This journal is c The Royal Society of Chemistry 2012 Catal. Sci. Technol., 2012, 2, 1221–1233 1221 Cite this: Catal. Sci. Technol., 2012, 2, 1221–1233 Fischer–Tropsch reaction–diffusion in a cobalt catalyst particle: aspects of activity and selectivity for a variable chain growth probability David Vervloet,* a Freek Kapteijn, b John Nijenhuis a and J. Ruud van Ommen a Received 2nd February 2012, Accepted 27th February 2012 DOI: 10.1039/c2cy20060k The reaction–diffusion performance for the Fischer–Tropsch reaction in a single cobalt catalyst particle is analysed, comprising the Langmuir–Hinshelwood rate expression proposed by Yates and Satterfield and a variable chain growth parameter a, dependent on temperature and syngas composition (H 2 /CO ratio). The goal is to explore regions of favourable operating conditions for maximized C 5+ productivity from the perspective of intra-particle diffusion limitations, which strongly affect the selectivity and activity. The results demonstrate the deteriorating effect of an increasing H 2 /CO ratio profile towards the centre of the catalyst particle on the local chain growth probability, arising from intrinsically unbalanced diffusivities and consumption ratios of H 2 and CO. The C 5+ space time yield, a combination of catalyst activity and selectivity, can be increased with a factor 3 (small catalyst particle, d cat = 50 mm) to 10 (large catalyst particle, d cat = 2.0 mm) by lowering the bulk H 2 /CO ratio from 2 to 1, and increasing temperature from 500 K to 530 K. For further maximization of the C 5+ space time yield under these conditions (H 2 /CO = 1, T = 530 K) it seems more effective to focus catalyst development on improving the activity rather than selectivity. Furthermore, directions for optimal reactor operation conditions are indicated. Introduction Selecting an appropriate catalyst dimension for heterogeneous catalyzed reactions is crucial for realizing optimum catalyst utilization and selectivity, as expressed by the catalyst effective- ness factor (Z). The Thiele modulus (f) is the key parameter that defines the interplay between reaction rate(s) (R i ) in a porous catalyst (with characteristic length l cat ) and mass transport by effective diffusion (D i,eff ). The derivations and expressions for f are well-known for numerous types of kinetics. 1 The heterogeneously catalyzed Fischer–Tropsch (FT) synthesis, in which syngas is converted into hydrocarbons and water, may be strongly affected by diffusion limitations. 2,3 Therefore, an analysis of the Thiele moduli for the reactants (H 2 and CO) is crucial for catalyst and reactor design purposes, irrespective of the reactor type in which the catalyst is applied. Furthermore, the selectivity towards desired hydrocarbon chain-lengths, typically C 5+ in low-temperature Fischer–Tropsch synthesis (FTS), is a key factor. This is generally expressed by the chain growth probability parameter a, which depends on the local tempera- ture (T) and reactant concentrations (c i ). 4 An analysis of the diffusivities of the reactants reveals that the ratio of diffusivities of H 2 over CO in a typical liquid hydro- carbon product (e.g. C 28 n-paraffin, following the relations by Wang et al. 5 ) at typical low temperature FT temperatures (e.g. 500 K) is approximately 2.7; this is similar to values reported by other authors, e.g. ref. 6. Not only is hydrogen diffusion faster than that of CO, but its concentration in the liquid phase is typically also higher. Although the CO solubility is approximately 1.3 times higher than that of H 2 in a typical liquid product medium at 500 K (following the relations and parameter values for the Henry coefficients by Marano and Holder 7 ), bulk syngas feed ratios of 2 (or slightly lower) are typically chosen for stoichiometric reasons, resulting in a liquid H 2 /CO concentration ratio of approximately 1.6. The consumption ratio of H 2 over CO on the other hand is a value between 2 (for production of infinitely long hydrocarbon chains) and 3 (for production of methane), so depending on a. It can be shown mathematically, analogous to, 8 that the consumption ratio of H 2 over CO follows the remarkably linear result (3 a), given the assumption that a is independent of the chain length. For typical desired a values, between 0.9 and 0.95, the conclusion is that the diffusivity and concentration ratios do not match the consumption ratio of H 2 and CO. Therefore, under typical reaction conditions, a syngas ratio (H 2 /CO) gradient is expected inside the catalyst