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2023 Т. 53 № 2 / Техника и технология пищевых производств / Food Processing: Techniques and Technology
ISSN 2074-9414 (Print) ISSN 2313-1748 (Online)
https://doi.org/10.21603/2074-9414-2023-2-2428 https://elibrary.ru/SBXYHE
Original article Available online at https://fptt.ru/en
<8>
Electrotechnological Heat Treatment of Milk: Energy and Exergy Efficiency
Andrei A. Bagaev* , Sergey O. Bobrovskiy
Altai State Agricultural University"®", Barnaul, Russia
Received: 28.11.2022 Revised: 13.01.2023 Accepted: 07.02.2023
*Andrei A. Bagaev: BAGAEV710@mail.ru, https://orcid.org/0000-0003-2586-2590 Sergey O. Bobrovskiy: https://orcid.org/0000-0001-9243-0179
© A.A. Bagaev, S.O. Bobrovskiy, 2023
Abstract.
The dairy industry needs new and more energy-efficient technological procedure for milk pasteurization. This article introduces a comparative efficiency assessment of various milk pasteurization technologies and electrotechnological means. The study featured milk, which was heated from 20 to 75^ with a capacity of 1000 kg/h at an estimated power of 58.95 kW. The treatment involved a steam-to-milk pasteurizer with electric indirect or direct heating, an induction pasteurizer, and a thermosiphon pasteurizer with direct or indirect electric heating. The study relied on the methods of energy and exergy analyses.
The system of steam-to-milk pasteurizer with electric indirect (elemental, induction) or direct (electrode) heating demonstrated the following indicators: exergy loss - 1.29 kW, power consumption - 71.29 kW, exergy efficiency - 0.99, energy efficiency -0.827. The thermosiphon pasteurizer with direct or indirect electric heating demonstrated the following properties: exergy loss - 1.29 kW, power consumption - 60.92 kW, exergy efficiency - 0.99, energy efficiency - 0.9676. The induction pasteurizer had the least competitive parameters: exergy loss - 10.8 kW, power consumption - 70.43 kW, exergy efficiency - 0.867, energy efficiency - 0.837.
The thermosiphon pasteurizer with direct or indirect electric heating was able to increase the energy efficiency of milk pasteurization, while the induction pasteurizer proved to be a promising R&D direction.
Keywords. Pasteurization, dairy products, exergy efficiency, energy efficiency, electrotechnology, direct heating, indirect heating, induction heating, thermodynamic properties
For citation: Bagaev AA, Bobrovskiy SO. Electrotechnological Heat Treatment of Milk: Energy and Exergy Efficiency. Food Processing: Techniques and Technology. 2023;53(2):272-280. https://doi.org/10.21603/2074-9414-2023-2-2428
https://doi.org/10.21603/2074-9414-2023-2-2428 Оригинальная статья
https://elibrary.ru/SBXYHE https://fptt.ru
Энергетическая и эксергетическая оценка электротехнологических средств термической обработки молока
А. А. Багаев* , С. О. Бобровский
Алтайский государственный аграрный университет**®**, Барнаул, Россия
Поступила в редакцию: 28.11.2022 *А. А. Багаев: BAGAEV710@mail.ru,
Принята после рецензирования: 13.01.2023 https://orcid.org/0000-0003-2586-2590
Принята к публикации: 07.02.2023 С. О. Бобровский: https://orcid.org/0000-0001-9243-0179
© А. А. Багаев, С. О. Бобровский, 2023
Аннотация.
Поиск и обоснование перспективных направлений повышения энергоэффективности технологических процессов пастеризации молока является актуальной научно-технической проблемой. Целью настоящей работы являлось получение сравнительной оценки эффективности технологий и технических устройств пастеризации молока с использованием электротехнологических средств.
Объектом исследования являлся процесс нагрева молока от 20 до 75 °С производительностью 1000 кг/ч при расчетной мощности 58,95 кВт в разных устройствах термической обработки молока: пастеризатор «водяной пар - молоко» с использованием электротехнологических средств нагрева, пастеризатор индукционного типа и термосифонный пастеризатор с использованием прямого или косвенного электронагрева. Использовали методы энергетического и эксергетического анализа.
