doi: 10.1002/cctc.201100186 statistical analysis of …...doi: 10.1002/cctc.201100186 statistical...

DOI: 10.1002/cctc.201100186

Statistical Analysis of Past Catalytic Data on OxidativeMethane Coupling for New Insights into the Compositionof High-Performance CatalystsUlyana Zavyalova,[a] Martin Holena,[b, c] Robert Schlçgl,[a] and Manfred Baerns*[a]

Introduction

Catalytic coupling of methane

The oxidative coupling of methane (OCM) comprises heteroge-neous catalytic and homogeneous noncatalytic processes forconverting methane mainly into C2 hydrocarbons [Eqs. (1) and(2)]:

2 CH4þ0:5 O2 ! C2H6þH2O ð1Þ

C2H6þ0:5 O2 ! C2H4þH2O ð2Þ

Besides these two selective reactions, nonselective oxidationof the hydrocarbons to COx takes place. There is a unanimousopinion that the initial step of the reaction is the formation ofmethyl radicals, which have been proven to exist.[1, 2] Once theformation of the radicals is initiated on a catalytic surface, gas-phase reactions are believed to proceed to a large extent. Theradicals should recombine selectively to ethane, which is thendehydrogenated to ethylene oxidatively or possibly also ther-mally. Methoxy species formed on the surface or in the gasphase finally react to carbon dioxide.

In particular, at temperatures from 950 to 1200 K typical ofthe OCM reaction, homogeneous processes mainly control thecoupling reaction.[3] Hence, at very high temperatures, theyield of hydrocarbons is limited irrespective of the amount ofcatalytically active sites and hence methyl radicals. Therefore, ahigh-performance OCM catalyst should not only initiate theformation of CH3 radicals at lower temperatures but also sup-press nonselective surface oxidation of methane and hydrocar-bon products to carbon dioxide. The required multifunctionali-ty of a catalyst could be the reason why a multitude of oxidesolids with different solid-state properties show activity in theOCM reaction. The catalytic materials can be classified into

four groups: 1) reducible metal oxides, 2) nonreducible metaloxides, 3) halogen-containing oxide materials, and 4) solid elec-trolytes.[4]

Since the pioneering works of Keller and Bhasin,[5] Baernsand Hinsen,[6] and Ito and Lunsford,[7] a huge body of data onOCM catalysts and their performance have been accumulated.The comprehensive literature search in databases provided byCAplus (American Chemical Society), Web of Science (ThomsonReuters), and Science Direct (Elsevier) resulted in more than2700 research articles and reviews on the OCM reaction. In ad-dition, about 140 patents on the OCM reaction have been pub-lished in the last 30 years; this is illustrated in Figure 1.

About one third of the references available from the litera-ture focus on the intrinsic reactions between reactants and cat-alyst surfaces over hundreds of different catalytic materials andnumerous metal or metal-oxide loadings. Most of the initial ex-

A database consisting of 1870 data sets on catalyst composi-tions and their performances in the oxidative coupling ofmethane was compiled. For this goal, about 1000 full-text ref-erences from the last 30 years have been analyzed and about420 of them, which contained all the necessary information,were selected for the data extraction. The accumulated datawere subject to statistical analysis : analysis of variance, correla-tion analysis, and decision tree. On the basis of the results, 18catalytic key elements were selected from originally 68 ele-ments. All oxides of the selected elements, which positively

affect the selectivity to C2 products, show strong basicity. Anal-ysis of binary and ternary interactions between the selectedkey elements shows that high-performance catalysts aremainly based on Mg and La oxides. Alkali (Cs, Na) and alkaline-earth (Sr, Ba) metals used as dopants increase the selectivity ofthe host oxides, whereas dopants such as Mn, W, and the Clanion have positive effects on the catalyst activity. The maxi-mal C2 selectivities for the proposed catalyst compositionsrange from 72 to 82 %, and the respective C2 yields range from16 to 26 %.

[a] Dr. U. Zavyalova, Prof. Dr. R. Schlçgl, Prof. Dr. M. BaernsDepartment of Inorganic ChemistryFritz-Haber Institute of Max-Planck SocietyFaradayweg 4-6,d-14195 Berlin (Germany)Fax: (+ 49) 30-8413-4401E-mail : baerns@fhi-berlin.mpg.de

[b] Dr. M. HolenaLeibniz-Institute for Catalysis at Rostock UniversityAlbert-Einstein-Strasse 29a,D-18059 Rostock (Germany)

[c] Dr. M. HolenaInstitute of Computer ScienceAcademy of Sciences of the Czech RepublicPod vod�renskou vez� 2, CZ-18200 (Prague)

Supporting information for this article is available on the WWW underhttp://dx.doi.org/10.1002/cctc.201100186 as a pdf or, alternatively, as anMS Excel file underwww.fhi-berlin.mpg.de/acnew/department/pages/ocmdata.html

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perimental work on catalyst screening was done from 1985 to1995 in laboratory-scale catalytic fixed-bed reactors. A greatdeal of effort has been devoted to overcome the hurdle ofeconomic constraints of low yield of C2 hydrocarbons, Y(C2),caused by two reasons: first, by catalysts, which partly favornonselective oxidation steps on the solid surface and subse-quently by methoxy species in the gas phase; and second, bythe loss of C2 hydrocarbons selectivity S(C2) due to the highconcentrations of the gas-phase oxygen needed to achievehigh degrees of methane conversion. Eventually, the inabilityto discover a selective catalyst led to a gradual loss of interestin the OCM reaction. In the mid-1990s, research activity in thisarea began to decline significantly, as evidenced by the de-creasing number of patents filed and peer-reviewed publica-tions. Lately, many new concepts on the reactor and processdesign have been proposed for suppressing the detrimentaleffect of high oxygen concentration.[4, 8–10] Although an upperbound of Y(C2) of about 25 % has been predicted by Yinget al.[11] on the basis of assumed fundamental kinetics bychanging the rate constants for all reaction steps, at least 24different catalysts providing Y(C2)�25 % have been reported;such catalysts with corresponding references are shown inFigure 2. Some of these catalysts are close to the target for theindustrial application of the OCM process: single-pass conver-sions of methane of at least 30 % and S(C2) of around 80 %.

Although extensive research has been done on the OCM re-action in the last 30 years, many fundamental aspects, whichdetermine the choice of catalytic components, for example,distribution between surface-to-gas phase reactions, the partic-ipation of nonequilibrium sites in the OCM process, as well asthe essential features for an optimal catalyst compositionremain unknown.

From an economic point of view on catalyst research anddevelopment in the OCM, the question about key componentsof a catalyst that lead to high C2 selectivity has to be first an-

swered before further fundamental work can be targeted on aspecific group of catalysts for their further optimization.

