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Original papers
Materials for energy and environment, next-generation photovoltaics, and green technologies УДК 662.216.4 DOI: 10.17277/jamt.2022.02.pp.122-134
Predictive estimate of the calorific value of substances with negative oxygen balance depending on the value of oxygen balance
© Valerii Yu. Dolmatova^, Alexander N. Ozerinb, Evgeny D. Eidelmanc'd, Anatoly S. Kozlova, Sergey Yu. Naryzhnya, Valerii A. Martchukova, Asko Vehanene, Vesa Myllymakie
a Special Design and Technological Bureau "Technology, 33-a, Sovetskiy pr., St. Petersburg, 192076, Russian Federation, b Enikolopov Institute of Synthetic Polymeric Materials of the RAS, 70, Profsoyuznaya St., Moscow, 117393, Russian Federation, cIoffe Institute, 26, Politekhnicheskaya St., St. Petersburg, 194021, Russian Federation, d Saint Petersburg State Chemical and Pharmaceutical University of the Ministry of Healthcare of the Russian Federation, 14A, Professor Popov St., St. Petersburg, 197022, Russian Federation, e Carbodeon Ltd. Oy, Vantaa, Pakkalankuja 5, 01510, Finland
И diamondcentre@mail.ru
Abstract: In recent years, it has become necessary to determine the calorific value of pure combustible substances, since the error of the previously used formula by D.I. Mendeleev reaches 20 %, which is not acceptable. The method for determining the calorific value by M.S. Karash is also widely known. This method is based on the interaction principle between the electron fields of atoms and atomic groups - any interaction of the atom fields is accompanied by a change in the energy of the system. According to the Karash method, the calculated calorific value refers only to the liquid state, while for each class of organic compounds its own calculation formula is proposed, taking into account correction factors for all atomic groups. The need for at least a quantitative account of the molecule structure and the mutual arrangement of atomic groups complicates the calculation. The authors of this work have found a relationship between the calorific value of substances with a negative oxygen balance and the value of oxygen balance. The formula calculated by the authors has the form Ql = 0.1387ЮВ, MJ-kg^1 and only one variable (oxygen balance). The determination accuracy is not worse than using the well-known formula by D.I. Mendeleev (6 variables), but the calculation is much simpler.
Keywords: calorific value; oxygen balance; forecast; fuel; calculation formulas.
For citation: Dolmatov VYu, Ozerin AN, Eidelman ED, Kozlov AS, Naryzhny SYu, Martchukov VA, Vehanen A, Myllymaki V. Predictive estimate of the calorific value of substances with negative oxygen balance depending on the value of oxygen balance. Journal of Advanced Materials and Technologies. 2022;7(2):122-134. DOI: 10.17277/jamt.2022.02.pp.122-134
Прогнозная оценка теплотворной способности веществ с отрицательным кислородным балансом в зависимости от величины кислородного баланса
© В. Ю. Долматов аИ, А. Н. Озери^, Е. Д. Эйдельман^, А. С. Козлов", С. Ю. Нарыжный^ В. А. Марчуков^ A. Веханен^ В. Мюллюмяки
а Специальное конструкторско-технологическое бюро «Технолог», Советский пр., 33-а, Санкт-Петербург, 192076, Российская Федерация, b Институт синтетических полимерных материалов им. Н. С. Ениколопова РАН, ул. Профсоюзная, 70, Москва, 117393, Российская Федерация, с Физико-технический институт им. Иоффе, ул. Политехническая, 26, Санкт-Петербург, 194021, Российская Федерация, d Санкт-Петербургский государственный химико-фармацевтический университет Министерства здравоохранения Российской Федерации, ул. Профессора Попова, 14, лит. А, Санкт-Петербург, 197022, Российская Федерация, e Carbodeon Ltd. Oy, Паккаланкуя 5, Вантаа, 01510, Финляндия
И diamondcentre@mail.ru
Аннотация: В последние годы появилась необходимость определения теплотворной способности (ТС) чистых горючих веществ, так как погрешность ранее применяемой формулы Д. И. Менделеева доходит до 20 %, что не приемлемо. Широко известен и метод определения ТС М. С. Караша. В основе метода лежит принцип взаимодействия электронных полей атомов и атомных группировок - всякое взаимодействие полей атомов сопровождается изменением энергии системы. По методу Караша подсчитываемая ТС относится только к жидкому состоянию, при этом для каждого класса органических соединений предлагается своя формула расчета с учетом поправочных коэффициентов для всех атомных группировок. Необходимость хотя бы количественного учета структуры молекулы и взаимного расположения атомных группировок затрудняет расчет. Авторами настоящей работы найдена взаимосвязь между ТС веществ с отрицательным кислородным балансом и величины кислородного баланса. Рассчитанная авторами формула имеет вид Qh = -0,1387-КБ, МДж-кг"1, и только одну переменную (КБ). Точность определения не хуже, чем известной формуле Д.И. Менделеева (6 переменных), но расчет значительно проще.
