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METHOD FOR MODELING THE ADIABATIC BURNING TEMPERATURE OF CHEMICAL
SUBSTANCES USING DESCRIPTORS OF GRAPHS OF STRUCTURAL FORMULAS
Trushina Veronika Pavlovna, Osipov Aleksandr Leonidovich, Novosibirsk State University of Economics and Management, Novosibirsk
E-mail: alosip@mail.ru
Abstract. A mathematical method for modeling the adiabatic burning temperature depending on the molecular fuel structure is considered. The method was tested on experimental data in comparison with other methods.
Key words: method, modeling, structural formula, burning temperature, computer system, structural elements.
Introduction. Problems concerned with fire and explosion hazard of chemical substances and materials have not been solved up to now. They require further improvement of experimental methods, their unification and standardization, development and improvement of methods for predicting the fire and explosion hazard indicators, and consideration of specific technological conditions of processes that require determining characteristics that are not included in the standard [1].
Analysis of the present-day state of investigation in this field shows that there is a substantial gap between theory and practical task of determining the fire and explosion hazard indicators. It is caused by the complex mechanism of the organic compound oxidation process that includes many elementary stages whose kinetic parameters are either unknown or insufficiently studied. This fact caused development of a great number of empirical and semi-empirical calculation methods for predicting fire and explosion hazard of organic compounds [2]. Calculation methods are the only way for satisfying the ever growing demand for fire and explosion hazard data because experimental estimation of the indicators is concerned with laborious investigation. The calculation methods are particularly useful for a predictable estimate of fire and explosion hazard of substances used since this estimate will lead to correction of the product obtaining process and its instrumentation. Calculations
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are also important at the stage of design investigation for estimating the influence of possible fluctuations of compositions of reactive mixtures in chemical-technological processes.
Mathematical modeling the adiabatic burning temperature. Many calculation methods concerned with calculating such an important parameter as a concentration limit inferior of inflammation require a knowledge of the adiabatic burning temperature [3, 4]. In these calculations, one proceeds from the energy system balance in the form of equality between energy supplied by the fuel and energy expended by the system in the required heating up to the adiabatic burning temperature (normally, 1550 K) of the retarder present in the limiting mixture. The calculation accuracy of the concentration limit inferior of inflammation by the combustion potential is determined by the degree of closeness of the adiabatic burning temperature to 1550 K. This leads to the necessity of modeling the adiabatic burning temperature Tb at the lower level, depending on the structural fuel formula.
The central point in finding the dependence of Tb on the fuel structure is to t solve the question: what struc-tural elements of the molecule govern the burning f
process at the limit inferior. To model the dependence of Tb on the fuel structure, we
will use the simplest sample of partial structural increments. The structural elements in the sample are pairs of bonded atoms in view of belonging of the bonds to certain chemical elements, and also atoms in view of the valent state. There are known applications of the structural increment method to calculating various physical -chemical parameters [5, 6].
The availability of program facilities to input molecular structures to a computer and automatically generate structural elements with a prescribed complexity allows us to propose the following tasks:
- full automation of calculations by models described in the literature;
- revision of structural-additive models using new structural elements;
- development of new structural-nonadditive models.
The first task is being under solution, and some automated databanks and a system for calculating fire and explosion hazard characteristics of organic compounds by the described models are available [7-11].
Solution of the second task is limited by that as the structural elements become more complicated their number drastically grows along with the number of model coefficients to be determined. Since the volume of available experimental data (training samples) is limited, in practice it is possible to use only the simplest structural elements. In what follows we will present some examples (structure -physical-chemical properties correlation) to illustrate the possibility of progress in solving the task by invoking the concept of partial contributions of structural elements.
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In the paper, we used the structural-nonadditive models:
Tb =2 Ttxt, (1) k
where Tk is the partial contribution of the k th structural element to the
parameter Tb ■ xk is the portion of the k th structural element in the molecule:
n
x = k/
m
I n,
i = 1
(here m is the number of structural elements (molecular fragments) and nk is the
number of structural elements of the k th type in the molecule). Model (1) takes into account dependence of the parameters on the qualitative (relative) composition of molecules contrary to the structural-additive models that take into account dependence of the parameters on the quantitative composition. ^ To refine structural-additive models of the form of (1), one should take into
account the reciprocal influence of structural fragments (the dependence of one fuel
components on the others) or, more precisely, the dependence of the increments Tk
on the molecule structure as a whole, that governs the changes of the electron density distribution on the fragments as well as their geometrical characteristics. This model allows one to take this fact into account in considering the hierarchies of regularly complicating structural elements:
- atoms without regard to surrounding (the chemical kind of the atom and the distribution of bonds between these atoms and other atoms, i.e., the valent state, or hybridization, are considered);
- atom - bond - atom;
- atoms with regard to the first surrounding (the elements of the description atoms without regard to surrounding are supplemented with a list of directly bonded atoms, their valent state either indicated or not indicated);
- atoms with regard to the first and second surroundings, i .e., with indication of the set of atoms spaced from the central one by no less than two bonds.
