2986
Ind. Eng. Chem. Res. 2004, 43, 2986-2999
Microreactor Modeling for Hydrogen Production from Ammonia Decomposition on Ruthenium S. R. Deshmukh, A. B. Mhadeshwar, and D. G. Vlachos* Department of Chemical Engineering and Center for Catalytic Science and Technology (CCST), University of Delaware, Newark, Delaware 19716-3110
Ammonia decomposition for the production of hydrogen in a newly fabricated, aluminum framework post microreactor is modeled. A detailed microkinetic model describing the chemistry of ammonia decomposition on Ru is developed. A PFR model is used as a low hierarchical tool for developing a reduced rate expression using a computer-aided methodology. This reduced chemistry model is used in computational fluid dynamics simulations of microreactors, and good agreement with experimental data is observed. It is found that the overall conversion in the post microreactor better approximates that of a PFR than that of a CSTR. It is shown that the posts play an important role in enhancing the transverse mass transfer and providing a high catalyst surface area and that interesting flow patterns and back-diffusion occur at lower flow rates. Finally, parametric studies are performed, and a tradeoff between pressure drop and conversion is observed under certain conditions. Introduction Microchemical devices emerged more than a decade ago enabled by advances in the fabrication of microelectromechanical systems. Initial efforts on microchemical systems focused on high-throughput systems for the screening of catalyst, materials, and pharmaceuticals; the remote and/or on demand production or handling of toxic and explosive chemicals; the manipulation of selectivity; the demonstration of reduced gradients for extraction of chemistry using ideal reactor models; etc.1-7 New applications, ranging from heat sources for soldiers to portable power generators for telecommunications and electronic devices such as laptops and computers, have recently created strong interest in microchemical systems. All of these applications rely on efficient power generation. Fuel cells are being considered as battery replacements for some of these applications because of their high efficiency and environmentally benign operation.8-10 The primary idea of an integrated microchemical device (fuel processor plus fuel cell) is to convert chemical energy into electricity. Hydrogen-based proton exchange membrane (PEM) fuel cells show good potential for the production of electricity.8-10 However, widespread commercialization of portable PEM fuel cells will depend on the cheap and environmentally benign production of hydrogen at the small scale based on some type of a microreactor. The higher energy density of hydrocarbons, methanol, and ammonia (nearly 100-fold) compared to conventional Li-based batteries makes them ideal candidates for the production of hydrogen and eventually electricity. Traditionally, hydrogen has been produced using steam reforming, partial oxidation, and autothermal reforming.11-16 Independent of the production route, syngas has to be processed to produce “pure” hydrogen, given the low tolerance of the catalyst of PEM fuel cells. Membrane separation or water-gas shift and * To whom correspondence should be addressed. E-mail:
[email protected]. Tel.: (302) 831-2830. Fax: (302) 8311048
selective catalytic removal of CO are currently being investigated as possible routes to overcome the problem of hydrogen purity. Among fuels, ammonia is a COxfree source of hydrogen that might turn out to be a viable candidate for portable devices. Its ease of liquefaction is an added advantage in terms of storage and transportation. Whereas ammonia synthesis is a mature commercial process,11,17 the reverse path of decomposition for hydrogen production has been of interest only recently.18,19 As a result, there is a lack of predictive models to describe the decomposition chemistry. The small scales of microchemical devices have inherent advantages, including high heat- and mass-transfer coefficients and large surface-area-to-volume ratios. At the same time, small scales impose certain challenges in the practical realization of microchemical systems for high-temperature applications. Enhanced mixing to overcome the low Reynolds numbers, high catalyst loadings in microdevices to achieve desirable conversions, and low pressure drops must be simultaneously achieved. Recently, novel microreactor designs have been fabricated using electrodischarge machining,20 silicon etching,21 and sacrificial beaded beds22 to address these challenges. On the modeling side, computational fluid dynamics (CFD) simulations for simple microreactor geometries, such as a T-microreactor,23 straight channel microburners,24,25 a tubular microreactor,26 and a capillary microreactor27 have been employed to explain corresponding experiments. However, results from these studies do not easily extend to the design and optimization principles of complex structured microreactors. It is our objective to perform simulations in such microreactors in order to elucidate the relevant physics. In this paper, we model ammonia decomposition in a complex, post microreactor geometry, depicted in the inset of Figure 1, for hydrogen production. We propose a detailed microkinetic model for the ammonia decomposition on Ru, accounting for the N-N lateral interactions for the first time, to predict the experimental microreactor data. A one-step, easy-to-use kinetic rate expression is then derived. Using this reduced chemistry
10.1021/ie030557y CCC: $27.50 © 2004 American Chemical Society Published on Web 02/06/2004
Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004 2987
Figure 1. PFR simulations with full and reduced reaction models compared to the experimental data of Ganley et al.20 The detailed reaction model can describe well the experimental data without any adjustment in kinetic rate parameters. Our computer-assisted reduced reaction model E4 is in very good agreement with the detailed model. Predictions of the reduced reaction rate expressions (E1-E3) from the literature deviate from the experimental data. The parameters are as follows: inlet volumetric flow rate of 15 sccm, area-to-volume ratio of ∼31 cm-1, and length of ∼1 cm. The inset shows a schematic of the post microreactor used in the experiments of Ganley et al.20 Details of the microreactor geometry are illustrated in Figure 5.
