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Page 1 Modeling coupled processes Solving multi‐field problems with object‐ oriented numerical methods Application examples in geotechnics and hydrology Olaf Kolditz
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Modeling coupled processesSolving multi‐field problems with object‐oriented numerical methodsApplication examples in geotechnics and hydrology
Olaf Kolditz
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Variety of problems
T
H
M
C
Yajie Wu
Karsten Rink
Thomas KalbacherNorbert Böttcher
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GeothermalEnergy
GeotechnicalSystems
WaterQuality
Water Resources
Variety of geoscientific problem requires system analysis
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OutlineIntroduction / Motivation• Geotechnics• Hydrology, soil science
Governing equations
Software issues• Object‐oriented methods• HPC and visualization
Applications• CO2 sequestration• Nuclear waste deposition• Coupled hydrosystems• Geothermal energy (Norihiro Watanabe)
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HIGRADE Course onTHM Mechanics
http://www.ufz.de/index.php?en=17985
HIGRADE Course 2011onReactive Transport
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Continuum Mechanics
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Heat transport
Fluid flow
Reactive transport
Deformation
Hydraulics
Chemistry
Mechanics
Thermodynamics
Multi‐Physics: THMC coupled processes
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Porous Media: Phases and Components
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Theoretical background:Heat transport in porous media (T)
Governing equation
Boundary and initial conditions
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Theoretical background:Non‐isothermal flow in porous media (H)
Governing equation
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Theoretical background:Non‐isothermal flow in porous media (H)
Boundary and initial conditions
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Theoretical background:Deformation in porous media (M)
Governing equation
Boundary and initial conditions
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Constitutive theoryWang, Görke et al. (2007‐10)
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Constitutive theoryWang, Görke et al. (2007‐10)
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Constitutive theoryWang, Görke et al. (2007‐10)
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Constitutive theoryWang, Görke et al. (2007‐10)
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Governing Equations
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EOSEquations of state
Böttcher et al. (2010)
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GOVERNING EQUATIONSH3 Problem
gf
gfs
gf
h
qt
h
∇−=
=⋅∇+∂∂
Kq
q
gf
gfφ
( )zk
qtS
r
sfs
+Ψ∇−=
=⋅∇+∂∂
Kq
q
sf
sfφ
ofj
s
l
ofs
aa
hS
CH
qt
H
∇−=
=⋅∇+∂∂
−
+
1
1of
of
q
qφ
Diffusive wave surface flow
Richards flow in soil Groundwater flow in aquifer
10 ≤≤ aφ
Borden AquiferOK et al. (JHI 2008)
Jens‐Olaf Delfs
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Computational Mechanics
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Finite element approach:Weak forms with the test function
Heat balance equation (T)Mass balance equation (H)Momentum balance equation (M)
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Finite element approach:Applying the Galerkin method to the weak forms leads to the coupling equations
Thermal and hydraulic equations
•Mass and Laplace matrices
Mechanical equation
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Finite element approach:The derived coupling equations are solved in the problem‐dependent staggered/monolithic manner
H1H2
M
T
H1H2
M
T
Heat emitting waste CO2
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Numerical Methods ‐ Summary
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OO Software ConceptHPC Developments and Applications
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Heat transport
Fluid flow
Reactive transport
Deformation
Hydraulics
Chemistry
Mechanics
Thermodynamics
Multi‐Physics: THMC coupled processes
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Version 4: Object‐Orientationfor Multifield Problems
PCS
MSH
GEO
GeometryPointsPolylinesSurfacesVolumesDomains
TopologyNOD NodesELE Meshes
IC BC ST
MATMFPMSPMMPMCP
NUM
FEMFDMFVM
FCT
I/O
CProcess::Create()CProcess::Config()CProcess::Execute()
EQS
Kolditz & Bauer (2004)J Hydroinformatics
Source code reduction: 10 (V3) ‐> 3 MB (V4)
Ax = b
x = A‐1b
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OO‐ELEElement Objects
Wang & Kolditz (2007)J Num Methods Eng
Version 4.4 – OO‐FEM
Aij(xj)xi = bi
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Processor 0
...
