Contribution to computational geotechnics [Elektronische Ressource] : non-isothermal flow in low-permeable porous media / vorgelegt von Joëlle De Jonge

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• Publié par: eberhard_karls_universitat_tubingen
• Publié le: 01 janvier 2005
• Nombre de lectures: 32
• Langue: Deutsch
• Poids de l'ouvrage: 4 Mo

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Contributions to computational geotechnics

Non-isothermal flow in low-permeable
porous media






Dissertation
zur Erlangung des Grades eines Doktors der Naturwissenschaften


der Geowissenschaftlichen Fakultät
der Eberhard-Karls-Universität Tübingen









vorgelegt von
Joëlle De Jonge
aus Ixelles (Belgien)

2005




























Tag der mündlichen Prüfung: 24. Juni 2005
Dekan: Prof. Klaus G. Nickel, Ph.D.
1. Berichterstatter: Prof. Dr. Olaf Kolditz
2. Berichterstatter: Dr. Stefan Finsterle, USA
Zusammenfassung
Um thermische (T), hydraulische (H) und mechanische (M) Prozesse, ihre Kopplungen und
ihren Einflu? auf das Systemverhalten besser zu verstehen, werden T-H-M Modelle entwick-
elt. Diese Modelle lassen Modellierungen im Nahbereich des Systems zu. Die Simulierung von
nicht-isothermen, thermo-hydraulischen (TH) Prozessen ist f¨ur Anwendungen wie Geothermie,
W¨armeunterstu¨tzteGrundwassersanierung, undAtommu¨llentsorgungwichtig. DieseDoktorar-
beit richtet sich spezifisch an den Anwendungen f¨ur Atommu¨llentsorgung aus, vor Allem an
den thermischen und hydraulischen Prozessen in diesem Bereich.
Thermische Prozesse kommen durch die W¨armestrahlung des Abfalls zustande und zeichnen
sich durch den W¨armetransport vom Kanister zum Bentonitpuffer aus. Andere wichtige ther-
mische Prozesse sind Verdampfung und Kondensierung, die mit dem Phasenwechsel zwischen
w¨asseriger- und gas Phase assoziiert sind. Wichtige hydraulische Prozesse sind das Eindrin-
gen von Wasser von dem Gastgestein in den Puffer und dann in den Kanister, sowie quellen
und schrumpfen des Bentonitpuffers. Bentonit quillt durch das Eindringen von Wasser und
trocknet durch den W¨armetransport des Abfalls.
Das Ziel der Arbeit ist die mathematische Formulierung der Prozesse und ihre Integrierung in
den objekt-orientierten finite-elemente Code GeoSys/RockFlow.
Puffer, Gastgestein und Fluide (in der w¨asserigen und gas Phase) formen gemeinsam ein
mehrphasiges-mehrkomponenten System (por¨oses Medium). Das TH Modell ben¨otigt drei
Bilanzgleichungen, eine fu¨r die Wasserkomponente, eine fu¨r die Luftkomponente und eine fu¨r
Energie. Die drei Prim¨arvariablen sind Gasdruck, Wassers¨attigung und Temperatur.
UmdieBilanzgleichungenzul¨osen, werdenGleichungen, diedasSystembeschreiben, ben¨otigt.
Dies sind Materialparameter, wie zum Beispiel Kapillardruck - S¨attigungsbeziehungen oder
Dichtegleichungen. Fu¨r die beschriebenen Prozesse sind diese Materialparameter und Zus-
tandsgleichungen meist nicht-linear und meist Funktionen der Temperatur, der S¨attigung und
des Drucks. Nicht nur das Material, sondern auch der thermodynamische Zustand des Sys-
tems mu? beschrieben werden. Dies wird mit Zustandsgleichungen erreicht, zum Beispiel
Funktionen zur Berechnung des Wasserdrucks, oder der Massenfraktionen. Materialparame-
ter und Zustandsgleichungen werden in die Bilanzgleichungen substituiert, es resultieren die
drei Modellgleichungen in Differentialform. Diese Gleichungen werden nach Umformungen von
GeoSys/RockFlow gel¨ost.
Die Implementierung l¨a?t Phasenwechsel zwischen den Fluidphasen (wasser und gas) explizit
zu. Das Modell erm¨oglicht Simulationen von sehr undurchl¨assigem Tonmaterial mit hohen
Kapillardru¨cken. Beispiele der Modellvalidierung werden gezeigt, wo Ton durch hohe Temper-
aturen ents¨attigt wird.
2Summary
Tobetterunderstandthecouplingofthermal(T),hydraulic (H)andmechanical(M)processes
(T-H-M processes) and their influence on the system behaviour, models allowing T-H-M cou-
pling are developed. These models allow simulations in the near-field of the system. The
modeling of non-isothermal thermo-hydraulic (TH) processes is important for applications
such as geothermal energy generation, heat supported environmental remediation, and nuclear
waste disposal. The work presented herein focuses on deep geological disposal of nuclear
waste, and more specifically on the thermal and hydraulic processes in this application.
Thermal processes result directly from the heat radiation of the waste and include heat trans-
port from the core to the bentonite buffer. Other processes of importance are vaporization and
condensation associated with phase changes between the liquid and gaseous phases. Hydraulic
