CeO2 wet oxidation catalysts

Applied Catalysis B: Environmental 30 (2001) 141–150

Neural network kinetic prediction of coke burn-off on spent MnO2 /CeO2 wet oxidation catalysts Fa¨ıçal Larachi∗ Department of Chemical Engineering & CERPIC, Laval University, Québec, Canada G1K 7P4 Received 25 June 2000; received in revised form 22 August 2000; accepted 31 August 2000

Abstract Combustion kinetics of coke laydown on wet oxidation catalysts is studied by means of temperature-programmed oxidation “TPO” and mass spectrometry “MS” in the temperature range from 30 to 600◦ C. The study is designed to allow a better understanding of the influence of wet oxidation conditions (catalyst-phenol contacting time and temperature) on the combustion kinetics of coke deposited on MnO2 /CeO2 and 1 wt.% Pt-MnO2 /CeO2 catalysts during phenol degradation. In this respect, the experimental procedure involves the continuous monitoring of carbon oxides and O2 fluxes resulting form the combustion of carbonaceous deposits in a 5% O2 /He mixture. Based on the experimental data, an artificial neural network-based (ANN) modeling approach is implemented to represent, as accurately as possible, the complex combustion phenomenon so as to provide the opportunity to predict its evolution. In this context, the resulting ANN model is used as a “black-box” to approximate the complex non-linear conversion rate of the wet oxidation coke. The conversion rate is thus, expressed in terms of the TPO ramp temperature, running oxygen concentration, wet oxidation temperature, and phenol oxidation time. The proposed ANN-based modeling approach proved to be an accurate, reliable and effective tool for the quantification of the coke burn-off kinetics. The method has then great potential as a means to compensate for the lack of efficient phenomenological kinetic modeling techniques. It can also be used in the design of regenerative units downstream of catalytic wastewater treatment reactors based on wet oxidation. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Wet oxidation; Catalyst deactivation; Burn-off kinetics; Artificial neural networks

1. Introduction Several abiotic processes are known to be efficient in transforming water dissolved biorefractory contaminants into environmentally innocuous entities. In this respect, catalytic wet oxidation (CWO) is gaining in popularity to become well established in industry, especially in wastewater treatment where pollutant loads are neither suitable for conventional ∗ Tel.: +1-418-656-3566; fax: +1-418-656-5993. E-mail address: [email protected] (F. Larachi).

biotreatment nor for incineration. Highly active solid catalysts combined with pressurized O2 under mild temperature/pressure are indeed able to trigger the oxidation of pollutants dissolved in wastewater to a deeper level till complete mineralization [1]. Efforts are focused on the need to provide efficient CWO solid catalysts capable of accomplishing oxidative destruction of aqueous pollutants under acceptably moderate conditions. The trend in favor of the development of cost-effective processes is created by the need to respond to industrial economic concerns and, at the same time, comply with strict environ-

0926-3373/01/$ – see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 6 - 3 3 7 3 ( 0 0 ) 0 0 2 3 6 - 8

