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Large-scale numerical simulation of groundwater flow and solute transport in discretely-fractured crystalline bedrock

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Large-scale numerical simulation of groundwater ﬂow and solute transportin discretely-fractured crystalline bedrock
Daniela Blessent
a,
⇑
, Rene Therrien
b
, Carl W. Gable
c
a
Department of Civil, Geological and Mining Engineering, École Polytechnique, Montreal, C.P. 6079, succ. Centre-ville, Montréal, Québec, Canada H3C 3A7
b
Department of Geology and Geological Engineering, Université Laval, Ste-Foy, Québec, Canada G1V 0A6
c
Computational Earth Sciences Group, Earth and Environmental Sciences Division, Los Alamos National Laboratory, T003, Los Alamos, NM 87545, USA
a r t i c l e i n f o
Article history:
Received 17 May 2011Receivedinrevisedform13September2011Accepted 15 September 2011Available online 22 September 2011
Keywords:
OlkiluotoFracture zonesBoreholesNumerical modelingTetrahedra
a b s t r a c t
Alarge-scaleﬂuidﬂowandsolutetransport modelwasdevelopedforthecrystallinebedrockatOlkiluotoIsland, Finland, which is considered as potential deep geological repository for spent nuclear fuel. Sitecharacterization showed that the main ﬂow pathways in the low-permeability crystalline bedrock onthe island are 13 subhorizontal fracture zones. Compared to other sites investigated in the context of deep disposal of spent nuclear fuel, most deep boreholes drilled at Olkiluoto are not packed-off but areinstead left open. These open boreholes intersect the main fracture zones and create hydraulic connec-tions between them, thus modifying groundwater ﬂow. The combined impact of fracture zones and openboreholes on groundwater ﬂow is simulated at the scale of the island. The modeling approach couples ageomodel that represents the fracture zones and boreholes with a numerical model that simulates ﬂuidﬂow and solute transport. The geometry of the fracture zones that are intersected by boreholes is com-plex, and the 3D geomodel was therefore constructed with a tetrahedral mesh. The geomodel wasimportedintothenumericalmodeltosimulateapumpingtestconductedonOlkiluotoIsland. Thepump-ing test simulation demonstrates that fracture–borehole intersections must be accurately discretized,because they strongly control groundwater ﬂow. The tetrahedral mesh provides an accurate representa-tion of these intersections. The calibrated ﬂowmodel was then used for illustrative scenarios of radionu-clide migration to show the impact of fracture zones on solute transport once the boreholes werebackﬁlled. Thesemass transport simulations constitute base cases for future predictiveanalyses andsen-sitivity studies, since they represent key processes to take into consideration for repository performanceassessment.
2011 Elsevier Ltd. All rights reserved.
1. Introduction
Quantifying ﬂuid ﬂow and solute transport in fractured rock isrelevant in the ﬁelds of (i) groundwater withdrawal for watersupply, (ii) exploitation of mineral, petroleum and geothermal re-sources, (iii) geotechnical and mine engineering issues, and (iv)deep disposal of hazardous waste, in particular spent nuclear fuel.The concept of deep disposal of spent nuclear fuel in low-perme-ability geologic formations relies on isolating spent fuel from thebiosphere. The disposal system consists of iron/copper canistersplaced in vaults at a depth of at least 500m within a suitablegeological formation. Buffers and backﬁlls, such as bentonite, ﬁllthe gaps between the canister and the deposition hole walls [29].Recent research and development have increased the understand-ing of howundergrounddisposal facilities will functionover aboutone million years, which is the time frame usually considered forpost closure safety assessment studies, and have enhanced conﬁ-dence in the ultimate safety of the deep geological disposal of spent nuclear fuel [28]. Repository performance assessment aimsat demonstrating, through numerical simulations, that the spentfuel will remain isolated over the considered time frame. There-fore, mathematical modeling is required to investigate rockmechanics, rock–ﬂuid chemistry, tectonics, groundwater ﬂow andmass transport in geological formations considered for deep dis-posal and it must rely on appropriate conceptual and numericalmodels.For groundwater and mass transport modeling, which are thesubjects of this paper, different conceptual models for fracturedrockexistandthechoiceofaconceptualmodelforagivenapplica-tion depends on the scale of the problem, the geological formationproperties and the modeling objectives. The simplest conceptualmodel is based on the equivalent continuum approach, which wastheﬁrstapproachusedformodelingﬂowandtransportinfracturedmedia [9]. More complex models are based on two continua thatdistinguish ﬂuid ﬂow and solute transport in the fractures and in
0309-1708/$ - see front matter
2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.advwatres.2011.09.008
⇑
Corresponding author.
