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P O S I V A O Y
O l k i l u o t o
F I -27160 EURAJOKI , F INLAND
Te l +358-2-8372 31
Fax +358-2-8372 3709
Lee Har t l ey , Jaap Hoek , Dav id Swan
Dav id Rober ts , S teve Joyce
Sven Fo l l i n
August 2009
Work ing Repor t 2009 -61
Development of a Hydrogeological DiscreteFracture Network Model for the Olkiluoto Site
Descriptive Model 2008
August 2009
Base maps: ©National Land Survey, permission 41/MML/09
Working Reports contain information on work in progress
or pending completion.
The conclusions and viewpoints presented in the report
are those of author(s) and do not necessarily
coincide with those of Posiva.
Lee Hart ley , Jaap Hoek , Dav id Swan
Dav id Roberts , Steve Joyce
Serco TAS
Sven Fo l l i n
SF GeoLog ic AB
Work ing Report 2009 -61
Development of a Hydrogeological DiscreteFracture Network Model for the Olkiluoto Site
Descriptive Model 2008
ABSTRACT
The work reported here (2008 OHDFN) constitutes the hydrogeological discrete
fracture network (Hydro-DFN) model for the Olkiluoto site descriptive model 2008.
The report collates the structural-hydraulic information gathered in 40 long (KR) and 16
short (KRB) sub-vertical boreholes drilled from the surface. This information was
compared with the structural-hydraulic information gathered in seven short (PH) sub-
horizontal pilot boreholes drilled from the ONKALO tunnel. The report presents:
An interpretation of the hydraulic information (fracture core data and Posiva flow
log (PFL) data) in the context of structural subdomains defined in the Geo-DFN
developed from surface, borehole and pilot-hole data.
The derivation of a Hydro-DFN model for each sub-domain, which were further
sub-divided by depth, suitable for describing flow and transport properties in the
rock between the deterministically defined hydro zones.
Predictions of frequencies, orientations and transmissivities of water conducting
fractures in two pilot holes (PH) not drilled at the time of this work (PH8 and PH9).
Equivalent continuum porous medium (ECPM) hydraulic properties for the rock
between hydro zones in sub-domains in the immediate vicinity of the repository.
Transport properties based on particle tracking through the rock between hydro
zones in sub-domains in the immediate vicinity of the repository.
Site-scale groundwater flow and transport pathway statistics.
Site-scale ECPM model paramaterisation in support of the FEFTRA ECPM site
modelling.
The analyses carried out provide an input to the hydrogeological DFN descriptions of
the bedrock in between hydro zones needed for the construction of 3D groundwater
flow models of the Olkiluoto site as well as in the subsequent safety performance
assessment. It would be useful to review if the methodology reported here could be
refined with a view to integrate with hydrochemistry, which was never part of the study.
Keywords: Hydrogeology, discrete fracture network, hydraulic properties, modelling
Hydrogeologisen rakoverkkomallin kehittäminen vuoden 2008 Olkiluodon paikkamalliin
TIIVISTELMÄ Tässä raportissa kuvataan Olkiluodon 2008 paikkamallin osaksi muodostettu hydro-
geologinen rakoverkkomalli (Hydro-DFN). Geometrialtaan ja hydraulisilta ominai-
suuksiltaan malli perustuu tietoon pinnalta kairatuista 40:tä pitkästä (KR) ja 16:ta
lyhyestä (KRB) kairanreiästä. Näistä kerättyä rakoilutietoa on verrattu seitsemästä
ONKALOn pilottireiästä (PH) kerättyyn aineistoon.
Raportissa esitetään tulkinta hydraulisista havainnoista geologisessa rakoverkomal-
lissa määritellyissä kallioperän voluumeissa kairansydän ja Posivan virtausmittari-
aineistoon perustuen. Olkiluodon geologisessa rakoverkkomallissa tutkimusalueen
kallioperä on jaettu pinta-, kairanreikä- ja pilottireikähavaintojen pohjalta kahteen
alivolyymiin.
Hydro-DFN malli on esitetty kallioperän eri alivolyymeille. Geologisen rakoverkko-
mallin alivolyymijaon lisäksi Hydro-DFN malli on jaettu syvyysvyöhykkeisiin, joita
käytetään determinististen vyöhykkeiden välissä olevan taustarakoilun virtaus- ja
kulkeutumisominaisuuksien kuvaamiseen.
Vettäjohtavien rakojen tiheydet sekä asento- ja vedenjohtokykyjakaumat on ennus-
tettu kahdelle ONKALOn pilottireiälle (PH8 ja PH9), joita ei tämän työn tekemisen
aikaan vielä ollut kairattu.
Rakoverkkomalliin perustuen esitetään arvio ekvivalenteista hydraulisista ominai-
suuksista (ECPM) determinististen rakenteiden välisessä taustarakoilussa kallio-
perän eri alivolyymeissa loppusijoitustilan ympäristössä.
Raportissa arvioidaan myös kulkeutumisominaisuuksia taustarakoilussa loppu-
sijoitustilan välittömässä läheisyydessä,
sekä virtaus- ja kulkeutumisominaisuuksia tutkimuspaikan mittakaavassa.
Rakoverkkomallinnuksen avulla on myös arvioitu ECPM mallin parametrisointia
tutkimuspaikan mittakaavassa huokoisen väliaineen mallinnuksen (FEFTRA) tueksi.
Mallinnuksen tuloksia voidaan käyttää hyväksi muodostettaessa rakoverkkomalliin
perustuva tutkimuspaikan mittakaavan pohjaveden virtausmalli. Tätä kautta työn tulok-
sia voidaan käyttää hyväksi myös turvallisuusanalyysissä.
Avainsanat: Hydrogeologia, rakoverkkomalli, hydrauliset ominaisuudet, mallinnus
1
TABLE OF CONTENTS
ABSTRACT
TIIVISTELMÄ
1 INTRODUCTION .................................................................................................. 5
1.1 Background ........................................................................................................... 5 1.2 Objectives and scope ............................................................................................ 5
1.2.1 Objectives ................................................................................................. 5 1.2.2 Scope ........................................................................................................ 6
1.3 Structure of this report ........................................................................................... 6 1.3.1 Phase I ...................................................................................................... 6 1.3.2 Phase II ..................................................................................................... 7 1.3.3 Addendum work ........................................................................................ 8
2 NOMINAL MODEL AREAS OF OLKILUOTO ........................................................ 9
3 HYDRO ZONES AND FRACTURE DOMAINS .................................................... 11
3.1 Model of hydro zones .......................................................................................... 11 3.2 Model of fracture domains ................................................................................... 12
4 PRIMARY DATA ................................................................................................. 15
4.1 Single-hole hydraulic tests .................................................................................. 15 4.2 Quality assurance assessment ........................................................................... 18
4.2.1 KR and KRB boreholes ........................................................................... 18 4.2.2 Pilot holes ............................................................................................... 18
5 FRACTURE DATA ANALYSIS ............................................................................ 21
5.1 Assumptions ....................................................................................................... 21 5.2 Methodology ....................................................................................................... 23 5.3 Fracture orientation ............................................................................................. 24
5.3.1 Hard sectors ............................................................................................ 24 5.3.2 Contoured stereonets showing all fractures and the PFL data ................. 26 5.3.3 Discrete stereonets showing the PFL transmissivities ............................. 29
5.4 Fracture intensity ................................................................................................ 31 5.4.1 Depth zones ............................................................................................ 31
6 HYDROGEOLOGICAL DFN MODELLING .......................................................... 41
6.1 Overview ............................................................................................................. 41 6.2 Fracture set definitions ........................................................................................ 43 6.3 Model domain ..................................................................................................... 43 6.4 Modelling approach ............................................................................................. 44
6.4.1 Case A – power-law size distribution ....................................................... 44 6.4.2 Case B – log-normal size distribution ...................................................... 45 6.4.3 Step 1...................................................................................................... 45 6.4.4 Step 2...................................................................................................... 49 6.4.5 Step 3...................................................................................................... 49
6.5 Comparison of the two fracture size distribution models ...................................... 49 6.6 Simulation of Posiva Flow Log (PFL-f) tests ........................................................ 59
6.6.1 Modelling approach ................................................................................. 59 6.6.2 Comparison of the three fracture transmissivity-size models ................... 60
6.7 Summary of Hydro-DFN models ......................................................................... 66
2
6.7.1 FDb: Depth zone 1 (0 to –50m elevation) ................................................ 67 6.7.2 FDb: Depth zone 2 ( –50 to –150m elevation) ......................................... 68 6.7.3 FDb: Depth zone 3 (–150 to –400m elevation) ........................................ 69 6.7.4 FDb: Depth zone 4 (–400 to –1 000m elevation) ..................................... 70
7 PREDICTION OF WATER CONDUCTING FRACTURES IN TWO TUNNEL PILOT HOLES – PH8 AND PH9 ......................................................................... 71
7.1 Pilot holes PH8 and PH9 ..................................................................................... 71 7.2 Modelling approach ............................................................................................. 71 7.3 Hydro-DFN .......................................................................................................... 72 7.4 Prediction ............................................................................................................ 72 7.5 Uncertainty assessment ...................................................................................... 74
8 REPOSITORY-SCALE EQUIVALENT CONTINUUM POROUS MEDIUM (ECPM) BLOCK PROPERTIES ........................................................................................ 79
8.1 Objectives ........................................................................................................... 79 8.2 Model set-up ....................................................................................................... 79 8.3 Example visualisations ........................................................................................ 79 8.4 Studied cases ..................................................................................................... 79 8.5 Effective hydraulic conductivity............................................................................ 82 8.6 Effective kinematic porosity ................................................................................. 82 8.7 Summary of the upscaling study ......................................................................... 83
9 REPOSITORY-SCALE FRESHWATER FLOW AND TRANSPORT .................... 89
9.1 Objectives ........................................................................................................... 89 9.2 Model set-up ....................................................................................................... 89 9.3 Fraction of deposition holes connected to the DFN ............................................. 92
9.3.1 Case A-C/SC/UC-FDb-DZ3 ..................................................................... 92 9.3.2 Case A-C/SC/UC-FDb-DZ4 ..................................................................... 93 9.3.3 Case A/B-SC-FDb-DZ3 ........................................................................... 94 9.3.4 Case A/B-SC-FDb-DZ4 ........................................................................... 94
9.4 Travel times and F-quotients ............................................................................... 95 9.4.1 Directional values for Case A-C/SC/UC-FDb-DZ3 ................................... 96 9.4.2 Minimum values for C/SC/UC in DZ3 and DZ4 ........................................ 98 9.4.3 Minimum values for Case A and Case B in DZ3 and DZ4 ..................... 100
9.5 On the role of HZ for DFN connectivity .............................................................. 101 9.6 Summary .......................................................................................................... 102
10 SUMMARY AND CONCLUSIONS OF PHASE I ............................................... 105
10.1 General ............................................................................................................. 105 10.2 Results from Phase I ......................................................................................... 105
10.2.1 Hydro zones, fracture domains and Geo-DFN ....................................... 105 10.2.2 Primary data .......................................................................................... 105 10.2.3 Key assumptions ................................................................................... 106 10.2.4 Fracture orientations ............................................................................. 106 10.2.5 Fracture intensity ................................................................................... 106 10.2.6 Fracture size ......................................................................................... 107 10.2.7 Fracture transmissivity .......................................................................... 108 10.2.8 Prediction of water conducting fractures ................................................ 108 10.2.9 Repository-scale ECPM block properties .............................................. 109 10.2.10 Repository-scale freshwater flow and transport PA properties ............... 109
10.3 Discussion ........................................................................................................ 110 10.4 Outstanding issues – data interpretation ........................................................... 110
3
11 SITE-SCALE EQUIVALENT CONTINUUM POROUS MEDIUM (ECPM) BLOCK PROPERTIES ................................................................................................... 113
11.1 Objectives ......................................................................................................... 113 11.2 Model set-up ..................................................................................................... 113 11.3 Visualisations .................................................................................................... 113 11.4 Effective hydraulic conductivity.......................................................................... 113 11.5 Effective kinematic porosity ............................................................................... 115 11.6 Block property statistics .................................................................................... 118
12 SITE-SCALE FRESHWATER FLOW AND TRANSPORT ................................. 123
12.1 Objectives ......................................................................................................... 123 12.2 Model set-up ..................................................................................................... 123 12.3 Example visualisations – Case 1-1 .................................................................... 125
12.3.1 Transport statistics ................................................................................ 130 12.3.2 Case 1-1 – a single realisation of the model with one particle per start
position .................................................................................................. 130 12.3.3 Case 1-10 – a single realisation of the model with ten particles per start
position .................................................................................................. 136 12.3.4 Case 10-10 – ten realisations of the model with ten particles per start
position .................................................................................................. 141
13 SITE-SCALE SALTWATER FLOW AND TRANSPORT .................................... 143
13.1 Objectives ......................................................................................................... 143 13.2 Model set-up ..................................................................................................... 143 13.3 Results .............................................................................................................. 143
14 SUMMARY AND CONCLUSIONS OF PHASE II .............................................. 149
14.1 General ............................................................................................................. 149 14.2 Results from Phase II ........................................................................................ 149
14.2.1 Upscaling .............................................................................................. 149 14.3 Flow and transport ............................................................................................ 150 14.4 Outstanding issues – site modelling .................................................................. 151 14.5 Future Hydro-DFN studies ................................................................................ 151
REFERENCES ......................................................................................................... 153
Appendix A: Pilot holes PH1-7 .................................................................................. 155
Appendix B: Repository-scale ECPM properties ....................................................... 163
Appendix C: Repository-scale particle tracking results .............................................. 189
Appendix D: Hydro zone properties .......................................................................... 221
Appendix E: Primary HYDRO-DFN data references.................................................. 223
Appendix F: On the role of the ‘guard zone’ technique and different spatial scales for the calculation of ECPM block conductivity ........................................... 225
4
5
1 INTRODUCTION
1.1 Background
A hydrogeological discrete fracture network (Hydro-DFN) study of Olkiluoto is
required as part of the 2008 site descriptive model (SDM) to provide an integration of
fracture geometrical and hydraulic data from boreholes (KR and KRB), pilot holes (PH)
and tunnels with site-scale groundwater flow and solute transport modelling. The
objective being to give better support to the description of groundwater flow and
transport processes and parameters based on detailed data from the field.
There are several interfaces to other disciplines required by this type of work. The
conceptual framework for fracturing was taken from the geological discrete fracture
network (Geo-DFN) as input, along with fracture mapping and Posiva Flow Logging
(PFL) of flowing features, and the structural model of deformation zones.
1.2 Objectives and scope
1.2.1 Objectives
For practical reasons, the work was divided into two phases. The aims for the 2008
Hydro-DFN study of Olkiluoto (2008 OHDFN) include:
Phase I (June 2008)
To produce a Hydro-DFN model for the sub-domains defined in the Geo-DFN
calibrated on surface borehole and pilot-hole data (fracture core data and PFL data)
suitable for describing flow and transport properties in the immediate repository
target volume
To make predictions of frequencies, orientations and transmissivities of water
conducting fractures in two pilot holes not drilled at the time of this work.
To provide hydraulic properties to support the FEFTRA EPM modelling.
To investigate groundwater flow and transport pathway statistics through the
bedrock appropriate to the bedrock immediate to the repository.
Phase II (November 2008)
To investigate groundwater flow and transport pathway statistics through the
bedrock on a site-scale.
To derive site-scale equivalent continuum porous medium (ECPM) hydraulic and
transport properties in support of FEFTRA ECPM modelling.
To describe the Hydro-DFN in a supporting document to the SDM 2008.
6
1.2.2 Scope
Phase I
Performing a statistical analysis of fracturing observed in 56 sub-vertical surface
boreholes (KR and KRB) and 7 sub-horizontal tunnel pilot holes (PH) with
particular focus on water conducting fractures.
Specifying an appropriate conceptual model for a Hydro-DFN, e.g. defining
appropriate hydraulic fracture domains based on spatial trends including depth and
fracture domain.
Parameterise a Hydro-DFN suitable for describing flow and transport properties in
the immediate repository target volume.
Making predictions on frequencies, orientations and transmissivities of water
conducting fractures in two planned tunnel pilot holes.
Calculate 50m ECPM block-scale properties for a bedrock volume appropriate to
the repository-scale.
Investigate groundwater flow and transport pathway statistics through the bedrock
immediate to the repository volume.
Phase II
Parameterise all remaining hydraulic fracture domains calibrated on deep borehole
and pilot-hole data (fracture core data and PFL data).
Calculate 50m ECPM block-scale properties for a bedrock volume appropriate to
the site-scale.
Produce a site-scale Hydro-DFN model including the hydro-structural features for
calculating groundwater flow and transport pathway statistics through the bedrock.
Reporting the findings and responding to review comments.
1.3 Structure of this report
1.3.1 Phase I
Section 2 presents an overview of the nominal model areas of Olkiluoto.
Section 3 presents the deterministically modelled hydrogeological zones (also called
hydro zones and denoted by HZ) and a suggested division of the bedrock in between
the hydro zones into two fracture domains. These are here referred to as FDa and
FDb. FDa occurs above the suite of zones referred to as HZ20A-B, whereas FDb
occurs below this suite of zones. The division is in line with the hanging wall and
footwall bedrock concept suggested in the geological DFN model.
7
Section 4 presents an overview of the primary data gathered with the PFL method in
the KR, KRB and PH boreholes. The presentation is made with regard to the
modelled hydro zones and fracture domains. Section 4 also provides a list of reasons
why it was not possible to use all the all PFL data coinciding with the two fracture
domains in the Hydro-DFN modelling reported here.
Section 5 collates the fracture data gathered in the KR and KRB boreholes with
regard to fracture type (all, open, PFL), fracture set (orientation; NS, EW, SH),
bedrock segment (HZ, FDa, FDb) and elevation (depth zone; DZ1, DZ2, DZ3,
DZ4). The primary output of the data compilation is the computed Terzaghi
corrected linear (1D) fracture intensities. The linear intensities are used as estimates
of the fracture surface area per unit volume of bedrock. Appendix A collates the
fracture data gathered in the PH boreholes. The PH borehole statistics are for
verification tests in the Hydro-DFN modelling reported here, see Section 7.
Section 6 concerns numerical simulations with the objective to derive optimal model
parameter values for fracture size and fracture transmissivity in fracture domain
FDb using data from the KR and KRB boreholes. The modelling is done in
sequence, fracture size model parameter values being determined first.
- The size analysis explores two different distribution models, power-law (Case
A) and log-normal (Case B), based on a decision by Posiva /Löfman and Poteri
2008/. Optimal parameter values for each size model are determined with regard
to the computed Terzaghi corrected linear fracture intensities. A key component
in the optimisation is the requirement of fracture connectivity.
- The transmissivity analysis explores three different models relating fracture
transmissivity and fracture size: correlation without uncertainty, correlation with
uncertainty (semi-correlation) and no correlation (random uncertainty). The
optimisation is made with regard to several criteria, the most important of which
being the histogram of measured specific capacities (Q/s, also called specific
flow rates). Hydro-DFN model parameters are collated with regard to the four
depth zones DZ1-DZ4 in fracture domain FDb.
Section 7 presents predictions of frequencies, orientations and transmissivities of
water conducting fractures in two, planned tunnel pilot holes, PH8 and PH9.
Section 8 presents ECPM effective hydraulic properties for the bedrock immediate
to the repository.
Section 9 presents groundwater flow and transport pathway statistics through the
bedrock immediate to the repository.
Section 10 discusses the findings during Phase I.
1.3.2 Phase II
Section 11 presents ECPM equivalent hydraulic properties for the Olkiluoto site-
scale bedrock.
8
Section 12 presents freshwater flow and transport pathway statistics for the
Olkiluoto site-scale bedrock.
Section 13 presents saltwater flow and transport pathway statistics for the Olkiluoto
site-scale bedrock.
Section 14 discusses the findings during Phase II
1.3.3 Addendum work
Update of kinematic porosities used in Phase I
The effective kinematic porosity is calculated as the cumulative volume of the flowing
pore space divided by the block volume. In Phase I, the contribution to the flowing pore
space was calculated from the following function (cf. section 8.6):
et = 0.46 T (8-3)
where et is the transport aperture and T is the fracture transmissivity.
In Phase II, the contribution to the flowing pore space was calculated from the cubic law
for the connected fractures (cf. section 11.5):
eh = (T / ( g))1/3
(11-2)
et = 4 eh (11-3)
Posterior to the completion of the flow modelling work, it was decided to update the
kinematic porosities derived in the ECPM effective hydraulic properties for the bedrock
immediate to the repository. The update is reported as an addendum to Appendix B.
Upscaling of equivalent block conductivities
In Phase I (Chapter 8), the „guard zone‟ technique in ConnectFlow /Jackson et al. 2000/
was used where flow is calculated in a domain, 150 m, but only the flux through central
50 m block is used to calculate the equivalent hydraulic conductivity tensor, Keff. In
Phase II (Chapter 11), the „guard zone‟ technique was not used while the equivalent
hydraulic conductivity tensor was calculated for the 50 m block.
It was suggested in Chapter 14 that it is the use of the „guard zone‟ technique that cause
the lower mean hydraulic conductivities in depth zones 2-4 of the repository-scale
model compared those of the site-scale model, cf. Table 14-1.
In Chapter 14, it was also suggested that the dependence of upscaled hydraulic
properties on spatial scale needs to be studied further to quantify the uncertainty in
groundwater fluxes depending on the choice of spatial resolution in ECPM models.
In conclusion, while completing this modelling report it was decided to investigate the
issues further to better quantify the origin of the differences seen. The upscaling cases
studied are: „50 m‟, „30 m‟ and „guard zone (50 m)‟. The results are reported in the
addendum in Appendix F.
9
2 NOMINAL MODEL AREAS OF OLKILUOTO
Olkiluoto is situated on an island in the southwest of Finland within the municipality of
Eurajoki about 200 km west of Helsinki. Figure 2-2 shows a map of the Olkiluoto area.
The site area is located in the centre of island and the ONKALO area is located in the
centre of the site area.
Figure 2-1. A plane view of the nominal model areas of Olkiluoto. The location of the
Olkiluoto site area is shown in the centre. Reproduced from /Mattila et al. 2008/.
Figure 2-2 shows a close up of the site (investigation) area together with boreholes and
investigation trenches. The site area is modelled in 3D. Figure 2-3 shows a 3D view of
the Olkiluoto island showing the model volume of the geological site model (GSM).
The present version of the GSM (version 1) is described in /Mattila et al. 2008/ and is an
update of the initial version (version 0) described in /Paulamäki et al. 2006/. Version 1
combines the results of geological surface mapping, drill core studies and tunnel
mapping, with interpretations of geophysical data from airborne and ground surveys,
and geophysical borehole measurements. The development has greatly benefited from
the discussions with the end users of the model, i.e. rock mechanics, hydrogeology and
hydrogeochemistry, during the many integration meetings after the release of the initial
version. It should be noted that the GSM activities run parallel with activities related to
modelling of a much smaller model volume, whose upper surface is represented by the
ONKALO area (see Figure 2-1). The aim of the ONKALO model, which essentially
contains the ONKALO access tunnel and will contain the future ONKALO rock
characterisation facility, is to support the rock engineering effort and provide rock
mechanics and hydrogeological predictions as tunnelling proceeds.
10
Figure 2-2. Map of the Olkiluoto site (investigation) area with surface boreholes OL-
KR1 to OL-KR43. (Data from OL-KR1 to OL-KR40 are used in the work reported
here.) Reproduced from /Mattila et al. 2008/.
Figure 2-3. A 3D view of Olkiluoto island showing the model volume of the geological
site model described in /Mattila et al. 2008/. The sub-vertical boreholes drilled from the
surface and the ONKALO access tunnel are shown within the model volume.
Reproduced from /Mattila et al. 2008/.
11
3 HYDRO ZONES AND FRACTURE DOMAINS
A cornerstone of the bedrock hydrogeological description concerns the hydraulic
characterisation of the more intensely fractured deformation zones and the less fractured
bedrock in between (outside) these zones. The approach taken by Posiva combines a
deterministic representation of the hydrogeologically active deformation zones (HZ)
with a stochastic representation of the less fractured bedrock outside these zones using a
hydrogeological discrete fracture network (Hydro-DFN) concept. The HZ and Hydro-
DFN models are parameterised hydraulically with data from single-hole Posiva Flow
Log (PFL) pumping tests.
3.1 Model of hydro zones
From a hydrogeological perspective, the geological deformation zones describe the
potential pathways for fluid flow. The hydro zone (HZ) model presented by /Ahokas et
al. 2007/ and /Vaittinen et al. 2009/ describes site-scale hydrogeologically active
deformation zones, where high transmissivities are common and hydraulic connections
between boreholes are detected as pressure and flow responses during pumping tests
and other field activities. One zone is based on anomalous low head observations. These
studies suggest that the most important hydrogeological zones in the Olkiluoto site area
are zones HZ19A-C, HZ20A-B and HZ21. However, due to known heterogeneity of
hydraulic properties, no particular definition for measured transmissivity has been
determined for the definition of a hydro zone. Figure 3-1 shows the site-scale hydro
zones provided for the work reported here.
Figure 3-1. Visualisation of the site-scale hydro zone (HZ) model based on /Vaittinen et
al. 2009/.
12
3.2 Model of fracture domains
The idea of the fracture domain concept is to homogenise the spatial variations observed
in the fracture data in between zones. Ideally, the rock units within a well defined
hydrogeological fracture domain show less variation in the fracture characteristics
(orientation, intensity (frequency), size, spatial distribution) and fracture transmissivity
than between fracture domains.
The attempted division of the bedrock within the Olkiluoto site area into two fracture
domains is based on a notion suggested in the geological DFN modelling. According to
/Buoro et al. 2009/, the bedrock in the surroundings of the ONKALO tunnel can be
separated into an upper rock block (hanging wall bedrock) and an intermediate zone,
and a lower rock block (footwall bedrock). The extension of the intermediate zone is
approximately given by the extension of the of two large gently-dipping geological
deformation zones, BFZ080 and BFZ098. According to /Ahokas et al. 2007/ and
/Vaittinen et al. 2008/, zone BFZ080 and zone BFZ098 intersect almost the same
borehole sections (intervals) as zone HZ20A and zone HZ20B. The transmissivity of the
two hydrogeological zones vary typically between 10–6
and 10–5
m2/s /Ahokas et al.
2007/ and /Vaittinen et al. 2008/.
Following the notion of a hanging wall segment and a footwall segment, the bedrock
above zone HZ20A is here referred to as „fracture domain above‟ (FDa) and bedrock
below zone HZ20B as „fracture domain below‟ (FDb). For the sake of the work reported
here, an algorithm was defined and used to determine if a particular fracture in between
the hydrogeological zones occur in fracture domain FDa or in FDb. The algorithm was
defined by manually fitting a plane to the bottom of zone HZ20B and computing the
normal equation of that plane:
0)cos()cos()cos( pzyx (3-1)
where cos( ), cos( ) and cos( ) are the direction cosines of the normal to the fitted
plane and p is the distance from the plane to the origin of the coordinate system. For
fractures above the plane, i.e. fractures in FDa, the left hand side of Equation (3-1) > 0
and vice versa. The values of cos( ), cos( ), cos( ) and p are shown in Table 3-1.
Figure 3-2 shows a visualisation of the boreholes and the positions of the PFL data
provided for hydrogeological DFN modelling in the work reported here. Fracture
domain FDa occurs above the highlighted zones HZ20A and HZ20B, whereas fracture
domain FDb occurs below.
Table 3-1. Parameter values of the normal equation of the plane used to determine
whether a particular fracture occurs in fracture domain FDa or fracture domain FDb.
cos( ) cos( ) cos( ) p
0.251157128 –0.29931741 0.920504853 1650080.0
13
Figure 3-2. Visualisation of the boreholes and the positions of the PFL data based on
/Vaittinen et al. 2009/. Fracture domain FDa occurs above the highlighted zones
HZ20A and HZ20B, whereas fracture domain FDb occurs below. View towards the
southwest.
14
15
4 PRIMARY DATA
This section describes the data used in the construction of Hydro-DFN models of the
bedrock in between the hydrogeological zones, i.e. fracture domains FDa and FDb and
their associated depth zones (cf. section 3). Hydraulic data (fracture transmissivities) are
determined with the Posiva Flow Log (PFL) and the associated geometrical data
(fracture positions and orientations) are determined from drill core mapping and/or
borehole TV images.
The PFL method is a geophysical logging device developed to detect continuously
flowing fractures in sparsely fractured crystalline bedrock by means of difference flow
logging, see Figure 4-1. The physical limitations of the measurement device and the
principles for operation are explained in the measurement reports. The practical lower
measurement limit (threshold) of the PFL method in terms of transmissivity is typically
T 10–9
m2/s. For an example, a view of high transmissivities (T > 10
–6 m
2/s) observed
in KR1-KR39 is presented in Figure 4-2.
4.1 Single-hole hydraulic tests
Fracture transmissivities are measured systematically with PFL method in the following
boreholes:
40 KR surface boreholes: (OL-)KR1 to KR40
16 KRB surface boreholes: (OL-)KR15B-20B, KR22B-23B, KR25B, KR27B,
KR29B, KR31B, KR33B, KR37B, KR39B-40B
7 PH tunnel boreholes: (ONK-)PH1-PH7
Due to practical reasons, the names of the boreholes are in this report given without OL-
and ONK-prefixes, e.g. OL-KR1 is in this report referred to as KR1, OL-KR15B as
KR15B, ONK-PH1 as PH1, etc. Moreover, the tunnel boreholes PH1-7 are here referred
to as pilot holes. The pilot holes are sub-horizontal boreholes, whereas the surface
boreholes are sub-vertical.
Appendix E lists the references that describe the data acquisition in each of the used
boreholes. An overview of the hydrogeological database is found in /Tammisto et al.
2009/.
Table 4-1 shows the number of PFL data in each borehole with regard to fracture
domains and hydro zones. >T< denotes the total number of PFL data in the two fracture
domains, FDa and FDb, that were not possible to use in the Hydro-DFN modelling for
one or several reasons, e.g. missing position data, orientation data or transmissivity data,
see Section 4.2.
16
WinchPumpComputer
Flow along the borehole
Rubberdisks
Flow sensor-Temperature sensor is located in the flow sensor
Single point resistance electrode
EC electrode
Measured flow
Figure 4-1. Schematic drawing of the down-hole equipment used for difference flow
logging in Olkiluoto. Reproduced from /Sokolnicki and Rouhiainen 2005/.
View from southwest
Boreholes KR1-KR39
Red=T>1E-5
Purple=T>1E-6
View from southwest
Boreholes KR1-KR39
Red=T>1E-5
Purple=T>1E-6
Figure 4-2. Position of PFL transmissivities in boreholes KR1-KR39 (T >10–5
m2/s are
shown in red, 10–6
<T<10–5
m2/s are shown in purple). View towards the northeast.
Discs representing transmissivities do not show the orientation of fractures i.e. they all
are perpendicular to the axis of a borehole. Reproduced from /Ahokas et al. 2007/.
17
Table 4-1. Compilation of the number of PFL data in each borehole with regard to
fracture domains (FDa and FDb) and hydro zones (HZ). >T< denotes the total number
of PFL data in the two fracture domains that were not possible to use in the Hydro-
DFN modelling for one or several reasons, e.g. a missing transmissivity value, position
and/or orientation.
KR 1 2 3 4 5 6 7 8 9 10 11 12 13 14
FDa 16 14 0 11 0 0 21 46 50 14 16 31 55 74
FDb 37 21 59 6 39 55 28 0 5 16 14 20 15 8
HZ 14 3 0 10 5 1 11 21 6 2 3 3 2 2
>T< 7 2 6 3 4 11 11 1 1 4 3 6 8 5
KR 15 15B 16 16B 17 17B 18 18B 19 19B 20 20B 21 22
FDa 27 15 41 12 26 12 18 17 0 0 10 25 0 28
FDb 6 0 0 0 0 0 0 0 100 12 26 0 22 1
HZ 2 6 2 2 1 1 2 2 5 0 6 0 0 10
>T< 15 3 9 5 6 2 5 5 9 0 4 1 6 7
KR 22B 23 23B 24 25 25B 26 27 27B 28 29 29B 30 31
FDa 19 38 18 10 31 9 19 71 11 21 8 12 22 45
FDb 0 0 0 1 10 0 0 0 0 3 4 0 0 0
HZ 0 8 0 3 10 0 0 9 0 15 9 0 2 11
>T< 0 3 3 2 6 3 2 5 0 9 3 0 4 11
KR 31B 32 33 33B 34 35 36 37 37B 38 39 39B 40 40B
FDa 17 35 0 0 60 32 43 27 19 26 6 6 13 3
FDb 0 15 70 8 0 0 0 0 0 6 22 0 3 0
HZ 0 0 0 0 6 4 3 5 0 8 0 0 2 0
>T< 1 3 15 1 8 5 4 8 5 16 31 17 29 15
PH 1 2 3 4 5 6 7 Sum KR Sum KRB Sum PH
FDa 27 58 25 22 5 18 3 1 005 195 158
FDb 0 0 0 0 0 0 0 612 20 0
HZ 0 0 0 0 0 0 0 206 11 0
>T< 1 27 11 3 17 5 4 297 (18% of FDa+b)
61 (28% of FDa+b)
68 (43% of FDa+b)
18
4.2 Quality assurance assessment
The observations made for the KR, KRB and PH boreholes during the data quality
assurance assessment are listed below. The list shows the reasons behind the figures
denoted by >T< in Table 4-1.
4.2.1 KR and KRB boreholes
There are 46 005 fracture records in the primary fracture data supplied by Posiva. Of
these, 2 188 records are defined as PFL records. The PFL records are defined with a
non-null value in the column marked up as “Prg_tec depth”.
Of the 2 188 PFL records, 192 PFL records were discarded because they had not
been associated with a fracture in the core/image logs (lacked an “M_FROM”
value), which is needed to calculate position, i.e. elevation, from the borehole
trajectory files (called PTH files), thus leaving 1 996 PFL records with useable
elevations.
A further 18 PFL records were discarded because they did not have an angle of
inclination to the core (either an ALPHA or ALPHA_CORE value), required to
calculate a Terzaghi corrected value, thus leaving 1 978 useable PFL records.
A further 146 PFL records were then discarded because we could not determine
their orientation because the records lacked both a DIP/DIP_CORE and/or a
DIR/DIR_CORE value, thus leaving 1 832 useable PFL records.
In conclusion, a total of 1 832 PFL records were used in the fracture frequency
calculations reported here in section 5. It should also be noted that in terms of fracture
transmissivity, in 14 of the 1 832 PFL records, a transmissivity value was not specified,
but these records were still used in the fracture frequency calculations.
4.2.2 Pilot holes
There are 1 892 fracture records in the primary fracture data supplied by Posiva. Of
these, 226 records are defined as PFL records. The PFL records are defined with a
non-null value in the column marked up as “Prg_tec depth”.
Of the 226 PFL records, 40 PFL records were discarded because they had not been
associated with a fracture in the pilot hole core/image logs (i.e. they lacked CORE
DEPTH value), which meant that they could not be matched with the corresponding
“M_FROM” value, thus leaving 186 PFL records with useable elevations.
A further 7 records were discarded because they did not have an inclination to the
core (i.e. either an ALPHA or ALPHA_CORE value), required to calculate a
Terzaghi corrected value, thus leaving 179 useable PFL records.
A further 21 PFL records were then discarded because we could not determine their
orientation because the records lacked both a DIP/DIP_CORE value and/or
DIR/DIR_CORE value, thus leaving 158 useable PFL records.
19
In conclusion, a total of 158 PFL records were used in the fracture frequency
calculations reported here in Appendix A. It should also be noted that in terms of
fracture transmissivity, in 4 of the 158 PFL records a transmissivity value was not
specified, but these records were still used in the fracture frequency calculations.
20
21
5 FRACTURE DATA ANALYSIS
This section considers the orientation and intensity data of the fractures mapped in the
cored-drilled KR and KRB boreholes shown in Figure 3-2. The fracture statistics are
collated in a variety of ways to try to discover any patterns in the occurrence and nature
of the flowing connected open fractures detected with PFL method, see Figure 5-1.
5.1 Assumptions
The following assumptions have been made in the data compilation:
The location of the fractures has been determined by borehole core logs and
borehole TV images. In those cases, where both types of log data exist, the borehole
TV images were used to determine the location.
The locations of the first and last fracture mapped in the borehole core logs
approximate well the total length of borehole mapped.
The errors in the orientation data in the borehole TV images are small.
The measurement process for recording length down the borehole for the occurrence
of PFL data are sufficiently consistent with the measurement process for the
borehole TV images that the correlations of flows and individual fractures made in
preparation of /Tammisto et al. 2009/ are valid.
Fracture sets of continuously flowing fractures can be categorised based on
orientation only, and the definitions of the mean pole and trend defined in the
geological DFN for all fractures are of relevance to the hydraulic fractures.
However, it is noted that the only significant result of that work used here is the hard
sector classification.
Three fracture sets are defined in the geological DFN by /Buoro et al. 2009/, two
sub-vertical (NS and EW) and one sub-horizontal (SH). Roughly, fracture with dips
50º (plunges <40 ) belong to the two sub-vertical sets; fractures with dips <50º
(plunge 40 ) are assigned to the sub-horizontal set (see Section 5.3.1 for details).
The Terzaghi correction /Terzaghi 1965/ can be used to estimate fracture intensities
unbiased by the direction of a sample borehole. Having calculated unbiased
(corrected) 1D fracture intensities, P10,corr, for individual boreholes, these can be
combined over boreholes of varying trajectories to estimate average values of the
fracture surface area per unit volume of bedrock, P32, i.e.
P32 P10,corr (5-1)
Stereonets are plotted as equal area lower hemisphere plots. The maximum
correction factor used in the Terzaghi correction process is 7, corresponding to a
minimum angle of 8° between a fracture and the axis of the core.
The PFL-anomalies identified in each borehole are comparable, i.e. have similar
practicable lower detection limit, i.e. 10–9
m2/s. (The geometric mean of the
minimum interpreted transmissivities over the boreholes is 10–9
m2/s).
22
The frequency of open fractures is the upper limit of the intensity of potential
flowing fractures. The open fractures are a subset of all fractures. Based on
/Tammisto et al. 2009/, the number of open fractures is here defined as:
open = all – tight – 24 % of filled (5-2)
A flowing fracture requires connectivity between transmissive fractures. An open
fracture is in this regard a potentially flowing fracture. The connected open fractures
(cof) are a subset of the open fractures and the PFL data represent a subset of the
connected open fractures. That is, the PFL data represent connected open fractures
with transmissivities greater than the practicable lower detection limit, see Figure
5-1:
P10,all > P10,open > P10,cof > P10,PFL (5-3)
Figure 5-1. The frequency of 1) all fractures intersecting the borehole, 2) open
fractures, 3) connected open fractures (cof) and 4) flowing fractures that have a
transmissivity greater than c. 10-9 m2/s. BC1 and BC2 are constant-head boundary
conditions. Reproduced from /Follin et al. 2007/.
23
5.2 Methodology
The workflow for analysis and collation of fracture geological and hydrogeological
information follows the steps:
1. The fracture categories to be quantified include: all fractures, open fractures
(Equation (5-2)), and fractures associated with the PFL data. The database analysed
is here referred to as /Tammisto et al. 2009/.
