IN
DEGREE PROJECT ,
SECOND CYCLE, 30 CREDITS STOCKHOLM SWEDEN 2020 ,
Evaluation of the new Power &
Biomass to Liquid (PBtL) concept for production of biofuels from woody biomass
ROBERT DAHL
SUPERVISOR: PROF. MAGNE HILLESTAD EXAMINER: PROF. KLAS ENGVALL
KTH ROYAL INSTITUTE OF TECHNOLOGY
SCHOOL OF ENGINEERING SCIENCES IN CHEMISTRY,
BIOTECHNOLOGY AND HEALTH
Robert Dahl
Evaluation of the new Power &
Biomass to Liquid (PBtL) concept for production of
biofuels from woody biomass
Degree Project in Chemical Engineering, Second Cycle - KE200X
Stockholm, August 2020
Supervisor: Professor Magne Hillestad
Norwegian University of Science and Technology Faculty of Natural Sciences
Department of Chemical Engineering
i Acknowledgements
I want to send a great thanks to the PBtL group at Department of Chemical Engineering at NTNU, with special thanks to Professor Magne Hillestad for taking me as a master thesis student. The much required help I received from PhD Candidate Umesh Pandey, who at any hour of the day took his time any explaining the ASF theory. Postdoctoral Fellow Rao Kotteswara Putta similarly has my gratitude assisting me with Aspen Plus.
Prof. Klas Engvall for examining my master thesis project.
Prof. Hanna Knuutila for helping me find this project at NTNU.
Lastly, I want to thank Erasmus+ for funding my stay abroad in Trondheim, Norway and the
help I received from Erasmus+ coordinator Ingela Vanderzwart at KTH.
ii
Abstract
In this report, the new Power & Biomass to Liquid (PBtL) concept was evaluated. The PBtL concept is a new alternative to the more well-established Biomass to Liquid (BtL) concept where electricity is added to the process. The main purpose for developing the PBtL is that the BtL process exhibits poor carbon efficiency compared to the PBtL process. The electricity here is used to produce H 2 in electrolysis. The report is part of a larger PBtL project pursued for several years at the Department of Chemical Engineering at NTNU and SINTEF. The evaluation was done by simulating different types of low temperature Fischer-Tropsch reactors in simulation software Aspen Plus. A conversion reactor and a kinetic reactor was developed. A conversion reactor based on the result from the kinetic reactor was also developed.
The conversion-based reactor was modeled with the ASF distribution theory which describes the distribution of products formed in Fischer-Tropsch synthesis along with a method of lumping higher hydrocarbons, previously described in Hillestad [1]. The distribution between paraffins, olefins and oxygenates was based on experimental data from Shafer et al. [2] with similar operating condition with a Slurry reactor. The kinetic-based reactor was modeled with ASF distribution theory with a consorted vinylene mechanism previously described in Rytter and Holmen [3]. The reactors were added to a process for which the biomass gasification section had previously been developed by the PBtL group. The Fischer-Tropsch products were as well separated in order to evaluate the subsequent step of separation of waxes, middle distillate and lighter hydrocarbons. This enabled the option of recycling of tail gas to the Fischer-Tropsch reactor to be evaluated. A smaller contribution included addition of a biomass dryer prior the biomass gasification section. The PBtL concept is also shortly discussed from a practical point- of-view.
It was found that for the operating condition of 210 °C, 25 bar and H 2 /CO = 1.95 for the
conversion-based reactor yielded a carbon selectivity towards CH 4 and C 5+ of 14.77 and 75.40
mol C% respectively. For the same operating condition, the kinetic-based reactor yield a carbon
selectivity towards CH 4 and C 5+ of 7.612 and 86.00 mol C% respectively. It could be seen from
the conversion-based reactor that elevating temperature, pressure and H 2 /CO (to a certain
extent) results in higher carbon selectivity towards lower hydrocarbons. From the product
iii separation with the kinetic reactor it was observed that C 8 -C 16 production was higher than the C 17+ production in terms of mole flow but lower in terms of mass flow. For both models, carbon selectivity increases with carbon number and peaks around carbon number 13 and then starts to decrease.
Keywords: PBtL, Fischer-Tropsch Synthesis, Biofuels, BtL, ASF product distribution, Aspen Plus
Sammanfattning
I den här rapporten utvärderas det nya konceptet Power & Biomass to Liquid (PBtL). PBtL är ett alternativ till den tidigare och mer etablerade Biomass to Liquid (BtL) processen. Med PBtL förbättras utbytet av kol jämfört med BtL genom att elektricitet läggs till i processen.
Elektriciteten används för att producera H 2 , som används för att höja H 2 /CO förhållandet istället för att använda WGS som i vanlig BtL process. Rapporten är en del i ett större PBtL projekt som bedrivits vid Institutt for kjemisk prosessteknologi vid NTNU och på SINTEF.
Utvärderingen utfördes genom flera simuleringar av lågtemperaturs Fischer-Tropsch reaktorer i simuleringsprogrammet Aspen Plus. Omvandling och katalytiska reaktorer utvecklades och togs fram i programmet.
Produktfördelningen i omvandlingsreaktorn modellerades med ASF distribution theory tillsammans med en metod för sammanslagning av högre kolväten. Fördelningen av paraffiner, olefiner och oxygenater baserades på experimentella resultat från Shafer et al. som studerade en slurryreaktor under liknande förhållanden. Den kinetiska reaktorn modellerades med en ariant a ASF f rdelningsteori kallad consorted in lene mechanism fr n R tter och Holmen. Reaktorerna adderades till förgasningsprocess, som utvecklats tidigare av PBtL gruppen. I förgasningsprocessen förgasas biomassa till syntesgas, dvs H 2 och CO. För att möjliggöra en utvärdering av det efterföljande steget med separering av vax, mellandestillat och lättare kolväten så antogs en väl fungerande separation av Fischer-Tropsch produkterna.
En enklare separation av med flash förångning gjordes också, dels för fortsättningen av PBtL
processen och för att kunna studera tailgasrecirkulering. Ett mindre bidrag var simulering av en
torkningsprocess för biomassa innan inloppet till förgasningsprocessen. PBtL konceptet
diskuterades även ur ett praktiskt perspektiv.
iv Resultaten visar att vid driftbetingelser på 210 °C, 25 bar och H 2 /CO = 1,95 så gav omvandlingsreaktorn en kolselektivitet för CH 4 respektive C 5+ på 14,77 respektive 75,40 mol%
C. Högre temperatur, tryck och H 2 /CO förhållande i reaktorn resulterar i en högre kolselektivitet mot lägre kolväten. Vid samma driftbetingelser gav den katalysreaktorn en kolselektivitet för CH 4 respektive C 5+ på 7,612 respektive 86,00 mol% C. Resultaten visar att C 8 -C 16 produktionen var högre än C 17+ med avseende på molflöde men lägre beträffande massflöde för katalysreaktorn. Generellt så ökar kolselektiviteten med ökande kolnummer till ett maximum runt 13 för att sedan minska.
Abbreviations
BtL Biomass to Liquid
PBtL Power & Biomass to Liquid EF gasifier Entrained flow gasifier
WGS Water-gas shift
RWSG Reverse water-gas shift SOEC Solid oxide electrolysis cell
ASF Anderson Schulz Flory PFR Plug flow reactor
FTS Fischer-Tropsch synthesis FT reactor Fischer-Tropsch reactor FT products Fischer-Tropsch products
Nomenclature
𝑻 Temperature °𝐶
𝑷 𝒊 Partial pressure of component 𝑖 𝑀𝑝𝑎 𝑿 𝒊 Conversion of component 𝑖
𝑭 𝒊 Mole flow per hour for component 𝑖 WHSV Weighted hourly space velocity
H 2 Hydrogen
CO Carbon monoxide
v N 2 Nitrogen
CO 2 Carbon dioxide H 2 O Water
Concepts
Biofuels / bio-based fuels Fuels produced from organic matter/waste and is a renewable energy source [4].
