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Natural gas conversion
The Reforming and Fischer-Tropsch processes
by
Sarah Lögdberg
Hugo A. Jakobsen
TKP 4145 Reactor technology
Compendium
ii
Prelude
This compendium consists of two parts. The first part deals with natural gas reforming in
general, whereas the second part treats the modelling of trickle bed reactors and the Fischer-
Tropsch synthesis.
iii
Table of contents
Prelude .................................................................................................. ii
Reforming of natural gas .................................................................... 1
1. Introduction ........................................................................................................................ 2
2. Different natural gas reforming concepts ........................................................................... 3
2.1 Reactions and thermodynamics: ................................................................................... 5
2.2 Steam reforming (tubular reforming) ........................................................................... 8
2.3 Adiabatic pre-reforming ............................................................................................. 13
2.4 Partial oxidation ......................................................................................................... 14
2.5 Autothermal reforming and secondary reforming ...................................................... 15
2.6 Heat exchange reforming ........................................................................................... 18
3. Different reforming concepts for different applications................................................... 21
3.1 Introduction ................................................................................................................ 21
3.2 Methanol synthesis ..................................................................................................... 23
3.3 Ammonia synthesis .................................................................................................... 24
3.4 Fischer-Tropsch synthesis .......................................................................................... 24
4. New reforming concepts under development ................................................................... 26
5. Some notes on modeling of CPOX and ATR .................................................................. 28
Modeling of trickle-bed reactors ...................................................... 31
1. Fixed-bed reactors vs trickle-bed reactors ....................................................................... 32
2. Dispersion model equations for multiphase systems ....................................................... 34
3. Special issues in modeling of trickle-bed reactors ........................................................... 38
3.1 Introduction ................................................................................................................ 38
3.2 Catalyst wetting and relating kapp to k ........................................................................ 39
3.3 Liquid hold-up and mass transfer ............................................................................... 41
3.4 Heat transfer ............................................................................................................... 44
3.5 Effectiveness factor .................................................................................................... 45
3.6 Backmixing ................................................................................................................ 46
3.6.1 One-parameter models ............................................................................................ 46
3.6.2 Two-parameter model ............................................................................................. 49
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3.7 Conclusion .................................................................................................................. 51
The Fischer-Tropsch process ............................................................................................... 52
4.1 Introduction ................................................................................................................ 52
4.2 Different reactor types and reaction conditions ......................................................... 54
4.2.1 HTFT ....................................................................................................................... 55
4.2.2 LTFT ....................................................................................................................... 56
4.3 Scope of the work ....................................................................................................... 58
4.4 Modeling of the trickle-bed FT-reactor ...................................................................... 59
4.4.1 Wang et al. [2003] ................................................................................................... 61
4.4.2 Jess et al. [1999] ...................................................................................................... 70
4.5 Modeling of the slurry phase reactor .......................................................................... 73
4.5.1 Different flow regimes and estimation of gas hold-up ............................................ 73
4.5.2 Mass transfer ........................................................................................................... 76
4.5.3. Mixing .................................................................................................................... 77
4.5.4 Heat transfer ............................................................................................................ 78
4.5.5 The model ................................................................................................................ 78
4.5.6 The results ............................................................................................................... 81
5. Conclusion/discussion ...................................................................................................... 83
References ........................................................................................... 85
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Reforming of natural gas - The different concepts
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1. Introduction
The largest natural gas reserves are located in the former USSR, Iran and Qatar. There are
also large reserves in the North Sea. About 40 % of the resources are in the former USSR.
[www.gasforeningen.se] In 1993, Norway produced 1.1 % of the world natural gas production
[Kirk-Othmer, 1995]. Natural gas stands for approximately 21 % of the world’s energy
consumption [www.iea.org].
Except for being used as fuel, natural gas is the most common feedstock for hydrogen
production or syngas production for synthesis of base chemicals (such as methanol and
ammonia), oil refining, and in many other industrial applications (iron ore reduction,
hydrogenation of fats, production of oxo alcohols). Of the total hydrogen production by
catalytic reforming, 50 % is used for ammonia production, 10 % for methanol production and
35 % for hydrotreatment in petrochemical processes (hydrocracking, hydrodesulfurization
etc.) [Ullman’s, 1985].
Syngas may however be produced from a range of feedstocks (naphtha, coal, biomass etc.).
For heavy hydrocarbons as feedstock, partial oxidation with steam and oxygen is used for
syngas production. Also for solid feedstocks, such as coal and biomass, partial oxidation with
steam and oxygen is used for the syngas production, but in this case it is often referred to as
gasification. When producing syngas from natural gas or light hydrocarbons, steam reforming
is often the preferred route if a high H2/CO ratio is desired. Steam reforming can be
performed in the presence of oxygen or CO2. A combination of steam reforming and partial
oxidation is called autothermal reforming, in which the endothermic and exothermic reactions
are coupled [Moulijn et al., 2003].
For light hydrocarbons, partial oxidation is usually not economical since it requires an
expensive cryogenic air separation unit. However, for special applications, a high CO/H2 ratio
in the syngas is desired, which can be accomplished by partial oxidation. Partial oxidation
may be carried out with or without a catalyst [Moulijn et al., 2003].
It is desirable to operate at higher pressures, if the syngas is to be used for production of
chemicals such as methanol, ammonia or Fischer-Tropsch fuels. This is because these fuel
synthesis operate at elevated pressures, and hence a pressurized syngas removes the cost of
compressing. Furthermore, plants operating at elevated pressures can have higher capacities
due to their smaller gas volumes, which in turn means lower investment costs [Ullman’s,
1985].
The gasification process may be conducted with or without a catalyst. The use of a catalyst
makes it possible to come closer to the equilibrium conversion, but catalysts can only be used
for gaseous feeds or for distillate liquid feeds.
In this report, the state-of-the-art of reforming of natural gas into synthesis gas will be
described. Different commercial concepts will be discussed and compared, as well as
concepts being developed at present, not yet commercialised.
3
2. Different natural gas reforming concepts
Table 1 shows the approximate molar H2/CO ratios that are achieved upon different natural
gas reforming concepts. Wilhelm et al. [2001] summarized the advantages and disadvantages
with the major natural gas syngas production concepts in Table 2.
Table 1. Ways to increase/reduce H2/CO ratios, and approximate H2/CO ratios from different concepts [Wilhelm
et al., 2001].
4
Table 2. Advantages and disadvantages of several natural gas reforming concepts. SMR = steam methane
reforming, ATR = autothernal reforming, POX = partial oxidation. aSMR followed by oxygen-blown secondary
reforming [Wilhelm et al., 2001].
5
2.1 Reactions and thermodynamics:
The standard enthalpies of reaction (at 298 K) are given in brackets. The most important
reactions in steam reforming (SR) of methane are [Moulijn et al., 2003]:
1. CH4 + H2O CO + 3H2 (+206 kJ/mol)
2. CO + H2O CO2 + H2 (water-gas-shift, WGS, -41 kJ/mol)
3. CH4 + CO2 2CO + 2H2 (dry reforming, +247 kJ/mol)
The last one is called “dry reforming” because it can be used to produce a CO-rich syngas
without steam as reactant.
These main reactions may be accompanied by coke formation according to:
4. CH4 C + 2H2 (decomposition of methane, +75 kJ/mol)
5. 2CO C + CO2 (the Boudouard reaction, -173 kJ/mol)
Reactions (4) and (5) are reversible. At temperatures above 650 ºC, also higher hydrocarbons
may be thermally cracked into coke, and this reaction is irreversible. [Dybkjaer, 1995] The
carbon formation will be discussed more deeply in 2.2 Steam reforming.
In the presence of oxygen, the following reactions may occur [Moulijn et al., 2003]:
6. CH4 + ½O2 CO + 2H2 (-36 kJ/mol)
7. CH4 + 2O2 CO2 + 2H2O (-803 kJ/mol)
8. CO + ½O2 CO2 (-284 kJ/mol)
9. H2 + ½O2 H2O (-242 kJ/mol)
Since the reaction with methane and steam (1) is highly endothermic, and the reactions
involving O2 (6 – 9) are highly exothermic, the production of syngas from methane can me
allothermal or autothermal. Allothermal means that the required heat for the reaction is
produced outside of the reactor. This is the case for pure steam reforming, or when only little
amount of O2 is present. Autothermal means that all heat required for the steam reforming
reaction is formed inside of the reactor by means of exothermic reactions with O2, and hence
no external heating is needed. It is the steam/oxygen ratio that determines the mode of
operation [Moulijn et al., 2003]. When the reaction is exothermal it takes place in adiabatic
reactors.
Dybkjaer [1995] remarked that also higher hycrocarbons are present in natural gas, and that
they will react according to the following endothermal reaction:
CnHm + nH2O nCO + (n+m/2)H2 (10)
This reaction is irreversible and proceeds to full conversion. The overall heat of reaction of
(1), (2) and (10) may be positive, zero or negative, depending on the process conditions. At
low steam/carbon (S/C) ratios, and at low catalyst exit temperatures, the overall reaction is
only slightly endothermal or even exothermal, if the feed contains high concentrations of
6
higher hydrocarbons. This is due to that the CO formed in reaction (10) is converted into CH4
according to the reverse of reaction (1). In this case, the process may be carried out without
external heating, e.g. in an adiabatic pre-reformer. However, if a syngas with a low methane
content is desired, a high exit temperature is required and the overall heat of reaction will be
endothermal, and external heat is necessary [Dybkjaer, 1995].
As shown in Figure 1, at high temperatures (> 800 ºC) the equilibrium H2/CO-ratio of the
syngas reaches a value of 3/1 in case of pure steam reforming (1), and 2/1 in case of partial
oxidation (POX) (6), respectively. These values are valid if the feed has the stoichiometric
CH4/H2O and CH4/O2 ratios for the steam reforming and partial oxidation reactions,
respectively. The data in Figure 1 are obtained if respect is taken to all reactions 1 – 3 for the
left picture (a), and 1 – 3 and 6 – 9 for right picture (b). Their similar appearance is due to the
fact that the same reactions actually occur in both cases, except for the reactions in which O2
are involved which only occur in the partial oxidation case [Moulijn et al., 2003].
Figure 1. Effect of temperature on equilibrium composition at 1 bar in steam reforming of methane (a), and
partial oxidation of methane (b). H2O/CH4 = 1/1 in (a), O2/CH4 = 0.5/1 in (b) [Moulijn et al., 2003].
The peak in CO2 concentration is explained by that formation of CO2 is favoured at low
temperatures, since CO2 is only formed in exothermal reactions. At higher temperatures, the
CO2 is consumed in the endothermal reforming reactions, since these reactions are favoured
by higher temperatures [Moulijn et al., 2003].
Figure 2 shows the pressure dependence of the equilibrium composition in case of pure steam
reforming with stoichiometric feed. A higher pressure shifts the steam reforming equilibrium
towards the reactants since they compose fewer molecules. At 30 bar, a temperature of 1400
K is needed to reach an equilibrium in which only the products CO and H2 exist. However,
the maximum temperatures used in industry for steam reforming are around 1200 K due to
reactor material constraints [Moulijn et al., 2003].
7
Figure 2. Effect of temperature and pressure on equilibrium composition in steam reforming of methane.
H2O/CH4 = 1/1. (a) H2 and CH4, (b) CO, H2O and CO2 [Moulijn et al., 2003].
Since most syngas applications, such as methanol and ammonia synthesis, require high
pressures, the syngas production is often performed at high pressure in order to avoid an
expensive compression and to make the reformer size small. A high pressure is not favourable
for equilibrium of the syngas production, and hence a high temperature and steam in excess is
used as compensation, otherwise the methane conversion is too low. Figures 3 shows the
effect of pressure and the effect of steam/methane ratio on unconverted methane (the methane
slip), respectively. The most economical operation is as high pressure and temperature as
possible, the tube material setting the limits. [Moulijn et al., 2003] In other cases, the pressure
is set by the requirements of downstream separation or purification processes, such as PSA
units, membranes or cryogenic units. [Dybkjaer, 1995].
Figure 3. Effect of pressure (left) and steam/methane ratio (right) on unconverted methane as a function of
temperature [Moulijn et al., 2003]
8
2.2 Steam reforming (tubular reforming)
The overall steam reforming (SR) is highly endothermic and it is carried out at high
temperature (900 ºC) and at pressures between 15 and 30 bar [Moulijn et al., 2003] over a
Ni/Al2O3 catalyst [Bharadwaj and Schmidt, 1995]. The composition of the gas at the reactor
outlet reflects the equilibria of reaction (1) and (2) above. In some cases, it is advantageous to
add CO2 at the inlet of the reformer. This is done in order to save hydrocarbon feedstock and
decrease the H2/CO ratio in the product gas. The CO2 coming out from the reformer is then
recycled, and in some cases CO2 is also imported. CO2 then is supposed to react to form CO
via the reverse WGS-reaction, and this is favored at low S/C ratios. However, low S/C ratios
leads to high methane concentrations in the outlet. To compensate for this, a higher
temperature can be used [Dybkjaer, 1995].
The Ni-catalyst is needed since methane is a very thermodynamically stable molecule even at
high temperatures. The steam reformer consists of two sections – a convection section and a
radiant section (see Figure 4). In the convection section, methane and steam are preheated to
500 ºC [Ullman’s, 1985] by heat exchange with the hot flue gases from the fuel combusted in
the reformer furnace, and in the radiant section the reforming reactions take place in the
catalyst filled tubes which are hanging in rows inside of the reformer furnace [Moulijn et al.,
2003]. The process gas is heated gradually to approximately 800 C inside of the tubes
[Ullman’s, 1985]. All tubular reformers use catalyst inside the tubes in order to reduce the
operating temperature. This is important in order to reduce the tube stresses resulting from
high pressure and high temperatures [Froment and Bischoff, 1990]. HP-steam is also
produced in the convection zone, which may be converted to electricity which is used for
compression of the produced syngas in case of methanol or ammonia synthesis. Steam for the
reforming is produced from the heat in the product gas out from the reformer. One furnace
can contain 500 – 600 tubes with inner diameters of 70 –130 mm and lengths of 7 – 12 m
[Moulijn et al., 2003]. The wall thickness of the tubes is between 10 – 20 mm [Ullman’s,
1985]. The tubes have small diameters in order to achieve the highest possible heat flux to the
catalyst, and hence to achieve the highest possible capacity for a given amount of catalyst
[Froment and Bischoff, 1990].
The heat needed in the tubular reformer is the enthalpy difference between inlet and exit gas.
The heat duty consists of the heat of the reaction and the heat needed to bring the products to
the exit temperature. Approximately 50 % of the heat produced by combustion in the burners
is transferred to the process gas. The other 50 % exits the system in the hot flue gases from
the burners, and this heat is recovered in the convection section as described above. The
overall thermal efficiency of the reformer may approach 95 % [Dybkjaer, 1995]. In the case
where there is no need for surplus energy, and hence production of HP-steam is not desirable,
one solution is to install smaller tubes inside the reformer tube. The catalyst is placed in the
space between the main and the smaller tubes. After being preheated, the steam and methane
enter the catalyst-filled space, where it is heated and reforming takes place as usual. At the
end of the reformer tube, the gas then enters the smaller tubes and transmits some heat to the
catalyst bed before being discharged at the top. This reduces the amount of heat transmitted
by the reformer tube and hence the number of tubes and their surface area by approximately
20 % [Ullman’s, 1985].
9
Figure 4. Schematic picture of a steam reformer, showing the radiation and convection sections [Moulijn et al.,
2003].
Methane reforming can be described by a first-order reaction, irrespective of pressure. At high
temperatures the overall rate can be limited by pore diffusion, but at low temperatures the
molecular diffusion rate is much higher than the reaction rate so that the catalyst activity can
be fully used [Ullman’s, 1985]. According to Dybkjaer [1995], the overall rate in steam
reforming is limited by the heat transfer, at high temperatures. The Ni-catalyst is often in the
form of thick-walled Raschig rings, with 16 mm in diameter and height, and a 6 – 8 mm hole
in the middle. If the heat load per unit area is too high, the limits of such catalysts will be
reached, and hence smaller particles will be necessary in order to make use of more of the
catalyst. Smaller particles will however lead to increased pressure drop. Therefore, special
packing shapes such as spoked wheels or rings with several holes have been developed for
these smaller particles [Ullman’s, 1985].
The Ni-catalyst is poisoned by sulfur, which is present in practically all gaseous feedstocks,
why desulfurization is a necessary step prior to reforming (see Figure 4). The desulfurization
is often made with zinc-oxide absorption beds working at 350 – 400 ºC. Zinc oxide absorbs
several different sulfur species such as hydrogen sulfides (H2S), carbonyl sulfide and
mercaptans. However, cyclic organic sulfur compounds such as thiophenes normally require
hydrogenation over Co-Mo or Ni-Mo catalysts to H2S. The H2S is then adsorbed over the
zinc-oxide bed. The hydrogenation and zinc-oxide catalysts can be combined into one vessel.
Residual sulfur content is < 0.2 mg/m3 [Ullman’s, 1985].
There are four types of burner configurations used in tubular reforming as shown in Figure 5.
Top-fired reformers can have several parallel rows of tubes, while wall- or side-fired
reformers only can have one row. The homogeneity of the heat transfer to the tubes is
determined by burner geometry, flame length and diameter, tube-to-tube and row-to-row
spacing, fired tube length and distance from the flame to the reformer wall. The temperature
of the flame is approximately 1800 C at the hottest place, and 1100 C at the coldest place.
The heat transfer in the wall-fired reformers is mainly by the radiant side-wall, while in top-
fired reformers, the heat is transferred through radiation from the flame and hot flue gases
[Ullman’s, 1985].
10
Figure 5. Typical configurations of reformer furnaces [Dybkjaer, 1995].
Typical reformer wall temperature profiles in the top- and side-fired reformers are shown in
Figure 6 (left). The top-fired reformer is characterized by a temperature peak in the top, and it
has the highest heat flux where the metal temperature is at its maximum. The side-fired
reformer allows a better temperature control, and the maximum temperature is at the outlet of
the tube. The highest heat flux is at a rather low temperature. The side-fired reformer has a
higher average heat flux than the top fired. Moreover, the short residence time in the flames in
the side fired reformer ensures very low emissions of NOx in the flue gases [Dybkjaer, 1995].
A central problem in steam reforming is to balance the heat input through the tube with the
heat consumption by the endothermic reforming reaction, while at the same time limiting the
stress on the tubes by minimising the maximum tube wall temperature and the maximum tube
wall temperature difference. The side-fired reformer is ideally suited to solve this complex
interrelation [www.topsoe.com]. Godfrey and Shackcloth [1970] and Stehlik [1991] have
made some modelling of the radiation heat transfer from burner to steam reformer tube.
