Kinetic modeling of oxidative dehydrogenation of propane (ODHP) over a vanadium–graphene catalyst: Application of the DOE and ANN methodologies

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JIEC-1591; No. of Pages 12 Journal of Industrial and Engineering Chemistry xxx (2013) xxx–xxx

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Kinetic modeling of oxidative dehydrogenation of propane (ODHP) over a vanadium–graphene catalyst: Application of the DOE and ANN methodologies Moslem Fattahi a, Mohammad Kazemeini a,*, Farhad Khorasheh a, Alimorad Rashidi b a b

Department of Chemical and Petroleum Engineering, Sharif University of Technology, Azadi Avenue, P.O. Box 11365-9465, Tehran, Iran Nanotechnology Research Center, Research Institute of Petroleum Industry, Tehran, Iran

A R T I C L E I N F O

Article history: Received 9 June 2013 Accepted 29 September 2013 Available online xxx Keywords: Kinetic modeling Artificial neural network DOE Oxidative dehydrogenation of propane Non-linear regression

A B S T R A C T

In this research the application of design of experiment (DOE) coupled with the artificial neural networks (ANN) in kinetic study of oxidative dehydrogenation of propane (ODHP) over a vanadium–graphene catalyst at 400–500 8C and a method of data collection/fitting for the experiments were presented. The proposed reaction network composed of consecutive and simultaneous reactions with kinetics expressed by simple power law equations involving a total of 20 unknown parameters (10 reaction orders and 5 rate constants each expressed in terms of a pre-exponential factors and activation energies) determined through non-linear regression analysis. Because of the complex nature of the system, neural networks were employed as an efficient and accurate tool to model the behavior of the system. Response surface methodology (RSM) and ANN methods were constructed based upon the DOE’s points and were then utilized for generating extra-simulated data. The three data sets including the original experimental data, those simulated by the ANN and RSM methods were subsequently used to fit power law kinetic rate expressions for the main ODHP and side reactions. The results of kinetic modeling with simulated data sets from the ANN and RSM models compared with collected experimental data. Both methods were able to satisfactorily fit the experimental data for which the ANN data set showed the best fitting amongst them all. ß 2013 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved.

1. Introduction Although the oxidative dehydrogenation (ODH) of paraffins for the production of light olefins (ethylene, propylene or butenes) continues to be of interest at laboratory research level, industrial applications are still hindered by unsatisfactory yields (due to the formation of carbon oxides) and technical conditions (flammability of the reaction mixture and reactor choice) [1]. Vanadium catalysts are generally used [2] and the majority of reported studies deal with catalyst preparation techniques, evaluation of catalyst performance in terms of the selectivity-conversion trend and correlations between catalytic activity, vanadium co-ordination and catalyst properties [3,4]. There are several studies that focus on determination of the kinetic parameters of the reactions involved in the ODH process and several reaction mechanisms have been proposed [5–8]. Kinetic study of the oxidative dehydrogenation of alkanes is one

* Corresponding author. Tel.: +98 21 6616 5425; fax: +98 21 6602 2853. E-mail addresses: [email protected] (M. Fattahi), [email protected] (M. Kazemeini), [email protected] (F. Khorasheh), [email protected] (A. M. Rashidi).

approach to elucidate the reaction mechanism and to facilitate the selection of the appropriate catalyst. Previous studies [5–13] on ODHP over oxide catalysts have not completely explained the reaction mechanism and some controversies in determination of the macroscopic steps of the reaction still exist. Most models applied to ODHP reaction were simplified. Though it is well-known that the kinetic studies are not able to determine the molecular mechanism of the reaction, they allow to exclude some of the possible paths and to determine the reaction network. Kinetic studies have provided useful information about the reaction and the role of catalyst. On the basis of these studies, one can identify the intermediate products and examine the importance of particular reaction routes (parallel and consecutive reaction paths, branching of the reactions, etc.) which play an important role on the observed selectivity of the process. One can also identify the rate-determining step in a sequence of consecutive reactions. The Mars–van-Krevelen (MvK) or steady state adsorption models (SSAM) have been used with or without the Eley–Rideal (ER) or Langmuir–Hinshelwood (LH) mechanisms. The models were evaluated using a wide range of experimental data on propane conversion and selectivities to propylene and COx for different contact times, temperatures and initial propane

1226-086X/$ – see front matter ß 2013 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jiec.2013.09.056

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concentrations [14]. Kinetic investigations revealed a low reaction order for oxygen and reaction orders in the range of one for propane [15,16]. Previous studies [17,18] have underlined the theory of MvK mechanism as a microkinetic model suggesting that lattice oxygen takes part in the reaction. Quantum chemical calculations by means of density functional theory (DFT) are currently exploring energetically favorable reaction sites in ODHP. For silica supported vanadia catalysts, calculations suggested that monomeric and dimeric vanadium oxide surface species to take part in ODHP [19]. It was suggested that for a model (0 1 0) surface of V2O5 system at least two V5 5O groups bonded by a V–O–V bond were required for the dissociative adsorption of propane [20]. Alkene selectivities in ODHP decreased markedly as conversion increases [21,22]. One important reason for these yield limitations was the typically higher energies of the C–H bonds in alkane reactants compared with those in the desired alkene products [23] leading to rapid alkene combustion at the temperatures required for C–H bond activation in alkanes. On VOx-based catalysts, the evolution of oxide structures from monovanadate to polyvanadate species as VOx results in surface density increases leading to an increase in both ODH and propylene combustion rates, apparently because similar sites are required for the two reactions [11]. The greater reactivity of propylene arises in part because the weakest C–H bond in propane (at the methylene group) is significantly stronger than the allylic C–H bond in propylene [23]. In recent years, the concept of neural networks which arose from attempts to model the functioning of the human brain, has gained wide popularity in many areas of chemical engineering including dynamic modeling of chemical processes, catalyst design, estimation of catalyst deactivation, reaction modeling, modeling of chemical reactors and modeling of complex chemical processes [24–26]. The main feature of the ANN approach which has resulted in its wide range of applications is that models based on ANN exhibit the rule-following behavior without containing any explicit representation of those rules. The ANN appears to be a promising tool for kinetic studies involving complex reactions where the governing mechanisms cannot be formulated due to insufficient knowledge or lack of sufficient data. In studies where experimental data is used to estimate kinetic parameters, DOE might have several benefits because of the constraints on time limitation, cost and technical considerations. Selection of an appropriate experimental design is critical in a successful experimental research. Although non-standard optimal designs have been successfully used in kinetic studies of heterogeneous catalytic reactions [27,28], standard designs have not been considered as much. Because of the exponential dependency of reaction rates on temperature (Arrhenius behavior), kinetic rate equations exhibit a non-linear behavior. Juusola et al. [27] indicated that using factorial or central composite design (CCD) to obtain parameter estimates for highly non-linear mechanistic models will almost always lead to highly correlated (and hence unreliable) estimations of these parameters. Providing the experimental points with optimal designs makes it possible to efficiently reduce the experimental points required to fit the model and determine the co-variance of the model parameters. Application of ANN for modeling can facilitate the prediction of catalyst activity. Based on our literature survey, there was no attempt on ANN modeling of catalyst performance for ODH reactions. In this paper, we have demonstrated the use of the ANN in prediction of the performance of V2O5 over graphene in ODHP. Applying the standard experimental designs of RSM (CCD) made it possible to use regression/statistical tools for the modeling. It was also possible to use the RSM models to generate simulated data. The combination of the standard DOE with ANN helped the current kinetic study to be conducted more efficiently from the standpoints of the kinetic test minimization and information maximi-

