Modeling of graphite oxidation in oxygen
The problem of nuclear grade graphite oxidation at high temperatures is considered in the paper. A simulation model of the nuclear grade graphite oxidation is developed, taking into account the porosity, granulometric composition and sample density. Analysis of the results approbation showed satis...
Збережено в:
| Дата: | 2014 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2014
|
| Назва видання: | Вопросы атомной науки и техники |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/80355 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Modeling of graphite oxidation in oxygen / A.M. Odeychuk, A.I. Komir // Вопросы атомной науки и техники. — 2014. — № 4. — С. 60-65. — Бібліогр.: 26 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-80355 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-803552015-04-17T03:01:58Z Modeling of graphite oxidation in oxygen Odeychuk, A.M. Komir, A.I. Физика радиационных повреждений и явлений в твердых телах The problem of nuclear grade graphite oxidation at high temperatures is considered in the paper. A simulation model of the nuclear grade graphite oxidation is developed, taking into account the porosity, granulometric composition and sample density. Analysis of the results approbation showed satisfactory agreement with experimental data. Рассматривается проблема окисления ядерно-чистого графита при высоких температурах. Разработана имитационная модель окисления ядерно-чистого графита с учетом пористости, гранулометрического состава и плотности образца. Анализ результатов апробации показал удовлетворительное согласие с экспериментальными данными. Розглядається проблема окислення ядерно-чистого графіту при високих температурах. Розроблена імітаційна модель окислення ядерно-чистого графіту з урахуванням пористості, гранулометричного складу і щільності зразка. Аналіз результатів апробації показав задовільну згоду з експериментальними даними. 2014 Article Modeling of graphite oxidation in oxygen / A.M. Odeychuk, A.I. Komir // Вопросы атомной науки и техники. — 2014. — № 4. — С. 60-65. — Бібліогр.: 26 назв. — англ. 1562-6016 http://dspace.nbuv.gov.ua/handle/123456789/80355 621.039.532.21 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Физика радиационных повреждений и явлений в твердых телах Физика радиационных повреждений и явлений в твердых телах |
| spellingShingle |
Физика радиационных повреждений и явлений в твердых телах Физика радиационных повреждений и явлений в твердых телах Odeychuk, A.M. Komir, A.I. Modeling of graphite oxidation in oxygen Вопросы атомной науки и техники |
| description |
The problem of nuclear grade graphite oxidation at high temperatures is considered in the paper. A simulation
model of the nuclear grade graphite oxidation is developed, taking into account the porosity, granulometric
composition and sample density. Analysis of the results approbation showed satisfactory agreement with
experimental data. |
| format |
Article |
| author |
Odeychuk, A.M. Komir, A.I. |
| author_facet |
Odeychuk, A.M. Komir, A.I. |
| author_sort |
Odeychuk, A.M. |
| title |
Modeling of graphite oxidation in oxygen |
| title_short |
Modeling of graphite oxidation in oxygen |
| title_full |
Modeling of graphite oxidation in oxygen |
| title_fullStr |
Modeling of graphite oxidation in oxygen |
| title_full_unstemmed |
Modeling of graphite oxidation in oxygen |
| title_sort |
modeling of graphite oxidation in oxygen |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2014 |
| topic_facet |
Физика радиационных повреждений и явлений в твердых телах |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/80355 |
| citation_txt |
Modeling of graphite oxidation in oxygen / A.M. Odeychuk, A.I. Komir // Вопросы атомной науки и техники. — 2014. — № 4. — С. 60-65. — Бібліогр.: 26 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT odeychukam modelingofgraphiteoxidationinoxygen AT komirai modelingofgraphiteoxidationinoxygen |
| first_indexed |
2025-07-06T04:19:26Z |
| last_indexed |
2025-07-06T04:19:26Z |
| _version_ |
1836869816322883584 |
| fulltext |
60 ISSN 1562-6016. ВАНТ. 2014. №4(92)
UDC 621.039.532.21
MODELING OF GRAPHITE OXIDATION IN OXYGEN
A.M. Odeychuk, A.I. Komir
Science and Production Establishment
“Renewable Energy Sources and Sustainable Technologies”,
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
E-mail: anodeychuk@kipt.kharkov.ua; tel. +38(057)335-60-43
The problem of nuclear grade graphite oxidation at high temperatures is considered in the paper. A simulation
model of the nuclear grade graphite oxidation is developed, taking into account the porosity, granulometric
composition and sample density. Analysis of the results approbation showed satisfactory agreement with
experimental data.
