developments in a coupled thermal- hydraulic … · design phase - half scale test - supercontainer...
TRANSCRIPT
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
1
(Belgian Nuclear Research Centre)
Copyright © 2013 SCK•CEN
COMSOL ConferenceRotterdam 2013
Outline
Potential applications
Objective
Governing equations
COMSOL-MATLAB
Sample Benchmarks
Conclusions and perspectives
2
Copyright © 2013 SCK•CEN
COMSOL ConferenceRotterdam 2013
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
Copyright © 2013 SCK•CEN
COMSOL ConferenceRotterdam 2013
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
Copyright © 2013 SCK•CEN
COMSOL ConferenceRotterdam 2013
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
Copyright © 2013 SCK•CEN
COMSOL ConferenceRotterdam 2013
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)
Copyright © 2013 SCK•CEN
COMSOL ConferenceRotterdam 2013
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
Copyright © 2013 SCK•CEN
COMSOL ConferenceRotterdam 2013
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
Copyright © 2013 SCK•CEN
COMSOL ConferenceRotterdam 2013
Benchmark 1
Infiltration under isothermal conditions (Hydro-mechanical coupling)
9
.l ll l mK z
t
. 0f sP P C : ε I I b
Copyright © 2013 SCK•CEN
COMSOL ConferenceRotterdam 2013
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
Copyright © 2013 SCK•CEN
COMSOL ConferenceRotterdam 2013
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
Copyright © 2013 SCK•CEN
COMSOL ConferenceRotterdam 2013
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
Copyright © 2013 SCK•CEN
COMSOL ConferenceRotterdam 2013
Temperature and pore water pressure evolution
13
Copyright © 2013 SCK•CEN
COMSOL ConferenceRotterdam 2013
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.
Copyright © 2013 SCK•CEN
COMSOL ConferenceRotterdam 2013
Benchmark 3
Chemo-osmotic flow
15
0.l ll l mK
t
.l ii i i
cD c c
t
lv
Copyright © 2013 SCK•CEN
COMSOL ConferenceRotterdam 2013
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
Copyright © 2013 SCK•CEN
COMSOL ConferenceRotterdam 2013
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)
Copyright © 2013 SCK•CEN
COMSOL ConferenceRotterdam 2013
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
Copyright © 2013 SCK•CEN
COMSOL ConferenceRotterdam 2013
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.
19
Copyright © 2013 SCK•CEN
COMSOL ConferenceRotterdam 2013
Copyright © 2013 - SCKCEN
PLEASE NOTE!This presentation contains data, information and formats for dedicated use ONLY and may not be copied,
distributed or cited without the explicit permission of the SCK•CEN. If this has been obtained, please reference it as a “personal communication. By courtesy of SCK•CEN”.
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
20