Single idealized cracks: a tool for understanding fractured glass block leaching
Laure Chomat1, Frédéric Bouyer1, Stéphane Gin1 and Stéphane Roux2
1
CEA Marcoule, DEN/VRH/DTCD/SECM/LCLT, BP 17171, F-30207 Bagnols-sur-Cèze Cedex
2
LMT Cachan, 61 Avenue du Président Wilson F-94 235 Cachan Cedex
ABSTRACT
Within the scope of the long term behaviour of the R7T7 glass, which is the French
nuclear glass, leaching and its coupling with transport mechanisms is studied. Experiments
carried out on a SON 68 glass (inactive R7T7 type glass) model cracks in static basic conditions
show a strong coupling between solution transport and glass leaching, depending on crack
aperture. Moreover, gravity driven convective transport was evidenced for vertical model cracks,
whereas only molecular diffusion was detected for horizontal model cracks under the same
alteration conditions. In addition, an original device was developed to study the influence of
temperature gradients on alteration kinetics as a convective driving force. These experiments
show conclusively that thermally- or gravity-induced convective flow must be taken into
account, even if such convective effects have not been established experimentally in neutral
condition, which is more realistic condition for geological storage. A modeling, based on a
porous geochemical software (HYTEC) accounting for both chemistry and transport, has been
successfully applied to describe alteration within simple silicate glass cracks. It will be extended
to study SON 68 glass model cracks, and more complex fracture networks.
INTRODUCTION
In France, vitrification is the process used for the immobilization of HL radwastes. A
large amount of glass with radioelement is cast into an iron canister. During the cooling process,
thermal stresses (unavoidable for such meter scale canisters) lead to a multiple fragmentation and
a complex crack network appears in the glass block, thereby increasing its specific surface.
Considering the aim of geological disposal, this aspect may have a major influence on the long
term behaviour, which must be ensured during several tens of thousand years. Indeed, when
exposed to water, the glass leaching rate is proportional to the reactive surface. Moreover, glass
dissolution involves complex couplings between incongruent leaching, secondary phase
precipitation [1] and transport. Thus the study of the glass block alteration requires to consider
separately different scales to single out the relevant elementary phenomena. Therefore,
experiments were conducted on single ideal cracks in static and dynamic alteration conditions.
The dynamic conditions were produced by a temperature gradient, which induced well defined
flow rate. This paper presents the experimental approach designed for the study of an ideal crack
and aims to highlight the different transport mechanisms and their couplings with the chemical
reactions taking place during water alteration. As a perspective, the alteration modeling within
cracks will be briefly presented.
EXPERIMENTS
Static alteration condition on single model crack
Most of these experiments were conducted on SON 68 glass and consisted in leaching simplified
model cracks (two well polished glass pieces of 25×25 mm2 or 25×50 mm2 area, separated by a
calibrated Teflon spacer or polyamide yarn of variable thickness) maintained in vertical or
horizontal position in basic condition (NaOH 0.27  0.03 mol/l) at a constant prescribed
temperature of 90  1 °C, inducing a pH value above 11. The use of a basic pH and high
temperature enhances chemical reaction rates [2], so that alteration can be conveniently and
accurately followed thanks to SEM imaging of the altered surface.
Table 1 presents the range of experiments carried out, indicating crack apertures, lengths
and positions.
Table 1. Studied crack apertures and lengths according to the position imposed to the model
crack (uncertainty of measurement is 10 µm (resp. 20 µm) for distances below (resp. above) 160
µm). 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.
Length (mm)
25
25
25
25
25
25
25
25
25
50
Vertical :
aperture (m)
Top
free
free
free
200
free
free
40
60
60
60
Bottom
60
80
160
200
220
550
40
60
120
60
Horizontal :
aperture (m)
Right
40
60
80
220
550
x
110
200
x
60
Left
40
60
80
220
550
x
80
100
x
60
In addition, control experiments were conducted on a 60 µm aperture model crack in pure
water at 90  1 °C to check whether conclusions derived in basic condition may be extended to
neutral conditions.
Dynamic alteration conditions in model cracks : Thermoconvection experiments
The assessment of the influence of a temperature gradient, as a convective transport
drive, on alteration within the model crack is studied thanks to a specific leaching device. The
latter is designed to generate a convective transport between two cells filled with pure water and
maintained at different controlled and regulated temperatures. The bridging between these two
cells consists in two model cracks in parallel with a fixed aperture separated by a 94 mm vertical
distance; consequently a convection loop is induced into these two model cracks (see figure 1).
