Hierarchical Multiscale Modeling of Methane ... - ACS Publications

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Hierarchical Multiscale Modeling of Methane Steam Reforming Reactions De Chen,*,† Rune Lødeng,‡ Hallvard Svendsen,† and Anders Holmen† † ‡

Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), N-7491 Trondheim, Norway SINTEF Materials and Chemistry, N-7465 Trondheim, Norway ABSTRACT: In this work, a hierarchical multiscale modeling approach is demonstrated. Models at the atomic and molecular level, on Ni crystal, in catalyst pellets and reactor tubes in a steam methane reformer are included. The kinetics of steam reforming, including carbon formation on the supported Ni catalyst, was studied experimentally in a tapered element oscillating microbalance (TEOM) reactor at relevant industrial conditions. A predictive microkinetic model of steam reforming including filamentous carbon formation was developed. The activation energy and pre-exponential factor of each elementary step were estimated using the unity bond index-quadratic exponential potential (UBI-QEP) approach and transition-state theory, respectively. Only a few parameters in the model were refined based on the experimental results and DFT calculations. The hybrid kinetic model combining a traditional kinetic model and a microkinetic model was used in simulations to significantly reduce the computational load. Maps of the kinetic carbon potential in the catalyst pellets and tubular reformer were established at different operating conditions. It was found that intraparticle diffusion resistance increases the carbon potential. High carbon potentials were found near both the inlet and the outlet of the reactor.

1. INTRODUCTION Steam reforming is the most common catalytic technology for converting natural gas to synthesis gas and hydrogen.1 In this process, two stable molecules are converted into the more reactive synthesis gas; hence, the overall reaction is strongly endothermic. To supply sufficient heat, the catalyst is loaded into a large number of special alloy tubes placed inside a furnace equipped with burners. Typically, the catalyst temperature can vary from 450-650 °C at the inlet to 700-950 °C at the outlet of the tubes. Steam reforming on nickel catalysts always involves the risk of carbon formation.2,3 The presence of carbon could decrease the heat transfer to the catalyst, cause deactivation and even destroy the catalyst mechanically, as well as increase the pressure drop through the reformer tubes. In industry, the catalyst properties and operating conditions must be carefully selected to minimize carbon formation. A steam-to-carbon ratio of about 3 is typical in industrial operation. However, reducing the steam-tocarbon ratio could be economically beneficial because of a higher volumetric throughput of natural gas. The resulting increased risk of carbon formation has to be offset by improved operation achieved by optimization at different scales, including the reaction on the catalyst surface and at the catalyst pellet, actual reactor, and process levels.4 Such an approach should rely as much as possible on a fundamental and detailed understanding of the reaction system. The chemical process involves different scales, including those of atoms (∼10-11 m), metal crystals (∼10-10 m), catalyst particles (∼10-3-10-2 m), the reactor (∼100-101 m), and the plant (>101 m).5 Research is typically dedicated to one particular scale (i.e., homogeneous models) or possibly two scales as in common heterogeneous models. To obtain a more fundamental tool for predicting carbon formation, the catalyst r 2010 American Chemical Society

surface and possibly atomic levels should also be included. finding an approach that merges these levels into one model in a consistent manner is not straightforward at all. Discussions have continued for a long time about how to overcome different jumps in scale, for example, the gap between surface science at the atomic scale and applied catalysis at the particle scale and further at the reactor scale. Recently, hierarchical multiscale modeling has received much attention as a method to seamlessly and dynamically link models and phenomena across multiple length and time scales, spanning from the quantum to the macroscopic scale in a two-way information flow modeling structure.6,7 Microkinetic modeling plays an important role with regard to emerging scientific fields that span many disciplines, including physics, chemistry, mathematics, statistics, chemical engineering, mechanical engineering, and materials science.7 It provides perfect boundaries for models covering different scales. The present work presents such an effort connecting models at different scales with each other, providing a tool for obtaining useful diagnostics in terms of predicting coking potential on Ni catalysts in industrial reformers. The main objective is to build a kinetic carbon potential map for a steam reformer based on a detailed microkinetic model. A hierarchical approach is discussed to deal with the complexities of the different scales. The article starts with a brief overview of hierarchical multiscale modeling approaches and an introduction of modeling at different scales. This is followed by the development of a microkinetic model of the Special Issue: IMCCRE 2010 Received: March 16, 2010 Accepted: August 25, 2010 Revised: August 4, 2010 Published: September 10, 2010 2600

dx.doi.org/10.1021/ie1006504 | Ind. Eng. Chem. Res. 2011, 50, 2600–2612

Industrial & Engineering Chemistry Research Scheme 1. Representation of the Hierarchically Multiscale Approach

steam reforming of methane including filamentous carbon formation. Then, a two-dimensional heterogeneous reactor model is developed using hybrid kinetic models to simulate the concentration and temperature, as well as site coverage profiles in the pellets throughout the reactor. Based on these data, a map for coking potential is built.

2. HIERARCHICAL MULTISCALE MODELING Vlachos and co-workers8 developed a hierarchical multiscale approach to a new thermodynamically consistent microkinetic C1 model on Rh for methane catalytic partial oxidation and reforming, as well as for the thermal decomposition of C1 oxygenates (methanol and formaldehyde). In the present work, we extend this approach to a multiscale model of an industrial reformer, combining the models at the atomic and molecular level on Ni crystals with models of the catalyst pellets and tubular reactor. A hierarchical approach is employed to take into account the complexity of reactions at the different scales, such as Ni surfaces and pellets. The extended approach is illustrated in Scheme 1. It has been shown that microkinetic modeling9-11 of a reaction system at the atomic or molecular level can be very useful for a detailed understanding of the reaction mechanism and the catalyst structure-activity relationship. Much progress has been achieved in the development of a methodology for microkinetics, such as methods for dealing with thermodynamic consistency,12 microkinetic analysis and derivation of rate expressions based on microkinetics,13 and the approach for refining kinetic parameters.7,14,15 This has made microkinetic modeling a powerful method for elucidating reaction mechanisms, performing predictive modeling, and optimizing reactor configurations. Microkinetic modeling has been successfully applied to many reaction systems.9,10,16,17 Because no rate-determining step (RDS) is assumed and the kinetic parameters are determined or estimated on a physical basis, microkinetic models are, in principle, much more widely applicable than traditional models. However, microkinetic modeling presents a formidable challenge because of the high number of thermodynamic and kinetic parameters that must be determined. Surface science studies9 and ab initio quantum chemical calculations1,10,18 provide important sources of relevant data. The latter can be considered as a high-level theoretical tool, on the right side of Scheme 1. Significant progress in the prediction of kinetic parameters has been made with density functional theory (DFT).1,10,18 However,

