Assessment of Overall Rate Expressions and Multiscale, Microkinetic ModelUniqueness via Experimental Data Injection: Ammonia Decomposition onRu/γ-Al2O3 for Hydrogen Production

V. Prasad, A. M. Karim, A. Arya, and D. G. Vlachos*

Department of Chemical Engineering and Center for Catalytic Science and Technology UniVersity ofDelaware, Newark, Delaware 19716-3110

We introduce a framework for parameter estimation of microkinetic models via injecting data, collected inoptimal regions of the “entire” experimental operating space, in models. We demonstrate this framework bycombining differential conversion experimental data without transport limitations and models for ammoniadecomposition on Ru/γ-Al2O3 for hydrogen production. Experiments indicate that there is significant H2

inhibition even at low ammonia conversions. Statistical model discrimination techniques indicate that multiplemicrokinetic parameter sets are able to describe quantitatively the experimental data, and some global rateexpressions are also adequate. Among the best microkinetic models, nitrogen adsorption/desorption and theNHx dehydrogenation reactions are the kinetically significant reactions. It is found that macroscopic data(conversion) are insufficient for complete model discrimination; microscopic scale data are proposed for furthermodel discrimination.

Introduction

In the quest for clean and efficient energy production, fuelcells have been identified as a viable candidate. Hydrogen isthe primary fuel for low temperature fuel cells, and ammoniais a prime candidate for the production of hydrogen.1 The majoradvantages of ammonia as a hydrogen storage material are itsability to be stored and transported as a liquid at relatively lowpressures, its relatively high energy density and hydrogen storagecapacity (∼17 wt %), and the widespread infrastructure forammonia synthesis. In addition, the hydrogen produced is freeof CO and CO2, and there is minimal downstream processingrequired to remove the unreacted ammonia from the hydrogenstream.

In spite of these obvious advantages of hydrogen productionby the catalytic decomposition of ammonia, the underlyingchemistry is still not well understood. Most previous studieshave focused on ammonia synthesis, due to its importance forfertilizers. While research on ammonia decomposition hasrecently increased,2-23 there is still no consensus on the rate-determining step (RDS) and the most abundant reactiveintermediate (MARI). The associative desorption of N2 and theN-H bond scission have both been proposed to be the RDS inNH3 decomposition.4,19 Also, either elemental hydrogen ornitrogen has been predicted to be the MARI.19,24,25 Differentoperating conditions and catalyst synthesis methods may explainthese differences. In addition, some of the experimental studieshave been performed at ultrahigh vacuum conditions on singlecrystals, and the pressure and material gaps make it difficult toextrapolate these results to conditions that are relevant to fuelcells (high ammonia concentration, atmospheric pressure).

While first principle models are emerging as a powerful toolfor predicting trends, their quantitative capabilities are stilllimited. The large number of parameters of complex reactionsin conjunction with the inherent uncertainty of the catalyststructure and active site often require the use of free-energytype and semiempirical correlations that introduce further

parameter uncertainty. Data injection into microkinetic modelsis therefore necessary to render these models predictive.Parameter refinement is typically cursed with nonuniqueness(multiplicity in values) due to the nonlinear nature of kineticmodels. Given the physical and thermodynamic constraintsimposed on the parameters of microkinetic models, a naturalquestion raised though is whether such physically based (ratherthan purely fitting-based) models are unique.

In this contribution, we first formulate a framework thatcombines experiments, high throughput microkinetic modeling,and an informatics-based design of experiments to render themodel quantitative in a “global” sense. The approach isillustrated in the catalytic decomposition of ammonia onruthenium (Ru) to study the chemistry at fuel cell relevantoperating conditions and to clarify aspects of the chemistry, suchas the RDS and the MARI. In the following sections, wedescribe the experimental procedure and results, the microkineticand global rate expression models developed, and their com-parison with experimental data and conclude on the uniquenessof microkinetic models and the predicted RDS and MARI.

Experimental Details

Ru/Al2O3 catalyst was prepared using an incipient wetnesstechnique. γ-Al2O3 was dried at 120 °C overnight prior toimpregnation. Ru nitrosyl nitrate solution (Aldrich) (1.7 wt %Ru by weight) was added dropwise to the Al2O3 powder andthe powder was shaken to ensure even distribution; then, thepowder was dried at 80 °C. The process was repeated until 4wt % Ru loading was achieved. The catalyst was dried at 80°C overnight and then calcined at 500 °C for 5 h.

The kinetics of ammonia decomposition on Ru/Al2O3 catalystwas measured in a 1/4 in. stainless steel reactor. MKS calibrateddigital mass flow controllers were used to control the flow rateof NH3, H2, N2, and He. Figure 1 shows a schematic of thereactor and the locations of the thermocouples. In order toeliminate temperature and concentration gradients, the catalystpowder was diluted with inert Al2O3 of the same particle size(50-75 µm) and, then, packed in the reactor. The catalyst bed

* To whom correspondence should be addressed. E-mail: vlachos@udel.edu.

Ind. Eng. Chem. Res. 2009, 48, 5255–5265 5255

10.1021/ie900144x CCC: $40.75 2009 American Chemical SocietyPublished on Web 04/27/2009

length was 1.9-3.8 cm depending on the catalyst loading anddilution. Prior to reactivity measurements, the catalyst wasreduced at 450 °C (10 °C/min ramp rate) for 2 h in 10% H2

(balance He) at 200 sccm total flow rate. The reactor productswere sampled with a gas-sampling valve, and the compositionwas monitored with a HP Series 6890 gas chromatograph (GC),using a thermal conductivity detector. Ammonia conversion wascalculated using the H2 and N2 mole fractions in the products.Attention has been paid to eliminate transport gradients (seethe Appendix).

