Developments in a Coupled Thermal- Hydraulic … · Design phase - Half scale test - Supercontainer CHM: Impact of bitumen waste on Boom clay H, CM , CH: ... Hydraulic Thermal osmosis

Copyright © 2013 SCK•CEN

COMSOL ConferenceRotterdam 2013

Developments in a Coupled Thermal-Hydraulic-Chemical-Geomechanical Model

for Soil and Concrete

S.C. Seetharam* and D. Jacques24th October 2013

*[email protected]

1

(Belgian Nuclear Research Centre)



Outline

Potential applications

Objective

Governing equations

COMSOL-MATLAB

Sample Benchmarks

Conclusions and perspectives

2



Potential applications

Significant experimental and numerical research on coupled THCM behaviour for soil and concrete applications.

Current interest

Nuclear waste repository

PetroleumGround freezing

Geotechnical in general

3

Deep disposal

Near-Surface disposal



Potential applications…

THCM:In situ Processes in deep disposal repository in Boom Clay

4

THMDesign phase -Half scale test -Supercontainer

CHM:Impact of bitumen waste on Boom clay

H, CM , CH:Near surface disposal concept based on concrete as predominant materialhttp://science.sckcen.be/en/Institutes_groups/EHS



Well known process interaction matrix for Porous media applications

Temperature Hydraulic Chemical Mechanical

Temperature Conduction(Fourier‘s Law)

Convection Dufour effect Volumetric deformation

Hydraulic Thermal osmosis Pressure flow(Darcy‘s law)

Chemical osmosis Volumetric deformation

Chemical Soret effect Advection Diffusion(Fick‘s

Law)+Reactions

Volumetric deformation

Mechanical Thermal expansion Swelling/Shrinkage Swelling/Shrinkage Stress/Strain Equilibrium

5



Objective

Develop a generic fully coupled THCM model within COMSOL-MATLAB environment

6

THCM Model(COMSOL)

Geochemical ModelSource term for the "C

component"(e.g. PHREEQC)



Governing equations

THERMAL

HYDRAULIC (GEO)MECHANICAL

CHEMICAL

PORE WATER

PORE GAS

Stress equilibrium

Energy conservation

Mass conservationMass conservation – pore gas pressure

Mass conservation – pore water pressure

7

Weakly or Strongly coupled

1 ps s

pl l l r g v

pv g v pda g da

pl l pv g vl g v r

pda g da

n C

C S T T LnSn

C S C S

tC C

T L T TC

lv

v vv v

v

0.

. .

v gl ll l m

l v g

K zt t

vv v

.g da dada g g g a

g

Dt

v

. ln

ln

l i

i i ii i e

i i i i

i i i ii

ct

D z FcD cRT

D c RD c c

T cT

lv

0

l e

li i

F c z

ELECTROCHEMICAL

Charge conservation

. 0f sP P th ieC : ε - ε - ε I I b



Inbuilt solute interface(introduce cross

coupling terms using source term)

PDE form(based on

equations in slide 7)

Implementation

T

HPf

Pg

3 governing equations (TH)

C

Multi-component (as many governing equations as the number of chemicals, Ci)

8

Inbuilt solid mechanics interface

(introduce cross coupling terms (e.g. pore water

pressure) and geomechanical constitutive laws applicable for

soil and concrete)M

Geomechanical (M)

Implemented soil models (useful for describing Boom clay behaviour) using COMSOL's generic plasticity feature:• Mohr-Coulomb• Drucker-Prager• Etc…

Dilute species model used because it offers numerical stability schemes – this means

the formulation requires further adaptation to include porosity



Benchmark 1

Infiltration under isothermal conditions (Hydro-mechanical coupling)

9

.l ll l mK z

t

. 0f sP P C : ε I I b



Infiltration under isothermal conditions…

Test equipment (CIEMAT, Spain) and model idealisation for the infiltration experiment under isothermal conditions