142

F. Larachi / Applied Catalysis B: Environmental 30 (2001) 141–150

mental requirements. While the process is developed to provide “clean” but “zero-added-value” treated water with virtually no immediate profits, the need to comply with existing regulations relating to discharge tolerances is always accompanied by extra costs. Integration of CWO multiphase reactors into viable water treatment units must take into account one key aspect of solid catalysts, that is catalyst regeneration. Coke formation leading to catalyst deactivation represents an inevitable parasitic chemical reaction that occurs concomitantly with the pollutant mineralization [2–5]. As the carbonaceous overlayer tends to deactivate the catalyst, “coke” burn-off is, as a result, explored as an optional means to restore the catalyst activity. The CWO deposits dealt with in this work show various similarities with carbonaceous deposits formed in the course of a reaction of hydrocarbons in the presence of H2 over cracking and reforming catalysts [6–8]. While the coke formed as a result of hydrocarbon conversion is the subject of thorough investigations over the last decades, literature relating to catalytic wet oxidation “coke” is virtually non-existent. This deficiency highlights the strong need to bring further knowledge that provides new insights into the behavior of carbonaceous materials building up over wet oxidation catalysts. As a result, wastewater treatment units will be designed to last long and to successfully deal with the catalyst coke laydown deactivation. Artificial neural network or ANN-based modeling techniques are commonly accepted and well established as a substitute for mechanism-based models that are hard to establish or not well identified [9–10]. Hence, the prime purpose consists in using a feed-forward perceptron ANN to model the combustion kinetics of carbonaceous deposits in the temperature-programmed oxidation mode (TPO). As already stated, the carbonaceous deposits build up on spent MnO2 /CeO2 and 1 wt.% Pt-MnO2 /CeO2 catalysts used for catalytic wet oxidation of phenolic aqueous solutions. The fundamental process involved in the learning procedure that consists in creating internal states or, in other words, finding the optimal neural architecture that models the external events, here the combustion phenomenon, is described. The ability of the final network to generalize, that is to perform correctly on instances that differ from those in the training examples, is also discussed.

2. Experimental 2.1. Coke deposition The equipment and techniques used to form the carbonaceous deposits, or “coke”, on the catalysts have already been described in detail [11,12]. As illustrated in Fig. 1, the phenol “coking” tests were performed using a stainless steel high pressure autoclave batch slurry reactor (model 4842, Parr Instrument, Inc.). The aqueous phenol solutions, typically 100 ml, underwent catalytic wet oxidation (CWO) over MnO2 /CeO2 and 1 wt.% Pt-MnO2 /CeO2 catalysts. In each CWO run, 100 mg of catalyst was “coked” in an atmosphere of oxygen (0.5 MPa) under varying temperature conditions (80–130◦ C) using 0.1 g phenol in water. The MnO2 /CeO2 and 1 wt.% Pt-MnO2 /CeO2 catalysts were synthesized in our laboratory. First, the MnO2 /CeO2 catalyst (bulk ratio = 7/3) was synthesized by coprecipitation of MnCl2 (Fisher Scientific Co.) and CeCl3 (Sigma Chemicals Ltd.). The precipitate was filtered, washed, and air-dried overnight at 100◦ C. It was then calcined for 3 h under flowing air at 350◦ C. Platinum was next loaded on the composite oxide support by impregnation (incipient wetness method) using H2 PtCl6 precursor. Subsequently, to reduce Pt, the promoted catalyst was calcined in air at 350◦ C, then cooled to room temperature, and finally exposed for 2 h to flowing H2 at 250◦ C.

Fig. 1. Layout of the experimental facilities used in the phenol coking tests in a three-phase slurry reactor.

F. Larachi / Applied Catalysis B: Environmental 30 (2001) 141–150

The catalysts were contacted in the CWO slurry reactor for up to 4 h using phenolic solutions. Several CWO batches were run under identical conditions and thence quenched in order of increasing oxidation reaction times. The procedure is designed to establish the catalyst activity loss profiles versus time. Subsequent to each reaction quenching, the (partially) deactivated catalyst was withdrawn at regular 5 min intervals from the slurry reactor, then washed and air-dried. For each operating condition, the spent catalyst was divided into 50–100 mg batches to provide the ability to conduct the TPO-MS studies and the elemental analysis determinations. 2.2. TPO-MS facility As illustrated in Fig. 2, the basic configuration of the TPO-MS facility includes a 1/4 in. i.d. flow through U-shaped tubular quartz microreactor placed in an electrically heated and temperature-program controlled ceramic furnace. At about mid-height deep in the furnace, 50–100 mg of spent catalyst is placed inside the reactor and sandwiched in-between two glass wool plugs. Such small amounts of catalyst are required to prevent large temperature fluctuations of the gas stream associated to the exothermicity of combustion and excessive peak broadening resulting

Fig. 2. Layout of the experimental facilities used in the temperature-programmed oxidation of the spent catalyst.

