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Proceedings of ICAPP ‘10
San Diego, CA, USA, June 13-17, 2010
Paper 10159
On the Oxidation Kinetics and Erosion of Graphite during a Massive Air or
Water Ingress in HTRs
Mohamed S. El-Genk1,2,3 and Jean-Michel P. Tournier1,2
1Institute for Space and Nuclear Power Studies, 2Chemical and Nuclear Engineering Department
3Mechanical Engineering Department
University of New Mexico, Albuquerque, NM
Tel: (505) 277–5442, Fax: – 2814 , Email: mgenk@unm.edu
Abstract – A massive air or steam ingress in High Temperature Reactors (HTRs) nominally operating at 600-950 oC is
a design-basis accident requiring the development and validation of graphite oxidation and erosion models to examine the
impact on the potential fission products release and the integrity of the graphite core and reflector blocks. Nuclear
graphite is of many types with similarities but also differences in the microstructure, volume porosity, impurities, type and
size of filler coke particles, graphitization and heat treatment temperatures, and the thermal and physical properties. These
as well as the temperature, types and partial pressures of oxidants affects the prevailing oxidation mode and kinetics of the
oxidation processes of graphite in HTRs. This paper reviews the graphite crystalline structure, the fabrication procedures,
characteristics, chemical kinetics and modes of oxidation of nuclear graphite for future model developments.
I. INTRODUCTION
Analysis of air or steam ingress in high temperature
reactors (HTRs) requires accurate models for predicting
the corrosion and oxidation rates of the porous nuclear
graphite in the prismatic and pebble bed reactor core
designs. The nature and progress of these reactions are
complex and strongly coupled. They primarily depend on
temperature, partial pressures of oxidants and the burn off
fraction of graphite. Other important parameters include:
(a) multi-species diffusion coefficients and the rate of
transport of various oxidants to the surface and into the
internal pores; (b) available area for reaction within the
pores and at the external surface; and (c) rate of removal
of the reaction products. The prevailing exothermic
reactions of graphite generate heat that raises the
temperature, accelerating the oxidation and corrosion
processes. On the other hand, the gas species produced by
both exothermic and endothermic reactions decrease the
partial pressures of oxidants, slowing down the
progression of graphite oxidation.
Oxidation processes at the external surface and within
the volume pores are qualitatively well understood,
however quantitative predictions of their rates over time is
still a challenge. This is attributed to the complex nature
and strong coupling of these processes and the difficulty of
extracting detailed information from experiments to
validate them. Modeling the erosion and oxidation of
graphite is further complicated by a progressively
changing microstructure, including volume pores, active
surface area and active sites with time. Thus, predictive
models must track the simultaneous changes in these
parameters as well as in temperature, chemical kinetics of
prevailing reactions, multi-species inter-diffusion rates of
oxidants and gaseous reaction products, and the
microstructure and physical and thermal properties of
graphite.
The objective of this paper is to review the graphite
crystalline structure and fabrication procedures,
characteristics, chemical kinetics and modes of oxidation
of nuclear graphite as function of temperature and partial
pressure of oxidants for future development of predictive
models of the impact of a massive air or steam ingress on
the safety of HTRs.
II. GRAPHITE STRUCTURE
Graphite is an aggregate of crystallite grains,
generally of identical properties.1 The interaction among
misaligned crystallites while changing shape builds up
stresses at the grain boundaries. The graphite crystal (Fig.
1) has a hexagonal structure with predominant ABABA
stacking of planes and large c/a (6.7/2.46 = 2.72). The
crystal height, c is twice the inter-layer spacing d and the
Proceedings of ICAPP ‘10
San Diego, CA, USA, June 13-17, 2010
Paper 10159
nearest distance between carbon atoms in these planes is
1.42 Å. In a perfect crystal, the basal planes, stacked with
an inter-layer spacing (d) of 3.35 Å, have strong covalent
bonding, made up largely of (2s, 2px, 2py) trigonal
hydrides, but the bonding of planes due to Van der Waal’s
forces is much weaker.2 The (2pz) orbitals form the
electronic conduction band, giving the graphite crystal its
anisotropic properties, with the conductivity in the c
direction about two orders of magnitude larger than in the
direction parallel to the basal planes. In well graphitized
materials, the size of the crystallites varies between 400
and 800 Å.
d
a
c
d
a
c
FIG. 1. Unit Cell of Graphite Crystal.1
The size of graphite crystallites in the c direction is
limited by the so-called Mrozowski cracks. The micro-
pores (~5% porosity) forming in the cokes particles during
cool-down introduce micro-cracks due to the large
anisotropy in the crystals’ thermal expansion and Young’s
modulus. At ~ 1800oC, the microstructure hardens and
the large shrinkage in the c direction produces horizontal
cracking in the basal planes, the weakest link in the
structure. This cracked graphite structure enhances its
shock resistance, allowing large expansion in the c
direction without inter-crystalline cracking.3
These cracks, the internal pores forming by the
evolution of gases during the heat treatment of graphite
and the anisotropic thermal shrinkage during cool-down
partially accommodate irradiation-induced crystal growth
during HTR operation. The intensification of the local
stress promotes crack initiation from favorably oriented
volume pores. The propagating cracks are drawn toward
the pores in their vicinity by the induced stress in the
surrounding.4 The cracked crystallites join together and
follow the general shape of the coke particle. Many larger
cracks and fissures exist and tend to follow the shape of
the coke particles.
