Developing global reaction rate model for CO oxidation over Au catalysts from past data in literature using artificial neural networks

Applied Catalysis A: General 468 (2013) 395–402

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Applied Catalysis A: General journal homepage: www.elsevier.com/locate/apcata

Developing global reaction rate model for CO oxidation over Au catalysts from past data in literature using artificial neural networks M. Erdem Günay a , Ramazan Yildirim b,∗ a b

Department of Energy Systems Engineering, Istanbul Bilgi University, 34060 Eyup-Istanbul, Turkey Department of Chemical Engineering, Bo˘gazic¸i University, 34342 Bebek-Istanbul, Turkey

a r t i c l e

i n f o

Article history: Received 24 April 2013 Received in revised form 18 June 2013 Accepted 31 August 2013 Available online 8 September 2013 Keywords: Power law model Reaction kinetics Artificial neural networks Knowledge extraction CO oxidation

a b s t r a c t In this work, the literature for CO oxidation kinetics over Au based catalysts was analyzed using artificial neural networks to test the possibility of developing global reaction rate models representing the entire literature. A database was constructed using the data obtained from nineteen papers published between the years 1997 and 2011; then, the reaction rate was modeled as a function of catalyst preparation and operational variables by using neural networks. Next, global reaction rate equations in the form of power law were developed for each support type by the help of the neural network model, and the order of reaction with respect to each reactant and the parameters of Arrhenius relation were estimated. These power law models were successfully validated by using the information reported in the literature; hence, it was concluded that they can be used for the initial estimation of the reaction rates in the absence of more specific rate equations. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Developing an effective catalyst is a challenging task that requires significant amount of experimental works to optimize the catalyst preparation and operating conditions as well as to understand the physical and chemical processes over the catalyst surface. Fortunately, the research capacity and resource allocation for the catalysis in the world continuously increases resulting large number of contributions from all over the world even for the simplest catalytic systems. Although researchers generally try to focus their efforts on the conditions that have not been fully explored, there are significant amount of repetitions, similarities and correlations among the works published in the literature. Today, it is quite likely that the works already been published and the number of data points generated, in a popular research area that have been studied for a couple of years, may be large and diverse enough to cover the entire experimental region. Hence, it may be possible to extract the knowledge hidden within the network of the data, which have already been published, and identify pattern, rules and generalizations. Such valuable information may help to understand the catalytic phenomena better, and even to predict the outcome of the untested conditions without performing an actual experiment. Data mining is the collection of methods such as classification, clustering and estimation, which help to detect trends and

∗ Corresponding author. Tel.: +90 212 359 7248; fax: +90 212 287 2460. E-mail address: [email protected] (R. Yildirim). 0926-860X/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.apcata.2013.08.056

patterns, derive conclusions or make predictions from a set of data [1,2]. The applications of the data mining methods have become quite widespread in various areas due to the great development of hardware and software especially in the last two decades. Likewise, in the field of catalysis, many successful implementations of these techniques have been reported by various researchers including our group; the examples are the decision trees and logistic regression for classification [3–6], k-means clustering and Kohonen networks for clustering [3], artificial neural networks and support vector machines for estimation [6–12]. In all these works, the corresponding data mining method were employed on a limited set of experimental data produced by the same research group. However, as far as we know, there are also at least three (two of them by our group) successful applications of knowledge extraction from the entire published literature for a catalytic system using data mining tools [13–15]. In our first communication adopting this approach, we constructed a neural network model for selective CO oxidation over CuO/CeO2 catalysts using 1337 data points harvested from 20 publications in the literature and tested this model to predict the outcome of the unstudied experimental conditions [14]. The CO conversions reported in each publication were successfully predicted by the model constructed from the remaining nineteen publications unless that publication contained some unique variables, which were not used in the other studies (like a specific type of a promoter). The model constructed was also quite successful in determining the effects of various catalyst preparation variables (such as Cu loading, second metal additive, support type and

