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α-Olefin Readsorption Product Distribution Model for the Gas-Solid Fischer-Tropsch Synthesis
NATURAL GAS CONVERSION V Studies in Surface Science and Catalysis, Vol. 119 A. Parmaliana et al. (Editors) o 1998 Elsevier Science B.V. All rights reserved.
179
a - O l e f i n R e a d s o r p t i o n P r o d u c t Distribution M o d e l for the G a s - S o l i d F i s c h e r - T r o p s c h Synthesis G.P. van der Laan and A.A.C.M. Beenackers Department of Chemical Engineering, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands 1. I N T R O D U C T I O N Increasing crude oil prices may cause a shift to coal and natural gas as the feed stock of the chemical industry and transportation fuels market. These can be converted into CO and Ha by partial oxidation or steam reforming processes which subsequently can be converted to hydrocarbons in the Fischer-Tropsch (FT) process. The FT synthesis product spectrum consists of a complex multi-component mixture of linear and branched hydrocarbons and oxygenated products. Main products are linear paraffins and a-olefins. The FT synthesis has been recognized as a polymerization reaction [ 1]. The reactants, CO and H2, adsorb and dissociate at the surface of the catalyst and react to form chain initiator (CH3), methylene monomer (CH2), and H20. The most important growth mechanism for the hydrocarbon formation is the surface carbide mechanism by CHa insertion into adsorbed alkyl chains. Termination can take place by dehydrogenation to ot-olefins or hydrogenation to paraffins [ 1,2]. The FT product yield decreases exponentially with increasing chain length. The so-called Anderson-Schulz-Flory (ASF) distribution is often used to describe the entire product range by a single parameter, o~, the probability of the addition of a carbon intermediate to a chain [3]. However, significant deviations from the ASF distribution are reported in literature: (i) a relatively high yield of methane [4,5], (ii) a relatively low yield of ethene [4] relative to the ASF distribution, and (iii) an exponential decrease of the ot-olefin to paraffin ratio and change in chain growth parameter, an, with increasing chain length. These deviations are caused by secondary reactions, readsorption and hydrogenation, of a-olefins [4,6]. However, secondary hydrogenation is strongly inhibited by CO and HzO relative to readsorption [7]. Readsorption of ot-olefins leads to chain initiation and results in a decrease of the olefin to paraffin ratio and an increase of the chain growth parameter with chain length. A new product distribution model is presented to explain the deviations from the ASF distribution. This model combines a mechanistic model of olefin readsorption with kinetics of chain growth and termination on the same catalytic sites. In this study, the emphasis is on modeling the selectivity to linear olefins and paraffins. 2. THEORY The ot-Olefin Readsorption Product Distribution Model (ORPDM) accounts for secondary readsorption of ot-olefins on FT growth sites on the precipitated iron catalyst (see Fig. 1). Here,
180
COG and COs denote the gas phase and the adsorbed CO, respectively. CM,S refers to adsorbed monomeric building units (CH2,s), and Cn,s is an adsorbed alkyl species with carbon number n. Conversion of CO to CM,S follows a sequence of elementary reaction steps, but is shown as a single step. Chain growth initiates by hydrogenation of CM,S to CH3,s, while chain propagation proceeds via insertion of CM,S into adsorbed alkyl chains. Chain termination by dehydrogenation of adsorbed alkyl chains gives olefins, whereas paraffins are formed by hydrogenation of alkyl species. Based on the reaction network shown in Fig. 1, a-olefins may readsorb on growth sites and continue to grow via propagation with monomers or terminate as hydrocarbon product.
