KING, a KInetic Network Generator

Chemical Engineering Science, Vol. 47. No. 9-11. Printed in Great Britain.

pp. 2713-2718.

KING,

a Kinetic

1992.

Network

0

ooo9-2m9/92 $5.00+0.00 1992 Pergamon Press Ltd

Generator

F.P. Di Maio and P.G. Lignola Department of Chemistry - Chemical Eng. Branch University of Calabria 87030 Arcavacata di Rende (CS) - Italy

Abstract. Computer simulation of chain branching reactive processes by means of detailed kinetic network is an important tool to improve the understanding of the complex phenomena that may arise. Among the different systems, combustion processes, which lead to complex dynamic behaviouts, can be profitably studied by means of detailed kinetic modeling. The kinetic mechanisms of interest involve a large number of species in a large set of elementary reactions. Consequently, traditional network analysis by hand appears overwhelming. In order to generate automatically such complex mechanisms, a computer program, Kinetic Network Generator (KING), has been developed. In the code, the Bond Electron (BE) matrices are used to represent the chemical species and matrix operators are used to describe reactions. The problem of multiple representation of the same species has been solved by means of BE matrices eigenvalues. Automatic identification of chemical species allows removal of redundant branches of kinetic network that have different matricial representations but are kinetically equivalent. Tests have been performed, by means of KING, to generate a simple kinetic mechanism such as that of hydrogen-oxygen combustion. Results show that the code is indeed capable of generating the well known hydrogen-oxygen combustion mechanism. Application of the code and of the method to acetaldehyde combustion processes is discussed in the paper, and comparison is made with traditionally generated models existing in the literature. Introduction. Simulation of reactions evolving through complex kinetics in homogeneous phase systems can be an important tool for improving the comprehension of the different phenomena which occur in such systems. Among them, combustion of hydrocarbons and related compounds can be considered an exhaustive example. Indeed combustion processes exhibit a rich variety of phenomena, caused by thermal and kinetic interactions of numerous radical and molecular intermediates, through a broad kinetic network. The number of species and of reactions increases with the number of carbon atoms in the hydrocarbon molecule, reaching the order of magnitude of hundreds of species and of thousands of reactions even for not so large reactant molecules (Westbmok et al., 1988). The large dimension of such systems hinders the traditional by hand development, following successive approximations. This work is aimed at assessing the feasibility of a novel approach, based on automatic computer generation of a comprehensive kinetic network. Algorithms for the implementation of such generators can be divided into two categories. The first category includes those algorithms which. having recognized the compounds as belonging to a certain class, generate only the reactions which are known to be characteristic of that class (Chevalier et al., 1990). Algorithms, based on combinatorial methods, constitute the second category. They are able to generate the whole set of possible reactions, by taking into account only the congruence of electronic configuration of reagents and products. The first category of algorithms produce compact reaction networks, but require the u priori 2713

F. I’. DI MAIO and P. a.

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knowledgeof possible productsand of specific reactionsoccurringwith each class of compounds.They appearto be applicableto processes.which are alreadyknown, at least in principle,and they are able to generateonly known reactions. Combinatorialmethods,on the otherhand, aIleapplicableto any process and they m able even to discover new reactiontypes. They requireno previous knowledge of products to be formed or of possible reactionsfor each class of compounds. Networksgeneratedby such algorithmsare in general very large and often requireto be reducedby means of thermodynamicand thennokineticcriteria. In this work, in orderto have a wide appmach,a combinatorialalgorithmhas been developed. Representation

of compounds.

Compoundscan be describedmathematicallyby means of Bond Electron(BE) matrices(Ugi et . al., 1979). A BE matrix B for a compound with n atoms Al, AZ, . . A, is a squarematrix of dimension n, the i”l row of which correspondsto electron configurationof atom Ai. In particularthe bij element representsthe number of covalent bonds between atoms Ai and Aj, whereas the element on main diagonal bii representsthe number of free valence electrons, i.e. those not involved in bonds. Being bij = bji. matrix B is symmetric.All the matrix elements bij are generally integers,since they rep=sent either free or bonding valence electrons. Resonance structures,however, can be representedby fractionalnumbers. A set of compounds is depicted by a block matrix, each block representingone compound. For a chemical compound made up of N atoms there exist N! different ways of numbering atoms, each correspondingto a differentBE matrix. It can be easily proved that the N! matricesdiffer each from the other for a permutationof rows and columns, i.e. Bi=PBjPT, where P is a permutationmatrix. In order to avoid the analysis of N! matrices, which are chemically equivalent, since eigenvalues are invariantwith permutationand real because of symmetry of B, an ordenzdvector v of the eigenvaluesis associatedto each B matrix.This method implies the calculation of eigenvalues.but does not requirethe comparisonof N! matrices. Reactions.

