Modelling the leaching of fractured SON 68 glass block
Laure CHOMAT, Frédéric BOUYER*, Stéphane Gin
CEA, Marcoule DEN/VRH/DTCD/SECM/LCLT BP 17171 30207 Bagnols-sur-Cèze Cedex
Stéphane ROUX
LMT Cachan, 61 avenue du président Wilson 94235 Cachan Cedex
Abstract : experimentations carried out on SON 68 glass model cracks in static condition, show a
strong coupling between transport and leaching, depending to a form factor (aperture). Moreover,
convective transport induced by gravity was observed in vertical model cracks, whereas only diffusion was
detected in horizontal model cracks. Besides, an original device was developped to study the impact of
gradient temperature, as a convective driving force, on alteration. These experimentations allow to build a
model of the alteration in simplified cracks. First of all, the transport is deduced from Poiseuille’s law. The
so evaluated velocity is introduced in a porous geochemical software (HYTEC1), which allows us to model
the alteration. This model development has been applied to describe alteration within simple silicate glass
cracks. It will then be extended to study all simple compositions glasses, as well as R7T7 glass model
cracks, and more generally network of fractures.
Context
In France, vitrification is the process used for the immobilisation of HL radwastes. A
large amount of glass with radioelement is cast in iron canister. During the cooling process
in those canisters a cracks network appears in the glass block, increasing the developed
surface. When considering the geological disposal concepts, this aspect may have a great
influence on the long term behaviour, which must be ensured during several tens of
thousand years. Indeed, exposed to water, the altered glass releases a total amount of
elements proportional to the reactive surface. Moreover, the glass dissolution is a
complicated coupling between incongruent leaching, secondary phases precipitation and
transport. The study of the glass block appears to be too complex and shows the necessity to
consider simplified object to determinate a model describing the elementary phenomenon
involved in cracks. Thus, experiments were conducted on single ideal cracks in different
configurations and in different alteration conditions. Besides, the use of modelling aims
highlighting the different transport mechanisms and its coupling with chemical reactions in
cracks, and finally will help to predict the behaviour of real cracked media.
Experiments
Static alteration condition on a single model crack
The experiments were conducted on SON 68 glass and consisted in leaching simplified
model cracks (two well polished glass pieces of 25 * 25 mm2 area, separated by a calibrated
Teflon rubber or polyamide yarn) maintained in vertical or horizontal position. The
alteration condition is NaOH 0.25 mol/l at 90  1 °C for all experiments. The use of basic
*
corresponding author (frederic.bouyer@cea.fr)
pH permits to enhance chemical reactivity2, and to make observable the coupling between
chemistry and transport. The chart below presents the range of experimentations carried out,
indicating apertures and position of the studied model crack.
Vertical :
Top
aperture (m)
Bottom
Horizontal :
Right
aperture (m)
Left
free
60
40
40
free
80
60
60
free
160
90
90
free
220
220
220
free
550
550
550
40
40
110
80
60
60
200
100
60
120


Table 1: apertures studied according to the position imposed to the model crack (until a <
160 m, uncertainty of measurement is 10 m, above it’s 20 m)
When the upper aperture is indicated as free, only one clamping device was applied on the
bottom of the vertical model crack so that the upper aperture was not ensured to be at the
same bottom value.
The first studies carried out on 60 m aperture model crack show a significant impact of the
transport on alteration within cracks. This will be pointed out by an altered glass layer
thickness deeper on the exit edges than in the middle of the crack (see figure 1). The new
phase resulting from the incongruent glass leaching and silicon recondensation is regarded as
the glass altered layer and was observed by SEM. This figure depicts different transport
mechanisms, depending on the position vertical or horizontal of the fracture.