COG
CH4
C2H, C 2 H 6
S
~[C~s
1 k,
CnH2. CnH2n+2
RlI lkTillkTtk ,
k2
k-
C3H 6 C3H 8
2kO
2t,P
2
kO kt, p
RI ikko k~p ,~.................
kp J C3s
I I-I ' ,
......... ~ CN, S .................9 .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.......................... 9
Figure 1. Reaction network c~-Olefin Readsorption Product Distribution Model Steady state mass balances for alkyl species with carbon number n, On, can be derived to account for readsorption [4,7]: kpOMOn-1 -- (kt,oOv q- kt.eOn + kpOM)On -- k*RCC,,H2,,
(1)
where 0/-/is the surface coverage of adsorbed hydrogen and 0v is the fraction of vacant catalytic sites. The actual concentration of the olefin at the catalyst surface, Cc,,/-/2,,,s, can be related to the reaction rate: RC,,H2,, -- kt,oOvOn - k*RCC,,H2,,,S
(2)
The steady-state mass balance for ot-olefins in an ideally mixed continuous reactor is: RC,, IG, --
~v,RPC, H2,, W R TR
(3)
where P G I G , / R T R is the gas-phase concentration of olefins in the reactor with carbon number n, ~,,,R is the volumetric flow rate of the gas-phase at reactor conditions, and W is the weight of the catalyst. The interfacial effects of reactive olefins at the gas-wax and wax-catalyst surface should be taken into account. Several authors stated that a greater solubility of larger hydrocarbons results in an increase of readsorption rates for larger olefins [5,6]. Vapor-liquid equilibria of Breman et al. [8] and Caldwell and Van Vuuren [9] show that the solubility of hydrocarbons increases exponentially with the chain length. Data on the adsorption of hydrocarbons on solids show that the enthalpy of adsorption increases linearly with carbon number [10]. Adsorption equilibria constants increase exponentially with chain length [4]. In multi-component mixtures (Fischer-Tropsch product specu'um) these effects result in a physisorbed layer with mainly long-chain hydrocarbons. Therefore
181
we assume the olefin gas phase concentration to relate to the concentration at the catalyst surface as: Cc,, H2,, , S
(4)
o( e cn
Pc,, H2,,/ R TIe
where c is a positive constant depending on the exponential increase of the physisorption and solubility with chain length. Rearranging and solving Eqs. 1 - 4 yields: On On-1
=
kpOM kt,oOv/ (1 + kRe cn) + kt, eOl-I + kpOm
=
p t o / ( 1 + kRe cn) + 1 + p
= o6,
(5)
where kR -- k*nWPRTo/(C~vPoTR) (PR= reactor pressure and ~v= flow rate at P0 = 0.1 MPa and To= 273 K). Propagation and termination to olefins are relative to the termination rate of paraffins: p -- kpOm/kt, pOH, and to -- kt,oOv/kt,pOt-l. The surface fractions of alkyl chains with carbon number n can be determined by successive calculation of the chain growth parameter with increasing carbon number: ~ ~
01
ffi
--
(6)
tY2"Ot3"''Otn
i=2
Solving Eqs. 2 and 3 gives the following molar selectivities" to oti and mc,,lh,, -- 1 + kRe c'-'~Ot
mc,,lh,,+2 -- Ol i=2
(7)
lYi
i=2
The molar selectivity to product i is calculated from the experimental mole fraction, Yi, relative to the mole fractions of all products considered: (8)
Yi m i - - ~-2i Yi
Higher surface mobility or reactivity of C1 and C2 precursors and rapid readsorption of ethene give the most reasonable explanation for the deviations of the short-chain hydrocarbons from the ASF distribution. The selectivities of Cl and Ca products are calculated separately: mcz-14 -- t~,01,
mC2H6 -- t~,02 --t20t201,
mGl-i 4 --
1 +k 2
o2
(9)
with t~ -- k t , p / k t , p , t~, - kat,p/kt,p, and t~ - t2to (see Fig. 1). The model reduces to the ASF distribution when olefins can not readsorb, i.e. kR -- 0. Therefore, Eqs. 5-7 can also be used for the ASF distribution with substitution of kR -- 0. The ORPDM accounts for the chain-length dependent readsorption of olefins on FT sites. The readsorption step depends on carbon number, resulting in a net decrease of the termination to olefins with increasing carbon number until no olefins are formed. At high carbon numbers, the chain growth parameter, Otn, approaches a maximum constant value of oeoo = p / ( 1 + p). The increased readsorption of long-chain olefins results in a decreasing olefin/paraffin ratio with chain length.