Database on the catalytic OCM reaction

From many selectivity- and activity-determining factors, thechemical composition of a catalyst is certainly of highest im-portance. Therefore, for assessing and comparing the relation-ships between the composition and performance of OCM cata-lysts, only references with quantitative data on the elementalcomposition of the catalyst tested in a fixed-bed reactor withfully described reaction conditions have been selected. Quanti-tative information about reactant partial pressures, operatingtemperature, total pressure, contact time, as well as degrees ofreactant (methane, oxygen) conversion and selectivities of thereaction products have been considered as necessary for theevaluation and comparison of the literature data. For the vari-ous data sets, the elements were grouped into the domains ofactive components, supports, or promoters as defined by therespective authors. As a rule, supports are defined as inert ma-terials on which the catalytic components are deposited. Alldata are available in the Supporting Information as a pdf andfrom the authors website in MS Excel format; the assumptionhad to be made that the published data used for the statisticalanalysis are reproducible within the frame of experimentalaccuracy.

Surprisingly, only a relatively small amount of references thatdeal with catalyst development were usable for the data as-sessment procedure. According to the applied criteria, 343 ref-erences, which include research articles, reviews, PhD thesis,scientific reports, conference proceedings, and 78 patents,have been selected for the extraction of data in the OCM data-base (see Table 1). Till January 2011, the OCM database con-tained 1868 data sets (with collection of data on catalyst com-position and its performance presented in a tabular form) oncatalytic tests in the OCM reaction, which have been evolvedfrom 421 references.

Figure 1. Chronological distribution of a) research articles and b) patents re-lated to the OCM reaction (analysis by SciFinder).

Figure 2. Elemental compositions of OCM catalysts with Y(C2)�25 % report-ed in the literature. All the catalysts were tested in a fixed-bed reactor in theco-feed mode under atmospheric pressure at temperatures from 943 to1223 K, p(CH4)/p(O2) = 1.7–9.0, and contact times from 0.2 to 5.5 s.

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M. Baerns et al.

The data collected in the OCM database include data on cat-alytic materials that comprise a total of 69 different elementsthat are catalytically active. The sources from which those datawere extracted have been presumably, in general, motivatedby the search for the best-performing catalyst. Therefore, theyare not equally distributed among the 69 elements, nor amongdifferent values of each of them. Instead, they are biasedtoward areas in which the authors expected the best catalysts.

For convenience, the references and corresponding datasets are listed chronologically. Different types of literature pub-lished within 1 year are arranged alphabetically in the follow-ing sequence: research articles>conference proceedings>PhD thesis>patents. The data are logged within three sectionsof input variables, namely, elemental composition of catalysts,preparation techniques, and applied process parameters, andone section with output data on the catalytic performance ofthe catalytic materials used. The arrangement is illustrated inFigure 3.

Elemental compositions of catalysts include cations andanions of the active component, promoters, and supports. Anactive component of a catalyst is considered as “host oxide,”which may incorporate minor concentrations of various othercomponents designated as dopants. Catalyst compositions areexpressed in molar fractions. Oxygen was not included in theelemental composition, because in most cases the exactoxygen stoichiometry is unknown under conditions of theOCM reaction. Similarly, easily decomposing anions, such as hy-droxides and nitrates, were considered only when the oxidicform of the catalytic component was likely to be essential atreaction temperatures. When elements such as F, Cl, B, and Sare part of the catalyst composition, they are logged into theOCM database as anions of active components. In other cases,they are defined as promoters assisting the catalytic process.

As a rule, inert materials, for ex-ample, oxides of Al, Si, Ce, andPr, are used as supports. Howev-er, in some cases, metal oxidesactive for the OCM reaction, forexample, oxides of Nd and Sm,were also defined as supportmaterials by some authors.

Five preparation techniques,namely, thermal decomposition, precipitation, impregnation,sol–gel, and spray pyrolysis, had been applied. Due to the lackof data, the stability of the catalysts and their phases was notconsidered as the criterion. Inclusion of important catalystproperties, such as ion and electronic conductivity, acidity and/or basicity, electronegativity, crystal and pore sizes, and specificsurface area, in the database was also not possible, because ofthe lack of such information in most references considered.However, this might be done in the future for a limitednumber of key compounds identified by statistical means.

Against the above background, statistical means have beenapplied in the present work to a huge body of past experimen-tal data for identifying the key catalytic components and theircombinations needed for the high values of S(C2) and Y(C2).For quantifying the effect of various fractions of elements onthe catalytic performance, analysis of variance (ANOVA), corre-lation analysis, and regression tree analysis were applied. Itwas anticipated that the methodology used in the presentwork should have an impact on the improvement of OCM cat-alysts for which a broad basis of preceding work exists. The ex-perimental validation of the results already in progress will becommunicated at a later stage.

Results

Assessment of performance data on single oxides

For identifying the key components that contribute to S(C2)and Y(C2), first the catalytic performances of single unsupport-ed oxides without any promoters were compared from 237data sets of single-oxide catalysts. For illustration, cations ofsuch unsupported single oxides are presented in Figure 4 inthe form of a periodic table as a matter of convenience, in

which their S(C2) ranges areindicated.

For 19 single unsupportedoxides, at least three sets of datafor their performance are avail-able in the OCM database. Inthis way, the mean values ofY(C2) and S(C2) could be derivedfor each of them, as shown inFigure 5.

The unpromoted oxides of thealkaline-earth metals are activein the OCM reaction. In particu-lar, Sr, Ba, and Ca exhibit selec-tivities ranging from 50 to 70 %

Table 1. Overview of the considered literature on the OCM reaction.

Literature search on OCM[a] Science articles, reviews, PhD theses Patents Total

Considered abstracts 2706 136 2842Selected full texts related to catalyst development 870 94 964Selected full texts suitable for the data extraction 343 78 421

[a] State for January 2011.

Figure 3. Data logging in the OCM database.

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Oxidative Methane Coupling

and yields from 8 to 9 %. Among the lanthanides, La, Sm, Nd,Eu, Gd, and Yb are compounds that lead to selectivities from50 to 60 % and yields from 8 to 11 %. Most single transition-metal oxides are generally active only for nonselective oxida-tion reactions. However, oxides based on Pb, Sb, Bi, Mn, and Yshow an average selectivity of 45–65 % and yields of 2–9 %.Needless to say, the catalytic performance of single-oxide cata-lysts is influenced by their solid-state properties, which in turnare affected by the synthesis techniques applied for their prep-aration. It is necessary to note that the performance datashown in Figures 4 and 5 have been obtained under quite dif-ferent reaction conditions: temperatures from 600 to 1200 K;ratios of p(CH4)/p(O2) from 0.8 to 16; contact times from 0.2 to18 s; the resulting degree of oxygen conversion amountedusually from 80 to 99 %, occasionally being significantly lower.Moreover, the various single oxides were quite different intheir numbers, which provide catalytic performance data.Oxides, based on Ba, Ca, La, Mg, and Sm, have been quite ex-tensively studied according to the literature, whereas there areonly a few data on the other single metal oxides. Therefore,the mean values of S(C2) and Y(C2) in Figure 5 can be usedonly as a rough indication for well-performing OCM catalysts.