The binder, surrounding the polycrystalline grains of
coke particle is a conglomerate of smaller graphite crystals
and less well graphitized material with volume pores.5
The binder is stronger than the filler particles because of
double and single C-C bonds. When graphite is under
compression, slip deformation initially occurs in the filler
grains by cleavage between the basal planes and the binder
hardly deforms plastically.6 The binder phase is a
superposition of “domains” extending > 100 µm in length
with common basal plane alignment, and of “mosaics,”
regions of small and randomly-oriented pseudo-crystallites
< 10 µm with common basal plane orientation.4 Cleavage
of “domains” occurs at stress levels well below the fracture
stress, and thus such regions are sites for crack initiation,
particularly in the vicinity of volume pores. On the other
hand, propagating cracks are arrested or deflected by the
“mosaic” regions, which fracture only at stress levels close
to the fracture stress.4 During an air ingress accident in a
HTR, the binder region, with open porosity and more
impurities than the filler crystallites, is oxidized more
readily.7 The oxidants transport through the open porosity
and the impurities act as a catalyst for oxidation. This
preferential oxidation of the binder region degrades
graphite strength.8
III. NUCLEAR GRAPHITE
Nuclear graphite is a non-homogeneous composite
comprised of filler or coke particles and binder. In
medium-grained graphite, the size of the filler particles
ranges from 100 µm to 4 mm, compared to ~ 10 µm and 2
µm in fine-grained and ultra-fined grained graphites,
respectively. The broad range of grain sizes and the
micro-pores, voids, agglomerates and inclusions cause
large variations in the microstructure, affecting
mechanical properties and gas diffusivity. The graphite’s
porous structure, with open and closed volume porosities,
can be characterized by the size distribution, effective
length and accessible internal surface area of the pores.
Volume porosity of manufactured nuclear graphite varies
from 20% to 30%, compared to < 1% for single crystals
graphite. High purity chars have an internal surface area
of 0.10 to 103 m2/g, compared to ~ 0.10 – 10 m2/g for
high-density graphite and as much as 100 m2/g for porous
graphite. The volume pores are comprised of large macro-
pores > 200 Å, transitional pores of size 20 – 200 Å, and
small micro-pores < 20 Å.
The density of high-density pyrolitic graphite is ~
2.23 g/cm3, while that of graphite single-crystals nearly
equals the theoretical density, ~ 2.266 g/cm3. Early types
of nuclear graphite had densities of ~1.6 g/cm3 (~ 29%
volume porosity); however, in order to increase the
Young’s modulus and mechanical strength, the density has
increased to ~ 1.75 g/cm3 (~ 23% porosity) currently, and
could reach ~ 1.81 g/cm3 (~ 20% porosity) in the future.
High graphitization and purity are required. The first
Proceedings of ICAPP ‘10
San Diego, CA, USA, June 13-17, 2010
Paper 10159
increases the thermal conductivity (~140 – 150 W/m/K at
room temperature), while the latter reduces neutron
activation9 and may decrease the oxidation rate of
graphite.3
Mixing
Nuclear
graphite
Carbonization
@ 800-1100
o
C
Forming (Extrusion, Pressure molding, Vibration molding, Isostatic pressing)
Graphitization
@ 2800
o
C
Impregnation(s)
Green
article
Pitch binder
15-20%
graphite
powder
Coal tar
pitch
Grinding,
sieving,
blending
Mixing
Raw
petroleum
coke
Pitch binder
Isotropic coke
aggregate
Vibration or
Isostatic
molding
Carbonization
@ 1000
o
C
Petroleum
coke or
pitch
Conventional
filler
Calcination
@ 1300
o
C
Grinding,
sieving,
blending
Purification
@ 2500
o
C
Machining
A
B
(Optional)
(Optional)
Mixing
Nuclear
graphite
Carbonization
@ 800-1100
o
C
Forming (Extrusion, Pressure molding, Vibration molding, Isostatic pressing)
Graphitization
@ 2800
o
C
Impregnation(s)
Green
article
Pitch binder
15-20%
graphite
powder
Coal tar
pitch
Grinding,
sieving,
blending
Mixing
Raw
petroleum
coke
Pitch binder
Isotropic coke
aggregate
Vibration or
Isostatic
molding
Carbonization
@ 1000
o
C
Grinding,
sieving,
blending
Mixing
Raw
petroleum
coke
Pitch binder
Isotropic coke
aggregate
Vibration or
Isostatic
molding
Carbonization
@ 1000
o
C
Petroleum
coke or
pitch
Conventional
filler
Calcination
@ 1300
o
C
Grinding,
sieving,
blending
Petroleum
coke or
pitch
Petroleum
coke or
pitch
Conventional
filler
Conventional
filler
Calcination
@ 1300
o
C
Grinding,
sieving,
blending
Purification
@ 2500
o
C
Machining
A
B
(Optional)
(Optional)
FIG 2. Manufacturing Processes of Nuclear
Graphite.1,3,10-12
III.a Fabrication of Nuclear Graphite
Nuclear graphite is manufactured by a partial re-
crystallization, at high temperatures, of carbonaceous
materials basically consistig of cokes fillers and
viscoplastic coal tar pitch binders.1 The cokes, either a
petroleum, coal by-product or naturally occurring pitch,
vary considerably in structure, size and purity. They are
calcined at 900 – 1300 oC to densify and remove volatile
impurities, preventing excessive dimensional changes in
subsequent processes.3,10 The calcined cokes are crushed,
milled and graded to the desired particle sizes (Path A in
Fig. 2), and mixed with a pitch binder in a fairly uniform
plastic mass, known as the “green article”. The green
article is then formed into the desired shape or blocks, by
extrusion, pressure molding, isostatic molding, vibration
molding,11 or warm molding in the plastic temperature
range of the binder resin (Fig. 2). The randomly oriented
filler grains produce macroscopically isotropic graphite.
Alternatively, “secondary” precursor cokes with isotropic
structure can be produced commercially using inexpensive
anisometric pitch coke (Path B in Fig. 2).1,11,12
The blocks of green article are graphitized at up to
2600 – 3000oC (Fig. 2). The heat treatment at > 1900oC
increases a and c of the crystals and the graphitization and
thermal conductivity, but decreases the mechanical
strength, modulus of elasticity and rate of oxidation.
Above 2300 oC, these parameters stabilize, and opposite
changes occur at temperatures > 2600oC due to carbon
vaporization. During graphitization, crystals are formed,
the material becomes softer and easier to machine, the
electrical and thermal conductivity dramatically improve
and many impurities are driven off. The purity of graphite
can be increased by reheating to ~2400 oC in an Acheson
furnace with a halogen gas flow (Fig. 2). The TRISO-
coated fuel particles are mixed with graphite powder and
thermoplastic resin, then shaped into hexagonal elements
or pebbles for HTRs.13
Modern techniques that use finer coke particles and
cold isostatic pressing or vibration molding to form the
green article produce isotropic nuclear graphites with
uniform properties. For example, IG-110, a fine-grained,
nearly isotropic graphite contains much smaller
petroleum-based coke particles than H-451.14 The filler
particles in IG-110 are typically 10-150 µm in size (20 µm
mean) compared to 100-1500 µm (500 µm mean size) in
H-451.4 Furthermore, the internal pores in the IG-110 are
considerably smaller (16 µm mean) than in H-451 (42
µm).
