Chemical Engineering Science 58 (2003) 81–87www.elsevier.com/locate/ces

Catalyst design for methane oxidative coupling by using arti&cial neuralnetwork and hybrid genetic algorithm

Kai Huang∗, Xiao-Li Zhan, Feng-Qiu Chen, De-Wei L3uDepartment of Chemical Engineering, Zhejiang University, Hangzhou, 310027, China

Received 5 February 2002; received in revised form 10 May 2002; accepted 30 August 2002

Abstract

A new method for catalyst design was discussed based on arti&cial neural network, which was developed to simulate the relationsbetween catalyst components and catalytic performance in the previous research. For enhancing e8ciency of catalyst design, a new hybridGA tested by TSP was generated for global optimization to design the ‘optimal’ catalyst. A multi-turn design strategy was described.Based on the previous research, the design method was applied for designing multi-component catalyst for methane oxidative coupling,some better catalysts, in which C2 hydrocarbon yields were greater than 25% were designed. When reacting on the best catalyst, GHSVwas 33313 cm3 g−1 h−1, CH4 : O2 was 3, reaction temperature was 1069 K, methane conversion and C2 hydrocarbon selectivity were37.79% and 73.50%, respectively (C2 hydrocarbon yield was 27.78%), which was higher than that of previous reported catalysts on nodiluted gas condition, and showed a better prospect for industrialization of methane oxidative coupling. The research also showed thatthe new catalyst design method is highly e8cient and universal.? 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Catalyst; Design; Optimization; Oxidative coupling of methane; Neural network; Hybrid genetic algorithm

1. Introduction

For a new chemical reaction, it is important to develop ahighly e8cient catalyst, and the key to obtain a highly ef-&cient catalyst is the catalyst design. Usually, a traditionalmethod (Trimm, 1980) for catalyst design is based on fore-casted reaction mechanism to decide the main componentsof catalyst and determine the best catalyst by several experi-ments. Some better catalysts can be designed when reactionmechanism is clear by using the traditional method. But un-fortunately, for most of the new chemical reaction process,the catalytic mechanism could not be known well, so it is im-possible to design some highly e8cient catalysts for a newreaction in a short time by the traditional design method.With the development of information technology,

computer-aided-design catalyst (CADC) becomes an im-portant direction for catalyst design. Compared with thetraditional method, the CADC method does not need plentyof catalytic mechanisms and could design some better cat-alysts by a few experiments in a short time. In the past

∗ Corresponding author. Tel.: +86-571-87952728;fax: +86-571-87951227.

E-mail address: huangkai@cmsce.zju.edu.cn (K. Huang).

20 years, several softwares based on Expert system weredeveloped to aided-design catalyst, such as DECADE(Banares-Alcantara, Westerberg, Ko, & Rychener, 1887,1988), INCAP (Hattori & Kito, 1991), ESKA ( Speck et al.,1989), Catalyst (Dumesic et al., 1987), Hu System (Hu,Henry, & Stiles, 1991), IACES (Sun & Li, 1992), ESY-CAD (Koerting & Baerns, 1993), ESMDC (Huang et al.,1996) and GACD (Ji & Lin, 1998). But in those softwares,some catalytic information database based on designingcatalyst should be founded &rstly; secondly, an inferenceengine based on catalytic mechanism should be developedto give some useful information, lastly, some better cata-lyst could be designed for the catalytic reaction. Accordingto the above design Pow, it would spend much time andmoney designing a highly e8cient catalyst, and those de-sign methods may not be universal. So it is necessary todevelop a new method for catalyst design.In the past 20 years, arti&cial neural network (ANN) was

introduced to design catalysts by some researchers, such asKito (Hattori & Kito, 1991) (Kito, Hattori, & Murakami,1990, 1991, 1992, 1993, 1994, 1995; Hattori & Kito, 1995;Hattori et al., 1994; Hou, Dai, Wu, & Chen, 1997) and(Huang, Chen, & L3u, 2001), who succeeded in designing

0009-2509/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved.PII: S0009 -2509(02)00432 -3

82 K. Huang et al. / Chemical Engineering Science 58 (2003) 81–87

catalysts for propane ammoxidation (Hou et al., 1997) andcatalysts for methane oxidative coupling (Huang et al.,2001). Those researches indicate that computer-aided cata-lyst design by ANN is feasible and over many experimentscan be avoidable. But it should be pointed out that theselection of optimization method, especially for global opti-mization, is very important to design an ‘optimal’ catalyst,after simulating the relations between catalytic perfor-mances (such as conversion of reactants and selectivity ofaim products) and catalyst components by ANN.In this paper, on the basis of previous research (Huang et

al., 2001), a new method for catalyst design by using ANNand genetic algorithm is discussed and applied to design amulti-component catalyst for oxidative coupling of methane.

