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Numerical modeling of groundwater andair flow between compacted bentonite and

fractured crystalline rock

Benoît Dessirier

Department of Physical GeographyStockholm University

Stockholm 2016

c© Benoît Dessirier, Stockholm University 2016Cover illustration: Modeling processes at a bentonite/rock interface, by Benoît Dessirier.ISBN: 978-91-7649-294-9ISSN: 1653-7211Type set with LATEX using Department of Physical Geography thesis templatePublished articles typeset by respective publishers, reprinted with permissionPrinted by: Holmbergs, Malmö, 2016Distributor: Department of Physical Geography, Stockholm University

Abstract

The geological repository for final storage of spent nuclear fuel, envisioned by the SwedishNuclear Fuel and Management Company (SKB), relies on several barriers: copper canisters de-posited in holes in the floor of underground tunnels in deep bedrock, embedded in a buffer ofcompacted bentonite. The initially unsaturated buffer would take up water from the surroundingrock mass and swell to seal any potential gaps. This initial two-phase (gas and liquid) regimewith two components (air and water) may impact the final density, swelling pressure and bio-geochemical conditions in the buffer. A main objective of this work is to identify factors andmechanisms that govern deposition hole inflow and bentonite wetting under the prevailing two-phase flow conditions in sparsely fractured bedrock. For this purpose, we use the numericalcode TOUGH2 to perform two-phase flow simulations, conditioned by a companion field exper-iment (the Bentonite Rock Interaction Experiment or BRIE) performed in a 417m deep tunnelof the Äspö Hard Rock Laboratory in southeastern Sweden. The models predict a significantde-saturation of the rock wall, which was confirmed by field data. To predict the early bufferwetting rates and patterns, the position of local flowing fractures and estimates of local rock ma-trix permeability appear more important than the total open hole groundwater inflow. A globalsensitivity analysis showed that the buffer wetting time and the persistence of unsaturated condi-tions over extended periods of time in the rock depend primarily on the local fracture positions,rock matrix permeability, ventilation conditions in the tunnel and pressure far in the rock. Dis-mantling photographs from BRIE were used to reconstruct a fine-scale snapshot of saturationat the bentonite/rock interface, showing tremendous spatial variability. The high level of het-erogeneity in the rock generates complex two-phase flow phenomena (air trapping, dissolution),which need to be accounted for in buffer design and rock suitability criteria. In particular, resultssuggest that uncertainties regarding two-phase flow behavior are relatively high close to resid-ual air saturation, which may also have important implications for other applications involvingtwo-phase flows, such as geological storage of carbon dioxide.

Sammanfattning

Det geologiska slutförvar för använt kärnbränsle i Sverige som förespråkas av Svensk Kärn-bränslehantering AB (SKB) bygger på flera barriärer: kopparkapslar som nedsänks i deponer-ingshål från tunnlar i djup berggrund, inbäddade i en buffert av kompakterad bentonit. Denursprungligen omättade bufferten kommer att ta upp vatten från den omgivande bergmassan ochsvälla, vilket tätar eventuella mellanrum. Denna initiala tvåfasregim (gas och vätska) med tvåkomponenter (luft och vatten) kan påverka slutlig densitet, svälltryck och biogeokemiska förhål-landen i bufferten. Ett huvudsyfte med denna avhandling är att identifiera faktorer och mekanis-mer som styr inflöde till deponeringshål och vätning av bentonit under de tvåfasflödesförhål-landen som råder i det sprickiga berget. För detta ändamål utför vi tvåfasflödessimuleringarmed den numeriska koden TOUGH2, givet observationsdata från ett fältexperiment (BentoniteRock Interaction Experiment eller BRIE) som utförts i en 417 meter djup tunnel i Äspölabo-ratoriet i sydöstra Sverige. Simuleringarna förutspår att en betydande omättnad zon utvecklasi bergväggen, vilket bekräftades av fältdata. För att förutsäga hur snabbt bufferten vattenmät-tas och hur tidiga mönster för denna mättnad ser ut, verkar lokalt flödande sprickors positionsamt permeabiliteten hos den lokala bergmatrisen vara mer betydelsefulla än storleken på to-tala grundvatteninflödet till deponeringshålet. En global känslighetsanalys visade att buffertmät-tningstiden samt tiden som omättade förhållanden råder i berget i första hand beror på de lokalasprickornas positioner, bergmatrisens permeabilitet, ventilationsförhållandena i tunneln och vat-tnets bakgrundstryck långt in i berget. Demonteringsfotografier från BRIE som användes för attrekonstruera en högupplöst ögonblicksbild av vattenmättnad i bentonit/berg-gränssnittet, visadeen enorm rumslig variabilitet. Den höga heterogeniteten i berget skapar komplexa tvåfasflödes-fenomen (luftfickor, fasövergångar), som måste beaktas i buffertens design och lämplighetskri-terier för berget. I synnerhet tyder resultaten på att osäkerheterna kring tvåfasflöde är relativthög då gasen (luften) närmar sig residualmättnad, vilket också kan ha stor betydelse för andratillämpningar som innefattar tvåfasflöde, såsom geologisk lagring av koldioxid.

Thesis content

This doctoral compilation dissertation consists of a summarising text and the four articleslisted below. A description of author contributions are given for each article.

Paper I Dessirier, B., Frampton, A., Jarsjö, J., 2016. Impact of near-wall rock charac-teristics on bentonite buffer wetting: In-situ study of nuclear fuel depositionholes in deep bedrock. Manuscript.

BD designed the study with the help of JJ, ran all the simulations and wrote themajority of the manuscript.

Paper II Dessirier, B., Jarsjö, J., Frampton, A., 2014. Modeling two-phase-flow interac-tions across a bentonite clay and fractured rock interface. Nuclear Technol-ogy, 187(2), 147–157

BD, AF and JJ designed the study, BD ran the simulations and wrote the major-ity of the manuscript.

Paper III Dessirier, B., Frampton, A., and Jarsjö, J., 2015. A global sensitivity analysisof two-phase flow between fractured crystalline rock and bentonite with ap-plication to spent nuclear fuel disposal. Journal of contaminant hydrology,182, 25–35

BD designed the study, set up all simulations and wrote the major part of themanuscript with guidance and help from JJ and AF.

Paper IV Dessirier, B., Frampton, A., and Jarsjö, J., 2016. Reconstruction of the sat-uration profile at the interface between a compacted bentonite column andfractured crystalline bedrock. Mansucript.

BD proposed and developed the reconstruction method, he also wrote themanuscript with help and guidance from JJ and AF.

Contents

1 Introduction: geological disposal of spent nuclear fuel 11.1 The KBS-3 method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 The buffer material . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 The host rock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Background and objectives 5

3 Data and representations of physical processes 73.1 The Bentonite Rock Interaction Experiment (BRIE) . . . . . . . . . . . 73.2 Processes and models of flow in porous/fractured media . . . . . . . . . 7

3.2.1 Advective flow . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2.2 Air dissolution, groundwater degassing and vapor pressure . . . 93.2.3 Binary molecular diffusion . . . . . . . . . . . . . . . . . . . . 103.2.4 Constitutive relationships: permeability and capillary pressure . 103.2.5 Swelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.3 Simulation frameworks and implementations . . . . . . . . . . . . . . 113.3.1 Visco-capillary two-phase flow . . . . . . . . . . . . . . . . . . 123.3.2 Richards unsaturated flow . . . . . . . . . . . . . . . . . . . . 12

4 Summary of results 134.1 Numerical modeling of early saturation of BRIE deposition holes (PA-

PER I) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.2 Scenario and global sensitivity analyses of bentonite saturation time,

rock wall de-saturation and potential air dissolution in BRIE depositionholes (PAPERS II & III) . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.3 Reconstruction of saturation at the rock-bentonite interface (PAPER IV) 20

5 Discussion and future perspectives 235.1 DFN modeling and upscaling . . . . . . . . . . . . . . . . . . . . . . . 235.2 Further investigations of two-phase flow processes . . . . . . . . . . . 235.3 Coupled processes and full scale repository modeling . . . . . . . . . . 245.4 High Performance Computing and other applications of multi-phase flow

modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

6 Conclusions 27

7 Acknowledgements 29

References 31

1 Introduction: geological disposalof spent nuclear fuel

Deep geological repositories are envisioned as the leading solution for final disposal oflong-lived high-level radioactive waste such as spent nuclear fuel (International AtomicEnergy Agency, 2011). Tentative repository designs rely on a multi-barrier concept in-cluding a natural barrier, i.e the geological formation to host the repository, and engi-neered barriers such as backfilling and buffer materials as well as metal canisters (Pusch,2009). Different rock formations have been studied to potentially host high-level wasteincluding salt domes (Hansen and Leigh, 2011), argillaceous layers (Marschall et al.,2005; Trotignon et al., 2007) and deep crystalline bedrock (SKB, 2010). Backfilling andbuffer materials under test include clays, usually bentonite, and mixtures of clays withother materials like sand (Pusch, 2009).