143

from multiple-readsorption. While the temperature of the gas stream can be measured using a thermocouple positioned flush to the microreactor wall, the pressure reading can be conducted through a pressure gauge located at the reactor outlet. The experimental procedure carried out using the TPO-MS facility amounts to first exposing each batch of spent catalyst to flowing helium (30 ml/min) and, at the same time, starting, at a heating rate of 10◦ C/min, a linear temperature-program from the ambient temperature to 120◦ C. The final temperature is then maintained for 20 min before a cooling down process to room temperature is initiated. The heating and cooling down treatment is systematically conducted so as to provide the ability to remove physisorbed water from the catalyst sample without thermally damaging the deposited coke [11]. The next step consists in heating the catalyst up to 650◦ C at a rate of 8◦ C/min. The catalyst heating-process is designed to progress under a controlled flow of 5% O2 /He passing through the catalyst bed to burn-off the carbonaceous deposit at a constant gas flow rate of 30 ml/min. Measures taken to ensure that the average particle size of the fresh and spent catalysts is enough small (approximately 70 ␮m) combined to the high molecular diffusivity of O2 in He provide the opportunity to prevent mass transfer control. Besides, the influence of heat transfer on the combustion process is considered negligible as the heat of combustion estimated at approximately 30 kJ/g [13] induces a temperature difference less than 0.01 K between the catalyst surface and the gas bulk. The oxygen uptake is determined by means of a thermal conductivity detector (TCD). The O2 , CO and CO2 fluxes evolving in the gas phase downstream from the microreactor are continuously monitored using a mass spectrometer based on a transpector quadrupole (Leybold Inficon, Inc.). A fraction of the gases flowing out of the quartz reactor are diverted into a multiple-stage pressure reduction system. The latter consists of a metering valve designed to provide the ability to control and shunt the gases into the mass spectrometer. The gas flow is provided by means of mechanical pumps and a turbo-molecular pump operating at a vacuum pressure maintained at approximately 10−6 Torr. A computer linked to the experimental set up via data acquisition boards is used to record, every 5 s, signals from the TCD and the MS.

144

F. Larachi / Applied Catalysis B: Environmental 30 (2001) 141–150

The MS signals corresponding to the O2 , CO and CO2 fluxes are converted into production/consumption rates using the microreactor outlet conditions. h

−1 ◦ −1

Rate ␮mole(g of cat.)

C

i

JP0 Q 106 = SPd RT βwcat

(1)

The units specific to the evolution rates are determined from: • the electrical current, J (in mA), measured for each species, i.e. O2 , CO, CO2 ; • the tabulated mass spectrometer sensitivity factor, S, in mA/atm, for each species; • the MS-side total pressure, Pd in atm; • the microreactor-side total pressure P0 in atm, determined to be 1.2 atm for all the runs; • the mass of catalyst, wcat in g; • the combustion temperature, T in ◦ C; • the heating rate, β in ◦ C/min; • the microreactor flow through volumetric rate, Q at reaction conditions in l/min. The total carbon oxide (COx ) rate is expressed as the carbon conversion rate to allow the kinetic modeling of the combustion phenomenon: J P0 Q 106 dX = dT S Pd RT β[C]0 wcat

(2)

Table 1 Description of CWO operating parameters for the TPO-MS profiles of spent Pt-MnO2 /CeO2 a Run

WO temperature, τ WO (◦ C)

WO reaction time, θ WO (min)

R0 (fresh) R1 R2 R3 R4 R5 R6 R7 R8

– 80 80 90 90 130 130 130 130

– 15 90 5 120 5 10 15 30

a

PO2 = 0.5 MPa, 1 g cat./l, 1 g phenol/l.

currents resulting from the burn-off of the deposits are converted into moles of consumption/production or conversion rates per unit mass of catalyst using appropriate signal conversions (Eq. (1)). The influence of the ramp temperature on the COx , i.e. CO + CO2 , production and O2 consumption rates is displayed in Fig. 3. In this respect, it is possible to compare the results obtained for low severity (i.e. low conversion, run R1) and high severity (high conversion run R2) of phenol oxidation. As can be seen from Fig. 3, the oxygen consumption rate, obtained

where R is the ideal gas constant, [C]0 , in ␮mol/g catalyst, represents the concentration of the total carbon measured using the Carlo Erba CHN analyzer (Model 1106), and X the conversion of carbon.

