Article pubs.acs.org/IECR
Modeling of Dual-Zone Structured Reactors for Natural Gas Steam Reforming Juray De Wilde*,† and Gilbert F. Froment‡ †
Division of Materials and Process Engineering (IMMC-IMAP), Université catholique de Louvain, Place Sainte Barbe 2, B-1348 Louvain-la-Neuve, Belgium ‡ Chemical Engineering Department, Texas A&M University, 3122 TAMU, College Station, Texas 77843, United States ABSTRACT: The performance of dual-zone structured catalytic reactors in natural gas steam reforming under typical commercial operating conditions is evaluated by means of detailed Computational Fluid Dynamics (CFD) simulations, including detailed reaction kinetics. A hybrid CFD model is developed, combining a porous medium type description of the reactor core zone and a detailed description of the reactor internals in the near-wall region. The porous medium model parameters are determined from specific pressure drop measurements in a wide mass flow rate range. Additional pressure drop measurements with the complete structure and with pellets serve for CFD model validation. The influence of the flow and catalyst distribution over the different reactor zones and the influence of the catalyst loading are then numerically studied. A comparison with a conventional packed bed reactor is made, and advantages of the dual-zone structured reactors with respect to pressure drop, heat transfer, and catalyst effectiveness are illustrated. suspended in a gas fired furnace.2 To achieve an optimal heat flux profile and to avoid pronounced radial temperature gradients a tube diameter of 4 in. (10.16 cm) is generally retained. Nevertheless, the throughput is limited by the heat transfer from the tube inner wall to the process gas and by constraints on the tube outer wall temperature. The size of the catalyst particles follows from a trade-off of the pressure drop over the reactor and intraparticle diffusion limitations.4 In steam reforming the catalyst effectiveness is quite low, and this has led to catalyst particles with a layer of active material on an inert core. To reduce intraparticle diffusion limitations and increase the catalyst effectiveness, cylindrical catalyst particles with one or multiple perforations are used. Lobed particles have been introduced to increase the geometric surface area. Particle shapes have also been optimized with respect to pressure drop. Structured catalytic reactors have been developed to deal with the throughput limitations of conventional packed bed reactors.5 A thin layer of catalyst is coated on the reactor internals, thus reducing or eliminating intraparticle diffusion limitations. The reactor internals are designed to minimize the pressure drop over the reactor and intensify the heat transfer between the tube inner wall and the process gas. Reactor internals made of highly conductive materials and conductive monolithic catalysts have also been considered.6 In the Catacel reactor, axial corrugated channels are used.7 Dual-zone structured reactors use a different concept and contain a core and a casing which are interconnected. In so-called ZoneFlow reactors (Figure 1), the core consists of stacked perforated smooth and corrugated cones, the casing of sectors with centrifugal and centripetal blades guiding the flow alternatively
1. INTRODUCTION Steam reforming of natural gas is the most important process for the large-scale production of hydrogen and synthesis gas, a
Figure 1. (a) Classical packed bed and (b) ZoneFlow type structured reactor with casing and core.
mixture of CO and hydrogen. Whereas synthesis gas is used for the production of methanol, aldehydes, or synthetic fuels, hydrogen is used in ammonia synthesis and different hydrogenation and hydrotreatment processes.1 The commercial extraction of shale gas has renewed interest in the conversion of natural gas. Steam reforming of natural gas uses Ni/MgAl2O4 as a catalyst.2 Pt and Rh on various carriers have been shown to be active as well1,3 but are relatively expensive and more sensitive to poisoning by sulfur. The reactions producing CO and H2 are strongly endothermic, and this has led to the choice of a multitubular fixed bed reactor and a large number of tubes © XXXX American Chemical Society
Received: May 9, 2013 Revised: August 27, 2013 Accepted: September 5, 2013
A
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toward and away from the wall, thus improving heat transfer with the latter.8 Radial fins partially separate the centrifugal and centripetal sectors in the casing. Communication between them is achieved via a small spacing between the casing and the tubular reactor wall but also via the reactor core. The permeability of the core can be adapted to optimize the distribution of the flow between the core and the casing. In prior work, a first ZoneFlow reactor design and its performance in methane steam reforming under typical commercial operating conditions was studied by means of detailed Computational Fluid Dynamics (CFD) simulations.9,10 The present paper deals with 2 variants, referred to as R1 and R2. These two reactors essentially differ in the design of the core, i.e. the number and size of the holes.10 The R2 reactor core has larger holes and achieves an intrinsically lower pressure drop than the R1 reactor core. Therefore, it is expected that relatively more flow is directed toward the casing in the R1 reactor, improving heat transfer between the tubular reactor wall and the process gas and reactor internals in the casing. In the present paper, the performance of these reactors in methane steam reforming under typical commercial operating conditions was evaluated by means of detailed simulations using a hybrid CFD model. These aimed in particular at illustrating the influence of the catalyst loading, the permeability of the core, and the catalyst distribution between core and casing.