2. Group the fracture categories (all, open and PFL) according to whether they are
inside a hydro-structural zone (HZ), or in one of the two fracture domains (FDa and
FDb) using Equation (3-1).
3. Calculate linear (1D) fracture intensities, P10, in each borehole according to various
sub-sets of types of fracture.
4. Calculate Terzaghi corrected linear fracture intensities, P10,corr, in each borehole
according to various sub-sets of types of fracture.
5. Investigate possible correlations between fracture intensity and fracture domain,
inside or outside a hydro-structural zone, and by depth.
6. Calculate average fracture intensities across boreholes by using borehole length
weighted averages, and use Terzaghi corrected fracture intensities to limit the bias
due to borehole orientations.
7. Generate equal area lower hemisphere stereonets for each rock subdivision to
investigate variations in fracture orientations between boreholes, and consider
variations in fracture orientation by depth.
8. Use Terzaghi corrected stereographic density plots for each rock subdivision to
identify major sets and compare these with the hard sector definitions of sets defined
in geological DFN model for Olkiluoto /Buoro et al. 2009/.
9. Generate stereographic pole plots for the fractures associated with PFL data
colouring the poles according to the interpreted transmissivity to identify the
orientation of fractures with the greatest hydrogeological significance.
10. Collate fracture intensities for various fracture sub-sets with each of the three
fracture sets (NS, EW and SH) identified in the geological DFN model for Olkiluoto
/Buoro et al. 2009/.
11. Calculate fracture intensities within each zone identified in the HZ model for
Olkiluoto /Ahokas et al. 2007; Vaittinen et al. 2008/
The objectives of this analysis are to collate basic statistics of the three fracture
categories (all, open and PFL) in a variety of ways to guide and support the
development of a conceptual model for a hydrogeological DFN (Hydro-DFN).
24
5.3 Fracture orientation
5.3.1 Hard sectors
The three fracture sets derived in the geological DFN model for Olkiluoto /Buoro et al.
2009/ were used as a starting point. However, it is noted that the only significant result
of that work used here is the hard sector1 classification, see Figure 5-2. The hard sectors
are given by a non-symmetric curve on the lower hemisphere stereonet. The curve
separates the fractures into one sub-horizontal set and two sub-vertical sets. The curve is
defined by four points with the following values of pole trend and plunge in degrees:
Point 1: 320/30. Point 2: 30/35. Point 3: 130/40. Point 4: 220/40:
The sub-horizontal set (SH) set is given by fractures with a plunge inside of the
curve.
The sub-vertical east-west (EW) set is defined by fractures north of points 1 and 2,
and by fractures south of points 3 and 4.
The sub-vertical north-south (NS) set is defined by fractures west of points 4 and 1,
and by fractures east of points 1 and 2.
Figure 5-2. All fracture poles in the geological DFN model coloured with regard to the
hard sector definitions defined in /Buoro et al. 2009/.
1 Using a stereographic projection (stereoplot), the orientation data (fracture poles) is manually separated
into three different sets by use of curved boundaries on the stereo plot, these are the hard sectors. The data
inside the hard sectors are analysed for orientation and clustering. The analyses are based on the
distribution of the intensity of fractures (amount of fractures) inside the hard sectors. The definition of the
orientation of the representative vector (fracture set pole) of the fractures inside the hard sectors is based
on the areas with high fracture intensity only.
25
In the work reported here, the following hard sector algorithm (VBA code) was used to
determine the orientation set belonging of the fracture data (all, open and PFL):
(5-4)
The hard sector boundaries used here are shown in Figure 5-3. Table 5-1 collates the
number of fractures for each set with regard to bedrock segment (HZ, FDa, FDb) and
fracture type (all, open and PFL).
Figure 5-3. All fracture poles in the hydrogeological DFN model coloured with regard
to the hard sector definitions defined in the work reported here.
26
Table 5-1. Summary of the number of fractures for each set with regard to bedrock
segment (HZ, FDa, FDb) and fracture type (all, open, PFL) based on the hard sector
algorithm in (5-4). The values representing open fractures are derived with Equation
(5-2). The 1 200 PFL data encountered in FDa constitutes 8.0 % of all intersected
fractures in this fracture domain. The 632 PFL data encountered in FDb constitutes 3.6
% of all intersected fractures in this fracture domain.
Segment HZ FDa FDb
Type all open PFL all open PFL All open PFL
1 EW 292 185.32 14 1611 981.04 97 2314 1350.44 71
2 NS 222 142.04 13 1799 1149 105 2251 1328.04 65
3 HZ 2414 1578.64 190 11530 7002.84 998 13217 7743.88 496
5.3.2 Contoured stereonets showing all fractures and the PFL data
Figure 5-4 through Figure 5-7 show the stereonets of all fractures and the PFL data,
respectively, with regard to the two fracture domains FDa and FDb, i.e. in the bedrock
in between the hydro zones (HZ). The border between FDa and FDb is defined by
Equation (3-1).
The stereonets are plotted as Terzaghi corrected Fisher concentration plots using equal
area lower hemisphere projection. Concentration plots are used since they indicate
which sets have the highest density of fractures. The Terzaghi correction is used to
reduce the bias due to the orientation of the borehole to make comparisons between
boreholes of different orientation more meaningful than simple pole plots. The measure
of concentration is a relative one defined in terms of % of total per 1 % area, meaning
that for each 1 % area on the lower hemisphere, the number of poles within that area are
counted and divided by the total number of poles to give the percentage. The contoured
stereonets in Figure 5-4 through Figure 5-7 suggest:
The stereonets for all fractures indicate that the sub-horizontal SH set is dominant in
both fracture domains, but the two mean pole trends differ. In FDa, the mean pole
trend of the SH set is c. 325 , whereas it is c. 355 in FDb. Noteworthy, the two
mean pole trends of the sub-vertical EW set appear to differ in a similar fashion as
well; c. 345 in FDa and c. 005 in FDb. By contrast, the two mean pole trends of
the sub-vertical NS set appear to be fairly similar, c. 85 in both FDa and FDb.
The stereonets for the PFL data resemble by and large the stereonets for all
fractures. Noteworthy, there is a fairly large amount of PFL data centred on trend c.
170 and plunge c. 50 in fracture domain FDb.
It is noted that the stereonets for the open fractures are not shown since they closely
resemble the stereonets for all fractures. Furthermore, the stereonets for the fracture data
within the hydro zones (HZ) are not shown since the fracture networks within the HZ
are not modelled in the work reported here. The symbols shown in Figure 5-4
through Figure 5-7 indicate the trend and plunge of the mean poles of the three fracture
sets. The contour lines centred on these points encompass c. 68 % of the data within
each fracture set. The evaluated Fisher distribution parameter values for each fracture
27
set (NS, EW, SH), fracture type (all, PFL) and bedrock segment (FDa, FDb) are shown
in Table 5-2.
Table 5-2. Summary of the evaluated Fisher distribution parameters values for the
stereonets shown in Figure 5-4 through Figure 5-7.
Segment, data FDa, all FDa, PFL FDb, all FDb, PFL
EW, Trend () 356.2 176.1 359.2 185.9
EW, Plunge () 0.0 2.6 1.3 4.6
EW, Concentration (-) 9.2 10.0 8.7 11.0
NS, Trend () 273.0 89.6 90.5 90.2
NS, Plunge () 1.9 0.2 0.3 6.2
NS, Concentration (-) 6.9 7.3 7.5 8.1
SH, Trend () 309.8 305.2 332.9 300.6
SH, Plunge () 73.2 78.1 73.0 85.6
SH, Concentration (-) 7.1 7.3 6.4 6.1
Figure 5-4. Contoured stereonet for fracture domain FDa: all fractures outside the
hydro zones (HZ) described in /Tammisto et al. 2009/. The symbol denotes the trend
and plunge of the mean poles of the three fracture sets. The contour lines centred on
these points encompass c. 68 % of the data within each set. The corresponding Fisher
distribution parameter values are shown in Table 5-2.
28
Figure 5-5. Contoured stereonet for fracture domain FDa: PFL data outside the hydro
zones (HZ) described in /Tammisto et al. 2009/. The symbol denotes the trend and
plunge of the mean poles of the three fracture sets. The contour lines centred on these
points encompass c. 68 % of the data within each set. The corresponding Fisher
distribution parameter values are shown in Table 5-2.
Figure 5-6. Contoured stereonet for fracture domain FDb: all fractures outside the
hydro zones (HZ) described in/Tammisto et al. 2009/. The symbol denotes the trend
and plunge of the mean poles of the three fracture sets. The contour lines centred on
these points encompass c. 68 % of the data within each set. The corresponding Fisher
distribution parameter values are shown in Table 5-2.
29
Figure 5-7. Contoured stereonet for fracture domain FDb: PFL data outside the hydro
zones (HZ) described in /Tammisto et al. 2009/. The symbol denotes the trend and
plunge of the mean poles of the three fracture sets. The contour lines centred on these
points encompass c. 68 % of he data within each set. The corresponding Fisher
distribution parameter values are shown in Table 5-2.
5.3.3 Discrete stereonets showing the PFL transmissivities
Section 5.3.2 considered the relationship between the orientations of all fractures with
respect to the orientation of the PFL data in terms of hard sectors. Here, we considered
if these sectors are also useful in interpreting the orientations of high-transmissivity,
flowing features, i.e. if there is any anisotropy in flow. By a high-transmissivity, we
mean here transmissivities greater than 10–6
m2/s. Figure 5-8 shows two stereographic
pole plots of the PFL data associated with fracture domains FDa and FDb.
30
Figure 5-8. PFL data outside the hydro zones (HZ) described in /Tammisto et al. 2009/.
Top: Fracture domain FDa. Bottom: Fracture domain FD. The poles are coloured by
log10 (transmissivity) and use an equal area lower hemisphere projection. The
symbol denotes the trend and plunge of the mean poles of the three fracture sets. The
contour lines centred on these points encompass c. 68 % of the data within each set.
The corresponding Fisher distribution parameter values are shown in Table 5-2.
The two plots suggest:
For both fracture domains, there is huge spread in the PFL data. However, the
frequency of high-transmissivity flowing connected open fractures is dominated by
the sub-horizontal SH fracture set.
For FDa, SH fractures tend to dip SE, a small handful of sub-vertical, high-
transmissive flowing fractures strike NW or N and dip towards W.
31
For FDb, SH fractures typically tend to dip S or N, a small handful of sub-vertical,
high-transmissive flowing fractures strike NW or N and dip towards E.
5.4 Fracture intensity
5.4.1 Depth zones
The variation of the fracture intensity with depth was analysed by dividing the two
fractured domain into twenty 50 m thick intervals by depth (elevation). Figure 5-9
shows the Terzaghi corrected linear (1D) intensity of all fractures, P10, all, corr, and the
PFL data, P10, PFL, corr. The maximum magnitude of the Terzaghi correction factor
(weight) was set to 7 (cf. the geological DFN model by /Buoro et al. 2009/).
The corrected intensity plots for fracture domains FDa and FDb are shown in Figure
5-10. Figure 5-11 shows the average hydraulic conductivity for each 50-m interval. For
the sake of comparison, we show in Figure 5-12 the corrected intensities of all fractures,
P10,all,corr, and the PFL data, P10,PFL,corr, in the hydro zones (HZ) and the two fracture
domains combined. The plots shown in Figure 5-9 to Figure 5-12 suggest:
The corrected intensity of all fractures shows a moderate decrease with depth in
both the hydro zones and in the two fracture domains combined. By contrast, the
corrected intensity of the PFL data shows a significant decrease with depth in these
bedrock segments.
For all of the studied elevations, the corrected intensity of all fractures in the hydro
zones is greater than the corrected intensity of all fractures in the two fracture
domains combined. For an example, the corrected intensity of all fractures in the
hydro zones is c. four times the corrected intensity in the two fracture domains
combined at –400m elevation.
For all of the studied elevations, the corrected intensity of the PFL data in the hydro
zones is c. ten times the corrected intensity of the PFL data in the two fracture
domains combined.
There is a depth trend in the average hydraulic conductivity down to c. –600 m
elevation. Above this elevation, the average hydraulic conductivity in the hydro
zones is c. two orders of magnitudes greater than the average hydraulic conductivity
in the two fracture domains combined.
Fracture domain FDb appears to be slightly more fractured and hydraulically
conductive than fracture domain FDa for all depths above –550 m elevation. Below
this elevation, there are no data gathered in fracture domain FDa.
In order to create fairly homogeneous sub-volumes with regard to the depth trend in
the Terzaghi corrected intensity of flowing fractures (corrected frequency of PFL
data) seen, it was decided to subdivide each fracture domain into four depth zones
DZ1-4 as follows, see Figure 5-13:
o DZ1: 0 to –50 m elevation DZ2: –50 to –150 m elevation
o DZ3: –150 to –400 m elevation DZ4: –400 to –1 000 m elevation
32
Fracture intensity of all fractures by depth
0
1
2
3
4
5
6
7
8
50 0-5
0-1
00-1
50-2
00-2
50-3
00-3
50-4
00-4
50-5
00-5
50-6
00-6
50-7
00-7
50-8
00-8
50-9
00-9
50
Elevation (m)
P1
0co
rr (
m-1
)
Fracture intensity of PFL fractures by depth
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
50 0-5
0-1
00-1
50-2
00-2
50-3
00-3
50-4
00-4
50-5
00-5
50-6
00-6
50-7
00-7
50-8
00-8
50-9
00-9
50
Elevation (m)
P1
0co
rr (
m-1
)
Figure 5-9. Terzaghi corrected intensity of all fracture data, P10,all,corr, and the PFL
data, P10,PFL,corr, by elevation in terms of 50-m thick intervals. The maximum
magnitude of the Terzaghi correction factor (weight) was set to 7. Top: P10,all,corr.
Bottom: P10,PFL,corr. Note the difference in scale of the ordinate axes.
33
Fracture intensity of PFL fractures above HZ20B by depth
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
50 0-5
0-1
00-1
50-2
00-2
50-3
00-3
50-4
00-4
50-5
00-5
50-6
00-6
50-7
00-7
50-8
00-8
50-9
00-9
50
Elevation (m)
P1
0c
orr
(m
-1)
Fracture intensity of PFL fractures below HZ20B by depth
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
50 0-5
0-1
00-1
50-2
00-2
50-3
00-3
50-4
00-4
50-5
00-5
50-6
00-6
50-7
00-7
50-8
00-8
50-9
00-9
50
Elevation (m)
P1
0c
orr
(m
-1)
Figure 5-10. Terzaghi corrected intensity of the PFL data, P10,PFL,corr, by elevation
in terms of 50-m thick intervals. The maximum magnitude of the Terzaghi correction
factor (weight) was set to 7. Top: Fracture domain FDa. Bottom: Fracture domain
FDb.
34
Hydraulic conductivity above HZ20B by depth
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
50 0-5
0-1
00-1
50-2
00-2
50-3
00-3
50-4
00-4
50-5
00-5
50-6
00-6
50-7
00-7
50-8
00-8
50-9
00-9
50
Elevation (m)
T/
L (
m/s
)
Hydraulic conductivity below HZ20B by depth
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
50 0-5
0-1
00-1
50-2
00-2
50-3
00-3
50-4
00-4
50-5
00-5
50-6
00-6
50-7
00-7
50-8
00-8
50-9
00-9
50
Elevation (m)
T/
L (
m/s
)
Figure 5-11. Average hydraulic conductivity by elevation in terms of 50-m thick
intervals. Top: Fracture domain FDa. Bottom: Fracture domain FDb.
35
Fracture intensity of all fractures by depth in HZ
0
5
10
15
20
25
30
35
50 0-5
0-1
00-1
50-2
00-2
50-3
00-3
50-4
00-4
50-5
00-5
50-6
00-6
50-7
00-7
50-8
00-8
50-9
00-9
50
Elevation (m)
P1
0co
rr (
m-1
) Fracture intensity of all fractures by depth
0
1
2
3
4
5
6
7
8
50 0-5
0-1
00-1
50-2
00-2
50-3
00-3
50-4
00-4
50-5
00-5
50-6
00-6
50-7
00-7
50-8
00-8
50-9
00-9
50
Elevation (m)
P1
0co
rr (
m-1
)
Fracture intensity of PFL fractures by depth in HZ
0
1
2
3
4
5
6
7
8
50 0-5
0-1
00-1
50-2
00-2
50-3
00-3
50-4
00-4
50-5
00-5
50-6
00-6
50-7
00-7
50-8
00-8
50-9
00-9
50
Elevation (m)
P1
0co
rr (
m-1
)
Fracture intensity of PFL fractures by depth
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
50 0-5
0-1
00-1
50-2
00-2
50-3
00-3
50-4
00-4
50-5
00-5
50-6
00-6
50-7
00-7
50-8
00-8
50-9
00-9
50
Elevation (m)
P1
0co
rr (
m-1
)
Hydraulic conductivity by depth in HZ
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
50 0
-50
-10
0
-15
0
-20
0
-25
0
-30
0
-35
0
-40
0
-45
0
-50
0
-55
0
-60
0
-65
0
-70
0
-75
0
-80
0
-85
0
-90
0
-95
0
Elevation (m)
T/
L (
m/s
)
Hydraulic conductivity by depth
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
50 0-5
0-1
00-1
50-2
00-2
50-3
00-3
50-4
00-4
50-5
00-5
50-6
00-6
50-7
00-7
50-8
00-8
50-9
00-9
50
Elevation (m)
T/
L (
m/s
)
Figure 5-12. Plot of three types of data by elevation in terms of 50-m thick intervals.
Top row: Terzaghi corrected intensity of all fracture data. Middle row: Terzaghi
corrected intensity of the PFL data. Bottom row: Average hydraulic conductivity for
each 50-m interval. The maximum magnitude of the Terzaghi correction factor (weight)
was set to 7. Left column: Hydro zones (HZ). Right column: Fracture domains FDa and
FDb combined.
36
HZ20A+B
FDa
FDb
26131648PFL
HZFDbFDaSegment
26131648PFL
HZFDbFDaSegment
97211449PFL
HZFDbFDaSegment
97211449PFL
HZFDbFDaSegment
66218102PFL
HZFDbFDaSegment
66218102PFL
HZFDbFDaSegment
28721PFL
HZFDbFDaSegment
28721PFL
HZFDbFDaSegment
DZ1: 0 to –50 m
DZ2: –50 to –150 m
DZ3: –150 to –400 m
DZ4: –400 to –1 000 m
Figure 5-13. Schematic visualisation of the number of PFL data by bedrock segment
(FDa, FDb, HZ) and depth zone (DZ1-4).
Table 5-3 shows the sample lengths and numbers of fractures with regard to bedrock
segment (FDa, FDb, HZ) and fracture type (all, open, PFL). Figure 5-14 shows the
Terzaghi corrected intensity, P10,corr, by bedrock segment (FDa, FDb, HZ) and fracture
type (all, open, PFL).
Table 5-4 shows the sample lengths and numbers of fractures with regard to bedrock
segment (FDa, FDb, HZ), depth zone (DZ1-4) and fracture type (all, open, PFL).
Figure 5-15 shows the Terzaghi corrected intensity, P10,corr, by bedrock segment (FDa,
FDb, HZ) and depth zone (DZ1-4) of all fractures and the PFL data, respectively. This
demonstrates that there is either no or only a weak depth trend in fracture intensity of all
fractures, but a consistent decrease in the intensity of water conducting fractures
detected by PFL with depth for FDa, FDb and HZ.
37
Table 5-3. Summary of sample lengths and numbers of fractures with regard to bedrock
segment (FDa, FDb, HZ) and fracture type (all, open, PFL).
Segment FDa FDb HZ
borehole length 7 830.92 11 185.16 499.86
all fractures 14 940 17 782 2 928
allcorr 22 070.80 28 776.80 4182.47
P10, all, corr 2.82 2.57 8.37
open fractures 9 132.88 10 421.6 1 906
opencorr 13 474.31 16 864.08 2 719.16
P10, open, corr 1.72 1.51 5.44
PFL data 1 200 632 217
PFLcorr 1 728.29 1073.03 307.17
P10, PFL, corr 0.22 0.10 0.61
0
1
2
3
4
5
6
7
8
9
all open PFL
Fracture category
P10,c
orr
(m
–1)
FDa
FDb
HZ
Figure 5-14. Terzaghi corrected intensity, P10,corr, by bedrock segment (FDa, FDb, HZ)
and fracture type (all, open, PFL).
38
Table 5-4. Summary of sample lengths and numbers of fractures with regard to depth
zone (DZ1-4), fracture type (all, open, PFL) and bedrock segment (FDa, FDb, HZ).
Depth zone DZ1: (0 to –50) masl DZ2: (–50 to –150) masl
Segment FDa FDb HZ FDa FDb HZ
BH length 1 797.46 364.97 27.08 2 810.14 1 236.81 146.79
all fractures 4 839 1 087 145 5 832 3 504 795
allcorr 6 775.11 1 691.91 196.25 8 912.82 5 540.75 1 080.00
P10, all, corr 3.77 4.64 7.25 3.17 4.48 7.36
open fractures 3 083.44 652.28 101.64 3 474.44 2 027.08 575.88
opencorr 4 316.05 1 022.51 139.95 5 274.23 3 219.46 779.02
P10, open, corr 2.40 2.80 5.17 1.88 2.60 5.31
PFL data 648 131 26 449 211 97
PFLcorr 889.95 218.52 34.76 687.80 369.51 135.58
P10, PFL, corr 0.50 0.60 1.28 0.24 0.30 0.92
TPFL / BH length 2.07E-07 3.62E-07 9.49E-06 1.03E-07 3.92E-08 4.92E-06
Max TPFL 6.03E-05 4.94E-05 1.63E-04 1.24E-04 9.42E-06 1.01E-04
Min TPFL 5.21E-10 2.95E-10 2.76E-09 1.55E-10 3.16E-10 1.18E-09
Mean (Log(T)) -7.30 -7.29 -6.07 -7.67 -7.84 -6.16
St. dev. (Log(T)) 0.89 1.06 1.10 0.92 0.91 1.20
Depth zone DZ3: (–150 to –400) masl DZ4: (–400 to –1000) masl
Segment FDa FDb HZ FDa FDb HZ
BH length 2 981.55 4 558.52 169.24 241.77 5 024.86 156.75
all fractures 4 074 7 349 1 080 195 5 842 908
allcorr 6 091.73 12 075.62 1 590.13 291.14 9 468.52 1 316.09
P10, all, corr 2.04 2.65 9.40 1.20 1.88 8.40
open fractures 2 466.56 4 348.56 707.88 108.44 3 393.68 520.6
opencorr 3 713.07 7 182.02 1 045.27 170.95 5 440.09 754.93
P10, open, corr 1.25 1.58 6.18 0.71 1.08 4.82
PFL data 102 218 66 1 72 28
PFLcorr 149.50 378.78 98.75 1.04 106.22 38.08
P10, PFL, corr 0.05 0.08 0.58 0.00 0.02 0.24
TPFL / BH length 1.99E-08 9.52E-09 2.48E-06 1.28E-10 1.66E-09 2.43E-07
Max TPFL 2.96E-05 1.68E-05 1.28E-04 3.09E-08 6.23E-06 1.41E-05
Min TPFL 2.04E-10 3.31E-10 2.03E-09 – 5.01E-10 1.19E-09
Mean (Log(T)) -7.91 -8.08 -6.24 -7.51 -8.13 -7.18
St. dev. (Log(T)) 0.96 0.90 1.12 - 0.77 0.94
39
0
1
2
3
4
5
6
7
DZ1 (0 to –50) DZ2 (–50 to –150) DZ3 (–150 to –400) D4Z (–400 to –1000)
Depth zone
P10,a
ll,c
orr
(m
–1)
FDa
FDb
HZ
0
0.2
0.4
0.6
0.8
1
1.2
1.4
DZ1 (0 to –50) DZ2 (–50 to –150) DZ3 (–150 to –400) D4Z (–400 to –1000)
Depth zone
P10,P
FL
,co
rr (
m–1)
FDa
FDb
HZ
Figure 5-15. Terzaghi corrected intensity, P10,corr, by depth zone (DZ1-4) and bedrock
segment (FDa, FDb, HZ). Top: all fractures. Bottom: PFL data.
40
41
6 HYDROGEOLOGICAL DFN MODELLING
6.1 Overview
A flowing fracture requires connectivity between transmissive fractures. An open
fracture is in this regard a potentially flowing fracture. A sealed fracture is regarded as
impervious. Partly open fractures (i.e. partial break in the core) are classified as open
fractures.
The connected open fractures (cof) are a subset of the open fractures and the PFL data
represent a subset of the connected open fractures. That is, the PFL data represent
connected open fractures with transmissivities greater than the practicable lower
detection limit, see Figure 5-1:
P10,all > P10,open > P10,cof > P10,PFL (6-1)
The key input to Hydro-DFN simulations is the open fracture surface area per unit
volume of bedrock, P32. Since P32 is based on a volume sample, it is not dependent on a
sample direction as with linear (P10) and area (P21) samples, i.e. it is unbiased. However,
P32 is not readily measured directly. In practice, P32 can be estimated from P10,corr and
adjusted if necessary by calibration against numerical simulations.
Besides models for fracture orientation and fracture intensities, a Hydro-DFN model
consists of descriptions for:
the spatial distribution of the fracture centres in space,
the fracture size distribution, and
the fracture transmissivity distribution.
Here, we have assumed that the locations of the fracture centres in space can be
mimicked by a Poisson process. Fracture trace lengths (not sizes) can be measured as
seen on outcrops and in tunnels. Because it is not possible to directly measure, fracture
size is normally derived via mathematical modelling. Table 6-1 shows the two size
models attempted here based on a decision by Posiva /Löfman and Poteri 2008/. Case A
used a power-law size model, whereas Case B used a log-normal size model.
Table 6-1. Two fracture size models were attempted in the work reported here based on
a decision by Posiva /Löfman and Poteri 2008/.
Case Potentially water conducting fractures
Not water conducting fractures
Fracture size model and parameter values
A Open fractures All other fractures
Power-law fracture size distribution with the location parameter equal to the borehole radius
The shape parameter to be determined as part of Hydro-DFN flow simulations to match PFL intensities
B PFL fractures All other fractures
Log-normal fracture size distribution with a log10 standard deviation around ¼ order of magnitude The log10 mean to be determined as part of Hydro-DFN flow simulations to match PFL intensities
42
The key parameters for a power-law fracture size distribution, measured in terms of the
radius r of a disc, are the shape parameter (kr) and the location parameter (r0). The
distribution, f(r), is often defined only in a truncated range, between rmin and rmax.
1
0)(r
r
k
k
r
r
rkrf (6-2)
where rmax ≥ r ≥ rmin≥ r0, r0 > 0, and kr >0.
In comparison, the key parameters for a log-normal fracture size distribution, measured
in terms of the radius r of a disc, are the mean (m) and the standard deviation (s) of the
common logarithm (log10) of r. The distribution, f(r), is often defined only in a truncated
range, between rmin and rmax:
2
2
½ 2
)(logexp
)2()10ln(
1)(
s
mr
srrf (6-3)
where rmax ≥ r ≥ rmin and s 0.
In both cases, the quantitative calibration of fracture transmissivity was attempted for
three different size-transmissivity models, see Table 6-2.
Table 6-2. Transmissivity parameters used for all sets when matching measured PFL-f
flow distributions.
Type Description Relationship Parameters
Correlated Power-law relationship log(T) = log(a r b) a , b
Semi-correlated Log-normal distribution about a power-law correlated mean
log(T) = log(a r b) + σ log(T) N(0,1) a , b, σ log(T) = 1
Uncorrelated Log-normal distribution about a specified mean
log(T) = μ log(T) + σ log(T) N(0,1) μ log(T) , σ log(T)
To assess the „goodness of fit‟ for the tested fracture transmissivity models, the
following statistics were calculated:
Average total flow to the abstraction borehole over 40 realisations;
Histogram of flow rate to borehole divided by drawdown (notated Q/s) as an
average over 40 realisations. The comparison of histogram shape was quantified
by the correlation coefficient of the number of flowing features with each
histogram bin (½ order of magnitude in Q/s);
43
Bar and whisker plot of minimum, mean minus standard deviation, mean, mean
plus standard deviation, maximum of log(Q/s) for the inflows within each
fracture set taken over all realisations;
The average numbers of fractures within each set giving inflows to the
abstraction borehole above the measurement limit for the PFL-f tests.
In the work reported here, the same transmissivity assignments were used for each
fracture set and at each depth in order to quantify how well a simplistic model could
reproduce the data. That is, in the first instance we try to explain variations in flow by
variations in fracture intensity and the resultant network connectivity. Moreover, we
have constrained the Hydro-DFN modelling in section 6 to treat the conditions in the
bedrock below the hydro zones HZ20A and HZ20B mainly, i.e. fracture domain FDb.
However, we do report one Hydro-DFN model for fracture domain FDa, see section 7.
6.2 Fracture set definitions
All modelling performed in this study uses the hard sector definition of fracture sets
defined by the script in Equation (5-4). The Univariate Fisher distribution parameters
used to model the PFL fracture orientations obsereved in fracture domain FDb are given
in Table 6-3. The corresponding data for fracture domain FDa are provided for the sake
of comparison. It is noted that the settings differ slightly compared to Table 5-2.
Table 6-3. Parameters values used in the Univariate Fisher distribution for fracture
orientations in fracture domains FDa and FDb.
Fracture domain Set Trend Plunge Concentration
FDa EW 175.1 3.5 10
FDa NS 269.4 0.2 7.4
FDa SH 304.3 78 7.3
FDb EW 185.5 5.3 10.4
FDb NS 90.7 7.5 8.1
FDb SH 301.3 85.0 6.1
6.3 Model domain
Because of the variations in borehole orientation, all calibration of the Hydro-DFN
models derived was performed on the basis of comparing the estimated P32,open and
P32,PFL values deduced from Terzaghi corrected measurements, i.e.:
P32,open P10,open,corr (6-4a)
P32,PFL P10,PFL,corr (6-4b)
with the equivalent simulated Terzaghi corrected values of open fractures, i.e.:
44
P10,open,corr P10,open,sim,corr (6-5a)
P10,PFL,corr P10,cof,sim,corr (6-5b)
The model domain extended 400m in each of the horizontal directions and 1 140 m in
the vertical direction. The simulated borehole was 1 km long, inserted through the
middle of the model, 40 m below the top of the model and 100 m above the bottom. The
lateral model extension of 400 m was chosen as an approximate average horizontal
spacing between the deterministically modelled hydro zones. Apart from the vertical
boundaries, the model domain contained no other hydro zones.
The borehole geometry was chosen to represent the deep core drilled boreholes which
are typically 1 km long and cased in the upper 40 m. The top of the casing is positioned
at an elevation of 0m in the mode. An example of the model set up is shown in Figure 6-
1.
Figure 6-1. Example of a DFN model used in the calibration. The right picture shows
all the fractures and the left just the domain and central vertical borehole. The fractures
are coloured according to the depth zone in which their centres are generated. Here, a
Poisson point process is assumed for the generation of fracture centres.
6.4 Modelling approach
6.4.1 Case A – power-law size distribution
The methodology used for deriving a Hydro-DFN model for each fracture domain for
Case A involves the following steps:
1. Perform DFN simulations based on Equation (6-4a) using an “average” power-law
size model with kr = 2.6 and r0 = 0.038m based on previous experience /Follin et al.
45
2007/. Check that the geometrical data for each fracture set given in Table 6-3 can
be used in DFN simulations to yield on average the measured fracture intensity of
open fractures specified in Table 5-4.
2. Based on step 1, perform connectivity analyses to test if the “average” power-law
size model can mimic the Terzaghi corrected frequency of PFL data measured in the
boreholes, i.e. P10,cof,sim,corr P10,PFL,corr.
3. Based on step 2, optimise the “average” power-law size model for each fracture set,
i.e. to give a frequency of connected open fractures consistent with the set specific
frequencies of PFL data measured in the boreholes, i.e. P10,cof,sim,corr = P10,PFL,corr.
4. Perform DFN flow simulations to calibrate hydraulic parameters and possible
relationships between fracture size and transmissivity. The parameters are derived
for each set, each depth zone and each rock domain. A direct correlation between
fracture size and transmissivity is considered, as well as alternatives based on a
semi-correlated and a completely uncorrelated model.
6.4.2 Case B – log-normal size distribution
The methodology used for deriving a Hydro-DFN model for each fracture domain for
Case B involves the following steps:
1. Perform DFN simulations based on Equation (6-4b) using an “average” log-normal
size model with a mean length mlog(r) = 0.45, and standard deviation mlog(r) = 0.25.
Check that the geometrical data for each fracture set given in Table 6-3 can be used
in DFN simulations to yield on average the measured fracture intensity of PFL data
specified in Table 5-4.
2. Based on step 1, perform connectivity analyses to make sure that the “average” log-
normal size model indeed reproduces the Terzaghi corrected frequency of PFL data
measured in the boreholes, i.e. Equation (6-4b).
3. Based on step 2, optimise the “average” log-normal size model for each fracture set,
i.e. to give a frequency of connected open fractures consistent with the set specific
frequencies of PFL data measured in the boreholes i.e. P10,cof,sim,corr = P10,PFL,corr.
4. Perform DFN flow simulations to calibrate hydraulic parameters and possible
relationships between fracture size and transmissivity. The parameters are derived
for each set, each depth zone and each rock domain. A direct correlation between
fracture size and transmissivity is considered, as well as alternatives based on a
semi-correlation and a completely uncorrelated model. (The DFN flow simulations
run to calibrate hydraulic parameters and possible relationships between fracture
size and transmissivity are presented in section 6.6.)
6.4.3 Step 1
Comparisons of the generated and measured Terzaghi corrected fracture intensities (for
the individual fracture sets and for all sets combined) based on an ensemble over 40
realisations of the Hydro-DFN for the FDb fracture domain are presented in Figure 6-2
46
and Figure 6-3 for Case A and Case B, respectively. As can be seen, the fracture
intensities for the generated realisations are in good agreement with the measured
values.
The intensities for the generated realisations are slightly lower than the measured
intensities for some sub-vertical sets. A maximum Terzaghi weight of 7 was used in this
analysis. Increasing this maximum weight might have improved the match, but then the
corrected intensity might have become overly sensitive to the contribution from a few
fractures near-parallel to the borehole. This was not done for this study given the small
magnitude of the discrepancies.
-50 to 0 masl
0.000
0.500
1.000
1.500
2.000
2.500
3.000
ALL EW NS SH
Fracture se t
P1
0corr
(1/m
)
MEASURED (all BH)
SIMULATED (kr=2.6,r0=0.04)
-150 to -50 masl
0.000
0.500
1.000
1.500
2.000
2.500
3.000
ALL EW NS SH
Fracture se t
P1
0corr
(1/m
)
MEASURED (all BH)
SIMULATED (kr=2.6,r0=0.04)
-400 to -150 masl
0.000
0.200
0.400
0.600
0.800
1.000
1.200
1.400
1.600
1.800
ALL EW NS SH
Fracture set
P10
corr
(1/m
)
MEASURED (all BH)
SIMULATED (kr=2.6,r0=0.04)
-1000 to -400 m asl
0.000
0.200
0.400
0.600
0.800
1.000
1.200
ALL EW NS SH
Fracture se t
P1
0corr
(1/m
)
MEASURED (all BH)
SIMULATED (kr=2.6,r0=0.04)
Figure 6-2. Comparisons by depth of the generated and measured open fracture intensities (P10,open, corr) in a borehole for each fracture set
and for the Case A (power-law) fracture size model, for the FDb fracture domain.
47
-50 to 0 masl
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
ALL EW NS SH
Fracture set
P1
0c
orr
(1/m
)
MEASURED(all BH)
SIMULATED(m=0.45, s=0.25)
-150 to -50 masl
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
ALL EW NS SH
Fracture set
P1
0c
orr
(1/m
)
MEASURED(all BH)
SIMULATED(m=0.45, s=0.25)
-400 to -150 masl
0.000
0.010
0.020
0.030
0.040
0.050
0.060
0.070
0.080
0.090
ALL EW NS SH
Fracture set
P1
0corr
(1/m
)
MEASURED (all BH)
SIMULATED (m=0.45,s=0.25)
-1 000 to -400 m asl
0.000
0.005
0.010
0.015
0.020
0.025
ALL EW NS SH
Fracture se t
P1
0corr
(1/m
)
MEASURED (all BH)
SIMULATED(m=0.45,s=0.25)
Figure 6-3. Comparisons by depth of the generated and measured PFL fracture intensities (P10,PFL, corr) in a borehole for each fracture set
and for the Case B (log-normal) fracture size model, for the FDb fracture domain.
48
49
6.4.4 Step 2
The approach used in the connectivity analyses is to generate realisations of the open
fractures (Case A) within the specified domain without any borehole present initially.
The intersections between any two fractures and between a fracture and a boundary of
the domain are calculated. Then, fractures that either have no connection via the
network to a boundary of the domain, or ones that have only one intersection (i.e. a
dead-end) are removed. Finally, the vertical borehole is inserted through the remaining
connected network to obtain the intensity of connected open fractures. This procedure
avoids retaining, and counting, fractures that only form connections via the borehole.
For the Case B models, we fixed the fracture size distribution parameters so that no
more than a small proportion of the fractures generated are disconnected from the rest of
the fracture network.
Examples of the connectivity analysis are shown in Figure 6-4 and Figure 6-5 below.
They demonstrates how small fractures tend not to contribute to connectivity and are far
less likely to form potential flow paths, leaving areas of rock through which there is
little flow or no flow. This effect becomes more exaggerated for parts of the rock with
low intensity of open fractures, as found at greater depth.
6.4.5 Step 3
Figure 6-6 and Figure 6-7 show the results from the optimisation of the “average”
power-law size and log-normal size models for each fracture set, i.e. to give a frequency
of connected open fractures consistent with the set specific frequencies of PFL data
measured in the boreholes, i.e. Equation (6-5b). The error bars indicate the standard
deviation in P10,cof,corr over 40 realisations. Table 6-4 and Table 6-5 summarise the
parameters used in the calibrated size models of Case A (power-law) and Case B (log-
normal) for fracture domain FDb.
6.5 Comparison of the two fracture size distribution models
In Figure 6-8, Figure 6-9 and Figure 6-10, we compare the different fracture size
distributions at the initial fracture generation stage and the connectivity analysis stage of
the modelling process. In summary, we make the following observations:
For both size models, the connected open fracture size distribution approaches the
generated fracture size distribution for sufficiently large fracture sizes
The Case A and Case B size models produce different connected fracture size
distributions with their current fracture size distribution parameters. In particular the
Case B size model has a higher proportion of large connected fractures (50 m) and
far fewer connected fractures smaller than (10 m) compared to the Case A size
model.
The Case A connected open fracture size distributions could possibly be
approximated by log-normal distributions, but with different mean and variance
parameters than we have used in Case B model.
50
The Case A connected open fracture size distributions provide some justification for
increasing the mean size of the connected fractures as depth increases. This trend is
perhaps counter-intuitive as the power-law size distributions of open fractures
generated in Case A do not vary very much with depth, e.g. kr is constant over the
bottom three depth zones.
Figure 6-4. Illustration of fracture connectivity for Case A (power-law) fracture size distribution and the FDb fracture domain. Top left:
The open fractures generated. Top right: A slice through the open fractures generated. Bottom left: Connected open fractures. Bottom
right: A slice through the connected open fractures.
51
Figure 6-5. Illustration of fracture connectivity for Case B (log-normal) fracture size distribution and FDb rock domain. Top left: The
fractures generated. Top right: A slice through the fractures generated. Bottom left: The connected fractures. Bottom right: A slice through
the connected fractures.
