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Wall-to-particle heat transfer in steam reformer tubes: CFD comparison of catalyst particles
Chemical Engineering Science 63 (2008) 2219 – 2224 www.elsevier.com/locate/ces
Wall-to-particle heat transfer in steam reformer tubes: CFD comparison of catalyst particles Anthony G. Dixon a,∗ , M. Ertan Taskin a , Michiel Nijemeisland b , E. Hugh Stitt b a Department of Chemical Engineering, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609-2280, USA b Johnson Matthey, P.O. Box 1, Belasis Avenue, Billingham, Cleveland TS23 1LB, UK
Received 25 July 2007; received in revised form 8 January 2008; accepted 11 January 2008 Available online 20 January 2008
Abstract Computational fluid dynamics (CFD) was used to simulate non-reacting heat transfer in a steam reforming packed reactor tube of tubeto-particle diameter ratio (N) equal to 4, with cylindrical multi-hole catalyst particles. These simulations extend those of our previous study [Nijemeisland, M., Dixon, A.G., Stitt, E.H., 2004. Catalyst design by CFD for heat transfer and reaction in steam reforming. Chemical Engineering Science 59, 5185–5191] to provide accurate tube wall temperatures, runs at constant pressure drop in addition to those at constant mass flow rate and simulations of particles with different sizes of holes. At constant pressure drop, particles with higher void fractions allowed higher mass flow rates, resulting in tube wall temperatures and radial temperature profiles in order: solid cylinders > one-hole particles > multi-hole particles. Little difference was seen between three-hole and four-hole particles. The particles with multiple holes gave a substantial reduction in tube wall temperature, with only a small decrease in core tube heat transfer. The effect of hole size was small, for the cases investigated in this study. 䉷 2008 Elsevier Ltd. All rights reserved. Keywords: Computational fluid dynamics; Catalyst design; Heat transfer; Packed bed; Chemical reactors; Reaction engineering
1. Introduction The design of catalyst particles for fixed bed reactors is governed by several competing considerations, such as pressure drop of the bed, catalyst effectiveness for reaction, particle crush strength, and heat transfer efficiency. For methane steam reforming, the gas flow rate is very high, which forces the use of large catalyst particles to reduce pressure drop, and the reactions are highly endothermic, which requires the use of slim tubes so that heat may be supplied efficiently through the tube wall. The fixed bed reactor tubes have low tube-to-particle diameter ratio (N), often in the range of 4–8. Due to the strong diffusional limitations, reaction takes place in a thin layer near the particle surface (Pedernera et al., 2003) so that the particles behave like “egg-shell” catalysts, and activity is observed to be proportional to external geometric surface area (Stitt, 2005). ∗ Corresponding author. Tel.: +1 508 831 5350; fax: +1 508 831 5853.
E-mail address: [email protected] (A.G. Dixon). 0009-2509/$ - see front matter 䉷 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2008.01.017
To improve steam reforming reactor performance, modern catalyst pellet design has evolved from simple cylinders and rings to include pellet shapes with internal holes and external features, such as lobes and grooves (Sie and Krishna, 1998). Larger external surface area for reactant access into the pellets leads to higher catalyst activity, and lower tube wall temperatures and thus longer tube life (Bruno et al., 1988; Stitt, 2005). Lower pressure drop, or higher plant rates at the same pressure drop, can be obtained, as well as lower methane slip and closer approaches to equilibrium (Stitt, 2005). Simulations of steam reformer tubes usually represent the complex pellet shapes by equivalent 1-D shapes such as annular rings (e.g. Pedernera et al., 2003). Considerable efforts are being made to improve the computation of effectiveness factors by defining shape factors for complex 3-D pellet shapes such as multi-hole and multi-lobe cylinders (Mariani et al., 2003) and “wagon-wheel” type tablets (Keegan et al., 2006). These shape factors may then be used in 1-D models to approximate the reaction behavior of 2-D or 3-D pellets.
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The effects of these catalyst designs on tube wall heat transfer have not been studied in detail necessary to understand their consequences for tube temperature profiles and wall temperatures. Classical heat transfer approaches have empirically correlated heat transfer parameters for packings of cylinders and rings (Bauer and Schünder, 1978; Dixon, 1988; Winterberg and Tsotsas, 2000) while more complex shaped particles have been studied more recently, such as “wagon wheels” (Landon et al., 1996) and multi-hole cylinders (Smirnov et al., 2004; Kagyrmanova et al., 2006). The use of CFD simulations in reaction engineering is increasing rapidly (Kuipers and van Swaaij, 1998; Ranade, 2002). In particular, CFD is being recognized and developed as a tool for obtaining detailed flow and scalar transport information in packed beds or representative segments of packed beds. Recent developments in packed bed CFD have been reviewed (Dixon et al., 2006), including automata-based simulation methods such as the lattice Boltzmann method as well as finite volume or finite element solution of the continuum equations of change, for both fluid and solid regions in the original packing geometry. Nijemeisland et al. (2004) used CFD to study the effects of some aspects of cylindrical catalyst pellet design on near-wall heat transfer, under conditions typical of steam reforming. That study focused on a simple qualitative comparison of the temperature and flow fields for four types of particle with different numbers of internal voids, in the form of holes of the same dimensions running longitudinally through the pellets, under constant mass flow rate. The work presented here continues that of the previous paper, and extends it as follows: (i) The tube wall temperature is accurately computed, using a boundary-layer mesh on the tube wall. (ii) Comparisons are presented on the basis of constant pressure drop, in addition to extensions of runs under the constant mass flow rate basis of the earlier study. (iii) The four original particle types are supplemented by two new ones to provide more information on the effects of the diameters of the holes in the particles, on heat transfer. 2. Simulation model A 120◦ wall segment model geometry was created to provide a packed bed environment for a single central test particle near the tube wall. In previous work, we showed that a periodic 120◦ wall segment model with symmetry side conditions gave
