Computing and Visualization in Science manuscript No. (will be inserted by the editor) Numerical simulation of gas migration through engineered and geological barriers for a deep repository for radioactive waste Brahim Amaziane · Mustapha El Ossmani · Mladen Jurak Received: March 28, 2012 / Accepted: date Abstract In this paper a finite volume method ap- proach is used to model the 2D compressible and im- miscible two-phase flow of water and gas in heteroge- neous porous media. We consider a model describing water-gas flow through engineered and geological barri- ers for a deep repository of radioactive waste. We con- sider a domain made up of several zones with differ- ent characteristics: porosity, absolute permeability, rel- ative permeabilities and capillary pressure curves. This process can be formulated as a coupled system of par- tial differential equations (PDEs) which includes a non- linear parabolic gas-pressure equation and a nonlinear degenerated parabolic water-saturation equation. Both equations are of diffusion-convection types. An implicit vertex-centred finite volume method is adopted to dis- cretize the coupled system. A Godunov-type method is used to treat the convection terms and a conforming finite element method with piecewise linear elements is used for the discretization of the diffusion terms. An upscaling technique is developed to obtain an ef- fective capillary pressure curve at the interface of two media. Our numerical model is verified with 1D semi- analytical solutions in heterogeneous media. We also present 2D numerical results to demonstrate the signif- B. Amaziane UNIV PAU & PAYS ADOUR, IPRA–LMA, CNRS-UMR 5142, Av. de l’universit´ e, 64000 Pau, France. E-mail: [email protected]M. El Ossmani Universit´ e Moulay Isma¨ ıl, LM2I-ENSAM, Marjane II, B.P. 4024, Mekn` es, 50000, Maroc. E-mail: [email protected]M. Jurak UNIV PAU & PAYS ADOUR, IPRA–LMA, CNRS-UMR 5142, Av. de l’universit´ e, 64000 Pau, France. E-mail: [email protected]icance of capillary heterogeneity in flow and to illus- trate the performance of the method for the FORGE cell scale benchmark. Keywords Finite volume · Heterogeneous porous media · Hydrogen migration · Immiscible compressible · Nuclear waste · Two-phase flow · Vertex-centred PACS 47.40.-x · 07.05.Tp · 02.30.Jr · 47.11.Df · 47.56.+r · 47.55.Ca · 28.41.Kw · 47.55.-t Mathematics Subject Classification (2000) 74Q99 · 76E19 · 76T10 · 76M12 · 76S05 1 Introduction The modeling of multiphase flow in porous formations is important for both the management of petroleum reser- voirs and environmental remediation. More recently, modeling multiphase flow received an increasing atten- tion in connection with the disposal of radioactive waste and sequestration of CO 2 . The long-term safety of the disposal of nuclear waste is an important issue in all countries with a significant nuclear program. Repositories for the disposal of high- level and long-lived radioactive waste generally rely on a multi-barrier system to isolate the waste from the bio- sphere. The multi-barrier system typically comprises the natural geological barrier provided by the reposi- tory host rock and its surroundings and an engineered barrier system, i.e. engineered materials placed within a repository, including the waste form, waste canisters, buffer materials, backfill and seals. In this paper, we focus our attention on the numeri- cal modeling of immiscible compressible two-phase flow in heterogeneous porous media, in the framework of the geological disposal of radioactive waste. As a matter of
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Computing and Visualization in Science manuscript No.(will be inserted by the editor)
Numerical simulation of gas migration through engineered andgeological barriers for a deep repository for radioactive waste
Brahim Amaziane · Mustapha El Ossmani · Mladen Jurak
Received: March 28, 2012 / Accepted: date
Abstract In this paper a finite volume method ap-
proach is used to model the 2D compressible and im-
miscible two-phase flow of water and gas in heteroge-
neous porous media. We consider a model describing
water-gas flow through engineered and geological barri-
ers for a deep repository of radioactive waste. We con-
sider a domain made up of several zones with differ-
ent characteristics: porosity, absolute permeability, rel-
ative permeabilities and capillary pressure curves. This
process can be formulated as a coupled system of par-
tial differential equations (PDEs) which includes a non-
linear parabolic gas-pressure equation and a nonlinear
degenerated parabolic water-saturation equation. Both
equations are of diffusion-convection types. An implicit
vertex-centred finite volume method is adopted to dis-
cretize the coupled system. A Godunov-type method isused to treat the convection terms and a conforming
finite element method with piecewise linear elements
is used for the discretization of the diffusion terms.