Biomass A renewable energy source derived from organic matter/waste, from for example forest or agricultural industry as well as organic municipal waste.
Carbon e ciency The proportion of the biomass carbon that ends up in FT products containing at least
e carbon atoms [5].
Carbon number The number of carbon atoms a hydrocarbon molecule contains.
Growth probability, 𝜶 The probability for the hydrocarbon to react with syngas and grow with one carbon number.
Syngas The mixture of H 2 and CO.
Conversion reactor Conversion-based reactor simulates a
reactor, without specifying the type of
reactor. It works by specifying a conversion
of one of the reactants.
vi Kinetic reactor A reactor for which the type and its
associated kinetics are specified, for example Langmuir-Hinshelwood (LHHW) adsorption kinetics.
Carbon selectivity A useful measure when evaluating FTS.
Unlike normal selectivity, carbon selectivity also considers that longer hydrocarbon contains more carbon by multiplying the carbon number to the selectivity.
Tail gas The lightest hydrocarbon fraction and unreacted syngas.
FT reactor operating conditions Refers to the temperature, pressure and
H 2 /CO ratio at the Fischer-Tropsch reactor
inlet.
vii
Table of Contents
1 INTRODUCTION ... 1
1.1 S COPE OF THE PROJECT AND OUTLINE ... 2
2 BACKGROUND ... 2
2.1 T HE P OWER & B IOMASS TO L IQUID (PB T L) PROCESS ... 2
2.2 P RE - TREATMENT ... 3
2.3 B IOMASS GASIFICATION ... 6
2.4 R EVERSE WATER GAS SHIFT (RWGS) ... 7
2.5 S OLID OXIDE ELECTROLYSIS CELL (SOEC) ... 7
2.6 G AS CLEANING , WATER REMOVAL AND A CID GAS REMOVAL ... 8
2.7 F ISCHER -T ROPSCH SYNTHESIS (FTS) ... 9
2.8 U PGRADING OF FT PRODUCTS ... 12
3 METHOD ... 13
3.1 C ONVERSION - BASED REACTOR MODEL ... 13
3.1.1 Modeling the ASF product distribution theory ... 13
3.1.2 Modeling the deviation from the ASF theory ... 17
3.1.3 Conversion reactor Aspen implementation ... 17
3.2 K INETIC - BASED REACTOR MODEL ... 21
3.2.1 Consorted Vinylene Mechanism ... 21
3.2.2 Kinetics for main reactions ... 23
3.2.3 Kinetics for the deviation from the ASF theory and WGS ... 24
3.2.4 Catalyst deactivation ... 26
3.2.5 Kinetic reactor Aspen implementation ... 27
3.2.6 Conversion reactor model based on results from kinetic reactor model with variable X
CO... 31
3.3 S EPARATION OF FT PRODUCTS AND FT LOOPING ... 31
3.3.1 Kinetic reactor with base case separation ... 31
3.3.2 Kinetic reactor with C
6-C
7extraction ... 32
3.3.3 Kinetic reactor with recycling back to FT reactor ... 33
3.3.4 Kinetic reactor with recycling back to FT reactor and C
6-C
7extraction ... 34
3.4 B IOMASS D RYER ... 34
3.5 P RODUCT E VALUATION ... 36
4 RESULT & DISCUSSION ... 37
4.1 C ONVERSION - BASED REACTOR MODEL ... 37
4.2 K INETIC - BASED REACTOR MODEL ... 41
4.2.1 Conversion reactor model based on results from kinetic reactor model with variable X
CO... 43
4.3 R EACTOR MODELS DISCUSSION AND COMPARISON ... 44
4.4 K INETIC REACTOR WITH S EPARATION OF FT PRODUCTS AND FT LOOPING ... 45
4.4.1 Kinetic reactor with base case separation ... 45
4.4.2 Kinetic reactor with C
6-C
7extraction ... 47
4.4.3 Kinetic reactor with recycling back to FT reactor ... 48
4.5 B IOMASS D RYER ... 49
viii
4.6 S HORT DISCUSSION ABOUT THE PB T L PROCESS ... 50
5 CONCLUSIONS... 51
6 AREAS SUBJECT TO FURTHER WORK ... 51
REFERENCES ... 52
1
1 Introduction
One of the biggest challenges in today's world is the transition from fossil-based fuels into sustainable bio-based fuels. Power & Biomass to Liquid (PBtL) is a new concept of producing biofuels from biomass and electrical power. In short, the process consists of a biomass gasification part in which biomass is gasified into syngas as its main component. Hydrogen is then added to the syngas to increase its H 2 /CO ratio. This is followed by one or several FT reactors, in which syngas is consumed to produce hydrocarbons of various carbon lengths.
Finally, are the hydrocarbons separated and the longer hydrocarbons cracked. This report is part of PBtL project who has been pursued for several years at NTNU.
The PBtL process can produce various hydrocarbons. Bio-based aviation fuel is of particular interest, considering the aviation transport section is far from electrical and fuel cells driven powertrains. The concept with Power & Biomass to Liquid (PBtL) could be an adequate option in the near future as much of the technology for such process already are known and proven.
The fuel produced in this process is compatible with today's aircraft engines and also other types of combustion engines. It has also very low sulfur content due the low levels present in the biomass and the additional sulfur removal prior to Fischer-Tropsch synthesis.
The PBtL process is of particular interest for Norway, having 98 % renewable electricity and 22 % of productive woodland covering the country [6]. Utilizing residues from the forest industry as feedstock is very suitable for biofuel production. As stem wood usually is the main product from forest harvesting, tops, branches and stumps are often left in the forest. Stumps are yet however still cumbersome to make use of. Furthermore, is bark, a waste product in pulp and paper and sawmill industries also possible to utilize [7].
Unfortunately, there is presently no operation or logistics apparatus for collection, handling and distribution of forest residues in Norway. At the moment, buyers need to be willing to pay a price that motivates forestry companies to start collecting it. But in line with the increasing willingness to use renewable resources, there is reason to think it will start to be collected in the future. Also, since there are other applications for forest residues than for biofuel production, including biochemical products and combined heat and power (CHP). The theoretical potential of tops and branches in Norway corresponds to 7.1 million m 3 or 13.8 TWh * based on the 2018 harvest. The technical potential is estimated to about 60 to 80 % of
The volume is converted into energy by formula derived by Kofman P.D assuming a 40% moisture content
[50].
2 the available theoretical quantity. The realistic potential after environmental and production considerations is even lower. Therefore, the real is potential about half of the available technical volume of tops and branches, corresponding to about 2.5 million m 3 or 4.86 TWh * or 555 MW [7].
However, in neighboring country Sweden collection of tops and branches is rather common, giving possible learning and trading opportunities [8] [9]. Sweden has also unutilized tops and branches and stumps of 138-161 ** TWh, which is nearly as much energy that goes into the pulp and paper and sawmill industries (167 TWh) from the stem wood. Only 15 TWh is made use of, in CHP-plants [10] [11].
Similar BtL (with PBtL consideration) projects are investigated, for example at Luleå Tekniska Universitet (LTU), focusing on maximizing jet fuel production from the feedstock forest residues. A demo-plant is intended to be built in 2020 with potential commercialization in year 2023 [12].