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computational cost is still a major barrier for its wide application. DFT results have demonstrated that the adsorption energy of any molecule is approximately proportional to the adsorption energy of the central C, N, O, or S atom.19 A phenomenological approach, namely, the combination of a scaling model with a Brønsted-Evans-Polanyi-type correlation, has been developed into a general framework for estimating the reaction energies of surface reactions.19-21 This makes it possible to construct the full potential energy diagram for a surface-catalyzed reaction for any transition metal on the basis of the C, N, O, and S chemisorption energies and a calculation for a single metal. The semiempirical unity bond index-quadratic exponential potential (UBI-QEP) technique [previously known as the bond order conservation-Morse potential (BOC-MP) approach] has long provided a framework for predicting adsorption heats and activation energies within an accuracy range of 1-3 kcal/ mol.22-24 However, the error could occasionally be substantially larger. Both scaling methods and the UBI-QEP approach can be thought of as low-level theoretical tools, on the left side of Scheme 1. UBI-QEP theory is a simple bridge between the binding energy of adsorbed species on a surface and the reaction activation energy, providing estimations with reasonably good accuracy.23 The method has been applied quite frequently for different reaction systems as a tool for understanding reaction mechanisms on metal surfaces.24-26 Recently, UBI-QEP was successfully applied to the microkinetic simulation of different reactions24 such as ethane hydrogenolysis, the water-gas shift reaction,27-29 oxidative conversions of hydrogen and methane on Pt and Rh surfaces,30 ammonia decomposition,31 C1-C2 product formation in a Fischer-Tropsch synthesis over cobalt,32 and the steam reforming of methane.33,34 A hierarchical approach combines the advantages of low- and high-level methods, enabling the use of surface experiments and DFT calculations to refine the parameters, such as the reaction index in UBI-QEP approach. This increases the accuracy of the UBI-QEP method, while still retaining its simplicity. Transition-state theory allows details of molecular structures to be incorporated approximately into rate constant estimations, especially in the estimation of the pre-exponential factor by determining entropy changes using statistical thermodynamics. All of the partition functions can be estimated by DFT calculations to determine entropy changes between the reactant and transition state at a high level.35 At a low level, the pre-exponential factor can be estimated based on assumptions about the mobilities of surface intermediates.9 Dumesic and co-workers16 developed an approach to simplify the method by substituting the estimation of entropy values of each species with an estimation of entropy changes between the reactants and transitionstate species. It was assumed that the adsorption of a molecule from gas phase to a metal surfaces leads to the loss of one to three degrees of freedom in translational movement, but maintains the vibrational and rotational freedom. The atomic heats of adsorption of C, O, and H are important input parameters to the UBI-QEP model. Shustorovich and Sellers23 suggested using values estimated from experimental heats of adsorption of CO, H2, and O2. These values can also be estimated by density functional theory. The hybrid DFT and UBI-QEP method can also be used to calibrate the reaction index in the UBI-QEP approach,14 which is fixed as a constant value of 0.5 in the original UBI-QEP model. Detailed microkinetics can well describe the surface chemistry on metal surfaces. It can be considered as a numeric version of the 2601

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Industrial & Engineering Chemistry Research

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Langmuir-Hinshelwood-Hougen-Watson (LHHW) kinetic equation. Through a combination of microkinetics with dynamic Monte Carlo simulations, the heterogeneity of a surface, such as steps and different faces of metal nanoparticles, can be taken into account in kinetic modeling.36,37 The mean-field approximation simplifies the modeling significantly by ignoring the catalyst heterogeneity. However, even when using the mean-field approximation, direct application of a microkinetic model in detailed reactor simulations and optimizations remains a challenge with respect to computational cost. The LHHW approach has been widely employed in reactor simulations by lumping the details of the reaction mechanism into a simple algebraic equation. The hybrid DFT and UBI-QEP method was developed to provide the LHHW equation from the microkinetic model, where one or a few reactions are set as the ratedetermining step (RDS).13,27 The RDS is the output of the microkinetic simulation, which is clearly different from the conventional kinetic modeling where the RDS has to be assumed. In terms of reactor modeling, computational fluid dynamics (CFD) can solve and analyze problems that involve reactive fluid flows. However, implementing microkinetic models into a CFD code still remains unfeasible. Idealized reactor models such as continuous stirred-tank reactors (CSTRs) and plug-flow reactors (PFRs) are the most commonly used in microkinetic modeling. A two-dimensional heterogeneous reactor model including a microkinetic model can be used to describe the temperature and concentration profiles, as well as the site coverage of adsorbed species, both inside the pellets and in the reactor. A hybrid modeling technique is developed in the present work to dramatically reduce the computational efforts. The LHHW kinetic model developed by Xu and Froment38 is first used to estimate the temperature and concentration profiles inside both the pellets and the reactor. Then, the microkinetic model is used to simulate the surface site coverage profile, inside each pellet, based on the simulated temperature and concentration profiles. 2.1. UBI-QEP Model for Chemisorption and Activation Energy at the Atomic and Molecular Level. Steam methane reforming (SMR) constitutes a complex reaction network and is described by the steam and dry reforming reactions, the water-gas shift reaction, and the carbon forming reactions. Syngas production can be described by three independent reactions CH4 þ H2 O ¼ CO þ 3H2

ðR1Þ

CO þ H2 O ¼ CO2 þ H2

ðR2Þ

CH4 ¼ C þ 2H2

ðR3Þ

Carbon can also be formed by the Boudouard reaction 2CO ¼ C þ CO2

ðR4Þ

The reactions can be described by a detailed mechanism based on the results of extensive surface science and kinetic studies,39 as well as theoretical catalysis.1 As presented in Table 1, 13 elementary reaction steps are involved. The methods of estimating kinetic parameters in the model have been reported previously.33 The initial pre-exponential factors were estimated by transition-state theory, employing reasonable chemical assumptions about surface mobility. Dumesic

Scheme 2. Illustration of the Mechanism of Filamentous Carbon Formation

et al.9 summarized typical ranges of these values used in microkinetic analysis studies. For the reaction A* þ B* f C* þ D*, the pre-exponential factor is typically 1013 s-1, assuming immobile surface intermediates. The activation energies were estimated by the UBI-QEP method. No attempt will be made here to review the UBI -QEP theory, but the basic principles are illustrated by the following two equations, which show how the activation energy can be estimated from the bond strength. The detailed formulas and rules for calculation can be found in the review by Shustorovich and Sellers.23 They are also summarized in ref 32. The chemisorption heat for strong adsorption at zero coverage is given by QAB ¼

QA 2 QA þ DAB

ð1Þ

For CO (A-B) adsorption on a Ni surface, the adsorption energy can be estimated from the dissociation energy of C-O in the gas phase and the bond strength of Ni-C, which can be determined experimentally or estimated by DFT. For dissociation on a metal surface, represented by ABS f AS þ BS, the activation barrier is given by 1 QA QB þ QAB - QA - QB ΔEAB, S ¼ DAB þ ð2Þ 2 QA þ QB Equation 2 is one of the Brønsted-Evans-Polanyi-type correlations, where the reaction heat is (QAB - QA- QB) with a coefficient of 0.5. The number 0.5 is defined as the reaction index in UBI-QEP theory. As pointed out by Vlachos and co-workers,8 this reaction index can be refined by DFT results. 2.2. Microkinetic Model on Ni Crystals. The reaction rate in a microkinetic model is calculated as the turnover frequency. The rate for a reaction step, including forward and reverse reactions, rR, is G n Gþ Iþ1 Y X E Y aij Ai exp pj aij θaij rR i ¼ ð3Þ RT i¼1 j¼1 j¼ G þ 1 The reaction elementary steps involved in filamentous carbon formation are presented in Scheme 2, where the mechanism is adopted from Snoeck et al.40,41 The mechanism of filamentous carbon formation1,33,40-43 seems to be generally accepted. The steps involved are surface reactions leading to the formation of surface carbon, segregation of the surface carbon into the layer 2602