45
Top of the crack
Bottom of the crack
40
altered glass thickness (m)
35
30
25
20
15
10
5
0
0
5
10
15
20
25
situation in crack (mm)
horizontal model crack
vertical model crack
Figure 1: altered glass thickness according to the position of the crack and the situation
into, measured by SEM (case of the vertical /horizontal ideal fractures, with an aperture
of 60 µm)
The dissymmetric altered glass layer thickness profile, observed in vertical model crack,
indicates that a convective transport mechanism prevails, whereas in horizontal crack the
Brownian diffusion mechanism induces a symmetric profile. Besides, the minimum
alteration thickness, where local saturation is reached very rapidely, is close to the bottom of
the cracks, indicating that a flux goes from the top to the bottom of the crack. The results of
the whole range of experiments confirm theses assessments and the type of altered glass
layer thickness profile for each case are depicted on the following synoptic figure.
Horizontal crack :
athreshold : 220-220 / 550-550 µm
a
550-550 µm
a
40-40, 60-60, 90-90
220-220 µm
a
80-110, 100-200 µm
symetric
flat
Vertical crack :
athreshold : 160-free / 220-free µm
a
60-free 90-free, 160-free µm
40-40, 60-60 µm
a
60-120 µm
flat
dissymetric
a
220-free, 550-free µm
Figure 2: synoptic figure presenting different altered glass layer profile as a function of
the aperture
Those different experiments show also that the coupling between chemistry and transport
appears until a threshold aperture is reached, which is between 220 and 550 m or 160 and
220 m for respectively horizontal or vertical model crack with a length of 25 mm. So, the
significance of the coupling between transport and chemistry depends of a form factor.
Though, model cracks presenting variable aperture according to crack length indicate the
same shape profile than these expected for constant aperture crack in the same position. So,
a variation of aperture until 100 m, inducing different local leaching conditions, can’t
explain the dissymmetric profile. A convective transport appears to be the only way to
understand that phenomenon. Besides, experiment conducted on a vertical model crack and
analysed by ToF SIMS confirmed the dissymmetric profile in pure water alteration
condition : the way of accelerating reactive processes (i.e. the use of NaOH for the alteration
of SON68 glass) does not affect these conclusions.
Therefore, the whole range of experiments described previously demonstrate in an original
way that, in vertical configuration, convective transport induced by density gradient must be
considered. Compared to gravity, temperature gradient seems to be an unlikely cause of
convective transport, as experiments were performed in drying furnace. Nevertheless, it is
expected into glass block. That’s the reason why its influence has been also studied on model
fracture.
Thermoconvection experiments
To evaluate the impact of a temperature gradient, as a convective velocity motor on
alteration within model crack, a leaching device was especially designed. It allows producing
a convective transport between two cells filled of pure water and maintained at different
controlled and regulated temperatures. The linkage between these two cells consists in two
model cracks with a fixed aperture separated by around 9.4 cm high; consequently an equal
but opposite velocity is produced into these two model fractures.
The first range of parameter introduced in this experiment was a temperature gradient of 4-5
°C and an aperture of 60 m. It’s difficult to maintain the temperature gradient with an one
degree accuracy, because of the variation of the room temperature. So, the temperature
gradient imposed as well as the evolution of a KCl tracer introduced in the hotter vault were
indexed. These data indicate that the temperature gradient is about 4 °C during the first ten
days, then increase to achieve a constant value of about 5 °C after twenty days. The tracer
analysis points out a velocity around 2-0.7 10-5 m.s-1. After one month of leaching, although
the study of the altered glass layer leads to thickness measurement difficulties and
interpretation, the analysis of the altered glass layer into the two cracks shows an undeniable
presence of convective transport, as expected (a thermo-convective velocity is imposed).
Another experiment with an aperture of 82 m and a temperature gradient of 5 °C was
performed. The KCl tracer evolution indicates a velocity of 10-4 m.s-1 and the altered glass
layer thickness will be soon analysed. Afterwards, an aperture of 200 m will be considered
with the same temperature gradient. The results of these experimentations are particularly
interesting for modelling, because the alteration condition is well defined.
Modelling
The interest of modelling comes from the possibility to describe what occurs within
fractures (so at the fracture scale), that is chemical reactivity, flow and species transport. This
model, validated on our experimentations, will allow us to simulate what happens at large
time scale as well as on crack network at the glass block scale.