zation through fitting the rate equations with simulated points. In this investigation a strategy was presented based on the DOE coupled with ANN to collect the experimental points for subsequent generation of simulated data and kinetic parameter estimation. Moreover, in the current kinetic model, all possible main and side reactions as well as components were considered while their corresponding reaction rates were determined. Finally, this study determined values of a large number of unknown (i.e., 20) parameters involved in a fairly precise manner. 2. Materials and methods 2.1. Catalyst preparation Vanadium pentoxide (V2O5) (supplied by Aldrich) and graphene (produced in-house [29,30]) in carbon to vanadium (C/V) molar ratio of 1:1, were dissolved in 200 ml of ethanol. The solution temperature was raised to 90 8C under vigorous stirring for 120 min. This solution and 50 ml of water were added to a Teflonlined autoclave with a stainless steel shell kept at 180 8C for 48 h. After cooling to room temperature, the autoclave was heated up again to 180 8C for an additional 24 h. The resulting precipitate was filtered and washed to get neutralized. This precipitate was then washed with a solution of ethanol and n-hexane subsequently dried at 100 8C for 24 h to get vanadium oxide over graphene. The sample was then calcined at 500 8C for 2 h under nitrogen atmosphere and under air atmosphere at 500 8C for an additional 2 h. The resulting catalyst prepared by the hydrothermal method was designated as V-G-1. The catalyst was grained and sieved to obtain very fine powder particles. 2.2. Reactor and intrinsic kinetic tests The kinetic experiments were carried out in a tubular fixed bed micro-reactor. The catalyst was diluted with quartz wool for heat dissipation during the dehydrogenation process. The reaction was carried out in 10 mm diameter tube. The reaction tube was placed in a furnace equipped with a temperature controller. Prior to the reaction, the catalyst was activated in situ using N2 (50 ml/min) at 400 8C for 2 h. After reduction, purified air and propane were fed into the reactor. The flowrates of propane and air were controlled by two mass flow controllers (Brooks). The exited gases were analyzed for light hydrocarbons, CO and CO2 using an online gas chromatograph equipped with TCD and FID detectors. The moisture (i.e., water) trap, packed with silica gel, placed before the product gas entered the GC column. The schematic diagram of the reactor is presented in Fig. 1. CCD with three factors was employed by Design Experts Software (Version 8.0.1). Post-processing including analysis of the experimental results for estimation of the correlations was also performed by the software. To predict the curvature of responses, the behavior of propane conversion, propylene, ethylene and COx selectivities were described by an empirical second-order polynomial. The typical form of such a polynomial is: Y ¼ a0 þ

k k k X k X X X ai j x i x j þ e ai xi þ aii x2i þ i¼1 i¼1 i j i< j

(1)

where Y is the predicted response, a0 is a constant, ai is the ith linear coefficient, aii is the ith quadratic coefficient, aij is the ith interaction coefficient, xi is the independent variable, k is number of factors and e is the associated error. The coefficients of the model were predicted by regression of experimental data. To investigate the effect of process variables such as temperature, feed ratio and total feed flowrate on propane conversion,

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Fig. 1. Schematic diagram of experimental apparatus utilized in this research.

propylene, ethylene and COx selectivities, the experimental design approach was utilized. The variables and their corresponding ranges presented in Table 1. A total of 30 experiments were selected to be performed according to CCD. The catalysts were extremely fine particles, so that intraparticle diffusion could be neglected. It was also observed that propane conversions remained unchanged at constant contact time but with different feed flowrates of identical composition indicating that the external mass transfer resistance was also negligible [31]. The first set of runs was carried out in order to determine the kinetic limiting operating conditions. Propane conversions were measured by fixing the hydrocarbon to air ratio in the feed and varying the amount of catalysts in the packed bed reactor. It is widely accepted that external diffusion can be excluded when the propane conversion curves overlap for different amounts of catalyst [31]. The results indicated that contact times Table 1 Levels for process variable in actual values. Independent variable

(A) Temperature (8C) (B) Propane/air (C) Feed flowrate (ml/min)

(defined in reference to the amount of catalyst) smaller than 0.1 gcat s ml1 should ensure conditions where external mass transfer limitations would be absent. In addition, a series of classical empirical checks [31] were also performed to evaluate the absence of temperature and concentration gradients, both outside and inside the catalyst particle. These checks are summarized in Table 2. The required parameters to perform the calculations that are presented in Table 2 were either determined experimentally (reaction rate, particle diameter, particle porosity and reactant concentrations) or calculated through well-established empirical correlations (diffusivities or mass transfer coefficients). Once the kinetic operating region was firmly established, experimental measurements of the reaction rates were carried out for space times of 0.02–0.10 gcat s ml1. A physical mixture of Table 2 Criteria [31] applied to evaluate the influence of mass transfer limitations. T (8C)

Carberry number <0.05/n

Weiz modulus

Hudgins <1/n

Dreactor/ dpowder > 10

400 450 500

2.11  106 5.69  106 8.24  106

1.90  107 6.23  107 9.72  107

2.21  106 4.79  106 7.94  106

180 180 180

Level Min.

Center

Max.

400 0.2 60

450 0.6 90

500 0.8 180

The process was considered to be first order (n = 1) with respect to propane concentration.