good agreement with full bed simulations over the center 60◦ section containing the test particle (Taskin et al., 2007). The CFD approach for packed bed heat transfer was validated by comparison to experiments (Nijemeisland and Dixon, 2001). The particles were equilateral cylinders of size 25.4 mm, and the radius of the segment was 50.8 mm, giving a tube-toparticle-diameter ratio N = 4. The diameter of a standard hole running axially through the particles was 7.28 mm; the hole diameter of the one-big-hole particle was twice the standard diameter, while the hole diameters of the four-small-holes par√ ticles had diameters reduced by a factor 2 of the standard diameter. The focus particle was in the middle row of the three axial rows of particles, and located tangentially near the center of the segment model, at a 45◦ angle to the column axis. This configuration was the one observed most frequently in our study of the packing of cylindrical particles in a tube (Nijemeisland, 2003), which has been confirmed by the more extensive and detailed study presented recently by Zhang et al. (2006). The particles in the top and bottom layers made up the periodic boundaries. Illustrations of the solid, one-hole, three-hole and four-hole particle designs have been shown in our previous work (Nijemeisland et al., 2004). The wall-adjacent particles in an orthographic projection for the new four-small-holes and one-big-hole particles are shown here in Fig. 1, together with the standard four-hole particles for comparison. The particle numbering scheme used in this work is given in the standard four-hole picture, the focus particle was number 2. For the present work, the Fluent CFD code, version 6.2, was used with an unstructured (UNS) tetrahedral mesh, except for the tube wall where a boundary-layer prism mesh was used. This was a similar approach to that of Calis et al. (2001) and Romkes et al. (2003) who used layers of prismatic cells on both tube wall and particles for laminar flow in narrow tubes of spheres. Our boundary-layer treatment for the present turbulent flow consisted of four layers of prisms, first layer height 3 × 10−5 m, corresponding to y + values in the range of 1–2, and a growth factor of 1.2, resulting in a total prism depth of 1.6 × 10−4 m. This enabled the steep temperature gradients at the tube wall to be resolved. At the particle-fluid interfaces prism layers were not used, as the temperatures of the particles and fluid were expected to be very close, in the absence of reaction and at steady-state. To take advantage of the mesh structure, the k– RNG turbulence model was chosen, with the enhanced wall treatment which adapts to either low-Re or coarse meshes (Fluent, 2005). The simulation conditions were the same as for the earlier study. A user-defined fluid was used with the properties
Fig. 1. Orthographic projections of the four-hole, four-small-holes, and one-big-hole particles, with particle numbers for the standard four-hole configurations.
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of a typical inlet steam reforming reaction mixture: = 6.1616 kg/m3 , cp = 2395.38 J/kg K, kf = 0.0876 W/m K, and = 3.0 × 10−5 Pa s. A total pressure of approximately 21.6 bar, and an inlet temperature of 824.15 K were set, along with a wall heat flux of 113.3 kW/m2 . The solid thermal properties, s , cps and ks , were those of alumina. The base mass flow rate corresponded to a particle Reynolds number of approximately 9500 based on superficial velocity and the particle diameter of a sphere of equivalent volume to the cylindrical particle, ignoring voids. The solution of flow and energy equations was decoupled, as any temperature-dependence of the gas properties was not expected to influence flow at the extremely high industrial flow rates simulated here. This assumption allowed the flow to be treated as periodic, independent of the temperature field, and isothermal flow simulations were carried out first, with the temperature field determined subsequently for a fixed flow field. The gas heated up as it passed through the segment, so the temperature field could not be treated as periodic. The first energy simulation for each packing had to use a uniform inlet temperature, which was not realistic for a typical bed position. To overcome this thermal entry effect, the segments were virtually “stacked” with the outlet conditions from one segment becoming the inlet conditions for the next (Nijemeisland and Dixon, 2004). This technique provided a developed temperature field for the test segment. All results presented here are for the third segment in the stack. For analysis of results, the 120◦ wall segment was divided into four sections of 30◦ each along the arc-length of the segment wall. Section 1 corresponds to the left-hand side of the segment geometry as viewed in Fig. 1, while Section 4 corresponds to the right-hand side. The main focus of the analysis below is on the center of the segment surrounding particle 2, in Sections 2 and 3. The temperature profiles reported in this work were generated from these center sections only.
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Fig. 2. Near-wall radial profiles of axial velocity for the solid and four-hole particles, showing the decrease in velocity at the tube wall to satisfy the no-slip condition. Inset shows profiles over entire radius.
Fig. 3. Radial temperature profiles for the solid particles, for standard and fine meshes at constant mass flow rate.