E-mail address:
daniela.blessent@polymtl.ca (D. Blessent).Advances in Water Resources 34 (2011) 1539–1552
Contents lists available at SciVerse ScienceDirect
Advances in Water Resources
journal homepage: www.elsevier.com/locate/advwatres
the rock matrix [6]. Another approach is the discrete fracturemodel, or discrete fracture network (DFN) model, that allows forthe explicit representation of fracture geometries. A distinctioncanbemadebetweenDFN,wherethesurroundingporousrockma-trixcontributionisneglected,anddiscretely-fracturedporousmed-ia, where ﬂuid ﬂows simultaneously along fractures and throughthe porous rock matrix surrounding the fractures [7].Andersson and Dverstorp [5] stated that ﬁeld investigations of ﬂow in fractured rock clearly demonstrate that modeling the rockasahomogeneouscontinuummightbeanoversimpliﬁcation.Like-wise, Neuman[26]statedthat allevidencesuggeststhatrarelycanone consistently model ﬂow and transport in fractured rock bytreatingit as a uniformor mildlynonuniformisotropic continuum.Althoughadiscretefracturemodelmayappearbettersuitedthanacontinuum model because transport mechanisms in individualfractures are explicitly taken into account, it increases the compu-tationaleffortandgenerallyrequiresmoreﬁelddata[9].Inconcep-tual models for discretely-fractured porous media, a distinction ismade between networks of fractures that are randomly locatedinspace[5,10,11]andthosewherethelocationofthediscretefrac-turesis known[3]. Irrespectiveof theconceptual approachchosen,modeling groundwater ﬂowin fractured rock is relatively complexbecause fractures can be as difﬁcult to observe and characterize asthey are to represent in a numerical model [34]. Moreover, it is akeychallengetodiscretizethestructural complexityof thegeolog-ical formations while maintaining model dimensions and meshresolution that are practical for ﬂow simulations [31].The hydrogeological modeling methodology for a geologicalrepository usually requires that several different types of numeri-cal models for ﬂuid ﬂow be developed, including a bedrock model[42]. The bedrock model focuses on the large-scale, or site-scale,groundwater ﬂow dynamics and simpliﬁes the geometry, proper-ties and water ﬂow processes close to and at ground surface byconsidering saturated groundwater ﬂow only [42]. The bedrockmodel usually covers an area of a few tens of square kilometersand extends to several hundred meters in depth. Examples of hydrogeological or hydrogeochemical modeling of crystalline rockenvironments related to the disposal of spent nuclear fuel havebeen described by several authors, such as Laaksoharju et al.[20], Maryška et al. [22], Molinero and Samper [25], Normani
et al. [27], and Selroos et al. [34].