Two sets of molecules, A and 8, are defined as isomeric if they are made up of the same number of atoms of the same elements. Two isomeric sets have the same empirical formula. In a chemical reactionreactantsand productsare isomericsets. Indeedchemical reactiontransformsthe set of reactantsin the set of products operating on valence electrons but conserving the number of atoms of each elements. The reaction: A --+ B can be written:

f(A) = B where f is a matrix operatorthat distributesthe valence electrons. The operatorshould have several properties. In particular it should be invertible and should conserve the number of electrons:

The sum is the simplestoperatorto be chosen. Hence equation(1) can be written: A+R

= B

(3)

where R is the reaction matrix. Condition (2) then becomes: IS %j = C bij = C and then: aij

+

C

qj

Since %j andbij are non-negative,elementsof R should satisfy also: ifrijC0

then

lrijl

<

qj

A genericmatrixR can be derivedas a linearcombinationof two elementaryreactionmatrices. The first describesthe transferof one electronfrom atomj to atom i:

KING,

F16

a KImtic Network

2715

Generator

.

Uij

0 . . .

. .

+ 1

. *

=

ii

. . The second describes the formation of one covalent bond between atom i and atom j: i

j . . .

Vij

=

+

\ i

1 . . .

* . . .

-

1 . .

. .

j /

Matrix R can thus be given by: R = a ZVij

+ p XUij

a and p being generic parameters. If one does not include the case of ionic reactions, limiting the analysis to gas phase reactions, reaction matrices R am given by: R=

a

ZVij

(3

Since each element can have only a certain electronic configuration, given valence schemes for each elements, BE matrices which in the i* row contains a forbidden electronic configuration for the Ai atom, can be excluded from the feasible set. Algorithm implementation. Only the reactant matrix A, is required at the start_ Different R matrices anz cyclically generated according to expression (5). If the B matrix of products satisfies the mathematical and chemical constraints, the reaction: A+R=B

(6)

is considered a feasible reaction and is added to the kinetic scheme, after a check in order to avoid reaction duplicates. If the reaction (6) is not possible or has been already included in the list of reactions, a new R matrix is generated. Otherwise content of B matrix is assigned to reactant A matrix. The procedure is repeated until a B matrix which fulfils the above requirement has been found. A branch of a tree is thus generated, the nodes of which are A matrices. Once a terminal node has been reached, the branch is followed backward. At each node the existence of other possible branches is inspected and followed if inspection is positive. The algorithm stops if the terminal node coincides with the starting reactant matrix A,. A chemical reaction can be recognized if the involved compounds are identified as possible chemical species. Coding of compounds can also reduce computation time, since equivalent reaction branches can be excluded automatically from being generated, e.g. cracking of a molecule generates H and CHs radicals, since alI four CH bonds am equivalent, it is immaterial which H radical is released. As a consequence only one reaction exists, though four matrix representations are possible each of which is able to generate a branch of the kinetic tree: identification of compounds avoids the repetition

