Code_Aster ®
Version
7.3
Titrate:
WTNP112 - Resaturation of a column
Date:
03/01/05
Author (S):
Key S. GRANET
:
V7.32.112-A Page:
1/8
Organization (S): EDF-R & D/AMA
Handbook 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.
Handbook of Validation
V7.32 booklet: Thermo hydro-mechanical in porous environment unsaturated
HT-66/05/005/A
Code_Aster ®
Version
7.3
Titrate:
WTNP112 - Resaturation of a column
Date:
03/01/05
Author (S):
Key S. GRANET
:
V7.32.112-A Page:
2/8
1
Problem of reference
1.1 Geometry
The studied field is a semi medium infinite horizontal. In practice it measures 3m.
y
C
D
With
X
B
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)
1000
Viscosity
1
Parameters
Permeability K
1,625E-5m/s
homogenized
Porosity
0.3
0 81667
.
Isotherm of sorption
S (
C
P) = 0 1833
.
+
.
0
[
.
2 0304
1 + (2 9227
.
P)
C
] 5075
Relative permeability
W
Kr (C
P) = (7,3Pc)
E
0 49
.
1 97
.
.
0 82
.
2 5.
-
1
S -
0 18
,
= E
Initial State
Pressure
P0 =
m
15
.
1
C
1.3
Boundary conditions and initial
They are expressed on the capillary pressure:
P (X)
0
, = P0 =
m
15
.
1
C
C
P (,
0 T) = 0 and P
,
3
(T) =
m
15
.
1
C
C
One is in condition of Richards: P (X, T) = atm
1
gz
Handbook of Validation
V7.32 booklet: Thermo hydro-mechanical in porous environment unsaturated
HT-66/05/005/A
Code_Aster ®
Version
7.3
Titrate:
WTNP112 - Resaturation of a column
Date:
03/01/05
Author (S):
Key S. GRANET
:
V7.32.112-A Page:
3/8
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 steps 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
1 hour
1,2
2 hours
1
3 hours
0,8
4 hours
0,6
5 hours
PC
6 hours
0,4
7 hours
0,2
8 hours
0
9 hours
10 hours
0
1
2
3
X (m)
Handbook of Validation
V7.32 booklet: Thermo hydro-mechanical in porous environment unsaturated
HT-66/05/005/A
Code_Aster ®
Version
7.3
Titrate:
WTNP112 - Resaturation of a column
Date:
03/01/05
Author (S):
Key S. GRANET
:
V7.32.112-A Page:
4/8
Semi-analytical solution of Pillips
1,2
1h
2h
1
3h
0,8
4h
0,6
PC
5h
0,4
6h
7h
0,2
8h
0
9h
0
1
2
3
10h
X (m)
Saturation along the column 40 elements
1 hour
1
2 hours
0,9
3 hours
4 hours
0,8
5 hours
S 0,7
6 hours
0,6
7 hours
0,5
8 hours
9 hours
0,4
10 hours
0
1
2
3
X (m)
3.4 Value
tested
X (m)
Time (S)
PRE1 Aster
Capillary pressure (Philips)
Relative error
1. 36000s
0.461
0.460
0.2%
Handbook of Validation
V7.32 booklet: Thermo hydro-mechanical in porous environment unsaturated
HT-66/05/005/A
Code_Aster ®
Version
7.3
Titrate:
WTNP112 - Resaturation of a column
Date:
03/01/05
Author (S):
Key S. GRANET
:
V7.32.112-A Page:
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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 steps 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
1,2
1 hour
1
2 hours
0,8
3 hours
0,6
4 hours
PC
5 hours
0,4
6 hours
0,2
7 hours
8 hours
0
9 hours
0
0,5
1
1,5
2
2,5
3
10 hours
X (m)
Handbook of Validation
V7.32 booklet: Thermo hydro-mechanical in porous environment unsaturated
HT-66/05/005/A
Code_Aster ®
Version
7.3
Titrate:
WTNP112 - Resaturation of a column
Date:
03/01/05
Author (S):
Key S. GRANET
:
V7.32.112-A Page:
6/8
Semi-analytical solution of Pillips
1,2
1h
2h
1
3h
0,8
4h
0,6
PC
5h
0,4
6h
7h
0,2
8h
0
9h
0
1
2
3
10h
X (m)
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
1 hour
1
2 hours
0,9
3 hours
0,8
4 hours
5 hours
S 0,7
6 hours
0,6
7 hours
0,5
8 hours
0,4
9 hours
0
0,5
1
1,5
2
2,5
3
10 hours
X (m)
Handbook of Validation
V7.32 booklet: Thermo hydro-mechanical in porous environment unsaturated
HT-66/05/005/A
Code_Aster ®
Version
7.3
Titrate:
WTNP112 - Resaturation of a column
Date:
03/01/05
Author (S):
Key S. GRANET
:
V7.32.112-A Page:
7/8
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 steps of 0,5 hours time.
5.3 Results
The results are obviously the same one as for modeling B.
Handbook of Validation
V7.32 booklet: Thermo hydro-mechanical in porous environment unsaturated
HT-66/05/005/A
Code_Aster ®
Version
7.3
Titrate:
WTNP112 - Resaturation of a column
Date:
03/01/05
Author (S):
Key S. GRANET
:
V7.32.112-A Page:
8/8
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 blocked 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 steps of 0,5 hours time.
6.3 Results
The results are obviously the same one as for modeling B.
7 Bibliography
[1]
Plane Alliances project of qualification, notes ANDRA CNT-ASCS 02-075B
Handbook of Validation
V7.32 booklet: Thermo hydro-mechanical in porous environment unsaturated
HT-66/05/005/A
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