model, a hierarchy of chemical reactors is employed, ranging from ideal reactors, such as plug-flow reactors (PFRs) and continuous stirred tank reactors (CSTRs), to CFD simulations in straight tubes (tubular reactors with explicit 2D axisymmetric flow and mass-transfer treatment) and complex geometries (post microreactor). The ideal reactors are used as a rapid screening tool and as a threshold for comparison with the overall flow/ chemistry characteristics of complex structured reactors. Parametric studies delineate the role of operating conditions and geometric features in reactor performance. Ammonia Decomposition Chemistry In this section, proposed kinetic rate expressions in the literature are first assessed. Subsequently, a microkinetic model for ammonia decomposition on Ru is employed and compared to experimental data using a PFR (a low hierarchical reactor model). A computerassisted methodology is employed for the PFR to derive a reduced rate expression that can be used in CFD simulations. Finally, the important chemistry under atmospheric-pressure microreactor conditions is identified. Assessment of Literature Rate Expressions. Although extensive research has been devoted to ammonia synthesis,28-36 the decomposition kinetics is not as well established. Of all the transition metals studied so far, Ru has been found to give the highest conversion,37,38 and hence, it is selected for this study. Reduced rate expressions describing ammonia decomposition on Ru have been proposed, for example, by Bradford et al.19 and Tsai and Weinberg,39 and are listed in Table 1. Expression E1 was derived assuming N-H bond cleavage and recombinative N2 desorption as the ratedetermining steps (RDSs) and N* as the most abundant reactive intermediate (MARI).36 This expression was shown to be qualitatively consistent with the reaction order in NH3 observed under the UHV experiments of Tsai and Weinberg, namely, zeroth order at low temperatures and first order at high temperatures. On the other hand, expression E2 assumes adsorbed nitrogen atoms to be in equilibrium with the gas-phase NH3 and
H2, with recombinative N2 desorption being the RDS and N* again being the MARI. E2 explains only the inhibitive influence of H2 as described in refs 40 and 41. Expression E3 was derived for high temperatures (>750 K) and can be rationalized for surface-reactionlimited conditions with NH3* being the only important surface species. These reduced kinetic rate expressions were based on Langmuir-Hinshelwood kinetics with the aforementioned assumptions and aimed at describing certain experimental trends. These expressions have not been used for quantitative reactor performance predictions at atmospheric conditions. To assess the performance of these expressions for atmospheric data, PFR simulations were carried out for conditions corresponding to the microreactor experiments of Ganley et al.20 Although our choice of a PFR is not yet obvious and will be discussed below, our aim here is to explore the differences between the predictions of these rate expressions and a set of experimental microreactor data. In the absence of data on reaction rate constants (for E1 and E2), values were obtained from transition state theory (TST)30 and the semiempirical unity bond index-quadratic exponential potential (UBI-QEP) theory, also known as bond order conservation (BOC),42,43 indicated in Tables 2 and 3 (discussed later), whereas for E3, the molecular flux is calculated using the kinetic theory of gases. In all simulations below, the surface-area-to-volume ratio is taken to be ∼31 cm-1 (unless otherwise specified). This is ∼20% lower than the actual geometric area per unit volume of ∼38.15 cm-1 of the experimental post microreactor of Ganley et al.20 to account for the uncertainty in the catalyst surface area. A site density of 1015 sites/cm2 is used. Alternatively, one could reduce the site density while keeping the surface-area-tovolume ratio equal to the actual one. Furthermore, different values of prefactors will most probably lead to a different value of the area-to-volume ratio. Therefore, the value given here should be taken as just an order-of-magnitude estimate. Finally, the residence time is computed from the volumetric flow and reactor temperature (e.g., ∼0.3 s for an inlet flow rate of 15 sccm, an entrance cross section of 0.26 cm2, and a reaction zone length of ∼1 cm). Note that the velocity accelerates in the posts, because of the increasing number of moles and the reduced cross-sectional area that is open for flow, and thus, the contact time in the reaction zone is lower than 0.3 s. As seen in Figure 1, the literature rate expressions differ considerably from each other, because of the different underlying assumptions and conditions, as well as from the microreactor experimental data (this is especially true for E2 and E3). Development and Assessment of a Detailed Microkinetic Model. Because of the lack of predictive capabilities of the rate expressions available in the literature, a detailed surface reaction mechanism for ammonia decomposition on Ru is developed, using the multistep methodology described in ref 44. The mechanism is listed in Table 3 and consists of six reversible elementary steps comprising adsorption/desorption of NH3, N2, and H2 and hydrogen-abstraction steps from NHx intermediates and their reverse. The heats of chemisorption as a function of species coverages are an input to UBI-QEP, which in turn calculates coverage-dependent activation energies for all reaction steps. Orderof-magnitude estimates of preexponential factors are determined using TST.30
2988 Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004 Table 1. Expressionsa for the Rate of NH3 Decomposition on Ru no.
expression for the rate of ammonia decomposition [mol/(cm2 s)] k11 k9 PNH3 k12
E1 σNH3 )
( x
k9k11 P 2k4k12 NH3
1+
E2
σNH3 ) K)
E3 E4
(
(1 + xK)2
k9k11k7k5 P k6k8k12 NH3
)( ) 2
k2 k1PH2
3
σNH3 ) 0.5FluxNH3 exp[-5000/(1.987T)]
( x
σNH3 )
ω)
-2(k4ω2 - k3PN2) k11 P + k12 NH3
k3 P + k4 N2
x
ref 19
(i) N* is in equilibrium with NH3 and H2 (ii) N2 desorption is the RDS (iii) N* is the MARI
19
(i) high temperatures (>750 K) (ii) NH3* surface reaction is decomposition-limited small reaction rates and species coverages are neglected from species balances and site conservation, respectively
39
2
k4K
1+
a
)
assumptions (i) N2 desorption and N-H cleavage are the RDSs (ii) N* is the MARI
k1 P +ω k2 H 2
)
2
this work
x
k2 k7k9k11 P P -0.5 k1 2k4k10k12 NH3 H2
Kinetic parameters (k) appearing here that have been used in our simulations (except for expression E3) are given in Table 3.
Table 2. Heats of Chemisorption of Species in NH3 Chemistry on Ru at Zero Coverage species
heat of chemisorptiona (kcal/mole)
refs
N* H* NH3* NH* NH2*
135.0-35.0θNb,c 63.0 18.2 86.8 60.0
45-47, 54 31 31 our UBI-QEP calculations our UBI-QEP calculations
a UBI-QEP was used to calculate the bare surface heats of chemisorption of NH2* and NH*. b θ indicates the coverage of surface species. c N-N adsorbate-adsorbate interactions of 35 kcal/mol/ML were taken from the DFT simulations of refs 45-47.
The heats of chemisorption for various species, taken here from surface science experiments (see ref 31 and references therein), are listed in Table 2. Because of the high surface coverages of N* and the strong N-N repulsions, a coverage-dependent heat of chemisorption for N, taken from the density functional theory (DFT) calculations of Jacobi,45 Mhadeshwar et al.,46 and Logadottir and Norskov (reported in ref 47), is included. Adsorbate-adsorbate interactions between H atoms could be taken as 3.5 kcal/mol.48 However, their effect on model predictions is small, and for simplicity, they are left out. NHx-NHx interactions might be significant given the similarity of these species to N*, but because of the relatively low coverages of NHx species at the high temperatures of practical interest, these interactions are also not taken into account. The N-N adsorbateadsorbate interactions result in coverage-dependent activation energies of several steps (discussed further below). Finally, because N2 dissociation on Ru is activated, according to surface science experiments49 as well as quantum mechanical DFT calculations,35,45,50 this reaction is taken into consideration in our analysis through the UBI-QEP framework (see Table 3). This mechanism is hereafter called the screening or unoptimized mechanism. Screening mechanisms can typically describe experiments only in a semiquantitative manner, and rigorous fine-tuning is necessary for quantitative model prediction.51-53 Note that this is typically true even when highest-level DFT simulations are used
Table 3. Proposed Surface Reaction Mechanism (Unoptimized) for Ammonia Decomposition on Rua
no.