Ключевые слова: теплотворная способность; кислородный баланс; прогноз; топливо; формулы расчетов.
Для цитирования: Dolmatov VYu, Ozerin AN, Eidelman ED, Kozlov AS, Naryzhny SYu, Martchukov VA, Vehanen A, Myllymaki V. Predictive estimate of the calorific value of substances with negative oxygen balance depending on the value of oxygen balance. Journal of Advanced Materials and Technologies. 2022;7(2):122-134. DOI: 10.17277/jamt.2022.02.pp. 122-134
1. Introduction
The issue of assessing the calorific value of fuel Q with sufficient accuracy without experimental determination, given its complexity, is quite acute.
D.I. Mendeleev proposed his empirical formula for the lowest calorific value of all types of natural fossil fuels, for which it is necessary to know the elemental composition, i.e. the percentage of the following elements in it: oxygen (O), hydrogen (H), carbon (C), sulfur (S), ash (A) and water (W) [1]. For the calculation, the lowest thermal conductivity Ql is usually used, which takes into account heat losses with water vapor. For solid and liquid fuels, the value of Ql (MJ-kg-1) is approximately determined by the formula:
Ql = 0.339[С] + 1.025[H] + 0.1085[S] -- 0.1085[0] - 0.025[W],
(1)
where parentheses indicate the percentage (wt. %) content of the corresponding elements in the fuel composition. Comparison of calculated and experimental data on the calorific value of various fuels (wood, peat, coal, oil) showed that the calculation by D.I. Mendeleev formula gives an error not exceeding 10 %. Checking the calculated Ql for individual combustible compounds (alcohols, gases, aliphatic and aromatic compounds, sugars) by D.I. Mendeleev formula in comparison with the experimentally determined Ql gave a spread of errors up to 20 %.
The paper [2] describes the most used method for calculating the combustion heat of substances (the method of M.S. Karash). The Karash method is based on the interaction principle between the electron
fields of atoms and atomic groups: any interaction of the atom fields is accompanied by a change in the energy of the system. The fundamentals of the method are given by Karash in the form of five postulates.
1. The combustion heat is a consequence of the energy release during the movement of electrons between atoms and molecules. Oxidation is the result of the movement of electrons. Therefore, it is possible to relate the combustion heat to the total number of electrons moved.
2. The combustion heat of an organic compound is a function of the total number of electrons moved. It is a quantity equal to the amount of heat corresponding to the movement of one electron, multiplied by the number of moved electrons:
Ql = xn,
(2)
where x is a constant equal to the amount of heat released when an electron moves; n is the number of transferred electrons.
3. The amount of energy released in the form of heat when one electron moves from the position that exists in the hydrocarbon molecule (for example, in methane) to the position characteristic of the CO2 and H2O type is approximately equal to x = 26.05 kcal-(mol-electron)-1. The constant x = 26.05 is determined from normal octane, which, according to numerous and verified data, has a calorific value of 1302.9 kcal-mol"1, and the number of displaced electrons in the combustion process is 50. Then
Qcv 1302.9
x = =-= 26.05 .
n 50
(2a)
Octane is taken as the basis for calculating x, not only because the calorific value is known exactly, but also because it has a sufficiently long chain and the influence of terminal methyl groups does not distort the value, which is mainly characteristic of the CH2 increment. In addition, according to the Karash method, the calculated calorific value refers to the liquid state.
4. The movement of electrons from a location in methane to an arrangement like CO2 and H2O occurs in stages. The farther the electrons are from the carbon atom and closer to the oxygen atom, the less energy is released during combustion.
In methyl alcohol, the position of the hydrogen atom in the OH group is exactly the same as in water, i.e. the entire energy of moving one electron (26.05 kcal) has already been released. The position of the electron in the C—O bond is only partially shifted, therefore, with a complete shift its amount will be less than 26.05 kcal-(mol-electron)-1, although heat will be released. In the carboxyl group, all the electrons have already been completely moved, and during the combustion of formic acid, energy is released from the movement of only two electrons in the C—H bond. The final movement of these two electrons results in the formation of finished oxidation products.
This example shows that any partial movement of electrons from the position in CH4 to the position of CO2 and H2O leads to an increase in the formation heat and reduces the combustion heat. When considering the structural formula of a substance, this provision allows drawing qualitative conclusions about the order of the combustion heat.
5. A pair of electrons common to two carbon atoms is not displaced, and during combustion the movement of this pair gives the same amount of heat as a pair of electrons in a position like methane. Based on these postulates, Karash offers calculation formulas for each class of organic compounds.
1. Limit hydrocarbons
Qcv = 26.05«. (3)
2. Unsaturated ethylene hydrocarbons
Qcv = 26.05« + 13a, (4)
where a is the number of double bonds.
3. Primary alcohols
Qcv = 26.05« + 13b, (5)
where b is the number of OH groups.
4. Secondary alcohols
Qcv = 26.05« + 6.5b. (6)
5. Tertiary alcohols
Qcv = 26.05« + 3.5b. (7)
6. Polyhydric alcohols
Qcv = 26.05« + 13b + 6.5c, (8)
where b and c are the numbers of primary and secondary alcohol groups, respectively.