Microkinetic Models

Microkinetic models26 are generally superior to global rateexpressions in terms of being able to describe data over widerranges, having a physical basis for most parameters, and beingable to identify changes in the important chemistry. Microkineticmodels take into account all relevant elementary reactions anddo not make a priori assumptions about an RDS, the MARI, orpartial equilibrium (PE) conditions.

The microkinetic model we use in this work builds on a modelpreviously developed by our group to describe ammoniadecomposition on Ru.7,14 The rate constant of elementaryreactions is expressed in the modified Arrhenius form

ki ) A0i( TTref

)�iexp(- Ei

RT), i ) 1, ..., m (1)

where m is the number of reactions. The elementary reactionsconsidered for ammonia decomposition are (* denotes vacantsites, and H*, N*, etc. denote adsorbed species):

H2 + 2* {\}k1f

k1b

2H* (R1)

N2 + 2* {\}k2f

k2b

2N* (R2)

NH* + * {\}k3f

k3b

N* + H* (R3)

NH2*+* {\}k4f

k4b

NH* + H* (R4)

NH3*+* {\}k5f

k5b

NH2*+H* (R5)

NH3 + * {\}k6f

k6b

NH3* (R6)

There are two major sets of parameters in microkineticmodelssthe activation energies and the pre-exponential factors.We employ the bond-order conservation (BOC) method27 toestimate activation energies, using heats of chemisorption as

inputs (obtained from density functional theory (DFT) calcula-tions or experiments). Surface coverage effects determined fromDFT simulations are included in the activation energies, asdetailed in ref 28. The pre-exponential factors A0i

are estimated(in an order of magnitude sense) using transition state theory(TST). To improve the quantitative capabilities of a mechanism,in previous work, some of the pre-exponential factors wereestimated by fitting the model predictions to limited experi-mental data, subject to thermodynamic consistency.29 Theparameters to be estimated were chosen based on sensitivityanalysis. The microkinetic model is then combined with a reactormodel, and is solved numerically to obtain predictions of gas-phase mole fractions, fractional coverage of surface species,conversion, and other relevant quantities. In this work, we modelour experimental reactor as a plug flow reactor (PFR) at steadystate, given that the Peclet number is larger than 10 (convectionsignificantly faster than diffusion).

The method employed to generate relevant experimental datafor estimation and refinement of the parameters in the model isdescribed in the next section.

Informatics-Based Design of Experiments

The computational effort in calculating all parameters of largemicrokinetic models from first principles is prohibitive. Inaddition, there is an inherent uncertainty in parameter valuesassociated with estimation methods, even with DFT. Anadditional uncertainty arises from the complex and often poorlyknown catalyst structure. In order to render microkinetic modelsquantitative and predictive, parameter refinement is thereforenecessary. To achieve this, we use rational model-basedtechniques (described in detail in ref 30) in order to refineuncertain parameters and assess the global (i.e., in the entireexperimental parameter space) model robustness. We employinformatics based approaches to identify optimal experimentalregions; other applications of systems and informatics ap-proaches in catalysis and kinetics may be found in refs 31-33.

The overall methodology can be outlined as follows. Anexhaustive search of the operating space is conducted to identifyoperating conditions that are optimal for estimation of param-eters of a microkinetic model. This search is performed usinga Monte Carlo method and results in a massive set of generatedconditions (high throughput modeling). We have developedphysics-aided methods (sensitivity, PE, and MARI) and statistics-based methods (A, D, and E optimal designs) for the design ofexperiments. In the statistical approaches, we use suitablemetrics, obtained from the Fisher information matrix (FIM),constructed from the normalized sensitivity coefficients (NSCs).The massive information is refined using informatics methods,such as principal component analysis (PCA) and clustering, toidentify optimal regions for conducting experiments in thefollowing manner: First, operating conditions are classified basedon the optimality metric (D optimal metric or NSC value), andpoints with a high value of the metric are chosen. These pointsare then grouped into clusters using the partitioning amongmedoids (PAM) method.34 Conditions that belong to the samecluster share common underlying characteristics. Next, patternsindicating optimal regions are extracted from the clusters byidentifying regions that have high probability of finding pointsthat score high on the optimality metric. Performing a relativelysmall number of experiments in these optimal regions enablesus to refine the parameters of a model, and improve its predictivecapability and its reliability in identifying important chemistry.

Our analysis illustrates that the D optimal and sensitivity-based designs are the most promising methods and generate

Figure 1. Schematic of packed bed reactor used for kinetic studies.

5256 Ind. Eng. Chem. Res., Vol. 48, No. 11, 2009

conditions that delineate important chemistry. We have shown30

that a standard design around the D optimal point may not beuseful for (highly nonlinear) kinetics problems, and informaticsmethods are proposed instead to identify optimal regions of theoperating space. We have found that the experiments conductedwithin these regions have a high probability in providing usefulkinetic information.

The methodology described above is used to design optimalexperiments for parameter estimation in our multiscale modelfor ammonia decomposition. In this work, we conduct a set ofexperiments in an optimal region identified using the methodsdescribed above. The main characteristics of this optimal regionare that the inlet composition space is bounded by the limits(in terms of mole fractions) 0.6 and 0.75 for NH3 and 0 and0.25 for H2. Reactor temperatures lie between 623 and 723 K,and total flow rates are either 100 or 200 sccm. This data isused to refine parameters of the microkinetic model (called“fitting set” in the sections below). A separate data set is usedfor model assessment. This data set uses a much broadersampling of the feasible experimental space. For example, themole fractions of NH3 at the inlet range from 0.1 to 1.0, andthe inlet mole fractions of H2 at the inlet range between 0 and0.4. Total flow rates range between 100 and 400 sccm, andreactor temperatures are in the range 573-723 K. This set willbe called the “assessment set” in the following sections.