The buffer would be introduced unsaturated and left to swell and seal potential gapsas it collects groundwater from the surrounding rock mass. In this early stage, the depo-sition hole would be subject to two-phase (gas and liquid) flow of air and groundwater.The modeling of multi-phase flow in geological porous media is an active subject ofresearch motivated by the development of technologies such as Carbon Capture andStorage (CCS) (Chasset et al., 2011; Niemi et al., 2012, e.g.), enhanced oil recovery(EOR), the combination of the two (CCS-EOR) (Dai et al., 2013, e.g.) and pollutedsoil remediation (Hu et al., 2010, e.g.). The work presented in this thesis will focus onthe case of radioactive waste disposal and on buffer and rock types envisioned by theSwedish Nuclear Fuel and Waste Management Co. (SKB) for the planned repository forhigh-level radioactive waste, following a method called KBS-3.

1.1 The KBS-3 method

The KBS-3 (kärnbränslesäkerhet-3) method is a multi-barrier design under developmentin Sweden and Finland. It targets a sparsely fractured crystalline bedrock formationlocated approximately 500 m below ground. It includes, in order from the waste out tothe biosphere (Fig.1.1):

• iron inserts inside copper canisters,

• a bentonite clay buffer and backfill material, and

• the crystalline bedrock.

The KBS-3 method is designed to be maintenance-free once in place.The application for building a repository for spent nuclear fuel in Forsmark (central

eastern Sweden) is currently under review by the Swedish High Environmental court(Mark- och miljödomstolen) and the Swedish Radiation Safety Authority (Strålsäker-hetsmyndigheten) to help the government reach a final decision. Research activities are

1

Numerical modeling of groundwater and air flow between compacted bentonite and fractured crystalline rock

Figure 1.1. Breakdown of the KBS-3 method developed for final disposal of spent nu-clear fuel in Sweden and Finland. The multiple barrier design includes: crystalline hostrock and engineered barriers, i.e., the copper canister, bentonite clay buffer and tunnelbackfill. (Source SKB. Illustrator: Mats Jerndahl.)

Figure 1.2. Conceptual representation of the bentonite-rock interface with physical pro-cesses. Blue arrows and text represent advective groundwater flow, while red arrowsor text stand for air flow or air related processes. Dashed arrows represent interac-tions with intact rock or “matrix”, comparatively smaller than fracture flows. The highsuction and the swelling behavior of the buffer are represented in green and purple re-spectively.

2

Benoît Dessirier

taking place in Forsmark as well as at the Äspö Hard Rock Laboratory (HRL), the Ben-tonite Laboratory and the Canister Laboratory, in Oskarshamn (southeastern Sweden),and at the Onkalo site (western coast of Finland), to increase our understanding of thephysical and biogeochemical processes occurring in the different components of KBS-3.The Äspö HRL is an ensemble of tunnels and niches stemming from a main helicoidalaccess tunnel leading from the surface down to 460 m depth (Banwart et al., 1997). Ithas been the scene of numerous experiments on flow and transport processes in fracturedrock at different scales (Jarsjö and Destouni, 2000; Andersson et al., 2007; Laaksoharjuand Rockström, 2013, e.g), or on underground microbial populations (Pedersen, 2010).

1.2 The buffer material

A candidate buffer material fulfilling the KBS-3 criteria is a montmorillonite-rich sodiumbentonite extracted in Wyoming (USA) and commercially known as MX-80. It wouldbe prepared either in the form of pre-compacted blocks or pellets (SKB, 2010). In thedeposition holes, disk or ring-shaped blocks would be used to embed the canisters, andpellets would be used to fill the remaining space between the rock walls and the installedblocks (SKB, 2010). Similarly, in the tunnels, blocks would be used to fill the centralpart and pellets would be used in the interstitial space between the blocks and the rockwall (Bennett, 2015). The buffer is intended to fulfill different functions. The presenceof montmorillonite in its composition grants it a complex microstructure that evolveswith its hydration state, resulting in an overall swelling behavior as it gets hydrated. Thefirst function of the buffer is then to absorb groundwater from the nearby rock mass toswell and seal potential gaps left open during the installation. The second function ofthe buffer is to limit the intrusion of compounds that could jeopardize the integrity of thecanisters such as sulphides. Here high density bentonite plays a double role: it limits thesource of sulphides inside the buffer itself by hindering microbial development throughhigh swelling pressure and it limits the diffusive transport of sulphides produced in therock mass to the canister surface (Pedersen, 2010). Lastly, bentonite has a high retarda-tion capacity for radionuclides, which contributes to the final function of the bentonitebuffer: retarding the transport of radionuclides from the canister to the host rock in caseof canister failure (Neretnieks, 1985).

1.3 The host rock

The bedrock at Forsmark and Äspö consists mainly of altered granite, along with someoccurrences of other intrusive rock types such as diorite and pegmatite (Stanfors et al.,1999; Stephens et al., 2007), all of which will further be referred to as hard crystallinerock for the sake of hydrogeology. Groundwater flow in hard rock is dominated at theregional and repository scale by deformation zones (Rhén et al., 2003; Stephens et al.,2007). At the tunnel scale and away from the intersection with large scale deformationzones, the inflow is conveyed by a sparse network of fractures (Painter and Cvetkovic,2005). Flow through intact rock blocks, also called rock matrix, is very small in compari-son. The rock matrix offers, however, many sorption sites for radionuclides. This resultsin a strong solute retardation capacity via a joined diffusion/sorption process into therock matrix (Neretnieks, 1980; Cvetkovic et al., 1999, 2002; Frampton and Cvetkovic,2011). Long term stability, low groundwater flow rates and strong radionuclide retar-dation capacity are the arguments to consider sparsely fractured crystalline rock as asuitable host of a spent nuclear fuel repository (Nguyen et al., 2009).

3


4

2 Background and objectives

Laboratory studies have provided detailed accounts of the thermo-hydro-mechanical(THM) processes in compacted bentonite (Åkesson and Kristensson, 2008; Åkessonet al., 2009). Full scale experiments, such as the prototype repository in Äspö (Jo-hannesson et al., 2007) and the FEBEX at Grimsel in Switzerland (Alonso et al., 2005),have been commissioned to test the interactions between the different repository materi-als in situ, beyond controlled laboratory settings, and help assess the applicability of theenvisioned repositories. The high number of coupled physical processes in action andthe uncertainty due to the natural in situ conditions make the interpretation and mod-eling of full-scale experiments a very complex task (Alonso et al., 2005). Recognizingthis complexity, international platforms were created to foster cooperation and compar-ison between researchers. Two such examples are the SKB Task Force on Modelingof Groundwater Flow and Transport of Solutes (GWFTS) and the SKB Task Force onEngineered Barrier Systems (EBS). Common modeling tasks, tackling knowledge gaps,are submitted to distinct modeling groups within the task forces to compare the resultsand build a deeper understanding of the processes and features at play in the repositorydesign. The modeling tasks are usually scheduled to interact with experimental workcarried out in the underground laboratories, either to support experiment design, to at-tempt blind predictions of experimental results or to perform inverse modeling. An insitu experiment, the Bentonite Rock Interaction Experiment (BRIE), and a joint model-ing task between the GWFTS and EBS Task Forces (task 8) were set up to investigatethe isothermal wetting of bentonite after installation in sparsely fractured rock. The aimswere to increase our understanding and to build confidence in the models used to makeassessment and predictions for envisioned repositories. The work presented in this the-sis summarizes the author’s contribution in a modeling team from Stockholm Universityinvolved in task 8 and in the modeling of BRIE.

The saturation state of bentonite is important to determine the swelling pressure(Fig.1.2) and the final density patterns in the buffer (Rutqvist et al., 2011). But theexact water availability at the rock/bentonite interface is difficult to assess. Furthermore,the insertion of an unsaturated buffer exerting a high suction can potentially de-saturatethe near rock domain (Fig.1.2 and 2.1) which significantly and durably alters the flowregime around the deposition holes and makes the estimation of the water delivery tothe bentonite all the more uncertain. Low pressures around the deposition holes canlead to groundwater degassing (Fig.1.2) of dissolved nitrogen, methane, hydrogen orcarbon dioxide for example (Jarsjö and Destouni, 2000; Rosdahl et al., 2011). Gas phasepersistence near the deposition hole would result in profoundly different flow patternscompared to saturated flow. The dissolution of gas installed with the buffer, such asoxygen, could alter the prevailing biogeochemical conditions in the early years of therepository (Fig.1.2 and 2.1) and for example trigger microbial activity (Yang et al., 2007).

