TRM@OGS: Thermo-Richards-Mechanics
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L A T E X Tik Zposter TRM@OGS: Thermo-Richards-Mechanics Sonja Kaiser, J ¨ org Buchwald, Wenqing Wang, Dmitri Naumov, Thomas Nagel TRM@OGS: Thermo-Richards-Mechanics Sonja Kaiser, J ¨ org Buchwald, Wenqing Wang, Dmitri Naumov, Thomas Nagel TRM Concept & Overview Motivation and URL Link Quantitative evaluation of Thermo-Hydro-Mechanical (THM) processes are essential in the course of barrier integrity analyses and for safety assessment in general. THM processes are studied in several laboratory and in-situ experiments such as heater experiments in sev- eral Underground Research Laboratories (URL) such as in Mont Terri (Switzerland, the figure left shows a plane view including various experiments in the old and new galleries). The Full-Scale Emplacement (FE) experiment in Mont Terri is of particular interest for study of THM pro- cesses in Opalinus clay and was selected as Task C in the current DECOVALEX 2023 phase. Figure sources: swisstopo, visualization by Karsten Rink (UFZ) Benchmarking Concept The benchmarking concept is organized in a hierarchic way with an increasing complexity: ‚ Single processes (T,R,M), ‚ binary processes (TR, TM, RM), ‚ and finally the trinary TRM (Thermo-Richards-Mechanics) process. for a systematic testing of all possible couplings (see also companion poster on TH 2 M processes by Grunwald et al.). The generic approach allows the evaluation of various hydraulic processes (single phase flow, unsaturated (Richards) flow, and two-phase flow) in the context of thermal and mechanical interactions. Governing Equations Energy balance: p%c p q B T B t ´ ∇ ´ ´λ eff T ∇ T ` φ% L c p l T v L ` φ% v c p v T v L ¯ “ Q T Mass balance: φ „ p% L ´ % v q B S B p `p1 ´ S q B % v B p ` % L β p d S p dt ` „ φp1 ´ S q B % v B T ´ % L ´ φSα L T ` 3pα B ´ φqα S T ¯ d S T dt ` ∇ ¨pq L ` q v q` S% L p∇ ¨ 9 uq“ Q H Momentum balance: ∇ ¨ ´ σ eff ´ α B Sp I ¯ ` %g “ 0 with 9 σ eff “ C:p 9 ´ 9 th ´ 9 inel ´ 9 sw q Literature References [1] W. Wang et al. “Non-isothermal flow in low permeable porous media: A comparison of Richards’ and two-phase flow approaches” . In: Environmental Earth Sciences 62.6 (2011). cited By 52, pp. 1197–1207. DOI: 10.1007/s12665-010-0608-1. URL: https://www.scopus.com/inward/record.uri? eid=2-s2.0-79952073715&doi=10.1007%2fs12665-010-0608-1&partnerID=40&md5=41dca1366e09b40cfb6dd784e6fb7a2c. [2] X. Wang et al. “Numerical analysis of thermal impact on hydro-mechanical properties of clay” . In: Journal of Rock Mechanics and Geotechnical Engineering 6.5 (2014). cited By 13, pp. 405–416. DOI: 10.1016/j.jrmge.2014.07.002. URL: https://www.scopus.com/inward/record.uri?eid=2- s2.0-84925287928&doi=10.1016%2fj.jrmge.2014.07.002&partnerID=40&md5=82e8fab8283a935f0a79dc178a59db07. TRM Benchmarks & Applications Benchmarks ‚ FullySaturatedFlowMechanics (HM), from RM ‚ Liakopoulos from RM ‚ LinearMechanics, from M, RM ‚ RichardsFlow2D, from RM ‚ Simple3DThermoMechanics from TM, a simple 3D thermal stress problem ‚ HeatTransportInStationaryFlow for TH: Liakopoulos results: DECOVALEX 2023 Task C THM modelling of the FE experiment: ‚ Step 0: 2D benchmarks with increasing complexity (T, TH+vapour, THM) (see figure below) ‚ Theory: Non-isothermal Richards flow with me- chanics (TRM), isobaric gas phase ‚ Porosity evolution: pφq 1 S “ pα B ´ φq ´ div puq 1 S ` K ´1 SR pp FR q 1 S ´ 3α T S pT q 1 S ¯ H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 H12 T1 T2 T3 T4 T5 T6 Numerical approach: ‚ Method: Finite Elements (FEM) ‚ Coupling scheme: Monolithic ‚ Nonlinear solver: Newton-Raphson ‚ Spatial discretization: 3460 tri+quad elements (see figure above) ‚ Temporal discretization: Backward Euler ‚ Code: OpenGeoSys (OGS 6.3.2) Results The figure left shows the distribution of temperature, saturation, and horizontal stresses at t “ 1000 days indicating the anisotropy of the Opalinus clay. The temporal evolution of the TRM variables (tem- perature, saturation, displacement) in the given ob- servation points (see figure above) are depicted in the figures below. 