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Flow, Transport, and Reaction Interactions in Shaped Cylindrical Particles for Steam Methane Reforming Anthony G. Dixon,*,† Justin Boudreau,†,‡ Anne Rocheleau,†,§ Alexandre Troupel,† M. Ertan Taskin,†,∥ Michiel Nijemeisland,⊥ and E. Hugh Stitt⊥ †

Department of Chemical Engineering, Worcester Polytechnic Institute, 100 Institute Road, Worcester, Massachusetts 01609-2280, United States ⊥ Johnson Matthey, P.O. Box 1, Belasis Avenue, Billingham, Cleveland TS23 1LB, U.K. ABSTRACT: Complex interactions between steam methane reforming reaction rates, conduction, and diffusion inside cylindrical catalyst particles with holes, and the external flow and temperature fields near the heated tube wall were shown in detail using computational fluid dynamics and compared to prior work on full cylinders. This work highlights the differences caused by the particle features. Simulations were done under industrial tube inlet conditions at a constant pressure drop for one-, three-, four-, and six-hole cylinders. Heat and mass fluxes were within 10% for all particle surfaces; the holes provided the reactant good access to the particles. The six-hole catalyst particles offered the best temperature distribution and reaction rate. However, the four-hole particles gave a higher mass flow rate and lower tube-wall temperature for a set pressure drop.

1. INTRODUCTION Steam methane reforming (SMR) is a widely used process to convert hydrocarbons (mainly methane) into a mixture of hydrogen and carbon monoxide (syngas).1 Currently, SMR is used in the petrochemical industry for the refining of fossil fuels; it is also used in the production of ammonia. As a result of the application of SMR in these industries, the process is well-known and highly efficient (around 65−75%). The cost of steam reforming is largely dependent on the price of natural gas, but currently, it is one of the most economical options for hydrogen production. Because of its maturity, high efficiency, and relatively low cost, steam reforming is considered a viable option for supporting a future hydrogen economy. The importance of steam reforming in the refining and chemical industry today as well as its potential uses in the future gives impetus for further studies of the process. The primary reactions that take place in steam reforming are CH4 + H 2O ↔ CO + 3H 2 (1) CO + H 2O ↔ CO2 + H 2

(2)

CH4 + 2H 2O ↔ CO2 + 4H 2

(3)

Commercial catalyst pellet design must satisfy several criteria, including low pressure drop, high catalyst activity, good heat transfer, and high mechanical strength.2−4 The major factor affecting the activity of catalyst particles for SMR is the ratio of the particle’s geometric surface area (GSA) to volume. One-dimensional particle simulations of SMR imply that reaction occurs within 3−5% of the particle radius from the surface,5 so the reaction effects may be regarded as limited to this region. Thus, in steam reforming, it is very important to provide a high GSA, which will allow higher catalyst activity. This requirement is conventionally met by using smaller particles; however, at the flow rates of interest commercially, small particles result in prohibitively high pressure drops. Other catalyst design criteria are good heat transfer and mechanical durability. High strength in particles avoids breakage during handling and filling of the beds. Strength will not be addressed in the present analysis of the catalyst geometries, but it should be noted that, although no catalyst is strong enough to resist the stresses of tube contraction during cooling, the fracture patterns are important in preventing an increase in the pressure drop.1 One of the main problems with steam reforming is the formation of hot patches and thermal banding on the reformer tubes. The reactor tubes are exposed to fired heaters and must effectively transfer heat to the catalyst particles and gas mixture inside the reactor. If heat is dissipated unevenly, temperature gradients on the tube wall can strain the tube and reduce its life span significantly. For example, a tube-wall temperature increase of 20 °C can reduce the tube life by half, from 10 to 5 years.1 Because the cost of retubing is around $5−8 million, there is great incentive to maximize internal heat transfer and

Because of the highly endothermic nature of reactions 1 and 3, reformers are operated at high temperatures (usually between 800 and 900 K). A conventional steam reformer consists of several hundred fixed-bed reactor tubes. These tubes are usually heated by open-flame furnaces to reach the desired temperature. A pretreated methane feed is sent down the tubular reactors, where the reactions take place in the presence of a catalyst. The catalyst is usually nickel supported by alumina (Al2O3) pellets. The reformed gas then exits the reactor array and is often sent for further treatment in a series of water−gas shift reactions (WGSRs). Although steam reforming is an efficient and cost-effective method of producing hydrogen, there are several challenges associated with the design of catalysts for the process. © 2012 American Chemical Society

Received: Revised: Accepted: Published: 15839

November 23, 2011 October 1, 2012 November 16, 2012 November 16, 2012 dx.doi.org/10.1021/ie202694m | Ind. Eng. Chem. Res. 2012, 51, 15839−15854

Industrial & Engineering Chemistry Research

Article

Figure 1. Model geometry: (a) four particle types compared in this work; (b) WS viewed from the tube wall, with test, top, and bottom particles; (c) WS viewed from the bed center; (d) planes through test particles with some surfaces and particles removed for clarity.

reduce the tube-wall temperature. At the high flow rates typical of SMR, radial heat transfer in the bed of particles is good, and there are only small temperature gradients across the bulk of the tube. The heat transfer from the wall to the gas has the highest resistance, and there is a large temperature difference across the boundary layer.1 In the industrial range of the tubeto-particle diameter ratio (N) from 3 to 10, a large fraction of the catalyst particles are at the tube wall. An understanding of the heat-transfer performance of catalyst particles at the tube wall is therefore critical to improving tube and catalyst design. Recently, shaped cylindrical catalyst particles have been studied6,7 because they have a better GSA to volume ratio than conventional cylindrical shapes of the same outside diameter and length and allow the reactants better access to the particles. Shaped pellets typically feature internal holes and/or external grooves (flutes) along the length of the particle. Shaped particles also give rise to lower pressure drop because their internal and external voids increase the bed void fraction. The reforming industry often uses particles of a length-to-diameter ratio in the range of 0.8−1.2, although lower aspect ratios are not uncommon. The number of internal holes varies from 1 to 10, with 4-, 7-, and 10-hole pellets being used by major SMR catalyst technology suppliers. External grooves are more recent, and a variety of these are beginning to appear in the patent literature. There is virtually nothing in the open literature on the science behind the various choices and the trade-offs between them. In order to assist in meeting the challenges associated with catalyst design in steam reforming, it is helpful to understand the fluid mechanics, heat transfer, diffusion, and reaction kinetics taking place in and around the catalyst particle. The classical models of reaction engineering depend on averaging and simplified geometries to represent complex particle shapes, although recent developments7 extended the classical particle

model to account for some effects of interior holes and looked at optimal dimensions for one- and three-hole cylinders. These approaches necessarily miss many of the details of the transport and reaction phenomena. On the other hand, it is not feasible to experimentally determine what is happening inside the reactors under realistic conditions because of the high operating temperatures of reformers (in the range 800−1100 K). Because of these limitations, computational fluid dynamics (CFD) is increasingly being used in packed-tube modeling,8 in order to provide a more fundamental understanding of the transport and reaction phenomena in such reactors. CFD can supply insight into the complex interactions of three-dimensional velocity, species, and temperature fields that is needed to improve engineering approaches. In CFD, the Navier−Stokes momentum equations and, optionally, the energy and species balances are solved numerically. Studies of the packed-tube performance have been made9 using the lattice Boltzman method with reaction on solid surfaces, but these have been restricted to low Re values and isothermal conditions. Simulations using a finite-volume CFD code have been done more recently,10 again with surface reactions only. The inclusion of heterogeneous chemical reaction inside catalyst particles is only recently becoming a routine capability. Our group has studied the heat effects of SMR, in spherical, cylindrical, and multihole catalyst particles.11−13 More recently, we have developed the capability of coupling diffusion, reaction, and conduction within the catalyst pellet to the fluid flow and convective heat and mass transfer in the external fluid. We considered two industrially important strongly endothermic reactions in heated multitubular reactors and restricted our attention to the detailed study of a single full cylinder in plausible surroundings near the tube wall.14 The operating conditions chosen were SMR under heat-transfer-limited conditions near the entrance of a typical tube, and under 15840