Table 1. Reactions Considered and Reaction Rate Expressions Useda reactions and reaction rate expressions
CH4 + H 2O ⇔ CO + 3H 2
(Reaction-1)
⎛ pH3 pCO ⎞ k1 ⎜ 2 ⎟/(DEN)2 r1 = 2.5 − p p K1 ⎟⎠ pH ⎜⎝ CH4 H2O 2 (water gas shift)CO + H 2O ⇔ CO2 + H 2 r2 =
(Reaction-2)
pH pCO ⎞ k2 ⎛ − 2 2 ⎟/(DEN)2 ⎜p p pH ⎝ CO H2O K2 ⎠ 2
CH4 + 2H 2O ⇔ CO2 + 4H 2
(Reaction-3)
⎛ pH4 pCO ⎞ k3 ⎜ 2 2 2⎟ r3 = 3.5 − p p /(DEN)2 CH H O K3 ⎟⎠ pH ⎜⎝ 4 2 2 with: DEN = 1 + K COpCO + K H2pH + K CH4pCH + K H2OpH O /pH 2
4
2
2
a
Derivation, assumptions, and the thermodynamic and rate constants can be found in Xu and Froment.12
Stokes (RANS) equations for the casing can be written as follows:4 Species continuity equations: ∇·(ρg mA u ̅ ) = ∇·(ρg DAm,eff ∇mA )
2. HYBRID CFD MODEL In previous CFD work on the ZoneFlow reactor, all details of the reactor geometry were included, and the single phase
(1)
Total mass continuity equation:
∇·(ρg u ̅ ) = 0
(2)
Momentum continuity equation: ∇·(ρg uu ̅ ̅ ) = −∇Peff + ∇·( σeff ) + b ̅
(3)
Energy continuity equation: ∇·(ρg Eu ̅ ) = −∇·(uP ̅ eff ) + ∇·( σeff · u ̅ ) + ∇·(λf,eff ∇T ) − ∇·(∑ hiJi )
(4)
i
At the temperatures typically encountered inside the simulated SMR reactor tube, the contribution of radiation to heat transfer is negligible, as shown by De Wilde and Froment.11 On the reactor internals coated with catalyst, interfacial mass transfer equals in the steady state the consumption or production of species A by reactions in the catalyst layer, so that the boundary condition for eq 1 can be written as
Figure 2. Hybrid CFD model with a detailed description of the geometry of the casing and a porous medium type description of the core.
s ̃ (mAs kg,A − mA ) = ρs dcatMA ∑ αA, kηk rk(m̅ ss , Ts) k
(5)
The overall unit in (5) is [kg A/(m interface • s)]. The reaction scheme and the intrinsic reaction rate equations used in the present work were derived by Xu and Froment12 and are summarized in Table 1. The thermodynamic and rate constants for the ICI 46-9 S catalyst (NiO: 16 wt %; K2O: 2 wt % in bulk, 1.2 wt % at the surface) are also given in Xu and Froment.12 Intraparticle diffusion limitations for the different reactions are accounted for through the mean catalyst effectiveness factors. They were obtained from the typical intraparticle concentration profiles calculated by Xu and Froment.13 For reactions 1 and 3 an effectiveness factor of 0.5 is used, for reaction 2 an effectiveness factor of 1. Equation 5 allows calculating the 2
Reynolds-Averaged Navier−Stokes (RANS) equations were solved together with an appropriate turbulence model and detailed reaction kinetics.9 The large number of small holes in the versions dealt with here requires an unrealistic meshing and number of grid cells. Even with multiple processors in parallel, the resulting computation time would be unrealistically high. Therefore, a hybrid CFD model, illustrated in Figure 2, was developed. It describes the geometry of the casing in detail but models the core as a porous continuum medium. 2.1. Modeling Mass, Heat and Momentum Transfer in the Casing. The steady state Reynolds-Averaged Navier− B
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species concentrations at the catalyst surface, msAs. Similarly, for eq 4, on reactor internals coated with catalyst, in the steady state, interfacial heat transfer equals the heat effect of the reactions hf (Ts − T ) = ρs dcat ∑
ηk rk(m̅ ss ,
Ts)( −ΔHk)
k
core core ∇·(ε coreρg uu σeff ) + ε coreb ̅ ̅ ̅ ) = −ε ∇Peff + ∇·(ε
⎛μ K 2ρg ⎞ −⎜ + | u |⎟ u 2 ̅⎠ ̅ ⎝ K1
from which the interstitial velocity in the porous medium core model can be calculated. The last two terms in 11 describe the pressure drop in the porous medium and are usually dominant. The term containing K1 represents the laminar contribution, the term containing K2 the turbulent contribution. K1 is the socalled permeability, with 1/K1 the viscous resistance, and K2 is the inertial resistance factor. For a packed bed of spherical particles, K1 and K2 have been modeled as a function of the bed porosity and the particle diameter:18
(6)
where the overall unit is [J/(m2 interface•s)]. Whereas under commercial operating conditions, interfacial mass transfer ̃ → ∞ and msAs limitations can usually be neglected (i.e., kg,A = mA), this is not the case for interfacial heat transfer limitations.4 At the externally heated tubular reactor wall, a heat flux is calculated based on the imposed axial profile of the inner wall temperature and the calculated species concentration, flow, and temperature fields: Q hw = hf (Thw,i − T )
K1 =