The work presented here focuses on site-scale ﬂuid ﬂow andsolute transport in the crystalline bedrock at Olkiluoto Island, Fin-land, where site investigations have been conductedfor more than30yearstosupporttheconstructionofadeepgeologicalrepositoryfor spent nuclear fuel. The suitability of the Olkiluoto bedrock as ahost geological formation for the repository has been studiedthrough site characterization and performance assessmentanalyses. About 50 deep boreholes were drilled down to depthsof several hundred meters and have been used for various ground-water investigations. The crystalline bedrock contains several sub-horizontal major fracture zones whose spatial extent exceeds1km. These fracture zones control groundwater ﬂow at the site-scale. A 69-day pumping test was conducted in 2004, and draw-downwas monitoredat observationboreholeslocatedat distancesthat varyfromtens to hundreds of metersfromthe pumpingbore-hole. Because of its duration and the large spatial scale investi-gated, the pumping test provides a unique data set for calibratingagroundwater ﬂowmodel. Incomparisontoother bedrockstudiesmentioned previously, the site is also unique because the deepboreholes are left open and they create hydraulic connections be-tween the major fracture zones.Theobjectiveof thisworkis todevelopalarge-scalegroundwa-ter ﬂow model suitable to reproduce the complex geometry of thenetwork of irregular fracture zones and inclined boreholes and tosimulate the hydraulic response during the long-term pumpingtest. Additional objectives were to apply the modeling methodol-ogy presented by Blessent et al. [8] to a real ﬁeld-scale problemand demonstrate that irregular tetrahedral meshes are more suit-able than regular structured meshes (based on blocks or prisms)to simulate subsurface water ﬂow through networks of inclinedfracture zones and boreholes, and ﬁnally to present simulationsthat illustrate the impact of fracture zones on site-scale radionu-clidemigration.Themodelingmethodologyisbasedon(i)thecon-structionofathree-dimensionalgeologicalmodel(geomodel)fromﬁeld data such as borehole coordinates and fracture observations,(ii) the discretization of the geomodel with a tetrahedral mesh,and (iii) the simulation of groundwater ﬂow and solute transportusing a discretely-fractured porous rock conceptual model.
2. Study area and conceptual model
The Olkiluoto Island is located on the coast of the Baltic Sea insouthwestern Finland (Fig. 1). The annual precipitation is525mm. Karvonen [18] estimated that 60% of the annual precipi-tation returns to the atmosphere by evapotranspiration, that 35%becomes runoff and that the recharge to bedrock is approximately5–25mm/year [18].Various geological, hydrogeological and geophysical investiga-tions have been conducted at Olkiluoto since the 1980s to charac-terize the crystalline bedrock. The Olkiluoto bedrock is mainlygneiss from the Precambrian Fennoscandian Shield. Soil and over-burden layers overlie the crystalline bedrock and their averagethickness is 4m [18]. Analysis of core samples indicates that thebedrock average fracture frequency is 1–3 fractures/m. This fre-quency decreases with depth and most fractures are located intheﬁrst200m[38].Thesefracturesaredeﬁnedasbackgroundfrac-tures, as they have generally limited spatial extension, less thanhundred meters, and low transmissivity [40]. Field investigationsindicated that the upper portion of the bedrock, which extends toa depth of about 70m, has a higher hydraulic conductivity thanthe lower bedrock. In the lower part of the bedrock, the mosthydraulically-conductivefeaturesaresub-horizontalfracturezonesthathavepoorverticalconnectivity.Severalmethodssuchaslong-term pumping tests, pressure responses, vertical seismic proﬁlereﬂectors, and mise-a-la-masse geophysical surveys have helpeddeﬁnethegeometryandextentofthesefracturezones[2,39]. Theyare characterized by spatial extents and transmissivities much lar-ger than those of the background fractures. The major fracturezones considered here are listed in Table 1, where the acronymHZ stands for hydraulic zone and BFZ for brittle fault zone [4].Although other fracture zones have been observed, the fracturezones listed in Table 1 are the most important hydraulic featuresat the site-scale. Average fracture transmissivities were estimatedfrom ﬂow rate measurements at borehole–fracture intersections[40]. For each fracture zone, a constant aperture was then calcu-lated from its transmissivity based on the cubic law (Table 1).Construction of the ONKALO underground research laboratorystarted in 2004 for detailed hydrogeological characterization of the bedrock as well as for testing and demonstration purposes[38]. The ONKALO laboratory consists of an access tunnel of about5kminlengthandthreevertical shafts that reachadepthof about450m. During construction, the water table elevation was moni-tored in shallow and deep boreholes and piezometers. The long-termmeanelevationofthewatertableisshowninFig.2.Thewatertableelevationrangesbetween0m,whichisthesealevel,and9m.The unsaturated zone is only a few meters deep on the Island. Theanalysis of long-term hydraulic head data indicates that there is anatural seasonal decrease in hydraulic heads [1]. For the summers1991, 1994, 1996 and for the longer period January 2002–May2003, an average decreasing trend of 1cm/day was measured.