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preparation method) and operational variables (such as reaction temperature, feed composition and F/W ratio). Next, we extended our efforts to a larger and more complex data set (5610 data points from 80 publications) involving CO oxidation over noble metal (Pt, Au, Pd, Rh, Ru and Ir) catalysts and performed a more detailed analysis using a combination of various data mining tools [15]. First, we classified the catalysts in the database by using decision trees to determine the conditions that lead to high CO conversion. Then, we determined the relative importance of various catalyst preparation and operational variables for CO conversion using artificial neural networks. Finally, we separated the entire database into smaller sets according to their similarities by genetic algorithm based clustering technique, and modeled each cluster by artificial neural networks to make predictions. This provided the extraction of useful trends, rules and correlations, which were not easily comprehensible by the naked eyes. In these two works summarized above, we mainly focused on the catalytic performance and used the data from the publications that aim to optimize the catalyst preparation and operational variables or to understand their effects on the catalytic performance; we excluded the data involving reaction kinetics, which are also vital to model and understand the catalysis phenomena, because they required a special treatment. In the present communication, we analyzed the publications involving CO oxidation kinetics over Au based catalysts by using artificial neural networks to test the possibility of deriving a global model valid within the entire database and a global reaction rate equation in the form of power law. Such knowledge can provide the initial estimation of the reaction rates in the absence of specific models developed for those specific conditions.

developed in the present work since they represent the data generated in these publications. The catalyst preparation variables (base metal percent, support type, catalyst preparation method and calcination conditions) together with the operating conditions (CO, O2 , H2 , H2 O and CO2 partial pressures, reaction temperature and time on stream) were used as the input variables while the output variable was the reaction rate. Some of these variables were continuous (like base metal percent, temperature and feed compositions) while the others were categorical (such as catalyst preparation method and support type). Each continuous variable was treated as one input within the minimum–maximum range of the values reported in the database. Each option for the categorical variables, on the other hand, was treated as an individual input variable having the value of one or zero depending whether it was used or not [14].

2. Materials and methods

r

2.1. Experimental data

The reaction rate constant, k, was written as a function of temperature (Arrhenius relation) and inserted into Eq. (1) leading the following equation.

Nineteen publications on CO oxidation kinetics over gold based catalysts were reviewed and the experimental data presented in these works were extracted (882 data points). Table 1 shows the year of publication (from 1997 to 2011), the catalyst preparation method applied, the support type and the number of data points extracted from each publication used in the database. All these publications described the intrinsic kinetics assuming that the mass transfer limitations were negligible. Consequently, the same assumption is valid for the global reaction rate models

2.2. Procedure of analysis The procedure of developing global reaction models for selective CO oxidation was as follows (Fig. 1): first a neural network model for entire database was constructed using the data obtained from all the related publications found in the literature. Then, input significance analysis was performed to determine the relative importance and the effects of input variables on CO oxidation rate. Then, we tried to construct an empirical global rate equation valid in the entire range of experimental conditions reported in the literature. As customary in the field, we defined the equation as a power law function of the partial pressures of CO, O2 and H2 as shown in Eq. (1). Hydrogen is also considered as a reactant throughout the analysis, if it is present in the feed because it affects the CO reaction rate.

r







mol CO g−1 s−1 = k · PCO (atm)˛ · PO2 (atm)ˇ · PH2 (atm) Au

mol CO g−1 s−1 Au



 =

A·e

−Ea (j mol-1 ) RT (K)

(1)

 · PCO (atm)˛

·PO2 (atm)ˇ · PH2 (atm)

(2)

where A is the pre-exponential term, Ea is activation energy, R is the universal gas constant, T is the reaction temperature in K. Then,

Table 1 Details of the publications used for database construction. Reference

Year of publication

Preparation method

Support

Number of data points

Visco et al. [16] Okumura et al. [17] Kahlich et al. [18] Park and Lee [19] Schumacher et al. [20] Schubert et al. [21] Calla and Davis [22] Rossignol et al. [23] Lomello-Tafin et al. [24] Pansare et al. [25] Han et al. [26] Quinet et al. [27] Avgouropoulos et al. [28] Aguilar-Guerrero and Gates [29] Denkwitz et al. [30] Piccolo et al. [31] Xu et al. [32] Davran-Candan et al. [33] Ulguel [34]

1997 1998 1999 1999 2004 2004 2005 2005 2005 2005 2007 2008 2008 2008 2009 2009 2010 2011 2011