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Table 3 Experimental kinetic data designs by CCD in a fixed bed microreactor. Run

T (8C)

Propane/ air ratio

Feed flowrate (ml/min)

Propane Con. (%)

Propylene Sel. (%)

Ethylene Sel. (%)

COx Sel. (%)

Propylene yield (%)

R C3 H8 (mol/(s g))

R C3 H6 (mol/(s g))

R C2 H4 (mol/(s g))

RCOx (mol/(s g))

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

425 475 425 500 400 475 450 450 475 425 450 425 475 450 450 400 400 400 400 500 500 500 500 415 415 435 435 460 460 480

0.65 0.35 0.65 0.5 0.5 0.65 0.5 0.5 0.65 0.35 0.8 0.35 0.35 0.2 0.5 0.2 0.2 0.8 0.8 0.2 0.2 0.8 0.8 0.3 0.7 0.3 0.7 0.4 0.7 0.3

150 150 90 120 120 90 120 60 150 150 120 90 90 120 180 60 180 60 180 180 60 180 60 80 140 80 140 140 80 160

2.29 4.74 2.08 4.98 1.85 4.43 4.46 3.64 4.93 2.16 4.69 1.87 4.27 4.09 4.89 1.88 1.86 1.93 2.09 4.99 4.74 5.09 4.82 1.95 2.06 1.92 2.13 3.65 3.21 3.69

90.78 92.35 89.63 92.45 88.02 91.25 91.39 92.18 92.39 89.12 91.69 88.71 91.86 90.48 93.12 89.46 90.76 91.65 90.47 92.08 93.89 92.14 92.69 90.65 91.04 91.38 89.05 89.02 89.17 90.16

0.76 1.01 0.77 1.65 0.72 1.25 0.89 0.91 0.92 0.79 0.81 0.81 1.02 0.85 0.87 0.75 0.79 0.65 0.72 1.39 1.24 1.43 1.18 0.88 0.82 0.89 0.96 0.99 0.93 1.04

8.18 6.39 8.93 5.19 10.75 7.36 6.93 6.76 6.56 9.72 6.89 10.23 6.69 8.21 5.52 8.84 7.63 7.01 8.23 5.67 4.21 5.48 5.54 7.59 7.24 6.78 9.02 9.01 8.91 7.88

2.08 4.38 1.86 4.60 1.63 4.04 4.08 3.35 4.55 1.92 4.30 1.66 3.92 3.70 4.55 1.68 1.69 1.77 1.89 4.59 4.45 4.69 4.47 1.77 1.87 1.75 1.89 3.25 2.86 3.32

1.87492E06 2.55405E06 1.02179E06 2.76004E06 1.02532E06 2.17622E06 2.47184E06 1.00869E06 4.03641E06 1.16387E06 3.46576E06 6.04567E07 1.38048E06 1.13339E06 4.06524E06 2.60486E07 7.73144E07 7.13103E07 2.31666E06 2.07419E06 6.56757E07 5.64201E06 1.78091E06 4.98803E07 1.64542E06 4.91129E07 1.70131E06 2.02292E06 1.46511E06 1.88778E06

1.70205E06 2.35867E06 9.15834E07 2.55166E06 9.02484E07 1.9858E06 2.25902E06 9.29812E07 3.72923E06 1.03724E06 3.17775E06 5.36312E07 1.26811E06 1.02549E06 3.78555E06 2.33031E07 7.01706E07 6.53559E07 2.09588E06 1.90991E06 6.16629E07 5.19855E06 1.65073E06 4.52165E07 1.49797E06 4.48794E07 1.51502E06 1.80081E06 1.30644E06 1.70202E06

1.42494E08 2.57967E08 7.86778E09 4.55407E08 7.38228E09 2.72027E08 2.19994E08 9.17908E09 3.71349E08 9.19462E09 2.80726E08 4.89704E09 1.40809E08 9.63382E09 3.53676E08 1.95364E09 6.10784E09 4.63517E09 1.66815E08 2.88312E08 8.14379E09 8.06808E08 2.10147E08 4.38946E09 1.34923E08 4.37105E09 1.63326E08 2.00269E08 1.36255E08 1.96329E08

1.53368E07 1.63204E07 9.12458E08 1.43246E07 1.10222E07 1.60169E07 1.71299E07 6.81874E08 2.64788E07 1.13128E07 2.38791E07 6.18472E08 9.23543E08 9.30514E08 2.24401E07 2.30273E08 5.89909E08 4.99885E08 1.90661E07 1.17606E07 2.76495E08 3.09182E07 9.86624E08 3.78591E08 1.19127E07 3.32985E08 1.53458E07 1.82265E07 1.30541E07 1.48757E07

0.02–0.30 g of catalyst and the required amounts of inert quartz particles were used to form a bed height of 1 cm when loaded into the reactor. The kinetic test data are represented in Table 3. To investigate gas volume variations due to the involved reactions, the exit gas flowrate were measured by a soap bubble flow meter. Duplicates of some selected runs (5 runs) performed and showed more than 93% reproducibility confirming no sensible change in conversion and selectivities. The low propane conversions ensured that the reactor could be considered as a differential reactor allowing for the reaction rates to be determined as follows: ri ¼

F i Xi mcat:

(2)

where Xi is the conversion of component i, ri is the rate of reaction for component i (mol/g s), mcat. is the catalyst mass (g) and Fi is the molar flow of component i (mol/s). Moreover, deactivation of the catalyst was not observed for a 6 h time-on-stream (time generally required to complete a set of experimental measurements). Data analysis was performed with the developed in-house code in MATLAB and processing with the Simulink subroutine. The adjustable parameters of the non-linear reaction rates were obtained by a genetic algorithm (GA) method. In order to obtain the kinetic constants, the adjustable parameters of the GA method were changed to determine the stable answers and find the absolute extrema.

formation of flexible nanomaterials with a black color. There is almost no sign of mineral clusters in Fig. 2 implying most of the mineral impurities of graphene were removed in the purification process. Fig. 2 also confirmed that the vanadium oxide species were properly precipitated on the surface of graphene and a rather uniform nanostructure of VOx-graphene was formed during the synthesis process. The V2O5 was readily adsorbed on graphene (i.e., about 90%, based on the weight of the sample after drying to the initial weight of vanadium oxide and graphene). The morphology of the catalyst was belt-like, homogeneous and uniform in size. Fig. 3 showed the FTIR spectra of the synthesized catalyst. The signals between 400 and 1000 cm1 attributed to vibrations of various V–O groups. The broad IR spectra indicated strong absorptions at 528–541 cm1, related to symmetric and asymmetric stretching vibrations of V–O–V and at 915–924 cm1 assigned to the stretching of short V5 5O bonds from the vanadyl

3. Results and discussion 3.1. Catalyst characterization Fig. 2 illustrated the FESEM micrographs for V-G-1 indicating that the obtained nanostructure was an ordered, well-structured and homogenous material. The growth of the V2O5 within the porous graphene network by the hydrothermal method led to the

Fig. 2. FESEM micrograph of V2O5 over graphene prepared by the hydrothermal method (The scale is 5 mm).