2. Catalyst modeling

In the previous research (Huang et al., 2001), amulti-component catalyst, which consisted of Na, S, W, P,Mn, Zr, and supported on SiO2, was introduced for methaneoxidative coupling, and the preparation method was alsodiscussed. Because there existed a complex interactionamong diRerent elements and supports, the reaction mecha-nism did also not known well for designing better catalysts,it was useful for catalyst design to develop a robust catalystreaction model by using ANN which did not depend onclear reaction mechanism. The primary research succeededin designing catalyst for methane oxidative coupling. Thecatalyst network model developed in the previous paper,contained six input units, 24 &rst-hidden-layer units, ninesecond-hidden-layer units and two output units. The molec-ular ratio of six elements in the catalyst would be six inputunits, methane conversion and C2 hydrocarbon selectivitywould be output units, according to the reaction property.Activation function of each layer was a sigmoid function;Levenberg–Marquardt method was chosen to train the net-work. Therefore, the previous model would be used in thispaper, and the previous results were also used as initialtraining patterns.

3. Optimization

Since the relations between catalytic performances andcomponents in the catalyst have been expressed by an ANN,some optimization methods should be introduced to designthe ‘optimal’ catalyst based on the network, which could beseen as a ‘function’. Local optimization method and globaloptimization method were used simultaneously for diRerentroles.

3.1. Local optimization

Since the number of catalysts in the training group isnot large enough to obtain the best generalization ability of

network at the beginning of the design, it is unavoidableto adjust the weight matrix of the trained neural network.Compared with adding the catalysts prepared randomly tothe training group, it is e8cient for improving the trainednetwork to add some catalysts designed by some local opti-mization methods as training patterns.Although more advanced methods could be employed to

perform a local optimization in the parameter space, such asvarious conjugate gradient methods and quasi-Newtonmeth-ods (Deng, 1992), it was di8cult to calculate &rst and sec-ond derivatives from the model expressed by an ANN in thisresearch. Therefore, some numeric optimization methodswere available for this purpose, such as complex method andSWIFT method. The complex method was used commonlyfor local optimization, but its convergence rate was unsat-is&ed. When a certain initial point was given the sequentialweight increasing factor technique (SWIFT) ( Sheela & Ra-mamoorthy, 1975) method could &nd local maximum andcould be faster than the complex method. For the constrainedoptimal problem expressed in (Huang et al. (2001)), theepoch periods of SWIFT method were not greater than 400after giving an initial point, and that of complex method wasnot less than 1000; on the other hand, SWIFT method waseasier to be programmed and executed on a computer thanother methods.In a general way, diRerent local optimization methods

were chosen for getting the fastest convergence rate accord-ing to the complexity of the catalyst design system.

3.2. Global optimization

For catalyst design, the &nal aim is to design the bestcatalyst; the introduction of global optimization could helpto design highly e8cient catalysts.One of the global optimization methods is genetic algo-

rithm (GA) (Chen, Wang, Zhuang, & Wang, 1996), whichwas developed by simulating evolution process, and couldbe used in global optimization e8ciently. Recently, GA suc-ceeded in using for selection and optimization of heteroge-neous catalytic materials by Wolf, Buyevskaya, and Baerns(2000) and Rodemerck et al. (2001). There are three opera-tions in GA, such as selection, crossover and mutation. But,it should be known that the ability of local searching is weakin GA so that it would lead to convergence slow or uncon-vergence. It would be a good choice to design a new hybridGA by combining standard GA with other local optimiza-tion methods. For strong ability of local searching, SWIFTmethod was chosen for combining with standard GA to gen-erate a new hybrid GA. The principle of the hybrid GA isshown in Fig. 1.The optimization steps of the hybrid GA is shown as

follows:

(1) Initialization. An initial feasible solutions populationconsists of several diRerent feasible solutions generatedrandomly.