Processor 1 Processor n
Version 4.5 – MPI‐FEM
• MPI parallelization
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MPI‐Efficiency for THM coupled problems
Wenqing Wang
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MPI‐Efficiency for THM coupled problems
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MPI‐Efficiency for THM coupled problems
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Version 4.7 – OpenMP
Theory vs. OpenMP
0
10
20
30
40
50
60
70
80
90
100
110
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Number of Threads
% ti
me
in c
ompu
tatio
n
ICC Real time Theory
OpenMP OpenMP OpenMP
MPI MPI
SMP Node
• OpenMP parallelization
• Hybrid parallelization (GRID computing)
Test bed (8 x DualCore)
Simple test example
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• SX6 (HLRS)0.3 TFlop/s
• SX8 (HLRS)15 TFlop/s
• Cray XT3 (PSI)8.5 TFlop/s, 1664 CPUs
• BlueGene/L (FZJ)Test node
• LiClus (UFZ)256 CPUs (QuadCore)
• Strider (HLRS)256 Opteron CPUs
• Merlin 3 (PSI)256 Opteron CPUs
• HYDRA (ZAG)8 AMD Opteron CPUs
HPC Platforms
Linux ClusterSuper‐Computer
NEC‐SX8HYDRA
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Flexibility of OO codes, but …
THMCcoupling
Surface/subsurfacecouplingFracture networks
OpenMP
MPI
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Monte‐Carlo simulation on Parallel Clusters
Measurements
THM model
Stochastic reservoir model
Virtual reservoir1 …
Prediction1
Virtual reservoir2 Virtual reservoir N
Scenario / Assumptions
Prediction2 Prediction N…
Statistical property of sample data
Data analysis
THM model THM modelParallelization
Norihiro Watanabe
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(Parallel) Threading for Root‐Soil SystemsThomas Kalbacher
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Geochemical SimulatorsCoupled to OGS
MultiCompTransport
CHEMAPP
?FlexibleThermodynamics(High T, high C)
Special Data for nuclideThermodynamicsSorption & desorptionUncertainty
EQlinkPHREEQC
World wide distributedAquatic geochemistryLow T, low C, kineticFree code
BRNS
BiogeochemicalMicrobiologicalprocesses
GEMS
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PHREEQC ChemApp
BRNS GEMS
OGS Focus ‐ Reactive Transport
HIGRADE Course 2011: Reactive Transport
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Maintenance of scientific software ‐ OpenSource
(6 Partners from 4 countriesIn all about 100 people)
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Plattform‐independent: CMakeAutomated benchmarking: CTestScientific Visualization 3D data explorer: Qt
OGS 5 – a scientific open source project
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TESSIN ‐ Helmholtz Topic Center for Terrestrial Environmental System Simulation and INtegration
Data modelingHigh performance computingScientitic visualization
Water resourcesGeotechnics (CO2)Geothermal energyLandscape modeling
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Process UnderstandingBenchmarks / Code comparisonReal Applications
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Multiphase flow (H2)Chan‐Hee Park, Wenqing Wang
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3D multiphase flow
Chan‐Hee Park
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Known Numerical Issues and Workarounds: Multiphase flow
Local mass conservatory method• Finite difference method • Finite volume method• Mixed‐finite element method
Non‐local mass conservatory method• Standard Galerkin finite element method
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Primary Variables:Multiphase flow
Oil science: Pw and Pnw
Soil science: Pc and Pnw
Water resources science: Pw and Sw or Snw
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H2(PwSnw and PcPnw): Kueper’s Experiment ‐Heterogeneity (Water and Oil)
Selection of primary variables … don‘t forget about physics
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H2 (PwSnw): CO2 workshop in Stuttgart Germany 2008 (Water and CO2)
Is CO2 wetting or non‐wetting to media of our interests?