The heat transfer coefficient in the near-wall region, hf, was calculated by means of the model of Jayatilleke.14 To describe the effects of turbulence, the standard k-ε model with wall functions and enhanced wall treatment was adopted.15−17 In the species, momentum and energy continuity equations, the effect of turbulence is then accounted for by means of an effective diffusivity, effective viscosity, and effective conductivity, respectively. More details on their calculation can, for example, be found in Froment et al.4 2.2. Modeling Mass, Heat, and Momentum Transfer in the Core. The reactor core, with its perforated cones, is modeled as a porous continuum medium with isotropic porosity. Mass transport through this medium occurs through convection with superposed effective diffusion.4 The steady state continuity equations can then be written as Species continuity equations:
=
∑
k
(13)
(14)
On the internals of the core coated with catalyst, interfacial heat transfer equals in the steady state the heat effect of the reactions: hf aVcore(Ts − T ) = ρs dcataVcore ∑ ηk rk(m̅ ss , Ts)( −ΔHk ) k
= ρBcore ∑ ηk rk(m̅ ss , Ts)( −ΔHk ) k
(15)
Ts)
To account for the effect of turbulence in the porous medium core, an effective diffusivity, Dcore Am,eff, and an effective conductivity, λcore eff , were introduced in eqs 8 and 14. Unlike the effect of the pressure drop, the effect of diffusion and conduction in the core is relatively weak9 so that the heat and mass transfer correlations for porous media were used as such. The effective conductivity consists of a static and dynamic contribution, λcore = λ0 + λt.4,19,20 The static contribution eff depends on the conductivity of the fluid and the solid core internals:
(9)
where acore V is the specific geometric surface area of the core, and the reaction rates are calculated as shown in Table 1. Total mass continuity equation: ∇·(ε coreρg u ̅ ) = 0
(1 − ε) ε 3d p
core + ∇·(λeff ∇T )
k
= ρBcore MA ∑ αA, kηk rk(m̅ ss , Ts)
(12)
core ∇·(ε coreρg Eu ̅ ) = −∇·(ε coreuP σeff · u ̅ ) ̅ eff ) + ∇·(ε
(8)
s ̃ aVcore(mAs − mA ) SA = kg,A
αA, kηk rk(m̅ ss ,
ε3 150 (1 − ε)2
Extension of the approach for particles with a more complex shape is possible to a certain extent.4 For a structured reactor core, these model parameters depend on the core design and have to be determined from pressure drop measurements in a sufficiently wide flow rate range, as described in the next section. Because of the angle of the cones with the vertical axis and the corrugated cones (Figure 1b), a pronounced nonisotropic flow resistance in the axial and radial direction is unlikely. This is evidenced by earlier CFD simulations considering the full core geometry but with less and larger perforations in the core.9 It is mainly the flow resistance in the axial direction that determines the flow distribution over the core and the casing. For this reason only axial pressure drop measurements were carried out to determine the porous medium model parameters. Energy continuity equation:
In 8, εcore is the porosity of the core. The geometrically determined value of 0.9 has been adopted in the porous medium model. The source term for interfacial mass transfer, SA, is expressed in [kg A/(m3 reactor • s)]. At steady state, mass transfer between the gas phase and the solid equals the consumption or production of species in the catalyst layer on the internals of the core
ρs dcatMA aVcore
d p2
K 2 = 3.5
(7)
core ∇·(ε coreρg mA u ̅ ) = ∇·(ε coreρg DAm,eff ∇mA ) + SA
(11)
(10)
λ 0 = ε coreλg + (1 − ε core)λs
Momentum continuity equation: C
(16)
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The dynamic contribution essentially depends on the turbulence. For packed beds, De Wasch and Froment19 modeled λt as a function of the Reynolds number, Re = dp•G/μ: λt =
0.0105 ⎡ 3600⎢1 + 46 ⎣
dp 2 ⎤
( ) ⎥⎦ dt
Re (17)
In the present work, λt is calculated by means of 17 using an equivalent particle diameter for the core derived from 13 and the experimentally determined K2 and assuming complete analogy between turbulent momentum and heat transfer. An equivalent particle diameter approach was shown to hold for a variety of porous metals.21 With εcore = 0.9, deq p was calculated to have a value of 1.7 mm for R1 and 2.8 mm for R2. Assuming complete analogy between heat and mass transfer: core DAm,eff = λt /(εcoreρg c p)
(18)
3. EXPERIMENTAL STUDY OF THE PRESSURE DROP AND ESTIMATION OF THE PARAMETERS OF THE POROUS MEDIUM MODEL A schematic representation of the experimental setup for the measurements of the pressure drop is shown in Figure 3a. Figure 4. Pressure drop versus the (a) process gas mass flow rate and (b) average (superficial) axial gas velocity for standard methane steam reforming pellets and low pressure drop pellets and for different structured reactor core and/or casing configurations. Reactor design details: see Table 2. The lines in (b) show the fit with a porous medium type model, eq 11, with optimized model parameters K1 and K2.
