ARTICLE pubs.acs.org/IECR
Fuel Reformation and Hydrogen Generation with Direct Droplet Impingement Reactors: Parametric Study and Design Considerations for Portable Methanol Steam Reformers Mark J. Varady and Andrei G. Fedorov* Multiscale Integrated Thermofluidics Research Laboratory, GWW School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0405, United States ABSTRACT: In a companion article (Varady and Fedorov Ind. Eng. Chem. Res. 2011, DOI: 10.1021/ie200563e), the concept of a direct droplet impingement reactor (DDIR) was introduced as a promising approach to liquid fuel reformation for distributed hydrogen generation. Considering the overall device as an array of unit cells enabled simplified modeling of the device on a unit-cell basis. In this study, the unit-cell model is utilized to study the effects of the important reactor operating parameters for the specific case of methanol steam reforming. The performance of the baseline DDIR is compared to the ideal limit of an isothermal plug-flow reactor (PFR). The effects of DDIR shape, size, heat input and location, and droplet initial conditions were varied from the baseline design to identify possible performance improvements. It was found that the selectivity displays a distinct maximum at a Peclet number (Pe) of ∼3 because of the interplay between back-diffusion of the products and thermal resistance of the catalyst bed. The spatial heating distribution also plays a key role, where an optimized matching of the heat input locations to the areas of heat consumption due to liquid vaporization and endothermic reaction results in an improved reactor performance, albeit at the penalty of a more complex reactor design and increased cost. Impingement of the droplet stream on the catalyst interface is necessary for proper operation, which requires certain initial droplet conditions to be satisfied, as expressed in the form of an operating regime map. Although the results are presented only for methanol steam reforming, the DDIR model is comprehensive and sufficiently general in terms of incorporated physical phenomena that it should be useful for developing similar operating criteria for other fuels and reactions requiring vaporization of a liquid feed followed by reaction over a fixed catalyst bed.
’ INTRODUCTION In an accompanying article,1 a novel concept for catalytic reforming of liquid fuel reforming was introduced in which the liquid reagent was atomized and directed toward a hot catalyst where the droplets impinged, vaporized, and reacted to form the desired gaseous species. This basic reactor concept was introduced by Schmidt’s group at the University of Minnesota for renewable hydrogen generation from a variety of fuels through high-temperature catalytic oxidation.2,3 The key distinguishing feature of this direct droplet impingement reactor (DDIR) model is controlling the reactor performance on the level of an individual fuel droplet impinging and reacting on a dedicated catalyst layer, thus forming a “DDIR unit cell” that can be optimized for a given feedstock and a set of reactions. Further, unparalleled control over the droplet delivery parameters (such as diameter, direction of motion, velocity, and spacing) not only allows for new capabilities for managing reactor behavior, but also enables reactor scaleup to high throughputs without sacrificing the performance achieved through optimization of the DDIR unit cell. As stated in the companion article,1 successful application of the unit-cell results to a scaled-up reactor requires each unit cell to have identical operating conditions, which is satisfied when the total number of unit cells is large compared to the number of unit cells exposed to the ambient on the periphery. Moreover, the concept of the DDIR unit cell, which has sufficient geometric simplicity and experiences periodically repeating but identical droplet impingement events, permits development of a comprehensive reactiontransport model based on first principles with minimal empiricism. The model simulation results were validated by comparison with r 2011 American Chemical Society
relevant literature results, as well as experimental results from an apparatus approximating a unit cell of the reactor, to validate both the physics of the phenomena incorporated into the model and the simulation methodology. In this work, a 100-W steam reforming reactor based on an array of 400 unit cells was constructed and tested to further demonstrate the concept, but without the benefit of the design rules developed later in this article. The DDIR unit-cell model, which is shown in Figure 1, was then applied to identify and study the effects of critical reactor operating parameters on the performance of a methanol steam reforming reactor, including droplet spacing and initial conditions, unit-cell shape and size, and magnitude and distribution of heat input. The baseline for comparison was taken as an ideal (isothermal) plug-flow reactor, which served both to establish basic performance trends and to define a theoretical performance optimum for comparison with DDIR results. The shortcomings of the nonoptimized experimental reactor are highlighted in association with a discussion of the optimum operating regimes revealed by the simulation results. Demonstration of DDIR for 100-W Output. A methanol steam reforming DDIR utilizing an array of unit cells was constructed to achieve a hydrogen output equivalent to 100 W. This reactor was constructed prior to development of the performance trends and resulting design rules detailed in this article. Received: March 20, 2011 Accepted: June 28, 2011 Revised: June 18, 2011 Published: June 29, 2011 9514
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Industrial & Engineering Chemistry Research As a result, this reactor exhibited significant performance deficiencies; the reasons for these shortcomings and possibilities for improvement are presented as the corresponding simulation results are detailed in the following sections. Much of the instrumentation used in this reactor is identical to that used in the validation of the unit-cell model described in the companion article1 where details are available. The primary differences are in the layout of the reactor, where, in this reactor, a 20 20 array of unit cells spaced at 780 μm makes up the required reactant throughput, and in the heat input, an electrical heater is deployed at the periphery of the catalyst bed, as shown in Figure 2. The droplet generator is a microelectromechanical system (MEMS) ultrasonic atomizer array with 400 nozzles described in detail elsewhere.46 The heater consists of a 30gauge NiCr alloy wire wrapped around a 1/8-in. ceramic tube and encased in an aluminum block that surrounds the catalyst bed. A copper wire mesh screen attached to the aluminum block
Figure 1. Schematic of DDIR unit cell showing the geometric parameters, droplet parameters, liquid film accumulation on the catalyst interface, and heaters at the catalyst interface and unit-cell periphery.