particle for diffusion limited systems, having an impact on the catalyst performance in terms of reaction rate and selectivity. To avoid limitation in one of the reactants, a Product & Process Engineering, Delft University of Technology, Faculty of Applied Sciences, Julianalaan 136, 2628 BL Delft, The Netherlands. E-mail: [email protected]b Catalysis Engineering, Delft University of Technology, Faculty of Applied Sciences, Julianalaan 136, 2628 BL Delft, The Netherlands Catalysis Science & Technology Dynamic Article Links www.rsc.org/catalysis PAPER Published on 28 February 2012. Downloaded on 25/03/2018 07:46:28. View Article Online / Journal Homepage / Table of Contents for this issue
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This journal is c The Royal Society of Chemistry 2012 Catal. Sci. Technol., 2012, 2, 1221–1233 1221
Fischer–Tropsch reaction–diffusion in a cobalt catalyst particle: aspects
of activity and selectivity for a variable chain growth probability
David Vervloet,*aFreek Kapteijn,
bJohn Nijenhuis
aand J. Ruud van Ommen
a
Received 2nd February 2012, Accepted 27th February 2012
DOI: 10.1039/c2cy20060k
The reaction–diffusion performance for the Fischer–Tropsch reaction in a single cobalt catalyst
particle is analysed, comprising the Langmuir–Hinshelwood rate expression proposed by Yates
and Satterfield and a variable chain growth parameter a, dependent on temperature and syngas
composition (H2/CO ratio). The goal is to explore regions of favourable operating conditions for
maximized C5+ productivity from the perspective of intra-particle diffusion limitations, which
strongly affect the selectivity and activity. The results demonstrate the deteriorating effect of an
increasing H2/CO ratio profile towards the centre of the catalyst particle on the local chain
growth probability, arising from intrinsically unbalanced diffusivities and consumption ratios of
H2 and CO. The C5+ space time yield, a combination of catalyst activity and selectivity, can be
increased with a factor 3 (small catalyst particle, dcat = 50 mm) to 10 (large catalyst particle,
dcat = 2.0 mm) by lowering the bulk H2/CO ratio from 2 to 1, and increasing temperature from
500 K to 530 K. For further maximization of the C5+ space time yield under these conditions
(H2/CO = 1, T = 530 K) it seems more effective to focus catalyst development on improving the
activity rather than selectivity. Furthermore, directions for optimal reactor operation conditions
are indicated.
Introduction
Selecting an appropriate catalyst dimension for heterogeneous
catalyzed reactions is crucial for realizing optimum catalyst
utilization and selectivity, as expressed by the catalyst effective-
ness factor (Z). The Thiele modulus (f) is the key parameter that
defines the interplay between reaction rate(s) (Ri) in a porous
catalyst (with characteristic length lcat) and mass transport by
effective diffusion (Di,eff). The derivations and expressions for fare well-known for numerous types of kinetics.1
The heterogeneously catalyzed Fischer–Tropsch (FT) synthesis,
in which syngas is converted into hydrocarbons and water, may be
strongly affected by diffusion limitations.2,3 Therefore, an analysis
of the Thiele moduli for the reactants (H2 and CO) is crucial for
catalyst and reactor design purposes, irrespective of the reactor
type in which the catalyst is applied. Furthermore, the selectivity
towards desired hydrocarbon chain-lengths, typically C5+ in
low-temperature Fischer–Tropsch synthesis (FTS), is a key
factor. This is generally expressed by the chain growth
probability parameter a, which depends on the local tempera-
ture (T) and reactant concentrations (ci).4
An analysis of the diffusivities of the reactants reveals that the
ratio of diffusivities of H2 over CO in a typical liquid hydro-
carbon product (e.g. C28 n-paraffin, following the relations by
Wang et al.5) at typical low temperature FT temperatures
(e.g. 500 K) is approximately 2.7; this is similar to values
reported by other authors, e.g. ref. 6. Not only is hydrogen
diffusion faster than that of CO, but its concentration in the
liquid phase is typically also higher. Although the CO solubility
is approximately 1.3 times higher than that of H2 in a typical
liquid product medium at 500 K (following the relations and
parameter values for the Henry coefficients by Marano and
Holder7), bulk syngas feed ratios of 2 (or slightly lower) are
typically chosen for stoichiometric reasons, resulting in a liquid
H2/CO concentration ratio of approximately 1.6.