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Table 1. Reaction Mechanism and Kinetic Parameters in Microkinetic Modeling of Steam Methane Reforming on Nia kforward

reaction 1 2 3

kreverse

6.5 107e-57500/RT

CH4 þ 2* = *CH3 þ *H *CH3 þ * = *CH2 þ *H

1.5 1010e-80900/RT

13 -99900/RT

2.0 1012e-49600/RT

13 -97000/RT

1.0 1013e-73700/RT

13 -189700/RT

1.0 10 e

*CH2 þ * = *CH þ *H

1.0 10 e

4

*CH þ 2* = **C þ *H

1.0 10 e

1.0 1013e-173000/RT

5

H2O þ * = *H2O

2.4 10

6

1.0 1013e-68900/RT

16 -86700/RT

1.0 1013e-42700/RT

13 -86800/RT

6.73 1011T-3.03e-103600/RT

6 7

*H2O þ * = *OH þ *H

1.0 10 e

**C þ *OH = *CHO þ 2*

1.0 10 e

18 -0.968 -108900/RT

8 9

**COOH þ *H = *CHO þ *OH þ * *CHO þ * = **CO þ *H

3.38 10 T e 1.0 1011e-16800/RT

1.0 1013e-24900/RT 1.0 1011e-66700/RT

10

**CO = CO þ 2*

2.0 1012e-122400/RT

5.9 107

12 -97600/RT

11

2*H = H2 þ 2*

3.1 10 e

1.1 108e-5600/RT

12

CO2 þ 2* = **CO2

1.0 10

6

1.0 1013e-27300/RT

13

**CO2 þ *H = **COOH þ *

1.0 10

13

1.0 1013e-18400/RT

a

Activation energies estimated by the UBI-QEP method. Reaction rate constant (k) calculated using the Arrhenius form k = A exp[-E/(RgT)]or k = (s/σ)[RgT/(2πM)]1/2 exp[-E/(RgT)] (where A is the pre-exponential, s is the sticking coefficient, σ is the site density, E is the activation energy, Rg is the ideal gas constant, and T is the absolute temperature).

near the gas-solid surface, diffusion of the carbon from the gas-solid side to the solid-support side either through bulk Ni or through the surface, and precipitation on the support side of the Ni particles. Scheme 2 illustrates these steps, where surface carbon is treated as an important precursor for both synthesis gas and carbon filament generation. The driving force for carbon diffusion is the difference between the chemical potentials of carbon on the front side (gas-Ni surface interface) and rear side (carbon-Ni interface). Atomic carbon on the gas-Ni surface interface and filamentous carbon on the carbon-Ni interface have completely different carbon structures. Therefore, they have very different chemical potentials, which result in different carbon solubilities. The driving force for carbon diffusion can thus be simplified to the carbon concentration difference between these two interfaces. Based on the mechanism leading to filamentous carbon formation, surface carbon is a result of a kinetic balance of all of the elementary steps on the surface as shown in Table 1. Additional steps from surface carbon to filamentous carbon are presented in eqs S.1-S.3 ðS:1Þ Segregation : C ¼ CNi;f þ 2 Diffusion : CNi;f f CNi;r Precipitation :

CNi;r ¼ Cf

ðS:2Þ ðS:3Þ

where **C is the surface carbon, CNi,f is the carbon in the thin layer on the front side of a Ni particle, CNi,r is the carbon on the rear side of the Ni, and Cf is the filamentous carbon. The kinetic knowledge on elementary steps involved in carbon formation is very limited. Because no kinetic information about the segregation and precipitation of filaments is available in the literature, these two steps are assumed to be fast and at equilibrium. Moreover, the reported equilibrium data between carbon and Ni, presented in terms of solubilities of surface carbon in Ni, vary significantly in the literature. For example, the reported carbon solubilities range from 35 to 157 mol/m3 at 500 °C and from 82 to 574 mol/m3 at 700 °C.44,45 Isett and Blakely45 reported a Langmuir equation (eq 4) to estimate the weight fraction of carbon (xb, in grams of carbon per

gram of Ni) in the segregation layer of Ni ΔGseg θC xb ¼ exp where 1 - θC 1 - xb RT

ð4Þ

ΔGseg ¼ - 4:52 104 - 14:23T ð J=molÞ where θC is the surface coverage of carbon and ΔGseg is the Gibbs free energy for segregation. As in the approach of Snoeck et al.,40,41 eq 4 was selected here to describe the equilibrium between the surface and subsurface carbon, that is, the segregation of surface carbon. Based on experimental observations on Ni(100) with a maximum carbon site coverage of 0.5,46 an ensemble size of adsorption of carbon was set to be 2. A correction factor of 2 was therefore used for θC in eq 4. The rate of carbon diffusion through nickel is described as r¼

DC aNi ðCNi;f - CNi;r Þ dNi

ð5Þ

where DC is the effective diffusivity through nickel crystals; dNi is the effective diffusion path;33,41,43 aNi is the specific surface area of Ni; and CNi,f and CNi,r are the carbon concentration on the front and rear sides, respectively. 2.3. Conservation Equations in the Catalyst Pellets. Because the partial pressure gradients are limited to a very thin layer near the surface, planar geometry was used.38,47 Dimensionless equations for the conservation of mass and heat in the pellets are given as r2 βS, i - ð1 þ θS ÞT0 rβS, i rθS P r θS 2

FC ri ð1 þ θS ÞT0 Rp 2 ¼ 0 ð6Þ εDe, i

ri FC ð - ΔHi ÞRp 2 ¼0 kcat T0

with boundary conditions ξ ¼0:

rβS; i ¼ 0

rθS ¼ 0 ξ ¼1: 2603

kg; i ðβSS; i - βS; i Þ ¼ rβS; i

ð7Þ

ð8Þ ð9Þ ð10Þ


Industrial & Engineering Chemistry Research hf aðθSS - θS Þ ¼ rθS

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ð11Þ

where De,i is assumed to be constant in the pellets. 2.4. Conservation Equations in the Fixed-Bed Reactor. A mass balance gives the equation ν Þ - rðcDi rxi Þ ¼ kg, i ðcSS, i - ci Þ ð12Þ rðcxi ! The concentration term in this equation was converted to partial pressure using the ideal gas law. A dimensionless equation is then derived as βi βi Di L 1 2 rβi rθ rθ - ru þ rβi ¼ r βi uuz0 R 2 1þθ 1þθ u kg aL S þ ðβ - βi Þ uuz0 S, i

ð13Þ

" # 5 L X u u S rθ ð14Þ ru ¼ kg, i ðβS, i - βi Þ þ rβ þ βuz0 i¼1 β 1þθ with boundary conditions Ω ¼ 0 and Ω ¼ 1 :

rβi ¼ 0

βi ¼ βi0

Z ¼0:

u ¼1 Z ¼1:

rβi ¼ 0

ru ¼ 0

ð15Þ ð16Þ ð17Þ ð18Þ ð19Þ

The dimensionless energy balance equation is rθ ¼

kbed Luuz0 2 hf aL r θþ ðθS - θÞ Fg Cp uuz0 S Fg C p R 2

ð20Þ

with boundary conditions Ω ¼0: Ω ¼1:

rθ ¼ Z ¼0:

Z ¼1:

rθ ¼ 0

ð21Þ

hw R ðθw - θÞ kbed

ð22Þ

θ ¼0

ð23Þ

rθ ¼ 0

ð24Þ

The pressure drop in the radial direction was assumed to be negligible. The pressure drop along the axial direction is described by an Ergun-type equation48 " #-1 2 Fg uð1 - εÞ L 150μg ð1 - εÞ rβ ¼ þ 1:75 ð25Þ Pt0 Φdp ε3 ðΦdp Þ2 ε3 with the boundary condition Z ¼0:

β ¼0

ð26Þ

2.5. Carbon Potential. Formation of filamentous carbon cannot be tolerated in a tubular reformer. The important problem is whether or not carbon is formed, not the rate at

which it is formed.49 Thermodynamic criteria based on the affinity concept have been used for a long time to check for the possibility of coke formation. As pointed out by RostrupNielsen and Sehested49 and Froment,50 coke limitation is a kinetic issue, so a kinetic approach is required. The microkinetic model can generally predict the coking rate well under different conditions in dry reforming.33,43 The present work focuses on the evaluation of the possibility of carbon formation in a reactor, rather than coking rates. The relative driving force for the diffusion of carbon through a Ni particle is defined as a kinetic carbon potential (CP) CP ¼

CNi;f - Csat Csat

ð27Þ

CP e 0 means there is no potential for carbon formation, whereas CP > 0 indicates a risk for carbon formation. CP = 0 represents a coking threshold condition with a zero coking rate. In the mapping of the overall reactor, the maximum carbon potentials in each catalyst pellet at different positions in the reactor are estimated. 2.6. Numerical Methods. All of the model equations were implemented in MATLAB. The partial differential equations were solved by finite differences in the radial direction of the reactor (five points) and in the catalyst pellets (six points). The discrete nonlinear algebraic equations (eqs 6-11) were solved with the MATLAB function fsolve. The resulting differential equations in the axial direction of the reactor were solved by an ODE solver for stiff problems. The nonlinear algebraic conservation equations for surface coverage were solved by a similar ODE solver. It was found that the detailed microkinetic model created a very stiff problem. The CPU time increased significantly (to more than 100 h), and the solution of the nonlinear algebraic equations in the catalyst pellets was the most time-consuming. A comparison between a traditional kinetic model for steam reforming from Xu and Froment38 and our microkinetic model was performed for a one-dimensional isothermal reactor model. Both models predicted equally well the conversions at different temperatures, where the properties of metal surface reported38 were taken into account in the microkinetic simulation. Therefore, a hybrid kinetic model was used in the present work to reduce the computation cost. The simulation procedure was divided into steps: First, the two-dimensional reactor model was solved using the kinetic model of Xu and Froment38 to obtain an estimate of the concentration and temperature profiles. In step two, the surface coverage and carbon potential in the reactor and pellets were simulated based on the concentration and temperature profiles obtained in step one. This approach reduced the CPU time dramatically by a factor of about 20-50. The simulation results reported in section 4.1 were obtained from this hybrid model. It should be pointed out that the LHHW kinetic model of steam reforming could also be obtained by a microkinetic model by setting an elementary step as the ratedetermining step based on the microkinetic modeling results, instead of assuming a RDS as in the conventional approach.

3. EXPERIMENTAL SECTION The experimental study was performed in a tapered element oscillating microbalance (TEOM) reactor51 at 2 MPa total pressure and at temperatures in the range of 550-650 °C over an industrial steam reforming catalyst containing 11 wt % Ni on 2604


Industrial & Engineering Chemistry Research CaAl2O4 spinel carrier. The BET surface area was 5.5 m2/g, as measured by N2 adsorption, and the Ni surface area was 0.33 m2/g, as determined by H2 chemisorption. The TEOM reactor and experimental setup are described elsewhere.34 The reactor was filled with approximately 8 mg of catalyst with a particle size of 0.4-0.6 mm. About 70 mg of MgAl2O4 spinel with a similar particle size was used as an inert diluent. Catalyst reduction was performed in a H2/Ar (50/50 mL/min) mixture by increasing the temperature from ambient to 650 °C at a rate of 2 °C/min and maintaining this temperature for about 6 h. The product was analyzed online by a HP5890 II gas chromatograph with a carbosieve S-II column and a thermal conductivity detector. Kinetic data for carbon formation and steam reforming were obtained by varying the steam-to-carbon (S/C) ratio in the range 0.5-2.5 at a constant methane pressure of 0.38 MPa. The H2 level in the feed during the reaction was 2.5% relative to CH4. The space time used in the study was 0.074 gcat h/mol in most experiments, which gave low conversions (923 K

ð29Þ

The reason for the lower coking thresholds at higher temperatures (>923 K) is possibly the fragmentation of large Ni crystals, where a few carbon nanofibers or tubes, referred to as filamentous carbon here, can grow on one Ni crystal. This phenomenon has often been observed in carbon nanotube synthesis.65,66 It is also well documented that the Ni crystal size has a significant effect on carbon formation in steam reforming and that less carbon formation takes place on small Ni crystals.1,67 The smaller Ni crystals resulted in a higher solubility of carbon filaments.67 The possible changes in Ni particle size lead to a discontinuity in the changes of Csat with the temperature as shown in Figure 3.

ð30Þ

Here, the activation energy of carbon diffusion in Ni is 112.9 kJ/ mol, which is not very different from the value estimated by DFT. However, it is difficult to distinguish the subsurface and bulk diffusion mechanisms here. The value is lower than those reported (125-138 kJ/mol) in the literature.72 Figure 2 shows that the microkinetic model describes the coking rate generally well under different conditions, except for the predictions at very low S/C ratios. This might be due to the experimental procedures used in the present work. The experiments were started at a low S/C ratio that was gradually increased. Starting carbon formation at a low S/C was done on purpose to generate as many filaments as possible in order to eliminate the initiation period. This is expected to reduce the effect of filament number on the steady-state growth rate.40,41 The steady-state growth rates were measured on almost identical numbers of filaments in this way. However, encapsulating carbon on the Ni surfaces is expected to be formed at low S/C ratios, which might be the reason for the relatively large deviation of the experimental coking rate compared to that predicted by the model. 4.2. Two-Dimensional Heterogeneous Reactor Modeling of Steam Reformer. A hypothetical large-scale primary tubular steam reformer was simulated. The input data for the reactor and geometric parameters of the catalysts were identical to the values reported by Xu and Froment.47 The catalyst properties were identical to those in the Experimental Section. The inlet temperature was 873 K, and the initial gas velocity was 1.1 m s-1. The inlet pressure was about 2.9 MPa, and the molar ratios in the reactant mixture were H2/CH4 = 0.15 and CO2/ CH4 = 0.072. The effect of the steam-to-carbon (methane) (S/C) ratio was evaluated. More detailed information about parameters in the model can be found in the literature.47,73,74 2607



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Figure 5. Distributions of (A) carbon and (B) hydrogen site coverage and (C) carbon potential in the pellet at the axial center of the reactor along the reactor length. (D) Three-dimensional carbon potential mapping in the reactor. Initial S/C ratio = 2.

