Applied Catalysis A: General 219 (2001) 61–68

Artificial neural network-aided design of a multi-componentcatalyst for methane oxidative coupling

Kai Huang∗, Feng-Qiu Chen, De-Wei LüDepartment of Chemical Engineering, Zhejiang University, Hangzhou 310027, PR China

Received 8 November 2000; received in revised form 2 April 2001; accepted 20 April 2001

Abstract

Based on the properties of neural network, an improved back-propagation network, including the structural organization,the training method and the generalization ability of network, was developed to simulate the relations between components ofcatalyst and aspects of catalytic performance, which include C2 selectivity and conversion of methane. Levenberg–Marquardtmethod is presented to train the network and get better results than are available with traditional gradient method. The catalyst,which was found by SWIFT method, was proved to be better than any other catalyst in training pattern. When reacting on theoptimum catalyst, GHSV was 33,313 cm3 g−1 h−1, CH4:O2 was 3, reaction temperature was 1069 K, CH4 conversion was27.54%, C2 selectivity reached 75.40% (C2 yield was 20.77%) and the activity of catalyst did not decrease obviously in 10 h.© 2001 Elsevier Science B.V. All rights reserved.

Keywords: Artificial neural network; Catalyst; Computer-aided design; Oxidative coupling of methane

1. Introduction

It is important to choose a catalyst for a chemicalreaction, but it is difficult to design a high-efficientcatalyst by the tradition method [1], which is based onreaction mechanism to decide the main componentsof catalyst and performance of some experiments tofind the best catalyst. It is obvious that there are manydisadvantages in using this method. Firstly, one mayspend much time and money to do many experiments;secondly, if the mechanism of the chemical reaction isnot clear, the best catalyst could not be found; finally,the ‘optimum’ catalyst found by this method may not

∗ Corresponding author. Tel.: +86-571-87932477;fax: +86-571-87951227.E-mail address: huangkai@cmsce.zju.edu.cn (K. Huang).

be the best catalyst. So, it is important to find a moreeffective method for design of catalyst.

With developing of information technology andmathematics theory, design of catalysts by computerhas become an effective method. Many scholars wereengaged in this field and have developed many soft-wares, such as DECADE [2,3], INCAP [4], ESKA[5], catalyst [6], Hu system [7], IACES [8], ESYCAD[9] and ESMDC [10]. But most of those softwares arebased on Expert System, which would spend muchtime founding an Expert System database, and maynot be universal. Recently, artificial neural networkis widely applied for designing catalyst and in otherfields of catalytic research [11–13]; a good examplehas been reported to design a catalyst for ammoxi-dation of propylene [14]. Farther research indicatesthat this method is easy to understand and could beused for designing catalyst of different chemical

0926-860X/01/$ – see front matter © 2001 Elsevier Science B.V. All rights reserved.PII: S0926 -860X(01 )00659 -7

62 K. Huang et al. / Applied Catalysis A: General 219 (2001) 61–68

reaction by changing structural organization of theneural network.

In this paper, the application of artificial neuralnetwork in design of catalyst for oxidative couplingof methane (OCM) is discussed.

2. Experimental

2.1. Basic consideration

Direct catalytic conversion of methane to C2hydrocarbons by OCM is a potential route for theproduction of useful chemicals and fuels from abun-dant natural gas. A large number of catalysts havebeen developed to catalyze OCM, as has been doc-umented in a review article [15]. At the same time,most of OCM catalysts are made up of two to threecomponents, and only some aspects of catalytic per-formance, such as selectivity, could be enhanced onmost of catalysts; the other aspects of performance,such as conversion and stability of catalyst, were notgood yet. If a high-efficient element could not befound to catalyze OCM, it is necessary to developa multi-component catalyst to enhance the catalyticperformance of OCM.