182
The accuracy of the fitted model relative to the experimental data was obtained from the M A R R (Mean Absolute Relative Residual) and R R (Relative Residual) functions: m ;XP
MARR
1x
. rood --
rrt i -
-
-
i
l,r t e X p i
-
exp
100
n
RR
--
mi
. rood -
expm i
X 1O0
( 1O)
m i
where n is the total number of optimized selectivities of all experiments together, m; xp is the experimental selectivity of the ith data point, and m- ,noa is the model prediction of the mole fraction. i 3. E X P E R I M E N T A L Fischer-Tropsch experiments were carried out with a gas-continuous Spinning Basket Reactor (SBR) with a reactor volume of 285 ml. The stainless steel reactor had the catalyst particles placed in four baskets mounted on the stirrer shaft. A detailed description of the experimental set up, analysis, and experimental procedures is given by Van der Laan [11]. The gaseous phase was analyzed with a Hewlett-Packard 5980A gas chromatograph. The gaseous components were linear paraffins Ci-C10, c~-olefins C2-Cl0, CO2, H20, CO, and H2. The catalyst applied was a commercial precipitated iron catalyst (type LP 33/81) synthesized by Ruhrchemie AG (Oberhausen, Germany). The synthesis procedure was described by Frohning et al. [12]. The catalyst pellets were calcined in air at 573 K for 5 h and crushed and sieved to particle diameters between 0.125 and 0.160 ram. The baskets were loaded with 2.34 g of unreduced catalyst. The catalyst was pretreated with hydrogen with a flow rate of 0.83 10-3 Nm 3 kgcJt s -~ according to Bukur et al. [ 13]. After reduction, synthesis gas was fed to the reactor at reference conditions o f T = 523 K, P= 1.50 MPa, Hz/CO feed ratio= 2 and dOv/W= 1.51 10 -3 Nm 3 kgcalt s -1 . The experimental conditions were varied as follows: P= 0.8 - 4.0 MPa, H2/CO feed ratio= 0.25 4.0, and C b v / W = 0 . 5 - 2.0 10 -3 Nm 3 kgcal/ s - l at a constant temperature of 523 K.
4. RESULTS AND DISCUSSION 16 kinetic experiments were carried out in the SBR with the Ruhrchemie precipitated iron catalyst at 523 K. Fig. 2 shows a typical distribution of the hydrocarbon products and the corresponding molar ratio of olefin to paraffins as a function of carbon number. We observed a decrease of the molar 0t-olefin/paraffin ratio with increasing carbon number and a curved line for the distribution of paraffins alone and paraffins and olefins combined. The ASF model was optimized with two model parameters (p and to), within each experiment. The number of parameters in model ORPDM was equal to 7: p, to, kR, c, tip, t 2, and k~ (see Eqs. 6-9). Four parameters were found to be independent of the experimental conditions (see table 1). Table 2 shows the accuracies of the optimized models expressed with the M A R R function for the paraffins and olefins, respectively as well as the total number of product mole fractions, n, for the complete set of experimental values at 523 K. The ASF model results in large deviations between model and experiment. The curved paraffin distribution cannot be described with the ASF model. The model ORPDM describes n-dependent readsorption of olefins, resulting in a curved distribution of paraffins and a decreasing O/P ratio with carbon number. An example of a predicted product distribution with the optimized model values from model ORPDM is shown in Fig. 2a-b. The observed deviations from the ASF model are accurately described by our model, resulting in lower MARR values relative to the ASF model (see table 2).
