Couplex-Gaz

Couplex-Gaz: Test Case 1
… with Tough2 and Tough2_MP
ANDRA Workshop on
Couplex-Gaz: Test case 1
4th/5th April 2007
A. Poller, G. Mayer & J. Croisé
Colenco Power Engineering Ltd
Outline
2
•
Suitability of Tough2 for Couplex-Gaz
•
Motivation for Tough2_MP
•
How does Tough_MP work?
•
Couplex-Gaz (Case 1b):
Numerical and physical aspects
•
Selected results
•
Conclusion
Workshop Couplex-Gaz, April 4/5 2007
Suitability of Tough2 for Couplex-Gaz
3
•
Established multi-phase multi-component code for flow
and transport in porous media
•
Special module EOS5 for hydrogen release and migration
=> Fluid properties for given P-range and given
temperature (<20MPa, 30°C)
•
Variety of Pcap(S)- and krel(S)-relationships
•
Available as source code => adaptable to special needs
Workshop Couplex-Gaz, April 4/5 2007
Tough2-module EOS5
4
•
Components:
H2O & H2
•
Phases:
liquid & gas
•
Ideal gas law for gas phase
•
Interpolation of gas mixture viscosity for given P and T
•
Dalton‘s law
•
Solubility of H2 according to Henry‘s law
•
Primary variables:
–
1 phase:
P, XH2, T
–
2 phases:
Pg, Sg, T
Workshop Couplex-Gaz, April 4/5 2007
Motivation for Tough2_MP
5
•
Experience with Tough2
•
Reputed to be robust (Yucca Mountain project)
•
Very appealing for large problems
(e.g. Couplex-Gaz Case 2)
•
Efficient utilization of our linux cluster
Workshop Couplex-Gaz, April 4/5 2007
Tough2_MP – Overview
6
•
Developed at Lawrence Berkeley National Laboratory
(Zhang et al., 2003)
•
Based on Tough2 V1.4
•
Parallel computing of
–
Jacobian assemblage
–
Solving linearized system
•
Partitioning of the model domain with METIS graph
programs (Karypsis and Kumar, 1998)
•
Iterative linear solver from Aztec Software package V2.1
(Tuminaro et al., 1999)
•
Communication via MPICH
(Message passing interface)
Workshop Couplex-Gaz, April 4/5 2007
Tough2_MP – Domain Partitioning with METIS
7
•
Even partitioning
=> equal utilization
•
Minimum number of
connections
=> communication slows down
•
Distribution of required
memory
=> large grids
•
Little global communication
=> e.g. for calculating norms
From Tough2_MP User‘s manual
Workshop Couplex-Gaz, April 4/5 2007
Couplex-Gaz Case 1b – Spatial Discretization
8
Workshop Couplex-Gaz, April 4/5 2007
Couplex-Gaz Case 1b –
Deviations of Physical Model Specified
•
9
Permeability of clearance: 10-15 m2 instead of 10-12 m2
=> Remaining permeability contrast to adjacent concrete units: > 3 orders of
magnitude
•
Initial gas present: Mixture of H2 and vapor (not air)
=> Initial mass < 1% of total H2 generated
=> little influence on H2-breakthrough at boundaries
•
Slightly different Henry constant
(7.62e-6 mol/m3·Pa instead of
7.65e-6 mol/m3·Pa
at 30°C)
•
Tough2 viscosity model used (Hirschfelder et al., 1954)
•
Tough2 diffusion model used (see below)
•
Initial saturation in EDZ: 99% instead of 100%
=> slight retardation of pressure rise in initial gas phase (see below)
Workshop Couplex-Gaz, April 4/5 2007
Couplex-Gaz Case 1b –
Diffusion Model Used
•
•
Diffusion of dissolved H2 in liquid phase
Couplex-Gaz:
D Hw2 = S w
ω
D H2 / H2O
τ2
Tough2:
DHw2 = k rw
ω
D H2 / H 2 O
τ2
Diffusion of dissolved H2 in gaseous phase
Couplex-Gaz:
D Hg 2 / vap = (1 − S w )
Tough2:
DHg 2 / vap = k rg
ω g
DH2−H20
τ2
ω g
DH2−H20
τ2
Workshop Couplex-Gaz, April 4/5 2007
10
1.0E+07
Couplex-Gaz Case 1b – Initial Conditions
Capillary Pressure
4.0E+06
6.0E+06
8.0E+06
Primary package
Concrete of package
Clearance
Filler concrete
Fractured zone
Disturbed zone
Callovo-Oxfordian
0.0E+00
2.0E+06
P cap [Pa]
11
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
S w [-]
Workshop Couplex-Gaz, April 4/5 2007
L:/andra/Couplex-g az//postprocessing .RMon Apr 02 15:40:19 2007