Froment.9 To avoid outlet effects, the second internal pressure measurement was at 0.805 m. The reactor tube was either loaded with a packed bed of standard- or low pressure drop pellets, with a ZoneFlow reactor consisting of core and casing, or with the casing and a blocked core, or with a core and a blocked casing (a smaller diameter tube was used in the latter case). Both the R1 and lower pressure drop R2 cores were tested. All measurement probes were calibrated, and each experiment was repeated 4 times. As can be seen from Figure 4, the experimental error was relatively small. Figure 4 shows the pressure gradient in the reactor as a function of the (a) gas flow rate and (b) average (superficial) axial gas velocity, respectively. The latter allows accounting for the difference in cross sectional surface area available for flow when measuring the pressure drop over the core or casing individually. Both reactors are seen to offer a significant pressure drop advantage, with respect to standard and low pressure drop pellets. For typical commercial mass flow rates and compared to standard pellets, the R1 reactor leads to a roughly 50% reduction in the pressure drop, the R2 reactor with larger holes in the core a roughly 70% reduction. Figure 4 shows how the low pressure drop in the dual-zone structured reactors results from the very low pressure drop in the casing, which is identical in all variants studied. The cores have an intrinsically higher pressure drop, aiming at generating a nonuniform distribution of the flow over the core and casing. As mentioned earlier, reducing the permeability of the core is expected to increase the fraction of the flow through the casing
Figure 3. (a) Schematic representation of the experimental setup. (b) Structured reactor core. (c) Structured reactor casing.
Compressed air was fed via a mass flow controller at about 60 °C. The compressor can deliver mass flow rates up to 800 N m3/h at a 0.8 bar overpressure. The pressure in the reactor was controlled by means of a pressure controller at the reactor exit − atmospheric pressure was imposed in the experiments presented. The density of the air fed to the reactor depends on the feed pressure and temperature but was about 1.25 kg/m3, compared to 4 to 8 kg/m3 for the gas mixture typically fed to a commercial steam reformer. The temperature was measured at the reactor inlet and outlet. The pressure was measured right upstream and downstream of the reactor and at two internal positions in the reactor. To avoid inlet effects, the first internal pressure measurement was at an axial distance of 0.4 m in the reactor, distance shown to be sufficient by De Wilde and D
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Table 2. Reactor Design Parameters and Operating Conditions ZoneFlow reactors length diameter simulated sector casing core R1 R2 catalyst layer R1/ R2UC/ CC-36
R1/ R2UC/ CC-80
1m 0.102 m 11.25° geometry described in detail porous medium: εcore = 0.9 = 1100 m2 interface/m3 reactor core acore V K1 = (5 ± 0.2)·10−9; K2 = 297 ± 30 acore = 1006 m2 interface/m3 reactor core V K1 = (7 ± 0.5)·10−9; K2 = 212 ± 35 36 μm (Ni/Mg−Al2O4) ρB,eff ≈ 23.55 kg cat. eff/m3 reactor (R1CC-36) (comparable to packed bed of Xu and Froment12) 80 μm (Ni/Mg−Al2O4)
ρB,eff ≈ 47.38 kg cat. eff/m3 reactor (R2CC-80) ρB,eff ≈ 51.81 kg cat. eff/m3 reactor (R1CC-80) operating conditions total feed rate inlet temperature feed composition (mole fractions) N2 CH4 CO CO2 H2O H2 S/C-ratio outlet pressure wall temperature
534.17 N m3/h 793.15 K Xu and Froment12 inlet conditions 0.0348 0.2128 0.0 0.0119 0.7145 0.0260 3.18 29 bar 985 K
equilibrium inlet composition (793.15 K) 0.0332 0.1762 0.0016 0.0354 0.6278 0.1258
Figure 5. Hybrid CFD model validation comparing experimentally measured and calculated pressure drops for given operating conditions as described in Section 3. Reactor design details: see Table 2. (a) Pressure drop versus air (mass) flow rate. (b) Parity plot.
and to intensify the heat transfer between the reactor tube inner wall and the process gas and reactor internals coated with catalyst in the casing. The CFD simulations presented in the next section will confirm this. The lines in Figure 4b correspond to the pressure drop for a porous medium calculated by means of eq 11, with model parameters K1 and K2 determined from the experimental data by means of regression assuming that the porous medium related last two terms in eq 11 dominate the pressure drop. The estimated values of K1 and K2 and the standard deviations are shown in Table 2. The turbulent contribution is significantly smaller than the laminar because of the small width of the channels between the cone blades in the core. Because the CFD calculations presented hereafter were carried out using only a porous medium type description of the core, the pressure drop measurements of the complete dualzone structured reactors − core and casing − can be used for validation of the hybrid CFD model which includes a detailed description of the casing.