Statistical analysis of performance data of multicomponentcatalysts

The complete OCM database contains 1868 catalyst-perfor-mance data sets composed of 68 different elements: 61 cationsand 7 anions (Cl, F, Br, B, S, C, and P) except oxygen. Thereby,almost all possible combinations of the 68 elements with amultitude of different fractions are available. For comparison,the statistical analysis was performed on the complete 1868data sets as well as on 317 data sets with the so-called “well-performing” catalysts, defined as catalysts that exhibit S(C2)�50 % and Y(C2)�15 %.

The numbers of catalysts that contain a particular elementor, in other words, the frequency of its occurrence within thecomplete data and within the data on well-performing cata-lysts is shown in Figure 6.

In literature, alkaline-earth metals with an alkali dopant, inparticular magnesia doped with lithium, have been most fre-quently studied. From the 10 elements presented in theFigure 6, 6 elements with the highest frequency of occurrenceare alkaline-earth and alkali metals disregarding La, Mn, and Cl.Most probably, a human factor has played a vital role in thedesign of the experiments. That is to say, scientists might havebeen induced in using well-performing catalysts by the guid-ance of prior published data. The frequency of the occurrenceof La, Ba, Sr, Cl, Mn, and F within the 317 well-performing cata-lysts is higher, whereas the frequency of the occurrence of Caand K is lower as compared with that within the complete setof 1868 data sets.

To identify the highly significant elements of the catalysts,multiway ANOVA (analysis of variance) for main effects wasperformed. The results are shown in Table 2, which lists theachieved significances of the presence of individual elements(without elements of support) for Y(C2) and S(C2) in all datasets and in the well-performing catalysts with S(C2)�50 % andY(C2)�15 %. The quantitative statistical analysis of the nonlin-ear relationships shows an influence of varying the values ofindividual fractions of elements on the variance of Y(C2) orS(C2).

The significant elements for the 317 well-performing cata-lysts with S(C2)�50 % and Y(C2) � 15 % differ from the signifi-

Figure 4. S(C2) of various unsupported single oxides tested in the OCM reac-tion in the co-feed mode.

Figure 5. Mean values of Y(C2) and S(C2) obtained on unsupported singlemetal oxides tested in the co-feed mode under atmospheric pressure.

Figure 6. Frequency of occurrence (F) of elements for 317 well-performingcatalysts with S(C2)�50 % and Y(C2)�15 % and for all 1868 data sets. Foreach group, only 10 elements with the highest frequency of occurrence aredepicted.

M. Baerns et al.

cant elements identified for all1868 available experimental datasets. It should be underlinedthat the achieved significancelevel reflects only the influenceof various elements on the var-iance of S(C2) and Y(C2) withoutaccounting for a positive or neg-ative effect on the catalytic per-formance. Moreover, the statis-tics on the significant elementsidentified for the well-perform-ing catalysts (Yb, Mo, B, Ga, Sm,and Nb) is not very representa-tive, because there are fewerthan 5 data sets for each ofthese components within the317 data sets.

To establish correlations be-tween the fractions of individualelements and S(C2) and Y(C2), acorrelation analysis was per-formed. Correlations with rela-

tively high positive values of linear and Spearman’s correlationcoefficients are shown in Figure 7. Their maximal value 1would be achieved if the random variables for fractions of ele-ments and S(C2) and Y(C2) are increasing linear functions (linearcorrelation) or increasing monotone functions (general correla-tion) of each other.

According to the analyses, elements with positive values (>0.01) of the linear and Spearman’s coefficients of correlationfor both S(C2) and Y(C2) are Li, Na, Ca, Mg, Sr, Ba, La, Nd, Re, Cs,Bi, Mo, Yb, Ga, F, and B.

Pb and S have positive correlation with S(C2) but negativecorrelation with Y(C2), and on the contrary, Ti, W, Mn, Ce, andSm correlate positively with Y(C2) but negatively with S(C2).The adverse effects may have been caused by the interrela-tionships between the degree of methane conversion andboth S(C2) and Y(C2).

For the elements Al, Co, Sn, Zr, Sb, Nb, Mo, Ag, V, Cu, Cr, Pd,as well as K, Pr, C, and P, the linear and Spearman’s correlationcoefficients are negative for both Y(C2) and S(C2) (not shown inFigure 7). Notably, the coefficients of all the established corre-lations have values less than 0.5; that is, the relations are to beconsidered weak.

The results on the main effects as obtained by ANOVA (seeTable 2) and by the correlation analysis (Figure 7) can be sum-marized as follows:

· elements that correlate positively with both Y(C2) and S(C2)are alkali metals (Li, Na, Cs), alkaline-earth metals (Sr, Ba,Mg, Ca), as well as La, some other metals (Bi, Mo, Ga, Nd,Re, Yb), and fluorine;

· elements that correlate positively only with Y(C2) are Cl, W,Ti, Mn, Y, and Sm;

· elements that correlate negatively with both Y(C2) and S(C2)are Ag, V, K, and C (derived from carbonate species).

Table 2. Significant elements defined by ANOVA of Y(C2) or S(C2) for elements present in all catalysts and inthe well-performing catalysts.

ANOVA for all catalysts ANOVA for well-performing catalysts (S(C2)�50 %, Y(C2)�15 %)Element Significance

levelElement Significance

Li 3.36 � 10-28 Li 4.62 � 10-43 Cs 7.04 � 10-3 Yb 4.99 � 10-8

Na 4.13 � 10-24 Na 2.18 � 10-28 Bi 1.06 � 10-2 Mo 7.68 � 10-7

Sr 4.01 � 10-14 La 9.76 � 10-25 B 1.20 � 10-2 Ga 3.67 � 10-6

C 6.99 � 10-10 Ba 1.40 � 10-24 Mo 1.69 � 10-2 Cl 2.13 � 10-2

Ba 4.20 � 10-8 Sr 1.31 � 10-11 Ga 1.84 � 10-2 Sr 3.22 � 10-2

Ag 7.92 � 10-7 Ca 7.14 � 10-11 Re 2.52 � 10-2 Mg 3.36 � 10-2

Ca 1.22 � 10-6 F 7.40 � 10-10 W 3.14 � 10-2 Sm 9.02 � 10-2

Ti 1.38 � 10-6 C 1.19 � 10-9 F 5.97 � 10-2 Nb 9.74 � 10-2

Re 1.64 � 10-6 Sm 7.31 � 10-9 Mg 7.42 � 10-2

Pb 4.93 � 10-6 Nd 4.28 � 10-8 La 8.30 � 10-2

P 5.90 � 10-6 Zn 8.32 � 10-7

V 1.24 � 10-5 Mg 8.57 � 10-7

Sn 4.41 � 10-5 Mn 2.00 � 10-7

W 6.04 � 10-7

Ag 2.07 � 10-6

K 7.11 � 10-6

Y 1.42 � 10-5

Ga 6.46 � 10-5

Figure 7. Positive correlations between fractions of individual elements andS(C2) and Y(C2).