L:/andra/Couplex-g az//tmp_Cas1b_Cg 2e_21_mp/initial_pcap.wmf
1.0E+00
Couplex-Gaz Case 1b – Initial Conditions
Relative Permeability for Water
1.0E-04
1.0E-02
Primary package
Concrete of package
Clearance
Filler concrete
Fractured zone
Disturbed zone
Callovo-Oxfordian
1.0E-08
1.0E-06
k rl [-]
12
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
S w [-]
Workshop Couplex-Gaz, April 4/5 2007
L:/andra/Couplex-g az//postprocessing .RM on Apr 02 15:40:20 2007
L:/andra/Couplex-gaz//tmp_Cas1b_Cg 2e_21_mp/initial_krl.wmf
Couplex-Gaz: Test Case 1
Selected Results
H2-fluxes into host rock and across boundaries
14
500 a
10000 a
advectif de H2 à travers la limite supérieure
diffusif de H2 à travers la limite supérieure
advectif de H2 à travers la limite inférieure
diffusif de H2 à travers la limite inférieure
advectif de H2 du béton de remplissage à la zone fracturée
diffusif de H2 du béton de remplissage à la zone fracturée
JH2 [mol/a]
1e-05
1e-03
1e-01
1e+01
1e+03
Flux
Flux
Flux
Flux
Flux
Flux
0
10000
20000
30000
40000
50000
temps [a]
Workshop Couplex-Gaz, April 4/5 2007
L:/andra/Couplex-g az//postprocessing .RMon Apr 02 11:29:46 2007
L:/andra/Couplex-g az//tmp_Cas1b_Cg 2e_21_mp/h2_flx.wmf
Finding tend & H2-balancing
10000 a
Quantité de H2 initiale + quantité
produite
120000
140000
15
500 a
Flux diffusif de H2 à travers la
limite supérieure (cumulé)
100000
Flux diffusif de H2 à travers la
limite inférieure (cumulé)
Callovo-Oxfordien
80000
Zone fracturée
60000
Béton de remplissage
Jeux
Béton de colis
40000
nH2 [mol]
Zone endommagée
20000
Colis primaire
0
t f in = 77700 a
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
temps [a]
Workshop Couplex-Gaz, April 4/5 2007
L:/andra/Couplex-g az//postprocessing .RM on Apr 02 11:29:46 2007
L:/andra/Couplex-gaz//tmp_Cas1b_Cg 2e_21_mp/h2_balance.wmf
Pressure rise I
16
10.0
500 a
8.0
6.0
4.0
2.0
0.0
P g [MPa]
10000 a
Colis primaire, x=0.82, z=61.99
Béton de colis, x=0.82, z=64.9
Jeux, x=0.82, z=69.2
Béton de remplissage, x=0.82, z=69.9
Zone f racturée, x=0.82, z=71.25
Zone endommagée, x=0.82, z=73.28
Callovo-Oxf ordien, x=0.82, z=77.69
10
30
100
300
1000
3000
temps [a]
Workshop Couplex-Gaz, April 4/5 2007
10000
50000
Pressure rise II
100 110 120 130
17
70
60
0
10
20
30
40
50
z [m ]
80
90
0a
250 a
500 a
1000 a
5000 a
7500 a
10000 a
20000 a
40000 a
50000 a
0.0
1.0
2.0
3.0
4.0
P g [MPa]
L:/andra/Couplex-g az//postprocessing .RMon Apr 02 11:29:48 2007
5.0
6.0
7.0
Workshop Couplex-Gaz, April 4/5 2007
L:/andra/Couplex-g az//tmp_Cas1b_Cg 2e_21_mp/Pg_x103.wmf
Initial conditions
18
Workshop Couplex-Gaz, April 4/5 2007
Maximum pressure – 10000 a
19
Workshop Couplex-Gaz, April 4/5 2007
Countercurrent flow of gas and water
20
Workshop Couplex-Gaz, April 4/5 2007
Conclusion
21
•
Tough2 capable of handling Couplex-Gaz-like problems
•
Tough2_MP promising for large problems (Case 2)
•
Tough2_MP more robust than Tough2
•
Tough2_MP said to speed-up almost linearly the solution
of large problems (YM experience)
Workshop Couplex-Gaz, April 4/5 2007
Conclusion for Couplex-gaz (Case 1b)
22
•
Influence of deviations from Couplex-Gaz specifications
on results is most likely small
•
„Coarse“ grid leads to some inaccuracy in predicting the
gas-water front position, but …
•
Maximum pressure build-up in the drift is mainly related to
the single-phase (water) flow resistance in the undisturbed
clay and therefore accurately predicted
•
Convergence issues prohibit to determine the time at
which gas phase disappears (tend)
Workshop Couplex-Gaz, April 4/5 2007
Acknowledgement
23
We would like to thank Mr. Keni Zhang from
LBL for providing a test version of
Tough2_MP and for his help with code
installation and useful hints.
Workshop Couplex-Gaz, April 4/5 2007