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to V4+ cations consistent with previous observation in this regard [34]. 3.2. Generation of simulating data

Fig. 3. FTIR spectra of the V-G-1 catalyst prepared by the hydrothermal method.

bonds [32]. The absorption frequencies at 528–541 cm1 indicated that these vibrations arise from different V–O bonds in the VOx layers. The weak band appearing at 1003–1008 cm1 was due to initial disorder from VO2(B) octahedral arrangement. The spectra suggest that the structure of vanadium layers were rearranged over graphene as was also suggested by the FESEM image in Fig. 2 showing nano-tubular or belt-like structures. The absorption band at 1615–1623 cm1 (assigned to the deformation mode of H2O) appeared due to water. The absorption bands of surface OH-groups are also observed at 3200–3500 cm1. These phenomena were associated with an increase of dispersity (specific surface area) [33]. In situ growth of vanadium within the graphene network led to an interpenetrating network structure. The X-ray diffraction (XRD) pattern for the catalyst was presented in Fig. 4 indicating that vanadium grown within the composites contained smaller crystalline domains. All diffraction peaks might have been indexed to the VO2(B) monoclinic structure with lattice constants of a = 12.03 A˚, b = 3.693 A˚ and c = 6.42 A˚ and b = 106.68 (JCPDS #311438). No peaks of any other phases or impurities were observed revealing that VO2(B) nanomaterials with high purity could be obtained from the present synthesis process. Moreover, the peak separation clearly noticed at 2u = 17.18, 20.68, 24.78 and 29.68 for the graphene-based catalyst. The products were dark in color after the hydrothermal process indicating that V5+ cations were reduced

A computer program written in MATLAB 2009a (version 7.8) was used to implement the ANN. These networks consisted of input, hidden and output layers. A layer consists of processing elements called neuron or nodes. Neurons are interconnected to the hidden and output layers. The number of neurons in input layer was set equal to the number of input factors (being variables) and the number of neurons in output layer was set equal to the number of responses or targets. The number of neurons in the hidden layer had to be adjusted in order to achieve the best fit of the experimental data. The information contained in the input layer was mapped to the output layer through the hidden layers. The strength of the connections amongst the neurons was referred to as the weight. A neuron accepted a weighted set of inputs with a bias. The sum of weighted inputs with a bias was then subjected to the activation function. The experimental points had to be employed to train the network with suitable learning algorithms. The learning algorithm adjusted the values of connection weighting coefficients of the processing nodes by minimizing the possible errors of the network output. In this study, a feed forward two hidden layers ANN was developed with 3 input and four output neurons. The input neurons included temperature, propane to air ratio and total feed flowrate whereas the propane conversion, propylene, ethylene and COx selectivities were considered as the outputs of the respective network. The 30 experimental points collected according to the CCD method were used to train and test the network. The number of neurons in the hidden layer was adjusted to create the best fit. To avoid over fitting, the 30 experimental points were divided into three sets for training, validating and testing. The validation data was used to measure the network generalization and halted the training when generalization stopped improving. The testing data had no effect on training and only provided an independent measure of the network performance. The Levenberg–Marquardt (LM) optimization algorithm was used in the training process and the performance function was the mean squared error (MSE) of output and targets. The obtained models from the RSM were used to produce 120 simulated points for propane conversion, and propylene, ethylene and COx selectivities. The RSM model based upon CCD generated these simulated data at different temperatures, feed ratios and total feed flowrates within ranges as indicated in Table 1 resulted in propane conversions in the range of 1.3–5.5%. The purpose was to investigate the potential of the RSM simulated data in the kinetic study and its capability in prediction of catalyst performance for the ODHP reaction. These simulated data were used to obtain the reaction rates for components in the differential reactor system and to calculate the partial pressure of propane, propylene, ethylene and COx at the reactor exit. The simulated experimental data was then employed in the curve fitting process to estimate the parameters of rate equations. The ANN model was also employed to generate 120 simulated data under different reactor conditions within ranges specified in Table 1. This ANN simulated data were also used to obtain the kinetic rate parameters. 3.3. ANN and RSM models Three data sets were used to fit the reaction rates by means of non-linear regression:

Fig. 4. XRD patterns for V-G-1 catalyst by the hydrothermal method.

 Data set 1 (30 data): 30 experimental rate data from CCD experiments in the temperature range of 400–500 8C, feed ratio

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of 0.2–0.8 and feed flowrate of 60–180 ml/min, with propane conversions in the range of 1.85–5.09%.  Data set 2 (150 data): 120 simulated rates from RSM models with propane conversion in the range of 1.3–5.5% and 30 experimental rate data.  Data set 3 (150 data): 120 simulated rates based on ANN model and 30 experimental rate data. The goal was to compare the efficiency of these data sets in the curve-fitting process and to investigate the capability of RSM and ANN models for accurate prediction of conversion and product selectivities. The data sets 1–3 were used to obtain the kinetic parameters and rate constants that were expressed in terms of the Arrhenius equation. It is noteworthy that, in this investigation the ratio of the number of experimental data points to the unknown parameters was taken to be greater than 1.5. This ultimately guaranteed an acceptable fitting. The RSM models for propane conversion and products selectivities as well as the important statistical parameters are presented in Table 4. The high values of R2 and R2ad j for responses indicated that the models are capable of fitting the experimental data. Table 4 also presented the ANOVA results of RSM model. The ANOVA results indicated that the regression is significant and that the modified second order polynomial equations are statistically significant and adequate to represent the actual relationship between inputs (temperature, feed ratio and feed flowrate) and outputs (propane conversions and product selectivities). The parity plots of predicted output versus actual values are presented in Fig. 5 indicating a fairly good agreement between the experimental data and the correlated values. The statistical importance of the generated models evaluated by the Fisher test (i.e., F-test) was quantified by dividing the

Model Mean Square by its Residual Mean Square to follow the ANOVA. The ANOVA results displayed in Table 4 confirming that, these models might have been applied to the considered design space. The F-value for the Y1 and Y3 were 8.67 and 14.29, respectively. For both these responses, there was only a 0.01% chance that a ‘‘Model F-Value’’ having a greater magnitude than the aforementioned ones occurred due to a noise. A very low probability value for both models implied that, they were significant thru the 95% confidence interval. It is noteworthy that, a p-value less than 0.05 indicated being significant in that range. The F-value for Y2 and Y4 were 3.65 and 0.91 (chance) providing the acceptable range. Insignificant terms in the model had p-values greater than 0.100, which might have been dropped out manually from the models to enhance the regression quality and optimization results. Adequate precision for Y1 and Y4 denoted that the values were greater than 4. These statistical criteria indicated that these were significant for describing the undertaken process. ‘‘Goodness of fit’’ of the predicated values for response of the model was measured by the predicted R2. For an adequate model, the R2 was within 0.2 of the adjusted R2. Table 4 revealed that, all responses passed these criteria successfully. Moreover, the coefficients of determination for both responses were close to unity. This provided further support of a ‘‘good correlation’’ between the actual and predicted values. A multi-layer ANN with tangent sigmoid transfer function (tansig) at the hidden layer and a linear transfer function (purelin) at the output layer was used. The experimental data was divided into an input matrix [p] and a target matrix [t]. The original data was divided into training, validation and test subsets. 10% of the data was taken as the validation set, 10% as the test set and 80% as the training set. The experimental data was loaded into the

