ARTICLE pubs.acs.org/IECR
Numerical Analysis of Fractal Catalyst Structuring in Microreactors Venkat Reddy Regatte and Niket S. Kaisare* Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600036, India ABSTRACT: The objective of this work is to verify the feasibility of implementing fractal structuring to reduce the amount of active catalyst surface required in microreactors. This work follows up on the work by Phillips et al. [Chem. Eng. Sci., 2003, 58, 24032408], where the authors reported the use of Cantor triads to reduce the total amount of active catalyst in a mass-transferlimited system. They considered flat-plate geometry with infinitely fast reactions. This work is extended to realistic microreactors with finite rate chemistry to study the effect of catalyst structuring in the presence of flow confinement. Fractal and periodic patterns are formed by removing the catalyst from various sections along the reactor wall, resulting in alternating catalytic and noncatalytic segments. Two-dimensional computational fluid dynamics (CFD) simulations of tubular microreactor channel with catalyst structuring are performed. Our results show that the role of catalyst structuring confined geometry is rather modest, compared to the open (flat-plate) geometries considered so far. We also show that singularities (boundary of noncatalytic and catalytic segments) formed with catalyst structuring, and not the fractal pattern itself, are responsible for improved conversion from the microreactor. Large gradients at singularities result in enhanced mass transfer, which is analyzed using Sherwood number correlations. The effect of various operating parameters is investigated.
’ INTRODUCTION Heterogeneous catalysis of gas-phase reactions has been an active area of research for scientists and engineers alike, because of its industrial and environmental importance. Fritz Haber’s synthesis of ammonia on metal catalyst in 1909 and its subsequent scaleup by Carl Bosch and his team at BASF by 1913 is the most significant milestone in industrial chemistry. Ever since, the importance of solid-catalyzed gas-phase reactions has increased exponentially. It finds applications in the fields of petrochemicals, pharmaceuticals, automobiles (catalytic converters), and biotechnology. The overall mechanism involves diffusion of the reactants from the bulk to the catalyst surface (external diffusion), diffusion to the active site (internal diffusion), adsorption at the active site, various surface reactions, desorption of the products, and their diffusion back to the bulk gas. This mechanism relies on the availability of a large surface area per unit volume of the active catalyst, which increases the probability of reactant molecules to come into contact with the catalytic surface. Various methods have been proposed to improve the yield and efficiency of existing catalytic processes. Loffler and Schmidt1 investigated the effect of introducing surface heterogeneities to increase the yield and selectivity of product in mass-transferlimited systems. Forced unsteady-state operation has been proposed improve the performance of catalytic reactors beyond that which can be achieved in steady-state operation.2,3 Sheintuch and co-workers4,5 have exploited spatial structures in catalytic reactors that reveal patterns different from those existing in reactiondiffusion systems that have been subjected to uniform conditions. Selective placement of catalysts that promote methane combustion, reforming, and water-gas shift reactions was proposed for periodically operated reverse-flow microreactors to improve the productivity by enhancing reaction rates in low- and hightemperature regions of the reactor.6 Cote et al.7 proposed using an auxiliary catalyst in addition to implementing a layered patterned strategy to alleviate the equilibrium limitation for paraffin r 2011 American Chemical Society
dehydrogenation and methanol synthesis. In the past decade, catalytic microreactor technology has been proposed for chemical synthesis, chemical kinetics studies, and process development, because of the high surface:volume ratio and high heat- and mass-transfer rates.8 In summary, research has focused on using spatial and/or temporal patterns to enhance the efficiency of existing catalytic processes. Advances in microreactor technology allow us to push the envelope further, by carefully designing and controlling flow, temperature, and catalyst patterns. High yields can be obtained with millisecond contact times,9 because of enhancement in heat- and mass-transfer rates.10,11 In mass-transfer-limited systems, significant reduction in active catalyst can be achieved while maintaining the same conversion by segmenting the catalyst surface into catalytically active and inactive (i.e., noncatalytic) sections.1,12 Hybrid microcombustors, consisting of