III.b Type of Nuclear Graphites
The nuclear graphite NBG-10 currently being
developed is medium-grained and nearly isotropic. It uses
coal tar pitch coke with a grain size < 1.6 mm, and is
formed by extrusion and doubly impregnated.15,16 The
PCEA nuclear graphite,16,17 a candidate for replaceable
reflector and core blocks in the prismatic Next Generation
Nuclear Plant reactor (NGNP), uses petroleum-based coke
with grain sizes < 0.8 mm and is also manufactured by
extrusion.15,17 Both NBG-10 and PCEA have similar
densification to that of H-451. Other types of nuclear
graphite are the NBG-17 and NBG-18.15 Both use pitch
coke, are vibration molded and exhibit nearly isotropic
properties. The medium-grain (300 µm mean) NBG-18
graphite is being considered for the core structure of the
Pebble Bed Modular Reactor (PBMR), while NBG-17, a
finer-grained version of NBG-18, is a candidate for the
prismatic HTR fuel compact and core structure.
The graphite’s microstructure, density and porosity,
and its reactivity in the presence of oxidizing species
depend on the choice of the precursor coke, the
fabrication, molding process and heat treatment. The rate
of heating, final heat treatment temperature and duration
at temperature are particularly important. These variables
affect the alignment and size of the crystallites, which
control the proportion of reactive edge sites and the size
distribution and structure of the internal pores forming
during heat treatment. These pores give the oxidants
access to the interior surface during an air or steam
ingress in HTRs. The larger the crystallites, the lower the
chemically Active Surface Area (ASA), and the smaller
Proceedings of ICAPP ‘10
San Diego, CA, USA, June 13-17, 2010
Paper 10159
the accessible pore diameters. The rate of graphite
oxidation can therefore be reduced by increasing the heat
treatment temperature and time at temperature, since both
increase the crystallites size. With particles sizes > 100
µm, cracking may occur inside the pores as volatiles
escape during the heat treatment. The resulting carbon
deposition reduces graphite reactivity for oxidation. Rapid
heating could reduce such an effect, since it increases the
release rate of volatiles, reducing contact time for cracking
and the carbon deposition in the pores.18
III.c Preferential Oxidation of Binder in Graphite
In the coarse and fine-grained nuclear graphites,
preferential oxidation of the binder occurs,19-22 because it
is relatively disordered and more chemically active than
the filler calcined petroleum or pitch coke particles. The
volume pores in the binder increase the effective surface
area for oxidation, and the impurities and impregnates, if
present, act as a catalyst for oxidation, accelerating the
corrosion process. Degradation in mechanical properties
of graphite by preferential oxidation of the binder,
propagation of cracks at the binder-grains interface,
and/or the increase in volume porosity in the binder have
been reported.8,9,19-22
Figure 3 presents oxidation data of nuclear graphite
V483T and fuel pebbles’ graphite matrix A3-27 as a
function of burn-off fraction. The latter is comprised of
graphitized filler particles and a larger fraction (about
10%) of un-graphitized coked binder (1.74 g/cm3, < 60
ppm ash content). The relatively low heat treatment
temperatures (< 1950oC) of the matrix to avoid damaging
the TRISO fuel particles in the pebbles cause the binder to
not be fully graphitized. Also, there were 2 pronounced
maxima in the pore size distribution (at ~ 0.03 µm and 1
µm).20 On the other hand, V483T nuclear graphite is
fine-grained (< 100 µm size, 1.81 g/cm3, < 340 ppm ash
content), fully-graphitized and has a more homogeneous
pore size distribution. It is heat treated at > 2500oC.19 As
shown in Figs. 3a and 3b, the oxidation rate of V483T
graphite in air at 773 K and 1023 K with an activation
energy of 165 kJ/mole increases with increased burn-off,
X, to a maximum at ~ 0.40, then decreases with further
increase in burn-off. For the same burn-off fraction, the
total loss rate was higher at the higher temperature. By
contrast, A3-27 exhibited a more complex behavior, with
the loss rate first peaking at a burn-off fraction of only
0.05 (activation energy = 123 kJ/mole), corresponding to
preferential oxidation of binder coke (Fig. 3b). The second
peak in the rate due to the oxidation of the filler particles
at higher activation energy of 165 kJ/mole occurred at ~
0.40 burn-off fraction.22
0
1
2
3
4
5
0
0
.
2
0
.
4
0
.
6
0
.
8
V483T nuclear graphite
A3-27 fuel matrix graphite
(a)
Oxidation in air at 773 K
(Kühn, Hinssen and Moormann, 2004)
Rate x 105 (% / s)
0
4
8
12
16
2
0
0 0.2 0.4 0.6 0.8
A3-27 fuel matrix graphite
V483T nuclear graphite
(b)
Oxidation in air at 1023 K
(Kühn, Hinssen and Moormann, 2004)
Burn-Off Fraction, X
Rate x 10
3
(% / s)
FIG. 3. Oxidation Rate of V483T and A3-27 Graphites in
Air at: (a) 773 K; (b) 1023 K.20
IV. MODES OF GRAPHITE OXIDATION
The oxidation of graphite following an air or water
vapor ingress in a HTR proceeds through a number of
successive transport processes:23
(a) Diffusion of oxygen and other oxidants to the graphite
surface and into the open pores;
(b) Adsorption of oxidizing molecules onto graphite,
simultaneous formation of C-O and C-H bonds, and
the breaking of the C-C bonds. The gas molecules
typically dissociate as they adsorb onto graphite
(dissociative chemisorption);18
(c) Desorption of gaseous reaction products, such as CO
and CO2, from the surface and their transport through
the boundary layer, to the bulk gas mixture.
