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21Сегодня преимуществом такого метода улучшения системы пожаротушения, работающего в составе с промышленными телевизионными установками, по сравнению с управляющими вручную лафетными стволами является возможность замены человека машиной в экстремальных условиях, высвобождение значительного числа пожарных для решения других тактических задач по борьбе с пожарами, способность в зависимости от характера пожара действовать по различным программам.
Список литературы
1. Федеральный закон от 27.12.2002 N 184-ФЗ (ред. от 29.07.2017) «О техническом регулировании» // http://www.consultant.ru
2. Федеральный закон от 30.12.2009 № 384-ФЗ (ред. от 02.07.2013) «Технический регламент о безопасности зданий и сооружений» // http://www.consultant.ru
3. Федеральный закон от 22.07.2008 N 123-ФЗ (ред. от 27.12.2018) «Технический регламент о требованиях пожарной безопасности» // http://www.consultant.ru
4. Государственный доклад «О состоянии защиты населения и территорий Российской Федерации от чрезвычайных ситуаций природного и техногенного характера в 2017-2019 гг.» // https://www.mchs.gov.ru/dokumenty/4602
5. Антонченко В.В. Проблемы профилактической работы в сфере обеспечения пожарной безопасности // Актуальные проблемы российского права. 2019. № 1 (98). С. 73-79.
6. Яковлев С.Е. Требования пожарной безопасности к производственным зданиям и помещениям // Аллея науки. 2019. Т. 1. № 8 (35). С. 343345.
7. Барануков Р.К., Сметанкина Г.И., Дорохова О.В. Система пожарной безопасности объектов производственного назначения // Мировая наука. 2019. № 2 (23). С. 94-97.
8. Новиков И.В., Сметанкина Г.И., Дорохова О.В. Деклалирование пожарной безопасности // Мировая наука. 2019. № 2 (23). С. 192-195.
9. Горбань Ю.И. Системы пожаротушения для защиты машинных залов тэц, аэс и гэс: проблемы и решения http://www.firerobots.ru/ru/press-center/info/item 5563.html
METHOD FOR CALCULATING KINETIC PARAMETERS OF HETEROGENEOUS-CATALYTIC
REACTIONS
Kontsevoi A.,
Candidate of Technical Sciences (PhD), Associate Professor, Department of Inorganic Substances, Water Treatment and General Chemical Technology.
Igor Sikorsky Kyiv Polytechnic Institute, Ukraine
Kontsevoi S.,
Candidate of Technical Sciences (PhD), Associate Professor, Department of Inorganic Substances, Water Treatment and General Chemical Technology.
Igor Sikorsky Kyiv Polytechnic Institute, Ukraine
Ivanenko I.
Candidate of Chemical Sciences (PhD), Associate Professor, Department of Inorganic Substances, Water Treatment and General Chemical Technology.
Igor Sikorsky Kyiv Polytechnic Institute, Ukraine
Abstract
The complexity of heterogeneous-catalytic reactions often leads to a rejection of kinetic equations based on the mass action law in favor of kinetic equations, the form of which is determined by the Langmuir-Hinshelwood mechanism. In this article is proposed the methodology of processing on a personal computer of experimental data to determine the possible mechanism of the reaction, envisaging various variants of adsorption of the reagents and reaction products. The step-by-step algorithm offers the development of an Excel program that is designed to calculate the reaction rate constant, the adsorption coefficients of the reaction components, the pre-exponential factor, the activation energy and the heat of adsorption for catalytic heterogeneous processes occurring in the kinetic region.
Keywords: heterogeneous-catalytic reactions, Langmuir-Hinshelwood kinetic equations, mechanism of the reaction, algorithm, Excel program, rate constant, adsorption coefficients, activation energy, heat of adsorption.
