CO2 Reforming of Methane. Carbon Filament Formation by the

ICI Katalco, P.O. Box 1, Billingham, Cleveland TS23 1LB, England. A rigorous kinetic model was derived for the formation on a nickel catalyst of filam...
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Ind. Eng. Chem. Res. 2002, 41, 4252-4265

Steam/CO2 Reforming of Methane. Carbon Filament Formation by the Boudouard Reaction and Gasification by CO2, by H2, and by Steam: Kinetic Study J.-W. Snoeck† and G. F. Froment*,‡ Laboratorium voor Petrochemische Techniek, Universiteit Gent, Krijgslaan 281, B-9000 Gent, Belgium

M. Fowles ICI Katalco, P.O. Box 1, Billingham, Cleveland TS23 1LB, England

A rigorous kinetic model was derived for the formation on a nickel catalyst of filamentous carbon by the Boudouard reaction and for the gasification of filamentous carbon by carbon dioxide, by hydrogen, and by steam. The experimental study was performed in an electrobalance unit. Carbon formation and gasification experiments were performed at temperatures ranging from 773 to 848 K. The partial pressures of the various components were chosen in the ranges encountered in industrial steam reformers. The influence of the carbon formation reaction on the subsequent gasification process was also investigated. The mode of experimentation ensured that the rates of growth or gasification of the carbon filaments were always based on the same number of carbon filaments. The same reaction mechanism was derived from the study both of methane cracking and the Boudouard reaction and of the reverse reactions, gasification by hydrogen and carbon dioxide. Using the results of the parameter estimation, energy diagrams were constructed for the Boudouard reaction and for gasification by carbon dioxide and by hydrogen. Introduction Natural gas, consisting primarily of methane, is the main source for synthesis gas production by nickelcatalyzed steam reforming. A major problem encountered in this process is the deposition of carbon, leading to deactivation and even disintegration of the catalyst particle and causing blockage of the reactor tubes and fouling in downstream equipment.1-3 Criteria for predicting conditions that would lead to carbon formation are an absolute requirement in steam/CO2 reforming. Until now, these criteria have been based on the thermodynamics of the carbon-forming reactions, even if the crystallographic nature of the carbon is not known. It is obvious that the criteria would have to be based instead on the kinetics of the phenomenon. There is more, however. Electron microscopy studies have revealed that, on Ni catalysts, the carbon is deposited in the form of filaments or whiskers, carrying Ni particles on the top. This phenomenon is known to consist of a number of steps: formation of carbon at the surface of the Ni particle embedded in the support, diffusion of carbon through the Ni particle, segregation at the rear, and lifting of the Ni particle from the support by a growing carbon filament. During gasification, the sequence of steps is reversed and the filament shrinks until Ni reintegrates with the support surface. Clearly, the complexity of this phenomenon prohibits its description in terms of only a reversible surface reaction subject to thermodynamic equilibrium constants. * To whom correspondence should be addressed. † Present address: BASF Antwerpen, Scheldelaan 600, B-2040 Antwerpen, Belgium (E-mail: joost.snoeck@ notes.basant.be). ‡ Present address: Department of Chemical Engineering, Texas A&M University, College Station, TX 77843-3122 (E-mail: [email protected]).

The present paper is part of a study aiming at the development of rate equations for carbon filament formation and gasification in steam/CO2 reforming. In previous papers,4,5 the mechanisms of filamentous carbon formation and gasification occurring in methane cracking on a Ni catalyst were discussed in detail and kinetic equations were derived from this analysis using an extensive experimental database. In the present paper, reaction schemes and kinetic equations are derived for carbon formation by the Boudouard reaction

2CO f C + CO2

(1)

and for gasification by hydrogen, CO2, and steam, following the approach developed for methane cracking. Coking and gasification thresholds are determined experimentally, and the results are compared with values calculated from thermodynamics, assuming carbon in either the graphite or carbide modification. For lack of experimental data on the fine details of filament formation and retraction, the full model, accounting for diffusion and segregation, is simplified into a model valid for Ni particles saturated with carbon. The rate equations can then be cast into the form of a truly reversible reaction by introducing the experimentally determined threshold constant. Experimental Procedure and Program The experiments were performed in an electrobalance unit, described in detail in a previous paper4 and yielding weight versus time data for carbon formation or gasification. The rate of carbon formation or gasification is obtained from the slope of these curves. The experimental procedure was also described in a previous paper.5

10.1021/ie010666h CCC: $22.00 © 2002 American Chemical Society Published on Web 07/24/2002