0 1 2 3 4 5 -1.0 -0.5 0.0 0.5 1.0 1.5 Displacement t a u / mm X Z H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 H12 T1 T2 T3 T4 T5 T6 O1 O2 O3 O4 O5 O6 0 1 2 3 4 5 20 40 60 80 100 120 Temperature t a T / °C THM TH H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 H12 T1 T2 T3 T4 T5 T6 O1 O2 O3 O4 O5 O6 0 1 2 3 4 5 0.2 0.4 0.6 0.8 1.0 Saturation t a S - THM TH H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 H12 T1 T2 T3 T4 T5 T6 O1 O2 O3 O4 O5 O6 First lessons from Step 0: The modelling teams obtained plausible results (e.g. effect of anisotropy). Differ- ences in the results were traced back to open points in the problem specification which were clarified in a new task specification. Further testing now includes mesh effects, reduced vs. full two-phase flow formulations, different storage terms, initial stress conditions etc. Contact: Sonja Kaiser ([email protected]) and Dmitri Naumov, Institute of Geotechnics at the TU Bergakademie Freiberg, Chair of Soil Mechanics and Foundation Engineer- ing; J¨ org Buchwald and Wenqing Wang, Helmholtz Centre for Environmental Research (UFZ), Department of Environmental Informatics (ENVINF) Acknowledgements The contribution of SK was funded by the Bundesgesellschaft f¨ ur Endlagerung (BGE), the German federal company for radioactive waste disposal. The authors furthermore acknowledge the funding provided partially by the German Federal Ministry of Education and Research (BMBF) for the iCROSS project (grant number 02NUK053E), as well as the Helmholtz Association (Helmholtz-Gemeinschaft e.V.) through the Impulse and Networking Funds (grant number SO-093). Radioactive Waste Management (grant agreement No 847593). The authors deeply appreciate the support of the DECOVALEX Task C Leader Kate Thatcher (Qunitessa) and Bastian Graupner (ENSI) as well as the help by the OGS developer team. We are very grateful to swisstopo for the support in the Mont Terri project. Funding
Transcript of TRM@OGS: Thermo-Richards-Mechanics
LATEX TikZposter
TRM@OGS: Thermo-Richards-Mechanics
Sonja Kaiser, Jorg Buchwald, Wenqing Wang, Dmitri Naumov, Thomas Nagel
TRM@OGS: Thermo-Richards-Mechanics
Sonja Kaiser, Jorg Buchwald, Wenqing Wang, Dmitri Naumov, Thomas Nagel
TRM Concept & Overview
Motivation and URL Link
Quantitative evaluation of Thermo-Hydro-Mechanical(THM) processes are essential in the course of barrierintegrity analyses and for safety assessment in general.THM processes are studied in several laboratory andin-situ experiments such as heater experiments in sev-eral Underground Research Laboratories (URL) suchas in Mont Terri (Switzerland, the figure left showsa plane view including various experiments in the oldand new galleries).
The Full-Scale Emplacement (FE) experiment in MontTerri is of particular interest for study of THM pro-cesses in Opalinus clay and was selected as Task C inthe current DECOVALEX 2023 phase.
Figure sources: swisstopo, visualization by Karsten Rink (UFZ)
Benchmarking Concept
The benchmarking concept is organized in a hierarchic way with an increasing complexity:‚ Single processes (T,R,M),
‚ binary processes (TR, TM, RM),
‚ and finally the trinary TRM (Thermo-Richards-Mechanics) process.for a systematic testing of all possible couplings (see also companion poster on TH2M processes by Grunwald etal.). The generic approach allows the evaluation of various hydraulic processes (single phase flow, unsaturated(Richards) flow, and two-phase flow) in the context of thermal and mechanical interactions.
Governing Equations
Energy balance:
p%cpqBT
Bt´∇
´
´λeffT ∇T ` φ%LcplTvL ` φ%vcpvTvL
¯
“ QT
Mass balance:
φ
„
p%L ´ %vqBS
Bp` p1´ Sq
B%vBp` %Lβp
dSp
dt
`
„
φp1´ SqB%vBT
´ %L
´
φSαLT ` 3pαB ´ φqα
ST
¯
dST
dt`∇ ¨ pqL ` qvq ` S%Lp∇ ¨ 9uq “ QH
Momentum balance:∇ ¨
´
σeff´ αBSp I
¯
` %g “ 0
with 9σeff “ C:p 9ε´ 9εth ´ 9εinel ´ 9εswq
Literature
References
[1] W. Wang et al.“Non-isothermal flow in low permeable porous media: A comparison of Richards’ and two-phase flow approaches”. In: Environmental Earth
Sciences 62.6 (2011). cited By 52, pp. 1197–1207. DOI: 10.1007/s12665-010-0608-1. URL: https://www.scopus.com/inward/record.uri?
eid=2-s2.0-79952073715&doi=10.1007%2fs12665-010-0608-1&partnerID=40&md5=41dca1366e09b40cfb6dd784e6fb7a2c.