reaction
R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12
H2 + 2* f 2H* 2H* f H2 + 2* N2 + 2* f 2N* 2N* f N2 + 2* NH* + * f H* + N* H* + N* f NH* + * NH2* + * f H* + NH* H* + NH* f NH2* + * NH3* + * f H* + NH2* H* + NH2* f NH3* + * NH3 + * f NH3* NH3* f NH3 + *
activation sticking energyb coefficient (kcal/mol) (unitless) or preexponential at at factor (s-1) θ* ) 1 θN* ) 0.3 1 1.0 × 1013 1 1.0 × 1013 1.0 × 1011 1.0 × 1011 1.0 × 1011 1.0 × 1011 1.0 × 1011 1.0 × 1011 1 1.0 × 1013
1.9 23.7 6.2 50.3 5.8 37.2 19.1 17.4 17.5 13.2 0 18.2
1.9 23.7 14.1 37.2 10.4 31.4 19.1 17.4 17.5 13.2 0 18.2
a The mechanism is enthalpically consistent at 300 K. To ensure entropic consistency, preexponential factors (A) of unimportant reactions can be adjusted. This can be achieved, for example at 300 K, by setting A5 ) 4.98 × 1011 s-1, A6 ) 4.48 × 1010 s-1, and A8 ) 4.48 × 1010 s-1. b The activation energies in column 4 are calculated in the zero coverage limit (θ* ) 1). In the detailed microkinetic model, activation energies are coverage-dependent as determined using the UBI-QEP framework with the heats of chemisorption listed in Table 2. Activation energies at θN*)0.3 are also indicated in the last column and are used in the reduced reaction rate expressions E1, E2, and E4 (see Table 1).
for parameter estimation. The activation energies in the screening mechanism are solely based on UBI-QEP. Next, we briefly discuss the reaction energetics that differ from previously reported values (a detailed comparison of the literature energetics of NH3 chemistry on Ru can be found in ref 46). Typical DFT calculations in the literature are carried out on a flat surface. The heats of H*-abstraction reactions in our mechanism differ from those of Zhang et al.54 (in our case, reaction R5 is exothermic and reactions R7 and R9 are endothermic, whereas in Zhang et al.’s work,54 the first and third H*-abstraction steps are endothermic while the second H*-abstraction step is exothermic). Furthermore, DFT-predicted energetics of H*-abstraction reactions on a flat surface are opposite from those on steps in terms
Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004 2989
of heats of reaction.54,55 These differences arise from different binding energies between various studies. Our energetics is more consistent with the DFT energetics on a stepped surface,55 compared to that on a flat surface.54,55 It should be also noted that the activation energies of reactions R3-R6 are strongly dependent on the N* coverage. Our screening mechanism, based on UBI-QEP, is enthalpically consistent.44,51 However, the order-ofmagnitude preexponential factors obtained from TST do not satisfy entropic consistency. Following the discussion on thermodynamic consistency of surface reaction mechanisms in ref 53, the present mechanism can be made fully thermodynamically consistent, say, at 300 K, by minor tuning of insensitive preexponential factors, such as those of reactions R5, R6, and R8, as discussed in footnote a of Table 3. This thermodynamically consistent screening or unoptimized mechanism is used below. We emphasize again that some prefactors differ from those used in previous work because parameter fine-tuning is not our goal here. For example, the sticking coefficient of H2 (SH2) varies significantly as a function of the surface coverage, as well as the type of the catalyst surface. Savargaonkar et al.48 observed that this parameter varies between 0.01 and 0.35 on Ru(0001) and between 0.003 and 0.2 on Ru/SiO2 as a function of H* coverage. Christmann and Muschiol56 observed SH2 ≈ 1 on Ru(1010). Such variation is common; in fact, SH2 on Pt is also found to vary from e0.001 on defect-free Pt(111) to 0.01 on Pt(111) to 0.9 on Pt(332) 57. The most important point here is that the overall conclusions reached below regarding the important reactions and species and the post microreactor behavior are practically the same upon mechanism optimization (not shown). Thus, the screening mechanism proposed herein is sufficient for microreactor analysis. Rigorous optimization of the chemistry and validation against a comprehensive set of data and reaction model analysis will be the focus of a forthcoming paper.58 The ideal PFR model is used again as a rapid means of detailed assessment of the reaction mechanism. Steady-state PFR runs are carried out at atmospheric pressure in the temperature range of 673-923 K. No gas-phase reactions are considered in the model. Pure ammonia is assumed to be present at the inlet. The mass balance equations are solved using DDASSL.59 The predictions for the experimental conditions of ref 20 are in fairly good agreement with the published data, as shown in Figure 1, without tuning of any of the reaction parameters. Hierarchical Detailed Chemistry Reduction. The full microkinetic model, though useful in providing detailed information on the chemistry involved, makes CFD simulations demanding, especially when parametric and/or optimization studies need to be carried out. A simple one-step rate expression, on the other hand, is much faster to run, provided it is sufficiently accurate. Here, we use a recently introduced systematic, computeraided chemistry reduction methodology.60 This methodology is based on reaction path analysis (RPA) and involves identification of the important reactions and species under desired conditions, along with the use of small-parameter asymptotics (zeroth-order models), followed by simple algebraic manipulations. The chemistry model reduction is done very efficiently and cheaply in a PFR and subsequently used in CFD. This idea (train in a simple reactor, use in a complex reactor) was illu-
Figure 2. Steady-state reaction rates at the reactor exit at three temperatures obtained from isothermal PFR simulations using the detailed microkinetic model of Table 3. There is a large disparity in reaction rates. Reactions with small rates might still be important for some of the surface species. The parameters are those of Figure 1.
strated before for flame chemistry61 and works well when the transport time scales of different reactors are comparable. The reduction approach is illustrated next. Using the mechanistic steps in Table 3, the following steady-state balances for the surface species are obtained
dθH* ) 2r1 - 2r2 + r5 - r6 + r7 - r8 + r9 - r10 ) 0 dt (1) dθN* ) 2r3 - 2r4 + r5 - r6 ) 0 dt
(2)
dθNH* ) -r5 + r6 + r7 - r8 ) 0 dt
(3)
dθNH2* dt dθNH3* dt
) -r7 + r8 + r9 - r10 ) 0
(4)
) r11 - r12 - r9 + r10 ) 0
(5)
The overall site conservation equation is
θNH3* + θNH2* + θNH* + θN* + θH* + θ* ) 1
(6)
where r represents the reaction rate and θ the species coverage. The first step in the methodology is to identify the important reactions and species. PFR simulations used above for the assessment of the full reaction model provide valuable information regarding the values of the steady-state coverages of various surface species and the individual reaction rates in the screening mechanism. Typical magnitudes of these parameters are shown in Figures 2 and 3. At low temperatures, the surface is mostly covered by NH3* (∼60%) as the thermal energy to overcome the activation barrier for surface reaction is low. The coverage of N* (∼35%) is higher than that of H* (only ∼10%) owing to the larger activation energy barrier for N2 desorption (see also Table 2). Finally, very few surface vacancies exist. At higher temperatures, the surface is dominated by NH3* and N* at short distances, but ammonia reacts rapidly, giving rise to H*, N*, and some vacancies. The changes in the species coverages are more rapid in the initial 1% of the reactor length.