Below 400 oC, graphite oxidation is negligible. The
prevailing oxidation modes are categorized based on
temperature as follows:23-26
Mode (a): Chemical reaction kinetics (< 400 – 600
oC) (Fig. 4a);
Proceedings of ICAPP ‘10
San Diego, CA, USA, June 13-17, 2010
Paper 10159
Mode (b): Limited oxidants transport through
volume pores (600 – 900 oC) (Fig. 4b);
Mode (c): Counter-current diffusion of oxidants
and reaction products through boundary
layer to the graphite’s external surface
(> 900 oC) (Fig. 4c).
FIG. 4. Oxidation Modes of Graphite.
IV.a Reaction Kinetics Mode (a)
At temperatures of 400 – 600 oC, graphite oxidation
occurs within the volume pores, progressively increasing
its porosity with time (Fig. 4a and 5a). The decrease in
graphite density could eventually compromise structural
integrity, particularly of the support columns in the lower
plenum of a prismatic core HTR. A 10% decrease in
graphite density could reduce its structural strength by up
to 50%, depending on the type of graphite.25,27,28 Owing to
the low rates of reaction, oxidants concentration in this
mode is uniform throughout the pores (Figs. 4a and 5a).
The effective surface area of open and interconnected
pores strongly affects the corrosion rate of graphite by this
mechanism (Figs. 4a and 5a). It does not change the
outside dimension but increases the size of the volume
pores. The increased diameter of the pores effectively
increases the diffusion of oxidants into the pores, further
increasing the corrosion of the interior, and could
eventually compromise the integrity and mechanical
strength of graphite. The resulting oxidation products,
however, increasingly hinder the diffusion of oxidants to
the interior of the pores, decreasing the total oxidation rate
with further increase in burn-off. The pores eventually
break through, decreasing the internal surface area (Fig.
5), and reducing the corrosion rate.25,26 This reduction in
reactivity may be moderated by an increase in surface area
through access to originally closed pores.
Mechanistic models before 1979 for predicting the
enlargement and deepening of the pores and their
coalescence with other contiguous pores are detailed in the
excellent review by Essenhigh.18 Recent models of note
since are the Overlapping Grains Model29 and the Monte
Carlo model.30 The former assumes the porous solid is
made up of overlapping and partially sintered spherical
grains, while the latter uses percolation theory to describe
the effect of solid connectivity on oxidation, and dynamic
scaling to describe the distribution of the fragments. This
model tracks the evolution of the porous structure, but no
equations are solved explicitly for the oxidation rate.
A promising model of predicting the evolution of
internal surface area of the pores with burn-off has been
developed independently by Gavalas31 and Bathia and
Perlmutter.32 It assumes a solid porosity consisting of
infinitely-long overlapping random cylinders, and
accounts for the widening and the random overlap of
reacting surfaces (or coalescence) of the pores. The model
encompasses several treatments (grain-shape and order-of-
reaction models18) as special cases and relates the
important geometrical parameters of the porous solid to
the fundamental statistics of the pores using first
principles.
ln (Reaction Rate)
1 / T
Ea
Eb= Ea/2
Ec
Mode (a):
Chemical
Kinetics
Mode (b):
Diffusion through
volume pores
Mode (c):
Diffusion through
Boundary-layer
(a) Reaction Rate
Co
δδ
Boundary-layer
C (x)
Concentration
Boundary-layer
C (x)
C (x)
(b) Oxidants Concentration Gradient
ln (Reaction Rate)
1 / T
Ea
Eb= Ea/2
Ec
Mode (a):
Chemical
Kinetics
Mode (b):
Diffusion through
volume pores
Mode (c):
Diffusion through
Boundary-layer
(a) Reaction Rate
Co
δδ
Boundary-layer
C (x)
Concentration
Boundary-layer
C (x)
C (x)
Co
δδ
Boundary-layer
C (x)
Concentration
Boundary-layer
C (x)
C (x)
(b) Oxidants Concentration Gradient
FIG. 5. Oxidant Distribution and Oxidation Rate of
Graphite.
Using a pores volume distribution function,
determined from measurements, the initial volumetric
porosity, surface area and effective pore length per unit
volume are given by:32,33
dr
r
rf
So
o
v∫
=
+∞
0
)(
2, dr
r
rf
Lo
o
v∫
=
+∞
02
)(
π
, drrfoo ∫
=
+∞
0
)(
ε
(1)
The model characterizes the solid microstructure using a
structural parameter, Ψ and a particle size parameter,
σ
(often very large, and with little effect on results), given
by:
(
)
2
)()1(4 o
vo
o
vSL
επ
−=Ψ , and
(
)
o
o
voSR
εσ
−= 1.
(2)
Proceedings of ICAPP ‘10
San Diego, CA, USA, June 13-17, 2010
Paper 10159
In Mode (a), the oxidation rate is uniform on all
surfaces and proportional to the internal surface of the
solid (Figs. 4a and 5). Typically,
σ
is large (
σ
>>
τ
), and
the volumetric surface area and fractional burn-off vary
with time32,33 as:
o
vv SSXX
d
dX =−Ψ−×−= )1ln(1)1(
τ
. (3)
The dimensionless time,
τ
, is given by:
(
)
o
o
v
ntSCk
ετ
−
′′
=1 . (4)
0
30
60
90
120
150
180
0 0.2 0.4 0.6 0.8 1.0
One sample
Individual samples
Ψ
= 806 (best fit)
Ψ
= 765 (measured)
R
T
(t = 0) = 11.3
µ
g / s
Random
Cylinders
Model
IG-110 graphite cylinders oxidized in air at 750
o
C
(Fuller and Okoh, 1997)
Burn-Off Fraction, X
R
T
(
µ
g / s)
FIG. 6. Oxidation of IG-110 Graphite.25
This model for predicting the reaction surface area in
terms of the initial pores structural parameter, Ψ, is valid
only in the absence of new pores generation and in Mode
(a). Extending this model to other modes occurring at
higher temperatures (Figs. 4 and 5), requires a numerical
solution of the equations. As
σ
∞, the pores maximum
surface area occurs at
[
]
ΨΨ−−= /)2/1(exp1
max
X.