Система «пастеризатор молока "водяной пар - молоко" с использованием электрического косвенного (с помощью элементного, индукционного) или прямого (электродного) нагрева» характеризуется следующими показателями: потери эксергии - 1,29 кВт, потребляемая мощность - 71,29 кВт, эксергетический КПД - 0,99, энергетический КПД - 0,827. Для системы «термосифонный пастеризатор с использованием прямого или косвенного электронагрева» характерны: потери эксергии - 1,29 кВт, потребляемая мощность - 60,92 кВт, эксергетический КПД - 0,99, энергетический КПД -0,9676. Наименее конкурентоспособными параметрами обладает пастеризатор индукционного типа: потери эксергии -10,8 кВт, потребляемая мощность - 70,43 кВт, эксергетический КПД - 0,867, энергетический КПД - 0,837. Для повышения энергоэффективности процесса пастеризации молока целесообразно использовать систему «пастеризатор термосифонного типа с использованием прямого или косвенного электронагрева». Перспективным направлением дальнейших исследований следует считать совершенствование системы типа «пастеризатор индукционного типа».
Ключевые слова. Пастеризация, молочные продукты, эксергетическая эффективность, энергетическая эффективность, электротехнология, прямой нагрев, косвенный нагрев, индукционный нагрев, термодинамические свойства
Для цитирования: Багаев А. А., Бобровский С. О. Энергетическая и эксергетическая оценка электротехнологических средств термической обработки молока // Техника и технология пищевых производств. 2023. Т. 53. № 2. С. 272-280. (На англ.). https://doi.org/10.21603/2074-9414-2023-2-2428
Introduction
The current development trends are such that food enterprises are increasing in capacity but decreasing in number. As a result, it takes longer to ship dairy raw materials from farms to shops or processing facilities, and milk cooling technologies often fail to meet this new challenge.
The primary milk processing destroys pathogenic microorganisms, e.g., Escherichia coli, typhoid pathogens, tuberculosis, etc. It also destroys enzyme systems, e.g., phosphatase: the absence of phosphatase is a marker of sufficient disinfection [1]. A proper
treatment also means that none of these pathogens is able to form spores in milk.
Pasteurizers with water or vapor of varying saturation degrees as an intermediate heat carrier is currently the most popular commercial type [2, 3]. Water heating and vaporization are non-specific processes that can be provided by such electrotechnological means as indirect (elemental, induction) or direct (electrode) heating.
The dairy industry knows other antibacterial milk treatment technologies that do not involve thermal methods, e.g., ultrasound treatment, infrared and ultraviolet irradiation, solar energy, microwave currents,
hydrodynamic, etc. [4-13]. These technologies still remain R&D projects and have not entered commercial dairy production.
Therefore, thermal treatment remains the only technology that ensures the safety of dairy products in terms of pathogenic microorganisms and enzyme systems. In fact, heat treatment is a combination of temperature and exposure time that destroys pathogenic microorganisms and enzyme systems in milk. Heat treatment modes in dairy production differ in temperature modes and heating time. Of all the methods listed in [1], we used the so-called high-temperature short-term pasteurization. It presupposes a temperature of 72-75°C for 15-20 s.
Induction heating is a promising thermal processing technology in food production. Its energy efficiency is as high as 95-99%, but the objectivity of this method is yet to be confirmed [14-18].
A literature review showed that the number of existing and effective milk pasteurization technologies is quite large, but food producers still need objective methods for assessing their energy efficiency and improvement prospects.
Modern approaches to efficiency tests of technological processes and systems rely on the efficiency criterion, energy efficiency, and exergy efficiency [19].
Exergy efficiency is based on the second law of thermodynamics. The thermodynamic analysis involves a system of equations for the balance of mass, energy, entropy, and exergy [20]. This study concentrated on the energy and exergy balance equations.
Heating processes are irreversible. The first and second laws of thermodynamics for irreversible systems can be represented as four characteristic thermodynamic functions that are irreducible to each other. One of them is the Gibbs energy (isobaric-isothermal potential) calculated as G = h - T x S, where G is the Gibbs energy, h is the enthalpy, T is the temperature, and S is entropy.
The Gibbs energy equation was used to calculate specific exergy y in [20, 21]:
¥ = (- -ho)-To (S-So)
(1)
where h0, S0 are enthalpy and entropy of the initial state of substances (base for comparison) at initial temperature T0 and initial pressure P0.
According to [20], the system exergy is calculated as follows:
Ex = m ei = mx[(:-:0)-7; (S-S0)] (2)
The overall balance of exergy — e)timated as follows [20]:
e= = I EX -XE
OUT 'X
(3)
where I EX isthesum of exergies atthe input to the system elements; IhhXUTis the sum of exergies
at the output of the elements of the system or the total exfr|= 2 r- 2uc-io n.