Introduction. Any study of kinetics in heterogeneous catalysis starts with identifying the relationship between the concentration of adsorbed reactants and their concentrations in the gas phase (which can be measured directly, in comparison with the surface concentration). This relationship with some approximation can be estimated using the Langmuir adsorption model. The complexity of heterogeneous-catalytic reactions often leads to a rejection of kinetic equations based on the mass
action law in favor of kinetic equations, the form of which is determined by the Langmuir-Hinshelwood mechanism [1-5]. In this article is proposed the method of processing on a personal computer (PC) of experimental data to determine the possible mechanism of the reaction, envisaging various variants of adsorption of the reagents and reaction products. The purpose of the work is processing of experimental data on a PC for the
determination possible reaction mechanism by designing of program, which calculates reaction rate constant, adsorption coefficients of the reaction components, pre-exponential factor, activation energy and heat of adsorption for heterogeneous catalytic processes, that are limited in kinetic region.
Research methodology. In the case of monomo-lecular substitution of all adsorption sites on the catalyst surface by one gaseous reactant, fractional occupancy of surface area 8 is:
e_ kiP _ bP
(k2 + kp) 1 + bP ' (1)
where ki and k2 - adsorption and desorption constants respectively;
b=k1/k2 - adsorption ratio (if adsorption is reversible, the b - equilibrium constant between reactant on the catalyst surface and reactant in the gas phase);
P - partial pressure of the gaseous reagent.
In the case of adsorption of mixture, which consists of n components, fractional occupancy of surface area by i component can be determined by the equation:
bP
0.■ =
(1+E bP)
(2)
If substance A dissociates into z particles during adsorption (usually z = 2: N2, H2, O2), each of which occupies one adsorption site, then:
0, =
(bAPA)7
1 + (bAPA)'
(3)
It should be highlighted, that the Langmuir model is used to describe physical adsorption and can be used for formal description of chemisorption, due to the fact that the chemical adsorption is always a monomolecu-lar (monolayer sorption). According to the Langmuir-Hinshelwood approach, the rate of heterogeneous catalytic reactions determined by the surface action law, which is similar to the mass action law for homogeneous reactions. As a first approximation, the law states that the rate of reaction is proportional to the product of numbers of surface sites, occupied by reagents (surface concentration) each raised to power of respective stoi-chiometric coefficient:
W = ki-0aA (4) Stoichiometric coefficients in this case demonstrate in which ratio substances interact on the surface of the catalyst (in the adsorbed state), and may not coincide with the stoichiometric coefficients of these substances as if they interact in the absence of a catalyst. This makes it necessary to determine the experimental values of a=n1 and b=n2 which are called orders of catalytic reaction for A and B components respectively.
Adsorption coefficient b depends on temperature according to next equation:
[A]JAL-Mo • 14
b = b0e
-AH®ic/ Qaöc/
/rt = b0e /rt ,
(5)
where b0 - a factor related to the adsorption entropy;
Hads, Qads - the enthalpy and heat of adsorption process respectively.
According to equations (1) (if 1>>bAPA and including the Arrhenius equation) and (5) next equation for A component can be obtained:
W = K ■ b
'A = K0 b0
-(E-Qads)/
■ P = K ■
PA = K0
-(Ekaj)/
/RT ■ p PA
(6)
where Ekaj=E - Qads - apparent activation energy of catalytic reaction, which is less than the true activation energy E by the amount of heat absorption.
The mathematical processing of experimental data for various mechanisms is presented below.
Mechanism 1: Interaction of adsorbed components A and B including influence of the reaction product C adsorption for reaction aA+bB^cC+rR.
Schematic representation of the heterogeneous catalytic reaction mechanism, which is described by the equations:
niA +ni( ) • ni(A)
n2B + n2( ) •^(B)
n1 (A) + n(B) = (C) +R +( n1 +n -1)( )
(C) • C + ( ),
where ( ) is here and below the vacant adsorption site on the surface.
The underlined reaction proceeds with the lowest rate, which means that it is the limiting stage of the process. Component R is not adsorbed. According to the surface action law, next equation describes rate for the reaction:
W = -
k■(bA ■ Paf (bB ■ PB)
(1 + bA ■ Pa + bB ■ Pb + bc ■ Pc )
(7)
where k - rate constant;
bA, bB, bc - adsorption coefficients of A, B, C components respectively;
PA, P, P - partial pressure of A, B, C component respectively;
n1, n2 - order of reaction for A, B components respectively;
S = n1 + n2 - value, which describes the adsorption effect on the rate of chemical reactions.