For the identification of ele-ments that contribute to thebest catalytic performance, thequantitative values of Y(C2) andS(C2) were approximated with apiecewise-constant function asapplied in regression tree analy-ses. The trees for the regressionof S(C2) and Y(C2) as a functionof the presence of individual ele-ments in the well-performingcatalysts are shown in Figure 8.

The paths from the root tothe leaf describe the conditionsfor the average values of Y(C2) orS(C2) in the presence (non-crossed-out elements) or ab-sence (crossed-out elements) ofan individual element. Data wererecursively split by using valuesthat lead to maximally homoge-neous branches. Splitting wasstopped when a further splitwould lead to leaves with lessthan 5 % of the considered data.In our case, this leads to thelowest leaf size of 15 data sets.

In summary, the results showthat the main groups of catalyststhat comprise the well-perform-ing materials are based on alkaliand alkaline-earth metals (Li, Na,Mg, Sr, Ba, Ca) as well as on La,W, and F and Cl anions.

The group of well-performingcatalysts has an overall meanS(C2) = 65 % and mean Y(C2) =

19.5 %. From the obtained rulesabout the data, it can be statedthat the mean value of S(C2) ishigher than the mean valueS(C2) = 65 % for the whole group of the catalysts in the pres-ence of the following elements:

· mean S(C2) = 69 % in the presence of Mg or promoters Cl, B,and S;

· mean S(C2) = 68 % in the presence of the combinationLa*Sr ;

· mean S(C2) = 66 % in the presence of W.

The mean value of Y(C2) is higher than the mean valueY(C2) = 19.5 % for the group of well-performing catalysts in thepresence of the following elements:

· mean Y(C2) = 21.7 % in the presence of promoters such asCl, B, and S;

· mean Y(C2) = 20.9 % in the presence of Al or Si oxide sup-ports ;

· mean Y(C2) = 20.3 % in the presence of Li.

In addition, the nature of promoters and supports apparent-ly plays an important role. Therefore, the catalytic key ele-ments selected on the basis of the presented statistical resultscan be divided into three major groups with respect to theirfunction in a catalyst :

· main components: Sr, Ba, Mg, Ca; La, Nd, Sm; Ga, Bi, Mo, W,Mn, and Re;

· dopants: Li, Na, Cs;· promoters : F, Cl.

Mn was selected as the catalytic key element potentiallysuitable for the design of high-performance OCM catalysts be-

Figure 8. Regression trees for the dependencies of a) S(C2) in percent and b) Y(C2) in percent (red values) on thepresence (non-crossed-out elements) or absence (crossed-out elements) of various elements in the well-perform-ing catalysts. Decoding of the promoter numbers: 1, B; 3, Cl ; 4, Cl+B; 5, F; 7, S; support numbers: 1, Al ; 2, Al+Si ;3, Ce; 8, Nd; 9, Pr; 10, Si ; 12, Sm.

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cause it was identified as ahighly significant element withrespect to the variance of Y(C2)and it has a positive correlationwith Y(C2). In addition, 11 fromthe 24 reported catalysts withY(C2)�25 % are based or includeMn (underlined in Figure 2). Reand Ga were also selected as sig-nificant elements with positivelinear and Spearman’s coeffi-cients with both Y(C2) and S(C2).However, it should be men-tioned that there are only 3 datasets on Re-containing catalystsand only 1 for a Ga-containingmaterial in the whole OCM data-base.

Analysis of interactions be-tween catalytic key compo-nents

Since there are not sufficientdata to analyze all possible com-binations between 68 elementsin the OCM database, interac-tions between only 18 selectedkey elements (i.e. , Sr, Ba, Mg, Ca;La, Nd, Sm; Ga, Bi, Mo, W, Mn,Re; Li, Na, Cs; F, Cl) were tested by ANOVA. Hereby, interactions(indicated by *) between the selected key elements significantfor the variance of Y(C2) and S(C2) were identified within all cat-alysts and within the well-performing ones; the results arelisted in Table 3.

The identified significant binary and ternary interactions canbe classified into the following groups according to the chemi-cal nature of their components [Note: Here * stands for inter-action]:

a) alkaline-earth * transition metal (Mn, Mo, or W): i.e. , Mg*W,Ca*W, Mg*Mn, Ca*Mn, Mg*Mo, Sr*Mo;

b) alkali (Na or Cs) * alkaline-earth metal, La, or Mn: i.e. ,Na*La; Na*Mg, Na*Ca, Na*Sr, Cs*Mg, Na*Mn;

c) alkali metal * W: i.e. , Na*W, Li*W, Cs*W;d) two alkaline-earth metals : i.e. , Ca*Ba, Ca*Sr, Ba*Sr, Mg*Sr,

Mg*Ba;e) alkaline-earth metals * Cl or Mn * Cl: i.e. , Mg*Cl, Ba*Cl,

Mn*Cl, Ca*Cl ;f) La*Sr ;g) binary combinations of the groups (a) or (d) with dopants

such as Na, Li, or Cl : i.e. , Mg*Ba*Cl, Na*Mg*W, Na*Ca*Sr,Li*Ba*Sr, Na*Mg*Mn.

To find the best combinations of elements having a poten-tial for the design of a high-performance OCM catalyst, someof the significant combinations listed above were excluded

from further consideration because of low performance. Suchcombinations do not belong to the well-performing catalysts(Ca*W, Ca*Mn, Sr*Mo, Mg*Ba*Cl, Na*Ca*Sr), or they occur inonly one well-performing catalyst: (Mg*W, Mg*Mo, Na*Sr, Li*W,Cs*W, Ca*Sr, Na*Mg*W, Li*Ba*Sr).

To elucidate whether the 17 selected significant combina-tions that occur among more than one well-performing cata-lysts have a positive or negative effect on the catalytic perfor-mance, the mean values of Y(C2) and S(C2) were compared incases of the presence and absence of these combinations.Figure 9 shows the mean values of Y(C2) and S(C2) calculatedamong those catalysts that contain the respective combinationof elements (full columns) and among those that do not (slash-ed columns).