The informatics-based design of experiments provides condi-tions that are best to estimate parameters. Fuel cell conditionsform part of the sampling space. However, the best conditionsmay not be those of fuel cell operation. The global nature ofthe models ensures that they apply at fuel cell conditions.

Parameter Estimation and Model Discrimination

We have employed methods based on numerical optimizationfor estimating the parameters of the microkinetic modelstheseinclude gradient-based methods (the “fmincon” function inMATLAB’s optimization toolbox) and simulated annealing.35

Initial guesses for these searches were supplied using modelsdeveloped earlier in our group and in the literature.14,36,37 Itshould be noted that none of the literature models provideadequate fits over the entire experimental space studied priorto parameter estimation. An example is shown later, in Figure9a.

The objective function used in the parameter estimation isgiven below

φ ) minθ (∑

i)1

N (Xmodel - Xexpt

Xexpt)2) (2)

where X denotes ammonia conversion, N is the total number ofdata points in the set used for estimation, and θ is the set ofparameters to be estimated. Note that a quadratic objectivefunction is being optimized with respect to the relative differencebetween model predictions and experimental data. Uncertaintyin the experimental conversion scales as a percentage (ap-proximately 10%) of the measured value and, thus, does notaffect the objective function for the optimization. The set ofparameters to be estimated includes the pre-exponential factorsof elementary reactions, binding energies for nitrogen andhydrogen (these are inputs to the BOC calculation for computingactivation energies) and their dependence on surface coverage(mainly of atomic nitrogen), and the BOC bond-index param-eters for the two most important elementary reactions based onsensitivity analysis (R2: N2 + 2* ) 2N* and R4: NH2* + * )NH* + H*). Entropic thermodynamic consistency of the overall

ammonia decomposition mechanism is applied as a constraintin the estimation of pre-exponentials (using thermodynamicconstraints and a reaction basis set, as described in ref 29), andenthalpic thermodynamic consistency is ensured by the use ofBOC for calculating activation energies and heats of reaction.

Since microkinetic models are highly nonlinear, many localminima are found in the optimization. Each of the parametersets, corresponding to a local optimum, provides a reasonablygood fit to the experimental data. To decide on the mostappropriate model (parameter set), we use a model discrimina-tion criterion developed in ref 38 on the best models based ongoodness of fit. This is a modified Box-Henson criterion thatis based on Bayesian statistics. Assuming normally distributederrors in the experiments, the posterior probability of each modelbeing correct is calculated using

p(Mj|Y, σ) ∝ p(Mj)2-pj/2 exp(- Sj

2σ2) (3)

Here, p(Mj|Y,σ) is the posterior probability of model j (givendata Y with variance σ), p(Mj) is the prior probability, pj is thenumber of parameters estimated in model j, and Sj is the sumof squared errors for model j. The probability of model j beingcorrect is calculated by normalizing the posterior probabilityover all models

π(Mj|Y, σ) )p(Mj|Y, σ)

∑k

p(Mk|Y, σ)(4)

The model with the highest probability is chosen as the(statistically) most likely model.

Results

In the following sections, we describe first experimentalresults. Catalyst characterization results are presented at theoutset, and the catalyst surface area estimated experimentallyis kept constant in all the models. Next, we describe the effectof temperature and feed composition changes, including the inletammonia mole fraction and inhibition by co-feeding the products(H2 and N2). The presentation in terms of one-parametervariation helps establishing major experimental trends that anymodel should be capable of predicting. For parameter refine-ment, experiments are conducted in the optimal regions identi-fied using clustering. Details of optimal regions and normalizedsensitivity coefficients for the nominal model may be found inref 30. Model parameters are refined using this data (the fitting/training set), and model predictions are then compared againstexperimental data in the entire operating range (training andassessment sets). We include a comparison of the performanceof global rate expressions along with those of full microkineticmodels against the experimental data. Finally, we discuss modeldiscrimination.

Catalyst Characterization. Scanning transmission electronmicroscopy (STEM) was performed on a JEOL 2010F FASTEMfield emission gun scanning transmission electron microscope.

Figure 2 shows a typical STEM image of the spent catalyst.Over several images, we measured the particle size of about200 Ru particles. The corresponding particle size distributionis shown in Figure 3. The Ru number average particle diameter(Navg ) ∑i nidi/∑i ni, di being the particle diameter and ni thenumber of particles) was 7 nm. The mean surface diameter (Ns

) ∑i nidi3/∑i nidi

2) was 8.6 nm, which corresponds to a Rudispersion of 15%.39

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The total Ru surface area of the fresh catalyst was measuredby CO pulse chemisorption using an automated chemisorptionanalysis instrument from Altamira (AMI-200). A 250 mg portionof the 4 wt % Ru/Al2O3 catalyst was loaded into a 1/4 in. quartztube. Prior to the pulse CO chemisorption measurement, thecatalyst was reduced at 450 °C for 2 h in 10% H2 (balance Ar)at 40 sccm total flow rate and then cooled down to roomtemperature in He at 30 sccm. The CO uptake was 22 µmol/g,and the corresponding calculated Ru dispersion was 10%,assuming a CO:Ru stoichiometry of 0.6:1.19,40 The Ru surfacearea for the spent catalyst was also measured, and the calculatedRu dispersion was 8.5%. Microscopy and chemisorption dataare in reasonable agreement. The latter is used for the catalystsurface area in all our models. This ensures that the surfacearea (or the number of active sites) is not an adjustable parameterfor the models, and avoids any compensation effects betweenthe surface area and pre-exponential parameters in parameterestimation.