1.1 Scope of the project and outline
The purpose of this report is to evaluate the Power & Biomass to Liquid (PBtL) process concept proposed by Hillestad et al. [5]. This is done by simulating various Fischer-Tropsch reactor models in the software Aspen Plus. A conversion reactor was first modeled and its operating conditions were varied. This is followed by a kinetic plug-flow reactor in which the conversion of CO, 𝑋 𝐶 is studied. Separation of Fischer-Tropsch products was also considered. The PBtL concept is as well discussed.
2 Background
2.1 The Power & Biomass to Liquid (PBtL) process
A previously proposed PBtL process by Hillestad et al. [5] is presented in Figure 2.1. It is a comprehensive process made up of a pre-treatment part, an Entrained flow (EF) gasifier, followed by a Reverse water gas shift reactor (RWGS) and a Waste heat boiler (WHB). A subsequent, extensive gas cleaning part is also followed in order to remove water and H 2 S. The cleaned syngas converts hydrocarbons in three Fischer-Tropsch reactors. The produced fuels are upgraded into more valuable products resulting in advanced Biofuels. As opposed to similar
138-161 TWh is from extrapolating the 20-25 TWh of tops and branches reported from Sveaskog, who has
14% of the market share in Sweden.
3 BtL processes external H 2 is added. The main reason for this is that the Fischer-Tropsch synthesis (FTS) is said to be more favorable with a higher H 2 /CO ratio, around 1.85. H 2 is produced through high-temperature electrolysis, a SOEC unit (around 850 °C) powered by electric energy, therefore the name Power & Biomass to Liquid. One benefit of this arrangement is that O 2 is also produced, eliminating the need for an air separation unit for biomass gasification.
Figure 2.1: Simplified block flow diagram for the PBtL process [5].
Adding a Water-gas shift reactor (WGS) is also an option for increasing the H 2 /CO ratio.
However, as WGS consumes CO, the carbon efficiency of the overall process becomes lower.
The carbon needed for the Fischer-Tropsch synthesis is in the form of CO.
2.2 Pre-treatment
Since EF gasifier has high requirements for the input feed, a thoroughly pre-treatment section is needed. The biomass used is wet woody biomass, namely forest residues from the forest industry. It is usually too wet to be used without drying, therefore a biomass dryer is adequate.
The dryer uses ue gas from the re heater associated to the SOEC and also possibly tail gas
from the FTS. The Pre-treatment section was also proposed in Hillestad et al. [5], see Figure
2.2.
4 Figure 2.2: Previously proposed pre-treatment process flow diagram by Hillestad et al.
[5].
Pyrolysis or alternatively torrefaction, a form of low-temperature pyrolysis, is also needed in
order to facilitate the subsequent gasification process. This is done by initiating the primary
reactions of biomass thermo-chemical conversion in which solid char and volatiles are formed,
shown in Figure 2.3, described in more detail in reaction (1). The process pre-dominantly
releases H 2 O and CO 2 , resulting in a decrease of both O/C and H/C ratios for the biomass. This
is favorable later in the gasification since lower oxygen content reduces oxidation during the
gasification [13]. The process does also make the biomass more brittle, improving the
grindability. The torrefaction process is performed without catalysts or addition of any
oxidizing medium, as air or oxygen.
5 Figure 2.3: Reaction scheme of gasification process from K. Engvall [14].
𝑏𝑖𝑜𝑚𝑎𝑠𝑠 𝛥𝐻
𝑝𝑦𝑟𝑜𝑙𝑦𝑠𝑖𝑠 𝑐ℎ𝑎𝑟 𝑡𝑎𝑟𝑠 𝐶𝑂 2 𝐻 2 𝑂 𝐶𝐻 4 𝐶𝑂 𝐻 2 𝐶 2−5 (1) The volatiles produced, i.e. steam and CO 2 as well as other gases and primary tars is directly fed into the gasifier. The primary tars contain oxygenates and primary organic condensable molecules [13]. Char is also produced at this stage which is passed into a grinder where the particle size is reduced down to particle size requirements for EF gasifiers [15]. The pyrolysis process is endothermic and can utilize ue gas from the re heater and tail gas from FTS as heating medium. The tail gas can be heated by the steam produced in the waste heat boiler (WHB). Reasons for not employing other thermochemical pre-treatment process, is that pyrolysis and torrefaction is less complex compared to for example carbonization, as such requiring less expensive equipment and material resulting in potentially best economical option [16].
The operating temperature is debatable. Kumar et al. [17] argues using that temperatures lower
than 300 °C, as in torrefaction is more favorable than pyrolysis. In the temperature window of
torrefaction, the hemicellulose decomposes from 150 to 280 °C to more un-condensable vapors
and less tar. For the higher pyrolysis temperatures, the cellulose starts to decompose with
higher yields of condensable vapors, increasing the potential risk of tar clogging in the volatile
pipe flow as the tar dew point is around 350 °C [13] [18].
6
2.3 Biomass gasification
The biomass gasification is the process converting the pretreated biomass into permanent gases and heat. The process can be varied extensively in order to influence the producer gas. For woody biomass as feedstock, the producer gas is a mixture of H 2 , CO, CO 2 , H 2 O, CH 4 , C 2 -C 5 , N 2 (of air is supplied as gasifying agent), tars, char and ash [14]. Unlike fossil fuels, woody biomass contains very little inorganic constituents [13].
It can be adjusted by temperature, pressure, gasification technology, particle size and residence time. The reactions occurring in gasification of char is first of all the endothermic gasification reactions, which is favored in high temperatures.
𝐶 𝐶𝑂 2 ↔ 2𝐶𝑂 H = +172 kJ/mol (Boudouard reaction re erse ) (2) 𝐶 𝐻 2 𝑂 ↔ 𝐶𝑂 𝐻 2 H = +131 kJ/mol (Water gas reaction) (3) The exothermic reaction includes hydrogasification.
𝐶 2𝐻 2 ↔ 𝐶𝐻 4 H = - 75 kJ/mol (The methanation reaction) (4)
There is also exothermic combustion reaction possible occurring when O 2 is added to the gasifier.
𝐶 ½𝑂 2 ↔ 𝐶𝑂 H = -111 kJ/mol (5)
𝐶 𝑂 2 ↔ 𝐶𝑂 2 H = -283 kJ/mol (6)
In the presence of CO and H 2 WGS and RWGS would occur.
𝐶𝑂 𝐻 2 𝑂 ↔ 𝐶𝑂 2 𝐻 2 H = -42 kJ/mol (WSG) (7)
Also, steam reforming is favored with higher temperatures.
𝐶𝐻 4 𝐻 2 𝑂 ↔ 𝐶𝑂 3𝐻 2 H = +159 kJ/mol (Steam reforming) (8)
The gasification technology considered is EF, due to its products mainly being syngas with negligible amounts of tar. The proposed high temperature of 1300 °C and high pressure of 40 bar in the gasifier is for the intention of maximizing syngas production. Gasification is a partial oxidation, where oxygen is with an oxygen stoichiometric value, of preferably around 0.3.
is the ratio bet een the actual molar o rate of o gen used for gasi cation to the total
stoichiometric o rate needed for complete biomass combustion [5].
7 The particle size of the biomass has high influence on the gasifier output. Generally, smaller particle sizes result in higher and better gas yields [19]. This is due to processes with larger particles being more influenced by diffusion effect between the particle and the bulk (the solid- gas reactions) and heat transfer control, affecting the conversion of biomass into products negatively. This can be explained by smaller particle having higher surface/volume ratio.
However, numerical studies of particle size by Mermoud et al. [20] indicated that diffusive effect begins to overcome already at 1.8 mm.