MODELS ANALYSIS OF CARBON
MATERIALS OXIDATION
At present developing nuclear power systems
Generation IV caused need of carrying out researches of
active zone components. In particular study of the
properties and behavior of nuclear grade graphite in
oxidizing environments at high temperatures. A large
amount of experimental work is executed on the
studying dependencies of the carbon materials oxidation
processes [1, 3, 4, 8, 9], which allowed for a overview
of the main phases of the process of oxidation, as well
as perform the appropriate physical and mathematical
description. However not enough attention is paid to
researches on modeling of such processes: influence of
grain-size distribution and graphite porosity.
For example, in [1] the IG-110 graphite oxidation
was considered under different conditions. Experiments
were carried out in two temperature ranges (540…600,
700…1500 °С), puffing rate ((3…18), 40 l/min),
oxygen concentration (2.5…32, 2.5…20%), with the
area available for reaction 19.792 mm
2
. In this work
Arrhenius equation was used, for which the coefficients
specified: n = 0.75 ± 0.146 and the activation energy
Ea = (218±4) kJ/mol. It is claimed that the proposed
model includes the parameters corresponding to the
range of high-temperature gas-cooled reactors.
Modeling of the oxidation process was carried out in
a cylindrical coordinate system. During the simulation
the following graphite specimen parameters were
calculated: temperature, density and specific heat, while
blowing it upwards parallel to the side surface of the
specimen. Concentration distribution also is given in
article for О2, CO, CO2 in the surrounding space.
However, the paper does not take into account of the
porosity and grain-size distribution of the sample, and
changing of the sample cell volume with radius
increase, which may lead to the error in the modeling of
oxidation.
In work [2] the following graphite oxidation stages
are analyzed:
a) oxidizer transfer on a graphite surface;
b) oxidizer adsorption on a graphite surface
(physical adsorption);
c) formation of carbon-oxide bonds (chemisorption);
d) formation of carbon-hydroxide bonds (for
reaction with water);
e) breakage of carbon-carbon bonds;
f) desorption of carbon monoxide or other product of
reaction;
g) transfer of products of reaction from a surface.
From above-mentioned stages follows that the
factors influencing the rate of oxidation reactions are:
a) intensity of oxidant inflow to the surface;
b) partial pressure of oxidizer;
c) reactionary zone is available to an oxidizer on
surface;
d) amount and distribution of catalytic impurities in
graphite;
e) temperature;
f) removal rate of the reaction products;
g) graphite damage by fast neutrons;
h) amount of previously oxidized (radiolytic or
annealed) material;
i) effective diffusion coefficient.
It is noted that at temperatures less than 350
o
С
oxidation of graphite is practically absent. With
increasing temperature, starting from 400
o
С, oxidation
becomes measurable. Water as an oxidizer, raises a
threshold of oxidation reaction to 800
o
С.
Mohamed S. El-Genk [3] investigated the properties
of graphite grades IG-110, IG-430, and NBG-25.
Dependence between diffusion rates of oxidizer deep
into graphite on temperature is considered also. It is
suggested to divide oxidation process into 3 modes:
– mode is limited by diffusion in the boundary layer
(in this mode, oxidant concentration decreases linearly
in a thin boundary layer);
– diffusion mode, diffusion is limited by diffusion
inside of pores (at this mode an oxidizer is in the sample
volume and its concentration falls linearly to zero at a
specific depth of the sample);
– mode, which is limited by the chemical kinetics (in
this mode an oxidizer fills the entire sample volume
some nonlinear slightly decreasing deep concentration).