7. Ketones
Qcv = 26.05« + 6.5. (9)
8. Acids
Qcv = 26.05«. (10)
9. Nitro compounds
Qcv = 26.05« + 13d, (11)
where d is the number of —NO2 groups.
When all electrons are taken into account, the formula should be written as follows
Qcv = 26.05« - 13d. (11a)
10. Primary amines
Qcv = 26.05« + 13e, (12)
where e is the number of NH2 groups.
11. Amides, anilides, amino acids
Qcv = 26.05«. (13)
In polyfunctional compounds, a combined formula, which includes correction factors for all atomic groups, is used. In this form, the use of the Karash method is cumbersome and inconvenient, since it is necessary to have a set of formulas and coefficients. M.Kh. Karapetyants [3] proposed a generalized formula for calculating the combustion heat of any organic compound
Qcv = 26.05(4C + H - p)+iTk& - qf, (14)
1
where 26.05 kcal-(mol-electron)-1 is the electron displacement energy equal to the total heat of C—H and C—C bonds breaking and subsequent formation of CO2 and H2O; C is the number of carbon atoms in a substance molecule; H is the number of hydrogen atoms in a substance molecule; the sum 4C + H is the number of moving electrons for normal hydrocarbons (4C + H = « in Karash formulas); p is the number of partially or completely displaced electrons in a substance molecule (C—O and O—H bonds); kt is the number of identical i-substituents; fy is thermal correction, taking into account the change in the energy of the substance due to changes in the electronic structure (polarization) caused by the introduction of this substituent; qf is the latent heat of the substance fusion.
The combustion heat according to the formula (14) is calculated at p = const for a liquid substance.
If the experimental value qf is not known, the latter can be calculated approximately using the Walden formula:
qf = 56.5Tf kJ-kg-1 . (15)
V.O. Kulbakh notes that the nature of the correction factor is more complicated than Karash originally believed.
The correction factor is the net effect of the partial displacement of the electron pair and the substituent-induced displacement of the electronic field of the entire organic compound.
Thus, the correction factors make it possible to clarify the changes that occur in the energetics of a molecule with the introduction of one or another
Table 1. Values for thi
p g Groupings and bonds
atomic group. Such corrections are inevitable, since at present the change in energy with a change in structure cannot be expressed analytically. Therefore, any new attempts to create a calculation method based on some other principle always lead to a whole range of correction factors. Moreover, if in the Karash method the issue of corrections as a whole is solved quite simply and corrections are known for many types of compounds, this is not the case in other methods, so the calculation accuracy is much less and applicability is limited.
Table 1 shows the correction values proposed by Karash et al.
When using the Karash method, a template should be avoided, since disregard of the interaction of groups in a molecule can lead to incorrect data. A typical example is the correction for the nitro group.
ochemical corrections
Thermochemical correction
Structure
kcal-mol-1 MJ-kmol-1 nA
1
2
3
4
5
6
1 Sulfo group in aromatic hydrocarbons
2 Bonding of condensed aromatic nuclei
3 Nitro group in aliphatic and aromatic compounds
4 Carboxyl group in aromatic acids
5 Nitro group in heme-dinitro compounds
6 Bonding of aromatic radicals Aromatic radical with vinyl radical Aromatic radical with acetylene radical Nitro group in trinitromethane Aromatic radical and nitrile
Urea group
7 Aromatic and aliphatic radicals Aromatic radical and nitrogen (such as ammonia)
Quaternary carbon atom Acid amides
8 Carboxyl group in acids Alcohol nitrates
Nitro group in tetranitromethane
9 Tertiary alcohols Phenols Nitroamines
Ar—SO3H
R—NO2
Ar—COOH R—CH(NO2)2 Ar : Ar Ar : C = C Ar : C ^ C Alk—C(NO2)3 Ar : CN C = ON = Ar : Alk
Ar—N =
(R)4C R—CONH2 Alk—COOH R—ONO2 C(NO2)4 (R)3—C—OH
Ar—OH R—NHNO2
-23.4 -20.0
-13.0
-10 -6.5
-3.5
+3.5
-98 -84
-54.4
-41.8 -27.2
-14.6
+14.6
-7A -6A
-4A
-3A -2A
-1A
+1
0
0
0
Continuation of the Table 1
1
2
3
10 Secondary alcohols
Ethylene bond in the ring
Aliphatic and aromatic ketones Aromatic primary amines Substituted amides
Aromatic radical and chlorine Hydroxy acid type
Esters of aromatic acids Anhydrides of carboxylic acids
11 Alcohols primary Ethylene bond
Aliphaticandaromaticaldehydes
Aliphaticprimaryamines
Aliphaticsecondaryamines
Lactones
Aliphatic radical and chlorine (bromine) Aromatic radical and bromine Estersofaromaticacids C=C bond in transconnections Trimethylene and cyclobutane rings in carboxylic acids
Aliphatic esters
Aliphatic radical and nitrile Quinone group
(R)2CHOH
(R)2=C=O Ar—NH-
ff R r-c-n-ncr
Ar—COO—Ar R—OH
Alk —NH2 Ar —NH —Ar
Alk : Cl(Br)5 Ar : Br Ar —COO —Ar
+6.5
-27.2 +2
+10
+13
+41.8 +3
+54.4 +4
+16.5 +69.1 +5
C=C bond in cis compounds
4
5
6
Continuation of the Table 1
2
3
12
13
14
15
16 17
Simple ethers
Secondaryaliphaticamines
Tertiaryaromaticamines
Tertiaryaliphaticamines
Oximes
Acetylenebond (fully substituted)
Isonitriles in the aliphatic series
Iodine derivatives of aliphatic and aromatic glyoximes
Acetylene bond
R1—O—R2 (Alk)2NH (Ar)3N
(Alk)3N
R—C=C—R R—N=C
R—I
H—C=H(R)
+19.5
+26
+33.1
+91.6
+108.8
+6A
+8A
+138.5 +10A
+40.1 +167.8 +12A +46.1 +192.2 +14A
1
4
5
6
Correction for the primary nitro group is R—NO2£, = -13 kcal, however, in the case of gem-di, three-tetra- and nitro groups, the corrections should be different.