dx.doi.org/10.1021/ie202694m | Ind. Eng. Chem. Res. 2012, 51, 15839−15854


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quantitative comparison of the reaction performance for the different particles. 2.1. Geometry. The cylinder and particle geometry were based on our previous packed-bed models;8,11−15 it was a 120° wedge or wall segment (WS) with two side planes of symmetry and had periodicity on the top and bottom surfaces, which were created to be identical. The wedge contained 12 particles and had a tube-to-particle diameter ratio of 4. Each particle was created at the origin and then translated and rotated to its final position. One full particle was located at the center of the middle row, marked as “Test” in Figure 1b, with the particles directly below and above it marked as “Bottom” and “Top”, respectively. The segment is illustrated from the tube-wall viewpoint in Figure 1b and from the center-tube viewpoint in Figure 1c for the case of six-hole cylinders. The near-wall center test particle was located at an angle of 45° at the center of the model. This configuration was chosen based on our experimental observations of many cylinder packings in a transparent tube in the laboratory.11 It was the only particle completely in the WS. The other particles in the geometry were only partly in the WS model, and they were placed to provide typical surroundings for the test particle, again based on our experimental observations. The packed-bed-tube section had a radius of 0.0508 m and a height of 0.0508 m, and the particles had radii of 0.0127 m and lengths of 0.0254 m. In all but the six-hole case, the particle holes had a radius of 3.64 × 10−3 m; for the six-hole case, the holes had a radius of 2.54 × 10−3 m in order for all of the holes to fit in the particle. The particles did not touch, so it was not necessary to avoid contact points, as is usually the case in packings of spheres.8 The side walls of the WS model had symmetry conditions placed on them. For spheres near the wall, this would be very close to the actual angular symmetry of the packing. For cylinders, there is no such symmetry, and the flow results near the sides of the WS will not be realistic. We performed an initial study to address this point,16 where we compared a WS model with cylinders truncated at the symmetry boundaries to a 360° full bed of complete cylinders built to extend the 120° segment. (This bed was not used for the main study both because of the computational expense and because the extra particles were not able to be located in physically realistic positions.) The comparison showed that velocity and temperature distributions for the middle 60° of the WS, which included the test particle, were in very good agreement with the corresponding distributions in the full-bed model. More recently,15 we extended this study to include species and reaction simultaneously with flow and heat transfer and confirmed that the mass fraction and reaction rate results for the center test particle were again unchanged by the imposition of the symmetry conditions on the side walls. 2.2. Reactive Particles Method. The equations for the fluid phase are the usual equations of conservation of mass, momentum, and energy. These are well-described in any standard reference for CFD. For the convenience of the reader, we repeat here the brief description of our solid particle method for simulating diffusion and reaction in catalyst particles14 and refer to the original publication17 where a more complete description may be found. The solid-particle method is used in preference to the earlier porous-particle approach,18−20 for which we found that a spurious convective flux across the particle−fluid interface was introduced, which was an artifact of the numerical method. This nonphysical convective flux leads

equilibrium-limited conditions at midtube, and propane dehydrogenation (PDH), which is less strongly diffusionlimited. Simulations for PDH were extended to include deactivation by carbon deposition.15 The results of our work with full cylinders illustrated that the flow around a typical near-wall particle can exhibit strong lateral displacement around the particle base, accelerated flow across the curved surface, the development of vortices due to the blocking of flow by the particle above, and recirculating flow following the downstream end. These flow features can contribute to significant local variations in the temperature and species present in a reacting catalyst particle near a heated wall. A primary cause is the strong heat flux from the tube wall, which can result in strong temperature, species, and reaction rate variations in the direction perpendicular to the wall. Our simulations revealed nonsymmetric temperature and species fields within the particles and nonuniform surface distributions, which were quite contrary to the conventional assumptions in catalyst pellet models. It was also seen that the flow field had a strong influence on the diffusion/reaction limitations, and lowvelocity flows contributed to the development of regions of reactant depletion in confined regions on the particle surface. Our full-cylinder simulations also confirmed that the reactions were primarily taking place in a thin “egg-shell” region near the particle surface. In this study, we determine how the features typically found on shaped catalyst particles affect the fluid flow around the particles and heat and mass transfer to the particles. Our particular focus is on the effects of cylindrical particle holes and whether they improve or worsen desirable properties of the pellets compared to the plain cylinders of the previous work. Do the results described in the previous paragraph carry over to shaped particles, are they mitigated by the presence of the holes, and do we see any new phenomena unique to the shaped particles? It should be noted that none of the particles studied here is intended to represent a particular commercial catalyst; they have been chosen to represent a typical range of the number and placement of holes. The present work is restricted to equilateral cylinders (L = D) as being the middle of the commercial range. The particles do not have domed ends, which are often seen in commercial pellets to improve the packing characteristics.

2. SIMULATION MODEL DEVELOPMENT This work presents the results of simulations that were focused on the behavior of shaped cylindrical catalyst particles, located at the wall of a heated reactor tube. This configuration allowed a highly resolved study of the transport and reaction in and around the particles. A detailed picture of the local variations in the temperature, species, and reaction rate could be obtained. The simulations were not intended to represent the overall behavior of a reactor tube, for which a larger assembly of particles would be necessary. The four particle types for which we present new simulations are shown in Figure 1a and are all variations on the equilateral cylinder. The study is split into two parts. In the first part, the one- and four-hole particles were compared at constant mass flow rate ṁ to the previous full-cylinder results14 to see how the qualitative distributions of temperature species and reaction would be affected by the presence of holes in the particles. In the second part, the four particle types shown in Figure 1a were compared at constant pressure drop ΔP to provide a 15841



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The solid- and fluid-phase diffusivities for each species are given by

to overestimation of the interphase transport rates. This was shown for heat transfer, by a comparison to standard literature correlations for a single particle, in our original work.17 This comparison is extended in the present work to mass transfer in Figure 2, where the mass-transfer coefficient between the

e ⎧ (solid) ⎪ ρDk Γk = ⎨ ⎪ ⎩ ρDk + μt /Sct (fluid)

(8)

The fluid value is the sum of the molecular and turbulent diffusivities, and the solid value is an effective Fickian diffusivity derived by Hite and Jackson22 from the dusty gas model and is given by N

1 = Dke

1

∑l =sp1 Δ

kl

(y − y ) N̲ l k N̲ k

l

N

N̲

1 − yk ∑l =sp1 N̲ l

(9)

k

where 1 1 1 = e + e e Δkl Dkl DKk DKl ∑m

particle surface and bulk fluid based on the mass fraction driving force is shown as a function of the flow rate. Results from the porous-particle method are clearly much higher than those from the solid-particle method, which are in reasonably good agreement with the classical Ranz−Marshall correlation21 (4)

NR

Si = ρs ∑ (αijrj)Mi

The solid-particle method mass-transfer coefficients are within 20% of the correlation values, but the porous-particle masstransfer coefficients are 500−700% of the correlation values because of the extra incorrect convective flux. In the solid-particle method, we use Nsp − 1 user-defined scalars ϕk, in both the fluid and solid phases. These scalars represent the species mass fractions. The kth scalar in the fluid phase satisfies the steady-state equation ∇·(ρ u̲ φk − Γk∇φk ) = 0

j=1

NR

Q = ρs ∑ rj( −ΔHj)

(5)

j=1

(6)