Co-precipitation Deposition precipitation, chemical vapor deposition Co-precipitation Deposition precipitation Deposition precipitation Deposition precipitation Deposition precipitation Low-energy cluster beam deposition Simple oxidation Deposition precipitation Ultrasound deposition precipitation Anionic exchange method Deposition precipitation Unspecified Deposition precipitation Deposition precipitation Deposition precipitation Deposition precipitation Deposition precipitation

Fe2 O3 Al2 O3 , TiO2 , SiO2 Fe2 O3 Al2 O3 , TiO2 , Fe2 O3 TiO2 Fe2 O3 Al2 O3 Al2 O3 , ZrO2 , SiO2 ZrO2 Al2 O3 Al2 O3 Al2 O3 CeO2 CeO2 TiO2 Fe2 O3 CeO2 Al2 O3 Al2 O3

60 25 28 140 40 60 60 50 41 45 4 116 5 19 128 5 10 20 26

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397

Fig. 1. The conceptual approach used to develop global rate equation.

Eq. (2) was linearized by taking the natural logarithm of both sides forming Eq. (3): ln r =



ln A −

Ea RT



+ ˛ ln PCO + ˇ ln PO2 +  ln PH2

(3)

It was observed from the initial analysis that the transformation of reaction rate and partial pressures by taking the natural logarithms (as in Eq. (3)) also improved the accuracy of the neural network models significantly. Although the neural networks normally have the ability to handle nonlinear problems quite well, some form of linearization seemed to be needed; hence, we performed this transformation at the beginning and used those networks throughout the analysis while the other variables were taken in their original form. 2.3. Computational details The artificial neural network models were created by using the neural network toolbox in MATLAB 7.13 (R2011b) environment. Levenberg–Marquardt Method of training was used for training and testing [14,35]. Hyperbolic tangent function was applied as the activation function in the hidden layers, and mean square error (MSE) was employed as the measure of fitness. Each network topology was trained 10 times to compensate the effects of random initialization of the neural network weights, and the best performances were recorded. To prevent overlearning of the neural network, the early-stopping technique was applied during the training process by using some random data points among the training set as the validation data. The optimal network topology was determined by constructing several networks and testing their performances according to their generalization accuracies (the ability to predict the data unseen during the training process) [36]. The root mean square

error (RMSE) of testing, which indicates the degree of the generalization accuracy [37], was estimated by applying k-fold (2-fold in this work) cross validation technique [11]. The entire database was divided randomly into k subsets, and then the data acquired from k − 1 sets were used to train the network to predict the outcome of the remaining one set. The errors between these predictions and the corresponding experimental results were recorded. This procedure was repeated k times covering all the data points, and the RMSE (Eq. (4)) calculated through the entire database was used as the indicator to determine the optimal neural network topology.

 n 1 RMSE =

(pi − ti )2 n

(4)

1

where pi is the predicted, ti is the target value and n is the total number of experiments. The test of relative importance (significance) for the catalyst variables was done by the change of root mean square error method. The test started with the removal of one of the input variables, and then, the network was trained with the remaining variables. After the training was complete, the RMSE value of the model calculated in the absence of this variable was compared with the value obtained in the presence of all inputs, and the difference was used as the indicator of the significance of this variable [10,11]. The procedure was repeated for all the input variables. 3. Results and discussion 3.1. Determining optimal neural network topology First, the reaction rates were modeled using the catalyst preparation and operating variables by artificial neural networks. For this

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Au wt.% preparation method calcination T (oC) calcination time (h) support type second metal type and wt.% reaction T(oC) CO vol.% O2 vol.% H2 vol.% output layer (rate of reaction)

H2O vol.% CO2 vol.% TOS (min) 1st hidden layer

2nd hidden layer

Input layer Fig. 2. The optimal neural network topology.