Recently, some new OCM catalysts are suggested.One catalyst is Na4P2O7-ZrOCl2, which shows a nicercatalytic performance (the optimum C2 yield were22%) [16], but the activity decreased rapidly in 2–3 h.The other OCM catalysts include Na+–Mn–W/SiO2[17] and Mn–S/SiO2 [18]. It is noticeable that the ox-ides of transition metals such as Mn and Zr, which areeffective for the deep oxidation, were introduced asthe main component in these three catalysts. In theory,the oxides of transition metals could increase the con-centration of lattice oxygen on the surface of catalyst,and quicken the activation of CH4; when promotedwith alkali metal compounds such as Na, the catalyticperformances in OCM could be improved signifi-cantly on some transition metals catalysts. At thesame time, a small quantity of S and P elements areadded to enhance the selectivity of C2 hydrocarbons,and the stability of catalyst could be improved byW element.

Based on such considerations, a multi-componentOCM catalyst could be prepared, which was supportedon SiO2, had Mn and Zr as main components, and S,

W and P as secondary components and was promotedby alkali metal compounds such as Na.

2.2. Catalyst preparation

A mixed solution of Na2CO3, Na2SO4, Na4P2O7and Na2WO4 was added to silica gel solution (the con-centration is 26%) to obtain a colloid. The colloid wasdried in air at 423 K for 3 h, calcined at 823 K for 2 hand at 1173 K for 6 h, and crushed to the particle sizeof 20–30 mesh. Then the particles were impregnatedwith a mixed solution of ZrOCl2 and Mn(CH3COO)2,dried in air at 423 K for 3 h, calcined at 823 K for 2 hand at 1173 K for 6 h, and crushed to the particle sizeof 20–30 mesh.

Twenty-five catalysts, which designed by the ortho-graphical method, were prepared by using this method,and the results of catalytic performance testing wouldbe taken as the training pattern. Eight catalysts, whichwere prepared by the above method and designed ran-domly, were taken as the testing pattern.

2.3. Catalytic performance testing

The apparatus and the procedure are in Fig. 1.The oxidative coupling reaction was carried out in aquartz tube. A thermocouple was positioned outsidethe quartz tube at the hottest part of reactor, whichwas heated by a furnace controlled by a controller.

Fig. 1. Schematic diagram of catalytic reaction apparatus: (1) CH4

gas cylinder; (2) mass flow controller; (3) O2 gas cylinder; (4)Ar gas cylinder; (5) gas mixer; (6) three-port valve; (7) fixed-bedreactor; (8) six-port valve; (9) sampling valve and (10) gas chro-matogram.

K. Huang et al. / Applied Catalysis A: General 219 (2001) 61–68 63

The length of the heated zone was 30 cm. The follow-ing reaction conditions were employed: the flow ratesof methane and oxygen were 30 and 10 cm3 min−1

(NTP), respectively (CH4:O2 = 3) and the catalystloading was 0.3 g. In all experiments, methane andoxygen were co-fed into reactor and a mass flow con-troller controlled their flow-rates. The catalyst waslocated in the hottest part of reactor. The productswere analyzed by two on-line TCD-equipped gaschromatographs. One column with organic support402 separated O2, H2, CH4, C2H4, C2H6 and CO2;another column with molecular sieve 5 Å separatedO2, CH4, and CO.

2.4. Experimental results

The performance of the above catalysts was testedon the apparatus shown in Fig. 1 under the samereaction conditions. The experimental results areshown in Tables 1 and 2.

Table 1Training pattern of the networka

Catalyst Input data (mol%) Output data (%) Yield (%)