Nsp − 1 sp

∑ k=1

φk

(12)

where ΔHj is the heat of reaction of reaction j, in joules per kilomole. The flow was turbulent at the industrial flow rates of the present study, and the Reynolds-averaged Navier−Stokes approach was used, with the shear-stress transport k−ω model for closure, which reduces to a traditional two-layer zonal model if the near-wall mesh is fine enough to resolve the laminar sublayer (y+ ≈ 1). It is important when using user-defined scalars that the equality of both the scalar values and their fluxes is enforced at the fluid−solid interfaces because the commercial code will not necessarily do this for user-defined variables, unlike heattransfer conjugate problems, where both the temperature and

again for k = 1, 2, ..., Nsp − 1, and where the source term on the right-hand side represents production of species k due to reaction. For both phases, the equation φN = 1 −

(11)

where ρs is the pellet density, αi,j represents the stoichiometric coefficient of component i in the reaction j, and Mi is the molecular weight of species i. The heat generation/ consumption by the reactions was calculated as

for k = 1, 2, ..., Nsp − 1, in which isotropic diffusion is assumed. In the solid phase, the kth scalar satisfies −∇·(Γk∇φk ) = Sφk

(10)

This approximate method assumes that pressure variation inside the catalyst pellet is small compared to the fluid pressure, without making the stricter assumption of constant particle pressure. In the fluid phase, the usual mass balances in terms of the mass fractions Yk are replaced by eqs 5, 7, and 8, which are solved for the user-defined scalars. The mass fractions Yk are required for each of the iterations, however, to obtain the average molecular weight, which is used in the computation of the fluid velocity field; both the fluid heat capacity and density depend on Yk. We therefore set Yk = ϕk in the fluid phase at the start of each iteration to ensure that the velocity field is modified (via the average molecular weight) as the composition of the gas phase changes due to reaction. Equations 6−8 are solved for the user-defined scalars in the solid phase. The sink/source terms in the catalyst particles were implemented by a user-defined code. In the code, the species source/sink terms were defined as

Figure 2. Comparison of the particle-to-fluid mass-transfer coefficients for porous- and solid-particle models to a standard literature correlation for 500 < Re < 22000.

Sh = 2.0 + 0.6Sc1/3Re 0.5

ym D Ke m

(7)

is added to obtain the last mass fraction, forcing their sum to be unity. 15842



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heat flux are fully coupled across boundaries. The fluxes for the user-defined scalars (species mass fractions) across the particle−fluid boundary were computed via a user-defined code using the standard expressions for diffusive flow across cell interfaces in a nonorthogonal mesh. This approach can only be applied for laminar flows or for turbulent flows with fine meshes which give y+ ≈ 1, because it does not take into account wall laws that are used for coarse meshes in turbulent flow. This was a further reason that the k−ω model was chosen for this work. 2.3. Meshing and Model Verification. The SMR reactions are known to result in very steep temperature and species gradients near the particle surface, with most reactions occurring in a narrow region within 3−5% of the nominal particle radius from the surface.5,14,15 Prism layers were therefore introduced inside the test particle at both the outer surface and the surfaces of the holes. Four prism layers were applied with a first layer height of 7.6 × 10−5 m (0.003 in.) and an increase ratio of 1.2. For the other particles, prism layers were introduced whenever the geometry of the particle allowed. The remaining regions in the particles were meshed by unstructured tetrahedral cells of 7.6 × 10−4 m (0.03 in.) size. To improve the resolution of the boundary layers on the solid surfaces, prism layers were implemented in the fluid domain on the tube wall and particle surfaces to create a fine enough grid structure to represent the laminar sublayer. From one to three prism layers of thickness 2.54 × 10−5 m (0.001 in.) were used, giving y+ values less than 1. In a test for mesh independence, we have previously reported13 a heat-transfer study of the number and thickness of the boundary prism layers on a single full cylinder in a box, at an angle of 45° to flow. The results showed that the most important factor in computing the particle heat transfer was a sufficiently thin first layer, to obtain y+ ≤ 1, and that the size of the UNS mesh was of secondary importance. An extension of that study14 considered the pressure drop in the full WS and confirmed the results of the single-particle study. It was shown that, for the WS cluster of particles, the pressure drop change was sufficiently small if the mesh on the solid surfaces was refined sufficiently to maintain y+ ≈ 1, which was obtained with a first-layer prism thickness of 2.54 × 10−5 m (0.001 in.). A further extension of the mesh-independence test was performed for simultaneous flow, diffusion, heat transfer, and reaction15 and showed that refining the mesh in that case produced no significant changes in the particle surface species flow or volumetric production rate. These tests led to the mesh sizes and strategy used for the present study. 2.4. SMR Operating Conditions and Settings. The operating conditions for the SMR simulations were taken from a Johnson Matthey detailed reformer model of a methanol plant steam reformer, at the tube inlet location.8 These values gave a Reynolds number of approximately 9500 based on the superficial velocity and particle diameter of a sphere of volume equivalent to that of the cylindrical particle. The corresponding conditions were set for the first part of the study with the constant mass flow rate runs. For the constant pressure-drop runs, the pressure drop was set to 3376 Pa/m and the mass flow rate adjusted to meet that criterion. The operating pressure was 2159 kPa, the inlet temperature was 824.15 K, and a constant wall heat flux of 113.3 kW/m2 was imposed. Average fluid properties were used, with heat capacity Cp = 2395.38 J/ kg·K, thermal conductivity kf = 0.0876 W/m·K, and viscosity μf = 3.0 × 105 Pa·s. The fluid through the packed bed was a

mixture of methane, hydrogen, carbon monoxide, carbon dioxide, and water vapor. The mixture was assumed to be an ideal gas with an initial composition by mass of 19.66% methane, 0.05% hydrogen, 0.07% carbon monoxide, 17.53% carbon dioxide, and the balance steam. The solid particles were given the properties of alumina, with density ρs = 1947 kg/m3, specific heat cps = 1000 J/kg·K, and effective thermal conductivity keff = 1.0 W/m·K. Species diffusivities in the pellets were calculated using eqs 9 and 10 from straight-pore Knudsen and molecular diffusion coefficients corrected using pellet porosity and tortuosity values of ε = 0.44 and τ = 3.54. The source terms in the solid phase were based on the kinetic model of Hou and Hughes23 for SMR over a Ni/αAl2O catalyst, using the heats of reaction −ΔH1 = −206.1 kJ/mol, −ΔH2 = 41.15 kJ/mol, and −ΔH3 = −165.0 kJ/mol, corresponding to reactions 1−3. The reaction rates and parameter values were taken from the original reference and were based on the unit volume of the solid particle and combined with the stoichiometric coefficients to obtain the source terms needed for eqs 11 and 12. 2.5. Computational Procedure. The set of equations described above was solved using the finite-volume commercial CFD code Fluent, version 6.3. The pressure-based segregated solver was used, with the SIMPLE scheme for pressure− velocity coupling. All test results presented here used first-order upwind interpolation for the convection terms; all diffusion terms used second-order discretization. The second-order upwind interpolation for the convection terms usually became unstable at the pressure outlet surface because of the unavoidably large amount of recirculating flow there. In this type of simulation, it is not possible to move the exit plane far from the region of interest, as would usually be the practice. Underrelaxation factors were left at the Fluent default settings, unless some instability was observed in the iterations, when they were occasionally reduced. The flow simulations were not decoupled from the energy and species simulations in this work, in order to allow changes in the moles and temperature due to reaction to have their proper effect on the flow. Two runs were needed to obtain the final results in each particle geometry case. The first run was flow-only (isothermal and nonreacting), where the periodic inlet and outlet were linked together, and either the mass flow rate or the pressure drop was set. The resulting top velocity profile was saved in order to provide a nonuniform velocity profile for the inlet, which was considered to be more realistic than a constant inlet-velocity value. In the second run, both flow and reaction (including energy) were taken into consideration. This run was set to be nonperiodic, and the velocity profile from the flow run was used for the inlet velocity profile, which fixed the mass flow rate. As a consequence, the pressure drop could not be maintained at the desired value of 3376 Pa/m; because of changes in the temperature and molar flow rate from the reactions, it varied from case to case. To minimize the variation in the pressure drops, for each particle case, the flow run was repeated with adjustments made to the nonreacting pressure drop that was set. This gave different velocity inlet profiles and mass flow rates for the reacting runs, which, in turn, gave different pressure drops under reacting conditions. This process was repeated until a satisfactory reacting case pressure drop was achieved. In order to ease convergence in the reacting run, a “bootstrap” procedure was used to increase the reaction rate 15843



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up to the actual value. About 20 iterations were run using 1% of the reaction rate values. Next, the rates were increased to 10% of the actual values, and 20 more iterations were run. Finally, the reaction rates were restored to their actual values. To check for convergence, the reaction rates for each of the three reactions and the four species mass fractions were checked approximately every 3000 iterations. The simulations were considered converged when the percent difference between checks had an order of magnitude lower than 0.1%. The simulations were carried out on a system of parallel computers running 64-bit Red Hat Enterprise (release 4). The server had two dual-core AMD Opteron 2220 processors running at 2.8 GHz with a 1 MB cache and 12 GB of RAM. Each model had about 2 million cells and was run for about 6000 iterations for the flow-only run. For the reaction runs, convergence occurred for the three- and six-hole cases after about 24700 (approximately 185 h) and 20000 (about 135 h) iterations, respectively.