Figure 4. Partial pressure and temperature distributions in the pellets along the reactor length. S/C = 2.

The concentration and temperature profiles in the reactor and pellets were simulated using Xu and Froment’s kinetic model, involving steam reforming, the water-gas shift reaction, and dry reforming.38 The simulated results show no pressure and temperature gradients through the film on the surface surrounding the particle, which is in good agreement with the results of Xu and Froment.47 Figure 4 illustrates the temperature and partial pressure distributions inside catalyst pellets at the center of the reactor along the axial direction. The partial pressures and temperatures at rp = 4.2 mm represent data for the catalyst surface, which, because of the negligible film resistances, were also identical to the data in the gas phase. The axial distributions of temperature and partial pressure in the reactor are clearly shown. As expected, the temperature increased along the reactor, and the partial pressures of methane and water decreased. The conversion of methane was about 50% under these conditions. The primary reformer produced a gas mixture with a H2/CO ratio of 5.6, a H2/(CO þ CO2) ratio of 2.8, and also a remaining H2O/CH4 ratio of 2.4. The temperature at the exit of the reactor was about 820 °C. Based on the simulated concentration and temperature profiles (Figure 4), site coverages of different surface species were simulated using microkinetic modeling with kinetic parameters for each elementary step in Table 1. The surface coverage of species i (CH3, CH2, CH, C, H2O, OH, H, HCO, COOH, CO, CO2, and *) were obtained by solving the equations: dθi ¼ ri ¼ 0 dt m X

θi ¼ 1

ð31Þ ð32Þ

i¼1

where θi and ri are the site coverage and reaction rate, respectively, of surface species i and m is the total number of the surface species, which was 12 in the present work. The simulated distribution of site coverages of H and C, where H is the most

abundant surface species and C is the most important surface species to estimate the carbon potential, are presented in Figure 5. Parts A and B of Figure 5 present the distributions of C and H site coverages, respectively, inside the pellets along the axial direction. The carbon site coverage increases gradually along the reactor length, whereas the hydrogen site coverage shows a maximum at the middle of the reactor. The increased carbon site coverage along the axial direction is mainly attributed to the increase in temperature and the decrease in steam partial pressure, even though the partial pressure of hydrogen increased. Based on microkinetic analysis, increases in the steam and hydrogen partial pressure decrease the carbon site coverage, whereas increases in the temperature and the partial pressures of methane and CO increase the carbon coverage. The carbon coverage at different positions depends on the net effect of different parameters or, more precisely, on the net reaction of all elementary steps on the surface. The simulated results in Figure 5 indicate that an increase in temperature and a decrease in steam dominate and give higher carbon site coverage with reactor length. At isothermal conditions, higher carbon coverage reflects a higher carbon potential. However, the higher carbon coverage at higher temperatures does not mean a higher carbon potential, because higher temperature also result in a higher solubility of carbon filaments in Ni. The carbon potential calculated by eq 26 is presented in Figure 5C,D. Figure 5C illustrates the distribution of carbon potential in the catalyst pellets, and Figure 5D shows the carbon potential in the reactor. The distribution of carbon potential inside the catalyst pellets is more clearly demonstrated in the two-dimensional plot in Figure 6. A higher carbon potential is found inside the pellets in Figure 6, regardless of the position in the axial direction. This shows that the effect of increasing coke potential at lower steam partial pressure and higher CO partial pressure is more significant than the effect of increasing hydrogen pressure. Much lower gradients of carbon potential in the pellets were found at the outlet of the reactor, which might be due to the lower concentration gradients. However, it should be pointed that the carbon potential gradients are relatively small inside the pellets, mainly as a result of a low activity of the catalyst used in the simulation. For this specific case with very low Ni surface area, the model can be simplified into a 2608



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Figure 6. Radial development of carbon potential in the catalyst pellets at the inlet and outlet of the reactor. Initial S/C ratio = 2.

simple homogeneous model. However, for more active catalysts, a heterogeneous model is necessary. The maximum carbon potential found near the inlet of the reactor (at the reactor position of 0.5-0.8 m) corresponds to our experimental observation of a maximum coking threshold at 650 °C. The decrease in carbon potential after the maximum peak is mainly a consequence of a higher Csat value at higher temperatures. However, after the significant decrease in coking potential, the coking potential increases again because of an increase in the carbon site coverage as a result of increased temperature and CO concentration. An important conclusion from this analysis is that a higher carbon potential exists in the zone near the inlet, as well as in the zone near the outlet. It is of great interest to observe that the carbon potential at all positions inside the reactor is lower than zero, implying no risk of carbon formation at the initial steam-to-carbon ratio of 2. Another case with an initial S/C ratio of 1 was also simulated, and the carbon potentials in the reactor are presented in Figures 7 and 8. In this case, a risk of carbon formation was identified. The axial distribution of CO2 at an initial S/C ratio of 1in Figure 7 is rather different from the distribution for an S/C ratio of 2 as in Figure 4. The partial pressure of CO2 decreases at axial positions larger than 5 m, which is mainly due to the dry reforming as well as the reverse water-gas shift reaction, whereas the hydrogen site coverage also decreases dramatically. The carbon site coverage increases gradually in the axial direction, and the values are almost twice those found for steam reforming at an S/C ratio of 2. The estimated carbon potentials as presented in Figure 8C,D are larger than zero at the outlet of the reactor, whereas the carbon potential is almost zero at z = 0.8. The simulation was also performed at an S/C ratio of 1.5, and no coking risk was found throughout the entire reactor. It should be noted that this coking threshold in the reactor predicted by detailed microkinetic and reactor modeling is very low, possibly due to the presence of a relatively high partial pressure of hydrogen (inlet H2/CH4 = 0.15). Our experimental results showed a strong potential for reducing the coking threshold by increasing the hydrogen pressure.75 Another reason is the increasing filamentous carbon solubility with temperature and, thus, a lower coking potential due to a lower driving force for carbon diffusion. However, it should be pointed out that this parameter was purely estimated from the experiments in a

Figure 7. Partial pressure and temperature distributions in the pellets along the reactor length. S/C = 1.

limited temperature range (maximum temperature of 953 K due to the limitation of the TEOM reactor). There is a large uncertainty when extrapolating this parameter from low temperature to about 1073 K. Experiments at temperatures above 953 K will be very useful for the assessment of our model. Nevertheless, the present work demonstrates that detailed microkinetic and reactor modeling can be combined and used as a powerful diagnostic tool for the evaluation of coking potential in steam reformers.