A study by Hernández et al. [19] indicates that in an EF gasifier with woody biomass feedstock, higher residence time yields increasing amounts of H 2 , CO, CH 4 and C 2 -C 5 at lower CO 2 . Although, circulating fluidized bed (CFB) gasifier is also an option. It behaves in similarly to EF gasifiers in terms of effect of particle size and residence time. CFB generally operates at lower temperatures and pressures [14]. However, CFB with small particle size may be satisfactory for a PBtL process.
A waste heat boiler is placed after the gasifier in order to cool the producer gas leaving the gasifier at 1300 °C. It is desirable to cool the syngas down to a temperature where it is chemically stable, while also producing 700 °C steam which later is further heated to 850 °C in a fire heater fueled by purge gas from the FTS. The high temperature steam is needed and utilized in the SOEC producing the H 2 and O 2 .
2.4 Reverse water gas shift (RWGS)
In many previous BtL processes, a WGS is put after the gasifier in order to increase the H 2 /CO.
However, an increase of H 2 comes at the expense of carbon efficiency as CO is converted into CO 2 . The CO 2 acts as an inert in the FTS, meaning it does not contribute to the FT product yield [5]. Instead a RWGS could be added, converting CO 2 to CO at the expense of H 2 . As H 2
is added in the PBtL concept, one assures a high carbon efficiency while still maintaining the H 2 /CO high.
2.5 Solid oxide electrolysis cell (SOEC)
Distinguishing for PBtL compared to usual BtL, is that a solid oxide electrolysis cell (SOEC)
is added to the process. The SOEC is added as mentioned previously to increase the H 2 /CO
ratio. Other electrolysis cells are available e.g. alkaline water electrolysis (AWE), proton
exchange membrane water electrolysis (PEMWE) and molten carbonate electrolysis cell
(MCEC). Though has SOEC the best energy efficiency at high temperatures thanks to good
kinetics at high temperatures while also being a commercially available system [5].
8 When running the SOEC is it advantageous to run it above the thermoneutral temperature (T TN ), which is the temperature the cell strives to reach. If the temperature is below T TN , the cell temperature will increase from heat generated from ohmic resistance in the cell until T TN
is reached.
Using high temperature steam of >1000 °C and exceeding the T TN is beneficial, as the kinetics of the cell promotes a high energy efficiency since the Ohmic resistance is as good as absent and the electric e cienc becomes more than 100%. Using high temperature steam also decreases the electricity needed for the cell. Running above the T TN implies that the steam input will be cooled down by the cell.
As example, setting a conversion of steam into H 2 and O 2 of 80%. A steam inlet temperature of 850°C will result in a outlet temperature of 582°C and a required electrical input of 32.4 kWh kg -1 H2 , while with a 1000°C inlet, the outlet temperature will be 592°C and the required electrical input instead 31.4 kWh kg -1 H2 .
2.6 Gas cleaning, water removal and Acid gas removal
After the WHB, the gas is cleaned from particles and ammonia through a water wash. It is then cooled down in order to remove the wash water. For the reason of FTS being sensitive to sulfur, thus causing lower CO conversion, FT productivity and lower hydrocarbons an acid gas removal process step is adequate [21]. The sulfur level into the FTS is suggested in Hillestad et al. [5] to be in the ppb region, possibly 10 ppb. The proposed method is absorption with the Selexol process (licensed by UOP LLC). It is a physical absorption with pressure swings, resulting in a cleaner syngas without intensive solvent refrigeration or thermal regeneration processes needed.
The acid gas removal part, in short, consists of a cooler, which first cools the producer gas to 25 °C in order for the H 2 O to be separated in a demister. The H 2 S is then removed from the producer gas in an absorption spray column. The solvent is regenerated with a flash drum and a stripper. Lower amounts of H 2 and CO is also absorbed, so the gas from the flash is recycled back into the absorber. The Selexol solvent desorbs the H 2 S in the stripper and then cycle repeats. Considering the H 2 S level is at 1 ppm an additional cleaning step is demanded, this is done with a ZnO adsorption bed.
One advantage with the acid gas removal is that the sulfur content in the end product will be
very low. A drawback is the CO 2 is also adsorbed in the process, impairing the carbon
efficiency. The absorbed CO 2 could have been, after FTS partly been recycled to the gasifier
9 from the tail gas recycle (see Figure 2.1). The option to only have a ZnO bed have been discussed and is subject to further studies.
2.7 Fischer-Tropsch synthesis (FTS)
The Fischer-Tropsch synthesis (FTS) is a process step where the syngas is converted into more valuable products, namely FT products or FT fuels. The FTS dates back to 1925 but is still in development. The reactions involved in FTS is formation of paraffins (alkanes) which is the main reaction and olefins (alkenes) which is formed in smaller amounts, the reactions are shown in (9) and (10), respectively. The characteristics and possible issue are the high exothermicity, one mole 𝐶𝐻 2 formed gives 145 kJ of heat, which is high compared to other catalytic reactions, as oil refining.
𝑛 𝐶𝑂 2𝑛 1 𝐻 2 → 𝐶 𝐻 2 +2 𝑛 𝐻 2 𝑂 𝑛 1, 2, … , ∞ (9)
𝑛 𝐶𝑂 2𝑛 𝐻 2 → 𝐶 𝐻 2 𝑛𝐻 2 𝑂 𝑛 2, 3, … , ∞ (10)
Side reactions are the formation of oxygenates (monohydric alcohols and ethers) shown in reaction (11) and WGS, previously shown in reaction (7).
𝑛 𝐶𝑂 2𝑛 𝐻 2 → 𝐶 𝐻 2 +2 𝑂 𝑛 1 𝐻 2 𝑂 𝑛 1, 2, … , ∞ (11)
The growth probability and consequently hydrocarbon distribution in FT products can be described in a simplified, statistically way by the Anderson Schulz Flory (ASF) distribution [1]. It states a growth probability, 𝛼 and a probability of chain termination, 1 𝛼. With a constant 𝛼, the probability of producing a molecule with carbon number 𝑖, is given by
𝑥 1 𝛼 𝛼 −1 (12)
Where the 1 𝛼 factor is the chain termination and the 𝛼 −1 factor is the previous propagation(s). See Figure 2.4 for a depiction of the ASF theory. The majority of the products are paraffins and the rest is mostly only olefins, therefore does the chain growth differs between these products. Hence, a growth probability for paraffins, 𝛼 1 and olefins, 𝛼 2 is attained, where the 𝛼 2 is 70 % of 𝛼 1 . A chain growth for oxygenates is also introduced, 𝛼 3 . The growth probabilities, 𝛼 1 , 𝛼 2 and 𝛼 3 are dependent on the several parameters including:
- Pressure. CO is more easily adsorbed onto the catalyst surface than H 2 . Thus, with
higher pressure more CO is adsorbed onto the catalyst surface and the CO promotes
hydrocarbon chain growth, i.e. the growth probability increase [22].
10 - H 2 /CO ratio. The growth probability decreases with higher H 2 /CO ratio, since a higher H 2 /CO ratio promotes hydrogenation and also a decrease in olefins and oxygenates formation [22].
- Temperature. Higher temperature gives smaller growth probability. Desorption is an endothermic process, meaning higher temperatures more easily enable desorption of formed hydrocarbons [22].
- Space velocity. A function of Reactor size and length. A higher space velocity reduces the chain growth reactions since the FT products spends less time in contact with the catalyst resulting in less re-adsorption and less further chain growth [22].
- Catalyst. Cobalt and ruthenium give generally higher growth probability, thus diesel and waxes, while iron catalysts results in a lower growth probability with lighter hydrocarbons, as gasoline and also, more oxygenates [23]. See Figure 2.5. Nickel is an inexpensive catalyst compared to Co and Ru. However, it has a tendency promoting undesired methanation [2]. Iron and cobalt are most common, but cobalt-based catalysts are today the standard in modern FTS reactors, because of low activity towards WGS [23].