3. CONSTANT MASS FLOW RATE RESULTS SMR simulations were run corresponding to conditions at the inlet of the reactor tube. Heat transfer at tube inlet conditions is very important because it must supply the needs of the endothermic reactions and at the same time increase the particle temperature up to the range for which reforming to CO and H2 (eq 3) dominates over reforming to CO2 and H2 (eq 1). The distribution of temperature inside the particle is therefore of high interest. In addition, there are strong diffusion limitations in the particles. These conditions give rise to reaction rates that are significant only in the outer shell of the catalyst, so that for species surface distributions become of primary interest. In view of the above, the presentation of the results below is based on both intraparticle and surface variations. Intraparticle gradients were examined on two internal pellet planes in the test particle. Plane 1 cut the pellet lengthwise and was roughly perpendicular to the tube wall. Plane 2 was perpendicular to plane 1, also cutting the particle lengthwise, but was approximately parallel to the tube wall. These planes are shown in Figure 1d. Because test-particle side surfaces were exposed to large temperature gradients, we have focused on the temperature, species, and reaction rate variations on those surfaces. To examine the surface variations, the lateral surface of the test particle was “unwrapped”. To do this, we mapped the testparticle surface to a standard cylinder centered on the origin and aligned with the z axis. Any point on the surface could then be identified using the angle θ and the height Z, with the radius r remaining constant. Finally, a surface coordinate s was created as the product of the angle and radius (s = θr), and the unwrapped surface was plotted in s−Z coordinates. 3.1. Near-Wall Particle Surface Study. To simplify the comparison between the various geometries, the same color scale has been kept for the three contour maps in Figure 3. Notice that the overall mass flow rate has been kept constant for all geometries, and therefore the overall Reynolds number is also constant in all of these simulations. In agreement with the earlier results for full cylinders,14 a strong variation in the temperature can also be seen for oneand four-hole particles. For the same particles, one can notice a difference in the temperature of 50 K on the surface. The hottest zone (S ∼ 0.05 m) is the closest one to the reactor wall, whereas the coolest zone is the farthest from the reactor wall.

Figure 3. Surface temperature (K) contours of the test-particle unrolled side surface for full and one- and four-hole particles.

The temperature increases the more one moves toward the reactor wall and decreases the further one moves from it. Comparing the geometries, we can first notice a similarity in the temperature patterns. The hottest and coldest zones are roughly located at the same places, no matter how many holes are in the particle. However, significant variations appear in the values of the extrema. Though the full- and four-hole-particle temperature ranges are similar, it appears that the one-hole temperature range is significantly reduced. Its temperature range is only 30 K, which is 20 K lower than that for the other geometries. In order to understand this, one must focus on the flow around the particle. Figure 4 shows a comparison between the flows corresponding to the temperature contours on the particle surfaces. The top images (a−c) show the surface temperatures, and the lower images (d−e) show the pathlines of particles coming from the inlet (bottom surface). These pathlines are colored by velocity magnitude. Because these pathlines track particles coming from the inlet, a lack of pathlines in a particular region means no particle issued from the inlet passes through that region. In other words, a lack of pathlines will highlight stagnant fluid, and thus exchange of both energy and species with the bulk flow is only due to conduction or diffusion. In order to spot the hot spots on the test particle’s surface, the same view has been kept for all three particles in Figure 4. The first thing we can notice is that there is a strong correlation between localization of these hot spots and the flow. That is to say, the hottest spots can be found where there is no flow. This is perfectly understandable because, in these zones, hardly any fresh flow arrives, and it is well-known that heat transfer is much more efficient when convection is strong. The relative coolness of the one-hole geometry can also be understood thanks to flow. Indeed, it appears that the dead zones around the test particles are more confined and that the overall convection around these zones is better. 15844



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Figure 4. Comparison of the test-particle surface temperature hot spots (a−c) and pathlines over the hot-spot locations (d−f) for full (a and d), onehole (b and e), and four-hole (c and f) particles.

In order to understand the differences in the flow patterns, one needs to consider the particle that is just on top of the test particle. It appears that the particle on top of the test particle is blocking the flow coming from between the wall and test particle. Hence, for the full cylinder and, to a smaller extent, for the one-hole cylinder geometries, a swirling flow is formed, and velocities significantly decrease. Hence, the top particle acts like a barrier, and thus the path coming from in front of the test particle becomes a nonfavorable path. However, if one adds a hole to the top particle, fluid can now flow more easily, and the swirling flow becomes less important. The four-hole geometry might therefore be considered as the most favorable case in that flow should now easily pass through one of the four holes. It thus clearly seems that the fluid would flow more rapidly between the top and test particles for the four-hole case than it does for the other two geometries. These considerations would lead toward the expectation that the surface of the four-hole particle would be the coolest. The fourhole particle, however, has an interior hole located near the heated wall surface, which allows the hot gas flow to heat that portion of the pellet from within, so that the surface of the fourhole pellet there is relatively hot, warmer than that of the onehole particle. So, some aspects of the surface temperature distribution can be explained on the basis of good versus poor convective heat transfer to the external pellet surface, as in the prior case of full cylinders.14 For the shaped particles with internal holes, however, a new phenomenon comes into play, namely, direct convective transport of energy to the particle interior. The three plots in Figure 5 focus on the methane mass fraction. As before, the plots have been made from the test particle’s curved surface. The same holds for the following three contour plots of the hydrogen mass fraction for the three different geometries in Figure 6. As was the case for temperatures, gradients appear. Hence, for the methane mass fraction, a relative variation of over 4% can be noticed between the highest and lowest concentrations on the particle surface. The same is true with hydrogen, where the mass fraction ratio varies over a factor of 5. We can also clearly identify zones on

Figure 5. Surface methane mass fraction contours of the test-particle unrolled side surface for full and one- and four-hole particles.

the surface where the mass fraction is either high or low. Moreover, these zones seem to overlap with those that one could identify for temperature; i.e., hot zones have low methane and high hydrogen concentrations, and cold zones have high methane and low hydrogen concentrations. This is perfectly understandable because the two main reactions are highly endothermic. Hence, an increase in the temperature will lead to an increase in the reaction rates. One can also notice that, although the temperature and concentration zones are in good agreement, the maximum in the temperature and the respective maximum and minimum in methane and hydrogen do not have exactly the same location. The temperature maximum is roughly located at S ≈ 0.05 m, whereas the mass fraction extrema are located at roughly S ≈ 15845