Figure 6. Left: Tube wall temperature and heat flux profiles. Top- and side-fired reformers. Start of run. Right:
Tube wall temperature profiles at start and end of run. Top- and side-fired reformers [Dybkjaer, 1995]
11
The catalyst will deactivate and lose activity upon use. It is however actually possible to
retain the productivity essentially constant by a slight increase in temperature in the lower end
of the tube, provided the required heat is available. A decrease in activity will however result
in a large temperature increase in the top of the tube, especially in case of a top-fired reformer
(see Figure 6 (right)). This is since the reaction consumes less heat when the catalyst is
deactivated, and hence the driving force for heat transfer to the process gas decreases. Due to
these effects, the top fired reformers must be designed with a considerable margin above the
maximum temperature at the start of the run. There is also risk of carbon formation at the hot
wall [Dybkjaer, 1995].
In the side-fired reformer, a decrease in catalyst activity will lead to an increase in
temperature in the upper part, as well, but the temperature will still be highest in the lower
end. Therefore, in this case, the reformer does not have to be designed for much higher
temperatures than at the start of the run [Dybkjaer, 1995].
Carbon formation
As already mentioned above, a critical parameter in steam reforming is the molar S/C molar
ratio. Carbon deposits will occur that deactivates the catalyst by cooking, if this ratio is too
low. Large carbon deposits may also block the tubes and hence cause hot-spots, which might
destroy the tubes. A higher S/C ratio reduces the carbon formation, and a common
steam/carbon ratio lies between 2.5 and 4.5, the higher value being used for steam reforming
of naphtha. A higher S/C ratio than stoichiometric, also helps to shift the steam reforming (1)
equilibrium towards the products, and hence to increase the methane conversion (reduce the
methane slip) [Moulijn et al., 2003]. The carbon is formed according to [Ullman’s, 1985]:
2CO C + CO2 (The Boudouard reaction)
CH4 C + 2H2 (Decomposition of methane)
CO + H2 C + H2O (Heterogeneous water gas reaction)
The equilibrium for the Boudouard reaction and the decomposition of methane are shown in
Figure 7 and 8. However, it has been shown that for some catalysts the thermodynamically
predicted carbon formation can be suppressed at temperatures below 700 ºC. See for instance
line (f) in Figure 7, which shows the regions where carbon was formed and not for a nickel-
uranium catalyst, and compare with (d) or (e) that show the true thermodynamic constant for
the Boudouard reaction. Theoretically, carbon could form in the inlet of the steam reformer.
However, this does not occur below 650 ºC, but only at higher temperatures when the catalyst
has a low activity so that it fails to convert sufficient methane. The addition of CO2 to the feed
gas minimizes the risk of carbon formation as shown in Figure 7 and 8 [Ullman’s, 1985].
12
Figure 7. Reaction quote for Boudouard reaction (5): 2CO C + CO2 as a function of temperature. (a)
condition of rich gas from naphtha at inlet to tubular reformer, (b) equilibrium reached for WGS (2), (c)
equilibrium reached for SR of methane (1) and WGS (2), (d) and (e) show the equilibrium constant for the
Boudouard reaction according to two different references in Ullman’s [1985], (f) boarder between carbon
formation and no carbon formation for a nickel-uranium catalyst, (g) boarder between carbon formation and no
carbon formation for a sulfided catalyst. [Ullman’s, 1985]
Figure 8. Reaction quote for methane decomposition (4): CH4 C + 2H2 as a function of temperature. (a)
equilibrium reached for SR of methane (1) and WGS (2), (b) equilibrium reached for WGS (2), (c) equilibrium
constant for methane decomposition (4), (d) and (e) show working lines for methane reforming in a reactor tube
with a high activity catalyst and a low activity catalyst, respectively (figures at the lines are fractions of tube
length from reactor inlets) (f) equilibrium constant determined by experiments from a reference in Ullman’s
[1985], (g) connecting line between equilibrium constants determined by experiments at 410 and 525 ºC from
two references in Ullman’s [1985].
13
As described above, traditionally the S/C ratios have been rather high in order to avoid carbon
formation. However, new highly active steam reforming catalysts and the use of adiabatic pre-
reformers make it possible to use S/C ratios below 1.0. The lower S/C ratio is advantageous if
a CO-rich gas is wanted, and to make the overall reaction less endothermic [Dybkjaer, 1995].
In a pre-reformer (see 2.3 Adiabatic pre-reforming), the worst carbon precursors (i.e. higher
hydrocarbons) are removed up-stream the steam reformer. This is the reason for why the main
reformer is able to operate at a lower S/C ratio [Moulijn et al., 2003].
If CO2 is added to the reformer feed in order to make the syngas richer in CO, as discussed
above, less steam is actually needed for the suppression of carbon formation since CO2 is an
oxidizing agent [Moulijn et al., 2003].
2.3 Adiabatic pre-reforming
Adiabatic pre-reforming is used for reforming of natural gas to heavy naphtha. The process is
carried out in a fixed-bed upstream the tubular reformer (see Figure 9). Higher hydrocarbons
are completely converted into CO, H2 and CH4. The reactions taking place in the pre-
reformer, except for WGS, are [Dybkjaer, 1995]:
CnHm + nH2O nCO + (n+m/2)H2 (10)
3H2 + CO CH4 + H2O (reversed 1)
In case of natural gas as feedstock, the overall process is endothermic, and therefore will
result in a temperature drop since the reactor is adiabatic. For higher hydrocarbon feedstocks,
the pre-reforming is exothermic or thermoneutral. In the pre-reformer, the temperature is
relatively low. This makes the chemisorption of sulfur to the Ni-catalyst favorable. Therefore,
traces of sulfur from the desulfurization unit will be trapped in the pre-reformer [Dybkjaer,
1995].
Figure 9. Installation of a pre-reformer [Dybkjaer, 1995].
Advantages of installing a pre-reformer [Dybkjaer, 1995]:
14
- All higher hydrocarbons are completely converted into CO, H2 and CH4. Even for
naphtha, the natural gas steam reforming catalyst may be used in the prereformer.
- All traces of sulfur are removed, which increases the life-time of the tubular steam
reforming catalyst.
- Since no sulfur is poisoning the top layer of the catalyst in the steam reformer, risks of
hot spots are reduced.
- The production capacity of the plant may be increased. By installing a new pre-heat
coil or heater between the pre-reformer and the steam reformer, the load on the
reformer is reduced. This may be used as a capacity increase or as a decrease in firing
with unchanged capacity.
- The sensitivity of the steam reformer to variations in S/C ratios and feedstock
composition is essentially eliminated.
2.4 Partial oxidation
Partial oxidation (POX) is often used for gasification of heavy oil, but all hydrocarbons are
possible as feedstocks. Since no water is added, the H2/CO ratio is lower than compared with
steam reforming or autothermal reforming. Partial oxidation of natural gas is used in small
plants and in regions where natural gas is cheap. Reaction temperatures are 1350 – 1600 C
and pressures up to 150 bar. The concentrations of different compounds in the product
mixture are determined by several equilibria, which are quickly tuned in at these high
temperatures. Partial oxidation can be performed with or without a catalyst. If a catalyst is
used, the reaction temperature can be lower, the reactions still reaching equilibrium, since the
catalyst lowers the activation energies. A lower temperature, at this high temperatures, would
not significantly change the equilibrium composition [Ullman’s, 1985].
Bharadwaj and Schmidt [1995] claimed that the development over the years has been to
minimize the use of steam in reforming due to the following disadvantages:
- Endothermic reactions
- The product gas has a H2/CO ratio of 3
- Steam corrosion problems
- Costs in handling excess H2O
The trend is to move from steam reforming to “wet” oxidation (autothermal reforming) to
“dry” oxidation. The dry oxidation is the partial oxidation of methane (6). This reaction
directly gives the desired ratio H2/CO = 2 for Fischer-Tropsch or methanol synthesis, at
temperatures > 900 ºC, as shown in Figure 1 (b) above. However, the selectivites are also
affected by the H2O and CO2 formed in the complete oxidation reactions (7, 10) [Bharadwaj
and Schmidt, 1995].
Since the partial oxidation reaction is slightly exothermic, the partial oxidation reactor would
be much more energy efficient than the energy intensive steam reformer. Since the reaction is
fast, the reactor size could be reduced significantly compared to the SR reactor [Bharadwaj
and Schmidt, 1995].
The non-catalytic partial oxidation (POX) of methane is already commercialized, for instance
in the Fischer-Tropsch plant in Malaysia, Bintulu. However, there are several problems with
POX that can be avoided by catalytic partial oxidation (CPOX). In CPOX, only
heterogeneous reactions are taking place, lower temperatures are used and no soot or
unwanted by-products are formed. No burner is used. It is mainly the absence of
15
homogeneous reactions that prevent the formation of unwanted oxidation products or flames
which can lead to soot formation. The newly developed highly selective partial oxidation
catalysts can overcome the carbon problem without any steam input. It appears that high
selectivity to CO and H2, as compared to CO2 and H2O, can be achieved at short contact
times, i.e. at high GHSVs. Results showing high methane conversion at short contact times
have also been reported. Bharadwaj and Schmidt [1995] concluded that for partial oxidation
of methane, Rh seems to be the catalyst of choice to achieve selectivities to H2 and CO above
95 %, and methane conversions above 90 %. The major engineering challenge is to ensure
safe operation with the premixed CH4/O2 mixtures. The reaction mechanism seemed to be
direct oxidation via CH4 pyrolysis at contact times shorter than 0.1 s. At longer residence
times, reforming reactions with CH4 and H2O or CO2 and shift reactions also may take place.
However, the direct catalytic partial oxidation of methane has not yet been commercialized
because it is difficult to study since it involves premixing of CH4/O2 mixtures which can be
flammable or explosive [Bharadwaj and Schmidt, 1995].
Due to the high temperatures needed in order to reach high conversions and high selectivities
to H2 and CO, the CPOX-reactor needs extremely tolerant materials, which are expensive.
Current research at NTNU/SINTEF aims at developing catalysts that can give satisfactory
high reaction rates and high selectivities to H2 and CO at lower temperatures (650 ºC). This
would be possible if the catalyst could ensure that only the partial oxidation, i.e. reaction (6),
occurs, and hence that no water is formed. Reaction (6) is exothermic and hence favored at
low temperatures, and if no water is ever present in the reactor, a syngas with a H2/CO ratio of
2.0 could theoretically be formed at low temperatures in relatively cheap steel reactors
[Bjørgum, 2006].
According to Dybkjaer [1995] and Lødeng [2006], this far, no catalyst has shown selectivity
for CPOX of methane to CO and H2 at industrial conditions (i.e. at pressures above 20 bar)
yielding less CO2 than predicted by equilibrium of methane steam reforming and WGS. In
order to be economically attractive, catalytic POX of methane must be carried out at elevated
pressure and at high methane conversion. The composition of the product gas will always be
determined by the equilibrium at the reactor exit, irrespective of whether a fixed or fluidized
bed is used [Dybkjaer, 1995].
2.5 Autothermal reforming and secondary reforming
In autothermal reforming (ATR), partial oxidation of the fuel is conducted in order to produce
the heat required for the endothermic reforming reactions of the same fuel. External steam is
added. Characteristic of the autothermal process is that the oxygen added to generate heat is
chemically bound in the product gas, which results in that the H2/CO ratio in the product gas
is lower than in other processes. Both temperature and pressure is in between what is used in
steam reforming and partial oxidation. Typical operating conditions are 850 – 1000 C and 20
– 100 bar [Moulijn et al., 2003]. One advantage with autothermal reforming is that the
thermal efficiency (i.e. ratio of heat content of reformed gas to that of the hydrocarbon feed, at
0 C) is higher (88.5 %) than that of steam reforming (81 %, including fuel) and than that of
partial oxidation (83.5 %). The maximum temperature is not limited by the tube material but
by the stability of the catalyst and the refractory lining of the reactor. Autothermal reforming
is more flexible than tubular reforming, since the higher operating temperature can
compensate for the increase in methane slip which higher pressure would cause otherwise
[Ullman’s, 1985].
16
There are two types of autothermal reformers – pure catalytic, and with a pre-combustion
unit. In the pure catalytic reformer, the reactants (methane, oxygen and steam) enter the
catalyst bed directly after mixing. This performance, without any residence time in the empty
space above the catalyst bed, results in no carbon formation, even at low preheat temperatures
of the feedstock (methane). Steam reforming reactions take place more quickly than the
Boudouard reaction equilibrium is tuned in. This makes it possible to use less steam, and
hence less oxygen, which results in a higher CO/CO2 ratio in the product gas. The drawbacks
with this purely catalytic process are high thermal and mechanical loads on the catalyst in the
immediate vicinity of the burner. Temperature variations during start-up and shut-down, and
high gas velocities lead to attrition and catalyst disintegration, which in turn makes it
necessary to replace the catalyst every two years [Ullman’s, 1985].
Reforming with pre-combustion in the empty space above the catalyst bed is preferred for
gases that have very low risk of carbon deposition, i.e. gases with high H2 content and low
hydrocarbon content. This type of reforming requires slightly more oxygen than the pure
catalytic type, and the gas velocities must be lower [Ullman’s, 1985]. For natural gas
autothermal reforming, the concept with the pre-combustion zone is preferred, and will be
described further.
ATR, as a concept, is a stand-alone process in which the entire natural gas conversion is
carried out by means of internal combustion with oxygen. Secondary reforming is a process in
which partially converted process gas from a tubular steam reformer is further converted by
means of internal combustion. The secondary reformer in an ammonia plant will be air-blown,
while that of a methanol plant will be oxygen blown. [Dybkjaer, 1995]
The autothermal reforming is usually not used on its own, due to high investment costs for
separation of the oxygen from air. It is rather used downstream a steam reformer, i.e. as a
secondary reformer, in order to reform the unreacted methane from the steam reformer. This
makes it possible to increase the pressure, without increasing the temperature, in the steam
reformer (typical conditions are 1070 K and 30 bar), which is not favourable for the
equilibrium but economically favourable if the syngas will be used for a high-pressure
chemical synthesis. In case of ammonia production (> 100 bar), N2 is needed in the synthesis
and hence air can be used instead of oxygen in the autothermal reformer, which reduces the
cost for this reformer considerably. The two-step reforming concept with a SR combined with
a secondary reformer (ATR) is suitable also for methanol syngas production, since the
methanol takes place at high pressures (50 – 100 bar) [Moulijn et al., 2003].
Since the concentration of combustibles are different in the gas going to the ATR and the
secondary reformer, different designs of burner and reactor are needed, in order to ensure
suitable heat release and avoid soot formation in each case. The ATR and the secondary
reformer are however very similar in reactor design. They consist of a refractory-lined
pressure vessel (and therefore stands higher pressures and temperatures than the steam
reformer) with a burner, combustion chamber and catalytic bed. The reactor space can be
divided into three zones (see Figure 10) in which different reactions take place according to
Table 3. [Dybkjaer, 1995]
17
Figure 10. Schematic picture of an ATR [Moulijn et al., 2003].
Table 3. Reaction zones in an ATR
Reactor equipment Reaction zones
Burner - (provide mixing)
Combustion
chamber
Combustion zone
Thermal zone
Catalyst bed Catalytic zone
Burner:
The burner provides the mixing of the feedstreams in a turbulent diffusion flame. The core of
the flame has a high temperature, often above 2000 ºC, why it is important to minimize the
transfer of heat back to the burner from the flame. This can be made by recirculating the gas
from the thermal zone back to the burner [Dybkjaer, 1995]. The burner is the key element for
the oxygen-fired reformer. Careful design of the burner nozzles ensures a flow pattern with
efficient mixing that protects the refractory and burner from the hot flame core
[www.topsoe.com]
Combustion zone:
This is the turbulent zone in which the hydrocarbon and oxygen are mixed and combusted.
Often the principle “mixed-is burnt” is valid, since the exothermic combustion reactions are
very fast. The overall oxygen to hydrocarbon ratios in the combustion zone vary between 0.55
and 0.6, which means that the conditions are substoichiometric with respect to complete
combustion. The combustion reactions are numerous complex radical reactions, but for
modeling purposes, it is often enough to describe the reactions by an overall one molecular
reaction. In case of natural gas [Dybkjaer, 1995]:
CH4 + 3/2 O2 CO + 2H2O (11)
This reaction is a mixture of (6) and (7). All oxygen is consumed in the combustion zone, and
the unconverted CH4 will continue down to the thermal zone.
18
In case of a secondary reformer, also H2 will be burnt to water in the combustion zone
according to reaction (9).
Thermal zone:
In the thermal zone, the conversion of the hydrocarbon proceeds via homogeneous gas phase
reactions. The main reactions are thermal methane reforming (1) and WGS (2). Also pyrolysis
of higher hydrocarbons takes place. [Dybkjaer, 1995]
Catalytic zone:
The catalytic zone is a fixed-bed, in which the hydrocarbons are finally converted through
heterogeneous catalytic reactions. At the exit of the catalytic zone, the gas mixture will be in
equilibrium with respect to reactions (1) and (2) at the exit temperature and pressure, and the
catalyst will destroy any soot precursors formed in the combustion chamber. The syngas is
completely free of oxygen. The top of the catalyst bed is exposed to gases with temperatures
of 1100 – 1400 ºC. A Ni-catalyst supported on a magnesia-alumina spinel has the required
activity and high-temperature stability. The overall reaction rate is mainly controlled by the
external diffusion rate, i.e. the transport rate of the reactants through the gas film surrounding
the catalyst pellets. This means that the process can be carried out at very high space
velocities, since the catalytic reaction is very fast. It is also known that higher space velocities
reduce the film thickness surrounding the pellets. The amount of catalyst needed is actually
determined by optimal flow distribution and pressure drop in the reactor [Dybkjaer, 1995]. In
synthesis gas production, a S/C ratio as low as 0.6 is industrially proven. Soot-free operation
is achieved through optimised burner design and by catalytic conversion of soot precursors
over the catalyst bed [www.topsoe.com]. The ATR or secondary reformer is operated close to
adiabatically, and hence the temperature is given by the adiabatic heat balance [Aasberg-
Petersen et al., 2003].
Applications of the concepts ATR and secondary reforming are discussed in 3. Different
reforming concepts for different applications.
When steam reforming and autothermal reforming are combined, it is logical to use the heat
produced in the latter to warm the tubes in the former one. This configuration is called heat-
exchange reformer, and is described below.
2.6 Heat exchange reforming
The idea with heat exchange reforming is that part of the heat is supplied to the tubes by heat
exchanging with process gas. Heat exchange reforming eliminates the expensive fired
reformer. In this configuration, only medium pressure steam can be recovered from the syngas
plant and electricity for the syngas compressor must be imported. Figure 11 shows two
different types of heat-exchange reformer. The left is the ICI combined reforming process and
the right the Exxon CAR (combined autothermal reforming) process. In the ICI process, 75 %
of the methane is reformed in the steam reformer at 970 K and 40 bar, and the rest is
converted in the autothermal reformer. In the Exxon CAR process, steam reforming and
partial oxidation is combined in a single reactor and reaction zone. The reactor is a fluidised
bed, and oxygen is introduced in the middle of the bed [Moulijn et al., 2003].