The experimental and theoretical mass loss
dependence on the time of graphite grade IG-110
oxidation is analyzed, presented as graphs, numerical
evaluation of which shows that the average absolute
error is 21%. The work has also considered the
distribution of energy of adsorption and desorption of
the oxidizer and gasification sample rate.
However, as in [1], Mohamed S. El-Genk [3] doesn’t
take into account of granulometric composition of the
sample, which can significantly affect on the modeling
of the oxidation process.
ISSN 1562-6016. ВАНТ. 2014. №4(92) 61
In [4] specified refined coefficients of the Arrhenius
equation for isothermal conditions at temperatures 600,
612 and 625 °С and in the conditions of constantly
increasing temperature 1, 2, 10 °С/min. Dependence
of activation energy on sample burn-up and its mean
square error (Fig. 1) is analyzed. It is shown that the
average activation energy is 155 kJ/mol.
Fig. 1. The activation energy dependence on the
sample mass reducing [4]
The proposed analytical description of the oxidation
process poorly describes of the experimental data.
Also it should be noted that the description of
analytical models is provided in literature, for example
in [5-7], in which polynomial approximation of
experimental data is used. However this approach
doesn't consider the physical nature of oxidation that
leads to errors in calculations at the slightest exit from
the range of experimental data or insufficient sampling.
It is also heavy to approximate data from various
sources for creation of the general approximating curve.
In papers [8, 9] provide data on the effective
diffusion of oxygen and water into the graphite. The
analysis density of graphite after burn-up depending on
the depth after the oxidation process during 5 hours in
an atmosphere of air at 700
o
C. Developed in [8, 9]
models assume carrying out modeling with the diffusion
average on a sample that doesn't allow to consider of
graphite heterogeneity.
In most existing models used for the separation of
oxidation process previously mentioned modes, wherein
one of the model parameter is the diffusion of oxidant
into the sample, so during the numerical simulation is
necessary to take into account the porosity. Construction
of the model without this characteristic significantly
reduces the reaction surface for the graphite oxidation in
the temperature range 400…1200
o
С.
Also in [10] is investigating the effect of grinding on
the oxidation rate, and says that the speed increases by
mechanical action on the natural graphite. Therefore, in
developing an oxidation model should be considered
granulometric composition of the graphite structure.
In [11] was used model which contain three main
elements – filler binder and porosity for crack initiation
and propagation in pile grade A (PGA) reactor core
graphite modeling and also have microstructure with
good connection filler and binder.
Also various studies try to investigate microstructure
of nuclear grade graphite in oxidation conditions [12].
In this paper investigates oxidation behavior with
simultaneous study of different properties of
microstructure: shape, size. Also significant result is
shape of nuclear grade graphite oxidation with catalysts
and inhibitors.
Relative sizes of structure elements of filler and
binder in other work is filler in the size range
0.1…1.0 mm and these are dispersed in a matrix of fine
calcined filler particles, below 10 m [12].
Therefore, the development of a simulation model
for nuclear grade graphite oxidation at high
temperatures, which takes into account its porosity,
grain-size distribution, diffusion penetration of the
oxidizer, temperature and linear dimensions is pressing
issue. Consideration of these factors will allow
simulating of carbon components oxidation in the
operating conditions of nuclear power systems
Generation IV, graph of operating temperatures is
shown in Fig. 2 [13].
Fig. 2. Temperature range HTR (dotted)
and VHTR (solid) [13]
SIMULATION MODEL
Sample splitting into a set of cubic unit cells is the
basis of simulation model (Fig. 3).
The unit cell is characterized by the weight and the
linear sizes. Graphite sample described using a three-
dimensional matrix x y zv , which is hereinafter
denoted as v, where each element has a mass of i, j, k-th
unit cell.
The graphite sample (as a model material is
considered graphite GMZ) consists of a filler and binder
in the ratio three to one [14]. Filler is a coke granules
which have a specific size. In Table shows the
dimensions of the GMZ graphite granules [14].