alternating catalytic and noncatalytic segments, have been designed to operate under high velocities, to overcome the blow-out regions13,14 or selectively promote homogeneous combustion to improve the overall conversion in the system.15 Apart from microreactors, reduction in the active catalyst segments is also of interest to catalytic monoliths used for vehicular pollution abatement and solid-catalyzed gas-phase reactions in the industry. In this paper, the term “fractal catalyst structuring” refers to using fractal geometry to create such segments of alternating catalytic and noncatalytic regions in a reactor.12 Fractals, which were introduced by Mandelbrot,16 are fragmented geometric shapes consisting of self-similar, repeating patterns. The main Special Issue: Ananth Issue Received: February 27, 2011 Accepted: May 6, 2011 Revised: May 5, 2011 Published: May 06, 2011 12925
dx.doi.org/10.1021/ie2003957 | Ind. Eng. Chem. Res. 2011, 50, 12925–12932
Industrial & Engineering Chemistry Research
ARTICLE
Table 1. Model Equations and Boundary Conditions Governing Equations DF BÞ ¼ 0 Dt þ r 3 ðFu DðFuBÞ BuBÞ ¼ Dt þ r 3 ðFu
Continuity: Momentum:
rp þ r 3 τ
(8) (9)
where h i τ ¼ μ ðruB þ ruBT Þ 23r 3 uBI
Species transport:
DðFYi Þ BYi Þ Dt þ r 3 ðFu
¼ r 3 ðJBi Þ
(10)
Boundary Conditions
Figure 1. Schematic diagram of the tubular microreactor geometry with full catalyst loading and illustration of the fractal structuring of the active surface using a Cantor triadic bar.12 The shaded region is catalytic, whereas the blank region is noncatalytic. The catalyst loading for the first three fractal divisions is 66.67%, 44.44%, and 29.6%, respectively.
factors for the performance of heterogeneous catalysis are the geometrical details of the surface and the physicochemical nature of the reacting system. Fractal structures have found some applications in catalysis, although their use in chemical engineering is still immature.17,18 Jifen et al.19 computed information about the fractal dimension to provide a description of the catalytic activity and used it for catalyst selection. The qualitative and quantitative differences between fractal and uniform-pore catalysts suggest that the concentration field is markedly different and, consequently, the reaction rates, as well as the selectivity due to competition between such reactions, are expected to be crucially dependent on the concentration field.5 This work follows up on the idea of Phillips et al.,12 who investigated fractal segmentation using Cantorian triads. Catalyst was removed successively to yield alternating patterns of catalytic and noncatalytic segments, leading to self-similar fractal structure. They could achieve 76% reduction in the total catalyst for a flat-plate open geometry, with only a 2.3% reduction in reaction rate.12 They modeled the reaction to be infinitely fast. Depending on the operating conditions, microreactors may be reactionlimited, diffusion-limited, or both may be equally important.11 Moreover, Kaisare et al.20 showed that propane catalytic combustion shifts from diffusion-limited conditions to reaction-limited conditions, based on the thermal conductivity of the reactor wall material. We analyze fractal structuring for confined channels of microreactors (or individual channel of catalytic monolith) with a circular cross section. The effect of the Damk€ohler number (Da), Peclet number (Pe), and aspect ratio on the efficacy of fractal structuring is analyzed. Since the focus of this paper is on the effect of catalyst segmentation on mass-transfer enhancement in catalytic wall reactors, we have considered a generic reaction: A f products Therefore, the thermal effects and homogeneous reactions are neglected here. Traditionally, heat- and mass-transfer phenomena in confined channels of various geometries is explained through the Nusselt and Sherwood numbers (Nu and Sh, respectively).21 It is now well-known that the asymptotic value of Sh is dependent on the Pe and Da values.2226 The Sherwood number profile shows an “entrance effect”: the Sh value is very high at the inlet and falls asymptotically to a constant value. Large gradients due to singularities or light-off result in a “new entrance effect”,22 indicating a local increase in the Sherwood number profile before settling to the same23,24 or different25 asymptotic value. An analysis of the
flat velocity profile; Dirichlet conditions
inlet (x = 0) at catalytic surface at inert surface
nB 3 rYk ¼ Da r Yk nB 3 rYk ¼ 0
(11) (12)
Sherwood number profile in the presence of catalyst structuring is presented. In order to delineate the effect of segmentation on flow-diffusion-reaction coupling, an isothermal system is considered in this work. Finally, the effect of various parameters (such as number of catalyst segments, periodicity, and aspect ratio) on the net conversion is presented.