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The bypass of the catalyst basket by an important part of the feed necessitates differential operation to obtain the correct relationship between the experimentally observed rate of carbon formation or gasification and the feed composition. The catalyst used in this study is the ICI 46-9 steamreforming catalyst. It contains 16 wt % NiO and 2 wt % K2O on a calcium aluminate support. The catalyst was reduced in a 50 mol % H2/N2 mixture while the temperature was raised from ambient to 700 °C at a rate of 15 °C/min. The temperature was maintained at 700 °C for 45 min.4 The following phases were observed by X-ray diffraction: K2O, CaAl4O7, NiO (fresh catalyst), and Ni (reduced catalyst). A very small amount of NiO was also observed on the reduced catalyst. Ni spinels were not detected. A BET surface area of 13.7 m2/gcat was measured,4 and from TEM, an average carbon filament diameter between 15 and 20 nm was determined, corresponding to a nickel surface area of 3-5 m2/gcat. To avoid diffusional limitations, the catalyst was crushed and sieved so as to retain a size 0.25-0.50 mm. Further details are given in a previous paper.4 The gases, purchased from L’Air Liquide, had a purity of >99.95%. The experiments were performed in the temperature range 773-848 K, with an amount of catalyst between 10 and 15 mg. For all of the reactions studied, reaction products were added to the feed so as to enable also a kinetic study of the reverse reaction. Another reason is the necessity of achieving differential operation. In the case of gasification by carbon dioxide and by steam, the feed composition was also dictated by the necessity of maintaining the catalyst in the reduced state. For the Boudouard reaction, the partial pressure of carbon monoxide was varied between 0.3 and 5 bar, while partial pressures of carbon dioxide up to 25 bar were applied. The feed flow rate of 0.27 mol of CO per hour ensured differential operation. For gasification by carbon dioxide, the partial pressure of CO2 was varied between 1 and 8 bar and that of CO between 0.02 and 0.3 bar. A feed flow rate of 2.7 mol of CO2 per hour was necessary to achieve differential operation. For gasification by hydrogen, the partial pressure of H2 was varied between 0.25 and 6 bar and that of methane between 0 and 20 bar. The feed flow rate of hydrogen amounted to 2 mol/h. In gasification by steam, the partial pressure of steam was varied between 1 and 8 bar and those of CO and H2 between 0.15 and 0.5 bar. The feed flow rate of steam amounted to at least 2.5 mol/h to ensure differential operation. In the previous papers on this subject,4,5 it was shown that, for reliable kinetic modeling, the rates have to be based on the same number of carbon filaments. Therefore, the filamentous carbon was deposited prior to each gasification experiment by methane cracking under the following standard conditions: pCH4 ) 10 bar, pH2 ) 0.35 bar, T ) 550 °C. Carbon Formation by the Boudouard Reaction Weight and Rate versus Time Data. A typical rate versus time curve, derived from the observed weight versus time curve, for carbon formation by the Boudouard reaction is shown in Figure 1. Three periods are observed: a period of increasing rate, a short period

Figure 1. Typical rate versus time curve for the Boudouard reaction. Table 1. Relation between the Amount of Carbon Deposited, the Rate of Carbon Formation by the Boudouard Reaction, and the Subsequent Rate of Gasification by Carbon Dioxide carbon formationa

gasificationb

carbon content (wt %)

rC,B [molC/(gcat h)]

rg,CO2 [molC/(gcat h)]

11 19 37

0.142 0.186 0.124

0.068 0.089 0.099

a T ) 525 °C, p CO ) 1.2 bar, pCO2 ) 1.0 bar. pCO2 ) 4.8 bar

b

T ) 550 °C,

of constant rate, and a period of decreasing rate. The period of increasing rate is ascribed to the gradual nucleation of carbon filaments. It was observed in methane cracking that the nucleation proceeds more slowly under conditions with a low affinity for carbon formation. This also applies to the Boudouard reaction: the nucleation is slower at low partial pressure of CO, at high partial pressure of CO2, and at higher temperature, as would be expected from the exothermic character of the Boudouard reaction. The period of decreasing rate is explained by the gradual deactivation of the catalyst resulting from the formation of encapsulating carbon. This was observed for all partial pressures of CO and CO2 and at all temperatures, whereas in methane cracking, encapsulating carbon was only formed at low partial pressure of methane and in the absence of hydrogen.5 A similar observation was made by Kuypers et al.6 according to whom the hydrogenation of carbon deposited from methane resulted in the formation of methane only, whereas higher hydrocarbons were also formed when carbon was deposited by the Boudouard reaction. Carbon atoms deposited from the decomposition of methane are likely to be further apart from one another than carbon atoms resulting from carbon monoxide. The range of constant rate of carbon formation is very short for the Boudouard reaction. For methane cracking, a very clear period of constant rate was observed, during which no further carbon filament formation takes place. When a carbon formation experiment for the Boudouard reaction is interrupted at different points in time and the deposited carbon is gasified with CO2, the following observations were made: a period of increasing rate of gasification is already present when only a small amount of carbon is deposited, and the rate of gasification further increases after the maximum in the rate versus time curve for carbon formation (viz., Table 1). This means that encapsulating carbon is already present from the beginning of the carbon formation and that

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Figure 2. ln K versus 1/T plot for the threshold constant for the Boudouard reaction. Comparison with the equilibrium constant for graphite and nickel carbide.

further nucleation takes place after the small linear part of the weight versus time curve. This short constantrate zone is a transition between the first zone in which the nucleation of new filaments prevails and the zone in which the deactivation due to the formation of encapsulating carbon is more important than the nucleation of new carbon filaments. Experimental Results. Determination of the Coking Threshold. The coking threshold defines the conditions for which the rate of carbon formation equals the rate of gasification. It cannot be reliably calculated from thermodynamic data because the carbon modification is not accurately known. This is why the coking threshold was determined experimentally, in the same way as for methane cracking,4,5 for carbon formation by the Boudoaurd reaction, e.g., over a temperature range between 798 and 923 K, at CO partial pressures of 0.6 and 1.2 bar, with increasing partial pressure of the product, CO2, until the net rate of carbon formation becomes zero. The following expression was determined for the threshold constant, K/B

K/B

)

( ) pCO2

pCO2

(

) exp -

rC,B)0

exp

(

)

0 - 2µ0CO µC,fil + µCO 2

RT

) (

)

)

-170.44 162 483 exp (2) R RT

Depending on the nature of the carbon,7 equations can be derived for the equilibrium constant of the Boudouard reaction

for graphite formation

(

Kgr B ) exp -

192.3 180 965 exp R RT

) (

)

(3)

Figure 3. Boudouard reaction: Experimental observations corrected for the number of filaments and model predictions. Quasireversible model version. T ) 525 °C.