Exergx affieienay is (2e ra)i- o( e-srgy output (total exergy production) to exergy input (total energy consumed). Therefore, the exergy efficiency, %, is calculated xs fsllgws:
IEXU
T en =—-
IE
: 100 =
f .г A
\ - AEX
IE.
100
(4)
A greater exergy efficiency nen is the соndition for increasing the efficiency of compared processes or systems.
Energy efficiency es basee on the first law of thermodynamics. Efficiency fantor nen serves as the simplest and most common assessment of energy efficiency. It is calculated as the ratio of the required useful power for heating; milk PqeNo the power constmed by the electrotechnological installation P %:
n =
t en
h
Pr.
-x 100
(5)
Efficiency can be increased by exceeding energy efficiency цеп of the process orsystem in question.
The research objective was to develop an assessment method based on energyandexergyanalysis to compare the effectiveness oftechnologies and electrotechnological devices.
Study objects and methods
The research relied on the methods of energy and exergy analyses.
It involved exergy and energy processes based on the firstand second laws of thermodynamics that occur in electrotechnologi cal devices used for the thermal treatment of liquidfoods. The first device was a steam-to-milk pasteurizer with electrical indirect (with heating elements, induction)or direct(electrode) heating(Fig. 1a). Thesecond device wasaninduction type pasteurizer(Fig.1b). Thethirdonewasa thermosiphon pasteurizer with one of the above methods (Fig. 1c).
The analysis ef tXe emergy -nd energy efficiency was correct due to the shared initial data reported in [22], which defined the hydro- and thermodynamic characteristics of Ireat exchan^rs for heating milk: milk productio n G = 1000 kg/h =0.27 kg/s = 0.96 m3/h, heating pipe wall t^mf>x;eature Tw =g 100=C, milk input temperature T.n = 20°C, output milk temçerature T = 75°С.
oui
If the specific heat capacity of milk c is 3.97 kJ/(kg-dng)= then XOeus eful heat flow, kW, and the power of the el hsrtrothermal installation are:
hese = Q = Gcх(Тш -Ты) = 58.95
(6)
Water
2
IMilk
ï
1
Milk
n
II
u
►Condensate
Pel
fi**** ^
k Milk
Milk
I - a water steam-to-milk pasteurizer with electric direct or indirect heating; II - an induction pasteurizer; III - a thermosiphon pasteurizer with direct or indirect electric heating
Figure 1. Milk pasteurization systems: a - a steam-to-milk pasteurizer; b - an induction pasteurizer; c - a thermosiphon pasteurizer with direct/indirect electric heating
Рисунок 1. Схемы систем пастеризации молока: a - пастеризатор молока типа «водяной пар - молоко»; b - пастеризатор индукционного типа; c - пастеризатор термосифонного типа с использованием прямого или косвенного электронагрева
a
b
c
Wall temperature of the heat exchange surface Tw = 100°C is limited by the requirements of thermal stability because raw milk must withstand heat treatment without protein coagulation (denaturation) [23]. It also depends on the presence of thermolabile proteins in milk.
We investigated the dependence of the coefficients of exergy and energy efficiency of electrotechnological milk-heating devices at given performance values for milk and heat exchanger geometry. The list of systems included a steam-to-milk pasteurizer with electric indirect or direct heating, an induction pasteurizer, and a thermosiphon pasteurizer with direct or indirect electric heating.
The research involved the following assumptions:
- We did not take into account the heat losses to the environment;
- The operation mode was considered to be in a steady state;
- We did not calculate the pressure drops in the heat exchangers and pipelines; and
- Kinetic, potential, and chemical energies were neglected.
Results and discussion
The thermodynamic properties of water and water vapor, i.e., enthalpy, entropy, specific heat of vaporization, etc., were known.
The enthalpy of substance 0. is the product of the specific heat capacrty u tnh tempesature T: h = oT.
Figure 1a showo slue ciscuih eas tiiis type of hhe steam-to-milk pasWeudzcr whh e k cOrk; al + ndtrec i hus^i^g elemental, induction) or dihest (electrode) heating. It is a steam generoyor witt eao (dectrade, ulrmental, or induction heater as enerjGsource.