Na S W P Zr Mn XCH4 SC2

OCM-1 44.18 7.22 1.09 13.79 31.80 1.93 21.49 58.12 12.49OCM-2 48.55 3.74 2.25 9.52 32.94 3.00 21.61 63.19 13.66OCM-3 60.37 4.92 2.22 0.00 32.49 0.00 13.10 59.48 7.79OCM-4 86.89 4.67 0.00 5.95 0.00 2.50 15.87 52.99 8.41OCM-5 81.28 3.59 1.08 2.29 7.91 3.84 21.67 36.44 7.90OCM-6 39.42 11.03 1.66 7.02 36.45 4.42 24.03 61.94 14.88OCM-7 78.64 15.32 1.15 4.88 0.00 0.00 22.58 32.93 7.44OCM-8 71.74 7.80 2.35 7.45 8.59 2.08 16.95 49.74 8.43OCM-9 69.67 5.79 1.31 7.37 12.76 3.10 16.34 47.46 7.75OCM-10 67.25 5.91 0.00 0.00 26.05 0.79 16.14 51.79 8.36OCM-11 58.87 15.92 0.00 13.52 11.69 0.00 14.32 57.14 8.18OCM-12 57.80 15.36 1.54 0.00 22.56 2.74 12.85 60.54 7.78OCM-13 56.02 9.22 0.46 3.91 27.09 3.29 14.59 57.64 8.41OCM-14 66.97 8.91 1.79 1.89 19.64 0.79 14.79 53.05 7.85OCM-15 82.71 8.42 1.27 5.36 0.00 2.25 15.35 52.96 8.13OCM-16 41.35 16.25 1.84 2.59 35.81 2.17 20.29 63.96 12.98OCM-17 54.85 13.29 0.00 6.35 21.96 3.55 11.83 71.02 8.40OCM-18 76.43 13.25 1.00 8.44 0.00 0.89 12.43 62.52 7.77OCM-19 75.76 13.55 0.51 0.00 7.46 2.72 16.33 45.67 7.46OCM-20 74.79 9.81 1.48 3.12 10.80 0.00 10.82 69.24 7.49OCM-21 62.68 27.97 3.37 0.00 0.00 5.98 16.54 65.87 10.89OCM-22 66.36 18.29 1.65 4.66 8.06 0.98 12.52 64.24 8.04OCM-23 65.57 15.87 0.00 2.02 13.99 2.55 14.06 58.62 8.24OCM-24 64.00 11.23 0.68 4.29 19.80 0.00 8.82 81.75 7.21OCM-25 69.70 10.21 0.31 5.20 13.49 1.09 12.80 60.93 7.80

a Reaction conditions: catalyst loading = 0.3 g; flow rate = 40 cm3 min−1; CH4 = 25%; O2 = 75%; reaction temperature = 1069 K.

It could be found that the experimental results ofsome catalysts were similar to the result in Fig. 2,where conversion of CH4 would reach a maximumwith increasing temperature. The probable reason isas follows. There exist two main parallel by-reactions,shown as follows:

1. CH4 + 1.5O2 → CO + 2H2O2. CH4 + 2O2 → CO2 + 2H2O

Under the lower temperature, the rate of OCM wasfaster than reactions 1 and 2, and it could be foundthat selectivity of C2 was high. The Gibbs free energyof OCM increased with increasing temperature, butthat of reactions 1 and 2 remained constant in sub-stance [19], which indicated that a higher temperaturewas disadvantageous for OCM; the rates of reactions1 and 2 would gradually become fast, and make reac-tions 1 and 2 the main reactions. At the same time, theconsumed oxygen in reactions 1 and 2 was more thanthat in OCM, so the oxygen in feed was exhausted

64 K. Huang et al. / Applied Catalysis A: General 219 (2001) 61–68

Table 2Testing pattern of the networka

Catalyst Input data (mol%) Output data (%) Yield (%)

Na S W P Zr Mn XCH4 SC2

Cat-1 35.81 3.30 2.84 11.76 37.22 9.07 25.66 72.13 18.50Cat-2 52.00 10.76 6.79 3.65 20.22 6.57 22.11 77.58 17.15Cat-3 69.71 12.95 1.78 13.19 0.00 2.37 15.39 77.68 11.95Cat-4 49.20 3.71 0.56 9.75 33.71 3.07 23.85 78.83 18.80Cat-5 86.30 3.81 1.80 5.71 0.0 2.38 12.04 68.08 8.19Cat-6 69.71 12.95 1.78 13.19 0.0 2.37 15.39 77.68 11.95Cat-7 75.64 13.60 1.41 2.77 5.75 0.83 18.56 67.29 12.49Cat-8 49.20 3.71 0.56 9.75 33.71 3.07 13.28 55.95 7.43

a Reaction conditions: catalyst loading = 0.3 g; flow rate = 40 cm3 min−1; CH4 = 25%; O2 = 75%; reaction temperature = 1069 K.