The consumption ratio of H2 over CO on the other hand is a
value between 2 (for production of infinitely long hydrocarbon
chains) and 3 (for production of methane), so depending on a.It can be shown mathematically, analogous to,8 that the
consumption ratio of H2 over CO follows the remarkably
linear result (3 � a), given the assumption that a is independent
of the chain length. For typical desired a values, between 0.9 and
0.95, the conclusion is that the diffusivity and concentration ratios
do not match the consumption ratio of H2 and CO. Therefore,
under typical reaction conditions, a syngas ratio (H2/CO) gradient
is expected inside the catalyst particle for diffusion limited systems,
having an impact on the catalyst performance in terms of reaction
rate and selectivity. To avoid limitation in one of the reactants,
a Product & Process Engineering, Delft University of Technology,Faculty of Applied Sciences, Julianalaan 136, 2628 BL Delft,The Netherlands. E-mail: [email protected]
b Catalysis Engineering, Delft University of Technology,Faculty of Applied Sciences, Julianalaan 136, 2628 BL Delft,The Netherlands
CatalysisScience & Technology
Dynamic Article Links
www.rsc.org/catalysis PAPER
Publ
ishe
d on
28
Febr
uary
201
2. D
ownl
oade
d on
25/
03/2
018
07:4
6:28
. View Article Online / Journal Homepage / Table of Contents for this issue
This journal is c The Royal Society of Chemistry 2012 Catal. Sci. Technol., 2012, 2, 1221–1233 1225
drops much faster than that of H2, as a result of the lower
diffusion to consumption ratios. This is also visible in the top
left inset in Fig. 2A, where the concentration ratio of H2 over
CO varies over orders of magnitude towards the centre of the
catalyst. The dimensionless CO conversion rate first increases
towards the centre of the catalyst particle due to its negative
reaction order, as a consequence of the higher order of the
adsorption term in the rate expression, and then sharply drops
to zero upon further decrease in CO concentration, whereby the
reaction order of CO changes from negative to positive. Due to
this phenomenon the catalyst effectiveness exceeds unity.
Comparing the two cases for the selectivity (dashed lines:
a = 0.86, solid lines: a = variable) it is clear that the
dimensionless concentration profiles for CO are not very
different and that of H2 is somewhat lower for the variable acase. The H2/CO concentration ratio profile is lower for a
variable a case (top left inset, Fig. 2A) due to the a-dependentconsumption ratio. The catalyst effectiveness and overall CO
consumption rates do not differ much (Table 3).
The major difference between the two cases is visible in the
selectivity. In the variable a case the chain growth probability
deteriorates as the H2/CO ratio increases in the region where
the reaction rate is highest (z between 1.5 and 2.5). This causes
significant differences in the overall selectivity of the catalyst
particle, which results in a threefold reduction of the C5+
space time yield.