An upscaling technique is developed to obtain an ef-
fective capillary pressure curve at the interface of two
media. Our numerical model is verified with 1D semi-
analytical solutions in heterogeneous media. We also
present 2D numerical results to demonstrate the signif-
B. AmazianeUNIV PAU & PAYS ADOUR, IPRA–LMA, CNRS-UMR5142, Av. de l’universite, 64000 Pau, France.E-mail: [email protected]
M. El OssmaniUniversite Moulay Ismaıl, LM2I-ENSAM, Marjane II, B.P.4024, Meknes, 50000, Maroc.E-mail: [email protected]
M. JurakUNIV PAU & PAYS ADOUR, IPRA–LMA, CNRS-UMR5142, Av. de l’universite, 64000 Pau, France.E-mail: [email protected]
icance of capillary heterogeneity in flow and to illus-
zero and the gas flux is given by the gas source term.
At x = 0 m, for r ≤ 3 m, the boundary conditions
are of the Dirichlet’s type variable in time for water and
gas. The representation of these variations are given in
Figure 10. The gas pressure is deduced from the capil-
lary pressure law.
At all other parts of the boundary no flow boundary
condition is applied.
5.2 Output results
The benchmark requests different outputs from the sim-
ulation.
5.2.1 Evolution with time of fluxes through surfaces
Central concern of this benchmark is migration of the
gas produced by the canister corrosion. A good measure
of that migration is given by evolution in time of the
10 Brahim Amaziane et al.
Fig. 9 Boundary conditions in 2D computational domain.The waste canister is not a part of the computational domain.On its boundary the gas flux corresponding to the gas sourceterm is imposed.
phase fluxes through certain characteristic surfaces in
the model, which are given below.
Outer boundary of the model at r = 20 m (Sout in
Figure 11), fluxes counted positively out of the model.
Drift wall (Sdrift in Figure 11), fluxes counted pos-
itively toward the drift. Outside surface of the EDZ,
separated in 3 sections (see Figure 11): SEDZ1 (around
canister), SEDZ2 (around plug) and SEDZ3 (drift EDZ).
Fluxes counted positively out of the EDZ toward the
undisturbed rock. Inner cell surfaces (see Figure 11) :
Scell (section including interface and EDZ at canister-
plug junction), Sint1 (interface at canister-plug junc-
tion), Sint2 (interface at the drift wall). Fluxes counted
positively toward the drift.
5.2.2 Evolution with time along lines
Time evolution of all model variables are requested over
several lines. Lines at constant radius (see Figure 12):
Lint (passes through the interface), LEDZ (just outside
the cell EDZ), Lrock (inside the rock at a 5 m radius)
Lines at constant x (see Figure 12): Lx=0 m and
Lx=60 m (boundaries of the model), Lplug (in the mid-
dle of the plug), Lcell (in the middle of the canister).
5.2.3 Evolution with time at given points
Time evolution of all model variables are requested in
12 points (see Figure 13). Points 1 to 4, are at the same
radius as the centre of the interface: P1 and P4 (at the
boundaries), P2 (in the middle of the canister), P3 (at
canister-plug junction). Points 5 and 6 are at the same
radius as the centre of the cell EDZ: P5 (in the mid-
dle of the canister), P6 (at the canister-plug junction).
Point 7 is in the middle of the drift EDZ on x = 0
-4
-2
0
2
4
0.1 1 10 100 1000 10000 100000
Wate
r pre
ssure
[M
Pa]
Time [years]
Outer radius constant pressure
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
0.1 1 10 100 1000 10000 100000
Wate
r satu
ration
Time [years]
Outer radius constant saturation
Fig. 10 The Dirichlet boundary conditions on the Accessdrift boundary, for x = 0 and 0 ≤ r ≤ 3 m.
boundary. Points 8 to 12 are at 5 m radius: P8 and P12
(at the boundaries), P9 (at the same x as the middle ofthe canister), P10 (at the same x as the canister-plug
junction), P11 (at the same x as the intersection of the
drift and the interface).
5.3 Main difficulties
The geometry of the domain present the first difficulty
because of small diameter of the Interface (1 cm), com-
pared to other dimensions of the computational do-
main. Large computational time (100,000 years) force
us to use relatively coarse grid which then leads to a
grid with large difference in the elements size.
