Microkinetic modeling of the Fischer-Tropsch synthesis over cobalt catalysts

Article abstract of DOI:10.1002/cctc.201402662

We present a detailed microkinetic analysis of the Fischer-Tropsch synthesis on a Co/γ-Al₂O₃ catalyst over the full range of syngas conversions. The experiments were performed in a Carberry spinning basket batch reactor at initial H₂/CO ratios between 1.8 and 2.9, temperatures of 469 and 484 K, and initial pressures of 2 MPa. A reaction mechanism based on the H₂-assisted CO activation pathway, which comprises 128 elementary reactions with 85 free parameters, was proposed to explain the experimental results. Each of these elementary reactions belongs to one of the following reaction groups: adsorption-desorption, monomer formation, chain growth, hydrogenation-hydrogen abstraction, or water-gas shift. A twostage parameter estimation method, based on a quasi-random global search followed by a gradient-free local optimization, has been used to calculate the values of pre-exponential factors and activation energies. The use of data obtained from batch experiments enabled an effective analysis of dominating reactions at different stages of syngas conversions.

Full text of DOI:10.1002/cctc.201402662

DOI: 10.1002/cctc.201402662
Full Papers
Microkinetic Modeling of the Fischer–Tropsch Synthesis
over Cobalt Catalysts
Pooya Azadi, George Brownbridge, Immanuel Kemp, Sebastian Mosbach, John S. Dennis,
[a]
and Markus Kraft*
We present a detailed microkinetic analysis of the Fischer–
actions belongs to one of the following reaction groups: ad-
sorption–desorption, monomer formation, chain growth, hy-
drogenation–hydrogen abstraction, or water–gas shift. A two-
stage parameter estimation method, based on a quasi-random
global search followed by a gradient-free local optimization,
has been used to calculate the values of pre-exponential fac-
tors and activation energies. The use of data obtained from
batch experiments enabled an effective analysis of dominating
reactions at different stages of syngas conversions.
Tropsch synthesis on a Co/g-Al O catalyst over the full range
2
3
of syngas conversions. The experiments were performed in
a Carberry spinning basket batch reactor at initial H /CO ratios
2
between 1.8 and 2.9, temperatures of 469 and 484 K, and ini-
tial pressures of 2 MPa. A reaction mechanism based on the
H -assisted CO activation pathway, which comprises 128 ele-
2
mentary reactions with 85 free parameters, was proposed to
explain the experimental results. Each of these elementary re-
Introduction
[
1]
The foreseeable decline in the supply of conventional oil and
the recent development in the exploitation of unconventional
gas and large-scale gasification technologies have together re-
sulted in a renewed interest in the Fischer–Tropsch (FT) synthe-
number of experimental data points are available. The use of
systematic and semiautomated methods for parameter estima-
tion, as opposed to just manually adjusting parameter values,
makes it easier to detect and understand potentially underde-
termined parameters. Examples of recent efforts toward mod-
eling of the FT synthesis reactions are given in Refs. [7] and [8].
Herein, we present a detailed microkinetic analysis of the FT
reactions on a Co/g-Al O catalyst over the full range of syngas
sis. In this process, mixtures of CO and H are catalytically con-
2
verted into complex mixtures of hydrocarbons via successive
deoxygenation and hydrogenation of CO followed by the addi-
tion of the resultant CH monomers to growing hydrocarbon
x
2
3
chains. Despite the apparent simplicity of the chemistry, funda-
mental aspects of the surface reactions in FT synthesis, such as
the dominant CO activation pathway, have been highly contro-
versial subjects in the field of heterogeneous catalysis for sev-
conversions. A two-stage parameter estimation method, based
on a quasi-random global search followed by a local optimiza-
[9–11]
tion,
has been used to systematically calculate suitable
values of pre-exponential factors and activation energies. A re-
[
2–6]
eral decades.
action mechanism based on the H -assisted CO activation
2
[2–5]
Owing to the large number of reacting species, readsorption
and conversion of primary products, difficulties in measuring
surface intermediates, and coverage-dependent reaction rates,
detailed mechanistic modeling of FT synthesis is highly com-
plex. Furthermore, even if the smallest number of elementary
reactions sufficient to account for the major FT products is
considered, there remains more than one set of reaction rate
constants, corresponding to different fractional surface cover-
ages, from which the behavior of the system can be predicted.