3. Results We have shown pathline plots to illustrate the flow fields and temperature contour plots to illustrate the temperature fields, in several previous publications (Nijemeisland et al., 2004; Dixon et al., 2005, 2006), and we shall not repeat those here. Fig. 2 shows two examples of the near-wall radial profiles of axial superficial velocity, for the solid and four-hole particles, with the complete radial profiles presented in the insert. For constant mass flow rate the superficial velocities must average over the entire radius to the same for both cases, but the lower voidage of the solid packing leads to higher interstitial velocity. The velocities near the wall are higher for the solid cylinders as there is very little solid there and the superficial velocities in the figure are equal to the interstitial values. It should be noted that in both cases the decrease in velocity through the boundary layer down to the no-slip zero velocity at the wall is well captured by the mesh. The viscous boundary layer extends to approximately r/rt = 0.996 by these results, which is in very good agreement with estimates of viscous boundary-layer thickness (Tsotsas and Schlünder, 1990). The wall-affected region is larger, and
velocities at r/rt = 0.984 (r = 0.05 m) and above are clearly decreased due to viscous effects in the transition region. This trend is reinforced in the temperature plots following. Fig. 3 shows temperature profiles for the solid cylinders case with the original and a refined mesh. The finer mesh used eight prism layers on the tube wall, with first layer thickness half that of the standard case. Total thickness of the prism layers remained the same. The temperature profiles (and velocity profiles, not shown) are in good agreement, differences are less than 2% of the total temperature difference between wall and bed center. The standard mesh is accepted as providing a meshindependent solution. The results obtained by use of the prism layers on the tube wall are further illustrated in Fig. 4. The combined unstructured and prism mesh (UNS-PR) with enhanced wall treatment (EWT) of the present study is compared to the completely UNS mesh with standard wall functions (STWF) of the previous study (Nijemeisland et al., 2004) and a third alternative, the same completely UNS mesh with enhanced wall treatment. All three approaches give similar profiles throughout the bed,
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Fig. 4. Radial temperature profiles corresponding to different near-wall approaches, for the solid particles at constant mass flow rate. Inset shows details near the wall.
as shown in the main graph, but they differ close to the wall, as shown in the inset. The UNS (STWF) method over predicts the tube wall temperature by approximately 30 K, and departs significantly from the resolved profile. This result should not be surprising, as the average y + value for this mesh on the tube wall is equal to 14.2, considerably below the recommended range of y + > 30. This means that the wall function over estimates the resistance to heat transfer in the wall-affected region, resulting in a higher tube wall temperature. The UNS (EWT) method, on the other hand, predicts a tube wall temperature approximately 30 K too low. Again, the y + value is above the range recommended for low-Re two-region models (y + < 5) and below the range for the wall function models (y + > 30). Although the EWT method attempts to provide a reasonable compromise in this situation, by interpolating between the two approaches, it is clear that at least in this case satisfactory results are not obtained. A review of CFD simulations of flow in fixed beds (Dixon et al., 2006) found that many studies obtained y + values in this undesirable middle range when UNS meshes were used. The constraints imposed by computing cost usually prevent refining the mesh to obtain y + ≈ 1, while the close approach of the particles in the bed to each other and the wall will usually preclude a mesh coarse enough to allow the proper use of wall functions. For the steam reforming conditions in our study we determined that reliable values of temperature on the tube wall would not be obtained unless prism layers were used to control the y + to approximately unity and the boundary layer was reasonably well resolved. Results for the constant mass flow rate runs are shown in Fig. 5. A direct comparison of the effects of adding more holes is shown, for the solid, one-hole, three-hole, and four-hole particles. It may be seen that the bed temperature profile is relatively flat, with most of the temperature increase confined to a thin region next to the wall. The radial temperature profile for the solid particles is highest, while the wall temperature is lower than those of the multi-hole particles. Similarly, the temperature profile for the one-hole particle is lower, with
Fig. 5. Radial temperature profiles for the solid, one-hole, three-hole, and four-hole particles at constant mass flow rate. Inset shows details near the wall.
the profiles for the three-hole and four-hole particles slightly lower still, and indistinguishable from each other. The tube wall temperatures for the multi-hole particles lie somewhat above those of the solid and one-hole particles. The explanation for these trends is that as more internal void space is added to the particles (which decreases the structural integrity), the bed voidage increases, the pressure drop decreases and the interstitial velocity decreases. The near-wall heat transfer resistance increases, due to the lower interstitial velocity, which causes the tube wall temperature to increase. The trend for the heat transfer in the core of the bed is not as clear, but heat transfer overall worsens as voidage increases; this may be connected to the reduction in lateral displacement of fluid as alternative flow paths through the particles are provided. The apparent disadvantage for heat transfer of increasing the internal voids, as shown in Fig. 5, is a result of the decision to compare different particle types at constant mass flow rate. The lower voidage, however, implies that a higher mass flow rate can be accommodated at the same pressure drop, and thus pumping cost. This suggests that a more useful comparison of the different particles may be made at constant pressure drop, rather than constant mass flow rate. As voidage increases due to the provision of surface area by internal holes in the particles, the pressure drop decreases. A standard pressure drop value was chosen for a second set of simulations with variable mass flow rates, but at fixed pressure drop. This value was obtained by analyzing the pressure drops from the constant mass flow rate CFD simulations. These values were plotted against the group (1 − )/3 that appears in the inertial term of the Ergun equation, and a best-fit line was determined. This was then used with the voidage for the solid particles to calculate the standard pressure drop value for the runs. This procedure produced a standard value consistent with the CFD simulations but not biased toward any individual particle shape. The radial temperature profiles for the four base particles are again shown in Fig. 6, this time for constant P , with the
A.G. Dixon et al. / Chemical Engineering Science 63 (2008) 2219 – 2224
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appears to be overcome by the generally higher fluid velocity corresponding to the higher mass flow rates. These results show that lower tube wall temperatures can be obtained simultaneously with higher catalyst activity due to increased surface area. Fig. 7 presents the effects of changing hole diameter, for the constant P case. The four-hole temperatures lie below those for the four-small-holes in the bed center, and even more strongly in the wall boundary layer. Similarly the one-big-hole temperatures follow the same trends with respect to the onehole values. The decrease in temperature follows from the increase in voidage and mass flow rate (superficial velocity) as discussed above. The differences between the four cases are not very large, however, and these trends may not be significant. Fig. 6. Radial temperature profiles for the solid, one-hole, three-hole, and four-hole particles at constant pressure drop. Inset shows details near the wall.