Granulometric composition of GMZ graphite filler [14]
Size, mm 1.5±0.5 0.5±0.3 0.3±0.09 < 0.09
Content, % 26 13 14 47
Based on the provided data, it was offered to
carry out stage-by-stage model formation of a
graphite sample taking into account granulometric
composition.
Grain model formation was carried out using a
statistical approach, which was based on the
assignment of the distribution law of the unit cells
along the axes x, y, z, that allows to set the required
form of grains, depending on the grade features of the
graphite microstructure: size, shape, percentage of
filler granules in the sample.
62 ISSN 1562-6016. ВАНТ. 2014. №4(92)
a
b
Fig. 3. Scheme of the sample transformation in
three-dimensional matrix v: a a sample;
b unit cell i, j, k
Packing of granules in volume of a graphite sample
by full search of all possible provisions is extremely
difficult from the point of view of time of calculation.
Moreover, the complexity of this task increases with the
size of the sample. For solving this problem was
proposed and realized granules placement algorithm,
which comprising in realization of granules arbitrary
location that they may be crossed each other, then was
used the procedure of step movement of granules inside
of specimen volume till the moment of absence of
intersection.
Simulation results of the GMZ graphite sample are
shown in Figs. 4, 5. By red color specified material
located on the boundary of the sample, blue – inside.
Real graphite sample has an open and closed
porosity. The model assumed that all sample porosity is
open and it is proposed to set it unit cells in which the
mass of graphite equals to zero. Porosity distribution on
a sample has stochastic character [15].
a b c d
Fig. 4. Simulation of granulometric composition of nuclear grade GMZ graphite sample: a grains with size
(1.5±0.5) mm; b adding grains (0.5±0.3) mm; c adding grains (0.3±0.1) mm; d filler and binder
Fig. 5. Computer model of graphite: filler and binder
(increasing)
Therefore, the selection of a cell which is pore
performed by using a random number generator taking
into account the distribution of porosity in filler and
binder of the sample, which is based on Mersenne
twister [16-19].
In the simulation model are not considered the pores,
which are smaller than the size of the unit cell.
Sample unit cell weight is determined by the
formula:
3
, , , , ,i j k i j km a (1)
where a – size of the unit cell edge, m; , ,i j k – density
of i, j, k-th unit cell, kg/m
3
.
ISSN 1562-6016. ВАНТ. 2014. №4(92) 63
Mass of the sample is calculated by the formula
without taking into account of changing in linear
dimensions of the sample:
, ,
, ,
1, 1, 1
,
i j k
x y z
a a a
i j k
M m
1,2,..., ,i x 1,2,..., ,j y 1,2,..., ,k z
(2)
where mi,j,k – weight i, j, k-th unit cell, kg, wherein the
step of partitioning is multiple of all linear dimensions
of the sample.
As mentioned above, the nuclear power systems
Generation IV are operating at temperatures ranging
from 600 to 1000 °C [13], this simulation model is
considering the temperature range from 400 to 800
о
С,
that is corresponding of diffuse mode, which is
described in the papers [3, 20]. A feature of this mode is
the uniform distribution of oxidizer over the volume,
since the reaction rate is less than the diffusion rate of
oxidizer into the sample [8].
Mass reducing of the unit cell as a result of
oxidation is calculated by the formula:
, ,
, ,
1,1,1
, ,
1, 1, 1
1
,
i j k
i j k g
i h j l k
h l
dm
m K
dt
m
(3)
where
0, 0
1, 0
m
m
m
– unit impulse function;
Kg = K·(C0)
n
·S – oxidation rate, kg/s; K – reaction
constant, whose temperature dependence obeys the
Arrhenius equation, kg/(m
2
·s) [14]: 0
E
RTK K e
,
K0 – function of graphite properties, which is
characterized by a degree of crystallinity of the material
and its porosity, kg/(m
2
·s); Ea – surface activation
energy, J; R – gas constant, (m
2
·kg)/(s
2
·K·mol); T –
temperature, K; C0 – oxidizer concentration near the
surface; n – reaction order (n depends on many factors
including the oxidation mode and anisotropy and takes a
value from 0.5 to 3) [14]; S – reaction surface (the area
of one unit cell S = a
2
), m
2
, what is more, when leaving
the range of the mass cells matrix v, when the index is 0
or size is larger than matrix in the corresponding
dimension – mi,j,k equals zero. The rate of sample mass
change is calculated by adding of mass changes over all
sample cells:
, ,
, ,
1, 1, 1
.