The greatest corrections are given by such groups as OH, NO2, amines, double and triple bonds. In some cases, when it is impossible to take into account the mutual influence of groups or the isomerization effect, these corrections can be neglected, since usually they do not exceed 3-5 kcal. It is more difficult to calculate heterocyclic compounds, especially those containing several nitrogen atoms (triazoles, tetrazoles, etc.).
The need for at least a qualitative account of the molecule structure and the mutual arrangement of atomic groups complicates the calculation, and this is undoubtedly a disadvantage of the Karash method.
This work is devoted to the rapid determination of the calorific value of compounds and carbon used in pasty, solid and gaseous fuel systems. Priority is given to fully gasified combustion products. Such an important additive to fuels as carbon in the form of detonation nanodiamond is reflected in articles [4-6, 8], in the form of graphenes - [11-13] and in the form of nanotubes - [14-16].
2. Methods
In carrying out this work, the authors used the known reference data on the calorific value of substances, the calculation of oxygen balance (OB) of substances and finding the relationship between them in the form of a graphical dependence.
The authors used a well-known mathematical apparatus to find the mathematical relationship between the calorific value and oxygen balance, and also calculated the calorific value of substances
according to the formula they proposed and the formula by D.I. Mendeleev.
3. Results and Discussion
The Ql approximate value of fuel with a smaller error (as a rule, no more than 6 %) can be determined from the OB of the substance, determined for CaHbNcOd compounds, according to the well-known formula [17]:
[d-(2a + b/2)1x16
OB =-----x100%, (16)
M.w.
where M.m. is the molecular weight of the substance. Table 2 shows the experimental calorific value of various substances and carbon with a negative oxygen balance, which is then reflected together with OB in Figure 1, with which it is not difficult to determine Ql of other substances. In addition, the table shows the calculated calorific value according to D.I. Mendeleev formula and the proposed formula and their errors in relation to the experimental Ql (where it is available).
The calculation of the OB is based on the assumption that the fuel in a substance molecule (carbon and hydrogen) is oxidized during combustion or explosion by an oxidizer (oxygen in a molecule) to higher oxides - carbon to CO2 and hydrogen to H2O. Unlike the explosives, where only oxygen molecules are used, the combustion process is accompanied by the supply of an oxidizer (oxygen) from the outside -due to oxygen in the air or an oxygen-containing oxidizer in the fuel composition. In reality, some of the carbon is oxidized to carbon monoxide, releasing less energy. In addition, the experimentally determined Ql is not constant, the accuracy of their
determination is affected by the method of determination, the features of the equipment and the qualifications of the experimenter, sometimes Ql differs from each other (in various reference books) significantly. Taking into account the "ideality" of the calculating the OB, it should be expected that the calculation of Ql, as a rule, should give a higher value than the experimentally determined calorific value. It should be expected that the smaller the difference between the calculated value Ql (according to OB) from the experimentally
determined one, the more accurate the experimental data.
Table 2 (and Figure 1) shows the possible components of various types of fuels, their experimental and theoretical calorific value (calculated according to D.I. Mendeleev formula and the formula proposed in this work). In D.I. Mendeleev formula, it is necessary to take into account (and determine) up to 6 variables, while in the proposed formula - only oxygen balance. Table 1 also shows the calculation errors in relation to the experimentally determined Ql.
Table 2. Dependence of the calorific value (Ql) of organic substances on the OB
No.