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holds the catalyst in place. The heater was powered and controlled using a Harrick 24 VDC automatic temperature controller. Thermocouples monitored the temperature at the center of the catalyst bed and at its periphery at the impingement plane, and inert argon was introduced at 200 sccm parallel to the droplet flow through an MKS mass flow controller with a full scale of 1000 sccm. To attain the target power output of 100 W, the required molar flow rate of hydrogen, n_ H, was obtained using the formula P ¼ ηcell Φth I ¼ ηcell Φth ðηan n_ H NFÞ
ð1Þ
where ηcell is the fuel cell efficiency, Φth = 1.23 V is the theoretical single-cell voltage, I is the cell current, ηan is the fraction of hydrogen utilized at the fuel cell anode, N = 2 is the number of electrons produced per hydrogen molecule, and F = 96800 C/ mol is Faraday’s constant. Taking typical values of ηcell = 0.6 and ηan = 0.8 requires n_ H = 8.78 104 gmol/s and a corresponding volumetric flow rate of 0.018 mL/s for a 50% molar mixture of methanol/water at standard atmospheric conditions assuming 95% conversion of the reactants through the methanol steam reforming reaction. Given a total of 400 nozzles in the atomizer array and a nominal droplet ejection frequency of 1 MHz, the required droplet size is approximately 5 μm. To account for heat losses, the heater capacity was twice that required to heat and vaporize the feed and drive the steam reforming reaction. Several methanol steam reforming experiments were performed with catalyst bed temperatures between 473 and 513 K and at a catalyst loading of 20 g, which corresponds to a unit-cell aspect ratio of approximately 1.5. At each temperature, the flow rate from the ultrasonic atomizer was varied by adjusting the duty cycle in burst-mode operation. The results of these experiments are summarized in Figure 3. For temperatures of 493 and 513 K, the results show an increase of conversion with W/F, as expected, but the values are are still below the conversion for an ideal 473 K
Figure 2. Schematic and photograph of laboratory prototype reactor developed to demonstrate the DDIR concept for 100-W hydrogen output. 9515
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PFR. At 473 K, even more scatter in the data was observed. The reason for this finding is explored in connection with the simulation results in the Droplet Initial Conditions section. Figure 4 shows that a significant amount of CO appeared in the product stream. The primary reason for this is the high temperature observed at the edge of the catalyst bed, which increased the rate of the methanol decomposition reaction relative to steam reforming and therefore increased the amount of CO in the products. In a subsequent section of this article, it is shown that improved distribution of the heat throughout the catalyst bed would reduce the CO in the product stream.
reaction j. The reaction mechanism consists of methanol steam reforming, methanol decomposition, and the watergas shift reaction, for which the reaction kinetics were taken from Peppley et al.,8,9 and the chemical formulas are as follows
’ COMPARISON BASELINE CASE A baseline for evaluating DDIR performance was established by first examining the idealized and optimal performing case of an isothermal plug-flow reactor (PFR). The behavior of this reactor model can be described mathematically by7
ð5Þ
00
dni ¼ dz
∑j νij R j
ð2Þ
CH3 OH þ H2 O T 3H2 þ CO2
0 ΔH298 ¼ 49:5 kJ=mol
ð3Þ CH3 OH T 2H2 þ CO
0 ΔH298 ¼ 90 kJ=mol
H2 O þ CO T H2 þ CO2
ð4Þ
0 ΔH298 ¼ 47 kJ=mol
Important performance metrics for any fuel reforming devices include the methanol conversion, XM, and selectivity to steam reforming, SCO2/CO, which are defined in the usual manner.7 Additionally, for portable and mobile applications, energy conversion efficiency, η, and volumetric power density, ω, are important and are defined as
where n00i is the molar flux of species i, νij is the stoichiometric coefficient of species i in reaction j, and Rj is the reaction rate of
η¼
ðPout Qin Þ n_ f χM LHV M
ð6Þ
ω¼
ðPout Qin Þ "r
ð7Þ
where Pout is the molar flow rate of hydrogen at the reactor outlet multiplied by its lower heating value (LHV), n_ f is the molar flow rate of liquid fuel at the reactor inlet, χM is the mole fraction of methanol in the feed, "r is the reactor volume, and Qin is the heat input to the reactor to drive the reaction and vaporize the liquid fuel. For the case of an idealized plug-flow reactor, the last quantity is given by (
Qin ¼ n_ f
∑
i ¼ M, W
χi ½c̅ p, l, i ðTsat, i T0 Þ þ h̅ fg, i þ c̅ p, g, i ðTrxn Tsat, i Þ
þ χM ΔHrxn
Figure 3. Conversion for the methanol steam reforming reaction experiments on a 100-W DDIR compared with an isothermal plug-flow reactor at 473 K. The temperature range was between 473 and 513 K, and the catalyst loading was 20 g for all cases.