x y z
a a a i j k
i j k
dmdM
dt dt
Simulation model is constructed on the assumption,
that an internal pores of a sample contains an oxidizer
and it oxidizes of internal cells with the same speed, as
the outside oxidizer. Setting cell mass mi,j,k performed
by formula (1).
For determining of model accuracy (4) relative to
the dimensions of the unit cell was carried out
numerical simulation of the oxidation of graphite
sample at the temperature 560 °C (Figs. 6, 7).
Calculation of error modeling was carried out using the
mean absolute percentage error MAPE [24], which
describes how large modeling errors in comparison with
the experimental series values data:
1
1
100,
n
t t
t t
Y H
MAPE
n Y
(4)
where n – number of measurements; Yt – experimental
data [26]; Ht – modeling data.
Fig. 6. Mean absolute percentage error of the
graphite oxidation simulation model
Fig. 7. Dependence of the graphite sample mass loss
from time
Analysis of the results shows that the error under
reducing of the unit cell dimensions to 0.0001 m is
about 7%, however, with further decrease of the size
seen an increase of error associated with the fact that the
developed simulation model does not consider meso-
and nano-scale phenomena, which begin to play an
important role [22-24] under dimensions comparable
with the mean free path of the molecule [23]. Thus, the
results indicate that the area of application of the
developed simulation model with an error 7% is sample
discretization which commensurate with 0.0001 m.
64 ISSN 1562-6016. ВАНТ. 2014. №4(92)
APPROBATION OF SIMULATION MODEL
Approbation of the simulation model was carried out
using mathematical statistical apparatus [21] in the
medium of mathematical package Octave 3.6.4. Was
modeled of the nuclear grade GMZ graphite sample
oxidation process (as a model material), which has the
following characteristics: density 1850 kg/m
3
, porosity
20%, granulometric composition (see Table) [14], linear
sample dimensions width 0.002 m, length 0.003 m,
height 0.02 m, partitioning step of the sample on cubic
unit cell with given edge length – 0.0001 m.
Oxidation process parameters: temperature 560
о
C,
oxidizer concentration 10% О2, oxidation rate
710gK kg/s, duration of the process – 30 days. The
modeling results of the oxidation process of GMZ
graphite using the simulation model are shown in Fig. 8.
Analysis of simulation results (see Fig. 8) shows the
presence of oxidation dynamics of the sample, but
significant structural changes were observed after
10 days. After 20 days sample loses properties of
support structure, and after 30 days complete
destruction of the sample is observed. Moreover, it
should be noted that the simulation with taking into
account the porosity of the sample has allowed take into
account the non-linearity and stochasticity of the
graphite oxidation process. As seen from Fig. 8,d,
accounting at modeling oxidizer penetration into the
sample has a significant impact on the destruction
process, since oxidation takes place not only on the
outer surfaces, but also by the entire sample volume.
The obtained results of simulation with using the
developed simulation model are well correlated with the
experimental results obtained in the work [26].
CONCLUSIONS
Theoretical researches are conducted and the
simulation model of nuclear grade graphite oxidation is
developed. Model takes into account porosity,
factionalism, density of the sample and diffusion of
oxidizer for oxidation in the chemical kinetics regime,
which is in the temperature range 400…800
о
С.
Received results of researches were tested at
modeling of oxidation at high temperature of nuclear
grade GMZ graphite that agree satisfactorily with
experimental results.