1540
D. Blessent et al./Advances in Water Resources 34 (2011) 1539–1552
Thedecreaseatagivenlocationdepends,however,onlocalproper-ties such as topography, spatial location, and porosity [37].
2.1. Geological model: fracture network and boreholes
The site-scale geological model developed here covers an areaof about 17km
2
and has a thickness of 1200m. It is located be-tween coordinates 6,791,000 and 6,794,500 along the Northingdirection and between coordinates 1,523,000 and 1,528,000 alongthe Easting direction (Figs. 1 and 2). The geological model was de-ﬁnedbyspecifyingthesizeofthesimulationdomain,thegeometryof the fracture zone network, and the fracture–borehole intersec-tions. It was built with GOCAD (http://www.gocad.org/www/), anintegrated 3D geological object modeling and visualization soft-ware [13].The ﬁrst geometrical representation of each fracture zone con-sists in coarse and irregular facets obtained by connecting localfracture observations (Fig. 3a). Facet vertices correspond to frac-ture observations obtained from core samples, borehole wallimages or geophysical surveys. For ﬂuid ﬂow and solute transportmodeling, fractures had to be represented by triangular meshes of higher resolution than that used for the geometrical representa-tion. Some additional steps were thus required to generate a ﬁnerand more uniform triangular mesh until it was considered appro-priate for ﬂow and transport modeling (Fig. 3b). Because theconnectivity between fractures is of primary importance forgroundwater ﬂow and contaminant transport [10], the last step
in developing the geological model for the fracture network con-sisted in accurately representing intersections between fracturesurfaces. A conforming triangular mesh was required at the inter-section lines, such that the triangles belonging to two distinctintersecting fractures share a common edge (Fig. 3b). Along these
Table 1
Fracture zones in the Olkiluoto model.
Fracture zone name Fracture transmissivitygeometric mean(log10)
a
(m
2
/s)Fracture aperture (m)HZ1
7.9 2.60
10
5
HZ2
6.0 1.12
10
4
HZ3
6.2 9.60
10
5
HZ4
6.8 6.06
10
5
HZ8
5.0 2.4
10
4
HZ19A
5.8 1.3
10
4
HZ19C
5.5 1.64
10
4
HZ20A
5.1 2.2
10
4
HZ20AE
6.0 1.12
10
4
HZ20B_ALT
5.5 1.63
10
4
HZ21
7.8 2.81
10
5
HZ21B
6.1 1.04
10
4
BFZ99
7.8 2.81
10
5a
Vidstrand et al. [40].
Fig. 1.
Plan view of Olkiluoto Island and location of boreholes represented in the model. Grid shows Easting and Northing UTM coordinates in meters.
D. Blessent et al./Advances in Water Resources 34 (2011) 1539–1552
1541
intersections, the number of nodes is minimized to optimize thesize of the segments and to obtain the best ﬁtting line [14]. Bore-holeswerealsointegratedinthegeologicalmodelandthetriangu-lar mesh representing fracture surfaces was reﬁned around itsintersection with boreholes. Boreholes were discretized withone-dimensional line elements. The resulting site-scale geologicalmodel for the fracture network and open boreholes at Olkiluotois shown in Fig. 4.
