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 (Sonja.Kaiser@ifgt.tu-freiberg.de) 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