19
Figure 11. ICI combined reforming process (left) and Exxon CAR process (right)
In the case where two reformers are combined, the heat needed in the tubular SR reformer is
obtained from the hot product gas from the second reformer. The second reformer can be an
air- or oxygen fired ATR or a partial oxidation unit. This concept is used for production of
hydrogen or syngas for the methanol synthesis. In case of syngas production for the ammonia
synthesis, there is a poor correspondence between the heat required and the heat available in
the air-fired secondary reformer, and hence the concept of heat exchange reformer is not
common [Dybkjaer, 1995].
A problem associated with the heat exchange reforming described above, in which CO-rich
gases contact metals at high temperatures, is the risk of metal dusting corrosion. A certain gas
mixture will potentially form carbon via the exothermic Boudouard reaction at temperatures
below which the mixture satisfies the Boudouard reaction equilibrium. The temperature below
which a certain gas mixture may form carbon is called the Boudouard temperature. For a gas
mixture with a high Boudouard temperature, i.e. a CO-rich gas, the Boudouard reaction may
be catalyzed by hot metal surfaces. Therefore, it is important that a gas mixture with a high
Boudouard temperature does not come in contact with a metal surface of a slightly lower
temperature. If carbon deposition on the metal starts, there is a big risk of metal corrosion. If
carbon is deposited on the catalyst, this will of course lead to deactivation. Therefore, the
catalyst outlet temperature is always higher than the Boudouard temperature. However, a
temperature drop in the reformer could make carbon deposition possible [Dybkjaer, 1995].
Another type of heat exchange reformer is the convection reformer. In this reformer, the tubes
are heated mainly by the flue gas flowing upwards on the outside of the tubes, but also by the
reformer gas flowing upwards inside the tube [Dybkjaer, 1995].
The Topsoe convection reformer, see Figure 12 and 13, has a single burner, which simplifies
the design and control of the unit. The burner is separated from the tube section. It is called
convection reformer since it essentially means that the radiant tube section and the hot part of
the convection section are combined in a relatively small unit. The exit temperature from the
reformer is approximately 600 ºC for both product gas and flue gas after heat exchange. This
reduction in temperature means that 80 % of the fired duty is utilized in the process, compared
to 50 % in a conventional SR. In plants using the convection reformer, it is possible to
20
balance the energy need of the reformer by the energy available in the PSA off-gas, hence
avoiding the energy surplus in conventional systems [Dybkjaer, 1995].
Figure 12. The Haldor Topsoe Convection Reformer, HTCR, for hydrogen production [www.topsoe.com].
Figure 13. HTCR reformer (left) with burner, principle of heat transfer in the tubes (right) [www.topsoe.com]
21
3. Different reforming concepts for different applications
3.1 Introduction
A typical ATR plant is shown in Figure 14. It comprises a feed preheat section, an ATR-
reactor, a heat recovery section and a gas separation unit. The ATR plant contains much less
equipment than the conventional SR plant. Desulfurization is not needed if the feed is low-
sulfur natural gas. The schematic picture in Figure 14 shows the lay-out of an ATR plant for
the production of a syngas of H2/CO-ratio of 2.0. Such a lay-out can be used for syngas
production to a methanol plant, Fischer-Tropsch plant, for hydrogen production or for syngas
to an ammonia plant. In the ammonia case, air has to be used in the ATR [Dybkjaer, 1995].
Figure 14. Typical process lay-out for an ATR, for production of a syngas with H2/CO ratio of 2.0 [Dybkjaer,
1995].
The concept with secondary reforming is often used for syngas production to methanol or
ammonia synthesis. Figure 15 shows the lay-out of a plant for production of ammonia syngas.
Except from the tubular SR reformer and the secondary air-blown reformer, Figure 15 also
contains a pre-reformer. In case of natural gas as feedstock, the pre-reformer is usually not
necessary in the production of ammonia syngas. The concept with the pre-reformer is only
interesting when the steam production must be minimized.
22
Figure 15. State-of-the-art plant for production of ammonia synthesis gas [Dybkjaer, 1995].
Figure 16 shows the lay-out of the two-step production of syngas for methanol synthesis. The
conditions in the primary SR unit are mild. In the second reformer, oxygen and steam are
used. [Dybkjaer, 1995]
Figure 16. Two-step reforming plant for production of methanol synthesis gas [Dybkjaer, 1995].
The methanol synthesis takes place at 50 – 100 bar, and hence also for this application a
steam reformer and an autothermal reformer in series is sometimes used. However, since pure
oxygen is needed for the methanol synthesis, the autothermal reformer will be rather
expensive. Therefore, more than 80 % of the syngas production for methanol synthesis is
made solely with steam reforming of methane [Moulijn et al., 2003].
23
3.2 Methanol synthesis
The ideal syngas composition for methanol production is H2/CO = 2 and 5 vol% of CO2,
which increases the activity. It is actually the CO2, and not the CO, that reacts with H2 on the
catalyst surface, Cu/ZnO/Al2O3, to give methanol.
CO + 2H2 CH3OH ΔHR,298K = -90.8 kJ/mol
CO2 + 3H2 CH3OH + H2O ΔHR,298K = -49.6 kJ/mol
CO + H2O CO2 + H2 ΔHR,298K = -41 kJ/mol
The newly developed methanol catalysts have selectivities of up to 99 %. This is essential
since methanol is thermodynamically less stable than other possible products, for instance
CH4. The methanol synthesis is limited by equilibrium, why it is important to keep the
temperature low. This is obtained by quenching the reaction by cold feedgas at different
places in the bed as in the ICI-process (see Figure 17), or by several reactors with
intermediate cooling as in Haldor Topsoes process. Thus, the catalysts must be active at low
temperatures. Recycling is always performed in order to increase the overall yield. Typical
conditions for the methanol synthesis today are 50 – 100 bar and 500 – 550 K. Steam
reforming of methane is the most common way to produce the syngas, in which a H2/CO ratio
of 3 is obtained [Moulijn et al., 2003].
Figure 17. Flow scheme of the ICI low-pressure methanol plant [Moulijn et al., 2003].
In order to correct the H2/CO/CO2 ratio, prior to the methanol synthesis, either the surplus of
hydrogen is burnt or the CO content is increased. This can be done in two ways:
1. If CO2 is available it may be added to the reformer or to the raw syngas.
2. By installing an oxygen-fired ATR downstream of the SR, or by only using an ATR with
adjustment by CO2 removal in order to correct the carbon oxide content.
24
For both SR and ATR, the exit gas mixture is in equilibrium.
HP-steam is often produced at the exit of the ATR, or from the effluent gases from the
burners in the SR. This HP-steam can for instance be used to drive syngas compressors. When
SR and ATR are combined and heat exchanged, the high-temperature heat in the product gas
from the ATR is used to heat the steam reformer tubes, and hence only MP-steam can be
produced in this case.
3.3 Ammonia synthesis
The syngas for ammonia production requires a H2/N2 ratio of 3, which in 80 % is made from
steam reforming of natural gas followed by ATR with air.
N2 + 3H2 2NH3 ΔHR,298K = -91.44 kJ/mol
The equilibrium is favoured by low temperature and high pressure. However, the reaction rate
is very low below 670 K. The typical ammonia synthesis conditions are 675 K at inlet, 720 –
770 K at exit, and 100 – 250 bar. The same reactor solutions as used in methanol synthesis are
used in the ammonia synthesis, hence cold-feed quenching (see Figure 18) or several reactors
with intermediate cooling. The single-pass conversion is low (20 – 30 %) since the reaction is
limited by equilibrium, and hence recycling is necessary [Moulijn et al., 2003].
.
Figure 18. ICI quench reactor and temperature-concentration profile [Moulijn et al., 2003]
3.4 Fischer-Tropsch synthesis
The fundamentals in Fischer-Tropsch (FT) synthesis have been described thoroughly by
Lögdberg [2006]. Here, the choice of syngas production concept will be discussed. Figure 19
gives a schematic FT lay-out.
The preparation of synthesis gas from natural gas stands for 50 – 75 % of the capital cost in a
Fischer-Tropsch plant. According to Aasberg-Petersen et al. [2003], oxygen-blown ATR is
considered to be the best option for large-scale, safe and economic syngas production. Air-
blown ATR has shown to be less efficient and more cost intensive considering the whole
25
GTL-plant. The energy consumption for the air-blown alternative is much higher. The energy
consumption in the syngas section alone is 10 % higher for the air-blown ATR compared to
the oxygen-blown. The natural gas is often pre-reformed in an adiabatic reactor in order to
convert higher hydrocarbons to CH4, H2 and CO, by steam addition. The use of a pre-reformer
reduces the overall oxygen consumption.
According to Wilhelm et al. [2001], the syngas production for large-scale GTL plants in the
future will be the two-step reforming concept, or ultimately the ATR concept. They claimed
that air-blown reformers will never be competitive to oxygen-blown ones in GTL-plants,
although the investment cost for the air separation unit is eliminated. The reason is that the
air-blown reformer appears much less flexible, has lower thermal efficiency and requires high
air compression power. Furthermore, the usage of an air-blown reformer makes it impossible
to recirculate FT tail-gas, and the gas flows out from the reformer will be much larger which
in turn will increase the size of the equipment downstream the reformer. The FT-tailgas can
usually be used for power production by combustion in gas turbines. However, if it contains a
high concentration of N2, it will have a low heating value and the power production might not
be viable.
Figure 19. Schematic layout of Fischer-Tropsch plant [Aasberg-Petersen et al., 2003].
Steam to carbon ratios as low as 0.6 inside the ATR have been proven industrially. The
desired H2/CO ratio out from the ATR is, in case of FT, 2.0. This low ratio can only be
achieved at extremely low S/C ratios, see Figure 20, without recirculating CO2 [Aasberg-
Petersen et al., 2003].
Figure 20. H2/CO ratio as a function of S/C ratio in ATR outlet gas [Aasberg-Petersen et al., 2003].
26
Operation at low S/C ratios improves process economics, which is shown in Table 4.
However, low S/C increases the risk of carbon formation and hence catalyst deactivation. A
lot of research is going on in order to elucidate the causes of carbon formation, and the means
to prevent carbon formation or to destroy the carbon in the catalytic bed. Carbon formation
has been found to depend upon feed gas composition, temperature, pressure and especially
burner design. Pilot plant demonstrations have succeeded to run soot free operations at S/C
ratios as low as 0.2 [Aasberg-Petersen et al., 2003].
Table 4. Process economics with different S/C ratios [Aasberg-Petersen et al., 2003].
Bharadwaj and Schmidt [1995] seemed to have another opinion than Asberg-Petersen et al.
[2003] and Wilhelm et al. [2001]. They claimed that partial oxidation is much faster, highly
selective in a single reactor, and much more energy efficient than SR and ATR. It could hence
reduce the capital and operating costs of syngas production, and would hence be the choice of
reforming concept in the future. However, the catalytic partial oxidation (CPOX) is still not
commercialized, and was discussed more in 2.4 Partial oxidation.
According to Aasberg-Petersen et al. [2003], CPOX suffers from a highly flammable mixture
upstream the reactor at conditions relevant to GTL. The autoignition temperature is
approximately 250 ºC for the mixture, therefore the inlet temperature of the mixture to the
reactor is low, typically 200 ºC. Compared to an ATR with a pre-reformer, the CPOX concept
consumes more natural gas and oxygen for the same productivity. This is due to that much of
the natural gas must be completely oxidized in order to release enough energy to raise the
temperature in the reactor to the desired exit temperature. The exit compositions will be
essentially the same in both concepts, provided the amount and properties of the inlet streams
are the same. The authors meant that CPOX is not economical especially since it requires a lot
more oxygen than the ATR concept. Furthermore, the inherent safety constraints make the
CPOX less attractive. Air-blown CPOX could be an alternative in case of making fuels for
fuel cells, however not for FT or methanol synthesis, as discussed above.
4. New reforming concepts under development
Normal steam reforming accounts for 60 – 70 % of the investment costs of a methanol or FT-
plant based on natural gas, and the air separation unit stands for a major part. The
combination of steam reforming and autothermal reforming (the heat exchange reformer
concept) could to some extent reduce the investment and operating costs, and especially the
catalytic partial oxidation (CPOX) has a large potential to reduce the syngas production cost,
according to Moulijn et al. [2003]. CPOX is attractive since it has a high exergy efficiency,
which is due to the fact that no heat exchange is needed between a hot side and a cold side
since all reactions take place in the same vessel. Also the ICI combined reforming process
gives approximately 30 % lower exergy losses compared to a conventional steam reformer.
This is mainly due to that the need for irreversible combustion reactions to heat the furnace in
the steam reformer case is eliminated in the combined reforming process. However, Moulijn
et al. [2003] claimed that “a major breakthrough would be required to make any substantial
27
savings in the cost of producing syngas”. Some examples of such new ideas, still on the
development/demonstration stage are discussed below.
As discussed above, the air-separation unit is a cost intensive part of the syngas preparation in
the methanol and FT cases. It has, however, been shown economically advantageous to run
the ATR-burner on oxygen compared to air, as discussed above. A more promising alternative
to eliminate the air-separation unit would be a ceramic membrane reactor. In this concept, an
ionic or oxygen transporting membrane makes it possible to combine air separation and
partial oxidation in one unit. The development of such membranes is still relatively early. The
membranes typically work at 750 ºC or higher. Oxygen is transported through the membrane
with a selectivity of 100 %. On the inside of the membrane it reacts with the hydrocarbon. If
the air must be compressed in order to ensure similar pressures on the two sides, the concept
might not be economical. If ambient pressure air can be used, the membrane must have a high
mechanical strength in order not to break at the high inner pressures desired for the syngas
production. The concept with ceramic membrane reforming seems promising, but its
feasibility must be proven [Aasberg-Petersen et al., 2003].
Membranes can also be used in order to remove the produced hydrogen from the product gas
(see Figure 21). This is called membrane reforming. In this way, the amount of hydrogen
produced is not limited by the equilibrium and hence much lower temperatures can be used,
and no traditional CO2 removal system is needed. [Moulijn et al., 2003]
Figure 21. Schematic picture of membrane reforming [www.co2captureproject.org].
Another technique under development is the chemical looping reforming, in which chemically
bound oxygen is used to oxidize methane. The system consists of two reactors, as shown in
Figure 22. In the air-reactor, metal particles are oxidized to metal oxide by air (exothermic
reaction), and in the fuel reactor, methane is partially oxidized to syngas by means of the
oxygen in the metal oxide (endothermic reaction). The oxygen carrier is continuously
circulated between the two beds, thus exchanging both oxygen and heat
[www.co2captureproject.org]. A possible alternative would be to install steam reformer tubes
in the fuel reactor, letting the complete oxidation of methane on the fluidized metal oxide
particles give heat to the steam reforming reactions inside of the tubes. Actually, the heat used
for the steam reforming would be released when the oxygen carrier is oxidized in the air
reactor, and transported to the fuel reactor with the metal oxide particles. The complete
combustion of methane outside of the steam reformer tubes is actually endothermic and this
process is needed in order to reduce the metal oxide back to the metal [Rydén, 2006]. The
advantage with chemical looping reforming is that the separation of oxygen from air is simple
and, in case of complete combustion, the CO2 can be captured easily since it is free from N2.
Another advantage is that partial oxidation could be performed without forming the explosive
gas mixtures of oxygen and methane discussed in 2.4 Partial oxidation.
28
Figure 22. Schematic picture of chemical looping partial oxidation [www.co2captureproject.org].
Another concept that implies CO2 capture from hot flue gases, which is gaining interest due to
the possibility of CO2 sequestration, combined with hydrogen production, is the sorption
enhanced steam reforming process (SERP). The idea is to mix the ordinary steam reforming
catalyst with a CO2 adsorbent, e.g. dolomite or lithium zirconate. CO2 is captured, which
shifts the equilibriums of reactions (1) and (2) towards hydrogen, and makes it possible to
perform the steam reforming reaction at much lower temperatures (450 – 630 ºC) than
conventional. Hence, investment and operational costs may be significantly reduced. It is
possible to obtain a product gas containing 97 % H2 on a dry basis. After saturation, the CO2-
saturated adsorbent is regenerated by heating. Kinetic limitations of the adsorbent however
hinder the concept from being commercialized [Ochoa Fernandéz et al., 2005].
5. Some notes on modeling of CPOX and ATR
De Groote et al. [1996] made a one-dimensional heterogeneous model to simulate the
adiabatic CPOX of methane in a fixed-bed reactor. A plug-flow was assumed. The reactions
considered were CO2 reforming, steam reforming, WGS, complete combustion, the
Boudouard reaction and methane cracking, for which kinetic rate expressions were set up.
Internal gradients in the catalyst pellets were accounted for by using effectiveness factors.
These effectiveness factors were very small (between 0.05 and 0.07) for all reactions except
for the WGS (0.7). It was concluded that when air is used as oxidant, or when steam and CO2
are added to the feed, acceptable temperatures are achieved in the bed. When oxygen is used,
29
a temperature maximum of 1500 ºC was achieved, which would destroy the Ni-catalyst.
When steam is added, the amount of coke becomes negligible. CO2 also reduces carbon
formation but increases the area in which coke is formed.
Hoang and Chan [2004] made a two-dimensional heterogeneous reactor model for an
adiabatic ATR. The application of the ATR was for hydrogen production to fuel cells. They
only included four reactions, i.e. the complete combustion of methane, methane steam
reforming to CO and H2 (and to CO2) and WGS. The carbon deposition reactions were
neglected since the chosen S/C and air to carbon (A/C) ratios would ensure no formation of
carbon. The combustion chamber was actually not modeled, but the complete reactor was
assumed filled with Ni-catalyst. It was assumed that the inlet temperature of the catalyst bed
was approximately 300 ºC, which is the light-off temperature, i.e. the temperature at which
the autothermal reaction can be self-activated.
Biesheuvel et al. [2003] made a one-dimensional ATR-reactor model for conversion of
methane. They divided the model in two sections: an upstream oxidation section and a
downstream reforming section. In the oxidation section, all of the oxygen is converted, with
partial conversion of the fuel. An empirical fuel utilization ratio is used to quantify which part
of the feed is converted in the oxidation section as a function of the relative flows of air and
steam. In the oxidation section, the gas temperature rapidly increases toward the top
temperature at the intersection with the reforming section. In this section the temperature
decreases while the fuel is further converted with water and CO2 as oxidant.