Net Rate of Carbon Formation. The experimental results at 525 °C, showing the net rates of carbon formation in the constant-rate zone, are represented in Figure 3. The decrease of the rate of carbon formation with the partial pressure of CO2 is logical, because the reverse reaction, gasification by CO2, becomes more important in this way. The coking threshold is very far away, certainly for higher partial pressures of CO (at pCO2 ) 10.7, 43, 172, 746, and 2984 bar for pCO ) 0.3, 0.6, 1.2, 2.5, and 5.0 bar, respectively). It can also be observed, e.g., for pCO ) 0.3 bar, that the rate of carbon formation becomes very low, although the coking threshold is far away. As in the case of methane cracking,4,5 this is because the difficult nucleation of filamentous carbon under conditions with a low affinity for carbon formation also leads to a smaller number of growing filaments on the catalyst sample. This effect would bias the kinetic modeling. For methane cracking, this difficulty was solved by performing sequential experiments on a catalyst on which carbon was first deposited under standard conditions with a high carbon formation affinity so as to obtain rates of carbon formation that are all based on the same number of growing filaments. In the case of the Boudouard reaction, however, the formation of encapsulating carbon made this impossible. The only solution was to gasify the deposited carbon after each carbon formation experiment with carbon dioxide under standard conditions (pCO2 ) 2 bar, pCO ) 0.1 bar, T ) 550 °C). The rates of gasification reflect the varying numbers of carbon filaments present on the catalyst sample and are used to correct the rates of carbon formation under conditions with a low affinity for carbon formation (high pCO2) (correction factor)1 ) rate of gasification when carbon is deposited at low pCO2

for Ni3C formation

(

3C KNi ) exp B

133 100 160.6 exp R RT

) (

)

(4)

If the carbon were formed on the surface as graphite and not modified by the subsequent steps of the filament formation, the threshold constant would agree with this 3C equilibrium constant. In the present case, K/B and KNi B / gr differ by a factor 40, but KB and KB agree quite well up to 900 °C (Figure 2).

rate of gasification when carbon is deposited at high pCO2

(5) Values ranging up to 3 were obtained for this correction factor. A second correction factor had to be introduced to correct the lower number of growing filaments present at higher temperatures. Nucleation is more difficult at higher temperatures (lower affinity for carbon forma-

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In terms of Fick’s law, the diffusion equation is written as

Table 2. Influence of the Temperature during Carbon Formation by the Boudouard Reaction on the Rate of Gasfication by CO2 and the Correction Factor T (°C)

rc,Ba [molC/(gcat h)]

T (°C)

rg,CO2b [molC/(gcat h)]

(correction factor)2c

500 525 550

0.189 0.168 0.145

550 550 550

0.0282 0.0205 0.0154

0.726 1 1.334

c

a p b CO ) 1.2 bar, pCO2 ) 1.0 bar. pCO2 ) 2.0 bar, pCO ) 0.1 bar. (correction factor)2 t ratio of number of filaments.

tion). As in the case of high pCO2, this also leads to a smaller number of growing carbon filaments at higher temperatures, which is reflected by the rates of gasification with CO2 under standard conditions (Table 2). Taking the number of growing filaments at 525 °C as a reference, the following correction factor was introduced

rC,diff )

DC,NiaNi (cC,{Ni,f} - cC,{Ni,sat}) da

(8)

It is thereby assumed that during steady-state carbon filament growth, supersaturation is negligible. Coupling eq 8 with the rate equations for adsorption and for the chemical steps of the finally retained model, the following implicit equation is obtained

k+ B KCOpCO rC,B )

(correction factor)2 )

(

-

pCO2 kB KCcC,{Ni,f} KO,CO2KCO pCO

1 + KCcC,{Ni,f} + KCOpCO +

)

pCO2

1

KO,CO2KCO pCO

2

(9a)

rate of gasification when carbon is deposited at 525 °C rate of gasification when carbon is deposited at 500/550 °C

(6) Mechanism and Kinetic Model. The formation of filament consists of a number of adsorption and elementary chemical steps followed by the dissolution of the surface carbon in the Ni particle, diffusion through the Ni, and precipitation at the rear, lifting the particle from the support. As more carbon is generated at the Ni surface, the filament develops and grows to a limit size. Different mechanisms have been tested for the Boudouard reaction in which adsorbed oxygen atoms act as an intermediate, because these are known to play an important role in the mechanism of steam reforming and the water-gas shift reaction. The following set of elementary steps was considered:

adsorption of CO CO + l a CO-l

(a.1)

CO-l + l a C-l + O-l

(f.1)

CO + 2l a C-l + O-l

(f.2)

carbon formation

reaction of the O-l intermediate O-l + CO-l a CO2-l + l

(ro.1)

O-l + CO-l a CO2 + 2l

(ro.2)

O-l + CO a CO2-l

(ro.3)

O-l + CO a CO2 + l

(ro.4)

or rC,B ) k+ B KCOpCO -

[ (

(

1 + KC cC,{Ni,sat} +

)

dissolution/segregation C-l a CNi,f + l

(ds.1)

k+ B KCOpCO rC,B )

(

1

rC,B ) (7)

)

pCO2

KO,CO2KCO PCO

(

k+ B KCO pCO -

precipitation/dissolution of carbon CNi,r a Cw

pCO2 kB′ KO,CO2KCO pCO

2

(10)

that can also be written in a form corresponding to a truly reversible process by introducing the experimentally determined threshold constant, K/B

diffusion of carbon in nickel CNi,f w CNi,r

2

(9b)

1 + KCOpCO +

(d.1)

]

pCO2 da 1 rC,B + KCOpCO + DC,NiaNi KO,CO2KCO pCO

At the coking threshold, the carbon concentration is uniform over the nickel particle while rC,B ) rC,diff ) 0. Under conditions with an affinity for carbon formation, a certain concentration gradient develops over the nickel particle, depending on rC,B, DC,Ni, aNi and da.4,5 For methane cracking, it was calculated that the concentration gradients are small for the majority of the experimental conditions. The agreement between the kinetically determined coking threshold obtained from the irreversible model and the experimentally determined threshold further justified the assumption of a negligible concentration gradient over the nickel particle. Therefore, in the following, the diffusion is considered to be intrinsically fast with respect to the chemical steps, meaning that the concentration of carbon dissolved in nickel is practically uniform and equal to the saturation concentration. If KCcC,{Ni,f} in eq 9b is incorporated into kB ′ while being neglected in the denominator, the rate equation takes a simpler and explicit form

desorption of CO2 CO2-l a CO2 + l

)

pCO2 kda B KC cC,{Ni,sat} + rC,B KO,CO2KCO DC,NiaNi pCO

(

1 + KCOpCO +

)