52
-50 to 0 masl
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
ALL EW NS SH
Fracture se t
P1
0cof,corr
(1/m
)
MEASURED (all BH)
SIMULATED (kr=2.6,r0=0.04)
SIMULATED (calibrated)
-150 to -50 masl
0.000
0.100
0.200
0.300
0.400
0.500
0.600
ALL EW NS SH
Fracture se t
P1
0cof,corr
(1/m
)
MEASURED (all BH)
SIMULATED (kr=2.6,r0=0.04)
SIMULATED (calibrated)
-400 to -150 masl
0.000
0.050
0.100
0.150
0.200
0.250
ALL EW NS SH
Fracture set
P1
0cof,corr
(1/m
)
MEASURED (all BH)
SIMULATED (kr=2.6,r0=0.04)
SIMULATED (calibrated)
-1000 to -400 m asl
0.000
0.020
0.040
0.060
0.080
0.100
0.120
ALL EW NS SH
Fracture se t
P1
0cof,corr
(1/m
)
MEASURED (all BH)
SIMULATED (kr=2.6,r0=0.04)
SIMULATED (calibrated)
Figure 6-6. Illustration of the Terzaghi corrected connected open fracture intensities, P10,cof,corr, for the individual fracture sets with the
measured fracture intensities of PFL in FDb, for the power-law fracture size distribution. The error bars indicate the standard deviation in
P10,cof,corr over 40 realisations.
53
-50 to 0 masl
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
ALL EW NS SH
Fracture set
P1
0c
of,
co
rr(1
/m)
MEASURED(all BH)
SIMULATED(m=0.05)
SIMULATED(m=0.45)
SIMULATED(m=1.45)
SIMULATED(calibrated)
-150 to -50 masl
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
ALL E-W N-S SubH
Fracture set
P1
0c
of,
co
rr(1
/m)
MEASURED(all BH)SIMULATED(m=0.05)SIMULATED(m=0.45)SIMULATED(m=1.45)SIMULATED(calibrated)
-400 to -150 masl
0.000
0.010
0.020
0.030
0.040
0.050
0.060
0.070
0.080
0.090
ALL E-W N-S SubH
Fracture set
P1
0cof,corr
(1/m
)
MEASURED (all BH)
SIMULATED(m=0.05)SIMULATED(m=0.45)
SIMULATED(m=1.45)SIMULATED(calibrated)
-1000 to -400 masl
-0.005
0.000
0.005
0.010
0.015
0.020
0.025
ALL E-W N-S SubH
Fracture set
P1
0cof,corr
(1/m
)
MEASURED (all BH)SIMULATED(m=0.05)SIMULATED (m=0.45)SIMULATED(m=1.45)SIMULATED(calibrated)
Figure 6-7. Comparison of the Terzaghi corrected connected open fracture intensities, P10,cof,corr, for the individual fracture sets with the
measured fracture intensities of PFL in FDb, for the log-normal fracture size distribution. The standard deviation slog(r) = 0.25 for all
cases. The error bars indicate the standard deviation in P10,cof,corr over 40 realisations.
54
55
Table 6-4. Summary of the parameters used in the calibrated Case A (power-law)
fracture size model for FDb. (masl denotes metres above sea level).
Elevation (masl) Set
Pole orientation
(trend, plunge), conc.
Case A power-law
(kr, r0)
rmin = r0 rmax = 564 m
Intensity
P32,open
(m, - ) (m2/m
3)
–50 to 0 EW (185.5, 5.3), 10.4 (2.6, 0.04) 0.44
N-S (90.7, 7.5), 8.1 (2.6, 0.04) 0.40
SH (301.3, 85), 6.1 (2.6, 0.04) 1.96
–150 to –50 EW (185.5, 5.3), 10.4 (2.7, 0.04) 0.50
NS (90.7, 7.5), 8.1 (2.7, 0.04) 0.49
SH (301.3, 85), 6.1 (2.7, 0.04) 1.61
–400 to –150 EW (185.5, 5.3), 10.4 (2.7, 0.04) 0.32
NS (90.7, 7.5), 8.1 (2.7, 0.04) 0.37
SH (301.3, 85), 6.1 (2.7, 0.04) 0.88
–1 000 to –400 EW (185.5, 5.3), 10.4 (2.7, 0.04) 0.22
NS (90.7, 7.5), 8.1 (2.7, 0.04) 0.24
SH (301.3, 85), 6.1 (2.7, 0.04) 0.62
Table 6-5. Summary of the parameters used in the calibrated Case B (log-normal)
fracture size model for FDb.
Elevation (masl) Set
Pole orientation
(trend, plunge), conc.
Case B log-normal
(mlog(r), slog(r)) rmin = 0.56m rmax = 564 m
3D intensity of fractures
P32,PFL
(-, - ) (m2/m
3)
–50 to 0 EW (185.5, 5.3), 10.4 (0.45, 0.25) 0.12
NS (90.7, 7.5), 8.1 (0.45, 0.25) 0.07
SH (301.3, 85), 6.1 (0.45, 0.25) 0.41
–150 to –50 EW (185.5, 5.3), 10.4 (0.45, 0.25) 0.07
NS (90.7, 7.5), 8.1 (0.45, 0.25) 0.06
SH (301.3, 85), 6.1 (0.45, 0.25) 0.17
–400 to –150 EW (185.5, 5.3), 10.4 (0.45, 0.25) 0.01
NS (90.7, 7.5), 8.1 (0.45, 0.25) 0.02
SH (301.3, 85), 6.1 (0.45, 0.25) 0.05
–1 000 to –400 EW (185.5, 5.3), 10.4 (1.45, 0.25) 0.00
NS (90.7, 7.5), 8.1 (1.45, 0.25) 0.00
SH (301.3, 85), 6.1 (1.45, 0.25) 0.02
-50 to -0 masl
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
-1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50
Log( fracture radius )
Lo
g(
fractu
re in
ten
sit
y )
P32 specified
P10,cor caseA - generated
P10, cor caseA - connected
-150 to -50 masl
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
-1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00
Log( fracture radius )
Lo
g(
fractu
re in
ten
sit
y )
P32 specified
P10,cor caseA - generated
P10, cor caseA - connected
-400 to -150 masl
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
-1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00
Log( fracture radius )
Lo
g(
fractu
re in
ten
sit
y )
P32 specified
P10,cor caseA - generated
P10, cor caseA - connected
-1000 to -400 masl
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
-0.80 -0.30 0.20 0.70 1.20 1.70 2.20 2.70
Log( fracture radius )
Lo
g(
fractu
re in
ten
sit
y )
P32 specified
P10,cor caseA - generated
P10, cor caseA - connected
Figure 6-8. Fracture size distributions for the Case A (power-law) size distribution model by depth zone for FDb. The fracture size
distribution parameters are taken from Table 6-4.
56
-50 to -0 masl
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
-1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50
Log( fracture radius )
Lo
g(
fractu
re in
ten
sit
y )
P32 specified
P10,cor caseB - generated
P10, cor caseB - connected
-150 to -50 masl
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
-1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50
Log( fracture radius )
Lo
g(
fractu
re in
ten
sit
y )
P32 specified
P10,cor caseB - generated
P10, cor caseB - connected
-400 to -150 masl
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
-1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50
Log( fracture radius )
Lo
g(
fractu
re in
ten
sit
y )
P32 specified
P10,cor caseB - generated
P10, cor caseB - connected
-1000 to -400 masl
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
-0.80 -0.30 0.20 0.70 1.20 1.70 2.20 2.70
Log( fracture radius )
Lo
g(
fractu
re in
ten
sit
y )
P32 specified
P10,cor caseB - generated
P10, cor caseB - connected
Figure 6-9. Fracture size distributions for the Case B (log-normal) size distribution model by depth zone for FDb. The fracture size
distribution parameters are taken from Table 6-5.
57
-50 to -0 masl
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
-1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50
Log( fracture radius )
Lo
g(
fractu
re in
ten
sit
y )
P10,cor caseB - connected
P10, cor caseA - connected
-150 to -50 masl
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
-1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50
Log( fracture radius )
Lo
g(
fractu
re in
ten
sit
y )
P10,cor caseB - connected
P10, cor caseA - connected
-400 to -150 masl
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
-1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50
Log( fracture radius )
Lo
g(
fractu
re in
ten
sit
y )
P10,cor caseB - connected
P10, cor caseA - connected
-1000 to -400 masl
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
-1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50
Log( fracture radius )
Lo
g(
fractu
re in
ten
sit
y )
P10,cor caseB - connected
P10, cor caseA - connected
Figure 6-10. A comparison of the fracture size distributions of connected fractures for the calibrated Case A and Case B models for FDb.
The fracture size parameters are taken from Table 6-4 and Table 6-5.
58
59
6.6 Simulation of Posiva Flow Log (PFL-f) tests
6.6.1 Modelling approach
The final stage of modelling is to account for the role of fracture transmissivity in
determining both the intensity of flowing features detected by the PFL tests and the
magnitudes of inflows measured in the boreholes as they are pumped. It is important at
this point to recollect what is actually measured with the PFL tests. For each PFL
transmissivity value identified, the change in flux (inflow) and head (drawdown) after
several days of pumping relative to conditions prior to pumping are calculated. A
transmissivity value is interpreted for the PFL-anomaly based on an assumed radius of
influence of c. 19 m. The choice of 19m reflects that tests are performed over several
days, and hence should represent an effective transmissivity of the whole fracture
intersected, and possibly adjoining parts of the network, but 19m is otherwise arbitrary.
Consequently, the interpreted values of transmissivity should not be viewed as
necessarily the transmissivity of an individual fracture, or the transmissivity of the
fracture local to the borehole intersect. They are more indicative of the effective
transmissivity over a larger scale. This remark influences the way we use the PFL-f data
in the Hydro-DFN modelling.
The Hydro-DFN is parameterised in terms of the transmissivity of individual fractures,
and may depend on the size of the fracture according to which transmissivity model is
used. Steady-state DFN flow simulations of the PFL-f test configuration are used to
predict the distribution of inflows to the boreholes. The idealised boundary conditions
used are zero head on the top and vertical boundaries, and a drawdown of 10m along the
whole 1km of borehole. Otherwise, the geometrical model configuration is the same as
the connectivity simulations described in the previous section. In the field, the
drawdown is typically 10m near the top, but gradually decreases, and hence the
normalised flow-rate of flux, Q, divided drawdown, s, is used for the comparison of
inflows. 40 realisations are performed for each simulation case.
In order to investigate variations with depth, the calculated values of flow rates, Q/s,
and the measurements from PFL are both divided according to the four depth zones, and
then used as ensembles to compare the distribution between modelled and measured
results. Three main measures are used to quantify how well the model simulates the
data:
A histogram of the distribution of flow-rates, Q/s, is compared with a bin size of
half an order of magnitude.
The total flow to the borehole, sum of Q/s.
The numbers of PFL-anomalies associated with each fracture set and the
distribution of Q/s for each set. This distribution is quantified in terms of the
mean, plus/minus one standard deviation, minimum and maximum of log(Q/s).
Each of these is compared for each depth zone. For the data, statistics are calculated
over the ensemble of measurements made in all boreholes for intervals within each
depth zone. The statistics (such as total flow and numbers of PFL-anomalies) are then
rescaled according to the thickness of the depth zone divided by the total length of
60
borehole sections measured within that depth zone. For the model, ensemble statistics
are calculated over the 40 realisations. Hence, the statistical variability between
realisations is used as an analogue of the spatial variability between boreholes.
The parameterisation of the Hydro-DFN model is non-unique as a number of decisions
have to be made in setting it up the model, including the relationship of transmissivity
to fracture size, the fracture size distribution and the interpretation of fracture intensities
for potentially open or flowing fractures. The various options are listed below.
Three models for the relationship of the fracture transmissivity to fractures size are
considered – correlated, semi-correlated and uncorrelated. The uncorrelated and
correlated models are two extremes, but a semi-correlated model, somewhere in
between, is included as it is likely be more physically realistic. The non-uniqueness of
the fracture size distribution is addressed by performing two cases of size models, Case
A and Case B. In Case A, the fracture size distribution is based on a power-law and the
source of the P32,open fracture intensity is P10, open, corr for open fractures. In Case B, the
fracture size distribution is log-normal and the source of the P32,PFL fracture intensity is
P10, PFL, corr for PFL fractures.
6.6.2 Comparison of the three fracture transmissivity-size models
The quality of the match to the observed distributions of PFL flows for the variant in
FDb with a semi-correlated transmissivity model is illustrated for Case A by Figure
6-11 through Figure 6-13 and for Case B by Figure 6-14 through Figure 6-16 below.
The match to the observed flow is poorest for the deepest depth zone (below -400 masl).
However, it should be noted that there are very few features carrying flow at this depth,
so the distributions of PFL detected inflows are not very well defined.
It was possible to find parameters for each of the three relationships between
transmissivity and fracture size that would give an acceptable match to observations.
Because the different types of relationship are parameterised in different ways, it is not
easy to compare the different relationships.
Number of intersections in range -50 masl to 0 masl
(per 50m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
< -1
0
-10 to
-9.5
-9.5 to
-9
-9 to
-8.5
-8.5 to
-8
-8 to
-7.5
-7.5 to
-7
-7 to
-6.5
-6.5 to
-6
-6 to
-5.5
-5.5 to
-5
-5 to
-4.5
-4.5 to
-4
-4 to
-3.5
-3.5 to
-3 > -3
log(Q/s) [m2/s]
Nu
mb
er
of
infl
ow
s p
er
50
m
Model (mean of 10 realisations)
Data (PFL_f)
Number of intersections in range -150 masl to -50 masl (per 100m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
< -1
0
-10 to
-9.5
-9.5 to
-9
-9 to
-8.5
-8.5 to
-8
-8 to
-7.5
-7.5 to
-7
-7 to
-6.5
-6.5 to
-6
-6 to
-5.5
-5.5 to
-5
-5 to
-4.5
-4.5 to
-4
-4 to
-3.5
-3.5 to
-3 > -3
log(Q/s) [m2/s]
Nu
mb
er
of
infl
ow
s p
er
10
0m
Model (mean of 10 realisations)
Data (PFL_f)
Number of intersections in range -400 masl to -150 masl (per 250m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
< -1
0
-10 to
-9.5
-9.5 to
-9
-9 to
-8.5
-8.5 to
-8
-8 to
-7.5
-7.5 to
-7
-7 to
-6.5
-6.5 to
-6
-6 to
-5.5
-5.5 to
-5
-5 to
-4.5
-4.5 to
-4
-4 to
-3.5
-3.5 to
-3 > -3
log(Q/s) [m2/s]
Nu
mb
er
of
infl
ow
s p
er
25
0m
Model (mean of 10 realisations)
Data (PFL_f)
Number of intersections in range -1000 masl to -400 masl (per 600m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
< -1
0
-10 to
-9.5
-9.5 to
-9
-9 to
-8.5
-8.5 to
-8
-8 to
-7.5
-7.5 to
-7
-7 to
-6.5
-6.5 to
-6
-6 to
-5.5
-5.5 to
-5
-5 to
-4.5
-4.5 to
-4
-4 to
-3.5
-3.5 to
-3 > -3
log(Q/s) [m 2/s]
Nu
mb
er
of
infl
ow
s p
er
600m
Model (mean of 10 realisations)
Data (PFL_f)
Figure 6-11. Histogram comparing the distribution of the magnitude of inflows divided by drawdown, Q/s, at abstraction boreholes in
FDb. The model has a semi-correlated transmissivity, with a power-law fracture size distribution. The PFL-f measurements are treated as
ensemble over all boreholes sections within FDb. The simulations represent the combined results of 10 realisations of the Hydro-DFN
model. The numbers of intersections are normalized to the length of borehole in the heading of each graph.
61
Inflows in range -50 masl to 0 masl (per 50m)
-10.0 -9.0 -8.0 -7.0 -6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0
PFL E-W
Model E-W
PFL N-S
Model N-S
PFL SH
Model SH
Fra
ctu
re s
et
log (Q/s) [m2/s]
1.4
0.9
1.9
1.2
13.6
13.3
Inflows in range -150 masl to -50 masl (per 100m)
-10.0 -9.0 -8.0 -7.0 -6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0
PFL E-W
Model E-W
PFL N-S
Model N-S
PFL SH
Model SH
Fra
ctu
re s
et
log (Q/s) [m2/s]
1.7
1.2
2.0
1.2
11.9
9.7
Inflows in range -400 masl to -150 masl (per 250m)
-10.0 -9.0 -8.0 -7.0 -6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0
PFL E-W
Model E-W
PFL N-S
Model N-S
PFL SH
Model SH
Fra
ctu
re s
et
log (Q/s) [m2/s]
1.3
0.7
1.1
0.9
8.9
8.3
Inflows in range -1000 masl to -600 masl (per 600m)
-10.0 -9.0 -8.0 -7.0 -6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0
PFL E-W
Model E-W
PFL N-S
Model N-S
PFL SH
Model SH
Fra
ctu
re s
et
log (Q/s) [m2/s]
0.5
0.3
0.8
0.4
6.6
4.1
Figure 6-12. Bar and whisker plots comparing statistics taken over each fracture set for the individual inflows, Q/s, for the PFL-f data
from borehole sections within FDb against statistics for an ensemble over 10 realisations of the Hydro-DFN model. The model has a semi-
correlated transmissivity, with a power-law fracture size distribution. The centre of the bar indicates the mean value, the ends of the bar
indicate 1 standard deviation, and the error bars indicate the minimum and maximum values. For the data statistics are taken over the
identified flowing fractures within each set. For the model, statistics are taken over the fractures generated within each set and over 10
realisations. The numbers of fractures are normalized to the length indicated in the graph heading.
62
63
Total normalized flow to borehole section
1.7
E-0
5
3.9
E-0
6
3.4
E-0
6
1.1
E-0
6
1.8
E-0
5
3.8
E-0
6
2.4
E-0
6
9.9
E-0
7
0.0E+00
2.0E-06
4.0E-06
6.0E-06
8.0E-06
1.0E-05
1.2E-05
1.4E-05
1.6E-05
1.8E-05
2.0E-05
-50 to 0 masl -150 to -50 masl -400 to -150 masl -1000 to -400 masl
Depth interval
Flo
w (
Q/s
) [m
2/s
]
model
PFL_f
Figure 6-13. Histogram comparing the sum of individual flows, Q/s, for the PFL-f data from
borehole sections within FDb, against statistics for an ensemble over 10 realisations of the
Hydro-DFN model. The model has a semi-correlated transmissivity, with a power-law
fracture size distribution. For the data, statistics are taken over the identified flowing
fractures. For the model, the median value of total flow is taken over 10 realisations. The
flows are normalized to the borehole length indicated by the range on the horizontal axis.
Number of intersections in range -50 masl to 0 masl
(per 50m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
< -1
0
-10 to
-9.5
-9.5 to
-9
-9 to
-8.5
-8.5 to
-8
-8 to
-7.5
-7.5 to
-7
-7 to
-6.5
-6.5 to
-6
-6 to
-5.5
-5.5 to
-5
-5 to
-4.5
-4.5 to
-4
-4 to
-3.5
-3.5 to
-3 > -3
log(Q/s) [m2/s]
Nu
mb
er
of
infl
ow
s p
er
50
m
Model (mean of 10 realisations)
Data (PFL_f)
Number of intersections in range -150 masl to -50 masl (per 100m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
< -1
0
-10 to
-9.5
-9.5 to
-9
-9 to
-8.5
-8.5 to
-8
-8 to
-7.5
-7.5 to
-7
-7 to
-6.5
-6.5 to
-6
-6 to
-5.5
-5.5 to
-5
-5 to
-4.5
-4.5 to
-4
-4 to
-3.5
-3.5 to
-3 > -3
log(Q/s) [m2/s]
Nu
mb
er
of
infl
ow
s p
er
10
0m
Model (mean of 10 realisations)
Data (PFL_f)
Number of intersections in range -400 masl to -150 masl (per 250m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
< -1
0
-10 to
-9.5
-9.5 to
-9
-9 to
-8.5
-8.5 to
-8
-8 to
-7.5
-7.5 to
-7
-7 to
-6.5
-6.5 to
-6
-6 to
-5.5
-5.5 to
-5
-5 to
-4.5
-4.5 to
-4
-4 to
-3.5
-3.5 to
-3 > -3
log(Q/s) [m2/s]
Nu
mb
er
of
infl
ow
s p
er
25
0m
Model (mean of 10 realisations)
Data (PFL_f)
Number of intersections in range -1000 masl to -400 masl (per 600m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
< -1
0
-10 to
-9.5
-9.5 to
-9
-9 to
-8.5
-8.5 to
-8
-8 to
-7.5
-7.5 to
-7
-7 to
-6.5
-6.5 to
-6
-6 to
-5.5
-5.5 to
-5
-5 to
-4.5
-4.5 to
-4
-4 to
-3.5
-3.5 to
-3 > -3
log(Q/s) [m 2/s]
Nu
mb
er
of
infl
ow
s p
er
600m
Model (mean of 10 realisations)
Data (PFL_f)
Figure 6-14. Histogram comparing the distribution of the magnitude of inflows divided by drawdown, Q/s, at abstraction boreholes in
FDb. The model has a semi-correlated transmissivity, with a log-normal fracture size distribution. The PFL-f measurements are treated as
ensemble over all boreholes sections within FDb. The simulations represent the combined results of 10 realisations of the Hydro-DFN
model. The numbers of intersections are normalized to the length of borehole in the heading of each graph.
64
Inflows in range -50 masl to 0 masl (per 50m)
-10.0 -9.0 -8.0 -7.0 -6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0
PFL E-W
Model E-W
PFL N-S
Model N-S
PFL SH
Model SH
Fra
ctu
re s
et
log (Q/s) [m2/s]
1.4
1.1
1.9
0.7
13.6
16.2
Inflows in range -150 masl to -50 masl (per 100m)
-10.0 -9.0 -8.0 -7.0 -6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0
PFL E-W
Model E-W
PFL N-S
Model N-S
PFL SH
Model SH
Fra
ctu
re s
et
log (Q/s) [m2/s]
1.7
1.1
2.0
0.7
11.9
11.1
Inflows in range -400 masl to -150 masl (per 250m)
-10.0 -9.0 -8.0 -7.0 -6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0
PFL E-W
Model E-W
PFL N-S
Model N-S
PFL SH
Model SH
Fra
ctu
re s
et
log (Q/s) [m2/s]
1.3
0.4
1.1
0.8
8.9
8.9
Inflows in range -1000 masl to -600 masl (per 600m)
-10.0 -9.0 -8.0 -7.0 -6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0
PFL E-W
Model E-W
PFL N-S
Model N-S
PFL SH
Model SH
Fra
ctu
re s
et
log (Q/s) [m2/s]
0.5
0.4
0.8
0.1
6.6
4.5
Figure 6-15. Bar and whisker plots comparing statistics taken over each fracture set for the individual inflows, Q/s, for the PFL-f data
from borehole sections within FDb against statistics for an ensemble over 10 realisations of the Hydro-DFN model. The model has a semi-
correlated transmissivity, with a log-normal fracture size distribution. The centre of the bar indicates the mean value, the ends of the bar
indicate 1 standard deviation, and the error bars indicate the minimum and maximum values. For the data, statistics are taken over the
identified flowing fractures within each set. For the model, statistics are taken over the fractures generated within each set and over 10
realisations. The numbers of fractures are normalized to the length indicated in the graph heading.
65
66
Total normalized flow to borehole section
1.7
E-0
5
4.7
E-0
6
2.0
E-0
6
1.1
E-0
6
1.8
E-0
5
3.8
E-0
6
2.4
E-0
6
9.9
E-0
7
0.0E+00
2.0E-06
4.0E-06
6.0E-06
8.0E-06
1.0E-05
1.2E-05
1.4E-05
1.6E-05
1.8E-05
2.0E-05
-50 to 0 masl -150 to -50 masl -400 to -150 masl -1000 to -400 masl
Depth interval
Flo
w (
Q/s
) [m
2/s
]
model
PFL_f
Figure 6-16. Histogram comparing the sum of individual flows, Q/s, for the PFL-f data
from borehole sections within FDb, against statistics for an ensemble over 10
realisations of the Hydro-DFN model. The model has a semi-correlated transmissivity,
with a log-normal fracture size distribution. For the data statistics are taken over the
identified flowing fractures. For the model, the median value of total flow is taken over
10 realisations. The flows are normalized to the borehole length indicated by the range
on the horizontal axis.
6.7 Summary of Hydro-DFN models
The inferred Hydro-DFN model parameters are here collated with regard to fracture
bedrock segment FDb, elevation (depth zone DZ1-DZ4) and size model (power-law,
log-normal).
67
6.7.1 FDb: Depth zone 1 (0 to –50 m elevation)
Table 6-6. Summary of Hydro-DFN parameters for the simulations of flow in fracture
domain FDb, depth zone DZ1 using a power-law size model (Case A).
Set Pole orientation
(trend, plunge) concentration
Case A power-law
(kr, r0)
Intensity
P32,open
rmin = r0
rmax = 564 m
Transmissivity model
C: (a,b) SC: (a, b, σlog(T))
UC: (µ log(T), σ log(T))
(-, m) (m2/m
3) T (m
2s
-1)
EW (185.5, 5.3) 10.4 (2.5, 0.04) 0.44
C: (1.5 10–8
, 1.2)
SC: (6 10–8
, 0.7, 0.8)
UC: (1.1 10–7
, 1.3)
NS (90.7, 7.5) 8.1 (2.5, 0.04) 0.40
C: (1.5 10–8
, 1.2)
SC: (6 10–8
, 0.7, 0.8)
UC: (1.1 10–7
, 1.3)
SH (301.3, 85) 6.1 (2.6, 0.04) 1.96
C: (4.5 10–8
, 1.2)
SC: (1.8 10–7
, 0.7, 0.8)
UC: (3.3 10–7
, 1.3)
Table 6-7. Summary of Hydro-DFN parameters for the simulations of flow in fracture
domain FDb, depth zone DZ1 using a log-normal size model (Case B).
Set Pole orientation
(trend, plunge) concentration
Case B log-normal
(mlog(r), slog(r))
Intensity
P32,PFL
rmin = 0.56m rmax = 564 m
Transmissivity model
SC: (a, b, σlog(T))
(m,m ) (m2/m
3) T (m
2s
-1)
EW (185.5, 5.3) 10.4 (0.45, 0.25) 0.12 SC: (2.3 10–9
, 0.7, 1.2)
NS (90.7, 7.5) 8.1 (0.45, 0.25) 0.07 SC: (2.3 10–9
, 0.7, 1.2)
SH (301.3, 85) 6.1 (0.45, 0.25) 0.41 SC: (7 10–9
, 0.7, 1.2)
68
6.7.2 FDb: Depth zone 2 ( –50 to –150 m elevation)
Table 6-8. Summary of Hydro-DFN parameters for the simulations of flow in fracture
domain FDb, depth zone DZ2 using a power-law size model (Case A).
Set Pole orientation
(trend, plunge) concentration
Case A power-law
(kr, r0)
Intensity
P32,open
rmin = r0
rmax = 564 m
Transmissivity model
C: (a,b) SC: (a, b, σlog(T)) UC: (µ log(T), σ log(T))
(-, m) (m2/m
3) T (m
2s
-1)
EW (185.5, 5.3) 10.4 (2.6, 0.04) 0.50
C: (3.3 10–9
, 1.1)
SC: (1 10–8
, 0.7, 0.7)
UC: (6.6 10–8
, 1.3)
NS (90.7, 7.5) 8.1 (2.6, 0.04) 0.49
C: (3.3 10–9
, 1.1)
SC: (1 10–8
, 0.7, 0.7)
UC: (6.6 10–8
, 1.3)
SH (301.3, 85) 6.1 (2.7, 0.04) 1.61
C: (1 10–8
, 1.1)
SC: (3 10–8
, 0.7, 0.7)
UC: (2 10–7
, 1.3)
Table 6-9. Summary of Hydro-DFN parameters for the simulations of flow in fracture
domain FDb, depth zone DZ2 using a log-normal size model (Case B).
Set Pole orientation
(trend, plunge) concentration
Case B log-normal
(mlog(r), slog(r))
Intensity
P32,PFL
rmin = 0.56 m rmax = 564 m
Transmissivity model
SC: (a, b, σlog(T))
(-, - ) (m2/m
3) T (m
2s
-1)
EW (185.5, 5.3) 10.4 (0.45, 0.25) 0.07 SC: (1 10–10
, 0.7, 1)
NS (90.7, 7.5) 8.1 (0.45, 0.25) 0.06 SC: (1 10–10
, 0.7, 1)
SH (301.3, 85) 6.1 (0.45, 0.25) 0.17 SC: (3.2 10–10
, 0.7, 1)
69
6.7.3 FDb: Depth zone 3 (–150 to –400 m elevation)
Table 6-10. Summary of Hydro-DFN parameters for the simulations of flow in fracture
domain FDb, depth zone DZ3 using a power-law size model (Case A).
Set Pole orientation
(trend, plunge) concentration
Case A power-law
(kr, r0)
Intensity
P32,open
rmin = r0
rmax = 564 m
Transmissivity model
C: (a,b) SC: (a, b, σlog(T)) UC: (µ log(T), σ log(T))
(-, m) (m2/m
3) T (m
2s
-1)
EW (185.5, 5.3) 10.4 (2.65, 0.04) 0.32
C: (1.3 10–9
, 1)
SC: (2.2 10–9
, 0.7, 0.7)
UC: (6.6 10–8
, 1)
NS (90.7, 7.5) 8.1 (2.65, 0.04) 0.37
C: (1.3 10–9
, 1)
SC: (2.2 10–9
, 0.7, 0.7)
UC: (6.6 10–8
, 1)
SH (301.3, 85) 6.1 (2.65, 0.04) 0.88
C: (4 10–9
, 1.1)
SC: (7 10–9
, 1.1, 0.7)
UC: (2 10–7
, 1)
Table 6-11. Summary of Hydro-DFN parameters for the simulations of flow in fracture
domain FDb, depth zone DZ3 using a log-normal size model (Case B).
Set Pole orientation
(trend, plunge) concentration
Case B log-normal
(mlog(r), slog(r))
Intensity
P32,PFL
rmin = 0.56 m rmax = 564 m
Transmissivity model
SC: (a, b, σlog(T))
(-, - ) (m2/m
3) T (m
2s
-1)
EW (185.5, 5.3) 10.4 (0.45, 0.25) 0.01 SC: (3.3 10–10
, 0.7, 1)
NS (90.7, 7.5) 8.1 (0.45, 0.25) 0.02 SC: (3.3 10–10
, 0.7, 1)
SH (301.3, 85) 6.1 (0.45, 0.25) 0.05 SC: (1 10–9
, 1, 1.2)
70
6.7.4 FDb: Depth zone 4 (–400 to –1 000 m elevation)
Table 6-12. Summary of Hydro-DFN parameters for the simulations of flow in fracture
domain FDb, depth zone DZ4 using a power-law size model (Case A).
Set Pole orientation
(trend, plunge) concentration
Case A power-law
(kr, r0)
Intensity
P32,open
rmin = r0
rmax = 564 m
Transmissivity model
C: (a,b) SC: (a, b, σlog(T)) UC: (µ log(T), σ log(T))
(-, m) (m2/m
3) T (m
2s
-1)
EW (185.5, 5.3) 10.4 (2.7, 0.04) 0.22
C: (1.3 10–9
, 1)
SC: (5 10–10
, 0.7, 0.7)
UC: (6.6 10–8
, 1)
NS (90.7, 7.5) 8.1 (2.7, 0.04) 0.24
C: (1.3 10–9
, 1)
SC: (5 10–10, 0.7, 0.7)
UC: (6.6 10–8
, 1)
SH (301.3, 85) 6.1 (2.7, 0.04) 0.62
C: (4 10–9
, 1.1)
SC: (1.5 10–9
, 1.1, 0.7)
UC: (2 10–7
, 1)
Table 6-13. Summary of Hydro-DFN parameters for the simulations of flow in fracture
domain FDb, depth zone DZ4 using a log-normal size model (Case B).
Set Pole orientation
(trend, plunge) concentration
Case B log-normal
(mlog(r), slog(r))
Intensity
P32,PFL
rmin = 0.56 m rmax = 564 m
Transmissivity model
SC: (a, b, σlog(T))
(-, - ) (m2/m
3) T (m
2s
-1)
EW (185.5, 5.3) 10.4 (1.45, 0.25) 0.00 SC: (7 10–11
, 0.7, 1)
NS (90.7, 7.5) 8.1 (1.45, 0.25) 0.00 SC: (7 10–11
, 0.7, 1)
SH (301.3, 85) 6.1 (1.45, 0.25) 0.02 SC: (1.5 10–10
, 1, 1.2)
71
7 PREDICTION OF WATER CONDUCTING FRACTURES IN TWO TUNNEL PILOT HOLES – PH8 AND PH9
7.1 Pilot holes PH8 and PH9
The locations of pilot holes PH8 and PH9 with regard to pilot holes PH1-7 presented in
Appendix A are shown in Figure 7-1. Pilot hole PH8 is planned to be drilled at a
location that partly coincides with fracture domain FDa and partly with fracture domain
FDb, whereas PH9 is planned to be drilled at a location that fully coincides with
fracture domain FDb. Pilot holes PH1-7 are all located in FDa.
PH8-9
… combined over boreholes of varying
trajectories to estimate average values …
… to make predictions
in two sub-horizontal pilot boreholes …
Figure 7-1. Location of pilot holes in PH1-9. The modelling approach is to use the
average Terzaghi corrected statistics deduced from the sub-vertical KR and KRB
boreholes to predict the frequency and magnitudes of water conducting fractures in two
sub-horizontal boreholes.
7.2 Modelling approach
The modelling approach shown in Figure 7-1 uses the average Terzaghi corrected
statistics of water conducting fractures deduced from the sub-vertical KR and KRB
boreholes to predict the frequency and magnitudes of water conducting fractures in two
sub-horizontal boreholes, PH8 and PH9. The success of this modelling approach is of
course uncertain as it implies that the statistics of the 56 sub-vertical KR and KRB
boreholes, 16 of which are very shallow, homogenised over the defined sub-domains
capture the same hydrogeological conditions as encountered by two specific, sub-
horizontal boreholes close to repository depth.
72
7.3 Hydro-DFN
In order to predict the frequency and magnitudes of water conducting fractures in pilot
hole PH8, it is necessary to compute the Hydro-DFN properties for FDa, since parts of
PH8 is located in depth zone 3 of this bedrock segment. (The Hydro-DFN model
presented in section 6 treats fracture domain FDb only.) Table 7-1 shows the properties
for the Case A fracture size model and the semi-correlated transmissivity model.
Table 7-1. Summary of Hydro-DFN parameters for fracture domain FDa, depth zones
DZ1-4 using a power-law size model (Case A) and a semi-correlated transmissivity
model (SC).
DZ Set
Pole orientation
(trend, plunge) concentration
Case A power-law
(kr, r0)
Intensity
P32,open
rmin = r0
rmax = 564 m
Transmissivity model
SC: (a, b, σlog(T))
(-,m ) (m2/m
3) T (m
2s
-1)
EW (175.1,3.5) 10 (2.5, 0.04) 0.32 SC: (2.7 10–8
, 0.7, 0.9)
1 NS (269.4,0.2) 7.4 (2.5, 0.04) 0.40 SC: (2.7 10–8
, 0.7, 0.9)
SH (304.3,78) 7.3 (2.5, 0.04) 1.68 SC: (2.7 10–8
, 0.7, 0.9)
EW (175.1,3.5) 10 (2.5, 0.04) 0.32 SC: (1.5 10–8
, 0.7, 1.1)
2 NS (269.4,0.2) 7.4 (2.5, 0.04) 0.35 SC: (1.5 10–8
, 0.7, 1.1)
SH (304.3,78) 7.3 (2.5, 0.04) 1.21 SC: (1.5 10–8
, 0.7, 1.1)
EW (175.1,3.5) 10 (2.65, 0.04) 0.26 SC: (1.5 10–8
, 0.7, 1.2)
3 NS (269.4,0.2) 7.4 (2.65, 0.04) 0.26 SC: (1.5 10–8
, 0.7, 1.2)
SH (304.3,78) 7.3 (2.65, 0.04) 0.73 SC: (1.5 10–8
, 0.7, 1.2)
EW (175.1,3.5) 10 (2.7, 0.04) 0.16 SC: (2 10–9
, 0.7, 0.7)
4 NS (269.4,0.2) 7.4 (2.7, 0.04) 0.22 SC: (2 10–9
, 0.7, 0.7)
SH (304.3,78) 7.3 (2.7, 0.04) 0.33 SC: (2 10–9
, 0.7, 0.7)
7.4 Prediction
Figure 7-2 and Figure 7-3 show the means over 40 realisations of the number of inflows
with regard to log(Q/s) for pilot hole PH8. Figure 7-2 shows the means for the
uppermost part of PH8, which is located in DZ3 in FDa (26 % of PH8 or c. 179 m of
borehole). Figure 7-3 shows the means for the lowermost part of PH8, which is located
in DZ3 in FDb (74 % of PH8 or c. 522 m of borehole). The difference in length in the
two fracture domains is not sufficient to explain the difference in the number of inflows.
From section 5.4 we conclude that P10,PFL,corr is about 60% higher in DZ3 of FDb than
in FDa, 0.08 m–1
vs. 0.05 m–1
, see Table 5-4 and Figure 5-15. The figures suggest it is
near certain at least one fracture of transmissivity > 1-3 10-8
m2/s will be encountered in
PH8, but it is much less likley that any fractures >3 10-7
m2/s will be seen.
73
Number of intersections in range -400 to -150 masl
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
< -1
0
-10 to
-9.5
-9.5 to
-9
-9 to
-8.5
-8.5 to
-8
-8 to
-7.5
-7.5 to
-7
-7 to
-6.5
-6.5 to
-6
-6 to
-5.5
-5.5 to
-5
-5 to
-4.5
-4.5 to
-4
-4 to
-3.5
-3.5 to
-3 > -3
log(Q/s) [m 2/s]
Nu
mb
er
of
infl
ow
s
Model (mean of 40 realisations)
Figure 7-2. Number of inflows with regard to log(Q/s) for the uppermost part of pilot
hole PH8, which is located in DZ3 in FDa. Mean over 40 realisations. Error bars show
the 5th and 95th percentiles over the 40 realisations.
Number of intersections in range -400 to -150 masl
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
< -1
0
-10 to
-9.5
-9.5 to
-9
-9 to
-8.5
-8.5 to
-8
-8 to
-7.5
-7.5 to
-7
-7 to
-6.5
-6.5 to
-6
-6 to
-5.5
-5.5 to
-5
-5 to
-4.5
-4.5 to
-4
-4 to
-3.5
-3.5 to
-3 > -3
log(Q/s) [m 2/s]
Nu
mb
er
of
infl
ow
s
Model (mean of 40 realisations)
Figure 7-3. Predicted number of inflows with regard to log(Q/s) for the lowermost part
of pilot hole PH8, which is located in DZ3 in FDb. Mean over 40 realisations. Error
bars show the 5th and 95th percentiles over the 40 realisations.
74
Figure 7-4 shows the means over 40 realisations of the number of inflows with regard to
log(Q/s) for pilot hole PH9, which is c. 280 m long and located in DZ3 in FDb. This
suggests that it is reasonably likely no fractures will be encountered with transmissivity
> 3 10-8
m2/s.