’ NUMERICAL PROCEDURE Figure 1 shows the schematic of a single catalytic channel of circular cross section that has been modeled in this work. The diameter of the microreactor is 500 μm, and the length of the reactor is 2.5 cm; this “nominal” case corresponds to an aspect ratio of L/d = 50. The inside walls of the channel are coated with catalyst, where a generic first-order reaction is assumed to occur. Internal mass-transfer limitations are neglected. The shaded region indicates catalytic region in the microreactor channel. The first case represents full catalyst loading (henceforth referred to as the “uniform” case). As a starting point for catalyst segmentation, the “Cantor triads” are chosen as the fractal structuring technique, as was implemented on a flat plate system by Phillips et al.12 The middle third of the catalyst is successively removed from each active surface area, thereby reducing the catalyst loading. This is one of the simplest and well-known fractals.16 The schematic shown in the second row in Figure 1 shows the first fractal division, where the middle one-third of the catalyst is removed. From each of these active surfaces, another one-third of the active catalyst is removed to yield the second fractal division (see the schematic depicted in the third row of Figure 1). The procedure is repeated once again to obtain the third fractal division (see the schematic depicted in the bottom row of Figure 1). These will be referred to as the “Fractal-1”, “Fractal-2”, and “Fractal-3” structures, respectively. The corresponding amounts of active catalyst loading are 66.7%, 44.4%, and 29.7% for the three cases, respectively, compared to the “uniform” case. The two-dimensional (2D) axisymmetric steady-state simulations are performed under isothermal laminar flow conditions. A first-order reaction23 is assumed; the pre-exponential is 3.5 107 kg mol/(m2 s), the activation energy is 95 kJ/(mol K), and a constant temperature of 685 K is maintained. The pre-exponential factor is varied to match the nondimensional Damk€ohler number (Da). Homogenous reactions are neglected to decouple the catalytic and homogeneous interactions and allow us to analyze the effect of catalyst structuring on the flowdiffusion catalytic reaction coupling. The inlet velocity is chosen to be 12926
dx.doi.org/10.1021/ie2003957 |Ind. Eng. Chem. Res. 2011, 50, 12925–12932
Industrial & Engineering Chemistry Research
ARTICLE
Figure 2. Closeup of the mesh near the channel wall at the boundary between catalytic and noncatalytic regions for the second fractal division. The dimensions are given in millimeters. The figure is scaled by a factor of 10 in the Y-direction.
2.5 m/s for the base case simulations. Since the first-order rate kinetics are used, the results are independent of the concentration of the limiting reactant at the inlet. Recent studies2832 in microreactors justify the assumption of isothermal boundary conditions. The Prandtl and Schmidt numbers (Pr and Sc, respcetively) are assumed to be 0.7 in all simulations. The Damk€ohler number and the axial Peclet number are varied; their nominal values are given as Da = 100 and Pe = 250. The aspect ratio is the third parameter that is varied in our simulations. Table 1 summarizes the model equations solved using the computational fluid dynamics (CFD) software FLUENT 6.3.26. The mesh is generated with GAMBIT. Initially, a grid independence study was conducted for various fractal divisions. It should be emphasized that coarse meshes were avoided; they lead to numerical difficulties, because of the presence of singularities (boundaries of catalytic and noncatalytic regions). The final simulations were carried out with appropriately fine mesh. A nonuniform grid is chosen, with more nodes near the catalytic wall (in the radial direction) and closer axial grid spacing near the boundary of the catalytic and noncatalytic sections. A closeup of the grid chosen for the fractal-2 geometry is shown in Figure 2. The axial spacing for the grid is 0.0125 mm in each of the catalytic sections. A nonuniform axial grid is used in the noncatalytic section. A fine mesh (as shown in the figure) is required to accurately capture mass fluxes and Sherwood number profiles in the reactor. The grid size varies from 20 000 to 150 000 nodes, depending on the number of fractal divisions and the aspect ratio. As shown in Table 1, a flat inlet velocity profile and Dirichlet boundary conditions are prescribed at the inlet and the temperature of the entire reactor is held constant. Second-order upwind differencing is used for the species balance equations. The resulting continuity, momentum, and species balance equations are solved using FLUENT 6.3. The residuals are monitored. Convergence was verified when the residuals were 10. The overall Sherwood number correlation used is similar to that proposed by Hawthorn:26 a b Sh ¼ 3:656 1 þ ð4Þ x where x* is the dimensionless axial distance, which is defined as x ð5Þ x ¼ d Re Pe Similar to the observations of Donsi et al.,22,23 we obtained the following values for the parameters a and b: a ¼ 0:015ðDaÞ0:12
ð6Þ
b ¼ 0:59ðDaÞ0:016
ð7Þ