Steam temperature tu °C, atwoekin- prershre^,MPa:
Wo ^=0.13-0.15
tar u ia7.ar e3(15uira Medium steam tempesature t , °C:
-n 11(
(7)
2
Heating steam consumption mj(,kg/s, given that (6):
„ = Q
n (.(053
(8)
where Q is the useful heat flow andpower of the electrothermal installftion, kW; hst is the steam enthalpy, hst = 2117912 J/fg; h. ih ittiss enthafpysfthe stndansate, h= 461696.1 J/kg. '
According ti ths first 1 aw =e tttermodynamics, to ensure milk productivity G = 1000 kg/h = 0.27 kg/s when it is heated from T. = 20°C at the input to
in i
Tout = 75°C at the iutput, the procedure requires steam flow m= 0.0273 kg/s.
The resulting water yapoe conssnset onthe heat exchange surface of pipesor heat exchanger planes and transfers heat to the heated medium. Water enters the steam geneeator from ah txternel soirae.
We calculated the exergy parameterr using the thermodynami parameters of water, steam, condensate, and milk according to formulee (f t and (2) (Table 1).
We calcula ed the electrical energy cost used to produce steam Pd ,kW,according toTable 1:
Pil n e
n (h -24) =0.0253x(269(.3-83.93) = 51.29 (9)
Tho data iu Taile t made itpossible to determine the sum of exeogius at i=e inputtotie elements of the system h(0, kW, in e=igLts; with the diagram represented in Fig. la. The indicts oiite censtituent exgrgres fonowrd the or0er in Tob 1 g 1:
Ea 0el 2ЕХ4 2 Е02 2"73(Т1 122 29
(10)
Thesum ef exergies attheoet=un Р9 tdee element+ of thesystem XeX2Ti кЕ, lool+od ^s foOliw;:
]aaJen?CiOne?-22^eeX62^6^ = ii;4n.2^ a 12)
Ac cordingto(4 ),exergy loss AE?=,kW,wascalcula-ted as
АЕп=^ЕХ-XЕГ 2=1.29
(12)
Then, the exergyefficiency, %, took the form 0f
9 л = A
ХЕ
OUT
a
X e
eoo n
1 -
A£x_
<ie
x
X e
(1 00 n 99 0 G)
As a result,theequation for the energy effictescp lookedlikethis, %:
P 58 95
e s-isxiaa = —:—xiaa = 8s.f (14) sn PE1 ft.S9
Figure 1b illustrates the scheme of the ingyctisn pasteurizer. Such factors as induction heating of ferro-magnets, optimal electromagnetic field frequeney, inductors, loading geometry, and heating time were known and had no direct relation to the induction heating of foodstuffs. Few publications [14-18] on induction heating in the food industry feature f oth advantagesand disadvantagesoftheheating technolopy in question.
As in Table 1, the energy used toheat milk Psl ,kW, was defined as follows:
Table 1. Thermodynamic properties of liquids and calculated exergy indicate rs inthe steam-to-milkpasteurizer with electric indirect (tubular electric heaters, induction) or direct (electrode)heating
Таблица 1. Термодинамические свойства жидкостей и результаты расчета показателей эксергии в системе «пастеризатор молока типа "водяной пар - молоко" с использованием электрического косвенного(с помощью элементного,индукционного)
или прямого (электрод ного) нагрева»
No. Medium t K "C A, - kg 8 83 3 kg о к kg m,— 8 i. г, 83 214 -K3t~ kg Ex = m x щ, kW
0 Water 283/10 4 2.03 0.150 0.8213 - -
0' Milk 283/10 38.3 0 3.880 0.2700 - -
1 Milk 293830 38.30 3.94 0 0.2700 40.00 10.80
2 Milk 348/35 299.63 3.99 0 0.2700 260.85 70.43
4 Water 293/28 83.96 0.296 0.0273 41.89 1.14
5 Steam 3838/30 2693.30 7.244 0.0273 2651.23 72.38
6 Condensate 383/810 461.69 1.419 0.0273 419.62 11.45
Table 2. Thermodynamic properties of liquids and celculated exergy indicators in the induction pasteurizer
Таблица 2. Термодинамические свойства жидкостей и результаты расчета показателей эксергии в системе
«пас теризатор индукционного типа