The differences between the mean values of Y(C2) and S(C2)in the presence and absence of the 14 combinations that con-tribute positively to Y(C2) or S(C2) are shown in Figure 10.

The following results were derived:

· combinations that contribute positively to S(C2): Cs*Mg>Mg*Cl = Mg*Ba>Mg*Mn = Na*Mg*Mn>Na*Mg>La*Sr>Na*W;

· combinations that contribute positively to Y(C2): Mn*Cl>Ba*Cl>Ba*Sr = Na*La>Na*Mn>Ca*Cl>Na*W;

· combinations that contribute negatively to both Y(C2) andS(C2): Mg*Sr, Ca*Ba, Na*Ca.

Table 3. Significant binary and ternary interactions between the selected key elements identified by usingANOVA on Y(C2) and S(C2) within all catalysts and within the well-performing catalysts.

ANOVA for all catalysts ANOVA for well-performing catalysts with S(C2)�50 %and Y(C2)�15 %

S(C2) Y(C2) S(C2) Y(C2)Interaction Significance

levelInteraction Significance

Binary interactionsNa*W 3.75 � 10-6 Mg*Mo 5.28 � 10-6 Na*La 3.70 � 10-3 Na*La 5.19 � 10-3

Na*Mg 1.35 � 10-3 Mg*Mn 2.70 � 10-5 Mg*W 3.86 � 10-3 Li*W 1.65 � 10-2

Na*Ca 1.79 � 10-3 Sr*Mo 5.67 � 10-4 Ca*W 4.32 � 10-3 Sm*Bi 9.23 � 10-2

Mg*W 3.86 � 10-3 Mg*W 7.01 � 10-4 Ca*Ba 5.85 � 10-3

Ca*W 4.32 � 10-3 Mg*Cs 7.68 � 10-4 Mg*Mn 8.56 � 10-3

Na*Sr 5.76 � 10-3 Ba*Cl 1.08 � 10-2 Mg*Mo 1.15 � 10-2

Ca*Ba 5.85 � 10-3 W*Cs 1.28 � 10-2 Ca*Sr 2.32 � 10-2

Ba*Cl 6.40 � 10-3 Ca*Sr 1.85 � 10-2 Ba*Sr 3.87 � 10-2

Mg*Mn 8.56 � 10-3 Mn*Cl 1.86 � 10-2

Mg*Mo 1.15 � 10-2 Sr*La 2.16 � 10-2

Mg*Cl 1.44 � 10-2 Na*La 2.23 � 10-2

Ca*Sr 2.32 � 10-2 Ca*Mn 2.64 � 10-2

Na*Mn 3.49 � 10-2 Mg*Sr 2.95 � 10-2

Ba*Sr 3.87 � 10-2 Na*Mn 3.33 � 10-2

Mg*Ba 3.51 � 10-2

Na*W 3.93 � 10-2

Na*Ca 4.03 � 10-2

Ca*Cl 4.67 � 10-2

Ternary interactionsMg*Ba*Cl 1.02 � 10-3

Na*Mg*W 3.04 � 10-3

Na*Ca*Sr 1.07 � 10-2

Li*Ba*Sr 2.07 � 10-2

Na*Mg*Mn 3.80 � 10-2

The mean values of Y(C2) and S(C2) presented in Figure 8-10were calculated not accounting for the other elements withinthe catalysts. The data sets that contain the significant combi-nations of the elements that contribute positively to Y(C2) orS(C2) were analyzed in more details ; the results are summarizedin Table 4.

Some particular catalyst compositions with the highestmean values of Y(C2) and S(C2) were selected from the availableexperimental data based on the identified combinations of ele-ments given in Table 5.

Each of these eight catalyst compositions has at least 3 datasets in the OCM database. Ranges of appropriate proportionsof elements in these catalysts are shown in Table 5. Notably, allthese catalysts were tested in the OCM reaction under atmos-

pheric pressure; the degrees of oxygen conversions were ap-proximately 85–99 %. The applied operating conditions are asfollows: temperatures from 973 to 1153 K; ratios of p(CH4)/p(O2) from 2 to 8; contact times from 0.1 to 7 s.

Except La*Mg*Ba catalysts obtained by thermal decomposi-tion, the other high-performance catalysts were prepared inthe majority of the cases by using the impregnation technique.

Despite the differences of the reaction conditions and of thevarious preparation methods as documented in the database,we believe that the simplification of not accounting for thesecircumstances may be acceptable as a first approximation.

From the multicomponent catalysts, the main components,with a potential for the design of a high-performance OCMcatalyst, were selected. The quantitative values of their propor-tions were approximated with a piecewise-constant function,as illustrated in Figure 11. Molar fractions (x) of the main com-ponents with positive effect on the mean value of S(C2) withinthe well-performing catalysts are given as follows:

· 78 %<x(Mg)<90 %!mean S(C2) of 71–77 %;· x(La)>67 %!mean S(C2) = 75 %;· x(Mn)>21 %!mean S(C2) = 67 %.

Molar fractions of the main components with positive effecton the mean value of Y(C2):

· x(Mn)>22 %!mean Y(C2) = 24.5 %;· 48 %<x(La)<89 %!mean Y(C2) of 19.2–19.9 %;· 76 %<x(Mg)<89 %!mean Y(C2) of 19.6–21.3 %;· x(W)<16 %!mean Y(C2) = 19.8 %;· x(Ba)>30 %!mean Y(C2) = 20.1 %;· x(Sr)<2.5 %!mean Y(C2) = 20.4 %.

Figure 9. Mean values of a) S(C2) and b) Y(C2) in the presence (full) and ab-sence (slashed) of the significant combinations of the key elements occur-ring in the well-performing catalysts.

Figure 10. Contributions to the mean values of S(C2) (gray) and Y(C2) (black)in the presence of the significant combinations in the well-performing cata-lysts. The combinations that contribute negatively to both Y(C2) and S(C2)are not shown.

M. Baerns et al.

Discussion

Statistical analysis for identifying compositions of high-per-formance catalysts from a large data pool of catalytic data

The purpose of the data analysis was to reveal empirical evi-dence on the catalytic performance on catalyst compositionand interactive properties among the single components ofthe analyzed variables and relationships between them. In par-ticular, the analyses revealed evidence of the following results:

· the presence of certain elements and their combinationssignificantly increases S(C2) and/or Y(C2) as identified bytheir variance (ANOVA);

· the extent to which the proportions of certain elements cor-relate with S(C2) or Y(C2), and whether this correlation ispositive or negative (correlation analysis) ;

· the combinations of the presence or absence of elementsshow the highest influence on changes in the average S(C2)or Y(C2) ; for certain elements, the combinations of their pro-portions also show such influence (decision trees).