The comparison between the Sh values obtained through CFD simulations and from eq 4 is shown in Figure 8 for the Fractal-2 case. For the sake of clarity, only the first two catalyst segments are shown. The presence of catalyst structuring downstream does not affect the Sh value near the entrance. This is evident from overlapping curves in Figure 7 for all four catalyst structures at the entrance. When fractal structuring is introduced, the Sh value decreases along the length of the reactor, except at singularities, where large concentration gradients cause a sudden increase in the Sh value. At each boundary between the noncatalytic and catalytic segments, a new entrancelike effect is observed. This effect is weaker than the true entrance effect: from Figure 8, it is clear that the Sherwood number correlation (described by eq 4) overpredicts the Sh value obtained from the CFD simulations. Interestingly, all the fractal structures show the same behavior. For example, at a dimensionless length of x/L = 0.667, we have singularity between noncatalytic and catalytic segments for all three fractal divisions. At this location, the Sh value computed through CFD simulations overlap for all three fractal divisions (other parameters being constant). Thus, we can conclude that the effect of singularity is dependent on the Damk€ohler and Peclet numbers, 12929
dx.doi.org/10.1021/ie2003957 |Ind. Eng. Chem. Res. 2011, 50, 12925–12932
Industrial & Engineering Chemistry Research
Figure 9. Conversion versus Peclet number (Pe) for various fractal divisions, under base case conditions.
Figure 10. Mass flux computed along the reactor wall at (a) Pe = 250 and (b) Pe = 1000 for uniform catalyst (solid lines) and second fractal structuring (dashed lines). The loss of mass flux in noncatalytic regions (shaded region) is mostly compensated by the net gain in mass flux at singularities (indicated by crosshatched lines) at the lower Pe values.
and the axial distance along the length of the reactor; it is independent of not only the conversion but also the presence of additional singularities either upstream or downstream in the reactor. Effect of Peclet Number. The effect of bulk flow on efficacy of fractal structuring is expressed in terms of the Pe value, which gives a measure of the relative importance of convective (axial) transport over radial diffusion. Following the discussion given in the previous section, simulations were performed for Da = 100, varying the value of Peclet number in the range of Pe = 101000.
ARTICLE
Figure 11. Effect of aspect ratio on catalyst patterning of microreactors. Left ordinate: conversion versus aspect ratio for different fractal divisions; right ordinate: percentage reduction in active length versus aspect ratio for the second fractal division. All other parameters are at their nominal values.
The simulations are performed for a constant Schmidt number (Sc = 0.7). Figure 9 shows the conversion versus the Peclet number for various fractal divisions, keeping all other parameters constant. At lower Pe values, a comparison is not made, because complete conversion is obtained within a very short length from the inlet. As we increase the Pe value to 100 and beyond, the complete reactor is utilized for reaction and the conversion decreases as we increase the fractal divisions. The increase in mass-transfer rate at the singularities does not completely compensate for the loss in conversion rate at the noncatalytic surfaces. This is clear from Figure 10, where we plot the axial profile of mass flux along the reactor wall for uniform catalyst loading and the second fractal division. It has been shown by Donsi et al.22 that the entrance effect is extended at higher Pe values. Consequently, at the first noncatalytic region of Fractal-2 (i.e., from x/L = 0.111 to x/L = 0.222 in Figure 10), there is a greater loss in mass-transfer rate for Pe = 1000 than Pe = 250. The area ratio (flux gained at singularities to flux lost) decreases from 0.97 to 0.90, as the Pe value increases from 250 to 1000. Therefore, the fractal structuring becomes less effective at higher Pe values, although the effect of Peclet number on efficacy of fractal structuring is not strong. These observations are consistent with the results of Phillips et al.12 Effect of Aspect Ratio. In the earlier work,1,12 the effect of aspect ratio was not explicitly studied, although Loffler and Schmidt1 have varied the lengths of catalytic and noncatalytic regions. Typically, microreactors and catalytic monoliths have large aspect ratios. The reactor diameter (5001000 μm) and length (110 cm) were changed, while keeping the other dimensionless numbers constant. The conversion is plotted for various aspect ratios for different fractal divisions in Figure 11. As the aspect ratio increases, the conversion increases for a given fractal, because of more residence time and higher catalyst loading. The loss in conversion increases as the fractals increase at a given aspect ratio. Also plotted is the percent reduction in active catalyst (computed using eq 3) for the second fractal division; the ideal value when Fractal-2 gives the same conversion as the uniform case is 55.6%. The percentage reduction in active length decreases as the aspect ratio is increased. This indicates that fractal structuring is more effective at lower aspect ratios. Indeed, 12930
dx.doi.org/10.1021/ie2003957 |Ind. Eng. Chem. Res. 2011, 50, 12925–12932
Industrial & Engineering Chemistry Research
Figure 12. Effect of the number of catalyst segments on conversion at different catalyst loadings. The horizontal lines refer to second and third fractal divisions, respectively. All other parameters are at their nominal values.