5. CONCLUSIONS Carbon formation during steam methane reforming has been studied in a TEOM reactor at relevant industrial conditions. Both the rate of filamentous carbon growth and the coking threshold have been studied as a function of steam-to-carbon ratio at different temperatures. The results reveal that the rate of filamentous carbon growth decreases with increasing steam-to-carbon ratio and reaches a coking threshold with a zero net growth rate. A maximum coking threshold, the highest steam-to-carbon requirement, was found at a temperature of 923 K. A microkinetic model was developed in the present work to describe the carbon formation during steam methane reforming, where the surface reaction steps of carbon segregation, diffusion, and precipitation were included. The surface carbon was considered as the precursor of carbon formation, and thus, surface carbon coverage was the most important parameter for modeling carbon formation. The surface carbon is a kinetic balance of surface reactions leading to synthesis gas formation or carbon dissolution. However, all of the surface reaction steps still affect the surface carbon coverage and, thus, carbon formation. The fitted diffusivity of carbon from experimental data is in good agreement with DFT predictions. The present work provides a unique way to describe carbon formation during steam methane reforming in great detail. The present work demonstrates hierarchically multiscale modeling as a powerful tool for reactor diagnostics by predicting 2609



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Figure 8. Distributions of (A) carbon and (B) hydrogen site coverage and (C) carbon potential in the pellet at the axial center of the reactor along the reactor length. (D) Three-dimensional carbon potential mapping in the reactor. Initial S/C ratio = 1.

coking potential in steam methane reforming. The multiscale approach provides much deeper insights into industrial process, as well as a bridge between fundamental studies and industrialscale applications. Maps of the carbon potential of an industrial reformer were established from detailed kinetic information of elementary steps on the surface. The effects of diffusion and radial and axial temperature and concentration distributions on the carbon potential have been analyzed by the multiscale model. The intraparticle diffusion increases the carbon potential. Two zones with higher carbon potential were found near the inlet and outlet of the reactor. The simulated results show that an industrial steam reformer can be safely operated at steam-tocarbon ratios of about 1.5 without carbon formation. However, one should keep in mind that the present work is the first effort toward such an approach, where the most important factors controlling carbon formation have been taken into account in some detail. In further research, effects of filamentous carbon solubility, pellet diameter, and catalyst sintering will also be taken into account.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT The support of this work by the Norwegian Research Council and STATOIL is gratefully acknowledged. ’ NOTATION aij = stoichiometric coefficient of i in the jth reaction aNi = Ni surface area, m2/gcat c = total concentration, mol/m3 CNif = carbon concentration at the front side of Ni particle, mol/m3 Cp = heat capacity of gas, J/(kg K) CP = carbon potential Csat = solubility of carbon filament in Ni, mol/m3 DAB = dissociation energy of A-B bond, J/mol

Dc = carbon diffusivity through Ni, m2/s De,i = effective diffusivity matrix of i, m2/s Di = dispersion matrix for component i, m2/s dNi = Ni diameter, m dp = equivalent diameter, m E = activation energy matrix, J/mol hf = heat-transfer coefficient through the film surrounding the catalyst particle, W/(m2 K) hw = heat-transfer coefficient through tube wall, W/(m2 K) kbed = thermal conductivity in a fixed bed, W/(m K) kcat = thermal conductivity in the catalyst, W/(m K) kg = mass-transfer coefficient through the film surrounding the catalyst particle, m/s L = reactor length, m P = pressure, Pa QA = chemisorption heat of atomic A, J/mol QAB = chemisorption heat of AB, J/mol r = radial reactor coordinate, m R = radius of fixed bed tube, m rp = radial catalyst pellet coordinate Rp = radius of catalyst pellets, m T = temperature, K u = gas velocity matrix, m/s xi = mole fraction of component i z = axial reactor coordinate, m Greek letters

ΔHi = heat of reaction for component i, J/mol ε = void fraction μg = viscosity of gas, N s/m2 Fc = catalytic density, kgcat/m3 Fg = density of gas, kg/m3 Φ = shape factor Dimensionless parameter

θ = (T - T0)/T0 u = uz/uz0 βi = Pi/Pt,o β = Pt/Pt,0 βz = (Ptout - Pt,0)/Pt,0 2610


Industrial & Engineering Chemistry Research Z = z/L Ω = r/R ς = rp/Rp Subscripts

0 = data at inlet of the reactor i = species i (CH4, H2O, CO, H2, CO2, N2) s = on the surface t = total w = tube wall z = data at position z

’ REFERENCES (1) Rostrup-Nielsen, J. R.; Sehested, J.; Norskov, J. K. Hydrogen and synthesis gas by steam- and CO2 reforming. Adv. Catal. 2002, 47, 65–139. (2) Rostrup-Nielsen, J. R. New aspects of syngas production and use. Catal. Today 2000, 63 (2-4), 159–164. (3) Armor, J. N. The multiple roles for catalysis in the production of H2. Appl. Catal. A 1999, 176 (2), 159–176. (4) Degroote, A. M.; Froment, G. F. Reactor modeling and simulations in synthesis gas production. Rev. Chem. Eng. 1995, 11 (2), 145–183. (5) Lerou, J. J.; Ng, K. M. Chemical reaction engineering: A multiscale approach to a multiobjective task. Chem. Eng. Sci. 1996, 51 (10), 1595–1614. (6) Vlachos, D. G. A Review of Multiscale Analysis: Examples from Systems Biology, Materials Engineering, and Other Fluid-Surface Interacting Systems. Adv. Chem. Eng. 2005, 30, 1–61. (7) Vlachos, D. G.; Mhadeshwar, A. B.; Kaisare, N. S. Hierarchical multiscale model-based design of experiments, catalysts, and reactors for fuel processing. Comput. Chem. Eng. 2006, 30 (10-12), 1712–1724. (8) Mhadeshwar, A. B.; Vlachos, D. G. Hierarchical Multiscale Mechanism Development for Methane Partial Oxidation and Reforming and for Thermal Decomposition of Oxygenates on Rh. J. Phys. Chem. B 2005, 109 (35), 16819–16835. (9) Dumesic, J. A.; Rudd, D. F.; Aparicio, L. M.; Rekoske, J. E.; Trevino, A. A. The Microkinetics of Heterogeneous Catalysis; American Chemical Society: Washington, DC, 1993, . (10) Broadbelt, L. J.; Snurr, R. Q. Applications of molecular modeling in heterogeneous catalysis research. Appl. Catal. A 2000, 200 (1-2), 23–46. (11) Froment, G. F. Single event kinetic modeling of complex catalytic processes. Catal. Rev.—Sci. Eng. 2005, 47 (1), 83–124. (12) Mhadeshwar, A. B.; Wang, H.; Vlachos, D. G. Thermodynamic consistency in microkinetic development of surface reaction mechanisms. J. Phys. Chem. B 2003, 107 (46), 12721–12733. (13) Vilekar, S. A.; Fishtik, I.; Datta, R. The steady-state kinetics of a catalytic reaction sequence. Chem. Eng. Sci. 2009, 64 (9), 1968–1979. (14) Mhadeshwar, A. B.; Vlachos, D. G. Hierarchical multiscale mechanism development for methane partial oxidation and reforming and for thermal decomposition of oxygenates on Rh. J. Phys. Chem. B 2005, 109 (35), 16819–16835. (15) Mhadeshwar, A. B.; Vlachos, D. G. Hierarchical, multiscale surface reaction mechanism development: CO and H2 oxidation, water -gas shift, and preferential oxidation of CO on Rh. J. Catal. 2005, 234 (1), 48–63. (16) Cortright, R. D.; Dumesic, J. A. Kinetics of heterogeneous catalytic reactions: Analysis of reaction schemes. Adv. Catal. 2001, 46, 161–264. (17) Lozano-Blanco, G.; Thybaut, J. W.; Surla, K.; Galtier, P.; Marin, G. B. Single-Event Microkinetic Model for Fischer-Tropsch Synthesis on Iron-Based Catalysts. Ind. Eng. Chem. Res. 2008, 47 (16), 5879–5891. (18) Hammer, B.; Norskov, J. K. Theoretical surface science and catalysis—Calculations and concepts. Adv. Catal. 2000, 45, 71–129. (19) Abild-Pedersen, F.; Greeley, J.; Studt, F.; Rossmeisl, J.; Munter, T. R.; Moses, P. G.; Skulason, E.; Bligaard, T.; Norskov, J. K. Scaling