Fundamental features of well-performing catalysts

Information from the presentdata analysis as well as from fun-damental studies lead to the fol-lowing main physicochemicalproperties of solid materials,which appear to be mostly re-quired for high-performanceOCM catalysts :

· intrinsic basicity;· p-type semiconductors with a

bandgap of 5–6 eV;·oxygen–anion conductivity ; oxygen vacancies due to metal

impurity ions and interstitial sites;· fast exchange rates between atomic oxygen species on the

surface and bulk oxygen-anion vacancies;· minimal rates of catalyst reoxidation as compared with

those of the OCM reaction;· low sticking coefficients of CH3 radicals on the catalyst sur-

face.[3, 19, 35–38]

In addition, the importance of structural defects of the cata-lytic materials for generating selective and nonselectiveoxygen species has been repeatedly reported for the OCM re-action. For these dependencies, reference is made to our earli-er studies.[35, 39]

The present work cannot contribute to this discussion direct-ly, but it is certainly helpful in understanding the main prereq-uisites, which should be an important feature besides catalystcompositions and which may provide guidelines for an ad-vanced design for high-performance OCM catalysts. For exam-ple, the catalytic key compounds that positively affect S(C2)mainly include Mg, La, Sr, and Ba oxides, as well as Li, Na, andCs dopants, which were identified by the various data analysismethods. All these components are strongly basic; that is, theresults confirm the positive effect of the basicity of solid mate-

Table 4. Compositions and catalytic properties of well-performing catalysts that contain the significant combinations of the key elements that contributepositively to Y(C2) or S(C2).

Interaction Elemental composition [mol %] Additional elements Number[a] Mean S(C2) [%] Mean Y(C2) [%]1 2 3

Cs*Mg 5–10 60–90 Li, Na, Cl 6 81.2 18.9Na*Mg 10–40 33–90 Mn, La, Li, Cs, Cl 14 68.6 18.7Mg*Cl 31–90 5–25 Li, Na, Cs, Bi 11 75.7 18.6Na*Mn*Mg 4–25 2–29 57–92 W 4 72.3 16.7Na*Mn 5–17 2–70 W, Mg, Nb, La, Zr, Cl, S, P, support 21 64.1 21.1Mn*Cl 30–80 10–20 Na, Li, K 4 55.7 24.0Na*W 2–20 1–8 Mn, Mg, support 16 65.8 20.1Na*W*Mn 2–20 1–5 2–4 support 7 66.8 20.4Na*La 7–33 25–90 Mg, Ba 9 59.0 21.4Sr*La 1–50 8–91 Li, Mg, Zr, F, Ca 26 67.6 17.8Sr*Ba 25–34 32–38 Ti, Li, Mg, Na 4 54.8 21.5Ba*Mg 2–10 83–96 La 4 75.8 15.9

[a] Number of corresponding data sets with S�50, Y�15.

Table 5. Selected catalyst compositions based on the significant combinations of the key elements with thehighest mean values of Y(C2) and S(C2).

Elemental composition Elemental composition [mol %] Number[b] Mean S(C2) [%] Mean Y(C2) [%]1 2 3 4

Na*Mg 9–15 85–91 4 79 25Na*Cs*Mg*Cl 3–10 3–10 60–90 5–20 3 82 20Na*Mn*Mg 4–25 2–29 57–92 4 72 18Na*La 7–75 25–93 4 71 22Sr*La 1–59 61–99 15 73 18La*Ba*Mg 2–9 2–8 87–96 4 72 16Na*Mn*Cl 17–33 34–67 17–33 3 53 26Na*W*Mn 50–53 24–27 26–27 7 67 20

[a] Number of corresponding data sets with S�50, Y�15.

rials on S(C2) in the OCM reaction. An extended statistical anal-ysis of the OCM database with respect to the physical proper-ties of the catalytic solids and their effect on catalyst perfor-mance will most probably result in additional understanding ofthe OCM catalysis.

The data were assessed by the simplification that the meth-ods of catalyst preparation and the resulting solid-phase struc-tures could be neglected (see also above). This approximationmay be justified because of a leveling-out effect attributable tothe large number of materials considered. This is to say, rathercomplex relationships between catalyst composition, structuralphases, and physicochemical properties have been subjectedto a “simple” statistical analysis.

The empirical evidence of properties and the relationshipsbetween the various variables that describe the catalysts isonly an intermediate, that is, secondary objective. The ultimateobjective would concern the understanding why certain com-positions of the catalytic materials lead to high-performancecatalysts. To this end, empirical evidence must be combinedwith existing chemical knowledge and catalytic results thatconcern particular high-performance catalysts.

Catalyst compositions pro-posed for the OCM reactionbased on the results of dataanalysis

Statistical analysis of past experi-mental data used in the presentwork for quantifying the effectof various fractions of the select-ed key elements on catalytic per-formance allows one to drawthe following conclusions impor-tant for the catalyst design:

· The significant componentswith a high extent of correla-tion (both linear and Spear-man’s correlation coefficients)with S(C2) are mainly stronglybasic alkali metals oxides, al-kaline-earth metals, and lan-thanide metals (see Figure 7).

· Within all the available data,Li was identified as the mostsignificant element with ahigh extent of correlationwith both S(C2) and Y(C2) (seeTable 2 and Figure 7). Howev-er, the mean S(C2) value inthe presence of Li within 317well-performing catalysts withS(C2)�50 % and Y(C2)�15 %was a bit lower than themean S(C2) value for thisgroup of catalysts (see Fig-ure 8 a). Notably, most lithium

compounds are highly volatile and hence detrimental tothe catalyst stability.

· Carbonate species being expressed as carbon in the statisti-cal analyses have significant negative influence on bothS(C2) and Y(C2).

Eighteen highly significant elements that correlate positivelywith S(C2) or Y(C2) were selected on the basis of the results ofANOVA and correlation analysis: Sr, Ba, Mg, Ca; La, Nd, Sm; Ga,Bi, Mo, W, Mn, Re; Li, Na, Cs; F, Cl.

The oxides of these elements, which include the halides,were used for the further analysis of their interactions.

The selected alkali metal oxides (Li, Na, Cs) used as dopantswith low ionization enthalpies and high electropositivity canwork as modifiers for morphology and defect structure of thehost oxides and considerably improve their S(C2).[39] The effectof Cl or F as gaseous promoters that positively affect the cata-lyst activity can be explained by chlorine or fluorine genera-tion, which initiates gas-phase reactions. However, it is oftennot a long-term effect, as the high catalytic performance de-creases with time on stream due to the loss of the gaseous

Figure 11. Regression trees for the dependencies of a) S(C2) in percent and b) Y(C2) in percent (red values) onmolar fractions of the main selected components.