casing with centrifugal blades, one sector of the casing with centripetal blades, and the radial fins separating the sectors. Hence, all main characteristics of the geometry are captured. Earlier simulations showed the flow to be fully developed after about 30 cm.9 The blades in the casing make an angle with the central axis (Figure 1b). Table 2 summarizes the most important characteristics of the simulated reactors. For the simulated sector, the grid contains a total of about 1.5 million cells. The effect of the flow distribution over core and casing on the reactor performance was investigated by varying the permeability of the core. The pressure drop related parameters of the porous medium model for the reactor cores were obtained from the pressure measurements described in previous section. The casing is always considered to be coated with catalyst. Coating the reactor core can, however, be questioned. Dual-zone structured reactors aim at introducing a nonuniform flow distribution with relatively more flow through the casing than through the core. Hence, whereas coating the core is costly, it may only marginally contribute to the overall performance of the reactor. To verify this, simulations were carried out with coated and uncoated reactor cores. The
4. STRUCTURED REACTOR DESIGNS, SIMULATION CONDITIONS, AND MODEL VALIDATION To reduce the calculation time, only a 11.25° sector of a reactor with a length of 1 m was simulated. It contains one sector of the E
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Figure 6. (a) Methane conversion in a cross section with centrifugal flow blades for different reactor core designs, catalyst distributions, and catalyst layers. (b) Radial profiles of the methane conversion in a cross section with centrifugal flow blades at different axial positions in the reactor for different reactor core designs, catalyst distributions, and an 80 μm catalyst layer. Reactor design parameters and operating conditions: see Table 2
for the main methane conversion reaction (reaction 1 in Table 1):
reactors with an uncoated core are referred to as R1UC (U for uncoated core and C for coated casing) or R2UC, whereas those with a coated core are identified as R1CC or R2CC. Finally, the influence of the thickness of the catalyst coating or ’catalyst bed density’ was studied by simulations with 36 and 80 μm catalyst coatings. The hybrid CFD model was validated using the data of the pressure drop measurements for the complete R1 and R2 reactors as described in Section 3. Simulations were carried out for different air flow rates in the range experimentally studied. Figure 5 compares the experimentally measured and simulated pressure drops. A good agreement is found demonstrating that the hybrid CFD model accurately describes the pressure drop in the core and casing and the related distribution of the flow over the core and the casing. For the calculation of the performance in methane steam reforming, the typical commercial operating conditions of Xu and Froment13 were adopted. They are summarized in Table 2. To evaluate the impact of the nonuniform flow distribution, reduced pressure drop, and improved heat transfer, a comparison between the structured reactors and packed beds of equal ’effective catalyst bed density’, ρB,eff, is made. The values for the effective catalyst bed density are based on the effectiveness factor of the catalyst
ρB,eff = ρB ·η1
(19)
Whereas for catalyst particles in a conventional packed bed reactor this effectiveness factor has a value of the order of 0.02, the thin catalyst coating layer in structured reactors leads to catalyst effectiveness factors close to 1. The combination with the very high specific geometric surface area of structured reactors leads to equal or higher effective catalyst bed densities than in a classical packed bed (PB). An equal ρB,eff can i.e. be obtained using less catalyst, as follows from 19. The advantage of operation at higher ρB,eff was evaluated separately from the simulations with different catalyst coating thickness.
5. STRUCTURED REACTOR PERFORMANCE AND INFLUENCE OF THE DESIGN Profiles of different flow and composition characteristics in a (rz)-cross section located in a sector with centrifugal flow blades are shown in Figures 6−10. Both contour plots and radial profiles at different axial positions in the reactor are shown. The profiles in the reactor zones with centrifugal and centripetal flow blades were found to be very similar. F
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Figure 7. (a) Temperature [K] in a cross section with centrifugal flow blades for different reactor core designs, catalyst distributions and catalyst layers. (b) Radial profiles of the temperature [K] in a cross section with centrifugal flow blades at different axial positions in the reactor for different reactor core designs, catalyst distributions, and an 80 μm catalyst layer. Reactor design parameters and operating conditions: see Table 2
Table 3. Comparison of Different ZoneFlow Type Dual-Zone Structured Reactors and Packed Bed Reactors in Terms of Methane Conversion, Pressure Drop, and Coefficient of Heat Transfer between the Tube Inner Wall and the Process Gas methane conversiona (z = 1 m) rel. impr. (%) methane conversiond Ta (K) (z = 1 m) c
PB-36eq R1UC-36 R1CC-36 PB-80eqc R1UC-80 R1CC-80 R2UC-80
0.088 0.190 0.278 0.106 0.200 0.318 0.187
/ 116 216 / 89 200 76
833 785 745 823 770 742 765
ΔP (Pa/m) over the reactor
hiwb (W/m2K) (z = 0.5 m)
27670 13350 12900 27500 13300 13300 8000
647 790 795 651 800 800 670
a Mass flow rate weighted cross sectional average. bBetween the tube inner wall and the process gas. cPB-36eq: ρB,eff as in the R1CC-36 reactor and as in Xu and Froment.13 PB-80eq: ρB,eff as in the R1CC-80 reactor. dCompared to a packed bed of equal ρB,eff.