The main research question I want to address in this thesis is how to use numericalsmodels to reach a better understanding of two-phase flow phenomena in highly hetero-

5


PRIOR CHARACTERIZATION IN SITU BENTONITE WETTINGMODELING

BRIEtime

dis

man

tlin

g o

f B

RIE

BENTONITEBLOCKS

INTACT ROCKMATRIX

LOCALFRACTURES

DEFORMATIONZONES

LABORATORY WATER UPTAKE TESTS- permeability (sat. & rel.)- retention curve

LABORATORY TESTINGON ROCK CORES- permeability (sat.)- retention curve

HOLE INFLOWMEASUREMENTS

HYDRAULIC TESTS&

FRACTURETRACE MAPPING

PAPER IV: FINAL SATURATION atBENTONITE/ROCK INTERFACE

PAPER I: CHARACTERIZATION and EARLY SATURATIONFULL BENTONITE SATURATION

ROCK WALL RE-SATURATIONMAXIMUM AIR DISSOLUTION

PAPERS II & III:

GAS FLOW

LIQUID

FLOW

DESATURATION GAS COMPRESSION

AIR DISSOLUTION

DIFFUSION

BIOGEOCHEMICALREACTIONS

years decadesdayshours

Figure 2.1. Overview of the BRIE data (left) and processes addressed in this thesis(right). The blue background represents the liquid phase in and around the depositionhole, whereas the red component represents the gas phase. The time scales are given asbroad references, this representation is only meant to be qualitative.

geneous fractured media. To this end, BRIE provides a rich dataset to test the modelsagainst a mixed engineered/natural system.

The detailed objectives of this thesis were therefore, by the use of numerical modelsand comparison to the field data obtained in BRIE (Fig.2.1):

A) to determine important features and processes to model near the bentonite/rock in-terface in order to obtain a reasonable simulation of the early wetting patterns in thebuffer,

B) to investigate the impact of different two-phase flow modeling assumptions and datauncertainty on: the final wetting time of the buffer, the persistence of unsaturatedzone in the rock, and the amount of air dissolving into the liquid phase,

C) to develop interpolation techniques to produce detailed reconstructions of the distri-bution of liquid saturation at the bentonite rock interface using both “hard” data frommonitoring and sampling as well as “soft” data such as dismantling photographs.

The objectives of this thesis are addressed by the appended articles and manuscripts.Paper I presents the development of a 3D flow model for the rock mass surroundingthe BRIE site and gives detailed modeling scenarios for the bentonite wetting observedduring BRIE, thus addressing objective A. Papers II and III introduce more generic flowmodels and configurations as well as longer simulation times to derive projected rangesfor important model outputs, such as buffer saturation time. They also rank the outputsensitivity to different model features or parameters, such as fracture location and rockmatrix permeability, in order to address objective B. Finally, paper IV explores the noveluse of geostatistical methods to include soft data in the reconstruction of the final stateof the bentonite at the end of BRIE (objective C).

6

3 Data and representations of phys-ical processes

This section will first describe a recent field experiment that has provided support forthe modeling work presented in this thesis. It will then summarize the processes andparameterizations considered to perform the modeling.

3.1 The Bentonite Rock Interaction Experiment (BRIE)

The Bentonite Rock Interaction Experiment (BRIE) was a field test, carried out at theÄspö HRL between 2008 and 2014, aiming at increasing the understanding of the in situwetting of a bentonite buffer in crystalline fractured rock (Fransson et al., 2012, 2015).It took place in several phases:

1. site selection,

2. site characterization,

3. deposition hole characterization,

4. in situ wetting and monitoring of bentonite parcels, and

5. dismantling and laboratory analyses of the bentonite parcels and the overcores ofthe rock wall.

Phases 1 and 2 consisted in drilling exploratory boreholes (76 mm in diameter) followedby hydraulic testing and laboratory characterization of drilled cores (Fig.2.1, 3.1). Forphase 3, two selected boreholes, tagged as 17 and 18, were enlarged to a diameter of 300mm to receive columns of compacted bentonite blocks, and were hydraulically charac-terized (Fig.2.1 and 3.1b).

Prior to the main bentonite wetting phase, laboratory water uptake tests were alsocarried on blocks of bentonite of the same size as those to be installed in the field(Fig.2.1). During the in situ wetting phase of bentonite, two columns of 3.5 and 3 mheight, equipped with sensors, were installed in the deposition holes for 419 and 518days respectively. After that, the bentonite columns and the surrounding rock mass wereovercored and transported to the laboratory for sampling and analyses (Fig.3.2).

3.2 Processes and models of flow in porous/fractured media

This section will summarize the different processes taken into account during the flowmodeling studies presented in this thesis (Papers I, II and III).

7


(a) Model features and mesh at the tunnel scale (b) Features and refined mesh at the deposition hole scale

Figure 3.1. (a) Modeling domain (black) including the main tunnel (grey), the BRIEtunnel (black), the four long boreholes (red) and the major deformation zones: wfrac1(blue), wfrac2 (green) and NW4 (purple). The rock cells between those features are notrepresented to improve clarity. (b) Refined deposition hole mesh. The BRIE tunnel flooris shown in black in the background, wfrac1 in blue to the right, the deposition holes 18(left, length: 3 m) and 17 (right, lenght: 3.5 m) in green, the local fractures in red, andthe local probing borehole intervals in black and labeled.

Figure 3.2. Photograph of the bottom of the retrieved bentonite column from hole 18(Photograph: Matthias Åkesson).

8

Benoît Dessirier

With regards to flow and if we define a control volume significantly larger than a sin-gle pore, intact rock and bentonite can be treated as porous media defined by a porosityΦ =

VpV that is the ratio of pore volume per bulk volume of medium, and a permeabil-

ity k that quantifies the propensity of this medium to allow flow (Gustafson and Walke,2012). The fractures in the rock are, here, represented either explicitly by elongatedsubdomains occupied by equivalent porous media with a higher permeability than thesurrounding rock mass for known deformation zones and local fractures intersecting thedeposition holes, or implicitly for other background fractures by including their effect onthe bulk rock permeability. Modeling a fractured medium by an equivalent continuumhas been explored by Finsterle (2000), who showed the applicability of this approachif the continuum model can be calibrated against data acquired at the same scale andinvolving the same processes as the desired flow prediction.

In the early pre-sealing conditions of the repository and in BRIE, the system is un-saturated, which means that the pore space is occupied by two distinct phases: liquidand gas. The ratio of occupancy of the pore space can be described by the liquid andgas phase saturations 0≤ Sl ≤ 1 and 0≤ Sg ≤ 1 defined by Sl =

VlVp

and Sg =VgVp

, Vl andVg being the volumes occupied by the liquid phase and gas phase respectively. Note theidentity Sl +Sg = 1 which implies the phase occupancy is fully determined by knowingone of the two saturations. Although, the two phases occupy distinct volumes in reality,here they are each represented as distributed across the whole representative volume, andthe hindrance to flow that they exert on each other has to be included into the adoptedconstitutive relationships for relative permeability (see section 3.2.4). Each phase is inturn composed of two components: air and water (air and vapor in the gas phase, liquidwater and dissolved air in the liquid phase). The ratio between components is usuallyrepresented by mole or mass fractions Xκ

βand xκ

β, defined as the number of moles or

mass of components κ in phase β over the bulk number of moles or mass in phase β .Here again, 0≤ Xκ

β≤ 1, 0≤ xκ

β≤ 1, ∑κ Xκ

β= 1 and ∑κ xκ

β= 1.

3.2.1 Advective flow

Each phase is subject to advective flow, that is the bulk displacement of fluids. At lowflow velocities, in the absence of turbulence, this phenomenon is driven by the gradient ofpressure between two points in the same phase (Gustafson and Walke, 2012; Marschallet al., 2005), which is an extension of Darcy’s law for two-phase flow systems. Theadvective flow qβ in phase β is then expressed as:

qβ =−ρβ · kβ (Sβ )

µβ

(∇Pβ −ρβ g

)(3.1)

where ρβ and µβ are the density and viscosity of phase β , kβ is the permeability of themedium to phase β depending on the phase saturation Sβ , ∇Pβ is the pressure gradientin phase β and g is the gravitational acceleration.