purpose, several neural network topologies were tested by using 2fold cross validation. The optimal topology with the minimum test error was found as 24-4-4-1 (24 input variables, 4 neurons in the first and second hidden layers, 1 output). Fig. 2 shows a schematic representation of the neural network. The statistical performance of this topology is shown in Fig. 3; the training and the testing data lie very close to the y = x line with the R2 values of 0.962 and 0.922 respectively indicating that this global model successfully represents the entire database. It should be remembered that the testing R2 is the measure of success in predicting the reaction rates not seen by the network during training; hence, the value of 0.922 is quite satisfactory for such purpose. 3.2. Analyzing effects of variables

(a) -3

(b) -3

ln(rate) predicted (mol CO.g Au-1.s-1)]

ln(rate) predicted (mol CO.g Au-1.s-1)]

The neural network topology constructed in the previous section was used to determine the relative importance of the catalyst variables using the change of root mean square error method as explained in computational details. In overall, the operational variables were found to be more significant than the catalyst

preparation variables (about 59–41%) as presented in Table 2. The temperature was found to be the most significant operational variable (with the relative significance of 51%) as expected, considering that the dependent variable was the reaction rate. This is followed by hydrogen as it known that its presence enhances the CO oxidation [33]. Although the CO and O2 concentrations are also the main variables for reaction rates, their relative impacts were found to be small for the following reason: Naturally, the relative significances are valid within the ranges of variables in the database, and CO and O2 concentrations are usually changed only around 1–2% (as expected in the feed) from a publication to publication resulting only small variations in the reaction rates. The same is also true for some other variables like Au loading, which are customary to be optimized into narrower ranges (1–2 wt.%) so that variation from paper to paper is insignificant. This lowers the apparent relative significances of these variables. The opposite is also true. For example the calcination conditions have very high relative significance because the optimum conditions for this step seem to be not well established yet: various procedures (no calcination, calcination before Au loading, calcination after Au loading) as well as

-6

-9 R2=0.962

-12

-6

-9 R2=0.922

-12 -12

-9

-6

ln(rate) experimental (mol CO.g Au-1.s-1)]

-3

-12

-9

-6

-3

ln(rate) experimental (mol CO.g Au-1.s-1)]

Fig. 3. Neural network predicted versus experimental reaction rates for: (a) training data, (b) testing data found by 2-fold cross validation.

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Table 2 Relative input significances of preparation and operational variables. Type of variables

Catalyst variables

Relative significance (%)

Group significance (%)

Preparation variables

Au wt.% Promoter type and amount Support type Preparation method Calcination conditions

10.5 2.2 18.6 14.0 54.6

41.1

Operating variables

CO vol.% O2 vol.% H2 vol.% H2 O vol.% CO2 vol.% Time on stream Reaction temperature

3.9 4.2 23.4 5.3 4.2 8.0 51.0

58.9

various calcination temperatures and times were used through the database. Whatever the reason is, however, the high relative significance indicates that corresponding variable can be further refined to have better catalytic performance. We also presented the plots of the reaction rate versus calcination and reaction temperatures, which are the most significant preparation variables for this database, for two support types. Fig. 4 shows the effect of calcination temperature (in the range of 473–773 K) on the reaction rate for the Au/TiO2 and the Au/Fe2 O3 catalysts by keeping the partial pressures of CO and O2 at 0.02 and 0.04 atm, respectively; the reaction temperature was taken as 373 K. It was found that the calcination temperature had a negative influence on the reaction rate for both catalyst types. This result is in good agreement with the findings of Park and Lee [19], who attributed this negative effect to the fact that the gold phase changes from an oxidized gold phase (more active) to metallic Au (less active) as the calcination temperature increases. In Fig. 5, the reaction rates over Au/Al2 O3 and Au/TiO2 catalysts were compared in the temperature range of 313–373 K by keeping the other variables constant at average values. According to the figure, Au/TiO2 yielded higher rate than Au/TiO2 as also observed by Rossignol et al. [23], who reported that gold nanoparticles are dispersed on alumina and titanium supports with the same size distribution however with a CO conversion on TiO2 higher than on Al2 O3 . The effect of temperature, which is stronger in case of TiO2 support, was also quite obvious. The effect of reaction temperature, partial pressures of CO, O2 and H2 will be further discussed in the following sections when the reaction rate equations were developed.