3. The large-scale KR24 pumping test
To predict the effect of the ONKALO underground laboratory ongroundwater ﬂow and to support the large-scale (100m to 1km)characterization of properties of hydraulically conductive fracturezones, a 69-day pumping test was conducted in deep boreholeKR24 from March 25 to June 2 2004, prior to starting constructionof the laboratory [37]. The location of borehole KR24 correspondsto that of the future ventilation shaft of the ONKALO such thatKR24 does not exist anymore. The borehole was cased down to adepth of 20.13m and, prior to the pumping test, a 1m packerequipped with a by-pass tube of length and diameter equal to 1m and 4mm, respectively, was installed at a depth of 80.60–81.60m [40], therefore creating a lower and upper section in theborehole. A submersible pump was installed in the upper sectionand, during pumping, water ﬂowed from the lower to the uppersection through the by-pass tube. The lower section of KR24 waspartially isolated by the packer during the test and the maximumdrawdown in that lower section was 2m, which was smaller thanthe maximum drawdown of 18m observed in the upper section.The upper section of borehole KR24 was intersected by fracturezone HZ19A only, while fracture zones HZ19C, HZ20A, andHZ20B_alt intersected the lower borehole section.During the test, groundwater was pumped at a constant rate of 18l/min with the submersible pump, while hydraulic heads weremeasured inshallowboreholes, multilevel piezometers, deepopenboreholes (without packers), and packed-off boreholes. Moreover,vertical proﬁles of ﬂow rates in and out of the borehole werelogged along the length of 12 open boreholes [37], which is a un-ique characteristic of this pumping test. The location and depthof boreholes are shown in Fig. 1 and in Table 2, respectively. The
boreholesareall inclined, except vertical KR24, andarecasedfromthe ground surface to depths of about 10m, to prevent groundwa-terclosetothesurfacefromﬂowingintotheboreholes[39].Atotalof 139 measuring sections in 68 observation boreholes and theupper and lower sections in pumped borehole KR24 weremonitored.
Fig. 2.
Interpolated observed mean water table elevation at Olkiluoto Island.
Fig. 3.
Modeling of fracture surfaces: (a) fracture facets obtained directly from ﬁeld data and (b) ﬁnal triangular mesh, with two intersection lines from other fractures.1542
D. Blessent et al./Advances in Water Resources 34 (2011) 1539–1552
Drawdown measured in deep open boreholes KR4, KR7, KR8,KR10,KR14,KR22,andKR28isshowninFig.5. Formostboreholes,there was an initial sharp increase in drawdown, occurring in theﬁrst few days after the test was started. Although the rate of in-crease in drawdown slowed down after a few days, it continuedto increase until the end of pumping. Part of the drawdown ob-served after the initial sharp increase was attributed to the naturaltrendindecliningheadsmentionedpreviously.Drawdownsharplydecreased immediately when the pumping stopped after 69days,but it did not return to the initial value of 0 after 90days, whichwas the end of the measurement period.