In contrast to the previous static experiment, neutral conditions were used.
l
Glass
h
water
z
Top crack
x
Glass
h
water
T1
T2
Glass
0
Bottom crack
a
g : gravity acceleration: 9.81 m/s2
h : height between the two cracks (m) : 94 mm
a : crack aperture (m)
l : crack length (m) : 25 mm
T : temperature (°C)
 : density
 kinematic viscosity Pa.s
 : water coefficient of thermal expansion (0,6596 kg/m3/°C)
Glass
Figure 1. Schematic description of the thermo-convective device (left) with arrows representing
the flow loop for T1 > T2 and table of relevant parameters.
Because of the small size of the cell and the slow flow rates induced by the
thermoconvection, inertial effects can be safely neglected (small Reynolds number) so that a
Stokes regime holds. Moreover, the aspect ratio of the model crack is large enough to allow for
a further simplication to the so-called Reynolds or lubrication approximation. Henceforth, the
flow in the crack is of Poiseuille type (parabolic velocity profile through the thickness). Finally
the model crack flows can be described as obeying a simple Darcy law, whereas the pressure in
the two lateral isothermal cells is essentially hydrostatics. Yet, because of the temperature
difference, both cracks are subjected to a pressure difference, and hence a circulation loop sets
in. The solution of this problem is elementary and the mean velocity in the cracks reads [3] (with
notations explicited in Fig. 1).
gha 2
v
(T1  T2 )
24
(1)
Only few degree temperature differences will be studied for the 25 millimeter length
model crack to ensure that it won’t change alteration mechanisms. Table 2 summarizes the
different conditions studied with the thermo-convective set-up.
Table 2. Considered experimental conditions in the thermo-convective set-up.
T (°C)
Aperture
(m)
Time
(days)
60
44
4–5
82
36
5
+/- 1
1.03 10-4
200
28
4
+/- 1
5.2 10-4
+/- 1
Calculated flow
rate (m.s-1)
4.6 10-5 / 5.8 10-5
For a 60 µm aperture crack, two flow rates are calculated corresponding to a temperature
difference of 4 °C, maintained during the first ten days of experimentation, and to a temperature
difference of 5 °C, reached after twenty days.
RESULTS
Static alteration conditions
The new mineral phase resulting from incongruent glass leaching and silicon recondensation,
denoted as the altered glass layer for simplicity, can be clearly observed by SEM in laboratory
basic pH conditions experiments. The first observations carried out on a 60 µm aperture model
crack revealed a significant influence of solute transport on glass alteration within the cracks.
This conclusion is based on the observation of a thicker altered glass layer at the exit edges than
in the middle of the crack. Figure 2 shows the altered layer thickness for a horizontal and vertical
model crack.
45
Top of the crack
Bottom of the crack
altered glass thickness (m)
40
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 2. Altered glass layer thickness as a function of the coordinate along the crack length for
a horizontal (empty symbol) and vertical (filled symbol), measured by SEM (model crack of
60 µm aperture).
The dissymmetric altered glass layer thickness profile observed for the vertical crack indicates
that a convective (gravity driven flow) transport mechanism prevails, whereas for the horizontal
crack a simple diffusion mechanism may hold. Indeed, the minimum alteration thickness, where
local saturation is reached at an earlier time, is close to the bottom of vertical crack, indicating
that convection takes place downward. All experimental observations comfort this conclusion.
Figure 3 proposes a synoptic presentation of all alteration thickness profiles.
Horizontal crack :
Location in crack
symmetric
Altered layer
thickness
a
80-110, 100-200 µm
2
a
550-550 µm
Altered layer
thickness
a
40-40, 60-60, 80-80
220-220 µm
1
flat
Location in crack
Vertical crack :
3
4
Altered layer thickness
dissymetric
a
220-free, 550-free µm
Location in crack
a
60-120 µm
Location in crack
a
60-free 80-free, 160-free µm
40-40, 60-60, 200-200 µm
Altered layer thickness
flat
Figure 3. Synoptic figures presenting different altered glass layer profiles as a function of the
aperture and orientation of the model crack.
As previously mentioned, experiments carried out in a constant aperture vertical model
crack present a minimum alteration position located in the last one-tenth of the crack length.