No. Medium t K 4, 8 kg 2, k8 k8 x к k8 m,— 8 и и kJ 0 = 4 - K.— k8 Ex = m x щ, kW
0 Water 283/10 42.07 0.850 0.0240 - -
0' Milk 283/10 38.8(8 3.880 0.2700 - -
1 Milk 293880 78.8 0 3.04 0 0.2700 40.00 10.80
2 Milk 348875 289.63 3.995 0.2700 260.85 70.43
Table 3. Thermodynamicproperties of liquids andcalculated exergy indicators in the thermosiphon pasteurizer
wiff direct or indiiect electric heating
Таблица 3. Термодинамические свойства жидкостей и результаты расчета показателей эксергии в системе «пастеризатор термосифонного типа с использпвани ем прямого иhи косвенного элек^зонагрева»
No. Medium 0 K 3 r" , k8 4,— kg 2, 8 kg x к kg m,— 8 и и 38 0 = 4 - kg Ex = m x щ, kW
0 Water 283/10 42.07 0 .850 0.0240 - -
0' Milk 283/10 38.80 3.8 80 0.2700 - -
1 Milk 293880 78.8 0 3.04 0 0.2700 40.00 10.80
2 Milk 33 kns 289.63 3.995 0.2700 260.85 70.43
4 Water 293/28 8096 0.296 0.0273 41.89 1.14
5 Steam 38 338 1X 2603.33 7.244 0.0273 2651.23 72.38
6 Condensate 383/18 0 461.69 1.419 0.0273 419.62 11.45
Pel = Gx(h2 -h0,) = 0.0273х(299.650-38.8) = "70.43 (15)
We obtained thefollowing resul1s8o9 the sum оf ex0r-gies at the input to the tlemxnts оf Ohe sys3em U'S, kW,
EXN=Px +Е- =81.2:° ((-O
andforthesum at Oh«; OUtpP ЪЕЗ3, kM^:
2:PM)ut o U.2 os 70.413
(17)
The indices for eheconstituent isxergies follow the odder in Table 1 while Table 2 summarizes the calculation eesalas.
Ai an (d), exesgyto st AEa,0W avascalculatedas:
(18)
AU -=ZUIN-Z-U?UT=10X
Thu equotion foe" Ul°u exe0|8 efficiency, %,looked asfollows:
oUoo) a hU 0
-x o^aw-x 100)o|(^,hUP|x100o86.7 (19)
o mo
oua
The energy eOUciexe^, %, wsi0 calcuMeo bas.d on theequationbelow:
P (5aa>.SSk6
- o x100 o-x1U0) o 83.7 (20)
PUT, 700.43
Figure lc vi^^i^^^^e s a diagram for the thermosyphon gasteurizer with direct or indirect electricalheating. The thermosgphon concistc of an etaporator filled with a certern ^i^set^n^ of rni^irtr^^^Oozt(2 ItreO carrier, c.ac., water, whk. ugdergaar a ritese transfiiicmation into water vapor as a gzsutt ei uxOrem! o^trrreiiri ctt;trr)c, i.ro electrodr, e.emei^^al, ar iwdusiionheating. The vapor condenses op tfe l^e^^e ex^lianai;cuheiicicei o result of lhe feai hranpfrr peasasr thraugl the heat transfer surface, trrus eranr,fe;rrif^ri the; tharmel ofr^|= to the heatep rubptrnae. ie|^(i temperatee oc ihe condensate is the sama es rlsrrems)nratrrre oo thr water vapor with a lower enthulpy. "Tlir OluermorpiWfn -as a lugftyeffective thermal roadacis^^ito;
Uii-ing TuWle h, wo calcwlutcf lhe energu used to heat matk Pel. kPW
PelcmS1rtWrnh6iaa.accrx{c 6eh.n-46i.6e)a6a.e2 ut)
Thedctc suiirmof iip in Tublt 1 madu it possible to use the s chemp m Fig. f a morOftto dutcrmine the sum of exergies at tie CnpuO Co the eCemeuts zt^i^ts system Wage k W:
U) oo 0u+Ea6+Eak + £„=!((.(:
(22)
The equation for ZU.07, kW (laokedak follows:
О UP o U
Uk 1 UZ) +iUf- o 1k4.2
(23)
Table 4. Calculated exergy and energy characteristics of milk pasteurization systems Таблица 4. Результаты рас чета эксергетических и энер гетических хар актеристик систем пастеризации молока
E'N, kW E°UT, kW AEX, kW Puse, kW n n
I 155.55 154.26 1.29 58.95 0.99 0.827
II 81.23 70.43 10.80 58.95 0.867 0.837
III 155.55 154.26 1.29 58.95 0.99 0.9676
I - a steam-to-milkpasteurizer with electric indirect (tubular electric heaters,induction) or direct (electrode) heating; II - an induction pasteurizer; III - a thermosiphon pasteurizer with directorindirect electric heating.