For the oxidation section, no kinetics were considered. The (partial) oxidation reaction in this
zone was assumed to take place instantaneously, and all oxygen reacted, and hence no need
for a catalyst. Experimental data of the top-temperature (i.e. the temperature at the start of the
catalytic bed (the reforming section)) as a function of inlet flows led to an empirical
expression for the fuel utilization ratio, i.e. how much of the steam and CH4 that was
converted in the oxidation section and the selectivity to H2 and CO, and H2O and CO2. In
order to find this relation, the heat release and heat loss in the oxidation section and the Cp-
values of the gas mixtures must of course be taken into account. Probably, the composition of
the gas exiting the oxidation section was found by iteration by solving mass and energy
balances over the oxidation section, for a guessed outlet composition, until the calculated
temperature agreed with the measured. Hence the authors could correlate a measured top
temperature to a certain gas composition/flow at the inlet of the reforming section, and then
the actual modelling of the reformer section was made based on these inlet data.
Figure 23 and 24 show some results from the simulation.
30
Figure 23. Oxidation section in ATR. γ = S/C ratio. Top temperature on left y-axis. Utilization factor (dashed
lines, fraction of methane converted in the oxidation section) and thermodynamic CH4 conversion (solid lines)
on right y-axis. T0 = 400 ºC, adiabatic [Biesheuvel et al., 2003].
Figure 24. Temperature profiles in the reforming section at different S/C ratios. The exit temperature and the
inlet gas composition will describe the composition of the product gas. Oxygen/carbon ratio = 0.57 [Biesheuvel
et al., 2003].
31
Modeling of trickle-bed reactors
- The Fischer-Tropsch reaction
32
1. Fixed-bed reactors vs trickle-bed reactors
In a conventional fixed-bed reactor, only gases and solid phases (the catalyst particles) are
present. This makes the modeling rather straight-forward. However, if a liquid phase is added
to the fixed bed, the modelling becomes a bit more complex. This concept is called trickle-
bed, and often means that the reaction takes place between a gaseous and a liquid reactant, the
gaseous reactant having to diffuse through the liquid phase to the catalyst surface and there
react with the other reactant already present in the liquid.
The downflow cocurrent column packed with catalyst may operate in mainly two different
flow regimes: “the trickle flow” in which the gas phase is continuous and the liquid phase
dispersed, and “the bubble flow” in which the gas phase is dispersed and the liquid phase
continuous. Increasing the gas flow rate will eventually lead to pulsed flow. Figure 1
illustrates the different regimes.
Figure 1. Flow regimes in cocurrently operated packed bed. G is the gas load in [kg/m
2, s] and L the liquid load
in [kg/m2, s] [Gianetto and Silveston, 1986].
The flow patterns in a trickle-bed range between gas-continuous and liquid-continuous
regimes, depending on shape and size of particles as well as on physical properties and flow
velocities of the gas and liquid
Trickle-beds are widely used in the refineries for processes such as hydrodesulfurization of
different petroleum fractions, hydrocracking of heavy gasoils and atmospheric residues,
hydrotreating of lubricant oils and for hydrogenation [Froment and Bischoff, 1990]. Trickle-
beds are also often used in the Fischer-Tropsch synthesis, in which syngas is converted into
hydrocarbons. In this case, the reactants are gaseous and the products gases and liquids.
33
The trickle-bed, with its stationary catalyst bed, is preferred to a slurry type operation, in
which the catalyst is suspended in the liquid, when the gas flow rate is relatively low because
it leads to a gas and liquid flow pattern that better approximates the plug flow. A plug flow,
with its high reactant concentration, is favourable if the total reaction order is positive. For
high gas flows, the slurry operation might be better suited since it avoids the pulsed flow
regime that can come up in a fixed-bed. However, Huang et al. [2004] reported that there
might be some advantages to work in the pulsing flow mode. The heat transfer is often poor in
the conventional trickle-flow regime. This is undesirable especially if the reaction is
exothermic, due to risk of run-away, and also due to formation of undesired by-products. One
way to enhance the heat transfer in trickle-beds is to operate in a high gas-liquid interaction
regime called pulsing flow by Huang et al. [2004]. In the pulsing flow mode, flows of gas-
continuous bases and liquid-rich slugs (pulses) are alternated. The heat transfer rates in the
pulses can be 3 – 4 times higher that those in the gas-continuous bases. The pulsing flow can
also enhance the wetting of the catalyst pellets and hence improve the liquid distribution,
which in turn will minimize the risk for hot spot formation. In the pulsing flow mode also the
mass transfer rates and the liquid hold-up can be significantly higher than in the conventional
trickle-flow mode.
The main difference between the modeling of a fixed-bed and a trickle-bed is the
hydrodynamics because of two fluid phases in the latter case. Furthermore, due to the extra
liquid phase in the trickle-bed, more mass and heat transfer resistances have to be
encountered, end hence gas-liquid and liquid-solid interfacial areas must be known. For a
conventional fixed-bed, the mass transfer coefficient, kg, and the geometrical external particle
surface area, av, is enough. For the mass transfer over the gas/liquid interface, usually Henry’s
constant, H, is used to estimate the concentration of a component at the interface.
Figure 2 shows schematic concentration profiles of reactants and products in the different
phases existing in a trickle-bed.
34
Figure 2. Idealized diffusion-reaction system in a three-phase trickle-bed reactor, where one reactant is in gas-
phase and the other in liquid phase [Gianetto and Silveston, 1986].
2. Dispersion model equations for multiphase systems
Typically, mass and energy balances for a 1-dimensional dispersion model of a trickle-bed
reactor, with A as the reactant of the gas phase and B as that of the liquid phase, would look
like this if the reaction only takes place at solid, and assuming constant superficial gas and
liquid velocities:
MB for component A in gas phase:
0)()( '
2
2
AL
AvL
AGiGL
AGeAGL C
H
paK
dz
dCu
dz
CdD
where ε and εL are the void fraction of packing and liquid hold-up ([m3 liquid/m
3 reactor]),
respectively. (ε - εL) is equal to the gas hold-up, εG, in [m3 gas/m
3 reactor]. uiG is the interstitial
velocity of gas in [m reactor/s] and hence the expression (ε - εL)*uiG is equal to usG, the
superficial gas velocity in [m3 gas/m
2 reactor, s]. If usG is not constant, it should be included in
the differential. av’ is the gas-liquid interfacial area per unit packed volume in [m
2
interface/m3 reactor]. KL is an overall mass transfer coefficient from gas bulk to liquid bulk in
terms of the liquid concentration gradient, according to:
GLL HkkK
111
where kL and kG are mass transfer coefficients from interface to liquid bulk based on
concentration as driving force, and from gas bulk to interface based on partial pressure as
driving force, respectively, in [m3 liquid/m
2 interface, s] and [kmol/m
2, bar, s].
35
MB for component A in liquid phase:
0)('''
2
2
s
AsALvAlALA
vLAL
iLLAL
eALL CCakCH
paK
dz
dCu
dz
CdD
MB for component B in liquid phase:
0)(''2
2
s
BsBLvBlBL
iLLBL
eBLL CCakdz
dCu
dz
CdD
where εL*uiL is the same as the superficial liquid velocity, usL, in [m3 liquid/m
2 reactor, s]. kl is
the mass transfer coefficient between liquid and catalyst surface in [m3 liquid/m
2 interface, s],
and av’’ is the liquid-solid interfacial area per unit packed volume in [m
2 interface/m
3 reactor].
MB for component A inside catalyst pellet, concentration gradients accounted for:
0)(1
1
2
2
NR
j
jAjs
As
effA rd
dC
d
dD
MB for component B inside catalyst pellet, concentration gradients accounted for:
0)(1
1
2
2
NR
j
jBjs
Bs
effB rd
dC
d
dD
where Deff is the effective diffusivity coefficient inside the catalyst pellet in [m2/s], ρs is the
catalyst density in [kg cat./m3 particle], NR is the number of reactions, αAj is the stoichiometric
coefficient of component A in the jth
reaction, and rj is the reaction rate for reaction j. The
sum of αAj*rj is negative for a component that is consumed. If mass transfer limitation inside
of the pellet can be neglected, for instance when the particle diameter is very small which
often is the case in slurry reactors, the last MB may be simplified with:
MB for component A at catalyst surface, no concentration gradients:
0)1()(1
''
j
NR
j
Ajs
s
AsALvAl rCCak
MB for component B at catalyst surface, no concentration gradients:
0)1()(1
''
j
NR
j
Bjs
s
BsBLvBl rCCak
36
The mass balances above are typical for any multiphase system. Simplifications are often
made such as assuming plug-flow of the gas. In slurry reactor models, in which the catalyst
particles are entrained with the liquid, the slurry phase is often modeled as a CSTR, while in
trickle beds the liquid phase often is treated as a plug flow. According to Shah and Sharma
[1987], in general, the number of equations that must be set up to solve a multi-phase system
equals the sum of all component balances for each phase plus the number of overall material
balances.
EB for gas phase:
0)(4)()()( '
2
2
gwgw
t
g
lgvapggiGLagL TTad
UTTah
dz
dTcu
dz
Td
where λag is the axial conductivity in the gas phase in [W/m gas, K], ha the heat transfer
coefficient from bulk gas to bulk liquid in [W/m2 interface, K], Ug is an overall heat transfer
coefficient for heat transfer between gas and tube wall in [W/m2 gas-wall interface, K] and
agw is the gas-wall interfacial area per inner tube wall area.
EB for liquid phase:
0)(4)()( '''
2
2
lwlw
t
ls
slvllgvapLLiLLalL TTad
UTTahTTah
dz
dTcu
dz
Td
where λal is the axial conductivity in the liquid phase in [W/m liquid, K], hl the heat transfer
coefficient between liquid and catalyst surface in [W/m2 interface, K], Ul is an overall heat
transfer coefficient for heat transfer between liquid and tube wall in [W/m2 liquid-wall
interface, K] and alw is the liquid-wall interfacial area per inner tube wall area.
EB in particle, intraparticle temperature gradients accounted for:
0)(1
2
2
j
NR
j
jsse rH
d
dT
d
d
While slurry reactors are often considered as isothermal, trickle-beds are not. Therefore it is
necessary to set up energy balances for the different phases. However, according to Jakobsen
[2003], the catalyst particles can often be considered as isothermal, and hence the last EB
could be simplified with:
EB at particle surface, no intraparticle temperature gradients:
0)()1()(1
''
j
NR
j
js
s
slvl rHTTah
37
However, according to Gianetto and Silveston [1986], commercial trickle-bed reactors are
normally considered as adiabatic, since the heat losses from the reactor are negligible
compared to the heat generated by the reaction, and heat conduction is neglected.
Furthermore, according to Shah [1979] and Gianetto and Silveston [1986], all phases at any
given axial position in the reactor is often assumed to have the same temperature. With these
assumptions, the EB for a trickle bed could be simplified with the following expression:
EB for adiabatic trickle-bed with temperature equality at any z-point in the reactor:
0)()1())((1
j
NR
j
jspggiGLpLLiLL rHdz
dTcucu
Momentum equation
In the case of trickle beds, a momentum equation has to be set up. The standard Ergun
equation was used by Wang et al. [2003] in the case of a Fischer-Tropsch reactor, in which
the liquid phase was assumed just to be a thin film surrounding the catalyst particles.
Froment and Bischoff [1990] give some alternative expressions for calculation of the pressure
drop in trickle beds, based on pressure drops measured for a certain bed with either liquid, δL,
and gas, δG, flow only. The equation below is one example:
666.0log
416.0log
2
2
G
LGL
where δ2 is the two-phase frictional pressure drop. The measured pressure drop, dPtot/dz, is
related to δ2 according to:
LL
tot gdz
dP 2
g is the acceleration of gravity in [m/s2]. The equations above are only valid if usG = usL, since
they are based on the assumption that the gas and liquid are quasi-homogeneous. See Froment
and Bischoff [1990] for further examples. Froment and Bischoff [1990] also discussed that in
trickle-bed operation, the liquid and gas flow rates are much lower than in for instance packed
absorbers, and hence single-flow pressure drop equations could be used as a first
approximation, with the void fraction reduced to account for the liquid hold-up.
38
3. Special issues in modeling of trickle-bed reactors
3.1 Introduction
What make trickle-beds a bit more complicated to model than other multi-phase reactors, are
the facts that the catalyst is often not completely wetted, insufficient liquid hold-up,
backmixing etc. [Shah and Sharma, 1987]. Gianetto and Silveston [1986] summarized the
main differences between transport and reaction in porous catalysts in multi-phase reactors
and conventional gas-solid reactors with the following points:
- The catalyst pores in multiphase reactors are often filled with liquid, and the diffusion in
liquids is approximately 4 orders of magnitudes lower than that in gases. Concentration of
solutes in most cases will be lower than the concentrations of the gas species. The low
concentrations and the slow diffusion result in a low catalyst surface utilization, which in turn
means that the overall rates are much slower than if the reaction could be performed in gas-
phase.
- When the pores are filled, the heat conductivity is about one order of magnitude higher than
for gas-filled pores. This means that the catalyst particles can be assumed isothermal at each
axial point in the reactor, provided the wetting of the catalyst is sufficient.
- In a multiphase system, the catalyst particle may be exposed to non-symmetrical surface
conditions. Part of the catalyst surface may be in contact with the flowing liquid, another part
in contact with a stagnant liquid, and the rest of the particle might be unwetted. This means
that the solute concentration will vary significantly over the external catalyst surface. When
the wetting is poor, the exothermic reactions can lead to evaporation of the liquid in some
pores. Those pores are hence dried out and completely filled with gas. In these cases, complex
temperature gradients will be present inside of the catalyst.
A poor wetting is also believed to be the major cause of poor effectiveness. The incomplete
wetting leads to non-symmetrical concentration gradients in the catalyst pores and
complicates the prediction of reaction rates and the analysis of kinetic data from trickle-beds.
In order to be able to evaluate the true rate constant, k, from laboratory experiments, it is
necessary to be able to correlate the observed rate constant, kobs, to the true one.
In Table 1, the advantages and disadvantages with trickle-beds as summarized by Shah [1979]
are given.
39
Table 1. Advantages and disadvantages with trickle-beds [Shah, 1979].
3.2 Catalyst wetting and relating kapp to k
Assuming first order kinetics of the reaction inside a trickle-bed, the apparent rate constant,
kapp, will for instance depend on the thickness of the liquid film surrounding the catalyst
pellets, which in turn is dependent on the liquid flow rate, and on the diffusion resistance
inside the pellets. The kapp will of course be different from (lower than) the true rate constant,
k, as long as the reaction is limited by mass transfer. If the reaction is not truly first order,
different kapp values will be obtained at different conversions.
Bondi [1971], a reference in Froment and Bischoff [1990], derived the following relation for
trickle-beds:
b
Lapp L
A
kk )/(
11 '
where 0.5 < b < 0.7
where A’ is a constant. The higher the LρL/Ω, the closer kapp/k is to 1 for hydrodesulfurization
of a heavy gasoil, which is understandable since the film thickness of liquid surrounding the
particles decreases with increased liquid flow rate, and the wetting of the pellets increases.
kapp/k would however never reach 1 as long as there are intraparticle concentration gradients.
40
In case of porous packing, two types of wetting can be defined [Shah, 1979]:
- Internal wetting or pore filling. This is often complete due to capillary action.
- External effective wetting, i.e. the amount of the particles’ outside area effectively
contacted by the liquid. Almost all mass exchange between the internal liquid and the
flowing liquid occurs through this area.
Little is known on how the liquid-solid contact efficiency depends upon the gas and liquid
flow rates. Higher gas and liquid loadings can increase the contact. Also a higher viscosity
and lower surface tension increases the contacting efficiency. Satterfield, a reference in Shah
[1979], defined the contacting effectiveness in terms of the apparent rate constant, kapp,
obtained from laboratory experiments in trickle-beds, and the true rate constant, k, obtained in
a CSTR, and found the correlation depictured in Figure 3.
Figure 3. Contacting effectiveness vs liquid loading, as proposed by Satterfield. GL is the superficial liquid flow
rate per unit cross-section (usL) [Shah, 1979].
According to Koros, another reference in Shah [1979], there is little correlation between flow
uniformity and contacting effectiveness. The contacting efficiency may increase even if the
flow uniformity is poor. The interstitial bed geometry, catalyst shape and size play important
roles in the contacting effectiveness. At high liquid mass velocities, high contacting
effectiveness can be achieved even for reactor : catalyst diameter ratios as low as 1.4 : 1. For
some systems, no correlation between the contacting effectiveness and mass velocity can be
found.
Mears [1974], another reference in Froment and Bischoff [1990], meant that correlating the
kapp to k and liquid flow rate (or liquid dynamic hold-up) was not correct, and instead
suggested that kapp should be proportional to the external wetted area of the catalyst, which in
turn depends on parameters such as μL, σL, σL,c etc. This is understood since in conventional
trickle-beds both components in gas and liquid are reactants that must meet and react at the
catalyst surface. The lower the degree of wetting, the smaller the interfacial contact area
between liquid and solid and hence the slower the mass transfer rates of B to the catalyst
active sites. The transport of the gas phase reactant A will however be faster the lower the
41
degree of wetting, which might actually increase the global reaction rate if A is the limiting
reactant. In the hydroprocessing of oils, a sufficiently large liquid hold-up is essential, since if
this is too low, the whole capacity of the catalyst will not be used, due to incomplete wetting.
In case of Fischer-Tropsch, where all reactants are in the gas phase, the degree of wetting
should primarily affect the mass transfer rates from gas to catalyst surface, probably giving a
higher overall rate the lower the degree of wetting, provided that the reaction rate is diffusion
controlled. Gianetto and Silveston [1986] concluded that in trickle-beds, essentially all
reaction occurs by mass transfer of reactant from the gas-covered part of the catalyst surface.
3.3 Liquid hold-up and mass transfer
Biswas et al. [1988], a reference within Froment and Bischoff [1990], performed experiments
that led to the conclusion that in order for the catalyst particles to be fully wetted, an efficient
liquid distribution at the top is required, and the column-to-particle diameter should exceed 20
– 25 to avoid liquid bypassing along the wall. This is of course of big importance if the
trickle-bed involves reaction between components in the gas and the liquid, in order to fully
utilize the capacity of the catalyst loaded into the reactor.