183
)
(b)
0.1 O/P
in i
0.01 9 9
Paraffins Olefins
~,,."~ "~
0.001
0
0
2
4
6
8
Carbon number
10
2
J
0
I
2
i
I
i
4
i
6
t
I
8
i
I
10
Carbon number
Figure 2. a. Product distribution as a function of carbon number, T= 523 K, P= 1.50 MPa, (H2/CO)feed=2, dPv/W= 1.5 10 -3 Nm 3 kgc~ s -l, 1011 hours-on-stream, b. Corresponding molar O/P ratio. Lines are predictions of model ORPDM (p= 7.18, to= 9.18, kR= 0.78). Symbols are experimental data points. Table 1 Model parameters for ORPDM Parameter Value t~, (6.6 4- 1.9) t2 (1.6 + 0.3) k~ (12.6 4- 3.5) kRe 2c c 0.29 4- 0.07
Table 2 Accuracies of the kinetic models MARR % model paraffins olefins ASF 49.9 42.5 ORPDM 10.1 9.1
(Eq. 10) n 443 443
Fig. 3 shows that the relative residuals between model and experiment, calculated with Eq. 10, are almost always within 25 % for all experiments. The residuals for methane, ethene, paraffins and olefins are shown separately to indicate that the model can accurately describe the well-known deviations of the ASF distribution. Fig. 4 shows the effect of carbon number on the chain growth parameter calculated with Eq. 5 according to model ORPDM for the experiment mentioned in Fig. 2. The calculated chain growth parameter is high at n = 2 due to rapid readsorption of ethene and increased termination to C2 products, minimal for C3 and increases to the asymptotical value of ot~ = p/(1 + p). 5. C O N C L U S I O N S A product distribution model, which accounts for n-dependent olefin readsorption, proves to be able to describe accurately the deviations in the observed product distributions in both olefins and paraffins from ASF distributions: i.e. a relatively high yield of methane, a relatively low yield of ethene and an exponential decrease of the olefin to paraffin ratio and change of the chain growth parameter with chain length. For each experimental product distribution three parameters were
184
50
....
!
. . . . . . . .
i
. . . . . . .
~
. . . . . . . .
i
a 40
o
30
*
20
,~
" A
O~
oO. ,o
oO
A
o~
~
o
t
+ 25%_
o
Otoo
0.90
0 ~
.,.,.. ~.,
"~' :o~ -
o ~ _~~176
0.95
u
o o Ao ~o 0~ % | , g o ~ o.a ,,
%
AAO
~,
1.00
-
o
o
o oO
f
-
0.85 Ot n 0.80
"
e- ~8"o
o
~
L."
~
-
I , a o,2~ A~ go ~ , ~176 -20 ._ .... ,_:__,__: . . . . ~ . . . . . . _, _ __A__~7/;
0.75 0.70
-30 [-
o"
I
o I
o
I
*
,,,,,.t,,~
|
"
Olefins(n=3-10)
o
-40 ~-
.
o
,
I .50
h
I .....
I
. . . . . . . .
0.001
I
,
I
0.01
mi ~'
"
Paraffins (n= 2-10) 0.65
E~n~
. . . . . . . . . . . . . . .
0.1
(-)
Figure 3. Relative residuals versus experimental values. Model ORPDM
]
!
0.60 0
5
10
15
20
25
30
35
Carbon number Figure 4. Calculated chain growth parameter as function of carbon number. Experimental conditons, see Fig. 2. Model ORPDM
optimized, whereas four model parameters were optimized for the entire set of experiments. The superior accuracy of the olefin readsorption model in predicting experimentally observed product distributions is obtained from adding one extra parameter only, without the assumption of multiple catalytic chain growth sites. REFERENCES 1. 2. 3. 4. 5. 6. 7.
8. 9. 10. 11. 12. 13.
A.T. Bell, Catal. Rev.-Sci. Eng. 23 (1981) 203. M.E. Dry and J.C. Hoogendoom, Catal. Rev.-Sci. Eng. 23 (1981) 265. L.S. Glebov and G.A. Kliger, Russ. Chem. Rev. 63 (1994) 185. T. Komaya, and A.T. Bell, J. Catal. 146 (1994) 237. E.W. Kuipers, C. Scheper, J.H. Wilson, and H. Oosterbeek, J. Catal. 158 (1996) 288. E.W. Kuipers, I.H. Vinkenburg, and H. Oosterbeek, J. Catal. 152 (1995) 137. E. Iglesia, S.C. Reyes, R.J. Madon, and S.L. Soled, Selectivity control and catalyst design in the Fischer-Tropsch synthesis: sites, pellets, and reactors. In E. Eley, H. Pines and P. Weisz (Eds.), Advances in Catalysis 39 (1993) 221. B.B. Breman, A.A.C.M. Beenackers, E.W.J. Rietjens, and R.J.H. Stege, J. Chem. Eng. Data 39 (1994) 647. L. Caldwell and D.S. van Vuuren, Chem. Eng. Sc. 41 (1986) 89. D.M. Ruthven, P r i n c i p l e s o f a d s o r p t i o n a n d a d s o r p t i o n p r o c e s s e s . New York, 1984. G.P. van der Laan, PhD Thesis (in preparation), University of Groningen, The Netherlands. C.D. Frohning, H. K61bel, M. Ralek, W. Rottig, E Schuur, and H. Schulz, Fischer-TropschSynthese. In J. Falbe (Ed.), Chemierohstoffe aus Kohle, Chapter 8, Stuttgart, 1977. D.B. Bukur, L. Nowicki, R.K. Manne, and X. Lang, J. Catal. 155 (1995) 366.