Moreover, those different experiments show that, in basic condition, model crack
aperture increase lead to flatter altered glass layer thickness profile. Consequently, the
significance of the coupling between transport and chemistry depends on a form factor (a, see
figure 1). However, model crack types labelled as 2 and 4 in figure 3 present similar shape
profiles to those observed respectively for model crack types labelled as 1 and 3. Therefore, an
aperture variation smaller than 100µm, inducing different local leaching conditions, cannot
account for a dissymmetric profile. A convective transport appears to be the only way to
understand that phenomenon. The whole range of experiments described previously
demonstrates in an original way that, in vertical configuration, convective transport induced by
water density gradient must be considered. As compared to gravity, temperature gradient seems
to be an unlikely cause of convective transport, as experiments were performed under regulated
temperature.
25 mm and 50 mm long cracks showed a similar behaviour. For the vertical model crack,
the minimum alteration position lies approximately at the same relative position as shown in
Figure 4.
50
leaching layer thickness (m)
45
l = 25 mm
l = 50 mm
40
35
30
25
20
15
10
5
0
0
0.2
0.4
0.6
0.8
1
nomarlized distance within model crack from the top to the bottom (mm)
Figure 4. Altered glass thickness profile along the crack length normalized by the total length,
measured by SEM, for a 60 µm aperture.
Although the conclusions of the above set of experiments clearly indicate the relevance
of convection mechanisms, one has to check that this effect remains present for unaccelerated
(i.e. non-basic) leaching conditions. The slow kinetics of neutral leaching did not allow us to
conduct similar experiments, however a discussion of this point is proposed in Section 4.
Dynamic alteration conditions: Thermoconvection experiments
Maintaining temperature gradient with a one degree accuracy is difficult, because of room
temperature variations. So, the imposed temperature gradient was chosen to be about 4 or 5 °C.
Both temperature and the evolution of a KCl tracer introduced in the hotter cell were monitored.
The latter was used to measure the flow rate and is compared in Table 2 to the theoretical
expectation as given in Eq. 1 for the three experiments.
Table 2. Experimental data of the three different experiments, carried out in thermo-convective
device, compared to the theoretical flow rate given from Eq. 1.
Aperture
(m)
Measured flow
rate (m.s-1) +/- 15 %
Calculated flow
rate (m.s-1)
60
1.8 10-5
4.6 10-5 / 5.8 10-5
82
3.5 10-5
1.03 10-4
200
In analysis
5.2 10-4
Considering the large uncertainty of the temperature monitoring, the agreement between
measured and calculated flow rates can be considered as fair, thereby validating our set-up and
procedure.
After leaching, the altered glass layer thickness was intended to be quantified through
SEM imaging. The low alteration thickness and the damaging of the layer during coating and
polishing lead to measurement and interpretation difficulties. Yet, the analysis of the altered
glass layer into the two 60 µm aperture cracks whose profile is shown in Fig. 5 suggests that
convective transport plays a significant role because of the absence of typical symmetric shape
of the alteration layer thickness profile characteristic of diffusion transport. However, the
peculiar w-shape of these profiles is not yet fully understood. This type of experiments
constitutes a very discriminating test case for modeling.
Flow direction
leaching layer thickness (m)
8
7
6
5
bottom crack
top crack
4
3
2
1
0
0
5
10
15
20
25
distance within crack according to the termoconvective flow direction (mm)
Figure 5. Measurement of the leaching layer thickness within the two cracks altered in the
thermo-convective device (60 µm aperture).
DISCUSSION
Static (carried out in basic conditions) and thermo-convective (neutral) experiments show
a significant influence of convective transport on the alteration kinetics within cracks, whatever
the convective driving force, gravity or temperature gradient.
One may wonder why such a coupling has not, so far, been observed in the case of
neutral condition and vertical crack in static conditions? The difficulty is that the altered glass
layer thickness obtained after 290 alteration days is close to the SEM detection limit. Moreover,
theoretical estimates of the convection flow rates are a subtle issue due to the intricate coupling
between chemistry and transport. However, a model, based on simplified assumptions, was
developed to get a crude order of magnitude of the involved flow rates. The free surfaces within
the crack and out of the crack are considered to be altered at constant (but different) rates,
deduced from leached layer thickness within the crack (respectively the average and the
maximum deduced rate). This alteration releases different amounts of chemical species in the
crack and in the surrounding solution (out of the crack), according to the incongruent leaching
[2][4]. They induce different fluid densities within the crack and the surrounding solute, and so
convection flow rate. This latter is determined considering Poiseuille law in model crack,
diffusion transport negligible and stationary state. This model gives consistent values for flow
rates induced by density variations in experiments carried out in basic condition (see table 3).