In the trickle-bed, the liquid holdup, εL, consists of liquid inside the pores (internal liquid
hold-up) and outside of the pores (external liquid holdup). The external liquid hold-up
consists, in turn, of the dynamic hold-up, εL’, and the static hold-up. The static hold-up was
related to the Eötvös number, δL*g*dp2/σL (σL is the surface tension of the liquid in [N/m]),
and it varies between 0.02 and 0.05 (Charpentier et al. [1968], a reference within Froment and
Bischoff [1990]). Froment and Bischoff [1990] presented the following expression for the
dynamic hold-up. Note that it is only dependent on the liquid flow rate and not on the gas
flow rate:
)(
2
23
'
pv
L
Lp
L
pL
L dagdLd
c
where L is the volumetric liquid flow rate in [m3 liquid/s], Ω the cross sectional reactor area
[m2 reactor], μL the liquid viscosity in [kg/m, s] and av is the external particle surface area per
unit of reactor volume in [m2 particle/m
3 reactor]. c, α, β and γ are constants (see Froment and
Bischoff [1990]). Although not discussed by Froment and Bischoff [1990], this dynamic hold-
up could probably find use in a so-called two-zone model, in which the liquid is looked upon
as a flowing fraction and a stagnant fraction, as described below in Backmixing.
Henry and Gilbert, a reference in Shah [1979], claimed that a certain minimum liquid hold-up
is required for 100 % catalyst utilization, as illustrated in Figure 4.
42
Figure 4. Effect of fluid dynamics on hold-up [Shah, 1979].
The liquid hold-up was claimed to depend on (FrL/ReL)1/3
, where FrL = usL/ρL2dpg and ReL =
usLdp/μL.
There are some correlations that might be used to estimate interfacial areas in the trickle-bed.
One example is the following expression, originally developed for a countercurrent packed
column, for ρLL/Ω = 1.5 kg/m2, s:
18.0
,135.004.0'
Re05.1
L
cL
L
v
v Wea
a
where We = ρLL2dp/Ω
2σL, and σL,c is the critical surface tension above which the packing
cannot be wetted.
Respecting the mass transfer between gas and liquid in trickle-beds, there are some specific
results for cocurrent operation available in literature. For low liquid and gas flows,
Charpentier [1977] (a reference in Froment and Bischoff [1990]) developed the following
correlation for the liquid side mass transfer:
9
'
104.20011.0
AL
LvL
DEak [s
-1]
where DAL is the diffusivity in liquid in [m2/s], assuming that the liquid viscosity is not too far
from that of water, and EL = (ΔPtot/Δz)*usL in [W/m3]. Reiss, a reference in Shah [1979],
found a correlation for the liquid side mass transfer at higher gas and liquid rates (pulsing or
spray flow):
5.0' 173.0 LvL Eak
Figure 5 illustrates the above discussion.
43
Figure 5. Correlation between liquid side mass transfer coefficient kLaL values for cocurrent downflow in packed
beds. aL in the figure is the gas-liquid interfacial area, i.e. av’. U0L in the figure is the superficial liquid velocity,
i.e. usL [Shah, 1979].
The gas-side mass transfer, kGav’, is also depending on the liquid and gas flow rates which is
illustrated in Figure 6.
Figure 6. Energy correlation for kG. U0 is the superficial liquid velocity (us). ε is the bed voidage. Ψ is the
packing shape coefficient, values are found in Table 2 below [Shah, 1979].
44
Table 2. Values for porosity and packing shape coefficients used in Figure 6 [Shah, 1979].
For the liquid-solid mass transfer, jD correlations for single-phase flow can be used as a first
approximation. These correlations are given in Froment and Bischoff [1990].
Dealing with mass transfer limitations inside of the catalyst pellets in a trickle-bed is done in
the same way as for single-flow fixed beds, i.e. with particle equations or effectiveness
factors. However, the trickle-bed case is much more complex, since in the case of liquid
evaporation (in hydrodesulfurization or hydrocracking) the pores will be filled with both
vapour and liquid, and the theory of the effectiveness factor for such a situation still has to be
worked out.
3.4 Heat transfer
The trickle-bed is characterized by poor heat transfer rates, compared to reactor
configurations in which the liquid is continuous. The transition from homogeneous trickling
flow to pulsed flow correspond to an increase of several hundred percent in the radial heat-
transfer rate. There are not many studies about the heat transfer in trickle-beds. One relation
describing the heat transfer in the trickle-mode was derived by Weekman and Myers, a
reference in Shah [1979]:
GG
l
g
LL
ll
e
k
k
kk
kPrRe172.0PrRe00174.0
71.7
where ke is the effective conductivity of the bed, kl and kg the liquid and gas conductivities.
ReG and ReL are the gas and liquid Reynolds numbers based on superficial velocities and tube
diameter. PrG and PrL are the gas and liquid Prandtl numbers. The overall heat-transfer
coefficient was related to the effective conductivity as:
Z
cucurk
rU
pGsGpLsLt
e
t
)(183.0892.2
[cal h-1
cm-2
K-1
]
where rt is the tube radius in [cm] and usL and usG are in [g/h, cm2]. cpG
* is the specific heat of
saturated air in [cal/g, K]. Z is the axial distance from the inlet in [cm]. These relations were
found for an air-water cocurrent downward system with packing of spheres with sizes
between 38 mm and 65 mm. The radial heat transfer coefficients were found to be much
larger than those observed for single phase liquid flow. The effect of the gas on the heat
transfer was mainly that it increased the velocity of the liquid phase. The radial velocity in the
liquid was larger in two-phase flow.
45
3.5 Effectiveness factor
The use of effectiveness factors instead of solving the particle equations is convenient.
According to Gianetto and Silveston [1986], the effectiveness factor change much more
slowly through the reactor than do the reaction rate or concentration. Thus, the effectiveness
factor only has to be estimated at the inlet, in the middle and at the outlet of the reactor.
Gianetto and Silveston [1986] reported expressions for the Thiele modulus and effectiveness
factor for various kinetic reaction rate expressions.
However, when the wetting is not complete, conventional intraparticle effectiveness factors
are not applicable since the concentration of reactant at the external catalyst surface is not
uniform. According to Gianetto and Silveston [1986], it is necessary to consider mass transfer
from gas to liquid, from liquid to the portion of the particle in contact with flowing liquid, and
direct transport from gas to the part of the particle in contact with the gas. Expression for an
overall effectiveness factor in case of spherical catalyst particles partly in contact with
flowing liquid, and partly in direct contact with gas, was derived by Gianetto and Silveston
[1986] for first order kinetics. The whole idea is that the overall effectiveness factor, ηo, is
divided into two parts – one for the wetted catalyst surface (f) and one for the “dry” catalyst
surface (1-f), where f is the wetting efficiency:
glo ff )1(
where ηl and ηg are effectiveness factors for entire particle surface (i.e. overall effectiveness
factors that include external mass transfer resistance as well as internal) covered by liquid and
gas, respectively. The particle effectiveness factor, η, i.e. the one concerning internal mass
transfer restrictions only, is included in the expressions for ηl and ηg. See Gianetto and
Silveston [1986] for the complete expression. The overall rate, r, of formation/disappearance
of one component can then be expressed as:
*
lokCr
where Cl* is the liquid phase concentration in equilibrium with the bulk gas concentration.
Partial wetting should only affect the overall rate/effectiveness factor if ηg > ηl. In order to
estimate the role of wetting on the overall rate, it is necessary to know the wetting efficiency f.
A correlation useful for scale-up is:
75.0
,2.005.036.1exp1L
cL
ll WeGaf
where Gal = dp3g/υl
2, and υl the kinematic viscosity of the liquid in [m
2/s].
46
3.6 Backmixing
3.6.1 One-parameter models
The 1-dimensional dispersion models characterize the backmixing with just a single
parameter – the dispersion coefficient. The assumption that all the mixing processes follow a
Fick’s law type of diffusion becomes increasingly dubious with increasing degree of
backmixing. But the dispersion models are still very widely used due to their simplicity, since
they describe the backmixing (or RTD) by simply one parameter. In multiphase reactors, the
degree of backmixing is accounted for in each phase. The degree of backmixing is often much
higher for the slow moving liquid phase compared to the fast moving gas phase, which often
leads to a plug-flow model (zero dispersion/backmixing) for the latter [Shah, 1979]. The
effective axial dispersion coefficient, Dea, is expressed in dimensionless form as the Peclet
number (based on particle diameter):
ea
pi
aD
duPe
where ui is the interstitial velocity in [m reactor/s] of the phase encountered. The Peclet
number, at a Reynolds number of 10 (based on particle diameter), is approximately 0.2 for the
liquid phase in the trickle-bed, compared to approximately 2 for the fluid in a single-phase
operation [Froment and Bischoff, 1990].
Froment and Bischoff [1990] claimed that in laboratory-scale, the minimum reactor length for
absence of axial dispersion in the gas phase can be an order of magnitude higher for a trickle-
bed than for single-phase fixed beds. However, in industrial reactors, the axial dispersion in
gas phase can be neglected.
Elenkov and Kolev [1972], a reference in Froment and Bischoff [1990], developed the
following expression for estimation of Dea in the liquid in a trickle-bed:
33.0
23
278.0
4068.0
Lv
L
Lv
L
vea
sL
a
g
a
L
aD
u
Deviations from plug-flow in the gas-phase of trickle-bed reactors are often not concerned. Of
course the conventional way to find Dea is to make a tracer experiment in the phase of interest,
and then to calculate the E(t), the residence time distribution function. The E(t) describes the
dimensionless outlet tracer concentration (Cout(t)/Cout(t) integrated from t0 - t) as a function
of time, and by setting up mass balances and boundary conditions / initial values for the tracer
(including the dispersion term), the numerical solution (i.e. Cout(t)) expression may be fitted to
the experimentally found E(t) by choosing a suitable Dea.
According to Shah [1979], maldistribution of the flow is common in laboratory-scale trickle-
beds. The maldistribution, such as channeling, dead zones and bypassing etc. result in
complex RTD evaluation. If such phenomena cannot be avoided in the system, micromixing
models (see Fogler [1999] for an explanation) have to be set up to correlate such unusual
shapes of RTD curves. Micromixing models describe how molecules of different ages
encounter one another in the reactor, unlike the macromixing models (i.e. the RTD) which
only describe the distribution of residence times.
47
RTDs for each phase is needed in order to describe the backmixing. However, as mentioned
above, the gas phase is often considered to be a plug flow. Figures 7-10 below show an ideal
RTD and RTDs for systems with maldistributional flows for typical trickle-bed reactors.
Figure 7. An ideal RTD curve, and a RTD curve with tailing [Shah, 1979].
Figure 8. RTD curve for a reactor with channeling [Shah, 1979].
Figure 9. RTD curve for a reactor with large dead space [Shah, 1979].
48
Figure 10. RTD curve for a reactor with bypassing [Shah, 1979].
Channeling and bypassing are undesirable phenomena since they reduce the utilization of the
catalyst. Proper design of the liquid distributor and a calming section in large-scale trickle-
beds can essentially eliminate the maldistributions of flows. It is also important to use the
same type of particles (same porosity) in the large-scale as in the laboratory scale since tailing
will occur due to the static liquid hold-up in the pores, shown in Figure 7.
Shah [1979] presented several models for describing the backmixing/macromixing in trickle-
bed reactors. The most common, although with a rather poor capability of predicting the
backmixing, are the axial dispersion models, as described above in 2. Dispersion model
equations for multiphase systems. The dispersion model gives satisfactory correlation to the
measured RTD data as long as radial-flow nonuniformities are minimized by keeping a large
reactor diameter / particle diameter (> 25). Michell and Furzer, a reference in Shah [1979],
claimed that a dispersion model of the liquid phase does not describe the true nature of
trickling flow. In their so called “bypass model”, the liquid phase is modeled as a laminar film
flow over a series of packing elements with imperfect mixing, or bypassing, at each packing
junction. The liquid film is assumed plug-flow, and the static liquid hold-up at the junctions
well-mixed by hydrodynamic effects, such as ripples, that cause axial dispersion in the
reactor. At each junction, a fraction q of the flow enters the perfectly mixed regions, while the
rest of the flow bypasses the mixing. This is illustrated in Figure 10.
Figure 10. Schematic picture of the bypass model [Shah, 1979].
49
Michell and Furzer derived the following expression for the mean residence time, tmL, of the
liquid:
MFmL tqtt
where η is the bed height divided by packing diameter, tF is the mean residence time of a
single film and tM the mean residence time in a single mixer. Expression for tF and tM are
given below:
f
p
Fu
dt
sL
pstatLL
Mqu
dt
where uf is the mean flow velocity in the film, εstatL the static liquid hold-up and usL the
superficial liquid velocity in [m3 liquid/m
2 reactor, s]. uf is related to the wetted surface area,
aw, according to:
3/13/2
48
4
L
L
Lw
sLf
g
a
uu
The expression for E(t) for a Dirac pulse tracer input, in case of the bypass model equations,
will be:
Mx
x
M
xx
t
t
t
t
xxx
qqtqtE exp
)!1()!1()!(
)1(!)()1()(
1
1
Since aw and usL often can be estimated from experiments, the only unknown parameter that
has to be found, in order to fit the experimental results to the model, is q. Hence, both the
dispersion and bypass models are typical single-parameter models (Dea and q).
3.6.2 Two-parameter model
Shah [1979] presented three two-parameter models and one three-parameter model for
description of the backmixing in multiphase reactors. Below, one two-parameter will be
shown as an example.
This model was referred to as the two-parameter modified mixing-cell model in Shah [1979],
and as the two-zone model in Froment and Bischoff [1990]. According to Froment and
Bischoff [1990], the deviations from plug-flow in the liquid phase of a multi-phase packed-
bed reactor are mainly caused by insufficient contact between the gas and liquid. The reason
for this phenomenon may be preferential paths in the packing or stagnant zones. These effects
can often not be described satisfactorily by effective diffusion models. A more appropriate
50
description could be made using a two-zone model. Briefly, in such a model, only a fraction
of the liquid flows through the packing, and the rest of the liquid is considered stagnant. The
stagnant liquid phase is assumed to be well-mixed and exchanges mass with the flowing
fraction of the liquid and with the catalyst particles. Note that in the one-parameter bypass
model described above, no mass transfer between the film and stagnant zones was
encountered.
The mass balance for A in the gas-phase is written as shown in 2. Dispersion model equations
for multiphase systems. The mass balance for A in the liquid phases can be written [Froment
and Bischoff, 1990]:
MB for A in flowing fraction of liquid:
0)()( ''''
s
As
f
ALvl
f
ALA
vL
d
AL
f
ALT
f
ALiL
f
L CCakCH
paKCCk
dz
dCu
where uiL’ is the interstitial velocity of the flowing fraction of the liquid, kl is the mass transfer
between the flowing fraction and the solid, kT the mass transfer between the flowing and
stagnant liquid. The superscripts f and d stand for flowing fraction and stagnant fraction,
respectively.
MB for A in stagnant fraction of liquid:
)()( ' s
As
d
ALl
f
AL
d
ALT CCkCCk
where kl’ is the mass transfer coefficient between stagnant liquid and solid.
MB for A at catalyst:
)1()()( ''' sA
s
As
d
ALl
s
As
f
ALvl rCCkCCak
kT and kl’ contain interfacial areas that are not yet well established.
In order to solve the equations, the flowing fraction of liquid, f, must be determined, so that εLf
can be estimated. It is f and kT that comprise the two parameters needed to fit the experimental
tracer data with E(t). The expression for E(t) can be found in Shah [1979]. f can be estimated
by:
m
i
t
tf 1
where ti and tm are the time when the tracer first appears in the effluent, and the average
residence time of liquid in the reactor, respectively. The variance of the RTD is given by:
mT tkf /2 22
51
ti, tm and σ2 are easily achieved from the RTD curve, and hence both f and kT can be estimated
rather easily from the RTD experiment.
3.7 Conclusion
There is still not enough knowledge in order to make a model that can predict the different
results obtained in laboratory-scale and large-scale trickle-bed reactors, and hence the design
practice for trickle-beds is still in an early stage of development. The high degree of
backmixing that can arise in multiphase systems is often difficult to describe with a
conventional dispersion model, as discussed above. This is due to the complex phenomena
that often take place, such as droplets breaking loose from the liquid phase and getting
mixed/entrained with the gas flow, or in the case of slurry reactors gas bubbles coalesce and
break continuously. Some liquids will also form foam in the column at certain conditions,
which is not easy to predict. In the multiphase systems the interfacial contact areas between
the different phases is important for the mass and heat transfer since the resistance towards
transfer mainly exist in the interfacial “films”. At certain conditions, these films will break up
and the mass and heat transfer rates may therefore change drastically. [Jakobsen, 2006]
Shah [1979] summarized the problems with RTD and scale-up for trickle-beds with the
following points:
- RTD data from laboratory-scale experiments cannot be used for large-scale units.
Often the prevailing flow regimes are different in different scales.
- In trickle-beds, maldistribution of the flow is common, which makes it difficult to
evaluate RTD data. Maldistribution, such as channeling, dead zones and bypassing,
often exist in laboratory-scale units but not in larger scale.
52
The Fischer-Tropsch process
4.1 Introduction
The Fischer-Tropsch (FT) synthesis, in which synthesis gas is converted to liquid fuels such
as gasoline and diesel is also called GTL (Gas-To-Liquids). Feedstocks for the synthesis gas
can be coal, natural gas, biomass etc. The FT-process was discovered in the early 1920’s and
has been used from time to time at places short of petroleum, such as Germany during WW2,
and in South Africa during the oil embargo. In the last ten years, the FT-process has gained
new world-wide interest due to the forecasts about diminishing petroleum reserves, and due to
the more stringent emission legislations coming up due to the green-house effect. FT-fuels are
much cleaner than petroleum-based fuels since they are essentially free from sulfur and
aromatics. Furthermore, they can be CO2-neutral if made from biomass.
The commercial-scale FT-plants existing in the world today are three coal-based plants in
South Africa (150 000 barrels1 per day (bpd), Sasol), one natural-gas based plant in South
Africa (23 000 bpd, PetroSA), and one natural-gas based plant in Malaysia (15 000 bpd,
Shell). From this year and within the next 5 years there will be several commercial-scale
natural-gas based FT-plants set up in Qatar, which is a country with huge natural-gas
resources. The companies active in this country are Qatar Petroleum/Sasol Chevron, Shell,
ExxonMobile and ConocoPhillips. Statoil recently erected a natural-gas based FT-
demonstration unit in South Africa, which is a slurry reactor with a capacity of 1 000 bpd. In
Germany, Choren/Shell are building a commercial-scale biomass-based FT-plant. Sweden has
currently one pilot-plant for gasification of biomass in Växjö, and one for gasification of
black liquor (a rest product from the pulp industry) in Piteå. Still, the Swedish energy has not
decided what fuels will be made from the syngas produced at this pilot-plants. A feasibility
study made by Ekbom et al. [2005] showed that approximately 25-30 % of the transportation
fuels in Sweden can be replaced by CO2-neutral fuels (FT-fuel, DME or methanol) if all pulp
mills in Sweden replace their old recovery boilers by new black liquor gasifiers. This option
would still cover the steam and energy need of the pulp mills.
In the Fischer-Tropsch (FT) synthesis, synthesis gas (CO + H2) is converted over Fe or Co-
based catalysts into hydrocarbons and water according to reaction (1) [Sie and Krishna, 1999].