Number of intersections in range -400 to -150 masl
0.0
1.0
2.0
3.0
4.0
5.0
6.0
< -1
0
-10 to
-9.5
-9.5 to
-9
-9 to
-8.5
-8.5 to
-8
-8 to
-7.5
-7.5 to
-7
-7 to
-6.5
-6.5 to
-6
-6 to
-5.5
-5.5 to
-5
-5 to
-4.5
-4.5 to
-4
-4 to
-3.5
-3.5 to
-3 > -3
log(Q/s) [m 2/s]
Nu
mb
er
of
infl
ow
s
Model (mean of 40 realisations)
Figure 7-4. Predicted number of inflows with regard to log(Q/s) for pilot hole PH9,
which is located in DZ3 in FDb. Mean over 40 realisations. Error bars show the 5th
and 95th percentiles over the 40 realisations.
7.5 Uncertainty assessment
As a means to address the uncertainties in the methodology as well as in comparison
between sub-vertical versus sub-horizontal statistics, we made two additional prediction
tests. In the first of the two additional prediction tests, we predicted the number of
inflows to pilot holes PH2 and PH6, respectively. In the second one, we predicted the
number of inflows to pilot holes PH1+PH2 combined and to PH3+4+5+6 combined.
The first prediction test checks the approach used to predict the number of inflows to
pilot holes PH8 and PH9, whereas the second prediction tests the suitability of the
modelling approach as such. That is, if the first prediction test fails to do the job,
whereas the second prediction test is more successful, we may conclude that the spatial
variability between pilot holes is probably very large and that the average predictions
shown in Figure 7-2 through Figure 7-4 only indicate the range of possible conditions
that may be encountered, but not the pattern that is likely to be seen in an individual
pilot hole. An interesting question is then how many (if any) of the 40 realisations
carried out are close to the measured distribution.
Figure 7-5 and Figure 7-6 show the results from the first prediction test and Figure 7-7
and Figure 7-8 show the results from the second. The outcome looks like the
expectation. That is, the second prediction test is more successful. Table A-4 shows that
75
P10,PFL,corr is 0.24 m–1
in PH1 and 0.85 m–1
in PH2, which make an average of 0.545 m-1
.
In comparison, Table 5-4 shows that the average value of P10,PFL,corr for the 56 sub-
vertical boreholes is 0.50 m–1
in DZ1. By the same token, Table B-4 shows that the
average value of P10,PFL,corr for PH3+4+5+6 is 0.245 m–1
, and Table 5-4 shows that the
average value of P10,PFL,corr for the 56 sub-vertical boreholes in DZ2 is 0.24 m–1
. The
conclusion is that the Hydro-DFN model can be used to predict the distribution of
tunnel inflows taken as an ensemble gathered from tunnel sections totalling at least
1km, but predicting the inflows that may seen within individual tunnel sections on order
of a few hundred metres is much more uncertain.
A noteworthy difference is that there are several transmissivities of large magnitudes
(>10–4
m2/s) among the 56 sub-vertical boreholes, whereas the highest values recorded
for pilot holes PH1-7 is ca 100 times smaller. Examples of relevant question that may
be raised here are if this difference is due to:
local diffferences in the near-surface geological conditions investigated by PH1 and
PH2 boreholes, and
differences in the transmissivity between different fracture set in the superficial
bedrock (e.g. the SH set has a higher probability of intersectin the sub-vertical
KR/KRB boreholes).
Number of intersections in range -50 to -0 masl
0.0
5.0
10.0
15.0
20.0
25.0
< -1
0
-10 to
-9.5
-9.5 to
-9
-9 to
-8.5
-8.5 to
-8
-8 to
-7.5
-7.5 to
-7
-7 to
-6.5
-6.5 to
-6
-6 to
-5.5
-5.5 to
-5
-5 to
-4.5
-4.5 to
-4
-4 to
-3.5
-3.5 to
-3 > -3
log(Q/s) [m 2/s]
Nu
mb
er
of
infl
ow
s
Model (mean of 40 realisations)
Data (PFL_f)
Figure 7-5. Measured vs. predicted number of inflows with regard to log(Q/s) for pilot
hole PH2, which is located in DZ1 in FDa. Mean over 40 realisations. Error bars show
the 5th and 95th percentiles over the 40 realisations.
76
Number of intersections in range -150 to -50 masl
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
< -1
0
-10 to
-9.5
-9.5 to
-9
-9 to
-8.5
-8.5 to
-8
-8 to
-7.5
-7.5 to
-7
-7 to
-6.5
-6.5 to
-6
-6 to
-5.5
-5.5 to
-5
-5 to
-4.5
-4.5 to
-4
-4 to
-3.5
-3.5 to
-3 > -3
log(Q/s) [m 2/s]
Nu
mb
er
of
infl
ow
s
Model (mean of 40 realisations)
Data (PFL_f)
Figure 7-6. Measured vs. predicted number of inflows with regard to log(Q/s) for pilot
hole PH6, which is located in DZ2 in FDa. Mean over 40 realisations. Error bars show
the 5th and 95th percentiles over the 40 realisations.
Number of intersections in range -50 to 0 masl
0.0
5.0
10.0
15.0
20.0
25.0
< -1
0
-10 to
-9.5
-9.5 to
-9
-9 to
-8.5
-8.5 to
-8
-8 to
-7.5
-7.5 to
-7
-7 to
-6.5
-6.5 to
-6
-6 to
-5.5
-5.5 to
-5
-5 to
-4.5
-4.5 to
-4
-4 to
-3.5
-3.5 to
-3 > -3
log(Q/s) [m2/s]
Nu
mb
er
of
infl
ow
s
Model (mean of 40 realisations)
Data (PFL_f)
Figure 7-7. Measured vs. predicted number of inflows with regard to log(Q/s) for pilot
holes PH1+2, which are located in DZ1 in FDa. Mean over 40 realisations. Error bars
show the 5th and 95th percentiles over the 40 realisations.
77
Number of intersections in range -150 to -50 masl
0.0
5.0
10.0
15.0
20.0
25.0
< -1
0
-10 to
-9.5
-9.5 to
-9
-9 to
-8.5
-8.5 to
-8
-8 to
-7.5
-7.5 to
-7
-7 to
-6.5
-6.5 to
-6
-6 to
-5.5
-5.5 to
-5
-5 to
-4.5
-4.5 to
-4
-4 to
-3.5
-3.5 to
-3 > -3
log(Q/s) [m 2/s]
Nu
mb
er
of
infl
ow
s
Model (mean of 40 realisations)
Data (PFL_f)
Figure 7-8. Measured vs. predicted number of inflows with regard to log(Q/s) for pilot
holes PH3+4+5+6, which are located in DZ2 in FDa. Mean over 40 realisations. Error
bars show the 5th and 95th percentiles over the 40 realisations.
78
79
8 REPOSITORY-SCALE EQUIVALENT CONTINUUM POROUS MEDIUM (ECPM) BLOCK PROPERTIES
8.1 Objectives
Effective hydraulic conductivity tensors, Keff, and kinematic porosities, eff, were
calculated for a 50m block size (approximately the grid size in FEFTRA) in the bedrock
immediate to the repository using the statistics derived in the previous sections. The
results were generated for one realisation as the objective was to provide preliminary
hydraulic properties in support of the ECPM modelling with FEFTRA.
8.2 Model set-up
The model domain is a cube with size (500 m)3. The model domain is sub-divided into
103 50m blocks. Each 50 m block considered in the statistics has a „guard zone‟ of 50m
in each direction to prevent fractures that are unconnected to the wider fracture network
contributing to the conductivity of the block. Hence, a maximum of 93 (729) 50 m
blocks are considered in each simulation.
The fracture size distribution and transmissivity values are taken from the flow
calibration. Different depth zones are considered in separate models. If there are no
connected fractures generated inside a block then that block will have zero hydraulic
conductivity. These cases are excluded from the calculation of hydraulic conductivity
statistics. The fraction of blocks that have at least some connected fractures is presented
in the results as the percolation fraction.
8.3 Example visualisations
Figure 8-1 shows the front side of the fractures generated in the semi-correlated Case A
model, –400 to –150 m elevation. Figure 8-3 shows a 2D slice through the centre of this
realisation. Figure 8-2 and Figure 8-4 show the Kxx (E-W) hydraulic conductivities
corresponding to two E-W slices through the centres of the 2 models.
8.4 Studied cases
Table B-1 through Table B-11 and Figure B-11 through Figure B-21 show upscaling
results for the following combinations of models and depth zones, see Table 8-1.
80
Table 8-1. Summary of stucied combinations of size and transmissivity models.
Model description
Fracture size distribution model T model DZ (masl)
Case A: power-law SC DZ1: 0 to –50
Case A: power-law SC DZ2: –50 to –150
Case A: power-law SC DZ3: –150 to –400
Case A: power-law SC DZ4: –400 to –1 000
Case A: power-law C DZ3: –150 to –400
Case A: power-law C DZ4: –400 to –1 000
Case A: power-law UC DZ3: –150 to –400
Case A: power-law UC DZ4: –400 to –1 000
Case B: log-normal SC DZ2: –50 to –150
Case B: log-normal SC DZ3: –150 to –400
Case B: log-normal SC DZ4: –400 to –1 000
Figure 8-1. Vertical WE visualisation of the fractures generated in the semi-correlated
Case A model, –400 to –150 m of elevation. The fractures are coloured by
transmissivity.
81
Figure 8-2. Kxx hydraulic conductivities for the vertical WE slice shown in Figure 8-1.
Figure 8-3. A vertical WE slice through the centre of the model region shown in Figure
8-1.
82
Figure 8-4. Kxx hydraulic conductivities for the vertical WE slice shown in Figure 8-3.
8.5 Effective hydraulic conductivity
In ConnectFlow, a symmetric positive definite 6 component tensor is calculated. The
effective hydraulic conductivity, Keff, is calculated as either:
Keff = (Kxx Kyy Kzz)1/3
(8-1)
where Kxx = K11, Kyy = K22, and Kzz = K33, or slightly more rigorous
Keff = (Kmax Kint Kmin)1/3
(8-2)
i.e. the geometric mean of the principal components (or eigenvalues of the matrix). The
results reported here are based on Eq. (8-2).The statistics found in Appendix B show:
The 10, 25, 50, 75, 90 percentiles of Keff based on all cells whether Keff is zero or
not.
The geometric mean and standard deviation of those values that have Keff >10–13
m/s
(keff = 10–20
m2).
The percentage of cells that have Keff >10–13
m/s.
8.6 Effective kinematic porosity
The effective kinematic porosity is calculated as the cumulative volume of the flowing
pore space divided by the block volume. In Phase I, the contribution to the flowing pore
space was calculated from the following function (N.B. it was modified in Phase II):
83
et = 0.46 T (8-3)
where et is the transport aperture and T is the fracture transmissivity. The physical basis
for Eq. (8-3) is uncertain, cf. /Dershowitz et al. 2003/.
8.7 Summary of the upscaling study
Table 8-2 and Table 8-3 together with and Figure 8-5 through Figure 8-7 summarise the
upscaling results shown in Appendix B. We make the following observations:
The median ratio of (max[Kxx, Kyy]/Kzz) is a factor of 2 or 3 at all depth zones, and
for all the modelling variants.
For the semi-correlated power-law model, the geometric mean effective
conductivity decreases with depth from around 7.4 10-8
m/s for DZ1, 2.2 10-9
m/s
for DZ2, 1.9 10-10
m/s for DZ3 to 2.4 10-11
m/s for DZ4. Likewise, the geometric
mean kinematic porosity decreases with depth from around 1.3 10-4
for DZ1-2,
1.3 10-5
for DZ3 to 3.7 10-6
for DZ4.
The spread around the mean values increases with depth.
The percolation fraction decreases with depth from around 1.0 for DZ1-2 to around
0.9 for DZ3, to around 0.4 for DZ4. These fractions do not vary much with the
modelling variant.
The models with log-normal fracture size distribution show a slightly higher mean
conductivity and lower spread compared to models with a power-law fracture size
distribution, but these differences may not be statistically significant.
Table 8-2. Summary of upscaling results for repository-scale 50m Keff.
Model description Parameter
Fracture size distribution
T model Depth zone (masl)
m of log(Keff)
[m/s]
s of log(Keff)
[m/s]
Fraction of percolation
Power-law SC 0 to –50 -7.13 0.39 1.00
Power-law SC –50 to –150 -8.65 0.63 1.00
Power-law SC –150 to –400 -9.72 0.94 0.89
Power-law SC –400 to –1 000 -10.62 0.70 0.46
Power-law C –150 to –400 -9.73 0.90 0.89
Power-law C –400 to –1 000 -9.87 0.76 0.45
Power-law UC –150 to –400 -9.59 1.02 0.90
Power-law UC –400 to –1 000 -9.84 0.94 0.48
Log-normal SC –50 to –150 -8.78 0.31 1.00
Log-normal SC –150 to –400 -9.30 0.83 0.98
Log-normal SC –400 to –1 000 -9.46 1.19 0.37
84
Table 8-3. Summary of upscaling results for repository-scale 50 m eff.
Model description Parameter
Fracture size distribution
T model Depth zone (masl)
m of log( eff)
[m/s] s of log( eff)
[m/s]
Fraction of percolation
Power-law SC 0 to –50 -3.88 0.05 1.00
Power-law SC –50 to –150 -4.50 0.05 1.00
Power-law SC –150 to –400 -4.89 0.08 0.89
Power-law SC –400 to –1 000 -5.43 0.07 0.46
Power-law C –150 to –400 -5.05 0.10 0.89
Power-law C –400 to –1 000 -5.25 0.07 0.45
Power-law UC –150 to –400 -4.46 0.08 0.90
Power-law UC –400 to –1 000 -4.68 0.05 0.48
Log-normal SC –50 to –150 -4.87 0.07 1.00
Log-normal SC –150 to –400 -4.92 0.12 0.98
Log-normal SC –400 to –1 000 -5.22 0.24 0.37
85
FDb, semi-correlated, CaseA
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
-6 to
-5.5
-5.5
to -5
Block K [m/s]
CD
F
SC caseA DZ1
SC caseA DZ2
SC caseA DZ3
SC caseA DZ4
FDb, semi-correlated, CaseA
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
-6 to
-5.5
-5.5
to -5
Block K [m/s]
PD
F
SC caseA DZ1
SC caseA DZ2
SC caseA DZ3
SC caseA DZ4
Figure 8-5. Summary of upscaling results for: FDb, Depth zones DZ1-4, Case A
(Power-law size distribution), Semi-correlated transmissivity. Top: CDF of Keff.
Bottom: PDF of Keff.
86
FDb, semi-correlated, CaseB
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
-6 to
-5.5
-5.5
to -5
Block K [m/s]
CD
F
SC caseB DZ2
SC caseB DZ3
SC caseB DZ4
FDb, semi-correlated, CaseB
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
-6 to
-5.5
-5.5
to -5
Block K [m/s]
PD
F
SC caseB DZ2
SC caseB DZ3
SC caseB DZ4
Figure 8-6. Summary of upscaling results for: FDb, Depth zones DZ2-4, Case B (Log-
normal size distribution), Semi-correlated transmissivity. Top: CDF of Keff. Bottom:
PDF of Keff.
87
FDb, CaseA
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
-6 to
-5.5
-5.5
to -5
Block K [m/s]
CD
F
C caseA DZ3
C caseA DZ4
SC caseA DZ3
SC caseA DZ4
UC caseA DZ3
UC caseA DZ4
FDb, CaseA
0.00
0.05
0.10
0.15
0.20
0.25
0.30
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
-6 to
-5.5
-5.5
to -5
Block K [m/s]
PD
F
C caseA DZ3
C caseA DZ4
SC caseA DZ3
SC caseA DZ4
UC caseA DZ3
UC caseA DZ4
Figure 8-7. Summary of upscaling results for: FDb, Depth zones DZ3-4, Case A
(Power-law size distribution), Correlated transmissivity, Semi-correlated transmissivity
and Uncorrelated transmissivity. Top: CDF of Keff. Bottom: PDF of Keff.
88
89
9 REPOSITORY-SCALE FRESHWATER FLOW AND TRANSPORT
9.1 Objectives
Particle tracking simulations were carried out to investigate freshwater flow and
transport pathway statistics through the bedrock model in close proximity to the
repository volume. The objective is to provide preliminary information about
performance assessment (PA) properties of the Hydro-DFN model in close proximity to
the repository, i.e. the F-quotient and the travel time t.
9.2 Model set-up
The model domain is a cube with size (200 m)3. The particles are released from an
array of 100 points. The array of release points has rows and columns spaced at 5 m
intervals.
At each release point, a sphere of radius 2.5 m is searched for fractures connected to
the flowing fracture network. The radius of 2.5 m was chosen to approximate the
height of a canister deposition hole. If no connected fractures intersect the sphere
surrounding the release point the particle is not released. Ten particles are released
at each release point. If there is more than one fracture within the 2.5 m radius
around the release point the choice of release is weighted by the flux through the
possible fractures.
The fractures are generated according to the fracture size distribution parameters
and fracture transmissivity parameters produced in the flow calibration stage of
modelling. To make the model computationally tractable the smallest fractures
(down to 0.28 m radius) are only generated in the region immediately surrounding
the release points. The depth zones –150 to –400 and –400 to –1 000 masl are
considered separately.
The transport aperture te of the fractures is assigned according to the relationship
shown in Eq. (8-3). It is noted that the physical basis for this relationship is
uncertain, cf. /Dershowitz et al. 2003/.
Pathlines are calculated for cases when the pressure gradient is in the X (E-W)
direction, Y (N-S) direction and Z (vertical) direction. The pressure gradient is 1 %
in each case. The model boundary conditions are a linear pressure gradient on each
of the six faces.
The particle pathlines are calculated for 40 realisations of the model.
Table 9-1 shows the models studied. Figure 9-1, Figure 9-2 and Figure 9-3 visualise the
model set-up. Figure 9-4 through Figure 9-7 show the fraction of active particles (those
for which a connected fracture is found within the release volume) in each DFN model.
The results are tabulated in Appendix C. An excerpt of the results for the travel time and
the F-quotient is shown in Figure 9-8 through Figure 9-13.
90
Table 9-1. Summary of the cases studied.
Model ID Fracture size distribution model
T model DZ (masl)
A-SC-FDb-DZ3 Case A: power-law SC DZ3: –150 to –400
A-SC-FDb-DZ4 Case A: power-law SC DZ4: –400 to –1 000
A-C-FDb-DZ3 Case A: power-law C DZ3: –150 to –400
A-C-FDb-DZ4 Case A: power-law C DZ4: –400 to –1 000
A-UC-FDb-DZ3 Case A: power-law UC DZ3: –150 to –400
A-UC-FDb-DZ4 Case A: power-law UC DZ4: –400 to –1 000
B-SC-FDb-DZ3 Case B: log-normal SC DZ3: –150 to –400
B-SC-FDb-DZ4 Case B: log-normal SC DZ4: –400 to –1 000
Figure 9-1. Upper left: Model region showing the array of release points. There are
100 release points in 10 rows. Each row is spaced 5m apart. Upper right: Horizontal
slice through the model showing the location of the deposition holes. Lower left: For
the power-law fracture size distribution model fractures with radii down to 0.28 m are
generated in a region surrounding the release points. Outside this region fractures with
radii greater than 2.26 m are generated. Lower right: All fractures generated in the
model region. The fracture size distribution and fracture transmissivity parameters are
taken from the results of the flow calibration; in this case for a semi-correlated
transmissivity, case A model (power-law distribution), for the FDb fracture domain in
depth zone –150 to –400 masl.
91
Figure 9-2. Fractures connected to the deposition holes for a single realisation. This
example is for the depth zone –150 to –400 masl. For the depth zone –400 to –1 000
masl the fracture network is even sparser.
Figure 9-3. Ensemble of pathlines produced over 40 realisations for a single release
point. The pressure gradient is in the X direction. Semi-correlated transmissivity, Case
A (power-law) model, fracture domain FDb, depth zone DZ3 (–150 to –400 masl).
92
9.3 Fraction of deposition holes connected to the DFN
Figure 9-4 compares statistics for estimates of the percentage of deposition holes that
are intersected by at least one connected fracture for the Case A size model and either
correlated, semi-correlated or uncorrelated transmissivity model in depth zone 3.
9.3.1 Case A-C/SC/UC-FDb-DZ3
A-C-FDb-DZ3
0%
10%
20%
30%
40%
50%
60%
70%
Min m-1sd 50% m m+1sd Max
Fra
cti
on
of
pa
rtic
les
in
DF
N (
%)
X
Y
Z
A-SC-FDb-DZ3
0%
10%
20%
30%
40%
50%
60%
70%
Min m-1sd 50% m m+1sd Max
Fra
cti
on
of
pa
rtic
les
in
DF
N (
%)
X
Y
Z
A-UC-FDb-DZ3
0%
10%
20%
30%
40%
50%
60%
70%
Min m-1sd 50% m m+1sd Max
Fra
cti
on
of
pa
rtic
les
in
DF
N (
%)
X
Y
Z
Figure 9-4. Histograms showing the percentages of released particles that are
connected to the fracture network for Case A, FDb and DZ3. Top: Correlated model
(C), Middle: Semi-correlated model (SC), Bottom: Uncorrelated model (UC).m = mean,
50% = median, sd = standard deviation.
93
9.3.2 Case A-C/SC/UC-FDb-DZ4
Figure 9-5 compares statistics for estimates of percentage of deposition holes that are
intersected by at least one connected fracture for the Case A size model and either
correlated, semi-correlated or uncorrelated transmissivity model in depth zone 4.
A-C-FDb-DZ4
0%
10%
20%
30%
40%
50%
60%
70%
Min m-1sd 50% m m+1sd Max
Fra
cti
on
of
pa
rtic
les
in
DF
N (
%)
X
Y
Z
A-SC-FDb-DZ4
0%
10%
20%
30%
40%
50%
60%
70%
Min m-1sd 50% m m+1sd Max
Fra
cti
on
of
pa
rtic
les
in
DF
N (
%)
X
Y
Z
A-UC-FDb-DZ4
0%
10%
20%
30%
40%
50%
60%
70%
Min m-1sd 50% m m+1sd Max
Fra
cti
on
of
pa
rtic
les
in
DF
N (
%)
X
Y
Z
Figure 9-5. Histograms showing the percentages of released particles that are
connected to the fracture network for Case A, FDb and DZ4. Top: Correlated model ©,
Middle: Semi-correlated model (SC), Bottom: Uncorrelated model (UC).m = mean,
50 % = median, sd = standard deviation.
94
9.3.3 Case A/B-SC-FDb-DZ3
Figure 9-6 compares statistics for estimates of percentage of deposition holes that are
intersected by at least one connected fracture for the Case A and Case B size model with
the semi-correlated transmissivity model in depth zone 3.
A-SC-FDb-DZ3
0%
10%
20%
30%
40%
50%
60%
70%
Min m-1sd 50% m m+1sd Max
Fra
cti
on
of
pa
rtic
les
in
DF
N (
%)
X
Y
Z
B-SC-FDb-DZ3
0%
10%
20%
30%
40%
50%
60%
70%
Min m-1sd 50% m m+1sd Max
Fra
cti
on
of
pa
rtic
les
in
DF
N (
%)
X
Y
Z
Figure 9-6. Histograms showing the percentages of released particles that are
connected to the fracture network for SC, FDb and DZ3. Top: Case A, Bottom: Case
B.m = mean, 50 % = median, sd = standard deviation.
9.3.4 Case A/B-SC-FDb-DZ4
Figure 9-7 compares statistics for estimates of percentage of deposition holes that are
intersected by at least one connected fracture for the Case A and Case B size model with
the semi-correlated transmissivity model in depth zone 4.
The last 4 figures demonstrate the percentage of deposition holes connected to the wider
fracture network is much lower in depth zone 4, around 4 %, compared to around 20 %
in depth zone 3. Also, the statistics do not depend on the fracture size model used. The
reason is that both models have been calibrated to give an intensity of connected open
fractures that is based on the measured intensity of water conducting fractures detected
by PFL.
95
A-SC-FDb-DZ4
0%
10%
20%
30%
40%
50%
60%
70%
Min m-1sd 50% m m+1sd Max
Fra
cti
on
of
pa
rtic
les
in
DF
N (
%)
X
Y
Z
B-SC-FDb-DZ4
0%
10%
20%
30%
40%
50%
60%
70%
Min m-1sd 50% m m+1sd Max
Fra
cti
on
of
pa
rtic
les
in
DF
N (
%)
X
Y
Z
Figure 9-7. Histograms showing the percentages of released particles that are
connected to the fracture network for SC, FDb and DZ4. Top: Case A, Bottom: Case
B.m = mean, 50 % = median, sd = standard deviation.
9.4 Travel times and F-quotients
Figure 9-8 compares percentiles of travel time for released released particles for the
Case A size model with the correlated, semi-correlated and uncorrelated transmissivity
model in depth zone 3 and three axial flow directions.
96
9.4.1 Directional values for Case A-C/SC/UC-FDb-DZ3
A-FDb-DZ3-x_dir
1E-02
1E-01
1E+00
1E+01
1E+02
1E+03
1E+04
1E+05
1E+06
1E+07
min 10% 25% 50% 75% 90% max
Tra
ve
l ti
me
in
DF
N (
y)
x: C
x: SC
x: UC
A-FDb-DZ3-y_dir
1E-02
1E-01
1E+00
1E+01
1E+02
1E+03
1E+04
1E+05
1E+06
1E+07
min 10% 25% 50% 75% 90% max
Tra
ve
l ti
me
in
DF
N (
y)
y: C
y: SC
y: UC
A-FDb-DZ3-z_dir
1E-02
1E-01
1E+00
1E+01
1E+02
1E+03
1E+04
1E+05
1E+06
1E+07
min 10% 25% 50% 75% 90% max
Tra
ve
l ti
me
in
DF
N (
y)
z: C
z: SC
z: UC
Figure 9-8. Histograms showing the average percentiles of the travel time in three
orthogonal directions for Case A, FDb and DZ3: C = the Correlated model, SC = the
Semi-correlated model and UC = the Uncorrelated model.
Figure 9-9 compares percentiles of F-quotient for released released particles for the
Case A size model with the correlated, semi-correlated and uncorrelated transmissivity
model in depth zone 3 and three axial flow directions.
97
A-FDb-DZ3-x_dir
1E+01
1E+03
1E+05
1E+07
1E+09
1E+11
min 10% 25% 50% 75% 90% max
F-q
uo
tien
t (y
/m)
x: C
x: SC
x: UC
A-FDb-DZ3-y_dir
1E+01
1E+03
1E+05
1E+07
1E+09
1E+11
min 10% 25% 50% 75% 90% max
F-q
uo
tien
t (y
/m)
y: C
y: SC
y: UC
A-FDb-DZ3-z_dir
1E+01
1E+03
1E+05
1E+07
1E+09
1E+11
min 10% 25% 50% 75% 90% max
F-q
uo
tien
t (y
/m) z: C
z: SC
z: UC
Figure 9-9. Histograms showing the average percentiles of the F-quotient in three
orthogonal directions for Case A, FDb and DZ3: C = the Correlated model, SC = the
Semi-correlated model and UC = the Uncorrelated model.
98
9.4.2 Minimum values for C/SC/UC in DZ3 and DZ4
The minimum of each percentile is calculated over the 3 alternative flow directions
(based on axial head gradients) for the travel time in Figure 9-10 and F-quotient in
Figure 9-11 for Case a size (power-law), FDb, depths zones 3 and 4. The three
transmissivity models give similar results, although the correlated model has tendency
toward lower travel time than the other 2 models. F-quotients tend to be less sensitive to
the transmissivity model.
min(A-FDb-DZ3-x/y/z_dir)
1E-02
1E-01
1E+00
1E+01
1E+02
1E+03
1E+04
1E+05
1E+06
1E+07
min 10% 25% 50% 75% 90% max
Tra
vel
tim
e i
n D
FN
(y)
C
SC
UC
min(A-FDb-DZ4-x/y/z_dir)
1E-02
1E-01
1E+00
1E+01
1E+02
1E+03
1E+04
1E+05
1E+06
1E+07
min 10% 25% 50% 75% 90% max
Tra
vel
tim
e i
n D
FN
(y) C
SC
UC
Figure 9-10. Histograms showing the minimum values of the average percentiles of the
travel time in three orthogonal directions for the Correlated (C), the Semi-correlated
(SC) and the Uncorrelated (UC) transmissivity model. Top: Case A, FDb and DZ3.
Bottom: Case A, FDb and DZ4.
99
min(A-FDb-DZ3-x/y/z_dir)
1E+01
1E+03
1E+05
1E+07
1E+09
1E+11
min 10% 25% 50% 75% 90% max
F-q
uo
tien
t (y
/m)
y: C
y: SC
y: UC
min(A-FDb-DZ4-x/y/z_dir)
1E+01
1E+03
1E+05
1E+07
1E+09
1E+11
min 10% 25% 50% 75% 90% max
F-q
uo
tien
t (y
/m)
y: C
y: SC
y: UC
Figure 9-11. Histograms showing the minimum values of the average percentiles of the
F-quotient in three orthogonal directions for the Correlated (C), the Semi-correlated
(SC) and the Uncorrelated (UC) transmissivity model. Top: Case A, FDb and DZ3.
Bottom: Case A, FDb and DZ4.
100
9.4.3 Minimum values for Case A and Case B in DZ3 and DZ4
Here, we compare the minimum of each percentile over the 3 alternative flow directions
(based on axial head gradients) for the travel time in Figure 9-12 and F-quotient in
Figure 9-13 between case A (power-law) and case B (log-normal) fracture sizes for
FDb, semi-correlated transmissivity in depth zones 3 and 4. The statistics are slightly
lower for both travel time and F-quotient for case B since this fracture sizes distribution
is biased toward longer fractures.
min(FDb-DZ3-x/y/z_dir)
1E-02
1E-01
1E+00
1E+01
1E+02
1E+03
1E+04
1E+05
1E+06
1E+07
min 10% 25% 50% 75% 90% max
Tra
vel
tim
e i
n D
FN
(y)
A:SC
B:SC
min(FDb-DZ4-x/y/z_dir)
1E-02
1E-01
1E+00
1E+01
1E+02
1E+03
1E+04
1E+05
1E+06
1E+07
min 10% 25% 50% 75% 90% max
Tra
vel
tim
e i
n D
FN
(y)
A:SC
B:SC
Figure 9-12. Histograms showing the minimum values of the average percentiles of the
travel time in three orthogonal directions for the Semi-correlated transmissivity model.
Top: Case A, FDb and DZ3. Bottom: Case B, FDb and DZ3.
101
min(FDb-DZ3-x/y/z_dir)
1E+01
1E+03
1E+05
1E+07
1E+09
1E+11
min 10% 25% 50% 75% 90% max
F-q
uo
tien
t (y
/m)
A:SC
B:SC
min(FDb-DZ4-x/y/z_dir)
1E+01
1E+03
1E+05
1E+07
1E+09
1E+11
min 10% 25% 50% 75% 90% max
F-q
uo
tien
t (y
/m)
A:SC
B:SC
Figure 9-13. Histograms showing the minimum values of the average percentiles of the
F-quotient in three orthogonal directions for the Semi-correlated transmissivity model.
Top: Case A, FDb and DZ3. Bottom: Case B, FDb and DZ4.
9.5 On the role of HZ for DFN connectivity
The DFN simulations considered (cf. Figure 9-1 for an example) were not superimposed
on the Olkiluoto hydro zone (HZ) model, hence the connectivity analysis carried out
prior to the flow and transport simulations tacitly assumed that the HZ model do not
significantly alter the entity known as the connected open fracture area per unit volume
of rock, P32,cof. In order to demonstrate the relevance of this assumption, the same DFN
realisation was generated twice for Case A, where one of the simulations was
superimposed on top of the HZ model and the other was not prior to the connectivity
analysis. The simulated repository is located around –400 (c. 400 m depth), which is
also the interface between depth zones DZ3 and DZ4. A fraction of the layout area in
each depth zone intersected HZ20, see Figure 5-13 and Table 9-2.
Table 9-2. Distribution of the simulated repository area with regard to HZ20 and DZ3-
4.
DZ % above HZ20 % below HZ20
DZ3 6.8 93.2
DZ4 4.8 95.2
102
The results of the connectivity analysis for the two simulations are shown in Table 9-3
and Figure 9-14. It is noted that the analysis address the spatial average within the
model domain. Local effects along individual boreholes were not studied. We conclude
from the numbers shown that the HZ model does not alter P32,cof. in a significant way.
Table 9-3. DFN fracture intensities without and with HZ, respectively.
Depth zone P32,o
(m2/m
3)
P32,cof without HZ
(m2/m
3)
P32,cof with HZ
(m2/m
3)
DZ3 - below HZ20 3.07E-01 5.67E-02 5.79E-02
DZ3 - above HZ20 2.30E-01 3.03E-02 3.78E-02
DZ4 - below HZ20 1.83E-01 1.63E-02 1.73E-02
DZ4 - above HZ20 1.23E-01 5.42E-03 7.87E-03
0.00E+00
5.00E-02
1.00E-01
1.50E-01
2.00E-01
2.50E-01
3.00E-01
3.50E-01
DZ3 - below DZ3 - above DZ4 - below DZ4 - above
P32 - connected
without HZ
P32 - open
P32 - connected
with HZ
Figure 9-14. DFN fracture intensities without and with HZ, respectively.
9.6 Summary
For the depth interval –150 to –400 masl, a mean of 21-26 % of deposition holes are
intersected by water-conducting fractures. The results for Case B (log-normal
fracture size distribution) are higher because the fractures are generally longer.
o The worst case model (case B) has a 50-percentile F-quotient about 4 104 y/m,
and 10-percentile F-quotient about 2 103 y/m.
o The F-quotient for vertical flow is around 1-4 times higher than horizontal flow
because sub-horizontal fracturing causes more tortuous, longer paths.
o The worst case is the semi-correlated transmissivity model. Uncorrelated is
similar to SC. The Correlated models are higher by a factor ~5 in the F-quotient
for horizontal flow, but similar for vertical.
o Uncorrelated models have longer more tortuous paths, increasing the F-
quotients. Correlated models typically have higher F-quotients, because a
deposition hole is less likely to intersect a high transmissivity feature.
103
o The results for Case A and B are similar. There are lower travel times for Case B
models, presumably because the fractures tend to be longer.
For the depth interval –400 to –1000 masl, a mean of 3-5 % of deposition holes are
intersected by water-conducting fractures. The lower percentiles may suffer from
statistical convergence for this depth zone. Also the transmissivity distribution in
these models may not be as well constrained due to the limited number of PFL-
anomalies.
o The worst case model has a 50-percentile F-quotient of about 2 104 y/m, 10-
percentile about 3 102 y/m.
o The correlated transmissivity model has the lowest F-quotients. Here, there are
only a few possible connections and those that are have a high transmissivity.
This suggests that the importance of the correlation of the transmissivity to the
fracture size depends on fracture intensity.
o The semi-correlated models and uncorrelated models give 50-percentile F-
quotients of around 1 105 y/m. Again, these two models are quite similar
o Case B is similar to Case A, but with shorter travel times.
The HZ model does not alter P32,cof. of the connected DFN in a significant way for
the studied size model (Case).
104
105
10 SUMMARY AND CONCLUSIONS OF PHASE I
10.1 General
The work described in section 2 to section 9 refers to Phase I of the 2008
hydrogeological discrete fracture network model of Olkiluoto. Phase I collates the
structural-hydraulic information gathered in 40 long (KR) and 16 short (KRB) sub-
vertical boreholes drilled from the surface. The information is compared with the
structural-hydraulic information gathered in seven short sub-horizontal pilot boreholes
(PH) drilled from the ONKALO tunnel. In conclusion, Phase I contains:
A Hydro-DFN model for the sub-domains defined in the Geo-DFN has been
calibrated based on fracture core data and PFL data suitable for describing flow and
transport properties in the immediate repository target volume.
Predictions of frequencies, orientations and transmissivities of water conducting
fractures in two pilot holes not drilled at the time of this work.
Preliminary ECPM effective hydraulic properties in support of the FEFTRA
modelling.
Preliminary transport properties. These were deduced by means of freshwater flow
and transport simulations through DFN realisations of the bedrock immediate to the
repository neglecting the influence of any hydro zones.
10.2 Results from Phase I
10.2.1 Hydro zones, fracture domains and Geo-DFN
The bedrock is divided into two fracture domains, FDa and FDb. FDa occurs above the
suite of zones referred to as HZ20A-B, whereas FDb occurs below this suite of zones.
The division is in line with the hanging wall and footwall bedrock concept suggested in
the geological DFN model.
10.2.2 Primary data
The primary data consists of fracture transmissivities determined with the PFL and the
associated fracture positions and orientations determined from drill core mapping and/or
borehole TV images. The modelling is based on the information gathered in the
following boreholes:
40 KR boreholes: (OL-)KR1 to KR40
16 KRB boreholes: (OL-)KR15B-20B, KR22B-23B, KR25B, KR27B, KR29B,
KR31B, KR33B, KR37B, KR39B-40B
Table 4-1 shows the number of PFL data in each borehole with regard to fracture
domains and hydro zones. >T< denotes the total number of PFL data in the two fracture
domains, FDa and FDb, that were not possible to use in the Hydro-DFN modelling for
106
one or several reasons, e.g. missing position data, orientation data or transmissivity data,
see section 4.1.
10.2.3 Key assumptions
Section 5 lists a number of assumptions that are used in the data analyses and in the
modelling. Three key assumptions are:
1. The Terzaghi correction /Terzaghi 1965/ can be used to estimate fracture intensities
unbiased by the direction of a sample borehole. Having calculated unbiased
(corrected) 1D fracture intensities, P10,corr, for individual boreholes, these can be
combined over boreholes of varying trajectories to estimate average values of the
fracture surface area per unit volume of bedrock, P32, i.e.:
P32 P10,corr (10-1)
2. The frequency of open fractures is the upper limit of the intensity of potential
flowing fractures. The open fractures are a subset of all fractures. The number of
open fractures is here defined as:
open = all – tight – 24% of filled (10-2)
3. A flowing fracture requires connectivity between transmissive fractures. An open
fracture is in this regard a potentially flowing fracture. The connected open fractures
(cof) are a subset of the open fractures and the PFL data represent a subset of the
connected open fractures. That is, the PFL data represent connected open fractures
with transmissivities greater than the practicable lower detection limit, see Figure
5-1:
P10,all > P10,open > P10,cof > P10,PFL (10-3)
10.2.4 Fracture orientations
The contoured stereonets shown in Figure 5-4 through Figure 5-7 suggest:
The stereonets for all fractures indicate that the sub-horizontal SH set is dominant in
both fracture domains, but the two mean pole trends differ. In FDa, the mean pole
trend of the SH set is c. 325 , whereas it is c. 355 in FDb. Noteworthy, the two
mean pole trends of the sub-vertical EW set appear to differ in a similar fashion as
well; c. 345 in FDa and c. 005 in FDb. By contrast, the two mean pole trends of
the sub-vertical NS set appear to be fairly alike, c. 85 in both FDa and FDb.
The stereonets for the PFL data resemble by and large the stereonets for all
fractures. Noteworthy, there is a fairly large amount of PFL data centred on trend c.
170 and plunge c. 50 in fracture domain FDb.