REFERENCES
1. E.S. Kim, H.C. No. Experimental study on the
oxidation of nuclear graphite and development of an
oxidation model // Journal of Nuclear Materials. 2006,
v. 349, Issue 1-2, p. 182-194.
2. Irradiation damage in graphite due to fast
neutrons in fission and fusion systems // IAEA-
TECDOC-1154. 2003, p. 207-213.
3. M.S. El-Genk, J.-M.P. Tournier. Comparison of
oxidation model predictions with gasification data of
IG-110, IG-430 and NBG-25 nuclear graphite // Journal
of Nuclear Materials. 2012, v. 420, Issue 1-3, p. 141-
158.
4. H. Badenhorst, B. Rand, W.W. Focke. Modelling
of natural graphite oxidation using thermal analysis
techniques // Journal of Thermal Analysis and
Calorimetry. 2010, v. 99, Issue 1, p. 211-228.
5. W.S. Cornwall. Wigner Stresses: United
Kingdom Atomic Energy Authority, TRG Report 40(R),
1962, 133 p.
6. M. Lasithiotakis, B.J. Marsden, T.J. Marrow.
Application of an independent parallel reactions model
on the annealing kinetics of BEPO irradiated graphite //
Journal of Nuclear Materials. 2012, v. 427, p. 95-109.
a b c d
Fig. 8. The view of the GMZ graphite sample during oxidation in the oxidizing environment at oxidizer
concentration 10% О2 at temperature 560
о
C: a initial state; b after 10 days; c after 20 days;
d after 30 days (on the right is shown scale of the mass change of the unit cell)
ISSN 1562-6016. ВАНТ. 2014. №4(92) 65
7. H. Li, A.S.L. Fok, B.J. Marsden. An analytical
study on the irradiation-induced stresses in nuclear
graphite moderator bricks // Journal of Nuclear
Materials. 2008, v. 372, p. 164-170.
8. J.J. Lee, T.K. Ghosh, S.K. Loyalka. Oxidation
rate of nuclear-grade graphite NBG-18 in the kinetic
regime for VHTR air ingress accident scenarios //
Journal of Nuclear Materials. 2013, v. 438, Issue 1-3,
p. 77-87.
9. R.P. Wichner, T.D. Burchell, C.I. Contescul.
Penetration depth and transient oxidation of graphite by
oxygen and water vapor // Journal of Nuclear
Materials. 2009, v. 393, Issue 3, p. 518-521.
10. H. Badenhorst, W. Focke. Comparative analysis
of graphite oxidation behaviour based on microstructure
// Journal of Nuclear Materials. 2013, v. 442, p. 75-82.
11. P.J. Heard etc. Crack initiation and propagation
in pile grade A (PGA) reactor core graphite under a
range of loading conditions // Journal of Nuclear
Materials. 2010, v. 401, p. 71-77.
12. H. Badenhorst, W. Focke. Comparative analysis
of graphite oxidation behaviour based on microstructure
// Journal of Nuclear Materials. 2013, v. 442, p. 75-82.
13. M. Davies. Qualification of selected graphites
for a future HTR. Technical Meeting on High-
Temperature Qualification of High Temperature Gas-
Cooled Reactor Materials. 1013 June 2014. IAEA
Vienna [Electronic resource]. Access mode:
http://www.iaea.org/NuclearPower/Meetings/2014/2014
-06-10-06-13-TM-NPTD.html. Header from screen.
14. V.V. Goncharov et al. Effect of irradiation on
graphite of nuclear reactor. M.: «Atomizdat», 1978,
p. 9-38.
15. V.S. Ostrovsky et al. Changes in the porosity and
permeability of the carbon material during heat
treatment. Structural materials on basis of graphite. The
collection of works N 3. M.: «Metallurgy», 1967,
p. 204-208.
16. V.P. Kichor et al. Economic and statistical
modeling and forecasting. Lviv: Publishing House of
National University “Lviv Polytechnic”, 2007, 156 p.