1 pCO2 K/B pCO pCO2 1

KO,CO2KCO pCO

)

2

(11)

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Table 3. Boudouard Reaction Final Parameter Estimates Based on the Simultaneous Regression of Experiments at All Temperatures, t Values and Approximate 95% Confidence Intervals, F Value, and Adequacy Test for the Selected Model (Rate Eq 11)a estimate k+ B KCO KO,CO2 F value FC

t value

lower limit

A+ B E+ B (J/mol) ACO 0 ∆Ha,CO (J/mol) AO,CO2 0 ∆HO,CO (J/mol) 2

26 732 820 19.1b 2.01b 108 379 8.4 82 580 1.0245 × 10-6 9.1b 0.088b -92 543 -3.6 -144 200 30 190 322 6.0b 27.4b 89 805 2.2 8717 774 2.94 < Ftab(49, 7; 95%) ) 3.32

upper limit 2.48b 134 200 0.138b -40 310 55.2b 170 900

a Quasireversible model description based on experimental results corrected for the number of growing filaments. b For reparametrized coefficients.

with

K/B

)

( ) ( pCO2 p2CO

)

)

2 k+ B KCO KO,CO2

rC,B)0

kB′

Figure 4. Parity diagram for the Boudouard reaction.

)

rC,B)0 2 k+ B KCO KO,CO2

kB KccC,{Ni,sat}

(12)

This model is rigorously valid at the coking threshold only, where rC,B ) 0 and cC,{Ni,f} ) cC,{Ni,r} ) cC,{Ni,sat}, but its application is also justified when the concentration gradients over the nickel particle are sufficiently small. From the chemical steps of the scheme in eqs 7, 12 rival equations were derived, depending on the type of adsorption, molecular (eq a.1) or dissociative (eq f.2), of carbon formation (eq f.1 or f.2), the reaction of O-l, and the rate-determining step. The rate parameters of the models were obtained by means of nonlinear regression of the experimental data using the Marquardt algorithm.8,9 Reparametrization around the mean temperature was applied to facilitate the estimation. The fit of the various sets of equations was tested by means of an F-test. The parameters were tested by their 95% confidence interval and by physicochemical criteria such as the Arrhenius and van’t Hoff equations and the Boudart rules.8-10 The finally retained model corresponds to molecular adsorption of CO (eq a.1), carbon formation from adsorbed CO (eq f.1), reaction of O-l according to (eq ro.2) reflecting the weak adsorption of CO2 and with the cleavage of the CO-l represented by eq f.1 as the rate-determining step

CO + l a CO-l

KCO

CO-l + l a C-l + O-l

rds/k+ B and kB

O-l + CO-l a CO2 + 2l

KO,CO2

C-l a CNi,f + l

1/KC

The corresponding rate equation was already given above in eq 11. It is the only rate equation in which all of the parameters are significantly positive. They are given in Table 3. The CO adsorption constant KCO ) exp(-115/R) exp(92 543/RT) satisfies the Boudart criteria.10 The curves in Figure 3 show the fit of the experimental data at 525 °C, and Figure 4 is a parity plot including all of the data.

Figure 5. Energy diagram for the Boudouard reaction.

Tottrup11 considered the same scheme and ratedetermining step, but without reversibility in the surface reaction. The temperature dependence of the parameter estimates was not very reliable. The results of the kinetic modeling of the Boudouard reaction are visualized in the energy diagram of Figure 5, which contains the various steps of the scheme with their corresponding standard enthalpy changes and, for the rate-determining step, the activation energy. Using the parameter estimates and thermodynamic data, it is possible to calculate a value for the heat of adsorption of oxygen. This is done in the following way. The enthalpy change for the oxidation of CO is determined from thermodynamic data

CO + 1/2O2 a CO2

0 ∆H798 ) -283.3 kJ/mol

The heat of adsorption of carbon monoxide was estimated as

CO + l a CO-l

0 ∆Ha,CO ) -92.5 kJ/mol

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Figure 6. Typical rate versus time curve for gasification by CO2. Carbon deposited by the Boudouard reaction.

This value agrees well with the literature data (127 kJ/ mol12). The enthalpy change of the following reaction can now be determined

CO-l + 1/2O2 a CO2 + l

∆H0 ) -189.8 kJ/mol

The enthalpy change for the reaction of an adsorbed CO molecule with an adsorbed oxygen atom can be derived from the parameter estimation

CO-l + O-l a CO2 + 2l

0 ∆HO,CO ) 89.8 kJ/mol 2

From the enthalpy changes of the last two reactions, a value for the heat of adsorption of oxygen can be calculated 1

/2O2 + l a O-l

∆H0a,O ) -279.6 kJ/mol

This value agrees very well with values available in the literature. Toyoshima et al.12 mention a heat of adsorption of 255 kJ/mol. Panas et al.13 give a chemisorption energy between 115 and 130 kcal/mol. With a bond dissociation enthalpy of 119.1 kcal/mol for O2, a heat of adsorption of oxygen of 233-295 kJ/mol is calculated. Carbon Gasification by Carbon Dioxide Weight and Rate versus Time Data. Prior to each gasification experiment, carbon was deposited on the catalyst under standard conditions, because it has been extensively shown for methane cracking5 and for the Boudouard reaction that the conditions during carbon formation influence the number of growing carbon filaments and thereby also the rate of gasification. When carbon is deposited by the Boudouard reaction (T ) 550 °C, pCO ) 1.2 bar, pCO2 ) 1.0 bar, 16 wt % of carbon deposited), the weight or rate versus time curve for gasification by CO2 shows three zones (Figure 6): one with an increasing rate of gasification, a short one with a constant rate, and one with a decreasing rate. These three zones are the mirror image of the three zones observed during carbon formation by the Boudouard reaction. These zones were determined by the competing processes of carbon filament nucleation and surface deactivation by the formation of encapsulating carbon. In the early stages of gasification, encapsulating carbon is removed. As a result, the rate of gasification of the filaments increases. Near the end, the decrease of the number of filaments prevails. There is an intermediate zone with an almost constant rate. It was also observed that the period of increasing rate of gasification is much longer when conditions are applied with a low affinity