[2] X. Wang et al.“Numerical analysis of thermal impact on hydro-mechanical properties of clay”. In: Journal of Rock Mechanics and Geotechnical Engineering
6.5 (2014). cited By 13, pp. 405–416. DOI: 10.1016/j.jrmge.2014.07.002. URL: https://www.scopus.com/inward/record.uri?eid=2-
s2.0-84925287928&doi=10.1016%2fj.jrmge.2014.07.002&partnerID=40&md5=82e8fab8283a935f0a79dc178a59db07.
TRM Benchmarks & Applications
Benchmarks
‚ FullySaturatedFlowMechanics (HM), from RM
‚ Liakopoulos from RM
‚ LinearMechanics, from M, RM
‚ RichardsFlow2D, from RM
‚ Simple3DThermoMechanics from TM, a simple 3Dthermal stress problem
‚ HeatTransportInStationaryFlow for TH:
Liakopoulos results:
DECOVALEX 2023 Task C
THM modelling of the FE experiment:
‚ Step 0: 2D benchmarks with increasing complexity(T, TH+vapour, THM) (see figure below)
‚ Theory: Non-isothermal Richards flow with me-chanics (TRM), isobaric gas phase
‚ Porosity evolution: pφq1S “
pαB ´ φq´
div puq1S `K´1SR ppFRq
1S ´ 3αTSpT q
1S
¯
H1
H2
H3
H4
H5H6
H7
H8
H9
H10
H11H12
T1
T2
T3
T4
T5
T6
Numerical approach:
‚ Method: Finite Elements (FEM)
‚ Coupling scheme: Monolithic
‚ Nonlinear solver: Newton-Raphson
‚ Spatial discretization: 3460 tri+quad elements (seefigure above)
‚ Temporal discretization: Backward Euler
‚ Code: OpenGeoSys (OGS 6.3.2)
Results
The figure left shows the distribution of temperature,saturation, and horizontal stresses at t “ 1000 daysindicating the anisotropy of the Opalinus clay.
The temporal evolution of the TRM variables (tem-perature, saturation, displacement) in the given ob-servation points (see figure above) are depicted in thefigures below.
0 1 2 3 4 5
−1.
0−
0.5
0.0
0.5
1.0
1.5
Displacement
t a
u /
mm
X Z
H1H2H3H4H5H6H7H8H9H10H11H12T1T2T3T4T5T6O1O2O3O4O5O6
0 1 2 3 4 5
2040
6080
100
120
Temperature
t a
T /
°C
THM TH
H1H2H3H4H5H6H7H8H9H10H11H12T1T2T3T4T5T6O1O2O3O4O5O6
0 1 2 3 4 5
0.2
0.4
0.6
0.8
1.0
Saturation
t a
S−
THM TH
H1H2H3H4H5H6H7H8H9H10H11H12T1T2T3T4T5T6O1O2O3O4O5O6
First lessons from Step 0: The modelling teams obtained plausible results (e.g. effect of anisotropy). Differ-ences in the results were traced back to open points in the problem specification which were clarified in a newtask specification. Further testing now includes mesh effects, reduced vs. full two-phase flow formulations,different storage terms, initial stress conditions etc.
Contact:
Sonja Kaiser ([email protected]) and DmitriNaumov, Institute of Geotechnics at the TU BergakademieFreiberg, Chair of Soil Mechanics and Foundation Engineer-ing; Jorg Buchwald and Wenqing Wang, Helmholtz Centre forEnvironmental Research (UFZ), Department of EnvironmentalInformatics (ENVINF)
Acknowledgements
The contribution of SK was funded by the Bundesgesellschaft fur Endlagerung (BGE), the German federal company for radioactivewaste disposal. The authors furthermore acknowledge the funding provided partially by the German Federal Ministry of Education andResearch (BMBF) for the iCROSS project (grant number 02NUK053E), as well as the Helmholtz Association (Helmholtz-Gemeinschafte.V.) through the Impulse and Networking Funds (grant number SO-093). Radioactive Waste Management (grant agreement No847593). The authors deeply appreciate the support of the DECOVALEX Task C Leader Kate Thatcher (Qunitessa) and BastianGraupner (ENSI) as well as the help by the OGS developer team. We are very grateful to swisstopo for the support in the Mont Terriproject.
Funding
