View
215
Download
0
Tags:
Embed Size (px)
Citation preview
Summary of results to date
B. Garitte and A. Gens
2nd DECOVALEX 2011 workshop, 20th of October 2008, Wakkanai , Japan
Dept. of Geotechnical Engineering and GeosciencesTECHNICAL UNIVERSITY OF CATALONIA (UPC)
Comparison of the modelling results
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 50 100 150Time [days]
Wat
er lo
ss [
kg]
CEA JAEA Quintessa UoE CAS Sample A Sample B Sample C
Schedule of Task A
Step 0: Identification of relevant processes and of Opalinus Clay parameters. Modelling of the
laboratory drying test.
Step 1: Hydromechanical modelling up to the end of Phase 1.
Step 2: Hydromechanical modelling up to the end of Phase 2 using parameters
backcalculated from step 1. Advanced features as permeability anisotropy, rock damage and
permeability increase in the damaged zone may be considered.
Step 3: Hydromechanical and geochemical modelling of the full test. Conservative transport
and one species considered.
Step 4: Hydromechanical and geochemical modelling of the full test. Reactive transport and
full geochemical model (optional).
(T)H(M) formulation
Parameters and constitutive equations
Model setup
Comparison of the modelling results
Summary of the mechanisms
Conclusions and discussion on future work
Index
(T)H(M) formulation
wwg
wlg
wgl
wl fSS
t jj
Variation of the water mass in a certain volume (variation of liquid density, gas density, water saturation, gas saturation and porosity)
Main balance equation: water mass balance
In- and outflux of water to/from that volume (flux of water in the liquid phase and flux of water in the gas phase)
Source and sink terms
CAS CEA JAEA Quintessa UoE
Energy balance
Air mass balance
Stress equilibrium
(T)H(M) formulation
wwg
wlg
wgl
wl fSS
t jj
Variation of the water mass in a certain volume (variation of liquid density, gas density, water saturation, gas saturation and porosity)
In- and outflux of water to/from that volume (flux of water in the liquid phase and flux of water in the gas phase)
Source and sink terms
CAS CEA JAEA Quintessa UoE
Main balance equation: water mass balance
Energy balance
Air mass balance
Stress equilibrium
(T)H(M) formulation
wwg
wlg
wgl
wl fSS
t jj
Variation of the water mass in a certain volume (variation of liquid density, gas density, water saturation, gas saturation and porosity)
In- and outflux of water to/from that volume (flux of water in the liquid phase and flux of water in the gas phase)
Source and sink terms
CAS CEA JAEA Quintessa UoE
Main balance equation: water mass balance
Energy balance
Air mass balance
Stress equilibrium
wwg
wlg
wgl
wl fSS
t jj
(T)H(M) formulation
Variation of the water mass in a certain volume (variation of liquid density, gas density, water saturation, gas saturation and porosity)