Figure 2.4: Growth probability with ASF distribution, retrieved from Chemical Process
Technology, Second Edition, Wiley, 2013 [23].
11 Figure 2.5: FT Products as a function of 𝜶 with the ASF distribution. Retrieved from
Chemical Process Technology, Second Edition, Wiley, 2013 [23].
The conversion of syngas into products could be performed in a single FTS reactor or in several subsequent reactors. The estimated conversion in a single FTS reactor is suggested to be around 60%. Limiting the conversion means no risk of water partial pressure to become too high, which would result in fast deactivation of the cobalt catalyst and an increased rate of the WGS side reaction along with low syngas partial pressure. With multiple FTS reactors the products are extracted after each column while the unreacted syngas is sent to the next column. H 2 is added into every column in order to have a constant H 2 /CO ratio. The operating conditions is optimized in relation to products desired. Re-circulation of unreacted syngas is also an option.
The relevant types of FTS reactors are multi-tubular fixed bed and slurry-phase bubble columns, as shown in Figure 2.6. These reactors generally operate at lower temperatures, around 210-260 °C, with mostly cobalt catalysts, producing mainly wax and diesel. The multi- tubular ed-bed is well-proven and the most known FTS reactor. It is a column consisting of many small diameter tubes in parallel containing catalysts. Running above the upper limit could cause excessive carbon depositions leading to clogging.
The other option is a slurry-phase bubble column. It is also a low temperature process with
good heat transfer properties. The good heat removal is achieved since the catalysts are
dispersed in a liquid medium or slurr consisting of usually the products, mainly waxes. The
heat is removed from the slurry by internal cooling coils. A challenge has been the separation
of products, however today, it exists membranes which allows separation of the products from
the slurry [23].
12 Figure 2.6: a) Multi-tubular fixed bed b) Slurry-phase bubble column. BFW=boiler feed water. Retrieved from Chemical Process Technology, Second Edition, Wiley, 2013 [23].
2.8 Upgrading of FT products
The Fischer Tropsch process produces a very desirable diesel fuels, considering the longer hydrocarbons produced in FT are mostly linear, resulting in a high cetane number. It also has a negligible sulfur content. Though, focus on jet fuel is most favorable by reason of the aviation industry being highly interested in reducing its carbon emissions. International Air Transport Association (IATA) has also launched an initiative, CORSIA, where aviation technology, operational and infrastructure ad ances to continue to reduce the sector s carbon emissions.
Furthermore, is there are yet no realistic short-term alternatives to jet engines [5]. Planned commercial electric aircrafts have still limited range [24]. Therefore, is jet fuel a strategical product to be opted for.
As the FTS produces hydrocarbons of various lengths, several separation steps with flash
separation is proposed in order to produce streams with light gases (C 1 -C 5 ) and unreacted
syngas, kerosene (C 8 -C 16 ) and wax C 17+ . The wax is refined in a hydrocracking unit to produce
diesel, kerosene, naphtha and light gases of a yield around 76, 17, 4 and 5 wt.%. If gasoline is
to be a final product, the octane number needs to be increased by a hydrotreating unit [5].
13
3 Method
The work done in the report is a continuation of the Aspen file previously developed by Rao Kotteswara Putta in the PBtL group at NTNU [25]. His previous work on the file consists of a Biomass feed to process of 100 kg wet biomass/hr. A pyrolysis operating at 40 bar and 800°C and a biomass gasifier operation at 40bar and 1300°C. Furthermore, it also consists of simpler step involving ash, sulfur and CO 2 removal. An H 2 stream with a Design-spec block in order for it to feed right amount of mole flow of H 2 for yielding a specified H 2 /CO ratio. The file uses Peng Robinson Boston Mathias (PR-BM) property method. The property method is suitable for nonpolar and mildly polar mixtures under higher pressure. An ability Aspen is lacking in the properties section for pseudocomponents is that specification of melting point is missing, meaning that possible solidification and clogging are not detected by Aspen Plus.
3.1 Conversion-based reactor model
The Conversion-based reactor model simulates a FT reactor, without specifying the type or size of reactor, i.e. it is only a reactor which converts syngas to FT products. It catches the heat produced in FT by calculating heat of reaction for respective reaction and then doing a heat balance.
3.1.1 Modeling the ASF product distribution theory
The reactions implemented are previously described reactions (9), (10) and (11) but with stoichiometric coefficients for every hydrocarbon product, see reaction (13), (14) and (15). The method describing the products using the ASF theory are retrieved and more thoroughly described in Hillestad [1]. In practice, paraffins product up to C 20 (n-icosane) is added. Paraffins higher than C 20 is also produced but for convenience, those products are lumped into a pseudocomponent, named C 21+ lump with later calculated average carbon number. Similarly, olefins products up to C 10 (1-Decene) were added with C 11+ lump. CH 4 was also added into the olefins in order for the ASF theory to easier work.
For oxygenates, up to C 5 (n-Pentanol) were added with a C 6+ lump.
𝐶𝑂 𝑈 1 𝐻 2 → 𝜈 1,1 𝐶 1 𝜈 1,2 𝐶 2 ⋯ 𝜈 1, 21,∞ 𝐶 21+ 𝐻 2 𝑂 (13)
𝐶𝑂 𝑈 2 𝐻 2 → 𝜈 2,1 𝐶 1 𝜈 2,2 𝐶 2 ⋯ 𝜈 2, 11,∞ 𝐶 11+ 𝐻 2 𝑂 (14)
𝐶𝑂 𝑈 3 𝐻 2 → 𝜈 3,1 𝐶 1 𝜈 3,2 𝐶 2 ⋯ 𝜈 3, 6,∞ 𝐶 6+ 0.5𝐻 2 𝑂 (15)
14 The stoichiometric coefficients for paraffin growth are dependent on the chain growth factor for paraffins, 𝛼 1 and follows the ASF theory.
𝜈 1, 1 𝛼 1 2 𝛼 1 −1 (16)
𝜈 1, 21,∞ 1 𝛼 1 𝛼 1 21−1 (17)
where 𝑖 represents the carbon number. Furthermore, the stoichiometric coefficients for olefin growth are dependent on the chain growth factor for olefins, 𝛼 2
𝜈 2, 1 𝛼 2 2 𝛼 2 −1 (18)
𝜈 2, 11,∞ 1 𝛼 2 𝛼 2 11−1 (19)
Lastly, are the stoichiometric coefficients for olefin growth are dependent on the chain growth factor for olefins, 𝛼 3
𝜈 3, 1 𝛼 3 2 𝛼 3 −1 (20)
𝜈 3, 6,∞ 1 𝛼 3 𝛼 3 6−1 (21)
By summing up the stoichiometric coefficients multiplied with the carbon number for respective hydrocarbon product it must equal 1 since 1 CO is stated to be reacting in respective reaction, i.e.
𝑖𝜈 1,
∞
=1 ∞ =1 𝑖𝜈 2, ∞ =1 𝑖𝜈 3, 1 (22)
Summing up only the stoichiometric coefficients it equals 1 𝛼 for respective product group, i.e.