3.2.2 Air dissolution, groundwater degassing and vapor pressure

Dry air is assimilated to an ideal gas that mixes perfectly with water vapor so that Pg =Pa +Pv where Pg is the pressure of the gas phase, Pa is the partial pressure of dry air andPv the partial pressure of vapor.

The transfers of air between gas and liquid phases, also called dissolution and de-gassing, are assumed to take place significantly more rapidly than advection (Hunt et al.,1988; Staudinger and Roberts, 1996). Consequently, we will assume instant equilibrium

9


between air in the two phases and that air is always at solubility in the liquid phase.Solubility is defined by Henry’s law as:

Pa = Xag ·Pg = Kh ·Xa

l (3.2)

where Pg is the gas pressure, Xag and Xa

l are the mole fractions of air in the gas and liquidphase respectively and Kh = 1010 Pa is Henry’s constant for air and water at 15◦C, whichis the considered temperature throughout the simulations presented in this thesis (Pruesset al., 1999; Jarsjö and Destouni, 2000).

The vapor pressure Pv is most adequately modeled by Kelvin’s equation (Edlefsenand Anderson, 1943; Finsterle and Pruess, 1995):

Pv = Psat(T ) · exp( Mw ·Pc(Sl)

ρl ·R · (T +273.15)

)(3.3)

where Psat is the saturated vapor pressure as a function of temperature T , Mw is themolecular weight of water, Pc is the capillary pressure (See section 3.2.4), and R is theperfect gas constant. Optionally, the equation was approximated to Pv = Psat(T ) forsimulations in Papers I and II to obtain a faster resolution of the numerical problem, butthus neglecting potential vapor transport to the zones of strong capillary suction.

3.2.3 Binary molecular diffusion

Besides advection, strong mass fraction gradients can drive diffusive transport (Finsterleand Pruess, 1995). We are foremost interested, here, in the diffusion of dissolved airin the liquid phase. We use the parametrization of tortuosity by Millington and Quirk(1961) as implemented in TOUGH2 (Pruess et al., 1999) which yields a diffusive fluxof air in the liquid phase f a

l defined as:

f al =−Φ

4/3 ·S10/3l ·ρl ·da

l ·∇xal (3.4)

where dal is the diffusion coefficient of dissolved air in water and ∇xa

l is the air massfraction gradient. Diffusion of vapor in the gas phase is also implemented using thesame parametrization in paper III but it did not emerge as significant and was not studiedin detail.

3.2.4 Constitutive relationships: permeability and capillary pressure

In order to obtain a closed system of equations and solve the two-phase flow problem,one needs to define a permeability function as well as a relationship between gas andliquid pressure in the different media, also known as retention curve.

Traditionally, one defines the intrinsic permeability ksat of a medium as the perme-ability value observed for single phase flow (typically liquid phase), and then defines tworelative permeabilities kr,g(Sl) and kr,l(Sl) as functions of liquid saturation Sl with valuesin [0,1] to extend Darcy’s law to two-phase flow. A popular parameterization of liq-uid relative permeability for soils was proposed by Mualem (1976) and Van Genuchten(1980), and later extended to crystalline rock by e.g. Finsterle and Pruess (1995) andJarsjö and Destouni (2000). It takes the following form:

kr,l(Sl) =√

Sl ·(1−[1−S1/λ

l

]λ)2 (3.5)

where λ is a fitting parameter. The liquid phase permeability to introduce in Darcy’s lawthen becomes kl(Sl) = ksat · kr,l(Sl). For the gas relative permeability we use, here, thepermeability parametrization first given by Grant (1977) under the form:

kg(Sl) = ksat − kl(Sl) (3.6)

10

Benoît Dessirier

It is worth noting that this formulation distributes the intrinsic permeability between thetwo phases and disregards any effect of phase interference (mutual hindrance betweenthe two phases at intermediate saturations). The consequences of this modeling choiceare developed in the following discussion (section 5.2). For BRIE bentonite, the lab-oratory water uptake tests validated the adoption of the following liquid permeability(Fransson et al., 2015):

kl(Sl) = ksat ·Sαl (3.7)

where α is a fitting parameter. For low gas saturation, the complex changes in themicrostructure of the bentonite invalidate the common concept of intrinsic permeabilitydeveloped for porous media and one can observe a much higher permeability for gasthan the saturated permeability according to the intrinsic permeability concept (Alonsoet al., 2005). This is reflected by adopting the following parametrization:

kg(Sl) = ksat ·Γ · (1−Sl)β (3.8)

where β and Γ are fitting parameters and Γ represents the ratio between gas-saturatedand liquid-saturated permeabilities.

A retention curve Pc(Sl) = Pl−Pg is defined following the parametrization given byVan Genuchten (1980):

Pc(Sl) =−P0(S−1/λ

l −1)1−λ (3.9)

where P0 is the entry pressure and λ is a fitting parameter, both of which are fittedfor each material type. The laboratory water uptake tests enabled fitting the retentionparameters for bentonite. Analyses of BRIE rock cores allowed to build a retentioncurve for the intact rock matrix (Fransson et al., 2015). The scaling relation introducedby Leverett (1941) whereby:

P0(ksat) = P0,re f ·

√ksat,re f

ksat(3.10)

was used to define retention curve parameters for rock domains and fractures havingdifferent intrinsic permeabilities than the tested rock cores.

3.2.5 Swelling

Dueck and Börgesson (2007) proposed a simplified approach to including the effect ofbentonite swelling for confined conditions: the development of the swelling pressureis shown to partly counteract the suction exerted by the dry bentonite. This can be in-tegrated into the bentonite retention curve by calibrating it against an experiment thatwas realized under similar confined conditions. The bentonite water uptake tests pro-vided such a dataset and showed a good fit of the Van Genuchten model under confinedswelling conditions (Fransson et al., 2015).

3.3 Simulation frameworks and implementations

The different processes listed need to be assembled into balance equations to definecomplete flow problems that can be solved using numerical methods. This section willpresent two sets of equations that were used for the work presented in this thesis.

11


3.3.1 Visco-capillary two-phase flow

The isothermal two-phase flow system of equations, without any sink or source term,relies on two-mass balances, one for air and one for water (Pruess et al., 1999). This canbe written for κ = a,w (air and water) and β = l,g (liquid and gas):

Φ∂

∂ t ∑β=l,g

Sβ xκ

βρ

κ

β= ∇ · ∑

β=l,g

(qβ xκ

β+ f κ

β

)(3.11)

In the case of a non-isothermal system or if one needs to take into account the va-por pressure lowering with Kelvin’s equation, one adds the energy balance in the form(Pruess et al., 1999):

∂

∂ t

((1−Φ)ρRCRT +Φ ∑

β=l,gSβ xκ

βuβ (T )

)= ∇ ·

(−λT ∇T + ∑

β=l,gqβ hβ (T )

)(3.12)

where ρR and CR are the rock grain density and specific heat, T is the temperature, uβ isthe specific internal energy in phase β , hβ the specific enthalpy of phase β and λT is thethermal conductivity.

By inserting the previously introduced process parameterizations into the balanceequations, one can express the isothermal system as a non-linear system of two equationswith two unknowns, for example (Pg, Sl) for two-phase flow conditions and (Pg, xa

β)

for single phase flow conditions (Pruess et al., 1999). If thermal effects are at play,the complete system can be reduced to three unknowns with three equations. One candiscretize the equations using the integrated finite difference method (Narasimhan andWitherspoon, 1976) to obtain a non-linear system of algebraic equations which can beiteratively solved using the Newton-Raphson algorithm (Pruess et al., 1999). All flowsimulations carried out in this thesis used the implementation of the two-phase flowsystem and solver of the TOUGH2 code (Pruess et al., 1999): the equation of state 3(EOS3) was used in papers I and II for the simplified isothermal case and the equationof state 4 (EOS4) was used in paper III for implementing the full system with vaporpressure lowering due to capillary action.

3.3.2 Richards unsaturated flow

A simpler system of equations for isothermal unsaturated flow can be derived by makingsimplifications on the gas phase, namely that it is a passive bystander remaining at at-mospheric pressure. This reduces the mass balance to a single equation for liquid waterflow, also known as Richards’ equation (Pruess et al., 1999):

Φ∂

∂ t(Slρl) = ∇ ·

(kl(Sl)ρl

µl

[∇(Pc(Sl)+Patm)−ρlg

])(3.13)

where Patm is the atmospheric pressure.This system can be solved very efficiently. It is thus the preferred implementation of

unsaturated flow when the gas phase is unified, always connected to the atmosphere andno air trapping effects are expected (Finsterle et al., 2003; Wang et al., 2011). TOUGH2provides Richards’ equation as its equation of state 9 (EOS9). This framework is used inthis thesis for steady-state simulation of the rock mass prior to the insertion of bentonitesince no long-term air entrapment effect was expected in this stage. Richards’ equationis also compared to isothermal two-phase flow for the wetting of bentonite in paper II inorder to compare possible systematic differences induced by the adoption of Richards’equation.