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the three geometries. This is in perfect agreement with the fact that the full cylinder geometry has the highest temperatures. Hydrogen also confirms that last point because the highest mass fractions are obtained for the full cylinder pellets. 3.2. Near-Wall Particle−Intraparticle Study. Figure 7 represents the temperature variation on the two planes previously described. Notice that, for the four-hole cylinder geometry’s results, it appears as if the two holes displayed were not of the same diameter. This is simply due to the way planes 1 and 2 pass through the holes. They do not pass through the centers of the holes. First consider only plane 1, the one perpendicular to the reactor wall. Looking at the temperature variation inside the full cylinder particle, we can notice that the gradient is essentially located in the region of the pellets that is the closest to the wall. Past that zone, the temperature smoothes out rapidly. This becomes even more striking as we consider the other geometries. For instance, with the one-hole geometry, we can clearly see that the hole divides the plane in two. The left side presents a high gradient, whereas the right side has a more homogeneous temperature. This is showing that the right side of the test particle is too far from the wall to see any of the heat effects. If we now consider plane 2, we can see that temperature is quite homogeneous, no matter what geometry we consider. Besides, the mean temperature decreases on going from the full to four-hole cylinder. This can be explained by the fact that, as more holes are added, the larger the interface surface with the fluid will be. As is well-known, the SMR reaction is diffusionlimited. Therefore, if the interface surface increases, a larger amount of fresh reactant will be brought to the pellet, and more products will be converted. Consequently, there will be a larger heat sink and a lower mean temperature. Figure 8 shows the methane (a−c) and hydrogen (d−f) mass fractions for plane 1. The first thing we notice is a high gradient in methane near the solid−fluid interface. This is due to

Figure 6. Surface hydrogen mass fraction contours of the test-particle unrolled side surface for full and one- and four-hole particles.

0.065−0.07 m. For the full cylinder case,14 this was explained by the occurrence of regions of reactant depletion, where it was difficult for fresh flow to access the particle surface. For the one- and four-hole particles investigated here, the maxima and minima are not as strong as those for the full cylinders, which may be related to the shortening of the diffusion pathways because of convective transport of the reactants to the particle interior. If we once more compare the results of the three geometries, we can notice a close resemblance in the mass fraction patterns between the three. It is not surprising to notice that the full cylinder geometry has the lowest methane mass fraction among

Figure 7. Temperatures on the plane perpendicular to the tube wall (a−c) and on plane parallel to the tube wall (d−f) through the test particle for full (a and d), one-hole (b and e), and four-hole (c and f) particles. 15846



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Figure 8. Methane (a−c) and hydrogen (d−f) mass fraction profiles through the test particle for full (a and d), one-hole (b and e), and four-hole (c and f) particles.

diffusion limitations; i.e., the reactant that enters the particle reacts so quickly that it does not have time to reach the center of the pellet. Hence, we can see that the methane concentration is much higher at the interface than at the core of the particle. This holds true for all of the interfaces and confirms that the reaction zone is close to the surface for interior hole surfaces as well as for exterior surfaces. This suggests that methane has relatively good access to the interior of the particles via flow through the holes. The same thing can be seen for hydrogen. A relatively low concentration can be seen near the interface. The hydrogen that is produced by the reaction at the interface will diffuse where its gradient is most favorable, that is to say, toward the fluid zone where the hydrogen concentration is the lowest. We can see that the core of the pellets is almost homogeneous in concentration. It is as if diffusion is so limited that the system had enough time to reach the reaction equilibrium. Nevertheless, a slightly lower methane concentration and a slightly higher hydrogen concentration can be noticed in the near-wall region. With the reaction being endothermic, an increase in the temperature will be in favor of more hydrogen production. Also the system equilibrium will thus be moved toward a lower methane concentration.

Table 1. Summary of the Results for a Reactor Wedge catalyst geometry

void fraction

1-hole 3-hole 4-hole 6-hole

0.54 0.62 0.66 0.62

pressure drop (Pa/m) 3372 3393 3381 3378

mass flow rate (kg/s)

average tube-wall temp (K)

average temp of the exiting gas (K)

0.02875 0.03340 0.03505 0.03230

1054.5 1054.9 1052.7 1068.0

830.1 829.2 828.1 829.2

smaller in order to fit on the particle. The void fractions for the three- and six-hole geometries are equal, which provides an opportunity for a comparison of geometries with the same volume proportions but different surface areas. The target pressure drop for all runs was specified as 3376 Pa/m and should ideally stay the same for all of the cases. However, as discussed in Simulation Model Development, the actual pressure drops under reaction conditions varied slightly but all were still within 0.6% of the desired value. Some overall trends in the WS performance can be observed from Table 1. The mass flow rate increases proportionally to the void fraction; this is reasonable because the pressure drop is held constant. A small exception is provided by the three- and six-hole cases, which have the same void fraction, but the sixhole case has a lower mass flow rate. This is likely to be linked to the higher surface area of the six-hole particles, so that a lower flow rate causes the same friction drag contribution to the pressure drop. The average tube-wall temperature (Tw) changes little and possibly decreases as the number of holes and void fraction increase, as observed previously.12 However, Tw for the six-hole case is more than 10 K higher than that for the threehole case, although both have the same void fraction. Finally, the average exiting gas temperature decreases as the void fraction increases. This is due to the fact that more mass is flowing through the system at higher void fractions, providing higher thermal capacity for the same amount of heat transferred from the tube wall.

4. CONSTANT PRESSURE-DROP RESULTS The goal of the second part of the study was to compare the following characteristics for the extended range of catalyst one-, four-, three-, and six-hole geometries: the tube-wall temperature, the total heat sink, reaction rates, and effectiveness of the test particle, the overall mass flow rate for a set pressure drop, and the fluxes of heat and species on internal and external particle surfaces. Table 1 is a summary of the quantitative results for the reactor wedge for each of the four catalyst geometries. As holes are added to the base particle, the void fraction increases; the exception is the six-hole case because the hole diameters were 15847



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Table 2. Summary of the Results for the Test Particle catalyst geometry

GSA (m2)

surface weighted-average temp (K)

total heat sink (W)

surface heat flow (W)

methane flow (×10−7 kmol/s)

reaction rate 1 (×10−8 kmol/s)



1-hole 3-hole 4-hole 6-hole

0.00354 0.00453 0.00503 0.00523

802.3 803.7 803.8 803.4

43.67 56.87 64.18 65.77

43.72 56.86 64.07 65.89

−2.61 −3.39 −3.84 −3.92

1.43 1.92 2.20 2.23

−4.06 −5.21 −6.08 −6.09

2.46 3.19 3.60 3.69

Figure 9. Test-particle temperature (K) surface contour comparisons (particles 3 and 7 removed).

Figure 10. Intraparticle cross-sectional velocity (m/s) and temperature (K) contours for near-tube-wall four-hole particles.

Table 2 is a summary of the results of each case for the test particle specifically. The GSA of the particles is increased by the addition of holes. As the GSA increases, the reaction rate increases. This is reasonable because the reaction is believed to take place mainly in the outer 3−5% of the particle radius,5 and adding holes increases the surface area for this reaction and facilitates transport of the reactants and products for any reaction taking place in the particle interior. In the present case, the ratio of reaction rate 3 (the dominant reaction under tube-

inlet conditions) to GSA is almost constant, varying by only 1.4% so that, here, the catalytic activity is linearly proportional to GSA. Despite the different heat sinks and reaction rates in the particles, the weighted-average temperatures of the testparticle surfaces showed no distinguishable trend. The results in Table 2 also allow us to perform model verification tests by checking the material and energy balances on the test particle. The total heat sink computed from the product of the heat of reaction and reaction rate, summed over 15848



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Figure 11. Velocity (m/s) pathline comparisons through bottom- and test-particle holes, colored by velocity magnitude.

