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

Presented at the **COMSOL** Conference 2010 Boston

**Hydro**-**Mechanical** **Model ing**

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 **in**cludes the isolation and conta**in**ment **of** used nuclear

fuel **in** a Deep Geological Repository (DGR).

• A shaft seal is one **of** the eng**in**eered barriers considered **in** isolat**in**g

and conta**in****in**g used nuclear fuel **in** a Deep Geological Repository

(DGR).

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**Shaft** **Seal****in**g Concept

**Shaft** **Seal****in**g Concept

AECL @1993

**Shaft** **Seal**

A shaft seal

•would be **in**stalled 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** **Seal****in**g Concept

AECL @ 1993

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Full-Scale **Shaft** **Seal** at AECL’s URL

(Dixon, Mart**in**o & Onagi 2009)

The objective **of** the seals at URL is to

limit the mix**in**g **of** groundwater with

higher sal**in**ity below the FZ with

lower sal**in**ity above the FZ.

•The seal construction is funded by

Natural Resources Canada (NRCan)

under the Nuclear Legacies Liability

Program (NLLP).

•Monitor**in**g is funded by Enhanced

**Seal****in**g Project (ESP) (NWMO,

Posiva Oy, SKB and ANDRA).

**Seal**s at the AECL’s Underground Research

Laboratory (Mart**in**o et al. 2010)

• THM responses be**in**g monitored

**in**clude: temperatures, displacements,

stra**in**s, 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 **in**stalled at a

fracture zone **in** a hypothetical geosphere.

The f**in**al objective:

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

(e.g., coupl**in**g 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 : Crystall**in**e Rocks

7.3 m

A, B, and C are **in**

unsaturated conditions at **in**stallation

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Stages **of** Numerical **Model ing**

1. Stage 1 simulates groundwater flow **in**to open shaft and stress condition

prior to seal **in**stallation.

Duration: time between excavation and shaft seal **in**stallation (100 y)

2. Stage 2 simulates groundwater flow after shaft seal **in**stallation.

Duration: depend**in**g 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

• **Seal****in**g **com**ponents are **in**itially unsaturated,

• Clay-based seal**in**g **com**ponents have large volume change

coupl**in**g **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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Coupl**in**g **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** = L**in**ear 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

l**in**e

CL

y

Impermeable

Symmetry

u w = 0.2 MPa

x

Symmetry

No flow

at symmetry Impermeable l**in**e

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 l**in**e

Initial

p = 0.5 MPa

Symmetry

x

(c)

**Mechanical**

9

Results **of** HM Numerical **Model ing**

**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

l**in**e

CL

y

Impermeable

Symmetry

u w = 0.2 MPa

No flow

at symmetry Impermeable l**in**e

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 l**in**e

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 **Model ing**

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 : Crystall**in**e Rocks

7.3 m

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Porewater Pressure, Stage 1

Stage 1, groundwater flow **in**to 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 **in**to 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 **in**to 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 **in**to 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 l**in**ear elastic model

– to implement a custom SWCC and permeability model observed from

the results **of** laboratory test**in**g **of** the bentonite-sand mixture

specimens.

• The results **of** the numerical model**in**g **of** a shaft seal us**in**g **COMSOL** shows

a logical hydraulic and mechanical processes, which **in**dicated that

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

geological repository.

• Us**in**g current **com**puter capability, the solution time required to **com**plete 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** build**in**g more **com**plex

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

conditions.

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Re**com**mendations

• Future studies re**com**mended to improve simulation **of** a shaft seal

**in**cludes:

– Development **of** coupl**in**g formulation **of** multi-phase flow with

mechanical constitutive model to improve HM simulation.

– Coupl**in**g 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** **Model ing**

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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