12

4 Summary of results

This section summarizes the specific methods and results obtained in the appended pa-pers.

4.1 Numerical modeling of early saturation of BRIE deposi-tion holes (PAPER I)

Paper I is directly linked to BRIE. The first task of the study was to build a flow modelof the rock mass surrounding the BRIE site (Fig.3.1a) including the tunnels and themain deformation zones. Boundary conditions were extracted from a regional model ofthe Äspö area (Svensson et al., 2008). The characterization of the deformation zonesfrom the early phases of BRIE (Fransson et al., 2015) were directly used and simplehomogeneous equivalent properties were fitted and assigned to the rest of the rock massin order to respect the observed tunnel inflow values. Long term pressure values inboreholes were also used for comparison in order to build confidence in the tunnel scalemodel. Richards’ equation was assumed to be a suitable physical representation of theflow at this stage and used as implemented in TOUGH2-EOS9 (see Paper I for moredetails). No formal calibration or inversion was performed.

The second stage in paper I consisted in refining the flow model in the vicinityof the BRIE deposition holes (Fig.3.1b) and developing scenarios regarding the per-meability structure close to the deposition hole wall. Two inflow values separated byapproximately one order of magnitude were observed in holes 17 and 18 (see Frans-son et al. (2015) and Table 4.1). Realistic permeability structures were assigned nearthe deposition hole including the available information on intersecting flowing frac-tures and permeability measurements made on BRIE cores in the laboratory. Two caseswere distinguished based respectively on the average of core intrinsic permeabilities(He—km = 1.0 10−20 m2) or the lower end of the measured permeabilities (HHe—km = 2. 10−21 m2, see Table 4.1). In each case the fracture transmissivity is fitted todeliver the observed inflow value.

Synthetic cases are added to the realistic ones in order to extend the investigationto other configurations relevant for the planned repository. We considered cases with10 times the highest field inflow value (hole 17), denoted as 17’, to finally extend theinvestigated span of inflow values to two orders of magnitude (rows in Table 4.1). Andin addition to the realistic cases including detailed fracture information, we defined caseswhere the deposition hole wall is assigned a homogeneous matrix permeability value tohonor the observed inflow without the presence of fracture (Ho). The combination of allinflow values and permeability structures forms a matrix of 9 scenarios (Table 4.1).

The insertion and saturation of a bentonite column is simulated for each case in Table4.1. The realistic cases (He17, HHe17, He18 and HHe18) allow direct comparison withBRIE data through (i) the time evolution of the saturation recorded by relative humiditysensors installed in the bentonite columns (Fig.4.1, 4.2 and 4.3) and (ii) for the final

13


Table 4.1. Matrix of deposition hole scale scenarios — Horizontally: Permeability dis-tribution at the deposition hole wall - Homogeneous: homogeneous permeability aroundthe whole deposition hole, Heterogeneous and Highly Heterogeneous: a single dippingfracture intersecting the borehole and a homogeneous permeability elsewhere — Verti-cally: Inflow level — Inside: km is the permeability of the local homogeneous matrix,Tf is the transmissivity of the considered fractures if applicable, Q f is the steady statefracture inflow into the open deposition hole and Qm is the steady state matrix inflowinto the open deposition hole.

Permeability distribution→ Homogeneous Heterogeneous Highly Heterogeneousprefix Ho prefix He prefix HHe

Inflow rate ↓ No fracture km = 1.0 10−20 m2 km = 2.0 10−21 m2

10 times BRIE hole 17suffix 17’ km = 1.3 10−18 m2 Tf = 4.66 10−11 m2/s Tf = 4.68 10−11 m2/s

Q∼ 3. 10−5 kg/s Q f : N/A Q f = 3.0 10−5 kg/s Q f = 3.0 10−5 kg/sor 1.8 mL/min Qm = 3.0 10−5 kg/s Qm = 1.2 10−8 kg/s Qm = 2.5 10−9 kg/s

BRIE deposition hole 17suffix 17 km = 1.45 10−19 m2 Tf = 4.1 10−12 m2/s Tf = 2.35 10−11 m2/s


BRIE deposition hole 18suffix 18 km = 1.8 10−20 m2 Tf = 1.8 10−13 m2/s Tf = 4.2 10−13 m2/s


B9

B8

B12

B13

B14

B15

0.0m

2.1m

2.3m

2.6m

2.7m

3.45m

frac

ture

W4

W6W5

W1

W2W3

DSU

DSL

F

bottom steel plate

sand

(a)

2.3m

2.7mW11W12

W10

216°

-

288°-

2.15m

0.0m

Legend:

cross-sectionfracture strike

sensor location

2.95mbottom steel plate

sand

W9

W8

W7

frac

ture

B9

(b)

Figure 4.1. Sensor positions and cross-section lines (a) in hole 17 and (b) in hole 18.

14

Benoît Dessirier

0.4

0.5

0.6

0.7

0.8

0.9

1.0

liqui

d sa

tura

tion

(-)

W1 W2 W3

sensorHHe17He17Ho17HHe17'He17'Ho17'

0 100 200 300 400time (days)

0.4

0.5

0.6

0.7

0.8

0.9

1.0

liqui

d sa

tura

tion

(-)

W4

0 100 200 300 400time (days)

W5

0 100 200 300 400time (days)

W6

Figure 4.2. History of liquid saturation at sensor locations in hole 17 given the initialinflow measured in the field (black set of curves) and 10 times the initial inflow measuredin the field (gray set of curves).

0.4

0.5

0.6

0.7

0.8

0.9

1.0

liqui

d sa

tura

tion

(-)

W7 W8 W9

0 100 200 300 400 500time (days)

0.4

0.5

0.6

0.7

0.8

0.9

1.0

liqui

d sa

tura

tion

(-)

W10

0 100 200 300 400 500time (days)

W11

0 100 200 300 400 500time (days)

W12sensorHHe18He18Ho18

Figure 4.3. History of liquid saturation at sensor locations in hole 18.

15


0.0 0.1 0.2 0.3 0.4 0.5radius (m)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

liquid

satu

rati

on (

-)

rockbentonite

Cross-section Hole 18

rock measurementscross-sectionHHe18 216 ◦

He18 216 ◦

Ho18 216 ◦

HHe18 288 ◦

He18 288 ◦

Ho18 288 ◦

measurements inbentonite B9 216 ◦

measurements inbentonite B9 288 ◦

0.0 0.1 0.2 0.3 0.4 0.5radius (m)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

liquid

satu

rati

on (

-)

rockbentonite

Cross-section Hole 17 F

rock measurementscross-section DSUHHe17He17Ho17measurements inbentonite B8-B9cross-section DSLHHe17'He17'Ho17'

0.0 0.1 0.2 0.3 0.4 0.5radius (m)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

liquid

satu

rati

on (

-)

rockbentonite

Cross-section Hole 17 DSL


0.0 0.1 0.2 0.3 0.4 0.5radius (m)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

liquid

satu

rati

on (

-)

rockbentonite

Cross-section Hole 17 DSU


a)

d)c)

b)

Figure 4.4. Final liquid saturation profile along cross-section DSU (a), DSL (b) andF (c) in deposition hole 17 (Fig.4.1a) and the cross-section in deposition hole 18 (d)(Fig.4.1b) according to data and the different scenarios.

profiles of saturation in the bentonite and the rock wall along certain sampled crosssections (Fig.4.1 and 4.4). The comparison of results for the bentonite wetting betweenmodeling cases gives a measure of the impact of the local permeability structure onthe prediction (comparison between columns), and of the open hole inflow (comparisonbetween lines).

The analysis of the liquid saturation history at several locations (Fig.4.2) reveals thatfor the cases including the local fracture explicitly (He17, HHe17 vs. He17’, HHe17’),there is a smaller difference induced by a change of a factor 10 in initial depositionhole inflow (between corresponding black and grey curve) than by a change of a factor5 in rock matrix intrinsic permeability (between solid and dashed curves of the samecolor). The same conclusion can be drawn by looking at the cross-sections of saturation(Fig.4.4). The models without fracture (dotted lines) predict very rapid wetting patternssince the homogeneous permeability field distributes the wetting front very efficientlyacross the whole column (Fig.4.2). One conclusion is thus that the knowledge of thegeometry of the features around the deposition holes as well as the rock matrix perme-ability between the fracture traces are more important factors than the initial total inflowto issue a correct bentonite wetting prediction in holes where the inflow is clearly domi-nated by sparse fractures. It is worth noting that the matrix permeability value giving the

16

Benoît Dessirier

closest fit to the data (HHe17) was representative of the very low end of the measuredvalues on rock cores from the BRIE site.