ð8Þ
where hfg,i, cp,l,i, and cp,g,i are the molar heat of vaporization and molar specific heats in the liquid and gaseous phases, respectively; T0, Trxn, and Tsat,i are the initial liquid feed temperature, the reaction temperature, and the species i saturation temperature, respectively; and ΔHrxn is the heat of reaction for methanol steam
Figure 4. (a) Fraction of CO in products for different reaction temperatures and W/F values. (b) Measured temperature at the edge of the catalyst bed compared to the temperature at the center of the catalyst bed, showing the spatial temperature variation. 9516
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Figure 5. Variation of reactor performance metrics with contact time (W/F) for an isothermal plug-flow reactor executing the methanol steam reaction at 523 K.
Table 1. Operating Parameters for Baseline DDIR for Methanol Steam Reforming parameter
description
value
Rd,0
initial droplet radius (μm)
10.0
Vd,0 Td,0
initial droplet velocity (m/s) initial droplet temperature (K)
5.0 300
XM,d,0
initial droplet methanol mole fraction
0.5
f
droplet delivery frequency
105
q00i
heat flux at catalyst interface (W/cm2)
1.97
q00w
heat flux at unit-cell periphery (W/cm2)
0
Rcell
unit-cell radius (m)
0.004
Hcell
distance from droplet generator to catalyst (m)
0.001
Hcat ε
length of catalyst bed (m) catalyst porosity
0.006 0.3
dp
catalyst average particle size (mm)
0.1
ks
catalyst thermal conductivity (W/m 3 K)
1.0
reforming. Although the minor reactions of methanol decomposition and watergas shift also contribute to the thermal behavior of the reactor, they are ignored in this ideal analysis. Figure 5 shows the tradeoffs between conversion/efficiency and power density/selectivity for methanol steam reforming based on the results for an isothermal plug-flow reactor model at 523 K for varying W/F, which is the ratio of catalyst mass to molar fuel flow rate and is also a measure of reactant contact time with the catalyst bed. This temperature was chosen as an optimal operating point for the Cu/ZnO/Al2O3 steam reforming catalyst. (Note that significant amounts of CO are formed at temperatures higher than 573 K.10) The results show that the selectivity and power density peak at low contact time, which corresponds to low conversion and efficiency. Because the power density is a critical metric for portable devices, operating at low W/F seems desirable. However, this results in much wasted fuel unless a product recycling scheme is employed, with this tradeoff being discussed in previous studies.11 To this point, it seems that product recycling has not been seriously considered for small-scale reformers in the literature, but could be a fruitful direction for further research. Because of the value of the fuel and the desire to not waste it, a minimum acceptable conversion is usually set somewhere above 90% in most studies.1214 The isothermal PFR model was used to
Figure 6. Contours of gas-phase pressure and velocity with streamlines for baseline case of DDIR for methanol steam reforming.
find the minimum contact time required to achieve 95% conversion at an operating temperature of 523 K. This value of W/F = 72 kgcat 3 s/gmol was used in the baseline DDIR study with a catalyst bed aspect ratio (AR = Hcell/Rcell) of 1.5. This value of AR was chosen based on the demonstration DDIR for methanol steam reforming with a 100-W capacity, discussed in the previous section. The other parameters in the baseline DDIR model are outlined in Table 1. The selection of spacing, Hcell; droplet size, Rd,0; and velocity, Vd,0, ensured that impingement occurred without significant evaporation or slowing of the droplet stream. Additionally, the heat input was just sufficient to vaporize and heat the liquid feed to reaction temperature and to drive the endothermic reaction. This corresponds to a ratio of heat input to fuel flow rate of Qin/m_ in= 2.8 MJ/kg, a parameter that is used throughout this work. In this baseline case, all of the heat was applied only at the catalyst interface heater, corresponding to q00w = 0 and q00i = 1.97 W/cm2 in Figure 1. Examination of the velocity, temperature, and species fields for the baseline case (Figures 6 and 7) reveals some important operating trends for the DDIR for methanol steam reforming. In these figures, the droplets emanate from the left side along the center line of the domain, and the catalyst interface is denoted by a vertical line dividing the domain. At the interface, the accumulated liquid film is represented by the enclosed white area. Note that the liquid film takes the shape of a hemispherical cap outside the catalyst, and the imbibed portion of the liquid film is cylindrical. This approximation is discussed in more detail and justified in the companion article.1 Figure 6 shows a recirculation zone close to the center line of the unit cell created by the viscous drag of the droplets on the surrounding gas. Also, in the baseline case, a liquid film has accumulated at the catalyst interface, and vaporization results in elevated pressure at the film interface, with resulting flow of the vapor normal to the isobars. Some of the vaporized liquid 9517
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Figure 7. Contours of (a) temperature (top) and rate of methanol steam reforming (bottom) and (b) rates of methanol decomposition (top) and watergas shift (bottom) for the baseline case of DDIR for methanol steam reforming.