F. P. DI MAIO and P. G.

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of four kinetically equivalent branches. In order to reduce the extension of kinetic network several other constraints, beyond those above, can be imposed to compounds and reactions, e.g. the number of molecules or radicals that interact can be fixed, as well as the number of broken and formed bonds and so on. It is known that in combustion reactions there is also the possibility of formation of hydrocarbons larger than the reactant. This feature has also been implemented. Results. In order to evaluate KING’s ability to generating the maximum set of feasible reactions and to asses the capacity of the method to providing a tool for analysis and postulation of kinetic networks, it has been applied to the kinetic scheme of H 2 - O2 reaction (Di Maio and Lignola, 1991). Comparison with mechanisms currently available in the literature indicated that indeed the aim of the work has been achieved. KING has then been applied to the study of C!H&HO combustion process. Since in this paper the attention is not focussed on the discussion of CH$HO combustion kinetics, but only on demonstrating that it is indeed possible and useful the automatic generation of kinetic complex networks, the amplitude of the full feasible scheme has been limited on purpose. Hence KING was run with the constraints of Table I, which reports also the kinetic network automatically generated. It consists of 32 intermediates (Table II) involved in 193 reactions. Kaiser er al. (1986) proposed a rather comprehensive detailed mechanism of acetaldehyde oxidation in the negative temperature coefficient regime. Kaiser model consists of 40 intermediates involved in 153 reactions. Because of the constraints adopted in this application of KING, those compounds and reactions which do not satisfy the constraints are not expected. Intermediates which do not appear are: C2H502H, qH502. CH302CH3, C~HSO, C!zHg. CzHg. CH2, CH. Comparison between the two kinetic schemes shows that 63 reactions are in common (marked with asterisks in Tab. I), 90 reactions of Kaiser scheme do not appear in KING scheme, as they should not, because these reactions either imply the presence of three radicals per reaction, or the break or formation of more than two bonds, or the presence of five or six hydrogen atoms. 130 reactions appear exclusively in the KING scheme. Among these reactions, analysis shows that 29 are combinations of elementary steps (marked with crosses in Tab. I), whereas 101 reactions, according to combustion kinetics knowIedge seem to be feasible reactions, which in principle should be included in an exhaustive kinetic network. Discussion of inclusion or exclusion of the 101 reactions is beyond the scope of this paper, but certainly for combustion researchers this result can direct both experiments and modeling toward a better simulation of the pmcess. In conclusion KING, the kinetic network generator, performed as expected and by this first application revealed a powerful tool for developing comprehensive kinetic schemes. The different options and selectable constraints can be used for a thorough analysis of even very complex processes, with the confidence that the maximum set of the intermediates and reactions will be generated. Available knowledge provides the means for suitable reduction or can indicate which reactions are candidates for further experimental and/or theoretical investigation.

Acknowledgement. This work was performed in the frame of activities of the CNlZ Institute of research on membrane and chemical reactor modeling. It was partly funded by MURST of Italy and by CNR grant CTE3 89.00270/12.

References. Chevalier, C., Wamatz, J. and Melemk, H., 1988,Proceedings ofXU Task Leaders Meeting IEA, 18I-l%, Tokyo. Di Maio, F.P. and Lignoia, P-G., 1991,Meeting of Ztalian section of The Combustion Institute, FGa. Kaiser, E.W., Westbrook, C.K. and Pi& W.J., 1986.ht. J. C&em. Kin., 18.655-688. Ugi, I., Bauer, J.. Brandt, J., Friedrich,J., Gasteiger,J., Jochum,C. and Shutirt,W., 1979,Angew. Chem. Int. EdEngi., 18.111-123.

Westbrook, C.K., Warn&z, J. and Pitz. W.J., 1988,22& Symp. (ht.) Institute,Pittsburgh.

on Combustion, 893-901.

The Combustion

a Kinetic

KlNG.

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Table I Kinetic network automatically generated by KING Max Max Max Max

# # # #

of of of of

C atoms in compound= H atoms in compound= 0 atoms in compound= free electrons in camp.=

Max # of broken/formed bonds= 2 Max # of compounds in reaction= 5 Max # of radicals in reaction= 2

2 4 3 1

* Reaction included in the kinetic scheme develorxd by Kaiser et al. x reaction that is combination of elementary steps *