K. Huang et al. / Chemical Engineering Science 58 (2003) 81–87 83

GA

SWIFT

GA

SWIFT

SWIFT

GA

Fig. 1. Principle of a Hybrid GA.

0 1000

20

40

60

80

100

120

140

160

180

Standard GA Hybrid GA (GA+SWIFT)

Path

leng

th

200 300 400Epoch times

Fig. 2. Comparison between standard GA and Hybrid GA (GA+SWIFT)in TSP.

(2) Execute SWIFT searching for half individuals in thepopulation and obtain some local maximums.

(3) Execute standard GA searching for remained half indi-viduals in the population and obtain some maximums.

(4) Execute genetic operations, such as selection,crossover and mutation for the local maximums ob-tained in steps 2 and 3.

(5) Repeat the searching course in steps 2–4 until the ter-minated conditions were satis&ed.

The hybrid GA was applied to solute TSP problem inorder to prove feasibility of the hybrid algorithm and com-pared with standard GA, the result is shown in Fig. 2.It could be known that the convergence rate of hybrid GA

was faster than that of standard GA. It should be also pointedout that the generated hybrid GA was still a global optimiza-tion method, but the ability of local searching and the con-vergence rate were improved strongly. In Fig. 2, the scale ofpopulation was 72; generation gap was 0.9; crossover prob-

Com. 2

Com. 3

Com. i

……

…

……

…Perf. 1

Perf. j

Input

Layer

First

Hidden

Layer

Second

Hidden

Layer

Layer

Com. 1

……

…

……

Output

Fig. 3. Structural organization of the neural network. Com — element orcombination of element; Perf. — catalytic performance.

ability Pc and mutation probability Pm were 0.75 and 0.005,respectively; roulette wheel rule was applied to selection op-eration, simple crossover operation was adopted; the factors�, �, � were chosen to be 1.0, 0.5, 2.0; initial penalty factorwas 1.0.

4. Design strategy

Since an accurate robust catalyst model could not beestablished by using a few training patterns, multi-trainingand multi-optimization strategy should be introduced todesign catalysts. Details of the strategy are described asfollows:

(1) An initial training group, which contained several cata-lysts designed by the orthographical method, was usedto train the neural network, which had a certain struc-tural organization, and show in Fig. 3. An initial trainednetwork model could be established.And the network model could also be expressed by

[X; S] = f(xi);

ai6 xi6 bi: (2)

(2) By using the optimization method discussed in Section3, based on formula (2), several catalysts could bedesigned and the predicted reaction results could alsobe known.

(3) These designed catalysts were prepared and tested toobtain the actual reaction results.

(4) Compared the actual results with predicted results. Ifthe error was acceptable, turn to step 7; otherwise, turnto the next step.

(5) Add the designed catalyst and actual reaction resultsto the training group and set the weights of the lasttraining as the initial weights of the next training.

84 K. Huang et al. / Chemical Engineering Science 58 (2003) 81–87

(6) Re-training the neural network, and repeat steps 3–5.(7) Some better catalysts were designed.

5. Catalyst design for methane oxidative coupling(Huang, 2001)

5.1. Introduction

Oxidative coupling of methane is one important tech-nology for methane conversion. The key to this reactionis to design a catalyst, which should be highly e8cient,with high-stability and reacting on lower temperature. In theprevious researches, a multi-component catalyst (C2 yieldreached 20.77%) was designed based on ANN model. Inorder to design better catalysts for oxidative coupling ofmethane, further research is carried out based on ANN andthe hybrid GA in this section.

5.2. Catalyst design

The model established in Huang et al. (2001) was set asinitial catalyst reaction model, SWIFT method and hybridGA were used to design some catalysts, the actual reactionresults were compared with the predicted results, and thosedesigned catalysts and reaction results were added into thetraining group to re-train the network. Repeating the abovedesign step, six-turn catalyst design for methane oxidativecoupling was processed, and the comparison between pre-dicted results and actual results of typical designed catalystsis shown in Table 1.From Table 1, the errors between predicted results and ac-

