Proceedings of Global 2009
Paris, France: September 6-11, 2009
Paper 9038
Long-term behavior of vitrified waste packages
Isabelle Ribet*, Sophie Bétrémieux **, Stéphane Gin *, F. Angeli *, Christophe Jégou *
*CEA, Centre de Marcoule, DTCD, B.P. 17171, 30207 Bagnols sur Cèze, France
**AREVA NC, BU-T / DIRP / RDP, Tour AREVA, 1 Place Jean Millier, 92084 PARIS - LA DEFENSE 6, France
Email: isabelle.ribet@cea.fr
Abstract – The VESTALE project (from the French acronym for “long-term alteration of glass in
interim storage and in a waste repository) was undertaken to develop long-term behavior models of
vitrified waste packages. The first stage of the project was completed in 2005, meeting the deadline set
by the 1991 French nuclear waste management act, with the submission of long-term behavior models
taking into account the current state of knowledge at that time. The subsequent waste management act
of 2006 selected a clay medium (in the Meuse-Haute Marne area of northeastern France) as the
reference option for a geological repository site. The second stage of the VESTALE project (2006–
2012) is therefore devoted to consolidating long-term behavior models of vitrified waste packages, by
taking into account more precisely defined repository environmental conditions. The project
addresses two main areas of investigation: first, a study of intrinsic glass behavior under the
responsibility of the waste producers, which is the subject of this article; and second, a study of
environmental coupling, especially as applied to the conditions prevailing in the Bure underground
laboratory, under the responsibility of the French radioactive waste management agency, ANDRA,
and which is not detailed here. The work now in progress on intrinsic glass behavior seeks not only to
strengthen the hypotheses adopted in the existing models developed for the glass formulations
currently in production, but also to acquire data for characterizing the long-term behavior of future
glass packages. The following topics are covered: (1) self-irradiation effects: effects on the glass
structure, consequences on macroscopic properties, helium behavior at high alpha doses;
(2) alteration kinetics, especially over the long term: mechanisms controlling the residual glass
alteration rate, modeling the alteration kinetics, assessment of glass composition effects;
(3) estimation of the reactive surface area: thermomechanical modeling of the initial crack density,
development of cracking under the effect of external mechanical stresses, coupling with the alteration
kinetics to determine the quantities of altered glass in full-scale blocks; (4) natural and archaeological
analogs: the issues of long-term validation of the experimental and modeling results.
•
I. INTRODUCTION
Reprocessing is the reference process for spent fuel from
pressurized water reactors in France; the resulting fission
product solutions are then vitrified. This article focuses on
research concerning the “R7T7” containment glass produced
by AREVA NC in its La Hague plant. The French nuclear
waste management act of 2006 specified geological disposal
as the reference disposition route for vitrified wasteforms.
Characterization of the long-term behavior of the glass in
collaboration with the waste producers provides input data for
investigations by ANDRA of package interaction with the
repository environment. In this context, the VESTALE
project is designed to develop glass behavior models that can
be coupled with models of the other components of waste
storage vaults to allow performance calculations of dose
release from the repository.
Two main issues must be addressed in characterizing
long-term behavior:
Glass behavior in a closed system: characterization of the
potential changes in the glass structure due to heat and
self-irradiation.
• Glass behavior in a water-saturated open system: specification of the glass source term, i.e. the quantity of altered
glass (or of radionuclides released) over time.
A predictive behavior model known as V0Vr was
developed and published in 2005 [1]. This conservative
model incorporates the state of scientific knowledge available
in 2005; its main hypotheses are reviewed in the next section
of this article. The following sections discuss recent progress
and prospects concerning self-irradiation effects for very high
doses, the long-term alteration kinetics, estimating the
reactive surface area and its potential long-term evolution,
and validation by natural and archaeological analogs.
The main milestone in the ongoing program is in 2012,
when a summary of available knowledge must be submitted
under the ANDRA repository licensing process.