Table 2. Comparison of Baseline DDIR for Methanol Steam Reforming Reaction with the Equivalent Isothermal Plug-Flow Reactora
a
MeOH conversion
SCO2/CO
outlet CO (%)
efficiency (%)
power density (W/cm3)
isothermal PFR
0.95
13.5
1.8
84
12.9
baseline DDIR
0.69
9.3
3.1
55
8.19
For both cases, W/F = 72 kgcat 3 s/gmol, Qin/m_ in = 2.8 MJ/kg.
enters the droplet transit zone and has a primarily radial velocity before re-entering the catalyst zone axially. Clearly, vapor generated from the liquid film interface takes a varying amount of time to reach the reactor outlet depending on which streamline is followed, which is a significant departure from plug-flow behavior. Figure 7a shows cold zones along the unit-cell center line and surrounding the accumulated film because the cold droplet stream acts as a heat sink and the vapor leaving the film surface is at its saturation temperature. The cold zone near the catalyst interface results in low reaction rates and poor catalyst utilization in this region. Additionally, large temperature gradients are observed near the film interface with a hot spot near the edge of the unit cell furthest from the impingement point. The hot spot results in increased methanol decomposition in those areas and higher levels of CO in the products; however, this is partially ameliorated by an increased watergas shift reaction rate around the same location in the catalyst bed as shown in Figure 7b. Farther downstream of the catalyst interface, the bed temperature approaches the design value of 523 K. A performance comparison between the isothermal PFR and baseline DDIR is made in Table 2. Clearly, the baseline DDIR shows deficiencies in all performance metrics, which is primarily due to the cold zone at the droplet impingement point and nonisothermality of the catalyst bed discussed above. Of course, it must be remembered that the thermal resistance of the catalyst bed is not considered in the isothermal PFR model, making its performance an ideal limit.
’ EFFECTS OF OPERATING PARAMETERS Investigation of the effects of key operating parameters of the DDIR was carried out to identify potential improvements in reactor performance over the baseline case presented in the preceding section, in addition to finding operating regimes to avoid. This analysis resulted in a set of basic design rules for the DDIR as applied to methanol steam reforming. Unit-Cell Aspect Ratio and Throughput. Two critical DDIR parameters are the unit-cell aspect ratio and throughput. The aspect ratio is important because it determines the spacing between droplet streams, how the applied heat is distributed through the catalyst bed, and the portion of the catalyst interface covered by the liquid film. A more general parameter containing the aspect ratio is the Peclet number, or the ratio between diffusive and advective time scales in the reactor. Here, the velocity scale used is the mass flow rate of droplets injected into the unit cell, m_ d = 4/3πRd,03Flf, divided by the unit-cell crosssectional area, and the relevant length scale is taken as the length of the catalyst bed in the axial direction, Hcat ! uHcat m_ d Hcat Pe ¼ ¼ ð9Þ De Fg πRcell 2 De The unit-cell reactant throughput determines the required size of the unit cell and also the number of unit cells needed to achieve 9518
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Figure 8. DDIR performance as a function of Pe for unit-cell throughputs defined by droplets with Rd,0 = 2.5, 5, and 10 μm delivered at a frequency of 100 kHz. For all cases, W/F = 72 kgcat 3 s/gmol and Qin/m_ in = 2.8 MJ/kg. (a) Methanol conversion and reactor efficiency, (b) selectivity to methanol steam reforming, (c) maximum interface temperature and average outlet temperature, and (d) power density.