Fig. 2. Influence of temperature on catalytic performance. Reactionconditions: catalyst loading = 0.3 g; flow rate = 40 cm3 min−1;CH4 = 25%; O2 = 75%; reaction temperature = 1069 K. Catalyst:OCM-6.

rapidly by parallel reactions. Thus, OCM could notreact adequately because of absence of oxygen, andconversion of CH4 would decrease gradually. It waspointed out that deactivation of catalyst did not takeplace in the above reaction.

3. Computer-aided catalyst design

3.1. Catalyst modeling

An artificial neural network, which consists ofmany simple process units, can simulate the structuralorganization and function of a human brain. One typi-cal form is called connectionist model, which is madeup of many single process units called neurons andweights. The weight wij denotes the strength of the

function between neurons i and j. Generally, an artifi-cial neural network can divided into input layer, hid-den layer(s) and output layer. Error back-propagationnetwork, which is used in this paper, is one forwardfeedback network and is used in many fields becauseof its strong learning capability [14].

There exist strong interactions between differentcomponents of a catalyst. Based on the property of ar-tificial neural network, the relation between catalyticperformances (such as the selectivity of reaction andthe conversion of reactant) and the components ofcatalyst could be expressed effectively. The structuralorganization of network could show the complexityof catalyst system, and the weight matrix could showthe interactions between different components.

As the activation function, a sigmoid function,which is used frequently, is adopted. If the input dataof a set of training patterns (such as the componentsof catalyst) and the output data (such as the catalyticperformances) were given, the network would calcu-late a set of output data and adjust the interconnectionpattern (such as the weights) so as to make the calcu-lated data as close to the given output data as possibleby the back-propagation algorithm. Thus, a trainednetwork may be thought of as a ‘function’, whichrepresents the relation between the input data and theoutput data. If the trained network was used as theobjective ‘function’, better catalyst components couldbe predicted by using the proper optimization method.

It is important to select the catalysts for the trainingpattern in order to find the best catalyst in a certainrange of catalyst components by optimization. So,the distribution of the catalyst for the training patternshould be well proportioned; here the orthographical

K. Huang et al. / Applied Catalysis A: General 219 (2001) 61–68 65

Fig. 3. Structural organization of the neural network.

method was used to design the catalysts in Table 1.The form of the input layer was optimized throughpreliminary experiments, and it could get the best re-sults by using atom ratio as the form of the input layer.The structural organization of the neural network isschematically shown in Fig. 3. In this neural network,which consists of an input layer, two hidden layersand an output layer, the components of catalyst wereused as input units, while selectivity of C2 and conver-sion of CH4 were used as output units. After severaltimes of learning, the conversion of methane (XCH4 )and the selectivity of C2 (SC2 ) could be representedas a ‘function’ of the catalyst components, shown inFormula (1). The generalization ability of the trainednetwork was tested by the testing pattern; the catalystfor the testing pattern should be different from the cat-alyst for the training pattern, and should be designedrandomly in a certain range of catalyst components.

(XCH4i ,SC2i) = f (Nai , Si , Wi , Pi , Zri , Mni ) (1)

Because the convergent rate is very slow in traditionalback-propagation algorithm, a new training algorithmwill be adopted in this paper to improve convergenceof the network. At the same time, a structural orga-nization of the network and an optimization methodare also discussed in this paper.

3.2. The training method of neural network

If the structural organization of a neural networkis to be certain, it was important to choose a right

Fig. 4. Comparison of two algorithms: (1) traditional algorithmand (2) Levenberg–Marquardt algorithm.

training method. The convergence of traditionalback-propagation algorithm based on gradient descentis very slow, and this method would result in failuresthat correspond to getting trapped in a local minimumduring gradient descent. It is necessary to find anothereffective method for training of the neural network.With the Delta rule presented in training, Levenberg–Marquardt method [20] is the best choice for train-ing. The comparison is shown in Fig. 4. The timeof calculation in the Levenberg–Marquardt methodis much less than in the gradient–descent searchingmethod.