Proceedings of Global 2009
Paris, France: September 6-11, 2009
Paper 9038
II. THE V0Vr MODEL
This model is designed to quantify the quantity of altered
glass over time. It therefore postulates the very conservative
hypothesis that all the radionuclides are released at the same
rate as the glass alteration tracers, such as boron. The
following additional hypotheses are assumed:
• The effects of heat and self-irradiation do not degrade the
physical and chemical properties of the glass over time.
The glass matrix remains homogeneous and helium
production due to the decay of alpha emitters does not
lead to the formation of bubbles at micrometer scale. This
hypothesis has been largely demonstrated for the glass
packaged that are now produced industrially.
• As long as the medium remains reactive with respect to
silicon from the glass matrix, the glass alteration rate is
assumed equal to the maximum observed rate, i.e. the
initial rate V0, which depends only on the temperature and
pH. The reactive surface area during this alteration phase
is only a fraction of the total consisting of the external
(geometric) surface area (S0) and the surface area of largeaperture cracks. The cracking factor is designated 0. The
quantity of glass altered per unit time during this phase is
equal to the product of V0 × S0 × 0.
• After the initial phase of rapid alteration due to chemical
reactions in the immediate environment of the glass (Si
sorption on metal canister corrosion products), the
alteration kinetics reach a residual rate (Vr) under
conditions in which the water renewal rate is very low, as
in the case of a geological repository. The reactive surface
area comprises all the external surfaces and the crack
surfaces. The cracking factor is designated r. The
quantity of glass altered per unit time during this phase is
equal to the product of Vr × S0 × r.
The model parameters (alteration rates V0 and Vr, cracking
factors 0 and r) were determined as a function of the
temperature (between 25 and 100°C), the pH (between 7 and
10) and the glass composition throughout the R7T7
composition range. The uncertainties on the parameter values
were also determined. The model can be used to calculate the
lifetime of the glass from the time/temperature profile, the pH
of the medium, the date of water ingress in contact with the
glass, and the quantity of accessible silicon sorption sites on
the canister metal products.
Figure 1 is a typical calculated glass lifetime plot for two
hypotheses concerning the quantity of unsaturated sorption
sites during the initial rate phase, assuming water ingress in
contact with the glass after 4000 years [1]. The graph
illustrates the importance of the residual rate phase in
determining the total package lifetime, and the need to better
understand the mechanisms responsible for this rate regime.
Figure 1. Total altered glass fraction in two cases:
 allowing for saturation of the canister corrosion
products alone,  allowing for saturation of the canister
and overpack corrosion products. In both cases alteration
begins after 4000 years. The corresponding uncertainties
are indicated in broken lines, especially in the reference
case .
Compared with the state of knowledge in 2005, the
objective of the ongoing studies is to consolidate the
hypotheses of the V0Vr model in the following areas:
• More precise characterization of the reactivity of the
surrounding environment with respect to the glass; this is
the subject of a study organized by ANDRA and is not
discussed here.
• Confirmation that the glass properties are not degraded at
high alpha doses.
• Clarification of the mechanisms controlling the residual
rate.
• Comparison of the cracking factors 0 and r obtained by
indirect measurements with the estimated glass thermomechanical cracking factor.
III. SELF-IRRADIATION EFFECTS ON GLASS
PROPERTIES
Increasingly higher fuel burnup implies the vitrification of
fission product solutions with minor actinide concentrations
higher than those initially specified. This requires an
assessment of R7T7 glass behavior at alpha decay doses of
about 1019 /g of glass. Actinide solubility tests in R7T7-type
glass have shown that the minor actinide concentrations in
question do not limit their incorporation in the glass network.
Irradiation damage studies combine several approaches:
• Glass specimens subjected to external irradiation: these
methods are used to accumulate high doses in a thin glass
layer near the surface, and allow a broader range of
characterization methods than doped glass (Raman
spectroscopy, XANES).
Proceedings of Global 2009
Paris, France: September 6-11, 2009
Paper 9038
•
Atomistic modeling (molecular dynamics): computation
of cumulative displacement cascades is a mean of
estimating the impact of irradiation on macroscopic
properties such as the density or the modulus of elasticity.