17. M. Matsumoto, T. Nishimura. Mersenne Twister:
A 623-Dimensionally Equidistributed Uniform
Pseudorandom Number Generator // ACM Transactions
on Modeling and Computer Simulation. 1998, v. 8, N 1,
p. 3-30.
18. SIMD-oriented Fast Mersenne Twister (SFMT):
twice faster than Mersenne Twister [Electronic
resource]. Access mode: http://www.math.sci.
hiroshima-u.ac.jp/~m-mat/MT/SFMT/index.html.
Header from screen.
19. R. Tor. Collusion-Secure Fingerprinting. A
simulation of the Boneh and Shaw Scheme. Coding
theory and cryptography [Electronic resource] //
Bergen: Department of Informatics Universitas
Bergensis, 2005, 119 p. Access mode:
http://www.ii.uib.no/~georg/coding/Students/Tor/collusi
on_secure_fp.pdf. Header from screen.
20. H. Badenhorst. Graphite Oxidation // DST Chair
in Carbon Materials and Technology. 2009, 38 p.
21. A.M. Odeychuk, A.Yu. Gud. Simulation model
for the study heteroskedastic time series in information
systems // Visnyk of the Academy of Customs Service of
Ukraine. 2010, N 1, p. 102-110.
22. Processes of micro- and nanotechnology.
Educational and methodical complex on St .P. SETU
discipline. St.-Petersburg, 2010, 266 p.
23. N.F. Morozov, R.V. Goldshtein, V.A. Gorod-
stov. Modeling of the mechanical behavior of
nanostructured formations. St.-Petersburg State
University, Institute for Problems in Mechanics named
A. Yu. Ishlinsky RAS. M., 2009, 35 p.
24. A.S. Lobasov, A.V. Minakov. Computer
modeling of heat and mass transfer processes in
microchannels with using CFD-package Flow //
Computer studies and simulations. v. 4, N 4, 2012,
p. 781-792.
25. A.N. Odeychuk. Generalized criterion for
efficiency of time series forecasting models in
information systems // Bionica Intellecta: scientific-
technical magazine. 2009, N 1 (70), p. 113-119.
26. S.J. Gregg, R.F.S. Tyson. The kinetics of
oxidation of carbon and graphite by oxygen at 500–
600 °С // Carbon. 1965, v. 3, Issue 1, p. 39-42.
Статья поступила в редакцию 01.07.14 г.
МОДЕЛИРОВАНИЕ ОКИСЛЕНИЯ ГРАФИТА В СРЕДЕ КИСЛОРОДА
А.Н. Одейчук, А.И. Комир
Рассматривается проблема окисления ядерно-чистого графита при высоких температурах. Разработана
имитационная модель окисления ядерно-чистого графита с учетом пористости, гранулометрического состава
и плотности образца. Анализ результатов апробации показал удовлетворительное согласие с
экспериментальными данными.
МОДЕЛЮВАННЯ ОКИСЛЕННЯ ГРАФІТУ В СЕРЕДОВИЩІ КИСНЮ
А.М. Одейчук, А.І. Комір
Розглядається проблема окислення ядерно-чистого графіту при високих температурах. Розроблена
імітаційна модель окислення ядерно-чистого графіту з урахуванням пористості, гранулометричного складу і
щільності зразка. Аналіз результатів апробації показав задовільну згоду з експериментальними даними.
http://www.multitran.ru/c/m.exe?t=4540392_1_2&s1=generalized%20criterion%20for%20efficiency%20of%20time%20series%20forecasting%20models%20in%20information%20systems
http://www.multitran.ru/c/m.exe?t=4540392_1_2&s1=generalized%20criterion%20for%20efficiency%20of%20time%20series%20forecasting%20models%20in%20information%20systems
http://www.multitran.ru/c/m.exe?t=4540392_1_2&s1=generalized%20criterion%20for%20efficiency%20of%20time%20series%20forecasting%20models%20in%20information%20systems
|