Second difficulty is the large difference in the capil-
lary pressure curves in the Interfaces and the curves in
the EDZ and the Bentonite plug. The continuity of the
capillary pressure through the material interface makes
the saturation in the Interface very sensible to varia-
tions of the saturations in surrounding materials, the
EDZ and the Bentonite plug. This instability is very
Numerical simulation of gas migration for radioactive waste 11
Fig. 11 Schematic representation of the surfaces troughwhich fluxes will be calculated.
Fig. 12 Schematic representation of the lines along whichresults should be calculated.
Fig. 13 Schematic representation of the points where resultsshould be calculated.
strong in the Interface near the plug and to avoid nu-
merical oscillations in the Interface, which can prevent
the Newton solver from converging, the time step must
often be reduced. This is serious difficulty because of
large final time of simulation.
Remark. Benchmark test case presented here is sim-
plified with respect to the original benchmark in two
aspects. First, we did not model gas dissolution in wa-
ter and dissolved gas transport by the convection and
the diffusion. We assume that all generated gas will be
present in the gas phase and we study its migration.
Second, we have changed the permeability of the In-
terface near the Canister, from originally 10−12 m2 to
10−18 m2. Original, very large permeability in the In-
terface near the Canister prevented the Newton solver
from converging, except for small time steps. No other
changes to the original data were done (see also foot-
note on page 8).
6 Simulation results
6.1 Simulation code and the grid
We have used simulation code developed in house based
on the numerical scheme presented in Section 3. The
non linear system of discretized equations is solved by
the inexact Newton method, using ILU preconditioned
GMRES linear solver. For linear and non linear solvers
we have used PETSc package, [5]. Fully implicit time
stepping was controlled by the convergence of the New-
ton solver.
Fig. 14 Simulation grid.
The grid used in the simulation, shown in Figure 14,
is composed of 1932 elements in the primary grid and it
is mostly uniform rectangular grid, except in the Access
drift and the EDZ, where general quadrilaterals and
triangles are used to fit the given geometry. In the EDZ
we have used five layers of elements, and four layers
in the Interfaces. Dimensions of the elements in radial
direction go from 25 mm in the Interface, to 1.6 m in
the Geological medium.
The effective capillary pressure curves were calcu-
lated as tables in all interface points before beginning
of the simulation; 9000 points are used in each table.
Since the effective capillary pressure curves depend on
local mesh geometry, we obtain one curve in each ver-
tex on the material interface. As an illustration, in Fig-
ure 15 we show one effective capillary pressure curve at
12 Brahim Amaziane et al.
the material interface between the EDZ and the Geo-
logical medium. Corresponding material curves are also
shown. From Figure 15 we see, as well as from the def-
inition (9), (10), that the effective capillary pressure
curves have the same monotonicity properties as the
material curves and represent a mesh dependent mean
value of the material capillary pressure curves. In Fig-
ure 16 we show one effective capillary pressure curve
on the boundary of the EDZ and the Interface near the
Canister. Since the geometry of the primary grid near
the Canister is very regular all effective curves are clus-
tered in a few groups of almost identical curves. We
can also note in Figure 16 that the material curve of
the Interface is too small to be represented at the scale
of the figure.
0
5
10
15
20
25
0 0.2 0.4 0.6 0.8 1
Capill
ary
pre
ssure
[M
Pa]
Water saturation
effectiveEDZ
Geol. med.
Fig. 15 The effective capillary pressure between the EDZand the Geological medium.
0
10
20
30
40
50
60
70
80
90
100
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Capill
ary
pre
ssure
[M
Pa]
Water saturation
effectiveInterface
EDZ
Fig. 16 The effective capillary pressure between the EDZand the Interface.
6.2 Gas pressure evolution
The gas pressure is a primary variable in our model.
It is taken to be equal to the water pressure in wa-
ter saturated region. From imposed initial conditions
the gas pressure is initially discontinuous. It is assumed
that the fully saturated materials (EDZ and Geological
medium) are initially put into contact with unsaturated
materials (Interfaces and Access drift) which results in
discontinuity of water and gas pressures in the initial
moment. After the start of the simulation the gas pres-
sure becomes immediately continuous, as it can be seen
from Figure 17, for t = 1 day. Then, in the EDZ and the
Access drift, it stays relatively small and uniform until
sufficient quantity of gas is generated, when it starts to
grow (see Figure 17 for t = 2, 000 years). The maximum
gas pressure is attained at one corner of the Canister
at the end of the gas production interval (t = 10, 000
years).