3.3. Developing a global power law model Although the artificial neural network is quite successful as a global model to predict the reaction rates, a simpler power low model was also searched. No single model for the entire database was possible because the support type affected the rate significantly and it was not possible to insert this variable into the equation due to its discrete nature. Hence, a specific global power law model was developed for each support type. Although this approach puts some limits on the generalization of the results, the global reaction rates derived this way will be still useful considering that only a limited number of supports are utilized for a certain class of reaction; each of these models (especially the ones for common supports like Al2 O3 ) would be general enough to find wide applications in the literature. The analysis for Al2 O3 support were presented and discussed below while similar results found for TiO2 and F2 O3 are given in “Supplementary Material”. The reaction rates for various values of reactants (CO, O2 and H2 ) partial pressures in the entire experimental region were computed using the neural network model. Then, the reaction rate parameters (k, A, Ea , ˛, ˇ, ) shown in Eq. (2) were estimated from the predicted reaction rates by employing linear regression as the common procedure employed in the field: the plot of reaction rate versus the partial pressure for each reactant was constructed in logarithmic scale by keeping the reaction temperature and the partial pressure of the other reactants constant. Next, the order of the reaction with respect to each reactant was determined from the slopes of the lines.

Au/TiO2 Au/TiO2

Au/Fe2O3

Au/Al2O3

0.006

rate (mol CO.gAu -1.s-1)

rate (mol CO.gAu-1.s-1)

0.016

0.012

0.008

0.004

0.002

0.004

0.000

0.000 400

500

600

700

800

Calcination Temperature (K) Fig. 4. Effect of calcination temperature on Au/TiO2 and the Au/Fe2 O3 catalysts simulated by the optimal neural network.

300

320

340

360

380

Reaction temperature (K) Fig. 5. Effect of support type on Au/Al2 O3 and the Au/TiO2 catalysts simulated by the optimal neural network.

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H2=0.4atm

H2=0 atm

-5.0

-4.5

ln(rate) (mol CO.gAu-1.s-1)

ln(rate) (mol CO.gAu -1.s-1)

y = 0.41x -3.55 R² = 0.99 -5.5

-6.5 y = 0.70x -4.18 R² = 1.00 -7.5

-8.5 -5.0

-4.0

-3.0

-5.2

-5.4

y = 0.27x -4.89 R² = 1.00

-5.6

-5.8

-2.0

-3.2

-2.2

ln CO (atm) Fig. 6. Estimating the order of reaction for CO by using the predictions of the neural network model for the Au/Al2 O3 catalyst (1.22% Au).

3.3.1. Determining order of reaction with respect to CO (˛) The trained network was used to estimate the rate of reactions at 10 different partial pressures of CO in the range of 0.008–0.080 atm, by keeping the reaction temperature constant at 373 K and the partial pressure of O2 as 0.04 atm. The neural network estimated logarithmic rate versus the partial pressure of CO is presented in Fig. 6 both in the presence and absence of hydrogen (with a partial pressure of 0.4 atm) in the feed. The plot was successfully fitted to a straight line with R2 values of approximately 1.00 for both the absence and the presence of hydrogen. The slopes of the lines indicate that the reaction order with respect to CO is 0.70 and 0.41 for the absence and presence of hydrogen, respectively. 3.3.2. Determining order of reaction with respect to O2 (ˇ) Similar to the analysis done for CO, the trained network was used to estimate the rate of reactions at 10 different partial pressures of O2 in the same range as CO by keeping the reaction temperature constant at 373 K and the partial pressure of CO as 0.02 atm. Again the straight lines were fitted almost perfectly resulting the order of reaction with respect to O2 as 0.41 and 0.54 for the absence and presence of hydrogen, respectively (Fig. 7). 3.3.3. Determining order of reaction with respect to H2 () This time the partial pressures of both CO and O2 were kept constant at 0.02 and 0.04 atm, respectively; and the partial pressure H2=0.4atm

-1.2

-0.2

ln H2 (atm) Fig. 8. Estimating the order of reaction for H2 by using the predictions of the neural network model for the Au/Al2 O3 catalyst (1.22% Au).