10.2.5 Fracture intensity
The plots shown in Figure 5-9 to Figure 5-12 suggest:
107
The corrected intensity of all fractures shows a moderate decrease with depth in
both the hydro zones and in the two fracture domains combined. By contrast, the
corrected intensity of the PFL data shows a significant decrease with depth in these
bedrock segments.
For all of the studied elevations, the corrected intensity of all fractures in the hydro
zones is greater than the corrected intensity of all fractures in the two fracture
domains combined. For an example, the corrected intensity of all fractures in the
hydro zones is c. four times the corrected intensity in the two fracture domains
combined at –400 m elevation.
For all of the studied elevations, the corrected intensity of the PFL data in the hydro
zones is c. ten times the corrected intensity of the PFL data in the two fracture
domains combined.
There is a depth trend in the average hydraulic conductivity down to c. –600m
elevation. Above this elevation, the average hydraulic conductivity in the hydro
zones is c. two orders of magnitudes greater than in the average hydraulic
conductivity in the two fracture domains combined.
Fracture domain FDb appears to be slightly more fractured and hydraulically
conductive than fracture domain FDa for all depths above –550 m elevation. Below
this elevation, there are no data gathered in fracture domain FDa.
In order to create fairly homogeneous sub-volumes with regard to the depth trend in
the Terzaghi corrected intensity of flowing fractures (corrected frequency of PFL
data) seen, it was decided to subdivide each fracture domain into four depth zones
DZ1-4 as follows:
o DZ1: 0 to –50 m elevation DZ2: –50 to –150 m elevation
o DZ3: –150 to –400 m elevation DZ4: –400 to –1 000 m elevation
10.2.6 Fracture size
In Figure 6-8, Figure 6-9 and Figure 6-10, we compare the two fracture size
distributions studied, Case A (power-law) and Case B (log-normal), at the initial
fracture generation stage and the connectivity analysis stage of the modelling process.
In summary, we make the following observations:
For both size models, the connected open fracture size distribution approaches the
generated fracture size distribution for sufficiently large fracture sizes.
The Case A and Case B size models produce different connected fracture size
distributions with their current fracture size distribution parameters. In particular
the Case B size model has a higher proportion of large connected fractures (50 m)
and far fewer connected fractures smaller than (10 m) compared to the Case A size
model.
108
The Case A connected open fracture size distributions could possibly be
approximated by log-normal distributions, but with different mean and variance
parameters than we have used in Case B model.
The Case A connected open fracture size distributions provide some justification for
increasing the mean size of the connected fractures in the Case B model as depth
increases. This trend is perhaps counter-intuitive as the power-law size distributions
of open fractures generated in Case A do not vary very much with depth, e.g. kr is
constant over the bottom three depth zones.
10.2.7 Fracture transmissivity
A quantitative calibration of fracture transmissivity was made for three different size-
transmissivity models, see Table 6-2. The quality of the match to the observed
distributions of PFL flows for the variant in FDb with a semi-correlated transmissivity
model is illustrated for Case A by Figure 6-11 through Figure 6-13 and for Case B by
Figure 6-14 through Figure 6-16 below. The match to the observed flow is poorest for
the deepest depth zone (below –400masl). However, it should be noted that there are
very few features carrying flow at this depth, so the measured distributions of PFL is not
well resolved.
It was possible to find parameters for each of the three relationships between
transmissivity and fracture size that would give an acceptable match to observations.
Because the different types of relationship are parameterised in different ways, it is not
easy to compare the different relationships.
10.2.8 Prediction of water conducting fractures
The modelling approach shown in Figure 7-1 uses the average Terzaghi corrected
statistics of water conducting fractures deduced from the sub-vertical KR and KRB
boreholes to predict the frequency and magnitudes of water conducting fractures in two
sub-horizontal boreholes, PH8 and PH9. The success of this modelling approach is of
course uncertain as it implies that the statistics of the 56 sub-vertical KR and KRB
boreholes, 16 of which are very shallow, represent the same hydrogeological conditions
as encoutered by two specific, sub-horizontal boreholes close to repository depth.
As a means to address the uncertainties in the methodology as well as in comparison
between sub-vertical versus sub-horizontal statistics, we made two prediction tests. In
the first test, we predicted the number of inflows to pilot holes PH2 and PH6,
respectively. In the second one, we predicted the number of inflows to pilot holes
PH1+PH2 combined and to PH3+4+5+6 combined.
The first prediction test checks the approach used to predict the number of inflows to
pilot holes PH8 and PH9, whereas the second prediction tests the suitability of the
modelling approach as such. That is, if the first prediction test fails to do the job,
whereas the second prediction test is more successful, we may conclude that the spatial
variability between boreholes is probably very large and that the average predictions
shown in Figure 7-2 through Figure 7-4 only indicate the range of possible conditions
that may be encountered, but not the pattern that is likely to be seen in an individual
109
pilot hole. An interesting question is then how many (if any) of the 40 realisations
carried out are close to the measured distribution.
A noteworthy difference is that there are several transmissivities of large magnitudes
(>10–4
m2/s) among the 56 sub-vertical boreholes, whereas the highest values recorded
for pilot holes PH1-7 is ca 100 times smaller. The question raised here is if this
difference shows that the SH set is more transmissive, or if the identification of high-
transmissive hydro zones in the 56 sub-vertical boreholes should be revisited.
10.2.9 Repository-scale ECPM block properties
Block-scale hydraulic conductivity tensors are calculated for a 50 m block size in the
bedrock immediate to the repository using the statistics derived in the previous sections.
The objective is to provide preliminary hydraulic properties in support of the ECPM
modelling with FEFTRA. We make the following observations:
The median ratio of (max[Kxx, Kyy]/Kzz) is a factor of 2 or 3 at all depth zones, and
for all the modelling variants.
For the semi-correlated power-law model, the geometric mean effective
conductivity decreases with depth from around 7.4 10-8
m/s for DZ1, 2.2 10-9
m/s
for DZ2, 1.9 10-10
m/s for DZ3 to 2.4 10-11
m/s for DZ4. Likewise, the geometric
mean kinematic porosity decreases with depth from around 1.3 10-4
for DZ1-2,
1.3 10-5
for DZ3 to 3.7 10-6
for DZ4.
The spread around the mean values increases with depth.
The percolation fraction decreases with depth from around 1.0 for DZ1-2 to around
0.9 for DZ3, to around 0.4 for DZ4. These fractions do not vary much with the
modelling variant.
The models with log-normal fracture size distribution show a slightly higher mean
conductivity and lower spread compared to models with a power-law fracture size
distribution, but these differences may not be statistically significant.
10.2.10 Repository-scale freshwater flow and transport PA properties
For the depth interval –150 to –400 masl, a mean of 21-26 % of deposition holes are
intersected by water-conducting fractures. The results for Case B (log-normal fracture
size distribution) are higher than for Case A (power-law) because the fractures are
generally longer.
For the depth interval –400 to –1000 masl, a mean of 3-5 % of deposition holes are
intersected by water-conducting fractures. The lower percentiles may suffer from
statistical convergence for this depth zone. Also the transmissivity distribution in these
models may not be as well constrained due to the limited number of PFL-anomalies.
The results suggest that the importance of the correlation of the transmissivity to the
fracture size depends on fracture intensity.
110
10.3 Discussion
In the work reported here, the same transmissivity assignments were used for each
fracture set and at each depth in order to quantify how well a simplistic model could
reproduce the data. That is, in the first instance we try to explain variations in flow by
variations in fracture intensity and the resultant network connectivity.
The limited success in the prediction of the frequency of transmissivities of water
conducting fractures in individual pilot holes PH2 and PH6 suggest that there may be a
necessity to introduce further complexity such as anisotropy between sets and spatial
heterogeneity. Alternatively, there may be a limited number of PFL data measured in
the sub-vertical boreholes that should be associated with hydro zones instead of fracture
domain FDa.
Moreover, we have constrained the Hydro-DFN modelling presented here to treat the
conditions in the bedrock below the hydro zones HZ20A and HZ20B mainly, i.e.
fracture domain FDb. It is noted that in section 7, we present a limited Hydro-DFN
model for FDa, i.e. Case A (power-law size distribution) and a semi-correlated
transmissivity model. The differences between FDa and FDb are marginal.
The simulation domain used in the connectivity analyses presented in Section 9 does not
contain any hydro zones, which means that the deduced DFN connectivity is governed
by the geometrical and hydraulic properties of the connected open fractures vis-à-vis the
distance to the vertical boundaries of the model domain. The simulation results shown
in Section 9.4 do not suggest, however, that the inclusion of hydro zones significantly
alter the net P32,cof of the connected DFN. The site-scale freshwater and saltwater DFN
flow and transport PA simulations reported in Sections 1 and 13, respectively, includes
hydro zones.
10.4 Outstanding issues – data interpretation
In order to minimise uncertainties in the interpretation of the hydraulic data the
following recommendations are made:
A consistent core classification of open fractures be made that could guide the
identification of potential water-conducting fractures;
Attempts be made to resolve the problems encountered with assigning some
detected PFLs due to missing information relating them to features seen in the
fracture database based on the core and image logs.
In implementing the Hydro-DFN on a site-scale only localised fracture domains
based on HZ20 are defined in the Geo-DFN. This means extrapolating the
fracture domains far beyond the extent of HZ20. A more extensive description
of the geological structural model is required for site modelling.
Other information should be used in confirmatory testing of the developed
Hydro-DFN based on some of the following data: hydraulic interference tests,
111
tunnel hydraulic tests, integration with palaeo-hydrogeology, and tracer/dilution
tests.
The core classification of open fractures has several values. Besides providing
information about the nature of the fractures‟ openness (apertures), which is of interest
in the transport modelling, the Terzaghi corrected linear frequency of open fractures,
P10,open,corr, constitutes an estimate of the upper bound of the potential 3D intensity of
flowing fractures.
The difference flow logging measurements carried out with the Posiva Flow Log may
be regarded as a means to determine the intensity of connected open fractures that have
a transmissivity value greater that the lower measurement limit of the Posiva Flow Log,
P10,PFL,corr. In general terms, the transmissivity threshold of these data is of the order of
10–9
m2/s.
The difference in intensity between P10,open,corr and P10,PFL,corr may be regarded as a
measure of the intensity of fracture with transmissivities below the lower measurement
limit of the Posiva Flow Log. However, not all open fractures are connected. The
difference in fracture intensity between P10,open,corr and P10,PFL,corr can be split into three
subgroups:
isolated open fractures with transmissivities less than the lower measurement limit
of the Posiva Flow Log,
isolated open fractures with transmissivities greater than the lower measurement
limit of the Posiva Flow Log connected open features, and
connected open fractures with transmissivities less than the lower measurement limit
of the Posiva Flow Log.
The Hydro-DFN approach used in this report models the connectivity and specific
inflow rates, Q/s) of open fractures in cored boreholes that have a transmissivity value
greater than the practical lower measurement limit of the Posiva Flow Log. In Section
4.2.1, it was concluded that a fraction of the flowing fractures in the KR/KRB boreholes
and the PH boreholes detected with the Posiva Flow Log were not used in the flow
modelling because their geometrical or hydraulic properties were unknown for one
reason or the other. The effect of this data discrimation was not evaluated in the work
reported here, though. Such an analysis could be made if required but it would invoke
some uncertainties, e.g. for those PFL data that lack positions it is difficult to determine
the correct depth zone belonging, and for those data that lack orientation it is impossible
to determine the Terzaghi corrected intensity. In general terms, however, it can be stated
that the effect of a lower value of P10,PFL,corr is that the sizes of the flowing DFN
fractures become larger than for a higher value of P10,PFL,corr.
Finally, it is important at this point to recollect what is actually measured with the PFL
tests. For each PFL transmissivity value identified, the change in flux (inflow) and head
(drawdown) after several days of pumping relative to conditions prior to pumping are
calculated. A transmissivity value is interpreted for the PFL-anomaly based on an
assumed radius of influence of c. 19 m. The choice of 19m reflects that tests are
performed over several days, and hence should represent an effective transmissivity of
112
the whole fracture intersected, and possibly adjoining parts of the network, but 19 m is
otherwise arbitrary. Consequently, the interpreted values of transmissivity should not be
viewed as necessarily the transmissivity of an individual fracture, or the transmissivity
of the fracture local to the borehole intersect. They are more indicative of the effective
transmissivity over a larger scale. This remark influences the way we use the PFL-f data
in the Hydro-DFN modelling.
113
11 SITE-SCALE EQUIVALENT CONTINUUM POROUS MEDIUM (ECPM) BLOCK PROPERTIES
11.1 Objectives
Equivalent block hydraulic conductivity tensors, Keff, and kinematic porosities, eff,
based on an underlying Hydro-DFN model were calculated for a 50m block size using
the statistics derived in the previous sections. The objective was to provide hydraulic
properties from a single site-scale Hydro-DFN realisation in support of the site-scale
ECPM modelling with FEFTRA.
11.2 Model set-up
The model domain is similar to that used in the FEFTRA site-scale modelling /Löfman
et al. 2009/. It is based on a rectangle in North and East axial directions that
encompasses the FEFTRA model. The bottom of the model is at -2000 masl. The
lineaments are not used. The domain was sub-divided into a total of 803 088 blocks of
side 50m, and for each equivalent hydraulic properties were computed in the same
fashion as previously done on the repository scale, cf. Section 8. The only exception
was that the „guard zone‟ method used in Section 8 was not applied on the site-scale
model.
The results shown here represent one realisation of a DFN model with two fracture
domains, FDa and FDb (in Section 8 we studied one fracture domain at a time), a
power-law size model (Case A) and a semi-correlated transmissivity model (SC). If
there were no connected fractures generated inside a block then that block was assigned
a zero hydraulic conductivity. These cases are excluded from the calculation of
hydraulic conductivity and kinematic porosity statistics. The fraction of blocks that have
at least some connected fractures is presented in the results as the percolation fraction.
11.3 Visualisations
Figure 11-1 shows the surface of the site-scale model domain coloured by the upscaled
conductivity values Kxx (E-W). Figure 11-2 shows three vertical slices through the
model domain coloured by the upscaled conductivity values Kxx. Figure 11-3 through
Figure 11-6 show four horizontal slice through the site-scale model domain again
coloured by the upscaled conductivity values Kxx. The slices were chosen to cut through
depth zones 1-4 to demonstrate the decrease in hydraulic conductivity with depth. The
contrast in the ECPM properties that is visible in some of the slices is due to the slight
difference in the Hydro-DFN properties between fracture domains FDa (SE corner) and
FDb (NW corner), cf. Table 5-4.
11.4 Effective hydraulic conductivity
The upscaling methodology produces a directional hydraulic conductivity tensor,
fracture kinematic porosity and other transport properties (such as the fracture surface
114
area per unit volume). In CONNECTFLOW a flux-based upscaling method is used that
requires several flow calculations through a DFN model in different directions.
To calculate the equivalent hydraulic conductivity for a block, the pressure and flow
distribution in the fractures that have any part of their area within the block is calculated
for a linear head gradient in each of the axial directions. Due to the variety of
connections across the network, several flow-paths are possible, and may result in cross-
flows non-parallel to the head gradient. Cross-flows are a common characteristic of
DFN models and can be approximated in an ECPM by an anisotropic hydraulic
conductivity. In 3D, CONNECTFLOW uses six components to characterise the
symmetric hydraulic conductivity tensor. Using the DFN flow simulations, the fluxes
through each face of the block are calculated for each head gradient direction. The
hydraulic conductivity tensor is then derived by a least-squares fit to these flux
responses for the fixed head gradients.
A detailed description of the upscaling method to calculate the ECPM hydraulic
conductivity tensor is given in /Jackson et al. 2000/. Briefly, the method can be
summarised by the following steps:
Define a sub-block within a DFN model;
Identify the fractures that are either completely inside or cut the block;
Calculate the connections between these fractures and their connection to the
faces of the block;
Remove isolated fractures and isolated fracture clusters, and dead-end fractures
if specified;
Specify a linear head gradient parallel to each coordinate axis on all the faces of
the block;
Calculate the flow through the network and the flux through each face of the
block for each axial head gradient;
Fit a symmetric anisotropic hydraulic conductivity tensor that best fits (least-
squares) the flux response of the network;
Fracture kinematic porosity is calculated as the sum (over all fractures that are
connected on the scale of the block) of fracture area within the block multiplied
by the transport aperture of the fracture.
One important aspect of this approach is that the properties are calculated on a particular
scale, that of the blocks, and that a connectivity analysis of the network is performed
only on the scale of the block. Bulk flows across many blocks will depend on the
correlation and variability of properties between blocks.
By diagnonalising the resulting hydraulic conductivity tensor into the 3 principal
components (or eigenvalues of the matrix), the effective hydraulic conductivity, Keff,
was calculated as the geometric mean of these eigenvalues:
115
Keff = (Kmax Kint Kmin)1/3
(11-1)
11.5 Effective kinematic porosity
The effective kinematic porosity was calculated as the cumulative volume of the
flowing pore space divided by the block volume. The contribution to the flowing pore
space was calculated from the cubic law for the connected fractures:
eh = (T / ( g))1/3
(11-2)
et = 4 eh (11-3)
Figure 11-1. View of the site-model domain showing the Kxx component.
116
Figure 11-2. Three vertical slices showing the variation of Kxx with depth.
Figure 11-3. Horizontal slice at 25m depth. The conductivities shown represent Kxx.
117
Figure 11-4. Horizontal slice at 100m depth. The conductivities shown represent Kxx.
The contrast in the ECPM properties is due to the slight difference in the Hydro-DFN
properties between fracture domains FDa (SE corner) and FDb (NW corner), cf. Table
5-4.
Figure 11-5. Horizontal slice at 275m depth. The conductivities shown represent Kxx.
118
Figure 11-6. Horizontal slice at 500m depth. The conductivities shown represent Kxx.
11.6 Block property statistics
The results from the site-scale upscaling are shown in Figure 11-7 through Figure 11-12
and summarised in Table 11-1 and Table 11-2. The statistics encompass:
the 10, 25, 50, 75, 90 percentiles of Keff based on all cells whether Keff is zero or not;
the mean and standard deviation of log(Keff) for those values that have Keff >10–13
m/s (keff = 10–20
m2);
the percentage of cells that have Keff >10–13
m/s.
The percentages of percolating blocks in Figure 11-7 compare well with the results for
FDb in Table 8-2. Figure 11-12 demonstrates the depth trend in hydraulic conductivity
associated with the depth zones. Comparing Table 11-1 with Table 8-2 the mean
effective hydraulic conductivities are higher for the site-scale model than in the block
modelling for DZ2-4. There are three contributing factors to these differences:
in the site-scale model, statistics are calculated by depth combining fracture domains
FDa and FDb whereas they are just based on FDb in Table 8-2;
in the site-scale model, long fractures can extend protrude from the depth zone
above to raise the conductivity of some blocks within the lower depth zone;
the use of a guard zone in the block-scale modelling in Section 8 (i.e. calculating
flow through a larger domain) may have resulted in lower conductivities due to
scale dependency of the network connectivity.
The porosities in Table 11-2 are consistent with those in Table 8-3.
119
ECPM-50m Keff = (Kmax Kint Kmin)(1/3)
803088
362821
18252
36504 36443
10951295281
638820
212845
18252
1E+04
1E+05
1E+06
Available Conductive
No. of elements
DZ1-4
DZ1
DZ2
DZ3
DZ4
33%87%100%100%45%
Figure 11-7. Fraction of percolation for the connected fractures by depth zone.
ECPM-50m Keff = (Kmax Kint Kmin)(1/3)
1E-11
1E-10
1E-09
1E-08
1E-07
1E-06
Keff-10 Keff-25 Keff-50 Keff-75 Keff-90
Percentile
Hyd
rau
lic c
on
du
cti
vit
y (
m/s
)
DZ1
DZ2
DZ3
DZ4
Figure 11-8. The 10, 25, 50, 75, 90 percentiles of Keff. by depth zone.
120
ECPM-50m (Kmax / Kmin)
1E+00
1E+01
1E+02
1E+03
K-max/K-min-10 K-max/K-min-25 K-max/K-min-50 K-max/K-min-75 K-max/K-min-90
Percentile
Maxim
um
an
iso
tro
py r
ati
o y
(-)
DZ1
DZ2
DZ3
DZ4
Figure 11-9. The 10, 25, 50, 75, 90 percentiles of the ratio of Kmax/ Kmin.by depth zone.
ECPM-50m Keff = (Kmax Kint Kmin)(1/3)
-7.11
0.49
-7.55
0.67
-8.37
1.00
-9.37
1.03
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
m-log(Keff) s-log(Keff)
Entity
DZ1
DZ2
DZ3
DZ4
Figure 11-10. The mean and standard deviation of log(Keff) by depth zone.
121
ECPM-50m
1E-06
1E-05
1E-04
Phi-10 Phi-25 Phi-50 Phi-75 Phi-75
Percentile
Kin
em
ati
c p
oro
sit
y (
–)
DZ1
DZ2
DZ3
DZ4
Figure 11-11. The 10, 25, 50, 75, 90 percentiles of eff by depth zone.
ECPM-50m
-4.39
0.19
-4.62
0.29
-5.06
0.39
-5.37
0.36
-6
-5
-4
-3
-2
-1
0
1
2
m-log(phi) s-log(phi)
Entity
DZ1
DZ2
DZ3
DZ4
Figure 11-12. The mean and standard deviation of log( eff) by depth zone.
122
Table 11-1. Summary of upscaling results for site-scale 50 m Keff by depth zone (Note:
mixed fracture domains).
Model description Parameter
Fracture size distribution
T model Depth zone (masl)
m of log(Keff)
[m/s]
s of log(Keff)
[m/s]
Fraction of percolation
Power-law SC 0 to –50 -7.11 0.49 1.00
Power-law SC –50 to –150 -7.55 0.67 1.00
Power-law SC –150 to –400 -8.37 1.00 0.87
Power-law SC –400 to –2 000 -9.37 1.03 0.33
Table 11-2. Summary of upscaling results fort repository-scale 50 m eff by depth zone
(Note: mixed fracture domains).
Model description Parameter
Fracture size distribution
T model Depth zone (masl)
m of log( eff)
[–]
s of log( eff)
[–]
Fraction of percolation
Power-law SC 0 to –50 -4.39 0.19 1.00
Power-law SC –50 to –150 -4.62 0.29 1.00
Power-law SC –150 to –400 -5.06 0.39 0.87
Power-law SC –400 to –2 000 -5.37 0.36 0.33
123
12 SITE-SCALE FRESHWATER FLOW AND TRANSPORT
12.1 Objectives
Particle tracking simulations were first carried out for a freshwater system (i.e.
neglecting the effects of buoyancy due to variations in salinity). The objective was to
provide information about the PA transport properties of the derived Hydro-DFN model
on a site-scale in support of the Olkiluoto site descriptive model 2008. By PA transport
properties we mean the distributions and moments of F [TL–1
] and t [T], where F is the
quotient between the flow wetted surface area and the flow rate and t is the advective
travel time for non-sorbing tracers. Here, the integral values of these two entities are of
key interest, i.e. their cumulative (or total) values from the release area to the exit
positions.
12.2 Model set-up
The model domain is an extension of the FEFTRA site-scale model, see
section 11.2. The transmissivity of the hydro zones (cf. Appendix D) and the array
of release points were the same as in the FEFTRA site-scale modelling by /Löfman
et al. 2009/.
The boundary conditions were no-flow on the bottom surface and all vertical sides
of the model domain and a specified residual pressure at the trace of fractures on the
top boundary that was based on pressure values calculated in FEFTRA on the top
surface of that model for present-day conditions. The FEFTRA model specifies head
on the top surface equal to the measured watertable where it is available and
elsewhere the watertable is assumed to be half of the topographical elevation above
sealevel. Nearest neighbour interpolation was used to transfer the FEFTRA pressure
in the CPM to the nodes on fracture traces in the DFN model.
The fractures were generated according to the fracture size distribution parameters
and fracture transmissivity parameters produced in the Hydro-DFN flow calibration
stage of modelling. To make the model computationally tractable, the smallest
fractures in the large fracture sets were set to 11.2 m radius throughout the domain,
except around the repository smaller fractures were also generated, with a minimum
size of 0.5 m radius.
The model has no tunnels. At each release point a sphere of radius 2.5 m is searched
for intersecting fractures connected to the flowing fracture network. The radius of
2.5 m was chosen to approximate the height of a canister deposition hole. If no
connected fractures intersect the sphere surrounding the release point the particle is
not released. One or ten particles were released at each release point. If there is more
than one transport node within the 2.5 m radius around the release point, the choice
of destination is weighted by the flux through the possible fractures.
124
In the transport calculations, the transport aperture, et (L) of the fractures was deduced
from the cubic law, i.e.:
3/13/1 04.0)12
(44 Tg
Tee ht (12-1)
where he [L] is the hydraulic aperture and T [L2T
–1] is the fracture transmissivity. The
F quotient [TL–1
] and the advective travel time t [T] of the fractures were calculated as:
(12-2)
(12-3)
where W [L] is the fracture width, L [L] is the fracture length and Q [L3T
–1] is the
fracture water flow rate. The latter comes from the solution of the head field and can be
written as:
JTWvWQ (12-4)
where v [L2T
–1] is the water velocity per unit width and J [–] is the hydraulic head
gradient. From (12-1) and (12-2) it can be concluded that the relationship between the F
quotient and the advective travel time t depends on the definition of the transport
aperture. Rearranging (12-1), (12-2) and (12-3) and solving for the F quotient we get:
(12-5)
Equation (12-5) merely shows how the problem was formulated in the work reported
here. In reality, the transport aperture, et, is quite uncertain implying that knowing the
advective travel time t does not necessarily imply that we also know the F quotient. In
conclusion, it is of particular interest to study how the total value of the F quotient and
the advective travel time t at the exit position of a pathway, Ftot and ttot, relates to the
geometrical and hydraulic properties of the initial fractures at the start positions, i.e. the
fractures that connected to the canisters.
In the calibration of the Hydro-DFN model described in the previous sections we used
different relationships between fracture transmissivity T and fracture size r, see
Table 6-2. Here, we adopted the semi-correlated model, i.e. the correlation between
fracture transmissivity and fracture size is uncertain. In operation, the random deviate
log(T) will create a randomness to Equation (12-5).
To begin with, particle pathlines were calculated for one realisation of the model with
one particle released at each start position (Case 1-1). In a second step, a single
realisation with ten particles per start position was studied (Case 1-10), and in the third
and final step, particle pathlines were calculated for ten realisations of the model with
ten particles released at each start position (Case 10-10).
125
12.3 Example visualisations – Case 1-1
Figure 12-1 and Figure 12-2 visualise a single realisation of the model, where the hydro
zones and the DFN fractures are coloured by their head values. Figure 12-1 shows three
vertical slices in the WE direction. Figure 12-2 shows a horizontal slice at 400 m depth
through the centre of the model area where the repository is located. The repository area
contains a total of 6 816 canisters /Löfman et al. 2009/.
Figure 12-2 shows that the greatest head values at 400m depth appear east of the
repository area. Moreover, there is a “crest of higher heads” running across the
repository area in the WE direction, which suggests a groundwater divide with lateral
head gradients towards north and southwest.
Out of a total 6 816 canisters, 369 (~5 %) are connected in this particular DFN
realisation. These start positions are shown as red dots in Figure 12-3. Figure 12-4
shows that the exit positions are mainly to the north and to the southwest of the release
area, indeed. Apparently, very few of the particles exit where the hydro zones outcrop.
Figure 12-5 and Figure 12-6 visualise the pathways between the start positions and the
exit positions. The two pictures show the importance of the sea as a boundary condition
and that many particles flow in the stochastic DFN rather than in the hydro zones.
However, Figure 12-6 shows the importance of hydro zones HZ21 and HZ099 for the
pathway to the north, and though exit points do not correspond with the outcrop of
HZ21, a large part of their path is in HZ21 until they find a short-cut to the top surface
through large sub-vertical stochastic fractures.
Figure 12-7 visualises the exit locations for the single realisation of the model with 369
start positions and one particle per start position shown in section 12.4. Some exit
locations cluster on linear features associated with large stochastic fractures. Figure
12-8 visualises the exit positions for ten realisations of the model, each with c. 350-380
start positions, depending on realisation, and ten particles per start position.
Figure 12-7 and Figure 12-8 indicate that large stochastic features play a greater role for
the positions of the exit positions than the hydro zones do. That is, there is no structure
in the exit positions that is common to all realisations, which is what one would expect
if the outcropping hydro zones governed the exit positions. Still, the overall spread in
the exit positions is fairly concentrated. This implies that the position of the shoreline
governs which of the “stochastic short-cuts” that comes into play.
126
Figure 12-1. Three vertical slices through the site-scale model domain. The hydro
zones and the DFN fractures are coloured by their head values.
Figure 12-2. Plan view of the centre of the model area where the repository is located
at c. 400 m depth. The hydro zones and the DFN fractures are coloured by their head
values.
127
Figure 12-3. A horizontal slice at c. 400m depth through a single realisation of the
model with one particle per start position. Red = start positions. The hydro zones and
the DFN fractures are coloured by their head values.
Figure 12-4. A horizontal slice at 100m depth through a single realisation of the model
with one particle per start position. Red = start positions. Pink = exit positions. The
DFN fractures are coloured by their head values. The hydro zones (thicker lines) are
coloured by transmissivity. The dashed circles are inserted to guide the eye to find the
particles’ start positions (red circle) and exit positions (black circles). Apparently, very
few of the released particles exit where the hydro zones outcrop.
128
Figure 12-5. A horizontal slice at 100m depth through a single realisation of the model
with one particle per start position. 369 start positions (red), pathways (blue) and exit
positions (pink). The hydro zones (thicker lines) are coloured by transmissivity.
Figure 12-6. Cross sectional of the picture shown in Figure 12-5. The exit positions are
mainly to the north and to the southwest of the release area. The participating hydro
zones are HZ21 and HZ099.
129
Figure 12-7. Plan view of the exit positions for a single realisation of the model with
369 start positions and one particle per start position.
Figure 12-8. Plan view of the exit positions for ten realisations of the model with 350-
380 start positions depending on realisation and ten particles per start position. The
exit positions of the ten realisations are shown in different colours. Some realisations
occur very local.
130
12.3.1 Transport statistics
Since the release area is large and hence samples a range of different groundwater flow
pathways, the distributions of the F-quotient and advective travel time t for one
realisation of the model with one particle per start position (Case 1-1) may not be so
different from studying one realisation with ten particles per start position (Case 1-10)
or studying ten realisations with ten particles per start position (Case 10-10). For the
sake of clarity, however, we begin by showing some results of the F quotient and the
advective travel time t for Case 1-1. Secondly, we show some additional results that can
be deduced from Case 1-10 only, e.g. the variability in the F quotient depending on the
route taken at a given start position intersected by several fractures. Finally, we end by
showing some results for Case 10-10.
12.3.2 Case 1-1 – a single realisation of the model with one particle per start position
The figures in this sub-section display statistics for the realisation of the model shown
in Section 12.3, i.e. out of a total of 6816 canister positions 369 (~ 5 %) are connected
to the DFN. Figure 12-9 and Figure 12-10 show the histograms of the (cumulative) F
quotient and the advective travel time t. From these histograms, we make the
observation that the distributions of F and t look somewhat bimodal.
Figure 12-11 suggests that there is a pronounced correlation in the transport properties
between the total F quotient and the total advective travel time t. Figure 12-12 reveals
that there is also a correlation between the total F quotient and the initial water velocity
at the start position, and Figure 12-13 suggests that there is a more limited correlation
between the total F quotient and the transmissivity values of the initial facture. The
strong correlation between F and t follows from the relationship (12-5), which implies
that the spread in F will be in proportion to the cube root of the spread in transmissivity.
The range of transmissivities is about 6 orders of magnitude, and so the spread in F is
less than 2 orders of magnitude fro a given travel time.
Figure 12-14 shows the contribution to the total F quotient as a function depth. The
diagram is divided into eight 50m thick depth intervals and the distribution of the
contribution at each depth interval is shown in terms of eleven percentiles. The largest
contribution is gained at the repository depth. Above repository depth, the contribution
of each 50 m depth interval falls gradually with step changes at the boundary between
the depth zones, i.e. -400 masl, -150 masl and -50 masl. Hence, retention is primarily in
the fracture network immediate to the repository. The analysis of transport properties in
Section 9 are therefore expected to give a reasonable approximation of near-field
retention, although the site-scale model allows the hydraulic gradient directions and
magnitude to be quantified more realistically.
The four pie charts shown in Figure 12-15 visualise the relative contribution of the
hydro zones and the three DFN fracture sets to the total F quotient for the chosen
segments of the F quotient distribution shown in Figure 12-9. Apparently, the hydro
zones play a minor role and among the DFN fracture sets, apart from in the 0-30
percentiles. The sub-horizontal (SH) set dominates all parts of the F distribution. The
same conclusion is drawn from Figure 12-16 through Figure 12-18, which show three
scatter plots.
131
0
10
20
30
40
50
60
70
80
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7
log (t) [y]
Fre
qu
en
cy
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 1 p/st pos
St pos = 369
log50 = 1.67
Median = 47 y
Figure 12-9. Histogram of log(t) for a single realisation of the site model with one
particle per start position.
0
10
20
30
40
50
60
2 3 4 5 6 7 8 9 10 11 12
log (F) [y/m]
Fre
qu
en
cy
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 1 p/st pos
St pos = 369
log50 = 5.85
Median = 7E5 y/m
Figure 12-10. Histogram of log(F) for a single realisation of the site model with one
particle per start position.
132
1E+02
1E+04
1E+06
1E+08
1E+10
1E+12
1E-01 1E+01 1E+03 1E+05 1E+07
t [y]
F [
y/m
]
Figure 12-11. Scatter plot of total F versus total t for a single realisation of the site
model with one particle per start position.
1E+02
1E+04
1E+06
1E+08
1E+10
1E+12
1E-10 1E-08 1E-06 1E-04 1E-02 1E+00 1E+02
vi [m2/y]
F [
y/m
]
Figure 12-12. Scatter plot of total F versus the initial water velocity vi at the start
position for a single realisation of the site model with one particle per start position.
133
1E+02
1E+04
1E+06
1E+08
1E+10
1E+12
1E-12 1E-10 1E-08 1E-06 1E-04
Ti [m2/s]
F [
y/m
]
Figure 12-13. Scatter plot of total F versus the initial fracture transmissivity Ti at the
start position for a single realisation of the site model with one particle per start
position.
Distribution of F for 369 particles per 50m depth interval
-400
-300
-200
-100
0
1E+00 1E+02 1E+04 1E+06 1E+08 1E+10
F-quotient (y/m)
Ele
va
tio
n (
m)
0.95
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.05
Figure 12-14. Contribution to the total F quotient as a function depth for a single
realisation of the model with one particle per start position. The diagram is divided
into eight 50m thick depth intervals and the distribution of the contribution at each
depth interval is shown in terms of eleven percentiles.
134
Interval 0-5%
Mean F-quotient = 4.8E+03 y/m
HZ
DFN Set 1 - EW
DFN Set 2 - NS
DFN Set 3 - SH
Interval 20-30%
Mean F-quotient = 8.3E+04 y/m
HZ
DFN Set 1 - EW
DFN Set 2 - NS
DFN Set 3 - SH
Interval 50-60%
Mean F-quotient = 1.3E+06 y/m
HZ
DFN Set 1 - EW
DFN Set 2 - NS
DFN Set 3 - SH
Interval 80-90%
Mean F-quotient = 2.1E+08 y/m
HZ
DFN Set 1 - EW
DFN Set 2 - NS
DFN Set 3 - SH
Figure 12-15. Four pie charts that show the relative contribution of the hydro zones
and the three DFN fracture sets to the total F quotient for four segments of the F
quotient distribution shown in Figure 12-9.
1E+02
1E+03
1E+04
1E+05
1E+06
1E+07
1E+08
1E+02 1E+03 1E+04 1E+05 1E+06 1E+07 1E+08
Sum of F in DFN [y/m]
To
tal F
(H
Z +
DF
N)
[y/m
]
F<1E3 y/m
F<1E4 y/m
F<1E5 y/m
F<1E6 y/m
F<1E7 y/m
F<1E8 y/m
Figure 12-16. Scatter plot of the total F vs. the contribution of the DFN realisation.
135
1E+02
1E+03
1E+04
1E+05
1E+06
1E+07
1E+08
1E+02 1E+03 1E+04 1E+05 1E+06 1E+07 1E+08
Sum of F in HZ [y/m]
To
tal F
(H
Z +
DF
N)
[y/m
]
F<1E3 y/m
F<1E4 y/m
F<1E5 y/m
F<1E6 y/m
F<1E7 y/m
F<1E8 y/m
Figure 12-17. Scatter plot of the total F vs. the contribution of the hydro zones.
1E+02
1E+03
1E+04
1E+05
1E+06
1E+07
1E+08
1E+02 1E+03 1E+04 1E+05 1E+06 1E+07 1E+08
Sum of F in SH DFN [y/m]
To
tal F
(H
Z +
DF
N)
[y/m
]
F<1E3 y/m
F<1E4 y/m
F<1E5 y/m
F<1E6 y/m
F<1E7 y/m
F<1E8 y/m
Figure 12-18. Scatter plot of the total F vs. the contribution of the sub-horizontal
fracture set.
Figure 12-11 through Figure 12-13 show a handful of particles with abnormally low F-
quotient, and so it is important to understand under scenarios these can arise. On
inspection it was found that these are associated with a case where two long sub-
136
horizontal stochastic fractures intersect one another and extend down to the repository.
Figure 12-19 shows a visualisation of the pathways of ten start positions with very low
F quotients in Case 1-1 showing the two extensive stochastic sub-horizontal fractures in
different colours. The initial fracture is very close to all of the ten start positions. In fact
this case only arose in this one amongst the 10 realisations, suggesting it is rare, but still
possible in the derived Hydro-DFN model.
Figure 12-19. A visualisation of the pathways of ten start positions with very low F
quotients in Case 1-1.
12.3.3 Case 1-10 – a single realisation of the model with ten particles per start position
The figures in this sub section display statistics for the single realisation of the model
shown in Section 12.3. In contrast to Case 1-1, however, the figures shown here
represent ten particles per start position. In the model, it was possible to release 10
particles per start position at 351 of the 369 start positions studied in Case 1-1. Thus, at
18 start positions, the number of particles releases in the model varied between one and
nine.
Since the number of fractures at the different start positions varies, the probabilities of
the ten random releases at a given start position depend on the relative strength of the
flow rate of each pathway at that start position.
137
Figure 12-20 shows the total F quotient versus the fracture transmissivity at the start
positions, Ti, for a single realisation of the model with ten particles per start position. It
is noted that low values of the total F quotients apparently can occur for a wide range of
values of the initial fracture transmissivity.
By the same token, Figure 12-21 shows the total F quotient versus the fracture size at
the start positions, ri, for a single realisation of the model with ten particles per start
position. It is noted that low values of the total F quotients can occur regardless of the
size of the initial fracture, presumably because a small fracture can connect directly into
a large stochastic fracture or hydro zone. The vertical lines on the right side of this
graph correspond to several particles starting in individual large stochastic fractures.