3. Results and discussion 3.1. Variables influencing the TPO-MS burn-off kinetics The spent MnO2 /CeO2 and Pt-MnO2 /CeO2 catalysts are produced under the phenol wet oxidation conditions summarized in Table 1. All the experiments are performed using constant oxygen partial pressure of 0.5 MPa, an identical initial phenol concentration of 1 g/l, and a constant catalyst concentration of 1 g/l. Therefore, only the effects of wet oxidation temperature (τ WO ) and time (θ WO ) on coke burn-off will be studied. Furthermore, the TPO-MS electrical

Fig. 3. Experimental evolution rates of COx and O2 during TPO in 5% O2 /He mixture at a heating rate of 8◦ C/min of 1% Pt-MnO2 /CeO2 coked in phenol wet oxidation (runs R1 and R2).

F. Larachi / Applied Catalysis B: Environmental 30 (2001) 141–150

145

under both conditions, mirrors almost perfectly the COx production rate. The carbonaceous deposit undergoes otherwise important modifications with increasing exposure time, θ WO , and oxidation temperature, τ WO , during phenol oxidation in the slurry reactor. Moreover, the deposit formed under low severity, i.e. low θ WO and/or τ WO , exhibits TPO-MS COx evolution profiles with quasi-symmetrical Gaussian single-peak culminating near 250◦ C (e.g. run R1, Fig. 3). These combustion peaks have indeed been successfully modeled using the conventional power-law grain model [14]. At high severity or high phenol conversion, i.e. high θ WO and/or τ WO , the carbon oxide profile exhibits, as shown in Fig. 3, multiple-feature combustion peaks (R2). It can also be noticed that one sharp “low-temperature” peak clearly overlaps with a broad “high temperature” bell-shaped peak. Similar complex peaks associated to the other runs corresponding to high severity wet oxidation presented in Table 1 can also be systematically observed. The burn-off temperature range for the deposits remains unaffected by neither θ WO nor τ WO . This observation suggests the predominance of a transition metal oxide mediated burn-off route. The latter can be easily explained by the abundance of surface manganese oxide and ceria, a well-known oxygen storage promoter, over the partially deactivated catalyst [15]. 3.2. Power-law grain model As stated above, a modeling approach based on the widely used power-law grain model (PLGM) has been attempted earlier [14] to represent the variation of the combustion rate dX/dT as a function of temperature. Functionally in the PLGM, the non-isothermal coke burning rate can be expressed as [14]: dX = k0 e−(E/RT) [O2 ]m (1 − X)n dT

(3)

in which the activation energy, E, the pre-exponential factor, k0 , the oxygen partial order, m, and the deposit partial order, n, are the usual adjustable parameters that could be estimated using standard non-linear regression techniques. The performance of the power-law grain model is illustrated in Fig. 4a and b in the case of runs R1 and R2, respectively. Clearly, the burn-off kinetics of

Fig. 4. Experimental vs. predicted evolution rates of COx during TPO in 5% O2 /He mixture at a heating rate of 8◦ C/min of 1% Pt-MnO2 /CeO2 coked in phenol wet oxidation. Run R1 (a), run R2 (b): model predictions obtained by fitting a power-law grain model.

low-severity cokes is successfully modeled by means of the PLGM. However, this model fails to represent the multiple-feature combustion peaks recorded using high severity cokes. Other sophisticated phenomenological models such as the pore tree, the random pore, the random capillary, and the bifurcated pore models have also been evaluated but did not provide further gain with respect to the much simpler PLGM. Thorough discussions on these attempts can be found in [14]. As an alternative to these conventional approaches, we will illustrate in the next section the potential of artificial neural network computing in providing a trustful representation of the coke burn-off