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Multiphase flow (H2T)Non‐isothermal effectsNorbert Böttcher, Ashok Singh
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Test case definition
for supercritical fluids(Böttcher et al. 2010)
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Non‐isothermal effects for supercritical fluids
for supercritical fluids(Böttcher et al. 2010)
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Multiphase flow consolidation (H2M)Defining test casesJoshua Taron, Uwe Görke
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Known Numerical Issues and Workarounds: Conversion of primary variables on nodal points to cell centers or the other way around
What if mechanical deformation is involved?• Merge of FEM and FVM or FDM
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A benchmark proposal for H2M ‐ Definition
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H2M: German test site for CO2 storage in deformable media
Fluid properties Medium properties
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A benchmark proposal for H2M ‐ Results
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A benchmark proposal for H2M ‐ Results
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Multiphase flow consolidation (H2M)Shear slip during CO2 injection
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H2M Problem Definition:
Shale
Sandstone
3 km
100 m
4 m
6 m
σV=76.5 MPa
σH=0.6σv
Line source of CO2 injection: 500 tones per year
Vertical cross-section at 3 km depth
100 m
1 km
∆x=1m and ∆z=0.5m
{pw=31 MPa and Snw=0} or {pc=19 kPa and pnw=pw+pc}
1 mqnw(50,1)= 1.87e-3 m3/day
σH=0.6σv
x
z
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CO2 Saturation with 20 Years of the Injection
1 year
10 years
20 years
100 years
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Safety Factors for Shear Slip Failure:The realistic failure mode
1 year
10 years
20 years
100 years
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A systematic for CO2 benchmarking #1 Processes
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A systematic for CO2 benchmarking #3 Scenarios
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Multiphase flow consolidation (TH2M)Non‐isothermal effects
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DECOVALEXDECOVALEX‐‐IV IV TaskTask DD
DEvelopment of COupled modelsAnd their VAlidation against EXperiments
Task D – Teams:DOE/LBNL Lawrence Berkeley National LaboratoryCAS Chinese Academy of ScienceJAEA/JNC Japan Atomic Energy Agency
Japan Nuclear Cycle Develoment Inst.Hazama Corporation
BGR/UFZ Federal Institut for GeosciencesHelmholtz Center forEnvironmental Sciences
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THM1/2 Task Definitions
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Geomechanical ProcessesShort‐Term Effects
Significant geomechanical effects are expected in response to heat release from the decaying radioactive waste
FEBEX type:
Drying / wetting of bentoniteinduces shrinkage and swelling in thebuffer
Yucca Mountain type:
High temperature dryout zone byboiling effects
Thermally induced stresses will act upon rock mass:
thermal expansion effects might be recoverable but …
Final DECOVALEX‐IV Reporting (Birkholzer et al. 2008)
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Geomechanical ProcessesLong‐Term Effects
thermal stresses may lead to irreversible impacts
Changes in the stress field during the heating period can lead to inelastic mechanical response induced by fracture shear slip or crushing of fracture asperities
Elevated temperatures and stresses will be maintained for long time periods ‐> increased microcracking, crack growth
‐> irreversible changes
in hydraulic properties
Final DECOVALEX‐IV Reporting (Birkholzer et al. 2008)
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THM Simulations ‐ T Process
THM1‐FEBEX THM1‐YuccaMountain
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THM Simulations ‐M Process
THM1‐FEBEX THM1‐YuccaMountain
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THM Simulations ‐ H ProcessTHM1‐FEBEX THM1‐YuccaMountain
Stress dependent
permeability
changes
for Yucca Mountain
type
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THM Teams – Flow models
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Time [Year] (Log scaling)
Satu
ratio
n
10-3 10-2 10-1 100 101 102 103 104 105 1060.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
Present multi-phase modelRichards model
Time [Year] (Log scaling)
Air
pres
sure
[Pa]
10-3 10-2 10-1 100 101 102 103 104 105 1060.0E+00
2.0E+06
4.0E+06
6.0E+06
8.0E+06
1.0E+07
V1V2
Richards vs Two‐Phase Flow
Special Issue(2009)
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Richards vs Two‐Phase Flow
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Richards vs Two‐Phase Flow
Intrinsic permeability10‐13m2
Intrinsic permeability10‐18m2
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Richards vs Two‐Phase Flow
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Reactive Transport
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Results of THC Simulations1D‐TestMineral
Abundances
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Richards vs. Two‐Phase‐Flow Models
Figure 20: Alteration of Annite and Pyrite, Multiphase flow / Richards flow
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Reactive nuclide transport
120 species have to beconsidered to represent thegeochemical system
non‐ideal solid solutions
60 in PSI data base Haibing Shao (PhD thesis 2010)
Reactive TransportNuclear Waste Deposition
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Approaching the RealityGeometry matters …
Björn Zehner, Lars Bilke
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HPC in real applications of THM codes
Whiteshell URLCanada
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HPC in real applications of THM codes
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HPC in real applications of THM codes
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PresentationNorihiroWatanabe
Geothermal reservoir simulation
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Benchmarking projects in
CO2 storage: CO2BENCH
Hydrology: HNBENCH
Geothermics: GEOBENCH
BENCHMARKING
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Conclusions
Community efforts are necessary …• Observation & Data assimilation• Conceptual modelling• Numerical methods• Computer sciences• Open source philosophy• Transparent and efficient work platforms• Cooperation between NLs and Universities• …Computer power & man power …• more complexity must coincide with a better understanding
• …
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Thank you for your attention
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Hydrology II
TERENOwww.tereno.net
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Database
Bode ModelWork flow
Karsten RinkFeng Sun
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BODE BASINSELKE CATCHMENT
OGS‐DE
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SELKE CATCHMENTFirst results
mHM: Groundwater recharge OGS: Groundwater discharge
Wenqing WangLuis SamaniegoJens Delfs
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Hydrology I Yajie Wu
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106 grid nodes
Density‐dependent flow