CO + 2H2 -CH2- + H2O ΔHR,298K = -165 kJ/mol (1)
Mainly straight-chain saturated hydrocarbons from CH4 up to heavy waxes may be produced.
Some olefins and oxygenates are also produced. The reaction mechanism is a polymerisation
process in which the building block, or monomer, is the CH2-unit. Due to the step-wise
growth mechanism, the hydrocarbon products will always be a range of products of C1+,
described by the ASF (Anderson, Schulz, Flory) -distribution, shown in figure 1. The chain
growth probability, α, is a common parameter used to characterise a FT product distribution.
A higher α means that the product contains higher hydrocarbons, and hence less CH4. It is
known that the higher the pressure, and the lower the temperature, and the lower the inlet
H2/CO-ratio, the higher is α. The chain growth probability is also dependent on the
characteristics of the catalyst (e.g. pellet size, pore size, active site density, promoters etc.). It
is commonly accepted that the highest yield to diesel (the most promising FT-fuel due to a
1 1 barrel equals 159 dm
3.
53
very high cetane number realised by the un-branched straight hydrocarbon chains) is achieved
by first making wax, which is then hydrocracked into the diesel fraction (C12 – C20). In this
way you will minimise the formation of shorter byproducts, especially CH4. Hence, the
world-wide FT-research is today focused on how to prepare catalysts that give high α, and
how to increase the dispersion of the Co in order to minimize the amount of expensive Co
needed for a certain productivity. A normal α today is around 0.9 for a wax-producing FT-
process.
The molar usage ratio of H2/CO is about 2 over a Co-based catalyst (see reaction (1)). The
reaction is strongly exothermic, which makes a rapid heat removal necessary from the reactor.
An efficient heat removal is a key point in the design of FT reactors, due to the risk of run-
away, and also due to the temperature sensitivity of the product selectivity.
For Fe-based catalysts, the water-gas-shift (WGS) reaction (reaction (2), [Jess, 1999]) takes
place simultaneously with reaction (1) in the reactor, and hence lowering the usage ratio,
which makes it possible to feed the FT-reactor with a molar inlet ratio of H2/CO of less than
2. Such hydrogen poor synthesis gas is obtained from gasified coal or biomass. The WGS
reaction is known for its equilibrium composition which is located “in the middle” between
the reactants and products. Therefore, the WGS equilibrium is often tuned in in chemical
processes.
CO + H2O CO2 + H2 ΔHR,298K = -41 kJ/mol (2)
However, for the case of low-temperature FT (LTFT), which is used when high waxes are
wanted, the WGS reaction is slow and does often not reach equilibrium [Dry, 1996]. Hence,
no commercial FT-process exists today that can handle, directly in the FT-reactor, such a low
H2/CO-ratio as 1.0, which is the ratio in for instance gasified biomass. Instead, external WGS-
units are used in order to correct the H2/CO-ratio in the syngas before entering the FT-reactor.
The FT-reaction is not limited by equilibrium, as is the case in, for instance, the methanol
synthesis. Over a Co-based catalyst, the reaction products (HCs and water) are not believed to
affect the reaction rate, and hence a high conversion per pass is possible (above 90 % possible
in a slurry phase reactor). Over a Fe-based catalyst, water has shown to limit the reaction rate,
and hence the conversion per pass is rather low and water is knocked out prior to
recirculation. Below, two generalised rate expressions for FT over a Fe- and Co-based catalyst
are presented, respectively [Dry, 2002].
For Fe:
For Co:
Co is often preferred to Fe if the syngas is not poor in hydrogen. This is due to its higher
activity, the lack of WGS-activity (which would otherwise lead to a too high H2/CO-ratio
inside of the reactor), and the fact that the reaction rate is not limited by the presence of water.
What limits the conversion per pass over a Co-based catalyst is actually the ability of heat
54
removal in the reactor. Several different reactor solutions have been developed for FT during
the years. They will be presented in the next section.
4.2 Different reactor types and reaction conditions
In a FT-plant, the production of syngas, if produced from natural gas, accounts for 60 - 70 %
of the total capital and running costs. Economy of scale is very important for the syngas
production, and therefore the downstream FT-reactors must also have a high capacity.
Therefore, the ease of up-scaling is very important when making the selection of type of FT-
reactor. [Dry, 2002]
The FT-synthesis takes place in a three-phase system. The gas phase contains the reactants
and water vapour and gaseous hydrocarbon products. The higher hydrocarbons compose the
liquid phase, and the catalyst is the solid phase. In some cases, often high-temperature FT
(HTFT), all products are vaporised under reaction conditions and hence there are only two
phases present. The amounts of syngas and product molecules that must be transferred
between the phases are quite large in FT compared to the hydrogen molecules transferred in
the hydrotreatment of petroleum oils in today’s refineries. Therefore, in FT synthesis there is
a demand for a high interfacial mass transfer. [Sie and Krishna, 1999]
A nearly isothermal reactor, i.e. a reactor in which the temperature control is good, is possible
to operate at a slightly higher average temperature than a non-isothermal reactor in which
there are risk of hot spots and hence run-away. A slightly higher temperature gives a slightly
higher reaction rate, and therefore a higher productivity [Schulz, 1999]. Hence, a reactor with
a good temperature control can have a higher productivity per gram catalyst, or put in another
way, can host a more active catalyst.
Many of the early FT-reactors (before and during WW2) were only possible for low
capacities (15 bbl/day) due to inefficient heat removal and required very large cooling
surfaces. Low pressure was used (even down to atmospheric) which required very low gas
flows in order to reach high conversions. The lower gas flows gave poor heat transfer.
[Krishna and Sie, 2000]
Other early FT-reactors had external cooling, i.e. the hot outlet gas or liquids were cooled and
then recycled into the reactor. This solution requires very large recycle streams in order to
remove the generated heat in the reactor, which in turn results in large pressure drops and high
energy consumption for the circulation. [Krishna and Sie, 2000]
High heat exchange rates are today accomplished by forcing the syngas at high linear
velocities through long narrow tubes packed with catalyst particles (tubular fixed-bed reactor,
TFBR) to achieve turbulent flow and each tube cooled by boiling water, or by using a slurry
phase reactor (SPR) in which the catalyst is dispersed in the liquid products and in which very
high heat transfer rates are achieved. For HTFT in which α < 0.71, fluidised catalytic bed
reactors are used which have very good heat transfer and temperature equalisation
characteristics. Due to the risk of heavy products depositing on the catalyst pellets, fluidised
beds cannot be used when high waxes are produced. [Dry, 2002; Sie and Krishna, 1999]
There are currently two FT operating modes: [Dry, 2002; Wender, 1996]
55
1. High-temperature FT (HTFT); 300 – 350 ºC, Fe-based catalysts, production of
gasoline and linear low molecular mass olefines. Significant amounts of oxygenates
are also produced. Diesel may be produced by oligomerization of the olefins.
2. Low-temperature FT (LTFT); 200 – 240 ºC, either Fe- or Co-based catalysts,
production of high amounts of paraffins and linear products and the selectivity to high
molecular mass linear waxes can be very high. The primary diesel cut and the
hydrocracking of the waxes yield exellent diesel fuels. The primary gasoline cut needs
further treatment to obtain a high octane number.
The reactor operating conditions also depend on the reactor type. The pressure is between 1
and 40 atm (= 4 MPa). The SV is between 100 – 1000 h-1
. [Williams, 2002]
4.2.1 HTFT
The Sasol FT plants existing in 1982 all had circulating fluidized beds (CFBs) for their HTFT
process, see Figure 11 (left picture). The CFB reactors are also called the Synthol reactors. In
CFBs there are two phases of fluidized catalyst – dense and lean. The catalyst particles move
down the standpipe in dense phase while they are transported up the reaction-zone in lean
phase. In order to avoid that the feedgas goes up the standpipe, the differential pressure over
the standpipe must always exceed that of the reaction zone. During operation at high
temperature, carbon is deposited on the catalyst particles (the Fe-based) which lowers the bulk
density of the catalyst and hence the differential pressure over the standpipe. Therefore it is
not possible to raise the catalyst loading in the reaction section in order to compensate for the
normal catalyst deactivation with time on stream. [Dry, 2002]
Sasol performed pilot scale experiments in fixed fluidized beds (FFBs, see Figure 11 (right
picture)) in the 1970s. They discovered that the FFB reactor had a higher performance than
their commercial CFB unit. 1989 a commercial FFB unit was brought on-line successfully.
Between 1995 and 1999, the 16 second generation CFB reactors at Secunda were replaced by
eight FFB reactors called Sasol Advanced Synthol (SAS). [Dry, 2002] The fluid bed FT
synthesis at Sasol is mainly used for production of olefins (C2-C7). [Schulz, 1999]
For the fluidised HTFT reactors, the catalyst pellets can be small (< 100 um), and hence
internal diffusion limitations are expected to be absent even though the catalyst pores are
filled with wax. [Dry, 1996]
The advantages of FFBs over CFBs are: [Dry, 2002; Wender, 1996]]
- 40 % lower construction costs. For the same capacity, the FFB reactor is much
smaller.
- Lower pressure-drop.
- Due to the wider reaction section, more cooling coils can be installed, which increases
the capacity of the FFB reactor due to the more isothermal behaviour
- At any moment, all of the charged catalyst participates in the reaction.
- The lowering of bulk density due to fouling is of less significance in the FFB which
implies that less on-line catalyst removal and replacement with fresh catalyst is
required to maintain high conversions, which lowers the overall catalyst consumption.
- The FFB reactor requires less maintenance due to the lower linear velocities. The CFB
reactors are complex and subjected to considerable erosion at the bends in the reactor.
56
Figure 11. HTFT reactors [Wender, 1996].
4.2.2 LTFT
In top-fed multitubular fixed-bed reactors (TFBR, see Figure 12 (left picture)), the waxes
trickle down and out of the catalyst bed. In slurry phase reactors (SPRs, see Figure 12 (right
picture)) the waxes accumulate inside the reactors and so the net wax produced needs to be
continuously removed from the reactor. [Dry, 2002]
In the FT plant in Sasolburg that was started 1955, five multitubular ARGE reactors were
installed for wax production. They are still in operation. Each reactor consists of 2050 tubes
(5 cm i. d., 12 m long). They operate at 2.7 MPa and 230 C. The production capacity of each
reactor is 21 000 t/year. An additional reactor was installed in 1987 operating at 4.5 MPa.
[Dry, 2002]
In the Shell plant at Bintuli there are four large multitubular reactors with a capacity of 125
000 t/year each. There are ca. 10 000 tubes in each reactor. In this plant, Co-based catalysts
are used. These are much more active than the Fe-based catalysts used in the Sasol plants.
This implies that the tube diameters of the Shell reactors are narrower in order to be able to
handle the higher rate of heat release. [Dry, 2002]
Due to pressure drop constraints in packed beds, the catalyst pellet diameter used in the TFBR
is often larger than 1 mm. When the catalyst pellet diameter is larger than 0.5 mm,
intraparticle diffusion can be rate limiting (H2/CO = 2, 21 bar, 200 – 240 C, pore diameter =
10 – 65 nm) [Sie and Krishna, 1999]. This problem can however be overcome by using egg-
shell impregnation, in which only the outmost layer of the pellets contains the active metal. In
this way, the diffusion distance for the reactants to the active sites is not governed by the size
of the pellets. Since Co is expensive, it is important that all of the impregnated metal is used
in the reaction. [Espinoza et al., 1999]
57
In the 1950s, slurry phase reactors (SPRs) as alternative to fixed bed reactors were first
encountered. Not until 1993 the first commercial unit based on a SPR for wax production was
brought on-line by Sasol. Its capacity is ca. 100 000 t/year, which equals the total capacity of
the five ARGE reactors, and the catalyst is Fe-based. SPRs require efficient filtration devices
in order to separate the produced waxes from the catalyst slurry. [Dry, 2002]
The SPR consists of a shell in which cooling coils are present for steam generation. The
syngas is fed to the bottom of the reactor and it rises through the slurry. The slurry consists of
liquid products (mainly waxes) with catalyst particles suspended in it. The reactant gases
diffuse through the liquid phase to the catalyst particles. The heavy products form part of the
slurry and the lighter gaseous products and water diffuse through the liquid. The gaseous
products and unreacted reactants pass through the slurry to the freeboard above the slurry bed
and then to the gas outlet. [Espinoza et al., 1999]
In the SPR, the catalyst pellets can be smaller than in the fixed bed, since they are dispersed in
the liquid phase and hence there are essentially no pressure drop constraints. The smaller
catalyst pellets prevent internal diffusion limitations on the overall rate. However, since the
pellets are suspended in the liquid wax, diffusion of the reactants from the gas phase through
the wax to the solid catalyst may be rate limiting. [Dry, 1996]
One advantage with the multitubular fixed-bed reactor is that there are no problems in
separating the wax product from the catalyst. [Espinoza et al., 1999] The advantages of slurry
phase reactors over multitubular reactors are: [Dry, 2002; Wender, 1996; Espinoza et al.,
1999]
- The cost of the reactor is only 25 % of the cost of a multitubular reactor.
- The pressure drop over the reactor is four times lower which results in lower gas
compression costs.
- Lower complexity, easier scale-up.
- A lower catalyst loading is possible, which results in a four times lower catalyst
consumption per tonne of product.
- The slurry bed can operate at higher temperatures and hence results in higher average
conversions due to the more isothermal behaviour. This makes it easier to control the
product selectivities. The SPR can handle catalysts with higher activities than the
multitubular fixed-bed reactor can.
- On-line removal/addition of catalyst allows longer reactor runs due to frequent catalyst
renewal, which is necessary in order to obtain a steady selectivity profile for a single
reactor.
The periodic replacement of the catalyst in the multitubular reactor is cumbersome and
maintenance and labour intensive, and it causes disturbances in the operation of the plant. The
cooling system, with cooling only on the shell-side of the tubes, gives rise to axial and radial
temperature profiles in the tubes. For maximum reaction rates, a maximum average
temperature is desired. This temperature is however limited by the maximum allowable
temperature peak. This maximum temperature is set in order to avoid catalyst sintering and
fouling. The product selectivities are temperature dependent, why it is desirable to be able to
vary the temperature. In tubular fixed bed reactors, the temperature control is however
severely complicated by the need to avoid exceeding the maximum peak temperature.
[Espinoza et al., 1999]
58
One disadvantage with a fluidized bed (such as in the SPR) is that if a poison, like H2S,
should enter the reactor, the whole amount of catalyst will be poisoned. In the case of a fixed
bed, only the layers of the catalyst closest to the entrance will be poisoned. [Dry, 2002] To
achieve this, the removal of sulphur for slurry bed application must be very effective. This is
one of the critical aspects for successful commercialisation of SPRs operating with a Co
catalyst. [Espinoza et al., 1999]
Figure 12. LTFT reactors [Wender, 1996].
The slurry phase LTFT process is by many authors regarded as the most efficient process for
FT clean diesel production today. This FT technology is also under development by Statoil
(Norway) for use to convert associated gas at offshore oil fields into a hydrocarbon liquid.
[Schulz, 1999] Shell however claims that their TFBR works as well as a SPR [Presentation at
GasFuel05 in Brugge, Belgium]. Fixed-bed reactors are also more commonly used for
laboratory-scale experiments, due to faster and simpler operation for screening of different
catalysts.
4.3 Scope of the work
The scope of this report is to describe how to model a fixed-bed (also called trickle-bed) for
the LTFT-synthesis. The laboratory-scale of these reactor types are used at NTNU and by
Statoil for screening of catalysts. The kinetic information from these reactors can also be used
to model slurry phase reactors. In the kinetic experiments, the pellet size of the catalyst in the
fixed-bed is between 53 and 90 μm, in order to avoid mass transfer limitations on the
measured rate. The tube diameter is 10 mm, and the bed height approximately 50 mm. In
larger-scale fixed-beds, this pellet size would result in high pressure drop.
For comparison, the modelling of a slurry phase FT-reactor will be discussed briefly.
Modelling of reactors is made in order to be able to scale-up a process from laboratory results,
to extrapolate the performance of a reactor at conditions outside the conditions on which the
59
model is built, to predict hot-spots and run-away, to predict optimum operating conditions
respecting temperature control, recycling ratio etc.
4.4 Modeling of the trickle-bed FT-reactor
As mentioned above, high heat exchange rates in the TFBR is accomplished by forcing the
syngas at high linear velocities through long narrow tubes to achieve turbulent flow. Each
tube is cooled by boiling water. The wish is to obtain an isothermal reactor, and hence the
reaction heat should be removed by radial transport (mainly conduction). However, the heat
conductivity is rather poor, especially at the tube wall, compared to fluidised beds and this
often results in radial temperature gradients, see Figure 13. These gradients affect the
selectivity and may also lead to increased deactivation of the catalyst. The gradients are
highest near the entrance of the reactor since the reaction rates are highest there, and since the
liquid phase is rather small. Further down in the reactor, the reaction rates are slower due to
depletion of reactants and more and more liquid wax is present, which reduces the radial
temperature gradients. [Krishna and Sie, 2000; Sie and Krishna, 1999]
Figure 13. Concentration and temperature profiles in a reactor of the ‘Mitteldruck ’ Fischer–Tropsch process [Sie
and Krishna, 1999].
The radial heat transport is enhanced by larger catalyst pellets and higher gas velocities. There
must be a compromise between the heat transport/pressure drop and the effectiveness, η, of
the catalyst. The larger the catalyst particle, the larger is the Thiele modulus, which can be
thought of as “a reaction rate” / “a diffusion rate”. A large Thiele modulus will result in a low
effectiveness factor, as shown in Figure 14, which means that the usage of the catalyst particle
is low, i.e. only the outer part of the catalyst particle is taking part in the reaction.
60
Fig. 14. Catalyst effectiveness η as a function of the Thiele modulus Φ for various cobalt and iron catalysts.
Hydrogen/ carbon monoxide molar ratio 2, P = 2.1 MPa, T = 473–513 K [Sie and Krishna, 1999].
Both the effective radial thermal conductivity, λeff, and the wall heat transfer coefficient, αw,
increase with increased Reynolds number (Rep) (see Figure 15). [Sie and Krishna, 1999]
Figure 15. Effective radial thermal conductivity λeff and wall heat transfer coefficient αw as functions of the
particle Reynolds number Rep. dp is the particle diameter and λG is the thermal conductivity of the gas [Sie and
Krishna, 1999].