• Actinide-doped glass specimens quickly reach high
cumulative doses throughout the glass volume. The doped
glass with the highest activity prepared for this study
contained 3.5 wt% curium-244 oxide; by 2008 it had
reached an accumulated dose of 1019 /g, corresponding
to the dose sustained by R7T7 glass after 10 000 years.
The three approaches all yield consistent results: due to the
effect of alpha decay the glass density diminishes slightly and
its mechanical properties appreciably improve, especially its
resistance to cracking. The variations in these properties
reach a saturation level and stabilize beyond 2 × 1018 /g
(Figure 2).
Accumulated alpha dose (α/g)
0.0E+00
0.1
2.0E+18
4.0E+18
6.0E+18
8.0E+18
1.0E+19
0
Density variation (%)
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6
-0.7
0.04wt% 244CmO2
0.4wt% 244CmO2
3.25wt% 244CmO2
fit Marples model
1.2wt% 244CmO2
Figure 2. Density of R7T7-type glass versus alpha decay
dose. Data from [2] [3].
Nuclear interactions caused by recoil nuclei induce slight
structural changes, especially a drop in the boron
coordination number and residual depolymerization of the
borosilicate network (~1%). These changes are comparable to
the effects of local thermal quenching of zones partially
disorganized by recoil nuclei.
A local thermal quenching accumulation model has been
developed to describe the origin of these structural changes:
each alpha disintegration locally damages the glass, which
stabilizes in a new glass structure corresponding to a
hypothetical high-temperature state. The accumulation of
these events throughout the glass volume gradually produces
a new glass corresponding to this slightly modified structure.
This description accounts for the stabilization of the macroscopic properties observed beyond 2 × 1018  disintegrations
per gram of glass by postulating a damage threshold affecting
the entire material volume. [4].
The results of these studies reveal no measurable specific
effect of helium generation in the glass up to the maximum
dose of 1019 /g. The data acquired establish that the
properties of R7T7-type glass will be not modified by an
accumulated dose of about 1019 /g glass, and do not call into
question its long-term behavior. [5]
In order to pursue our research on a possible accumulation
limit of alpha decay in the glass (above 1019 /g), a program
specifically targeting helium behavior in the glass was
undertaken to assess feasibility of subjecting glass to higher
doses. The program should allow us to predict the
consequences of helium behavior over the very long term
(diffusion as a function of the temperature and degree of glass
network damage; bubble formation; effect on the cracking
factor). It will include the examination of glass specimens
irradiated in a reactor to generate large quantities of helium
by the 10B(n,)7Li reaction.
IV. GLASS ALTERATION KINETICS:
The GRAAL Model (Glass Reactivity
with Allowance for the Alteration Layer)
Observations during R7T7-type glass leaching
experiments in a closed system or with very slow renewal
have shown that very low alteration rates are reached (about
5 nm/year at 50°C). A detailed investigation of glass
alteration mechanisms identified the following features when
glass is placed in contact with water (Figure 3) [6]:
• Exchange and hydrolysis reactions involving the mobile
glass constituents (alkalis, boron, etc.) rapidly occur
during the initial instants.
• Slower hydrolysis, especially of silicon, results in the
existence of an initial glass dissolution rate.
• The difference between these two kinetics results in the
creation of an amorphous layer at the glass/solution
interface regardless of the alteration conditions. This layer
is gradually reorganized by hydrolysis and condensation
mechanisms.
• The amorphous layer dissolves as long as the solution is
not saturated with respect to its constituent elements (Si,
Zr, Al, Ca, etc.). Renewal of a pure water solution
sustains the dissolution process.
• The amorphous layer constitutes a barrier against the
transport of water toward the glass and of solvated glass
ions into solution. The existence of this transportinhibiting effect rapidly causes this layer to control glass
alteration.
• Some glass constituent elements precipitate as
crystallized secondary phases. The precipitation of these
crystallized phases on the external surface or in solution
can sustain glass alteration.
Proceedings of Global 2009
Paris, France: September 6-11, 2009
Paper 9038
Water diffusion through the PRI
100000
PRI dissolution from
the outer face
Tracers
Pristine glass
PRI
Precipitation of
secondary phases
GRAAL Modeling
H2O
Glass
hydration
at the
glass/PRI
interface
Mass of altered g
based on boron t
release at the en
each experime
(mg of glass)
Log scale is chose
that each experim
can have the sa
weight on the fig
10000
1000
100
Water
10
Figure 3. The four processes involved in glass alteration.