Effect of Ammonia Mole Fraction. The points in Figure 4show the experimentally estimated ammonia conversion as afunction of temperature and ammonia mole fraction in the inlet.The lines are refined model predictions and will be discussedlater. The total gas flow rate was kept constant at 200 sccm.Data (not shown) was also collected at 400 sccm total flow ratein order to get differential conversions (0-15%). The calculatedNH3 reaction order, based on data of Figure 4, is between0.25-0.45 (with the increasing ammonia mole fraction, thespace velocity changes linearly, whereas conversion decreasessublinearly giving rise to a positive reaction order). A transition

from zero order at low temperatures to first order in ammoniaat high temperature has been reported in the literature.8,19

The calculated apparent activation energy was 95-100 kJ/mol (see Figure A2 in the Appendix). The activation energyreported in the literature for supported Ru catalysts rangesbetween 61 and 138 kJ/mol.4,6,22,23,41 It should be noted that inall the literature studies cited here, Ru chloride was used as theprecursor for catalyst preparation, while we used Ru nitrosylnitrate. Chlorine is known to be a poison for ammonia synthesisand decomposition catalysts.15,42-44 Transport limitations, es-pecially heat transfer, were not checked for and eliminated insome literature studies. Chlorine poisoning and transport limita-tions could be responsible for the large spread in the apparentactivation energy reported in the literature.

H2 and N2 Inhibition Effect on Ammonia Decom-position. The effect of flowing H2 and N2 with NH3 in the inletwas studied. H2 was found to significantly inhibit the ammoniadecomposition reaction. Figures 5-7 show the effect of H2

inhibition on ammonia decomposition at the same spacevelocity. It is evident that NH3 decomposition is stronglyinhibited by H2 in the inlet, even at inlet mole fractions as lowas 10%. This indicates that differential data analysis that leavesproduct inhibition out will lead to errors. Nitrogen, on the otherhand, has no effect on NH3 conversion even with up to 70%N2 mole fraction in the inlet (data not shown). The inhibitionby H2 and insensitivity to N2 partial pressure on ammoniadecomposition has been reported previously in the literature.8,23

However, as shown in Figures 5-7, the inhibition by H2 persistsat all temperatures. This is in contrast to the work by Egawa et

Figure 2. Typical STEM image of the spent Ru/Al2O3 catalyst.

Figure 3. Ru particle size distribution.

Figure 4. Effect of NH3 mole fraction in the inlet on the NH3 conversion.Total flow rate ) 200 sccm, balance He. A 96 mg portion of catalyst wasdiluted with 150 mg inert Al2O3.

Figure 5. Effect of H2 on ammonia decomposition. Total flow rate ) 200sccm. Inlet NH3 mole fraction ) 0.3, balance He. A 96 mg portion ofcatalyst was diluted with 150 mg inert Al2O3.

5258 Ind. Eng. Chem. Res., Vol. 48, No. 11, 2009

al., where they reported no H2 inhibition at temperatures higherthan 327 °C.8 It should be noted that our study was conductedunder atmospheric pressure, while the work by Egawa et al.was done at ultrahigh vacuum. Also, Tsai et al. studied the effectof hydrogen inhibition on ammonia decomposition on platinum,and they reported a pressure dependence of the degree ofhydrogen inhibition on ammonia decomposition;18 the higherthe total pressure, the higher the degree of hydrogen inhibition,and therefore the higher the temperature at which the decom-position of ammonia becomes insensitive to H2 partial pressure.On the other hand, Chellappa et al. reported a zero order reactionrate in H2 on Ni-Pt/Al2O3 at temperatures 520-660 °C,5 whichis higher than the temperature range explored in our study.

Global Rate Expression Refinement and Assessment. Inaddition to microkinetic models, we have investigated thepossibility of a global rate expression being able to describethe system in the entire experimental space. Most of these globalexpressions have been derived using an a priori assumption(s)of an elementary reaction being the RDS and a particular surfacespecies being the MARI. Table 1 summarizes the global rateexpressions investigated, the assumptions used in their deriva-tion, and the goodness of fit (based on the objective functionof eq 2 for each model over all experimental data, includingfitting and assessment sets). Table 2 summarizes the parametervalues obtained for the best fit with each global expression, andFigure 8 shows parity plots obtained for all the models. Notethat the differential reactor assumption is not applied; the globalrate expressions are used with a reactor model (PFR) thatcorresponds to experimental conditions. The parameter estima-tion has been carried out using the same optimization methods

as with the microkinetic models; also, the catalyst surface areahas been fixed at the value obtained from the chemisorptionresults. The best-fit parameter values provided goodness of fitvalues that were clearly better (by approximately a factor of 2)than the other local minima.