2990 Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004
Using such information, reduced balances are derived as follows
dθH* ) 2r1 - 2r2 + r9 - r10 ) 0 dt
(1′)
dθN* ) 2r3 - 2r4 + r5 - r6 ) 0 dt
(2′)
dθNH* ) -r5 + r6 + r7 ) 0 dt
(3′)
dθNH2* dt
Figure 3. Steady-state species coverages along the length of the reactor at three temperatures obtained from isothermal PFR simulations using the detailed microkinetic model of Table 3. The parameters are those of Figure 1. Significant changes occur in the first 1% of the reactor length. At low temperatures, NH3* is the dominant species, whereas at high temperatures, H* and N* dominate.
The coverage of N* remains almost constant along the reactor length. At low temperatures, NH3* dominates because of its slow decomposition, and at high temperatures, H* is the dominant surface species, with N* being the second dominant species. This finding is at first counterintuitive because H* desorbs more rapidly from the surface than N*, and one would expect the coverage of H* to be low. From a comparison of the reaction rates at various temperatures shown in Figure 2 and a more detailed analysis that follows below, it is found that the ammonia and hydrogen adsorption/desorption reactions have high rates and that these species are in partial equilibrium (PE). The PE of H* with H2 and the high mole fraction of H2 in the gas phase at high ammonia conversions explains the significant coverages of H*. Obviously, this situation is very different from that encountered under UHV conditions, where no or very little readsorption of products occurs and species inhibition is caused only by the slow chemistry and desorption of products. As a result, the previously proposed reduced rate expressions based on N* being the MARI are not expected to hold at atmospheric-pressure, flow-reactor-type conditions. To become quantitative in our analysis, the relative contribution of each reaction in each species’ balance is determined, according to Figure 2, and summarized in Table 4. Threshold limits are set for the contribution of reaction rates (10%) and surface coverages (1%). Reactions or species whose contributions are below the threshold are neglected in eqs 1-5 or 6, respectively. Figures 2 and 3 indicate that the importance of each reaction changes with temperature. To develop a reduced rate expression that is applicable over the entire temperature range, RPA is carried out at various temperatures at the exit of the PFR. Once the important reactions and species are determined at different conditions, their union is used. Alternatively, one could use principal component analysis to determine the important steps at different conditions.62,63 Finally, because the PFR is an evolutionary (initial-value) problem, RPA was also carried out along the length of the reactor at various temperatures. We found that, for reactor lengths greater than 1% of the total length, the important chemistry remains practically the same as that at the reactor exit. The small differences near the inlet of the reactor have only a slight effect on the ammonia conversion and, for the sake of simplicity, are neglected.
dθNH3* dt
) r9 - r10 ) 0
(4′)
) r11 - r12 ) 0
(5′)
θNH3* + θN* + θH* + θ* ) 1
(6′)
Equations 4′, 5′, and 1′ (in conjunction with eq 4′) indicate that the desorption/adsorption of NH3*, reactions R9 and R10, and the desorption/adsorption of H* are in PE. The coverages of H* and NH3* can easily be determined as
θH* ) θ*
x
k1 P k2 H2
k11 θNH3* ) θ* PNH3 k12
(7) (8)
Solving the quadratic expression resulting from substitution of eq 3′ into eq 2′ and using eq 4′, the coverage of adsorbed nitrogen atoms N* is obtained as
θN* ) θ*ω
(9a)
with
ω)
x
k3 P + k4 N2
x
k2 k7k9k11 P P -0.5 (9b) k1 2k4k10k12 NH3 H2
The coverage of vacancies * can easily be determined from eqs 6′ and 7-9 as
θ* )
1 k11 1+ P + k12 NH3
x
k1 P +ω k2 H2
(10)
Because hydrogen and ammonia are nearly in PE, the net rate of the overall reaction is calculated using the rates of the nitrogen adsorption and desorption steps. The rate of N2 production is
σN2 ) k4θN*2 - k3PN2θ*2 ) (k4ω2 - k3PN2)θ*2 (11a) The rates of hydrogen production and ammonia decomposition are obtained from the overall reaction stoichiometry and are
σH2 ) 3σN2
and
σNH3 ) -2σN2
(11b)
The final reduced rate expression for ammonia decomposition can be written as
Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004 2991 Table 4. Reaction Path Analysis at Various Temperaturesa species
T (K)
R1
R2
H*
650 850 950
9.3 46.5 49.9
9.5 52.1 49.9
N*
650 850 950
NH*
650 850 950
NH2*
650 850 950
NH3*
650 850 950
R3
R4
0.01 15.2 31.9
32.3 28.7 33.9
R5
R6
R7
R8
R9
R10
0.2 0.01 0.01
0.0 0.0 0.0
0.1 0.0 0.0
0.0 0.0 0.0
40.6 0.6 0.1
40.5 0.6 0.1
48.8 33.4 11.8
1.2 2.6 2.2
0.2 0.4 1.0
0.0 0.0 0.2
50.0 50.0 49.8
49.8 49.6 49.0
0.0 0.1 0.2
0.0 0.1 0.2
66.1 41.5 19.0
1.6 14.6 15.2
48.8 47.4 47.8
1.2 16.6 38.2
R11
R12
50.0 49.9 49.8
50.0 49.9 49.8
a Each value indicates the percent contribution of a reaction in the balance for a particular species. Blanks in the table indicate that a particular reaction does not involve the species under consideration. The sum across each row of the table might not be exactly equal to 100% because of rounding of decimals.