A model describing all these mechanisms was developed.
The glass-related parameters are the solubility limit of the
passivating reactive interphase (PRI), the water diffusion
coefficient in this interphase, the gel dissolution rate, and the
initial hydration rate of the pristine glass at the internal
interface. The other model parameters concern the secondary
phases likely to precipitate, depending on the chemical
elements supplied by the glass or by the surrounding
medium: phase solubility limits and precipitation kinetics.
When R7T7 glass is leached in initially pure water, the
secondary phases are mainly phyllosilicates (Figure 4). The
simulations show a good agreement with experimental data
(Figure 5) [7].
Figure 4. SEM image of an R7T7 glass sample altered for
4 months in initially pure water at 150°C, showing the
outer layer of phyllosilicates precipitated from solution,
the porous gel formed by in situ condensation, and the
underlying pristine glass.
10
100
1000
10000
100000
Experimental Measurements
Figure 5. Altered glass mass calculated by the model
compared with experimentally measured values.
Calculations were performed at the last sampling interval
of each experiment.
A simplified analytical solution of the model shows that
the residual glass alteration rate depends on the water renewal
rate. With rapid renewal the residual rate is limited by the
dissolution kinetics of the passivating reactive interphase;
with slow or zero renewal the residual rate is governed by the
secondary phase precipitation kinetics.
Work is now in progress to refine the model parameters as
a function of the temperature, pH and glass composition, but
especially to identify the secondary phases and their kinetic
parameters in order to couple this glass alteration model with
a geochemistry-transport model describing the glass
environment (a diffusive reactive medium characteristic of a
repository environment).
Moreover, very sophisticated experimental approaches
have been developed to study the gel structure (highresolution solid-state NMR [8] [9]]) and its morphology
(small angle X-ray scattering, neutron scattering, ToF-SIMS
[10]). These techniques have been coupled with mesoscopic
scale models (kinetic Monte Carlo method [11] [12]). This
approach has identified pore closure processes, establishing
for the first time a direct cause-effect relationship between
the altered layer morphology and the alteration kinetics in
simplified borosilicate glass simulating nuclear containment
glass compositions. It has been shown that substituting an
insoluble oxide for a significant fraction of silica retards the
gel structural reorganization and, by inhibiting the pore
closure mechanism, leads to greater alteration. The very large
drop in the leach rate observed for some glass compositions is
due to pore closure by gel densification, which transforms the
glass from a state in which dissolution is controlled mainly by
hydrolysis to a state in which it is controlled by the
accessibility of the reaction interface to water.
Under these conditions, saturation of the solution with
respect to silica becomes a prerequisite to the formation of a
passivating layer but is not a criterion for the end of
alteration. Regardless of the degree of reaction progress, even
Proceedings of Global 2009
Paris, France: September 6-11, 2009
Paper 9038
under “saturation” conditions, aqueous alteration of nuclear
glasses always leads to the diffusive release of glass
constituents, even if in only very minute quantities [13] [6].
The alteration film constitutes a diffusion barrier with (in the
case of R7T7 nuclear glass) an apparent diffusion coefficient
of about 10-21 to 10-24 m-2·s-1 [13] [14], very near the values
found in solids. Such very low values could not be reached if
the porosity were open, allowing percolation of the elements
released from the glass into solution, because the
interdiffusion coefficients (for transfer by direct contact
between the pristine glass and solution) are much higher [15].