146

F. Larachi / Applied Catalysis B: Environmental 30 (2001) 141–150

kinetics especially that obtained under high severity conditions. 3.3. Neural networks for modeling the reaction kinetics A full description of the combustion kinetics of “coke” laydown on spent wet oxidation catalysts using conventional mechanistic pathways appears, at this stage, extremely difficult. In this context, attempt is made to implement a feed-forward ANN as a way to approach the unknown combustion mechanism. The final purpose is to approximate the relationship between the wet oxidation parameters (τ WO , θ WO ), the burn-off operating conditions (T, [O2 ]) and the coke conversion rate dX/dT. The advantage of the ANN-based modeling approach lies in the ability to intrinsically embed the rule following behavior of a non-linear system without the need of an explicit representation of its governing rule [16]. The use of the ANN amounts to find an explicit mapping function Φ that maps the dependent variable dX/dT with the independent variables τ WO , θ WO , T and [O2 ]: RX =

dX = Φ(T , [O2 ], θWO , τWO ) dT

(4)

3.4. Feed-forward perceptron ANN architecture As shown in Fig. 5, the ANN used represents a three-layered architecture possessing a cascade of connected nodes. Each processing unit or node is set to perform the simple task of receiving a weighted sum of inputs from the neighboring cells of the precedent layer and generating an output. The input to a processing unit can be either the output from the connected neighboring units or data fed from outside the network. Moreover, the output from a processing unit is used either as input to neighboring units of the next layer or as output from the network. Within the adopted architecture, input units, stimulated or fed with input data corresponding to the bias and four variables identified previously as affecting the coke burn-off kinetics, determine the state of the hidden units and activate the output units to generate the coke conversion rate, dX/dT.

Fig. 5. Schematic representation of the three-layer feed-forward perceptron artificial neural network used in this work.

The neural network designed to predict the combustion kinetics in terms of the COx TPO-MS data is described by the following set of generic equations:  −1  +1  JX  (5) Rˆ X = 1 + exp − ωj Hj    j =1

"

(

5 X Hj = 1 + exp − ωij Ui

)#−1 (6)

i=1

  ˆ 2 , U3 = θˆWO , U4 = τˆWO U1 = Tˆ , U2 = O

(7)

where the hat symbols designate the variables normalized in the interval (0−1), U5 and HJ +1 are the bias constants set equal to one, ωi and ωij are the connectivity weights of the ANN, J represents the number of nodes in the hidden layer. A supervized learning algorithm is used to train the neural network. The supervized learning rules require simultaneous procurement of the desired network input-output data to adjust the weight matrix ω (or ωi and ωij ANN parameters) in order to minimize the loss function, usually a quadratic criterion

F. Larachi / Applied Catalysis B: Environmental 30 (2001) 141–150

147

between measured and predicted outputs defined as follows: El (ω) =

l X (ymeas. − ypred. )2

(8)

1

where ymeas. represents the measured coke conversion rate, ypred. the network prediction, and l designates the number of measurements in the learning set. The basic idea behind the supervized learning procedure consists in feeding the ANN input data patterns so as to produce associated output data patterns that closely match the target or desired output data. The approach amounts to identifying a set of connectivity weights, i.e. matrix ω, that minimizes a cumulative relative error (Eq. (8)) between the ANN output data and the measured data using the least-squares method. Indeed, the kinetic data is split into two subsets. While the first subset is used for training the neural network, the second is designed to provide the opportunity to investigate the generalization capability of the resulting network architecture. In this context, it is worthwhile noting that the Broyden– Fletcher–Goldfarb–Shanno (BFGS) method has been used to train various ANNs in such a way as to find the optimal architecture. The usual heuristic consists in using two-thirds of the rate data for the identification of the weight matrix and keeping the remaining one-third for the investigation of the model robustness. The NNFit package [17] is used to carry out the desired ANN simulations. The standard deviation used to evaluate the neural networks learning capabilities is defined as follows.   El (ω) 1/2 (9) σl = l Besides, the ability of the final network to generalize, that is to perform correctly on instances that differ