tual results were so large that accuracy of the &rst turn trainednetwork was not good and the network had to be further ad-justed. But it should also be found that the C2 hydrocarbonyield reached 22.67% and a 2% increase was obtained com-pared with 20.77% in previous research (Huang et al., 2001).In order to obtain an accurate catalyst model, further train-ing proceeded. The C2 hydrocarbon yields were 24.40%,26.07% and 27.08%, respectively, after second turn, thirdturn and fourth turn training, and the errors between pre-dicted results and actual results were also decreased grad-ually. This showed that the catalyst model was improvedgreatly, and some better catalysts were designed based onthe improved model. After the &fth turn training, the bestC2 hydrocarbon yield was only 24.73%, which was smallerthan 27.08% in fourth turn training; a conceivable reasonwas that the zone of lower C2 hydrocarbon yield was im-proved greatly, but the improvement fell into an error inthat of higher yield. So sixth turn training proceeded toamend the mistake, and a catalyst, in which C2 hydrocar-bon yield was 27.78%, was designed, and did not deactivatein 10 h.It could be found that the errors after sixth turn training

were not less than 1% yet. On the other hand, re-testedexperiments for the same catalyst showed that the error was

about 1%. So further training was unnecessary because thesimulated error approached the experimental error.From Table 1, it could also be found that the improve-

ment of catalyst ingredients was irregular during the designprocess, and no apparent rules could be deduced to directcatalyst component design. In fact, the interactions amongcomponents were complex and could not be expressed bya simple rule or formula because of the indistinct reactionmechanism about the designing multi-component catalyst;so it was useful for the catalyst design to establish an ac-curate robust model by using ANN. It could also be provedthat the traditional catalyst design method was not goodfor designing multi-component catalyst, especially for thecatalyst system, in which complex interactions among com-ponents existed.In order to check generalization ability of the &nal net-

work model, several catalysts designed randomly wereprepared to test the network, and the results are shown inTable 2.From Table 2, all errors between predicted results and

actual results were not greater than 3%. Considering theexperimental error, the generalization ability was acceptable.By the six turn design, some better catalysts for methane

oxidative coupling were designed, listed in Table 3.For most of the catalysts in Table 3, methane conversion

exceeded 35% and C2 hydrocarbon selectivity was greaterthan 70%. There were two catalysts in which C2 hydrocar-bon yield exceeded 27%, seven reached 26%, and the com-positions of these catalysts were diRerent from each other.On the same reaction conditions, in which no diluted gas

(such as nitrogen, helium) was added, performance of thecatalyst, in which C2 hydrocarbon yield was 27.78%, wasbetter than that of the previous reported catalysts.Based on above research, it could be known that the

new catalyst design method is highly e8cient for cata-lyst design, and it could be used for designing other cat-alysts by adjusting the structural organization of neuralnetwork.

6. Conclusion

In this paper, a new method for catalyst design was dis-cussed based on ANN and hybrid GA. Neural network wasapplied for catalyst modeling. In order to design the ‘opti-mal’ catalyst, SWIFT method was used for local optimiza-tion to improve the network model. A hybrid GA was gen-erated by standard GA and SWIFT, and used for global op-timization based on the trained catalyst model to improvethe rate of optimization. Amulti-training, multi-optimizationdesign strategy was introduced to the catalyst design. Themethod was applied for designing catalyst for methane ox-idative coupling. By six turn design, some better catalystswere designed, and C2 hydrocarbon yield of the best cata-lyst reached 27.78%, which was higher than that of previ-ous reported catalysts when no diluted gas was added. The

K. Huang et al. / Chemical Engineering Science 58 (2003) 81–87 85

Table 1Parts of typical optimal results

Catalyst Catalyst components (103 mol=g SiO2) Experimental results Network prediction Error

Na S W P Zr Mn XCH4 (%) SC2 (%) YC2 (%) XCH4 (%) SC2 (%) YC2 (%) XCH4 (%) SC2 (%) YC2 (%)