As any serviceable FT mechanism involves upwards of 40 free
parameters (i.e., pre-exponential factors and activation ener-
gies), the system can remain underdetermined even if a large
pathway,
comprising 128 elementary reactions with 85 free
parameters, was implemented to simulate 1176 measured data
points across 8 experiments. The experiments were performed
in a batch reactor at H /CO ratios between 1.8 and 2.9, temper-
2
atures of 469 and 484 K, and initial pressures of approximately
2 MPa. The experiments were run to completion, which meant
that several different reactions were dominant at different
stages of the process. At low conversions, the primary reac-
tions (e.g., monomer formation and chain growth) dominated;
however, as the process progressed, the secondary reactions
(e.g., alkene readsorption and water–gas shift) became more
important.
The agreement between experiment and model responses
was quantified by using a least-squares objective function,
which is explained in the Computational Methods section. The
initial values of the activation energies and pre-exponential
factors were chosen from previous studies on the basis of DFT
and transition state theory, respectively. However, owing to the
oversimplified nature of these first-principle methods, particu-
larly with respect to surface composition, the findings of such
[
a] Dr. P. Azadi, G. Brownbridge, I. Kemp, Dr. S. Mosbach, Prof. J. S. Dennis,
Prof. M. Kraft
University of Cambridge
New Museums Site
Pembroke Street, Cambridge CB2 3RA (United Kingdom)
E-mail: mk306@cam.ac.uk
Supporting information for this article is available on the WWW under
http://dx.doi.org/10.1002/cctc.201402662.
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studies are often associated with large uncertainties
and they can provide only a limited insight into the
kinetics of FT synthesis (see the Supporting Informa-
tion). Hence, the search for the optimum value of
each parameter was conducted within reasonable
bounds around its initial value determined from rele-
vant first-principle calculations.
Results and Discussion
The key assumptions behind the presented kinetic
model are as follows: 1) the reactor is isothermal and
homogeneous; 2) the rate of the reaction is con-
trolled by intrinsic surface kinetics and not mass
transfer; 3) the catalyst contains only one type of active site,
and all reactions occur competitively on the surface of metal
nanoparticles; 4) the pre-exponential factors and activation en-
ergies are coverage independent; and 5) the yields of oxygen-
ated hydrocarbons throughout the reaction are negligible.
A schematic diagram of the essential pathways in FT synthe-
sis, represented by simplified reaction groups and typical links
among them, is shown in Scheme 1. To minimize the number
of parameters in the model, parallel pathways within each re-
action group (i.e., each box in
Scheme 1. Flow diagram for the reaction mechanism.
a C H
molecule can be generated through hydrogenation
growing chain or through readsorption and subse-
2n+1
n
2n+2
of a C H
n
quent hydrogenation of a previously desorbed C H molecule.
n
2n
The elementary reaction steps included in the presented mi-
crokinetic model, along with their respective pre-exponential
factors and activation energies, are given in Table 1. The exper-
imental results and model responses for single carbon com-
pounds, paraffins, and olefins are plotted in Figures 1–3, re-
spectively. In line with the findings of previous DFT and isotope
Scheme 1) were avoided. For ex-
ample, with regard to the mono-
mer formation group, only ele-
mentary reactions representing
Table 1. List of elementary reactions and their pre-exponential factors and activation energies obtained from
parameter estimation.