Fig. 6. Parity plot of predicted vs. measured COx emission rate using a 2-6-1 network topology: empty symbol (learning set), filled symbol (generalization set).

from those in the examples used during the learning process, is tested using the following standard deviation.   Eg (ω) 1/2 (10) σg = N −l 3.5. Training of the neural networks One good measure of performance of the final network is commonly known as the generalization ability. It consists in investigating how closely an ANN output predicted using input data that has never been presented as learning patterns approximates the desired or target output data. The procedure is designed to show that the final network has the capability to recover the general rule underlying the task. To identify the optimal network topology, various ANN architectures have been trained and tested using J hidden neurons varying from 2 to 25. In this

Table 2 Optimum network topologies vs. learning procedures Run

Net topology

Weights

Total data set

σ Learning

R8 R3, R8 R4, R5, R8 R3–R8

2-06-1 4-05-1 4-07-1 4-10-1

25 31 43 61

262 809 1274 2617

8.4 1.7 2.6 3.4

× × × ×

10−5 10−4 10−4 10−4

2 RLearning (%)

σ Test

99.98 99.91 99.78 99.59

9.0 1.8 1.9 4.2

× × × ×

2 RTest (%)

10−5 10−4 10−4 10−4

99.98 99.90 99.88 99.34

148

F. Larachi / Applied Catalysis B: Environmental 30 (2001) 141–150

context, different learning sets of kinetic data have been constructed to evaluate the effect of the experimental conditions (visited domain of learning data) on the learning ability of the constructed networks

(see Table 2). An ANN having an optimal topology is bound to exhibit the best trade-off between an under-parameterized network that might fail to describe the training sets, and an over-parameterized

Fig. 7. Comparison of measured rate data profiles with the ANN predictions for various values of τ WO , θ WO , T, [O2 ]: (a) run R3, (b) run R4, (c) run R5, (d) run R6, (e) run R7, (f) run R8. Smooth lines show ANN prediction.

F. Larachi / Applied Catalysis B: Environmental 30 (2001) 141–150

149

network that might unduly overfit the training set, leading to a loss of generalization. Even if this criterion is fulfilled, a number of candidate networks can provide almost the same statistical performance. This is ascribable to the highly non-linear character of ANNs that seldom reach a “global” minimum. Besides, depending on the inventory of the training set, the initialization of the connectivity weights and the number of iterations, training might converge towards a local minimum. Under these circumstances, potential advantages such as simplicity highlight the need to use small networks.

Last but not least, it is important to mention that although ANNs can handle swiftly complex non-linear processes, they must be viewed exclusively as representational tools and not as explanatory models. Hence, ANNs should be used only for predicting behaviors for conditions falling within the ranges prescribed during the training step. Venturing outside these ranges can be misleading and is usually not recommended.

3.6. Testing of the neural networks

Manganese-cerium composite oxide catalysts exhibits deactivation by coke deposits in the course of the phenol wet oxidation obtained in the batch slurry reactor. The experimental results reveal that the chemical structure of the deposits evolves under varying wet oxidation operating conditions. The combustion of the carbonaceous deposits was monitored via the conversion rate of the carbon oxides, COx , and the consumption rate of oxygen in the temperature-programmed oxidation mode. Both measured fluxes were used to model the combustion kinetics of the deposits by means of a novel neural network-based approach. In this context, the perceptron artificial neural network is thus, shown to be an efficient non-linear regression tool for modeling complex heterogeneous combustion kinetics of coke deposits over deactivated wet oxidation catalysts. Indeed, ANNs proved to be very effective representation models of intrinsic rate equations when reaction mechanisms and/or their corresponding phenomenological kinetic models are non-existent or too sophisticated. The results provided herein illustrate the great potential of ANNs for the quick and precise formulation of kinetic models relevant to catalyst regeneration in the context of heterogeneous wet air oxidation. Hence, ANNs can be advantageously used to provide simplified reactor models required for the design of catalyst regeneration units.