M. Baerns et al.

promoters. The other 13 catalytic key elements, considered asmain components of a host oxide stable under OCM condi-tions, include the following:

a) alkaline-earth metals : Sr, Ba, Mg, Ca;b) lanthanide metals : La, Nd, Sm;c) other metals located in III, V, VI, and VII groups of the peri-

odic table: Ga, Bi, Mo, W, Mn, and Re.

It is well known that various promoters and dopants consid-erably improve the catalytic performance of single-oxide cata-lysts.[4, 38–40] For the OCM reaction, structural defects in single-phase catalysts act as active centers ; they are due to oxygenvacancies and ions of transitional-metal impurities ; for highcatalytic performance of multiphase catalysts, particular phasesappear to be required.[40] In multicomponent catalysts, addi-tive, synergistic, or adverse effects may occur. Usually, thedesign of high-performance catalysts implies finding composi-tions with synergistic effects, whereby the combination of indi-vidual components often results in catalytic performances notobtainable by any of the components independently.[41]

Analysis of catalytic performance in the presence of highlysignificant interactions that occur in more than one well-per-forming catalyst shows the following:

· most combinations that contribute positively to S(C2) arebased on Mg oxide;

· the presence of Cl and Mn in multicomponent combina-tions leads to high Y(C2) ;

· the presence of Na*W interactions contributes positively toboth high S(C2) and Y(C2) ;

· the other combinations that contribute positively to S(C2)have a negative influence on methane conversion (low ac-tivity) and Y(C2), and vice versa (see Figure 10). However,these effects cannot be clearly distinguished;

· it appears that there is a synergistic effect in La*Sr combina-tions. The presence of this interaction results in meanS(C2) = 68 %, whereas the mean S(C2) in the presence of Laand Sr alone is lower (see Figure 8);

· most interactions of Li within the group of well-performingcatalysts were identified as less significant for the varianceof Y(C2) and S(C2) compared with those of Na (see Table 3).Moreover, in catalysts that contain Li-doped MgO, the meanY(C2) is a bit lower as the mean Y(C2) for all 317 well-per-forming catalysts (see Figure 8 b). Hence, the most frequent-ly studied catalytic system does not appear to be a promis-ing material for the OCM according to the results of thedata analysis ; this finding is in agreement with a recentreview on Li-doped MgO catalysts.[42]

After careful consideration of all elements in the group ofwell-performing catalysts based on the combinations of ele-ments given in Table 4, one can conclude that the majority ofthe high-performance catalysts can be divided into three maingroups:

a) Mg oxide doped by alkali metals (Cs, Na), by Mn, and/orpromoted by the Cl anion;

b) La oxide doped by Na or alkaline-earth metals (Sr, Mg, Ba);c) Mn oxide doped by Na, W, and/or promoted by the Cl

anion.

The catalysts based on Mg and La may possess the highestvalues of S(C2) of 72–82 % and of Y(C2) in the range of 16–26 %,whereas Mn-based catalysts from the third group result inhigh Y(C2) of 20–26 % and are less selective with S(C2) = 53–67 % but more active, as compared with the catalysts from thefirst and second groups.

Taking into account additional information about propor-tions of the main components obtained from the regressiontree analysis (see Figure 11), the following recommendationsfor the design of high-performance OCM catalysts can bemade:

A high-performance OCM catalyst is a multicomponent ma-terial that may consist of the following:

a) host oxides:- Mg oxide with molar fraction 76<x<89 %; or- La oxide with molar fraction 67<x<89 %; or- mixtures of La oxide with Mg, Sr, or Ba oxides;b) dopants that positively affect S(C2): Na and/or Cs;c) dopants that positively affect Y(C2): Mn and/or W;d) the Cl anion as a promoter that positively affects Y(C2).

Some particular catalyst compositions with the highestmean values of Y(C2) and S(C2) were selected from the availableexperimental data (see Table 5), namely: oxides of Na/Mg, Na–CsCl/Mg, Na/Mn–Mg, La–Ba–Mg, Na/La, Sr–La, NaCl/Mn, andNa/W–Mn.

For preparing catalysts of not only optimal qualitative butalso optimal quantitative compositions, two approaches mightbe used, which will contribute to a further fundamental under-standing of the OCM catalysis. The first approach might bebased on already existing generic fundamental knowledgeusing the above compositions for high-performance OCM cata-lysts. Such knowledge is, however, still limited; it certainlycomprises crystalline bulk and surface structure, crystalline dis-order, segregation phenomena, and other physical–chemicalproperties. The optimal performance of such a catalyst will bedetermined not only by the composition but also by themethod of preparation. The second approach based on theempirical knowledge gained in the present study would targeton an optimal catalyst composition within the compositionalmultiparameter space. An evolutionary procedure connectedwith a high-throughput experimentation should be used in thesearch for new catalyst compositions; also different catalystsynthesis methods should be considered. By using this proce-dure, optimal catalyst compositions should be identified.[43] Onthe basis of these results, a few catalysts of optimal composi-tions will result, which then should be prepared, tested, andextensively characterized for gaining an advanced fundamentalunderstanding of such OCM catalysts. The results of characteri-

zation will certainly lead to new insights, which, in turn, mightfurther improve the optimal catalysts.

Conclusions

The comprehensive statistical analysis applied to data frompast OCM experiments allowed one to extract information rele-vant for the design of potential catalytic materials with im-proved performances. At the same time, it provided a quanti-tative assessment of the effect of catalyst composition on cata-lytic performance, which can contribute to insights into thefundamental features of high-performance catalysts.

Metal oxides and their binary and ternary combinations thatare important for high-catalyst performance in the OCM reac-tion were derived. Mn- and Mo-containing catalysts, whichhave been more recently described in the open literature aswell as in patents, were also identified as promising catalysts.

It was also confirmed that alkaline-earth oxides as well asrare-earth oxides both doped with alkali metal oxides have ahigh potential for application. The Li–MgO system (see above),favored quite often in the past, was, however, not identified bythe statistical analysis as a promising high-performance materi-al ; this is in agreement with the conclusion of an extendedreview on Li–MgO catalysts.[42]

A new strategy is proposed that uses synergetic effects inmulticomponent materials based on strongly basic oxides (Mg,La) with dopants having positive effects on both C2 selectivity(Cs, Na, Sr, Ba) and catalyst activity (Mn, W, Cl anion).