It should be noted, that without the denominator, equation (7) actually turns into equation of the mass action law.
Variable concentrations of components during the reaction should be presented through the degree of conversion X of component A and initial concentration of the components, also change in the volume during the reaction should be taken into consideration A n = (c+r) - (a + b):
+ An-[A] ■ X 1 + An-[A] ■ X
(1 -X)= A-(1-X) ;
(8)
[ »]=-
[ 4 - b [ 4 ■ X
a
a
■[ 4
+ An ■ [ A]0 ■ X 1 + X
[C ] = 1
[C ]o + C ■[ 4 ■ X
a
a
■[ A]o
/a [ A. ]
f
-X
An■ [A]o ■ X 1 + An■ [A]q ■ X
Co ]
c/
\/ a
\ \
= b ■ A ■(d - X) ; (9) a
[Ao]
■ + X
= (f + X) ; (10) a
A =
[ A]o
1 + *"■ [ 4,-X' ~b/a [ A. ]
d = JBL ; f = [C]
/a [ Ao ]
(11)
The values of A, d and f were introduced to simplify the processing of the equation on a PC. Experimental data is presented in series of dependences of the reaction rate from the conversion degree of basic component, thus the speed, which is presented like the change of a component partial pressure in the time, should be introduced like a change of the degree of conversion in time:
P-[4,1-dX A-dX tjt dX W
L J " W = — = — , (12)
dz A
dP
W ' = - A
dr 1 + n■ [A ]■ X^dr dr
where P - total pressure in the system, bar.
According to the Dalton law, partial pressure of component can be presented as the product of total system pressure and molar fraction, therefore the equation for reaction rate transforms into:
k-bf-Pn1 -[AT1 bB"2-Pn2 -[Bln2
--(13)
W = ■
{A (1 + bA-P■ [ A] + bB-P- [ B] + bc-P■ [C ])}■
For further transformation, total pressure in the system is assumed to be 1 bar (atmospheric pressure) and concentrations of the components are presented by the initial concentration and the degree of conversion of component A:
f , \n2
kAn1 ■(! - X )n1 ■ b/2■ bA I ■( d - X )
W = -
a
A 1 + /■A■ (1 - X ) + / ^ bA |(d - X ) + bc CA f + X )
(14)
The equation for reaction rate transforms into next form:
W = -
K ■An1+"2-1 ■(! - X)" 1 ■(d - X)n
{1 + A-(b\-(1 - X ) + b\-( d - X ) + bc■ ( f + X ))}
(15)
where
b\ = bA ; b\ = \ ; bc = C-bc:
a a
K = k^A"1
= k ■ b * A" ■ bB"2. (15a)
b
b c of
(b A
--bB
va y
To calculate coefficients K , b A, b B
equation (15) Excel Solver add-in is used: the sum of squared deviations (SD) of experimental ( We) and calculated ( W) values of reaction rate should be minimized (We-W)2^min. Then constants k, bA , bB , bc should be calculated using formulas mentioned above (15a).
Mechanism 2: Interaction of adsorbed component B with component A from the gas phase (Eley-Rideal mechanism) including the influence of reaction product C adsorption for reaction aA +bB^cC+rR.
Schematic representation of the mechanism of heterogeneous catalytic reactions is described by the equations:
n2B + n2( ) •^(B)
aA + n(B) = (C) +R +(n2 -1)( )
(C) • C + ( ).