Figure 7. Typical rate versus time curve for gasification by CO2. Carbon deposited by methane cracking.

for gasification (low pCO2, high pCO, low temperature), indicating that the removal of the encapsulating carbon is more difficult. It is, therefore, questionable whether encapsulating carbon is removed to the same extent for all of the experimental conditions. This could cause a distortion of the rates of gasification, especially at low temperature and at high partial pressure of CO. When carbon is deposited by methane cracking (T ) 550 °C, pCH4 ) 10 bar, pH2 ) 0.35 bar, 30-50 wt % of carbon deposited), only two zones are observed in the weight or rate versus time curves (Figure 7): one with a constant rate and one with a decreasing rate of gasification. Because of the absence of encapsulating carbon, a period of constant rate of gasification is observed, and this ensures that an accurate and reliable rate of gasification can be obtained for all experimental conditions. The rates of gasification by means of CO2 of carbon deposited by methane cracking and the Boudouard reaction are comparable. This is logical when the standard conditions chosen for both reactions have a high affinity for carbon formation. Differences appear when conditions with a low affinity for gasification are applied, because the encapsulating carbon, formed by the Boudouard reaction, is not easily removed. For this reason, methane cracking was preferred for the deposition of carbon prior to each gasification experiment. Experimental Results. Determination of the Gasification Threshold. The gasification threshold was determined experimentally in the same way as the coking thresholds. For various temperatures and partial pressures of carbon dioxide, the partial pressure of CO was determined for which the net rate of gasification was zero and the gasification threshold was calculated / from KCO ) pCO2/pCO2. 2 When carbon was deposited by methane cracking, the following expressions were obtained for the threshold constant at various partial pressures of CO2

pCO2 ) 1 bar

/ KCO ) exp 2

168 527 exp((177.8 R ) RT ) (13)

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Table 4. Comparison of the Enthalpy Change in the Formation of Filamentous Carbon from Graphite Calculated from the Experimentally Determined Expressions for the Threshold Constants for Methane Cracking and for Gasification by CO2 gasification by CO2 pCO2 (bar) 1 4 8

0 ∆Hgrffil

pCO2 ) 4 bar

methane cracking

(kJ/mol)

pCH4 (bar)

0 ∆Hgrffil (kJ/mol)

12.4 24.8 32.3

1.5 5 10

16.4 49.8 57.5

/ KCO ) exp 2

156 129 exp((164.8 R ) RT ) (14)

pCO2 ) 8 bar

/ KCO ) exp 2

148 389 exp((156.3 R ) RT ) (15)

When carbon was deposited by the Boudouard reaction, the following equation was derived for pCO2 ) 4 bar / KCO ) exp 2

148 550 exp((157.7 R ) RT )

(16)

Equation 16 leads to values that are in agreement with those obtained when coke is deposited by methane cracking, so that the thermodynamic properties of the carbon filaments are not influenced in a marked way by the reaction that forms them. The threshold constant derived from carbon gasification by CO2 is in good agreement with that for the carbon formation by the Boudouard reaction, as required. The threshold constant for gasification by CO2 depends slightly on the gas-phase composition, in analogy with methane cracking.5 The threshold shifts toward the gasification side when the partial pressures increase, so that more CO or methane is required to establish affinity for carbon formation. The expressions for the threshold constant and for the equilibrium constant based on graphite allow the enthalpy change for the formation of filamentous carbon from graphite to be calculated (Table 4). With increasing partial pressures, the enthalpy change in the formation of filamentous carbon from graphite evolves in the same direction at increasing partial pressures for methane cracking and CO2 gasification. The explanation for these phenomena is not clear. It certainly does not originate from the conditions during the nucleation of the carbon filaments, because carbon was always deposited under the same standard conditions prior to gasification by CO2. The only useful indication is that the change in partial pressure causes a change in the carbon surface coverage because of the competition for the same sites between carbon segregation and gas adsorption.5 This was observed to influence the thermodynamic properties of surface carbon:14 the lower the carbon coverage, the higher the deviation from graphite. This coincides with the actual results: the higher the partial pressure, the stronger the deviation from graphite. How the thermodynamic properties of the filamentous carbon that determine the threshold4 could be altered is not clear. Net Rate of Gasification by Carbon Dioxide. The experimental results at 550 °C are shown in Figure 8, together with the model predictions. The partial pres-

Figure 8. Gasification by CO2: Experimental observations and model predictions. Quasireversible model version. T ) 550 °C. Carbon deposited by methane cracking.

sure of carbon monoxide had to be limited at the lower end by the requirement of operating under differential conditions. Although the conversion calculated on the basis of an estimate of the feed flow rate through the catalyst in the basket was very small ( 1 bar, and less pronounced at high temperature (T ) 575 °C), where a partial pressure of hydrogen of 4 bar is required before the rate of gasification decreases. This behavior points toward a strong adsorption of hydrogen. At high partial

Figure 11. Gasification by H2: Experimental observations and model predictions. Rate of gasification versus partial pressure of hydrogen. pCH4 ) 0.5 bar. Quasireversible model version. T ) 500, 525, 550, and 575 °C. Carbon deposited by methane cracking.

pressure of methane, the rate of gasification monotonically increases because of the proximity of the coking threshold. Mechanism and Kinetic Model. In the kinetic modeling of gasification by hydrogen, it was assumed that the adsorbed carbon atoms are gradually hydrogenated into methane. Hydrogen is assumed to adsorb dissociatively. The first step is the segregation of carbon, dissolved in nickel, to the surface of the nickel particle. The carbon atoms are provided by the carbon filament (cf. gasification by CO2).