The hierarchy can be extended up to the maximal consideration of surrounding in which for each atom considered as a central one we take into account as a surrounding all other atoms of the molecule.
The hierarchy of bonds is constructed in a similar way. For this purpose, in the hierarchy of bonds pre-sented above it is sufficient to replace the central atom by a bond, i.e., a pair of chemically bonded atoms in view of their valent state.
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The traditional way for refining the structural-additive models is concerned with complication of structural fragments. This requires a great body of experimental data that should form a statistic sufficient for calculating the fire hazard parameters with the necessary accuracy. A more complicated level of the previous hierarchy is a result of dramatic increase of the number of structural elements as well as parameters (increments) to be deter-mined. Hence, only the first three levels of the hierarchy have found practical application. Storing considerable experimental data on fire and explosion hazard characteristics of chemical substances in databases will make the approach much more universal.
The most important factors determining the value of Tb are relative
characteristics of the fuel molecule. Let us introduce the notion of the adiabatic burning temperature Tk of a hypothetical fuel having structural ele-ments of the k
th type or sort solely. We will consider the real fuel molecules as complexes formed from hypo-thetical fuel molecules and assume that the contributions of these hypothetical fuels to the adiabatic burning temperature at the limit inferior of the real fuel are additive. This leads to model (1). Let us give a physical- chemical f interpretation of such a formal model.
According to present-day thermal flame propagation theory, equations for the
normal flame velocity uf , [12] may be represented as u2 = Fexp(-E / RT), where E
f
and T the activation energy and the temperature of the leading stage of the process, respectively; F is the function of physical-chemical parameters of the fuel mixture (diffusion coefficients, heat capacities, concentrations, heat loss, kinetic parameters of chemical conversion stages, etc.); R is the gas constant. For our case, when T is the same as the adiabatic burning temperature Tb , and E is the effective activation energy, we have
T = E 1
b R ( ^ ln
F,
.2
u
f
J
The activation energy is well modeled by an equation of the form of E = £ E x [5].
k k k
Taking into account that at the limit inferior the u f values depend slightly on the
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kind of organic fuel and that the
2 is under the logarithm sign, we may assume
f
sufficient smoothness of the function ln
f
and approximate it by the following
expression: ln
f
= I f x;.
i i
We obtain for Tb a linear-fractional model of the form T = 1
i i
Expanding the linear-fractional function into series and restricting ourselves to the linear terms, we obtain the desired model Tb = £ Tkxk ■
Modeling results. The efficiency of this approach was investigated on a sample of 100 organic compounds taken from a wide class of chemical substances or structural formulas of organic molecules consisting of C, H, O, CI, Br, and N atoms written as an empirical formula CnHmOkNlClsBri [13]. Results of the investigation
are presented by relative RMS errors: 1.56, 1.68 (in training), and 2.87, 2.75 (at examination) for two types of structural elements: ''atom - bond - atom" and "atoms with valent surrounding", respectively.
We will note that the relative RMS error for the adiabatic burning temperature in [14] was 2.86 in train-ing on a sample of 83 chemical substances, there was no
examination in this research.
Using chemical substances cited in [14], we formed an examination sample of substances that were not in-cluded in our training sample. Results of this examination are demonstrated in tabl. 1 and tabl.2.