In the reactors without coating on the core, methane is only converted on the internals in the casing. As shown in Figures 6a and 6b, radial mixing between the core and casing is seen to be relatively slow in both reactors but slightly faster in the R1UC reactor. Comparing the methane conversion in the R1UC and R2UC reactor casings with an 80 μm catalyst layer shows that similar conversions are obtained, despite the much higher axial flow velocities and resulting smaller space time (or contact time between process gas and catalyst) in the R1UC casing (Figure 8a). This is due to a higher degree of turbulence in the R1UC
than in the R2UC reactor (Figure 9a). Turbulence significantly improves the heat transfer between the heated tubular wall of the reactor and the process gas and internals coated with catalyst in the casing (Figure 9b), as well as radial mixing, in particular between the core and the casing (Figure 6). The intensified heat transfer and radial mixing in the R1UC reactor is also reflected in the temperature profiles (Figures 7a and 7b). Despite the higher flow rate through the casing and similar methane conversions, the temperature in the R1UC reactor is seen to increase more rapidly than in the R2UC reactor, both in G
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Figure 8. (a) Axial velocity [m/s] and (b) relative pressure [Pa] in a cross section with centrifugal flow blades for different reactor core designs and an 80 μm catalyst layer coated on the casing. Reactor design parameters and operating conditions: see Table 2.
Figure 9. (a) Turbulent kinetic energy [J/kg] (log scale) and (b) effective conductivity [W/(m•K)] (log scale) in a cross section with centrifugal flow blades for different reactor core designs and an 80 μm catalyst layer coated on the casing. Reactor design parameters and operating conditions: see Table 2.
the casing and the core. Values of the estimated coefficients of heat transfer between the tube inner wall and the process gas in the casing are given in Table 3. A more important fraction of the flow through the casing of the R1UC reactor than through that of the R2UC reactor and comparable methane conversions in the two reactor casings results in a higher outlet methane conversion in the R1UC reactor, as seen in Table 3 showing the mass flow rate weighted cross sectional average methane conversion at the outlet of the different simulated reactors. The lower permeability of the R1UC core compared with that of the R2UC core results in a higher fraction of the flow going through the casing, increased turbulence and intensified heat transfer, but comes at the cost of a somewhat higher pressure drop (Figure 8b). As was experimentally measured and shown in the simulations (Table 3), both reactors offer a significant pressure drop advantage with respect to classical packed beds. The R2UC reactor offers roughly 70% reduction in pressure drop, the R1UC reactor roughly 50%. The predicted pressure drop reduction corresponds well with the experimentally measured values (Figure 4). This indicates that the pressure drop in the casing, which was not fitted with the experimental data, and the corresponding flow distribution between core and casing are well predicted by the hybrid CFD model. The radial temperature profiles at different axial positions in the reactor (Figure 7b) exhibit some points with significantly lower values in the casing. A line drawn in the radial direction for visualization purposes crosses the casing blades which have a given angle with respect to the horizontal axis (Figure 1b).
The strongly endothermic reactions take place on these blades (coated with catalyst), resulting in significantly lower temperatures on and in their vicinity. A similar effect is seen in the axial velocity profiles (Figure 8a) because of the no-slip condition imposed on the blades. The results point toward interfacial heat transfer limitations between the process gas and the blades in the casing, already mentioned by De Wilde and Froment.9 The differences between reactors with a coated core (R1CC) and an uncoated core (R1UC) are clearly illustrated in Figures 6, 7, and 10. A coated core contributes to the conversion of methane but only significantly in the first half meter of the reactor where the heat provided with the feed gas sustains a certain conversion (Figure 6). Further downstream, when heat transfer between the casing and the core becomes limiting, the methane conversion in the core contributes only marginally to the overall conversion. That heat transfer between the casing and the core becomes limiting in the R1CC reactor is clearly seen from Figures 7a and 7b showing the temperature profiles in the different reactors. Transfer of species between the core and casing zones is also found to be relatively slow. Radial heat and mass transfer in the casing is, however, very efficient and the more so as the fraction of the flow through it and turbulence increases, as discussed earlier. The high consumption of energy by the reactions in the casing, through which most of the flow is directed, and the efficient radial H
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Figure 10. Radial profiles of the (a) H2 mole fraction, (b) CO mole fraction, and (c) CO2 mole fraction in a cross section with centrifugal flow blades at different axial positions in the reactor for different reactor core designs, catalyst distributions, and an 80 μm catalyst layer. Reactor design parameters and operating conditions: see Table 2.
methane conversion (Figure 6a) and temperature (Figure 7a) profiles. The latter and the methane outlet conversions reported in Table 3 clearly illustrate that the heat transfer between the tube inner wall and the process gas and reactor internals coated with catalyst becomes more limiting as the catalyst layer thickness increases.