CNi,f + l a C-l

KC

H2 + 2l a 2H-l

KH

C-l + H-l a CH-l + l

1/K5

CH-l + H-l a CH2-l + l

1/K4

CH2-l + H-l a CH3-l + l

1/K3

CH3-l + H-l a CH4-l + l

1/K2

CH4-l a CH4 + l

1/KCH4

and

(29)

Ind. Eng. Chem. Res., Vol. 41, No. 17, 2002 4261

or CH3-l + H-l a CH4 + 2l

Table 7. Gasification by H2 Final Parameter Estimates Based on the Simultaneous Regression of Experiments at All Temperatures, t Values and Approximate 95% Confidence Intervals, and F Value (Rate Eq 31)a

1/K2

All of the steps were considered as possible ratedetermining steps. Rate equations were derived in the same way and under the same assumptions as for gasification by CO2 for all of the possible reaction mechanisms and rate-determining steps. Simplifications of these rate equations, obtained by omitting certain terms in the denominator (meaning that the surface concentrations of certain intermediate species were neglected), were also considered. A total of 91 possible rate equations was obtained. The model discrimination led to the same rate equation as deduced for methane cracking.5 The rate-determining step is the last hydrogenation step, in which an adsorbed methyl group is hydrogenated and adsorbed methane is formed. The surface concentrations of CH-l and CH2-l are negligible. The retained mechanism can be written as

CNi,f + l a C-l

KC

H2 + 2l a 2H-l

KH

C-l + 3H-l a CH3-l + l

1/Kr

CH3-l + H-l a CH4-l + l

rds/k+ H and kH

CH4-l a CH4 + l

1/KCH4

K+ H′ K′′r KCH4 F value b

A+ H′ E+ H′ (J/mol) A′′r ∆H0r ′′ (J/mol) ACH4 395

estimate

t value

lower limit

upper limit

2.52 × 109 159 736 7.45 × 1011 191 555 3.58

8.6b 10.8 4.2b 6.3 9.4

0.072b 130 000 0.121b 131 100 2.82

0.115b 189 500 0.342b 252 000 4.35

a Quasireversible model, carbon deposited by methane cracking. For reparametrized coefficients.

(30)

with the following rate equation in the quasireversible model version

rg,H2 )

(

(

k+ 1 H′ p 2 - / pCH4 K′′r H2 K

1+

H

)

1 p 3/2 + KCH4pCH4 K′′r H2

)

2

(31)

and + 1/2 k+ H ′ ) kH K H

Kr ) K3K4K5

Figure 12. Energy diagram for gasification by hydrogen.

K′r ) Kr/KH3/2 K′′r ) K′r/KCcC,{Ni,sat} K/H, the threshold constant in eq 27, becomes

K/H )

( ) ( pCH4 pH22

)

rg,H2)0

)

k+ H′KCcC,{Ni,f} kHK′r

)

rg,H2)0

k+ H′KCcC,{Ni,sat} kHK′r

(32)

All of the other models could be rejected on the basis of a lack of fit or significantly negative parameter estimates. The paramater values are presented in Table 7. The heat of adsorption of methane was not significantly different from zero, so that the adsorption coefficient was estimated without temperature dependence. The experimental and calculated rates are compared in Figure 9 for a temperature of 550 °C and in Figure 11 for various partial pressures of hydrogen. The

nonmonotonic behavior of the rate of gasification with the partial pressure of hydrogen is very well predicted. It originates from the strong increase of the surface coverage of the methyl species (term in pH23/2) with increasing partial pressure of hydrogen. The evolution of this effect with the temperature is also correctly described: the effect is very strong at 500 °C and becomes weaker as the temperature increases. On the basis of the results of the parameter estimation and literature data for the heat of adsorption of hydrogen,5 the energy diagram for gasification by hydrogen was constructed (Figure 12). Carbon Gasification by Steam Experimental Results. Determination of the Threshold for Gasification by Steam. The direct determination of the threshold for gasification by steam only was impossible, because several reactions take place simultaneously. An equation for the threshold constant was derived from the relationship between gasification by steam and carbon dioxide

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adsorbed oxygen atom is chosen as the rate-determining step, because it was already found to be rate-determining in the study of gasification by CO2. Gasification by steam cannot be modeled separately because it is always accompanied by gasification by hydrogen.

CNi,f + l a C-l

KC

H2 + 2l a 2H-l

KH

C-l + 3H-l a CH3-l + 3l

1/Kr

CH3-l + H-l a CH4-l + l

rds/k+ H and kH

CH4-l a CH4 + l

1/KCH4

H2O + l a O-l + H2

1/KO,H2O

(37)

or

Figure 13. Gasification by H2O: Experimental results and model predictions. T ) 550 °C. Quasireversible model version. Simultaneous parameter estimation for gasification by H2 and H2O.

C + CO2

a 2CO

/ KCO 2

CO + H2O a CO2 + H2

KWGS

C + H2O

/ KH 2O

a H2 + CO

(33)

The threshold constant for gasification by carbon dioxide or for the Boudouard reaction has been determined experimentally before, and the equilibrium constant for the water-gas shift reaction can be calculated from thermodynamic data / K/B ) 1/KCO ) exp(-170.4/R) exp(162481/RT) (34) 2

KWGS ) exp(-33.8/R) exp(36 564/RT)

K H 2O

H2O-l a O-l + H2

1/KO,H2O

C-l + O-l a CO-l + l

rds/k+ O and kO

CO-l a CO + l

1/KCO

In the derivation of the rate equations, it was assumed that the diffusivity of carbon in nickel is sufficiently high to maintain a practically uniform carbon concentration in the nickel particle equal to the saturation concentration. The model discrimination led to a model with a dissociative adsorption of steam and the rate equation

where / / KH ) KCO K 2O 2 WGS

H2O + l a H2O-l

(35)

rg,H2,H2O )