Hco+cH~=cHgrfo

x

HCHO+CH3=CH3CHO+H

C&CO2

*

cH,$=H+cH~

*

HCHO+CH3=HCO+CH,

C!H3CO2+CH2CO=H~+C!H3~

x

cq+Hco=cH&w0+H

*

HCHO+H=HCO+H2

CH3C02+HCO=CO+CH3CCb2H

*

co+cH+rcH3+Hco

*

HCHO+OH=HCO+H20

x

co+cH~+H-cH$xIo

*

co+H=HCO

HCHO

CH3CO+H-a+CO CH3CO

CH3CO=CH3+co

*

CH3CO+CH.$-CH3CH0+M3 CH3CO

+ HCO

0+0=02

*

H2+CH3CO=CH3CHO+H

* * *

H2+CO=H+HCO

*

CH3OH

+ U-&OH

CH3OH

+ C2H

= C&I2

+ CH2OH

= C2H2

+ CH30

CH3OH

+ C2H

*

CH30H

+ HCO

= HCHO

H02=02+H

X

CH3OIi

+ HCO

- CH3CH0

C&OH

+ CO = HCO

HZO,

+ C2H3

*

- CH2C0 = C2H4

+ HO2

*

X

*

HCCO+~=CH3+CH2C0

+ OH

+ CH2OH

CH30H+CO=CH3CO+OH CH3OH+CO=HCO+CM30

H202+H-H+2+H02 *

CH@H=CH3+OH CZ+OH=H+CZi30

H202=OH+OH *

H202=H+H02

HCCO+H=CH2CO

+ C!H30

CH30H=H+CH20H

+ HO2

Hp2+H=OH+H20

+ H = CH$O

+ CH2OH

HCHO+HCCO=HCO+CH2CO

H202+C2H=C2H2+H02

+ CH2CO

= C2H,, - HCHO

HCHO+C2H3=HcO+C~

H2=H+H

=CH3CO

+ C2H3 + HCO

CH30H CH3OH

H2+CH3=H+CH.,

+ CH3CHO

+ CH&%H

+ CM30

HCHO+CO-HCO+HCO

+ HCCO

HCCO

- CH3C0

= C,H,

HCHO=H+H+CO

+ CO

HCCO+H2=H+C&CO

+ CH3CH0 + C$-I,

X

H202

CH&O

CH3C0,

+ HCO

HCHO=H+HCO

*

.&

+ CW3CO2H

~~COZ+CHI=~~+W~C’?ZH

= CH,CHO

HCHO+C2H=HCO+C2H2

- CH3CHO

= HCO

*

+ H - CH3CHO

*

+ CH&O

+ HCHO

Hf12+CH3CO=CH@KI+H~

CH30H+H=CH3+H20 CH30H+H=H2+CH30

H2$12+CO=HCO+H02

*

C!H30H+H=H2+CH20H

HCCO+HCO=CO+CH2CO

*

H202+C!H3=CTQ+H02

X

CH30H+H=CH.,+OH

*

H20+H=H2+0H

*

H202+OH=m20+H02

X

CH30H+OH=CH3+H202

*

H20+HCCO=CH2CO+OH

*

H202+HCO=HCHO+H02

*

CH3OH

*

H20+CH3CO=C!H3CHO+OH

*

c!O2=co+o

*

CH30H+OH-H20+CH30

*

H20=H+OH

*

CH30=H+HCH0

C&OH

*

H20+CO=HCO+OH

*

CH2OH-

CH30H+CH3C02=CH30+CH3CX&H

*

H20+CH3=CH.,+OH

*

CH20H=H+HCH0

CH30H

+ HCCO

- CH2CO

+ CH30

*

C2H3+IS20-OH+C2H,+

*

CH202H=OH+HCH0

CH3OH

+ HCCU

- CH2C0

+ CH2OH

X

CH302=CH202H

C&OH

+ HO2

*

cH302=02+CH3

*

CH3Co3=q+CH3CO

C2H3 *

+ CH2CO

- HCCO

C2H3+H2=H+C2H, CzH3+cHq-cHJ

*

+ C2q

+CzH*

C$&+H=C.$-& C2H3

+ CH3CHo

- CH3Ccl+

c*

x

C2H3+HCO=CO+c2yq

*

%H2+H=C2H3

*

C2H+H20=OH+C2H2

*

C2H+H2=H+C2H2

x

*

= CH20H

= H24

CH30H

+ CH3CO

= CH3CHO

+ U+OH

CH@H

+ CH3CO

- CH&!HO

+ CH30

CH3C02H+H=CH,CTZO+OH

X

CH3OH

+ M&O

- CH3

CH3C02H

*

CH30H+CH3=CEQ+CH30

*

CHJoH+CH3=~+CH2OH

= CH3C0

+ OH

CH3C02H

+ OH = CH3CO

+ H202

CH3CO3H

+ H = Hz0

CH3C03H+H=CH3CHO+H02

C2H*~=CH3+C&2

C%ez+c2H1=~+~~

X

CH3C03H+H=CH~+&02

C2H+H=C2H2

CH3C02

+ CH2CO

- HCCO

+ C2H2

+ H = CH3C02H

CH3C03H

CH3C4+~-OH+CH3coLH cH3co2+H2oZ-Ho2+~&%H

+ CH3C02

CH3C03H+H-0H+C!H3C02H

~3C%-~3+co2 X

C2H

+ CH,C02H

CH3C03H+H=H2+CH3~

CH&=‘z+~=H+FP4’