The underlined reaction proceeds with the lowest rate, which means that it is the limiting stage of the process. According to the surface action law, next equation describes rate for the reaction:
S
W' =
k-PAnl (bB-PB )n2 (1 + Öb-Pb + bc-Pc )S
(16)
The transformation of this equation leads to the following equation:
W = -
K-An1+n 2-1 -(1 - X )n1 •( d - X )n 2
(17)
W = k-
(Öa-PA T'PB-PBJ2 (1 + bA-PA +J Öb-Pb2 +bc-Pc )
■(18)
The transformation of equation (18) leads to the following equation:
W = -
K • An1+n2/2-1 -(1- X)n1 •(d - X)'
(19)
¡1 + A-(bA (1-X )+>/b\-( d - X ) + bC-( f + X ))} where
b\ = bA ; b\ = b-bB ; b'c = c-bc ;
a a
K = k-bAn1 -|b-bB I = k-b\n1-b'Bn2/2. (19a)
a
b' c of
{l+A- (b'B- ( d - X ) + b'c-( / + X ))} where b ' B = bB ; b ' c = bc ;
K = k ■ (bB )"2 = k-b'/2 (17a)
To calculate coefficients K , b 'B, b 'c of equation (17) Excel Solver add-in is used: the sum of squared deviations (SD) of experimental ( We) and calculated ( W) values of reaction rate should be minimized
(X(We-W)2^-min). Then constants k, bB , bc should be
calculated using formulas mentioned above (17a). The
absence of coefficient b ' A was considered.
Mechanism 3 : interaction of adsorbed component A and adsorbed by dissociative mechanism component B2 including the influence of reaction product C adsorption for reaction aA+bB2^cC+rR.
Schematic representation of the mechanism of heterogeneous catalytic reactions is described by the equations:
niA +ni( ) — ni(A)
n2B2 + 2n2( ) — 2n2(B)
ni (A) + 2n(B) = (C) + R + ( ni +2n2 -1)( )
(C) - C+ ( ).
The underlined reaction proceeds with the lowest rate, which means that it is the limiting stage of the process. According to the surface action law, next equation describes rate for the reaction:
To calculate coefficients K, b A, b B
equation (19) Excel Solver add-in is used: the sum of squared deviations (SD) of experimental (We) and calculated (W) values of reaction rate should be minimized (X(We-W)2^-min). Then constants k, bA , bB , bc should
be calculated using formulas mentioned above (19a).
Mechanism 4: interaction between adsorbed by dissociative mechanism component B and component A from the gas phase including the influence of reaction product C adsorption for reaction aA+bB2^cC+rR.
Schematic representation of the mechanism of heterogeneous catalytic reactions is described by the equations:
n2B2 + 2n2( ) — 2n2(B) n (A) + 2n(B) = (C) + R + (2n2 -1)( ) (C) - C+ ( ).
The underlined reaction proceeds with the lowest rate, which means that it is the limiting stage of the process. According to the surface action law, next equation describes rate for the reaction:
W = k-
PAn1>B-PB2)
(1+ V Öb-PB2 + bc-Pc )
. (20)
The transformation of equation (18) leads to the next equation:
W = ■
K -An
-(1 - X )n1 -( d - X )
.(21)
{l + A-(^ b'B- ( d - X ) + b'c •( / + X ))}
where: b 'B = bB ; b 'c = bc ; K = k ■ (bB )"2 2 . (21a)
To calculate coefficients K , b , b of equation (21) Excel Solver add-in is used: the sum of squared deviations (SD) of experimental (We) and calculated (W) values of reaction rate should be minimized (X(We-W)2^min). Then constants k, bB , bc should be calculated using formulas mentioned above (21a). The absence of coefficient b ' A was considered.
Results of the research and discussion. Output data for two temperatures are given in Table 1. The values of the stoichiometric coefficients a=1, b=4, c=2 are determined by model chemical reaction: A + 4B = 2C+R. Component R is not adsorbed. It is accepted that the reaction is irreversible.