First optimal resultsFop1 3.4770 0.2212 0.3334 0.3376 0.9625 0.6120 32.84 62.50 20.52 54.11 66.00 35.71 −21:27 −3:50 −15:19Fop2 2.2845 0.7548 0.0000 0.3874 1.9756 0.4153 34.49 65.73 22.67 60.40 81.86 49.45 −25:91 −16:13 −26:78Fop3 2.4799 0.5301 0.3335 0.0001 1.4208 0.5452 27.39 61.83 16.94 79.56 65.49 52.10 −52:17 −3:66 −35:17Fop4 2.7616 1.2197 0.0947 0.0650 0.4746 0.6120 27.82 79.15 22.02 41.57 93.20 38.74 −13:75 −14:05 −16:72Fop5 4.0578 0.9261 0.3335 0.3004 0.9441 0.6120 30.52 60.78 18.55 39.69 88.44 35.10 −9:17 −27:66 −16:55Fop6 2.4982 0.6331 0.2937 0.2125 1.1559 0.3212 32.03 69.45 22.24 46.79 82.53 38.61 −14:76 −13:08 −16:37Fop7 2.4744 0.6416 0.0000 0.5956 1.8363 0.1404 32.33 62.73 20.28 39.87 85.38 34.05 −7:54 −22:65 −13:76Fop8 3.0291 1.1403 0.0775 0.0000 0.3924 0.6120 26.75 77.02 20.60 40.52 96.60 39.15 −13:77 −19:58 −18:54Fop91 3.0212 1.3133 0.1965 0.0002 0.2483 0.4802 26.58 84.78 22.53 55.40 95.00 52.63 −28:82 −10:22 −30:10

Second optimal resultsSop1 6.3095 1.4405 0.0000 0.7282 1.9474 0.6119 19.64 85.17 16.73 21.12 59.22 12.51 −1:48 25.95 4.22Sop2 8.9528 1.1815 0.2127 0.3882 2.0723 0.0000 14.28 77.69 11.09 48.91 65.12 31.85 −34:63 12.57 −20:76Sop3 3.1410 0.4261 0.0719 0.2149 1.0216 0.5112 22.33 78.76 17.59 31.25 69.45 21.70 −8:92 9.31 −4:12Sop4 4.9338 1.3753 0.2243 0.8674 0.3299 0.1155 21.02 78.67 16.54 49.33 66.99 33.05 −28:31 11.68 −16:51Sop5 2.0784 0.0928 0.0371 0.5295 1.7852 0.5189 29.65 63.48 18.82 37.21 84.72 31.52 −7:56 −21:24 −12:70Sop6 4.8367 1.1759 0.1919 0.9864 0.0522 0.3431 25.75 63.26 16.29 39.62 71.57 28.35 −13:87 −8:31 −12:06Sop7 2.2864 0.6806 0.0000 0.4614 1.9657 0.4063 32.02 76.19 24.40 45.61 73.73 33.63 −13:59 2.46 −9:23Sop8 3.8105 0.7429 0.3221 0.3522 1.9876 0.6120 34.65 69.54 24.10 42.91 88.69 38.05 −8:26 −19:15 −13:96Sop91 3.0841 0.0000 0.2544 0.5836 0.7755 0.6120 33.99 70.14 23.84 57.88 95.08 55.03 −23:89 −24:94 −31:19

Third optimal resultsTop1 5.9590 0.0001 0.2838 0.1853 0.8413 0.5437 19.52 69.80 13.62 32.78 66.04 21.65 −13:26 3.76 −8:02Top2 3.0330 1.3031 0.2132 0.0000 0.2700 0.4656 30.46 65.82 20.05 44.91 58.60 26.32 −14:45 7.22 −6:27Top3 4.1989 1.5849 0.0014 0.3412 2.8777 0.0022 10.98 76.25 8.37 20.74 81.03 16.80 −9:76 −4:78 −8:43Top4 9.8000 1.3417 0.0663 0.7731 0.6158 0.1759 15.22 48.06 7.31 28.69 66.61 19.11 −13:47 −18:55 −11:80Top5 6.2173 0.8743 0.0000 0.5755 0.4355 0.6113 15.12 64.77 9.79 29.76 74.37 22.13 −14:64 −9:60 −12:34Top6 5.7242 0.5636 0.0844 0.3793 0.2185 0.2960 21.35 77.39 16.52 13.59 66.12 8.99 7.76 11.27 7.54Top7 3.2473 0.3783 0.3058 0.0000 0.6640 0.6102 28.87 80.10 23.12 35.39 84.96 30.07 −6:52 −4:86 −6:94Top8 3.8125 1.3557 0.3221 0.0954 1.9753 0.5733 34.24 74.90 25.65 33.12 65.32 21.64 1.12 9.58 4.01Top9 5.6099 1.9135 0.2856 0.5101 1.5895 0.2838 36.29 71.84 26.07 43.39 72.45 31.44 −7:10 −0:61 −5:37Top10 3.8439 1.3509 0.3335 0.1909 1.9346 0.6119 32.72 74.09 24.24 53.66 85.13 45.69 −20:94 −11:04 −21:44Top11 3.2170 1.1631 0.0939 0.0000 0.4687 0.6120 21.63 83.12 17.98 40.28 95.67 38.53 −18:65 −12:55 −20:55Top121 4.3047 0.6761 0.3199 0.4118 0.8178 0.5435 36.23 71.30 25.83 72.39 86.87 62.89 −36:16 −15:57 −37:06