179
a - O l e f i n R e a d s o r p t i o n P r o d u c t Distribution M o d e l for the G a s - S o l i d F i s c h e r - T r o p s c h Synthesis G.P. van der Laan and A.A.C.M. Beenackers Department of Chemical Engineering, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands 1. I N T R O D U C T I O N Increasing crude oil prices may cause a shift to coal and natural gas as the feed stock of the chemical industry and transportation fuels market. These can be converted into CO and Ha by partial oxidation or steam reforming processes which subsequently can be converted to hydrocarbons in the Fischer-Tropsch (FT) process. The FT synthesis product spectrum consists of a complex multi-component mixture of linear and branched hydrocarbons and oxygenated products. Main products are linear paraffins and a-olefins. The FT synthesis has been recognized as a polymerization reaction [ 1]. The reactants, CO and H2, adsorb and dissociate at the surface of the catalyst and react to form chain initiator (CH3), methylene monomer (CH2), and H20. The most important growth mechanism for the hydrocarbon formation is the surface carbide mechanism by CHa insertion into adsorbed alkyl chains. Termination can take place by dehydrogenation to ot-olefins or hydrogenation to paraffins [ 1,2]. The FT product yield decreases exponentially with increasing chain length. The so-called Anderson-Schulz-Flory (ASF) distribution is often used to describe the entire product range by a single parameter, o~, the probability of the addition of a carbon intermediate to a chain [3]. However, significant deviations from the ASF distribution are reported in literature: (i) a relatively high yield of methane [4,5], (ii) a relatively low yield of ethene [4] relative to the ASF distribution, and (iii) an exponential decrease of the ot-olefin to paraffin ratio and change in chain growth parameter, an, with increasing chain length. These deviations are caused by secondary reactions, readsorption and hydrogenation, of a-olefins [4,6]. However, secondary hydrogenation is strongly inhibited by CO and HzO relative to readsorption [7]. Readsorption of ot-olefins leads to chain initiation and results in a decrease of the olefin to paraffin ratio and an increase of the chain growth parameter with chain length. A new product distribution model is presented to explain the deviations from the ASF distribution. This model combines a mechanistic model of olefin readsorption with kinetics of chain growth and termination on the same catalytic sites. In this study, the emphasis is on modeling the selectivity to linear olefins and paraffins. 2. THEORY The ot-Olefin Readsorption Product Distribution Model (ORPDM) accounts for secondary readsorption of ot-olefins on FT growth sites on the precipitated iron catalyst (see Fig. 1). Here,
180
COG and COs denote the gas phase and the adsorbed CO, respectively. CM,S refers to adsorbed monomeric building units (CH2,s), and Cn,s is an adsorbed alkyl species with carbon number n. Conversion of CO to CM,S follows a sequence of elementary reaction steps, but is shown as a single step. Chain growth initiates by hydrogenation of CM,S to CH3,s, while chain propagation proceeds via insertion of CM,S into adsorbed alkyl chains. Chain termination by dehydrogenation of adsorbed alkyl chains gives olefins, whereas paraffins are formed by hydrogenation of alkyl species. Based on the reaction network shown in Fig. 1, a-olefins may readsorb on growth sites and continue to grow via propagation with monomers or terminate as hydrocarbon product.