Table 4 ANOVA results and RSM models from regression of propane conversion and product selectivities. Source

Sum of squares

Degree of freedom (DF)

Mean square

Y1 Model Residual Correlation Total

40.09 8.79 48.88

10 19 29

4.01 0.46

8.67

0.0001

3.70 1.43

2.59

0.0365

14.29

0.0001

3.50

0.0091

R2 = 0.8202 Adjusted-R2 = 0.7256 Y2 Model 33.30 Residual 28.55 Correlation total 61.85

Adequate precision = 10.053

R2 = 0.5383 Adjusted-R2 = 0.3306 Y3 Model 1.39 Residual 0.22 Correlation total 1.61

Adequate precision = 6.884

Adjusted-R2 = 0.8049 R2 = 0.8654 Y4 Model 46.10 Residual 25.05 Correlation total 71.15

Adequate precision = 13.147

9 20 29

9 20 29

10 19 29

0.15 0.011

4.61 1.32

F-value

p-Value probability > F

R2 = 0.6479 Adjusted-R2 = 0.4627 Adequate precision = 8.070 Y1 (propane conversion) = 41.36899 + 0.16640  Temperature + 1.06763  Propane/air  5.55806E4  Feed flowrate  4.32683E3  Temperature  Propane/air  1.97013E5  Temperature  Feed flowrate  0.023046  Propane/air  Feed flowrate  1.46096E4  (Temperature)2 + 1.17380  (Propane/air)2 + 5.30374E5  (Feed flowrate)2 + 5.31239E5  Temperature  Propane/air  Feed flowrate Y2 (propylene selectivity) = 58.59726 + 0.12200  Temperature + 10.97580  Propane/air  0.067098  Feed flowrate  0.024775  Temperature  Propane/air  9.47203E5  Temperature  Feed flowrate + 0.010313  Propane/air  Feed Flowrate  8.15810E5  (Temperature)2  0.57303  (Propane/air)2 + 4.30529E4  (Feed flowrate)2 Y3 (ethylene selectivity) = 17.66601  0.080226  Temperature  0.11314  Propane/air  2.31350E4  Feed flowrate + 1.90624E3  Temperature  Propane/air + 7.85629E6  Temperature  Feed flowrate + 1.28237E3  Propane/air  Feed flowrate + 9.36825E5  (Temperature)2  0.92546  (Propane/air)2  1.54398E5  (Feed flowrate)2 Y4 (COx selectivity) = 27.77581  0.039235  Temperature  34.84514  Propane/air  0.035704  Feed flowrate + 0.082686  Temperature  Propane/air + 3.02729E4  Temperature  Feed flowrate + 0.21786  Propane/air  Feed flowrate  4.21867E5  (Temperature)2  1.24143  (Propane/air)2  3.90672E4  (Feed flowrate)2  5.11578E4  Temperature  Propane/air  Feed flowrate

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JIEC-1591; No. of Pages 12 M. Fattahi et al. / Journal of Industrial and Engineering Chemistry xxx (2013) xxx–xxx Design-Expert® Software Propane Conversion Color points by value of Propane Conversion: 5.09

Predicted vs. Actual

Design-Expert® Soft ware Propylene Selectivity

5.60

Predicted vs. Actual

Color points by value of Propylene Selectivity: 93.89

(a)

93.90

(b)

1.85 88.02

4.53

92.43

Predicted

Predicted

7

3.45

90.95

89.47

2.38

88.00

1.30

88.02

1.39

2.43

3.46

4.50

5.53

Actual Design-Expert® Soft ware Ethylene Selectivity

92.42

93.89

Predicted vs. Actual

Color points by value of COx Selectivity: 10.75

10.80

(d)

1.65

(c)

90.95

Actual Design-Expert® Software COx Selectivity

Predicted vs. Actual

Color points by value of Ethylene Selectivity: 1.65

89.49

4.21

0.65

9.08

Predicted

Predicted

1.40

1.15

7.35

5.63 0.90

3.90 0.65

3.94 0.65

0.90

1.15

1.40

5.64

7.34

9.05

10.75

1.65

Actual

Actual

Fig. 5. The parity plot of actual vs. predicted values of (a) proapne conversion, (b) propylene selectivity, (c) ethylene selectivity and (d) COx selectivity.

workspace at random for each subset. An optimization was carried out as an important task between the neuron number and mean squared error (MSE) for the best Back Propagation (BP) algorithm. The two-layer ANN was then evaluated by the BP algorithm for the optimal number of neurons at the hidden layer. The loss on the optimality of the estimates/results produced by BP training algorithms can be attributed to the combinatorial nature and non-linear structure of the experimental data. The optimal architecture of the ANN model and its parameter variation were determined based on the minimum value of the MSE of the training and prediction set. ANN predictions depend on many network parameters such as the number of hidden layers, the number of neurons in each layer, the learning rate and the initial weights. A learning rate of 0.01 resulted in a stable network performance and the initial weights were randomly assigned in the 0.55 to +0.55 range. The optimum number of hidden layers and the number of neurons in each hidden layer were subsequently determined by trial and error. Hidden neurons enable the network to learn difficult tasks by extracting progressively more meaningful features from the input patterns. Initially, only one hidden layer was employed and the mean squared error between the scaled predicted and experimental propane conversion and product selectivities were computed using 5–10 neurons. The network architecture was subsequently modified by adding a second layer

of hidden neurons. Again, the mean squared error between the scaled predicted and experimental results was computed after adding 7 neurons in the first hidden layer and varying the number of neurons in the second hidden layer in the range 7–12. In this design the obtained results were reasonable since the final mean squared error was small, the test set error and the validation set error had similar characteristics and no significant over-fitting had occurred. Table 5 compared different trained neural network models for the selection of the best design in this study. Model number 6 with the minimum mean squared error (0.00115), 2 hidden layers with 7 and 11 neurons in the first and the second hidden layer, respectively, was chosen as the most appropriate model to represent the experimental data. To consider the effect of the number of trains upon the determined answers in this method, optimum numbers of layers were varied. It was observed that, the optimum results changed very little (i.e., to the 3 decimal point and beyond) confirming no importance of such effects’ verification. Fig. 6 illustrates a comparison between the experimental and the estimated values using ANN model for propylene production. The regression R2 values measure the correlation between outputs and targets with a value of 1 indicating a close relationship. High values of R2 (0.99) were obtained for the network. The results indicated that the ANN model may not just be referred to as a black box.