a target overall throughput for a given application. In studying the effects of these parameters, we kept W/F and Qin/m_ in at their baseline values of 72 kgcat 3 s/gmol and 2.8 MJ/kg, respectively. Pe was varied by changing the aspect ratio Hcat/Rcell, whereas the unit-cell throughput was varied by changing the initial droplet radius, Rd,0, keeping the delivery frequency at the baseline value of 100 kHz. Additionally, the initial droplet Reynolds number, Red,0 = Rd,0Vd,0/νg, was kept constant at the baseline value of approximately 5 to ensure that the droplet stream impinged without significant evaporation or slowing. (Variations of Red,0 are studied in more detail in a subsequent section of this article in order to determine conditions for which droplet impingement on the catalyst does not occur, which has a negative impact on performance.) The results of this parametric study are summarized in Figure 8, showing the reactor performance metrics in addition to catalyst interface and outlet temperatures over ranges of Pe and unit-cell throughput values. First, notice that methanol conversion, reactor efficiency, and power density all increase with increasing unit-cell throughput over the entire range of Pe studied, whereas the selectivity decreases. Examining the temperature distribution, which is represented in Figure 8c, the catalyst bed approaches isothermality for lower unit-cell throughputs, but the reactor performance actually suffers based on all previously defined performance metrics except for selectivity. For higher unit-cell throughput, the maximum interface temperature is significantly higher over the entire range of Pe values. Because W/F is fixed for all cases, the unit-cell size must increase with unit-cell throughput. This
increase in size corresponds to an increase in thermal resistance of the catalyst bed and, in turn, of the temperature of the hot spot at the edge of the unit cell. For the highest unit-cell throughput studied here, the hotspot temperature increases from 565 to 600 K as Pe increases from 0.5 to 10. This is much higher than the recommended operating temperature of 523 K for the methanol steam reforming catalyst. Because the reaction rate follows an Arrhenius law and increases exponentially with temperature, this explains the increased conversion, efficiency, and power density with unit-cell throughput. In addition to increased reaction rate, the relative rate of methanol decomposition compared to steam reforming increases, explaining the decreased selectivity with increasing unit-cell throughput. It must be noted that, because these results were obtained using the kinetic expressions of Peppley et al.,8 which are only valid up to 573 K, there is a possibility that the results are quantitatively inaccurate above this temperature. However, it is expected that the trends observed still hold. Perhaps the most intriguing result is the maximum in selectivity observed in Figure 8b, which occurs at Pe ≈ 3 for all unitcell throughputs. To understand this behavior, only the highestthroughput case is examined in greater detail. Figure 9 shows contour plots of hydrogen mole fraction and fractional yield (defined as the ratio of the reaction rates of methanol steam reforming to methanol decomposition, rMSR/rMD) for (a) Pe = 0.6 and (b) Pe = 4. Clearly, the mole fraction of hydrogen is higher near the catalyst interface for lower Pe values because back-diffusion of products is more pronounced. Because the presence of hydrogen has an inhibiting effect on methanol steam 9519
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Figure 9. Contours of hydrogen mole fraction and fractional yield for Pe = (a) 0.6 and (b) 4. m_ d = 3.5 107 kg/s, W/F = 72 kgcat 3 s/mol, and Qin/m_ in = 2.8 MJ/kg for each case.
Figure 10. Variation of selectivity to methanol steam reforming with aspect ratio for the limiting cases Pe f ∞ and ke f ∞ for a unit-cell throughput of m_ d = 3.5 107 kg/s, W/F = 72 kgcat 3 s/gmol, and Qin/ m_ in = 2.8 MJ/kg.
reforming, the spatial average of the fractional yield is lower over the catalyst bed, resulting in a lower selectivity. If back-diffusion of products were the only factor in play, then the selectivity should monotonically increase with Pe. However, the thermal resistance of the bed also plays a role. Consider the case for a unit-cell droplet throughput of m_ d = 3.5 107 kg/s over the same range of aspect ratio, but for two ideal limiting cases: (1) De,i = 1 1010 m2/s and (2) ke = 10 W/m 3 K. Figure 10 demonstrates that for, case 1, where the back-diffusion is artificially eliminated, the behavior is dominated by the axial thermal resistance. As the aspect ratio increases, the axial thermal resistance increases, increasing the hot-spot temperature at the interface and decreasing selectivity. For case 2, the axial thermal resistance is significantly reduced, so the behavior is dominated by back-diffusion effects, and the expected monotonic increase in selectivity with aspect ratio is observed. One can think of the real reactor as a blend of these two limiting cases, resulting in an optimum Pe value for selectivity.