of H2 was changed from 0.05 to 0.50 atm. Again a perfect fit was achieved with a straight line whose slope indicates that the order of reaction with respect to H2 as 0.27 (Fig. 8). It should be noted that the hydrogen concentration was not systematically changed as the CO and O2 concentrations during the experiments reported in the literature; it was constant (and excess) at different values in each work reported in the literature. Hence, the exponent of the hydrogen () is not exactly a reaction order in the same sense as the reactants CO and O2 . Instead, it should be treated as an additional parameter accounting the difference in the reaction rates obtained at different studies performed under different hydrogen concentrations. 3.3.4. Determining Arrhenius parameters In order to find the Arrhenius parameters (A and Ea ) as shown in Eq. (2), the natural logarithm of the reaction rate versus the reciprocal of T was plotted for the temperature in the range of 293–393 K. The partial pressures of CO and O2 were kept as 0.02 and 0.04 atm, respectively; and the partial pressure of hydrogen was taken as 0.4 atm for the case of the presence of hydrogen. Again very successful linear fits were achieved as shown in Fig. 9, whose slopes indicate the Ea /R. Activation energies were calculated as 19.1 and 20.6 kJ/mol for the absence and the presence of hydrogen, respectively.

H2=0 atm

H2=0.4 atm

H2=0 atm

y = 0.54x -3.41 R² = 0.99

ln(rate) (mol CO.gAu -1.s-1)

ln(rate) (mol CO.gAu-1.s-1)

-4.5

-5.5

-6.5

-7.5 y = 0.41x -5.60 R² = 1.00 -8.5 -5.0

-4.0

-3.0

-2.0

ln O2 (atm) Fig. 7. Estimating the order of reaction for O2 by using the predictions of the neural network model for the Au/Al2 O3 catalyst (1.22% Au).

-5.0 y = -2,480.31x + 1.50 R² = 0.98

-7.0

y = -2,298.72x -0.79 R² = 1.00 -9.0 2.5E-03

3.0E-03

3.5E-03

1/T (K-1) Fig. 9. Estimating the Arrhenius parameters by using the predictions of the neural network model for the Au/Al2 O3 catalyst (1.22% Au).

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Table 3 Comparison of the parameters of the reaction rate equation reported in the literature with the neural network estimations for the Au/Al2 O3 catalysts in the absence of hydrogen. Variables

Okumura et al. [17]

Calla and Davis [22]

Rossignol et al. [23]

Quinet et al. [27]

Ulguel [34]

This work

Catalyst preparation variables

Au % Mg % Preparation methoda Calcination temperature (◦ C) Calcination time (h)

0.96 0 DP 300 4

1.16 0 DP 350 4

0.08 0 LCBD – –

1 0 AEM 300 4

1 1.25 DP 400 2

1.22 0 DP 280 3.5

Range of variables to calculate orders (˛ and ˇ)

CO range (atm) O2 range (atm) T (K)

– – –

0–0.07 0–0.07 295

– – –

– – –

0.02–0.08 0.01–0.06 403

0.008–0.080 0.008–0.080 373

Range of variables to calculate activation energy

CO (atm) O2 (atm) T range (K)

0.01 0.21 273–313

0.01 0.02 295–373

0.02 0.02 330–600

0.02 0.02 300–555

– – –

0.02 0.04 293–393

Reaction rate parameters computed

˛ (exponent of PCO ) ˇ (exponent of PO2 ) Ea (kJ/mol)

– – 32.0

0.32 0.36 12 ± 1

– – 22.0

– – 26.0

0.61 0.36 –

0.70 0.41 19.1

a

DP: deposition precipitation; LCBD: low-energy cluster beam deposition; AEM: anionic exchange method.