[a]
H -assisted CO deoxygenation
2
Elementary
step
Reaction
A
f
E
f
A
r
E
r
were considered and the carbide
mechanism was excluded from
the analysis. Likewise, the addi-
tion of carbene (CH ) to C H
2n+
Adsorption–desorption
3
12
1
2
3
4
5
H +2*$2H*
2
1.0ꢁ10
1.0ꢁ10
1.3ꢁ10
5.4ꢁ10
3.7ꢁ10
6.0ꢁ10
–
–
6.8ꢁ10
1.9ꢁ10
1.0ꢁ10
4.1ꢁ10
1.9ꢁ10
1.8ꢁ10
48.1
86.7
3
16
CO+*$CO*
2
n
7
17
C
C
C
2
3
n
H
H
H
4
+2*$C
+2*$C
2
H
H
4
**
**
2n**
32.2
71.9
155.0
91.9
(
nꢀ2) was assumed to be the
1
10
17[b]
8
13
6
3
6
sole pathway responsible for hy-
drocarbon chain growth, al-
though it is possible that the ad-
13[c]
13
–31
2n +2*$C
n
H
133.6
58.9
90.4
32
H O+2*$OH*+H*
2
123.0
Monomer formation
1
2
12
8
33
34
35
CO*+H*$HCO*+*
8.4ꢁ10
6.1ꢁ10
2.2ꢁ10
1.0ꢁ10
128.1
84.3
44.0
34.7
1.9ꢁ10
8.1ꢁ10
5.5ꢁ10
4.2ꢁ10
54.1
121.8
75.1
dition of other types of CHx
15
13
HCO*+H*$HCOH**
HCOH**+2*$CH***+OH*
monomers to C H growing spe-
10
10
n
y
1
3
cies also makes a considerable
contribution. Therefore, the rate
of conversion between any two
species within each group in the
present model essentially repre-
sents the overall conversion rate
resulting from all possible path-
ways among them.
36
CH***+H*$CH **+2*
18.8
2
Chain growth
1
1
4
2
5
37
38
39
CH
2
**+CH
2
**$C
2
H
4
**+2*
*+2*
*+2*
1.2ꢁ10
3.0ꢁ10
1.6ꢁ10
5.0ꢁ10
4.5
39.5
57.3
53.1
5.6ꢁ10
1.5ꢁ10
4.9ꢁ10
6.8ꢁ10
28.5
107.0
57.8
13
6
C
C
2
H
H
5
*+CH
*+CH
2
**$C
**$C
3
4
H
H
7
14
3
7
2
9
1
3[d]
11
40–65
CnH2n+1*+CH **$Cn+1H2n+3*+2*
2
163.0
Hydrogenation–H abstraction
1
1
4
6
9
66
67
68
CH
2
**+H*$CH
3
*+2*
1.5ꢁ10
6.8ꢁ10
1.5ꢁ10
1.1ꢁ10
3.4ꢁ10
1.5ꢁ10
1.1ꢁ10
69.6
126.6
59.2
4.7ꢁ10
2.8ꢁ10
4.1ꢁ10
1.9ꢁ10
52.9
34.1
53.3
68.2
7
C
C
2
3
H
H
4
**+H*$C
**+H*$C
2
H
H
5
*+2*
*+2*
13
10
12
6
3
7
1
1
1
1
4
7
4
5
The absence of parallel path-
ways within each reaction
group, however, does not rule
out the presence of parallel
pathways for the consumption
69–95
96
C H **+H*$CnH2n+1*+2*
66.8
n
2n
CH
3
*+H*!CH
4
+2*
141.0
131.0
138.8
9
9
7
C
C
2
H
H
5
*+H*!C
H +2*
2 6
8–125
n
2n+1*+H*!C
n
H2n+2 +2*
Water–gas shift
126
127
11
OH*+OH*!H O+O**
2
9.3ꢁ10
8.7ꢁ10
2.2ꢁ10
135.3
18.2
8
1
(or generation) of gas species.
CO*+O**!CO
2
+3*
6
1
28
H*+O**!OH*+2*
86.2
For instance, several pathways
for the consumption (and gener-
ation) of H2 gas exist in the
model (Scheme 1). For example,
ꢁ
1
[a] The units of activation energies (E
f
and E
of adsorption reactions and 0 for A
tion (1) with c=1.83. [c] Af,C4 in Equation (1) with c=0.73. [d] Af,C4 in Equation (1) with c=2.29.
r
) and pre-exponential factors (A
f r
and A ) are [kJmol ] and
ꢁ
n
ꢁ1
[Pa
s
], respectively; n=1 for A
f
f
of all other reactions. [b] Af,C4 in Equa-
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1 2
Figure 1. Partial pressures of C species at 469 K and with H /CO ratios of,
from top to bottom, 1.8, 2.2, 2.5, and 2.9.