Heat Input Distribution. In results reported in previous sections, the normalized heat input was held constant at Qin/ m_ in = 2.8 MJ/kg and uniformly distributed over the catalyst interface. Obviously, one can consider alternative heating arrangements, for example, when heat is also applied along the unit-cell periphery (at r = Rcell, Hcell < z < Hcell + Hcat) as shown in Figure 1. One method for implementing this approach is to integrate electric heaters within the catalyst bed so that each unit cell receives the same heat rate along the reactor length. This can be accomplished in practice by utilizing individual tubes wrapped with electric heaters for each unit cell. In this case, the unit cell becomes less of a conceptual construct and more of a physical object. Other methods for heating along the reactor length have been reported in the literature, including use of an exothermic reaction in adjacent channels using catalytic combustion of some of the methanol feed or of the unutilized hydrogen from the products.15,16 However, for this study, attention is confined to the case where the heat applied along the unit-cell periphery is spatially uniform, as in the case of the wound electric heaters. Three external heating scenarios are considered (see Figure 1): (1) the baseline case where all of the heat is applied uniformly at the catalyst interface, (2) the case where all of the heat is applied uniformly at the unit-cell periphery, or (3) the case where the total heat rate is divided between the catalyst interface and unit-cell periphery. For case 3, the heat is divided based on the simplified design premise that the heat applied at the catalyst interface goes toward vaporizing the impinging droplets, whereas the heat applied along the unit-cell periphery drives the endothermic steam reforming reaction. This results in heat fluxes at the catalyst interface, q00i , and unit-cell periphery, q00w, of 00
qi ¼ 9520
ð4=3ÞπFl Rd, 0 3 f ½hfg þ cp, g ðTrxn Tsat Þ πRcell 2
ð10Þ
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Figure 12. Difference between maximum interface and outlet temperature and average bed temperature for varying Pe with applied heat split between the interface and unit-cell periphery.
Figure 11. Effects of heater placement in the DDIR unit cell on (a) selectivity and (b) power density. Equal total heat rates were applied uniformly at the catalyst interface, unit-cell boundary, or split between the two as described in the text. For all cases, W/F = 72 kgcat 3 s/gmol, Qin/m_ in = 2.8 MJ/kg, and m_ d = 3.5 107 kg/s.
00
qw ¼
ð4=3ÞπFl Rd, 0 3 fyMeOH ΔHMSR 2πRcell Hcat
ð11Þ
For each of these three cases, Qin/m_ in = 2.8 MJ/kg, W/F = 72 kgcat 3 s/gmol, and m_ d = 3.5 107 kg/s are fixed, whereas Pe is varied between 1 and 20. Case 1, where all of the heat is applied at the catalyst interface, is described in detail in the previous sections. For case 2, the reactor is operable only below Pe ≈ 5 because flooding occurs above this point. This occurs because the total heat input is spread over a longer axial distance, and the heating intensity close to the impingement point decreases to the point where it becomes insufficient to vaporize the incoming droplet stream. It is clear from Figure 11 that optimal performance is achieved for case 3, which exhibits superior selectivity and power density compared to cases 1 and 2. Furthermore, this increase in performance becomes more pronounced as Pe increases and plug-flow behavior is approached. This is analogous to the situation shown in Figure 10 where ke f ∞, except that, instead of artificially altering the catalyst bed thermal conductivity, the heat input is spatially deployed in a more efficient manner. Figure 12 supports this conclusion, showing that the temperature difference along the reactor decreases and the average temperature of the catalyst bed approaches the design value of 523 K. Employing this distributed method for external heating comes with increased design complexity because two heaters must be independently controlled and each unit cell becomes an individual miniature reactor as described above. Returning to the experimental results, the spatial distribution of heat employed in the experimental reactor does not correspond to any of the simulated cases. However, heating only at the periphery for a unit cell results in the worst performance, and
this most closely corresponds to the experimental case with some additional radial spreading of heat enabled by the copper wire mesh at the catalyst interface. Additionally, the Pe value was approximately 20 for these experiments, much higher than the optimum of Pe ≈ 3 found using the comprehensive DDIR model, which also contributes to the high fraction of CO in the products. When an array of unit cells is employed in the distributed heating method, one method for practical implementation is to use an array of catalyst packed ceramic tubes wrapped with electrical heaters, packing them together, and employing a separate electrically actuated wire mesh heater at the inlet of the array of tubes. If a catalyst support with high thermal conductivity can be used, then the single-interface or single-side heating methods become more viable. Such work with highthermal-conductivity supports was successfully demonstrated by Horny et al. for methanol autothermal reforming.17,18 Droplet Initial Conditions. In all cases considered up to this point, the droplet stream impinges on the catalyst interface without significant evaporation or slowing of the droplets due to viscous drag. It is important to maintain these conditions for optimal operation of the DDIR, so finding the conditions under which the droplet stream transitions from impinging to not impinging is critical. In other words, there is some maximum distance between the droplet generator and catalyst interface at which the droplet stream would either completely evaporate or be overcome by drag. To find the dependence of this distance on droplet initial conditions, a constant droplet delivery rate of m_ d = 4.4 108 kg/s was studied using initial droplet radii of Rd,0 = 10, 5, and 2.5 μm at frequencies of f = 12.5, 100, and 800 kHz. The distance Hcell was then increased until one of the abovementioned scenarios was achieved. The other droplet parameters were set to W/F = 72 kgcat 3 s/gmol and Qin/m_ in = 2.8 MJ/kg as in previous baseline simulations. In this analysis, the droplet stream was assumed to be overcome by drag for Vd < 0.001Vd,0 and completely evaporated for Rd < 0.001Rd,0 because both velocity and radius follow an exponential decay and mathematically never reach zero. The results indicate that, because of the relatively mild operating conditions in the methanol steam reforming reactor, the droplet stream is overcome by drag in all cases before completely evaporating. Confining attention to this case, it is instructive to study the case of a single droplet (not a stream) traveling through a quiescent medium and to find the maximum distance it can travel before it nearly stops, that is, Vd = 0.001Vd,0. 9521
