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Boolean relation matrices

It should be added here that these huge reaction networks have to be generated by computer [Baltanas Froment, 1985]. Booleans relation matrices were used to describe the molecules and carbenium ions. Since a component analysis of a vacuum gas oil is not entirely feasible some lumping is inevitable but the rate coefficients for the reactions between the lumps can be constructed from those of the single events entering in the reactions of the components of the lump [Vynckier Froment, 1991]. [Pg.60]

The approach to hydrocarbon cracking taken by the Froment school is to model the actual elementary steps of radicals at the various molecular configurations [38]. These are relatively few initiation hydrogen abstraction from a primary, secondary, or tertiary carbon and radical decomposition by scission of a carbon-carbon bond in /3-position to the unpaired electron. Boolean relation matrices are used to reflect the structures of the hydrocarbon reactants by indicating the existence and location of all their carbon-carbon bonds. Computer software generates reaction networks on the basis of known rate coefficients and activation energies at the various positions. Froment states the number of components in naphtha cracking as around 200, that of radicals as 40, and that of elementary radical steps... [Pg.422]

These feedstock characterizations were the starting point for the development of the reaction network using Boolean relation matrices and characteristic vectors. Components of a hydrocarbon family which are known to be at equilibrium were grouped so as to limit the number of continuity equations to be integrated in reactor simulations. [Pg.759]

ABSTRACT. A fundamental approach is outlined for the kinetic modeling of complex processes like thermal cracking or catalytic hydrocracking of mixtures of hydrocarbons. The reaction networks are written in terms of radical mechanisms in the first case and of carbenium ion mechanisms in the second case. Since the elementary steps of the networks pertain to a relatively small number of classes, the number of rate coefficients is kept within tractable limits. The reaction networks are generated by computer through Boolean relation matrices. The number of continuity equations is limited by the elimination of radicals or carbenium ions through the pseudo-steady-state approximation. [Pg.409]

Evidently, these reaction schemes cannot be generated manually. Clymans and Froment (1984), Hillewaert et al (1988) devised a method for the computer generation of reaction networks based upon Boolean relation matrices. [Pg.415]

Hydrocarbons can be represented either by a Boolean relation matrix or by a vector. The species is preferably characterized by a vector because the matrices, although sparse, take a large amount of computer memory. The matrices are required, however, to carry out operations reflecting the elementary steps. They are easily generated out of the vectors stored in the computer memory whenever required by the pathway development. [Pg.90]

Boolean Relation Matrix and Label Representation of Molecules and ions. [Pg.147]

We have shown thus far how the system of equations representing a process can be related to a linear diagraph and its associated Boolean adjacency matrix. In the Section IV, we show how the location of the maximal loops in this adjacency matrix leads to identification of the subsystems of equations that must be solved simultaneously. [Pg.196]

Since the systems of equations to be considered are quite large, it is necessary to use some compact method to represent the information flow among them. A very convenient technique is to relate the system equations to a digraph and its associated Boolean matrix, which represent the structure of the information flow in the system. The Boolean matrix to be used is called the occurrence matrix (HI, S3), and is defind as follows (1) each row of the occurrence matrix corresponds to a system equation, and each column corresponds to a system variable (2) an element of the matrix, s -, is either a Boolean 1 or 0 according to the rule... [Pg.193]

T. Akutsu, S. Miyano, and S. Kuhara, Algorithms for identifying Boolean networks and related biological networks based on matrix multiplication and fingerprint fnnction. / Comput Biol 7(3 ) 331-343 (2000). [Pg.505]

The matrix condition IOC, stated by Theorem 2.2 or by Remark 2.6, is called the intrinsic order criterion, because it is independent of the basic probabilities p, and it only depends on the relative positions of the Os and Is in the binary n-tuples u, v. Theorem 2.2 naturally leads to the following partial order relation on the set 0,1 " (3). The so-called intrinsic order will be denoted by , and we shall write u > V (u < v)to indicate that u is intrinsically greater (less) than or equal to v. The partially ordered set (from now on, poset, for short) ( 0,1 ", on n Boolean variables will be denoted by / . [Pg.19]


See other pages where Boolean relation matrices is mentioned: [Pg.91]    [Pg.147]    [Pg.416]    [Pg.416]    [Pg.422]    [Pg.422]    [Pg.423]    [Pg.189]   
See also in sourсe #XX -- [ Pg.409 ]




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