(

(

H

2

(38)

with + 1/2 k+ H ′ ) kH K H

(36)

Net Rate of Gasification by Steam. The influence of the partial pressures of steam, carbon monoxide, and hydrogen on the rate of gasification is shown in Figure 13. As expected, the rate decreases with the partial pressures of the reaction products carbon monoxide and hydrogen. For high partial pressures of carbon monoxide and/or hydrogen, the rate of gasification increases monotonically with the partial pressure of steam. At low partial pressures of hydrogen and carbon monoxide, the rate of gasification exhibits a maximum when the partial pressure of steam increases. Mechanisms and Kinetic Model. The chemical steps at the surface are given in the scheme in eqs 37. The adsorption of steam is either molecular or dissociative. The reaction of an adsorbed carbon atom with an

)

1 1 pH2O 1 + pH23/2 + KCH4pCH4 + KCOpCO + K′′r KO,H2O pH2

The threshold constant for gasification by steam becomes / ) exp(136.7/R) exp(-125 916/RT) KH 2O

)

pH2O k+ k+ H′ O′ 1 pH22 - / pCH4 + - kOKCOpCO K′′r KO,H2O pH2 K

K′′r )

K′r KCcC,{Ni,sat}

)

Kr 3/2

KH KCcC,{Ni,sat}

(39)

+ k+ O′ ) kOKCcC,{Ni,sat}

or, in the quasireversible model version

rg,H2,H2O )

(

(

)

(

pH2O k+ k+ H′ 4′ 1 1 . pH22 - / pCH4 + . - / pCO K′′r K p K K O,H2O H2

1+

H

H 2O

)

)

1 1 pH2O pH23/2 + KCH4pCH4 + KCOpCO + K′′r KO,H2O pH2

2

(40)

Ind. Eng. Chem. Res., Vol. 41, No. 17, 2002 4263 Table 8. Parameter Estimates Based on the Simultaneous Regression of All Experiments at All Temperatures, t Values and Approximate 95% Confidence Intervals, and F Values for the Selected Model Simultaneous Parameter Estimation for Gasification by H2O and H2a

k+ O′

A+ O′ E+ O′ (J/mol) KO,H2O AO,H2O 0 ∆HO,H (J/mol) 2O + k+ ′ A ′ H H E+ H′ (J/mol) K′′r A′′r ∆H0r ′′ (J/mol) KCH4 ACH4 F value 806 a

Table 9. Comparison of the Estimates and Their 95% Confidence Intervals for the Activation Energy of k+ O′ Obtained in the Study of Gasification by CO2 and H2O E+ O′

estimate

t value

lower limit

upper limit

2 × 1010 166 397 4.73 × 10-6 -97 771 1.07 × 109 153 828 1.83 × 1013 216 145 3.49

16.0b 13.6 7.6b 3.0 10.4b 11.9 6.1b 10.0 9.6

0.239b 141 800 0.064b -163 100 0.078b 127 900 0.129b 170 300 2.765

0.307b 190 900 0.111b -32 450 0.116b 179 700 0.254b 259 300 4.216

Quasireversible model. b For reparametrized coefficients.

Figure 14. Parity diagram for gasification by steam. ICI 46-9S.

with / KH ) 2O

( ) pH2pCO pH2O

rg,H2O)0

)

k+ OKCcC,{Ni,sat} kOKCOKO,H2O

(41)

The parameter estimates obtained from the simultaneous regression of all experiments on gasification by hydrogen and by steam at all temperatures are shown in Table 8. The fit is excellent (F ) 806). All of the activation energies are positive. The only adsorption coefficient left in the denominator is the adsorption coefficient of methane. This was taken to be independent of temperature because the heat of adsorption could not be estimated as being significantly different from zero. The adsorption coefficient of CO was not estimated as being significantly different from zero and was omitted. The experimental values and the model predictions at 550 °C are compared in Figure 13. The parity diagram is shown in Figure 14. The observed behavior is quite well predicted by the model.

gasification by CO2 gasification by H2O

lower limit

estimate

upper limit

176 200 141 800

243 835 166 397

311 500 190 900

Table 10. Comparison of the Parameter Values at 525 °C Obtained from the Studies of the Boudouard Reaction and Gasification by CO2, and from Methane Cracking and Gasification by Hydrogen Respectively KCO 1/(KCOKO,CO2)

KCH4 1/K′′r

Boudouard reaction

gasification by CO2

1.2 0.021

27.4 0.0085

methane cracking

gasification by H2

0.21 10.1

3.58 4.6

steam and by carbon dioxide shows that both reaction schemes represent gasification of carbon by adsorbed oxygen atoms. Only the origin of the adsorbed oxygen atoms differs: dissociative adsorption of either steam or carbon dioxide. The same step is rate-determining, namely, the reaction between an adsorbed oxygen atom and an adsorbed carbon atom, so that the same rate coefficients are estimated in both studies. The estimates for the activation energies are compared in Table 9. Although the activation energy is higher for gasification by CO2, both confidence intervals overlap. The surface oxygen concentration is clearly higher during gasification by steam than during gasification by CO2, as can be concluded from a comparison of the values for 1/KO,H2O and 1/KCO/KO,CO2, e.g., at 525 °C: 1/KO,H2O ) 0.0844, 1/KCO/KO,CO2 ) 0.0085. Comparison of the Models Obtained from the Separate Studies of Carbon Formation and Gasification. The same models have been derived from the separate studies of the Boudouard reaction and gasification by CO2 and from studies of methane cracking5 and gasification by hydrogen. In each case, both the forward and the reverse reaction were modeled, which was possible because the feed always contained the reactants and the reaction products. In principle, analogous information should be obtained from these studies, and the rate equation obtained, e.g., during the study of methane cracking should be applicable to predictions of the rate of gasification by hydrogen. When the energy diagrams or the tables with the final parameter estimates are compared (Figures 5, 9, and 12 and Tables 3, 5, and 7 for methane cracking5), it becomes clear that the heats of reaction and adsorption are almost equal. The activation energies for the rate-determining step obtained from the studies of gasification reactions are clearly higher. When the parameter values at 525 °C are compared, for example, the differences are obvious (Table 10). In general, the adsorption terms in the denominator are much higher in the studies of gasification. This could point toward a strong competition for sites between the carbon that has to segregate from the bulk of the nickel phase to the surface and the gas-phase components.