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This is accomplished by integrating the droplet momentum conservation equation to find an analytical expression for Vd(t), determining the value of time t for which the above criterion of droplet slowing is met, and then integrating the kinematic equation for droplet position over this time period using the analytical expression for Vd(t). Defining time scales for droplet drag, τd,drag, and droplet transit, τd,trans, we write τd, drag ¼
Fl Rd, 0 2 F g νg
ð12Þ
τd, trans ¼
Hcell Vd, 0
ð13Þ
The transition between impingement and no impingement is then expressed in terms of these time scales as τd, drag 9 ð14Þ ≈ τd, trans 2 In the case of the DDIR, there is actually a stream of droplets that creates an entrained flow, as seen in Figure 6. This entrained flow clearly increases the maximum distance between the droplet generator and catalyst interface, and the transition criterion in eq 14 no longer applies. Another way to view this situation is that the time scale for drag is altered. Finding the appropriate augmented drag time scale, τ*d,drag, allows the transition criterion developed in eq 14 to still be used. To do this, consider that the velocity of the surrounding gas, u, is no longer neglected, which yields the following scaling
Figure 13. Regime map showing droplet impingement and no impingement zones, as obtained using the analytical model and scaling analysis, along with supporting simulation results using the comprehensive DDIR model (symbols). The solid line indicates the transition line for no evaporation of the droplets. The transition line shifts upward with significant droplet evaporation.
Fg νg ðVd, 0 us Þ Vd, 0 ¼ w τd, drag Fl Rd, 0 2 τd, drag ¼
Fl Rd, 0 2 Vd, 0 Fg νg ðVd, 0 us Þ
ð15Þ
where us is the velocity scale, which is obtained by scaling the gas-phase momentum equation in the axial direction assuming that the drag term balances the momentum source term from the droplets. (Please refer to the companion article1 for details.) νg us 6πνg Rd, 0 ðVd, 0 us Þf ≈ Rd, 0 2 Vd, 0 πRd, 0 2
ð16Þ
Solving for us and substituting into eq 15 gives the modified drag time scale, τd,drag*, which, when used in place of the original drag time scale in eq 14, yields the modified transition criterion between impingement and no impingement of the droplet stream on the catalyst ! τd, drag Fl Rd, 0 2 Vd, 0 6Rd, 0 f 9 ð17Þ ≈ 1 þ ≈ Vd, 0 2 τd, trans Fg νg Hcell This is written in a more compact form in terms of the dimensionless quantities, Remod = τd,drag/τd,trans, which is a modified Reynolds number, and St = Rd,0f/Vd,0, which is the Strouhal number Remod ≈
9 1 2 1 þ 6St
ð18Þ
Also, instead of using the initial droplet velocity, Vd,0, as the droplet velocity scale, a more appropriate scale is a positionaveraged velocity, as the droplet velocity decreases from Vd,0 to
Figure 14. Decrease in normalized droplet surface area throughout the droplet lifetime for different relative values of the time scales of droplet transit and evaporation.
0.001Vd,0 along the droplet trajectory, yielding 0.22Vd,0. Plotting the simulation results on axes of Remod versus St along with eq 18 shows that this equation is a good predictor of the transition between no impingement and impingement. Although Remod must be above a certain value to ensure impingement, another consideration is splashing of the droplet upon impact, which would possibly lead to unpredictable behavior. Previous work has shown that the Weber number (We = FVd2Rd/σ) upon droplet impact should be less than 80 to avoid splashing,19 and this criterion should be considered when interpreting the impingement/no-impingement regime transition. At the highest St case studied by the DDIR model, the noimpingement case lies above the solid transition line. This occurs because significant evaporation occurs throughout the droplet lifetime. A measure of this is the time scale for droplet evaporation, τd,ev. If τd,ev = ∞, then no evaporation occurs, and τd,trans/ τd,ev= 0, which is the solid line in Figure 13, whereas for nonnegligible values of τd,trans/τd,ev, the transition is shifted upward as shown by the dashed line in Figure 13. Figure 14 depicts the decrease in normalized droplet surface area throughout the 9522
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Industrial & Engineering Chemistry Research droplet lifetime for each of the cases studied here with the corresponding value of τd,trans/τd,ev. To account for the effects of evaporation, a family of transition curves corresponding to different values of τd,trans/τd,ev is required on the regime map of Remod versus St. For a sufficiently large value of τd,trans/τd,ev, complete evaporation of the droplet stream occurs. For exothermic reactions (e.g., fuel oxidation) resulting in high surrounding gas temperatures, this can occur and the possibility must be considered in general. Returning to the experimental results presented previously, it is now clear why these results are suboptimal. In these experiments, Remod ≈ 0.2 and St ≈ 0.2, which lies below the transition line in Figure 13, showing that significant deflection of the droplets from a straight-line path occurred, resulting in condensation on the side walls. Thus, a significant fraction of the liquid feed did not contact the catalyst bed, resulting in much lower conversion than expected, referring back to Figure 3.