6.3 Evolution with time of fluxes through surfaces
In the first year of the simulation the initial water pres-
sure discontinuity produce very strong flow of water
from the Geological medium to the EDZ. The water
flow through SEDZ1, after initial very strong flow into
EDZ, shortly changes direction and between 0.001 an
0.1 year flows to the Geological medium. After that
stays directed towards the EDZ (Figure 18). The water
flow through SEDZ3 (Figure 19) stays directed to the
EDZ until extinction of the gas source when its goes to
zero, but shows some small oscillations at later times,
obviously of numerical origin. The water flow through
SEDZ2 (Figure 18) is slightly positive (from the EDZ to
the Geological medium) which is a consequence of much
stronger water flow through the EDZ (surface Scell,
Figure 18) towards the Access drift. The flow of water
from the EDZ to the Access drift (surface Sdrift, Fig-
ure 19) stays very strong even after extinction of the gas
source. Water flow through the interfaces is negligible.
The EDZ is the main path for the water flow, which
goes from the Geological medium to the Access drift.
The Interfaces do not participate to the water flow since
they are mostly field with the gas (see Figure 26) keep-
ing water mobility very low. They prevent the flow of
water from the EDZ to the Bentonite plug, which resat-
urates primary from the Access drift. This slows down
the plug resaturations, which take approximately 2,000
years and explains small water flux from the EDZ to the
Geological medium through SEDZ2. Finally, the water
flux through the EDZ-Acess drift interface stops ap-
proximately at 23,000 years, when the hole domain, ex-
cept the Interfaces, is resaturated.
Numerical simulation of gas migration for radioactive waste 13
Fig. 17 Gas pressure (in MPa) in the domain at different times: 1 day, 1 year, 2,000 years and 100,000 years.
-150
-100
-50
0
50
100
0.1 1 10 100 1000 10000 100000
Wate
r flux [kg/y
ear
]
Time [years]
S_EDZ_2S_EDZ_1
S_cellS_int_1S_int_2
S_out
Fig. 18 Water fluxes through SEDZ1, SEDZ2, Scell, Sint1
and Sint2.
The gas flow in Figures 20 and 21 shows that the
gas is flowing through the EDZ in direction of the Ac-
cess drift (surface Scell, Figure 21) and and form the
EDZ to the Access drift, through Sdrift (Figure 21).
These two fluxes are the strongest ones. The flow of
the gas through the Interfaces (Sint1 and Sint2 in
Figure 20) is approximately 10-15 times smaller than
the flow through the EDZ in the direction of the Ac-
cess drift (Scell in Figure 21), and it is smaller than
the gas flow from EDZ into the undisturbed rock. We
may conclude, therefore, that importance of the inter-
-400
-200
0
200
400
0.1 1 10 100 1000 10000 100000
Wate
r flux [kg/y
ear]
Time [years]
S_driftS_EDZ_3
Fig. 19 Water fluxes through Sdrift and SEDZ3.
face for the gas migration is weak. The most of the
gas flows through the EDZ, whose properties has the
largest influence on behavior of the system. However,
the Interfaces keep their importance as a capillary bar-
rier that slows down the resaturation of the Canister
and the Bentonite plug.
Let us also note that in the first year of the simula-
tion the gas is flowing from the Access drift to the EDZ
(Sdrift in Figure 21) under the influence of the bound-
ary condition imposed on the boundary of the Access
drift and because the gas is replacing the water that is
entering into the Access drift.
14 Brahim Amaziane et al.
The flow of the gas from the EDZ to the Geologi-
cal medium (surfaces SEDZ1 and SEDZ2 in Figure 20) is
approximately 5-8 times smaller than the flow through
the EDZ and the Interface (surface Scell in Figure 21),
and is a consequence of the gas replacing the water that
is entering into the EDZ. Similarly, we have the flow of
the gas from the Access drift EDZ into undisturbed
rock (SEDZ3 in Figure 21) which is induced by a strong
flow of the water in the opposite direction. After ap-
proximately 23,000 years the gas is finally evacuated to
the Access drift and from there, through the boundary
with imposed pressure, out of the system.
6.4 Evolution with time at given points
In this subsection we show the water saturation and
the water and the gas pressures in some of prescribed
points.