3.3. The number of neurons and hidden layers

Although in theory, a three-layer neural networkcould simulate any continuous function, it is importantto find a right structural organization of network. Infact, the number of neurons and the hidden layers ofnetwork are chosen by experience, because no uniformmethod has been developed to decide it for variousproblems in theory yet.

For a six-component catalyst of methane oxidativecoupling, it is important to find the number of neuronsand hidden layers. By trying in time and again a betterstructural organization of network could be found; theresult is listed in Table 3.

From Table 3, the number of neuron is so few thatnetwork cannot well-simulate the relation between thecomponents of catalyst and catalytic performances,especially in selectivity of C2 in Net 1; Net 2 would

66 K. Huang et al. / Applied Catalysis A: General 219 (2001) 61–68

Table 3Comparison of various structural organizations of neural network (tested by the testing pattern)a

Net Catalyst Experimental results (%) Estimated results (%) Error (%)

XCH4 SC2 XCH4 SC2 XCH4 SC2

Net 1b Cat-1 25.66 72.13 25.4289 71.7935 0.2311 0.3365Cat-2 22.11 77.58 22.5138 78.0206 −0.4038 −0.4506Cat-3 15.39 77.68 15.9062 69.3038 −0.5162 8.3762Cat-4 23.85 78.83 23.7685 80.0307 0.0815 −1.2007Cat-5 12.04 68.08 12.1389 60.7666 −0.0989 7.3134Cat-6 15.39 77.68 15.4105 75.0670 −0.0205 2.6130Cat-7 18.56 67.29 18.1975 67.3076 0.3625 −0.0176Cat-8 13.28 55.95 13.3658 58.4484 −0.0858 −2.4984

Net 2c Cat-1 25.66 72.13 24.7689 75.3138 0.8911 −3.1838Cat-2 22.11 77.58 22.9058 76.2069 −0.7958 1.3631Cat-3 15.39 77.68 15.0871 74.3973 0.3029 3.2827Cat-4 23.85 78.83 24.5162 74.4226 −0.6662 4.4074Cat-5 12.04 68.08 12.1566 73.0097 −0.1166 −4.9297Cat-6 15.39 77.68 14.6589 75.5752 0.7311 2.1048Cat-7 18.56 67.29 18.7951 61.5453 −0.2351 5.7447Cat-8 13.28 55.95 13.5876 58.4047 −0.3076 −2.4547

Net 3d Cat-1 25.66 72.13 25.4956 72.0395 0.1644 0.0905Cat-2 22.11 77.58 22.1382 76.3761 −0.0282 1.1939Cat-3 15.39 77.68 15.4085 72.0518 −0.0185 5.6282Cat-4 23.85 78.83 23.5567 79.6529 0.2933 −0.8229Cat-5 12.04 68.08 12.0349 66.2673 0.0051 1.8127Cat-6 15.39 77.68 15.3547 71.7246 0.0353 5.9554Cat-7 18.56 67.29 18.7549 70.4659 −0.1949 −3.1759Cat-8 13.28 55.95 13.5764 50.2725 −0.2964 5.6775

Net 4e Cat-1 25.66 72.13 25.6479 71.57155 0.0121 0.5584Cat-2 22.11 77.58 22.1187 77.01131 −0.0087 0.5587Cat-3 15.39 77.68 15.3792 78.56976 0.0108 −0.8898Cat-4 23.85 78.83 23.8371 78.67106 0.0129 0.1589Cat-5 12.04 68.08 12.0375 66.95078 0.0025 1.1292Cat-6 15.39 77.68 15.4012 79.23214 −0.0112 −1.5521Cat-7 18.56 67.29 18.5746 66.50749 −0.0146 0.7825Cat-8 13.28 55.95 13.2754 57.14103 0.0046 −1.1910