In- and outflux of water to/from that volume (flux of water in the liquid phase and flux of water in the gas phase)
Source and sink terms
CAS CEA JAEA Quintessa UoE
Main balance equation: water mass balance
Energy balance
Air mass balance
Stress equilibrium
(T)H(M) formulation
Variation of the water mass in a certain volume (variation of liquid density, gas density, water saturation, gas saturation and porosity)
In- and outflux of water to/from that volume (flux of water in the liquid phase and flux of water in the gas phase)
Source and sink terms
CAS CEA JAEA Quintessa UoE
Energy balance
Air mass balance
Main balance equation: water mass balance
Stress equilibrium
CAS CEA JAEA Quintessa UoE
CAS CEA JAEA Quintessa UoE
CAS CEA JAEA Quintessa UoE
wwg
wlg
wgl
wl fSS
t jj
Parameters and constitutive equations
CAS CEA JAEA Quint. UoE
Physical
Solid grain density ρs [kg/m3] 2710 2710 2710 2700
Porosity φ 0.165 0.16 0.162 0.16
Hydraulic
Intrinsic permeability k [m2] 7.5E-20 2E-20 2E-20 1.69E-19 1.9E-20
Dynamic viscosity μ [Pa.s] 1E-5 2.9E-4
Liquid relative permeability λ’ 0.4 0.68 0.65 0.3
Vapour diffusion coefficient 6E-6 5E-6
Mechanical
Young modulus E [GPa] 6 1.5
Poisson coefficient ν 0.27 0.3
Friction angle φ [º]
Cohesion c [MPa]
Hydro-Mech. coupling
Suction bulk modulus Ks [GPa]
Air entry value (retention curve) P0 [MPa] 3.9 3.9 8 3.9
Shape parameter (retention curve) λ 0.128 0.128 0.15 0128
Maximum suction (retention curve)* Ps [MPa] 700 700 700 700
Second shape parameter (retention curve)* λs 2.73 2.73 2.73 2.73
Residual and maximum saturation (retention curve) Srl – Srs 0 – 1 0 – 1 0 - 1 0 - 1
2 /wgD m s
* Modified Van Genuchten
Parameters and constitutive equations
CAS CEA JAEA Quint. UoE
Physical
Solid grain density ρs [kg/m3] 2710 2710 2710 2700
Porosity φ 0.165 0.16 0.162 0.16
Hydraulic
Intrinsic permeability k [m2] 7.5E-20 2E-20 2E-20 1.69E-19 1.9E-20
Dynamic viscosity μ [Pa.s] 1E-5 2.9E-4
Liquid relative permeability λ’ 0.4 0.68 0.65 0.3
Vapour diffusion coefficient 6E-6 5E-6
Mechanical
Young modulus E [GPa] 6 0.15
Poisson coefficient ν 0.27 0.3
Friction angle φ [º]
Cohesion c [MPa]
Hydro-Mech. coupling
Suction bulk modulus Ks [GPa]
Air entry value (retention curve) P0 [MPa] 3.9 3.9 8 3.9
Shape parameter (retention curve) λ 0.128 0.128 1.5 0128
Maximum suction (retention curve)* Ps [MPa] 700 700 700 700
Second shape parameter (retention curve)* λs 2.73 2.73 2.73 2.73
Residual and maximum saturation (retention curve) Srl – Srs 0 – 1 0 – 1 0 - 1 0 - 1
2 /wgD m s
* Modified Van Genuchten
Pkr k
q k S Srl e e 1 1 12
/
1.00E-25
1.00E-24
1.00E-23
1.00E-22
1.00E-21
1.00E-20
1.00E-19
1.00E-18
0 0.2 0.4 0.6 0.8 1
Degree of saturation
per
mea
bil
ity
[m2]
CASCEAJAEAQuintessaUoE
* Modified Van Genuchten
Parameters and constitutive equations
CAS CEA JAEA Quint. UoE
Physical
Solid grain density ρs [kg/m3] 2710 2710 2710 2700