Figure 12-22 shows two histograms of the total advective travel time t. The histogram
with blue frequency bars represents the 351 particles at the 351 start positions that have
the lowest values of the total F quotient. Likewise, the histogram with purple frequency
bars represents the 351 particles at the same start positions that have the highest values
of the total F quotient. The histogram shown in Figure 12-23 suggests that the
geometric mean of the ratio of the total F quotients for these two types of particles is
less than ten. The pie charts shown in Figure 12-24 reveal that both types of particles
spend the majority of their advective travel time outside the hydro zones and that the
sub-horizontal fracture set dominates the advective travel times in the DFN realisation.
Figure 12-25 shows a scatter plot of the total F quotient versus the total advective travel
time t for the 141 pathways that have F quotients less than 104 y/m. A closer
examination at the simulation results shows that the 141 pathways can be associated
with 26 start positions. The pie chart shown in Figure 12-26 reveals that the 141
particles on the average spend 86 % of their total advective travel time t in the sub-
horizontal DFN fracture set.
1E+00
1E+01
1E+02
1E+03
1E+04
1E+05
1E+06
1E+07
1E+08
1E+09
1E+10
1E+11
1E+12
1E-11 1E-10 1E-09 1E-08 1E-07 1E-06 1E-05 1E-04
Ti [m2s]
F [
y/m
]
Figure 12-20. Total F quotient versus the fracture transmissivity at the start positions,
Ti, for a single realisation of the model with ten particles per start position.
138
1E+00
1E+01
1E+02
1E+03
1E+04
1E+05
1E+06
1E+07
1E+08
1E+09
1E+10
1E+11
1E+12
1E-01 1E+00 1E+01 1E+02 1E+03
ri [m]
F [
y/m
]
Figure 12-21. Total F quotient versus the fracture size at the start positions, ri, for a
single realisation of the model with ten particles per start position.
0
10
20
30
40
50
60
70
80
90
100
-1 0 1 2 3 4 5 6 7
log (t) [y]
Fre
qu
en
cy
t (Fmin)
t (Fmax)
N = 10 p/st pos
St pos = 351
Figure 12-22. Two histograms showing the total advective travel time t for a single
realisation with ten particles per start position. The histogram with blue frequency bars
represents the 351 particles at the 351 start positions that have the lowest values of the
total F quotient. Likewise, the histogram with purple frequency bars represents the 351
particles at the same start positions that have the highest values of the total F quotient.
139
2
113
99
52
33
22
137 5 2 2 1 0
0
20
40
60
80
100
120
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
log (Fmax/Fmin) [–]
Fre
qu
en
cy
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 10 p/st pos
St pos = 351
log50 = 0.82
Median = 6.6
Figure 12-23. Histogram of the ratio of the total F quotients for the two types of
particles shown in Figure 12-22.
Average Time in structure for Fmin
(single realisation, 10 p/start position)
9%
12%
20%59%
HZ
EW
NS
SH
N = 10 p/st pos
St pos = 351
F = 665 – 5E10 y/m
t50 = 17 y
F50 = 1.6E5 y/m
Average Time in structure for Fmax
(single realisation, 10 p/start position)
4%
14%
17%
62%
HZ
EW
NS
SH
N = 10 p/st pos
St pos = 351
F = 1.4E3 – 5E10 y/m
t50 = 139 y
F50 = 2.5E6 y/m
Figure 12-24. Pie charts showing the average travel time in different types of structures
for the two types of particles shown in Figure 12-22.
140
Figure 12-25. Scatter plot of the total F quotient versus the total advective travel time t
for the 141 pathways in Case 1-10 that have F quotients less than 104 y/m. A closer
examination at the simulation results shows that the 141 pathways can be associated
with 26 start positions.
Average Time in structure
(single realisation, 10 p/start position)
4%7%
3%
86%
HZ
EW
NS
SH
N = 141 p (3510 p)
P = 26 (351)
F = 665 – 9765 y/m
t50 = 0.51 y
F50 = 967 y/m
Figure 12-26. The 141 particles shown in Figure 12-25 spend on the average 86 % of
their total advective travel time t in the sub-horizontal DFN fracture set.
1E+02
1E+03
1E+04
1E-01 1E+00 1E+01
t [y]
F [
y/m
]
N = 141 p (3510 p)
P = 26 (351)
F = 665 – 9765 y/m
t50 = 0.51 y
F50 = 967 y/m
141
12.3.4 Case 10-10 – ten realisations of the model with ten particles per start position
Figure 12-27 shows the contribution to the total F quotient as a function depth for Case
10-10. The diagram is divided into eight 50m thick depth intervals and the distribution
of the contribution at each depth interval is shown in terms of box and whisker plots.
The largest contribution is gained at the repository depth. Above repository depth, the
contribution of each 50m depth interval is fairly constant up to c. 100m depth. Hence,
there is little difference between this plot and the plot representing Case 1-1 shown in
Figure 12-14. Figure 12-28 shows the exit locations coloured by total F quotient for
Case 10-10. The randomness in the spatial distribution of the F quotients is obvious, but
again the distribution of exit location is concentrated to north or southwest, and only a
few discharges occur on land associated with a small lake.
Distribution of F for 3712 particles (realisation # 2) per 50m depth interval
-1.0 1.0 3.0 5.0 7.0 9.0 11.0 13.0
> -25m
[-75, -25]
[-125m, -75m]
[-175m, -125m]
[-225m, -175m]
[-275m, -225m]
[-325m, -275m]
[-375m, -325m]
< -375m
De
pth
in
terv
al
log (F-quotient) [y/m]
Figure 12-27. Contribution to the total F quotient as a function depth for Case 10-10
(ten realisations of the model with ten particles per start position). The diagram is
divided into eight 50m thick depth intervals and the distribution of the contribution at
each depth interval is shown in terms of a box and whisker plot. The red and blue fields
represent 1 standard deviation of the ten means of log(F) at each depth interval. The
whiskers represent the minimum and maximum values of log(F) of all values over the
ten realisations at each depth interval.
Figure 12-28. Spatial distribution of the F quotients of Case 10-10 (ten realisations and ten particles per start position).
142
143
13 SITE-SCALE SALTWATER FLOW AND TRANSPORT
13.1 Objectives
In order to scope the affects of salinity, variable-density flow calulcations were
performed by importing a distribution of fluid density from a FEFTRA coupled
groundwater flow and salt transport calculation and then calculating consistent
distribution of residual pressure and flow in the site-scale DFN model. Particle tracking
simulations were then carried out on the basis of the calculated flow-field taking
account of buoyancy. The main objectives was to demonstrate that such calculations can
be carried out for a large model domain using a DFN model of the fractured bedrock at
Olkiluoto, and assess what types of differences might be seen relative to freshwater
simulations.
13.2 Model set-up
The model set-up mimics the freshwater system described in Section 1, except that the
fluid density field was taken from a variable-density flow solution of an ECPM model
studied with FEFTRA /Löfman et al. 2009/ (the base case calibrate model prediction of
present-day conditions was used). This approximation prohibited a more quantitative
comparison with the freshwater system studied in section 1 as the density field was not
based on an ECPM model consistent with the DFN realisation. Hence, the analysis was
limited to a comparison of the particle pathways „by eye‟.
13.3 Results
Figure 13-1 shows the imported density field from the ECPM model using FEFTRA. A
nearest neighbour interpolation method was used to distribute fluid denity within the
fracture system. The salinity increases rapidly at around -500masl. Figure 13-2 shows
the distribution of pointwater head in the DFN model consistent with this density
distribution such as to conserve mass flux, and this is compared with the equivalent
pointwater heads without variable-density. Likewise, the distribution of pointwater
heads at repository depth is compared with the freshwater head in Figure 13-3.
Figure 13-4 and Figure 13-5 show comparison of particle tracking for the saltwater and
freshwater cases. The exit points shown in Figure 13-5 are similar and many of the
clusters along linear features associated with large sub-vertical stochastic fractures are
common. However,
Figure 13-4 indicates that some of the long paths that go toward the southwest follow
deeper and longer paths fro the saltwater case than the freshwater case. This is probably
due to some particles starting below the saline interface in the southern part of the
repository. Such long paths may be a consequence of using a density field not based on
consistent hydraulic properties based on the DFN realisations. It is suggested that
saltwater simulations should be repeated in the future using density fields calculated
with an ECPM model that is based on the same underlying stochastic DFN realisation.
144
Figure 13-1. Vertical cross-sections showing the imported density field from the ECPM
model in FEFTRA.
145
Figure 13-2. Vertical cross-sections through the model domain. Top: Pointwater heads.
Bottom; Freshwater heads (cf. Figure 12-1).
146
Figure 13-3. Plan view of the centre of the model area where the repository is located
at c. 400 m depth. Top: Pointwater head values. Bottom: Freshwater head values (cf.
Figure 12-2).
147
Figure 13-4. Perspective view of particle pathways and exit positions. Top: Saltwater
case. Bottom: Freshwater case.
148
Figure 13-5. Plan view of the start positions (light blue) and the exit positions (red or
purple) for a single realisation of the model with 369 start positions and one particle
per start position. Top: saltwater case (red exit points). Bottom: Freshwater case
(purple exit points, cf. Figure 12-7).
149
14 SUMMARY AND CONCLUSIONS OF PHASE II
14.1 General
The work described in Sections 11-13 relate to the Phase II of the 2008 hydrogeological
discrete fracture network model of Olkiluoto. Phase II focuses on site-scale DFN
modelling and comprises:
Site-scale effective block hydraulic conductivity tensors, Keff, and kinematic
porosities, eff, in support of the ECPM modelling with FEFTRA;
Site-scale PA transport properties. These were deduced by means of freshwater flow
and transport simulations through DFN realisations of the bedrock at Olkiluoto;
A scoping study of variable-density flow and transport simulations through a DFN
realisation of the bedrock at Olkiluoto.
The analyses carried out provide input to the integration of site-scale hydrogeological
properties with modelling of palaeo-hydrogeology using FEFTRA ECPM models of the
Olkiluoto site as well as to subsequent safety performance assessment calculations.
14.2 Results from Phase II
14.2.1 Upscaling
Table 14-1 and Table 14-2 summarise the upscaling results of Phase I and Phase II for a
50 m block. It is noted that different formulae were used for the derivation of the
effective kinematic porosity, cf. Sections 8 and 11. The hydraulic conductivity
montonically decreases significantly with depth in both cases.
There are a number of important differences in the how the hydraulic conductivities
were calculated between Phase I and II:
In Phase I, the hydraulic conductivity was calculated only for fracture domain FDb,
whereas in Phase II both fracture domains, FDa and FDb, were considered and the
statistics calculated only by depth zone.
In Phase I, fracture network models were upscaled for each depth zone in isolation,
i.e. not in a layered system, while in Phase II extensive higher transmissivity
fractures could protrude from one depth zone down to the one below.
Finally, in Phase I the „guard zone‟ technique in ConnectFlow was used where flow
is calculated in a domain, 150 m, but only the flux through central 50 m block is
used to calculate the equivalent hydraulic conductivity tensor. These differences in
approach are the likely cause of the higher mean hydraulic conductivities in depth
zones 2-4 in the site-scale model taken as a whole, which was not invoking the
„guard zone‟ technique.. However, the fractions of blocks that percolate are similar,
as is the standard deviations of log(Keff), although tends to be higher in the site-scale
modelling. These issues could be investigated further to better quantify the origin of
the differences. The upscaled porosities are more consistent as they are based on
simpler geometrical parameters.
150
Table 14-1. Summary of upscaling results for 50m Keff of Phase I and Phase II.
Model description Parameter values of Phase I / Phase II
Fracture size distribution
T model Depth zone (masl)
m of log(Keff)
[m/s]
s of log(Keff)
[m/s]
Fraction of percolation
Power-law SC 0 to –50 -7.13 / -7.11 0.39 / 0.49 1.00 / 1.00
Power-law SC –50 to –150 -8.65 / -7.55 0.63 / 0.67 1.00 / 1.00
Power-law SC –150 to –400 -9.72 / -8.37 0.94 / 1.00 0.89 / 0.87
Power-law SC –400 to –1 000 / -2 000
-10.62 / -9.37 0.70 / 1.03 0.46 / 0.33
Table 14-2. Summary of upscaling results for 50m eff of Phase I and Phase II.
Model description Parameter values of Phase I / Phase II
Fracture size distribution
T model Depth zone (masl)
m of log( eff)
[m/s]
s of log( eff)
[m/s]
Fraction of percolation
Power-law SC 0 to –50 -3.88 / -4.39 0.05 / 0.19 1.00 / 1.00
Power-law SC –50 to –150 -4.50 / -4.62 0.05 / 0.29 1.00 / 1.00
Power-law SC –150 to –400 -4.89 / -5.06 0.08 / 0.39 0.89 / 0.87
Power-law SC –400 to –1 000 / -2 000
-5.43 / -5.37 0.07 / 0.36 0.46 / 0.33
14.3 Flow and transport
The results shown in Section 1 indicate that hydro zone form major pathways for
particles strting in the northern part of the repository area, but their ultimate exit
positions on the top surface is controlled by extensive sub-vertical fractures. There is no
systematic pattern in the exit positions that is common to all realisations, which is what
one would expect if the outcropping hydro zones governed the exit positions. Still, the
overall spread in the exit positions is fairly concentrated. This implies that the position
of the shoreline governs which of the “stochastic short-cuts” that comes into play. The
simulations show that the hydro zones play a very minor role in the total F quotient,
whereas the sub-horizontal fracture set of the DFN model is the key contribution to F
quotient in all transport simulations conducted in the work reported here. The
assumption that large stochastic features have constant properties can cause a limited
number of particle pathways with very rapid advective travel times and low values of
the F quotient.
Since the release area is large and hence samples a range of different groundwater flow
pathways, the distributions of the F quotient and advective travel time t for one
realisation of the model with one particle per start position (Case 1-1) is not very
different from studying one realisation with ten particles per start position (Case 1-10)
or studying ten realisations with ten particles per start position (Case 10-10).
151
14.4 Outstanding issues – site modelling
Coupled variable-density flow and transport simulations are very computational
intensive to carry out using a DFN model. However, the work reported here
demonstrates that such simulations are feasible, indeed, but that it is necessary to
use a density field consistent with each specific Hydro-DFN realisation. One
solution is to perform the coupled groundwater flow and chemistry simulations
(palaeo-hydrogeology) using ECPM models that corresponding to particular
realisations of an underlying DFN model, and then export the fluid density and
pressure boundary conditions back to the DFN model at relevant times to performed
detailed PA transport calculations.
Releases at future times need to be considered as the hydraulic boundary conditions
evolve.
The property assignment of the hydro zone model in the work reported here is based
on assumptions that are coherent with the corresponding modelling in FEFTRA.
However this neglects the role of depth dependency and/or spatial heterogeneity that
are likely to be realistic hydraulic characteristics of these features.
The dependence of upscaled hydraulic properties on spatial scale needs to be studied
further to quantify the uncertainty in groundwater fluxes depending on the choice of
spatial resolution in ECPM models.
The model domain reported here did not include any additional lineaments.
14.5 Future Hydro-DFN studies
It would be useful to review if the methodology reported here could be refined with a
view to integrate with hydrochemistry, which was never part of the study. Issues like
orientation distributions, definition of sets, choice of depth zones, transmissivity
contrasts between sets, combining different borehole orientations, appropriate scales for
ECPM models, etc. could be assessed. It is suggested that a pre-study is carried out and
that the results of the pre-study are documented in a memorandum and reported prior to
the work with 2010 OHDFN.
152
153
REFERENCES
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the layout planning and numerical flow model in 2006. Working Report 2007-01,
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Buoro, A., Dahlbo, K., Wiren, L., Holmén, J., Hermanson, J., & Fox, A. (editor). 2009.
Geological Discrete-Fracture Network Model (version 1) for the Olkiluoto Site,
Finland. Working Report 2009-77. Posiva Oy, Eurajoki.
Dershowitz W, Winberg A, Hermanson J, Byegård J, Tullborg E-L, Andersson P,
Mazurek M, 2003. Äspö Task Force on modelling of groundwater flow and transport of
solutes. Task 6c. A semi synthetic model of block scale conductive structures at the
Äspö HRL. Äspö Hard Rock Laboratory, International Progress Report IPR-03-13,
Svensk Kärnbränslehantering AB.
Follin S, Levén J, Hartley L, Jackson P, Joyce S, Roberts D, Swift B, 2007.
Hydrogeological characterisation and modelling of deformation zones and fracture
domains, Forsmark model stage 2.2. SKB R-07-48, Svensk Kärnbränslehantering AB.
Jackson CP, Hoch AR and Todman SJ, 2000. Self-consistency of a heterogeneous
continuum porous medium representation of a fractured medium, Water Resources
Research Vol 36. No 1, Pages 189-202.
Löfman J, Mészáros F, Keto V, Pitkänen P, Ahokas H, 2009. Modelling of groundwater
flow and solute transport in Olkiluoto – Update 2008. Working Report 2009-78. Posiva
Oy. Olkiluoto. (to be published).
Löfman J, Poteri A, 2009. Groundwater flow and transport simulations in support of
RNT-2008 analysis, Posiva Working Report 2008-52, Posiva Oy.
Mattila J, Aaltonen I, Kemppainen K, Wikström L, Paananen M, Paulamäki S, Front K,
Gehör S, Kärki A, Ahokas T, 2008. Geological model of the Olkiluoto site, Version 1.0,
Working Report 2007-92, Posiva Oy, Eurajoki.
Paulamäki S, Paananen M, Gehör S, Kärki A, Front, K, Aaltonen I, Ahokas T,
Kemppainen K, Mattila J, Wikström L, 2006. Geological model of the Olkiluoto Site,
Version 0, Working Report 2006-37, Posiva Oy, Eurajoki.
Sokolnicki M, Rouhiainen P, 2005. Difference flow logging of boreholes KLX07A and
KLX07B, Subarea Laxemar, Oskarshamn site investigation. SKB P-05-225, Svensk
Kärnbränslehantering AB.
Tammisto E, Palmén J, Ahokas H, 2009. Database for hydraulically conductive
fractures. Olkiluoto, Finland: Posiva Oy. 109 p. Working report 2009-30.
Vaittinen T, Ahokas H, Nummela J, 2009. Hydrogeological structure model of the
Olkiluoto Site – update in 2008. Posiva Working Report 2009-15, Posiva Oy.
154
155
APPENDIX A: PILOT HOLES PH1-7
Location
Figure A-1 and Figure A-2 show the location of the seven pilot holes in the ONKALO
access tunnel and the measured PFL transmissivities in these holes. The pilot holes are
sub-horizontal compared to the surface boreholes, which are sub-vertical. Moreover, all
of the seven pilot holes are located in fracture domain FDa.
Figure A-1. Cross section showing the location of the seven pilot holes in the ONKALO
access tunnel and the measured PFL transmissivities in these holes. Based on
/Tammisto et al. 2009/.
156
Figure A-2. Plan view showing the location of the seven pilot holes in the ONKALO
access tunnel and the measured PFL transmissivities in these holes. Based on
/Tammisto et al. 2009/.
Contoured stereonets showing all fractures and the PFL data
Table A-1 collates the number of fractures for each fracture set with regard to bedrock
segment (HZ, FDa, FDb) and fracture type (all, open and PFL).
Table A-1. Summary of the number of fractures for each set with regard to bedrock
segment (HZ, FDa, FDb) and fracture set (all, open and PFL) based on the hard sector
algorithm in (5-4).
Segment HZ FDa FDb
Type all open PFL all open PFL All open PFL
1 NS 0 0 0 313 212.2 42 0 0 0
2 EW 0 0 0 272 170.68 42 0 0 0
3 HZ 0 0 0 568 350.92 74 0 0 0
Figure A-3 and Figure A-4 show contoured stereonets of all fractures and the PFL data.
157
Figure A-3. Contoured stereonet for all pilot holes: all fractures outside the hydro
zones (HZ) described in /Tammisto et al. 2009/. The symbol denotes the trend and
plunge of the mean poles of the three fracture sets. The contour lines centred on these
points encompass 68 % of data within each set. The corresponding Fisher distribution
parameter values are shown in Table B-2.
Figure A-4. Contoured stereonet for all pilot holes: PFL data outside the hydro zones
(HZ) described in /Tammisto et al. 2009/. The symbol denotes the trend and plunge
of the mean poles of the three fracture sets. The contour lines centred on these points
encompass 68 % of data within each set. The corresponding Fisher distribution
parameter values are shown in Table B-2.
158
Discrete stereonets showing the PFL transmissivities
Figure A-5 shows a stereographic pole plot of the PFL data shown in Figure A-4.
Figure A-5. Pole plot of all PFL data for all pilot holes described in /Tammisto et al.
2009/. The poles are coloured by log10(transmissivity) and use an equal area lower
hemisphere projection. The symbol denotes the trend and plunge of the mean poles of
the three fracture sets. The contour lines centred on these points encompass 68 % of
data within each set. The corresponding Fisher distribution parameter values are
shown in Table A-2.
The symbols shown in Figure A-3 through Figure A-5 indicate the trend and plunge
of the mean poles of the three fracture sets. The contour lines centred on these points
encompass c. 68 % of the data within each fracture set. The evaluated Fisher
distribution parameter values for each fracture set (EW, NS, SH) and fracture type (all,
PFL) are shown in Table A-2.
Table A-2. Summary of the evaluated Fisher distribution parameter values for the
stereonets shown in Figure A-3 through Figure A-5.
Segment FDa, all FDa, PFL
EW, Trend () 342.5 341.9
EW, Plunge () 6.1 3.7
EW, Concentration (-) 9.4 9.3
NS, Trend () 299.1 284.9
NS, Plunge () 8.4 0.2
NS, Concentration (-) 9.7 7.2
SH, Trend () 317.9 327.5
SH, Plunge () 59.8 68.5
SH, Concentration (-) 8.7 7.1
159
The variation of the fracture intensity with depth was analysed by dividing the PH data
into twenty 50-m thick intervals by depth (elevation). Figure A-6 shows the Terzaghi
corrected intensity, P10, corr, by elevation of all fractures and the PFL data, respectively,
P10, PFL, corr. Figure A-7 shows the average hydraulic conductivity for each 50-m
interval.
Fracture intensity of all fractures by depth
0
1
2
3
4
5
6
7
8
50 0-5
0-1
00-1
50-2
00-2
50-3
00-3
50-4
00-4
50-5
00-5
50-6
00-6
50-7
00-7
50-8
00-8
50-9
00-9
50
Elevation (m)
P1
0c
orr
(m
-1)
Fracture intensity of PFL fractures by depth
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
50 0-5
0-1
00-1
50-2
00-2
50-3
00-3
50-4
00-4
50-5
00-5
50-6
00-6
50-7
00-7
50-8
00-8
50-9
00-9
50
Elevation (m)
P1
0co
rr (
m-1
)
Figure A-6. Terzaghi corrected linear intensity, P10,PFL,corr, in the pilot holes by
elevation in terms of 50-m thick intervals. The maximum magnitude of the Terzaghi
correction factor (weight) was set to 7. Top: all fractures. Bottom: PFL data. Note the
difference in scale of the two ordinate axes.
160
Hydraulic conductivity by depth
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
50 0-5
0-1
00-1
50-2
00-2
50-3
00-3
50-4
00-4
50-5
00-5
50-6
00-6
50-7
00-7
50-8
00-8
50-9
00-9
50
Elevation (m)
T/
L (
m/s
)
Figure A-7. Average hydraulic conductivity in the pilot holes by elevation in terms of
50-m thick intervals.
Table A-3 shows intensity data for the seven pilot holes PH1-7 with regard to bedrock
segment (FDa, FDb, HZ) and fracture type (all, open, PFL).
Table A-3. Summary of sample lengths and numbers of fractures for pilot holes PH1-7
with regard to bedrock segment (FDa, FDb, HZ) and fracture type (all, open, PFL).
Segment FDa FDb HZ
BH length 961.70 0.00 0.00
all fractures 1153 0 0
allcorr 1 968.13 0 0
P10, all, corr 2.05 0.00 0.00
open fractures 733.8 0 0
opencorr 1 209.30 0 0
P10, open, corr 1.26 0.00 0.00
PFL data 158 0 0
PFLcorr 273.61 0 0
P10, PFL, corr 0.28 0.00 0.00
161
Table A-4 shows intensity data for the seven pilot holes PH1-7 with regard to bedrock
segment (FDa, FDb), depth zone (DZ1-4) and fracture type (all, open, PFL).
Table A-4. Summary of sample lengths and numbers of fractures for pilot holes PH1-7
with regard to bedrock segment (FDa, FDb), depth zone (DZ1-4) and fracture type (all,
open, PFL).
Pilot hole 1 2 3 4 5 6 7
Segment / Depth zone
FDa / 1 FDa / 1 FDa / 2 FDa / 2 FDa / 2 FDa / 2 FDa / 3
BH length
157.32 118.25 140.80 94.56 202.53 152.99 95.25
all fractures
148 270 152 221 116 190 56
allcorr 239.90 475.08 282.59 351.59 188.14 331.33 99.49
P10, all, corr 1.52 4.02 2.01 3.72 0.93 2.17 1.04
open fractures
86 186 115 105 80 130 31
opencorr 129.74 319.34 215.55 154.03 132.77 212.73 45.14
P10, open, corr 0.82 2.70 1.53 1.63 0.66 1.39 0.47
PFL data 27 58 25 22 5 18 3
PFLcorr 38.36 100.56 44.24 34.92 9.74 38.75 7.05
P10, PFL, corr 0.24 0.85 0.31 0.37 0.05 0.25 0.07
TPFL / BH length
8.58E-08 6.82E-09 7.86E-09 2.67E-08 4.65E-09 2.94E-10 4.65E-12
Max TPFL 3.26E-06 1.77E-07 4.58E-07 8.01E-07 9.13E-07 2.48E-08 2.26E-10
Min TPFL 5.53E-09 3.63E-10 5.00E-11 5.17E-09 6.82E-10 7.78E-11 3.66E-11
162
163
APPENDIX B: REPOSITORY-SCALE ECPM PROPERTIES
Phase I results
Table B-1. Summary of Phase I upscaling model variants.
Model description
Table Figure Fracture size distribution
T model Depth zone
Power-law SC 1 B-11 B-11
Power-law SC 2 B-12 B-12
Power-law SC 3 B-13 B-13
Power-law SC 4 B-14 B-14
Power-law C 3 B-15 B-15
Power-law C 4 B-16 B-16
Power-law UC 3 B-17 B-17
Power-law UC 4 B-18 B-18
Log-normal SC 2 B-19 B-19
Log-normal SC 3 B-20 B-20
Log-normal SC 4 B-21 B-21
Table B-2. Summary of Phase I upscaling results for repository-scale 50m Keff.
Model description Parameter
Fracture size distribution
T model Depth zone (masl)
m of log(Keff)
[m/s]
s of log(Keff)
[m/s]
Fraction of percolation
Power-law SC 0 to –50 -7.13 0.39 1.00
Power-law SC –50 to –150 -8.65 0.63 1.00
Power-law SC –150 to –400 -9.72 0.94 0.89
Power-law SC –400 to –1 000 -10.62 0.70 0.46
Power-law C –150 to –400 -9.73 0.90 0.89
Power-law C –400 to –1 000 -9.87 0.76 0.45
Power-law UC –150 to –400 -9.59 1.02 0.90
Power-law UC –400 to –1 000 -9.84 0.94 0.48
Log-normal SC –50 to –150 -8.78 0.31 1.00
Log-normal SC –150 to –400 -9.30 0.83 0.98
Log-normal SC –400 to –1 000 -9.46 1.19 0.37
164
Table B-3. Summary of Phase I upscaling results for repository-scale 50m eff.
Model description Parameter
Fracture size distribution
T model Depth zone (masl)
m of log( eff)
[m/s] s of log( eff)
[m/s]
Fraction of percolation
Power-law SC 0 to –50 -3.88 0.05 1.00
Power-law SC –50 to –150 -4.50 0.05 1.00
Power-law SC –150 to –400 -4.89 0.08 0.89
Power-law SC –400 to –1 000 -5.43 0.07 0.46
Power-law C –150 to –400 -5.05 0.10 0.89
Power-law C –400 to –1 000 -5.25 0.07 0.45
Power-law UC –150 to –400 -4.46 0.08 0.90
Power-law UC –400 to –1 000 -4.68 0.05 0.48
Log-normal SC –50 to –150 -4.87 0.07 1.00
Log-normal SC –150 to –400 -4.92 0.12 0.98
Log-normal SC –400 to –1 000 -5.22 0.24 0.37
Update of kinematic porosities used in Phase I
The effective kinematic porosity is calculated as the cumulative volume of the flowing
pore space divided by the block volume. In Phase I, the contribution to the flowing pore
space was calculated from the following function (cf. section 8.6):
et = 0.46 T (8-3)
where et is the transport aperture and T is the fracture transmissivity.
In Phase II, the contribution to the flowing pore space was calculated from the cubic law
for the connected fractures (cf. section 11.5):
eh = (T / ( g))1/3
(11-2)
et = 4 eh (11-3)
Posterior to the completion of the flow modelling work, it was decided to update the
kinematic porosities derived in the ECPM effective hydraulic properties for the bedrock
immediate to the repository. There are three changes to the method used in Phase I:
The transport aperture model has been changed to match that used for phase 2. This
has the effect of reducing the porosities
The discard limit for fractures has been changed from 2.26m to 0.28 m.
The calculation is no longer done as part of the upscaling. Instead a single 50m
cube is used, fractures generated, and a connectivity analysis performed. Fractures
which are connected, or have an intersection with the connected network (dead-
ends), are retained and contribute to the porosity.
165
The effect of the second and third points is to increase the porosity. Also, only one
value is obtained so it is not possible to perform statistics on the distribution of
porosities. Previously we found the variation to be quite small (< 0.1 log( )).
The new results are described in Table B-4 below. The percolation fraction is taken
from the old upscaling results. Note that the kinematic porosities reported in Table B-1
through Table B-11 strictly apply to the modelling described in Chapter 8.
Table B-4. Summary of modified Phase I upscaling results for repository-scale 50m eff.
Model description Parameter
Fracture size distribution
T model Depth zone (masl)
rmin (m) log( eff) [m/s] Fraction of percolation
Power-law SC 0 to –50 0.28 -3.63
1.00
Power-law SC –50 to –150 0.28 -4.30
1.00
Power-law SC –150 to –400 0.28 -4.90
0.89
Power-law SC –400 to –1 000 0.28 -5.43
0.46
Power-law C –150 to –400 0.28 -4.87
0.89
Power-law C –400 to –1 000 0.28 -5.32
0.45
Power-law UC –150 to –400 0.28 -4.22
0.90
Power-law UC –400 to –1 000 0.28 -4.85
0.48
Log-normal SC –50 to –150 0.28 -5.18
1.00
Log-normal SC –150 to –400 0.28 -5.24
0.98
Log-normal SC –400 to –1 000 0.28 -5.96
0.37
Table B-11. Upscaling results for: FDb, Depth zone DZ1 (0 to –50m elevation), Case A (Power-law fracture size distribution), Semi-
correlated transmissivity.
Hydraulic conductivity
Block log(Keff) [m/s]
T model Size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
SC, FDb, 0 to –50 masl, Case A 50 2.26 -7.61 -7.37 -7.13 -6.85 -6.65 -7.13 0.39
Anisotropy of Hydraulic conductivity
T model Block size
rmin Mean(log(Kxx))
[m/s] Mean(log(Kyy)) [m/s]
Mean(log(Kzz))
[m/s]
SC, FDb, 0 to –50 masl, Case A 50 2.26 -6.98 -7.01 -7.19
Percolation
T model Block size
rmin Fraction of
percolation Kxx
Fraction of
percolation Kyy
Fraction of
percolation Kzz
SC, FDb, 0 to –50 masl, Case A 50 2.26 1.00 1.00 1.00
Anisotropy of Hydraulic conductivity
T model Block size
rmin Median(log(Kxx))
[m/s]
Median(log(Kyy))
[m/s]
Median(log(Kzz))
[m/s]
Median ratio
Khmax/Khmin
Median ratio
Khmax/Kzz
SC, FDb, 0 to –50 masl, Case A 50 2.26 -7.01 -7.01 -7.16 1.95 1.93
Porosity
Block log( ) [-]
T model size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
SC, FDb, 0 to –50 masl, Case A 50 2.26 -3.94 -3.91 -3.88 -3.85 -3.82 -3.88 0.05
166
167
BELOW, semi-correlated, CaseA, -50 to 0 masl.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
-6 to
-5.5
-5.5
to -5
Block K [m/s]
CD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
BELOW, semi-correlated, CaseA, -50 to 0 masl.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
-13
to -1
2.5
-12.
5 to
-12
-12
to -1
1.5
-11.
5 to
-11
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
Block K [m/s]
PD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
Figure B-11. Upscaling results for: FDb, Depth zone DZ1 (0 to –50m elevation), Case
A (Power-law fracture size distribution), Semi-correlated transmissivity. Top: CDF of
Kxx, Kyy and Kzz. Bottom: PDF of Kxx, Kyy and Kzz.
Table B-12. Upscaling results for: FDb, Depth zone DZ2 (–50 to –150 m elevation), Case A (Power-law fracture size distribution), Semi-
correlated transmissivity.
Hydraulic conductivity
Block log(Keff) [m/s]
T model Size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
SC, FDb, –50 to –150m, Case A 50 2.26 -9.46 -9.07 -8.60 -8.19 -7.87 -8.65 0.63
Anisotropy of Hydraulic conductivity
T model Block size
rmin Mean(log(Kxx))
[m/s]
Mean(log(Kyy))
[m/s]
Mean(log(Kzz))
[m/s]
SC, FDb, –50 to –150m, Case A 50 2.26 -8.45 -8.49 -8.59
Percolation
T model Block size
rmin Fraction of
percolation Kxx
Fraction of
percolation Kyy
Fraction of
percolation Kzz
SC, FDb, –50 to –150m, Case A 50 2.26 1.00 1.00 1.00
Anisotropy of Hydraulic conductivity
T model Block size
rmin Median(log(Kxx))
[m/s]
Median(log(Kyy))
[m/s]
Median(log(Kzz))
[m/s]
Median ratio
Khmax/Khmin
Median ratio
Khmax/Kzz
SC, FDb, –50 to –150m, Case A 50 2.26 -8.40 -8.48 -8.55 2.92 1.87
Porosity
Block log( ) [-]
T model size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
SC, FDb, –50 to –150m, Case A 50 2.26 -4.57 -4.54 -4.50 -4.47 -4.44 -4.50 0.05
168
169
BELOW, semi-correlated, CaseA, -150 to -50 masl.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
-6 to
-5.5
-5.5
to -5
Block K [m/s]
CD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
BELOW, semi-correlated, CaseA, -150 to -50 masl.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
-13
to -1
2.5
-12.
5 to
-12
-12
to -1
1.5
-11.
5 to
-11
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
Block K [m/s]
PD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
Figure B-12. Upscaling results for: FDb, Depth zone DZ2 (–50 to –150 m elevation),
Case A (Power-law fracture size distribution), Semi-correlated transmissivity. Top:
CDF of Kxx, Kyy and Kzz. Bottom: PDF of Kxx, Kyy and Kzz.
Table B-13. Upscaling results for: FDb, Depth zone DZ3 (–150 to –400 m elevation), Case A (Power-law fracture size distribution), Semi-
correlated transmissivity.
Hydraulic conductivity
Block log(Keff) [m/s]
T model Size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
SC, FDb, –150 to –400m, Case A 50 2.26 -10.98 -10.38 -9.66 -9.05 -8.58 -9.72 0.94
Anisotropy of Hydraulic conductivity
T model Block size
rmin Mean(log(Kxx))
[m/s]
Mean(log(Kyy))
[m/s]
Mean(log(Kzz))
[m/s]
SC, FDb, –150 to –400m, Case A 50 2.26 -9.58 -9.70 -9.79
Percolation
T model Block size
rmin Fraction of
percolation Kxx
Fraction of
percolation Kyy
Fraction of
percolation Kzz
SC, FDb, –150 to –400m, Case A 50 2.26 0.89 0.89 0.88
Anisotropy of Hydraulic conductivity
T model Block size
rmin Median(log(Kxx))
[m/s]
Median(log(Kyy))
[m/s]
Median(log(Kzz))
[m/s]
Median ratio
Khmax/Khmin
Median ratio
Khmax/Kzz
SC, FDb, –150 to –400m, Case A 50 2.26 -9.52 -9.61 -9.71 6.09 2.19
Porosity
Block log( ) [-]
T model size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
SC, FDb, –150 to –400m, Case A 50 2.26 -4.99 -4.94 -4.89 -4.84 -4.78 -4.89 0.08
170
171
BELOW, semi-correlated, CaseA, -400 to -150 masl.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
-6 to
-5.5
-5.5
to -5
Block K [m/s]
CD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
BELOW, semi-correlated, CaseA, -400 to -150 masl.
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
-13
to -1
2.5
-12.
5 to
-12
-12
to -1
1.5
-11.
5 to
-11
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
Block K [m/s]
PD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
Figure B-13. Upscaling results for: FDb, Depth zone DZ3 (–150 to –400 m elevation),
Case A (Power-law fracture size distribution), Semi-correlated transmissivity. Top:
CDF of Kxx, Kyy and Kzz. Bottom: PDF of Kxx, Kyy and Kzz.
Table B-14. Upscaling results for: FDb, Depth zone DZ4 (–400 to –1 000 m elevation), Case A (Power-law fracture size distribution),
Semi-correlated transmissivity.
Hydraulic conductivity
Block log(Keff) [m/s]
T model Size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
SC,FDb,–400 to –1 000m,Case A 50 2.26 -11.54 -11.15 -10.57 -10.14 -9.74 -10.62 0.70
Anisotropy of Hydraulic conductivity
T model Block size
rmin Mean(log(Kxx))
[m/s]
Mean(log(Kyy))
[m/s]
Mean(log(Kzz))
[m/s]
SC,FDb,–400 to –1 000m,Case A 50 2.26 -10.61 -10.67 -10.79
Percolation
T model Block size
rmin Fraction of
percolation Kxx
Fraction of
percolation Kyy
Fraction of
percolation Kzz
SC,FDb,–400 to –1 000m,Case A 50 2.26 0.46 0.47 0.46
Anisotropy of Hydraulic conductivity
T model Block size
rmin Median(log(Kxx))
[m/s]
Median(log(Kyy))
[m/s]
Median(log(Kzz))
[m/s]
Median ratio
Khmax/Khmin
Median ratio
Khmax/Kzz
SC,FDb,–400 to –1 000m,Case A 50 2.26 -10.50 -10.60 -10.78 9.07 2.07
Porosity
Block log( ) [-]
T model size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
SC,FDb,–400 to –1 000m,Case A 50 2.26 -5.50 -5.48 -5.44 -5.39 -5.33 -5.43 0.07
172
173
BELOW, semi-correlated, CaseA, -1000 to -400 masl.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
-6 to
-5.5
-5.5
to -5
Block K [m/s]
CD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
BELOW, semi-correlated, CaseA, -1000 to -400 masl.
0.00
0.05
0.10
0.15
0.20
0.25
-13
to -1
2.5
-12.
5 to
-12
-12
to -1
1.5
-11.
5 to
-11
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
Block K [m/s]
PD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
Figure B-14. Upscaling results for: FDb, Depth zone DZ4 (–400 to –1 000 m
elevation), Case A (Power-law fracture size distribution), Semi-correlated
transmissivity. Top: CDF of Kxx, Kyy and Kzz. Bottom: PDF of Kxx, Kyy and Kzz.
Table B-15. Upscaling results for: FDb, Depth zone DZ3 (–150 to –400 m elevation), Case A (Power-law fracture size distribution), Correlated
transmissivity.