Substance
S ë
o no te c 3 n
s
<D 5
M s
(D i"H Í-H <D
M T3 M S
<C
Empirical Experimenta
formula l calorific
and molecular value Ql,
weight kl-kg-1
o £
o c te
03
3
O
e
u
>
eg M
J
1? 13
> e T3 te
<D 3s 7
=3 60
0 ^
n e S ox of c 1 à J * 0
b
Q Ë n e M ™ ft
£ O CJ
b î-H 5? ^ 1!
g 0 ° £3 H
w O
I
o c c a
Î-H g
£ o
iS
s
. c
03 Ü
1 2 3 4 5 6 7 8 9 10
1 Adamantane* Solid C10H16, 136 no data 41974 - -329.4 45688 -
2 Amyl acetate Liquid C7H14O2, 130 29874 [18] 30272 +1.3 -233.8 32428 +8.5
3 1 -Aminoanthraquinone Solid C14H9NO2, 223 29814 [19] 28124 -5.7 -21.88 30348 +1.8
4 3-Aminobenzoic acid Solid C7H7NO, 137 24484 [19] 23487 -4.1 -181 25105 +2.5
5 Ammonia Gas NH3, 17 18585 [20] 18091 -2.7 -141.7 19654 +5.8
6 Aniline Liquid C6H7N, 93 36466 [19] 33963 -6.9 -266.3 36935 +1.3
7 Acetaldehyde Gas C2H4O, 44 27102 [19] 23864 -12 -181.8 25216 -7.0
8 Acetone Liquid C3H6O, 58 31403 [21] 28620 -8.9 -220.7 30611 -2.5
9 Benzoic acid Solid C7H6O2, 122 26455 [20] 25520 -3.5 -196.7 27282 +3.1
10 Benzene Liquid C6H6, 78 40576 [20] 39183 -3.4 -307.7 42678 +5.2
11 Hydrazine Liquid H4N2, 37 14644 [18] 12813 -12.5 -100 13870 -5.3
12 Glycerol Liquid C3H8O3, 92 16120 [18] 16523 +2.5 -121.6 16866 +4.6
13 1,4-diaminobenzene Solid C6H8N2, 108 30836 [19] 30196 -2.1 -237 32872 +6.6
14 1,5-diamino-
naphthalene Solid C10H10N2, 158 34625 [19] 32235 -6.9 -253.2 35119 +1.4
15 1,2-diaminopropane Liquid C3H10N2, 74 no data 30340 - -237.8 32983 -
16 3,5-dimethylbenzoic
acid Solid C9H10O2, 150 29115 [19] 28931 -6.3 -224 31069 +6.7
17 1,2-dimethylhydrazine Liquid C2H8N2, 60 29962 [19] 27223 -9.1 -213.33 29589 -1.2
18 N,N-dimethylurea Solid C2H8N2O, 88 20986 21212 +1.1 -163.6 22691 +8.1
19 Dimethyl sulfoxide Liquid C2H6SO, 78 20623 [20] 22570 +9.4 -164.1 22761 +10.4
20 Dioxane Liquid C4H8O2, 88 24887 23865 -4.1 -181.8 25216 +1.3
Continuation of the Table 2
1 2 3 4 5 6 7 8 9 10
21 Dimethylformamide Liquid C3H7NO, 73 26220 [20] 24180 -7.8 -186.3 25840 -1.4
22 Isopropanol Liquid C3H8O, 60 34190 [19] 31109 -9.0 -239.6 33233 -2.8
23 Methane Gas CH4, 16 55688 [19] 51050 -8.3 -400 55480 -0.4
24 Methanol Liquid CH4O, 32 23869 [19] 22359 -6.3 -150 20805 -12.8
25 Methylamine Gas CH5N, 31 33350 [19] 29656 -11.1 -232.3 32220 -3.4
26 Urea Solid CH4N2O, 60 10528 [21] 10723 +1.9 -80 11096 +5.4
27 Naphthalene Solid C10H8, 128 39390 [18] 38187 -3.1 -300 41610 +5.6
28 3-nitroaniline Solid C6H6N2O2, 138 21685 [22] 19629 -9.5 -150.7 20902 -3.6
29 2-nitro-1,3-
dimethylbenzene Liquid C8H9NO2, 151 27700 25364 -8.4 -196 27185 -1.9
30 Nitronaphthalene Solid C10H7NO2, 173 no data 26787 - -198.8 27574 -
31 Pyridine Liquid C5H5N, 79 33360 [23] 32235 -3,4 -253,2 35119 +5.3
32 Polypropylene Solid [-CH2-CH(CH3)-]„
[CbH6]„, 42 47140 [20] 43703 -8.5 -342.9 47560 +0.9
33 Polystyrene Solid [CH2CH (C6H5)-]n
(C8Hs)„, 104 40700 [22] 39175 -3.7 -307.7 42678 +4.9
34 Polyethylene Solid [-CH2-CH2-]n
(-C2H4-)n, 28 47140 [20] 43703 -7.3 -342.9 47560 +0.9
35 Polyethylenepolyamine * Liquid [-CH2-CHNH]n, (C2H5N)n, 43 no data 30840 -203.9 28281