Fig. 7. Radial temperature profiles for the four-small-holes, one-hole, one-bighole, and four-hole particles at constant pressure drop. Inset shows details near the wall.
insert giving the steep temperature rise across the boundarylayer. The profile for the solid particles is highest, then that for the one-hole particles, and the three-hole and four-hole profiles are almost indistinguishable, similarly to Fig. 5 for constant mass flow rate. In this case, however, the tube wall temperatures are also higher for the solid and one-hole particles than for the three-hole and four-hole particles. Tube wall temperature for the solid particles is approximately 20◦ higher than that for the multi-hole particles. Under the constant pressure drop condition, the mass flow rate increases with voidage, and tube wall temperature decreases as mass flow increases. The velocity in the near-wall region is essentially the interstitial velocity, which is almost constant for constant pressure drop. Since the heat transfer across the boundary region will be determined by the velocity there, it is also constant for this case. The higher flow rates through the bed for the single- and multi-holed particles compared to the solid cylinder case lead to higher fluid radial dispersion, and thus higher bed heat transfer, as the voidage increases. The decrease in fluid being laterally displaced around particles, as more internal flow paths are made available,
4. Conclusions The use of unstructured meshes that give y + values in the intermediate range of 5–30 gives tube wall temperatures that are not reliable, regardless of the wall treatment used, for the k– RNG model used here. The use of even a small number of prism layers, to control the y + value and resolve the boundary layer to some extent, appears to be a good approach for fixed bed CFD. Comparisons of the solid, one-hole, three-hole, and four-hole particles under constant mass flow rate appear to show that the solid particles give simultaneously higher core bed temperatures and lower tube wall temperatures. The one-hole particles appear to give the next best heat transfer performance, followed by the three-hole and four-hole particles which perform almost identically. However, this assessment neglects the aspect of pressure drop, which is higher for the solid particles and decreases with increasing void fraction, and is lowest for the four-hole particles. If comparisons are made under conditions of constant pressure drop, then the solid particles give the highest bed temperatures and the highest tube wall temperatures, followed by the one-hole particles and then the three-hole and four-hole particles, which again give almost identical temperatures. Thus, for comparable pressure drop costs, the multi-holed particles give a lower tube wall temperature, which prolongs tube life, at the cost of slightly worse heat transfer into the bed. The effects of changing particle hole sizes, as studied here via the four-small-holes and one-big-hole particles, were small. The comparisons presented here were made under nonreacting conditions, to examine the heat transfer behavior in isolation. Tube wall and bed temperatures, however, will also be affected by the presence of the endothermic steam reforming reactions in the catalyst particles, which may influence the comparative performance of the different particle geometries. This aspect is being investigated in a parallel study that includes heat sinks inside the particles. Notation cp cps k
fluid specific heat, J/kg K solid specific heat, J/kg K turbulent kinetic energy, J/kg
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kf ks N P r rt T vz y+
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fluid thermal conductivity, w/m K particle thermal conductivity, w/m K tube-to-particle diameter ratio pressure drop, Pa radial coordinate, m tube radius, m temperature, K axial superficial velocity, m/s dimensionless distance from wall
Greek letters s
bed voidage turbulence dissipation rate, J/kg s fluid viscosity, kg/m s fluid density, kg/m3 solid density, kg/m3
References Bauer, R., Schünder, E.U., 1978. Effective radial thermal conductivity of packings in gas flow. Part I convective transport coefficient. International Chemical Engineering 18, 181–188. Bruno, S.P., Barreto, G.F., Gonzalez, M.G., 1988. Effect of the geometric characteristics of commercial catalysts for steam reforming. The Chemical Engineering Journal 39, 147–156. Calis, H.P.A., Nijenhuis, J., Paikert, B.C., Dautzenberg, F.M., Van den Bleek, C.M., 2001. CFD modeling and experimental validation of pressure drop and flow profile in a novel structured catalytic reactor packing. Chemical Engineering Science 56, 1713–1720. Dixon, A.G., 1988. Wall and particle-shape effects on heat transfer in packed beds. Chemical Engineering Communications 71, 217–237. Dixon, A.G., Nijemeisland, M., Stitt, E.H., 2005. CFD study of heat transfer near and at the wall of a fixed bed reactor tube—effect of wall conduction. Industrial and Engineering Chemistry Research 44, 6342–6353. Dixon, A.G., Nijemeisland, M., Stitt, E.H., 2006. Packed tubular reactor modelling and catalyst design using computational fluid dynamics. Advances in Chemical Engineering 31, 307–389. Fluent, 2005. User’s Guide version 6.2, Fluent Inc., Lebanon, NH. Kagyrmanova, A.P., Zolotarskii, I.A., Vernikovskaya, N.V., Smirnov, E.I., Kuz’min, V.A., Chumakova, N.A., 2006. Modeling of steam reforming of natural gas using catalysts with grains of complex shapes. Theoretical Foundations of Chemical Engineering 40, 155–167. Keegan, S.D., Mariani, N.J., Martinez, O.M., Barreto, G.F., 2006. Behavior of catalytic pellets at high reaction rates. The effect of edges. Industrial and Engineering Chemistry Research 45, 85–97. Kuipers, J.A.M., van Swaaij, W.P.M., 1998. Computational fluid dynamics applied to chemical reaction engineering. Advances in Chemical Engineering 24, 227–328.