σNH3 )
(
1+
-2(k4ω2 - k3PN2) k11 P + k12 NH3
x
k1 P +ω k2 H2
)
2
(12)
Note that, when pure ammonia is fed into the reactor, the inlet pressure of H2 is zero in initial-value problems, such as a PFR, and eq 9b will not work. This difficulty is inherent to the problem that the RPA is different at very short length scales. However, the gaseous concentration of H2 accumulates rapidly to finite values even at dimensionless lengths on the order of 10-6 (see Figure 3 for corresponding coverages). Thus, use of a small (numerical) mole fraction of H2 at the entrance of 10-6 (recommended value) or below alleviates this mathematical problem and does not affect the predicted conversion, as long as this inlet value remains small enough (an alterative would require another reduced model for the entrance region, which complicates the analysis). The reduced reaction model can include coveragedependent activation energies, but doing so would require use of the entire UBI-QEP framework or a simplification of it. To simplify its use, we first fitted the activation energies from UBI-QEP as a function of N* coverage. The resulting values are, in kcal/mol
E(R3) ) 6.2 + 26.3θN* E(R4) ) 50.3 - 43.8θN* E(R5) ) 5.8 + 15.4θN* E(R6) ) 37.3 - 19.7θN* A further simplification can be employed by observing from Figure 3 that the coverage of nitrogen, θN*, is fairly constant along the reactor at all temperatures. Thus, an average value of θN* ) 0.3 is used in calculating the activation energies of the reduced model. These values are also listed in Table 3. The simplified rate expression E4 with constant activation energies captures the necessary coverage effects and the experimental data, as can be seen from Figure 1 (dashed line). Note that the reduced reaction model is significantly different from previously proposed rate expressions and takes into account poisoning arising from products. Its power
relies on the fact that it is derived from a detailed Langmuir-Hinshelwood reaction mechanism and captures the “right” physics as compared to a mere fit of experimental data. However, as happens with all model reduction procedures, one should be cautioned when using this model at conditions that are very different from the ones used here. This reduced model is subsequently used here for the CFD microreactor simulations. Important Chemistry Occurring during Ammonia Decomposition at Atmospheric Conditions. RPA identifies only low and high contributions of the chemistry in each species’ balance, but does not directly determine the RDS. In microkinetic modeling, the RDS can be easily determined though sensitivity analysis (SA). Figure 4a shows the sensitivity of ammonia conversion at the exit of the PFR at three temperatures. Note that similar SA results are obtained for the interior of the reactor and are omitted for brevity. The normalized sensitivity coefficient (NSC) is defined as (d ln x)/ (d ln A) [or (A∆x)/(x∆A) for the large perturbations used here] and is further normalized with the maximum value of the SA coefficients at each temperature. Here, A is the preexponential factor of a reaction step, and x is the conversion. The important reactions affecting the conversion are R1, R2, R7, and R9-R12. Among these reactions, the pairs R1 and R2, R9 and R10, and R11 and R12 are in PE. Reactions R1 and R2 represent the adsorption and desorption of H2, respectively. A decreased adsorption of H2 leads to an increase in conversion (a negative NSC) because of a reduction of occupied Ru sites. Conversely, a decreased desorption of H2 leads to a reduced conversion (a positive NSC). Similar behavior holds for reactions R11 and R12 at low temperatures, where NH3* blocks the majority of surface sites. On the other hand, at high temperatures, where the coverage of NH3* is low (surface-reactant-limited), the NSC changes sign, and the conversion could be enhanced by increased adsorption or decreased desorption of NH3*. Reaction R9 (the first H* abstraction) is important even though it is in PE with R10, because its reverse is fast and, on the net, NH3* decomposes slowly to NH2*. Finally, reaction R7 (the second H* abstraction) is slow, because of its higher activation energy, and irreversible. R7 limits the speed of ammonia decomposition to NH*. To provide insights into these arguments, the RPA shown in Table 4 is used. As an example, it is found
2992 Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004
Figure 5. Typical mesh consisting of about 100 000 nodes for the 2D post microreactor simulations. The postreactor has an open flow area of 3 mm (height) × 8.7 mm (width). The posts start 6 mm into the reactor. The enlargement shows the discretization around a post.
conditions. This difference stems from many factors, including synthesis studied previously vs decomposition explored here, the inclusion of N-N interactions in our model for the first time, and the prediction of energetics using UBI-QEP, as well as the lack of a priori assumptions about the MARI in our modeling. Microreactor Simulations
Figure 4. Sensitivity analysis (SA) of the conversion at three temperatures obtained from isothermal PFR simulations using the detailed microkinetic model of Table 3. Brute-force SA with a twofold reduction in preexponential factors was performed. Panel a shows SA with perturbation in one preexponential at a time, whereas panel b shows the pairwise perturbation case (see text for details). The parameters are those of Figure 1. Overall, the second H*-abstraction step controls the ammonia decomposition conversion.
that, at 850 K, only 0.2% of NH3* converts to NH2* (the rest desorbs) and only 0.4% of NH2* transforms to NH* (the rest is consumed back to NH3*). Overall, N* and H* formation is limited by the higher activation energy of R7, the low net speed of R9-R10, and the blocking of sites by H*. An important note is that, despite considerable blocking of Ru sites by N* at high temperatures, as shown in Figure 3, its formation process by R9-R10 and R7 is slower, and thus, N2 desorption is neither the most important process nor the RDS in controlling ammonia decomposition conversion. Even though the SA carried out in this manner reflects the important steps in NH3 chemistry, the perturbation in a single preexponential at a time can break down the partial equilibrium of some reactions. Furthermore, in a thermodynamically consistent mechanism, the preexponentials of forward and backward steps should be simultaneously perturbed by the same amount to maintain consistency. Figure 4b shows such a pairwise perturbation SA. The preexponentials of each reaction pair are decreased by a factor of 2, and the effect of this perturbation on the NH3 conversion (model response) is observed. Such a SA shows that, over the entire temperature range, reaction R7-R8 (NH2* + * T NH* + H*) is not in partial equilibrium and is the RDS in this microkinetic model. Our numerically reached conclusion is in contrast to a previously published hypothesis, albeit at different
In this section, we first describe the post microreactor, four reactor models, and the numerics. Subsequently, we compare simulation results to experimental data as functions of temperature and flow rate and then analyze flow and species patterns within post microreactors. Finally, the effects of post shape and post density are discussed. The Experimental Post Microreactor. An aluminum substrate was subjected to micro-electric discharge machining to create 300 µm × 300 µm posts with a distance of 260 µm between the posts. The height of the posts was 3 mm. Anodization was conducted to increase the available surface area (where some of the Al is converted to Al2O3), which was made catalytically active by wet impregnation of Ru. The total reactor length was about 2.1 cm, with a pre-reaction zone of 0.6 cm and a catalytic zone of ∼1 cm. The dimensions of the reactor are shown in Figure 5 and details can be found in ref 20. CFD Modeling and Numerics. Initial three-dimensional (3D) modeling showed that two-dimensional (2D) simulations adequately represent the conversion and pressure drop in this post microreactor (details will be presented in a forthcoming publication64). The commercial CFD software FLUENT (version 6.0) is used to obtain steady-state solutions of the problem. The gas flow in the microreactor is taken as compressible. The fluid density is calculated using the ideal gas law. The viscosity and thermal conductivity are calculated using the ideal gas mixing law, and Fickian diffusion is assumed for the mixture with a constant diffusivity. At the inlet, pure ammonia is assumed to flow into the reactor. The species inlet boundary conditions are Dirichlet, and the velocity profile is flat. At the exit, a fixed pressure of 1 atm is imposed, and the normal gradients for the species and temperature are set equal to zero. A no-slip boundary condition is applied for the flow at both the posts and the walls of the experimental setup. The ammonia decomposition reaction is assumed to occur at the post surface (given the small dimensions of the pores, with a typical pore diameter of ∼50 nm, internal mass transfer within the post is neglected because the effectiveness factor for these conditions is high). A user-defined function is used
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Figure 6. Comparison of the predictions of various reactor models (PFR, CSTR, CFD axisymmetric tubular reactor, and CFD post microreactor) with the experimental data as a function of temperature at a constant ammonia flow rate of 15 sccm. The conversion of the post microreactor is very close to that of a PFR. Perfect mixing in the CSTR leads to site blocking and higher product inhibition. Transverse mass transfer in the tubular reactor is relatively slow, highlighting the advantage of the posts.