Porosity φ 0.165 0.16 0.162 0.16
Hydraulic
Intrinsic permeability k [m2] 7.5E-20 2E-20 2E-20 1.69E-19 1.9E-20
Dynamic viscosity μ [Pa.s] 1E-5 2.9E-4
Liquid relative permeability λ’ 0.4 0.68 0.65 0.3
Vapour diffusion coefficient 6E-6 5E-6
Mechanical
Young modulus E [GPa] 6 0.15
Poisson coefficient ν 0.27 0.3
Friction angle φ [º]
Cohesion c [MPa]
Hydro-Mech. coupling
Suction bulk modulus Ks [GPa]
Air entry value (retention curve) P0 [MPa] 3.9 3.9 8 3.9
Shape parameter (retention curve) λ 0.128 0.128 1.5 0128
Maximum suction (retention curve)* Ps [MPa] 700 700 700 700
Second shape parameter (retention curve)* λs 2.73 2.73 2.73 2.73
Residual and maximum saturation (retention curve) Srl – Srs 0 – 1 0 – 1 0 - 1 0 - 1
k S Srl e e 1 1 12
/ i I imi iS D
273.15n
vaporm
g
TD D
P
1.00E-25
1.00E-24
1.00E-23
1.00E-22
1.00E-21
1.00E-20
1.00E-19
1.00E-18
0 0.2 0.4 0.6 0.8 1
Degree of saturation
per
mea
bil
ity
[m2]
CASCEAJAEAQuintessaUoE
2 /wgD m s
Parameters and constitutive equations
CAS CEA JAEA Quint. UoE
Physical
Solid grain density ρs [kg/m3] 2710 2710 2710 2700
Porosity φ 0.165 0.16 0.162 0.16
Hydraulic
Intrinsic permeability k [m2] 7.5E-20 2E-20 2E-20 1.69E-19 1.9E-20
Dynamic viscosity μ [Pa.s] 1E-5 2.9E-4
Liquid relative permeability λ’ 0.4 0.68 0.65 0.3
Vapour diffusion coefficient 6E-6 5E-6
Mechanical
Young modulus E [GPa] 6 0.15
Poisson coefficient ν 0.27 0.3
Friction angle φ [º]
Cohesion c [MPa]
Hydro-Mech. coupling
Suction bulk modulus Ks [GPa]
Air entry value (retention curve) P0 [MPa] 3.9 3.9 8 3.9
Shape parameter (retention curve) λ 0.128 0.128 0.15 0128
Maximum suction (retention curve)* Ps [MPa] 700 700 700 700
Second shape parameter (retention curve)* λs 2.73 2.73 2.73 2.73
Residual and maximum saturation (retention curve) Srl – Srs 0 – 1 0 – 1 0 - 1 0 - 1
2 /wgD m s
* Modified Van Genuchten
0
0.05
0.1
0.15
0.2
0.25
0.3
99.4 99.6 99.8 100 100.2 100.4 100.6
Diameter [mm]
Dis
tan
ce t
o b
ase
[m]
Initial
Sample A Diameter90º [m]
Sample B Diameter90º [m]
Sample C Diameter90º [m]
Bishop effective stress
Parameters and constitutive equations
CAS CEA JAEA Quint. UoE
Physical
Solid grain density ρs [kg/m3] 2710 2710 2710 2700
Porosity φ 0.165 0.16 0.162 0.16
Hydraulic
Intrinsic permeability k [m2] 7.5E-20 2E-20 2E-20 1.69E-19 1.9E-20
Dynamic viscosity μ [Pa.s] 1E-5 2.9E-4
Liquid relative permeability λ’ 0.4 0.68 0.65 0.3
Vapour diffusion coefficient 6E-6 5E-6
Mechanical
Young modulus E [GPa] 6 0.15
Poisson coefficient ν 0.27 0.3
Friction angle φ [º]
Cohesion c [MPa]
Hydro-Mech. coupling
Suction bulk modulus Ks [GPa]
Air entry value (retention curve) P0 [MPa] 3.9 3.9 8 3.9
Shape parameter (retention curve) λ 0.128 0.128 0.15 0128
Maximum suction (retention curve)* Ps [MPa] 700 700 700 700
Second shape parameter (retention curve)* λs 2.73 2.73 2.73 2.73