V. GLASS REACTIVE SURFACE AREA
After the melt has been poured, industrial nuclear glasses
exhibit a temperature gradient between the hot core and the
cool outer surface. The gradient results from a combination of
the thermal cooling scenario, the thermal power due to decay
of radioactive elements, and the low thermal conductivity of
the glass. This results in mechanical stresses whose release
leads to cracking. The glass surface area potentially
accessible to aqueous leaching thus exceeds the geometric
surface area of the package. The quantity of radionuclides
released during glass alteration under repository conditions is
directly proportional to surface area accessible to water,
which is currently taken into account in performance models
by two effective cracking factors, 0 and r. The cracking
factors are measured by leaching experiments performed on
full-scale inactive glass blocks [1]. These experiments are
designed to maintain the water renewal rate to ensure
leaching at the maximum rate, V0, based on well-known
parameter values. The accessible surface area is estimated
from the quantity of altered glass determined by analysis of
alteration tracers (boron, lithium). Leaching a large block in a
perforated basket in a Soxhlet device gives a value for 0.
Leaching the loose fragments of a large fractured block in the
same device provides an estimate of the total surface area
developed by the cracks, from which r is inferred.
Two areas of investigation were defined to consolidate
this phenomenological approach and to develop a model
capable of evaluating the potential progression of the
cracking under the lithostatic stress loading in a repository.
behavior law implemented in the ABAQUS code, and
finally a 3D cooling simulation. The second step will
produce a 3D simulation of package cracking based on a
damage and cracking law in the ABAQUS code.
• Experiments on small blocks, a few centimeters in size, to
determine the crack densities versus the applied stress
loading.
• Smaller scale experiments at crack scale are carried out to
evaluate the cracking mechanisms and to improve the
behavior laws and rupture criteria.
The model will be validated on full-scale inactive blocks on
which the crack network has been characterized by various
methods (tomography, particle size analysis).
V.B. Chemistry-transport coupling in the cracks;
modeling the quantity of altered glass in a full-scale block
Experiments with crack models (two glass tiles separated
by a known gap, typically 40 to 500 µm) identified coupling
in the cracks between chemistry and transport phenomena
with an intensity dependent on the crack aperture; the
coupling is characterized by a difference in the altered
thickness according to the position in the finest cracks (less
than about one hundred micrometers), whereas the thickness
is constant for cracks with larger apertures. Transport is
mainly diffusive in the finest cracks, but convection
phenomena can also occur (thermal convection or convection
due to density gradients in vertical cracks) (Figure 6) [16].
Figure 6. Photographs of crack models altered in
diffusive conditions (left) and in convective conditions
(right). The variation of color reflects the variation of
altered thickness.
V.A. Thermomechanical cracking
The objective is to develop a thermomechanical model to
obtain a sufficiently explicit statistical description of the
crack network (crack density, length, spacing) depending on
the active or inactive glass thermal scenario. The model can
then be used to quantify the initial cracking and its
progression under given mechanical stresses. The
methodology combines the following approaches:
• Simulation: the first step consists in a thermomechanical
analysis (finite-element calculation of structure stress and
strain phenomena) by solving the heat transfer equation
coupled with the equation of motion, using a viscoelastic
Coupling between chemistry and transport in the cracks
rapidly leads to a significant drop in the glass alteration rate
in the finest cracks, where the low solution renewal rate
causes a rapid transition to the residual rate regime; in the
case of R7T7 glass at 90°C the residual rate is four orders of
magnitude lower than the initial rate. This is perfectly
consistent with the fact that the effective cracking factor 0 is
much lower than the total cracking factor (for R7T7 glass, 0
is 5 ± 1 and r is 40 ± 17). When a large block is altered under
initial rate conditions, only the largest cracks contribute
significantly to the quantity of altered glass.
Proceedings of Global 2009
Paris, France: September 6-11, 2009
Paper 9038
The final step in increasing the robustness of the V0Vr
model is the coupling between the GRAAL mechanistic
alteration model and transport in the cracks in a full-scale
block to compute the quantity of altered glass versus time.
The methodology adopted is to model flow in the crack
network, define a simplified porous equivalent model, and
combine it with the GRAAL model.
VI. LONG-TERM VALIDATION ON
ARCHAEOLOGICAL ANALOGS (Embiez glass)
Validating predictive models is one of the major
difficulties of investigating the long-term behavior of
containment materials because the relevant time scales
largely exceed what is accessible to laboratory experimentation. Whenever possible, therefore, natural or archaeological
analogs are examined for this purpose.
quantitative agreement with the observations of the
archaeological glass block (Figure 8).