’ CONCLUSIONS Analysis of design tradeoffs of the direct droplet impingement reactor (DDIR) for methanol steam reforming was carried out using an isothermal (ideal) plug-flow reactor (PFR) as a baseline for comparison. Accounting for the additional heat load required for vaporization of the impinging droplet stream in the DDIR produces a cold zone and underutilization of the catalyst bed, resulting in performance deficiencies compared to the ideal isothermal PFR. Possible improvements were investigated by varying the critical DDIR operating parameters from their baseline values and observing the resulting trends in performance. The main conclusions of this analysis are summarized below. Once again, it is important to realize that applying these unit-cell results to the scaleup of an overall reactor requires that the number of unit cells in the interior (i.e., surrounded on all sides by other unit cells) should be much greater than the number of unit cells exposed to the surroundings.1 • Selectivity to steam reforming displays a clear maximum at a Peclet number of Pe ≈ 3, independent of the droplet delivery rate, and is due to a transition between product back-diffusion-dominated behavior at low Pe values to the catalyst-bed thermal-resistance-dominated behavior at high Pe values. However, as the average reactor temperature increases beyond the optimal range for steam reforming, the selectivity decreases, as expected, and the variation with Pe diminishes. • The spatial deployment of heat input in the reactor and unit-cell aspect ratio (defined as the ratio of lateral extent to axial length) both have significant impacts on reactor performance. O Employing heaters only at the catalyst interface where the droplet stream is impinging favors Pe ≈ 3 for optimal selectivity as explained above. Other performance metrics (conversion, efficiency, and power density) favor higher Pe values because the increased axial thermal resistance results in a greater hot-spot temperature at the edge of the catalyst interface. O Employing heaters only along the side walls of the unit cell also favors lower Pe values. As Pe increases, less heat is concentrated near the interface where it is required to drive vaporization and endothermic reaction. For this reason, flooding occurs above a certain Pe value, which depends on the total heat input to the reactor.
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O Splitting the heat load between an interface heater and side-wall heater such that the interface heating matches the thermal load required to vaporize and heat the feed whereas the side-wall heating matches the thermal load of the endothermic reaction always leads to the most favorable operation. Furthermore, the performance improvement is more pronounced for higher Pe values. However, this configuration is more complex and costly for practical implementation. • For a given droplet delivery rate, a minimum Reynolds number is required to ensure impingement on the catalyst interface, which is a decreasing function of the droplet Strouhal number. This minimum Reynolds number increases with increasing droplet evaporation rate. However, the Reynolds number should also be such that the Weber number is less than 80 at impingement to prevent splashing19 at the interface and subsequent unpredictable behavior. Beyond a Strouhal number of 1/2, the droplet stream collapses into a continuous jet that impinges at the catalyst surface. • Complete evaporation of the droplet stream before impingement is not observed either experimentally or in simulations because of the mild thermal conditions of the steam reforming reaction. Depending on the operating conditions, film operation could be preferred from the conversion/selectivity prospective, so flash evaporation is not necessarily an optimal mode for DDIR operation, especially for reactions requiring moderate temperatures. Investigation of other possible reaction pathways for hydrogen generation using the tools developed in this work could also prove useful. A prime example is that of autothermal (or oxidative) steam reforming20,21 in which air is mixed with the reactants in the proper ratio so that the heat produced by the exothermic reaction is just sufficient to vaporize the liquid feed and drive the endothermic reaction. It is expected that the conclusions drawn for this reaction would be quite different due to the mixing of the incoming air and vaporizing reactants and the heat generated at the impingement point upon vaporization and exothermic reaction at the interface. Other reaction schemes for different processes are also possible using the DDIR, which are likely to result in different optimal reactor designs. However, the analytical framework and simulation tools developed in this work are general enough to be successfully applied to other reactions and DDIR configurations.
’ AUTHOR INFORMATION Corresponding Author
*Tel.: +1 404 385 1356. Fax: +1 404 894 8496. E-mail:
[email protected].
’ ACKNOWLEDGMENT The authors acknowledge financial support of this work through NSF CBET Grant 0928716, which was funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). ’ REFERENCES (1) Varady, M. J.; Fedorov, A. G. Fuel Reformation and Hydrogen Generation with Direct Droplet Impingement Reactors: Model Formulation and Validation. Ind. Eng. Chem. Res. 2011, DOI: 10.1021/ ie200563e. 9523
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