Various ANNs of optimal topology are listed in Table 2 along with the number of weights, the total number of kinetic data (N) and the values of the standard deviation and the correlation coefficient obtained from the use of the training and test sets. As can be seen, highly accurate neural network-based approximations of the combustion kinetics have been obtained. Parity plots of the conversion rate data resulting from the experimental run R2 and the corresponding neural network-based predictions are shown in Fig. 6. To highlight the performance of the final network, the output data resulting from the learning process (empty circle) and the test (filled circle) sets have been purposely differentiated. Furthermore, the predictive ability of the R3–R8 ANN to handle effects of the wet oxidation temperature and exposure time in the slurry reactor as well as those associated to the TPO operating parameters (ramp temperature and instantaneous oxygen concentration) is illustrated in Fig. 7a–f. The learning process of various networks involved the use of 1744 samples obtained from the experimental runs R3–R8. On the other hand, the generalization capability of these ANNs has been investigated using a subset of 873 examples. The architecture that presents so far the best modeling performance is the 4 × 10 × 1 network with 10 processing units in the hidden layer. As can be seen, the predicted COx production rate is in a very good agreement with the measured COx conversion rate irrespective of the shape of the coke burn-off curve and regardless of the wet oxidation conditions.

4. Conclusion

Acknowledgements Financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC)

150

F. Larachi / Applied Catalysis B: Environmental 30 (2001) 141–150

and the Fonds pour la Formation de Chercheurs et d’Aide à la Recherche (Québec) is gratefully acknowledged. The author also thanks Drs. S. Hamoudi, K. Belkacemi and B.P.A. Grandjean for their help. The contribution of Mr. A. Bedrouni from the Department of Mechanical Engineering (ULaval) in the preparation of this manuscript is also acknowledged. References [1] Y.I. Matatov-Meytal, M. Sheintuch, Ind. Eng. Chem. Res. 37 (1998) 309. [2] A. Pintar, J. Levec, J. Catal. 135 (1992) 345. [3] S. Hocevar, J. Batista, J. Levec, J. Catal. 184 (1999) 39. [4] S. Hamoudi, F. Larachi, G. Cerella, M. Cassanello, Ind. Eng. Chem. Res. 37 (1998) 3561. [5] S. Hamoudi, K. Belkacemi, F. Larachi, Chem. Eng. Sci. 54 (1999) 3569.

[6] S.M. Augustine, G.N. Alameddin, W.M.H. Sachtler, J. Catal. 115 (1989) 217. [7] C. Li, T.C. Brown, Energy Fuels 13 (1999) 888. [8] A. Brito, R. Arvelo, F.J. Garcia, A.R. Gonzalez, Appl. Catal. A: Gen. 145 (1996) 285. [9] E. Molga, R. Cherbanski, Chem. Eng. Sci. 54 (1999) 2467. [10] I.M. Galvan, J.M. Zadilvar, H. Hernandez, E. Molga, Comput. Chem. Eng. 20 (1996) 1451. [11] S. Hamoudi, F. Larachi, A. Sayari, J. Catal. 177 (1998) 247. [12] S. Hamoudi, F. Larachi, A. Adnot, A. Sayari, J. Catal. 185 (1999) 333. [13] A.M.C. Janse, H.G. De Jonge, W. Prins, W.P.M. van Swaaij, Ind. Eng. Chem. Res. 37 (1998) 3909. [14] F. Larachi, K. Belkacemi, S. Hamoudi, A. Sayari, Catal. Today, 2000, in press. [15] A. Trovarelli, Catal. Rev. Sci. Eng. 38 (1996) 439. [16] K. Hornik, M. Stinchcombe, H. White, Neural Networks 2 (1989) 359. [17] P. Cloutier, C. Tibirna, B.P.A. Grandjean, J. Thibault, NNFit, logiciel de régression utilisant les réseaux à coucheshttp:// www.gch.ulaval.ca/∼nnfit.