Code_Aster
®
Version
7.3
Titrate:
WTNP112 - Resaturation of a column
Date:
03/01/05
Author (S):
S. GRANET
Key
:
V7.32.112-A
Page:
1/8
Manual of Validation
V7.32 booklet: Thermo hydro-mechanical in porous environment unsaturated
HT-66/05/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V7.32 booklet: Thermo hydro-mechanical in porous environment unsaturated
Document: V7.32.112
WTNP112 - Resaturation of a column
Summary:
The test presented here makes it possible to check the correct operation of the operators used for the resolution of
equations of a flow in unsaturated medium. This test corresponds to test 3.1 of the plan of qualification of the project
Al [bib1]. It represents the resaturation of a column.
Code_Aster
®
Version
7.3
Titrate:
WTNP112 - Resaturation of a column
Date:
03/01/05
Author (S):
S. GRANET
Key
:
V7.32.112-A
Page:
2/8
Manual of Validation
V7.32 booklet: Thermo hydro-mechanical in porous environment unsaturated
HT-66/05/005/A
1
Problem of reference
1.1 Geometry
The studied field is a semi medium infinite horizontal. In practice it measures 3m.
Co-ordinates of the points (m):
To 0 0
C 3 0.1
B 3 0
D 0 0.1
1.2
Properties of material
One gives here only the properties whose solution depends, knowing that the command file
contains other data of material (moduli of elasticity,…) who finally do not play any part
in the solution of the dealt with problem.
Liquid water
Density (kg.m
- 3
)
Viscosity
1000
1
Parameters
homogenized
Permeability K
Porosity
Isotherm of sorption
Relative permeability
1,625E-5m/s
0.3
()
[
]
5075
.
0
0304
.
2
)
9227
.
2
(
1
81667
.
0
1833
.
0
C
C
P
P
S
+
+
=
()
-
-
=
=
49
.
0
97
.
1
1
18
,
0
82
.
0
.
5
.
2
)
3
,
7
(
S
PC
C
W
E
E
P
Kr
Initial State
Pressure
m
P
C
15
.
1
0
=
1.3
Boundary conditions and initial
They are expressed on the capillary pressure:
m
P
X
P
C
C
15
.
1
)
0
,
(
0
=
=
0
)
,
0
(
=
T
P
C
and
m
T
P
C
15
.
1
)
,
3
(
=
One is in condition of Richards:
atm
T
X
P
gz
1
)
,
(
=
y
X
With
B
C
D
Code_Aster
®
Version
7.3
Titrate:
WTNP112 - Resaturation of a column
Date:
03/01/05
Author (S):
S. GRANET
Key
:
V7.32.112-A
Page:
3/8
Manual of Validation
V7.32 booklet: Thermo hydro-mechanical in porous environment unsaturated
HT-66/05/005/A
2
Reference solution
The reference solution is the semi-analytical solution of Philips [bib1].
3 Modeling
With
3.1
Characteristics of modeling A
Modeling THHD in plane deformations. 40 Q8 element
3.2 Functionalities
tested
Order Option
AFFE_MODELE
D_PLAN_THHD
DEFI_MATERIAU
THM_LIQU
THM_GAZ
THM_DIFFU
THM_INIT
ELAS
AFFE_CHAR_MECA DDL_IMPO PRE1
PRE2
TEMP
STAT_NON_LINE COMP_INCR
RELATION KIT_THH
RELATION_KIT
LIQU_GAZ
HYDR_UTIL
Discretization in time: 20 pitches of 0,5 hours time.
3.3 Results
The table below presents the capillary profiles of pressures and saturation along the bar and to
each hour: One intercalates between the 2 profiles, that corresponding to the semi-analytical solution of
Philips.
Capillary pressure along the column
40 elements
0
0,2
0,4
0,6
0,8
1
1,2
0
1
2
3
X (m)
PC
1 hour
2 hours
3 hours
4 hours
5 hours
6 hours
7 hours
8 hours
9 hours
10 hours
Code_Aster
®
Version
7.3
Titrate:
WTNP112 - Resaturation of a column
Date:
03/01/05
Author (S):
S. GRANET
Key
:
V7.32.112-A
Page:
4/8
Manual of Validation
V7.32 booklet: Thermo hydro-mechanical in porous environment unsaturated
HT-66/05/005/A
3.4 Value
tested
X (m)
Time (S)
PRE1 Aster
Capillary pressure (Philips)
Relative error
1. 36000s
0.461
0.460
0.2%
Saturation along the column 40 elements
0,4
0,5
0,6
0,7
0,8
0,9
1
0
1
2
3
X (m)
S
1 hour
2 hours
3 hours
4 hours
5 hours
6 hours
7 hours
8 hours
9 hours
10 hours
Semi-analytical solution of Pillips
0
0,2
0,4
0,6
0,8
1
1,2
0
1
2
3
X (m)
PC
1h
2h
3h
4h
5h
6h
7h
8h
9h
10h
Code_Aster
®
Version
7.3
Titrate:
WTNP112 - Resaturation of a column
Date:
03/01/05
Author (S):
S. GRANET
Key
:
V7.32.112-A
Page:
5/8
Manual of Validation
V7.32 booklet: Thermo hydro-mechanical in porous environment unsaturated
HT-66/05/005/A
4 Modeling
B
4.1
Characteristics of modeling B
Modeling THHD in plane deformations. 80 Q8 elements
4.2 Functionalities
tested
Order Option
AFFE_MODELE
D_PLAN_THHD
DEFI_MATERIAU
THM_LIQU
THM_GAZ
THM_DIFFU
THM_INIT
ELAS
AFFE_CHAR_MECA DDL_IMPO PRE1
PRE2
TEMP
STAT_NON_LINE COMP_INCR RELATION
KIT_THH
RELATION_KIT
LIQU_GAZ
HYDR_UTIL
Discretization in time: 20 pitches of 0,5 hours time.