2
Figure 2. Partial pressures of paraffins at 469 K and with H /CO ratios of,
from top to bottom, 1.8, 2.2, 2.5, and 2.9. The insets show the weight distri-
[
3,12]
bution (P ꢁn) of higher hydrocarbons corresponding to the last point in
each simulation.
studies,
the adsorption of H and CO (Table 1, reactions 1
n
2
and 2) and the first CO hydrogenation step (reaction 33) are
found to be equilibrated throughout each experiment.
To account for the dependence of the rates of alkene ad-
sorption–desorption (reactions 5–31) and alkyl growth (reac-
tions 40–65) on the number of carbon atoms, Equation (1) was
utilized to calculate the values of the pre-exponential factors
of these reactions as a function of the carbon number (n) and
the value of the pre-exponential factor for the relevant reac-
tion involving the C species (A ).
4
C4
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2
Figure 3. Partial pressures of olefins at 469 K and with H /CO ratios of, from
top to bottom, 1.8, 2.2, 2.5, and 2.9.
Figure 4. Fractional surface coverage against CO conversion at 469 K and
with initial H /CO ratios of, from top to bottom, 1.8, 2.2, 2.5, and 2.9.
2
ꢂ
ꢀ
ꢁꢃ
1
reasonably predict the evolution of paraffins and olefins (Fig-
ures 2 and 3). Importantly, the rapid decline in the yields of
olefins owing to readsorption and subsequent conversion at
high CO conversions is captured well by the model presented.
The fractional surface coverage profiles obtained from the
model for various initial compositions have been plotted as
functions of syngas conversions in Figure 4. Based on the sim-
ulation results, the fractional concentrations on the catalyst
ACn ¼ AC4 1 þ c 1 ꢁ
;
4 ꢂ n ꢂ 30,
ð1Þ
n ꢁ 2
For each type of reaction (i.e., adsorption, desorption, and
growth), a separate value of c was used (see Table 1) and each
was treated as a free parameter in the model.
As shown in Figure 1, the model responses for C species are
1
in close agreement with the experimental data. The model can
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surface decrease in the following order: CO>OH>H>free
sites>C H >CH >C H >O. The fractional surface cover-
Experimental Section
n
2n+1
x
n
2n
FT synthesis
ages of O (not shown in the figures) were considerably lower
than those of the other groups. There are uncertainties associ-
ated with the number of sites each surface species attaches to,
which then affects the number of free sites consumed or pro-
duced in the relevant reactions. Considering the range over
which the fractional concentration of free sites varies through-
out the simulations, the addition or elimination of one free site
from a reaction would be equivalent to a change in the activa-
The FT experiments were performed in a Carberry spinning basket
batch reactor (Autoclave Engineers, USA) (Figure 5) with a free
ꢁ
1
tion energy of up to 10 kJmol of that reaction.
The value obtained from the parameter estimation for the
heat of adsorption of H on cobalt is in agreement with calori-
2
[
13]
metric studies, which also indicated that the differential heat
of adsorption of hydrogen on cobalt is almost independent of
the H surface coverage. In contrast, the differential heat of ad-
2
sorption of CO on cobalt decreases dramatically with the in-
[
3,13]
Figure 5. Schematic diagram of the Carberry spinning basket batch reactor.
crease in CO surface coverage.
This phenomenon is primari-
ly attributed to the difference in the electronic structures of
different types of catalytic sites (e.g., planar, edge, corner, and
terrace). One can expect that the reactivity of an adsorbed CO
molecule is strongly affected by the atomic coordination
number of the catalytic site on which it is adsorbed. However,
owing to lack of quantitative information and to avoid further
complexities, the coverage dependency of the heat of adsorp-
tion and the subsequent reactions of the adsorbed molecules
of CO were not considered herein.
volume of 296 mL. The rotational speed of the basket was set at
approximately 260 rpm. After loading the catalyst, the reactor was
purged with nitrogen, evacuated, and heated up to the reaction
temperature with electrical band heaters. Then, the reactor was
charged to the desired pressure with syngas. The reactor pressure
was measured by using a pressure gauge (Swagelok, USA) with
a 2.5 MPa range and a precision of ꢃ0.02 MPa. The initial composi-
tions and reactor pressures for each experiment are listed in
Table 2. Gas samples were collected from the reactor during the
The size of the active material nanoparticles and the identity
of the catalyst support are among the factors that can, in prin-
ciple, substantially alter the activity of a given metal catalyst.