Hydraulic conductivity
Block log(Keff) [m/s]
T model Size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
C, FDb, –150 to –400 m, Case A 50 2.26 -10.93 -10.36 -9.73 -9.01 -8.57 -9.73 0.90
Anisotropy of Hydraulic conductivity
T model Block size
rmin Mean(log(Kxx))
[m/s]
Mean(log(Kyy))
[m/s]
Mean(log(Kzz))
[m/s]
C, FDb, –150 to –400 m, Case A 50 2.26 -9.75 -9.74 -9.89
Percolation
T model Block size
rmin Fraction of
percolation Kxx
Fraction of
percolation Kyy
Fraction of
percolation Kzz
C, FDb, –150 to –400 m, Case A 50 2.26 0.89 0.90 0.89
Anisotropy of Hydraulic conductivity
T model Block size
rmin Median(log(Kxx))
[m/s]
Median(log(Kyy))
[m/s]
Median(log(Kzz))
[m/s]
Median ratio
Khmax/Khmin
Median ratio
Khmax/Kzz
C, FDb, –150 to –400 m, Case A 50 2.26 -9.66 -9.66 -9.76 6.22 2.10
Porosity
Block log( ) [-]
T model size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
C, FDb, –150 to –400 m, Case A 50 2.26 -5.17 -5.13 -5.06 -4.98 -4.91 -5.05 0.10
174
175
BELOW, Correlated, CaseA, -400 to -150 masl.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
-6 to
-5.5
-5.5
to -5
Block K [m/s]
CD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
BELOW, Correlated, CaseA, -400 to -150 masl.
0.00
0.05
0.10
0.15
0.20
0.25
-13
to -1
2.5
-12.
5 to
-12
-12
to -1
1.5
-11.
5 to
-11
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
Block K [m/s]
PD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
Figure B-15. Upscaling results for: FDb, Depth zone DZ3 (–150 to –400 m elevation),
Case A (Power-law fracture size distribution), Correlated transmissivity. Top: CDF of
Kxx, Kyy and Kzz. Bottom: PDF of Kxx, Kyy and Kzz.
Table B-16. Upscaling results for: FDb, Depth zone DZ4 (–400 to –1 000 m elevation), Case A (Power-law fracture size distribution),
Correlated transmissivity.
Hydraulic conductivity
Block log(Keff) [m/s]]
T model Size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
C, FDb, –400 to –1000 m, Case A 50 2.26 -10.94 -10.46 -9.74 -9.28 -8.95 -9.87 0.76
Anisotropy of Hydraulic conductivity
T model Block size
rmin Mean(log(Kxx))
[m/s]
Mean(log(Kyy))
[m/s]
Mean(log(Kzz))
[m/s]
C, FDb, –400 to –1000 m, Case A 50 2.26 -9.87 -9.89 -10.08
Percolation
T model Block size
rmin Fraction of
percolation Kxx
Fraction of
percolation Kyy
Fraction of
percolation Kzz
C, FDb, –400 to –1000 m, Case A 50 2.26 0.46 0.45 0.46
Anisotropy of Hydraulic conductivity
T model Block size
rmin Median(log(Kxx))
[m/s]
Median(log(Kyy))
[m/s]
Median(log(Kzz))
[m/s]
Median ratio
Khmax/Khmin
Median ratio
Khmax/Kzz
C, FDb, –400 to –1000 m, Case A 50 2.26 -9.70 -9.74 -9.90 8.33 2.36
Porosity
Block log( ) [-]
T model size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
C, FDb, –400 to –1000 m, Case A 50 2.26 -5.35 -5.31 -5.26 -5.20 -5.15 -5.25 0.07
176
177
BELOW, Correlated, CaseA, -1000 to -400 masl.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
-6 to
-5.5
-5.5
to -5
Block K [m/s]
CD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
BELOW, Correlated, CaseA, -1000 to -400 masl.
0.00
0.05
0.10
0.15
0.20
0.25
-13
to -1
2.5
-12.
5 to
-12
-12
to -1
1.5
-11.
5 to
-11
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
Block K [m/s]
PD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
Figure B-16. Upscaling results for: FDb, Depth zone DZ4 (–400 to –1 000 m
elevation), Case A (Power-law fracture size distribution), Correlated transmissivity.
Top: CDF of Kxx, Kyy and Kzz. Bottom: PDF of Kxx, Kyy and Kzz.
Table B-17. Upscaling results for: FDb, Depth zone DZ3 (–150 to –400 m elevation), Case A (Power-law fracture size distribution),
Uncorrelated transmissivity.
Hydraulic conductivity
Block log(Keff) [m/s]
T model Size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
UC,FDb, –150 to –400 m, Case A 50 2.26 -10.79 -10.25 -9.58 -9.08 -8.39 -9.59 1.02
Anisotropy of Hydraulic conductivity
T model Block size
rmin Mean(log(Kxx))
[m/s]
Mean(log(Kyy))
[m/s]
Mean(log(Kzz))
[m/s]
UC,FDb, –150 to –400 m, Case A 50 2.26 -9.45 -9.43 -9.65
Percolation
T model Block size
rmin Fraction of
percolation Kxx
Fraction of
percolation Kyy
Fraction of
percolation Kzz
UC,FDb, –150 to –400 m, Case A 50 2.26 0.91 0.90 0.90
Anisotropy of Hydraulic conductivity
T model Block size
rmin Median(log(Kxx))
[m/s]
Median(log(Kyy))
[m/s]
Median(log(Kzz))
[m/s]
Median ratio
Khmax/Khmin
Median ratio
Khmax/Kzz
UC,FDb, –150 to –400 m, Case A 50 2.26 -9.35 -9.36 -9.56 5.37 2.44
Porosity
Block log( ) [-]
T model size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
UC,FDb, –150 to –400 m, Case A 50 2.26 -4.53 -4.51 -4.48 -4.45 -4.38 -4.46 0.08
178
179
BELOW, Uncorrelated, CaseA, -400 to -150 masl.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
-6 to
-5.5
-5.5
to -5
Block K [m/s]
CD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
BELOW, Uncorrelated, CaseA, -400 to -150 masl.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
-13
to -1
2.5
-12.
5 to
-12
-12
to -1
1.5
-11.
5 to
-11
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
Block K [m/s]
PD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
Figure B-17. Upscaling results for: FDb, Depth zone DZ3 (–150 to –400 m elevation),
Case A (Power-law fracture size distribution), Uncorrelated transmissivity. Top: CDF
of Kxx, Kyy and Kzz. Bottom: PDF of Kxx, Kyy and Kzz.
Table B-18. Upscaling results for: FDb, Depth zone DZ4 (–400 to –1 000 m elevation), Case A (Power-law fracture size distribution),
Uncorrelated transmissivity.
Hydraulic conductivity
Block log(Keff) [m/s]
T model Size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
UC,FDb, –400 to –1000 m, Case A 50 2.26 -11.10 -10.64 -9.75 -9.17 -8.59 -9.84 0.94
Anisotropy of Hydraulic conductivity
T model Block size
rmin Mean(log(Kxx))
[m/s]
Mean(log(Kyy))
[m/s]
Mean(log(Kzz))
[m/s]
UC,FDb, –400 to –1000 m, Case A 50 2.26 -9.95 -9.84 -10.12
Percolation
T model Block size
rmin Fraction of
percolation Kxx
Fraction of
percolation Kyy
Fraction of
percolation Kzz
UC,FDb, –400 to –1000 m, Case A 50 2.26 0.49 0.48 0.47
Anisotropy of Hydraulic conductivity
T model Block size
rmin Median(log(Kxx))
[m/s]
Median(log(Kyy))
[m/s]
Median(log(Kzz))
[m/s]
Median ratio
Khmax/Khmin
Median ratio
Khmax/Kzz
UC,FDb, –400 to –1000 m, Case A 50 2.26 -9.92 -9.90 -10.21 9.89 2.79
Porosity
Block log( ) [-]
T model size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
UC,FDb, –400 to –1000 m, Case A 50 2.26 -4.73 -4.72 -4.69 -4.65 -4.61 -4.68 0.05
180
181
BELOW, Uncorrelated, CaseA, -1000 to -400 masl.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
-6 to
-5.5
-5.5
to -5
Block K [m/s]
CD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
BELOW, Uncorrelated, CaseA, -1000 to -400 masl.
0.00
0.05
0.10
0.15
0.20
0.25
-13
to -1
2.5
-12.
5 to
-12
-12
to -1
1.5
-11.
5 to
-11
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
Block K [m/s]
PD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
Figure B-18. Upscaling results for: FDb, Depth zone DZ4 (–400 to –1000 m elevation),
Case A (Power-law fracture size distribution), Uncorrelated transmissivity. Top: CDF
of Kxx, Kyy and Kzz. Bottom: PDF of Kxx, Kyy and Kzz.
Table B-19. Upscaling results for: FDb, Depth zone DZ2 (–50 to –150 m elevation), Case B (log-normal size distribution), Semi-correlated
transmissivity.
Hydraulic conductivity
Block log(Keff) [m/s]
T model Size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
SC,FDb,–50 to –150m, Case B 50 2.26 -9.17 -8.99 -8.80 -8.58 -8.40 -8.78 0.31
Anisotropy of Hydraulic conductivity
T model Block size
rmin Mean(log(Kxx))
[m/s]
Mean(log(Kyy))
[m/s]
Mean(log(Kzz))
[m/s]
SC,FDb,–50 to –150m, Case B 50 2.26 -8.62 -8.66 -8.95
Percolation
T model Block size
rmin Fraction of
percolation Kxx
Fraction of
percolation Kyy
Fraction of
percolation Kzz
SC,FDb,–50 to –150m, Case B 50 2.26 1.00 1.00 1.00
Anisotropy of Hydraulic conductivity
T model Block size
rmin Median(log(Kxx))
[m/s]
Median(log(Kyy))
[m/s]
Median(log(Kzz))
[m/s]
Median ratio
Khmax/Khmin
Median ratio
Khmax/Kzz
SC,FDb,–50 to –150m, Case B 50 2.26 -8.63 -8.68 -8.97 1.60 2.45
Porosity
Block log( ) [-]
T model size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
SC,FDb,–50 to –150m, Case B 50 2.26 -4.95 -4.92 -4.88 -4.82 -4.77 -4.87 0.07
182
183
BELOW, semi-correlated, CaseB, -150 to -50 masl.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
-6 to
-5.5
-5.5
to -5
Block K [m/s]
CD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
BELOW, semi-correlated, CaseB, -150 to -50 masl.
0.00
0.10
0.20
0.30
0.40
0.50
0.60
-13
to -1
2.5
-12.
5 to
-12
-12
to -1
1.5
-11.
5 to
-11
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
Block K [m/s]
PD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
Figure B-19. Upscaling results for: FDb, Depth zone DZ2 (–50 to –150 m elevation),
Case B (Log-normal fracture size distribution), Semi-correlated transmissivity. Top:
CDF of Kxx, Kyy and Kzz. Bottom: PDF of Kxx, Kyy and Kzz.
Table B-20. Upscaling results for: FDb, Depth zone DZ3 (–150 to –400 m elevation), Case B (log-normal size distribution), Semi-
correlated transmissivity.
Hydraulic conductivity
Block log(Keff) [m/s]
T model Size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
SC,FDb,–150 to –400m, Case B 50 2.26 -10.38 -9.82 -9.22 -8.77 -8.29 -9.30 0.83
Anisotropy of Hydraulic conductivity
T model Block size
rmin Mean(log(Kxx))
[m/s]
Mean(log(Kyy))
[m/s]
Mean(log(Kzz))
[m/s]
SC,FDb,–150 to –400m, Case B 50 2.26 -9.01 -9.01 -9.39
Percolation
T model Block size
rmin Fraction of
percolation Kxx
Fraction of
percolation Kyy
Fraction of
percolation Kzz
SC,FDb,–150 to –400m, Case B 50 2.26 0.98 0.98 0.98
Anisotropy of Hydraulic conductivity
T model Block size
rmin Median(log(Kxx))
[m/s]
Median(log(Kyy))
[m/s]
Median(log(Kzz))
[m/s]
Median ratio
Khmax/Khmin
Median ratio
Khmax/Kzz
SC,FDb,–150 to –400m, Case B 50 2.26 -8.92 -8.91 -9.34 3.58 3.36
Porosity
Block log( ) [-]
T model size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
SC,FDb,–150 to –400m, Case B 50 2.26 -5.07 -5.00 -4.92 -4.84 -4.77 -4.92 0.12
184
185
BELOW, semi-correlated, CaseB, -400 to -150 masl.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
-6 to
-5.5
-5.5
to -5
Block K [m/s]
CD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
BELOW, semi-correlated, CaseB, -400 to -150 masl.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
-13
to -1
2.5
-12.
5 to
-12
-12
to -1
1.5
-11.
5 to
-11
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
Block K [m/s]
PD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
Figure B-20. Upscaling results for: FDb, Depth zone DZ3 (–50 to –150 m elevation),
Case B (Log-normal fracture size distribution), Semi-correlated transmissivity. Top:
CDF of Kxx, Kyy and Kzz. Bottom: PDF of Kxx, Kyy and Kzz.
Table B-21. Upscaling results for: FDb, Depth zone DZ4 (–400 to –1 000 m elevation), Case B (log-normal size distribution), Semi-
correlated transmissivity.
Hydraulic conductivity
Block log(Keff) [m/s]
T model Size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
SC,FDb,–400 to –1000m, Case B 50 2.26 -11.01 -10.26 -9.58 -8.46 -7.73 -9.46 1.19
Anisotropy of Hydraulic conductivity
T model Block size
rmin Mean(log(Kxx))
[m/s]
Mean(log(Kyy))
[m/s]
Mean(log(Kzz))
[m/s]
SC,FDb,–400 to –1000m, Case B 50 2.26 -9.41 -9.43 -9.66
Percolation
T model Block size
rmin Fraction of
percolation Kxx
Fraction of
percolation Kyy
Fraction of
percolation Kzz
SC,FDb,–400 to –1000m, Case B 50 2.26 0.37 0.37 0.38
Anisotropy of Hydraulic conductivity
T model Block size
rmin Median(log(Kxx))
[m/s]
Median(log(Kyy))
[m/s]
Median(log(Kzz))
[m/s]
Median ratio
Khmax/Khmin
Median ratio
Khmax/Kzz
SC,FDb,–400 to –1000m, Case B 50 2.26 -9.51 -9.54 -9.61 6.28 2.62
Porosity
Block log( ) [-]
T model size rmin 10-percentile 25-percentile 50-percentile 75-percentile 90-percentile Mean 1 s. d.
SC,FDb,–400 to –1000m, Case B 50 2.26 -5.53 -5.42 -5.25 -5.02 -4.88 -5.22 0.24
186
187
BELOW, semi-correlated, CaseB, -1000 to -400 masl.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
-6 to
-5.5
-5.5
to -5
Block K [m/s]
CD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
BELOW, semi-correlated, CaseB, -1000 to -400 masl.
0.00
0.05
0.10
0.15
0.20
0.25
-13
to -1
2.5
-12.
5 to
-12
-12
to -1
1.5
-11.
5 to
-11
-11
to -1
0.5
-10.
5 to
-10
-10
to -9
.5
-9.5
to -9
-9 to
-8.5
-8.5
to -8
-8 to
-7.5
-7.5
to -7
-7 to
-6.5
-6.5
to -6
Block K [m/s]
PD
F
K11 - 50m block
K22 - 50m block
K33 - 50m block
Figure B-21. Upscaling results for: FDb, Depth zone DZ4 (–400 to –1 000 m
elevation), Case B (Log-normal fracture size distribution), Semi-correlated
transmissivity. Top: CDF of Kxx, Kyy and Kzz. Bottom: PDF of Kxx, Kyy and Kzz.
188
189
APPENDIX C: REPOSITORY-SCALE PARTICLE TRACKING RESULTS
Fracture domain FDb, DZ3, Case A (power-law size model), Semi-correlated transmissivity model
Fraction of particles released that are connected to the fracture network
Direction of flow gradient X Y Z
mean 0.22 0.21 0.21
median 0.23 0.22 0.22
standard deviation 0.16 0.16 0.16
min 0.00 0.00 0.00
max 0.68 0.68 0.68
Flow gradient in X direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 6.3E-11 3.1E-02 53.9 7.3E-11 2.7E+01
0.1 percentile 5.3E-07 4.0E-01 92.6 3.3E-09 3.9E+03
0.25 percentile 3.0E-05 2.4E+00 126.9 1.1E-08 2.8E+04
50 percentile 7.7E-04 8.6E+00 175.4 7.0E-08 1.1E+05
75 percentile 5.8E-03 5.3E+01 215.2 3.4E-07 1.1E+06
0.9 percentile 6.4E-02 1.1E+03 287.9 1.2E-06 3.0E+07
max 1.3E+01 1.6E+06 558.1 2.1E-05 2.7E+10
Flow gradient in Y direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 4.7E-10 3.4E-02 49.8 7.3E-11 2.9E+01
0.1 percentile 5.8E-07 6.0E-01 83.1 3.0E-09 6.1E+03
0.25 percentile 3.1E-05 1.8E+00 121.7 1.1E-08 2.1E+04
50 percentile 4.3E-04 7.4E+00 173.2 7.0E-08 1.4E+05
75 percentile 1.1E-02 6.6E+01 217.4 3.3E-07 1.4E+06
0.9 percentile 6.5E-02 8.4E+02 261.4 1.2E-06 2.1E+07
max 8.6E+00 9.3E+05 437.9 2.1E-05 1.2E+10
Flow gradient in Z direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 2.7E-10 6.0E-02 51.7 7.3E-11 5.1E+01
0.1 percentile 3.6E-07 6.1E-01 89.1 3.3E-09 5.4E+03
0.25 percentile 1.9E-05 2.2E+00 120.4 1.1E-08 2.8E+04
50 percentile 4.9E-04 1.0E+01 187.0 7.2E-08 1.6E+05
75 percentile 6.9E-03 8.1E+01 255.1 3.4E-07 1.6E+06
0.9 percentile 4.7E-02 2.4E+03 377.9 1.2E-06 6.1E+07
max 5.1E+00 5.9E+05 741.8 2.1E-05 1.0E+10
190
Flow gradient in X direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1 1.4E+03 4.6E+03 9.5E+04
2
3
4 2.8E+07 5.6E+07 1.9E+08
5 9.4E+03 1.6E+04 4.2E+04
6 2.3E+04 5.3E+04 3.4E+05
7
8 7.3E+03 2.6E+04 5.0E+04
9 2.5E+02 2.8E+02 3.9E+02
10 8.8E+03 2.0E+04 7.0E+04
11 1.1E+05 1.5E+05 2.4E+05
12
13 2.4E+06 2.4E+06 1.2E+07
14 4.5E+02 9.1E+02 1.9E+05
15 6.7E+04 1.0E+05 1.3E+06
16 2.6E+02 3.5E+02 6.4E+04
17 3.5E+05 5.1E+05 9.1E+05
18 1.1E+04 1.5E+04 4.6E+04
19 6.6E+03 2.8E+04 1.6E+05
20 3.6E+04 7.6E+04 4.6E+05
21 3.3E+03 1.5E+04 1.6E+05
22 4.9E+03 1.4E+04 8.9E+04
23 1.5E+02 2.3E+02 3.7E+04
24 2.0E+04 3.3E+04 1.1E+05
25 1.4E+05 2.2E+05 7.4E+05
26 3.3E+04 4.4E+04 2.7E+06
27 1.5E+04 2.3E+04 6.0E+04
28 7.9E+06 1.3E+07 4.9E+07
29
30 2.2E+04 3.4E+04 8.7E+04
31 4.3E+03 4.9E+03 1.4E+05
32 2.7E+01 3.4E+01 4.1E+04
33 1.1E+04 1.6E+04 6.1E+04
34
35 2.9E+03 6.3E+03 5.4E+04
36 1.6E+03 2.0E+03 5.0E+03
37
38 1.8E+02 2.7E+02 2.2E+04
39 3.7E+05 5.0E+05 1.0E+06
40 1.3E+02 1.6E+02 7.3E+04
191
Flow gradient in Y direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1 3.5E+03 1.5E+04 2.8E+05
2
3
4 5.5E+06 1.1E+07 4.0E+07
5 4.8E+03 7.0E+03 1.2E+04
6 8.1E+04 1.4E+05 6.2E+05
7
8 1.1E+04 1.7E+04 2.9E+04
9 7.6E+02 9.5E+02 2.4E+03
10 2.4E+04 3.8E+04 8.4E+04
11 4.3E+05 5.7E+05 1.1E+09
12
13 3.3E+06 3.5E+06 1.3E+07
14 6.2E+02 7.1E+02 1.4E+05
15 6.6E+04 1.1E+05 2.4E+05
16 2.3E+02 3.0E+02 3.0E+05
17 7.7E+04 2.0E+05 7.9E+05
18 1.1E+04 1.7E+04 5.2E+04
19 9.3E+03 4.6E+04 4.8E+05
20 1.6E+04 2.3E+04 9.8E+04
21 3.8E+02 1.5E+03 2.5E+04
22 5.8E+03 8.4E+03 6.0E+04
23 4.2E+04 7.8E+04 1.6E+05
24 1.0E+04 1.4E+04 3.1E+04
25 6.4E+04 1.5E+05 5.2E+05
26 7.8E+03 1.5E+04 9.3E+06
27 2.9E+04 6.0E+04 1.8E+05
28 2.0E+06 3.1E+06 1.0E+07
29
30 5.4E+03 8.4E+03 4.4E+04
31 7.8E+03 1.7E+04 3.3E+05
32 2.9E+01 3.9E+01 6.8E+04
33 1.2E+04 3.3E+04 2.2E+05
34
35 6.2E+02 9.0E+02 5.5E+04
36 3.5E+03 9.8E+03 4.7E+04
37
38 4.8E+02 8.0E+02 9.6E+03
39 4.0E+05 6.0E+05 1.2E+06
40 5.4E+04 6.6E+04 1.3E+05
192
Flow gradient in Z direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1 7.4E+03 8.6E+04 1.1E+06
2
3
4
5 1.3E+04 2.4E+04 4.4E+04
6 1.5E+05 7.2E+05 3.3E+06
7
8 2.4E+04 3.5E+04 6.9E+04
9 3.0E+02 3.5E+02 6.2E+02
10 6.3E+03 9.6E+03 6.3E+04
11 1.4E+05 2.3E+05 6.9E+08
12
13 3.0E+06 3.1E+06 1.3E+07
14 4.8E+02 8.3E+02 3.1E+05
15 2.5E+04 3.2E+04 5.2E+05
16 4.2E+02 4.3E+02 3.0E+05
17 5.9E+04 1.1E+05 3.4E+05
18 6.5E+03 8.5E+03 1.6E+04
19 5.7E+03 2.0E+04 2.6E+05
20 1.0E+05 1.9E+05 5.2E+05
21 3.9E+03 8.2E+03 1.5E+05
22 2.0E+03 4.4E+03 4.7E+04
23 3.1E+02 4.0E+02 2.5E+04
24 9.6E+03 1.4E+04 2.7E+04
25 1.7E+05 4.0E+05 1.4E+06
26 5.9E+03 1.1E+04 6.1E+06
27 3.1E+04 4.2E+04 8.9E+04
28 2.8E+07 4.7E+07 1.5E+08
29
30 1.4E+05 3.4E+05 8.7E+05
31 2.1E+04 2.9E+04 9.5E+05
32 5.1E+01 6.6E+01 1.8E+05
33 1.6E+04 3.0E+04 8.9E+04
34
35 1.9E+04 2.8E+04 8.4E+04
36 2.7E+03 3.5E+03 1.1E+04
37
38 6.9E+02 7.4E+02 1.3E+04
39 2.4E+05 3.5E+05 6.0E+05
40 7.0E+04 9.2E+04 1.7E+05
193
Fracture domain FDb, DZ4, Case A (power-law size model), Semi-correlated transmissivity model
Fraction of particles released that are connected to the fracture network
Direction of flow gradient X Y Z
mean 0.04 0.04 0.03
median 0.00 0.00 0.00
standard deviation 0.09 0.09 0.08
min 0.00 0.00 0.00
max 0.33 0.33 0.33
Flow gradient in X direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 1.9E-09 5.0E-02 59.4 2.0E-10 1.0E+02
0.1 percentile 1.4E-06 1.4E-01 88.1 1.7E-09 2.7E+02
0.25 percentile 2.2E-05 8.4E-01 115.3 6.5E-09 2.9E+04
50 percentile 5.2E-04 1.1E+01 142.5 2.7E-08 3.9E+05
75 percentile 4.7E-03 5.6E+01 168.7 1.4E-07 2.5E+06
0.9 percentile 9.8E-01 1.5E+03 210.6 3.3E-06 3.8E+07
max 1.8E+00 2.7E+05 345.1 4.3E-06 7.3E+09
Flow gradient in Y direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 1.9E-09 5.0E-02 59.4 2.0E-10 1.0E+02
0.1 percentile 1.4E-06 1.4E-01 88.1 1.7E-09 2.7E+02
0.25 percentile 2.2E-05 8.4E-01 115.3 6.5E-09 2.9E+04
50 percentile 5.2E-04 1.1E+01 142.5 2.7E-08 3.9E+05
75 percentile 4.7E-03 5.6E+01 168.7 1.4E-07 2.5E+06
0.9 percentile 9.8E-01 1.5E+03 210.6 3.3E-06 3.8E+07
max 1.8E+00 2.7E+05 345.1 4.3E-06 7.3E+09
Flow gradient in Z direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 1.4E-09 1.2E-01 63.9 2.0E-10 2.6E+02
0.1 percentile 1.3E-06 2.2E-01 92.0 1.6E-09 4.7E+02
0.25 percentile 1.5E-05 8.8E-01 115.9 6.5E-09 7.0E+03
50 percentile 4.9E-04 7.4E+00 159.9 1.8E-08 3.3E+05
75 percentile 2.5E-02 4.8E+01 190.5 2.8E-07 2.8E+06
0.9 percentile 6.8E-01 2.2E+03 238.0 4.3E-06 7.7E+07
max 1.2E+00 2.0E+05 390.8 4.3E-06 5.9E+09
194
Flow gradient in X direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1
2
3
4 3.2E+04 3.7E+04 5.1E+04
5
6 2.3E+06 3.4E+06 1.7E+07
7
8
9
10 1.1E+09 1.2E+09 1.7E+09
11
12
13
14
15
16 1.6E+05 2.1E+05 5.6E+05
17 3.3E+03 3.5E+03 3.4E+04
18
19 3.6E+04 3.8E+04 5.0E+04
20
21
22
23
24 1.2E+06 1.4E+06 2.5E+06
25 6.6E+04 1.1E+05 3.3E+05
26
27
28
29
30 1.5E+05 2.3E+05 5.8E+05
31
32 1.0E+02 1.1E+02 2.1E+02
33 2.3E+05 2.7E+05 6.0E+05
34
35
36
37 1.6E+04 2.3E+04 9.8E+05
38
39
40 2.1E+05 2.5E+05 5.2E+05
195
Flow gradient in Y direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1
2
3
4 3.2E+04 3.7E+04 5.1E+04
5
6 2.3E+06 3.4E+06 1.7E+07
7
8
9
10 1.1E+09 1.2E+09 1.7E+09
11
12
13
14
15
16 1.6E+05 2.1E+05 5.6E+05
17 3.3E+03 3.5E+03 3.4E+04
18
19 3.6E+04 3.8E+04 5.0E+04
20
21
22
23
24 1.2E+06 1.4E+06 2.5E+06
25 6.6E+04 1.1E+05 3.3E+05
26
27
28
29
30 1.5E+05 2.3E+05 5.8E+05
31
32 1.0E+02 1.1E+02 2.1E+02
33 2.3E+05 2.7E+05 6.0E+05
34
35
36
37 1.6E+04 2.3E+04 9.8E+05
38
39
40 2.1E+05 2.5E+05 5.2E+05
196
Flow gradient in Z direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1
2
3
4 5.0E+04 5.0E+04 6.6E+04
5
6 1.3E+06 2.1E+06 5.9E+06
7
8
9
10 8.8E+07 9.5E+07 1.7E+08
11
12
13
14
15
16 1.9E+05 2.6E+05 4.3E+05
17 5.5E+03 6.2E+03 2.6E+04
18
19 6.9E+04 9.2E+04 1.4E+05
20
21
22 7.3E+05 9.5E+05 1.8E+06
23
24
25 1.9E+05 3.6E+05 5.7E+05
26
27
28
29
30 6.5E+06 1.1E+07 3.2E+07
31
32 2.6E+02 3.1E+02 4.8E+02
33 9.1E+04 1.1E+05 1.7E+05
34
35
36
37 4.3E+04 5.4E+04 1.2E+06
38
39
40
197
Fracture domain FDb, DZ3, Case A (power-law size model), Uncorrelated transmissivity model
Fraction of particles released that are connected to the fracture network
Direction of flow gradient X Y Z
mean 0.16 0.15 0.16
median 0.17 0.15 0.17
standard deviation 0.13 0.12 0.13
min 0.00 0.00 0.00
max 0.40 0.40 0.40
Flow gradient in X direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 3.8E-10 1.3E-01 53.5 1.2E-10 7.4E+02
10 percentile 4.8E-07 8.8E-01 115.2 1.0E-08 5.3E+03
25 percentile 2.0E-05 2.6E+00 149.0 4.5E-08 1.7E+04
50 percentile 1.1E-03 1.5E+01 193.5 1.8E-07 8.8E+04
75 percentile 1.5E-02 1.4E+02 250.4 8.0E-07 9.9E+05
90 percentile 5.8E-02 2.9E+03 307.7 2.9E-06 3.7E+07
max 3.2E-01 2.4E+06 596.3 1.9E-04 1.3E+10
Flow gradient in Y direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 7.5E-10 7.7E-02 52.7 1.2E-10 2.3E+02
10 percentile 5.0E-07 7.7E-01 104.8 1.0E-08 3.6E+03
25 percentile 4.3E-05 2.6E+00 151.6 4.8E-08 2.2E+04
50 percentile 1.2E-03 1.7E+01 193.5 2.1E-07 1.2E+05
75 percentile 9.1E-03 1.1E+02 253.5 8.7E-07 7.7E+05
90 percentile 7.3E-02 4.3E+03 330.5 2.9E-06 3.8E+07
max 1.7E+00 2.7E+06 655.2 1.9E-04 8.2E+09
Flow gradient in Z direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 1.2E-10 1.5E-01 53.1 1.2E-10 7.0E+02
10 percentile 1.9E-07 1.3E+00 102.8 1.0E-08 5.7E+03
25 percentile 7.7E-06 4.4E+00 154.5 4.7E-08 2.6E+04
50 percentile 7.5E-04 2.2E+01 213.3 2.0E-07 1.7E+05
75 percentile 9.6E-03 2.9E+02 280.1 8.1E-07 2.3E+06
90 percentile 3.4E-02 1.5E+04 341.3 2.9E-06 1.2E+08
max 6.5E-01 5.8E+06 1068.0 1.9E-04 1.6E+10
198
Flow gradient in X direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1 3.2E+08 3.2E+08 8.7E+08
2 2.8E+03 5.1E+03 8.8E+03
3 7.4E+02 1.0E+03 5.2E+03
4 1.5E+03 4.2E+03 2.2E+05
5 3.3E+03 6.4E+03 3.2E+04
6 1.7E+03 2.6E+03 1.0E+05
7 2.9E+04 9.7E+04 3.6E+05
8 4.8E+03 7.1E+03 2.5E+04
9 1.7E+03 2.7E+03 5.6E+03
10
11
12 6.9E+03 1.0E+04 2.9E+04
13 1.6E+03 3.3E+03 1.5E+05
14 1.2E+04 2.3E+04 1.3E+05
15 7.3E+04 1.3E+05 4.1E+05
16 6.4E+04 8.9E+04 1.1E+09
17 2.3E+04 2.8E+04 6.8E+04
18 4.3E+04 8.9E+04 2.1E+05
19 7.9E+04 1.2E+05 2.4E+06
20 1.0E+03 1.7E+03 6.3E+03
21
22 8.7E+04 1.7E+05 1.6E+06
23 2.8E+04 3.9E+04 6.7E+04
24
25 6.8E+03 2.8E+04 7.1E+04
26
27 1.3E+07 3.7E+07 1.7E+08
28 3.2E+03 6.9E+03 1.2E+04
29 1.6E+03 2.7E+03 1.8E+04
30 8.8E+07 8.8E+07 3.4E+08
31 6.3E+03 1.7E+04 5.7E+04
32 1.3E+05 2.5E+05 8.5E+05
33 1.6E+08 1.7E+08 2.0E+08
34 1.3E+05 1.7E+05 4.9E+05
35 3.2E+04 7.4E+04 2.3E+06
36 1.3E+04 2.0E+04 7.5E+04
37 4.1E+04 7.3E+04 1.0E+06
38
39 6.6E+04 8.5E+04 2.1E+05
40 2.9E+03 8.7E+03 6.6E+04
199
Flow gradient in Y direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1 9.8E+06 1.1E+07 1.2E+07
2 6.3E+02 9.2E+02 1.7E+03
3 2.3E+02 3.1E+02 1.1E+03
4 2.5E+03 1.2E+04 1.9E+05
5 1.1E+04 1.7E+04 4.5E+04
6 3.2E+03 7.5E+03 1.9E+05
7 2.0E+04 6.1E+04 2.9E+05
8 2.1E+04 2.9E+04 8.5E+04
9 1.2E+03 2.6E+03 7.4E+03
10
11
12 5.4E+03 1.2E+04 4.7E+04
13 9.2E+02 1.7E+03 5.8E+05
14 3.1E+04 4.2E+04 2.6E+05
15 2.3E+05 3.0E+05 6.8E+05
16 9.0E+04 1.2E+05 4.8E+06
17 2.9E+04 3.9E+04 9.7E+04
18 1.3E+04 3.1E+04 9.4E+04
19 3.8E+04 6.4E+04 2.1E+05
20 2.2E+04 4.0E+04 4.6E+05
21
22 4.1E+04 5.5E+04 1.8E+05
23 6.0E+04 1.0E+05 2.3E+05
24
25 5.1E+04 8.4E+04 1.7E+05
26
27 1.4E+06 1.7E+06 2.2E+07
28 2.1E+03 4.3E+03 1.6E+04
29 3.8E+03 8.6E+03 3.0E+04
30 9.7E+06 1.1E+07 2.0E+07
31 6.2E+03 9.7E+03 5.9E+04
32 7.5E+04 1.1E+05 4.3E+05
33 2.2E+08 2.2E+08 2.2E+08
34 2.1E+04 3.0E+04 6.4E+04
35 2.8E+07 3.6E+07 6.8E+07
36 6.2E+04 8.7E+04 2.0E+05
37 5.6E+04 1.0E+05 9.6E+05
38
39 3.9E+04 4.7E+04 1.2E+05
40 1.3E+05 1.6E+05 2.6E+05
200
Flow gradient in Z direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1 6.6E+06 6.6E+06 1.8E+07
2 7.7E+02 1.7E+03 6.2E+03
3 1.0E+03 1.5E+03 4.4E+03
4 1.1E+03 2.0E+03 2.1E+06
5 5.1E+03 6.8E+03 4.8E+04
6 3.0E+03 8.1E+03 4.7E+05
7 2.4E+04 4.5E+04 3.3E+05
8 1.5E+04 2.3E+04 4.2E+04
9 2.0E+03 7.2E+03 1.6E+04
10
11
12 5.0E+03 8.8E+03 6.7E+04
13 7.0E+02 1.2E+03 1.4E+06
14 8.7E+04 1.1E+05 6.7E+05
15 3.0E+05 4.1E+05 8.1E+05
16 9.9E+04 1.1E+05 3.6E+05
17 5.6E+04 6.3E+04 1.0E+05
18 8.9E+04 1.2E+05 2.3E+05
19 1.5E+04 2.0E+04 1.2E+05
20 4.7E+04 7.4E+04 1.6E+05
21
22 4.1E+06 6.2E+06 1.3E+07
23 7.6E+04 1.4E+05 2.3E+05
24
25 5.0E+04 8.7E+04 1.8E+05
26
27 1.2E+06 5.1E+06 3.0E+07
28 1.5E+03 2.4E+03 1.3E+04
29 2.9E+03 5.4E+03 1.9E+04
30
31 1.6E+04 2.7E+04 8.0E+04
32 3.8E+04 1.4E+05 8.2E+05
33 1.9E+09 1.9E+09 1.9E+09
34 2.8E+04 3.6E+04 1.2E+05
35 2.9E+04 5.0E+04 1.9E+06
36 6.8E+04 1.0E+05 2.4E+05
37 3.6E+04 5.7E+04 6.4E+05
38
39 9.7E+03 1.7E+04 3.4E+04
40 1.4E+05 7.3E+07 2.9E+08
201
Fracture domain FDb, DZ4, Case A (power-law size model), Uncorrelated transmissivity model
Fraction of particles released that are connected to the fracture network
Direction of flow gradient X Y Z
mean 0.05 0.06 0.06
median 0.00 0.00 0.00
standard deviation 0.08 0.09 0.09
min 0.00 0.00 0.00
max 0.29 0.29 0.28
Flow gradient in X direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 3.5E-09 5.2E-02 53.8 1.3E-09 1.5E+02
10 percentile 4.5E-07 1.0E+00 86.1 7.7E-09 2.1E+04
25 percentile 2.8E-05 2.6E+00 129.8 1.5E-08 3.0E+04
50 percentile 1.4E-03 9.3E+00 203.7 9.8E-08 6.6E+04
75 percentile 5.9E-03 1.0E+02 258.7 7.3E-07 1.2E+06
90 percentile 1.7E-02 5.2E+03 299.3 2.9E-06 4.1E+07
max 2.8E+00 8.1E+05 513.1 8.5E-05 2.4E+10
Flow gradient in Y direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 7.2E-10 9.9E-02 53.7 5.2E-10 2.8E+02
