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:
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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
:
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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

Outline document