When Ψ > 2, the maximum surface area, at 0 < Xmax <
0.393, is independent of temperature but depends on the
type of solid graphite. It has been confirmed
experimentally for nuclear graphite that Ψ > 100 and
0.387 < Xmax < 0.393. Results of air oxidation
experiments using cylinders of K018, K022 and IG-110
graphites confirmed that the maximum reaction rate
occurs at a burn-off of ~ 40% (Fig. 6).25
In Fig. 6, Ψ = 806 provides a best fit of the
experimental data, and the measured Ψ = 765 value
acceptably fits the data. Su and Perlmutter33 examined the
initial pore structure of coal chars using a combination of
mercury porosimetry, CO2 adsorption at 195 K and 273 K,
and pycnometry techniques, and compared values of Ψ
from their measurements with those used for fitting the
oxidation data in dry air at 653 K to 773 K. The
agreement of Ψ values validated the Random Cylinders
Model. However, this model neither accounts for opening
initially closed pores nor is applicable at a volume porosity
> 60%, when fragmentation of the graphite’s outer layer
likely occurs.
IV.b Limited Oxidants Transport Mode (b)
At temperatures above ~ 600 oC, the increase in
oxidation rate in the volume pores depletes oxidants as the
released reaction products increasingly obstruct their
diffusion into the pores. Thus, the diffusing gas is
consumed in a reactive zone that does not penetrate deep
to the center of the porous solid, marking the transition to
Mode (b) (Fig. 4b). In this mode, the oxidation rate is
limited by the oxidants transport into the volume pores
(Fig. 5a and 5b) and the activation energy of oxidation is
half that in Mode (a) (Essenhigh, 1981).
Results of experiments performed in the pores
diffusion-controlled Mode (b) (Fig. 4) at different oxygen
partial pressures indicated that Knudsen diffusion is the
relevant transport mechanism in the pebbles matrix
graphite, but not in standard nuclear graphite.20 Knudsen
diffusion, for which the mean free path of the oxidants is
much larger than the average pore diameter, effectively
reduces the overall reaction rate in Mode (b) (Fig. 4b).
These results suggest that micro-pores (< 0.002 µm) and
mesopores (0.002 – 0.050 µm) could play a role in the
oxidation of matrix graphite.
IV.c Boundary-Layer Diffusion Mode (c)
This mode of graphite oxidation prevails at > 800 –
900 oC, when the access of oxidants to the interior of the
volume pores is impaired, and corrosion reactions become
limited to the exterior surface (Figs. 4c and 5). The retreat
of the reaction from the internal pores to the external
surface of the graphite marks the transition to Mode (c)
(Figures 4c and 5). Graphite corrosion in this mode only
changes the outside dimensions, and its rate is controlled
by the diffusion of oxidants from the bulk gas mixture,
through the boundary layer, to the surface, and the
counter-current diffusion of the reaction products, such as
CO and CO2, from the surface to the bulk gas. Transition
temperatures to Mode (c) (Fig. 4c) are only suggestive,
because the reaction rate in this mode depends on several
parameters that include the shape and size of the graphite
block, the flow velocity of the bulk gas mixture and partial
pressures of the oxidizing species in the bulk gas flow.
IV.d Oxidation Reactions
The chemistry of corrosion reactions of graphite with
oxygen, CO and CO2, water vapor and hydrogen are well
understood. They are exothermic, except those with CO2
and water vapor to produce CO are endothermic. The
Proceedings of ICAPP ‘10
San Diego, CA, USA, June 13-17, 2010
Paper 10159
heterogeneous reactions occurring at the graphite surface
contribute to both the corrosion and the heating up of the
graphite. The homogeneous reactions occurring among
gaseous species in the bulk gas mixture and in the
boundary layer increase temperature. Such increase in
temperature increases the reaction rate constants, and the
mobility and diffusion of the oxygen molecules and other
oxidants from the bulk gas to the graphite surface.
The heterogeneous corrosion reactions are:23,34
)/5.393(
2
2
molkJHCOOC −=∆→+ (5a)
)/5.110(22 2molkJHCOOC −=∆→+ (5b)
These reactions proceed simultaneously and are combined
in the general form:
2
2
)1(2)1( COfCOfOCf −+→++ . (5c)
The coefficient f varies between 0 and 1; f = 0 indicates
oxidation proceeds by Reaction (5a) only, and for f = 1,
CO gas is generated by Reaction (5b) at twice the molar
volume of CO2 in Reaction (5a). This slows the inter-
diffusion of various gaseous species and sequesters twice
as many carbon atoms per oxygen atom supplied.
Reaction (5a) produces the largest amount of heat per unit
mass of graphite reacted, while reaction (5b) removes the
largest amount of graphite from the structure per unit
mass of oxygen reacted. It also produces less than a third
of the heat from reaction (5a). The Boudouard reaction is
highly endothermic and only occurs at high temperatures
(e.g. Mode (c)):
)/5.172(2
2
molkJHCOCOC +=∆⇔+ (5d)
The reactions of water vapor with graphite are either
endothermic (5e) or exothermic (5f), and negligible below
800 oC. At these temperatures, the reaction rates of
hydrogen with graphite (5g), though exothermic, are even
lower than those with water vapor:
)/5.131(
22 molkJHHCOOHC +=∆+⇔+ (5e)
)/4.82(22 222 molkJHHCOOHC −=∆+⇔+ (5f)
)/81.74(2 42 molkJHCHHC −=∆→+ (5g)
Reactions (5f) and (5g), typically associated with steam
ingress in HTR, generate the same amount of heat per unit
mass of graphite reacted. Reaction (5e) is an unlikely
contributor to graphite corrosion either by air or steam.
For example, at 800 oC and 0.1 atm, the relative rates for
the C–O2 (5b), C–H2O (5f), C–CO2 (5d) and C–H2 (5g)
reactions are 105, 3, 1 and 3 x 10-3, respectively.24
Homogeneous reactions of gaseous species are:23,34
)/0.283(22
2
2
molkJHCOCOO −=∆→+ (6a)
)/42(
2
2
2
molkJHHCOOHCO −=∆+→+ (6b)
)/4.481()(22
2
2
2
molkJHgOHHO −=∆→+ (6c)
Reactions (6a) and (6b) occur in the boundary layer and
the bulk multi-species gas mixture. The first reaction
competes for oxygen, and the second competes for water
vapor in the bulk gas. The highly exothermic Reaction
(6a) generates a large amount of heat per mole of oxygen,
increasing the temperature of the gas flow. These
exothermic reactions should be accounted for when
modeling graphite oxidation, following a massive steam
ingress into a HTR.