to incorporate the reduced rate expression for the calculation of the surface reaction rates. Uncertainties in the catalyst area and site density for the reactor are taken into account by using the same surface-area-tovolume ratio of 31 cm-1 as in the PFR model above. In the experimental setup, the post microreactor is enclosed in a constant-temperature furnace. Given the high conductivity of the metallic posts, the temperature is fairly uniform. In the simulation, the heat of reaction is set to zero in order to achieve isothermal conditions. A finite difference method is used to discretize the 2D continuity, momentum, energy, and species conservation equations. In our simulations, a nonuniform mesh is used, as shown in Figure 5. Computations were performed using meshes with varying nodal densities to determine the spacing that gives the desired accuracy and minimizes the computation time. It was found that a mesh of about 575 nodes in the x direction of flow and 220 nodes in the y transverse direction (a total of about 100 000 nodes and 800 000 unknowns) provides reasonable accuracy and computational cost. To solve the conservation equations, a segregated solver with an under-relaxation method is used. The segregated solver first solves the momentum equations, followed by the continuity equation and an update of the pressure and mass flow rates. The energy and species equations are subsequently solved, and convergence is checked. The latter is monitored through both the values of the residuals of the governing equations and the L2 norm of successive iterations of the solution. Simulations were performed on a 60-node Beowulf cluster (each processor is a 2.4-GHz Pentium IV) with a total of 60 GB of RAM. A typical calculation required about 6 CPU h on a single processor. Roles of Mass-Transfer, Kinetic, and Equilibrium Limitations. Figure 6 compares our simulation results with the experimental data as a function of temperature at a constant NH3 flow rate of 15 sccm, for four different reactors with the same surface-areato-volume ratio: (1) a PFR; (2) a CSTR; (3) a 2D, axisymmetric tubular reactor; and (4) the 2D post microreactor. The latter two reactors are simulated using CFD. All simulations are done with the reduced reaction rate expression. Note, however, that the full microkinetic model gives comparable results, as shown in Figure 1. The equilibrium conversion is also plotted for comparison purposes. The conversions predicted for
the post microreactor are in very good agreement with the experimental data without any parameter adjustment. The equilibrium conversion of ammonia increases sharply with temperature and is nearly 1 above 650 K. The low conversions seen in the post microreactor in the low-temperature regime are definitely not equilibrium-limited. The simulations of the PFR and post microreactor are in very close agreement, indicating that the post microreactor behaves effectively like a PFR. We discuss this issue in more detail below. The CSTR compares well at lower temperatures with the PFR but gives lower conversions at high temperatures. This probably indicates that the back mixing of products in the CSTR results in site blocking and reduced conversion, as compared to the PFR and post microreactor. To further illustrate this point, we performed simulations with full and reduced models in the ideal reactors where the sticking coefficients of H2 and N2 were set very low (product adsorption practically eliminated). For this numerical experiment, the conversion increased rapidly to ∼1 at about ∼670 K. These results show that product inhibition is very important in the microreactor and explains (a) the low conversions at lower temperatures (above 670 K) and (b) the poorer performance of the CSTR compared to the PFR. To further delineate the role of mass-transfer effects, a tubular reactor with an open cross section (lack of posts) was also modeled using axisymmetric 2D, CFD simulations. The tubular reactor was taken to have the same effective cross sectional area (with a radius of 2.884 mm), total length, and active reaction zone length as the post microreactor. Because its geometric areato-volume ratio of 6.93 cm-1 is lower than that of the post microreactor (38.15 cm-1), we artificially increased the reaction rates by a compensation factor of 5.502 (to numerically account for the elimination of the posts). Physically, this corresponds to a 5-fold increase of the catalyst surface area that is now all accumulated at the reactor walls. The conversion predicted for the tubular reactor is much lower than that of the PFR and post microreactor, especially at higher temperatures, indicating that there are significant mass-transfer limitations in the transverse direction (this point is further illustrated in the next section). This comparison further highlights the fact that, aside from the high surface area provided for catalyst deposition, the posts serve another important role in the low Reynolds number regime, namely, enhancing the transverse mass transfer in these microreactors. Figure 7 compares the conversions of different reactors to the experimental data as a function of flow rate at a constant temperature of 923 K. The predicted post microreactor and PFR conversions are in good agreement with the experimental data. The CSTR model consistently underpredicts the conversion. On the other hand, the conversion in the tubular reactor is significantly lower than that of the post microreactor, especially for faster flows, for which the residence time is reduced compared to the radial diffusion time for mixing. Model predictions with the full microkinetic model in the two ideal reactors (gray lines) are in good agreement with the reduced rate expression, despite the fact that the latter was developed at a single flow rate of 15 sccm. This indicates that the reduced reaction rate
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Figure 7. Comparison of the predictions of various reactor models (PFR, CSTR, axisymmetric tubular reactor, and post microreactor) with the experimental data as a function of flow rate at a constant temperature of 923 K. The gray, solid lines represent predictions using the detailed kinetic models. Both the PFR and CFD post microreactor simulations capture the experimental data well without any fitting, even for the fastest flows, whereas transverse mass transfer severely limits the tubular reactor performance. Perfect mixing and the high mole fractions of products at high conversions render the CSTR performance worse than those of a PFR and a post microreactor.