Degree of saturation

10

0102030405060708090

100

0 5000 10000 15000 20000 25000 30000

Rel

aive

hum

idity

(%)

Time (Hours)

z = 10 cm (COMSOL)z = 20 cm (COMSOL)z = 30 cm (COMSOL)z = 30 cm (measured)z = 20 cm (measured)z = 10 cm (measured)

Porosity: COMSOL (left) and Chen et al. (right) – scale not same

Linear elasticity

Nonlinear elasticity



Benchmark 2

THM response of the in-situ ATLAS III Experiment

11

1 ps s

rpl l l

pl l r

n CT T

n C S T

tT C T T

lv

. 0sP th ieC : ε - ε - ε I

.l ll l m

TK T

t



Conceptual model and data

Boom clay

Pore pressure fixed = 4.5 MPa

Key features:

• Fully coupled THM

• Axisymmetric

• Fully saturated

• Viscosity and density as a function of temperature

• Thermo-Elasto-plastic (Drucker Prager) model

• Two materials = steel + boom clay

• COMSOL computation time = 0.5 hours

12Chen and Li, 2009

2 3 sin3 sin

f J p c ctg

2 3 sin3 sin

g J p c ctg



Temperature and pore water pressure evolution

13



Radial displacement, mean effective stress and plastic strain

14

Note: Plastic region is insignificant and hence not shown (limited to few elements in the domain.



Benchmark 3

Chemo-osmotic flow

15

0.l ll l mK

t

.l ii i i

cD c c

t

lv



Keijzer’s experiment

16

0

1000

2000

3000

4000

5000

6000

7000

8000

0.00E+00 5.00E+05 1.00E+06 1.50E+06 2.00E+06

Pore

wat

er p

ress

ure

(Pa)

Time (seconds)

COMSOL

Measured (Bader andKooi, 2005)

Pressure evolution at the interface between the left porous stone and the clay

Clay zone

Transient pressure profile



Benchmark 3

Reactive transport (COMSOL-MATLAB)

17

.l ii i i i

cD c c R

t

lv

Phreeqc coupling via MATLAB – use sequential non-iterative approach (other approaches also tried, no difference for the specific problems chosen)



Ion exchange, Mineral dissolution verifications

18

CaCl2

Na-K-NO32-

+Exchanger

OutletInlet

Comparison made with open source code HP1, developed at SCK-CEN

Portlandite dissolution

Note: More complex chemistry successfully demonstrated in a forthcoming journal publication

Ca ≈ 20 mM, pH ≈ 12.5

Initial portlandite=4 mMLow pH

boundary

Advection-diffusion

Diffusion only

Input data: Patel, R.A., Perko, J., Jacques, D., De Schutter, G., Breugel, K. V., Ye, G. , 2013. A versatile pore-scale multicomponent reactive transport approach based on Lattice Boltzmann Method: Application to cementitious systems. Jour. Phy. and Chem. of the Earth (submitted)

0

1

2

3

4

5

0 20 40 60 80

Portland

ite (m

M)

Time (hrs.)

COMSOL

PHREEQC



Conclusions and perspectives

Model implementation and benchmark results highly encouraging.

Further work ongoing in terms of chemo-mechanical coupling, plus more and more verifications/validations.

Computational constraints especially iterating between COMSOL-MATLAB. Perhaps COMSOL can consider this in future versions.

COMSOL: easy to implement and serves as a powerful research tool.

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SCK•CENStudiecentrum voor Kernenergie

Centre d'Etude de l'Energie NucléaireBelgian Nuclear Research Centre

Stichting van Openbaar Nut Fondation d'Utilité PubliqueFoundation of Public Utility

Registered Office: Avenue Herrmann-Debrouxlaan 40 – BE-1160 BRUSSELSOperational Office: Boeretang 200 – BE-2400 MOL

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Documents

Developments in a Coupled Thermal- Hydraulic … · Design phase - Half scale test - Supercontainer CHM: Impact of bitumen waste on Boom clay H, CM , CH: ... Hydraulic Thermal osmosis