4.3 Results
The table below presents the capillary profiles of pressures and saturation along the bar and to
each hour, as for modeling A one intercalates the semi-analytical solution of Philips:
Capillary pressure along the column 80 elements
0
0,2
0,4
0,6
0,8
1
1,2
0
0,5
1
1,5
2
2,5
3
X (m)
PC
1 hour
2 hours
3 hours
4 hours
5 hours
6 hours
7 hours
8 hours
9 hours
10 hours
Code_Aster
®
Version
7.3
Titrate:
WTNP112 - Resaturation of a column
Date:
03/01/05
Author (S):
S. GRANET
Key
:
V7.32.112-A
Page:
6/8
Manual of Validation
V7.32 booklet: Thermo hydro-mechanical in porous environment unsaturated
HT-66/05/005/A
Semi-analytical solution of Pillips
0
0,2
0,4
0,6
0,8
1
1,2
0
1
2
3
X (m)
PC
1h
2h
3h
4h
5h
6h
7h
8h
9h
10h
4.4 Value
tested
X (m)
Time (S)
PRE1 Aster
Capillary pressure (Philips)
Relative error
1. 36000s 0.459
0.460
0.1%
Saturation along the column 80 elements
0,4
0,5
0,6
0,7
0,8
0,9
1
0
0,5
1
1,5
2
2,5
3
X (m)
S
1 hour
2 hours
3 hours
4 hours
5 hours
6 hours
7 hours
8 hours
9 hours
10 hours
Code_Aster
®
Version
7.3
Titrate:
WTNP112 - Resaturation of a column
Date:
03/01/05
Author (S):
S. GRANET
Key
:
V7.32.112-A
Page:
7/8
Manual of Validation
V7.32 booklet: Thermo hydro-mechanical in porous environment unsaturated
HT-66/05/005/A
5 Modeling
C
5.1
Characteristics of modeling C
Modeling THH 2D in plane deformations. 80 Q8 elements. It is exactly the same case as
modeling B but with a structure THH 2D and a coefficient of infinite Henry. This modeling has
only for goal to bring back itself to a structure of data THH 2D which is that known by
Alliances.
5.2 Functionalities
tested
Order Option
AFFE_MODELE
D_PLAN_THH 2D
DEFI_MATERIAU
THM_LIQU
THM_GAZ
THM_DIFFU
THM_AIR_DISS
THM_VAPE_GAZ
THM_INIT
ELAS
AFFE_CHAR_MECA DDL_IMPO PRE1
PRE2
TEMP
STAT_NON_LINE COMP_INCR
RELATION KIT_THH
RELATION_KIT
LIQU_AD_GAZ_VAPE
HYDR_UTIL
Discretization in time: 20 pitches of 0,5 hours time.
5.3 Results
The results are obviously the same one as for modeling B.
Code_Aster
®
Version
7.3
Titrate:
WTNP112 - Resaturation of a column
Date:
03/01/05
Author (S):
S. GRANET
Key
:
V7.32.112-A
Page:
8/8
Manual of Validation
V7.32 booklet: Thermo hydro-mechanical in porous environment unsaturated
HT-66/05/005/A
6 Modeling
D
6.1
Characteristics of modeling D
Modeling HMD in plane deformations. 80 Q8 elements. It is exactly the same case as
modeling B but with the mixing rate LIQU_GAZ_ATM specific to the modeling of Richards
(equivalent to modeling unsaturated with gas pressure imposed). One is locked in mechanics.
6.2 Functionalities
tested
Order Option
AFFE_MODELE
D_PLAN_HMD
DEFI_MATERIAU
THM_LIQU
THM_GAZ
THM_DIFFU
THM_INIT
ELAS
AFFE_CHAR_MECA DDL_IMPO PRE1
DX
DY
STAT_NON_LINE COMP_INCR
RELATION KIT_THH
RELATION_KIT
LIQU_GAZ_ATM
HYDR_UTIL
Discretization in time: 20 pitches of 0,5 hours time.
6.3 Results
The results are obviously the same one as for modeling B.
7 Bibliography
[1]
Project Alliances plan of qualification, notes ANDRA CNT-ASCS 02-075B