2
2
k
Table 1
Atom - Bond - Atom
Chemical substance Adiabatic burning temperature Calculation Difference Relative error, %
1,2-Dichloroethane 1650 1586.421 63.57866 3.853252
Amy I acetate 1502 1621.797 -119.797 7.975835
Amyl bromide 2071 1949.564 121.4356 5.863619
Amyl chloride 1598 1628.451 -30.451 1.905571
Acetaldehyde 1581 1176.041 404.9586 25.61408
Benzene 1605 1699.992 -94.9921 5 91851
Butene-1 1611 1629.161 -18.1606 1 127284
Butyl acetate 1615 1585.477 29.52322 1.828063
Butyl bromide 2101 2038.57 62.42999 2.971442
Butyl chloride 1618 1626.621 -8.62131 0 532837
Hexyl bromide 1888 1909.657 -21.6571 1.14709
Hexyl chloride 1560 1631.92 -71.9202 4.61027
Heptyl chloride 1529 1635.377 -106.377 6.957307
Glycerin 1587 1487.347 99.65342 6.279359
Divinyl 1685 1691.429 -6.42932 0.381562
Diethyl ether 1634 1585.058 48.94159 2 995201
Isobutane 1646 1559.103 86.89675 5.279268
lsobutyl alcohol 1567 1624.171 -57.1709 3.648431
Isooctane 1709 1621.047 87.95298 5.146459
Isopentane 1575 1661.69 -86.6898 5.50411 1
Isopropyl alcohol 1485 1651.089 -166.089 11.18445
Cumene 1620 1606.136 1 3.86437 0.855825
Methyl propylketone 1543 1560.49 -17.4901 1 133513
Methyl ethyl ketone 1538 1514.68 23.32013 1.516264
H-amyl alcohol 1586 1608.945 -22.9451 1.44673
Table 1 (continued)
H-butane 1643 1630.165 12.83468 0.781 173
H-butyl alcohol 1570 1605.049 -35.0491 2.232429
H-hexane 1648 1628.643 19.35674 1 17456
H-heptane 1650 1627.943 22.05681 1 336776
H-nonane 1647 1627.351 19.64884 1.193008
H-octane 1649 1627.56 21.43955 1.300155
H-pentane 1647 1629.253 17.74684 1.077525
H-propyl alcohol 1542 1601.033 -59.0334 3.828363
Ethylene oxide 1572 1637.255 -65.2554 4.1511 1
Pentene-1 1630 1620.966 9.03444 0.55426
Propane 1633 1635.439 -2.43947 0.149386
Propyl bromide 2205 2182.128 22.87199 1.037278
Propylene 1577 1555.907 21.09324 1.337555
Propyl chloride 1606 1628.198 -22.1977 1.382174
Styrene 1598 1613.597 -15.5974 0.976059
Toluene 1643 1676.539 -33.5391 2.041333
Cyclohexane 1656 1620.668 35.33243 2.133601
Ethanal 1585 1572.694 12.30598 0.776403
Ethyl acetate 1616 1520.809 95.19064 5.89051
Ethyl bromide 2392 2559.94 -167.94 7.020888
Ethylene glycol 1584 1529.466 54.53355 3.442774
Ethyl chloride 1661 1605.948 55.05249 3.314419
Table 2
Atoms with Valent Surrounding
Chemical substance Adiabatic burning temperature Calculation Difference Relative error, %
1,2-Dichloroethane 1650 1610.608 39.39215 2.387403
Amyl acetate 1502 1596.293 -94.2933 6.277847
Amyl bromide 2071 2002.296 68.70398 3.31743
529
Table 2 (continued)
Amyl chloride 1598 1624.584 -26.5836 1.663555
Acetaldehyde 1581 1516.25 64.75027 4 095526
Benzene 1605 1649.812 -44.81 17 2.792007
Butene-1 1611 1601.824 9.176101 0.56959
Butyl acetate 1615 1578.5 18 36.48215 2.258956
Butyl bromide 2101 2086.272 14.72764 0.700982
Butyl chloride 1618 1623.617 -5.6166 0.347132
Hexyl bromide 1888 1962.631 -74.6306 3.952892
Hexyl chloride 1560 1627.023 -67.0225 4.296315
Heptyl chloride 1529 1629.321 -100.321 6.561198
Glycerin 1587 1529.526 57.47372 3.621532
Divinyl 1685 1562.625 122.3752 7.262625
Diethyl ether 1634 1607.669 26.33055 1.61 1417
I so butane 1646 1581.376 64.62442 3.92615
lsobutyline 1600 1615.317 -15.3171 0.95731"
Isobutyl alcohol 1567 1583.14 -16.1396 1.02997
Isooctane 1709 1599.982 109.0176 6.37903
Isopentane 1575 1611.196 -36.1957 2.29814
Isopropyl alcohol 1485 1599.643 -114.643 7.720097
Cumene 1620 1622.97 -2.97022 0.183347
Methyl propylketone 1543 1583.959 -40.959 2.654504
H-amyl alcohol 1586 1601 927 -15.9267 1.004204
H-butane 1643 1619.043 23.95712 1.458133
H-butyl alcohol 1570 1598.84 -28.8402 1.836953
H-hexane 1648 1618.833 29.16696 1.76984
H-heptane 1650 1618.527 31.47331 1.907473
Table 2 (continued)
H-nonane 1647 1618.411 28.5895 1.735853
H-octane 1649 1618.418 30.58195 1.854575
H-pentane 1647 1618.962 28.03797 1.702366
H-propyl alcohol 1542 1595.112 -53.1 116 3.444332
Ethylene oxide 1572 1623.65 -51.6503 3.28564
Pentene-1 1630 1604.7 25.30002 1.552149
Propane 1633 1619.26 13.7396 0.841371