2
n
S
S
Table 1
Output data and results of calculations for the equation (15)_
T=453K
Series 1 Series 2 Series 3 Series 4
[A]o 0,005 [A]0 0,005 [A]0 0,03 [A]0 0,005
[B]o 0,025 [B]0 0,095 [B]0 0,135 [B]0 0,028
[C]o 0 [C]0 0 [C]0 0 [C]0 0,02
X We X We X We X We
0,2 0,0745 0,2 0,0448 0,2 0,0166 0,2 0,0346
0,3 0,0669 0,3 0,0402 0,3 0,0152 0,3 0,0298
0,4 0,0586 0,4 0,0354 0,4 0,0136 0,4 0,0250
0,5 0,0496 0,5 0,0303 0,5 0,0117 0,5 0,0201
0,6 0,0399 0,6 0,0249 0,6 0,0096 0,6 0,0154
0,7 0,0296 0,7 0,0192 0,7 0,0073 0,7 0,0108
K1 2749403 k 0,0041
b'A 504,08 bA 504,08
b'B 1146,82 bB 286,71
b'C 297,59 bC 148,8
T=463K
0,2 0,1304 0,2 0,0827 0,2 0,0312 0,2 0,0536
0,3 0,1147 0,3 0,0738 0,3 0,0279 0,3 0,0453
0,4 0,0980 0,4 0,0646 0,4 0,0244 0,4 0,0370
0,5 0,0806 0,5 0,0550 0,5 0,0205 0,5 0,0291
0,6 0,0627 0,6 0,0449 0,6 0,0163 0,6 0,0216
0,7 0,0446 0,7 0,0344 0,7 0,0117 0,7 0,0147
K1 2248861 k 0,0084
b'A 355,03 bA 355,03
b'B 866,4 bB 216,6
b'C 273,55 bC 136,8
E 123796 J/mol QB QC 48863 J/mol 14683 J/mol
k0 7,94E+11
Qa 61096 J/mol
Calculations. To perform the calculations for four mechanisms mentioned above, copy initial data for temperature 453 K (Table 1) to 4 individual worksheets in a Excel workbook, in each worksheet for all kinetic curves use only one equation that corresponds to a particular mechanism. Calculate in the relevant cells values d and f using initial data and assume the values of n1, n2, s depending on the chosen mechanism.
For all mechanisms assume n1 = 1, n2 = 2, s = 3. Variations in the course of calculations are possible, in particular, the value of s = 2. The maximum concentration of reagents is 16.5 % for series 3, the rest is inert gas. Ignore change in volume: An = 0, also in the mentioned above formulas A = Ao - see equation (11).
In Excel table 1 is supplemented with columns for calculating the reaction rate W and values of squared deviation (SD). To facilitate calculations of complex formulas, we recommend counting a numerator and denominator separately in additional columns. In the columns "numerator" and "denomina-tor" put numerators and denominators from kinetic equations (15) (17) (19) (21) respectively with an absolute references to cells of K1, b 'a, b B, b C, also it is necessary to provide the initial approximation of the unknown constants (0 - empty cell). By dividing the "numerator" by the "denominator", calculate the reaction rate W. The quality of the calculation depends heavily on the initial approximation K1, b 'a, b 'b, b 'c. In any case, after first calculation, it is required to repeat calculations using constants,
which were found in previous step, while previous and present calculations (values) do not match.
In the column "SD" for 6 points of each series put values of squared deviation (SD) for experimental We and calculated W reaction rates: SDi=(Wei-Wi)2. In the cell "sum of squared deviations " put SUM function to calculate the sum of SDi of experiments series - £1, £2, £3, £4. In the cell "total sum of squared deviation" (TSSD) calculate the sum of four SD,: TSSD= £1+ £2+ £3+ £4.
Refer to the Solver add-in, click Tools menu and select Add-ins, in the Add-ins window, select the check box on the left side of the add-in function, and then click OK, run the function, click Tools, then Solver. Set the "maximum number of iterations" to 1000, "relative error" to 0.00000101, "convergence" to 0.0001. Using the Solver add-on, find K1, b'A, b 'B, b'C provided that the total sum of squared errors of the deviation is minimum: TSSD ^min.
Comments. Setting of Solver add-in in Excel 2007 - copy this link to the browser window: http://www.solver.com/excel-solver-how-load-or-start-solver
Comparing values of total sum of squared deviations for different mechanisms (equations), the correct mechanism can be identified. The minimum value of total sum of squared deviations according to the table indicates the correct mechanism. Negative values of
constants or equal to 0 indicate a disparity of mechanism to physic-chemical catalytic basics of reaction, but it is possible that b'c = 0.