Links between the Models Obtained for the Separate Reactions

Conclusions

Link between Gasification by Steam and by CO2. A comparison of the mechanism for gasification by

Rate equations were derived from a set of experimental data on filamentous carbon formation by the

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Ind. Eng. Chem. Res., Vol. 41, No. 17, 2002

Boudouard reaction and its gasification by CO2. As a continuation of previous work on methane cracking,5 the gasification of carbon filaments by H2 and by H2O was also investigated. The rate equations explicitly reflecting certain typical features, such as the dissolution of carbon formed on the Ni particle surface into the metal, diffusion of carbon through the Ni, and segregation of the carbon at the rear of the particle, leading to the lifting of the latter by the growing filament or shrinking of this filament under gasifying conditions, contain parameters that are not accessible by the experimental techniques usually applied in chemical reaction engineering studies. Under certain assumptions, the rate equations can be reduced to a form encountered with reversible reactions, but to achieve accuracy, the thermodynamic equilibrium constant has to be replaced by an experimentally determined threshold constant, reflecting the thermodynamic properties of filamentous carbon. The thermodynamic properties of the filamentous carbon are not influenced in a marked way by the reaction leading to its formation. Common coking and gasification thresholds are found for the corresponding carbon formation and gasification reactions. An influence of the partial pressures of the gas-phase components on the threshold is observed, both for methane cracking and for gasification by CO2. The only possible explanation is their influence on the carbon surface coverage. How the thermodynamic properties of filamentous carbon are influenced is not clear. The fit of the rate equations to the experimental data is very good, but it follows from the parameter estimation that certain adsorption parameters and surface equilibrium constants appearing in the separately determined quasireversible rate equations for carbon formation as well as in that for gasification, do not have the same value (Table 10), meaning that the application of these equations is specific. It might well be that the surface coverages are quite different in the two cases because of the competition between gas-phase adsorption and carbon segregation for the same sites or that the essential assumption of carbon-saturated nickel is not satisfied under all experimental conditions. It is clear that further refinement of the kinetic model would be of interest. Nevertheless, the direct insertion of the threshold constants into the equations ensures a correct prediction of zones of carbon formation and of gasification. What remains to be done at this level is to derive kinetic criteria accounting for all of the reactions that produce and gasify carbon in steam/CO2 reforming. This issue will be addressed in a following paper.

da ) average diffusion path length (m) DC,Ni ) carbon diffusivity in nickel (m2/h) K/B ) experimentally determined threshold constant for the Boudouard reaction Kgr B ) equilibrium constant for the Boudouard reaction with formation of graphite 3C KNi ) equilibrium constant for the Boudouard reaction B with formation of nickel carbide

/ ) experimentally determined threshold constant for KCO 2 gasification by carbon dioxide

K/H ) experimentally determined threshold constant for gasification by hydrogen K/M ) experimentally determined threshold constant for methane cracking K ) symbol used for equilibrium coefficients k+ B , kB ) rate coefficients of the forward and reverse reactions of the rate-determining step of the Boudouard reaction k+ O, kO ) rate coefficients of the forward and reverse reactions of the rate-determining step of gasification by carbon dioxide k+ H, kH ) rate coefficients of the forward and reverse reactions of the rate-determining step of gasification by hydrogen l ) vacant catalyst site pi ) partial pressure of component i, bar rC,B ) rate of carbon formation by the Boudouard reaction [molC/(gcat h)] rg,CO2 ) rate of gasification by carbon dioxide [molC/(gcat h)] rC,diff ) rate of carbon diffusion through nickel [molC/(gcat h)] rg,H2 ) rate of gasification by hydrogen [molC/(gcat h)] rg,H2O ) rate of gasification by steam [molC/(gcat h)] rds ) rate-determining step µC,fil ) chemical potential of filamentous carbon

µ0CO ) standard chemical potential of CO 0 µCO ) standard chemical potential of CO2 2

Acknowledgment The authors are grateful to ICI Chemicals and Polymers Ltd., Billingham, U.K., for funding this research project. Literature Cited

Nomenclature aNi ) nickel metal surface area (m2/gcat) CNi,f ) carbon dissolved in nickel at the front of the particle, just below the selvedge CNi,r ) carbon dissolved in nickel at the rear of the particle cC,{Ni,f} ) concentration of carbon dissolved in nickel at the front of the particle, just below the selvedge (gas side) (molC/m3Ni) cC,{Ni,r} ) concentration of carbon dissolved in nickel at the rear of the particle (support side) (molC/m3Ni) cC,{Ni,sat} ) saturation concentation of filamentous carbon in nickel (molC/m3Ni) cw ) filamentous carbon (whisker carbon)

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Ind. Eng. Chem. Res., Vol. 41, No. 17, 2002 4265 (9) Froment, G. F.; Hosten, L. Catalytic Kinetics: Modeling. Catal. Sci. Technol. 1981, 2, 97-170. (10) Boudart, M.; Mears, D. E.; Vannice, M. A. Kinetics of Heterogeneous Catalytic Reactions. Congr. Int. Chim. Ind. [C. R. 35] 1967, 32 (Special issue, Part I), 281. (11) Tottrup, P. B. J. Catal. 1976, 42, 29. (12) Toyoshima, I.; Somorjai, G. A. Catal. Rev.-Sci. Eng. 1979, 19, 105.

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Received for review August 8, 2001 Revised manuscript received April 11, 2002 Accepted April 16, 2002 IE010666H