Model 145 is obtained by assuming reaction R2 (N2 adsorp-tion/desorption) to be the RDS and adsorbed nitrogen (N*) tobe the MARI. The parameters k2f and k2b represent the kineticparameters for the forward and backward directions of R2, andK7 represents the equilibrium constant for the composite reaction

NH3 + * {\}K7

N* + 32

H2 (R7)

which is assumed to be in PE. The fitted values of activationenergies for N2 adsorption and desorption are 40.8 and 20.1kcal/mol, respectively. The value for desorption is in reasonableagreement with the experimental TPD value (32.7 kcal/mol37)and DFT calculations (27.7 kcal/mol for B5 step sites46), andthat for adsorption is much larger than the literature values (7.937

and 9.2 kcal/mol46). The pre-exponential for k2f (assumed to beindependent of temperature in the range studied) is estimatedto be 2.3 × 104 1/s and that for k2b is 5.6 × 107 1/s. The valuefor k2f is larger than those reported in the literature (0.241 1/susing TST in ref 46; 56 1/(kPa s) from TPD experimentsconducted at atmospheric pressure in ref 37, even if the N2

pressure is assumed to be 1 atm, the maximum possible value).The value of k2b is approximately 5 orders of magnitude lowerthan that predicted using crude TST and 2 orders of magnitudelower than that estimated by Hinrichsen et al. (2 × 1010 1/s).The equilibrium constant (actually a function of temperature)K7 is not an independent parameter and is herein calculated ina thermodynamically consistent manner (such that the totalchange in enthalpy and entropy of the system of reactions R2and R7 matches that for the overall gas-phase ammoniadecomposition reaction). As Figure 8 and the goodness of fitgiven in Table 1 show, model 1 provides good fits to theexperimental data and is thermodynamically consistent. How-ever, the estimated pre-exponential for N2 desorption appearsphysically unrealistic.

Model 27 was derived from a full microkinetic model thatwas previously tested over a small range of operating conditions(no a priori assumption of a RDS was made). On the basis ofthe results, a posteriori assumptions were made about dominantsurface species and reactions being in partial equilibrium (PE).Reactions R1, R5, and R6 were in PE, and H* and N* werethe MARI. For parameter estimation, the activation energiesfor each elementary reaction were fixed at the values reportedin ref 7, with N-N adsorbate interactions included. Theimportant parameters in the fit using this model are k2f and k2b.The activation energies in the model are 14.1 and 37.2 kcal/mol, respectively, which are slightly higher than the literatureones. The pre-exponential factor for k2f is estimated to be 1.41/s (in the range reported in refs 37 and 46) and that for k2b is6.4 × 1013 1/s. Model 2 also provides very good fits to theexperimental data. The goodness of fit is insensitive to k2f overa couple of orders of magnitude, while the fit for model 1deteriorates quickly when k2f is varied. When N-N adsorbateinteractions are ignored in computing the activation energies,the fits are not satisfactory, possibly indicating the importanceof these interactions for ammonia decomposition as suggestedbefore.14

The estimated parameters of model 3,4 which assumesreactions R2 and R5 to be the RDS and N* to be the MARI,are k5f, k2b, k6f and k6b. The model is not able to capture the

Figure 6. Effect of H2 co-feed on ammonia decomposition. Total flow rate) 200 sccm. Inlet NH3 mole fraction ) 0.3, balance He. A 96 mg portionof catalyst was diluted with 150 mg inert Al2O3.

Figure 7. Effect of H2 co-feed on ammonia decomposition. Total flow rate) 200 sccm. Inlet NH3 mole fraction ) 0.6, balance He. A 96 mg portionof catalyst was diluted with 150 mg inert Al2O3.

Ind. Eng. Chem. Res., Vol. 48, No. 11, 2009 5259

inhibition of NH3 conversion with H2 in the feed and does notprovide good fits. Model 4,4 which is similar to model 1 butdoes not account for the N2 adsorption, provides almost identicalfits as model 1.

Finally, model 523,47,48 has also been derived using the sameassumptions as models 1 and 4 but has been put in theTemkin-Pyzhev form. Keq is the equilibrium constant for theoverall ammonia synthesis reaction. The parameters kapp and �are related to the apparent activation energy and reaction order.The apparent activation energy of 28.0 kcal/mol (approximately117 kJ/mol) is within the range reported in the literature.4,6,22,23,41

The reaction order with respect to NH3 () 2�) is estimated tobe 0.54. These values for the apparent activation energy andreaction order with respect to NH3 are in agreement with theexperimentally estimated values that we obtained, 95-100 kJ/mol and 0.25-0.45, respectively (see above and the Appendix).

While multiple models may describe the data, it appears thata single overall rate expression (model 2) is physically sound.The goodness of fit of model 2 is relatively insensitive to thepre-exponential factor for N2 adsorption. This may indicate thatmodel 2 has a more robust estimate of parameters than the othermodels.

Microkinetic Model Refinement and Assessment. In thissection, we describe the results obtained by refining themicrokinetic model described above using the optimal designof experiments. The parameters to be estimated include the pre-

exponential factor of each elementary reaction, binding energiesfor nitrogen and hydrogen and their dependence on surfacecoverage, and the BOC bond-index parameters for the elemen-tary reactions R2: N2 + 2* ) 2N* and R4: NH2* + * ) NH*+ H* (these were found to be important in the initial model).The fitting and assessment data sets used for the global rateexpressions and the microkinetic models are identical.

Figure 9a shows the performance of the model with thenominal (literature) parameter set, prior to estimation. Thereare systematic, large errors in the model predictions, indicatingthe necessity of optimal experiment design and parameterestimation. Figure 9b shows the performance of the refinedmodel on the fitting set of data, and Figure 9c shows theperformance on the assessment set. Figure 9d combines theinformation from panels b and c.