4. Numerical modeling of ﬂuid ﬂow and solute transport
4.1. Numerical simulator
HydroGeoSphere[35]isusedheretosimulatesaturatedsubsur-face ﬂow and solute transport in the discretely-fractured porousbedrock of Olkiluoto. The numerical solution of the ﬂow andtransport equations is based on the Control Volume Finite Elementmethod, CVFE, which produces discretized equations by applyingphysical conservation laws to control volumes surrounding meshnodes. The porous rock matrix is represented by 3D elements(blocks, prisms or tetrahedra), discrete fractures by 2D elements(triangles or squares), and wells, or boreholes, are representedby 1D linear elements. The common node approach used inHydroGeoSphere requires that fracture and borehole nodescorrespond to porous matrix nodes [35]. Common nodes ensurecontinuity of hydraulic head and concentration at fracture–matrixand borehole–matrix interfaces and there is no need to explicitlycalculate ﬂuid and mass leakage between fractures and porousrock matrix. The matrix equation is solved by a preconditionediterative solver, using either the ORTHOMIN, GMRES or BiCGSTABacceleration [35]. For the simulation presented below, theORTHOMIN acceleration was used.Details on the governing equations and on their discretizationare already presented by Therrien and Sudicky [36] and Therrienetal.[35]andarenotrepeatedhere,exceptforthediscretizedﬂowequation for the rock matrix. That equation is presented below todescribethecalculationoftransmissibilitycoefﬁcients,whichwereintroduced by Forsyth [15] and constitute the entries of the globalmatrix arising from the discretization of the governing equations.Thediscretizedequationfortransientsaturatedsubsurfaceﬂowin porous media, with no sources or sinks, is:
X
j
2
g
i
c
ij
ð
h
t
þ
D
t j
h
t
þ
D
t i
Þ¼
S
s
h
t
þ
D
t i
h
t i
D
t
!
v
i
ð
1
Þ
where
h
[L] isthehydraulichead,
S
s
[L
1
] isporousmediumspeciﬁcstorage,
v
i
[L
3
]isthecontrolvolumeassociatedtonode
i
, and
t
[T]istime. The left hand side of (1) represents ﬂuid ﬂow between node
i
and its neighbor nodes, indicatedby the subscript
g
i
in the summa-tion sign, which represents the set of nodes connected to node
i
.Transmissibility,
c
ij
[L
2
T
1
], is associated with the mesh segment joining nodes
i
and
j
and it corresponds to the integral of the Galer-kin ﬁnite element basis functions deﬁned on 3D ﬁnite elementsmultiplied by the medium hydraulic conductivity
K
[LT
1
]:
c
ij
¼
Z
v
r
N
i
K
r
N
j
d
v
ð
2
Þ
The integral can be solved analytically for 3D elements that are notdeformed compared to a reference element by using the inﬂuencecoefﬁcient technique presented by Huyakorn et al. [17] or by geo-metric considerations based on the Orthogonal SubdomainColloca-tion (OSC) method presented by Putti and Cordes [32] andimplemented in HydroGeoSphere by Blessent et al. [8]. The globalmatrix arising from the discretization of the governing equationsusing the OSC method leads to an M-matrix, a positive deﬁnite ma-trix with nonpositive off-diagonal entries. M-matrices are suitablewheniterativetechniquesareusedtosolvethesystemofequations,since they provide advantages in accuracy, stability, and runningtime[33].OneadvantageofM-matricesisthatsimulatednumericalﬂuxes between two connected mesh nodes are physically correctand unrealistic results are avoided, such as ﬂow in the directionof increasing hydraulic heads [12,19]. All simulations presentedhere are based on the OSC method.
4.2. Comparison of tetrahedral and block-based meshes
HydroGeoSphere can use either a tetrahedral mesh or a block-based mesh consisting of 8-node elements to discretize the spatialdomain. An example is described here to compare results fromblock-based and tetrahedral meshes. For this example, steady-state ﬂow was simulated in a cuboidal domain containing oneinclined pumping borehole intersecting one inclined discrete
Fig. 4.
Three-dimensional geological model of Olkiluoto Island showing boreholesand major fractures zones for (a) the whole domain and (b) a close-up of the modelin the areas of the boreholes.
Table 2
Boreholes in the Olkiluoto model.
Borehole name Borehole depth (m) Borehole inclination (
)KR4
870 77KR6
466 50KR7
750 70KR8
530 64KR9
530 70KR10
602 85KR12
761 70KR14
462 70KR22
410 60KR23
250 60KR24
540 90KR25
567 70KR27
430 55KR28
515 55
D. Blessent et al./Advances in Water Resources 34 (2011) 1539–1552
1543

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