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8 Table 5 Different neural network trained models.

Model number

Parameters

Number of hidden layers Number of neurons in hidden layers Transfer function Mean squared error Number of epochs

1

2

3

4

5

6

7

1 5 tansig 0.132 18

1 6 tansig 0.105 12

1 7 tansig 0.109 9

1 8 tansig 0.112 9

2 7 tansig 0.011 8

2 11 tansig 0.00115 16

2 12 tansig 0.005 12

k3

Similar to RSM models, this neural network was used to generate the simulated data for different conditions.

C3 H6 þ ð1:5 þ 1:5xÞO2 !3COx þ 3H2 O

3.4. ODHP reaction mechanism and kinetics

C3 H8 þ ð1 þ 0:5xÞO2 !C2 H4 þ COx þ 2H2 O

k4

Grabowski [5] concluded by means of transient experiments that the first step in the mechanism for propane conversion in ODHP followed an Eley–Rideal mechanism where propane reacted directly from the gas phase with the adsorbed oxygen on the catalyst. Chen et al. [35] showed that propane was dehydrogenated to propylene, and in parallel, the total oxidation of propane to carbon dioxide occurred. Carbon monoxide was exclusively formed by oxidation of propylene while carbon dioxide was produced by oxidation of both propane and propylene. Ethylene was also produced by cracking of propane and propylene. The following reaction scheme was employed based upon the above observations: k1

C3 H8 þ 0:5O2 !C3 H8 þ H2 O k2

C3 H8 þ ð2 þ 1:5xÞO2 !3COx þ 4H2 O

(3) (4)

k5

C3 H6 þ ð0:5 þ 0:5xÞO2 !C2 H4 þ COx þ H2 O

(5)

(6)

(7)

The first reaction corresponded to the oxidative dehydrogenation of propane. The second one represented the COx formation by total and partial oxidation of propane. Oxidation of propylene to COx was given by the third reaction. Ethylene formation represented by cracking reactions involving both propane and propylene. The above scheme of reactions represents both simultaneous and consecutive reactions that occurred alongside the principal reaction (3) for the oxidative dehydrogenation of propane. Assuming a power law rate expression for each reaction, the overall rate of formation of propane, propylene, ethylene and COx are given by: r C3 H8 ¼ k1 ½P C3 H8 a ½P O2 b þ k2 ½P C3 H8 c ½P O2 d þ k4 ½P C3 H8 g ½P O2 h

Fig. 6. Correlation between outputs and targets of ANN model.

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(8)

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r C3 H6 ¼ k1 ½P C3 H8 a ½P O2 b  k3 ½PC3 H6 e ½P O2  f  k5 ½P C3 H6 m ½P O2 n r C2 H4 ¼ k4 ½P C3 H8 g ½PO2 h þ k5 ½PC3 H6 m ½P O2 n

(9) (10)

r COx ¼ 3k2 ½P C3 H8 c ½PO2 d þ 3k3 ½P C3 H6 e ½PO2  f þ k4 ½PC3 H8 g ½P O2 h þ k5 ½P C3 H6 m ½P O2 n

(11)

A total of 20 parameters (reaction orders and Arrhenius parameters for each rate constant) need to be determined. In is worth mentioning that, to overcome the correlation between these parameters, a re-parameterization was required. This was achieved by expressing the rate constants in the present study as the classical Arrhenius type provided below:   E ki ¼ k0i exp  i (12) RT where k0i and Ei presented the pre-exponential factor of rate constant and corresponding activation energy for a given reaction, respectively. In Eqs. (8)–(11), k01 to k05 presented such values for the main, carbon oxide production from the propane and propylene as well as cracking of the propane and propylene reactions, respectively. The aforementioned parameters illustrated the criteria from both the order, as well as the importance of the understudied reactions. Moreover, the pre-exponential factors along with the related activation energies provided a clearer picture of such interactions. Given the large number of undetermined parameters, a ‘‘cascade’’ approach was used where reactions were examined separately. Ethylene was only produced by cracking of propane and propylene. Once the eight kinetic parameters for propane and propylene cracking reactions (k04, E4, k05, E5, g, h, m and n) were estimated using Eq. (10), k01, E1, k03, E3, a, b, e and f could be obtained from a balance of propylene production rate (Eq. (9)), and k02, E2, c and d could be obtained from a balance of propane consumption rate (Eq. (8)). The rate of COx production was used as a check for the obtained parameter estimates. The parameter estimation results were presented in Table 6 for each of the three data sets. The logical amount of the preexponential factors and activation energies in the investigated reaction space provided not only the extent of reaction taken place but also, checked the functional group of catalysts formed when compared to a similar system. In this venue, the pre-exponential

9

factors for different rate constants were within the same order of magnitude suggesting the presence of tetrahedral vanadate species (either isolate or as polyvanadates) on the graphene being consistent with a previous study [36]. How the surrounding environment and co-ordination of vanadium contributed to the process selectivity is still being debated in spite of numerous studies. Reaction order values indicated that the overall kinetic rate was more influenced by the hydrocarbon (reaction orders a, c, e and m) rather than the oxygen partial pressure (reaction orders b, d, f and n) except for reaction orders of g and h. According to the R2 and other statistical criteria, there were no significant differences in the predictive abilities of the models obtained from the three different aforementioned data sets. The average and maximum errors and standard deviations in the predicted reaction rates for the models using each of these three data sets presented in Table 7. These revealed the average errors for the sets using simulated data along with the original experimental data points were lower than those for the set #1 in which only the original experimental data employed. The errors and standard deviations reported in Table 7 also indicated that the performance of the model using Data set #3 in which the simulated data were generated by the ANN method was slightly superior to the model using Data set #2 containing simulated data from the RSM approach. The performance of the model using simulated data by the ANN method (i.e., Data set #3) illustrated in Fig. 7 where predicted and experimental reaction rates for propane, propylene, ethylene and COx presented in parity plots. The dashed lines in this figure showed 10% deviations. The authenticity of fitting around the diagonal line confirmed due to the fact that most of the data fell within the 10% margin. It can be seen that most of the points are distributed evenly on both sides of the diagonal which suggesting a good agreement between predicted and experimental reaction rates. Experimental and predicted reaction rates for different components are presented in Fig. 8 for different oxygen partial pressures using only those 20% of the experiments (i.e., sum of the validation and test set values) that were assigned for validating and not used in training of the ANN model. While all reaction rates increased with increasing oxygen partial pressure, oxygen partial pressure had a stronger influence on the reaction rate for propylene compared with propane. The effect of propane partial pressures on the reaction rate for different components illustrated in Fig. 9 using the same 20% of the experiments (due to 6 runs) assigned to the ANN model validation