COG
CH4
C2H, C 2 H 6
S
~[C~s
1 k,
CnH2. CnH2n+2
RlI lkTillkTtk ,
k2
k-
C3H 6 C3H 8
2kO
2t,P
2
kO kt, p
RI ikko k~p ,~.................
kp J C3s
I I-I ' ,
......... ~ CN, S .................9 .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.......................... 9
Figure 1. Reaction network c~-Olefin Readsorption Product Distribution Model Steady state mass balances for alkyl species with carbon number n, On, can be derived to account for readsorption [4,7]: kpOMOn-1 -- (kt,oOv q- kt.eOn + kpOM)On -- k*RCC,,H2,,
(1)
where 0/-/is the surface coverage of adsorbed hydrogen and 0v is the fraction of vacant catalytic sites. The actual concentration of the olefin at the catalyst surface, Cc,,/-/2,,,s, can be related to the reaction rate: RC,,H2,, -- kt,oOvOn - k*RCC,,H2,,,S
(2)
The steady-state mass balance for ot-olefins in an ideally mixed continuous reactor is: RC,, IG, --
~v,RPC, H2,, W R TR
(3)
where P G I G , / R T R is the gas-phase concentration of olefins in the reactor with carbon number n, ~,,,R is the volumetric flow rate of the gas-phase at reactor conditions, and W is the weight of the catalyst. The interfacial effects of reactive olefins at the gas-wax and wax-catalyst surface should be taken into account. Several authors stated that a greater solubility of larger hydrocarbons results in an increase of readsorption rates for larger olefins [5,6]. Vapor-liquid equilibria of Breman et al. [8] and Caldwell and Van Vuuren [9] show that the solubility of hydrocarbons increases exponentially with the chain length. Data on the adsorption of hydrocarbons on solids show that the enthalpy of adsorption increases linearly with carbon number [10]. Adsorption equilibria constants increase exponentially with chain length [4]. In multi-component mixtures (Fischer-Tropsch product specu'um) these effects result in a physisorbed layer with mainly long-chain hydrocarbons. Therefore
181
we assume the olefin gas phase concentration to relate to the concentration at the catalyst surface as: Cc,, H2,, , S
(4)
o( e cn
Pc,, H2,,/ R TIe
where c is a positive constant depending on the exponential increase of the physisorption and solubility with chain length. Rearranging and solving Eqs. 1 - 4 yields: On On-1
=
kpOM kt,oOv/ (1 + kRe cn) + kt, eOl-I + kpOm
=
p t o / ( 1 + kRe cn) + 1 + p
= o6,
(5)
where kR -- k*nWPRTo/(C~vPoTR) (PR= reactor pressure and ~v= flow rate at P0 = 0.1 MPa and To= 273 K). Propagation and termination to olefins are relative to the termination rate of paraffins: p -- kpOm/kt, pOH, and to -- kt,oOv/kt,pOt-l. The surface fractions of alkyl chains with carbon number n can be determined by successive calculation of the chain growth parameter with increasing carbon number: ~ ~
01
ffi
--
(6)
tY2"Ot3"''Otn
i=2
Solving Eqs. 2 and 3 gives the following molar selectivities" to oti and mc,,lh,, -- 1 + kRe c'-'~Ot
mc,,lh,,+2 -- Ol i=2
(7)
lYi
i=2
The molar selectivity to product i is calculated from the experimental mole fraction, Yi, relative to the mole fractions of all products considered: (8)
Yi m i - - ~-2i Yi
Higher surface mobility or reactivity of C1 and C2 precursors and rapid readsorption of ethene give the most reasonable explanation for the deviations of the short-chain hydrocarbons from the ASF distribution. The selectivities of Cl and Ca products are calculated separately: mcz-14 -- t~,01,
mC2H6 -- t~,02 --t20t201,
mGl-i 4 --
1 +k 2
o2
(9)
with t~ -- k t , p / k t , p , t~, - kat,p/kt,p, and t~ - t2to (see Fig. 1). The model reduces to the ASF distribution when olefins can not readsorb, i.e. kR -- 0. Therefore, Eqs. 5-7 can also be used for the ASF distribution with substitution of kR -- 0. The ORPDM accounts for the chain-length dependent readsorption of olefins on FT sites. The readsorption step depends on carbon number, resulting in a net decrease of the termination to olefins with increasing carbon number until no olefins are formed. At high carbon numbers, the chain growth parameter, Otn, approaches a maximum constant value of oeoo = p / ( 1 + p). The increased readsorption of long-chain olefins results in a decreasing olefin/paraffin ratio with chain length.