36 Sugar Solid C12H22O11, 342 16500 [18] 15283 -7.4 -112.2 15562 -5.7
37 Styrene Liquid C8H8, 104 42640 [20] 39175 -8.1 -307.7 42678 +0.1
38 Toluene Liquid C7H8, 92 40954 [20] 38869 -2.6 -300 41610 +1.6
39 Carbon Solid C, 12 33820 [20] 33900 +1.8 -266.7 36991 +9.4
40 Urotropin* Solid C6H12N4, 140 no data 26240 - -205.7 28531 -
41 Cyclohescan Liquid C6H12, 84 43825 [18] 43703 -0.3 -342.9 47560 +8.8
42 Cyclohexanol Liquid C6H12O, 100 35170 [22, 23] 34972 -0.6 -272 37726 +7.3
43 Ethyl acetate Liquid C4H8O2, 88 25400 [18] 20101 -20.9 -181.6 25188 -0.8
44 Ethylene glycol Liquid C2H6O2, 62 19351 [20] 15870 -17.9 -121.2 16810 -13.1
45 Ethanol Liquid C2H6O, 46 30562 [20, 22] 27248 -10.8 -208.7 28947 -5.3
Analysis of the data in Table 2 shows that 23 samples (No. 3, 4, 6-8, 11, 14, 17, 20-23, 25, 28, 29, 32-34, 37, 38, 43-45) have much higher accuracy calculation according to the proposed formula, compared with the experimentally determined Ql, than by D.I. Mendeleev formula; for six samples, the calculation error by D.I. Mendeleev formula and the proposed formula is close (9, 16, 19, 31, 33, 36), and in thirteen samples (No. 2, 5, 10, 12, 13, 18, 24, 26, 27, 31, 39, 41, 42 ) the calculation accuracy according to the proposed formula is lower than by
D.I. Mendeleev formula. However, for samples No. 5, 10, 12, 26, 27, 31, the error is quite acceptable -up to 6 %. For samples No. 1, 3, 40, which are one of the most interesting substances for further use, it was not possible to find reference data on QL.
Table 3 shows the dependence of the calorific value of explosives on their oxygen balance. It is impossible to determine the calorific value of explosives due to the rapid transition of their combustion to detonation. A slight difference is visible in the calculated calorific value of explosives
50000
45000
a
« 40000
35000
ss
25000
S 20000 «
15000
10000
5000
TO / / ' / ^
34
37 ■ 38 xO 41
22. 'V- 25 ' 33
S 45 „, 17 . 42 39 3 ]
24 -7 29 -O 21 4 20 'Y \ 8 2 n >
28 ..,* ^ 5
36 ■ 19
•26 ■12
-60
-110
-16U -210 -260
Oxygen balance
-310
-360
-410
Fig. 1. Dependence of the calorific value of fuels on their oxygen balance. 26 - urea; 11 - hydrazine; 36 - sugar; 44 - ethylene glycol; 12 - glycerol; 5 - ammonia; 24 - methanol; 28 - 3-nitroaniline; 18 - N,N-dimethylurea; 19 - dimethylsulphoxide; 4 - 3-aminobenzoic acid; 43 - ethyl acetate; 7 -acetaldehyde; 20 - dioxane; 21 - dimethylformamide; 29 - 2-nitro-1,3-dimethylbenzene; 9 - benzoic acid; 45 - ethyl alcohol; 17 - 1,2-dimethylhydrazine; 3 - 1-aminoanthraquinone; 8 - acetone; 16 - 3,5-dimethylbenzoic acid; 25 -methylamine; 2 - amyl acetate; 13 - 1,4-diaminobenzene; 15 - 1,2-diaminopropane; 22 - isopropanol; 14 - 1,5-diaminonaphthalene; 31 - pyridine; 6 - aniline; 39 - carbon; 42 - cyclohexanol; 38 - toluene; 27 - naphthalene; 33 -polystyrene; 37 - styrene; 10 - benzene; 32 - polypropylene; 34 - polyethylene; 41 - cyclohexane
Table 3. Dependence of combustion heat of explosives on their OB
Aggregate state
No.