expression model holds under some extrapolation in operating conditions. Flow and Species Patterns within Post Microreactors. Figures 6 and 7 indicate that the post microreactor behaves effectively like a PFR. To investigate how well the microreactor approximates the PFR and how the flow and species patterns evolve in the microreactor, flow and species contour maps can be used. However, because of the separation of scales (small post size compared to reactor size), small local variations are almost impossible to visualize from the contour maps of the entire reactor. Panels a and d of Figure 8 show the ammonia mass fraction contours for the two flow rates of 5 and 145 sccm, respectively, at 923 K. The Reynolds numbers, based on the inlet conditions and post diameter, are Red ) 0.098 for 5 sccm and Red ) 2.84 for 145 sccm. The corresponding axial Peclet numbers, based on the length of the reactive zone, average axial velocity in the microreactor, and molecular diffusivity, are 6.5 and 137.3, respectively. The corresponding transverse Peclet numbers, based on the half-width of the microreactor, are 0.8 and 15.4. Panels b and c of Figure 8 show the transverse profiles of the ammonia mass fraction at different locations near the entrance and the exit of the posts for 5 sccm flow, and panels e and f show the corresponding data for 145 sccm. The schematics in Figure 8c indicate the exact locations where the profiles are plotted. Specifically, location I1 is the midpoint of the first row of the posts, I2 is the midpoint between the first two successive rows of posts, and I3 is the midpoint of the second row of posts. The (100), 45° rotated configuration of posts in the microreactor is such that successive rows of posts have a certain degree of overlap at location I2. At each axial location, the cup-average mass fraction is indicated by horizontal dotted lines. The corresponding PFR mass fractions are also plotted for reference with horizontal solid lines. Figure 9 shows typical velocity magnitude contours for two flow rates (panels a and b) and velocity magnitude profiles for 5 sccm (panels c-e). As the flow impinges on the posts, reverse flow is created in the prereaction zone. The profile of the velocity magnitude is parabolic-like between the posts, with zero velocity
Figure 8. (a) NH3 mass fraction contours in the post microreactor and transverse NH3 mass fraction profiles (b) at locations I1-I3 and (c) at locations O1-O3 at a 5 sccm volumetric flow rate. Panels d-f show the corresponding data at 145 sccm flow rate. The solid horizontal lines indicate the PFR mass fractions, and the dotted horizontal lines indicate the cup-average mass fractions in the microreactor. All simulations were performed at 923 K. Significant back mixing occurs at low flow rates and high conversions, and slight local inhomogeneity in species mass fractions is seen at the post scale. For fast flows, a weak parabolic mass fraction profile develops that is perturbed by the posts.
Figure 9. Velocity magnitude contours in the post microreactor at (a) 5 and (b) 145 sccm flow rates, and radial velocity magnitude profiles (c-e) at locations I1-I3 at 5 sccm flow rate. All simulations were performed at 923 K. Significant local variation in velocity at the post scale is seen.
at the post surface. As the conversion in the reactor increases, there is an increase in the number of moles in the system, and the average velocity on the whole increases. The velocity magnitude at I2 is lower than that at I1 and I3 because of the greater amount of free area between the posts. The overall uniformity in the maximum velocity across the reactor observed here is consistent with previous CFD simulations in a crossflow packed-bed flow system.65 However, details of the porosity near the walls are different, resulting in higher velocities near the wall in ref 65 as compared to the lower velocities near the wall observed in our simulations.
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Figure 10. Conversions in the post microreactor, PFR, and tubular reactor as a function of reactive zone length at 923 K and the two flow rates indicated. Although the exit conversions of the post microreactor and PFR are nearly the same (see also Figures 6 and 7), back mixing and larger product inhibition near the entrance of the post microreactor at low flow rates result in significant longitudinal deviations between the two reactors. At high flow rates, back mixing is minimized, and the post microreactor better approximates the PFR. The tubular reactor shows lower conversions because of transverse mass-transfer limitations and behavior such as back mixing similar to that observed in the post microreactor.
Several interesting features of fluid flow and chemistry in this system are indicated in Figures 8 and 9. For slow flows, panels a and b of Figure 8 indicate that there is significant back mixing in the post microreactor. An ammonia conversion of about 40% is observed by the entrance of the posts! The low Peclet numbers [O(1)] at lower flow rates rationalize the back mixing observed in our simulations for the slower flows. On the other hand, the PFR has no axial diffusion, and so, there is no back mixing. However, within a few hundred microns, about 30% conversion is achieved, i.e., the conversion increases rapidly in the PFR to become slightly higher than that of the post microreactor. The presence of the posts and the parabolicity induced from the fluid flow, as shown in Figure 9, create moderate spatial nonuniformity in the transverse direction (only up to a few percent). The (100), 45° rotated configuration of the posts creates a coupling between the posts (essentially the free area between the even rows of posts corresponds to the posts in the odd row) and a local variation in the amplitude of the mass fraction in the longitudinal direction. Although the PFR starts with lower conversion at the beginning of the reaction zone, its rapid mass transfer and the minimization of site blocking created by the lack of back-diffusion (see also sensitivity analysis section above), renders the PFR superior within the first few rows of posts. Figure 10 summarizes these differences by depicting the conversion as a function of the location from the beginning of the reaction zone. The good agreement between the two reactors, seen in Figures 6 and 7, is due to compensation of effects. The maximum difference in conversion occurs at the entrance, but a difference of more than 10% is also seen at ∼4 mm in the reaction zone. At faster flows, the back mixing from axial diffusion is minimized, as shown in panels d and e of Figure 8 (about 3% conversion is seen at the entrance of the reaction zone for the 145 sccm case). The fast flow imposes parabolic mass fraction profiles downstream. The (100), 45° rotated configuration and overlap of the posts creates forks in the profile for faster flows, as shown in panels e and f of Figure 8. At high flow rates, the overall profile is flatter than that at lower flow rates. The
conversions of the PFR and post microreactor in the longitudinal direction are nearly the same, as shown in Figure 10, indicating that the transverse mass transfer in the post microreactor is sufficiently fast. This situation is reminiscent of the high Peclet number limit, under which a tubular reactor approaches the ideal PFR limit when the transverse mass transfer is sufficiently fast. Because of the observation of significant back mixing and a small concentration drop along a cross-flow packed bed reactor used for CO oxidation, it was concluded in ref 65 that the microreactor behaved like a CSTR. Our direct comparison in Figures 6 and 7 based on overall conversion indicates that the post microreactor with the specific geometric features considered here (e.g., larger posts compared to the particles in ref 65) is closer to a PFR for all conditions studied despite the significant back mixing observed at the lowest flow rates and highest temperatures. Further work is needed, however, to delineate the role of kinetics and geometric features in mapping a microreactor’s performance with that of a specific ideal reactor. In our case, the positiveorder kinetics in NH3 along with the blocking of sites by products (mainly by H*) makes reactors with back mixing, such as CSTRs, worse in terms of reactor conversion. We believe that our conclusions regarding microreactor performance are general and independent of the details of the reaction parameters as long as the major species (and thus blocking of sites) remain the same. Finally, CFD simulations in the tubular reactor, depicted in Figure 11, indicate that the development of profiles of parabolic nature with large gradients occurs only near the surface, especially for faster flows (panel b). Significant gradients in the tubular reactor in the transverse direction indicate that mass transfer is not sufficiently fast, even for a tube radius of 2.884 mm. Furthermore, back mixing is observed at lower flow rates (panel d) similar to the post microreactor. The significant back mixing at the entrance at lower flow rates gives the post microreactor some flavor of a CSTR. Overall, the post microreactor is closer to the PFR than the CSTR or the tubular reactor, and this is clearly the case at faster flows. A 1D diffusion, convection, reaction model for the microreactor to be presented in a forthcoming publication shows that the behavior can be captured quantitatively.64 Finally, in all simulations, the ammonia mass fraction near the surface, a usual signature of mass-transfer limitations, is far from being zero in most of the reactor. On the other hand, transverse mass transfer between posts is fast given the small gradients seen in Figure 8. This indicates that the chemistry is not sufficiently fast and is adsorptionlimited. An increase in the catalyst surface area and in the desorption of products (see comments in the discussion of sensitivity analysis) to liberate catalyst sites could be advantageous. The latter point will become more apparent next. Effect of Post Density. The role of the post density in the conversion and pressure drop was studied at the 15 sccm inlet volumetric flow rate. Figure 12 shows a comparison of the results of the nominal case of 275 (11 × 25) posts with that of the reduced post densities of 189 (9 × 21) and 105 (7 × 15) posts of the same size and in the same reactor volume as in the nominal case. The conversion and pressure drop in the microreactor decrease with decreasing post density, i.e., there is a
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Figure 11. (a) Velocity magnitude contours and (b) mass fraction of ammonia for 145 sccm flow rate in a tubular reactor. In image a, the scale of the velocity varies from 0.5 to 0 m/s. (c) Velocity magnitude contours and (d) mass fraction of ammonia for 5 sccm flow rate. In image c, the scale of the velocity varies from 0.07 to 0 m/s. The mass fraction scales in images b and d vary between 1 and 0. The reactive zone is present between the two vertical lines. (e) Transverse NH3 mass fraction profiles. Significant back mixing occurs at low flow rates, and transverse gradients in the reaction zone occur at all flow rates.