There are multiple sets of parameters that provide good fitsto the experimental data, and these results represent the model(parameter set) with the best fits. The model predictionsdescribed in Figures 2-5 are also based on this parameter setthat is listed in Table 3. Table 3 also lists the range of parametersover all local minima (over 100 in number). Approximateconfidence intervals for the parameters of the optimal set werecalculated from the FIM and the parameter covariance matrixusing the method described in ref 49. A notable feature is thatthe confidence intervals for the pre-exponential parameters(excluding the sticking coefficients) are of the order of 104 (for

Table 1. Global Rate Expressions Derived Using RDS and MARI Assumptions

model index model assumptions source goodness of fit

1

r )-k2bK7

2([NH3]2/[H2]

3) + k2f[N2]

(1 +K7[NH3]

[H2]3/2 )2

k2f ) A2f exp(-E2f

RT ), k2b ) A2b exp(-E2b

RT )

N2 + 2* ) 2N* is theRDS. N* is the MARI.

45 2.73

2

r )-2(k2bω

2 - k2fpN2)

(1 +k6f

k6bpNH3

+ �k1f

k1bpH2

+ ω)2

ω ) �k2f

k2bpN2

+ �k1b

k1f

k4fk5fk6f

2k2bk5bk6bpNH3

pH2

-0.5

NH3 and H2 adsorption/desorption and NH3* +* ) NH2* + H* are inpartial equilibrium. H*and N* are the MARI.

7 2.31

3

r )k5f

k6f

k6bpNH3

(1 + �k5fk6fpNH3

2k2bk6b)2

NH3* + * ) NH2* +H* and N2 adsorption/desorption are both theRDS. N* is the MARI.

4 1.7 × 103

4

r )k2bK7pNH3

2

pH2

3(1 + K7

pNH3

pH2

3/2)2

N2 adsorption/desorptionis the RDS. N* is theMARI.

4 12.2

5

r ) kapp[(pNH3

2

pH2

3 )�

-pN2

Keq2( pH2

3

pNH3

2)1-�]N2 adsorption/desorption

is the RDS. N* is theMARI.

23, 47, 48 8.5

5260 Ind. Eng. Chem. Res., Vol. 48, No. 11, 2009

example, the estimate for A3f is 1.4 × 1013 ( 8.9 × 103). Sincethe estimated values are typically in the range 1011-1013, withTST estimates placing bounds 2 orders of magnitude in eachdirection (i.e., between 1011 and 1015 for an estimate of 1013),this is a substantial improvement in the accuracy of theparameter estimates.

Microkinetic Model Discrimination. Since many (poten-tially hundreds) of local minima have been located for themicrokinetic models, a model discrimination exercise wasconducted using the methodology described in an earlier section(eqs 3 and 4), with a uniform prior being used. In addition tothe three best fit models (parameter sets), the global rateexpressions described by models 1 and 2 were considered (sincethey provided the best fits among the global rate expressions).

The parameter sets for the microkinetic models were separatedby orders of magnitude for the pre-exponentials/sticking coef-ficients related to adsorption of H2, N2, and NH3. The modeldiscrimination procedure indicates that the model (parameterset) described in Table 3 is statistically the most probable modelof the five considered, with a probability of 40%. However,other models also have significant probabilities in the range15-25%, indicating that the discrimination measure is not verystrong. The parameter sets corresponding to local minima fallroughly into eight families of solutions, of which five havephysically reasonable parameters.

The parameters of the statistically most probable microkineticmodel are within a couple of orders of magnitude of the valuesof the global rate expression model 2. The main difference is

Table 2. Parameter Values Obtained for the Best Fits with Models Described in Table 1a

model 1 model 2 model 3 model 4 model 5

k2f )

2.3 × 104 exp

(-40.8RT )

k1f ) 1.1 × 1014 exp

(-1.9RT )

k5f) 2.6 × 107 exp

(-18.9RT )

k2b) 3.2 × 109 exp

(-29.4RT )

kapp ) 6.0 × 108 exp

(-28.0RT )

k2b )

5.6 × 107exp

(-21.1RT )

k1b ) 4.8 × 1011 exp

(-23.7RT )

k6f

k6b) 5.8 × 10-1 K7 ) 8.3 × 10-2 � ) 0.27

k2f ) 1.4 × 100 exp

(-14.1RT )

k2b ) 6.0 × 108 exp

(-20.0RT )

k2b ) 6.4 × 1013 exp

(-37.2RT )

k4f ) 3.6 × 1012 exp

(-19.1RT )

k5f ) 1.5 × 1013 exp

(-17.5RT )

k5b ) 2.9 × 1013 exp

(-13.2RT )

k6f )

4.4 × 106 (non-activated)

k6b ) 1.9 × 1012 exp

(-18.2RT )

a Units of activation energies are kilocalories per mole, and those of pre-exponential factors are inverse seconds.

Ind. Eng. Chem. Res., Vol. 48, No. 11, 2009 5261

that the activation energies for nitrogen adsorption and desorp-tion (23.3 and 44.5 kcal/mol, respectively) of the microkineticmodel are slightly higher than those in model 2. However, the

parameters of the microkinetic model are physically reasonable,and this may be considered to be the most plausible model.

To exploit the most appropriate model from another perspec-tive, we have calculated the RDS for each of the parameter setsthat indicated a local minimum in the optimization (ap-proximately 100 in all). In addition, we calculated which ofthe reactions were predicted to be in PE for each of these modelsand also determined the MARI predicted by each model foreach operating condition in the fitting and assessment data sets.Some common features of the models (parameter sets) werethat either H* or N* were found to be the MARI in every case,and their surface coverage was comparable in many cases. N2

adsorption/desorption and at least one of the NHx dehydroge-nation reactions (R3-R5) were always predicted to be out ofPE, indicating that they are kinetically significant. This isconsistent with the assumptions made in deriving the globalrate expression model 2. While different reactions are predictedto be the RDS for different parameter sets at different operatingconditions, the most common reactions to be predicted as theRDS from all the possible solutions are reactions R2: N2 + 2*) 2N*, R3: NH* + * ) N* + H*, and R4: NH2* + * ) NH*+ H*. For the microkinetic models chosen from modeldiscrimination, reaction R3 is predicted to be the RDS, andreaction R2 is the next most sensitive reaction. H* is predictedto be the MARI, and reactions R2-R4 (and occasionally R5)are out of PE. It is interesting to note that model refinementchanged the order of important reactions; R3′s bond index wasnot included, and thus, it was modified. However, R3′s pre-exponential was fine-tuned and its activation energy dependson the elemental heats of adsorption that were estimated frompart of the data. As a result, adjustment of the bond index ofR3 is not necessary.