Figure 12. Test-particle methane mass fraction surface contour comparisons (particles 3 and 7 removed).

the particle volume, may be compared to the total heat flow across the particle surface. The values in the fourth and fifth columns of Table 2 show that these are in agreement to within 0.2%. The particle surface methane flow in column 6 in the table should be equal to the sum of the rates of reactions 1 and 3 in columns 7 and 9, and the results agree within about 1% error. To gain insight into the results in Tables 1 and 2, we examined the detailed pictures of the temperature and species distributions in the various particles. The high temperature seems to be localized near the bottom of the test particle (see Figure 9). In general, as the void fraction increases, the intensity of the hot spot increases. Despite the fact that the six-hole case

has the most holes, its void fraction is similar to that of the three-hole case. This explains why the two particles have similar temperature contours. To get a better understanding of why the intensity of the hot spot increases as the void fraction increases, a cross-sectional plane of the wedge was taken at the hot-spot location. The velocity contours at the cross-sectional plane can be seen in Figure 10a for the four-hole particles, while temperature contours on the same plane and for the same particles can be seen in Figure 10b. The holes within the particle allow for hot gas to pass through the holes near the hot spot. The hot gas flowing through these holes heats the particle even further, resulting in more intense hot spots. This is especially noticeable if the one-hole case is compared to the 15849



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multiholed cases. In the one-hole case, there are no holes near the hot spot, while in the other cases, there are one or more holes that contain hot gas near the hot spot. The velocity pathlines through the reactor wedge can be compared for each case. It was observed that flow is faster around the surface of the test particle in the one-hole case than in the multiholed case. Flow elsewhere in the one-hole case also appears to be more intense than in the multiholed cases. Figure 11 compares the velocity pathlines over and through the bottom particle and into the test particle. For the one-hole case, much of the flow hits the bottom of the test particle and is deflected in a radial direction. In general, the more holes there are, the more likely it is that flow is pulled through the holes instead of being deflected radially. This effect has its advantages and disadvantages. Flow going through the holes is kept close to the particle’s surface where the reaction takes place. As a result of this, not only do holes create more surface area, but they also help to redirect flow, which maximizes utilization of this surface area. However, the addition of more holes results in less radial flow. The reduction of radial flow reduces radial heat transfer and increases the tube-wall temperature. The tube-wall temperature not only increases with increasing void fraction but also depends on the configuration of the holes. For example, the difference in the tube-wall temperature from the three- and six-hole cases is greater than 10 K despite the fact that both cases have the same void fraction. Because there are double the number of holes in the six-hole case and these holes are spread out over the bottom surface of the particle, the chances of flow being “captured” by a hole is increased. Figure 12 shows the methane mass fraction gradients for each of the four catalyst geometries. The location of the holes in each of the cases has a significant impact on how effectively the holes are utilized. In the one-hole case, the hole is at the center of the particle. Below the test particle, there is another particle blocking flow (not shown). Because the single hole is in the center of the test particle, it is more difficult for flow to enter the hole and replenish it with methane. In the six-hole case, the larger number of holes results in less tortuous flow, and the holes are utilized more effectively than in the one-hole case. The test-particle rates of reaction 3 are shown in Figure 13 (that of reaction 1 is similar). The intensity of the reaction rates closely follows the intensity of the temperature hot spot (see Figure 9). This is expected because reactions 1 and 3 are highly endothermic. Because of the endothermic nature of these reactions, high temperature will drive the reaction forward. This is why the reaction rate is the highest where the temperature is the highest. The effects of flow on the temperature, methane mass fraction, and reaction rates were examined closely. A side-byside comparison of the various surface contours for the threehole case can be seen in Figure 14. Because reactions 1 and 3 are endothermic, the locations of the temperature hot spot and highest reaction rates correspond well. Because both reactions consume methane, the expected location of the minimum methane mass fraction would be at the maximum reaction rate location. However, this is not the case. The minimum methane mass fraction actually occurs slightly to the right of the maximum reaction rate (circled in red). In order to better understand why this was occurring, it was necessary to examine the flow patterns near the test particle.

Figure 13. Test-particle rate of reaction 3 contour comparisons (kmol/m3·s).

Two factors were found to influence the temperature contour on the test particle: the distance from the tube wall and the velocity of the fluid passing over the particle’s surface. On the far right of the test particle, away from the tube wall, the temperature is quite low. Moving further along the surface, the temperature starts to increase as the distance from the tube wall starts to decrease. However, near the tube wall, the velocity of the fluid starts to increase, similarly to the four-hole particle shown in Figure 4, because it is squeezed between the particle and wall. The region with the most intense velocity has a slightly lower temperature. At the location of the hot spot, the fluid is quite stagnant. Thus, the distance from the tube wall and velocity of the fluid passing over the surface determine where the hot spot occurs. Figure 14 shows the surface methane mass fraction on the three-hole test particle. The minimum surface methane mass fraction was found in an area of highly stagnant flow (circled in red). This suggests that methane is hardly being replenished. In addition to being starved of reactant, this location is further from the hot tube wall. The combination of these two factors results in an area with little reaction and very little methane. This explains why the minimum methane mass fraction was not found in the same area as the hot spot, in agreement with earlier results for the full cylinder.14 A question of interest to catalyst designers of shaped particles with interior holes is the following: Are the surfaces of the holes as accessible to the flow and to mass transfer as the outer particle surfaces? Also, if more holes are added, are the heatand mass-transfer rates across the surfaces increased proportionally or are there diminishing returns? These questions are addressed for the particle and hole sizes of the present study in Table 3. In Table 3, the average temperatures, heat fluxes, and methane molar fluxes are presented for the individual surfaces of each of the four shaped particles studied here. Both outside (side, top, and base) and interior (H1−H6 as appropriate) surfaces are included. In all cases, hole H1 is the one closest to the tube wall; holes are then numbered clockwise around the pellet top surface (refer to Figure 1a), with H6 being the center hole for the six-hole particle. The average temperatures tend to be higher on the curved side and base surfaces, probably as a result of their being directly exposed to the hotter reactant flow coming from below and being slightly closer to the tube wall. 15850



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Figure 14. Three-hole-particle surface contour comparisons of the temperature, methane mass fraction, and rates for the reforming reactions.

Table 3. Comparison of Particle-Surface Fluxes and Mass Flow Rates through Particle Holes catalyst geometry

surface

average temp (K)

molar flux (×10−5 kmol/m2·s)

heat flux (×10−4 W/m2)

mass flow rate (×10−3 kg/s)

1-hole

side top base H1

803.4 800.7 804.8 797.8

7.486 7.009 7.628 7.068

1.298 1.140 1.272 1.065

0.57

side top base H1 H2 H3

805.1 800.6 808.2 806.2 798.3 800.5

7.594 6.800 7.722 7.909 7.068 7.390

1.357 1.026 1.328 1.284 1.046 1.179

1.04 0.61 0.92

side top base H1 H2 H3 H4

805.1 801.0 811.4 805.5 799.5 802.9 799.8

7.729 6.832 8.088 8.018 7.355 7.716 7.384

1.379 1.020 1.460 1.340 1.111 1.137 1.178

1.10 0.70 0.67 0.99

side top base H1 H2 H3 H4 H5 H6

804.7 799.6 810.1 805.0 798.4 799.9 801.0 807.2 800.4

7.534 6.578 7.815 7.935 7.186 7.397 7.516 8.104 7.381

1.338 0.980 1.339 1.348 1.114 1.238 1.225 1.321 1.128

0.50 0.32 0.34 0.51 0.53 0.36

3-hole

4-hole

6-hole

The methane and energy fluxes appear to be quite close, for all surfaces. Some small trends can be discovered; the fluxes tend to be largest for the base and curved surfaces, for the same reasons as the temperature, and the surface fluxes on hole H1 (closest to the tube wall) tend to be larger, while those on the surface of hole H2 (further from the tube wall and more shielded from direct flow) tend to be smaller. The overall impression, however, is that all surfaces, interior or exterior, have approximately equal mass and energy surface fluxes, to within ±10%. Table 3 also presents mass flow rates for each hole in a particle. In most cases, hole H1 closest to the tube wall has the highest mass flow rate. This is due to the flow from below being less blocked for the holes nearest the tube wall. In the one-hole particle, H1 is further from the tube wall and, consequently, has a smaller flow rate. The mass flow rates through individual holes do not appear to be strongly affected by the added hole in going from three- to four-hole particles. In the six-hole case, the

holes are smaller so that lower mass flow rates in that case would be expected, as the simulations confirm. We can also obtain images of the distributions of flow, temperature, and species inside the holes in the catalyst particles, as illustrated in Figure 15 for the four-hole particle case. It is clear that the flow is not uniform across the holes, as shown in Figure 15a. The regions of higher flow (green and yellow) are located at the upper surfaces of the holes, i.e., at higher z, and are directly caused by the angle of the particle to the oncoming flow. It is also interesting to note that the simulations predict regions of backflow (negative velocities) within the holes. The backflow regions seem to align with colder regions with lower methane concentrations or nonrefreshed regions with local depletion, as in Figure 15b. The distributions of methane and hydrogen are also nonuniform within the holes, as shown in Figure 15c,d. When the resistance to mass and heat transfer inside a reacting pellet is important, it is usual to consider the effects of 15851