mixing in that zone results in a pronounced temperature gradient in the immediate vicinity of the wall. Figure 10a shows radial profiles of the hydrogen mole fraction at various bed depths and suggests a slightly better performance of the R2UC reactor than that of the R1UC reactor. This is due to the increased vertical velocity in the casing of the R1UC reactor and the resulting decreased space time. However, when accounting for the flow pattern, i.e. when calculating the mass flow rate weighted cross sectional average hydrogen production, the R1UC reactor performs better than the R2UC reactor. Figure 10 confirms that advantage of a coated core can only be taken in the first 0.5 to 1 m of reactor. It shows again that further downstream insufficient heat reaches the core to cause reaction in that zone. The radial profiles of the CO and CO2 mole fractions at various bed depths are shown in Figures 10b and 10c. In the range studied, the influence of the thickness of the catalyst layer is not negligible and is well reflected in both the
6. PROCESS INTENSIFICATION AND COMPARISON WITH CONVENTIONAL PACKED BED REACTORS Table 3 summarizes the advantages of the different simulated structured reactors for methane conversion, heat transfer, and pressure drop, when compared with conventional packed bed reactors. For the packed bed reactor simulations, the 1D equivalent model of Xu and Froment13 was used. Details on the reactor model can also be found in Froment et al.4 The R1CC36 reactor with a 36 μm catalyst layer has an effective catalyst bed density comparable with that of the packed bed simulated by Xu and Froment.13 With an 80 μm catalyst layer on the I
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LIST OF SYMBOLS av = external (or geometric) surface area (GSA) per unit reactor volume m2i /m3r cp = specific heat capacity J/(kg K) dcat = catalyst coating layer thickness m dp = equivalent particle diameter m dt = inner tube diameter m DAm,eff = effective diffusivity species A in a fluid m3f /(mfs) Dcore Am,eff = effective diffusivity species A in a porous medium m3r /(mrs) E = total energy, consisting of internal and kinetic energy J/ kg G = fluid mass flux kg/(m2r s) hf = coefficient of heat transfer over the film between a wall/ catalyst surface and the process gas J/(m2i s K) K = thermodynamic equilibrium constant k = turbulent kinetic energy J/kg k1 = rate constant of reaction 1 kg̃ = mass based mass transfer coefficient from gas to solid interface kg3f /(m2i s) MA = molecular weight species A kgA/kmolA mA = mass fraction species A kgA/kgf mSAS = mass fraction species A on the solid surface kgA/kgf pA = partial pressure component A Pa or bar P = total pressure Pa Peff = effective pressure Pa r = radial coordinate mr r1 = rate of reaction 1 per unit catalyst mass kmol/(kgcat s) rA = rate of reaction of component A per unit catalyst mass kmol A/(kgcat s) T = gas phase temperature K Thw,i = internal tube wall temperature K Ts = solid phase temperature K u̅ = gas phase velocity (interstitial) mr/s z = axial distance in the reactor mr αij = stoichiometric coefficient of component i in the jth reaction ε = bed/reactor void fraction m3f /m3r ε = turbulence dissipation rate m2r /s3 ηk = effectiveness factor reaction k for solid particle λcore eff = effective conductivity of the porous medium J/(mr s K) λ0 = static contribution to the effective conductivity of the porous medium reactor core J/(mr s K) λf,eff = effective thermal conductivity of the fluid J/(mf s K) λt = dynamic contribution to the effective conductivity of the porous medium reactor core J/(mr s K) μ = dynamic viscosity of the fluid Pa s μeff = effective viscosity Pa s ρg = gas density kgg/m3g ρB = bed or bulk density kg cat./m3r ρB,eff = effective catalyst bed density: ρB,eff = ρB·η1 kg cat. eff./ m3r ρs = catalyst density kg cat./m3p σeff = effective shear stress tensor kg/(m s2)
structured reactor internals, the effective catalyst bed density can be roughly doubled. Results with a theoretical packed bed with such a ρB,eff are also shown. The first three or last four rows in Table 3 (reactors with ≡ ρB,eff) clearly illustrate that the higher methane conversions achieved in ZoneFlow type structured reactors originate from two contributions: improved heat transfer and a higher flow through the wall region of the casing. Additional advantage results from a better catalyst distribution and effectiveness, as illustrated in Table 3 by the performance of reactors with uncoated and coated cores and with catalyst layers of respectively 36 and 80 μm. The pressure drop advantage of the structured reactors was already discussed in previous sections. Table 3 also shows lower mass flow rate weighted cross sectional average temperatures at z = 1 m in the structured reactors than in the packed beds. This is again explained by the significantly higher flow through the casing.