Residual and maximum saturation (retention curve) Srl – Srs 0 – 1 0 – 1 0 - 1 0 - 1
2 /wgD m s
* Modified Van Genuchten
0.1
1
10
100
1000
0 0.2 0.4 0.6 0.8 1
Degree of saturation
Pg
-Pl [
MP
a] Drying Path (Muñoz, 2003)
Wetting Path (Muñoz, 2003)
Gens (2000)
Drying path (Zhang, 2005)
Wetting path (Zhang, 2005)
Drying path (Villar, 2007)
CAS
CEA
Quintessa
Parameters and constitutive equations
CAS CEA JAEA Quint. UoE
Physical
Solid grain density ρs [kg/m3] 2710 2710 2710 2700
Porosity φ 0.165 0.16 0.162 0.16
Hydraulic
Intrinsic permeability k [m2] 7.5E-20 2E-20 2E-20 1.69E-19 1.9E-20
Dynamic viscosity μ [Pa.s] 1E-5 2.9E-4
Liquid relative permeability λ’ 0.4 0.68 0.65 0.3
Vapour diffusion coefficient 6E-6 5E-6
Mechanical
Young modulus E [GPa] 6 0.15
Poisson coefficient ν 0.27 0.3
Friction angle φ [º]
Cohesion c [MPa]
Hydro-Mech. coupling
Suction bulk modulus Ks [GPa]
Air entry value (retention curve) P0 [MPa] 3.9 3.9 8 3.9
Shape parameter (retention curve) λ 0.128 0.128 0.15 0128
Maximum suction (retention curve)* Ps [MPa] 700 700 700 700
Second shape parameter (retention curve)* λs 2.73 2.73 2.73 2.73
Residual and maximum saturation (retention curve) Srl – Srs 0 – 1 0 – 1 0 - 1 0 - 1
2 /wgD m s
* Modified Van Genuchten
0.1
1
10
100
1000
0 0.2 0.4 0.6 0.8 1
Degree of saturation
Pg
-Pl [
MP
a] Drying Path (Muñoz, 2003)
Wetting Path (Muñoz, 2003)
Gens (2000)
Drying path (Zhang, 2005)
Wetting path (Zhang, 2005)
Drying path (Villar, 2007)
JAEA
Parameters and constitutive equations
CAS CEA JAEA Quint. UoE
Physical
Solid grain density ρs [kg/m3] 2710 2710 2710 2700
Porosity φ 0.165 0.16 0.162 0.16
Hydraulic
Intrinsic permeability k [m2] 7.5E-20 2E-20 2E-20 1.69E-19 1.9E-20
Dynamic viscosity μ [Pa.s] 1E-5 2.9E-4
Liquid relative permeability λ’ 0.4 0.68 0.65 0.3
Vapour diffusion coefficient 6E-6 5E-6
Mechanical
Young modulus E [GPa] 6 0.15
Poisson coefficient ν 0.27 0.3
Friction angle φ [º]
Cohesion c [MPa]
Hydro-Mech. coupling
Suction bulk modulus Ks [GPa]
Air entry value (retention curve) P0 [MPa] 3.9 3.9 8 3.9
Shape parameter (retention curve) λ 0.128 0.128 0.15 0128
Maximum suction (retention curve)* Ps [MPa] 700 700 700 700
Second shape parameter (retention curve)* λs 2.73 2.73 2.73 2.73
Residual and maximum saturation (retention curve) Srl – Srs 0 – 1 0 – 1 0 - 1 0 - 1
2 /wgD m s
* Modified Van Genuchten
0.1
1
10
100
1000
0 0.2 0.4 0.6 0.8 1
Degree of saturation
Pg
-Pl [
MP
a] Drying Path (Muñoz, 2003)
Wetting Path (Muñoz, 2003)
Gens (2000)
Drying path (Zhang, 2005)
Wetting path (Zhang, 2005)
Drying path (Villar, 2007)
UoE
Parameters and constitutive equations
CAS CEA JAEA Quint. UoE
Physical
Solid grain density ρs [kg/m3] 2710 2710 2710 2700
Porosity φ 0.165 0.16 0.162 0.16
Hydraulic
Intrinsic permeability k [m2] 7.5E-20 2E-20 2E-20 1.69E-19 1.9E-20
Dynamic viscosity μ [Pa.s] 1E-5 2.9E-4
Liquid relative permeability λ’ 0.4 0.68 0.65 0.3