Substance
_ . , Explosion heat, Cakula^
of matter Gross formula _1 calorific value Oxygen
, and molecular , . g (D.I. Mendeleev balance,
under (charge density,
weight formula), %
normal g S-cm) QlJ-1
conditions L
Calorific
value calculated in the work, kJ-kg '
1 RDX (cylotrimethylene-trinitramine) C3H6N6O6, 222 5401 (1.5) [25] 3575 -21.6 2996
2 o-dinitrobenzene C6H4N2O4, 168 3643(1.5) [25] 12835 -95.2 13204
3 1,5-dinitronaphthalene C10H6N2O4, 218 2985 (1.5) [26] 18295 -139.4 19335
4 Tetryl (2,4,6-trinitro-N-methyl-N-nitroaniline) C7H5N5O8, 287 4554 (1.6) [25] 6864 -47.4 6574
5 TATB (1,3,5-triamines, 2,4,6-trinitrobenzene) Solid C6H6N6O6, 258 3973 (1.854) [25] 7813 -55.8 7740
6 2,4,6-trinitroaniline C6H4N4O6, 228 4266 (1.72) [25] 7931 -56.1 7781
7 1,3,5-trinitrobenzene C6H3N3O6, 213 4606 (1.66) [25] 6568 -58.3 7809
8 2,4,6-trinitrophenol (picric acid) C6H3N3O7, 229 4103 [25] 6694 -45.4 6297
by D.I. Mendeleev formula and by the formula proposed in this work. Column 5 of Table 3 shows the empirical value of the explosion heat, which, as a rule, is 1.5-6.0 times less than the combustion heat of the same substances. The substances presented in Table 3 are the most interesting for preparation of fuel compositions (tens of mass percent), and even the theoretical determination of their calorific value is decisive for the formation of such fuel compositions
Both formulas - D.I. Mendeleev and the one proposed in this paper, are competitive, however, using the latter, it is much easier to determine Ql (one variable) and, in general, it is more accurate. In addition, in the absence of reference data on Ql or the presence of doubtful data (a large scatter in value in various reference manuals), it is advisable to calculate Ql using both formulas and determine the arithmetic mean. Indeed, according to the proposed formula, the Ql value, as a rule, is slightly overestimated, and according to D.I. Mendeleev formula, on the contrary, it is usually underestimated.
The calorific value of carbon strongly depends on its allotropic form, for example, carbon in the form of diamond under normal conditions burns mainly to CO, and activated carbon to CO2, thus the thermal effect of combustion reactions can be very different.
Variance analysis: each experimental point is obtained as a result of multiple measurements, in order to determine the variance it is necessary to know the results of each specific measurement. This can only be done by the person who actually carried out these measurements.
In the table in column 10, "the error according to the formula proposed in this work, %" is defined -this is an analogue of the relative error.
The abscissa shows the oxygen balance, which is, in fact, a mathematically accurate value. As for the y-axis, the situation is different there. It contains the calorific value taken from reference books, and this is a purely empirical value. And although it is determined on hosted instruments, sometimes the numbers differ greatly in different reference books, so on average we determine the error at 5 % (the maximum correct error).
This means that the relative root mean square error is:
§ = A/(5x)2 + (Sy)2 =V(5%)2 +(1%)2 =V(26%)2 « 5 %.
(17)
On the graph, the boundaries of the confidence region at the selected significance level are given by lines:
y + A = -k(l + S)x = -1.05 • 0.1387x[mJ- kg -1 ] = = -0.1456x[mJ- kg-1]; (18)
y - A = -k(1 - S)x = -0.95 • 0.1387x[mJ kg-1 ] = = -0.1317 x[mJ- kg-1]. (19)
Points located outside the boundaries of the trust area are indicated in the Figure.
The confidence region is enclosed between the thin dotted lines in the Figure.
Points 26, 12, 44, 5, 24, 18, 19, 7, 45, 2, and 39 were outside the confidence area.
The correlation line is sought in the form y = kx + b, but it turned out that b is small.
Even for the smallest values of x from the table, taking into account b changes y within the error.
The coefficient k was obtained by linear regression using the least squares method [24].
A line approximating a system of points on a plane is called a line passing through the origin of coordinates and, therefore, satisfying the equation y = kx, if the sum of the distances from the points to this line is minimal.
When counting, we find
k = -0.1387 MJ-kg-1. (20)
The correlation coefficient is the value of the found k.
Thus, a directly proportional dependence of the calorific value of a substance on its oxygen balance has been demonstrated. A negative oxygen balance of a substance indicates a quantitative lack of oxygen until the substance is completely burned. The more negative the value of oxygen balance, the more oxygen is necessary for the complete oxidation of the fuel - hydrogen and carbon in the molecule due to extramolecular oxygen. Consequently, the more oxygen is needed for the complete oxidation of the fuel, the greater will be the thermal effect from redox reactions (combustion reactions). This is also indicated by the slope of the ascending line on the chart.
The dependence found is the total effect of numerous and complex combustion processes of organic and inorganic substances. A step-by-step study of such processes is a separate problem, the solution of which may be carried out in the future. A positive result of this work is a very simple way to calculate the calorific value of a substance.
4. Conclusions
A new method for calculating the calorific value of substances with a negative OB suitable for organic, inorganic compounds and elements is proposed.
Compared to the well-known formulas for calculating Ql according to formulas by D.I. Mendeleev and M.S. Karash, where the calculation error can reach up to 20 %, while according to the method proposed by the authors, the error, as a rule, does not exceed 6 %.
To determine the oxygen balance, the formula to calculate the oxygen balance of explosives of the universal formula CaHbNcOd is used:
Ql = -O.1387-OB, MJ-kg-1,
where M.w. is the molecular weight of the substance.
Calculation of the oxygen balance is based on the assumption that the fuel in a substance molecule (carbon and hydrogen) is oxidized during combustion by an oxidizer (oxygen) to higher oxides - carbon to CO2, and hydrogen to H2O.
It became possible to quickly and fairly accurately calculate the calorific value of explosives as well; it is impossible to determine the calorific value in a practical way due to the rapid transition of combustion to detonation.