in our earlier work,27 we found that the fractal structuring becomes is ineffective at higher aspect ratios for open flat-plate systems, and their effectiveness increases as the aspect ratio is reduced to L/d = 1. For typical microreactors, such small aspect ratios are unrealistic. Effect of Catalyst Segments. While fractal structuring is a convenient way to introduce singularities using self-similar structures, we now analyze the effect of periodicity and the number of singularities on the efficacy of catalyst segmentation. The results are summarized in Figure 12: the solid line with circular symbols refers to a 55.6% reduction in catalyst length and the dashed line with square symbols refers to a 70.3% reduction in catalyst length. The remaining catalyst is split into equal segments, which are placed at periodic intervals. The thin horizontal lines represent conversion from the Fractal-2 and Fractal-3 cases. First, we consider the Fractal-2 case. There are four segments of length x/L = 0.111, placed as shown in schematic (A) in Figure 12. The conversion from a reactor when the four segments are periodically placed with an equal length of noncatalytic segments separating them (as shown in schematic (B) in Figure 12) is indicated by the filled circle. The conversion from this system is same as that obtained from Fractal-2. Thus, the actual placement of the catalyst segments (as determined through fractals or placed periodically at equal intervals) does not affect the overall conversion. We further varied the length of the catalytic and noncatalytic segments to ensure the following: four catalytic and three noncatalytic segments, where ther first and last segments are catalytic, and total length of catalytic segments is constant (although not the length of each segment). Changing the length of these segments and their arrangement did not affect the conversion. In all the above simulations, the first catalyst segment was placed at the entrance (i.e., the n catalyst segments were separated by (n 1) noncatalytic segments). Next, simulations were repeated with the initial segment being noncatalytic; in other words, there were (n þ 1) equal noncatalytic segments separating the n catalytic segments, as shown in schematic (C) of Figure 12. Note that the length of each of the n catalytic segments was kept constant. With this arrangement, the conversion dropped from 85.8% (the Fractal-2 case) to 83.9%. This is indicated by the filled triangle in Figure 12. We repeated simulations for a few other cases to verify that this result is more
ARTICLE
general. Clearly, the true entrance effect at the inlet is stronger than the increase in mass transfer observed at the singularities. It is clear from these results that keeping the catalyst segment first (at the inlet) makes a slight improvement in conversion, compared to the second case. These results indicate that the creation of complex fractal patterns is not required to experimentally achieve the benefits of catalyst segmentation. The catalyst segmentation strategy relies on creating alternate regions of catalytic and noncatalytic segments. Such alternating periodic patterns are more feasible to achieve experimentally than the fractals. Finally, we studied the effect of changing the number of catalyst segments. The first catalytic segment is placed at the inlet. When we decreased the number of segments, keeping the same total length of the catalytic region (see Figure 12), the conversion was reduced. Conversely, increasing the number of segments increased conversion. Similar results were also observed by Loffler and Schmidt1 for ammonia oxidation on a platinum gauge. This is because more segments imply a greater number of singularities that cause the increase in mass flux, because of the large concentration gradients at these singular points. Conversion finally tapers off and does not exceed that obtained for the uniform case. Similar results also are observed for the Fractal-3 case. The conversion with 29.6% of the length being catalytic would settle at a value less than that for the previous case.
