and (h) Syngas Conversion (ucoolant/ufeed=15, Tinitial: 518.15 K)

Figure 6-32 3D Profiles of (a) Coolant Temperature Plane, (b) Coolant Temperature, (c) Syngas Conversion (ucoolant/ufeed=2, Initial Temperature: 518.15 K)

Table 6-20 The Effect of Coolant Velocity on Productivity

Parameter Run 1 Run 2 Run 3 Run 4

ucoolant/ufeed 1 3 5 9

H2O [g/gcat.h] 6.83E-02 5.61E-02 3.92E-02 4.56E-02

CH4 [g/gcat.h] 9.08E-03 6.31E-03 5.29E-03 4.37E-03

C5+ [g/gcat.h] 5.07E-02 4.28E-02 3.92E-02 3.56E-02

Xsyngas 61.787 50.86 46.076 41.337

%SOil 39.602 40.655 41.129 41.624

%SH2O 55.312 53.352 5.33E+01 53.269

%SCH4 7.0923 5.9985 5.54 5.1129

a b

c

79

Figure 6-33 Mass Fraction Rate of Reactants and Products in FT Tube

Figure 6-34 Bulk Temperature Profile in Different Solid Volume Fraction

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

02468

Pro

duct

s m

ass

frac

tio

n

Tube length [m]

w_CO w_H2 w_H2O

w_CH4 w_C5+

518

518.2

518.4

518.6

518.8

519

519.2

519.4

519.6

519.8

520

00.511.522.533.544.555.566.577.588.59

B

ulk

Tem

per

ature

[K

]

Tube length [m]

void=40% void=50% void=60% void=80%

80

Figure 6-35 Syngas conversion at the center tube in different feed temperature

Conclusion and Summary

The description of GTL technology was presented in this study, and it is one of

the important processes in converting natural gas to jet fuel products. The required steam

was derived in auto thermal reforming to achieve the exact mole ratio of H2/CO. The CFD

simulation of the Fischer-Tropsch recator was done to increase oil selectivity and

productivity, and syngas conversion. The entire GTL plant was designed in Aspen

HYSYS, and the results were compared to the CFD and pilot plant setup results. Finally,

a developed kinetic model was presented to ensure the reliability of the results.

0

10

20

30

40

50

60

70

80

90

100

490 493 496 499 502 505 508 511 514 517 520 523 526 529

%

Syngas

Co

nver

sio

n

Feed Temperature [K]

SV=391 SV=420

81

ABBREVIATIONS

c concentration [mol/m3]

Kbr Permeability [m2]

X Conversion [-]

S Selectivity [-]

Re Reynolds number [-]

Pr Prandtl number [-]

h Heat transfer coefficient [W/(m2.K)]

α carbon chain growth probability factor [-]

SV space velocity [Nml/gcat.h]

82

APPENDIX A

Component heat capacity 𝐶𝑝,𝑖 = 𝑎𝑖 + 𝑏𝑖𝑇 + 𝑐𝑖𝑇2 + 𝑑𝑖𝑇

3

Mixture heat capacity 𝐶𝑝,𝑚 = ∑𝑦𝑖 𝐶𝑝,𝑖

Component conductivity 𝑘𝑖 = 𝑎𝑖 + 𝑏𝑖𝑇 + 𝑐𝑖𝑇2 + 𝑑𝑖𝑇

3

Mixture heat conductivity 𝑘𝑖,𝑚 = ∑𝑦𝑖 𝑘𝑖,𝑚

Component viscosity 𝜇𝑖 = 𝑎𝑖 + 𝑏𝑖𝑇 + 𝑐𝑖𝑇2 + 𝑑𝑖𝑇

3

Mixture viscosity 𝜇𝑖,𝑚 = ∑𝑦𝑖 𝜇𝑖

Mixture Enthalpy ∆𝐻𝑖,𝑇 = ∆𝐻298.15 +𝑇−298

550−298(∆𝐻550 − ∆𝐻298)

Effective thermal conductivity 𝑘𝑒𝑓𝑓 = 𝜀𝑘𝑖,𝑚 + (1 − 𝜀)𝑘𝑐𝑎𝑡

The coolant equations were set up in CFD simulation:

𝜌𝑐 − 𝜌𝑑{∇. [𝜑

𝑑(1 − 𝑐𝑑)𝑢𝑠𝑙𝑖𝑝 − 𝐷𝑚𝑑∇𝜑

𝑑] +

𝑚𝑑𝑐

𝜑𝑑

} + 𝜌𝑐(∇. 𝑢) = 0 (1)

𝑢 =𝜑𝑐𝑢𝑐𝜌𝑐+𝜑𝑑𝑢𝑑𝜌𝑑

𝜌 (2)

𝑢𝑑 = 𝑢𝑐 + (1 − 𝑐𝑑)𝑢𝑠𝑙𝑖𝑝 −𝐷𝑚𝑑

𝜑𝑑

∇𝜑𝑑

(3)

𝜇𝑇 = 𝜌𝐶𝜇

𝑘2

𝜖

(4)

𝑃𝑘 = 𝜇𝑇[∇𝑢𝑐: (∇𝑢𝑐 + (∇𝑢𝑐)𝑇)] (5)

𝜌 = 𝜑𝑐𝜌𝑐 + 𝜑𝑑𝜌𝑑 (6)

𝑐𝑑 =𝜑𝑑𝜌𝑑

𝜌 (7)

𝐷𝑚𝑑 =𝜇𝑇

𝜌𝜎𝑇

(8)

83

Bo, 2004 theory:

𝑚𝑙𝑔 = (𝜑𝑒𝑣𝑎𝑝 + 𝜑𝑐𝑜𝑛𝑑)𝜌𝑔 (7)

Evaporation:

𝜑𝑒𝑣𝑎𝑝 = 𝑚𝑎𝑥 (0,𝜑𝑒𝑞−𝜑𝑔

𝑡𝑒𝑣𝑎𝑝 ) (8)

𝑡𝑒𝑣𝑎𝑝 =𝐾𝑒𝑣𝑎𝑝 𝑇𝑠𝑎𝑡

𝑚𝑎𝑥(𝑇−𝑇𝑠𝑎𝑡,𝑒𝑝𝑠) (9)

𝐾𝑒𝑣𝑎𝑝 = 0.005[𝑠] (10)

Condensation:

𝜑𝑐𝑜𝑛𝑑 = 𝑚𝑎𝑥 (0,𝜑𝑒𝑞−𝜑𝑔

𝑡𝑐𝑜𝑛𝑑 ) (11)

𝑡𝑐𝑜𝑛 =𝐾𝑐𝑜𝑛𝑑 𝑇𝑠𝑎𝑡

𝑚𝑎𝑥(𝑇𝑠𝑎𝑡−𝑇,𝑒𝑝𝑠) (12)

𝐾𝑐𝑜𝑛𝑑 = 0.025[𝑠] (13)

Volume fraction at equilibrium:

𝜑𝑒𝑞 =( 𝑥𝑒𝑞)

1.1

𝑥𝑒𝑞+(1− 𝑥𝑒𝑞)𝜌𝑐𝜌𝑑

(14)

𝑥𝑒𝑞 =𝐻−𝑐𝑝,𝑙𝑇𝑠𝑎𝑡

∆𝐻𝑔𝑙 (15)

𝐻 = 𝑐𝑝,𝑙𝑇𝑠𝑎𝑡 + 𝑥𝑔∆𝐻𝑔𝑙 + 𝑐𝑝(𝑇 − 𝑇𝑠𝑎𝑡) (16)

𝑃 =𝑅𝑇

𝑉𝑚−𝑏−

𝑎𝛼

𝑉𝑚2+2𝑏𝑉𝑚−𝑏2

𝑎 =0.45724𝑅2𝑇𝑐

2

𝑃𝑐

𝑏 =0.0778𝑅𝑇𝑐

𝑃𝑐

𝛼 = (1 + (0.37464 + 1.54226𝜔 − 0.26992𝜔2)(1 − 𝑇𝑟0.5))

2

𝑇𝑟 =𝑇

𝑇𝑐

84

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