182
The accuracy of the fitted model relative to the experimental data was obtained from the M A R R (Mean Absolute Relative Residual) and R R (Relative Residual) functions: m ;XP
MARR
1x
. rood --
rrt i -
-
-
i
l,r t e X p i
-
exp
100
n
RR
--
mi
. rood -
expm i
X 1O0
( 1O)
m i
where n is the total number of optimized selectivities of all experiments together, m; xp is the experimental selectivity of the ith data point, and m- ,noa is the model prediction of the mole fraction. i 3. E X P E R I M E N T A L Fischer-Tropsch experiments were carried out with a gas-continuous Spinning Basket Reactor (SBR) with a reactor volume of 285 ml. The stainless steel reactor had the catalyst particles placed in four baskets mounted on the stirrer shaft. A detailed description of the experimental set up, analysis, and experimental procedures is given by Van der Laan [11]. The gaseous phase was analyzed with a Hewlett-Packard 5980A gas chromatograph. The gaseous components were linear paraffins Ci-C10, c~-olefins C2-Cl0, CO2, H20, CO, and H2. The catalyst applied was a commercial precipitated iron catalyst (type LP 33/81) synthesized by Ruhrchemie AG (Oberhausen, Germany). The synthesis procedure was described by Frohning et al. [12]. The catalyst pellets were calcined in air at 573 K for 5 h and crushed and sieved to particle diameters between 0.125 and 0.160 ram. The baskets were loaded with 2.34 g of unreduced catalyst. The catalyst was pretreated with hydrogen with a flow rate of 0.83 10-3 Nm 3 kgcJt s -~ according to Bukur et al. [ 13]. After reduction, synthesis gas was fed to the reactor at reference conditions o f T = 523 K, P= 1.50 MPa, Hz/CO feed ratio= 2 and dOv/W= 1.51 10 -3 Nm 3 kgcalt s -1 . The experimental conditions were varied as follows: P= 0.8 - 4.0 MPa, H2/CO feed ratio= 0.25 4.0, and C b v / W = 0 . 5 - 2.0 10 -3 Nm 3 kgcal/ s - l at a constant temperature of 523 K.
4. RESULTS AND DISCUSSION 16 kinetic experiments were carried out in the SBR with the Ruhrchemie precipitated iron catalyst at 523 K. Fig. 2 shows a typical distribution of the hydrocarbon products and the corresponding molar ratio of olefin to paraffins as a function of carbon number. We observed a decrease of the molar 0t-olefin/paraffin ratio with increasing carbon number and a curved line for the distribution of paraffins alone and paraffins and olefins combined. The ASF model was optimized with two model parameters (p and to), within each experiment. The number of parameters in model ORPDM was equal to 7: p, to, kR, c, tip, t 2, and k~ (see Eqs. 6-9). Four parameters were found to be independent of the experimental conditions (see table 1). Table 2 shows the accuracies of the optimized models expressed with the M A R R function for the paraffins and olefins, respectively as well as the total number of product mole fractions, n, for the complete set of experimental values at 523 K. The ASF model results in large deviations between model and experiment. The curved paraffin distribution cannot be described with the ASF model. The model ORPDM describes n-dependent readsorption of olefins, resulting in a curved distribution of paraffins and a decreasing O/P ratio with carbon number. An example of a predicted product distribution with the optimized model values from model ORPDM is shown in Fig. 2a-b. The observed deviations from the ASF model are accurately described by our model, resulting in lower MARR values relative to the ASF model (see table 2).