Vapour diffusion coefficient 6E-6 5E-6
Mechanical
Young modulus E [GPa] 6 0.15
Poisson coefficient ν 0.27 0.3
Friction angle φ [º]
Cohesion c [MPa]
Hydro-Mech. coupling
Suction bulk modulus Ks [GPa]
Air entry value (retention curve) P0 [MPa] 3.9 3.9 8 3.9
Shape parameter (retention curve) λ 0.128 0.128 0.15 0128
Maximum suction (retention curve)* Ps [MPa] 700 700 700 700
Second shape parameter (retention curve)* λs 2.73 2.73 2.73 2.73
Residual and maximum saturation (retention curve) Srl – Srs 0 – 1 0 – 1 0 - 1 0 - 1
2 /wgD m s
* Modified Van Genuchten
0.1
1
10
100
1000
0 0.2 0.4 0.6 0.8 1
Degree of saturation
Pg
-Pl [
MP
a] Drying Path (Muñoz, 2003)
Wetting Path (Muñoz, 2003)
Gens (2000)
Drying path (Zhang, 2005)
Wetting path (Zhang, 2005)
Drying path (Villar, 2007)
Van Genuchten fit
Parameters and constitutive equations
CAS CEA JAEA Quint. UoE
Physical
Solid grain density ρs [kg/m3] 2710 2710 2710 2700
Porosity φ 0.165 0.16 0.162 0.16
Hydraulic
Intrinsic permeability k [m2] 7.5E-20 2E-20 2E-20 1.69E-19 1.9E-20
Dynamic viscosity μ [Pa.s] 1E-5 2.9E-4
Liquid relative permeability λ’ 0.4 0.68 0.65 0.3
Vapour diffusion coefficient 6E-6 5E-6
Mechanical
Young modulus E [GPa] 6 0.15
Poisson coefficient ν 0.27 0.3
Friction angle φ [º]
Cohesion c [MPa]
Hydro-Mech. coupling
Suction bulk modulus Ks [GPa]
Air entry value (retention curve) P0 [MPa] 3.9 3.9 8 3.9
Shape parameter (retention curve) λ 0.128 0.128 0.15 0128
Maximum suction (retention curve)* Ps [MPa] 700 700 700 700
Second shape parameter (retention curve)* λs 2.73 2.73 2.73 2.73
Residual and maximum saturation (retention curve) Srl – Srs 0 – 1 0 – 1 0 - 1 0 - 1
2 /wgD m s
* Modified Van Genuchten
0.1
1
10
100
1000
0 0.2 0.4 0.6 0.8 1
Degree of saturation
Pg
-Pl [
MP
a] Drying Path (Muñoz, 2003)
Wetting Path (Muñoz, 2003)
Gens (2000)
Drying path (Zhang, 2005)
Wetting path (Zhang, 2005)
Drying path (Villar, 2007)
Van Genuchten fit
CAS
CEA
JAEA
Quintessa
UoE
Model setup
10cm
28cm
1D
No flux
Evaporation
is the process by which molecules in a liquid state (e.g. water) spontaneously become gaseous (e.g. water vapour)
wg v
0wv0g
p 100 100
pRH
Relative Humidity
is a measurement of the amount of water vapour that exists in a gaseous mixture of air and water
0exp
273.15g l ww w w
g g g ll
p p M
R T
Psychrometric law
Model setup
CAS CEA JAEA Quintessa UoE
Rel
ativ
e h
um
idit
y [%
]
20%
50%
30%
Psychrometric law
Suction
Consequences:
water outflow under liquid form
fixed degree of saturation on boundary
Model setup
CAS CEA JAEA Quintessa UoE
Rel
ativ
e h
um
idit
y [%
]
20%
50%
30%
wgg
wggg
wgj
0
wg v
0wv0g
p 100 100
pRH
Relative Humidity
Consequences:
Evaporation boundary condition
Possibility to take the rock-air interface, wind velocity, etc into account (β coefficient). Comparison with free water surface evaporation.