7. CONCLUSIONS Studying the influence of the design of ZoneFlow type dualzone structured reactors on their performance in methane steam reforming for typical commercial operating conditions requires CFD simulations including detailed reaction kinetics. The hybrid CFD model that was developed allows a detailed description of the geometry of the structured reactor casing, while describing the reactor core as a porous medium. Two additional model parameters introduced by the latter could be determined from experimental pressure drop measurements with the reactor cores in a sufficiently wide gas flow rate range. Pressure drop measurements with the casing and cores joined allowed validation of the hybrid CFD model. Additional pressure drop measurements with standard- and low pressure drop pellets demonstrate the pressure drop advantage of the structured reactors at typical commercial mass flow rates. The origin is found in the design of the casing which offers an intrinsically extremely low pressure drop. The CFD simulations show an improved performance of the dual-zone structured reactors of the ZoneFlow type with respect to packed bed reactors due to (a) efficient heat transfer between the reactor tube inner wall and the process gas and reactor internals coated with catalyst in the casing, (b) a high geometric surface area and catalyst effectiveness, and (c) a nonuniform distribution of the flow with relatively more flow in the casing. These advantages are combined with a low pressure drop. The CFD simulations also show that the heat transfer between the casing and the core limits methane conversion in the core. Reducing the permeability of the core distributes the flow more toward the casing and intensifies turbulence and related heat transfer in the casing, thus increasing the methane conversion and hydrogen production. Increased turbulence also results in improved radial mixing and heat and mass transfer between the core and the casing.
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AUTHOR INFORMATION
Corresponding Author
*Phone: +32 10 47 8193. Fax: +32 10 47 4028. E-mail: Juray. DeWilde@UCLouvain.be.
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Author Contributions
REFERENCES
(1) Bartholomew, C. H.; Farrauto, R. J. Fundamentals of industrial catalytic processes, 2nd ed.; John Wiley & Sons: 2006. (2) Rostrup-Nielsen, J. R. Catalytic Steam Reforming. In Catalysis Science and Technology; Anderson, J., Boudart, M., Eds.; Springer: Berlin, 1984; Vol. 5:1.
All authors have given approval to the final version of the manuscript. Notes
The authors declare no competing financial interest. J
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(3) Wei, J.; Iglesia, E. Isotopic and kinetic assessment of the mechanism of reactions of CH4 with CO2 or H2O to form synthesis gas and carbon on nickel catalysts. J. Catal. 2004, 224, 370. (4) Froment, G. F.; Bischoff, K. B.; De Wilde, J. Chemical Reactor Analysis and Design, 3rd ed.; John Wiley & Sons: 2010. (5) Cybulski, A.; Moulijn, J. A. Structured catalysts and reactors, 2nd ed.; CRC Press: 2005. (6) Groppi, G.; Tronconi, E.; Cortelli, C.; Leanza, R. Conductive monolithic catalysts: Development and industrial pilot tests for the oxidation of o-xylene to phthalic anhydride. Ind. Eng. Chem. Res. 2012, 51 (22), 7590. (7) Thinnes, B. Stackable reactor enables superior heat transfer. Hydrocarbon Process. 2010, 89(8). (8) Feinstein, J. J. Reactor with primary and secondary channels. Patent: publ. no. EP1773492 (A2); 2007. (9) De Wilde, J.; Froment, G. F. Computational fluid dynamics in chemical reactor analysis and design. Application to the ZoneFlow reactor for methane steam reforming. Fuel 2012, 100, 48. (10) Tribute Creations LLC. Advanced hydrogen and syngas reforming with ZoneFlow catalytic reactors. Technical white paper book; 2011. (11) De Wilde, J.; Froment, G. F. CFD Analysis of the ZoneFlowTM Reactor for Steam Reforming. Report No. 2 for Tribute Creations LLC; July 9, 2007. (12) Xu, J. G.; Froment, G. F. Methane steam reforming, methanation and water-gas-shift: I. Intrinsic kinetics. AIChE J. 1989, 35, 88. (13) Xu, J. G.; Froment, G. F. Methane steam reforming: II. Diffusional limitations and reactor simulation. AIChE J. 1989, 35, 97. (14) Jayatilleke, C. L. V. The influence of Prandtl number and surface roughness on the resistance of the laminar sublayer to momentum and heat transfer. Prog. Heat Mass Transfer 1969, 1, 193. (15) Jones, W. P.; Launder, B. E. The prediction of laminarization with a two-equation model of turbulence. Int. J. Heat Mass Transfer 1972, 15, 301. (16) Wilcox, D. C. Turbulence Modeling for CFD, 2nd ed.; DCW Industries: Anaheim, 1998. (17) Schlichting, H. Boundary-Layer Theory, 7th ed.; McGraw-Hill: New York, 1979. (18) Ergun, S. Fluid flow through packed columns. Chem. Eng. Prog. 1952, 48 (2), 89. (19) de Wasch, A. P.; Froment, G. F. Heat transfer in packed beds. Chem. Eng. Sci. 1972, 27, 567. (20) Kunii, D.; Smith, J. M. Heat transfer characteristics of porous rocks. AIChE J. 1960, 6, 71. (21) Dukhan, N.; Patel, P. Equivalent particle diameter and length scale for pressure drop in porous metals. Exp. Therm. Fluid Sci. 2008, 32, 1059.
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