The problem with the poorest heat exchange rate in the inlet of the reactor, where the need for
heat removal is largest, can partly be solved by adding liquid in order to make sure that the
complete tube operates in the trickle-flow mode. [Sie and Krishna, 1999] Another way to
reduce the gradients at the inlet of the reactor is to lower the conversion per pass (to 20 – 30
%) and recycle the gas outlet. In this way, linear gas velocities are increased. The ARGE
process mentioned above, combines a low conversion per pass and recycling with higher
reaction temperature and pressure. Compared to the classical once-trough TFBR, the ARGE
concept results in an increase in capacity by a factor 25, a reduction in cooling area by a factor
12, and a reduction of the amount of catalyst and steel by a factor of 7. [Krishna and Sie,
2000]
As mentioned above, in FT synthesis there is a demand for a high interfacial mass transfer,
since capillary condensation of the formed waxes makes the pores filled with liquid. [Sie and
Krishna, 1999] Therefore, the modelling of the FT fixed-bed reactor involves description of
the interactions between complex chemical kinetics and transport phenomena.
According to Wang et al. [2003], only a few models for FT fixed-beds are reported in
literature. Atwood and Bennett [1979], a reference in Wang et al. [2003], made a one-
dimensional, heterogeneous plug-flow model. Bub et al. [1980] developed a two-dimensional,
pseudo-homogeneous plug-flow model. Jess et al. [1999] made a pseudo-homogeneous two-
dimensional model. In case of the pseudo-homogeneous models, the intraparticle diffusion
61
was not considered. In the heterogeneous model by Atwood and Bennett [1979], the
intraparticle gradients were encountered for by means of an effectiveness factor. According to
Wang et al. [2003], the use of an effectiveness factor instead of solving the catalyst
pellet/particle equations, makes a fundamental analysis of intraparticle diffusion-reaction
behaviour impossible.
4.4.1 Wang et al. [2003]
Wang et al. [2003] developed a one-dimensional heterogeneous model, with assumed plug-
flow in the gas-phase. Only two phases were accounted for - gas and solid/liquid. The catalyst
was Fe-based, and hence active for the WGS-reaction. Mass and energy balances were set up
for the two phases. The concentration of the components in the solid phase was expressed as
concentration in liquid, and hence the pores were assumed to be filled with liquid wax. Liquid
surrounding the pellets was not taken into account, and it was assumed that the mass transfer
restriction through the gas film surrounding the pellets was negligible. Hence, gas-liquid
equilibrium was assumed at the interface between the bulk gas and the liquid filled pellet. A
modified Soave-Redlich-Kwong (SRK) EOS was used to correlate the equilibrium between
the components in the gas bulk and the same components solved in the wax in the catalyst
pores. The description of this EOS is given in Wang et al. [1999]. For the heat transfer,
resistance between solid and gas was assumed to be located in a film around the pellets and
was expressed as a boundary condition for the pellet equation.
Wang et al. [2003] chose to include the reaction rate terms in the MB (and EB) for the gas
phase, however integrated over the volume of the pellet and then divided by the pellet volume
in order to obtain volume-average values. This was done due to the simplification that there
exist no mass transfer resistance between liquid and gas phase, an assumption which means
that the equilibrium values are attained immediately. From Bischoff and Froment [1990] we
have learnt that when interfacial gradients are accounted for, these terms would have been
replaced by the flux between the phases, i.e. by kgav(CAg - CS
AS) (and by hfav(Tss – Tg)). Wang
et al. [2003] did not estimate this kg, but instead simply just assumed equilibrium
concentrations in liquid and gas.
For the gas phase mass transfer, convection and flux from pellets was encountered. For the
energy balance in the gas phase, convective heat transport, heat flux from pellets and
conduction through tube wall were included.
For the solid phase mass transfer, diffusion and reaction was encountered. For the energy
balance, conduction inside pellets (dispersion term) and reaction were included.
The one-dimensional model cannot predict any radial gradients, which according to the
discussion above might be of significant magnitude in the fixed-bed.
62
Below follows the model equations used by Wang et al. [2003] with the same symbols as
used by Froment and Bischoff [1990]:
Bulk gas phase:
MB: drRdz
CudpR
NR
j
jijs
p
is 2
0 13
)1(3)(
(i = 1, nb of total components involved)
EB: )(4)()1(3 2
0 13 gw
t
RNR
j
jjs
p
g
pgs TTd
UdrH
Rdz
dTcu
p
Initial conditions:
z = 0: ci = ci,0 P = Pin Tg = Tin
Liquid/solid phase:
MB:
NR
j
jijs
is
ei rd
dC
d
dD
1
2
2)(
1
(i = 1, nb of key components involved)
EB:
NR
j
jjs
s
e rHd
dT
d
d
1
2
2)()(
1
Boundary conditions:
ξ = 0: 0d
dCis 0d
dTs
ξ = Rp: iV
i
L
ii xy
)( gs
e
fs TTh
d
dT
where yi and xi are the mole fractions of component i in gas and liquid, respectively, and φL
i
and φV
i are the fugacity coefficients in liquid and gas phase, respectively. This boundary
condition means that component i is in its equilibrium concentrations in the wax and the gas.
Wang et al. [2003] chose to describe the pressure drop in the bed with the classical Ergun
equation:
p
sg
pd
uf
dz
dP2
63
The Peng-Robinson EOS (equation of state) was used to calculate ρg and hence us. The ideal
gas-law can only be applied at low reactor pressures.
The rather complex kinetic rate expressions used in the model by Wang et al. [2003] can be
found in Wang et al. [2001]. Rate expressions were set up for the products, which included
CH4, paraffins and olefins of different carbon numbers, and CO2 (WGS-reaction). All reaction
rate expressions included the chain growth parameter, α, defined above. The chain growth
parameter used by Wang et al. [2001, 2003] was slightly modified compared to the original
αASF as defined by Anderson, Schulz and Flory. The modified α is not constant, but changes
with carbon number, and also accounts for the so-called olefin readsorption factor (βn). If the
catalyst has a high βn, the probability that a desorbed hydrocarbon chain will readsorb on the
catalyst surface and continue to grow is high. This phenomenon gives higher waxes and hence
higher α. The definition of βn can be found in Wang et al. [2001]. This factor can be
calculated knowing the rate constant for the olefin readsorption reaction, k-6, and the partial
pressures of the hydrocarbon products (paraffins and olefins). The βn however approaches 0
rather quickly with increasing carbon number. Practically, ethene, which is the shortest olefin,
has the highest readsorption ability, and it is often an order of magnitude higher than the
readsorption ability of propene.
651
1
2kPkPk
Pk
HCO
CO
ASF
)1(651
1
2 nHCO
CO
nkPkPk
Pk
The parameters k5 and k6 are rate constants for paraffin formation and olefin desorption,
respectively. The description of k1 was not given in Wang et al [2001], but is probably the rate
constant for consumption of CO.
Wang et al. [2001] characterized the wax by NMR and found it to be approximately n-C28H58
in all experimental runs, why this was also put into the model. Dispersion coefficients for H2,
CO and CO2 in this wax, Di, were taken from literature and could be fitted to expressions as a
function of temperature. Dispersion coefficients for the other components were approximated
by means of diffusivity correlations in infinitely dilute solutions:
6.0)/( iCOCOi VVDD
where V is the mole volume. The effective diffusivity of component i was calculated by
correcting the molecular diffusivities for the porosity and tortuosity of the catalyst pellets:
is
ei
DD
Clearly, this model should only work satisfactorily if the composition of the wax is close to n-
C28H58, and therefore should not be so accurate in predicting reactor operation under
conditions far away from those upon which the model is based.
64
In order to make the system of equations converge, the surface liquid concentrations in
equilibrium with the bulk gas concentrations were set as guess values for the unknown
concentrations inside the catalyst pellets.
Below, some of the results from the simulation are discussed. Figure 16 shows the
concentration profiles of CO, H2, CO2 and H2O inside of the wax-filled catalyst pores (0 is at
center and 1 at pellet surface).
Figure 16. Concentration profiles of key components in catalyst pellet [Wang et al., 2001].
The further the FT-reaction proceeds, the more water is produced, which is seen in the
increasing H2O concentration towards the middle of the particle. The more water, the more
CO is consumed in the WGS reaction, at the same time as it is consumed in the FT-reaction,
which explains the rapid decrease in CO concentration between 1 and 0.8Rp. This means that
the reaction zone is actually only in 0.2Rp, which is in good agreement with a value of 0.24Rp
reported in literature for catalyst pellets of 3 mm in diameter. The rapid decrease in CO
concentration in the outmost particle shell is also due to the far more severe diffusion
limitations on CO compared to H2. However, since the concentrations of CO2 and H2 are
rather high at this point (0.85Rp), the reversed WGS-reaction will be triggered, and hence
provide some CO for the FT-reaction even far inside of the pellet.
Since both the reaction order with reference to PH2 and PCO are positive, lower partial
pressures of these reactants will result in a lower reaction rate inside of the catalyst pellet
compared to at the surface. Furthermore, because of the higher H2/CO ratio inside of the
particle, see Figure 17, the selectivity to waxes will be lower here.
65
Figure 17. Variation of H2/CO ratio along the pellet dimension [Wang et al., 2001].
An improved diffusion of the CO would increase the reaction rate as well as the selectivity to
waxes.
The authors calculated the effectiveness factor for several different cases. The effectiveness
factor was calculated by dividing the true pellet-volume-averaged consumption rate of CO
with the pellet-volume-averaged consumption rate of CO if the CO concentration would be as
high as at the surface throughout the whole pellet. Figure 18 and 19 show the effectiveness
factor as a function of temperature and pellet diameter, respectively.
Figure 18. Variation of effectiveness factor with operation temperatures at different pressures [Wang et al.,
2001].
66
Figure 19. Variation of effectiveness factor with pellet size [Wang et al., 2001].
Figure 20 shows the HC distribution as a function of temperature. Figures 21 and 22 show the
selectivity to CH4 and CO2, and C2+ and C5+, respectively, as a function of pellet size.
Figure 20. Product distribution of hydrocarbons at different temperatures [Wang et al., 2001].
67
Figure 21. Selectivity variations of CO2 and CH4 with pellet radius [Wang et al., 2001].
Figure 22. Selectivity variations of C2+ and C5
+ products with pellet radius [Wang et al., 2001].
The conclusion is that small catalyst particles favour the formation of the desired products, at
the same time as the reaction rate is higher. However, in industrial applications the pellet size
should not be below 2 mm, in order to avoid a large pressure drop. The solution is to use so-
called egg-shell impregnation, in which the active metal, in this case Fe, is situated only in the
outmost shell of the pellet. The size of the inert core will have to be optimised in order to gain
a high selectivity to wax, at the same time keeping the total activity not so much under the
activity of the uniformly impregnated pellet. Figure 23 shows the effect of the inert core
radius on the selectivity to C5+ for a catalyst pellet with a radius of 1.5 mm.
68
Figure 23. Effect of inert core radius on C5+ selectivity [Wang et al., 2001].
Figure 24 shows that with an inert core radius of up to 80% of Rp, the reaction rate is actually
not lower compared to the uniform pellet. This indicates that the egg-shell impregnation can
improve the selectivity to waxes, avoiding a significant increase of the reactor volume to
obtain the same productivity as compared to uniform catalyst pellets.
Figure 24. Effect of inert core radius on effectiveness factor [Wang et al., 2001].
The model could satisfactorily predict the performance of different-scale demonstration
processes. The main conclusions from the modelling of Wang et al. [2003] were that a large
tube diameter was unfavourable for the total yield of higher HCs, and that the inner diameter
should not exceed 60 mm. This is a direct effect of the increased bed temperature as a larger
tube diameter implies a poorer heat removal (see Figure 25).
69
Recycling resulted in thermal stability of the reactor, avoiding the hot spot in the beginning of
the reactor, and also enhanced the yield of desired products. With a high recycle ratio the bed
was almost isothermal. The recycle operation means that the superficial gas velocity is
increased, but the space velocity of the fresh feed is unchanged. The lower overall
temperature decreases the CO-conversion, but the total syngas conversion is actually
increased due to the increase in H2/CO usage ratio (i.e. decrease in WGS-reaction rate).
However, from a practical point of view, the power consumption should always be taken into
consideration when choosing the recycle ratio.
An increase in cooling temperature can increase the syngas conversion, but lowers the yield of
higher HCs. Hence, a lower cooling temperature is recommended. An increase in pressure
favours both conversion and yield to desired products.
Fig. 25. Effect of process parameters on the axial temperature profile in the fixed-bed reactor. Base conditions:
dt=32 mm, L=7.0 m, GHSV=500 h−1
, Rcyc=3.0, Tw=Tg,0=523 K, Pin=25 bar. Fresh syngas composition (%): CO:
30.59; H2: 57.75; CO2: 7.0; N2: 4.08; CH4: 0.58 [Wang et al., 2003].
70
4.4.2 Jess et al. [1999]
Jess et al. [1999] developed a two-dimensional pseudo-homogeneous model for FT-synthesis
over a Fe-catalyst.
In the model by Jess et al. [1999], only mass transfer by convection (only in axial direction)
and reaction was considered in the MB. In the EB, radial conduction, advective heat transport
in axial direction, and reaction was encountered. Note that Jess et al. considered the radial
temperature gradients and radial heat transfer, while neglecting radial concentration gradients.
Below follows the model equations used by Jess et al. [1999] with the same symbols as used
by Froment and Bischoff [1990]:
MB: j
NR
j
ijs
is rdz
Cud
1
)1()(
(i = 1, nb of total components involved)
EB:
NR
j
jjspgser rHdz
dTcu
dr
dT
rdr
Td
12
2
)()1(1
Initial conditions:
z = 0, 0 r Ri: ci = ci,0 P = Pin Tg = Tin
Boundary conditions:
r = 0, all z: 0dr
dT
All z, all r: 0dr
dC
r = Ri, all z: )( ,,
,
iwiR
er
iwTT
dr
dT
r = Ro, all z: )( ,
,
coolow
w
owTT
dr
dT
where Ri is the tube inner radius, and Ro the tube outer radius, αw,i and αw,o [W/m2,K] the inner
and outer wall heat transfer coefficient, respectively. λw is the heat conductivity of the wall
[W/m,K].
Jess et al. [1999] expressed the consumption rate of CO as the sum of three rates, as shown in
Figure 26.
71
Fig. 26. Kinetic data of the three main reactions during FT-synthesis on the iron-catalyst (ARGE-Lurgi-
Ruhrchemie) [Jess et al., 1999].
The rate expressions above are not truly kinetic. Rather, they are only valid in the case of
mass transfer limitations inside the catalyst pellets. Hence, the rate expressions describe the
rate at which CO is consumed if diffusion of reactants through the catalyst pores is the rate
limiting step, and are, for pellet diameters > 2.5 mm, only valid at temperatures above 170 ºC.
External diffusion limitations could, according to Jess et al. [1999], be neglected up to 400 ºC,
but this is just a hypothetic value since the catalyst would rapidly deactivate at temperatures
above 260 ºC. These rate expressions corresponds to an effectiveness factor of 0.2 at 250 ºC,
and the activation energies in the expressions are approximately half of the true activation
energies, which is typical in the range of pore diffusion limitations [Fogler, 1999]. In their
pseudo-homogeneous model, Bub et al. [1980] also used “non-kinetic” rate data based on
laboratory experiments with rather large particle diameters. By using the same particle
diameter in the laboratory experiments as used in the pilot-scale reactor to be modeled, the
possible intraparticle mass transfer limitation on the overall rate was not necessary to be
considered.
Unlike Wang et al. [2003], the rate expressions of Jess et al. [1999] do not include the product
selectivity. It was not explained how the selectivity was calculated. Since the model is
pseudo-homogeneous, the diffusion of reactants through the waxes inside the catalyst pores is
72
baked in in the rate expressions, and in this way intraparticle gradients are somehow
accounted for, but this model should not be so accurate in predicting reactor operation under
conditions far away from those upon which the model is based. For instance, it can only be
applied if the catalyst pellets have exactly the same dimensions as the pellets used in the
“kinetic” measurements.
The object was to make a model that could predict the performance with a nitrogen-rich (50
vol-%) syngas. By producing the syngas by partial oxidation of natural gas with air, instead of
with pure oxygen, the need for the capital intense air separation unit is eliminated. Due to the
high inert concentration, this concept can (or must, in order not to build up inerts or to be
forced to bleed off a large stream) work without recycling of the tail gas and hence does not
need a recycle compressor.
The results of the modeling showed that nitrogen plays an important role in removing the heat
released by the FT-reaction. This led to an optimum tube diameter of 70 mm for a stable and
safe operation, compared to 45 mm for the nitrogen-free syngas. The production rate per tube
was about three times higher than in the case with a nitrogen-free syngas, due to the possible
high once-through conversion. This would decrease the investment cost of multitubular fixed-
bed reactors. However, since nitrogen is diluting the system, a higher total pressure will be
needed in order to preserve the partial reactant pressures, which is important for the kinetics.
The critical temperatures were defined as the temperatures not to be exceeded in order to
avoid a temperature runaway. The estimation of these temperatures can be found in Jess et al.
[1999]. Figure 27 shows how the tube diameter influences the critical temperatures in the
nitrogen-free and rich cases.
Fig. 27. Influence of the diameter of the single tubes of a FT-reactor on the critical maximum temperature for
nitrogen-rich and nitrogen-free syngas (volume rate of syngas according to τe = 25 s) [Jess et al., 1999].
73
4.5 Modeling of the slurry phase reactor
According to Krishna and Sie [2000], the best reactor choice is the slurry phase reactor (or as
they call it “the bubble column slurry reactor”) for large-scale plants with capacities around
40,000 bpd. It was calculated that for such a large total production, 10 TFBR, 17 slurry
reactors operating in the homogeneous regime or four slurry reactors operating in the
heterogeneous regime are needed. The limiting criterion was a maximum reactor weight of
900 tons.
4.5.1 Different flow regimes and estimation of gas hold-up
The homogeneous regime is characterized by a relatively low superficial gas velocity, usG,
and by small bubbles (db = 1 – 7 mm). When the superficial gas velocity reaches the value
Utrans, coalescence of the small bubbles occurs and larger bubbles are produced. The regime
with larger bubbles (db = 20 – 70 mm) and higher usG is called the heterogeneous regime.
(Figure 28 shows a schematic of the two regions.) These larger bubbles have a high rising
speed through the column (1 – 2 m/s) in a plug-flow manner. Smaller bubbles are also present
in the heterogeneous regime, and since they are entrained in the liquid phase, they are often
assumed to have the same backmixing characteristics as the liquid phase. When the catalyst
particles are small (< 50 μm), they are well mixed with the liquid, and the slurry phase can be
regarded as a pseudo-homogeneous phase. This assumption, with no catalyst settling, works
well at larger reactor diameters (> 0.5 m) at high gas velocities (usG > 0.2 m/s).
Fig. 28. Homogeneous and churn–turbulent regimes in a gas–liquid bubble column. The figure on the right
shows that increasing the system pressure delays the regime transition point [Krishna and Sie, 2000].