’ CONCLUSIONS This work followed up on the work of Phillips et al.,12 who found fractal structuring in a mass-transfer-limited flat-plate reactor to be extremely effective in reducing the catalyst by 76%, with a marginal reduction in activity. In this work, we have investigated the efficacy of using fractal structuring in catalytic microreactors. An initial conclusion of this work is that fractal catalyst structuring is less effective in catalytic microreactors than the open geometry.1,12 The efficacy of fractal catalyst structuring, when compared to using a single catalyst segment, shows a net improvement in conversion. The fractals were effective for mass-transfer-controlled systems and the effectiveness of the fractals decreased for Damk€ohler numbers of Da < 10. The Peclet number (Pe) had a rather weak influence on effectiveness of fractal structuring, although the effectiveness of fractal structuring decreased as the Pe value increased. The effect of aspect ratio was also studied; fractal structuring was more effective at lower aspect ratios. The effectiveness of fractals was studied by finding the equivalent length of reactor required to achieve the same conversion and comparing it with the fractal geometry. Under the best conditions considered, as much as 40% reduction in the active catalyst length can be achieved using the third fractal division. However, this number is nearly half of what can be achieved in the ideal case of a perfectly effective strategy. Since microreactors generally operate at higher Pe values and have a large aspect ratio, fractal catalyst structuring is not recommended as a general strategy for reducing the catalyst loading. The increase in conversion observed when using fractal structuring was due to the increase in mass-transfer rate at the boundaries of catalytic and noncatalytic sections. The “entrance effect” (i.e., a large value of the Sherwood number (Sh) at the reactor inlet) was same as that in the uniform catalyst loading case. The Sherwood number profile at the entrance was not 12931
dx.doi.org/10.1021/ie2003957 |Ind. Eng. Chem. Res. 2011, 50, 12925–12932
Industrial & Engineering Chemistry Research affected by the presence of downstream catalyst structuring. A large increase in the Sh value, similar to the entrance effect, was observed at the leading edge of each catalytic segment. This is attributed to the large concentration gradients at singularities (noncatalytic-to-catalytic boundary). This increase in the Sherwood number profile was somewhat weaker than the entrance effect at the inlet. Finally, the effect of singularities and periodicity of the patterns was studied. Increasing the number of singularities by further segmenting the available catalyst into multiple regions resulted in higher conversion. The location of the catalyst segments does not have an impact on the conversion, as long as the first catalyst segment is placed at the reactor inlet. Thus, the presence of singularities is more important than maintaining self-similar patterns of catalyst segments.
’ AUTHOR INFORMATION Corresponding Author
*Tel.: [þ91] (44) 22574176. E-mail:
[email protected].
’ REFERENCES (1) Schmidt, L. D.; Loffler, D. G. Catalytic Activity and Selectivity on Heterogeneous Surfaces with Mass Transfer. AIChE J. 1975, 21, 786–791. (2) Matros, Y. S. Unsteady Processes in Catalytic Reactors; Studies in Surface Science and Catalysis Series; Elsevier: Amsterdam, 1985. (3) Matros, Y. S. Forced unsteady-state processes in heterogeneous catalytic reactors. Can. J. Chem. Eng. 1996, 74, 566–579. (4) Sheintuch, M.; Shvartsman, S. Spatiotemporal patterns in catalytic reactors. AIChE J. 1996, 42, 1041–1068. (5) Sheintuch, M. On the intermediate asymptote of a diffusionlimited reactions in a fractal porous catalyst. Chem. Eng. Sci. 2000, 55, 615–624. (6) Kaisare, N. S.; Lee, J. H.; Federov, A. G. Operability analysis and design of a reverse-flow microreactor for hydrogen generation via methane partial oxidation. Ind. Eng. Chem. Res. 2005, 44, 8323–8333. (7) Cote, A. S.; Delgass, W. N.; Ramakrishna, D. Investigation of spatially patterned catalytic reactors. Chem. Eng. Sci. 1999, 54, 2627–2635. (8) Jensen, K. F. Microreaction engineering—Is small better?. Chem. Eng. Sci. 2001, 56, 293–303. (9) Liebman, L. S.; Schmidt, L. D. Catalytic partial oxidation of isobutane at millisecond contact times. Appl. Catal., A 1999, 179, 93–106. (10) Kaisare, N. S.; Stefanidis, G. D.; Vlachos, D. Millisecond production of hydrogen from alternative, high hydrogen density fuels in counter current multifunctional microreactor. Ind. Eng. Chem. Res. 2009, 48, 1749–1760. (11) Norton, D. G.; Deshmukh, S. R.; Wetzel, E. D.; Vlachos, D. G. Downsizing Chemical Processes for Portable Hydrogen Production. In Microreactor Technology and Process Intensification; Wang, Y., Holladay, J. D. Eds.; ACS: New York, 2005; pp 179. (12) Phillips, C.; BenRichoub, A.; Ambarib, A.; Federov, A. G. Catalyst surface at a fractal of cost—A quest for optimal catalyst loading. Chem. Eng. Sci. 2003, 58, 2403–2408. (13) Di Benedetto, A.; Sarli, V. D.; Russo, G. A novel catalytichomogenous micro-combustor. Catal. Today 2009, 1475, S156–S161. (14) Groppi, G.; Tronconi, E.; Forzatti, P. Investigations on catalytic combustors for gas turbine applications through mathematical model analysis. Appl. Catal. 1996, 138, 177–197. (15) Chen, G. B.; Chao, Y. C.; Chen, C. P. Enhancement of hydrogen reaction in a micro-channel by catalyst segmentation. Int. J. Hydrogen Energy 2008, 33, 2586–2595.