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Figure 15. Contours of (a) axial velocity vz (m/s), (b) temperature (K), (c) methane mass fraction YCH4, and (d) hydrogen mass fraction YH2 inside the holes for a four-hole particle.

the intraparticle gradients by an effectiveness (factor) η. This is a factor that multiplies the reaction rate at the particle surface conditions to yield the rate that is actually experienced when the conditions inside the particle are different. In practice, the effectiveness for reaction i may be calculated as ηi =

1 V

Reaction 3 is the dominant reaction compared to the others, by an order of magnitude of the reaction rates. The effectiveness was low, generally less than 0.2, and increased with increasing particle surface area or number of holes, except for the four- to six-hole comparison. Similar results with a somewhat higher effectiveness were seen for reaction 1, which was 1 order of magnitude slower than reaction 3. Reaction 2, the WGSR, is strongly equilibrium-limited because of the thermodynamic constraints at high temperatures. Therefore, there is a strong tendency to proceed in the reverse direction. The negative reaction rate obtained for the WGSR in the particle was due to this phenomenon. However, the surface reaction rate was in the forward direction, which implied that CO2 and H2 diffused to the bulk fluid more easily, and because the equilibrium level was not reached, the reaction proceeded in the forward direction, which resulted in a positive surface reaction rate value and a negative value for effectiveness. The overall trends in the effectiveness were in agreement with the industrial observations1 and pseudocontinuum modeling results.5,24 The literature modeling results, however, gave values for the effectiveness of the dominant reactions 1 and 3 that were lower than the values in Table 4 by 1 order of magnitude or more. This may be explained by considering that in the classical approach the pellet was modeled as onedimensional, symmetric, and isothermal with uniform surface conditions. In such a case, for steam reforming, equilibrium is established in the interior of the pellet, and the reaction rates drop to zero there, leading to low utilization of the catalyst particle volume. This behavior is typical of particles situated inside the bed, away from the tube walls. The simulated test particle is three-dimensional and asymmetric and is situated next to the tube wall, where it is subjected to a strong temperature gradient. This results in higher reaction rates next to the wall, as observed above, which create gradients in the species across the particle. There is therefore no opportunity for reaction equilibrium to be established inside the particles

V

∫0 ri(Cs , Ts) dV ri(Css , Tss)

(13)

where V is the pellet volume. To calculate the effectiveness based on this definition, the averaged reaction rate in the catalyst particle and the reaction rate on the particle surface were needed. For the reaction rate inside the particle, the rates were calculated for each computational cell, and the volume averages were taken. This was done by a user-defined code for the test particle. For the surface reaction rate calculation, the surface temperatures and species mass fractions were exported for each surface cell of the test particle and imported into a spreadsheet to calculate the reaction rates for each cell, and then the surface cell reaction rate values were averaged. These calculations were carried out for the three reactions of interest, and the effectiveness values for the test particle were obtained for each of the reactions and for the particle shapes studied and are presented in Table 4. The results for the full cylinder geometry are also included for comparison. Table 4. Effectiveness for the Three Reactions in Different Shapes of Wall-Located Particles catalyst geometry

η1

η2

η3

full 1-hole 3-hole 4-hole 6-hole

0.166 0.228 0.350 0.453 0.395

−0.490 −0.690 −1.05 −1.37 −1.15

0.0847 0.113 0.174 0.220 0.198 15852



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regions of backflow along the lower surfaces of the holes. Nevertheless, the holes appeared to be effective in bringing more fluid to the active surfaces of the particle. Heat- and masstransfer fluxes were comparable on both interior and exterior surfaces of the particles. The six-hole geometry offered the highest surface area and slightly higher reaction rates while still maintaining a more uniform surface temperature. However, the six-hole case had lower mass flow rates than the four-hole case for the set pressure drop. In addition, the six-hole case had a significantly higher tube-wall temperature compared to the four-hole wall temperature. The one- and three-hole cases had even lower tube-wall temperatures; however, these cases had significantly less surface area and void fraction compared with the four-hole case. Overall, the four-hole geometry offers high surface area for reaction, high void fraction for low pressure drops, and a reasonably uniform temperature over the particle, along with a lower average tube-wall temperature. An aspect of catalyst design that was not examined in this paper but that should be taken into consideration for future study is the strength of the geometries. Over time, catalyst particles get crushed inside the reactor bed and eventually clog the reactor. Thus, an optimal catalyst design would have high strength in addition to the characteristics discussed in this paper.

adjacent to the heated tube wall, so that there are nonzero reaction rates throughout the particle and the volume is utilized more effectively, as shown by the values in Table 4 that are higher than those in the literature results.

5. CONCLUSIONS The CFD simulations performed in this study expanded upon the previously studied full cylinder geometry14 by the addition of an extended range of catalyst geometries: one-, three-, four-, and six-hole. The simulations confirmed and extended several of the results of the earlier study: the reactions were confined to a thin region at the surface of the particle, and this was true for the interior as well as exterior surfaces; the shaped particles also showed significant local variations in the temperature, especially associated with the strong wall heat flux; the shaped particles also showed regions of reactant depletion on the particle surfaces, but compared to the full cylinder case, these appeared to be mitigated by the flow patterns caused by the holes. Hot spots were observed on the particle surfaces, generally near the closest approach to the tube wall, in regions of low flow. The one-hole hot-spot case was lower than the full- and four-hole-particle hot spots because of a higher flow rate in the right place to cool the particle; however, it was also possible for the redirected flow through a hole to increase the hot-spot temperature by carrying hot gases into the pellet and altering the local temperature gradient. On the other hand, the holes could also transport more reactants into the particles, increasing the reaction and, consequently, the endothermic heat sink, which then decreased the pellet temperature locally. The flow through the holes could also reduce regions of stagnant and swirling flow behind the pellet and improve heat transfer there. Particle features have the potential to change flow patterns locally and, through them, to change local distributions of temperature, species, and reaction rates. Results for the WS as a whole were obtained at constant pressure drop. As expected, as the void fraction increased, the mass flow rate increased. The average temperature of the exiting gas decreased as the void fraction increased because more mass was flowing through the tube with the same wall heat flux. The average reactor tube-wall temperature generally depended weakly on the void fraction. However, the average tube-wall temperature for the six-hole case was more than 10 K hotter than the three-hole case, which had the same void fraction. This was due to variations in flow; in particular, the six-hole case had less tortuous flow, which resulted in less effective radial heat transfer. So, pellets with the same void fraction may give a different heat-transfer performance because of the arrangement of holes and their effect on the flow field. Results for the test particle itself showed that, in general, the reaction rate in the particle was directly proportional to the GSA of the particle. The average particle surface temperature showed no trend with changing particle geometry. These observations suggest that the overall effect of adding features to a particle may be fairly simply characterized through the void fraction for the pressure drop and mass flow rate and through GSA for the catalytic activity. The effect of features on heat transfer appears to be somewhat more complex. Our simulations confirmed that the mass flow into the holes was substantial and did not appear to depend on the number of holes on a particle but did depend on the hole diameter and location of the hole. The flow did not move down the holes in plug flow for the 45°-angled particle; instead, it preferentially traveled along the top surface of the hole, and there were

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Addresses ‡

AECOM, 250 Apollo Drive, Chelmsford, MA 01824. Cornell University, Ithaca, NY 14853. ∥ HeartWare Inc., 14000 NW 57th Court, Miami Lakes, FL 33014. §

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Acknowledgment is made to the Donors of the American Chemical Society Petroleum Research Fund for support of this research.