processes of importance include water intrusion from the host rock to the buffer and eventually
to the core, as well as swelling and shrinking processes in the bentonite. Bentonite swells as
a result of water intrusion from the host rock and dries as a result of the heat transport from
the core.
The objective of the work is to formulate the processes mathematically and to integrate them
into the object-oriented simulator GeoSys/RockFlow.
Buffer, host rock, and fluids in the gas and liquid phase form a multiphase-multicomponental
system (porous medium). The TH model consists of a set of three balance equations. One
balance equation for the water component, one balance equation for the air component and
one energy balance equation. The three primary, or independent variables are gas pressure,
water saturation, and temperature.
To solve these balance equations, equations describing the material modelled are necessary.
Materialpropertiesincludeforexamplecapillarypressure-saturationrelationships,densityequa-
tions, or viscosity calculations. For those processes, material parameters and state variables
are highly non-linear and mostly functions of temperature, saturation, and pressure. Other
than describing the material, the thermodynamic state of the system has to be described.
This is achieved with equations of state, as for example functions for the calculation of liquid
pressure or mass fractions. When the material properties and the state functions are inserted
into the balance equations, governing equations in the differential form are obtained. After
numerical transformations, these equations are then solved by GeoSys/RockFlow.
The implementation allows phase changes between the fluid phases (gas and liquid) to occur
explicitly. The model allows the simulation of processes in very low permeability clays with
high capillary pressures. Examples for code validation are shown, where low permeability clay
is desaturated.
3Acknowledgement
I thank Prof. Olaf Kolditz for giving me the opportunity to work on this interesting topic, for
his input and excellent guidance and supervision during these three years. I thank him too for
contributing to an exceptional (musical) work atmosphere, as well as his encouragement and
understanding.
I thank the Federal Agency of Geosciences and Natural Resources (BGR) for their support of
this research project and making the funds available for this work. In particular I thank Dr.
Wallner and Dr. Shao, as well as Dr. Liedtke. I would also like to thank Thomas Nowak and
Herbert Kunz for constructive discussions and great help.
I would like to extend warm thanks to Stefan Finsterle and Rainer Helmig for their good guid-
ance and enthousiastic discussions and willingness to help at different stages of my work.
I would like to acknowledge the constant support of the DECOVALEX project members. Their
scientificinput and support wasinvaluable. In particular I wouldliketo thank Lanru Jing, Alain
Millard, Son Ngyuen, Sebastia Olivella, and Amel Rejeb.
Without my work group and other ZAG members this whole research would have been excep-
tionally difficult. I thank them for being so supportive scientifically and on personal matters,
and for creating a fun and light work atmosphere.
My heartfelt thanks go to my friends, in particular Jannine Bothner, Chris Fisher, Tobias Clau?
and Katrin Hieke. They have known how to encourage me, listened to my complaints and
turned hard times good.
Last but not least I would like to thank my parents, who although far away, were there when
I needed them and believed in me.
4Contributions to computational geotechnics 1
List of Symbols
a....... Component air [−] Saturation vector [−]S......
Jc Specific heat capacity [ ] S .... Effective saturation [−]effkg?K
Mass matrix, subscript: variable [kg]S ... Maximum saturation [−]C...... max
2m Residual saturation [−]D Diffusion coefficient [ ] S .....rs
mg...... Gravity vector [ ] s....... Solid phase, superscript [−]2s
g....... Gas Phase, superscript [−] Sat..... Saturated, subscript [−]
JEnthalpy [ ] Temperature [K]h...... T ......kg
Heat, subscript [−] T Temperature vector [K]h
kgFlux [ ] Time [s]J...... t.......m?s
Ju...... Internal energy [ ]Component (subscript) [−]k kg
2 3k...... Permeability [m ] V ...... Volume [m ]
m2 Velocity vector [ ]Permeability tensor [m ] vk s
k .... Relative permeability [−] Mass fraction [−]X......rel
WConductivity matrix [ ] Mass fraction vector [−]K...... Xm?K
1Henry coefficient [ ] w......K .... Water component, subscript [−]H Pa
Liquid phase, superscript [−]l.......
kgM ..... Molar mass [ ]
mol
1m...... Mass [kg] β ...... Fluid compressibi