10 percentile 8.0E-07 3.4E-01 76.7 9.7E-09 9.9E+02
25 percentile 1.2E-04 1.5E+00 100.3 3.1E-08 1.7E+04
50 percentile 2.1E-03 7.5E+00 138.0 1.1E-07 6.2E+04
75 percentile 9.6E-03 1.2E+02 180.3 1.9E-06 1.3E+06
90 percentile 1.1E-01 4.7E+03 229.9 2.5E-06 3.9E+07
max 8.4E-01 7.0E+06 503.5 5.7E-05 2.3E+10
Flow gradient in Z direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 8.7E-10 6.0E-02 64.0 4.0E-10 1.7E+02
10 percentile 6.2E-07 8.3E-01 92.3 7.7E-09 4.1E+03
25 percentile 3.7E-05 2.4E+00 116.5 2.5E-08 2.1E+04
50 percentile 5.8E-04 1.9E+01 147.1 1.1E-07 2.1E+05
75 percentile 6.4E-03 3.9E+02 208.8 1.6E-06 3.8E+06
90 percentile 2.9E-02 3.7E+03 263.9 2.4E-06 2.9E+07
max 6.5E-01 4.5E+05 410.7 8.5E-05 8.4E+09
202
Flow gradient in X direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1
2 8.5E+03 9.7E+03 1.1E+04
3
4 2.3E+06 3.2E+06 4.9E+06
5
6
7 4.1E+07 4.1E+07 1.2E+08
8
9 2.4E+04 3.9E+04 6.7E+04
10
11
12 2.3E+04 3.4E+04 6.7E+04
13
14
15
16 6.1E+05 7.3E+05 1.4E+06
17 2.5E+04 2.9E+04 3.2E+05
18 2.2E+04 2.6E+04 3.7E+04
19
20 1.5E+02 2.1E+02 1.1E+03
21
22
23
24
25 1.6E+05 2.1E+05 3.6E+05
26
27 1.9E+04 2.3E+04 2.9E+04
28
29 1.8E+04 2.1E+04 3.1E+04
30
31
32
33 6.4E+04 8.0E+04 1.4E+05
34 5.3E+06 5.8E+06 8.6E+06
35 2.0E+04 2.8E+04 3.0E+05
36
37
38 1.1E+04 2.9E+04 4.7E+06
39
40 2.7E+09 3.2E+09 7.1E+09
203
Flow gradient in Y direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1
2 6.3E+03 6.4E+03 8.8E+03
3 3.5E+02 5.0E+02 9.2E+02
4 4.1E+04 6.7E+04 2.7E+05
5
6
7 5.2E+07 5.2E+07 1.3E+08
8
9 2.9E+04 3.4E+04 4.4E+04
10
11
12 1.2E+04 1.5E+04 4.2E+04
13
14
15
16 8.6E+04 1.0E+05 1.7E+05
17 7.4E+03 8.7E+03 3.5E+04
18 1.4E+03 2.6E+04 5.9E+04
19
20 2.8E+02 3.0E+02 3.6E+02
21
22
23
24
25
26
27 6.6E+03 9.7E+03 2.2E+04
28 8.3E+05 1.2E+06 2.9E+06
29 2.2E+04 3.3E+04 6.2E+04
30
31
32
33 1.1E+04 1.3E+04 1.7E+04
34 5.1E+06 6.2E+06 8.5E+06
35 4.3E+03 7.1E+03 3.0E+04
36
37
38 1.6E+04 9.1E+04 8.1E+06
39
40
204
Flow gradient in Z direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1
2 4.6E+03 5.2E+03 7.2E+03
3 1.7E+03 2.7E+03 5.0E+03
4 3.1E+05 4.0E+05 5.9E+05
5
6
7
8
9 2.1E+04 3.4E+04 9.4E+04
10
11
12 1.8E+04 2.2E+04 7.3E+04
13
14
15
16 1.6E+06 2.2E+06 3.6E+06
17 1.0E+04 1.3E+04 6.4E+04
18 2.0E+03 9.0E+03 7.2E+04
19
20 1.7E+02 2.4E+02 7.2E+02
21
22
23
24
25 1.6E+05 2.1E+05 3.4E+05
26
27 1.4E+04 1.5E+04 2.3E+04
28 2.4E+06 3.8E+06 8.3E+06
29 1.8E+05 3.3E+05 5.2E+05
30
31
32
33 1.8E+04 2.0E+04 2.9E+04
34 9.8E+05 9.8E+05 1.2E+06
35 2.0E+03 4.2E+03 7.8E+05
36
37
38 6.0E+04 1.8E+05 2.1E+07
39
40 3.2E+09 3.2E+09 8.3E+09
205
Fracture domain FDb, DZ3, Case A (power-law size model), Correlated transmissivity model
Fraction of particles released that are connected to the fracture network
Direction of flow gradient X Y Z
mean 0.21 0.21 0.21
median 0.18 0.17 0.18
standard deviation 0.16 0.16 0.15
min 0.00 0.00 0.00
max 0.60 0.60 0.60
Flow gradient in X direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 6.6E-10 1.9E-01 51.3 4.2E-10 1.8E+03
10 percentile 4.1E-07 7.8E-01 99.7 4.6E-09 1.0E+04
25 percentile 1.6E-05 2.4E+00 142.0 1.2E-08 3.6E+04
50 percentile 3.8E-04 9.0E+00 190.1 3.3E-08 2.0E+05
75 percentile 4.4E-03 6.1E+01 268.7 1.1E-07 1.5E+06
90 percentile 2.0E-02 6.8E+02 331.2 2.0E-07 2.7E+07
max 2.7E-01 3.0E+05 563.7 5.9E-07 9.8E+09
Flow gradient in Y direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 2.0E-10 1.1E-01 49.8 3.8E-10 1.2E+03
10 percentile 5.5E-07 5.7E-01 101.6 4.6E-09 7.6E+03
25 percentile 2.9E-05 1.7E+00 139.8 1.2E-08 2.8E+04
50 percentile 5.5E-04 6.7E+00 178.3 3.2E-08 1.4E+05
75 percentile 5.3E-03 3.7E+01 237.2 1.1E-07 8.8E+05
90 percentile 2.3E-02 6.3E+02 321.8 2.0E-07 2.2E+07
max 4.2E-01 5.2E+05 588.5 5.9E-07 1.6E+10
Flow gradient in Z direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 2.9E-10 2.8E-01 55.9 3.9E-10 1.9E+03
10 percentile 3.9E-07 1.3E+00 117.2 4.6E-09 1.3E+04
25 percentile 1.3E-05 3.6E+00 171.1 1.3E-08 5.6E+04
50 percentile 3.6E-04 1.2E+01 237.1 3.3E-08 2.3E+05
75 percentile 3.3E-03 7.3E+01 314.2 1.1E-07 2.1E+06
90 percentile 1.7E-02 9.1E+02 373.9 2.0E-07 3.3E+07
max 1.9E-01 4.5E+05 624.0 5.9E-07 2.0E+10
206
Flow gradient in X direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1 1.7E+06 4.1E+06 6.4E+07
2 2.7E+03 3.6E+03 2.6E+04
3 2.8E+05 7.1E+05 1.6E+06
4 8.3E+04 1.2E+05 1.6E+06
5 2.0E+04 4.6E+04 3.6E+05
6 5.0E+03 6.8E+03 1.6E+04
7 2.6E+04 4.1E+04 1.1E+05
8 6.0E+03 1.2E+04 2.5E+04
9
10 6.4E+03 7.7E+03 1.2E+04
11 5.0E+04 7.1E+04 9.3E+06
12 1.6E+04 2.1E+04 1.1E+05
13 7.6E+03 1.4E+04 1.5E+05
14 5.5E+04 1.0E+05 6.5E+05
15 1.9E+03 4.4E+03 3.6E+04
16 1.5E+04 4.4E+04 2.5E+05
17
18 2.4E+06 2.4E+06 1.1E+07
19 6.2E+03 1.4E+04 6.8E+05
20 5.7E+04 7.0E+04 1.4E+05
21 6.7E+03 1.9E+04 7.2E+04
22 9.5E+04 1.1E+05 2.5E+05
23 3.8E+03 1.4E+04 5.8E+04
24 5.2E+03 1.7E+04 1.1E+06
25 2.7E+04 4.2E+04 2.6E+05
26 3.0E+04 3.6E+04 1.9E+05
27 5.1E+04 8.3E+04 1.2E+06
28 2.9E+04 3.5E+04 3.0E+05
29 1.4E+04 4.3E+04 2.0E+05
30 1.8E+03 2.1E+03 3.5E+03
31 6.0E+03 7.3E+03 9.4E+06
32 1.5E+04 2.4E+04 3.5E+05
33 8.3E+04 1.1E+05 1.9E+05
34 2.8E+04 2.2E+05 1.3E+06
35
36 2.0E+04 3.3E+04 2.0E+05
37 1.4E+05 2.5E+05 2.6E+06
38 1.0E+08 1.2E+08 4.8E+08
39 3.6E+04 1.1E+05 3.6E+05
40 2.1E+03 3.5E+03 1.1E+04
207
Flow gradient in Y direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1 2.1E+06 5.0E+06 7.3E+07
2 1.2E+03 1.7E+03 1.5E+04
3 1.7E+05 5.3E+05 1.3E+06
4 1.8E+04 3.9E+04 5.1E+05
5 4.2E+03 6.7E+03 1.2E+05
6 2.3E+03 2.9E+03 2.5E+04
7 4.3E+04 7.1E+04 1.9E+05
8 4.8E+04 6.3E+04 1.4E+05
9
10 2.1E+04 2.7E+04 4.0E+04
11 7.6E+04 1.1E+05 3.3E+07
12 1.1E+04 1.1E+04 1.2E+05
13 4.9E+03 9.3E+03 5.2E+05
14 8.1E+03 2.1E+04 5.2E+04
15 1.0E+04 1.4E+04 1.1E+05
16 9.8E+03 2.0E+04 1.2E+05
17
18 3.0E+07 1.1E+08 2.0E+08
19 4.7E+03 1.3E+04 3.7E+05
20 3.3E+03 3.9E+03 7.1E+03
21 8.2E+03 1.3E+04 6.0E+04
22 2.9E+05 4.0E+05 7.2E+05
23 3.3E+03 2.5E+04 2.3E+05
24 9.5E+03 1.7E+04 1.1E+06
25 3.3E+03 9.9E+03 3.6E+05
26 6.8E+04 1.2E+05 1.2E+06
27 6.1E+03 9.8E+03 3.9E+04
28 1.8E+04 2.2E+04 1.5E+05
29 2.9E+03 5.8E+03 5.0E+04
30 1.7E+03 2.2E+03 3.2E+03
31 3.3E+03 4.2E+03 3.8E+05
32 7.7E+03 1.2E+04 2.1E+05
33 2.4E+04 5.9E+04 2.3E+05
34 2.0E+04 6.2E+04 2.3E+05
35
36 2.2E+04 3.5E+04 2.5E+05
37 4.2E+05 1.1E+06 7.6E+06
38 2.7E+05 3.3E+05 5.5E+05
39 5.4E+04 9.2E+04 2.0E+05
40 4.5E+03 1.3E+04 4.0E+04
208
Flow gradient in Z direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1 1.9E+07 5.6E+07 2.3E+08
2 1.9E+03 3.5E+03 4.9E+04
3 2.9E+05 1.6E+06 3.9E+06
4 5.6E+04 6.4E+04 1.4E+06
5 2.3E+04 6.8E+04 2.4E+05
6 3.6E+04 4.8E+04 1.6E+05
7 2.0E+04 4.6E+04 1.3E+05
8 9.2E+03 2.3E+04 1.5E+05
9
10 1.7E+04 2.1E+04 4.1E+04
11 2.8E+05 4.6E+05 1.8E+07
12 6.9E+04 8.1E+04 4.8E+05
13 1.8E+04 3.6E+04 1.1E+06
14 7.9E+03 1.6E+04 1.2E+05
15 3.5E+03 7.1E+03 7.6E+04
16 2.2E+04 3.7E+04 1.5E+05
17
18 2.9E+06 7.6E+06 1.5E+07
19 3.2E+03 1.7E+04 1.5E+05
20 5.4E+03 6.6E+03 1.7E+04
21 3.2E+03 4.6E+03 1.2E+05
22 1.6E+06 1.9E+06 3.8E+06
23 1.8E+04 4.9E+04 1.4E+05
24 6.5E+03 8.2E+03 1.7E+08
25 1.1E+04 8.7E+04 8.1E+05
26 4.4E+04 6.0E+04 3.7E+05
27 1.3E+04 1.7E+04 2.6E+05
28 1.8E+04 2.4E+04 9.3E+04
29 2.9E+04 7.3E+04 4.2E+05
30 4.6E+03 6.9E+03 1.1E+04
31 4.1E+03 1.2E+04 2.8E+06
32 4.3E+04 1.8E+05 5.0E+05
33 5.6E+04 7.8E+04 1.6E+05
34 1.8E+04 4.9E+04 1.6E+05
35
36 6.2E+04 1.1E+05 3.8E+05
37 4.6E+05 1.2E+06 1.1E+07
38 2.2E+06 2.5E+06 1.3E+07
39 1.0E+05 2.2E+05 4.5E+05
40 9.4E+03 1.5E+04 4.7E+04
209
Fracture domain FDb, DZ4, Case A (power-law size model), Correlated transmissivity model
Fraction of particles released that are connected to the fracture network
Direction of flow gradient X Y Z
mean 0.04 0.03 0.04
median 0.00 0.00 0.00
standard deviation 0.09 0.08 0.09
min 0.00 0.00 0.00
max 0.42 0.42 0.42
Flow gradient in X direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 8.4E-10 1.3E-01 50.8 3.8E-10 4.6E+02
10 percentile 1.2E-06 2.8E-01 72.2 9.6E-09 1.8E+03
25 percentile 6.6E-05 4.5E-01 89.7 3.0E-08 4.4E+03
50 percentile 5.5E-03 2.5E+00 117.7 1.9E-07 2.2E+04
75 percentile 4.6E-02 8.7E+01 154.4 5.5E-07 1.4E+06
90 percentile 1.0E-01 3.4E+02 197.2 5.5E-07 8.3E+06
max 6.6E-01 2.0E+04 282.2 1.2E-06 1.0E+09
Flow gradient in Y direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 1.3E-09 1.1E-01 49.4 4.3E-10 4.6E+02
10 percentile 1.6E-06 1.9E-01 99.0 9.7E-09 8.6E+02
25 percentile 1.2E-04 3.3E-01 127.4 3.6E-08 2.1E+03
50 percentile 3.1E-02 7.8E-01 162.9 2.2E-07 6.3E+03
75 percentile 1.3E-01 9.3E+00 186.5 5.5E-07 4.0E+05
90 percentile 5.4E-01 1.3E+02 204.0 1.2E-06 4.0E+06
max 9.6E-01 4.2E+06 291.4 1.2E-06 4.6E+10
Flow gradient in Z direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 2.7E-09 1.8E-01 64.9 4.3E-10 6.5E+02
10 percentile 1.3E-06 2.2E-01 118.3 9.7E-09 1.4E+03
25 percentile 4.2E-05 1.2E+00 157.7 3.6E-08 1.2E+04
50 percentile 5.2E-03 2.9E+00 192.0 1.9E-07 2.4E+04
75 percentile 2.5E-02 6.4E+01 208.1 5.5E-07 1.3E+06
90 percentile 5.3E-02 3.6E+02 230.8 5.5E-07 7.0E+06
max 1.2E+00 3.1E+04 335.9 1.2E-06 9.0E+08
210
Flow gradient in X direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1
2 4.3E+04 5.2E+04 3.0E+06
3
4 4.0E+07 8.7E+07 1.2E+08
5 1.4E+04 1.6E+04 2.2E+04
6 8.7E+03 1.0E+04 1.7E+04
7
8
9
10
11
12
13
14
15
16 3.2E+05 3.2E+05 3.3E+06
17
18
19 6.7E+03 7.7E+03 1.4E+04
20
21 4.7E+05 6.4E+05 2.0E+06
22
23
24
25 1.3E+05 1.8E+05 6.3E+05
26 1.4E+04 1.7E+04 7.9E+04
27
28
29
30 1.2E+03 1.9E+03 3.8E+03
31 4.6E+02 7.5E+02 2.1E+03
32
33 1.6E+05 2.1E+05 1.5E+06
34 4.6E+04 1.1E+05 8.9E+06
35
36 1.3E+06 1.6E+06 2.7E+06
37
38
39
40
211
Flow gradient in Y direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1
2 1.3E+04 1.7E+04 2.9E+05
3
4
5 9.5E+02 1.0E+03 1.5E+03
6 4.2E+03 5.4E+03 8.2E+03
7
8
9 6.3E+09 9.1E+09 1.4E+10
10
11
12
13
14
15
16 5.5E+04 5.5E+04 5.7E+05
17
18
19 8.6E+03 9.6E+03 1.3E+04
20
21
22
23
24
25 5.8E+05 6.9E+05 1.1E+06
26 5.3E+03 5.7E+03 3.6E+04
27
28
29
30 1.2E+03 1.6E+03 3.1E+03
31 4.6E+02 5.3E+02 8.2E+02
32
33 3.7E+05 4.4E+05 3.7E+06
34 2.3E+04 2.7E+04 9.2E+05
35
36 8.8E+05 1.9E+06 7.4E+06
37
38
39
40
212
Flow gradient in Z direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1
2 1.1E+04 2.4E+04 5.6E+05
3
4 1.1E+08 1.8E+08 3.0E+08
5 1.1E+04 1.2E+04 1.5E+04
6 1.3E+05 1.7E+05 2.7E+05
7
8
9
10
11
12
13
14
15
16 6.9E+06 6.9E+06 7.0E+06
17
18
19 1.3E+04 1.5E+04 1.9E+04
20
21 8.0E+05 1.2E+06 2.4E+06
22
23
24
25 9.6E+04 1.1E+05 1.7E+05
26 7.8E+03 8.8E+03 1.3E+05
27
28
29
30 5.4E+03 8.6E+03 1.5E+04
31 6.5E+02 6.6E+02 7.3E+02
32
33 3.0E+06 5.8E+06 4.2E+07
34
35
36 2.3E+05 2.4E+05 2.3E+06
37
38
39
40
213
Fracture domain FDb, DZ3, Case B (log-normal size model), Semi-correlated transmissivity model
Fraction of particles released that are connected to the fracture network
Direction of flow gradient X Y Z
mean 0.26 0.26 0.26
median 0.26 0.26 0.26
standard deviation 0.16 0.16 0.16
min 0.00 0.00 0.00
max 0.59 0.59 0.59
Flow gradient in X direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 8.5E-10 3.7E-02 49.8 3.3E-11 7.7E+01
0.1 percentile 3.1E-05 3.0E-01 91.4 8.5E-10 1.8E+03
0.25 percentile 4.3E-04 7.7E-01 130.8 5.2E-09 1.2E+04
50 percentile 3.7E-03 2.4E+00 172.0 2.8E-08 4.5E+04
75 percentile 1.6E-02 7.2E+00 210.2 1.2E-07 2.5E+05
0.9 percentile 1.1E-01 3.2E+01 243.6 8.6E-07 1.3E+06
max 4.3E+00 3.7E+06 488.8 1.5E-05 1.9E+10
Flow gradient in Y direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 7.7E-10 5.5E-02 50.0 3.3E-11 5.6E+01
0.1 percentile 7.2E-05 2.3E-01 100.1 1.2E-09 1.4E+03
0.25 percentile 5.9E-04 8.3E-01 139.4 5.3E-09 1.1E+04
50 percentile 3.4E-03 1.9E+00 171.8 3.0E-08 4.1E+04
75 percentile 1.9E-02 4.7E+00 204.9 1.3E-07 1.6E+05
0.9 percentile 8.4E-02 1.8E+01 239.5 1.2E-06 7.1E+05
max 4.4E+00 5.6E+05 552.4 1.5E-05 1.4E+10
Flow gradient in Z direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 1.1E-09 8.7E-02 50.6 3.3E-11 2.3E+02
0.1 percentile 4.1E-05 4.7E-01 85.2 1.2E-09 3.3E+03
0.25 percentile 3.3E-04 1.4E+00 129.8 5.6E-09 2.2E+04
50 percentile 2.1E-03 3.6E+00 203.8 3.0E-08 7.8E+04
75 percentile 9.8E-03 9.6E+00 274.8 1.3E-07 2.8E+05
0.9 percentile 4.4E-02 4.9E+01 344.2 8.6E-07 1.5E+06
max 1.5E+00 6.8E+05 607.4 1.5E-05 7.4E+09
214
Flow gradient in X direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1
2 2.7E+03 1.1E+04 4.2E+05
3 1.1E+05 2.2E+05 4.7E+05
4 1.3E+04 1.9E+04 2.8E+04
5 3.6E+03 8.4E+03 1.7E+04
6
7 1.2E+02 3.9E+04 6.3E+04
8 6.1E+02 8.7E+02 2.7E+03
9 5.3E+03 1.4E+04 5.3E+04
10 3.2E+04 3.7E+04 6.3E+04
11 5.1E+04 7.3E+04 2.1E+05
12 7.3E+03 9.5E+03 1.6E+04
13 5.5E+04 7.4E+04 2.8E+05
14 7.7E+01 1.7E+02 3.4E+03
15 8.7E+03 1.4E+04 4.8E+04
16 1.1E+02 1.5E+02 4.2E+02
17 1.2E+05 1.5E+05 2.3E+05
18 7.8E+03 2.2E+04 6.7E+04
19 9.2E+03 2.2E+04 2.0E+05
20 7.3E+04 1.1E+05 2.2E+05
21 4.9E+02 7.1E+02 3.1E+05
22 1.2E+03 1.8E+03 4.1E+04
23 1.8E+03 2.6E+03 6.3E+03
24 3.5E+03 1.4E+04 3.5E+04
25 3.9E+05 6.2E+05 1.0E+06
26 1.9E+04 2.0E+04 2.1E+04
27 5.3E+02 1.5E+03 8.5E+03
28
29 2.7E+03 1.3E+04 7.0E+04
30 7.0E+03 1.9E+04 1.3E+06
31 1.1E+04 1.6E+04 2.3E+04
32 1.1E+04 1.4E+04 3.8E+04
33 1.3E+04 2.2E+04 6.9E+04
34 3.5E+05 1.0E+06 2.8E+06
35 3.0E+02 4.5E+02 1.2E+04
36 1.8E+04 2.3E+04 3.7E+04
37 3.4E+03 6.2E+03 4.5E+04
38 9.4E+03 1.1E+05 2.8E+05
39 3.3E+02 4.4E+02 1.3E+05
40 4.5E+04 7.5E+04 1.1E+06
215
Flow gradient in Y direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1
2 1.7E+04 4.3E+04 1.0E+05
3 7.7E+04 1.2E+05 2.6E+05
4 6.7E+03 1.7E+04 3.0E+04
5 1.9E+03 3.7E+03 9.6E+03
6
7 1.9E+02 1.8E+04 3.7E+04
8 7.2E+02 1.1E+03 1.8E+04
9 8.2E+03 2.6E+04 6.5E+04
10 1.5E+04 2.2E+04 4.2E+04
11 4.3E+04 5.6E+04 1.8E+05
12 3.2E+03 4.5E+03 8.6E+03
13 1.1E+04 1.8E+04 1.7E+05
14 5.6E+01 7.2E+01 1.3E+03
15 8.6E+03 1.4E+04 3.5E+04
16 1.8E+02 2.0E+02 2.7E+02
17 1.7E+05 2.2E+05 3.6E+05
18 1.9E+04 3.5E+04 8.3E+04
19 1.2E+04 1.9E+04 5.0E+04
20 2.0E+04 2.7E+04 4.7E+04
21 6.6E+02 8.0E+02 2.3E+05
22 3.7E+02 4.4E+02 6.1E+03
23 4.4E+02 2.4E+03 1.4E+04
24 5.9E+03 2.1E+04 1.2E+05
25 2.5E+05 2.9E+05 1.2E+06
26 1.5E+04 1.7E+04 2.3E+04
27 6.2E+02 8.1E+02 3.6E+04
28
29 3.1E+03 6.8E+03 2.2E+04
30 1.3E+04 6.9E+04 7.5E+05
31 1.7E+04 2.7E+04 5.7E+04
32 1.2E+04 1.4E+04 2.6E+04
33 9.8E+03 1.9E+04 5.2E+04
34 3.5E+05 4.5E+05 7.6E+05
35 2.0E+02 3.0E+02 1.6E+05
36 8.5E+03 1.1E+04 3.0E+04
37 1.9E+03 3.0E+03 1.6E+04
38 2.1E+04 5.1E+04 9.8E+04
39 7.8E+02 1.5E+03 3.9E+04
40 1.5E+04 2.2E+04 3.6E+04
216
Flow gradient in Z direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1
2 2.4E+03 1.7E+05 4.9E+05
3 3.3E+04 5.7E+04 2.2E+05
4 5.3E+03 8.4E+03 3.0E+04
5 2.8E+03 5.1E+03 1.1E+04
6
7 8.7E+02 4.5E+04 1.5E+05
8 2.6E+02 3.9E+02 2.9E+04
9 7.9E+03 2.1E+04 8.0E+04
10 8.5E+04 1.0E+05 1.9E+05
11 4.3E+04 5.3E+04 3.9E+05
12 1.7E+04 2.6E+04 5.1E+04
13 1.6E+04 4.5E+04 1.4E+05
14 2.3E+02 1.6E+03 2.3E+04
15 1.5E+04 1.9E+04 3.5E+04
16 7.0E+02 8.1E+02 9.5E+02
17 2.1E+04 2.3E+04 4.6E+04
18 8.6E+03 7.1E+04 4.3E+05
19 6.6E+03 1.0E+04 3.2E+04
20 1.3E+05 1.5E+05 2.5E+05
21 1.7E+03 2.5E+03 9.3E+04
22 5.9E+02 7.5E+02 2.0E+04
23 1.5E+03 3.3E+03 1.9E+04
24 1.8E+04 3.6E+04 1.1E+05
25 3.0E+05 5.4E+05 1.2E+06
26 6.9E+03 7.7E+03 7.9E+03
27 1.1E+03 1.4E+03 4.2E+04
28
29 1.3E+04 3.3E+04 1.2E+05
30 4.8E+03 6.0E+03 1.1E+06
31 1.1E+04 1.6E+04 8.2E+04
32 5.9E+04 7.6E+04 1.5E+05
33 6.6E+03 4.0E+04 8.5E+04
34 8.8E+05 1.2E+06 2.7E+06
35 7.3E+03 1.1E+04 1.1E+05
36 2.9E+04 4.4E+04 7.3E+04
37 3.8E+03 7.0E+03 3.3E+04
38 1.0E+05 1.2E+05 1.6E+05
39 2.3E+03 5.3E+03 6.5E+04
40 5.0E+04 6.5E+04 9.0E+04
217
Fracture domain FDb, DZ4, Case B (log-normal size model), Semi-correlated transmissivity model
Fraction of particles released that are connected to the fracture network
Direction of flow gradient X Y Z
mean 0.03 0.03 0.03
median 0.00 0.00 0.00
standard deviation 0.07 0.07 0.07
min 0.00 0.00 0.00
max 0.27 0.27 0.27
Flow gradient in X direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 3.4E-05 9.9E-02 72.3 1.2E-10 3.9E+02
0.1 percentile 1.2E-04 1.1E-01 118.0 1.2E-09 4.3E+02
0.25 percentile 5.5E-04 1.6E+00 128.0 1.3E-09 6.4E+04
50 percentile 9.5E-04 2.8E+00 142.0 3.2E-09 2.2E+05
75 percentile 2.3E-03 4.0E+00 165.5 6.2E-09 4.1E+05
0.9 percentile 4.4E-01 2.1E+01 229.3 1.0E-06 1.8E+06
max 6.6E-01 5.3E+01 397.0 1.0E-06 5.4E+06
Flow gradient in Y direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 3.7E-05 6.1E-02 61.5 1.2E-10 2.4E+02
0.1 percentile 1.2E-04 1.0E-01 76.9 1.2E-09 4.1E+02
0.25 percentile 5.8E-04 1.5E+00 90.6 1.3E-09 9.1E+04
50 percentile 8.4E-04 2.7E+00 138.4 3.2E-09 2.0E+05
75 percentile 2.6E-03 4.4E+00 158.2 6.2E-09 4.6E+05
0.9 percentile 2.9E-01 1.9E+01 176.9 1.0E-06 1.3E+06
max 5.0E-01 9.8E+02 306.1 1.0E-06 6.6E+07
Flow gradient in Z direction
Initial velocity (m^2/yr)
Travel time (yr)
Pathlength (m)
Transmissivity (m^2/s)
F-Quotient (yr / m)
min 5.4E-05 9.2E-02 54.2 1.2E-10 3.6E+02
0.1 percentile 9.2E-05 1.3E-01 62.4 1.2E-09 5.2E+02
0.25 percentile 2.3E-04 2.2E+00 76.7 1.3E-09 1.3E+05
50 percentile 5.1E-04 4.0E+00 115.6 3.2E-09 2.6E+05
75 percentile 1.1E-03 1.0E+01 162.7 6.2E-09 1.1E+06
0.9 percentile 2.3E-01 2.8E+01 230.7 1.0E-06 2.1E+06
max 3.6E-01 1.5E+02 311.7 1.0E-06 1.2E+07
218
Flow gradient in X direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1
2
3 1.9E+05 2.2E+05 3.3E+05
4
5 1.3E+05 1.4E+05 2.1E+05
6
7
8
9
10
11
12
13
14
15 3.8E+04 4.8E+04 6.7E+04
16
17
18 3.9E+02 4.0E+02 4.2E+02
19
20
21 2.7E+05 3.0E+05 3.9E+05
22
23
24
25
26 3.6E+04 4.0E+04 4.4E+04
27
28
29
30 1.2E+06 1.5E+06 1.9E+06
31
32
33
34
35
36 2.4E+06 2.8E+06 3.4E+06
37 1.4E+05 1.6E+05 1.9E+05
38
39
40
219
Flow gradient in Y direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1
2
3 1.5E+05 1.8E+05 3.1E+05
4
5 5.9E+04 7.5E+04 9.1E+04
6
7
8
9
10
11
12
13
14
15 3.2E+04 3.8E+04 1.3E+05
16
17
18 2.4E+02 2.8E+02 3.6E+02
19
20
21 3.8E+05 4.1E+05 4.5E+05
22
23
24
25
26 8.7E+04 1.1E+05 2.0E+05
27
28
29
30 8.9E+05 1.1E+06 1.4E+06
31
32
33
34
35
36 6.1E+06 6.3E+06 7.6E+06
37 6.8E+04 8.1E+04 1.3E+05
38
39
40
220
Flow gradient in Z direction
realisation min F-quotient (yr / m)
10 percentile F-quotient (yr / m)
50 percentile F-quotient (yr / m)
1
2
3 3.2E+05 3.4E+05 3.5E+05
4
5 6.8E+04 9.5E+04 1.7E+05
6
7
8
9
10
11
12
13
14
15 1.2E+05 1.3E+05 1.4E+05
16
17
18 3.6E+02 3.9E+02 4.6E+02
19
20
21 9.5E+05 1.0E+06 1.1E+06
22
23
24
25
26 1.0E+05 1.1E+05 1.2E+05
27
28
29
30 1.3E+06 1.6E+06 2.0E+06
31
32
33
34
35
36 3.1E+06 3.3E+06 3.7E+06
37 1.1E+05 1.3E+05 2.0E+05
38
39
40
221
APPENDIX D: HYDRO ZONE PROPERTIES
Transmissivity of main hydro zones [m2/s].
Hydro zone Task 7 Table 6.1 in *) Calibrated by VTT
HZ001 1.3 10-8
1.6 10-6
7.9 10-6
below 200 m 5.9 10-8
HZ004 1.6 10-7
1.3 10-7
*)
HZ008 1.0 10-5
3.2 10-6
*)
HZ19A 1.6 10-6
7.9 10-6
2.6 10-5
HZ19B – 3.2 10-6
3.2 10-7
HZ19C 3.2 10-6
4.0 10-6
6.3 10-5
HZ20A 8.1 10-6
5.0 10-6
1.5 10-5
HZ20B 3.2 10-6
3.2 10-6
9.0 10-6
HZ21 1.6 10-8
1.3 10-8
3.0 10-6
HZ099 1.6 10-8
2.0 10-7
*)
*) Vaittinen T, Ahokas H, Nummela J, 2009. Hydrogeological structure model of the
Olkiluoto Site – update in 2008. Posiva Working Report 2009-15, Posiva Oy.
Note: value for Task 7 for HZ099 is that used for BFZ001 and the one for HZ20B is the
one used for HZ20B_ALT.
222
223
APPENDIX E: PRIMARY HYDRO-DFN DATA REFERENCES
Surface boreholes
Pöllänen J, Rouhiainen, P, 1996a. Difference flow measurements at the Olkiluoto site
in Eurajoki, boreholes KR1-KR4, KR7 AND KR8, Work report PATU-96-43E, Posiva
Oy.
Pöllänen J, Rouhiainen, P, 1996b. Difference flow measurements at the Olkiluoto site
in Eurajoki, boreholes KR9 AND KR10, Work report PATU-96-44E, Posiva Oy.
Pöllänen J, Rouhiainen, P, 2000. Difference flow measurements at the Olkiluoto site in
Eurajoki, borehole KR11, Working report 2000-38, Posiva Oy.
Pöllänen J, Rouhiainen, P, 2001. Difference flow and electric conductivity measure-
ments at the Olkiluoto site in Eurajoki, boreholes KR6, KR7 AND KR12, Working
report 2000-51, Posiva Oy.
Pöllänen J, Rouhiainen, P, 2002a. Difference flow and electric conductivity measure-
ments at the Olkiluoto site in Eurajoki, boreholes KR13 and KR14, Working report
2001-42, Posiva Oy.
Pöllänen J, Rouhiainen, P, 2002b. Flow and electric conductivity measurements during
long-term pumping of borehole KR6 at the Olkiluoto site in Eurajoki, Working report
2001-43, Posiva Oy.
Pöllänen J, Rouhiainen, P, 2002c. Difference flow and electric conductivity measure-
ments at the Olkiluoto site in Eurajoki, boreholes KR15-KR18 and KR15B-KR18B,
Working report 2002-29, Posiva Oy.
Pöllänen J, Rouhiainen, P, 2002d. Difference flow measurements at chosen depths in
boreholes KR1, KR2, KR4 and KR11 at the Olkiluoto site in Eurajoki, Working report
2002-42, Posiva Oy.
Pöllänen J, Rouhiainen, P, 2002e. Difference flow and electric conductivity measure-
ments at the Olkiluoto site in Eurajoki, extended part of borehole KR15, Working report
2002-43, Posiva Oy.
Rouhiainen P, Pöllänen J, 2003. Hydraulic crosshole interference tests at the Olkiluoto
site in Eurajoki, boreholes KR14 - KR18 and KR15B - KR18B, Working report 2003-
30, Posiva Oy.
Rouhiainen P, 2000. Electrical conductivity and detailed flow logging at the Olkiluoto
site in Eurajoki, boreholes KR1 - KR11, Working report 99-72, Posiva Oy.
Pöllänen J, Pekkanen J, Rouhiainen P, 2005a. Difference flow and electric conductivity
measurements at the Olkiluoto site in Eurajoki, boreholes KR29, KR29B, KR30, KR31,
KR31B, KR32, KR33 and KR33B, Working report 2005-47, Posiva Oy.
Pöllänen J, Pekkanen J, Rouhiainen P, 2005b. Difference flow and electric conductivity
measurements at the Olkiluoto site in Eurajoki, boreholes KR19-KR28, KR19B,
KR20B, KR22B, KR23B, KR27B and KR28B, Working report 2005-52, Posiva Oy.
224
Pöllänen J, Rouhiainen, P, 2005. Difference flow and electric conductivity measure-
ments at the Olkiluoto site in Eurajoki, boreholes KR1, KR2, KR4, KR7, KR8, KR12
and KR14, Working report 2005-51, Posiva Oy.
Pöllänen J, 2006a. Monitoring measurements by difference flow method during the year
2005, boreholes KR2, KR4, KR7, KR8, KR10, KR14, KR22, KR22B, KR27 and KR28,
Working report 2006-39, Posiva Oy.
Pöllänen J, 2006b. Difference flow and electric conductivity measurements at the
Olkiluoto site in Eurajoki, boreholes KR34 - KR39, KR37B and KR39B, Working
report 2006-47, Posiva Oy.
Sokolnicki M, Pöllänen J, 2008. Difference flow and electric conductivity measure-
ments at the Olkiluoto site in Eurajoki, boreholes KR40, KR40B, KR41, KR41B,
KR42, KR42B, KR43, KR43B and PP56, Working Report 2008-xx, Posiva Oy (in
prep).
Tunnel (pilot) boreholes
Rouhiainen P, Pöllänen, J, 2005a. Flow measurements in boreholes PH01 and PH02 in
ONKALO, Working report 2005-18, Posiva Oy.
Öhberg A (ed), Heikkinen E, Hirvonen H, Kemppainen K, Majapuro J, Niemonen J,
Pöllänen J, Rouhiainen, P, 2006a. Drilling and the associated borehole measurements
of the pilot hole ONK-PH3, Working report 2006-20, Posiva Oy.
Öhberg A (ed), Heikkinen E, Hirvonen H, Kemppainen K, Majapuro J, Niemonen J,
Pöllänen J, Rautio T, Rouhiainen, P 2006b. Drilling and the associated drillhole
measurements of the pilot hole ONK-PH4, Working report 2006-71, Posiva Oy.
Öhberg A (ed), Hirvonen H, Jurvanen T, Kemppainen K, Mustonen A, Niemonen J,
Pöllänen J, Rautio T, Rouhiainen P, 2006c. Drilling and the associated drillhole
measurements of the pilot hole ONK-PH5, Working report 2006-72, Posiva Oy.
Öhberg A (ed), Hirvonen H, Kemppainen K, Niemonen J, Nordbäck N, Pöllänen J,
Rautio T, Rouhiainen P, Tarvainen A-M, 2007. Drilling and the Associated Drillhole
Measurements of the Pilot Hole ONK-PH6, Working report 2007-68, Posiva Oy.
Öhberg A (ed), Kemppainen K, Lampinen H, Niemonen J, Pöllänen J, Rautio T,
Rouhiainen P, Tarvainen A-M, 2008. Drilling and the Associated Drillhole
Measurements of the Pilot Hole ONK-PH7, Working report 2007-97, Posiva Oy.
225
APPENDIX F: ON THE ROLE OF THE ‘GUARD ZONE’ TECHNIQUE AND DIFFERENT SPATIAL SCALES FOR THE CALCULATION OF ECPM BLOCK CONDUCTIVITY
In Phase I (Chapter 8), the „guard zone‟ technique in ConnectFlow /Jackson et al. 2000/
was used where flow is calculated in a subdomain, 150m, but only the flux through
central 50m block is used to calculate the equivalent hydraulic conductivity tensor, Keff.
In Phase II (Chapter 11), the „guard zone‟ technique was not used while the equivalent
hydraulic conductivity tensor was calculated for the 50m block.
It was suggested in Chapter 14 that it is the use of the „guard zone‟ technique that
causes the lower mean hydraulic conductivities in depth zones 2-4 of the repository-
scale model compared those of the site-scale model, cf. Table 14-1.
In Chapter 14, it was also suggested that the dependence of upscaled hydraulic
properties on spatial scale needs to be studied further to quantify the uncertainty in
groundwater fluxes depending on the choice of spatial resolution in ECPM models.
In conclusion, while completing this modelling report it was decided to investigate the
issues further to better quantify the origin of the differences seen. The upscaling cases
studied are:
„50m without guard zone‟,
„30m without guard zone‟,and
„50m with guard zone‟.
The results are shown in Figure F-1 and confirm the hypothesis that it is the use of the
„guard zone‟ technique that causes the lower mean hydraulic conductivities in
Chapter 8. The differences seen between „50 m without guard zone‟ and „30 m without
guard zone‟, however, are not consistent, thus appear to depend on the differeces in the
Hydro-DFN properties between DZ1-4.
0
10
20
30
40
50
60
70
80
90
100
1E-18 1E-17 1E-16 1E-15 1E-14 1E-13
k main (m2)
Pe
rce
nti
le
DZ4(-450m): 50m
30m
G(50m)
DZ3(-275m): 50m
30m
G(50m)
DZ2(-100m): 50m
30m
G(50m)
DZ1(-25m): 50m
30m
G(50m)
Figure F-1. Upscaling results for a 50 m block without ‘guard zone’, a 30 m block without ‘guard zone’ and a 50 m block with ‘guard zone’. The
results are shown for the four depth zones in FDb.
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