Nevertheless, several studies have shown that the activity of
cobalt catalysts for FT synthesis is independent of the crystal-
lite sizes for nanoparticle sizes greater than approximately 6–
Table 2. Initial process conditions for the experiments with cobalt
catalysts.
Experiment
T
P
total
P
CO
P 2
H
P
Ar
m
cat
[
14–17]
8
nm,
which would correspond to metal dispersions of
[K]
[MPa]
[MPa]
[MPa]
[MPa]
[g]
1
2–16%. As the metal dispersion of typical cobalt catalysts, in-
1
2
3
4
5
6
7
8
469
469
469
469
484
484
484
484
1.90
2.10
2.10
2.08
1.97
2.01
2.01
1.99
0.65
0.64
0.58
0.52
0.50
0.57
0.61
0.49
1.19
1.39
1.44
1.48
1.39
1.37
1.33
1.42
0.06
0.07
0.08
0.08
0.08
0.07
0.07
0.07
5.0
5.0
5.0
4.3
5.0
5.0
5.0
5.0
cluding the catalyst used herein, is usually below these values,
the cobalt-catalyzed FT synthesis reactions are often consid-
ered to be size insensitive. In addition, within a typical range
of metal dispersion (e.g., 2–12%), the nature of the support
material has an insignificant effect on the turnover rates of
[
14]
cobalt catalysts for FT synthesis. The above evidence from
the literature in support of the structure insensitivity of the
cobalt-catalyzed FT synthesis reactions suggests that the pres-
ent analysis can, to a reasonable extent, be applicable to
a wide range of cobalt-catalyzed FT systems.
course of each experiment and analyzed with a gas chromato-
graph (Agilent 7890A, USA) equipped with thermal conductivity
and flame ionization detectors to determine the composition of
the reactor contents. Argon was used as an internal standard to
calculate the partial pressure of each compound from the GC re-
sults. Selected experiments were repeated to ensure the reproduci-
bility of the results.
Conclusions
A detailed microkinetic model of the Fischer–Tropsch synthesis
on a Co/g-Al O catalyst has been developed. The model can
2
3
predict Fischer–Tropsch product distribution (i.e., paraffins, ole-
fins, and carbon dioxide) over the full range of syngas conver-
Catalyst preparation and characterization
sions at initial H /CO ratios between 1.8 and 2.9 and tempera-
2
The experiments were performed with a Co/g-Al O catalyst
2
3
tures of 469 and 484 K. The model presented herein can serve
as a starting point for future studies targeting subsets of the
elementary reactions to fine-tune their rate parameters or for
microkinetic analyses performed with different catalysts.
(12 wt%) at a cobalt loading of 4.3–5.0 g. The catalyst was pre-
pared through the impregnation of the support with a cobalt ni-
trate precursor (Sigma–Aldrich, UK) by using an incipient wetness
method. After impregnation, the catalyst was dried at 363 K and
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ꢁ
1
calcined at 673 K for 4 h in flowing air (flow rate: 200 mLmin
STP). The catalyst was then reduced in flowing hydrogen (flow
example, the water–gas shift reactions (reactions 22–24) were
added only after most of the other reactions had been adjusted
satisfactorily. Despite focusing on the subsets of the parameters,
particularly during the early stages, all the parameters were includ-
ed in the optimization at each iteration owing to the high level of
interconnectivity between each part of the model and the concen-
trations of the measured species.
ꢁ1
rate: 200 mLmin STP) at 673 K for 4 h and finally passivated at
RT by exposing the catalyst to a gas mixture of 2% oxygen in ni-
trogen and progressively increasing the oxygen content to 10%
over the course of 4 h. The passivated catalyst was again reduced
in hydrogen in situ before the experiments. The XRD patterns
(
Figure 6) were collected on a Philips X’Pert X-ray diffractometer
At each iteration, the parameter estimation was performed by
[10,11]
using a two-stage algorithm.