The conclusion is slightly different for hole 18 (Fig.4.3) where the fracture-free sce-nario procures similar levels of saturation, if not better, especially close to the mappedflowing fracture. The dismantling analysis of the bentonite column in hole 18 latershowed that the top of the mapped fracture provided significantly more water than themiddle part close to which sensors W7-9 were installed (Fig.4.1). It appears thus that, atlow inflow values, internal variations in fracture transmissivity (channeling) and in rockmatrix permeability start to dominate the groundwater flow pattern to a greater degreethan the contrast between fractures and intact rock matrix.

One can however observe a general tendency to overestimate the bentonite satura-tion (Fig.4.2, 4.3 and 4.4), especially close to the mapped fractures. The analysis of thecross-sections is revealing of a lack of understanding of the two-phase flow processesin the near rock wall (Fig.4.4) where the liquid saturation is overestimated. Some per-meability reduction mechanism is not captured but appears to play a significant role.Possible underlying processes could be hypothesized such as stress effects, enhancedphase interference or hysteresis effects.

4.2 Scenario and global sensitivity analyses of bentonite sat-uration time, rock wall de-saturation and potential air dis-solution in BRIE deposition holes (PAPERS II & III)

Papers II and III extend the simulation of BRIE-size deposition holes, in time and tomultiple fracture configurations and two-phase flow parameter values. They use simpler2D radial geometrical representations of the tunnel and deposition hole (Fig.4.5a) toeasily parametrize the geometry and to reduce the computational burden.

Via the exploration of key scenarios using an approach similar to Chasset et al.(2011), Paper II explores the impact of different positions of the intersection betweenthe fracture and the deposition hole wall, as well as the impact of using the simplifiedRichards’ equation instead of a coupled two-phase flow system on the global wettingtime of the lower part of the buffer. We systematically disregard the upper part of theinstalled buffer that is directly influenced by its proximity to the tunnel. Furthermorewe define tα the time required to reach the degree of saturation α in the last cell of theconsidered buffer region. Results showed that Richards’ equation systematically yieldslower times to saturation tα than a two-phase system. The difference between the two ismoderate (< 15%) up to levels of saturation α = 95% but diverges significantly towardshigher saturations. The position of the fracture was shown to be an important factor todetermine the global wetting time of the bentonite buffer and a sustained de-saturationof the deposition hole wall was identified as an important phenomenon following theinstallation of a bentonite buffer, which was later confirmed by experimental data fromBRIE.

Following the exploration of scenarios in paper II, a formal framework, known as theelementary effects methodology or Morris OAT method, proposed by Morris (1991) andextended by Campolongo et al. (2007) was introduced to perform a global sensitivityanalysis in paper III. This method is particularly suitable for models with a long com-puting time and many input parameters since it requires fewer model runs in comparisonto other global sensitivity methods (Saltelli et al., 2008). It allows to rank the influenceof the input parameters on selected scalar model outputs, and to classify this influenceas negligible, linear, of higher order or in interaction with other parameters.

17


(a)

(b)

100 101 102 103 104

µ ∗ or time (days)

100

101

102

103

104

σ(days

)

3/4 deposition hole

zflgKr

p ctunnel

lgTf

αβ lgΓ

Pbnd

0.00

0.25

0.50

0.75

1.00

empiricalcdf

(c)

Figure 4.5. (a) Example of radial geometry and mesh used for the global sensitivity anal-ysis, (b) Example of snapshots of the saturation process at different times, (c) Empiricalcumulative density function of the required time to saturate 3/4 of the installed bufferto a saturation degree of 95% (in blue) and corresponding statistics of the elementaryeffects µ∗ and σ with centered 95% confidence intervals estimated by resampling. Threeparameters have negligible elementary effects with µ∗ and σ below 2 days and are thusnot shown in this plot.

18

Benoît Dessirier

The parameters retained for the sensitivity analysis were:

• the fracture position,

• the rock matrix intrinsic permeability,

• the rock matrix porosity,

• the equivalent suction exerted at the tunnel wall by ventilation,

• the fracture transmissivity,

• the fracture specific storage (represented as a porosity),

• the bentonite liquid permeability exponent α (see section 3.2.4),

• the bentonite gas permeability exponent β (see section 3.2.4),

• the ratio between gas-saturated and liquid-saturated permeability in bentonite Γ

(see section 3.2.4),

• the far field water pressure, and

• the diffusion coefficient for air in liquid water.

Each parameter was assumed to be uncorrelated with the others and uniformly dis-tributed in an assigned physical range. The cartesian product of these intervals defineda parameter space that was discretized in each dimension to obtain a finite grid. An el-ementary effect is the relative change in model output between two neighboring inputpoints on the parameter grid. The grid was scanned by the random procedure prescribedby Campolongo et al. (2007) resulting in a total of 120 simulations to compute the meanof the absolute value of the elementary effects µ∗ and the standard deviation of the ele-mentary effects σ in each parameter dimension (the method and the exact definition ofthe elementary effects is described in details in paper III).

The results of the sensitivity analysis for the time required to saturate 3/4 of the in-stalled buffer to a saturation degree of 95% or more are represented in Fig.4.5c. Thecumulative distribution function gives the range obtained and the spread for this out-put over the 120 simulations. This range is useful to determine when evaluating if anelementary effect is negligible or not. High values of µ∗ indicate an influential param-eter, and if so, low values of σ point to a linear impact while high values of σ point tonon-linear influence or parameters involved in interactions with others. Results for thecase of the time required to globally saturate the bentonite buffer up to 95% saturationshowed that the most influential parameters are the fracture position z f , the logarithmof the rock matrix intrinsic permeability lgKr, the far field pressure Pbnd and the suctionexerted by tunnel ventilation pc

tunnel . To a lesser degree, the bentonite relative permeabil-ity parameters α , β and Γ (see section 3.2.4) could have a significant impact, all otherparameters seem to have negligible influence on the time to saturation.

In summary, the global sensitivity analysis targeted three different kinds of modeloutputs: (i) the time to saturate the buffer to a degree of 95% (Fig.4.5c), (ii) the timeto re-saturate the rock wall and (iii) the maximum fraction of air introduced with thebuffer dissolving into the liquid phase as well as the time to this maximum (ii and iii areshown in paper III). Results indicate that the same parameters identified in Fig.4.5c, i.efracture position, rock matrix permeability, far field pressure and suction due to venti-lation, were consistently among the top six influential parameters for all tested outputs.Parameters related to bentonite gas relative permeability exert a significant impact on

19


the maximum amount of air dissolving into bentonite pore water, while the liquid phasediffusion coefficient seems to control the time to that maximum. None of the tested inputparameters could definitively be discarded as negligible for all selected model outputs.The Morris OAT analysis shows a complex sensitivity structure where several param-eters have a non-linear relationship with outputs and/or interact with other parameters,making predictions such as the time to global deposition hole saturation hard to estimatewith certainty.

4.3 Reconstruction of saturation at the rock-bentonite inter-face (PAPER IV)

Paper IV presents the processing of data from the BRIE experiment in order to producea fine scale reconstruction of the final saturation state of the surface of the bentonitecolumn in hole 18. The direct interpolation between samples, e.g. by inverse distanceweighted interpolation, gives a very smooth saturation field (Fig.4.6c) which contrastssharply with the visual aspect of the retrieved bentonite column , where wetter parts ofthe surface are relatively dark (Fig.3.2). Although, strictly, the shade of the bentonite hasnot been directly linked to its hydration state, it is striking that many of the dark tracesin the photographs correspond to the mapped fractures, which motivated the develop-ment of a method to incorporate “soft" data from the photographs into the interpolationprocess.

The first technical steps consisted in creating a coherent gray scale mapping of thesurface of the bentonite from the multiple photographs that were taken. Simple geo-metrical transformations and a leveling procedure at the overlaps are described in moredetails in paper IV and permitted to assemble the gray mapping shown in Fig.4.6a. Alinear regression between the sample gas saturation and the local average gray valueshowed a coefficient of determination of 0.48 (Fig.4.6b), implying that the photographscontain useful information for the reconstruction of the saturation profile. From there,a two-step reconstruction known as regression-kriging was performed (Pebesma, 2004;Bivand et al., 2008), whereby the gray mapping gives a trend of saturation via the fittedregression, and the residuals, i.e the local deviations from the regression line, are mod-eled by ordinary kriging as a space random function with a modeled semivariogram.

