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%

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,…)