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Hydro-Mechanical Modeling of a Shaft Seal in a ... - COMSOL.com

Presented at the COMSOL Conference 2010 Boston

Hydro-Mechanical Modeling of

a Shaft Seal in

a Deep Geological Repository

D. G. Priyanto

Presented at

COMSOL Conference 2010

Boston, 2010 October 7-9

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Background

• The Nuclear Waste Management Organization’s (NWMO) Adaptive

Phased Management (APM) approach to nuclear fuel waste

management includes the isolation and containment of used nuclear

fuel in a Deep Geological Repository (DGR).

• A shaft seal is one of the engineered barriers considered in isolating

and containing used nuclear fuel in a Deep Geological Repository

(DGR).

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Shaft Sealing Concept

Shaft Sealing Concept

AECL @1993

Shaft Seal

A shaft seal

•would be installed at strategic

locations, such as significant

fracture zone.

Deep Geological Repository (DGR)

•to limit the potential for fast

movement of groundwater from

repository level to the surface

via the shaft.

Shaft Sealing Concept

AECL @ 1993

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Full-Scale Shaft Seal at AECL’s URL

(Dixon, Martino & Onagi 2009)

The objective of the seals at URL is to

limit the mixing of groundwater with

higher salinity below the FZ with

lower salinity above the FZ.

•The seal construction is funded by

Natural Resources Canada (NRCan)

under the Nuclear Legacies Liability

Program (NLLP).

•Monitoring is funded by Enhanced

Sealing Project (ESP) (NWMO,

Posiva Oy, SKB and ANDRA).

Seals at the AECL’s Underground Research

Laboratory (Martino et al. 2010)

• THM responses being monitored

include: temperatures, displacements,

strains, pore pressures, & total

pressures at selected location.

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Objective

The objective of this presentation is:

• to evaluate the capability of COMSOL to simulate the hydraulic

& mechanical (H-M) processes of a shaft seal installed at a

fracture zone in a hypothetical geosphere.

The final objective:

• to simulate all required processes of an actual shaft seal.

(e.g., coupling H, M, T, Mass transfer)

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Hypothetical Shaft Seal Geometry

2D-axisymetrical geometry

CL

100 m

Hydraulic Properties of the

Geosphere

B

100 m

K FZ-Center = 10 -9 m/s

C

3 m

K FZ-Side = 10 -10 m/s

K rocks

D

E

1 m

A

C

B

6 m

3 m

100 m

4 m 2 m

Shaft

Elevations

(250 m)

Legend

A : Bentonite-Sand Mixture (BSM)

B : Dense Backfill (DBF)

C : Concrete

D : Fractured Zone (FZ)

E : Crystalline Rocks

7.3 m

A, B, and C are in

unsaturated conditions at installation

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Stages of Numerical Modeling

1. Stage 1 simulates groundwater flow into open shaft and stress condition

prior to seal installation.

Duration: time between excavation and shaft seal installation (100 y)

2. Stage 2 simulates groundwater flow after shaft seal installation.

Duration: depending the half life of the nuclear waste (0 – 1,000,000 y)

Stage 1 Stage 2

DBF

Open shaft

C

100 y

CS

C

BSM

CS

0-1,000,000 y

DBF

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Challenges

Challenge 1

Sealing components are initially unsaturated,

• Clay-based sealing components have large volume change

coupling of the unsaturated flow with structural mechanics

Challenge 2

• Properties and conditions at the seal location change abruptly

between Stages 1 and 2.

Challenge 3

• The durations of Stages 1 and 2 considered in this study are

anticipated to be in order of 100 years to 1,000, 000 years.

reasonable solution time

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Coupling of HM Formulation for

Unsaturated Soil

Detailed formulations are provided in

(Priyanto 2010)

H

p

C

SeS

KH

p

D Qs

S

t

S = f g ( p + f )

k

e

sat

w

k

0



3

1

1



1

H





1

m


C 1

m



0



s


p


2

n



1




m

K


2

0

3

0

for

for


1

S


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r

S

e

1

m

k sat

k

w r

H

e

H

1

m

p

p




0

0

m

for

for

H

H

p

p

0

0

100 mm

•Unsaturated flow = Richard’s equation

with vanGenuchten’s SWCC and

permeability models.

Mechanical = Linear elastic model

•Compare with laboratory triaxial test of

CL

the Bentonite-Sand CL

Impermeable Mixture (BSM)

CL

50 mm

y

Triaxial Specimen

(a)

50 mm

x

Symmetry

Symmetry

line

CL

y

Impermeable

Symmetry

u w = 0.2 MPa

x

Symmetry

No flow

at symmetry Impermeable line

Initial

u w = 0.2 MPa

u a = 0.101 MPa

w c = 18.75%

(b)

Hydraulic

Impermeable

Initial

u a = 0.101 MPa

w c = 18.75%

CL

y

Initial

p = 0.5 MPa

Symmetry

No y-displacement

at symmetry line

Initial

p = 0.5 MPa

Symmetry

x

(c)