a Reaction conditions: catalyst loading = 0.3 g; flow rate = 40 cm3 min−1; CH4 = 25%; O2 = 75%; reaction temperature = 1069 K.b Net 1 — six neurons in input layer, eight neurons in first hidden layer, four neurons in second hidden layer, two neurons in output layer.c Net 2 — six neurons in input layer, 25 neurons in first hidden layer, 15 neurons in second hidden layer, two neurons in output layer.d Net 3 — six neurons in input layer, 12 neurons in first hidden layer, 10 neurons in second hidden layer, seven neurons in third hidden

layer, 2 neurons in output layer.e Net 4 — six neurons in input layer, 20 neurons in first hidden layer, nine neurons in second hidden layer, two neurons in output layer.

overfit the experiment data because of overmanyneurons. At the same time, as shown in Net 3, therelation between components of catalyst and the re-action results would not be improved by increasingthe number of hidden layers when the total numberof neurons is the same. Net 4 is the best model of thissix-component catalyst by comparison.

3.4. Generalization ability

When the training finished, the generalization abil-ity of the network must be tested by data, which werenot included in the training group; the result are alsoshown in Table 3. We could find that the generaliza-tion ability of Net 4 is the best.

K. Huang et al. / Applied Catalysis A: General 219 (2001) 61–68 67

Table 4Comparison of the optimized results and experimental resultsa

Catalyst Experimental results (%) Estimated results (%) Error (%)

XCH4 SC2 XCH4 SC2 XCH4 SC2

Opt-1 27.54 75.40 27.8345 75.5619 −0.2945 −0.1619

a Reaction conditions: catalyst loading = 0.3 g; flow rate = 40 cm3 min−1; CH4 = 25%; O2 = 75%; reaction temperature = 1069 K.

Fig. 5. Activity change of catalyst with time. Reaction con-ditions: catalyst loading = 0.3 g; flow rate = 40 cm3 min−1;CH4 = 25%; O2 = 75%; reaction temperature = 1069 K. Catalyst:75.26 mol%Na–4.10 mol%S–2.19 mol%W–3.52 mol%P–9.70 mol%Zr–5.23 mol%Mn/SiO2.

3.5. Optimization

After founding the catalyst modeling by neural net-work, the optimal problem could be expressed in For-mula (2).

max(XCH4 , SC2) = f (xi) s.t. 0 ≤ xi ≤ 1,

i = Na, S, W, P, Zr, Mn (2)

Formula (2) was a constrained optimal problem ofnon-linear function, the aim function was the trainednetwork and the derivative was so difficult to calculatethat it could not be solved by analytical method. Asimple numerical method — SWIFT method [21] wasproved to be efficient to obtain good result.

Based on the optimal calculation, a better cat-alyst was found and proved by catalytic reaction.When GHSV was 33,313 cm3 g−1 h−1, CH4:O2 was3, reaction temperature was 1069 K, reacting on thebetter catalyst, CH4 conversion was 27.54%, C2 se-lectivity reached 75.40% (C2 yield was 20.77%); and

the activity of catalyst did not decrease obviouslyin 10 h, as shown in Fig. 5. The C2 yield of thiscatalyst is higher than that of any other catalyst onTables 1 and 2. Comparison of the optimized resultsand experimental results is shown in Table 4.

4. Conclusion

This paper provides the basic research on computer-aided designing of a multi-component catalyst formethane oxidative coupling. An improved back-propagation network, including the structural orga-nization, the training method and the generalizationability of network, was described. It was proved thatthe trained network could well simulate the relationsbetween components of catalyst and catalytic per-formances (such as conversion of CH4 and selec-tivity of C2). A better catalyst, which was found bySWIFT method, could get good catalytic performancein reaction. The experimental results of this catalystwere a little higher than those of the catalysts inthe training pattern and the testing pattern; furtherresearch should be performed in this field.

Acknowledgements

This work was partially supported by SINOPECBasic Research Foundation (no. X597017).

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