Landon, V.G., Hebert, L.A., Adams, C.B., 1996. Heat transfer measurement for industrial packed bed tubular reactor modeling and design. in: Heat Transfer—Houston 1996. 31st National Heat Transfer Conference. AIChE Symposium Series, Houston, p. 134. Mariani, N.J., Keegan, S.D., Martinez, O.M., Barreto, G.F., 2003. A onedimensional equivalent model to evaluate overall reaction rates in catalytic pellets. Transactions of the Institution of Chemical Engineers 81 (Part A), 1033–1042. Nijemeisland, M., 2003. Influences of catalyst particle geometry on fixed bed reactor near-wall heat transfer using CFD. Ph.D. Dissertation, Worcester Polytechnic Institute, Worcester, MA. Nijemeisland, M., Dixon, A.G., 2001. Comparison of CFD simulations to experiment for convective heat transfer in a gas-solid fixed bed. Chemical Engineering Journal 82, 231–246. Nijemeisland, M., Dixon, A.G., 2004. CFD study of fluid flow and wall heat transfer in a fixed bed of spheres. American Institute of Chemical Engineers Journal 50, 906–921. Nijemeisland, M., Dixon, A.G., Stitt, E.H., 2004. Catalyst design by CFD for heat transfer and reaction in steam reforming. Chemical Engineering Science 59, 5185–5191. Pedernera, M.N., Piña, J., Borio, D.O., Bucalá, V., 2003. Use of a heterogeneous two-dimensional model to improve the primary steam reformer performance. Chemical Engineering Journal 94, 29–40. Ranade, V., 2002. Computational Flow Modeling for Chemical Reactor Engineering. Academic Press, New York. Romkes, S.J.P., Dautzenberg, F.M., van den Bleek, C.M., Calis, H.P.A., 2003. CFD modeling and experimental validation of particle-to-fluid mass and heat transfer in a packed bed at very low channel to particle diameter ratio. Chemical Engineering Journal 96, 3–13. Sie, S.T., Krishna, R., 1998. Process development and scaleup: II. Catalyst design strategy. Reviews in Chemical Engineering 14, 159–202. Smirnov, E.I., Kuzmin, V.A., Zolotarskii, I.A., 2004. Radial thermal conductivity in cylindrical beds packed by shaped particles. Chemical Engineering Research and Design 82 (A2), 293–296. Stitt, E.H., 2005. Reactor technology for syngas and hydrogen. In: Derouane, E., Parmon, V., Lemos, F., Ramoa-Ribiero, F. (Eds.), Sustainable Strategies for the Upgrading of Natural Gas: Fundamentals, Challenges and Opportunities, NATO Science Series II, vol. 191. Kluwer Academic Publishers, Dordrecht, pp. 185–216. Taskin, M.E., Dixon, A.G., Stitt, E.H., 2007. CFD study of fluid flow and heat transfer in a fixed bed of cylinders. Numerical Heat Transfer A 52, 203–218. Tsotsas, E., Schlünder, E.U., 1990. Heat transfer in packed beds with fluid flow: remarks on the meaning and the calculation of a heat transfer coefficient at the wall. Chemical Engineering Science 45, 819–837. Winterberg, M., Tsotsas, E., 2000. Correlations for effective heat transport coefficients in beds packed with cylindrical particles. Chemical Engineering Science 55, 5937–5943. Zhang, W., Thompson, K.E., Reed, A.H., Beenken, L., 2006. Relationship between packing structure and porosity in fixed beds of equilateral cylindrical particles. Chemical Engineering Science 61, 8060–8074.
Wall-to-particle heat transfer in steam reformer tubes: CFD comparison of catalyst particles Anthony G. Dixon a,∗ , M. Ertan Taskin a , Michiel Nijemeisland b , E. Hugh Stitt b a Department of Chemical Engineering, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609-2280, USA b Johnson Matthey, P.O. Box 1, Belasis Avenue, Billingham, Cleveland TS23 1LB, UK
Received 25 July 2007; received in revised form 8 January 2008; accepted 11 January 2008 Available online 20 January 2008
Abstract Computational fluid dynamics (CFD) was used to simulate non-reacting heat transfer in a steam reforming packed reactor tube of tubeto-particle diameter ratio (N) equal to 4, with cylindrical multi-hole catalyst particles. These simulations extend those of our previous study [Nijemeisland, M., Dixon, A.G., Stitt, E.H., 2004. Catalyst design by CFD for heat transfer and reaction in steam reforming. Chemical Engineering Science 59, 5185–5191] to provide accurate tube wall temperatures, runs at constant pressure drop in addition to those at constant mass flow rate and simulations of particles with different sizes of holes. At constant pressure drop, particles with higher void fractions allowed higher mass flow rates, resulting in tube wall temperatures and radial temperature profiles in order: solid cylinders > one-hole particles > multi-hole particles. Little difference was seen between three-hole and four-hole particles. The particles with multiple holes gave a substantial reduction in tube wall temperature, with only a small decrease in core tube heat transfer. The effect of hole size was small, for the cases investigated in this study. 䉷 2008 Elsevier Ltd. All rights reserved. Keywords: Computational fluid dynamics; Catalyst design; Heat transfer; Packed bed; Chemical reactors; Reaction engineering
1. Introduction The design of catalyst particles for fixed bed reactors is governed by several competing considerations, such as pressure drop of the bed, catalyst effectiveness for reaction, particle crush strength, and heat transfer efficiency. For methane steam reforming, the gas flow rate is very high, which forces the use of large catalyst particles to reduce pressure drop, and the reactions are highly endothermic, which requires the use of slim tubes so that heat may be supplied efficiently through the tube wall. The fixed bed reactor tubes have low tube-to-particle diameter ratio (N), often in the range of 4–8. Due to the strong diffusional limitations, reaction takes place in a thin layer near the particle surface (Pedernera et al., 2003) so that the particles behave like “egg-shell” catalysts, and activity is observed to be proportional to external geometric surface area (Stitt, 2005). ∗ Corresponding author. Tel.: +1 508 831 5350; fax: +1 508 831 5853.