The fairly large range of parameter variation shown in Table3 indicates that despite the physical bounds and thermodynamicconstraints, multiple minima (parameter sets) still exist. It isclear that macroscopic data injection into multiscale models isinsufficient to provide complete model discrimination. Rather,some critical microscopic data is needed. For example, tem-perature programmed reaction is needed to resolve the MARIon the real catalyst and isotopic labeling experiments will behelpful to elucidate the RDS. Despite this multiplicity, the goodnews is that all these microkinetic models could be reliablepredictors of macroscopic response, such as ammonia conver-sion, needed for reactor design. The global search and infor-matics tools ensure that these models are useful in the entireexperimental parameter space (globally accurate).

Conclusion

First principle microkinetic models lack predictive capabili-ties. In order to render quantitative models, we introduced aframework for data injection into microkinetic models to refinethe model parameters and assess model uniqueness. Ourapproach was demonstrated for the catalytic decomposition ofammonia on Ru/γ-Al2O3 to produce hydrogen. Experimentswere designed to eliminate mass transfer limitations andminimize temperature gradients, while searching and organizingthe “entire” experimental parameter space using informaticstools. Traditional data analysis indicates a fractional reactionorder with respect to NH3, and strong H2 inhibition on theammonia conversion, even at low fractions of ammonia.

Multiple parameter sets were determined. Bayesian statisticswas employed to discriminate the microkinetic models andseveral global rate expressions. A major conclusion is that someof the best models describing the decomposition of ammonia

Figure 8. Parity plots showing the best fits of each of the global rateexpressions listed in Table 1 over the complete set of experimental data(fitting and assessment).

Figure 9. Parity plots showing (microkinetic) model predicted conversionagainst experimental conversion for (a) model before parameter estimation(assessment set), (b) model after estimation (fitting set), (c) model afterestimation (assessment set), and (d) model after estimation (fitting andassessment sets). Error bars in a indicate the uncertainty in the experimen-tally reported conversion.

5262 Ind. Eng. Chem. Res., Vol. 48, No. 11, 2009

on Ru/γ-Al2O3 have N2 adsorption/desorption and at least oneof the NHx dehydrogenation reactions out of partial equilibrium,and one of these reactions is the rate-determining step (RDS).H* or N* are the most abundant relative species (MARI) in allthese models. This finding indicates that the ambiguity in theliterature about N2 adsorption/desorption or the reactionNH2* + * ) NH* + H* being the RDS may result from thefact that models based on either premise can adequately describethe system with different parameter sets. It is entirely possiblethat there is not a single RDS, but instead N2 adsorption/desorption and some NHx dehydrogenation reactions are allkinetically significant reactions.

Our analysis indicates that (macroscopic) kinetic data alonemay be insufficient for microkinetic model discrimination;techniques such as temperature programmed reaction, isotopiclabeling, and in situ spectroscopy are needed to complementmacroscopic data and elucidate the key elementary reactionsand the most abundant species and, thus, to enable further modeldiscrimination. From an engineering viewpoint, the fact thatmultiple models (parameter sets) provide comparable accuracyin predicting experimental data implies that any of these models(with physically reasonable parameters) may be adequate forprocess design and systems engineering.

Acknowledgment

We acknowledge financial support from the US Departmentof Energy (DE-FG02-06ER15795). D.G.V. acknowledges Prof.V. Hatzimanikatis for useful discussions on sampling duringD.G.V.’s sabbatical visit at EPFL.

Appendix: Investigation of Transport Limitations andEffective Kinetic Parameters

High ammonia mole fraction (60-100%) in the feed was chosento test for transport limitations under conditions of high reaction

rates and low effective thermal conductivity (thermal conductiv-ity of NH3 is much lower than that of He). In order to checkfor temperature and concentration gradients in the catalyst bed,several experimental tests were conducted. External masstransfer limitation was investigated by varying the gas velocitywhile keeping the space velocity constant.50 This was done byvarying the catalyst loading and measuring the NH3 decomposi-tion rate. Higher gas velocity leads to higher mass transfer ratebetween the gas in the bulk and the catalyst pellets. At the samespace velocity, a higher mass transfer rate would lead to a higherNH3 conversion, if mass transfer limitations were present. FigureA1 shows that by doubling the gas velocity, the NH3 conversionis not affected. Therefore, we can conclude that the catalystbed is not affected by external mass transfer limitations.