V. KINETICS OF GRAPHITE OXIDATION
As indicated earlier, the oxidation modes of graphite
(Figs. 4 and 5) strongly depend on temperature, access of
oxidants to the graphite surface and the volume pores,
kinetics of prevailing chemical reactions and the removal
rate of the reaction products. The following subsections
discuss methods of modeling graphite’s oxidation reaction
kinetics (Figs. 4 and 5), and presents validation results of
models with experimental data, when available.
V.a Reaction Kinetics in Mode (a)
In this mode, oxidants have unobstructed access to the
volume pores and their concentration is uniform
throughout (Fig. 5). This is because of the low oxidants
concentration, low oxidation rate, and uniform carbon
gasification rate per unit of surface area of the open pores.
A one-step power law has been used successfully to predict
the reaction rate of graphite by air or oxygen in Mode (a)
as: 18,28,35
(
)
(
)
o
vv
n
O
TRE
o
vv
n
OSSPekSSPkR g
2
1
2
/
1−
==
′′ . (7)
In this expression, k is the rate constant, k1 is the pre-
exponential factor, E1 is the activation energy, and n is the
reaction order. The last term on the right-hand-side of
Eq. (7) accounts for the change in the porous structure of
graphite with burn-off. Graphite gasification by oxygen
generates both CO and CO2 reaction products (Eqs. (5a)
and (5b)); the measured ratio of [CO]/[CO2] in
experiments is fitted with an Arrhenius law as:
( )
TRE g
ekCOCO /
22 2
][][ −
=. (8)
Takeda and Ishida36 and Lim and No35 calculated the
rate of CO combustion in the bulk gas by the
homogeneous Reaction (6a), using the power law:37
2/1
2
2/1
2
/
3][][][
3OHOCOekR TRE
CO g×××=
′′ −. (9)
Proceedings of ICAPP ‘10
San Diego, CA, USA, June 13-17, 2010
Paper 10159
This equation accounts for the reaction enhancement in
the presence of steam using an activation energy, E3 =
125.6 kJ/mole. In their GAMMA code, Lim and No35
used the following correlation to predict the combustion
rate of CO in the bulk gas: (10)
(
)
(
)
2/14/1
2/14/1
/
4222
4
ggOggOHOCO
TRE
CO MMXYYekR g
ρρρ
−
=
′′
Because experimental data for the Boudouard Reaction
(5d) are not available for IG-110 graphite, the GAMMA
code calculates the reaction rate using the correlation
developed by Moorman34 for fine-grained A3-3 graphite
matrix:
(
)
(
)
2/1
/
6
/
52
6
2
5
21CO
TRE
CO
TRE
CO PekPekR gg −− +=
′′ . (11)
This correlation is only valid for temperatures between
1150 and 1300 oC, isothermal helium/CO2 mixtures at 0.1
MPa and high graphite burn-off. The activation energies
E5 and E6 are 207.9 and 58.2 kJ/mole. Xiaowei et al.26
used the following Langmuir-Hinshelwood equation,
developed by Velasquez et al.38 for H-451 graphite, to
calculate the rates of Reactions (5e) and (5f) by steam:
(
)
( )
.1 1
/
9
/
8
/
7
2
9
2
8
2
7
−
−−
−
++×
=
′′
OH
TRE
m
H
TRE
o
vvOH
TRE
C
PekPek
SSPekR
gg
g
(12)
This correlation is valid for PH2O < 300 Pa and 1%
graphite burn-off, when the exponent m = 0.75. Since the
gasification rate of graphite in steam is several orders of
magnitude lower than by oxygen, Xiaowei et al.26
neglected the heat of reaction, inhibition by reaction
products (k8 = 0) and changes in graphite microstructure
with time.
V.b Reaction kinetics in Mode (b)
In this mode of graphite oxidation, released reaction
products increasingly obstruct the diffusion of oxidants to
the interior of the pores, shifting the oxidation reactions
gradually with increasing temperature to the outer surface
of the graphite block. Thus, the oxidation rate is limited by
the transport of oxidants into the volume pores and to the
surface, making the kinetics of the reactions relatively
complex. Therefore, modeling oxidation reactions of
porous graphite in Mode (b) should include mathematical
formulations of the reaction rates in the volume pores.
Formulations developed for various geometries to describe
the porous solid use local density,
ρ
, volume porosity,
ε
,
massic surface area, Sm, volumetric surface area,
mv SS
ρ
=, and employ effective diffusion coefficients, Deff
of the gaseous species. The quasi-steady state local mass
balance, equating the rates of internal diffusion of
oxidants and chemical reaction, and neglecting any bulk
flow can be written for different geometries as:18
ivi
i
eff
i
s
sRSR
dr
dC
Dr
dr
d
r
′′
×=
′′′
=
−
−
1
1
1 . (13)
0.1
0.2
0.5
1
0.3
0.7
0.1 100.2 0.4 0.6 1 2 4 6
First-order
reaction
(n = 1)
Zero-order
reaction
(n = 0)
General Thiele Modulus, Φ
g
Effectiveness Factor,
η
FIG. 7. Effectiveness Factor.18
In this equation, a superposition of Fick’s second law and
rate equation in Mode (a), s = 1, 2, and 3 for a slab,
cylinder, and a sphere, respectively. For a solid cylinder, it
is solved for the reaction rate, i
R
′
′
, using the boundary
conditions:
Rii CtRrC ,
),( == , and oioi CtRC ,
),( =, (14)
Where 0 < Ro < R. In Mode (a) (Figs. 4a and 5), Ci,o =
Ci,R and Ro = 0, while in Mode (b) Ci,o = 0 at some depth
within the volume pores.