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NOMENCLATURE fluid specific heat, J/kg·K solid specific heat, J/kg·K concentration in the solid particle, kmol/m3 concentration on the surface of the solid particle, kmol/ m3 dp particle diameter, m k turbulent kinetic energy, J/kg kf fluid thermal conductivity, w/m·K keff effective particle thermal conductivity, w/m·K Lp particle height, m Mi molecular weight of species i N tube-to-particle diameter ratio Nsp number of species P static pressure, kPa Q heat generation/consumption term qwall wall heat flux, w/m2 r particle radial coordinate, m rt tube radius, m ri reaction rate i, kmol/m3·s cp cps Cs Css

15853


Industrial & Engineering Chemistry Research Re s Si T Ts Tss vz |v| y+ yk Yk Z

Article

Reynolds number, ρdpvz/μ arc length, m species source/sink term temperature, K temperature in the solid particle, K temperature on the surface of the solid particle, K axial velocity, m/s velocity magnitude, m/s dimensionless wall coordinate mole fraction of species k mass fraction of species k particle height coordinate, m

Reaction Heat Effects in Narrow Packed Tubes. Ind. Eng. Chem. Res. 2008, 47, 5966. (14) Taskin, M. E.; Troupel, A.; Dixon, A. G.; Nijemeisland, M.; Stitt, E. H. Flow, Transport and Reaction Interactions for Cylindrical Particles with Strongly Endothermic Reactions. Ind. Eng. Chem. Res. 2010, 49, 9026. (15) Behnam, M.; Dixon, A. G.; Nijemeisland, M.; Stitt, E. H. Catalyst Deactivation in 3D CFD Resolved Particle Simulations of Propane Dehydrogenation. Ind. Eng. Chem. Res. 2010, 49, 10641. (16) Taskin, M. E.; Dixon, A. G.; Stitt, E. H. CFD Study of Fluid Flow and Heat Transfer in a Fixed Bed of Cylinders. Numer. Heat Transfer 2007, 52, 203−218. (17) Dixon, A. G.; Taskin, M. E.; Nijemeisland, M.; Stitt, E. H. CFD Method to Couple Three-Dimensional Transport and Reaction inside Catalyst Particles to the Fixed Bed Flow Field. Ind. Eng. Chem. Res. 2010, 49, 9012. (18) Dixon, A. G.; Taskin, M. E.; Stitt, E. H.; Nijemeisland, M. 3D CFD Simulations of Steam Reforming with Resolved Intraparticle Reaction and Gradients. Chem. Eng. Sci. 2007, 62, 4963. (19) Kolaczkowski, S. T.; Chao, R.; Awdry, S.; Smith, A. Application of a CFD Code (Fluent) to Formulate Models of Catalytic Gas Phase Reactions in Porous Catalyst Pellets. Chem. Eng. Res. Des. 2007, 85, 1539. (20) Cheng, S.-H.; Chang, H.; Chen, Y.-H.; Chen, H.-J.; Chao, Y.-K.; Liao, Y.-H. Computational Fluid Dynamics-Based Multiobjective Optimization for Catalyst Design. Ind. Eng. Chem. Res. 2010, 49, 11079. (21) Ranz, W. E.; Marshall, W. R., Jr. Evaporation from drops. Chem. Eng. Prog. 1952, 48, 141. (22) Hite, R.; Jackson, R. Pressure Gradients in Porous Catalyst Pellets in the Intermediate Diffusion Regime. Chem. Eng. Sci. 1977, 32, 703. (23) Hou, K.; Hughes, R. The Kinetics of Methane Steam Reforming over a Ni/α-Al2O Catalyst. Chem. Eng. J. 2001, 82, 311. (24) Xu, J.; Froment, G. F. Methane Steam Reforming: II. Diffusional Limitations and Reactor Simulation. AIChE J. 1989, 35, 97.

Greek Letters

αi,j ΔHj ε ηi Γ ϕk μ ρ ρs τ ω

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stoichiometric coefficient of i in reaction j heat of reaction j, kJ/mol pellet porosity effectiveness for reaction i mass diffusion coefficient, kg/m·s kth user-defined scalar fluid viscosity, kg/m·s fluid density, kg/m3 solid density, kg/m3 pellet tortuosity specific dissipation rate, s−1

REFERENCES

(1) Stitt, E. H. Reactor Technology for Syngas and Hydrogen. In Sustainable Strategies for the Upgrading of Natural Gas: Fundamentals, Challenges and Opportunities; Derouane, E., Parmon, V., Lemos, F., Ramoa-Ribiero, F., Eds.; NATO Science Series II; Kluwer Press: Dordrecht, The Netherlands, 2005; Vol. 191, p 185. (2) Sie, S.; Krishna, R. Process Design and Scale up: II. Catalyst Design Strategy. Rev. Chem. Eng. 1998, 14, 159. (3) Bruno, S.; Barreto, G. F.; Gonzalez, M. G. Effect of the Geometric Characteristics of Commercial Catalysts for Steam Reforming. Chem. Eng. J. 1988, 39, 147. (4) Twigg, M. V. Catalyst Handbook, 2nd ed.; Wolfe Publishing Ltd.: London, 1989. (5) Pedernera, M. N.; Pina, J.; Borio, D. O.; Bucala, V. Use of a Heterogeneous Two-Dimensional Model To Improve the Primary Steam Reformer Performance. Chem. Eng. J. 2003, 94, 29. (6) Kagyrmanova, A. P.; Zolotarskii, I. A.; Vernikovskaya, N. V.; Smirnov, E. I.; Kuz’min, V. A.; Chumakova, N. A. Modeling of Steam Reforming of Natural Gas Using Catalysts with Grains of Complex Shapes. Theor. Found. Chem. Eng. 2006, 40, 155. (7) Kagyrmanova, A.; Zolotarskii, I.; Smirnov, E.; Vernikovskaya, N. Optimum Dimensions of Shaped Steam Reforming Catalysts. Chem. Eng. J. 2007, 134, 228. (8) Dixon, A. G.; Nijemeisland, M.; Stitt, E. H. Packed Tubular Reactor Modelling and Catalyst Design Using Computational Fluid Dynamics. Adv. Chem. Eng. 2006, 31, 307. (9) Freund, H.; Zeiser, T.; Huber, F.; Klemm, E.; Brenner, G.; Durst, F.; Emig, G. Numerical Simulations of Single Phase Reacting Flows in Randomly Packed Fixed-Bed Reactors and Experimental Validation. Chem. Eng. Sci. 2003, 58, 903. (10) Kuroki, M.; Ookawara, S.; Ogawa, K. A; High-Fidelity, C. F. D. Model of Methane Steam Reforming in a Packed Bed Reactor. J. Chem. Eng. Jpn. 2009, 42 (Supplement 1), s73. (11) Nijemeisland, M.; Dixon, A. G.; Stitt, E. H. Catalyst Design by CFD for Heat Transfer and Reaction in Steam Reforming. Chem. Eng. Sci. 2004, 59, 5185. (12) Dixon, A. G.; Taskin, M. E.; Nijemeisland, M.; Stitt, E. H. Wallto-Particle Heat Transfer in Steam Reformer Tubes: CFD Comparison of Catalyst Particles. Chem. Eng. Sci. 2008, 63, 2219. (13) Taskin, M. E.; Dixon, A. G.; Nijemeisland, M.; Stitt, E. H. CFD Study of the Influence of Catalyst Particle Design on Steam Reforming 15854


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