The volume fraction of catalyst in the liquid, εcat,L (εs in Figure 29) strongly affects the gas
hold up, εG (ε in Figure 29).
74
Fig. 29. Influence of increased particles concentration on the total gas hold-up in columns of (a) 0.1 m and (b)
0.38 m diameter. Air was used as the gas phase in all experiments. The liquid phase was paraffin oil (density,
ρL=790 kg m−3
; viscosity, μL=0.0029 Pa s; surface tension, σ=0.028 N/m) to which solid particles in varying
concentrations were added. The solid phase used consisted of porous silica particles (skeleton density=2100 kg
m−3
; pore volume=1.05 ml g−1
; particle size distribution, dp: 10%<27 μm; 50%<38 μm; 90%<47 μm). The solids
concentration s, is expressed as the volume fraction of solids in gas free slurry. The pore volume of the particles
(liquid-filled during operation) is counted as a part of the solid phase [Krishna and Sie, 2000].
For modeling purposes it is important to distinguish between the gas hold up in large bubbles
and that in the small bubbles. This can be made by instantaneously switching off the gas flow
to a slurry column at time t = 0. The gas hold-up will quickly decrease due to the escape of
large bubbles. After this quick reduction in gas hold-up, the small bubbles escape and the gas
hold-up is further reduced, as illustrated in Figure 30. From this experiment, the voidage of
gas in the dense phase (see Figure 30), εG,df, the gas hold-up in the large bubbles, εG,b, and the
superficial velocity through the dense phase, us,df, can be estimated. us,df is often taken to be
the same as Utrans.
Fig. 30. Dynamic gas disengagement experiments for air/paraffin oil and air/36 vol.% paraffin oil slurry in the
0.38-m-diameter column. The system properties are as given in the legend to Figure 29 [Krishna and Sie, 2000].
75
It is clearly seen that the higher the catalyst concentration in the slurry phase, εcat,L, the smaller
is the gas hold-up in the small bubbles. This is due to the increased coalescence of small
particles into bigger in the presence of solid particles. At εcat,L > 30 %, the population of small
bubbles is destroyed. The εG,df for a certain εcat,L is essentially constant at usG > 0.1 m/s for the
heterogeneous regime. Furthermore, the εG,df is essentially independent on reactor diameter
(DT). This is very useful for scale-up purposes, since a rather small reactor can be used to
determine the εG,df under actual reaction conditions.
The εG,b, however, of course increases with increasing superficial velocity through the large
bubble phase (usG-us,df), but seems to be independent on εcat,L in the range 0.16 < εcat,L < 0.36.
Unlike the εG,df, the εG,b (εb in Figure 31) is strongly dependent of the reactor diameter. The
εG,b is reduced at large diameters due to the increase in rise velocity, which, in turn is due to
the reduced wall effects at large diameters. Relationships to find the large bubble rise velocity
for different db/DT ratios is found in Krishna end Sie [2000].
Fig. 31. Influence of column diameter on the hold-up of large bubbles b in (a) paraffin slurries and (b) Tellus
oil [Krishna and Sie, 2000].
These relationships must be modified to be valid at higher pressures, as shown in Figure 32.
The modifications are presented in Krishna and Sie [2000]. Briefly, the expression for
calculation of the rise velocity of large bubbles, ub, is corrected for the higher density of a gas
at higher pressure compared to atmospheric pressure. ub for syngas at 30 bars, which is
common in FT, is for instance only 43% of the ub for air at atmospheric pressure, which is
easily understood since the gas densities are 7 kg/m3 and 1.29 kg/m
3 for the pressurized
syngas and the atmospheric air, respectively.
76
Fig. 32. The influence of elevated pressure on gas hold-up [Krishna and Sie, 2000].
When the ub is known, the εG,b can be calculated through the steps below. εG,df in a pressurized
system can be estimated by:
Lcat
dfGrefG
G
dfGdfG ,
0,,
48.0
,
0,,,
7.01
where εG,df,0 is εG,df at 0% catalyst concentration, ρG,ref is the density of gas at ambient
conditions, and ρG the density of the gas at pressurized conditions. The rise velocity of the
small bubbles, in atmospheric or pressurized systems, can be calculated by:
Lcat
small
smallsmallu
uu ,
0,
0,
8.01
where usmall,0 is the rise velocity at 0% catalyst concentration. This is not much affected by
pressure. The superficial gas velocity through the dense phase is estimated by:
dfGsmalldfs uu ,,
Since ub is known and defined as:
bG
dfssG
b
uuu
,
, )(
we can now calculate εG,b. The total gas hold-up in a pressurized slurry column can be
calculated according to:
)1( ,,, bGdfGbGG
4.5.2 Mass transfer
As mentioned above, in slurry reactors intraparticle diffusion limitations are often negligible,
due to the small pellets used. Mass transfer from gas to liquid can however be rate limiting.
This is often the case with highly active catalysts in high concentrations in slurry reactors
operating in the heterogeneous regime.
77
The large bubbles represent the major gas throughput. Conventional calculation of mass
transfer rates predicts a very low mass transfer between the gas and slurry phase for large
bubbles. Experiments have, however, shown that the real mass transfer rates are 5 – 10 times
higher than that expected from conventional calculations based on hold-up and bubble size.
The explanation to this is that during the characteristic time for mass transfer from the gas to
the liquid, the bubbles exchange gas with other bubble size classes. In conclusion, the large
bubbles represent the major gas throughput, but gas-liquid mass transfer is mainly determined
by the interfacial area between the small bubbles and the slurry. In most cases, the mass
transfer between gas and liquid is not limiting the overall rate in FT-synthesis. The volumetric
mass transfer (g/l) coefficient for the large bubbles, (kLa)large, can be calculated according to:
refL
L
bG
elL
D
Dak
,,
arg5.0
)(
where DL is the diffusivity in the liquid phase and DL,ref is a constant of 2 * 10-9
m2/s. The
diffusivities of the reactants CO and H2 at 240 ºC are 17.2 * 10-9
and 45.5 * 10-9
m2/s,
respectively. For the small bubbles, the expression has been found to be the same as for the
large bubbles, but with a constant of 1.0 instead of 0.5:
refL
L
dfG
smallL
D
Dak
,,
0.1)(
Note that the mass transfer coefficients kLa, are not the same as kL in Bischoff and Froment
[1990] in which this is a mass transfer coefficient from g/l interface to liquid bulk. kLa used
by Maretto and Krishna in this case is an overall mass transfer coefficient from gas bulk to
liquid bulk, including the interfacial area.
4.5.3. Mixing
The large bubbles concentrate in the middle of the column and carry the liquid upwards. At
the top of the column, the large bubbles escape from the slurry, and the liquid is recirculated.
The larger the reactor diameter, the bigger is the liquid velocity, VL, upwards in the middle
and downwards at the wall. However, by normalizing the liquid velocities by dividing VL(r)
with the liquid velocity at the central line, VL(0), the radial distributions are similar for all
reactor diameters. Hence, the liquid phase axial dispersion coefficient, Da,L, should be
proportional to VL(0). One useful relationship is:
8/1
32/1)(2.0)0(
L
TLg
UgDV
where υL is the kinematic viscosity of the liquid phase. Krishna and Sie [2000] showed that
the backmixing of the slurry phase is actually the same as for low viscosity liquids, such as
water, at the same superficial gas velocity. Measurements of the Da,L have led to the following
simple relationship:
TLLa DVD )0(31.0,
78
Estimation of Da,L in a commercial scale bubble slurry column with a reactor diameter of 7 m
and a superficial gas velocity of 0.35 m/s yields Da,L = 10 m2/s. This high value of the
dispersion coefficient suggests that the slurry phase is well mixed, and hence can be modeled
as a CSTR.
4.5.4 Heat transfer
The heat transfer is favored by high gas velocities and high εcat,L (εs in Figure 33), which are
typical for the heterogeneous regime.
Fig. 33. Estimate of the heat transfer coefficients to vertical cooling tubes [Krishna and Sie, 2000].
4.5.5 The model
The model, the results of which were briefly described in Krishna and Sie [2000], can be
found in Maretto and Krishna [1999]. A schematic picture of the model is given in Figure 34,
in which U = usG, and Udf = us,df.
Fig. 34. Generalized two-phase model applied to a bubble column slurry reactor operating in the churn–turbulent
regime [Krishna and Sie, 2000].
79
The slurry was assumed to have the properties of C16H34. The rate expression for the
consumption of syngas was taken from Yates and Satterfield [1991]:
2)1(
2
2
CO
COH
HCObp
papR
where a and b depend on the catalyst used, and are varying with temperature. Note that
according to the FT-reaction stoichiometry, RH2 = 2RCO. The selectivity was described with
the ASF-distribution and only paraffins (CnH2n+2) were assumed, the molar fraction of which
was expressed as:
1)1( n
ASFASFnx
αASF was set to 0.9.
As mentioned above, in the heterogeneous regime, which was modeled in this article, the
larger bubbles (20 – 70 mm) travel up the column at high velocities (1 – 2 m/s) in a plug-flow
manner, resulting in a well-mixed slurry. The smaller bubbles are hence entrained in the
slurry.
A one-dimensional heterogeneous model was made of a slurry reactor with a diameter of 7 m
and height of 30 m. The temperature was 240 ºC and pressure 30 bar. The large bubbles were
modeled as if being in plug-flow, with a superficial velocity of us-us,df, and the slurry phase
was assumed to be well-mixed. The temperature was assumed being constant in the reactor
and the catalyst particles, why no energy balances are needed. The model assumes that
resistance between liquid and catalyst surface is negligible, and also intraparticle gradients
were neglected. The catalyst pellets had a diameter of 50 μm.
MB large bubbles:
LCO
CO
elGCO
elCOL
elGCOdfssGC
H
Cak
dz
Cuud,
arg,,
arg,
arg,,,)(
))((
LH
H
elGH
elHL
elGHdfssGC
H
Cak
dz
Cuud,
arg,,
arg,
arg,,,
2
2
2
2
2 )())((
MB small bubbles:
ZCH
CakCCu LCO
CO
smallGCO
smallCOLsmallGCO
i
GCOdfs
,
,,
,,,,, )()(
ZCH
CakCCu LH
H
smallGH
smallHLsmallGH
i
GHdfs
,
,,
,,,,, 2
2
2
222)()(
80
where Ω is the cross sectional area of the reactor in [m2], Z is the dispersion height of the
reactor in [m], and superscript i means inlet of reactor. It was assumed that the concentration
of CO in the inlet gas is equal in large and small bubbles and equals CiCO,G. The same was
assumed for H2. The superficial gas velocity through small bubbles, us,df, was assumed
constant in the whole reactor.
MB liquid phase:
0)()(2,,
,,
,,
arg.,
0
arg,
HCOLLCO
o
sLLCO
CO
smallGCO
smallCOLLCO
CO
elGCOZ
elCOL RZCuCH
CakZdzC
H
Cak
02)()(222
2
2
22
2
2
2 ,,
,,
,,
arg.,
0
arg,
HCOLLH
o
sLLH
H
smallGH
smallHLLH
H
elGHZ
elHL RZCuCH
CakZdzC
H
Cak
where εL is the slurry hold-up, equal to 1-εG, since in the case with a slurry reactor the catalyst
particles are included in the slurry. The equations for the liquid phase are typical equations for
a CSTR, i.e. the concentrations in the slurry are assumed constant in the reactor, and also the
concentrations in the small bubbles, which means that the MB for the slurry is an overall MB
for that phase. Since the concentrations in the large bubbles are not constant, the mass transfer
between gas and liquid must be integrated along the reactor in order to fit in in the overall MB
for the slurry phase. The Henry’s constants were used as estimated solubilities for H2 and CO
in the wax, which was assumed to have the characteristics of C16H34, and equal to 2.478 and
2.964 at a temperature of 240 ºC for CO and H2, respectively.
It was also assumed that the contraction of gas volume due to reaction only affects the large
bubbles. The contraction factor, Ф, for 100 % syngas conversion was estimated to –0.648,
assuming 5 % inert in the syngas feed. Hence, the superficial gas velocity through large
bubbles decreases with conversion according to:
)1)(( ,, Xuuuu dfs
i
sGdfssG
where X is the conversion of CO (or H2). The conversion of CO equals the conversion of H2
in this case since the inlet molar H2/CO ratio is the same as the usage ratio in the reactor, i.e.
2. The reason for why this relationship was set up is that the authors only considered mass
balances and distribution between gas and liquid phase for the reactants (and not the
products). Therefore, there is lack of information considering how many moles of gas that
exist at different z-points in the reactor. The expression above estimates this information.
The solution to the equations above was found by means of an iterative procedure. This kind
of solution is typical when differential equations are coupled with algebraic ones, and in this
case most probably means that the concentration in the well-mixed phases are guessed as start
values, and then integration of the gas-phase along the reactor will give new guessed values of
the concentrations in the well-mixed phases, closer to the true ones. The authors mentioned
that it was possible to describe the concentration of one reactant as a function of the other,
which simplified the solution of the equations.
Simulations were made with usG = 0.12 – 0.4 m/s and εcat,L = 0.20 – 0.35. Since the reactor was
assumed to be isothermal, all reaction heat must be removed. This was modeled by assuming
81
vertical cooling tubes of 50 mm in diameter, with coolant of 230 ºC. The heat transfer
coefficient from slurry to coolant was estimated by:
)Pr(Re1.0 2
GFrSt
where the different dimensionless groups are explained in Deckwer et al. [1982], a reference
in Maretto and Krishna [1999]. The slurry density was calculated from:
LcatpLcat
Sk
LLSl ,,1
where ρp is the catalyst density in [kg/m3 of particle including voids] and ρSk is the catalyst
skeleton density in [kg/m3 of catalyst solids without voids]. The slurry viscosity was
estimated according to:
)5.41( ,LcatLSl
4.5.6 The results
Results from the simulation are shown in Figures 35 - 37. It can be seen that as the superficial
gas velocity, usG (or U in Figure 35), increases, the conversion decreases, but the productivity
increases. That the productivity increases as the space velocity is increased should be due to
an enhanced mass transfer. Practically, a single pass conversion in a slurry phase FT-reactor
should be around 90 % so that no recycling is necessary. For such a high conversion, it is
necessary to keep the superficial gas flow below 0.3 m/s.
Fig. 35. Fischer–Tropsch reactor simulation results: syngas conversion [Maretto and Krishna, 1999].
82
Fig. 36. Fischer–Tropsch reactor simulation results: total reactor productivity (column diameter DT=7 m;
dispersion height H=30 m) [Maretto and Krishna, 1999].
Increasing the catalyst concentration in the slurry, εcat,L (or εs in Figure 36), of course
increases both conversion and productivity, but the influence of εcat,L is not only because of
the increasing number of active catalyst sites, but also due to its reducing effect on the total
gas hold-up. So, increasing the εcat,L leads to lower εG and hence higher slurry hold-up, εL,
which in turn means that more catalyst can be loaded into the reactor. The higher the
productivity, the higher the number of cooling tubes needed (Figure 37).
Fig. 37. Fischer–Tropsch reactor simulation results: number of 50-mm-diameter cooling tubes [Maretto and
Krishna, 1999].
A sensitivity analysis was also performed to investigate the effect of the mass transfer
coefficient from gas to liquid, and the effect of the Yates-Satterfield kinetic constant a, on the
overall productivity. The superficial gas velocity, usG, was set to 0.4 m/s and the catalyst
concentration in the slurry to εcat,L = 0.25. A 10-fold increase or 3-fold reduction of kLa as
compared with the base case, had a negligible effect on the productivity. However, doubling
the kinetic constant a resulted in a 60 % increase of the productivity. Hence, it was concluded
that the slurry phase reactor at this base case is kinetically controlled.
83
5. Conclusion/discussion
It seems common for the few models describing FT in fixed-beds (trickle-beds) not to
consider the liquid as a separate phase. This is probably since the liquid essentially just is
existing as a thin film around the catalyst pellets, and hence the gas phase can be seen as the
continuous phase, and the liquid external hold-up, εL, is practically zero. One could of course
include the liquid phase in the model, as would be the case for other gas/liquid/solid systems
such as slurry reactors or more conventional trickle bed reactors (such as used in the
hydrotreatment of oils) in which the liquid hold-up is much larger and also the liquid flow.
The simplification with no separate liquid phase, in the case of the model by Wang et al.
[2003] who used true intrinsic kinetic rate expressions, is justified if the existence of the
liquid film around the pellets does not affect the overall rate, i.e. if no interfacial gradients
occur between gas and gas/liquid interface, and gas/liquid interface and liquid, and between
liquid and solid. Wang et al. [2003] did account for temperature gradients in a gas film around
the pellets. If mass transfer restrictions in the liquid film around the pellets can be neglected,
there is no need to find the interfacial areas, av´ and av´´, which otherwise seem rather
troublesome to find especially if the catalyst pellets are not completely wetted by the liquid.
The models described above developed by Wang et al. [2003] and Jess et al. [1999] did not
explain how the product yield was calculated. Probably, a material balance over the whole
reactor is needed since no liquid phase is accounted for, and the wax composition is assumed
to be constant, and hence cannot describe the proper product distribution.
In all models presented here, the composition of the wax is assumed to be constant. In order
to develop a model able to predict the performance of a wide range of conditions, the model
should be able to predict the composition of the wax phase. The composition of the wax
determines Dei inside the pores and also the concentrations of components at the gas/liquid
interface at the pore mouths. Maybe, it would be possible to solve such a problem iteratively,
by guessing a composition of the wax, and then integrate the gas phase over the reactor in
order to get a new guess value for the composition. For each composition of the wax, the
equilibrium values for gas-phase concentration and liquid-phase concentration of reactants
and products would be different. In a real FT-trickle-bed, the composition of the wax would
vary along the reactor, and, maybe more important, the thickness of the liquid film will
increase downwards the reactor. Another approach would be to assume that the wax
composition in a z-point is given by the selectivity in that point. In this case, of course the
selectivity is not constant in the reactor, but varies with for instance H2/CO ratio at catalyst
surface, as suggested by Wang et al. [2001].
The fact that the catalyst pores are filled with liquid wax, and that diffusion through wax is
much slower than diffusion through gas, leads to the choice of making a heterogeneous model
to account for interfacial and intraparticle gradients. This could have been made with an
effectiveness factor instead of solving the particle equations. However, such a model would
not be able to predict the product selectivity with a high accuracy outside the conditions used
for building the model, since the selectivity is very much dependent on the H2/CO ratio at the
active site on the internal catalyst surface. Only by solving the particle mass balance the true
H2/CO ratio at the active site can be predicted.
The complexity of the FT synthesis regarding the broad product distribution makes it
desirable to simplify the model equations most often by choosing a 1-dimensional model, and
84
also to treat the liquid and catalyst as a pseudo-homogeneous phase. It also seems to be
common only to consider the mass balances for the reactants.
85
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