Catalysts with the compositions identified by using dataanalysis perform close to the target required for an industriallyapplied OCM process. Further improvement in the perfor-mance of the catalysts based on the selected key componentsis expected by applying an evolutionary catalyst developmentapproach. From a scientific point of view, the results of thework presented will certainly contribute to further fundamentalunderstanding of the OCM catalysis.

Statistical analysis

The applied methods of statistical analysis of past experimentaldata collected are briefly introduced: 1) ANOVA for testing theeffect of various input variables (main effects and interactions) onthe variance of the dependent variables [Y(C2) and S(C2)] ; 2) Corre-lation coefficients for quantitative estimation of the correlation be-tween fractions of individual components with Y(C2) and S(C2);3) Regression trees for approximation of the dependent variables[Y(C2) and S(C2)] with a piecewise-constant function; 4) Comparisonof mean values of Y(C2) and S(C2) in the presence and absence ofvarious combinations of elements.In general, for all these methodsit has to be emphasized that the reproducibility of the results fromdata analysis depends on the sensitivity of the employed methodto changes of data. Hereby, the correlation analysis is least sensi-tive, that is, most robust. Also, ANOVA is quite robust, providedthe tacit assumption of the normality of data distribution is not in-validated by such changes.

ANOVA assumes that each dependent variable follows some basicstatistical model, in which the expectation of that variable isviewed as the sum of the effects of individual input variables,called main effects, possibly superimposed by their interactions ofvarious complexity. The amount of available data for each combi-nation of values of input variables determines the complexity ofthis basic model. The principle of ANOVA consists in testing the hy-pothesis that a particular main effect or an interaction can be leftout from that model without significantly changing the variance ofthe response variable. If the tested hypothesis is valid, then the un-explained part of the variance, that is, the model error, will be thesame for both models. Therefore, the ratio of both errors is com-puted in the ANOVA method, and if that ratio differs significantlyfrom the value 1, the tested hypothesis is rejected. Provided thatthe individual errors are normally distributed, the probability canbe computed that the error ratio is as high as the value corre-sponding to the measured data, or even higher. That probability iscalled achieved significance of the test. The lower it is, the moreunlikely it is that the measured data would occur if the simplifiedmodel is valid; consequently, the more significant is the effect orthe interaction that was left out from the model. For an overviewof the method from a catalysis point of view, the reader is referredto Baerns and Holena[43] and for a detailed statistical treatment tospecialized monographs, in particular Scheff�,[44] as well as Sahaiand Ageel.[45]

Correlation coefficients

The correlation coefficient describes quantitatively the correlationbetween the random variables A (input variable) and B (output var-iable) by their covariance. The linear correlation coefficient be-tween the random variables A and B is the covariance of A and Bafter their normalization to unit variance. The term linear refers tothe fact that this coefficient achieves its maximal value, which isthe value 1, if and only if A and B are increasing linear functions ofeach other, and it achieves its minimal value, �1, if and only if Aand B are decreasing linear functions of each other.Spearman’s correlation coefficient is a normalized expectation ofthe difference between the values of the joint distribution H of Aand B, and the values of the joint distribution of a two-dimensionalrandom vector with the same marginals F and G but independentcomponents. Hence, it is a normalized expectation of H(A,B)�F(A)G(B).Whereas the above correlation measures can assume any valuesbetween �1 and 1, the values of Schweizer and Wolff’s measureare always between 0 and 1. That explains why this measure canbe viewed as an intensity of correlation. It is obtained from Spear-man’s correlation coefficient through replacing the difference H(A,B)�F(A)G(B) with its absolute value. Hence, it is a normalized ex-pectation of jH(A, B)�F(A)G(B) j . A detailed statistical explanationof these as well as several other correlation coefficients can befound in Nelsen.[46]

Regression trees

Regression trees are models that, similarly to ANOVA, deal withcontinuous response variables. The underlying principle consists insplitting the value set of some input variable into two parts S1 andS2 in such a way that the sum of squared errors (SSEs), based onthe available data sample (x1, y1), …, (xn, yn), of the means of the re-sponse variable y corresponding to S1 and S2 is minimizedover all

M. Baerns et al.

possible splits (S1, S2) of the value sets of all input variables. If theconsidered input variable is continuous, then only splits of theform for some value n are considered.

S1 ¼ ðx < vÞ, S2 ¼ ðx > vÞ

Both S1 and S2 are then split again in the same way, possibly byusing different input variables. Such splits are performed conse-quently as long as needed, forming a hierarchy of rectangularareas in the space of continuous input variables.Depending on the number of such consecutive splits, trees of dif-ferent sizes can be obtained. The most appropriate tree size is usu-ally chosen by using cross-validation: The set of available data oncatalytic materials is randomly partitioned into k parts of approxi-mately equal size.With each possible tree size, k trees are constructed, using for theconstruction of each of them one k�1 part and leaving the re-maining kth part to measure the SSEs of predictions by the con-structed tree T [Eq. (3)]:

SSEðTÞ ¼X

xi2kth part

T xið Þ � yið Þ2 ð3Þ

To assess the appropriateness of each tree size, the SSE values forthe test data are averaged over all k trees with that size.For an overview of regression trees from a catalysis point of view,the reader is again referred to Baerns and Holena.[43] For a detailedstatistical treatment of the algorithms employed in the performedanalyses, see Breiman et al.[47] In this context, also the use of aclosely related model, that is, classification trees, which has beenapplied in catalyst development, should be recalled.[48, 49]

Supporting Information

All data used in the statistical data analysis can be found on theauthors website by following this link:www.fhi-berlin.mpg.de/acnew/department/pages/ocmdata.html

Acknowledgements

The authors acknowledge the inspiring and supportive discus-sions with members of the UNICAT Cluster of TU Berlin and withcolleagues from BASF.

Keywords: catalyst development · heterogeneous catalysis ·methane · oxidative coupling · catalyst composition · statisticalanalysis

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Received: June 3, 2011Published online on && &&, 0000

FULL PAPERS

U. Zavyalova, M. Holena, R. Schlçgl,M. Baerns*

&& –&&

Statistical Analysis of Past CatalyticData on Oxidative Methane Couplingfor New Insights into the Compositionof High-Performance Catalysts

The more the merrier: This paper dis-cusses the contributions of significantcombinations of elements to the meanvalues of selectivity and yield in the oxi-dative coupling of methane (OCM) reac-tion derived from the statistical analysisof about 1870 past catalytic data sets

(see figure). The applied methodologyallows the identification of the mainprerequisites in catalyst compositionsfor advanced design of high-perfor-mance OCM catalysts. Correlation coeffi-cients, decision trees, and analysis ofvariance are most useful tools.

doi: 10.1002/cctc.201100186 statistical analysis of …...doi: 10.1002/cctc.201100186 statistical...

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