The obtained reconstruction enforces local agreement with the samples while alsorendering the traces of known flowing fractures intersecting the deposition hole (bluesine-shaped linear traces in Fig.4.6d). It is thus considered as an interesting reference tohelp reconstruct the saturation profile in the whole volume of the bentonite column andto perform inverse modeling of the wetting process in hole 18. The assembling of thegray mapping is believed to be a main source of the deviation from the regression line,modeled here as random residuals. A better acquisition technique of the surface stateof the bentonite could improve the power of the regression and the quality of the finalreconstruction, which could be beneficial for analyzing other experiments such as theprototype repository in Äspö or envisioned full scale backfilling tests.

20

Benoît Dessirier

(a)

20 40 60 80 100 120 140 160pixel gray value

0.0

0.1

0.2

0.3

0.4

0.5

gas

satu

ratio

n

linear regression, R2 =0.48

(b)

(c) (d)

Figure 4.6. (a) Assembled gray scale mapping of the surface of the bentonite column forthe lowest meter of hole 18 with overlayed samples. (b) Regression between gray scaleand gas saturation. Reconstructions by (c) inverse distance weighted interpolation ofsample values and (d) regression-kriging using samples and gray scale mapping fromphotographs of the retrieved column.

21


22

5 Discussion and future perspectives

This section presents developments or alternative concepts that were not included in thework presented in this thesis but could extend the methodology.

5.1 DFN modeling and upscaling

The modeling cases presented in this thesis work, in 2D or 3D, include explicitly only asmall number of identified fractures and deformation zones. The rest of the rock masswas modeled by a simple homogeneous material with an estimated or fitted permeabilityto honor tunnel or deposition hole inflows. Other modeling approaches directly incorpo-rate the fractured nature of the rock by generating a Discrete Fracture Network (DFN).Assumptions are made regarding the possible fracture shapes, usually planar polygons orellipses, and regarding the fracture location, size and transmissivity distributions (Der-showitz, 1992; Adler et al., 2012). These assumptions can be based on observed fracturedistributions along scanlines at the surface, in tunnels or long boreholes (Holton et al.,2012), or they can be fitted (Niemi et al., 2000). Insights on the mechanical processesleading to the formation of the fractures can support the shape and parameter values ofthese distributions as well as prescribe rules for fracture termination (Davy et al., 2010,2013). New experimental microseismic methods currently developped at the field scalecould make passive mapping of the fractures in the rock mass available in the future(Geiser, 2006; Lacazette, 2013), which could help reduce the conceptual model uncer-tainty introduced by the assumptions necessary to generate the DFNs.

Different realizations of the DFN honoring the chosen statistics and/or criteria canthen be stochastically generated before running flow simulations. The generation andmeshing of DFNs raises technical issues (Adler et al., 2012; Hyman et al., 2014). Theunderstanding of the mechanics leading to the formation of a DFN, the transmissivitydistribution through the network and the practical implementation of DFN models, arevery active areas of research (Davy et al., 2013; Dreuzy et al., 2012; Hyman et al., 2015).

While DFN models can be used to directly perform simulations, they can also beused to derive equivalent rock mass properties (permeability, porosity) on a continuousvolume grid, a process also known as upscaling (Holton et al., 2012). Instead of fit-ting background permeability values to honor tunnel and deposition hole inflows as inPaper I, one could obtain equivalent permeability fields based on the upscaling of DFNrealizations respecting the fracture statistics gathered at the Äspö HRL.

5.2 Further investigations of two-phase flow processes

As evidenced by paper I, modeling the saturation in the rock domain near the depositionhole poses challenges. The retention curve built for BRIE cores is subject to uncertaintyand probable hysteresis effects (Fransson et al., 2015). The use and calibration of con-stitutive relationships accounting for hysteresis effects (Niemi and Bodvarsson, 1988;

23


Doughty, 2007, e.g.) would generate residual trapping of air which would maintain ahigher gas saturation during the re-saturation process of the rock wall (imbibition). Themeasurements of relative humidity in the rock later converted to saturation are also sub-ject to uncertainty as shown by the variability between repeated measurements (Frans-son et al., 2015). Moreover, a very non-linear relationship between relative humidityand saturation in the rock for liquid saturation levels in the range [0.5,1] amplifies theuncertainty on the final saturation plotted in Fig.4.4. The de-saturation of the rock wall,predicted by generic models in Papers II and III, was confirmed during BRIE, and it waseven shown that the phenomenon was more extensive than the estimates delivered bypredictive models for the final state of BRIE (Paper I).

Several factors could potentially improve the performance of the models:

1. accounting for potentially substantial variations of the transmissivity of the localfractures (channeling) and of the rock intrinsic permeability,

2. revising the representations of the relative permeabilities to liquid and gas phases,in particular accounting for the interference effects for the middle saturation ranges,

3. accounting for potentially strong hysteresis effect,

4. accounting for mechanical effects linked to the stress release generated by thedrilling of the tunnels and the deposition holes.

Point 1 is supported, for instance, by the variation in rock types observed on the BRIEcores or the range of permeability values obtained on the tested cores (Fransson et al.,2015). Point 2 addresses the relevance of the relative permeability curves used in paperI. Examples in the literature suggest strong phase interference effects in rough fracturereplicas, e.g. Pruess and Tsang (1990); Persoff and Pruess (1995); Jarsjö et al. (2001);Yang et al. (2013). A direct assessment of this phenomenon in BRIE could be to run theBRIE model with relative permeability relations including stronger phase interferenceeffects such as Corey (1954) or Watanabe et al. (2015).

Points 1-3 could be addressed by inverse modeling and sensitivity studies using thetype of model developed in paper I, and leveraging the intensive monitoring and sam-pling data provided by BRIE or enhanced data reconstructions, e.g paper IV. The inves-tigation of point 4 would require the explicit modeling of coupled mechanical effects.

In light of the very negative capillary pressures in the rock domain, a systematicquantification of the impact of vapor transport through the generalized use of Kelvin’sequation (see section 3.2.2) would also deliver important conclusions.

5.3 Coupled processes and full scale repository modeling

Paper III showed a potential dissolution of a large amount of the air introduced with thebuffer into the liquid phase, followed by a slow removal by diffusion and very low flowvelocities. The persistence of air points to revised input levels of oxygen in assessingthe potential biogeochemical reactions taking place in the near canister field (Yang et al.,2007) and their impact on the safety of the different components of the repository design.

Although, the simple approach to modeling the swelling behavior of bentonite inBRIE was deemed adequate in light of the results from the laboratory water uptake testsand a posteriori by observing only small variations in buffer density, a more generalstrategy would be to explicitly model coupled hydro-mechanical effects (Rutqvist et al.,2011; Loschetter et al., 2012; Blanco Martín et al., 2015). Such an approach, also in-cluding thermal effects due to the presence of heat-generating waste packages, would

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be a good opportunity to transfer the knowledge acquired in BRIE to the modeling ofmore complex in situ experiments such as the prototype repository at Äspö (Johannes-son et al., 2007) or the febex at Grimsel, Switzerland (Alonso et al., 2005; Rutqvist et al.,2011).

A general research question that could be approached by using two-phase and cou-pled models is to increase the understanding of the physical processes occurring in therock near the wall that lead to the observation of a so-called “skin effect". Observationsshow high pressure relatively close to the wall that would lead to significantly higherinflows than observed if one were to apply the average intrinsic permeability value esti-mated for the bulk of the surrounding rock mass up until the wall. To honor both tunnelinflow and borehole pressure measurements, one usually needs to apply a lower perme-ability near the wall to develop a steep gradient towards high pressures. Several factors,beyond the scale dependence, could influence the permeability near the tunnel wall andthus the inflow:

• the ventilation in tunnels shapes an unsaturated zone around tunnel that procuresa flow reduction (relative permeability effect),

• the stress redistribution generated by the excavation of the tunnel lowers the radialpermeability of the rock mass around the tunnel (Liu et al., 1999; Tsang et al.,2005),

• the damage induced by excavation operations, on the contrary, increases the frac-turation and the permeability of the rock near the wall,

• the oxidizing conditions in the unsaturated zone could create suitable environ-ments for enhanced microbial biofilm developments and subsequent clogging (Tsanget al., 2005).

The process understanding of EDZ and tunnel skin effects called by Tsang et al. (2005)has not yet been unified, and coupled physically-based models would be needed to per-form sensitivity analyses covering all the aspects involved.