Table 6 Estimates of kinetic parameters using the 3 data sets. Parameter

k01 k02 k03 k04 k05 E1 E2 E3 E4 E5 a b c d e f g h m n

Value

Unit

Data set #1

Data set #2

Data set #3

5.123  105 7.460  105 2.965  105 4.530  105 9.570  105 18.46 307.20 72.25 488.05 14.60 1.66 0.26 0.71 0.67 0.86 0.40 0.36 1.47 0.71 0.27

6.765  105 7.321  105 4.883  105 7.004  105 9.989  105 25.36 278.07 73.98 547.18 17.34 1.24 0.35 0.83 0.76 0.84 0.42 0.79 1.24 0.87 0.46

8.929  105 9.762  105 5.602  105 9.976  105 4.269  104 16.87 269.56 76.54 623.23 19.89 1.87 0.57 0.74 0.68 0.97 0.46 0.93 1.01 0.95 0.37

mol/(g s (atm)a+b) mol/(g s (atm)c+d) mol/(g s (atm)e+f) mol/(g s (atm)g+h) mol/(g s (atm)m+n) kJ/mol kJ/mol kJ/mol kJ/mol kJ/mol – – – – – – – – – –

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Table 7 The average and maximum errors in predicted reaction rates for models using different data sets. Rate

Error (%)

Date set #1

Date set #2

Date set #3

–r C3H8

Average Maximum S.D.a

3.74 18.19 9.51  107

3.46 15.69 8.72  107

2.82 16.12 5.89  107

r C3H6

Average Maximum S.D.a

4.86 17.87 6.05  107

3.92 19.37 5.75  107

2.93 18.38 5.63  107

r C2H4

Average Maximum S.D.a

5.37 22.01 7.48  107

4.65 19.11 7.93  107

2.75 20.15 6.94  107

r COx

Average Maximum S.D.a

7.47 25.64 8.37  106

5.93 24.75 4.29  106

3.43 23.21 2.02  106

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a

Standard deviation, S:D: ¼

Sn Si ðRateEx p: RatePred: Þ2 nk

where; n: number of experiments; k: number of adjustable parameters.

indicating that the reaction rate for all components enhanced with increasing the propane partial pressure. Moreover, it is worth mentioning that, a higher oxygen partial pressure resulted in a higher propane consumption rate, as well as a lower selectivity toward propylene. Furthermore, these effects of the oxygen partial pressure were consistent with those available in the open literature [10,13]. At the same time, however, the higher the propylene concentration, the greater are the rates of propylene combustion to COx and ethylene formation reactions. This behavior suggests that the partial pressure of oxygen has little influence on the rate-determining

step of the mechanism. These observations are in agreement with what has been reported by other authors for ODHP using different catalysts [37]. As the reaction of catalyst regeneration by gaseous oxygen is much faster than that of product formation, the overall reaction rate is only slightly influenced by the gaseous oxygen partial pressure. This is demonstrated by lower reaction orders reported in Table 6 for oxygen compared with those for propane. Creaser et al. [9] studied oxygen dependence and showed that the lower the oxygen partial pressure, the higher is the propylene selectivity. This is probably related to the fact that lattice oxygen is always available

Fig. 7. Parity plots of the observed and calculated reaction rates for propane, propylene, ethylene and COx using the kinetic parameters reported in Table 6 from the ANN based model (dashed lines represent 10% deviations).

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11

Fig. 8. Comparison of the experimental and predicted (due to the data set #3) reaction rates for propane, propylene, ethylene, and COx at different oxygen partial pressure.

Fig. 9. Comparison of the experimental and predicted (due to the data set #3) reaction rates for propane, propylene, ethylene, and COx at different propane partial pressure.

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even at low oxygen partial pressure. Thus, to observe an oxygen kinetic dependence, very low oxygen partial pressure must be used, which also influences the vanadium oxidation state. Our results are in contrary with Ref. [9] because the system that was studied therein was based on alumina as the template which had the oxygen in its structure. Moreover, as pointed out in Ref. [3], the hydrocarbon to oxygen ratio is the fundamental variable in the reconstruction of the catalytic site, since it influences the ratio between oxidation and reduction rates of the catalytic site that drives the selectivity toward propylene or combustion products [38]. Bottino et al. [15] have studied the kinetics of propane oxydehydrogenation using vanadium on alumina catalyst reporting similar results to those found by us. The apparent activation energies found by these authors are lower than those reported in the present study as their catalyst was less active in the higher temperature range. Moreover, the activation energies of the reactions were partially depended upon the catalyst loading. In addition, these energies were also depended upon the oxide support used to form the surface vanadia species. Value of the activation energy of the main reaction undertaken however, was determined to be different for the V2O5 catalyst over the metal oxide or wellstructured carbon supports. In order to compare the effect of the oxide support and loading simultaneously, it would be necessary to concurrently consider the pre-exponential factors and activation energies based on the catalysts’ vanadia loading. We also found the apparent reaction order for propane conversion was found to be greater than 1.0 with respect to propane partial pressure. Others [5,39,40] have that reported the order of propane conversion between 0.6 and 1.0 with respect to propane partial pressure. Previously, the ODHP kinetics over a Ni–Co molybdate catalyst in an integral reactor was investigated by non-linear regression techniques through which the CCD experiments performed to investigate the influence of propane and oxygen partial pressures, propane space-time and temperature [13]. They analyzed several kinetics models including the power-law (PL), Mars–van Krevelen (MvK), Eley–Rideal (ER) and Langmuir–Hinshelwood (LH) using the statistical and thermodynamical criteria. The patterns of the obtained results in the Ref. [13] were in a fairly good agreement with those obtained in the present work. Yet, in another study, the kinetics of the ODHP reaction over the V– Mo/g-Al2O3 and Sr–V–Mo/g-Al2O3 oxide catalysts in an integral reactor over the temperature range of 450–550 8C were investigated. The reaction network over the catalysts involved both the parallel and consecutive routes. Once again, the LH, ER and MVK kinetic models were employed [10]. Ultimately, the orders of magnitudes of the reaction rate constants as well as the orders of the reactions were in close agreement with currently obtained results. 4. Conclusions Kinetics of the ODHP over a Vanadium/graphene catalyst prepared by the hydrothermal technique was investigated in this research. Power law expressions were used to describe the network of reactions involving propane, propylene, ethylene and COx. A new method based upon the DOE coupled with the ANN simulating models was developed to study the kinetics of the ODHP process. Although the experimental designs conducted in a specific range of temperatures (400–500 8C), feed composition and total feed flowrate as process variables, the road was paved down to construct and train an artificial neural network based upon the available experimental data. Besides, employing such a network simulation utilizing a higher number of points including additional ones outside of the specified ranges of the aforementioned variables was made possible. In other words, with the aid of the ANN model it was possible to obtain simulated data at several different temperatures to estimate the activation energies through the Arrhenius relation. This approach overcame the correlation problem existed when the experimental points collected according