Table 4 Comparison of the parameters of the reaction rate equation reported in the literature with the neural network estimations for the Au/Al2 O3 catalysts in the presence of hydrogen. Variables

Calla and Davis [22]

Rossignol et al. [23]

Quinet et al. [27]

This work

Catalyst preparation variables

Au % Preparation methoda Calcination temperature (◦ C) Calcination time (h)

1.16 DP 350 4

0.08 LCBD – –

1 AEM 300 4

1.22 DP 280 3.5

Range of variables to calculate orders (˛, ˇ and )

CO range (atm) O2 range (atm) H2 range (atm) T (K)

0–0.03 0–0.03 – 295

– – – –

– – – –

0.008–0.080 0.008–0.080 0.05–0.50 373

Range of variables to calculate activation energy

CO (atm) O2 (atm) H2 (atm) T range (K)

0.01 0.02 0.57 295–373

0.02 0.02 0.48 330–600

0.02 0.02 0.48 300–555

0.02 0.04 0.40 293–393

Reaction parameters computed

˛ (exponent of PCO ) ˇ (exponent of PO2 )  (exponent of PH2 ) Ea (kJ/mol)

0.09 0.33 – 27 ± 4

– – – 19.0

– – – 34.0

0.41 0.54 0.27 20.6

DP: deposition precipitation; LCBD: low-energy cluster beam deposition; AEM: anionic exchange method.

3.3.5. Validating power law model with experimental results The artificial neural network model was proven to represent the experimental database successfully in Section 3.1. In the present section, we tested the success of the empirical rate equations by comparing the parameters in the equations and the rates predicted with the values reported in the literature. In Tables 3 and 4, the parameters in the rate equations developed above and the values reported in the literature are presented for the absence and presence of hydrogen, respectively. As Table 3 indicates, the reaction orders were computed to be very close to the values reported by Ulguel [34] while the activation energy was reasonably close to the value reported by Rossignol et al. [23] in the absence of hydrogen. The agreement between the activation energy found in this work and the one reported by Rossignol et al. [23] was also quite close in the presence of hydrogen as shown in Table 4. Since the values of reaction orders and activation energies vary in each publication as seen in Tables 3 and 4, it is inevitable that the model will be in agreement with only some of them or it will not be in agreement at all. On the other hand, the reaction rates computed by the global neural network, however, are quite close to the experimental rates reported in all publications in the database as presented in Fig. 2. This suggests that we should not compare the orders and activation energies of global models with individual

Ulguel (no H2)

Ulguel (H2 present)

Davran-Candan et al. (no H2)

Davran-Candan et al. (H2 present)

Calla and Davis (no H2)

Calla and Davis (H2 present)

ln(rate) predicted (mol CO.gAu -1.s-1)

a

-3.0

R2=0.920

-6.5

-10.0 -10.0

-6.5

-3.0

ln(rate) experimental (mol CO.gAu -1.s-1) Fig. 10. Reaction rates found by the neural network estimated reaction rate equation for the works of Ulguel [34], Davran-Candan et al. [33], Calla and Davis [22] versus their experimental reaction rates.

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models in the literature. Instead, we should test the ability of models to predict the reaction rates for given temperature and partial pressures because this correlation is physically meaningful and it is the main reason to develop such models in the first place. Hence, the reaction rate parameters determined in previous sections were inserted into Eq. (2), and the global rate equations obtained is used to predict the reaction rates given in three works (reporting full rate equations) in the literature. As seen from Fig. 10, the agreement is quite reasonable (with a very close distribution of data around y = x line with an R2 value of 0.920) suggesting that indeed a global rate equation can be used at least for the initial estimation of the reaction rates for a given partial pressure and temperature conditions. 4. Conclusions There is a continuous accumulation of experience in the past publications in the literature for the catalytic rate equations as in any other areas of scientific research. Although these works are empirical and valid for certain experimental conditions, the number of data points collected from the entire published works in the literature is quite large covering probably the entire experimental spectrum. This suggests that global models valid in a wider range can be developed by using some effective data mining tools. The present work demonstrated that this could be indeed achieved for the entire literature of selective CO oxidation over Au based catalysts by the help of artificial neural networks. The order of reaction with respect to each reactant and the parameters of Arrhenius relation were estimated to develop global reaction rate equations in the form of power law for each support type, and the power law models were successfully validated by using the information reported in the literature. To conclude, this approach can be extended to the other catalytic systems to develop global models that can be used at least for the initial estimation of the reaction rates. Acknowledgements The financial supports provided by the Scientific and Technical Research Council of Turkey through Project 109M207 and Bo˘gazic¸i University Research Fund Project 12A05M1 are gratefully acknowledged.

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Appendix A. Supplementary data [36]

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.apcata.2013.08.056.

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