Fourth optimal resultsRop1 2.1927 0.7204 0.0005 0.3754 2.0448 0.2177 31.24 65.00 20.31 24.65 66.69 16.44 6.59 −1:69 3.87Rop2 4.0723 0.8982 0.1775 0.3827 0.8148 0.6119 31.51 65.30 20.58 34.21 70.50 24.12 −2:70 −5:20 −3:54Rop3 6.1672 1.5165 0.0158 0.7080 2.0258 0.5981 23.49 63.31 14.87 25.64 72.55 18.60 −2:15 −9:24 −3:73Rop4 5.4866 1.9349 0.3300 0.2082 1.2670 0.1984 25.49 69.63 17.75 25.91 93.18 24.14 −0:42 −23:55 −6:40Rop5 3.1521 0.4410 0.3309 0.0000 0.8420 0.6120 36.91 73.36 27.08 46.26 70.75 32.73 −9:35 2.61 −5:65Rop6 2.4246 0.5724 0.3335 0.1071 1.0760 0.4621 26.80 75.75 20.30 38.51 78.11 30.08 −11:71 −2:36 −9:78Rop7 3.1904 0.4686 0.3335 0.0000 0.7887 0.6097 23.50 79.81 18.76 34.63 82.91 28.71 −11:13 −3:10 −9:96Rop81 4.2654 1.0519 0.1347 0.3276 0.7182 0.5895 36.95 72.22 26.69 75.54 88.32 66.72 −38:59 −16:10 −40:03

Fifth optimal resultsHop1 4.9484 1.3632 0.2525 0.8584 0.3303 0.1576 26.17 67.48 17.66 24.06 85.73 20.63 2.11 −18:25 −2:97Hop2 5.6436 0.6048 0.1214 0.3606 0.7328 0.6119 28.62 71.11 20.35 30.04 70.39 21.14 −1:42 0.72 −0:79Hop3 5.7521 0.6694 0.1104 0.2987 0.7040 0.6120 35.65 69.38 24.73 40.94 69.92 28.62 −5:29 −0:54 −3:89Hop4 3.9335 1.8993 0.0000 0.0674 0.8956 0.5393 30.59 70.57 21.59 39.31 74.22 29.18 −8:72 −3:65 −7:59Hop5 4.9220 1.3330 0.2191 0.8730 0.6879 0.4189 33.55 68.98 23.14 33.40 78.79 26.32 0.15 −9:81 −3:17Hop61 1.9899 0.1730 0.0744 0.6128 1.9127 0.5262 27.14 61.14 16.59 37.23 84.96 31.63 −10:09 −23:82 −15:04

Sixth optimal resultsXop1 2.7380 0.9620 0.2470 0.0868 1.1243 0.3742 36.54 73.07 26.70 35.51 78.14 27.75 1.03 −5:07 −1:05Xop2 3.9939 0.9070 0.2393 0.1350 0.9559 0.4488 37.12 72.26 26.82 38.56 77.39 29.84 −1:44 −5:13 −3:02Xop3 2.0190 0.0362 0.1222 0.7544 1.8279 0.5170 28.62 52.06 14.90 27.93 60.27 16.83 0.69 −8:21 −1:93Xop4 2.8085 0.3921 0.2420 0.1941 1.2851 0.5239 32.32 62.11 20.07 33.69 65.86 22.19 −1:37 −3:75 −2:12Xop5 3.2816 0.1194 0.3295 0.4905 1.0588 0.6120 36.49 71.98 26.27 36.80 75.68 27.85 −0:31 −3:70 −1:58Xop6 5.6543 0.2900 0.1450 0.4653 0.8103 0.6112 35.22 71.72 25.26 36.32 73.53 26.71 −1:10 −1:81 −1:45Xop7 4.8677 1.3240 0.2149 0.8613 0.6736 0.4067 36.03 71.17 25.64 40.29 68.21 27.49 −4:26 2.96 −1:84Xop81 3.5397 1.7537 0.0000 0.0161 0.6808 0.4944 37.79 73.50 27.78 45.66 66.32 30.28 −7:87 7.18 −2:51

1Obtained by using hybrid GA.Reaction conditions: catalyst loading = 0:3 g; Pow rate = 40 cm3 min−1; CH4 = 75%; O2 = 25%; reaction temperature = 1069 K.