ARTICLE
(16) Mandelbrot, B. The Fractal Geometry of Nature; W.H. Freeman: New York, 1983. (17) Levy, A. S.; Avnir, D. Fractal analysis of surface geometry effects on catalytic reactions. Surf. Sci. 1991, 248, 258–270. (18) Zhang, B.; Liu, X. Mechanism Discrimination in Heterogeneous Catalytic Reactions: Fractal Analysis. Ind. Eng. Chem. Res. 2000, 39, 573–574. (19) Jifen, W.; Bin, Z.; Shize, D.; Qiang, L. Catalyst Description by Using Fractal Measures. In Pattern Recognition, 1992, Vol. III, Conference C: Proceedings of the 11th IAPR International Conference on Image, Speech, and Signal Analysis; IEEE: Piscataway, NJ, 1992; pp 534536. (20) Kaisare, N. S.; Stefanidis, G. D.; Vlachos, D. G. Transport Phenomena in Microscale Reacting Flows. In Handbook of Microprocess Engineering: Fundamentals, Operations, and Catalysts; Renken, A., Wang, Y., Eds.; WileyVCH: Berlin, 2008. (21) Shah, R. K.; London, A. L. Laminar Flow Forced Convection; Academic Press: New York, 1978. (22) Donsi, F.; Di Benedetto, A.; Marra, F. S.; Russo, G. CFD Simulation of heat transfer in a circular channel: Effect of the Pe number. Int. J. Chem. React. Eng. 2005, 3, A36. (23) Donsi, F.; Di Benedetto, A.; Marra, F. S.; Russo, G. Effect of the Re number on heat and mass transport ina catalytic monolith. Catal. Today 2006, 117, 498–505. (24) Groppi, G.; Belloli, A.; Tronconi, E.; Forzatti, P. A comparison of lumped and distributed models of monolith catalytic combustors. Chem. Eng. Sci. 1995, 50, 2705–2715. (25) Gupta, N.; Balakotaiah, V. Heat and mass transfer coefficients in catalytic monoliths. Chem. Eng. Sci. 2001, 56, 4771–4786. (26) Hawthorn, R. D. AIChE Symp. Ser. 1974, 70 (137), 428. (27) Regatte, V. R.; Mukherjee, A.; Kaisare, N. S. Numerical analysis of fractal catalyst structuring in microreactors. In 19th International Congress of Chemical and Process Engineering CHISA, Prague, Czech Republic, 2010, http://www.chisa.cz/2010/default.aspx. (28) Ganley, J. C.; Seebauer, E. G.; Masel, R. I. Porous anodic alumina microreactors for production of hydrogen from ammonia. AIChE J. 2004, 50, 829–834. (29) Cao, E.; Gavriilidis, A. Oxidative dehydrogenation of methanol in a microstructured reactor. Catal. Today 2005, 110, 154–163. (30) G€orke, O.; Pfeifer, P.; Schubert., K. Kinetic study of ethanol reforming in a microreactor. Appl. Catal., A 2009, 360, 232–241. (31) Pfeifer, P.; K€olb, A.; Schubert, K. Kinetic investigations on methanol steam reforming on Pd-Zn catalysts in microchannel reactors and model transfer into the pressure gap region. Catal. Today 2005, 110, 76–85. (32) Thormanna, J.; Pfeifer, P.; Schubert, K.; Kunz, U. Reforming of diesel fuel in a micro reactor for APU systems. Chem. Eng. J. 2008, 135S, S74–S81.
12932
dx.doi.org/10.1021/ie2003957 |Ind. Eng. Chem. Res. 2011, 50, 12925–12932