Mechanical

9


Results of HM Numerical Modeling

of Unsaturated BSM Specimen

Dry density

CL

Impermeable

CL

X = 0 cm

100 mm

CL

50 mm

y

Triaxial Specimen

(a)

50 mm

x

Symmetry

Symmetry

line

CL

y

Impermeable

Symmetry

u w = 0.2 MPa

No flow

at symmetry Impermeable line

Initial

u w = 0.2 MPa

u a = 0.101 MPa

w c = 18.75%

(b)

x

Impermeable

Initial

u a = 0.101 MPa

w c = 18.75%

CL

y

Initial

p = 0.5 MPa

X = 0.5 cm

X = 1.0 cm

X = 1.5 cm

X = 2.0 cm

X = 2.5 cm

Symmetry

Symmetry

Degree of saturation

Symmetry

No y-displacement

at symmetry line

Initial

p = 0.5 MPa

(c)

x

X = 0 cm

X = 0.5 cm

X = 1.0 cm

X = 1.5 cm

X = 2.0 cm

Volume of Water Added (mL)

18

16

14

12

10

8

6

4

2

0

Volume of water added

to the specimen

Laboratory Test

COMSOL

0 2 4 6 8 10

Time (days)

X = 2.5 cm

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H-M Modeling of Shaft Seal

CL

100 m

Hydraulic Properties of the

Geosphere

B

100 m

K FZ-Center = 10 -9 m/s

C

3 m

K FZ-Side = 10 -10 m/s

K rocks

D

E

1 m

A

C

B

6 m

3 m

100 m

4 m 2 m

Shaft

Elevations

(250 m)

Legend

A : Bentonite-Sand Mixture (BSM)

B : Dense Backfill (DBF)

C : Concrete

D : Fractured Zone (FZ)

E : Crystalline Rocks

7.3 m

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Porewater Pressure, Stage 1

Stage 1, groundwater flow into open shaft

0 1 10 100

[Years]

Note that this results is only valid for the hypothetical assumptions

and properties used in this study.

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Porewater Pressure, Stage 2

(0-100 years)

Stage 2, groundwater flow into shaft seal

0 1 10 80 100

[Years]

Note that this results is only valid for the hypothetical assumptions

and properties used in this study.

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Porewater Pressure, Stage 2

(1e3-1e6 years)

Stage 2, groundwater flow into shaft seal

1,000 10,000 100,000 1,000,000

[Years]

Note that this results is only valid for the hypothetical assumptions

and properties used in this study.

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Porewater Pressure, Stage 2

Stage 2, groundwater flow into shaft seal

0 1 10 20 40

Note that this results is only valid for the hypothetical

assumptions and properties used in this study.

60 80 90 100 1,000

[Years]

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Saturation Degree and Dry Density

of the BSM

DBF

CS

C

BSM

r

CS

DBF

Time (Years)

1E-03 1E-02 1E-01 1E+00 1E+01 1E+02 1E+03

2.2

2.1

2.0

1.9

1.8

1.7

1.6

1.5

Dry Density [Mg/m 3 ]

Case 5:

MFR

r = 0

r = 1 m

r = 2 m

r = 3 m

r = 3.65 m

Note that this results is only valid for the hypothetical assumptions

and properties used in this study.

Time (Years)

1E-03 1E-02 1E-01 1E+00 1E+01 1E+02 1E+03

100

95

90

85

80

75

70

65

60

Degree of Saturation [%]

Case 5:

MFR

r = 0

r = 1 m

r = 2 m

r = 3 m

r = 3.65 m

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Conclusions

• This study has developed custom-additions in COMSOL

– to couple Richard’s equation and linear elastic model

– to implement a custom SWCC and permeability model observed from

the results of laboratory testing of the bentonite-sand mixture

specimens.

• The results of the numerical modeling of a shaft seal using COMSOL shows

a logical hydraulic and mechanical processes, which indicated that

COMSOL can be used as a tool for further study of a shaft seal in a deep

geological repository.

• Using current computer capability, the solution time required to complete the

analysis to simulate 1000000 years HM behavior of a shaft seal described in

this study was less than 1 hour, which is beneficial in building more complex

model and formulations to simulate an actual shaft seal in actual geosphere

conditions.

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Recommendations

• Future studies recommended to improve simulation of a shaft seal

includes:

– Development of coupling formulation of multi-phase flow with

mechanical constitutive model to improve HM simulation.

– Coupling between HM processes with other processes such as

thermal and mass transport.

– Implementation of elasto-plastic model.

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Thank you !

Acknowledgements

Hydro-Mechanical Modeling of a Shaft Seal in a Deep Geological Repository

Atomic Energy of Canada Limited (AECL)

D. G. Priyanto

Nuclear Waste Management Organization (NWMO)

COMSOL Conference 2010

Boston, 2010 October 7-9

AECL personnel, especially:

David Dixon, Paul Thompson, Peter Sargent,

Chang-Seok Kim, Blake Holowick,

Maureen MacDonald & Marlene Hall.

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