0
0.05
0.1
0.15
0.2
0.25
0 2 4 6 8water content [%]
dis
tan
ce t
o b
ase
[m]
CEA @ 21 days
CEA @ 99 days
CEA @ 142 days
JAEA @ 21 days
JAEA @ 99 days
JAEA @ 142 days
Quintessa @ 21 days
Quintessa @ 99 days
Quintessa @ 142 days
UoE @ 21 days
UoE @ 99 days
UoE @ 142 days
CAS @ 21 days
CAS @ 99 days
CAS @ 142 days
Initial water content
Measurements at 21 days
Measurements at 99 days
Measurements at 142 days
Comparison of the modelling results
CAS CEA JAEA Quintessa UoE21 days
0
0.05
0.1
0.15
0.2
0.25
0 2 4 6 8water content [%]
dis
tan
ce t
o b
ase
[m]
CEA @ 21 days
CEA @ 99 days
CEA @ 142 days
JAEA @ 21 days
JAEA @ 99 days
JAEA @ 142 days
Quintessa @ 21 days
Quintessa @ 99 days
Quintessa @ 142 days
UoE @ 21 days
UoE @ 99 days
UoE @ 142 days
CAS @ 21 days
CAS @ 99 days
CAS @ 142 days
Initial water content
Measurements at 21 days
Measurements at 99 days
Measurements at 142 days
Comparison of the modelling results
CAS CEA JAEA Quintessa UoE99 days
0
0.05
0.1
0.15
0.2
0.25
0 2 4 6 8water content [%]
dis
tan
ce t
o b
ase
[m]
CEA @ 21 days
CEA @ 99 days
CEA @ 142 days
JAEA @ 21 days
JAEA @ 99 days
JAEA @ 142 days
Quintessa @ 21 days
Quintessa @ 99 days
Quintessa @ 142 days
UoE @ 21 days
UoE @ 99 days
UoE @ 142 days
CAS @ 21 days
CAS @ 99 days
CAS @ 142 days
Initial water content
Measurements at 21 days
Measurements at 99 days
Measurements at 142 days
Comparison of the modelling results
CAS CEA JAEA Quintessa UoE142 days
Comparison of the modelling results
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 50 100 150Time [days]
Wat
er lo
ss [
kg]
CEA JAEA Quintessa UoE CAS Sample A Sample B Sample C
CAS CEA JAEA Quintessa UoE
Summary of the mechanisms
Evaporation
Desaturation
Reduction of the permeability
Dominant water transport mode: vapour diffusion in the gas phase (non advective)
Dominant water transport mode: Darcy flow in the liquid phase (advective)
Summary of the mechanisms
Ratio of vapour flux to liquid flux with elevations for selected times (y)
0
1
2
3
4
5
6
0 50 100 150 200 250 300
Distance from base (mm)
Rat
io V
apo
ut
flu
x to
liq
uid
fl
ux
141.902875109.9248673.94936536.974518.9870080.99931525
Quintessa
Summary of the mechanisms
Ratio of vapour flux to liquid flux with elevations for selected times (y)
0
1
2
3
4
5
6
0 50 100 150 200 250 300
Distance from base (mm)
Rat
io V
apo
ut
flu
x to
liq
uid
fl
ux
141.902875109.9248673.94936536.974518.9870080.99931525
Quintessa
0
0.05
0.1
0.15
0.2
0.25
0 2 4 6 8water content [%]
dis
tan
ce t
o b
ase
[m]
CEA @ 21 days
CEA @ 99 days
CEA @ 142 days
JAEA @ 21 days
JAEA @ 99 days
JAEA @ 142 days
Quintessa @ 21 days
Quintessa @ 99 days
Quintessa @ 142 days
UoE @ 21 days
UoE @ 99 days
UoE @ 142 days
CAS @ 21 days
CAS @ 99 days
CAS @ 142 days
Initial water content
Measurements at 21 days
Measurements at 99 days
Measurements at 142 days
Conclusions and future work
Objectives of step 0 are fulfilled:
Brainstorming about theoretical formulations to be used in Task A
Determination of a set of parameters for Opalinus Clay
Reproduction of a laboratory drying experiment (Floria et al, 2002)
Step 0 (second iteration): optional
Start of step 1 (defined in Oxford and in TaskA_description.doc)
Improvement of the models (diffusive flux of vapour and boundary
condition)
Advised common parameters (retention curve, porosity,…)