Transport modelling
When considering just a model crack, it’s not required to refer to Navier-Stokes equation,
Poiseuille’s law equation is fully sufficient. The lubrification approximation and a voluminal
laminar stationary flow of a Newtonian fluid can be considered as good approximation in
our cases. In this approach, the velocity profile in the crack is parabolic and depends on the
density variation, due either to temperature gradient or gravity.
In the case of gravity, the application of the Poiseuille’s law is more complex, because we
need to take into account the coupling between chemistry and transport to evaluate the
accurate difference between the element concentrations in and out of the crack. Neverthless,
simple assumptions can give good order of magnitude of the velocity induced. This model
can notably predicts a significant velocity (of the order of 10-4 m.s-1) even for little density
variation (concentration variation).
On the other hand, in thermoconvection experiments we only consider the impact of
temperature on Poiseuille’s law. The velocity obtained for an 60 m aperture is of the order
of 3-4 10-5 m.s-1, which is a little higher than the measured velocity thanks to KCl tracer in
the experiments. Moreover, this method gives also a velocity for 82 m aperture near to 8
10-5 m.s-1, closed to the experimental value. This simple Poiseuille’s law is in good agreement
with the experimental values and is sufficient to evaluate the convective driving force.
Geochemistry modelling
The modelling of glass alteration is very complex and requires to consider incongruent
leaching, secondary phases precipitation and transport. At the present time, no software can
associate Navier-Stokes resolution with a complex chemistry solver, because of very
different time scaling in both. As transport in model crack can be easily apprehended by
Poiseuille’s law, the use of a porous geochemical software (HYTEC 1) to describe the
complicated chemical reactions involved in glass leaching will be viewed as the best
compromise. HYTEC is the association (coupling) of a chemical module and a transport
module. Chemical reactions are based on thermodynamic equilibriums and an abundant
database is also available (thermodynamic and kinetic reactions can be easily added). The
transport can be represented by diffusion and by advection, but only by the mean of Darcy’s
law. We overcome the problem of the use of a geochemical model on simple ideal fractures
thanks to some tricks. Firstly, the surface interaction has been allowed by limiting diffusion
transport into glass medium to solid diffusion and by imposing a high contrast of
permeabilities between the glass and the species medium. Furthermore, the glass dissolution,
for which the kinetic’s law is depending on an inhibitor term, induces a secondary phase (socalled gel) thermodynamically more stable than the glass itself.
The velocity, calculated from the Poiseuille’s law, has been introduced as a constant value
within the geochemical model. Kinetics describing the glass alteration as well as the gel
appearance for a simple pure silicate glass have been investigated, in order to reproduce the
gel phase formation, as well as alteration profile within a fracture. The introduction of a
motion simulating a convective flow allows us to predict dissymmetric profiles. These first
results convince us to pursue in that direction in order to model SON 68 glass alteration, for
which only chemistry has to be refined.
Conclusion
The original experiments realized on SON 68 model cracks in static alteration conditions
show up that transport has a strong impact of alteration in model crack, until a threshold
form factor is reached. Besides, gravity induces a significant convective driving force
responsible for a dissymmetric altered glass layer thickness profile in the vertical model
fracture. Moreover, a special device permits us to study the effect of the flow motion
induced by gradient temperature (assumed to be present in glass block) on leaching in model
cracks. The experiments point out that a temperature gradient of some degrees produces a
velocity high enough to impact on the model cracks leaching. All those results enforce the
knowledge on transport mechanism and on the coupling between transport and chemistry,
which is the basis of the model crack leaching modelling. The use of the Poiseuille’s law and
a modified geochemical model allows us to simulate what occurs within simple ideal
fractures. This methodology will soon be applied to glasses of industrial interest for
describing and understanding phenomena involved in model crack, and afterwards in
network glass block.
Jan van der Lee, Laurent De Windt, Vincent Lagneau and Patrick Goblet, Computers &
Geosciences 29, p. 265-275 (2003)..
1
2
Solange Ribet, Stéphane Gin, Journal of Nuclear Materials 324, p. 152-164 (2004).