183
)
(b)
0.1 O/P
in i
0.01 9 9
Paraffins Olefins
~,,."~ "~
0.001
0
0
2
4
6
8
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Figure 2. a. Product distribution as a function of carbon number, T= 523 K, P= 1.50 MPa, (H2/CO)feed=2, dPv/W= 1.5 10 -3 Nm 3 kgc~ s -l, 1011 hours-on-stream, b. Corresponding molar O/P ratio. Lines are predictions of model ORPDM (p= 7.18, to= 9.18, kR= 0.78). Symbols are experimental data points. Table 1 Model parameters for ORPDM Parameter Value t~, (6.6 4- 1.9) t2 (1.6 + 0.3) k~ (12.6 4- 3.5) kRe 2c c 0.29 4- 0.07
Table 2 Accuracies of the kinetic models MARR % model paraffins olefins ASF 49.9 42.5 ORPDM 10.1 9.1
(Eq. 10) n 443 443
Fig. 3 shows that the relative residuals between model and experiment, calculated with Eq. 10, are almost always within 25 % for all experiments. The residuals for methane, ethene, paraffins and olefins are shown separately to indicate that the model can accurately describe the well-known deviations of the ASF distribution. Fig. 4 shows the effect of carbon number on the chain growth parameter calculated with Eq. 5 according to model ORPDM for the experiment mentioned in Fig. 2. The calculated chain growth parameter is high at n = 2 due to rapid readsorption of ethene and increased termination to C2 products, minimal for C3 and increases to the asymptotical value of ot~ = p/(1 + p). 5. C O N C L U S I O N S A product distribution model, which accounts for n-dependent olefin readsorption, proves to be able to describe accurately the deviations in the observed product distributions in both olefins and paraffins from ASF distributions: i.e. a relatively high yield of methane, a relatively low yield of ethene and an exponential decrease of the olefin to paraffin ratio and change of the chain growth parameter with chain length. For each experimental product distribution three parameters were
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optimized, whereas four model parameters were optimized for the entire set of experiments. The superior accuracy of the olefin readsorption model in predicting experimentally observed product distributions is obtained from adding one extra parameter only, without the assumption of multiple catalytic chain growth sites. REFERENCES 1. 2. 3. 4. 5. 6. 7.
8. 9. 10. 11. 12. 13.
A.T. Bell, Catal. Rev.-Sci. Eng. 23 (1981) 203. M.E. Dry and J.C. Hoogendoom, Catal. Rev.-Sci. Eng. 23 (1981) 265. L.S. Glebov and G.A. Kliger, Russ. Chem. Rev. 63 (1994) 185. T. Komaya, and A.T. Bell, J. Catal. 146 (1994) 237. E.W. Kuipers, C. Scheper, J.H. Wilson, and H. Oosterbeek, J. Catal. 158 (1996) 288. E.W. Kuipers, I.H. Vinkenburg, and H. Oosterbeek, J. Catal. 152 (1995) 137. E. Iglesia, S.C. Reyes, R.J. Madon, and S.L. Soled, Selectivity control and catalyst design in the Fischer-Tropsch synthesis: sites, pellets, and reactors. In E. Eley, H. Pines and P. Weisz (Eds.), Advances in Catalysis 39 (1993) 221. B.B. Breman, A.A.C.M. Beenackers, E.W.J. Rietjens, and R.J.H. Stege, J. Chem. Eng. Data 39 (1994) 647. L. Caldwell and D.S. van Vuuren, Chem. Eng. Sc. 41 (1986) 89. D.M. Ruthven, P r i n c i p l e s o f a d s o r p t i o n a n d a d s o r p t i o n p r o c e s s e s . New York, 1984. G.P. van der Laan, PhD Thesis (in preparation), University of Groningen, The Netherlands. C.D. Frohning, H. K61bel, M. Ralek, W. Rottig, E Schuur, and H. Schulz, Fischer-TropschSynthese. In J. Falbe (Ed.), Chemierohstoffe aus Kohle, Chapter 8, Stuttgart, 1977. D.B. Bukur, L. Nowicki, R.K. Manne, and X. Lang, J. Catal. 155 (1995) 366.