ARTICLE

Properties of Adsorption Energies for Hydrogen-Containing Molecules on Transition-Metal Surfaces. Phys. Rev. Lett. 2007, 99 (1), No. 016105-4. (20) Jones, G.; Bligaard, T.; Abild-Pedersen, F.; Norskov, J. K. Using scaling relations to understand trends in the catalytic activity of transition metals. J. Phys.: Condensed Matter 2008, 20, 064239. (21) Jones, G.; Jakobsen, J. G.; Shim, S. S.; Kleis, J.; Andersson, M. P.; Rossmeisl, J.; Abild-Pedersen, F.; Bligaard, T.; Helveg, S.; Hinnemann, B.; Rostrup-Nielsen, J. R.; Chorkendorff, I.; Sehested, J.; Nørskov, J. K. First principles calculations and experimental insight into methane steam reforming over transition metal catalysts. J. Catal. 2008, 259 (1), 147–160. (22) Shustorovich, E. The Bond-Order Conservation Approach to Chemisorption and Heterogeneous Catalysis: Applications and Implications. Adv. Catal. 1990, 37, 101–163. (23) Shustorovich, E.; Sellers, H. The UBI-QEP method: A practical theoretical approach to understanding chemistry on transition metal surfaces. Surf. Sci. Rep. 1998, 31 (1-3), 5–119. (24) Shustorovich, E. M.; Zeigarnik, A. V. The UBI-QEP method: Basic formalism and applications to chemisorption phenomena on transition metal surfaces. Chemisorption energetics. Russ. J. Phys. Chem. 2006, 80 (1), 4–30. (25) Bell, A. T.; Shustorovich, E. A comment on the analysis of CO hydrogenation using the BOC-MP approach. J. Catal. 1990, 121 (1), 1–6. (26) Bell, A. T.; Shustorovich, E. Analysis of the thermochemistry of C-2 hydrocarbons on transition-metal surfaces using a refined BOC-MP approach. Surf. Sci. 1990, 235 (2-3), 343–350. (27) Fishtik, I.; Datta, R. A UBI-QEP microkinetic model for the water-gas shift reaction on Cu(111). Surf. Sci. 2002, 512 (3), 229–254. (28) Zeigarnik, A. V.; Callaghan, C.; Datta, R.; Fishtik, I.; Shustorovich, E. Prediction of comparative catalytic activity in the series of single crystalline surfaces in a water-gas shift reaction. Kinet. Catal. 2005, 46 (4), 509–515. (29) Mhadeshwar, A. B.; Vlachos, D. G. Is the water-gas shift reaction on Pt simple? Computer-aided microkinetic model reduction, lumped rate expression, and rate-determining step. Catal. Today 2005, 105 (1), 162–172. (30) Aghalayam, P.; Park, Y. K.; Fernandes, N.; Papavassiliou, V.; Mhadeshwar, A. B.; Vlachos, D. G. A C1 mechanism for methane oxidation on platinum. J. Catal. 2003, 213 (1), 23–38. (31) Mhadeshwar, A. B.; Kitchin, J. R.; Barteau, M. A.; Vlachos, D. G. The role of adsorbate-adsorbate interactions in the rate controlling step and the most abundant reaction intermediate of NH3 decomposition on Ru. Catal. Lett. 2004, 96 (1-2), 13–22. (32) Storsaeter, S.; Chen, D.; Holmen, A. Microkinetic modelling of the formation of C-1 and C-2 products in the Fischer-Tropsch synthesis over cobalt catalysts. Surf. Sci. 2006, 600 (10), 2051–2063. (33) Chen, D.; Lodeng, R.; Omdahl, K.; Anundskas, A.; Olsvik, O.; Holmen, A. A model for reforming on Ni catalyst with carbon formation and deactivation. Catal. Deact. 2001, Proc. Int. Symp., 9th 2001, 139, 93–100. (34) Chen, D.; Bjorgum, E.; Lodeng, R.; Christensen, K. O.; Holmen, A. Microkinetic model assisted catalyst design for steam methane reforming. Nat. Gas Convers. VII, Proc. Symp., 7th 2004, 147, 139–144. (35) Blaylock, D. W.; Ogura, T.; Green, W. H.; Beran, G. J. O. Computational Investigation of Thermochemistry and Kinetics of Steam Methane Reforming on Ni(111) under Realistic Conditions. J. Phys. Chem. C 2009, 113 (12), 4898–4908. (36) Dooling, D. J.; Broadbelt, L. J. Microkinetic models and dynamic Monte Carlo simulations of nonuniform catalytic systems. AIChE J. 2001, 47 (5), 1193–1202. (37) Meskine, H.; Matera, S.; Scheffler, M.; Reuter, K.; Metiu, H. Examination of the concept of degree of rate control by first-principles kinetic Monte Carlo simulations. Surf. Sci. 2009, 603 (10-12), 1724–1730. (38) Xu, J. G.; Froment, G. F. Methane stem reforming, methanation and water-gas shift. 1. Intrinsic kinetics. AIChE J. 1989, 35 (1), 88–96. 2611