to the CCD. This study further indicated that employment of DOE/ ANN decreased the experimental points required for kinetic studies. Moreover, utilization of the experimental data to generate simulated ones using the RSM approach was undertaken. Three data sets including; experimental data (30 experiments), experimental data and an additional 120 simulated data generated by the ANN, as well as experimental data and an additional 120 simulated data generated by the RSM model utilized for the chemical kinetics parameter estimations. The estimated apparent activation energies, pre-exponential factors and reaction orders were close to one other for all data sets with the ANN based approach resulting in the lowest average error between the predicted and experimental reaction rates. Ultimately, it was shown that the 30 experimental points were sufficient to properly estimate the kinetic parameters of the rate equations in the ODHP process. References [1] G. Centi, F. Cavani, F. Trifiro`, Selective Oxidation by Heterogeneous Catalysis, Kluwer Academic/Plenum Publishers, New York, 2001. [2] F. Cavani, F. Trifiro`, Catalysis Today 24 (1995) 307. [3] M.D. Putra, S.M. Al-Zahrani, A.E. Abasaeed, Journal of Industrial and Engineering Chemistry 18 (2012) 1153. [4] T. Blasco, J.M. Lo´pez Nieto, Applied Catalysis A: General 157 (1997) 117. [5] R. Grabowski, Catalysis Reviews: Science and Engineering 48 (2006) 199. [6] D.C. Creaser, B. Andersson, Applied Catalysis A: General 141 (1996) 131. [7] H. Liu, Z. Zhang, H. Li, Q. Huang, Journal of Natural Gas Chemistry 20 (2011) 311. [8] T. Shishido, K. Shimamura, K. Teramura, T. Tanaka, Catalysis Today 185 (2012) 151. [9] D.C. Creaser, R.R. Hudgins, P.L. Silveston, B. Andersson, Canadian Journal of Chemical Engineering 78 (2000) 182. [10] M.D. Putra, S.M. Al-Zahrani, A.E. Abasaeed, Catalysis Communications 26 (2012) 98. [11] A. Khodakov, B. Olthof, A.T. Bell, E. Iglesia, Journal of Catalysis 181 (1999) 205. [12] R. Grabowski, B. Grzybowska, K. Samson, J. Sloczyn´ski, K. Wcislo, Reaction Kinetics and Catalysis Letters 57 (1996) 127. [13] M.M. Barsan, F.C. Thyrion, Catalysis Today 81 (2003) 159. [14] R. Grabowski, Applied Catalysis A: General 270 (2004) 37. [15] A. Bottino, G. Capannelli, A. Comite, S. Storace, R.D. Felice, Chemical Engineering Journal 94 (2003) 11. [16] B. Frank, A. Dinse, O. Ovsitser, E.V. Kondratenko, R. Schoma¨cker, Applied Catalysis A: General 323 (2007) 66. [17] E.V. Kondratenko, N. Steinfeldt, M. Baerns, Physical Chemistry Chemical Physics 8 (2006) 1624. [18] D. Creaser, B. Andersson, R.R. Hudgins, P.L. Silveston, Applied Catalysis A: General 187 (1999) 147. [19] X. Rozanska, R. Fortrie, J. Sauer, The Journal of Physics Chemistry C 111 (2007) 6041. [20] F. Gilardoni, A.T. Bell, A. Chakraborty, P. Boulet, The Journal of Physics Chemistry B 104 (2000) 12250. [21] H.H. Kung, Advances in Catalysis 40 (1994) 1. [22] S. Albonetti, F. Cavani, F. Trifiro`, Catalysis Reviews: Science and Engineering 38 (1996) 413. [23] A. Costine, B.K. Hodnett, Applied Catalysis A: General 290 (2005) 9. [24] G. Zahedi, A. Elkamel, A. Lohi, A. Jahanmiri, M.R. Rahimpor, Chemical Engineering Journal 115 (2005) 113. [25] K. Omata, N. Nukui, M. Yamada, Industrial and Engineering Chemistry Research 44 (2005) 296. [26] E.J. Molga, Chemical Engineering and Processing: Process Intensification 42 (2003) 675. [27] J.A. Juusola, D.W. Bacon, J. Downie, Canadian Journal of Chemical Engineering 50 (1972) 796. [28] S. Issanchou, P. Cognet, M. Cabassud, AIChE Journal 51 (2005) 1773. [29] Z. Sadeghian, A.M. Rashidi, Materials Science and Technology 26 (2010) 1191. [30] A. Ghozatloo, M. Shariaty-Niasar, A.M. Rashidi, International Communications in Heat and Mass Transfer 42 (2013) 89. [31] L. Petrov, NATO Science Series 69 (2002) 13. [32] J.-C. Valmalette, J.-R. Gavarri, Material Science and Engineering B 54 (1998) 168. [33] E. Skwarek, S. Khalameida, W. Janusz, V. Sydorchuk, N. Konovalova, V. Zazhigalov, J. Skubiszewska-Zie˛ba, R. Leboda, Journal of Thermal Analysis and Calorimetry 106 (2011) 881. [34] Ch.V. Subba Reddy, E.H. Walker Jr., S.A. Wicker Sr., Q.L. Williams, R.R. Kalluru, Current Applied Physics 9 (2009) 1195. [35] K. Chen, A. Khodakov, J. Yang, A.T. Bell, E. Iglesia, Journal of Catalysis 186 (1999) 325. [36] J.G. Eon, R. Olier, J.C. Volta, Journal of Catalysis 145 (1994) 318. [37] P.J. Gellings, H.J.M. Bouwmeester, Catalysis Today 58 (2000) 1. [38] A. Bottino, G. Capannelli, A. Comite, Journal of Membrane Science 197 (2002) 75. [39] A. Pantazidis, C. Mirodatos, Studies in Surface Science and Catalysis 101 (1996) 1029. [40] M.A. Chaar, D. Patel, H.H. Kung, Journal of Catalysis 109 (1988) 463.

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