Table I. Simulated thicknesses of the alteration products
at the crack tip
a
(µm)
Dsol
(m2∙s-1)
Total altered Total smectite
glass thickness
thickness
(µm)
(µm)
1.5 × 10-9
1.5 × 10-9
1.5 × 10-10
1.5 × 10-9
20
10
10
2
38
34
25
26
8
5.5
0.7
3
6 µm
< 0,3 µm
8 µm
20 µm
25 µm
Figure 7. Fractured archaeological glass sample
Archaeological glass blocks (Figure 7) from a shipwreck
discovered near the French Mediterranean island of Embiez
have been examined because of their morphological analogy
with nuclear glasses and their known, stable environment.
Like nuclear glasses, these blocks were fractured after
production; they were then leached for 1800 years in
seawater. A geochemical model capable of simulating the
alteration of a fractured archaeological glass block was
developed using the same methodology as for characterizing
the long-term behavior of nuclear glass (GRAAL). The
model was validated by comparing the results given by the
model with observations on the sampled materials [17] [18].
From these experiments we determined the kinetic
constants of the mechanisms involved (interdiffusion and
dissolution of the glass network) and the thermodynamic
parameters (affinity, secondary phases) of the model, which
was implemented in the HYTEC geochemical code to
simulate alteration in the cracks over 1800 years. The
simulations were carried out on internal cracks several
centimeters long and with variable apertures (again assuming
alteration in seawater at 15°C). Table I indicates the total
altered glass thicknesses and clay precipitates after 1800
years of alteration versus the crack aperture and diffusion
coefficient. The simulation results are in remarkable
10 µm
17 µm
< 0,7 µm
10 µm
30 µm
7 µm
< 0,3 µm
Figure 8. Micrographs of internal cracks in the
archaeological glass block: measured thicknesses of the
altered glass (black) and secondary phases (white).
Simulating the crack alteration over 1800 years accounts
for the thicknesses observed on the actual glass blocks.
Cracks with an initial aperture of 100 µm are sufficient to
allow renewal of the leaching medium. However, in the case
of smaller apertures (< 20 µm), with or without crack filling,
the model predicts total altered glass thicknesses of 25 to
38 µm near the crack tips, which corresponds to the
Proceedings of Global 2009
Paris, France: September 6-11, 2009
Paper 9038
thicknesses (between 5 and 30 µm) observed on the internal
cracks in the archaeological glass block. The simulation
results for the finest cracks (< 2 µm) should lead to even
smaller thicknesses. The saponite thicknesses are also
consistent with the measured values (1 to 5 µm near the crack
tips). The agreement of the simulated alteration thicknesses
and the values measured on the blocks validates the
predictive performance of the model.
The analogous behavior of archaeological and nuclear
glass allows us to consider applying the model to nuclear
glass under geological repository conditions.
The same methodology could be applied to much older
basaltic glasses for which the environment can be
characterized. These glasses not only exhibit the same
behavior, mechanisms, and kinetics as nuclear glasses in
short-term experiments, but their alteration products also
reveal strong similarities, especially between the palagonite
on basaltic glasses and the gel on nuclear containment
glasses, which can constitute a diffusion barrier. These
studies can contribute to a finer definition of the chemical
model of nuclear glasses and to the long-term validation of
the gel protective properties.
3.
4.
5.
6.
7.
8.
VII. CONCLUSIONS
An investigation of long-term glass behavior allowed us
to develop a conservative predictive model known as V0Vr.
Work is now in progress to consolidate the robustness of this
model by comparison with mechanistic approaches that
provide more accurate but more complex assessments of
long-term behavior. The ongoing work addresses the effect of
self-irradiation at high doses, modeling of helium behavior,
modeling of long-term alteration kinetics (GRAAL),
quantification of the initial cracking, coupling of chemistry
and transport phenomena in the cracks of a full-scale
fractured block, and long-term validation based on natural
and archaeological analogs.
9.
10.
11.
ACKNOWLEDGMENTS
The authors are grateful to AREVA and the CEA for their
financial support.
12.
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