E-mail address: [email protected] (A.G. Dixon). 0009-2509/$ - see front matter 䉷 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2008.01.017
To improve steam reforming reactor performance, modern catalyst pellet design has evolved from simple cylinders and rings to include pellet shapes with internal holes and external features, such as lobes and grooves (Sie and Krishna, 1998). Larger external surface area for reactant access into the pellets leads to higher catalyst activity, and lower tube wall temperatures and thus longer tube life (Bruno et al., 1988; Stitt, 2005). Lower pressure drop, or higher plant rates at the same pressure drop, can be obtained, as well as lower methane slip and closer approaches to equilibrium (Stitt, 2005). Simulations of steam reformer tubes usually represent the complex pellet shapes by equivalent 1-D shapes such as annular rings (e.g. Pedernera et al., 2003). Considerable efforts are being made to improve the computation of effectiveness factors by defining shape factors for complex 3-D pellet shapes such as multi-hole and multi-lobe cylinders (Mariani et al., 2003) and “wagon-wheel” type tablets (Keegan et al., 2006). These shape factors may then be used in 1-D models to approximate the reaction behavior of 2-D or 3-D pellets.
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The effects of these catalyst designs on tube wall heat transfer have not been studied in detail necessary to understand their consequences for tube temperature profiles and wall temperatures. Classical heat transfer approaches have empirically correlated heat transfer parameters for packings of cylinders and rings (Bauer and Schünder, 1978; Dixon, 1988; Winterberg and Tsotsas, 2000) while more complex shaped particles have been studied more recently, such as “wagon wheels” (Landon et al., 1996) and multi-hole cylinders (Smirnov et al., 2004; Kagyrmanova et al., 2006). The use of CFD simulations in reaction engineering is increasing rapidly (Kuipers and van Swaaij, 1998; Ranade, 2002). In particular, CFD is being recognized and developed as a tool for obtaining detailed flow and scalar transport information in packed beds or representative segments of packed beds. Recent developments in packed bed CFD have been reviewed (Dixon et al., 2006), including automata-based simulation methods such as the lattice Boltzmann method as well as finite volume or finite element solution of the continuum equations of change, for both fluid and solid regions in the original packing geometry. Nijemeisland et al. (2004) used CFD to study the effects of some aspects of cylindrical catalyst pellet design on near-wall heat transfer, under conditions typical of steam reforming. That study focused on a simple qualitative comparison of the temperature and flow fields for four types of particle with different numbers of internal voids, in the form of holes of the same dimensions running longitudinally through the pellets, under constant mass flow rate. The work presented here continues that of the previous paper, and extends it as follows: (i) The tube wall temperature is accurately computed, using a boundary-layer mesh on the tube wall. (ii) Comparisons are presented on the basis of constant pressure drop, in addition to extensions of runs under the constant mass flow rate basis of the earlier study. (iii) The four original particle types are supplemented by two new ones to provide more information on the effects of the diameters of the holes in the particles, on heat transfer. 2. Simulation model A 120◦ wall segment model geometry was created to provide a packed bed environment for a single central test particle near the tube wall. In previous work, we showed that a periodic 120◦ wall segment model with symmetry side conditions gave
good agreement with full bed simulations over the center 60◦ section containing the test particle (Taskin et al., 2007). The CFD approach for packed bed heat transfer was validated by comparison to experiments (Nijemeisland and Dixon, 2001). The particles were equilateral cylinders of size 25.4 mm, and the radius of the segment was 50.8 mm, giving a tube-toparticle-diameter ratio N = 4. The diameter of a standard hole running axially through the particles was 7.28 mm; the hole diameter of the one-big-hole particle was twice the standard diameter, while the hole diameters of the four-small-holes par√ ticles had diameters reduced by a factor 2 of the standard diameter. The focus particle was in the middle row of the three axial rows of particles, and located tangentially near the center of the segment model, at a 45◦ angle to the column axis. This configuration was the one observed most frequently in our study of the packing of cylindrical particles in a tube (Nijemeisland, 2003), which has been confirmed by the more extensive and detailed study presented recently by Zhang et al. (2006). The particles in the top and bottom layers made up the periodic boundaries. Illustrations of the solid, one-hole, three-hole and four-hole particle designs have been shown in our previous work (Nijemeisland et al., 2004). The wall-adjacent particles in an orthographic projection for the new four-small-holes and one-big-hole particles are shown here in Fig. 1, together with the standard four-hole particles for comparison. The particle numbering scheme used in this work is given in the standard four-hole picture, the focus particle was number 2. For the present work, the Fluent CFD code, version 6.2, was used with an unstructured (UNS) tetrahedral mesh, except for the tube wall where a boundary-layer prism mesh was used. This was a similar approach to that of Calis et al. (2001) and Romkes et al. (2003) who used layers of prismatic cells on both tube wall and particles for laminar flow in narrow tubes of spheres. Our boundary-layer treatment for the present turbulent flow consisted of four layers of prisms, first layer height 3 × 10−5 m, corresponding to y + values in the range of 1–2, and a growth factor of 1.2, resulting in a total prism depth of 1.6 × 10−4 m. This enabled the steep temperature gradients at the tube wall to be resolved. At the particle-fluid interfaces prism layers were not used, as the temperatures of the particles and fluid were expected to be very close, in the absence of reaction and at steady-state. To take advantage of the mesh structure, the k– RNG turbulence model was chosen, with the enhanced wall treatment which adapts to either low-Re or coarse meshes (Fluent, 2005). The simulation conditions were the same as for the earlier study. A user-defined fluid was used with the properties
Fig. 1. Orthographic projections of the four-hole, four-small-holes, and one-big-hole particles, with particle numbers for the standard four-hole configurations.