tradeoff between conversion and pressure drop. However, the pressure drop is very small in these microreactors. To isolate the effect of the lower catalyst surface area from the reduced transverse mass transfer resulting from the posts being farther apart, we increased the catalyst surface area of each post so that the total microreactor surface area was the same as in the nominal case (we call this case area-compensated, AC). The results depicted in Figure 12 show that the conversion is practically the same as in the nominal case. This indicates that the reduction in conversion with decreased post density is mainly an effect of reduced surface area rather than mass transfer, at least for these low flow rates. At higher flow rates, slight deviations in conversion from the nominal case are seen despite the area compensation (about 2% difference at 145 sccm and 923 K). For the most part, mass transfer is fast enough in the post microreactor. These results point to an important conclusion, namely, an increased catalyst surface area in the posts should lead to enhanced reactor performance. This might prove to be an important strategy for maintaining high conversions at the high flow rates of interest for high throughput of H2 (see the low conversions in Figure 7). Effect of Post Geometry. Simulations were carried out to examine the effect of post geometry on the
Figure 12. Effect of post density on (a) NH3 conversion as a function of temperature at 15 sccm flow rate and (b) pressure drop as a function of NH3 flow rate at 923 K. AC (area compensated) indicates that the total catalyst surface area has been compensated to be the same as in the nominal case of 275 posts. For these relatively low velocities, the density of the posts is high enough to create large transverse mass transfer. The catalyst surface area limits the conversion, especially at higher flow rates. Pressure drops are very low for these microreactors and flow rates.
conversion and pressure drop of post microreactors. In particular, diamond, circle, and triangle post shapes were investigated for a constant perimeter, i.e., the same catalyst area per post. The simulations were done with a nominal post density corresponding to the experimental value, and the effect of post shape on conversion was found to be insignificant (results not shown). The pressure drops are quite small but depend on the post shape. The simulated pressure drops are compared to the Ergun equation, typically used for porous media
µVs(1 - )2 FVs(1 - ) ∆P ) 150 + 1.75 2 3 L d d 3 s
(13)
s
using the equivalent surface diameter of the posts. The comparison is shown in Figure 13. The three post shapes result in different porosities , with the circles having the lowest and the triangles the highest porosity. The superficial gas velocities Vs were the same in all cases. The average values of viscosity µ and density F were used in eq 13. The viscous effects (first term in eq 13) dominate in this flow regime. The physical properties of the mixture do not vary as much given that the conversion is nearly the same, and thus, the porosity effects control the pressure drop. The circular posts give the highest pressure drop and the triangular the lowest. The Ergun equation, originally derived for spherical packings, provides a good repre-
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Figure 13. Effect of post shape on pressure drop in a post microreactor. Pressure drop estimates for diamond-shaped, triangular, and circular posts are shown as a function of NH3 flow rate at 923 K. Symbols (points) represent the values computed using CFD simulations, and solid lines represent the predictions of the empirical Ergun equation.
From a practical standpoint, the proposed microreactor achieves its goal for hydrogen production at the microscale for portable devices by providing a low pressure drop, reasonable surface area, high efficiency, and no movable parts. Our simulations indicate that microreactor optimization is definitely possible, for example, by using larger surface areas/catalyst loadings. The lack of CO in the ammonia decomposition reaction eliminates the water-gas shift and preferential oxidation of CO steps needed in reforming reactions, leading to more compact, simpler devices. On the other hand, the industrial production of ammonia from hydrogen and nitrogen along with its odor will limit its potential use to only small-scale, portable devices rather than large-scale fuel processors. Finally, the cost of Ru might be tolerable for small-scale devices. However, development of lower-cost/high-activity catalysts is obviously desirable. Acknowledgment
sentation for the pressure drop in circular post microreactors but fails to capture the effects of the other shapes. Conclusions In this paper, the decomposition of ammonia on a Ru/ Al2O3-catalyzed Al-framework post microreactor was modeled. To describe the system from first principles, the decomposition chemistry was first developed. A detailed, six-step reaction mechanism with parameters from UBI-QEP theory and TST and N-N lateral interactions from DFT was proposed. At atmospheric conditions and low temperatures, NH3* was found to be the dominant surface species, whereas at high temperatures, H* is the dominant species. We also found that the second H abstraction and the low net rate of the first H abstraction are important steps determining the conversion to H2. Although the surface coverage of N* is relatively high, N* is not the MARI. Furthermore, the desorption of N* is not the RDS. These conclusions are in contrast to the previously published mechanistic hypothesis, albeit in most cases under different conditions, and motivate further studies to understand the role of operating conditions in determining the important chemistry. Using an ideal PFR as a rapid screening tool, a computer-aided model reduction methodology was employed to generate a one-step rate expression that captures the physics of the full microkinetic model in the desired range of operating conditions. Using this reduced rate expression, 2D CFD simulations of post microreactors were undertaken. The results of these simulations are in good agreement with the experimental microreactor data of Ganley et al.20 Ideal reactors (PFR, CSTR) and CFD simulations (tubular and post reactors) were compared to delineate the effect of mass transfer and back mixing. An important finding of our simulations is that, aside from enhanced surface area, these posts create an effective transverse mixing that leads to higher conversions, compared to those obtained in a tubular reactor and a CSTR, at minimal pressure drops. At high post densities, the post microreactor behaves effectively like a PFR despite differences in flow and species patterns and back mixing observed at low flow rates and high conversions. A tradeoff between the conversion and pressure drop is observed with varying geometric characteristics (e.g., decreasing post density).
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Received for review July 2, 2003 Revised manuscript received November 21, 2003 Accepted December 1, 2003 IE030557Y