86 K. Huang et al. / Chemical Engineering Science 58 (2003) 81–87

Table 2Testing results of the 6-24-9-2 network model after six-turn training

Catalyst Catalyst components (103 mol=g SiO2) Experimental results Network prediction Error

Na S W P Zr Mn XCH4 (%) SC2 (%) XCH4 (%) SC2 (%) XCH4 (%) SC2 (%)

OCM T1 3.5691 1.7546 0.0000 0.0006 0.7461 0.5838 37.26 69.58 36.2035 67.9839 1.0565 1.5961OCM T2 3.6192 1.4076 0.0936 0.0000 1.9959 0.4994 25.05 39.95 27.0135 38.2932 −1:9635 1.6568OCM T3 2.0190 0.0362 0.1222 0.7544 1.8279 0.5170 28.62 52.06 27.3642 53.6143 1.2558 −1:5543OCM T4 4.2192 0.7547 0.1715 0.3772 0.0000 0.6120 28.64 69.42 26.3852 71.1043 2.2548 −1:6843OCM T5 5.0423 0.4298 0.2279 0.4022 0.0000 0.5810 10.74 77.11 6.8776 75.7554 3.8624 1.3546OCM T6 5.3361 1.8142 0.3235 0.4781 1.3863 0.0001 15.59 79.77 14.4331 81.3462 1.1569 −1:5762OCM T7 2.0649 0.0123 0.1810 0.0000 1.4280 0.5332 18.85 69.56 21.8023 68.3043 −2:9523 1.2557OCM T8 3.5400 1.7683 0.0016 0.0001 0.7037 0.4940 5.17 90.52 3.8042 93.1992 1.3658 −2:6792

Reaction conditions: catalyst loading = 0:3 g; Pow rate = 40 cm3 min−1; CH4 = 75%; O2 = 25%; reaction temperature = 1069 K.

Table 3Several OCM multi-component catalysts in which yield of C2 are greater than 25%

No. Catalyst components (103 mol=g SiO2) Experimental results

Na S W P Zr Mn XCH4 (%) SC2 (%) YC2 (%)

1 2.4240 0.5546 0.3309 0.0932 1.0827 0.4463 30.67 83.26 25.542 3.5691 1.7546 0.0000 0.0006 0.7461 0.5838 37.26 69.58 25.933 4.2654 1.0519 0.1347 0.3276 0.7182 0.5895 36.95 72.22 26.694 5.6099 1.9135 0.2856 0.5101 1.5895 0.2838 36.29 71.84 26.075 3.1521 0.4410 0.3309 0.0000 0.8420 0.6120 36.91 73.36 27.086 2.7380 0.9620 0.2470 0.0868 1.1243 0.3742 36.54 73.07 26.707 3.9939 0.9070 0.2393 0.1350 0.9559 0.4488 37.12 72.26 26.828 3.5397 1.7537 0.0000 0.0161 0.6808 0.4944 37.79 73.50 27.789 3.8125 1.3557 0.3221 0.0954 1.9753 0.5733 34.24 74.90 25.6510 4.8677 1.3240 0.2149 0.8613 0.6736 0.4067 36.03 71.17 25.6411 4.3047 0.6761 0.3199 0.4118 0.8178 0.5435 36.23 71.30 25.8312 3.2816 0.1194 0.3295 0.4905 1.0588 0.6120 36.49 71.98 26.2713 5.6543 0.2900 0.1450 0.4653 0.8103 0.6112 35.22 71.72 25.2614 4.1065 0.9661 0.3167 0.5927 1.7403 0.6120 36.25 73.76 26.7415 1.8921 0.7283 0.0545 0.1324 0.0000 0.6120 35.99 74.40 26.78

Reaction conditions: catalyst loading = 0:3 g; Pow rate = 40 cm3 min−1; CH4 = 75%; O2 = 25%; reaction temperature = 1069 K.

Application showed that the new method is highly e8cientand universal.

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