Industrial & Engineering Chemistry Research (39) Aparicio, L. M. Transient isotopic studies and microkinetic modeling of methane reforming over nickel catalysts. J. Catal. 1997, 165 (2), 262–274. (40) Snoeck, J. W.; Froment, G. F.; Fowles, M. Filamentous Carbon Formation and Gasification: Thermodynamics, Driving Force, Nucleation, and Steady-State Growth. J. Catal. 1997, 169 (1), 240–249. (41) Snoeck, J. W.; Froment, G. F.; Fowles, M. Kinetic Study of the Carbon Filament Formation by Methane Cracking on a Nickel Catalyst. J. Catal. 1997, 169 (1), 250–262. (42) Snoeck, J. W.; Froment, G. F.; Fowles, M. Steam/CO2 reforming of methane. Carbon formation and gasification on catalysts with various potassium contents. Ind. Eng. Chem. Res. 2002, 41 (15), 3548–3556. (43) Chen, D.; Lodeng, R.; Anundskas, A.; Olsvik, O.; Holmen, A. Deactivation during carbon dioxide reforming of methane over Ni catalyst: Microkinetic analysis. Chem. Eng. Sci. 2001, 56 (4), 1371–1379. (44) Isett, L. C.; Blakely, J. M. Binding energies of carbon to Ni(100) from equilibrium segregation studies. Surf. Sci. 1975, 47 (2), 645–649. (45) Isett, L. C.; Blakely, J. M. Segregation isosteres for carbon at the (100) surface of nickel. Surf. Sci. 1976, 58 (2), 397–414. (46) Chorkendorff, I.; Alstrup, I.; Ullmann, S. XPS study of chemisorption of CH4 on Ni(100). Surf. Sci. 1990, 227 (3), 291–296. (47) Xu, J. G.; Froment, G. F. Methane steam reforming. 2. Diffusion limitations and reactor simulation. AIChE J. 1989, 35 (1), 97–103. (48) Geankoplis, C. J. Transport Processes and Unit Operations; Prentice Hall: Upper Saddle River, NJ, 1993. (49) Rostrup-Nielsen, J. R.; Sehested, J. Whisker carbon revisited. Catal. Deact. 2001, Proc. Int. Symp., 9th 2001, 139, 1–12. (50) Froment, G. F. Production of synthesis gas by steam- and CO2reforming of natural gas. J. Mol. Catal. A: Chem. 2000, 163 (1-2), 147–156. (51) Chen, D.; Bjorgum, E.; Christensen, K. O.; Holmen, A.; Lodeng, R.; Bruce, C. G.; Helmut, K. Characterization of Catalysts under Working Conditions with an Oscillating Microbalance Reactor. Adv. Catal. 2007, 51, 351–382. (52) Zhu, Y.-A.; Chen, D.; Zhou, X.-G.; Yuan, W.-K. DFT studies of dry reforming of methane on Ni catalyst. Catal. Today 2009, 148 (3-4), 260–267. (53) Bengaard, H. S.; Norskov, J. K.; Sehested, J.; Clausen, B. S.; Nielsen, L. P.; Molenbroek, A. M.; Rostrup-Nielsen, J. R. Steam reforming and graphite formation on Ni catalysts. J. Catal. 2002, 209 (2), 365–384. (54) Al-Sarraf, N.; Stuckless, J. T.; Wartnaby, C. E.; King, D. A. Adsorption microcalorimetry and sticking probabilities on metal single crystal surfaces. Surf. Sci. 1993, 283 (1-3), 427–437. (55) Whitten, J. L.; Yang, H. Theory of chemisorption and reactions on metal surfaces. Surf. Sci. Rep. 1996, 24 (3-4), 55–124. (56) Zhu, X. Y.; White, J. M. Hydrogen interaction with nickel(100): A static secondary ion mass spectroscopy study. J. Phys. Chem. 1988, 92 (13), 3970–3974. (57) Bartholomew, C. H. Hydrogen adsorption on supported cobalt, iron, and nickel. Catal. Lett. 1990, 7 (1), 27–51. (58) Beebe, J. T. P.; Goodman, D. W.; Kay, B. D.; Yates, J. J. T. Kinetics of the activated dissociative adsorption of methane on the low index planes of nickel single crystal surfaces. J. Chem. Phys. 1987, 87 (4), 2305–2315. (59) Lee, M. B.; Yang, Q. Y.; Tang, S. L.; Ceyer, S. T. Activated dissociative chemisorption of CH4 on Ni(111): Observation of a methyl radical and implication for the pressure gap in catalysis. J. Chem. Phys. 1986, 85 (3), 1693–1694. (60) Lee, M. B.; Yang, Q. Y.; Ceyer, S. T. Dynamics of the activated dissociative chemisorption of CH4 and implication for the pressure gap in catalysis: A molecular beam-high resolution electron energy loss study. J. Chem. Phys. 1987, 87 (5), 2724–2741. (61) Watwe, R. M.; Bengaard, H. S.; Rostrup-Nielsen, J. R.; Dumesic, J. A.; Norskov, J. K. Theoretical studies of stability and reactivity of CHx species on Ni(111). J. Catal. 2000, 189 (1), 16–30.

ARTICLE

(62) Zhu, Y. A.; Dai, Y. C.; Chen, D.; Yuan, W. K. First-principles calculations of CH4 dissociation on Ni(100) surface along different reaction pathways. J. Mol. Catal. A: Chem. 2007, 264 (1-2), 299–308. (63) Steinr€uck, H. P.; Rendulic, K. D.; Winkler, A. The sticking coefficient of H2 on Ni(111) as a function of particle energy and angle of incidence: A test of detailed balancing. Surf. Sci. 1985, 154 (1), 99–108. (64) Rendulic, K. D.; Winkler, A.; Steinr€uck, H. P. The role of surface defects in the adsorption and sesorption of hydrogen on Ni(111). Surf. Sci. 1987, 185 (3), 469–478. (65) Serp, P.; Corrias, M.; Kalck, P. Carbon nanotubes and nanofibers in catalysis. Appl. Catal. A: Gen. 2003, 253 (2), 337–358. (66) De Jong, K. P.; Geus, J. W. Carbon nanofibers: Catalytic synthesis and applications. Catal. Rev.—Sci. Eng. 2000, 42 (4), 481–510. (67) Chen, D.; Christensen, K. O.; Ochoa-Fernandez, E.; Yu, Z. X.; Totdal, B.; Latorre, N.; Monzon, A.; Holmen, A. Synthesis of carbon nanofibers: Effects of Ni crystal size during methane decomposition. J. Catal. 2005, 229 (1), 82–96. (68) Zhu, Y. A.; Dai, Y. C.; Chen, D.; Yuan, W. K. First-principles study of C chemisorption and diffusion on the surface and in the subsurfaces of Ni(111) during the growth of carbon nanofibers. Surf. Sci. 2007, 601 (5), 1319–1325. (69) Zhu, Y. A.; Dai, Y. C.; Chen, D.; Yuan, W. K. First-principles study of carbon diffusion in bulk nickel during the growth of fishbonetype carbon nanofibers. Carbon 2007, 45, 21–27. (70) Zhu, Y. A.; Zhou, X. G.; Chen, D.; Yuan, W. K. First-principles study of C adsorption and diffusion on the surfaces and in the subsurfaces of nonreconstructed and reconstructed Ni(100). J. Phys. Chem. C 2007, 111 (8), 3447–3453. (71) Yang, R. T.; Chen, J. P. Mechanism of carbon filament growth on metal catalysts. J. Catal. 1989, 115 (1), 52–64. (72) Trimm, D. L. The Formation and Removal of Coke from Nickel Catalyst. Catal. Rev.—Sci. Eng. 1977, 16 (1), 155–189. (73) Dedeken, J. C.; Devos, E. F.; Froment, G. F. Steam reforming of natural gas—Intrinsic kinetics, difusional influences and reactor design. ACS Symp. Ser. 1982, 196, 181–197. (74) Grevskott, S.; Rusten, T.; Hillestad, M.; Edwin, E.; Olsvik, O. Modelling and simulation of a steam reforming tube with furnace. Chem. Eng. Sci. 2001, 56 (2), 597–603. (75) Sperle, T.; Chen, D.; Lodeng, R.; Holmen, A. Pre-reforming of natural gas on a Ni catalyst - Criteria for carbon free operation. Appl. Catal. A 2005, 282 (1-2), 195–204. (76) Ølgaard Nielsen, B.; Luntz, A. C.; Holmblad, P. M.; Chorkendorff, I. Activated dissociative chemisorption of methane on Ni(100): A direct mechanism under thermal conditions?. Catal. Lett. 1995, 32 (1), 15–30.

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