Analytical solutions of Eqs. (13) and (14) have been
developed assuming a constant diffusion coefficient and
either zero-order (n = 0) or first-order (n = 1) reaction.18,24
Approximate asymptotic solutions are also available for
the intermediate order reactions (0 < n < 1) and for the
general case of Langmuir-Hinshelwood rate equations for
i
R
′
′
. The maximum oxidation rate, max
T
R occurs when the
reactions in the volume pores involve the total internal
surface. Actual reaction rate in the porous solid is given
as:
max
TT RR ×=
η
. (15a)
The effectiveness factor,
η
< 1, depends on the fraction of
the interior surface of the pores involved in the oxidation
and decreases with increasing temperature. It is also a
function of the Thiele modulus, Φ, Fig. 7:18
η =
f
(Φ)
, where eff
DkR /
′′′
=Φ . (15b)
When the effective diffusion coefficient is large compared
to the reaction constant, oxidation is in Mode (a), where Φ
Proceedings of ICAPP ‘10
San Diego, CA, USA, June 13-17, 2010
Paper 10159
< 0.2 – 0.3. In Mode (b), Φ > 2 for slab, > 4 for cylinder,
and > 6 for sphere.
The graphite oxidation moves gradually from Mode
(a) to Mode (b), with increasing temperature, except for
zero-order reactions. For intermediate values (0 < n < 1),
approximate asymptotic solutions can be derived using the
Arrhenius form to calculate the reaction constant. In
oxidation Mode (b) (Fig. 4b), g
Φ≈ /1
η
, and the general
Thiele modulus is given by:18
1
2
)1( −
+
×
Φ
=Φ n
Rg C
n
s
. (16)
The total reaction rate, RT, per unit of external surface
area, Sp, is given by:18
.)(
2/)1(
2/)1( +
=
×
+
′′′
=
×
′′′
×
Φ
=
=
n
R
eff
n
R
g
Rr
i
eff
p
T
C
n
Dk
Ck
s
R
dr
dC
D
S
R
(17)
When Deff is assumed constant and independent of
temperature, Eq. (17) shows that in Mode (b) (Fig. 5) the
reaction order, na = (n+1)/2 and activation energy,
Eb = Ea/2. The curves of the effectiveness factor versus Φg
in Fig. 7 show that Φg < 1 represents Mode (a) and Φg > 1
represents Mode (b). This simple deduction indicates that
solving Eqs. (13) and (14) numerically to predict the
reaction rates in Mode (b) would be unnecessary. While
applicable to isothermal condition, the simple approach
cannot accurately predict the reaction rate for non-
isothermal processes, and does not provide information on
the penetration of oxidation in the volume pores (Fig. 4b).
The latter is needed to evaluate potential degradation in
structural strength of graphite as a function of time and
temperature. Furthermore, since effective diffusivities of
oxidants and gaseous products and the accessible surface
area in the pores for oxidation are strong functions of the
graphite burn-off, they vary significantly with
temperature, complicating Equations (13) and (14), which
must be solved numerically.
V.c Reaction Kinetics in Mode (c)
Graphite oxidation prevails in this mode at > 800 –
900 oC and occurs mostly at the external surface (Figs. 4c
and 5). This mode of oxidation is constrained by the
diffusion of oxidant gases through the boundary layer to
the surface and the counter-current inter-diffusion of the
reaction products from the surface to the bulk gas. The
counter-current diffusion of gaseous species in the
boundary layer, in terms of the mass transfer coefficient,
can be represented by the following equation:39
(
)
(
)
(
)
Riiim
Rr
ieff CCkdrdCD ,, −= ∞
= . (18)
In this oxidation mode, when the reaction rate is high, the
rate of mass transport of oxidants to the graphite surface
through the boundary layer is the limiting process. On the
other hand, the endothermic heterogeneous Boudouard
reaction (Eq. 4d) could significantly increase the rate of
graphite loss by oxidation.22 The CO produced by
exothermic gasification reaction in Eq. (5b) at the graphite
surface is oxidized in the bulk gas and the boundary layer
to CO2 (Eq. 5a), further gasifying the graphite by the
Boudouard Reaction (5d) to produce CO, and the process
continues. The gasification rate enhancement can be
explained by steeper concentration gradients and higher
local temperatures. In effect, CO2 in the bulk gas and the
boundary layer competes with oxygen as a gasifying agent,
while encountering little diffusion resistance to reach the
graphite surface.22
0.0001
0.001
0.01
0.1
1
10
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
21% O
2
(Fuller & Okoh, 1997)
21% O
2
(Chi & Kim, 2008)
Kim and No (2006):
20% O
2
10% O
2
5% O
2
2.5% O
2
Oxidation of IG-110 graphite
cylinders in dry air
Reciprocal Temperature, 10
3
/ T (K
-1
)
Oxidation Rate, R'' (
µ
g / cm
2
.s)
FIG. 8. Oxidation Data of IG-110 in Dry Air.25,40,41
V.d Progression of Graphite Oxidation and
Experimental Data
Experimental data of Contescu et al.21 for right
cylinders (D = H = 25.4 mm) of PGX, NBG-10, and R4-
650 graphite showed that the bend in the Arrhenius plot
(Fig. 8) occurs when the rate of oxygen supply falls below
10 times the consumption rate of carbon. This is
consistent with the reported experimental data for
cylinders of IG-11 and IG-110 graphite in dry air.25,26,40,41
The data also show that the transition from oxidation
Mode (a) to Mode (b) (Fig. 5) in the Arrhenius plot moves
to a higher temperature as the air or oxygen flow rate
increases. At a flow rate of only 0.020 liter/min, the
transition for the IG-11 cylinders (D = H = 1 cm) occurred
at 600 oC.26 At a higher flow rate (0.50 liter/min) with
IG-110 cylinders (D = 0.84 cm and H = 1.9 cm), Fuller
and Okoh25 obtained an Arrhenius plot for a carbon
consumption of 5.6% that was linear up to 750oC (Fig. 8).