Propyl bromide 2205 2205.755 -0.75509 0.034245
Propylene 1577 1598.792 -21.7922 1.381874
Propyl chloride 1606 1625.918 -19.9176 1.240198
Styrene 1598 1629.489 -31.4893 1.970542
Toluene 1643 1632.772 10.22776 0.622505
Cyclohexane 1656 1613.97 42.02964 2.538022
Ethanal 1585 1580.476 4.523983 0.285425
Ethyl acetate 1616 1554.742 61.25838 3.790741
Ethyl bromide 2392 2407.519 -15.5185 0.648767
Ethyl chloride 1661 1616.088 44.91201 2.703914
Ethylene glycol 1584 1553.155 30.84506 1.947289
For applications, the extremely important question is about the calculation reliability [14], which is determined by the maximum relative error.
The RMS errors and the reliability of the methods are easily calculated for structural elements: "atom - bond - atom" and "atoms with valent surrounding" from tabl.1 and tabl.2, and are equal to 4.06 and 1.88 (at examination) and 25.61 and 7.72, respectively.
When using the "atom - bond - atom" descriptors, Acetaldehyde is abruptly extracted at examination; it yields a great relative error and, thus, reduces prediction reliability. When this chemical substance was included in the training sample, the reliability of the method was considerably improved and became equal to 10.82, and the RMS error was 2.64.
Computer support system. An automated information-retrieval system was developed [15, 16]. It is equipped with programs of mathematical procedures of statistical modeling the fire and explosion hazard properties of chemical substances and includes:
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- subsystems to support professional structural-chemical knowledge and databases with the use of a graphic interface to manipulate with structural formulas of molecules;
- subsystems to predict fire and explosion hazard characteristics of organic molecules based on graphs of structural formulas to create training and examination samples from databases, set or select from the menu various chemical structure descriptions, and select structural-additive and nonadditive models used to find correlation between the structures and the properties.
Conclusion. The created computer information-retrieval system is a powerful tool for on-line dialog-mode prediction of fire and explosion hazard characteristics of chemical substances. It is also used for analyzing the relative information value of different groups of factors while studying the burning mechanisms of chemical substances. The obtained results ensure a good accuracy and high efficiency of the proposed methods in calculating the adiabatic burning temperature using descriptors of graphs of structural formulas of organic molecules.
Literature:
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7. O.A.Stepachev, V.M.Zatsepin, and Yu.M.Sorokin, Proc of the 7th AllUnion Conf on Application of Computers in Molecule Spectroscopy and Chemical Research (in Russian), IOS AN LatvSSR, Riga, 1986.
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9. A.L.Osipov, R.S.Nigmatullin, and V.M.Zatsepin, Informatsionnii Byulleten
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po Khimicheskoi Promishlennosti, no. 2, p. 119, 1988, NUTEKHIM, Moscow. 10. A.L.Osipov and M.V.Borisov, Proc. of the 2 nd All-Union Seminar on Nonequilibrium System Modeling (in Russian), IPTs KGTU, Krasnoyarsk,
11. A.L.Osipov, Ecology and Life (science, education, and culture) (in Russian), 2000, iss. 5.
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13. A.L.Osipov, V.M.Zatsepin, R.S.Nigmatullin, et al., Proc of the 8th AllUnion Conf. on Application of Computers in Molecule Spectroscopy and Chemical Research (in Russian), NIOKh SO AN SSSR, Novosibirsk, 1989.
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15. R.S.Nigmatullin, A.L.Osipov, A.P.Puzatkin, and V.A.Koptyug, Khimiko -Farmatsevtichesku Zhurnal. no. 2, 1985.
16. A.L.Osipov, R.D.Semenov, and V.M.Zatsepin, Optoelectronics, Instrumentation and Data Processing, no. 5, p. 78. 1995.
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