𝜈 1,
∞
=1 1 𝛼 1 (23)
𝜈 2,
∞
=1 1 𝛼 2 (24)
𝜈 3,
∞
=1 1 𝛼 3 (25)
The stoichiometric usage of hydrogen for paraffins is given through Eq. (26)
𝑈 1 ∞ =1 𝑖 1 𝜈 1, 1 ∞ =1 𝑖𝜈 1, ∞ =1 𝜈 1, 1 (26)
Using (22), (22) & Eq. (23) in Eq. (26)
𝑈 1 1 1 𝛼 1 1 3 𝛼 1 (27)
15 For olefins, the stoichiometric usage of hydrogen is given through Eq. (28). The 2𝜈 2,1 term comes from the CH 4 .
𝑈 2 2𝜈 2,1 ∞ =2 𝑖𝜈 2, 1 (28)
where 𝑖𝜈 2,
∞
=1 1 1𝜈 2,1 ∞ =2 𝑖𝜈 2, ⇒ ∞ =2 𝑖𝜈 2, 1 1𝜈 2,1 (29)
Using (29) in (28) gives
𝑈 2 2𝜈 2,1 1 1𝜈 2,1 1 2 𝜈 2,1 (30)
Lastly can Eq. (18) with 𝑖 1 be put in (30) to give
𝑈 2 2 1 𝛼 2 2 (31)
For oxygenates, the stoichiometric usage of hydrogen is similar to paraffins but differs since it produces half the H 2 O.
𝑈 3 ∞ =1 𝑖 1 𝜈 3, 1 3 2𝛼 3 (32)
With the lumping of components, the stoichiometric coefficients from carbon number 𝑁 to 𝑀 can be summed accordingly
𝜈 𝜈 , 1 𝛼 𝛼 −1 𝛼 (33)
where 1 𝛼 is the chain termination and 𝛼 −1 𝛼 is the chain propagation to the carbon number 𝑁 and then up to carbon number 𝑀.
The average carbon number of the lump from carbon number 𝑁 to 𝑀 can be calculated though
𝑛 , , − −1 − +1 −
1− − 1− (34)
which is simplified to
𝑛 , , − − −1 − +1 +
1− − (35)
The average carbon number of the lump is from 𝑁 to ∞ and thus simplified to expression (36).
𝑛 , ,∞ 𝑁
1− (36)
16 The average carbon number of the paraffins lump, 𝑛 ,𝐶 is multiplied by the molecular weight of CH 2 , 𝑀𝑊 𝐶𝐻 and then added with the molecular weight of two hydrogen atoms, 2𝑀𝑊 𝐻 in order to give the molecular weight of the paraffins lump pseudocomponent.
𝑀𝑊 𝐶 𝑛 ,𝐶 𝑀𝑊 𝐶𝐻 2𝑀𝑊 𝐻 (37)
And consequently, the molecular weight of the olefin lump pseudocomponent.
𝑀𝑊 𝐶 𝑛 ,𝐶 𝑀𝑊 𝐶𝐻 (38)
And lastly, the molecular weight of the oxygenates lump pseudocomponent.
𝑀𝑊 𝐶 𝑛 ,𝐶 𝑀𝑊 𝐶𝐻 𝑀𝑊 𝐻 (39)
The alpha model used in the conversion reactor is one formulated by Todic et al. [26]. It is a two-alpha model where 𝛼 1 , the growth probability of paraffins is seen in expression
(40).
𝛼 1 1
1+
(40)
where 𝑘 7 , 𝐾 2 , 𝑘 3 and 𝐾 1 has been simplified by Magne Hillestad [27].
𝑘 7 4.53 10 7 𝑒
. .
, (41)
𝐾 2 1.64 10 −4 𝑒
.
.
1
(42)
𝑘 3 4.14 10 8 𝑒
. .
, (43)
𝐾 1 6.59 10 −5 𝑒
.
.
1
(44)
The growth probability of olefins, 𝛼 2 is calculated according to expression (45).
𝛼 2 𝛼 1 𝑒 −0.27 (45)
No formula for the growth probability for oxygenates, 𝛼 3 has been formulated, therefore is it
assumed a value of 0.5. The boiling points of the lumps can be calculated through linear
interpolation of known boiling points of nearby carbon number alkanes, alkenes and
oxygenates.
17
3.1.2 Modeling the deviation from the ASF theory
There is a noticeable deviation from the ASF theory when it comes to methane produced, i.e.
it is higher than predicted by the theory. Reasons for this have been suggested, including mass transfer limitation in the catalyst favoring the thermodynamics for methane production instead of chain growth. Intuitively thinking it may not be so difficult to understand, hydrogenation of an adsorbed CH 2 should be a more simple reaction than the bimolecular chain growth [22].
Therefore, is an extra CH 4 producing reaction (46) added in addition to the extra CH 4 produced in the olefins reaction (14). The ethylene deviation is taken from Pandey et al. [28], due to the ethylene deviation in Hillestad [1] is described with kinetic and this model is solely conversion-based.
𝐶𝑂 3𝐻 2 → 𝐶𝐻 4 𝐻 2 𝑂 (46)
Moreover, the production of ethylene is much lower than predicted by the ASF theory, this is primarily due to the lower stability of ethylene intermediary species. Due to this fact, a significant fraction of ethylene supposed to be formed based on the ASF theory either gets converted to ethane as in reaction (47) or polymerizes to give higher olefins as in reaction (48) [28].
Considering it is a conversion reactor that is being modeled, reaction (48) can replaced with reaction (49) and then increasing the 𝑋 𝐶 for the olefins reaction (14).
𝐶 2 𝐻 4 𝐻 2 → 𝐶 2 𝐻 6 (47)
𝐶 2 𝐻 4 𝐶𝑂 𝐻 2 → 𝐶 3 𝐶 4 ⋯ 𝐶 11+ 𝐻 2 𝑂 (48)
𝐶 2 𝐻 4 𝐻 2 → 𝐶𝑂 3𝐻 2 (49)
3.1.3 Conversion reactor Aspen implementation Assumptions conversion reactor model
- No WGS reaction
- n-paraffins, 1-olefins and 1-oxygenates (alcohols) is the only formed hydrocarbons - No consideration of branching of hydrocarbons
- 5 °C increase after FT Reactor, because of a not 100% efficient cooling.
- Pressure drop 1 bar in FT reactor - 𝑝 𝐶 = 0.5 Mpa.
- The chain growth factors, 𝛼 1 , 𝛼 2 and 𝛼 3 are constant throughout the reactor
18 - Deviations from the ASF theory for oxygenates are neglected
- The chain growth factor for oxygenates, 𝛼 3 = 0.5 - Steady state
- No deactivation of catalyst considered - No heat losses
Th 𝑝 𝐶 varies notable along the length of the reactor. 𝑝 𝐶 is included in the calculation of 𝛼, because the calculator block in Aspen do not allow real time reading of the 𝑝 𝐶 along the length of the reactor, it can only be read at the reactor inlet. Therefore must 𝑝 𝐶 be assumed a mean value along the reactor. An appropriate average 𝑝 𝐶 along the reactor of 0.5 MPa is suggested by Pandey [27], deriving from experimental studies with similar conditions. In Figure 3.1, the conversion-based FT reactor model can be seen. The main reactions, oxygenates and the extra CH 4 reactions were performed in the FT-C Rstoic reactor and the ethylene deviation in the R- C2H4 Rstoic reactor for reasons described below.
Figure 3.1: Conversion reactor with boiling water reactor (BWR) in Aspen Plus.
Reactions (13), (14) and (15) were added into a Rstoic block named FT-C
along with the additional methane forming reaction (46), see Figure 3.2. In the conversion-
based model the conversion of CO, 𝑋 𝐶 was stated for each reaction. The 𝑋 𝐶 was adjusted for
each reaction in order for it to yield approximately same carbon selectivity (C%) as literature
values found in Shafer et al. [2]. Shafer et al. reported selectivities towards methane, paraffins,
olefins and oxygenates for a setup with a 25% Co -Al 2 O 3 catalyst at 220 °C, 27.6 bar, WHSV
19
= 2 5, H 2 /CO = 2 in a slurry reactor (CSTR), shown in Table 3.1. A total 𝑋 𝐶 was opted to 60% in a Rstoic block in Aspen plus.