Proceedings of ICAPP ‘10
San Diego, CA, USA, June 13-17, 2010
Paper 10159
At a higher flow rate of 10 liter/min, with right cylinders
of IG-110 graphite (H = D = 2.54 cm), the data of Chi and
Kim41 when the carbon weight loss was 5-10% exhibited a
bend near 820 oC (Fig. 8). At a much higher flow rate of
40 liter/min, with IG-110 cylinders (D = 2.1 cm and H = 3
cm) the bend in the Arrhenius plot during the induction
period (i.e., zero burn-off, X ~ 0) occurred at ~ 900oC
(Figure 8).40
The ratio of oxygen supply (in moles/min) to total
carbon consumption at the transition temperature where
the bend occurs are calculated as 9.8, 7.6 and 11.9 from
the data of Xiaowei et al.,26 Fuller and Okoh25 and Kim
and No,40 respectively. These ratios are consistent with
the ratio of 10 suggested by Contescu et al..21 Note that
the intrinsic carbon consumption rate data in Fig. 8,
expressed in units of mass flux (µg/cm2 s), is based on the
total initial reaction surface area. This is the sum of the
external surface of the cylindrical samples and the internal
surface of the open pores. The latter is obtained using a
specific surface area, Sv = 12,760 m2/m3 for IG-110.28 The
measured mass fluxes by Chi and Kim41 are nearly an
order of magnitude higher than those of Kim and No,40
because they were taken at a higher burn-off (X ~ 5 –
10%), which corresponds to a much higher internal
surface area. The data of Kim and No40 and Chi and
Kim41 in Fig. 8 also show that in Mode (c) occurring at
high temperatures (> 800 – 900 oC) the reaction rate
becomes almost constant. Using a semi-empirical model
that equated the chemical reaction rate to the mass
transfer rate through the boundary layer, Kim and No40
matched their experimental data in this mode.
VI. SUMMARY
The type and heat treatment of nuclear graphite
during fabrication strongly affect its behavior during a
massive air or steam ingress in HTRs. This event is a
design-basis accident requiring the development and
validation of graphite oxidation and erosion models to
examine the potential of fission products release from the
coated TRISO fuel particles, predict the rates of erosion
and assess the integrity of the graphite core and reflector
blocks as well as the supporting columns in prismatic core
HTRs. Similar concerns are applicable to the graphite
matrix of the pebbles in the PBMR. HTRs nominally
operate at 600 –950 oC and are cooled with inert helium
gas that may also function as the working fluid for the
Closed Brayton Cycle for energy conversion.
Nuclear graphite comes in many types with
similarities but also differences in microstructure, volume
porosity, impurities, type and size of filler coke particles,
graphitization and heat treatment temperatures, and
thermal and physical properties. These, as well as
temperature, types and partial pressures of oxidants in the
bulk gas mixture affect the prevailing oxidation mode, the
kinetics of oxidation and the erosion rates of graphite in
HTRs.
An extensive review is carried out and documented in
this paper of the graphite crystalline structure, the
characteristics, chemical kinetics and modes of oxidation
reactions of nuclear graphite as functions of temperature
and partial pressure of oxidants. Methods for predicting
the erosion rate of the graphite in the different modes and
for determining the reaction constants are also reviewed.
The contents of this review would be useful to future
model developments to assess the impact of a massive air
or steam ingress on the safety and integrity of the HTR
core and support structure.
Based on the present review, an accurate graphite
oxidation model for simulating air and water ingresses in
HTRs should couple the counter-current diffusion of
oxidants and reactant gases to the exterior surface and
within the interior of the volume pores to the appropriate
chemical reaction rate equation. In addition to predicting
the erosion rate, this coupling would make it possible to
predict the penetration of the oxidation front within the
porous graphite and the changes in volume porosity and
external dimensions as functions of time, burn-off fraction
and temperature. Validation of developed models with
experimental data may also require accounting for the
graphite removal by both erosion and fragmentation of the
outer surface. At higher temperatures, when the mass
transport through the boundary layer is a limiting rate, the
increase in graphite erosion by the Boudouard reaction
should be accounted for.
Because of a space limitation, the results of ongoing
work on examining reported models of graphite oxidation
and erosion during a massive air or steam ingress in HTRs
could not be included in this paper. The details of a
comprehensive phenomenological graphite oxidation
model that is being developed and validated with reported
experimental data of samples of different geometries will
be reported in a future publication.
ACKNOWLEDGMENTS
This research is partially funded by a DOE NEUP
contract No. 00044825 00002, Project No. 09-830, to the
University of New Mexico and the University of New
Mexico’s Institute for Space and Nuclear Power Studies.
NOMENCLATURE
C Concentration (mole/m3)
D Diffusion coefficient (m2/s)
E Activation energy (J/mole)
f Gas product fraction, ])[2]/([][
2
COCOCOf +=
fo Pores volume distribution function (m-1)
Proceedings of ICAPP ‘10
San Diego, CA, USA, June 13-17, 2010
Paper 10159
k Reaction rate constant, )/exp( TREkk gii −×=
km Mass transfer coefficient (m/s)
Lv Effective pore length per unit volume (m-2)
M Molecular weight (kg/mole)
n Reaction order (0 < n < 1)
Px Partial pressure of gaseous species x (Pa)
r Radius (m); radial coordinate
Rg Perfect gas constant (8.3144 J/mole.K)
R
′
′
Reaction rate per unit area (kg/m2.s)
R
′
′
′
Reaction rate per unit volume (kg/m3.s)
RT Total reaction rate (kg/s)
s Geometrical index
Sm Massic surface area for reaction (m2/kg)
Sv Volumetric surface area for reaction (m2/m3)
t Time (s)
T Temperature of gas mixture (K)
X Burn-off fraction
Xi Molar fraction of species i in gas mixture
Yi Mass fraction of species i in gas mixture
Greek
∆
Η
Enthalpy of reaction (J/kg)
ε
Volume porosity of solid graphite
η
Effectiveness factor
ρ
Mass density (kg/m3)
σ
Dimensionless particle size parameter
τ
Dimensionless kinetic time
Φ Dimensionless Thiele modulus
Ψ Dimensionless structural parameter
Subscript/Superscript
eff Effective
g General
i Gaseous species i
max Maximum value
o Initial condition at time = 0
R External surface of solid, r = R
∞ Mainstream value
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