The first stage was a global
search, over the region defined by the bounds of the parameters,
conducted by using low-discrepancy points generated using
[18]
a Sobol sequence. The second stage took the best points found
in the global search and refined the parameter values by using
a local valley-descending optimization routine. The Levenberg–
[19]
Marquardt gradient-based algorithm was initially used for the
local optimization, although for later iterations Hooke and Jeeves
[20]
algorithm was used instead because it was found to perform
better. The best set of values found after this stage was then used
to perform the next iteration.
A Sobol sequence was chosen to generate the points as they were
guaranteed to be more uniformly distributed, in a strict mathemat-
ical sense, than (pseudo-)randomly generated points. With this
number of parameters, the Sobol sequence was also a more effi-
cient sampling method than a full factorial design, which required
2 3
Figure 6. XRD patterns of the Co/g-Al O catalyst after multiple batch runs
and exposure to air.
2
85 points because it included every combination in which the
value of each parameter was set either high or low.
ꢁ
1
for 2q=20–808 at a scan rate of 0.00158s . The Scherrer equation
was used to calculate the metal dispersion from the XRD spectrum.
The BET surface area, support pore volume, and average pore di-
ameter were obtained for one sample of the catalyst with a Micro-
meritics catalyst characterization system (TriStar 3000, USA). The
characteristics of that catalyst sample are summarized in Table 3.
Compared to this, only a relatively small number of points (ꢄ50–
2000) were evaluated at each iteration, yet the inclusion of this
step still greatly improved the quality of the optima found during
the subsequent local optimization by allowing the optimization to
escape the local minima containing the initial point of each itera-
tion. This was particularly important, given that the objective func-
tion surfaces associated with chemical kinetic systems are known
to have a large number of local minima, making the probability of
finding the global one by using only local optimization algorithms
very small.
Table 3. Characteristics of the catalyst used in the FT experiments and
microkinetic analysis.
During both stages, the agreement between experimental and
model responses was quantified by using the least-squares objec-
tive function given in Equation (2).
Parameter
Value
2
ꢁ1
BET surface area
pore volume
pore diameter
pellet diameter
cobalt loading
dispersion
129 m g
3
ꢁ1
0.55 cm g
12.2 nm
3.0 mm
12.0 wt%
11.1%
!
Nspecies Nsamples
exp
model
ij
2
X X Pij ꢁ P
F ¼
ð2Þ
s
ij
i
j
exp
model
in which Pij is the experimentally measured partial pressure, Pij
is the corresponding model response, and s is used to calculate
ij
Computational Methods
the weight of the contribution of species i in sample j. Weighting
was required to compare responses that took values that differ
Parameter estimation
[10,11]
from each other by orders of magnitude.
The value of s for
each data point was calculated systematically based on the level of
uncertainty in the values measured in the experiments. The exact
A total of 128 elementary reactions (listed in Table 1) with 85 free
parameters were considered herein. The analysis was made more
difficult by the lack of information about the concentrations of the
species on the surface of the catalyst and disagreement among
the activation energies reported in DFT studies (see Table S2).
Owing to these complexities, the parameter estimation was per-
formed iteratively. At each iteration, the scope of the optimization
was increased, focusing on improving the fit of the model to the
partial pressures of a wider range of species. As part of this strat-
egy, the bounds on the parameters were often adjusted on the
basis of the results of previous iterations. If it was considered ap-
propriate, new reactions were also added to the mechanism; for
exp
relation used was s =aP +b, which accounted for the relative
ij
i
ij
i
precision of the measuring devices through a and their measure-
ment resolutions through b. The values used for a and b are given
in Table 4.
Acknowledgements
This work was partially supported by the E3C3 project (no. 4274),
which was selected by the European INTERREG IV A France
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[
8] A. J. Markvoort, R. A. van Santen,
P. A. J. Hilbers, E. J. M. Hensen,
Angew. Chem. Int. Ed. 2012, 51,
Table 4. Coefficients used in the objective function for calculating the weight of the compounds (sij).
Coefficient
CO
H
2
CO
2
CH
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Received: August 20, 2014
Published online on October 6, 2014
ChemCatChem 2015, 7, 137 – 143
www.chemcatchem.org
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