5.4 High Performance Computing and other applications ofmulti-phase flow modeling

The strategy developed in papers I, II and III to limit the computational requirementswas to restrict the number of nodes in the mesh via the use of flexible unstructured gridtypes and/or to simplify the geometry to a lower dimension. The rapid developmentof high performance computing techniques would offer an alternative to solve modelswith complex geometries and processes. Codes that support optimized parallel computa-tions for two-phase flow are e.g. Dumux (Flemisch et al., 2007), TOUGH2-MP (Zhanget al., 2008) and PFLOTRAN (Hammond et al., 2012). These types of codes are pow-erful platforms to investigate other multi-phase flow phenomena in porous media e.g.carbon dioxide sequestration (Yang et al., 2015), permafrost dynamics under climatechange (Frampton et al., 2013) and complex reactive transport phenomena (Trincheroet al., 2016). More efficient codes can be seen as opportunities to implement modelswith greater structural complexity or detailed physics. It is also a formidable advancetowards the use of heavy global sensitivity schemes and inverse modeling procedures inorder to identify key parameters and optimal levels of model complexity for each typeof application (Wainwright et al., 2014).

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The modeling of the migration of carbon dioxide in supercritical state after injec-tion into depleted oil fields or deep saline aquifers needs to address complex two-phaseprocesses. There is strong evidence that the trapping of carbon dioxide happens in dif-ferent phases: physical trapping of the supercritical phase under a caprock (Bachu et al.,1994), capillary (or residual) trapping of supercritical phase occurrences in the zone thatunderwent a cycle of drainage and imbibition (Juanes et al., 2006; Rasmusson et al.,2014, e.g.), solution trapping by dissolution into the brine phase enhanced by densitydriven Rayleigh-Bénard convection Fu et al. (2013), and mineral trapping by the precip-itation of carbonate minerals (Bachu et al., 1994). However, some uncertainties remainas to the efficiency of well seals and caprock integrity (Lesti et al., 2013, e.g.). Thenumerical modeling of the behavior of well seals constitutes a challenge as it involvescomplex fluid flow, reactive transport generating potential cracks and mechanical alter-ations (Lesti et al., 2013).

In the context of three phase flow for modeling permafrost dynamics, the effort hasbeen put up to this day on code development and benchmarking to build confidence(Rühaak et al., 2015). Studies have shown proofs of concept on generic geometries(Frampton et al., 2013, e.g.) but applications to specific natural systems are rare (Karraet al., 2014, e.g.). Significant efforts are also needed to develop coupling between surfaceand subsurface flow in the context of freezing/thawing dynamics (Karra et al., 2014).

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6 Conclusions

This thesis work investigated the isothermal wetting of a compacted bentonite bufferinserted in sparsely fractured crystalline bedrock. Different scenarios were simulatedusing numerical modeling to be compared with site characterization data and bentonitewetting data obtained in a field experiment denoted BRIE (Bentonite Rock InteractionExperiment) carried out in an underground research laboratory approximately 417 me-ters below ground. The objectives were to assess the performance of state of the art flowmodels to predict bentonite wetting rates and patterns, as well as to identify and rank thephysical processes and parameters exerting the most influence on the bentonite wetting.

Detailed 3D modeling focusing on early bentonite saturation development in BRIEdeposition holes (Paper I, up to 500 days in situ) permitted to show that:

• the knowledge on the presence and location of intersecting flowing fractures ismore determinant than the total deposition hole inflow to predict the wetting ofthe buffer in deposition holes where the inflow has been shown to be dominatedby sparsely distributed fractures,

• a detailed parametrization of the potentially heterogeneous local rock matrix per-meability is important to adequately distribute the water delivery from the inter-secting flowing fractures,

• at low inflow values the water delivery to the bentonite seems dominated by finescale channeling in the fracture plane (not included in the modeling cases), whichcould explain the similar performance of all the tested models (those includingplanar fractures as well as the homogenized ones),

• as of yet, there are two-phase flow, and possibly mechanical, processes unac-counted for in the rock mass surrounding the deposition hole, where the modeledde-saturation is not as pronounced as shown by field evidence from BRIE.

Scenario and global sensitivity analysis of generic deposition hole settings overlonger simulation times (Papers II and III, up to thousands of years) showed that:

• The prediction of the time required to reach a certain saturation in the buffer ac-cording to Richards’ equation yields systematic underestimation compared to theadopted two-phase coupled approach. The difference between both predictionsdiverges dramatically as one targets saturation levels close to full saturation.

• The considered factors that had the highest influence on the time required to nearlysaturate the bentonite buffer were found to be the position of the intersecting frac-tures, the rock matrix intrinsic permeability, the ventilation conditions in the tun-nel and the reference pressure far back in the rock (function of deposition tunnelspacing in the repository design for example),

27


• The hypothesized de-saturation of the rock wall, later confirmed by the field re-sults, can be predicted by the models and be quite significant. The model param-eters influencing the re-saturation time the most are similar to those affecting thebuffer wetting time to near full saturation.

• The dissolution of air into bentonite water can be significant and is very sensitiveto parameters for which there is a large uncertainty and few reported experiments,such as the gas relative permeability curve in compacted bentonite.

• The method of Morris revealed a complex sensitivity structure between the con-sidered parameters and the outcome of the bentonite wetting simulations, withmarked interactions between parameters and severe non-linear behaviors.

Observations and modeling of BRIE as well as predictions for longer periods oftime, have shown that two-phase flow phenomena in fractured rock after being exposedto high suction forces and undergoing a drainage event can be sustained and durablyimpact the physical conditions in the rock. Such phenomena are also occurring in carbondioxide injection projects, for instance, or when thermal fluxes generate cryosuction,as it is the case in permafrost zones or in artificially frozen ground for geotechnicalapplications. Our understanding of the detailed two-phase processes in fractured rockis still subject to uncertainties. Continued modeling and experimental work is neededto arrive at consistent and case-specific constitutive relationships and parameter sets.The understanding of the flow structure is in turn an important prerequisite for reactivetransport models including complex biogeochemical cycles.

Finally, the study of bentonite samples and photographs from the dismantling ofBRIE illustrated the possible use of soft data to support spatial statistical modeling andobtain detailed snapshots of the bentonite wetting process at the interface with the rockwall. Such fine scale reconstruction could help characterize the heterogeneity of waterdelivery at the rock/bentonite interface which was identified as an important factor tocapture the buffer wetting. The proposed methodology could be applied and developedto provide more information on the in situ saturation of bentonite if applied to ongoingand envisioned experiments. Methods developed for remote-sensing of soil moisturecould provide synergies and possibly leverage fine scale information obtained with non-visible spectral bands. Beyond the scope of radioactive waste disposal, similar recon-struction methods could be of interest to integrate results from geophysical investigationsinto groundwater flow models.

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7 Acknowledgements

I am very grateful to the many people who made this thesis work possible and a rich ex-perience. First among them is my main advisor Jerker Jarsjö: constantly supportive andoptimistic when discussing new results (or a lack thereof), it was my pleasure to com-plete my PhD studies under your guidance. Second, is my co-advisor Andrew Frampton,always eager to sit and discuss the bearings of new exciting results or to explore newideas, thank you. I gratefully acknowledge the financial support of the Swedish NuclearFuel and Waste Management Co. (SKB). I am very grateful to many people in the SKBTask Force for Modeling of Groundwater Flow and Transport of Solutes: Björn Gylling,Jan-Olof Selroos, Patrik Vidstrand, Bill Lanyon and all the members of the modelinggroups involved in task 8. I would like to address a special thank you to the team incharge of BRIE for providing all the experimental data that were used in the presentanalyses, as well as the staff at the Äspö HRL for their invaluable help in making theBRIE experiment possible.

I would like to thank my colleagues or former colleagues in the Physical Geographydepartment at Stockholm University, and at KTH. You are too many to thank properlyon this page. Let me just say that your company made my time in Stockholm a rich andhappy one.

I want to express my gratitude to the people who helped me during a short stay at theLawrence Berkeley National laboratory: Jim, Laura, Daisuke, Pierre, Michael, Jonnyand Carol.

I would also like to gratefully acknowledge the Bert Bolin Center for financial sup-port to attend conferences and a summer school. I would also like to thank the organizersof the 3rd summer school on flow and transport in porous and fractured media in Cargèse,in particular Joaquin and Pietro, for sharing their enthusiasm and inspiration.

I am also in great debt to Vladimir Cvetkovic, my former advisor and mentor, whointroduced me to the world of scientific research and always kept an eye on my achieve-ments since our paths crossed.

Finally to the people outside of geoscience, to my family, to my friends, in France,in Sweden and other places, and to V., my valient partner in life, thank you all for yourunconditional support throughout these past four years.

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