In Figure 22 we show water saturation in all points
outside of the EDZ and the Interface, and in Figure 23
we show the points in the Interface and the EDZ. We
see from Figure 22 that desaturation of the Geologi-
cal medium is very weak and that it is stronger in the
points closer to the Access drift, due to strog water flow
into the Access drift and some counter flow of the gas.
This weak desaturation is to be expected due to weak
permeability and strong capillary pressure curve of the
undisturbed rock.
In the points P2, P3 and P4 (Figure 23) which lay
in the Interface we observe a low water saturation un-
til 27,000 years when the resaturation of the Interface
starts. This behaviour is a consequence of very low
capillary pressure curve in the Interface (see Figure 7)
which keeps the Canister and the Bentonite plug iso-
lated of the EDZ and the Geological medium and slows
-0.01
0
0.01
0.02
0.03
0.04
1 10 100 1000 10000 100000
Gas flu
x [kg/y
ear]
Time [years]
S_EDZ_2S_EDZ_1
S_int_1S_int_2
S_out
Fig. 20 Gas fluxes through SEDZ1, SEDZ2, Sint1, Sint2 andSout.
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.1 1 10 100 1000 10000 100000
Gas flu
x [kg/y
ear]
Time [years]
S_driftS_cell
S_EDZ_3
Fig. 21 Gas fluxes through SEDZ3, Scell and Sdrift.
0.994
0.995
0.996
0.997
0.998
0.999
1
1.001
1.002
0.1 1 10 100 1000 10000 100000
Wate
r satu
ration
Time [years]
P1P8P9
P10P11P12
Fig. 22 Time evolution of the water saturation in points P1
and P8-P12.
down the resaturation of the Plug (and the Canister
in reality). Almost all gas must be evacuated from the
EDZ for resaturation of the Interface to start.
In the points P5 and P6 that lay in the center of
the EDZ a desaturation is significant only after 2,000
years (see Figure 23). This means that the generated
gas is efficiently evacuated to the Access drift until ap-
proximately 2,000 years, when the gas starts to accu-
mulate in the EDZ. In the point P7 the desaturation is
more significant (Figure 23), but this is influenced by
the boundary condition imposed on boundary of the
Access drift (compare to imposed water saturation in
Figure 10).
The gas pressure is shown in Figure 24 for points
P2-P7 which lay in the EDZ and in the Interfaces. In
the remaining points, P1 and P8-P12, we present the
water pressure in Figure 25.
In Figure 24 we show also the boundary condition
on the gas pressure imposed on the boundary of the
Numerical simulation of gas migration for radioactive waste 15
0
0.2
0.4
0.6
0.8
1
0.1 1 10 100 1000 10000 100000
Wate
r satu
ration
Time [years]
P2P3P4P5P6P7
Fig. 23 Time evolution of the water saturation in pointsP2-P7.
Access drift. This pressure is supposed to model inter-
action of the computational domain with the rest of the
repository. In this figure the gas pressure in the points
P2 and P5 are almost the same; similarly, the pressure
in the points P3 and P6 are almost the same, and the
pressures in P4 and P7 are almost equal to the gas pres-
sure imposed on the Access drift boundary. Since the
points P2, P5 and P3, P6 are close, this is to be ex-
pected. In the other hand, in the points P4 and P7 we
see strong influence of the Dirichlet boundary condition
at the boundary of the Access drift. The maximum gas
pressure achieved in the simulation is 5.43 MPa. This
results show that the pressurisation at the cell scale, due
to the gas generation by the canister corrosion, strongly
depends on interaction of the Canister with the rest of
the repository, which is represented here by time vary-
ing boundary condition on the Access drift.
0
1
2
3
4
5
6
0.1 1 10 100 1000 10000 100000
Gas p
ressure
[M
Pa]
Time [years]
P2P3P4P5P6P7
Fig. 24 Time evolution of the gas pressure in points P2-P7
and the gas pressure imposed on the boundary of the Accessdrift.
Evolution in time of the water pressures in the points
P1 and P8-P12 are presented in Figure 25. The initial
discontinuity of the water pressure produce immediate
pressure drop in the Geological medium. This pressure
drop attains it minimum before 100 years due to strong
initial water flux into the EDZ and the Access drift.
When these fluxes stabilize (see Figures 18 and 19) the
water pressure starts to increase, until reaching its ini-
tial value of 5 MPa after 10,000 years.