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of a typical inlet steam reforming reaction mixture: = 6.1616 kg/m3 , cp = 2395.38 J/kg K, kf = 0.0876 W/m K, and = 3.0 × 10−5 Pa s. A total pressure of approximately 21.6 bar, and an inlet temperature of 824.15 K were set, along with a wall heat flux of 113.3 kW/m2 . The solid thermal properties, s , cps and ks , were those of alumina. The base mass flow rate corresponded to a particle Reynolds number of approximately 9500 based on superficial velocity and the particle diameter of a sphere of equivalent volume to the cylindrical particle, ignoring voids. The solution of flow and energy equations was decoupled, as any temperature-dependence of the gas properties was not expected to influence flow at the extremely high industrial flow rates simulated here. This assumption allowed the flow to be treated as periodic, independent of the temperature field, and isothermal flow simulations were carried out first, with the temperature field determined subsequently for a fixed flow field. The gas heated up as it passed through the segment, so the temperature field could not be treated as periodic. The first energy simulation for each packing had to use a uniform inlet temperature, which was not realistic for a typical bed position. To overcome this thermal entry effect, the segments were virtually “stacked” with the outlet conditions from one segment becoming the inlet conditions for the next (Nijemeisland and Dixon, 2004). This technique provided a developed temperature field for the test segment. All results presented here are for the third segment in the stack. For analysis of results, the 120◦ wall segment was divided into four sections of 30◦ each along the arc-length of the segment wall. Section 1 corresponds to the left-hand side of the segment geometry as viewed in Fig. 1, while Section 4 corresponds to the right-hand side. The main focus of the analysis below is on the center of the segment surrounding particle 2, in Sections 2 and 3. The temperature profiles reported in this work were generated from these center sections only.
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Fig. 2. Near-wall radial profiles of axial velocity for the solid and four-hole particles, showing the decrease in velocity at the tube wall to satisfy the no-slip condition. Inset shows profiles over entire radius.
Fig. 3. Radial temperature profiles for the solid particles, for standard and fine meshes at constant mass flow rate.
3. Results We have shown pathline plots to illustrate the flow fields and temperature contour plots to illustrate the temperature fields, in several previous publications (Nijemeisland et al., 2004; Dixon et al., 2005, 2006), and we shall not repeat those here. Fig. 2 shows two examples of the near-wall radial profiles of axial superficial velocity, for the solid and four-hole particles, with the complete radial profiles presented in the insert. For constant mass flow rate the superficial velocities must average over the entire radius to the same for both cases, but the lower voidage of the solid packing leads to higher interstitial velocity. The velocities near the wall are higher for the solid cylinders as there is very little solid there and the superficial velocities in the figure are equal to the interstitial values. It should be noted that in both cases the decrease in velocity through the boundary layer down to the no-slip zero velocity at the wall is well captured by the mesh. The viscous boundary layer extends to approximately r/rt = 0.996 by these results, which is in very good agreement with estimates of viscous boundary-layer thickness (Tsotsas and Schlünder, 1990). The wall-affected region is larger, and
velocities at r/rt = 0.984 (r = 0.05 m) and above are clearly decreased due to viscous effects in the transition region. This trend is reinforced in the temperature plots following. Fig. 3 shows temperature profiles for the solid cylinders case with the original and a refined mesh. The finer mesh used eight prism layers on the tube wall, with first layer thickness half that of the standard case. Total thickness of the prism layers remained the same. The temperature profiles (and velocity profiles, not shown) are in good agreement, differences are less than 2% of the total temperature difference between wall and bed center. The standard mesh is accepted as providing a meshindependent solution. The results obtained by use of the prism layers on the tube wall are further illustrated in Fig. 4. The combined unstructured and prism mesh (UNS-PR) with enhanced wall treatment (EWT) of the present study is compared to the completely UNS mesh with standard wall functions (STWF) of the previous study (Nijemeisland et al., 2004) and a third alternative, the same completely UNS mesh with enhanced wall treatment. All three approaches give similar profiles throughout the bed,
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Fig. 4. Radial temperature profiles corresponding to different near-wall approaches, for the solid particles at constant mass flow rate. Inset shows details near the wall.
as shown in the main graph, but they differ close to the wall, as shown in the inset. The UNS (STWF) method over predicts the tube wall temperature by approximately 30 K, and departs significantly from the resolved profile. This result should not be surprising, as the average y + value for this mesh on the tube wall is equal to 14.2, considerably below the recommended range of y + > 30. This means that the wall function over estimates the resistance to heat transfer in the wall-affected region, resulting in a higher tube wall temperature. The UNS (EWT) method, on the other hand, predicts a tube wall temperature approximately 30 K too low. Again, the y + value is above the range recommended for low-Re two-region models (y + < 5) and below the range for the wall function models (y + > 30). Although the EWT method attempts to provide a reasonable compromise in this situation, by interpolating between the two approaches, it is clear that at least in this case satisfactory results are not obtained. A review of CFD simulations of flow in fixed beds (Dixon et al., 2006) found that many studies obtained y + values in this undesirable middle range when UNS meshes were used. The constraints imposed by computing cost usually prevent refining the mesh to obtain y + ≈ 1, while the close approach of the particles in the bed to each other and the wall will usually preclude a mesh coarse enough to allow the proper use of wall functions. For the steam reforming conditions in our study we determined that reliable values of temperature on the tube wall would not be obtained unless prism layers were used to control the y + to approximately unity and the boundary layer was reasonably well resolved. Results for the constant mass flow rate runs are shown in Fig. 5. A direct comparison of the effects of adding more holes is shown, for the solid, one-hole, three-hole, and four-hole particles. It may be seen that the bed temperature profile is relatively flat, with most of the temperature increase confined to a thin region next to the wall. The radial temperature profile for the solid particles is highest, while the wall temperature is lower than those of the multi-hole particles. Similarly, the temperature profile for the one-hole particle is lower, with
Fig. 5. Radial temperature profiles for the solid, one-hole, three-hole, and four-hole particles at constant mass flow rate. Inset shows details near the wall.