Figure 3.2: Main conversion reactor FT-C with reactions (13), (14), (15) and (46).
Table 3.1: Experimental results from Shafer et al. [2] for isothermal continuously stirred tank reactor with 25%Co -Al 2 O 3 catalyst at 220 °C, 27.6 bar, WHSV = 2–5,
H 2 /CO = 2.
Product group Carbon selectivity (C%)
Methane 14.98
Paraffins 66.10
Olefins 16.42
Oxygenates 2.51
Rstoic have the option to choose selectivity to be stated instead of the conversion of component.
However, Rstoic have not the option to choose a selectivity to a specific group of products (paraffins and olefins etc. respectively), only a product.
The ASF distribution theory for the reactions was calculated in a Calculator block named FT- CALC. The 𝛼 1 and 𝛼 2 expression (40) and (45) were added to the FT-CALC. The average carbon number, subsequent molecular weight and normal boiling point for the lumps pseudocomponents were as well calculated in the FT-CALC block.
The 𝛼 1 and 𝛼 2 with process parameters of 220 °C, 27.6 bar, H 2 /CO = 2 and associated ASF distribution were also pre-calculated in MS Excel and added into the FT-C reactor, since Aspen plus require the stoichiometry when it processes the input specification of the simulation.
The ethylene deviation reactions (47) and (49) were added to a separate Rstoic as those reactions work with conversion of C 2 H 4 and the C 2 H 4 can only be read after the FT-C reactor.
Reactions for block R-C2H4 are shown in Figure 3.3. The fractional conversion was set to 0.27
for reaction (47) and 0.67 for reaction (49) after Pandey et al. reports a reaction ratio for
20 reaction (47) and (48) of 0.27 and 0.67 respectively meaning 0.94 (0.27+0.67) or 94% of the ethylene predicted by the ASF theory is reacted to C 2 H 6 or to higher olefins [28].
Figure 3.3: R-C2H4 conversion reactor for the ethylene deviation reaction.
The BWR simulates the cooling of the FT reactor. The coolant used here was with water at 10 kmol/hr at 25°C which was vaporized to steam by the heat of reaction from the reactions in FT-C and R-C2H4, shown in Figure 3.4.
Figure 3.4: Addition of Heat of Reaction for the reactions in FT-C and R-C2H4.
When the 𝑋 𝐶 for each reaction was adjusted so that it gave approximately same carbon
selectivity as Shafer et al. [2] the process parameters were changed to 210°C, 25 bar and
H 2 /CO=1.95. A pressure drop of 1 bar was set at the R-C2H4 block outlet. The H 2 /CO,
pressure, temperature was also varied separately to 1.60, 20 bar and 220°C to study to effects.
21
3.2 Kinetic-based reactor model
The Kinetic-based reactor model simulates the FTS as a plug flow reactor, i.e. a multi-tubular fixed bed reactor. The block used in Aspen Plus is the RPlug. It uses Langmuir-Hinshelwood (LHHW) adsorption kinetics and the consorted vinylene mechanism, a modified ASF distribution model.
3.2.1 Consorted Vinylene Mechanism
In the kinetic modelling, the model used is the ASF but with a probabilistic distribution between the olefins and the paraffins, a consorted vinylene mechanism, proposed by Rytter and Holmen [3]. The oxygenates are not included in this model. A probability, 𝑏 is introduced which describes the probability to form an olefin, 𝐶 with carbon number, 𝑖. If not an olefin is formed then a paraffin, 𝐶 with carbon number 𝑖 is formed. See Eq. (50) and (51).
𝐶 𝑏 𝐶 (50)
𝐶 1 𝑏 𝐶 (51)
The 𝑏 is a function of β and is calculated through
𝑏 β −1 (52)
Beta, β is in itself a function of the partial pressure of CO, 𝑝 𝐶 , H 2 , H 2 O and temperature.
Although, Pandey et al. [28] reports a low dependence on partial pressure of H 2 and H 2 O while higher dependence of residence time which in more extent affect the 𝑝 𝐶 . Therefore, is a more straightforward β-model without including 𝑝 𝐻 and 𝑝 𝐻 pertinent.
β 1
1+
(53)
where
𝑘 β 𝑇 𝑘 β,r 𝑒 − −
.(54)
and 𝑘 β, 0.1135 𝑀𝑝𝑎 at 𝑇 483 𝐾, 𝐸 β 42.69 , 𝑅 8.314
,𝐾 .
A main alpha, 𝛼 is introduced , see expression (55), which describes the probability to overall
hydrocarbon chain growth. The expression for 𝛼 used in this simulation is a model developed
by Ostadi et al. and modified by Rytter et al. after Oosterbeek and Bavel reported 𝛼 independent
of 𝑝 𝐻 [28].
22
𝛼 1
1+ (55)
where 𝑧 0.17, 𝑦 0.095 and 𝑘 𝑇 is desribed in Eq. (56).
𝑘 𝑇 𝑘 , 𝑒 − − (56)
with 𝑘 , 0.1117 𝑀𝑝𝑎 at 𝑇 483𝐾 and 𝐸 4.77 .
Alpha 2, 𝛼 2 is also introduced which specifically describes the growth probability for olefins.
𝛼 2 𝛼β (57)
Thereby can a reaction be formulated for olefins and paraffins respectively as shown in (58) and (59). Olefins are lumped at 𝐶 11+ and Paraffins at 𝐶 21+ again.
𝐵𝐶𝑂 𝐵𝑈 2 𝐻 2 𝐵 𝑏 1 𝜈 1 𝐶 1 𝑏 2 𝜈 2 𝐶 2 ⋯ 𝑏 11 𝜈 11,∞ 𝐶 11+ 𝐵𝐻 2 𝑂 (58)
1 𝐵 𝐶𝑂 1 𝐵 𝑈 1 𝐻 2 1−𝐵 1 𝑏 1 𝜈 1 𝐶 1 1 𝑏 2 𝜈 2 𝐶 2 ⋯ 1
𝑏 21 𝜈 21,∞ 𝐶 21+ 1 𝐵 𝐻 2 𝑂 (59)
𝐵 describes the share of the reacted CO that reacts into olefins and 1 𝐵 describes the share of CO reacted that is not reacted into olefins, i.e. is reacted into paraffins and is calculated through
𝐵 1−
1− (60)
The left-hand side of Reaction (58) and (59) can be simplified by division of 𝐵 and 1 𝐵 respectively.
𝐶𝑂 𝑈 1 𝐻 2 𝐵 𝐶
𝐵
𝐶
𝐵 ⋯
,𝐶
𝐵 𝐻 2 𝑂 (61)
𝐶𝑂 𝑈 2 𝐻 2 1−𝐵 1− 𝐶
1−𝐵
1− 𝐶
1−𝐵 ⋯ 1−
,𝐶
1−𝐵 𝐻 2 𝑂 (62)
The stoichiometry for H 2 comsumption for production of olefins, 𝑈 1 and paraffins, 𝑈 2 is calculated in (64) and (63) respectively.
𝑈 1 2 1 𝛼 2 (63)
𝑈 2 2 1−
1−𝐵 1 1−
1− (64)
23 The stoichiometric coefficient for olefins is then
𝐵
β 1−
1 𝛼 2 2 𝛼 2 −1 (65)
The stoichiometric coefficient for the olefins lump is calculated through
,
𝐵 1 𝛼 2 𝛼 2 11−1 (66)
The stoichiometric coefficient for the paraffins can be described as the overall formation subtracted with the olefin formation.