Model results for variable /CO and H2/CO ratio
The calculations with variable a have been performed for a
wide range of conditions. In Fig. 3 aave, Z, RCO,total, SC5+, and
Table 2 Parameter values and condition ranges used in the model
Description Symbol Value Motivation/reference
Temperature T 470–530 K Varied rangePressure p 12–36 bar Varied rangeSyngas ratio in the bulk — 0.1–3.0 Varied rangeCatalyst particle diameter dcat 10–5000 mm Varied rangeCatalyst intrinsic (skeleton) density rcat 2500 kg m�3 TypicalCatalyst porosity ecat 0.5 TypicalCatalyst pore tortuosity tcat 1.5 TypicalYates and Satterfield reaction rate constant a(T) T-dependent relation/mol s�1 kgcat
�1 bar�2 24Yates and Satterfield adsorption constant b(T) T dependent relation/bar�1 24Catalyst activity multiplication factor F 1–10 Estimated catalyst activity improvement15
CO diffusion constant in product medium D0,CO 5.584 � 10�7 m2 s�1 5CO diffusion activation energy ED,CO 14.85 � 103 J mol�1 5H2 diffusion constant in product medium D0,H2
1.085 � 10�6 m2 s�1 5H2 diffusion activation energy ED,H2
13.51 � 103 J mol�1 5Henry coefficient Hi(T) T dependent relation/bar 7Chain growth probability a Model This work (eqn (7))Selectivity constant ka 56.7 � 10�3 This work (eqn (7))Selectivity exponential parameter b 1.76 This work (eqn (7))Selectivity activation energy difference DEa 120.4 � 103 J mol�1 This work (eqn (7))
Fig. 2 (A) Dimensionless concentration yi, reaction rateCi and a profiles in a spherical catalyst particle for a fixed a (dashed lines, a=0.86) and for the
variable amodel (solid lines). Conditions: T=490 K, p=30 bar, syngas ratio at the catalyst surface = 2, dcat = 1.5 mm, F=1; other parameters as in
Table 2. z=0 at the centre and z=3 at the surface of the particle. Inset: the syngas (H2/CO) ratio profile in the catalyst. (B) Graphical representation of
the dimensionless CO reaction rate profile in the catalyst sphere (variable a). An overview of other performance parameters is given in Table 3.
Table 3 Comparative overview of performance parameters for a fullcatalyst particle for the fixed a model versus variable a model.Conditions: T = 490 K, p = 30 bar, syngas ratio at catalystsurface = 2, dcat = 1.5 mm, F = 1; other conditions as in Table 2
1230 Catal. Sci. Technol., 2012, 2, 1221–1233 This journal is c The Royal Society of Chemistry 2012
achieved by a catalytic water gas shift functionality in the
reactor, whereby the relatively increasing CO is converted with
the produced water to CO2 and H2, keeping up the proper
desired H2/CO ratio. The indication to operate at low syngas
ratios is especially interesting when the syngas is produced
from coal or biomass, where typically low H2/CO ratios
are found.65 Using a strict boundary condition for the chain
growth parameter, for example aave = 0.9 (dotted line, Fig. 7
and 8) for carbon efficiency reasons, the conclusion is that the
maximum STYC5+for a single catalyst particle is achieved at
even lower bulk syngas ratios (H2/CO = 0.5–0.8) and high
temperature (T 4 520 K).
Operating at low H2/CO ratios may lead to additional
effects that are important for industrial application, such as
the changed olefin/paraffin ratio in the product distribution,4
or the catalyst deactivation rate.66 These elements are not
addressed in this modelling approach, and may be considered
for further analysis and deeper insight in economical viability.
Also, we note that the catalyst is an integral part of the reactor, in
which gradients (T, H2/CO, P) are to be expected and must be
taken into account. Reactor and overall process design—as other
units, such as syngas manufacturing and product upgrading,
roughly size with the amount of gas and liquid that needs to be
processed—are ultimately a decision based on capital invest-
ment, operating cost and total productivity. These results
aid in the exploration and selection of favourable operating
conditions, whether or not under additional constraints, for
maximum productivity.
As a final element, we readdress the earlier question on
whether to focus catalyst development on improving the activity
Fig. 8 C5+ space time yield (STYC5+in g gcat
�1 h�1) contour plots as a function of total pressure and bulk syngas ratio at constant catalyst
particle diameter (dcat = 50 mm) and various temperatures. (A) T = 490 K, (B) T = 500 K, (C) T = 510 K, (D) T = 520 K. Calculations
performed with a catalyst activity parameter F = 1. The dotted line indicates the isocontour for aave = 0.9.
Table 4 Performance analysis of a small catalyst particle (dcat = 50 mm) and a large catalyst particle (dcat = 1.5 mm) at a base case (F = 1 and1 � ka), improved catalyst activity (F = 10) and improved selectivity (0.1 � ka). Other conditions: T = 530 K, p = 36 bar and H2/CO = 1
This journal is c The Royal Society of Chemistry 2012 Catal. Sci. Technol., 2012, 2, 1221–1233 1233
Acknowledgements
This research is supported by the Dutch Technology Founda-
tion STW, which is the applied science division of NWO, and
the Technology Program of the Ministry of Economic Affairs,
Agriculture and Innovation.
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