The directly proportional dependence found by the authors is satisfactorily described by the formula y = 0.1387x, where y is the calorific value of the substance, MJ-kg-1; x is the absolute value of the oxygen balance, %.
The accuracy of the calculated calorific value of substances is not lower than according to the empirical formula by D.I. Mendeleev, and the calculation is simpler (one variable -oxygen balance).
5. Funding
This work was partly supported by the Russian Foundation for Basic Research, project No. 18-29-19112.
6. Conflict of interests
The authors declare no conflict of interest.
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Information about the authors / Информация об авторах
Valerii Yu. Dolmatov, D. Sc. (Eng.), Head of research laboratory, Special Construction and Technology Bureau "Technolog", St. Petersburg, Russian Federation; ORCID 0000-0001-8643-0404; e-mail: diamondcentre@mail.ru
Alexander N. Ozerin, D. Sc. (Chem.), Synthetic Supervisor, Enikolopov Institute of Synthetic Polymeric Materials of the RAS, Moscow, Russian Federation; ORCID 0000-0001-7505-6090; e-mail: ozerin@ispm.ru
Evgeny D. Eidelman, D. Sc. (Phys. and Math.), Senior Researcher, Saint Petersburg State Chemical and Pharmaceutical University of the Ministry of Healthcare of the Russian Federation, St. Petersburg, Russian Federation; ORCID 0000-0002-2030-9262; e-mail: Eidelman@mail.ioffe.ru
Anatoly S. Kozlov, Cand. Sc. (Chem.), Head of NPK-2, Special Construction and Technology Bureau "Technolog", St. Petersburg, Russian Federation; AuthorID (Scopus) 7402290001; e-mail: tool999@ yandex.ru
Долматов Валерий Юрьевич, доктор технических наук, начальник научно-исследовательской лаборатории, Специальное конструкторско-технологичес-кое бюро «Технолог», Санкт-Петербург, Российская Федерация; ORCID 0000-0001-8643-0404; e-mail: diamondcentre@mail.ru
Озерин Александр Никифорович, доктор химических наук, научный руководитель, Институт синтетических полимерных материалов им. Н. С. Ени-колопова РАН, Москва, Российская Федерация; ORCID 0000-0001-7505-6090; e-mail: ozerin@ispm.ru
Эйдельман Евгений Давидович, доктор физико-математических наук, старший научный сотрудник, Санкт-Петербургский государственный химико-фармацевтический университет Министерства здравоохранения Российской Федерации, Санкт-Петербург, Российская Федерация; ORCID 00000002-2030-9262; e-mail: Eidelman@mail.ioffe.ru
Козлов Анатолий Сергеевич, кандидат химических наук, начальник НПК-2, Специальное конструк-торско-технологическое бюро «Технолог», Санкт-Петербург, Российская Федерация; AuthorID (Scopus) 7402290001; e-mail: tool999@yandex.ru
Sergey Yu. Naryzhny, 1cat Design Engineer, Special Construction and Technology Bureau "Technolog", St. Petersburg, Russian Federation; e-mail: sergei.nar@bk.ru
Valerii A. Martchukov, Cand. Sc. (Chem.), Leading Design Engineer, Special Construction and Technology Bureau "Technolog", St. Petersburg, Russian Federation; AuthorlD (Scopus) 7801670746; e-mail: marvalal@yandex.ru
Asko Vehanen, Ph.D., Director, Carbodeon Ltd. Oy, Vantaa, Finland; AuthorlD (Scopus) 6701383667; e-mail: asko.vehanen@carbodeon.com
Vesa Myllymäki, Ph.D., CEO, Carbodeon Ltd. Oy, Vantaa, Finland; AuthorlD (Scopus) 55627561500; e-mail: vesa.myllymaki@carbodeon.fi
Нарыжный Сергей Юрьевич, инженер-конструктор 1 категории, Специальное конструкторско-технологическое бюро «Технолог», Санкт-Петербург, Российская Федерация; e-mail: sergei.nar@bk.ru
Марчуков Валерий Александрович, кандидат химических наук, ведущий инженер-конструктор, Специальное конструкторско-технологическое бюро «Технолог», Санкт-Петербург, Российская Федерация; AuthorlD (Scopus) 7801670746; e-mail: marvalal@yandex.ru
Аско Веханен, Ph.D., директор, Carbodeon Ltd. Oy, Вантаа, Финляндия; AuthorlD (Scopus) 6701383667; e-mail: asko.vehanen@carbodeon.com
Веса Мюллюмяки, Ph.D., главный исполнительный директор, Carbodeon Ltd. Oy, Вантаа, Финляндия; AuthorlD (Scopus) 55627561500; e-mail: vesa.myllymaki@carbodeon.fi
Received 17 February 2022; Accepted 15 April 2022; Published 01 July 2022
Copyright: © Dolmatov VYu, Ozerin AN, Eidelman ED, Kozlov AS, Naryzhny SYu, Martchukov VA, Vehanen A, Myllymaki V, 2022. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.Org/licenses/by/4.0/).