1−
1−𝐵
1−β 1−
1−𝐵
1
1−𝐵 1 𝛼 2 𝛼 −1 1 𝛼 2 𝛼 2 −1 (67) The stoichiometric coefficient for the paraffins lump is calculated through
1−
,1−𝐵
1−β 1−
1−𝐵
1
1−𝐵 1 𝛼 𝛼 11−1 1 β 1−
1− (68)
The carbon number for the lumps needs to be calculated as the molecular weights of the lumps needs to be specified in order for them to be used in the Aspen Plus simulation. Firstly, the carbon number of the olefins lump, 𝑛 ,𝐶 .
𝑛 ,𝐶 11 1
1− (69)
The molecular weight of the olefins lumps is calculated as in expression (38). The carbon number of the paraffins lump pseudocomponent is a derivation based on the overall formation minus the olefin with results in expression (70). Subsequently, the molecular weight of the paraffins lumps is equally calculated as in expression (37).
𝑛 ,𝐶
−
−
(70)
3.2.2 Kinetics for main reactions
The kinetics describing the FTS is of the type Langmuir-Hinshelwood-Haugen-Watson
(LHHW) adsorption kinetics. There are many models developed since the introduction of the
Fischer-Tropsch reactor. The kinetics considered in this work differs slightly from many earlier
models since it includes the effect of water, which do effect the FT reaction rate, 𝑟 , see
expression (71) [29] [28].
24 𝑟
1+∑ 𝐾
(71)
where 𝑘 is the known as the kinetic factor, while the rest of the factors in the numerator is known as the driving force expression. In this model, only the forward rate expression for the kinetics is considered. The expression in the denominator is known as the adsorption terms.
The model used in the simulation is a model developed by Rytter and Holmen [3] and fitted by Pandey et al. [28], shown in the expression (72). This model was fitted through a laboratory reactor of 1 cm diameter and 20 cm long with a 20% Co/0.5Re -Al 2 O 3 commercial catalyst with temperature sets of 210 and 230°C while variying the H 2 /CO ratio five time from 1.12 to 2.55 at 20 bar. The 𝑋 𝐶 was varied from 10 to 75%. Experimental points was also taken with 2 bar water (totaling 22 bar) in the feed.
𝑟
/
1+
1+ + +
(72)
where 𝑘 is described in eq (73). 𝑘 𝐻 0.1, 𝑎 11.96 1 , 𝑏 1.10 1
/, 𝑓 1.25 1
/.
𝑘 𝑘 𝑒 − − (73)
with 𝑘 7.05
, ,
., 𝐸 92.02 .
The kinetic expression 𝑟 is parted on the olefin reactions and paraffin reactions according to the consorted vinylene mechanism, shown in the expressions below [28].
𝑟 𝐵𝑟 (74)
𝑟 1 𝐵 𝑟 (75)
3.2.3 Kinetics for the deviation from the ASF theory and WGS
The methane deviation from the ASF theory is modelled as a separate reaction like in the conversion reactor.
𝐶𝑂 3𝐻 2 𝐶𝐻 4 𝐻 2 𝑂 (76)
25 The kinetic expression is the same as the 𝑟 expression in (72) but with a CH 4 kinetic factor, 𝑘 𝐶𝐻 , which is the kinetic factor, 𝑘 multiplied with stoichiometric coefficient for CH 4 , 𝜈 1 . The 𝑝 𝐻 is also added as it observed in Rytter and Holmen [30] that methane production increases with increasing 𝑝 𝐻 .
𝑟 𝐶𝐻 𝑘 𝐶𝐻 𝑝 𝐻 𝑟 𝐶𝐻
,𝑘 𝐶𝐻 𝑝 𝐻 1 𝛼 2 𝑟 (77)
where 𝑘 𝐶𝐻 6.38. Experimentally fitted by Pandey et al. [28].
The deviation for the ethylene is the same as used in the Conversion-based reactor model from Pandey et al. [28] which is formulated in two equation. Again, one part of the ethylene is to react with H 2 and form ethane. Another part is further polymerized to higher olefins with the distribution described in (61). The last part of the ethylene formed is retained as ethylene. The first ethylene deviation again reaction (48) but with kinetic expression (78). Similar to expression (77), the 𝑟 is multiplied with 𝜈 2 to get the 𝑟 𝐶 𝐻 −𝐶 𝐻 .
𝑟 𝐶 𝐻 −𝐶 𝐻 𝑘 𝐶 𝐻 −𝐶 𝐻 𝑟 𝐶 𝐻 , 𝑘 𝐶 𝐻 −𝐶 𝐻 1 𝛼 2 𝛼𝐵𝑟 (78)
where 𝑘 𝐶 𝐻 −𝐶 𝐻 0.27. Experimentally fitted in Pandey et al. [28].
The reaction of ethylene to higher olefins is a slightly complicated since it require another calculation of the stoichiometric coeffients in order for it to follow the ASF distribution. The associated reaction and kinetic expression is slightly modified compared how to Pandey et al.
[28] formulated it. Instead of being a consumption of CO expression as in (48), it is formulated as a consumption of C 2 H 4 expression, which it in reality is, see reaction (79). The water product gets cancelled which is explained below.
𝐶 2 𝐻 4 → 𝐶 3 𝐶 4 ⋯ 𝐶 11+ (79)
In the calculation of the stoichiometric coefficent for C 2 H 4 , the stoichiometric coefficient for CH 4 ,
𝐵 and C 2 H 4 ,
𝐵 from reaction (61) are subtracted from the stoichiometric coeffient of CO, 1, to the get stoichiometric coeffient for the C 2 H 4 as reactant. The stoichiometric coeffient for H 2 , 𝑈 1 is also subtracted with
𝐵 and
𝐵 .
1 𝐵 𝐵 2 𝐶𝑂 𝑈 1
𝐵 3
𝐵 4 𝐻 2 → 𝐶
𝐵
𝐶
𝐵 ⋯
,
𝐶
𝐵 1
𝐵 𝐵 2 𝐻 2 𝑂 (80)
26 Accordingly, the CO is replaced with C 2 H 4 as if the higher olefins are produced from C 2 H 4
instead of CO. The C 2 H 4 can be seen as an expression of the reaction of CO and H 2 .
2𝐶𝑂 4𝐻 2 ↔ C 2 H 4 2𝐻 2 𝑂 (81)
Solving for CO equals 𝐶𝑂 ↔ C H
2 𝐻 2 𝑂 2𝐻 2 (82)
Reaction (82) in reaction (80) gives
1− − 2
2 𝐶 2 𝐻 4 𝐶
𝐵
𝐶
𝐵 ⋯
,𝐶
𝐵 (83)
The associated kinetic expression is
𝑟 C H − r 𝑘 C H − r 𝑟 𝐶 𝐻 , 𝑘 C H − r 1 𝛼 2 2 𝛼 2 𝐵𝑟
(84) where 𝑘 C H − r 0.67. Experimentally fitted by Pandey et al. [28].
The WGS reaction is also included as a side reaction. CO 2 is observed to be formed in smaller amounts the FTS. It has also been observed that the CO 2 increases with increasing 𝑝 𝐻 and desreases with increasing H 2 /CO ratio [31]. A simple kinetic model for the WGS expression has been formulated by Moe [32].
𝑟 𝑘 𝐶 𝑝 𝐶 𝑝 𝐻 1
𝐾 𝑝 𝐶 𝑝 𝐻 (85)
where 𝑘 𝐶 and 𝐾 is described in (86) and (87) respectively.
𝑘 𝐶 𝑘 𝑒 − (86)
with 𝑘 119.14
, , . Experimentally fitted by Pandey et al. [28].
𝐾 𝑒
.