0
1
2
3
4
5
0.1 1 10 100 1000 10000 100000
Wate
r pre
ssure
[M
Pa]
Time [years]
P1P8P9
P10P11P12
Fig. 25 Time evolution of the water pressure in points P1
and P8-P12.
One of the main concerns in the nuclear waste repos-
itory safety assessment is the raise of the pressure of the
gas produced by the canister. In our simulation we find
that the pressure raise is quite small (0.43 MPa) and
therefore it does not present a threat to the safety of therepository. However, we have seen that the gas pressure
is strongly influenced by the gas pressure imposed on
the boundary of the Access drift, which is by itself an
assumption on interaction between one repository cell
with the rest of the repository. The other parameters
that influence the gas pressure buildup are the proper-
ties of the EDZ which determine the ability of the EDZ
to conduct the gas into the Acces drift, and thus reduce
the pressure buildup.
6.5 Evolution with time along lines
From solution over different lines we present only the
water saturation over line Sint which goes through the
Interfaces (Figure 26) which is the most interesting one,
since the behavior of the solution is the most complex
in the Interfaces. The Interfaces have a very small cap-
illary pressure curve which keeps it desaturated if there
is some quantity of the gas in the EDZ. Therefore we
16 Brahim Amaziane et al.
see that after initial partial resaturation at 2,000 years,
water saturation diminish and stays approximately con-
stant up to 25,000 years. Around 27,000 years the water
saturation decrease to its minimum value (see also Fig-
ure 23) – probably due to local accumulation of the gas
that is evacuated from the Geological medium and the
EDZ to the area close to the Interfaces – and then starts
slowly to increase again. The resaturation starts from
the Access drift side.
0
0.2
0.4
0.6
0.8
1
0 10 20 30 40 50 60
t=0.0 yearst=2000 years
t=10000 yearst=27000 yearst=60000 years
t=100000 years
Fig. 26 Water saturation over the line Sint given at severaltime instances.
It is of great importance to evaluate the role of the
Interfaces in the gas migration in the repository since
the meshing of the Interfaces in 3D model, on the scale
of whole repository, produces prohibitively large grids.
From our simulations we can conclude that the role ofthe Interface in the gas migration in minor compared
to the role of the EDZ. The main impact of the Inter-
face on the gas migration is to slow down resaturation
of the Bentonite plug (and the Canister). In the other
hand, modeling of the Interfaces as a porous medium
with very low capillary pressure curve is not an accurate
description of physical reality. We conclude, therefore,
that an upscaling of the Interfaces with the EDZ, that
is forming a new EDZ with slightly different properties
and eliminating the Interfaces, could produce a simpler
model of the repository, without perturbing important
gas migration characteristics.
7 Conclusion
We have presented a vertex centered finite volume nu-
merical scheme for the water-gas flow through highly
heterogeneous porous media. The method is fully im-
plicit and it includes a treatment of heterogeneities by
using an upscaling technique and the concept of the ef-
fective saturation. Our numerical model is verified with
1D semi-analytical solutions in heterogeneous media.
We also apply the method to the FORGE cell scale
benchmark developed for the evaluation of the hydro-
gen migration in an underground nuclear waste repos-
itory. Note that the benchmark deals with water-gas
flow in a porous medium under high and discontinuous
capillary pressures which leads to a degeneracy in the
system. The benchmark is presented in all details fol-
lowed by the numerical results obtained by our C++
homemade code based on the numerical scheme pre-
sented in this paper. The simulator uses the open source
library PETSc for solving discrete nonlinear systems.
The simulation shows that the most of the gas is
evacuated through the EDZ towards the Access drift.
Only a small quantity of the gas enters into the Geo-
logical medium and then slowly returns into the EDZ
to be evacuated from the system. The Interfaces have
only a secondary role in the gas transport, but they
slow down the process of re-saturation of the Bentonite
plug by keeping it isolated from the EDZ. The whole
system is strongly influenced by the Dirichlet boundary
condition imposed on the Access drift boundary.
Acknowledgements The research leading to these resultshas received funding from the European Atomic Energy Com-munitys Seventh Framework Programme (FP7/2007-2011) un-der Grant Agreement no230357, the FORGE project. Thiswork was partially supported by the GnR MoMaS (PACEN/CNRS,ANDRA, BRGM,CEA, EDF, IRSN) France, their supportsare gratefully acknowledged.
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