x

+ CH30

CH30H+H02=H202+CH20H

c~+#zH3cHo-c!H3co+~

C2H+HC!O=CO+C2H2

+ CH3C02H

*

CH3C?2+C2H4=C2H3+cH3C%H

c2H+w-J.4-c2~3+~%

+ CH3CO2

+ CIi2OI.Z

CH3CO&I+H=CSI3CO+H~O

CH3C02H=CH3+cO+OH

*

*

CH30

+ OH = H20

-CH3CO+

CH3C03H=CH3+CO+H02 *

CH3C03H=OH+CH3C02

HO2

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DI

x

*

-cH$I-Io

cH&m

- CHg2~

cH+xx$I

+

+ aI3

-a&

CH3C03H

+ CH3

- CH3C0,

HCCO

+ CHpcq +

+ %=3

+ OH - Hfl,

*w-Q

+ CH3CO3

CH3CQH

+ OH = HO,

+ CH3cO9-l

+ OH = H#

+ CH3C03

+ C,H + HCO

CH3C03H

+ Ho,

= C&

- Hz03

CH-JCQH

+ CO

CH3C03H

+ CH3C02

- HCO

CH3C03H

+ CH20H

CH3C03H

+ CM30

CH30fl

+ CH3C03

= HCHO

+ CH3CO3

+ CH3C-03 + CH3C02H

= CH3CO3 - CHpC03

+ CH3OH

CH303H+OH-

Hfi+CW30

*

CH303H+OH-

H20+CH303

CH&H+CO-HCO+C!H&

X

CH303H+OH-

Ho,+CH30H

- H + CHf13H

*

CH303H

- OH + CH30

-w2H+Cs3-

X

CH303H-H+

CH34

Cii30~H+H=H_P

+CH30

CH3O$+H-H2

+C!H20$l

CH303H+H-Hz

+CH3%

X

CH302H+H-M,

+Hq

x

cH30~+H=cH3

X

CH302H

+ H - OH

CH302H

+ CH3CO

-

C&Cl-IO

+ CH303H + CIi303

CH3%H

+ CH3CO

-

CH3CHO

CH&H

+ CH3CO

-

CH3

CH302H

+ CH3CO

CH302H

+ HCCO

-

CHfZO

+ CH30,

CHC

+ CH203H

= CT-I,0

- HCHO

+ CH34

CH&H

+ HCCO

-

- HCHO

+ CH2%H

CH302H

+ C2H -

C3H2

+ HCO + CO

- CH3CHO - HCO

+ Ho2

+ CH&H

*

C2H

c;?H2 CzH3 c2H4

CH2C0 CHzOzH CH*OH CH3

CH&HO CH3C0 CH3C02

x

*

X

CH302H

+ C,H

CH30,H

+ OH -

-

C3H2 H20

es++-302

CH303H+H%-

Hfi+CH&H

-303H+H4-

H2°2+M3%

CHjojH

+ CH3

- CH30

+ CH3OH

‘%02H+~3=cH4+cH302

+H202

HCO

CH30.$

x

X

+ CH,OH

WQ+WOaH

-3%H+-3--4+-

+ CH30H

+ HCO

C&O&l

FL6

LIGNOLA

CWOzH+c2H3-

+ CH3CD3

- CH3CO3

G.

- CH3 + Hq

X

+ =3-3

P.

CH302H

* CH3C4

CH3CO3H CH3CO3H

CH,CoJ

+ CH30H

- CH&O

-3w

cH3C03H

x

+ cH$o~

M3C03H

cHJOfl+ x

cqco

cH&qH

CF13C03H+

X

+

and

cH&H+co-cH3m+H~

CH303H a-I&K3+I

MAIO

+ CW3c03H + CH3CRH

+ CH2%H

CH303H

+ CH3C02

- CH30

CH302H

+ cH3C02

- CH20$I

+ CH3CQ3H

CH303H

+ CH3c0,

= CH302

CH30$-I

+ CH2OH

- CH20.94

CH302H

+ CH20H

- CH30,

*

CH303H

+ CH30

- CH20$4

*

CH30$I

+ C&I30

- CH,o,

CH302H

+ CH300,

- M&H

CH302H

+ CH3CO3

- CM34

+ CH3q + CH202H

CH,CO,H CH3C03 CH3C03H CH30 CH302 -WzH

CH30H CH4 co Co, H

Table II. Molecules and radicals generated by KING.

H2 H20

H202

HCCO HCHO HCO HO2 : OH

+ CH3~H + CH3~H + CH3OH + CH30H + CH3OH

+ CH30H + US3C03H + CH3CO3H