the profiles for the three-hole and four-hole particles slightly lower still, and indistinguishable from each other. The tube wall temperatures for the multi-hole particles lie somewhat above those of the solid and one-hole particles. The explanation for these trends is that as more internal void space is added to the particles (which decreases the structural integrity), the bed voidage increases, the pressure drop decreases and the interstitial velocity decreases. The near-wall heat transfer resistance increases, due to the lower interstitial velocity, which causes the tube wall temperature to increase. The trend for the heat transfer in the core of the bed is not as clear, but heat transfer overall worsens as voidage increases; this may be connected to the reduction in lateral displacement of fluid as alternative flow paths through the particles are provided. The apparent disadvantage for heat transfer of increasing the internal voids, as shown in Fig. 5, is a result of the decision to compare different particle types at constant mass flow rate. The lower voidage, however, implies that a higher mass flow rate can be accommodated at the same pressure drop, and thus pumping cost. This suggests that a more useful comparison of the different particles may be made at constant pressure drop, rather than constant mass flow rate. As voidage increases due to the provision of surface area by internal holes in the particles, the pressure drop decreases. A standard pressure drop value was chosen for a second set of simulations with variable mass flow rates, but at fixed pressure drop. This value was obtained by analyzing the pressure drops from the constant mass flow rate CFD simulations. These values were plotted against the group (1 − )/3 that appears in the inertial term of the Ergun equation, and a best-fit line was determined. This was then used with the voidage for the solid particles to calculate the standard pressure drop value for the runs. This procedure produced a standard value consistent with the CFD simulations but not biased toward any individual particle shape. The radial temperature profiles for the four base particles are again shown in Fig. 6, this time for constant P , with the
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appears to be overcome by the generally higher fluid velocity corresponding to the higher mass flow rates. These results show that lower tube wall temperatures can be obtained simultaneously with higher catalyst activity due to increased surface area. Fig. 7 presents the effects of changing hole diameter, for the constant P case. The four-hole temperatures lie below those for the four-small-holes in the bed center, and even more strongly in the wall boundary layer. Similarly the one-big-hole temperatures follow the same trends with respect to the onehole values. The decrease in temperature follows from the increase in voidage and mass flow rate (superficial velocity) as discussed above. The differences between the four cases are not very large, however, and these trends may not be significant. Fig. 6. Radial temperature profiles for the solid, one-hole, three-hole, and four-hole particles at constant pressure drop. Inset shows details near the wall.
Fig. 7. Radial temperature profiles for the four-small-holes, one-hole, one-bighole, and four-hole particles at constant pressure drop. Inset shows details near the wall.
insert giving the steep temperature rise across the boundarylayer. The profile for the solid particles is highest, then that for the one-hole particles, and the three-hole and four-hole profiles are almost indistinguishable, similarly to Fig. 5 for constant mass flow rate. In this case, however, the tube wall temperatures are also higher for the solid and one-hole particles than for the three-hole and four-hole particles. Tube wall temperature for the solid particles is approximately 20◦ higher than that for the multi-hole particles. Under the constant pressure drop condition, the mass flow rate increases with voidage, and tube wall temperature decreases as mass flow increases. The velocity in the near-wall region is essentially the interstitial velocity, which is almost constant for constant pressure drop. Since the heat transfer across the boundary region will be determined by the velocity there, it is also constant for this case. The higher flow rates through the bed for the single- and multi-holed particles compared to the solid cylinder case lead to higher fluid radial dispersion, and thus higher bed heat transfer, as the voidage increases. The decrease in fluid being laterally displaced around particles, as more internal flow paths are made available,
4. Conclusions The use of unstructured meshes that give y + values in the intermediate range of 5–30 gives tube wall temperatures that are not reliable, regardless of the wall treatment used, for the k– RNG model used here. The use of even a small number of prism layers, to control the y + value and resolve the boundary layer to some extent, appears to be a good approach for fixed bed CFD. Comparisons of the solid, one-hole, three-hole, and four-hole particles under constant mass flow rate appear to show that the solid particles give simultaneously higher core bed temperatures and lower tube wall temperatures. The one-hole particles appear to give the next best heat transfer performance, followed by the three-hole and four-hole particles which perform almost identically. However, this assessment neglects the aspect of pressure drop, which is higher for the solid particles and decreases with increasing void fraction, and is lowest for the four-hole particles. If comparisons are made under conditions of constant pressure drop, then the solid particles give the highest bed temperatures and the highest tube wall temperatures, followed by the one-hole particles and then the three-hole and four-hole particles, which again give almost identical temperatures. Thus, for comparable pressure drop costs, the multi-holed particles give a lower tube wall temperature, which prolongs tube life, at the cost of slightly worse heat transfer into the bed. The effects of changing particle hole sizes, as studied here via the four-small-holes and one-big-hole particles, were small. The comparisons presented here were made under nonreacting conditions, to examine the heat transfer behavior in isolation. Tube wall and bed temperatures, however, will also be affected by the presence of the endothermic steam reforming reactions in the catalyst particles, which may influence the comparative performance of the different particle geometries. This aspect is being investigated in a parallel study that includes heat sinks inside the particles. Notation cp cps k
fluid specific heat, J/kg K solid specific heat, J/kg K turbulent kinetic energy, J/kg
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kf ks N P r rt T vz y+
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fluid thermal conductivity, w/m K particle thermal conductivity, w/m K tube-to-particle diameter ratio pressure drop, Pa radial coordinate, m tube radius, m temperature, K axial superficial velocity, m/s dimensionless distance from wall
Greek letters s
bed voidage turbulence dissipation rate, J/kg s fluid viscosity, kg/m s fluid density, kg/m3 solid density, kg/m3
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