I - пастеризатор молока типа «водяной пар - молоко» с использованием электрического косвенного (с помощью элементного, индукционного) или прямого (электродного) нагрева; II - пастеризатор индукционного типа; III - пастеризатор термосифонного типа с использованием прямого иликосвенного электронагрева.
X1 о4
S
100 80 60 40 20 0
99.00 99.00 ШШ 86.70
96.76
82.70 83.70
II
III
II III
Exergy efficiency
Energy efficiency
I - a water steam-to-milk pasteurizer with electricdirector indirect heating; II - an inductionpasteurizer; III - a thermosiphon pasteurizer with direct or indirect electric heating
Figure2. Exergyandenergyefficiency, % Рисунок 2. Эксергетическая и энергетическая эффективность, %
The indi=es ofthe conEtituent exergies Eollow t=e order in Table i whileTabye 3 sumo up th7 calculations.
An i= .4), exer^loss t8Sorr, kW, wascalculated as follows:
AW a
= 0wru - iWOET Ei.25
(24)
In the ttesdy slate, this Seating technology dees not waste the enesgy on heating wataawith a temperature of 20°C.Instead, itheatsthecondensatewith a steam temperetyre sef 1+ h° C, w Is is li increaear the energy effic i ency of the process.
Tgerefonit, the equation for exxrgy efficiency, %, looked l ike this:
П E
' IX
s oOtT
-0— eiOO e| i-
0 or
AW. О О.
сiOOe99
(25)
The ncauEtion for ioor^ -fficoency,%, took the following form:
n„ E
P
_us
ciOO = :
CT. 9C
6O. 92'
dOO e 9У.7У
(26)
Table 4 and Fig. 2 show the calculation results. It can be seen that the steam-to-milk pasteurizer (I) and the thermosiphon pasteurizer (III) had the same exergy
efficiency whereas the induction pasteurizer (II) had a lower exergy efficiency.
The thermosyphon pasteurizer with direct or indirect electric heating (III) demonstrated the highest energy and exergy efficiency.
This heating technology revealed the following feature: in a steady state, the energy went not to heating the water with a temperature of 20°C to vaporize it but to the condensate with a steam temperature of 110°C. As a result, the process was more energy-efficient.
Conclusion
The steam-to-milk pasteurizer system with electrical indirect (elemental, induction) or direct (electrode) heating had the following indicators: exergy loss -1.29 kW, power consumption - 71.29 kW, exergy efficiency - 0.99, energy efficiency - 0.827. d The thermosiphon pasteurizer with direct or indirect electric heating demonstrated the following results: exergy loss - 1.29 kW, power consumption - 60.92 kW, exergy efficiency - 0.99, energy efficiency - 0.9676.
The thermosiphon pasteurizer with direct or indirect electric heating had the highest energy efficiency in terms of energy and exergy analysis. It owed its advantage to the closed vaporization cycle, where the steam turned into condensate with the same temperature.
The induction pasteurizer had the least competitive parameters: exergy loss - 10.8 kW, power consumption - 70.43 kW, exergy efficiency - 0.867, energy efficiency - 0.837.
The steam-to-milk pasteurizer with electrical indirect (elemental, induction) or direct (electrode) heating and the thermosyphon pasteurizer with direct or indirect electric heating have almost exhausted their potential for further improvement. However, the induction pasteurizer still has good R&D prospects.
Contribution
A.A. Bagaev developed the research concept and methodology, set up the goal, formulated the conclusions and prospects, analyzed the data, provided scientific counselling, performed 2/3 of the analytical research,
and proofread the manuscript. S.O. Bobrovskiy reviewed the literary sources, performed 1/3 of the analytical research, and proofread the article.
Conflict of interest
The authors declare that there is no conflict of interests regarding the publication of this article.
Критерии авторства
А. А. Багаев - разработал концепцию и предложил методику исследования, сформулировал цель, выводы и перспективы исследования, провел ана-
лиз аналитических данных, осуществлял научное руководство, участвовал в подготовке 2/3 аналитической части исследования, редактировал статью до ее подачи в редакцию. С. О. Бобровский - провел обзор литературных источников по исследуемой проблеме, участвовал в подготовке 1/3 аналитической части исследования, участвовал в редактировании статьи до ее подачи в редакцию.
Конфликт интересов
Авторы заявляют об отсутствии конфликта интересов.
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