The small catalyst pellets size (50-75 µm) was chosen inorder to eliminate internal diffusion limitation. The absence of

Table 3. Optimal Parameter Set for Microkinetic Model (Second Column) and Range of Parameter Values in Various Parameter Sets (ThirdColumn)a

parameter value range

QH, binding energy for H (kcal/mol) 66.7 47.4 - 77.4QN, binding energy for N (kcal/mol) 125.2 105.3 - 153.2bond index, reaction R2 0.8 0.19-0.80bond index, reaction R4 0.5 0.11-0.60S1f (sticking coefficient for H2 adsorption) 0.08 0.05-1.0Ea1f (activation energy for H2 adsorption, kcal/mol) 0.0 0.0A1b (pre-exponential, H2 desorption), 1/s 2.4 × 1013 (3.6-5.0) × 1013

Ea1b (activation energy for H2 desorption, kcal/mol) 25.9 0-47.2S2f (sticking coefficient for N2 adsorption) 2.2 × 10-7 1.0 × 10-7-0.43Ea2f (activation energy for N2 adsorption, kcal/mol) 23.3 0.0-39.6A2b (pre-exponential, N2 desorption), 1/s 1.6 × 1010 7.4 × 109-3.6 × 1012

Ea2b (activation energy for N2 desorption, kcal/mol) 44.5 10.8-77.3A3f (pre-exponential, forward reaction R3), 1/s 1.4 × 1013 1.2 × 1011-1.5 × 1013

Ea3f (activation energy, forward reaction R3, kcal/mol) 4.3 1.1-9.2A3b (pre-exponential, backward reaction R3), 1/s 8.8 × 1012 4.8 × 108-9.4 × 1012

Ea3b (activation energy, backward reaction R3, kcal/mol) 38.6 24.9-46.8A4f (pre-exponential, forward reaction R4), 1/s 7.2 × 1012 1.3 × 1012-2.0 × 1013

Ea4f (activation energy, forward reaction R4, kcal/mol) 19.3 3.5-28.2A4b (pre-exponential, backward reaction R4), 1/s 4.6 × 1012 9.1 × 109-1.3 × 1013

Ea4b (activation energy, backward reaction R4, kcal/mol) 15.6 0.9-24.4A5f (pre-exponential, forward reaction R5), 1/s 1.4 × 1013 1.4 × 1012-1.4 × 1013

Ea5f (activation energy, forward reaction R5, kcal/mol) 18.2 13.3-24.9A5b (pre-exponential, backward reaction R5), 1/s 8.8 × 1012 2.4 × 109-8.8 × 1012

Ea5b (activation energy, backward reaction R5, kcal/mol) 10.5 0.1-21.0S6f (sticking coefficient for NH3 adsorption) 0.63 6.1 × 10-5-1.0Ea6f (activation energy for NH3 adsorption, kcal/mol) 0.0 0.0A6b (pre-exponential, NH3 desorption), 1/s 4.4 × 1013 3.3 × 1011-7.6 × 1013

Ea6b (activation energy for NH3 desorption, kcal/mol) 14.0 9.8-20.9coverage dependence of QH on H-H interactions, kcal/mol -3.2 0.0-(-6.5)coverage dependence of QN on N-N interactions, kcal/mol -40.0 (-22.3)-(-47.1)

a Activation energies are specified in the zero coverage limit at 623 K.

Figure A1. External mass transfer limitation test. Both catalyst beds (4 wt% Ru/Al2O3) were diluted with Al2O3 in 1:1.5 ratio by weight. The gasvelocity for the 96 mg bed was double that of the 48 mg to fix the spacevelocity at the same value.

Ind. Eng. Chem. Res., Vol. 48, No. 11, 2009 5263

internaldiffusionlimitationswasconfirmedusingtheWeisz-Pratercriterion, (rA′ FcRp

2)/(DeCAs) , 1, where rA′ is the measured NH3

reaction rate (mol/(kg s)), Fc is the catalyst pellet density (1500kg/m3), Rp is the pellet radius (30 × 10-6 m), De is the effectivediffusivity of NH3 in the catalyst pellet (m2/s), and CAs is theNH3 concentration at the pellet surface (16.7 mol/m3 at 450 °C,assumed to be the same as in the gas-phase). The effectivediffusivity is calculated from the equation De ) DNH3-H2

φpσ/τ,where DNH3-H2

is the diffusion coefficient of NH3 in H2 at 450°C (4 × 10-4 m2/s51), φp is the pellet porosity, σ is theconstriction factor, and τ is the tortuosity. Typical values for acatalyst pellet are φp ) 0.4, σ ) 0.8, and τ ) 3. The measured

reaction rate at 450 °C, 100% NH3 at the inlet, and 400 sccmflow rate was 0.65 gmol/(kg s). The left-hand side equals 1.2× 10-3, which satisfies the criterion.

The apparent activation energy was calculated at 30%, 60%,and 100% NH3 mole fraction in the feed, and similar valueswere obtained (95-100 kJ/mol) as shown in Figure A2. Theapparent activation energy is expected to be lower under internalmass transfer limitations and increase if the system transitions(as the concentration increases) from diffusion- to reaction-limited conditions. These apparent activation energies are (withinexperimental error) independent of concentration and close tothose reported in the literature for Ru/Al2O3 catalysts (65-140kJ/mol).4,6,22,23,41 These results support the conclusion that thecatalyst bed is free of internal mass transfer limitations.

The typical experimental test to check for temperaturegradients in the catalyst bed consists of comparing the reactionrate at different bed dilution ratios.50 Figure A3 shows that thecatalyst bed is free of temperature gradients up to 400 °C. Asshown in Figure A4, higher dilution resulted in about 4-6%increase in NH3 conversion at 450 °C, which is withinexperimental error. Therefore, it can be concluded that with abed dilution ratio of 1:1.5, the catalyst bed is free of all transportlimitations up to 400 °C. At 450 °C, small temperature gradientscould exist in the catalyst bed. However, the effect of temper-ature gradients on the measured ammonia conversion at 450°C was within experimental error.

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ReceiVed for reView January 27, 2009ReVised manuscript receiVed April 1, 2009

Accepted April 7, 2009

IE900144X

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