Table 3. Average flow rates determined by a simple model evaluating average flow rate induced
by gravity in vertical model crack in basic and neutral conditions.
NaOH 0.27 mol/L
aperture (m)
average flow rate (m.s-1)
Pe
40
3.6 10-6
0.14
60
7.1 10-6
0.3
80
8.33 10-6
0.44
160
1.25 10-5
1.3
200
1.70 10-5
2.3
220
1.48
10-5
2.2
2.46
10-5
9
6.32
10-7
0.03
550
Pure water
60
The Péclet number Pe, which characterizes the relative importance of convective versus
diffusive flux, is classically defined through [5] [6]
Pe 
av
Dm
(2)
This dimensionless number is constructed from a characteristic length, which is the
aperture (a) for cracks, the average flow rate ( v ) and the diffusion coefficient (Dm = 10-9 m2.s-1).
A Péclet number larger (resp. smaller) than 1 indicates the predominance of convection (resp.
molecular diffusion).
The application of this crude model to neutral conditions for a 60 μm aperture vertical
crack gives an approximate average flow rate value of one order of magnitude lower than in
basic conditions. This model also shows up that, for the pure water experiment on 60 μm
aperture vertical crack, the Péclet number is very low compare to 1 which indicates than the
dominant transport mechanism, in this case, could be diffusion. Consequently, the flow rate in
neutral conditions may be too low to be observable from the altered glass layer thickness
dissymmetry. However, convection certainly takes place and should be taken into account in a
more detailed modeling of the kinetics of alteration.
PERSPECTIVES ON MODELING
Resorting to numerical modeling is essential in order to address more complex and
realistic geometries, and to investigate long term behavior in a faithful way, and hence
understanding the interplay between chemical reaction and transport mechanism. However, glass
alteration is very complex as it involves incongruent leaching of different species, secondary
phase precipitation and transport. At present, no commercial software addressing both flow and
chemistry is available. Since we have seen that in confined geometries such as crack, a simple
lubrication approximation is sufficient, the use of a porous geochemical software (HYTEC)
(whose ability to take account of the whole chemistry has been validated) appears to be the best
compromise. HYTEC [7] is the association of a chemical module and a transport module.
Chemical reactions are based on thermodynamic equilibriums and additional kinetic reactions,
which is necessary to represent the glass alteration [8]. Transport involves diffusion and
advection, but only through Darcy’s law. The extension to a non porous medium (such as a
realistic glass and its cracks) can be resolved within the same framework. Firstly, only surface
interaction is allowed by imposing molecular diffusion values corresponding to bulk glass and
choosing a high contrast of permeabilities between the glass and the solution. Secondly, the
dissolution rate depends on a Monod term, which limits chemical interaction to the surface, and
on a saturation term. The glass dissolution results in the precipitation of a secondary phase (socalled gel) thermodynamically more stable than the glass itself.
The flow rate, determined from the lubrication approximation, is introduced as a constant
value within the geochemical model. Kinetics describing the glass alteration as well as the gel
formation for a simple pure silicate glass has been investigated, in order to reproduce the
alteration profile within a fracture. The introduction of a flow rate in simulation predicts
dissymmetric profiles for pure silicate glass. These first results are encouraging for modeling
SON 68 glass alteration, for which chemistry has to be refined.
CONCLUSION
Original experiments performed on SON 68 model cracks in static and basic alteration
conditions proved that transport has a strong impact of alteration in model crack, for small
aperture cracks. For vertical cracks, the dissymmetric altered glass layer thickness profile shows
evidence of a gravity driven convection. The effect of a thermal gradient on leaching in model
cracks was also investigated thanks to a specifically designed device. Results indicate the
relevance of thermo-convection, in quantitative agreement with the theoretical expectation,
which influences notably the glass alteration.
Although, vertical crack convection has only been observed in basic conditions, and not
for neutral ones, its occurrence has been argued for through a crude modeling. This study shows,
in an original way, that convective transport, induced either by concentration variation or by
thermal gradient, can have a great influence on the alteration and hence must be taken into
account.
Modeling with a modified geochemical model is an encouraging direction which is
currently investigated for SON 68 glass, after a first validation on pure silicate glass. Another
considered perspectives is the extension of the modeling and experiments to more complex
geometries, i.e. crack networks involving several hundreds cracks.
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