For the chosen mechanism, process data for temperatures equal 463 K using the algorithm mentioned above.
Calculate rate constant k and adsorption coefficients bA, bB, be for both temperatures using the relevant equations - see (15a - 21a).
Using values of calculated reaction rate constants and component adsorption coefficients for specified temperatures, calculate:
- activation energy, J/mole:
R ■ T ■ T K E = R T T -ln- t
a T - T )
- pre-exponential factor, s-1
ko - '
-E/ - E/
'RT „ /RT
e ' 1 e
- heat of adsorption for each component J/mole:
Q -
R-T-T bT
R T1 T2 _J _ lTl
T - T) biT 2
The best results (the minimum total sum of squared deviations) among the four mechanisms are obtained for mechanism 1 - equation kinetics (15). Calculated reaction rate W practically do not differ from the experimental values We. Table 1 provides calculations of activation energy and heat of adsorption of components.
Conclusions. The proposed method for calculating kinetic parameters will facilitate better understanding by students and researchers of possible mechanisms of heterogeneous-catalytic reactions and performing calculations according to the proposed algorithm will deepen their skills in the advanced Excel.
References
1. G.S. Yablonskii, V.I. Bykov, V.I. Elokhin, A.N. Gorban (1991), Kinetic models of catalytic reactions, Elsevier Science, p. 391
2. Anna Kulik, Ramona Saliger. Seminararbeit «Heterogene Katalyse an Festkörperoberflächen», Technische Universität Braunschweig Institut für Physikalische und Theoretische Chemie, Braunschweig, 2006, 27 s.
3. Devanand Pintoa, Edgar A. Arriagab, Regine M. Schoenherrc, Shirley Shinn-Huey Chouc, Norman J. Dovichic (2003), Kinetics and apparent activation energy of the reaction of the fluorogenic reagent 5-fu-roylquinoline-3-carboxaldehyde with ovalbumin, Journal of Chromatography B, 793 (1), 107-114.
4. Koncevoj A.L. Issledovanie processa gidriro-vaniya primesi dioksida ugleroda v prirodnom gaze /A.L. Koncevoj, B.A. ZHidkov, O.G. CHernickij // Ki-netika i kataliz. - Kiev: Naukova dumka, 1982. -vypusk 20. - S.78-82.
5. Langmuir-Hinshelwood Kinetics. https ://www.sciencedirect.com/topics/chemistry/lang-muir-hinshelwood-kinetics (date of the application 06.01.22)
FORMATION OF A SET OF ALTERNATIVES FOR PERSONNEL DECISION ON COMPLETING VACANT POSITIONS OF MILITARY ORGANIZATIONAL STRUCTURES
Prokopenko O.,
ORCID 0000-0002-5482-0317 Adjunct of the Center for Military and Strategic Studies of the National Defence University of Ukraine named after Ivan Chernyakhovsky
Ukraine, Kyiv Rybydajlo A. ORCID 0000-0002-6156-469X Candidate of Technical Sciences (Ph.D), Senior Researcher, Leading Researcher of the Center for Military and Strategic Studies of the National Defence University of Ukraine named after Ivan Chernyakhovsky
Ukraine, Kyiv
Abstract
The proposed method of forming a set of alternatives for personnel decision on completing vacant positions of military organizational structures on the basis of the application of the developed model of artificial neural network.
Keywords: personnel decision; career management; military organizational structure; artificial neural network, decision support system, rating, classification.
Formulation of the problem. The modern stage of reforming the Armed Forces of Ukraine is carried out in the conditions of a difficult military-political and economic situation that has developed as a result of the armed aggression of the Russian Federation. This causes requirements for guaranteed and high-quality
staffing of military organizational structures by trained and motivated personnel.
The most effective mechanism for solving this problem is the development and implementation of appropriate information and analytical support for:
