Radionuclide transport report for the safety assessment SR-Site

Technical Report

TR-10-50

Radionuclide transport report forthe safety assessment SR-Site
Svensk Kärnbränslehantering AB

December 2010

Svensk Kärnbränslehantering AB

Box 250, SE-101 24 Stockholm
Phone +46 8 459 84 00

TR-10-50

CM Gruppen AB, Bromma, 2011

Swedish Nuclear Fueland Waste Management Co

ISSN 1404-0344
Tänd ett lager:
SKB TR-10-50
P, R eller TR.

Radionuclide transport report forthe safety assessment SR-Site
Svensk Kärnbränslehantering AB

December 2010

Keywords: SKBdoc 1266928, Advection, Colloid, COMP23, Corrosion, Deterministic
calculation, Far field, FARF31, Isostatic load, MARFA, Near field, Pinhole, Probabilistic
calculation, Radionuclide release, Radionuclide transport, Shear load.
A pdf version of this document can be downloaded from www.skb.se.

Preface
This document compiles radionuclide transport calculations of a KBS-3 repository for the safetyassessment SR-Site. The SR-Site assessment supports the licence application for a final repository
at Forsmark, Sweden.
The following persons have had the main responsibilities for specific subject areas: James Crawford,
Kemakta Konsult AB, Sweden (geosphere processes and site characteristics), Christina Greis, SKB
and Maria Lindgren, Kemakta Konsult AB, Sweden (near- and far-field calculations with COMP23
and FARF31), Scott Painter, Los Alamos National Lab, US (far-field calculations with MARFA) andthe undersigned (methodology, sensitivity analyses and analytical calculations).
The report has been reviewed by Jordi Bruno, Amphos, Spain; Alan Hooper, Alan Hooper
Consulting Limited, UK; Ivars Neretnieks, Royal Institute of Technology, Sweden; and Mike
Thorne, Mike Thorne and Associates Ltd, UK.
Stockholm, December 2010
Allan Hedin
Project leader SR-Site

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Summary
The safety assessment SR-Site is undertaken to assess the safety of a geologic repository at theForsmark site. The assessment supports SKB’s licence application for a final repository for spent
nuclear fuel at Forsmark. The results of the assessment are documented in the SR-Site Main reportand supporting documents. This report describes calculations of radionuclide release and transport
for the proposed repository at Forsmark and compares the resulting radiological doses to applicableregulatory limits. Release and transport in several additional scenarios that help illustrate barrier
function are also described. Site characteristics and processes affecting release and transport are also
described.
The dominant processes responsible for geosphere radionuclide transport include advection throughnetworks of fractures, diffusion in intact host rock adjacent to fractures, ion exchange and surface
complexation reactions on mineral surfaces within the host rock, radionuclide decay and in-growthof daughter radionuclides, and radionuclide sorption onto clay colloids that may be generated in
the buffer material under some conditions. The SR-Site project has developed a comprehensive
strategy for representing flow in fractures and engineered features of the repository (described
elsewhere). The outputs of that flow modelling activity, which represent inputs to the transportmodelling described here, are advective travel times and flow-related transport resistance parameters
for individual transport pathways and flow rates at individual deposition holes. Model uncertainties
related to the representation of flow are addressed by considering multiple conceptual models of thediscrete fracture network based on different degrees of correlation between fracture transmissivity
and length. Multiple realisations of the discrete fracture network are included to address uncertainties associated with the stochastic generation of fracture networks. Steady flow and chemical
conditions for the present day are used in the transport calculations for SR-Site; variant simulations
and screening analyses allowing transient flow and chemical conditions demonstrate that the steadyapproximation is an adequate representation. Sorption processes are represented by equilibrium sorption partitioning coefficients with appropriately defined probability distributions instead of detailed
modelling of ion-exchange and surface-complexation reactions.
Two scenarios for which canister failures and subsequent radionuclide release cannot be ruled out
are identified in SR-Site. The two scenarios are failure of the copper canister by corrosion and byearthquake-induced shear movements in fractures intersecting the canister positions. Two additional
hypothetical scenarios (a growing pinhole failure and failure due to isostatic load) are also analysed
to illustrate barrier functions although the analyses discussed in the SR-Site main report led to theconclusion that the canister failure modes associated with these scenarios can be ruled out. Importantnear-field processes are dependent on the release scenario, but generally include dissolution of thefuel matrix and corrosion of structural parts of the fuel assemblies and control rods, precipitation/
dissolution of secondary radionuclide-bearing minerals, and sorption onto clay buffer and backfill
material. Diffusion in the buffer material is the primary transport mechanism if the buffer material
remains in place; otherwise, advection is the primary transport mechanism in the near field.
Probabilistic calculations of radionuclide release and transport demonstrate that the mean releases
from the engineered barrier system give rise to doses below the dose corresponding to the regulatory
risk limit. The dose-equivalent releases are also significantly below estimates of dose corresponding
to background concentrations of uranium and radium. The releases are small because the geosphereand engineered barrier system protect the canisters by providing favourable hydrological and geo­chemical environments, thus resulting in small probability of failure for a few canisters and neg­
ligible probability of failure for the vast majority of canisters. In the shear-failure scenario, sorption
on buffer material also attenuates radionuclide release.
Radionuclide release from the engineered barrier system is further attenuated by the geosphere.
The geosphere attenuation is approximately a factor of 3 for the corrosion scenario (central caseconditions). The attenuation is relatively modest in the central corrosion case because the canisters
that are most likely to fail are associated with flow paths with modest retention. Geosphere attenuation is stronger for variant modelling cases that result in larger releases from the engineered barriersystem. Thus, in addition to protecting the canisters and limiting releases, the geosphere also reduces

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uncertainty in the estimated doses by attenuating the dose for variant cases that have larger releasefrom the engineered barrier system. For all probabilistic cases considered, the mean annual effective
dose is at least an order of magnitude smaller than the dose corresponding to the risk limit. For thecentral corrosion case, the peak of the mean annual effective dose is estimated to be 0.18 μSv/year.
For comparison, the dose corresponding to the risk limit is approximately 14 μSv/year and the dosecorresponding to typical background radiation is approximately 1,000 μSv/year.
Sorption to mobile clay colloids is an uncertain process that is handled pessimistically in SR-Site byneglecting a range of potential mitigating processes. When this process is included, the geosphereis not a significant barrier to radionuclide transport for the brief periods in which high colloid
concentrations are possible. However, these periods are brief and the small near-field release rates
are sufficient to keep dose-equivalent releases below the dose corresponding to the risk limit.
Results of simplified analytical models are in good agreement with results obtained with the numerical models. The agreement enhances confidence in the dose equivalent release calculations presented
here for two reasons. First, the comparison provides an important quality assurance check on the
numerical modelling of dose equivalent releases. Second, it demonstrates that potential doses arecontrolled by relatively simple processes that are straightforward to understand and model.

6TR-10-50

Sammanfattning
Säkerhetsanalysen SR-Site görs för att analysera säkerheten för ett geologiskt förvar i Forsmark.
Analysen ligger till grund för SKB:s ansökan om att uppföra ett slutförvar för använt kärnbränsle
i Forsmark. Resultatet av säkerhetsanalysen dokumenteras i SR-Sites huvudrapport och huvud­referenser samt i stödjande rapporter. Den här rapporten utgör en av huvud­referenserna och beskri­
ver beräkningar av frigörelse och transport av radionuklider för det föreslagna förvaret i Forsmark
och jämför beräknad radiologisk dos med den dos som motsvarar myndigheternas riskkriterium.
Frigörelse och transport beskrivs också för flera så kallade restscenarier som hjälp för att illustrera
betydelsen av enskilda barriärer och barriärfunktioner. Dessutom beskrivs platskaraktäristik ochprocesser som påverkar frigörelse och transport.
De viktigaste processerna som påverkar radionuklidtransporten i geosfären är advektion genom
nätverk av sprickor, diffusion i intakt bergmatris intill sprickor, jonbytes- och ytkomplexerings­
reaktioner på mineralytor i bergmatrisen, radioaktivt sönderfall och inväxt av dotternuklider. SR-Siteprojektet har utvecklat en omfattande strategi för att modellera vattenflöde i sprickor och tekniska
barriärer. Utdata från vattenflödesmodelleringen i form av advektiv gångtid och flödesrelaterade
tranportmotståndsparametrar för individuella transport­vägar och flödeshastigheter i individuelladeponeringshål används som indata till transport­modelleringen. Modellosäkerheter relaterade till
beräkningen av vattenflödet omhändertas genom att beakta flera konceptuella modeller av det
diskreta spricknätverket baserat på olika grad av korrelation mellan spricktransmissivitet och sprickstorlek. Flera realiseringar av det diskreta spricknätverket har använts för att beakta osäkerheten till
följd av den stokastiska genereringen av spricknätverken. Konstant flöde och konstanta kemiskaförhållanden motsvarande dagens situation används huvudsakligen i transportberäkningarna i
SR-Site. Variationsfall samt beräkningar med varierande flöde och kemiska förhållanden visar att
approximationen med konstanta förhållanden är adekvat. Sorptionsprocesser representeras med jämviktssorptionskoefficienter med lämpligt definierade sannolikhetsfördelningar i stället för detaljerad
modellering av jonbytes- och ytkomplexeringsreaktioner.
I SR-Site identifieras två scenarier för vilka det inte kan uteslutas att kapselns isolering går förlorad
och att radionuklider frigörs. De två scenarierna är korrosion av kopparkapseln och kapselskador till
följd av jordskalvsinducerade skjuvrörelser i sprickor som korsar kapselpositionen. Två hypotetiska
restscenarier (växande initialt pinnhål och skada på grund av isostatisk last) analyseras också för
att belysa barriärernas funktion, även om analysen som beskrivs i SR-Sites huvudrapport leder tillslutsatsen att dessa båda kapselskador kan uteslutas. Viktiga närzonsprocesser är scenarioberoende,
men generellt omfattar de upplösning av bränslematrisen och korrosion av metall i bränsleboxarna
och i styrstavar, utfällning/upplösning av sekundära mineraler som innehåller radionuklider samt
sorption på bentoniten i buffert och tunnelåterfyllning. Diffusion i buffertmaterialet är den primära
transportmekanismen, om buffertmaterialet är kvar, annars är advektion den primära transportmekanismen i närzonen.
Probabilistiska beräkningar av frigörelse och transport av radionuklider visar att medelutsläppet frånde tekniska barriärerna är lägre än den dos som motsvarar myndigheternas riskkriterium. Utsläppet
är också betydligt lägre än dosen från bakgrundskoncentrationer av uran och radium. De låga utsläppen beror på att geosfären och de tekniska barriärerna skyddar kapslarna genom att tillhandahålla engynnsam hydrologisk och geokemisk miljö, som resulterar i en låg sannolikhet för skador på ett fåtal
kapslar och försumbar sannolikhet för skador på en majoritet av kapslarna. I skjuvscenariot bidrarockså sorption på buffertmaterial till en dämpning av radionuklidutsläppet.
Radionuklidfrigörelsen från de tekniska barriärerna dämpas ytterligare av geosfären, vilket medför
en minskning med ungefär en faktor tre för korrosionsscenariot (centralfallet). Dämpningen är relativt begränsad i det centrala korrosionsfallet på grund av att de kapslar som har högst sannolikhet att
skadas är sammankopplade med flödesvägar med ringa retention. Geosfärens dämpning är större för
beräkningsfall som resulterar i högre utsläpp från de tekniska barriärerna. Förutom att skydda kapslarna och begränsa utsläppen, reducerar geosfären alltså också osäkerheter i de uppskattade doserna
genom att dämpa dosen mer för de fall som har högre utsläpp från de tekniska barriärerna. För alla
probabilistiska fall som beaktats är den effektiva årliga medeldosen åtminstone en storleksordning

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7lägre än dosen som motsvarar SSM:s riskkriterium. För det centrala korrosionsfallet är den högsta
årliga effektiva dosen beräknad till 0,18 μSv/år. Som jämförelse är dosen som motsvarar riskkriteriet
ungefär 14 μSv/år och dosen som motsvarar typisk bakgrundsstrålning omkring 1 000 μSv/år.
Sorption på mobila lerkolloider är en process av osäker omfattning som hanteras pessimistiskt i
SR-Site genom att försumma ett antal för säkerheten gynnsamma delprocesser. Då denna process
inkluderas, är geosfären inte en signifikant barriär mot radionuklidtransport under de kortvariga
perioder då höga kolloidkoncentrationer är möjliga. Dessa perioder är dock kortvariga och
utsläpps­takten från närzonen är tillräckligt låg för att hålla dosekvivalenta utsläpp under dosensom motsvarar myndigheternas riskkriterium.
Resultat av beräkningar med förenklade analytiska modeller stämmer väl överens med resultatfrån de numeriska modellerna. Överrensstämmelsen stärker tilltron till de dosekvivalenta utsläppsberäkningarna av två anledningar. Dels ger jämförelsen en viktig kvalitetskontroll av den numeriska
modelleringen av dosekvivalenta utsläpp och dels visar den att potentiella doser kontrolleras av
relativt enkla processer som är okomplicerade att förstå och modellera.

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Contents
1
2
2.1
2.2
2.3
2.4

2.5

3
3.1
3.2
3.3
3.4
3.5
3.6

3.7

4
4.1

4.2
4.3
4.4

4.5

Introduction
Processes and site characteristics affecting transport
Flow
2.1.1 Spatial variability and the nature of channelised flow
2.1.2 Evolution of flow over a glacial cycle
Chemistry
2.2.1 Spatial variability of groundwater chemistry
2.2.2 Evolution of groundwater chemistry over a glacial cycle
Background levels of naturally occurring radionuclides
Transport and retention processes
2.4.1 Non-linear sorption processes
2.4.2 Precipitation and dissolution in the far field
2.4.3 Sorptive interactions with fracture minerals
2.4.4 Consequences of neglected retention processes and temporalchanges in groundwater chemistry
Summary of geosphere non-flow related data
2.5.1 Diffusion-available porosity
2.5.2 Effective diffusivity
2.5.3 Rock matrix sorptivity
Conceptualisation of transport processes and conditions within SR-Site
Selection of radionuclides
Radionuclide release from the fuel3.2.1 Release of instantaneous release fraction
3.2.2 Release of activation products in metal parts
Near-field transport and retention
Geosphere transport and retention
Biosphere representation
Models used
3.6.1 COMP23
3.6.2 FARF31
3.6.3 MARFA
3.6.4 Summary of the transport model chain
3.6.5 Analytical models
3.6.6 Input data to the transport models
Summary of all data used
3.7.1 Probabilistic input data
3.7.2 Deterministic input data
3.7.3 QA-related issues
Canister failure due to corrosion
Introduction
4.1.1 Evolution of the canister after canister failure
4.1.2 Radionuclide release
4.1.3 IRF-pulse
Summary of calculation cases
Input data specific for the corrosion scenario
Central corrosion case
4.4.1 Deterministic calculations
4.4.2 Probabilistic calculations
4.4.3 Sensitivity analysis
4.4.4 Issues related to the probabilistic nature of the calculations
Alternative cases based on the semi-correlated hydrogeological DFN model
4.5.1 Disregarding thorium sorption in the near field
4.5.2 Including solubility limits in the near field
4.5.3 Decreased sorption of lead in the geosphere
4.5.4 Kd for U(VI) instead of U(IV) in the geosphere
4.5.5 Influence of correlation groups for Kd in the geospehere
4.5.6 Colloid-facilitated transport
4.5.7 Varying climate conditions
4.5.8 Varying climate conditions and colloid-facilitated transport
4.5.9 Initial advection

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4.6

Uncorrelated hydrogeological DFN model
4.6.1 Base case transport assumptions
4.6.2 Initial advection
4.7 Fully correlated hydrogeological DFN model
4.7.1 Base case transport assumptions
4.7.2 Initial advection
4.8 Cases addressing best available technique (BAT)
4.9 Alternative safety indicators for the central corrosion case
4.9.1 Finnish activity release constraints
4.9.2 Radiotoxicity flux from the geosphere – EU SPIN Project4.9.3 Naturally occurring fluxes of radionuclides at the site
4.10 Calculation with analytical models
4.11 Summary and conclusions for the corrosion scenario
5
Canister failure due to shear load
5.1 Introduction
5.2 Calculation of doses for the shear load scenario
5.2.1 Postulated failure of one canister at 100,000 years
5.2.2 Failure during the period 1,000 years to one million years
5.2.3 Early failure
5.2.4 Combination of shear load and buffer advection
5.3 Alternative safety indicators for shear load case 1,000 years to
one million years
5.3.1 Finnish activity release constraints
5.3.2 Radiotoxicity flux from the geosphere – EU SPIN Project
5.3.3 Naturally occurring fluxes of radionuclides at the site
5.4 Calculation with analytical models
5.5 Summary and conclusions for the shear load scenario
6
Hypothetical residual scenarios to illustrate barrier functions
6.1 Introduction
6.2 Canister failure due to isostatic load
6.2.1 Postulated failure of one canister at 10,000 years
6.2.2 Postulated failure of one canister at 100,000 years
6.2.3 Summary and conclusions for the isostatic load scenario
6.3 The growing pinhole failure
6.3.1 Base case, including the effect of spalling
6.3.2 Disregarding the effect of spalling
6.3.3 Lost swelling pressure in tunnel backfill, “Crown-space”
6.3.4 Different assumptions regarding EDZ
6.3.5 Summary and conclusions for the growing pinhole scenario
6.4 Exploration of geosphere barrier performance using the growing
pinhole case
6.4.1 Input parameters
6.4.2 Reference case
6.4.3 Issues related to the probabilistic nature of the calculations
6.4.4 Exploration of barrier function of geosphere components
6.4.5 Colloid-facilitated transport assuming irreversible sorption
6.5 Additional cases to illustrate barrier function
7
Summary and conclusions
8
References
Appendix A 	On the impact of channelised flow
Appendix B 	Scoping calculations involving fracture mineral retention processes
Appendix C 	Comparison between MARFA and FARF31
Appendix D 	Selection of radionuclides
Appendix E 	Inventory
Appendix F 	Solubility calculations
Appendix G 	Discretisation, diffusion resistances and boundary conditions
used in COMP23
Appendix H 	Transport parameters used in Section 6.4
Appendix I 	 Colloid facilitated transport model

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1Introduction

The safety assessment project SR-Site is undertaken by SKB to assess the safety, as defined in applicable Swedish regulations, of a potential geologic repository for spent nuclear fuel. The results ofthat assessment are documented in the SR-Site Main report1 and supporting documents. The Main
report forms part of SKB’s license application to construct and operate a repository at Forsmark
based on the KBS-3V concept.
Calculations of radionuclide release, transport and dose consequences for different scenariosand cases are important components of the safety assessment SR-Site. This report quantitatively
describes such calculations for all scenarios contributing to the calculated risk for the proposed
Forsmark repository and compares the resulting radiological annual doses to applicable regulatory
limits. The report also summarises transport assessments for residual scenarios that were selected
to illustrate performance of the repository barrier systems. As described in the Section 2.5.12 of theMain report, this report is one of 16 main references for the SR-Site Main report and is referred toas the Radionuclide transport report.
The SR-Site project team has developed an 11-step process for the SR-Site safety assessment(Figure 2-2 of the Main report). This report focuses on Step 10, Analyses of Selected Scenarioswith Respect to Isolation and Retardation. In addition, transport-related aspects of Step 2a,
Descrip­tion of Initial Site State and Step 7, Definition and Analyses of Reference Evolution are
also described.
Several scenarios that have the potential to cause radionuclide mobilisation and release from theengineered barrier system are identified in Chapter 11 of the Main report. The current reportanalyses consequences of the two scenarios identified as the most risk significant: canister failure
due to corrosion and canister failure due to shear load. In the ‘canister failure due to corrosion’scenario (called briefly the corrosion scenario below) canisters fail as a result of enhanced corrosion
due to advective conditions in the deposition hole following the loss of buffer through erosion. In
the ‘canister failure due to shear load’ scenario, canisters fail due to earthquake-induced secondary
shear movement along fractures intersecting the canister position. Details of the two scenarios are
discussed in the Main report. In addition, several residual scenarios that help understand geospherebarrier function are also analysed.
In addition to the analyses of selected scenarios, this report also briefly summarises site characteristics that affect radionuclide transport. Further, several radionuclide transport/retention processes thatare not explicitly included in SR-Site but require further analyses are discussed.
Some aspects of radionuclide transport are discussed in the Main report and are not discussed here,
including dose to non-human biota, risk summation, and gas-phase transport.

1
To improve readability, abbreviated names in bold font are used here to refer to the SR-Site Main report andits main references. Full report names are provided in the reference list.

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2

Processes and site characteristics
affecting transport

The migration of solutes through fractured rock is dependent on a number of processes and variables.
These are outlined in the Geosphere process report and can generally be categorised as being either
geological (i.e. relating to microstructural properties of the rock), hydrogeological (i.e. relating toflow), or hydrochemical in nature (i.e. relating to groundwater chemistry). Although the migration ofsolutes can also be related to a broader class of reactive transport processes governing ground­watercomposition, in this chapter the focus is primarily on features and processes of importance for thetransport of radionuclides from canister positions in the repository to the biosphere.
In this context, geological factors of importance relate primarily to the existence of a hydraulicallyconnected fracture system traversing the repository volume as well as the flow-wetted surface
and microporous structures both immediately adjacent to fracture surfaces and within the deeprock matrix. Although there is considerable overlap in the ontological description of features andprocesses that are considered geological and those categorised as being hydrogeological, both areimportant for the overall description of radionuclide transport processes. Hydrochemical features
include the groundwater chemistry parameters that govern the solubilities of radionuclides andinfluence the chemical reactions of nuclides with geological materials lining flowpaths through thenear field, far field, and biosphere. Hydrochemical features, although more precisely differentiatedthan geological or hydrogeological entities in this description, are still strongly dependent on the
couplings between geology, flow and chemical reactions involving other non-nuclide groundwaterchemical constituents. The following sections give an overview of the main features.

2.1

Flow

Groundwater flow is a primary control on radionuclide migration in the subsurface. The groundwaterflow system at Forsmark has been studied extensively and is described in detail in Section 10.3.6
of the Main report and supporting documents. At present, flow at Forsmark is primarily verticallyupward from the repository to a shallow bedrock aquifer associated with large, nearly horizontal
fractures/sheet joints because of the effects of a local topography-driven flow cell, then horizontallyin the shallow bedrock aquifer to discharge locations at topographic lows /Follin 2008/.
The existence of flow in fractured rock, its spatial distribution, and temporal variability are strongly
governed by the geological characteristics of the site and hydraulic boundary conditions. In somesituations, flow may be relatively evenly distributed throughout the available flow space, althoughin-situ observations suggest (e.g. /Abelin et al. 1991a, b, 1994/) that it is more likely to be channelised to varying degrees. Channelised flow can arise spontaneously on the level of regional fault
structures and more local scale heterogeneous fracture networks where water flow preferentiallyfollows the path of least resistance in connected hydraulic features. A comprehensive modelling
approach is used in SR-Site to represent the effects of such channelling at Forsmark. The modelling
approach uses a combination of discrete fracture network (DFN), continuous porous medium (CPM),
and equivalent continuum porous medium (ECPM) models. The latter class of models represents
flow in fractured rock by upscaling a DFN representation to a CPM representation. Models of flow
during the temperate period use nested DFN/ECPM models with explicit CPM representation oftunnels, boreholes and near-surface soil layers. Modelling of flow during the glacial and periglacial
periods has been carried out using ECPM representations without explicit representation of therepository engineered features.
Regardless of how the flow modelling is carried out, flow-related input to transport calculations islimited to three parameters: equivalent flow rate at the canister Qeq, the advective travel time tw, andthe flow-related transport resistance F. Definitions for these “flow triplet” parameters may be foundin /Joyce et al. 2010/.

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The flow triplets vary spatially and by realisation of the stochastically generated DFN. The Qeq
varies by canister location, release path (see Section 3.3), and DFN realisations. The tw and F
parameters are properties of the flowpath connecting a near-field release location to a geospheredischarge location. Thus, a unique pair of tw and F is required for each combination of DFN realisation, canister location, near-field release path, and flow path through the geosphere. Depending on
the transport code being used (3.6), spatial variability of tw and F along the flow path may also be
represented (e.g. element by element in a finite element representation of the flow). Cumulative
distributions of F for different realisations of the hydrological model are found in /Joyce et al. 2010/.
Within each realisation, the F values associated with different deposition holes span a large range.
The flow and transport modelling approach used in SR-Site represents spatial variability andchannelling phenomena down to the level of individual fractures. Channelling phenomena can occur
at even smaller scales because of physical features such as enlarged fracture intersections or withinfracture variability in fracture aperture. Channelling at the sub-fracture scale is not represented in
SR-Site. Technical bases for neglecting within-fracture channelling are discussed in Section 2.1.1
and Appendix A.
Future glacial cycles are expected to have significant effect on groundwater flow /Climate report/.
For most of the transport scenarios analysed here and in the Main report, these effects are ignoredand steady temperate-period flow and chemical conditions are assumed. Selected modellingcases presented later in this report are used to assess the impacts of climate variability and showthat the temperate-period results provide a reasonable approximation to peak mean annual dose.
Section 2.1.2 describes how flow evolution on a glacial cycle is represented in those selectedmodelling cases.

2.1.1 Spatial variability and the nature of channelised flow
On the scale of single fractures, the existence of a heterogeneous transmissivity field may result inthe merging of flow lines in high velocity regions of the fractures. Owing to the limited spatial extent
of these regions, this merging may decrease the flow-related transport resistance (F-factor) of certain
parts of the fracture relative to the estimate representing the average flow smeared evenly over thewhole fracture surface. As shown by /Cvetkovic et al. 1999/ increasing amounts of fracture-scale
heterogeneity results in a broadening of the F-factor and advective travel time distribution and anincreasing statistical average of these variables. Although an increasing average implies enhanced
retardation, this does not apply to the fast flowpaths in the fracture, which are of most relevance forsafety assessment calculations. When considering the fracture as a whole, broadening of the F-factor
and advective travel time distribution implies both a greater frequency of fast flowpaths together
with a greater frequency of slow flowpaths at the expense of middling flowpaths. Furthermore,this does not consider the location or extent of the solute source nor the setting in which individual
fractures reside (i.e. in a heterogeneous three dimensional network of connected structures). For thisreason it is important to not only consider heterogeneity on the level of individual fractures, but also
effects arising on the larger scale of the fracture network itself which also includes considerationof hydraulic boundary conditions and source term locations relevant for the solute transport underconsideration.
Calculations made by /Painter 2006/ indicate that internal variability in transport aperture and transmissivity has only a minor effect on the estimated flow-related transport resistance (F-factor) andthe advective travel time provided the internal variability is not greater than the fracture-to-fracture
variability. One cause of the insensitivity is a “choke-point effect” caused by the fact that fluid canenter and leave a fracture only on limited areas, thereby constraining the flowpath geometries. The
overall effect of fracture-to-fracture transmissivity variability and hydraulic connectivity are referred
to collectively as network scale effects in this report. In cases where the network scale variability
was less than the internal fracture variability, more severe channelling resulted in a greater frequency
of fast flowpaths with reduced F-factors. Although these calculations were made for non-contacting
fractures, similar results are likely for fractures with asperity contacts since the flow naturally
tends to seek out the path of least resistance. This does not necessarily mean that flow channellingis unimportant but merely that the effect in many cases may be weak in relation to the impact of
network scale stochastic variability.

14

TR-10-50

The problem remains, however, how to adequately account for flow channelling in safety assessment
calculations when it is not possible to make large scale hydrogeological simulations with sufficiently
well resolved spatial variability (i.e. on the level of individual fractures) to adequately capture
important flow channelling phenomena. Since the flow in sparse, heterogeneous fracture networks
tends to be governed by network scale effects, the issue essentially boils down to estimating theeffective flow-wetted surface that channelised flow makes contact with in individual fractures. In theprevious SR‑Can safety assessment /SKB 2006a/ this was handled by a heuristic assumption that theF-factor should be pessimistically reduced by a factor of ten relative to that estimated based on average fracture transmissivities and the assumption of flow contact with entire fracture surfaces. This
was not based on any specific quantitative reasoning, but primarily on subjective expert judgement
under the assumption that the bulk of the flow might only contact about 10% of the total fracturesurface area.
In the present SR‑Site safety assessment, the F-factor is not reduced by a factor of ten as was done
previously since this is considered to be an unnecessarily pessimistic assumption for three reasons.
First, fracture-to-fracture variability is generally larger than within-fracture variability in aperture.
Second, fluid can only enter and leave fractures on limited area, significantly constraining the meander of flowlines /Painter 2006/. Third, substantial portions of the non-contacting fracture surface
area outside of the dominant flow channels may still be accessible by diffusion within the fracture
pore space and thus provide additional surface area for radionuclides to interact with the rockmatrix. While this type of transverse dispersion can usually be neglected on the timescale of tracer
tests performed in fractured rock, it is of great significance at safety assessment timescales whererates of diffusive mass transfer can become commensurate with the rate of advective transport. On
balance this means that non-scaled F‑factor ranges can often be assumed for transport calculations
even in the presence of significantly channelised flow without introducing large errors provided a
set of reasonable conditions can be fulfilled. Calculations detailing the conditions under which thisassumption is considered reasonable are presented in Appendix A.

2.1.2 Evolution of flow over a glacial cycle
Understanding of climate evolution at the Forsmark site is described in detail in the Climate report.
Future glacial cycles will have a significant effect on groundwater flow and chemistry. For most of
the transport scenarios analysed here and in the Main report, these effects are ignored and steady
temperate-period flow and chemical conditions are assumed. Selected modelling cases presented
later in this report are used to assess the impacts of climate variability and show that the temperateperiod results provide a reasonable approximation to peak mean annual dose.
In those selected modelling cases that include unsteady conditions, a pessimistic abstraction of thegroundwater flow field evolution is used in place of the full details of the flow and chemical evolution during a glacial cycle. A simplification of the glacial cycle is developed in the Climate reportto support the abstraction, see Figure 2‑1. The simplified cycle has two temperate periods, threeperiglacial periods, two glacial periods, and two submerged periods in the 120 kyr cycle. It is notedthat the summed percentages of each climate period coincides with the corresponding percentages
for the original, non-simplified cycle. In the abstraction, the cycle repeats 8 times in the 1 million
year assessment period of interest. Table 2-1 provides times for each flow change in the first 120 kyr
cycle.
Detailed simulations of transient flow during a glacial cycle have been undertaken /Vidstrand et al.
2010/. These simulations show that both the direction and magnitude of groundwater flow areaffected by the glacial cycle. As an alternative to representing the full details of transient groundwater flow fields in the transport simulations, a pessimistic bounding abstraction is developed.
The abstraction includes changes in flow magnitude, but uses pathlines from the temperate period/­Joyce et al. 2010/ and ignores changes in flow direction. This abstraction is pessimistic because it
greatly overestimates the vertical component of the flow velocity compared with detailed simulations /Vidstrand et al. 2010/, and also ignores lengthening of the flow paths that may occur duringsome of the climate periods.

TR-10-50

15

Te
m

e
rat
6%

2

pe

S

rged
me
ub 6%
1

Climate domains

i al
Glac
24%

Temperate
Periglacial
GlacialSubmerged
conditions

lacialrig
Pe 34%

0

10

20

30

40

50

60

70

80

90

100

110

120

Time (kyrs after present)

Figure 2‑1. Simplified glacial cycle for use in the geosphere transport assessment /Climate report/.

Table 2‑1. Duration of each climate period in the simplified 120 kyr cycle. The percentage of eachaccumulated period is also indicated.
PeriodCalendar time (kyrs)

Duration (kyrs)

Accumulated duration (kyrs)

Temperate

0–8

8

8

Periglacial

8–12

4

4

Temperate

12–35

23

8+23=31 (26%)

Periglacial

35–58

23

4+23=27

Glacial

58–65

7

7

Submerged

65–75

10

10

Periglacial

75–89

14

27+14=41 (34%)

Glacial

89–11122

7+22=29 (24%)

Submerged

111–1209

10+9=19 (16%)

The glacial periods summarised in Figure 2‑1 and Table 2‑1 need to be further subdivided into
advancing, glacial maximum, and retreating phases because the groundwater velocity will be very
different in these three phases. For the advancing ice sheet, it takes 366 years for the ice sheet tomove between ice front locations I and IV, see /Vidstrand et al. 2010/ for details. For the retreating
ice sheet it takes 61 years to move between ice front locations IV and I. As an approximation, it isjudged that when the ice front is beyond these ice front locations, the influence of the ice front on
the repository will be small, i.e., conditions close to periglacial or submerged will prevail. However,even beyond these times, there is some influence, even if not comparable to the peak, see Figure 2‑2,
which shows the Darcy flux at repository depth within the repository footprint (measurement locality
2 in /Vidstrand et al. 2010/). Specifically, during the ice advance, the increase in Darcy flux relative
to temperate conditions prevails approximately for 2,000 years. It is decided to represent the glacialadvancing period as having duration of 1,800 years, which is much longer than the time to move
between ice front locations I and IV, but slightly shorter than the time 2,000 years. The more rapid
retreating phase is modelled as having duration of 300 years; i.e., the ratio in duration between
advance and retreat phases is maintained. It is also noted that the increase in Darcy flux during theadvancing phase is smaller than during the retreating phase. This is due to the fact that the advancing
phase is characterised by permafrost in front of the ice sheet, whereas the retreating ice sheet iswarm based such that no permafrost is present, see /Vidstrand et al. 2010/ for details.
Flow scaling factors for each climate domain are obtained from the calculated Darcy flux distributions at deposition hole locations in the super-regional groundwater flow model of /Vidstrand et al.
2010/. In Figure 6-18 of /Vidstrand et al. 2010/, the maximum, median, and minimum Darcy flux
distributions are shown normalised by the temperate period value. The normalised median values
from Figure 6-18 of /Vidstrand et al. 2010/ and the duration of each flow epoch from Table 2-1

16

TR-10-50

are used to obtain time-dependent flow factors (Figure 2-3). In developing the flow factors, theglacial state with a 2-km tongue of permafrost was assumed for the glacial advancing period, and theglacial state without permafrost was assumed for the glacial retreating phase. The latter assumption isregarded as slightly pessimistic because the fluxes in the glacial case without permafrost of /Vidstrand
et al. 2010/ were developed for an advancing ice sheet but applied here for a retreating ice sheet. In
the far-field calculations with MARFA, the advective travel time and flow-related transport resistancefor the temperate period are inversely scaled by the values in Figure 2-3 to obtain corresponding values
for other stages in the glacial cycle.
100

Normalised Darcy flux q/qtemp (-)

pre-LGM

LGM

post-LGM

10Glacial Casewith
Permafrost
Loc.2

1

0.1

0

2,000

4,000

6,000

8,000

10,00012,00014,00016,00018,00020,000Time (y)Figure 2‑2. Change in Darcy flux relative to the temperate period as the ice sheet advances and retreatsover the repository location. Figure is modified after Figure G-12 (Appendix G) of /Vidstrand et al. 2010/.

102

Flow factor [–]

101

100

10-1

10-2

0

20

40

60

80

100

120

Time [kyrs]

Figure 2‑3. Flow scaling factors for one glacial cycle (of eight during 1 million years) for use in far-fieldradionuclide transport simulations. The spikes at the end of the two glacial periods have duration of
300 years (not resolved on this scale). The scaling factor is defined relative to the Darcy flux in the tem­
perate period and is used to adjust both advective travel time and flow-related transport resistance.

TR-10-50

17

2.2

Chemistry

A broad overview of chemical processes of relevance for SR‑Site is given in the Geosphere processreport. In this section, chemical processes of specific importance for radionuclide migra­tion in thefar field are described. The chemical composition of groundwater and the reactions between aqueous
solutes is of great importance for understanding the sorption processes that give rise to the transport
retardation effects modelled in SR‑Site.
Although the partitioning of nuclides between the aqueous and surface sorbed phases is treated in a
simple fashion using a linear isotherm (Kd) approach, it is important to remember that the conditional
Kd value is simply the ratio of immobilised and dissolved solute that is specific for a particular solid
phase composition, water chemistry, and solute concentration and does not rely on any particularmechanistic argumentation regarding underlying sorption processes. In SR‑Site, the term sorption
is used to describe adsorption processes involving ion-exchange and surface complexation. Ionexchange refers to the electrostatic interactions of dissolved solutes with permanently charged sitesof minerals, usually phyllosilicates. Surface complexation, however, refers to the interactions of
dissolved solutes with surface reactive groups on mineral surfaces. Inner sphere surface complexation involves covalent bonding of solutes to these reactive groups, whereas outer-sphere surface
complexation refers to the electrostatic interaction of solutes with the reactive groups.
By their very nature, surface reactive groups are sensitive to the groundwater composition, inparticular pH, and the relative abundance of binding sites is therefore strongly dependent on
groundwater chemistry. Nuclides sorbed by way of ion-exchange or outer sphere surface complexation are sensitive to ionic strength since the electrostatic interactions are weak and they can easily
be displaced by competing solutes. Nuclides that form inner sphere surface complexes are typicallyconsidered less sensitive to ionic strength on account of their stronger bonds with the surface.
Direct and indirect competitive effects involving other dissolved species in groundwater influence
sorption of nuclides. Direct effects involve the presence of other groundwater solutes that, owing
to their much higher concentration, compete against nuclides for a limited number of sorption
sites even if they sorb less strongly than the migrating nuclide. Reactive ligands in solution suchas carbonate and hydroxyl ion also compete with sorption sites to bind radionuclides in the formof aqueous complexes. This is an example of an indirect competive effect. In general the free
concentration of a solute makes up a variable part of the total dissolved concentration of a substance.
The distribution of a nuclide between its various complexed forms (i.e. its speciation) has a strong
influence on the overall magnitude of sorption.
There are a number of different ligands present in groundwater that may influence the speciationof radionuclides. Chief among these are hydroxyl ions (involved in hydrolysis), carbonate, and to alesser extent chloride. Depending on redox conditions, the presence of sulphate or sulphide may also
play a role in radionuclide speciation. Certain nuclides are highly sensitive to redox potential and canswitch between largely immobile forms under reducing conditions to relatively more mobile forms
under oxidising conditions. The redox potential at which a transition is thermodynamically possible
from reduced to oxidised forms is also influenced by pH and carbonate concentration.
The two key variables that govern a large portion of radionuclide speciation are the pH and carbonate concentration (or equivalent partial pressure of carbon dioxide). These are considered to be ofprimary relevance for the sorption of many of the radionuclides in SR‑Site, particularly those thatsorb by way of a surface complexation mechanism. For solutes that sorb principally by ion-exchangeor outer-sphere surface complexation, the concentration of competing solutes given by the total
dissolved solids (TDS) or ionic strength is a key variable influencing sorption. Redox speciation isconsidered separately in SR‑Site owing to the overwhelmingly strong control that it exerts on themobility of certain radionuclides (principally, U, Np, Tc, and Pu).

18

TR-10-50

-2

-2

-2.2

-2.2

-2.4

-2.4

log 10CO2(mol/kgw )3 totallog 10CO2(mol/kgw )3 total2.2.1 Spatial variability of groundwater chemistry
The spatial distribution of groundwater composition at different times in the temperate phase of
repository evolution is shown in Figure 2‑4 for 2,000 years, and in Figure 2‑5 for 9,000 years.

-2.6
-2.8
-3
-3.2
-3.4

-2.6
-2.8
-3
-3.2
-3.4

-3.6

-3.6

-3.8

-3.8

-4
6

6.5

7

7.5

8

8.5

9

9.5

-4
-2

10

-1.8

-1.6

-2
-2.2

-2.4

-2.4

log 10CO2(mol/kgw )3 total(mol/kgw )log 10CO23 total

-2
-2.2

-2.6
-2.8
-3
-3.2
-3.4

8

pH

8.5

9

9.5

10

-0.6

-0.4

-0.2

0

-0.4

-0.2

0

-3.2
-3.4

-3.8
7.5

-0.8

-3

-3.6

7

-1

-2.8

-3.8
6.5

-1.2

-2.6

-3.6

-4
6

-1.4

log 10Ionic Strength (mol/kgw)

pH

-4
-2

-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

log 10Ionic Strength (mol/kgw)

Figure 2‑4. Distribution of groundwater compositions at 2,000 years in the temperate phase of repository
evolution. Data are given for total carbonate versus pH (left hand side), and total carbonate vs. ionicstrength (corresponding to the data calculated by /Salas et al. 2010/ and stored on SKB’s trac database).
The data are visualised in scatterplot form (top) and as a smoothed 2D histogram (bottom).

TR-10-50

19

-2.4

-2.4

-2.6
-2.8
-3
-3.2
-3.4

-2.6
-2.8
-3
-3.2
-3.4

-3.6

-3.6

-3.8

-3.8

-4
6

log 10CO2(mol/kgw)
3 totallog 10CO2(mol/kgw)
3 total

-2
-2.2

6.5

7

7.5

8

pH

8.5

9

9.5

-4
-2

10

-2

-2

-2.2

-2.2

-2.4

-2.4

log 10CO2(mol/kgw)
3 totallog 10CO2(mol/kgw)
3 total

-2
-2.2

-2.6
-2.8
-3
-3.2
-3.4

8

pH

8.5

9

9.5

10

-1.8

-1.6

-1

-0.8

-0.6

-0.4

-0.2

0

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

-3.2
-3.4

-3.8
7.5

-1.2

-3

-3.8
7

-1.4

log 10Ionic Strength (mol/kgw)

-2.8

-3.6

6.5

-1.6

-2.6

-3.6

-4
6

-1.8

-4
-2

log 10Ionic Strength (mol/kgw)

Figure 2‑5. Distribution of groundwater compositions at 9,000 years in the temperate phase of repository
evolution. Data are given for total carbonate versus pH (left hand side), and total carbonate vs. ionicstrength (corresponding to the data calculated by /Salas et al. 2010/ and stored on SKB’s trac database).
The data are visualised in scatterplot form (top) and as a smoothed 2D histogram (bottom).

2.2.2 Evolution of groundwater chemistry over a glacial cycle
The evolution of groundwater chemistry over time is described in some detail in the Main reportand only a brief overview of the most salient features is given here. Over a glacial cycle the changes
in groundwater chemistry are driven by different processes: infiltration of meteoric water in combination with land uplift during the temperate period (interglacial), alternating pulses of dilute, glacial
melt water and deep saline groundwater during the glacial advance and retreat (periglacial), andnearly stagnant conditions when a stable ice sheet exists over the repository. During various parts ofthe glacial phase, permafrost may also extend to a significant depth in the rock and prevent the flowof water.
The temperate period is characterised by a slow freshening of the groundwater surrounding therepository over many thousands of years under the influence of infiltrating meteoric water. During
this period, the groundwater evolves towards lower pH levels and higher carbonate concentrations.
This is also likely to result in a steady increase in the redox potential over time. The intruding
meteoric water displaces saline water in the fracture system and mixes by diffusive exchange withstagnant water in the rock matrix.
During the ice-front advance, the large hydraulic gradient near the advancing front of the ice marginresults in dilute glacial meltwater being forced to great depth in the rock before exiting downstreamof the advancing front although still short of the repository location. The meltwater comes in partfrom water under the ice itself held in a liquid state by isostatic pressure and partly from waterdraining from the surface of the ice through moulins near the ice margin. The disturbance in hydrogeological conditions displaces the existing saline water in the fracture system forcing it downwards

20

TR-10-50

and forwards. This results in saline upconing of deep brine groundwater to shallower depths in therepository vicinity. As the ice margin approaches and passes over the repository, the flows are partly
reversed and meltwater may penetrate the repository environment. Since the hydraulic connectivityof the fracture system and conductivity of the rock is very heterogeneous, some recharge flowpaths
experience very large and rapid changes in groundwater chemistry, whereas others are hardly
affected. Generally it is the flowpaths characterised by high Darcy fluxes and low F-factors thatexperience the greatest changes.
After the ice margin has passed, the flow gradually decreases until at some point nearly stagnant
conditions are achieved owing to the extremely low hydraulic gradients under the main part of theice sheet and the influence of permafrost, which reduces inflows to the groundwater system. The
large mass of ice on top of the land mass simultaneously pushes down on the crust, which has an
influence on hydraulic conductivity of the rock. During this phase of the repository evolution, flows
are much reduced relative to the temperate phase and flowpaths are longer to the discharge locations
downstream of the ice front. Salt stored in the rock matrix begins to diffuse back out into the diluted
fracture water and slowly restores salinity in the fracture system.
As the ice front begins to retreat, a similar sequence of processes is set in motion although in reverse.
In this case, the newly re-established saline groundwater in the fracture system is rapidly flushed
out by the forced intrusion of meltwater in the vicinity of the ice front. After the retreating ice front
passes over the repository location, additional episodes of saline upconing may occur. After the ice
front has retreated even further, the saline conditions typical of the temperate period becomes slowly
re-established. At this time, the isostatic load of the ice will depress the crust and result in the repository site being inundated with marine water and under sea level.
The subsequent uplift of the crust due to glacial rebound will slowly change the shoreline locationand topographic elevation of the land relative to the sea. The slowly changing topographical conditions and shoreline results in the repository eventually becoming an inland location. The slowly
evolving hydrogeological situation then results in a gradual freshening of groundwater in the repository environment due to infiltrating meteoric water and a return to temperate conditions.
Although this paints a broad picture of the main sequence of events characterising an individualglacial cycle, it is important to also consider that such cycles can be expected to reoccur with apredetermined periodicity and possibly deepening intensity with time as described in the Climate
report. There may also be transients (e.g. stadial and interstadial periods) and shorter glacial/interglacial periods over the total 120 ka timespan of the full glacial cycle. In the radionuclide transport
calculations, however, a much simpler tableau of glacial evolution is considered as indicated in
Figure 2‑1.

2.3

Background levels of naturally occurring radionuclides

A number of nuclides belonging to naturally occurring U-series decay chains are present in the
groundwater at Forsmark. To place in context the mean annual effective doses calculated later inthis report, it is useful to have an estimate of the corresponding dose from the naturally occurring
radionuclides.
Activities of U-238, U-234, Th-230, Ra-226, and Rn-222 (belonging to the U-238 decay chain)
have been measured during the site investigations as well as Th-232, Ra-228, Th-228 (belonging to
the Th-232 decay chain), and U-235 /Laaksoharju et al. 2008/. If one excludes Rn-222, the largest
contributors to the natural background activity in Forsmark groundwater are Ra-226, U-238, andU-234. These nuclides are shown in Figure 2‑6 as a function of sampling depth. Generally it isfound that Ra-226 activities are greatest at depth with a slight decrease towards the surface. The
opposite behaviour is observed for U with the lowest activities found at depth with a steady increase
towards the surface. Both these trends are in broad qualitative agreement with the understanding ofgroundwater chemistry at the site. The groundwater activity of Ra, for example, is well correlatedwith TDS (more so with Ca concentration) indicating a geochemical control by way of ion-exchangeor possibly solid solution involving calcite. Barite, which forms solid solutions with Ra, does notappear to be present in significant amounts in Forsmark fracture minerals, an observation which

TR-10-50

21

100

Background Activity (Bq/l)

10

1

226Ra
238U
234U

0.1

0.01

0.001
-1000

-900

-800

-700

-600

-500

-400

-300

-200

-100

0

Elevation (masl)

Figure 2‑6. Typical background activities of the main naturally occurring radionuclides of interest in
groundwater at the Forsmark site /Laaksoharju et al. 2008/ (numerical values are taken from the SKB
SIMON database). Rn-222 is neglected on account of its gaseous form and consequent rapid dilution in
the biosphere (it is also neglected in the calculation of far-field dose rates calculated in SR‑Site owing to
its low relative contribution to radiological risk).

is consistent with the only weak correlation between dissolved Ba and Ra concentrations at thesite. The decreasing trend of U activities with depth appears to be coupled to the decreasing redox
potential and carbonate concentration at increasing depths. Most sampled groundwaters at Forsmark
have a U-234/U-238 isotope ratio between 2–3 /Sandström et al. 2008/.
Assuming that the arithmetic average of sampled nuclide activities can be taken to be approximately
representative of the situation existing at 2000 AD in the corrosion scenario (central case), a com­­parative estimate of far-field release rates arising from these naturally occurring nuclides can be
made. The release rate (Bq/yr) of naturally occurring nuclides can be estimated by multiplying
the arithmetic average of the measured groundwater activities Ai (Bq/m3) with the discharge fluxvex (m3/m2yr) and surface area aex (m2) for release:N i ≈ Ai ⋅ vex ⋅ aex									2‑1

Since the naturally occurring background of dissolved nuclides is not restricted to the local or eventhe regional scale model area, the total release rate depends on the landscape surface area assumed
to make the calculation. In order to make a relevant comparison with the anthropogenic dose
rates, some reference area needs to be assumed. For the purposes of SR‑Site, the most appropriate
reference area is the predicted area for hypothetical nuclide release from the repository. The particle
tracking calculations used to estimate surface exit locations in the central case are used to estimate
this area in this analysis. The surface exit locations at 2000 AD for all realisations of the hydrogeological semi-correlated case (cf. Table 4-1) are shown in Figure 2‑7. The relevant surface area wasestimated by binning the particle release locations into a 2D histogram with 40 m × 40 m cells andcalculating the area of occupied cells.
The arithmetic mean of the groundwater activity is deemed an appropriate measure of groundwater
activity since the total release of nuclides represents a summation of groundwater activities originating from many different flowpaths. In accordance with this, the standard error of the mean activity

22

TR-10-50

6.7035x 10

66.70356.70256.7025

6.702

6.702

6.70156.7015

NS

6.703

NS

6.703

6.701

6.7005

6.7

6.7

6.6995

6.6995

6.699

6.699

1.6305 1.631

1.6315 1.632

1.6325 1.633

WE

1.6335 1.634

1.6345
x 10

6

6

6.701

6.70056.6985
1.63

x 10

6.69851.63

1.6305 1.631

1.6315 1.632

1.6325 1.633

1.6335 1.634

Figure 2‑7. Particle exit locations at 2000 AD for all realisations of the hydrogeological semi-correlatedcase (left). The approximate footprint of particle release locations for all simulations taken together as an
ensemble is also shown (right) where particles are sorted into a 2D histogram of 40 m × 40 m cells. The
convex hull of the full set of release locations is also shown as a reference (blue outline).

is deemed the relevant measure of uncertainty. The individual realisations of the hydrogeologicalmodel, however, may be considered as all equally valid with regard to estimated release area.
This means that the variance of the estimated area between realisations must be treated as a data
uncertainty rather than a measure of variability, given that in reality there should be only one true
value of the release area for a given set of boundary conditions.
Since the release area estimate is based on only a limited number of realisations, it is necessary
to calculate an expanded range of uncertainty that explicitly takes the limited sample size into
account. If it is assumed that the uncertainty of the estimated area can be modelled as a lognormally
distributed variable, then the correct form of the expanded uncertainty range is given by the student-t
distribution. A lognormal measure of the uncertainty is considered appropriate in this case since thevariation of the particle release area between realisations is sufficiently large that it would imply
negative areas if treated as a normally distributed uncertainty. Based on nine realisations of thehydrogeological model, the release area and its expanded uncertainty range are therefore estimatedto be (1.9±1.7)·106 m2. If, on the other hand, the ensemble of particle release locations from all
realisations were to be considered together, the estimated release area would be 4.1·106 m2.
The average groundwater discharge in a 5×5 km area surrounding the Forsmark site is given by/­Follin et al. 2007/ as roughly 2.6 mm/yr at an elevation of –100 m. This, however, is only a very
approximate estimate since the upward discharge varies with depth and one ideally would need toconsider that the discharge rate to the surface consists of water originating from different depths
representing different advective recharge histories and most likely different hydrochemical compo­
sitions (see Figure 2‑8). A large proportion of the upwards flow in the upper 100 m, for example,
derives from local flow cells that do not necessarily penetrate very deeply into the bedrock andtherefore may not carry representative amounts of naturally occurring nuclides. Based on the depth
dependent discharge fluxes calculated by /Follin et al. 2007/, less than 1% of the upward water flux
at an elevation of –100 m originates from repository depth and only about 13% originates fromelevations less than –200 m. Water sampled at elevations above –100 m is generally more dilute thangroundwaters sampled at greater depths owing to the larger turnover of water in the shallower flow
cells. Assuming, however, that the average groundwater activity measured at the site and depicted
in Figure 2‑6 is reasonably representative of the upwelling groundwater at an elevation of about–100 m then an approximate order of magnitude estimate of the natural background nuclide flux canbe made. This assumes that none of the naturally occurring activity originating from shallow flow
cells contributes in a meaningful way to the overall nuclide flux.

TR-10-50

1.6345
x 10

WE

23

6

7.68 mm/y

7.50 mm/y-10 m
3.83 mm/y

3.45 mm/y-50 m
2.57 mm/y

1.86 mm/y-100 m
0.95 mm/y

1.03 mm/y-150 m0.27 mm/y

0.34 mm/y-200 m0.17 mm/y

0.26 mm/y-250 m

0.09 mm/y

0.21 mm/y-300 m0.03 mm/y

0.01 mm/y-400 m
0.02 mm/y

0.01 mm/y-500 m0.01 mm/y

0.0 mm/y-600 mFigure 2‑8. Average vertical groundwater fluxes over a 5 km × 5 km surface area at different elevations
at the Forsmark site as calculated by /Follin et al. 2007/. Since the surface discharge represents a mix
of groundwaters with different advective histories, the upward flux at –100 m is chosen arbitrarily as
being approximately representative of water carrying the average nuclide activity based on the data in
Figure 2‑6.

Table 2‑2 gives the mean groundwater activity (Bq/m3), the estimated mean flux (Bq/m2yr), andestimated mean release of natural background activity (Bq/yr) calculated for U-238, U-234, andRa-226 at the Forsmark site. Since the mean release (Equation 2‑1) is equal to the product of several
variables with either normal or lognormally distributed uncertainties, it also has a lognormal uncertainty distribution. The estimated mean release and associated confidence interval given in Table 2‑2
implicitly assumes this.
Table 2‑2 Summary of natural background activities of naturally occurring radionuclides (U-238,
U-234, and Ra-226) estimated flux to the surface, and total release rate within the same releasefootprint as the semi-correlated case far-field transport calculations.

U-238
U-234
Ra-22624

Mean activity(Bq/m3)

Mean flux(Bq/m2yr)

Mean release(Bq/yr)Mean

94.1±31.5(2.42±0.81)·10–1(4.7±4.6)·105

CI (95%)47 – 1690.12 – 0.43

5.73·104 – 1.68·106

Mean

243±78(6.24±2.02)·10

CI (95%)125 – 429

0.32 – 1.1

1.52·105 – 4.31·106

Mean

1,530±325

3.94±0.84(7.61±7.02)·106

CI (95%)995 – 2,260

2.56 – 5.81

1.18·106 – 2.62·107–1(1.21±1.18)·106

TR-10-50

2.4

Transport and retention processes

The migration of radionuclides in fractured rock is controlled by a variety of processes including
advection and dispersion in water flowing through fractures, diffusion in the water in the pore spaceof the rock matrix, sorption processes, mineral precipitation/dissolution reactions, and interactions
with colloids /Geosphere process report/. The Geosphere process report further identifies thedominant mechanisms as advection/dispersion in flowing water in fractures, diffusion in the waterfilled pore space of the rock matrix, and sorption onto mineral grains. These processes are generally
modelled using the advection dispersion equation in the fractures coupled with a Fickian model
for matrix diffusion and a linear model for sorption in the rock matrix. Similar processes govern
the movement of radionuclides out of the canisters and through the buffer material with the maindifference being that precipitation/dissolution may be important within the canister for some radionuclides. Generally, these modelling simplifications of what is in reality a complex, coupled reactive
transport process are justified on the basis that the transported radionuclides are extremely dilute,
trace components within the groundwater /Geosphere process report/. However, a few neglected
processes require some additional discussion, which is given in the following subsections.

2.4.1 Non-linear sorption processes
A number of different non-linearities can influence the retardation of transported radionuclides. The
most direct effect is intrinsic non-linearity where sorptivity is limited by the finite number of bindingsites available for sorption. This is most frequently formalised in the Langmuir isotherm where theamount of solute sorbed as a proportion of the aqueous concentration decreases with increasing surface loading up to a maximum monolayer sorption capacity. Where there are multiple surface sites
with different reactive characteristics and maximum sorption capacities, the Freundlich isotherm
is sometimes used as an approximation. Multicomponent, Langmuirian non-linear behaviour also
arises where there is competition between different groundwater constituents for a limited numberof binding sites. These types of intrinsic non-linearities are explicitly represented in thermodynamic
models of ion exchange and surface complexation.
In many cases, the concentrations of migrating radionuclides are sufficiently low that intrinsic
non-linearities do not need to be considered and conditional Kd values appropriate for extremely
dilute nuclide concentrations can be assumed. This is frequently the case for radionuclides withstrong solubility controls governing the near-field source term. In these cases, although retention in
the immediate vicinity of the source may feature strongly non-linear characteristics a transition toapproximately linear behaviour is expected after a short migration distance as the release is dilutedby the retarded advective transport. The retardation effect achieved over the bulk of the subsequentmigration path can then be characterised by approximately linear sorption over the relevant concentration range, all other things being equal.
Even when nuclide concentrations are not dilute, the conditional Kd value may be considered effectively constant if the approximately static background concentration of naturally occurring isotopes
establishes the appropriate region of the non-linear sorption isotherm where the conditional Kd
value is evaluated. This is particularly relevant for radioelements such as Cs, Ra, U, Sr, Th, and to alesser extent the naturally occurring rare earth counterparts of the trivalent actinides and lanthanides.
Provided the transported concentration of anthropogenic nuclides does not exceed the backgroundlevels, the assumption of sorption linearity is an acceptable approximation.
Intrinsic non-linearity is considered relatively straightforward to handle since it is always possible
to establish a relevant concentration range over which a conditional Kd value can be defined thatpessimistically overpredicts radiological consequences. More important non-linearities, however,relate to the impact of variable groundwater chemistry on the magnitude of the conditional Kd value.
Selection of an appropriate Kd value therefore requires careful consideration of the ranges of groundwater chemistry that might be encountered and their spatial and temporal variability. As outlined
in /Crawford 2010/ the Kd data supplied for SR‑Site are associated with large uncertainties. A large
proportion of this uncertainty relates to variable or uncertain contact solution compositions used inlaboratory sorption measurements and how these relate to projected groundwater compositions in
SR‑Site.

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25

At present it is not possible to quantitatively relate changes in sorptivity with evolving groundwaterchemistry for many of the safety relevant nuclides. This is largely due to the lack of sufficiently
detailed, multidimensional data sets of unambiguous sorption data for granitic rock types. Also, at
any given time the concentration of major groundwater constituents can vary by two or more ordersof magnitude throughout the repository volume. As outlined in Section 2.2.1 and 2.2.2 the spatiallyvariable groundwater compositional profile also evolves over time under the influence of the prevailing hydrogeological boundary conditions. Fast flowpaths featuring low F-factors can be expected
to exhibit greater temporal changes in chemical composition than slower flowpaths featuring higher
F-factors. Since groundwater chemistry is not resolved on the level of individual flowpaths throughthe rock, a detailed knowledge of how groundwater composition influences the conditional Kd value
would not necessarily give narrower bounds of uncertainty for radionuclide transport and it is only
possible to speculate on the average impact of changing groundwater compositions throughout
the repository volume as a whole. More detailed discussion concerning the neglect of non-linear
sorption processes and its justification for the purposes of SR‑Site in the presence of evolving
groundwater chemistry can be found in /Crawford 2010/.

2.4.2 Precipitation and dissolution in the far field
Although precipitation and dissolution processes are considered to be of central importance fordetermining the source terms for solubility limited nuclides in the spent fuel canisters, theseprocesses are typically disregarded in the far-field transport modelling. Over long time scales it isconceivable that pure phase precipitates of solubility limited nuclides will form outside the canister
deposition holes in the near field. The further mobilisation of these nuclide enrichment zones along
a migration path is limited by the groundwater flow and solubility equilibria governing the aqueousconcentration of the nuclide in contact with the pure phase. For the redox sensitive radioelements,
U in particular, the groundwater redox buffering effect arising from the presence of the enrichment
zone itself may result in self-limiting transport dynamics which could conceivably give rise to rollfront behaviour not dissimilar to that observed in some natural analogues. Immediately downstreamof such mineralisations, however, the concentration of the nuclide will be diluted to below thesolubility limit by various other retention processes and no longer controlled by pure phase solubility
equilibrium. In these locations, the aqueous concentration will instead be governed by solid solutions
with fracture filling minerals (discussed in Section 2.4.3) as well as ion exchange and surface com­
plexation with fracture minerals. These processes may be considered to occur in addition to the
diffusion and sorption on rock matrix microsurfaces assumed in transport calculations. This is aparticularly relevant consideration if the abundance of potential co-precipitating fracture minerals
along a flowpath is such that they have a lower overall retention capacity than the sorptive surfacesthat can be effectively equilibrated in the rock matrix on the timescale of transport (as the scoping
calculations detailed in Appendix B indeed suggest).
The retardation effect that these retention processes impose on the migrating nuclide causes
further dilution of the nuclide until it reaches a concentration whereby sorption can be regarded as
approximately linear both within the rock matrix and the advective pore space. This hierarchy ofretardation processes and the continuous transition from highly non-linear sorption to approximately
linear behaviour over a short distance from the repository is one of the main justifications for theassumption of intrinsically linear sorptivity in the far field as already outlined in Section 2.4.1. In
an overwhelming majority of studied cases, the natural analogues used to support understanding ofradionuclide migration behaviour in the near field and far field exhibit these characteristics outlined
above (i.e. a hierarchy of processes active in different parts of the geosphere with increasing distancefrom the spent fuel analogue). Specific examples of these used in support of the corrosion scenario
are discussed in more detail in the Main report.
The background concentrations of naturally occurring nuclides and non-active counterparts ofanthropogenic radioelements, however, in many cases may be governed by solubility equilibria(in particular, U and Th). Deep within the rock matrix, recoil processes due to U-series radioactive
decay lead to the accumulation of various U, Th, and Ra isotopes in the pore water until secularequilibrium is attained. Microprecipitates of secondary U(IV) and Th(IV) phases are likely to govern
U and Th concentrations in the aqueous phase deep inside the rock matrix. On the other hand,and assuming that solid solution forming minerals such as calcite and barite are absent from therock matrix, the pore water concentration of Ra is likely to be governed by ion-exchange sorption.
26

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Porewater concentrations of rare earth element (REE) counterparts of the trivalent lanthanides andactinides are unlikely to be pure phase solubility limited owing to their extremely low concentrations. The background concentrations of these solutes are therefore largely expected to reflect theeffect of surface complexation sorption involving mineral surfaces in the rock matrix.
In the immediate vicinity of fracture surfaces, solubility limiting phases may be absent in which casethe formation of solid solutions with ferric oxyhydroxides and hematite as well as ion-exchange/
surface complexation sorption will instead control U and Th availability (concentrations of REE arealso expected to be influenced by this). Near the fracture surfaces, however, the interplay between
redox buffering due to the weathering of ferrous minerals and the redox potential of flowing groundwater (together with the groundwater pH and pCO2) govern the redox status of the predominant formof U in the groundwater. Amongst the redox sensitive radionuclides, U is particularly sensitive togroundwater composition and there is considerable evidence from U-series disequilibrium that U has
been mobilised as U(VI) and re-deposited as relatively immobile U(IV) many times in the Forsmark
fracture system over geological timescales (≥ 1 Ma) /Sandström et al. 2008/.
The solubility equilibria governing the aqueous phase concentrations of U and Th deep within therock matrix coupled with additional surface reactive processes and matrix diffusion near and at thefracture surfaces sets the relevant groundwater concentration range for conditional Kd evaluationeven though precipitation and dissolution of these solutes is not directly modelled in far-fieldtransport calculations.

2.4.3 Sorptive interactions with fracture minerals
Secondary minerals in the form of fracture coatings lining the advective flow space are expected tosorb migrating nuclides (both naturally occurring and anthropogenic). Although the term sorption
has been used consistently throughout the SR‑Site reports to refer specifically to ion exchange andsurface complexation, the description is extended here to also include surface reactions involving
solid solutions with minerals such as calcite, barite, and ferric oxides. There are many different
types of minerals present in fracture coatings at the Forsmark site. The most important of these froma perspective of potential nuclide retention, are calcite, hematite, chlorite, and other clay minerals(referred to here as a group although including illite, smectites, and various mixed layer clays).
Chlorite and clay minerals are expected to sorb nuclides by ion exchange and surface complexationinteractions whereas calcite and hematite can additionally form solid solutions with migrating
nuclides. Although precipitation/dissolution equilibrium is typically neglected in safety assessmenton account of the extremely low concentration of transported nuclides (outlined already in Section
2.4.2), solid solutions are extremely relevant for far-field transport processes in the geosphere on
account of the fact that, unlike pure phase equilibria, such processes are active already at very low
nuclide concentrations.
Generally, the retention processes involving fracture-filling minerals are considered to give anadditional transport retardation effect over and above that estimated by the customary handling ofretardation by matrix diffusion and sorption on rock matrix microsurfaces. For the central case where
static groundwater compositions and flow trajectories are assumed, it is pessimistic to neglect these
additional retardation processes because they only serve to lower far-field doses. Throughout theglacial cycle, however, groundwater chemistry is expected to change and in certain situations theneglect of the additional retention processes in the fracture minerals could potentially have negative
radiological consequences for the far-field doses. This has been handled in SR‑Site by screening
calculations of possible changes in solute retention on fracture filling materials as a function of
evolving groundwater chemistry, as discussed in Section 2.4.4.

2.4.4

Consequences of neglected retention processes and temporal changes
in groundwater chemistry
The neglect of sorption on fracture minerals lining the advective pore space is generally expected to
be a cautious assumption given that retention is relatively stronger in the fracture minerals than in
the rock matrix. If fracture surface retention processes were to be included in the safety assessment
modelling this would give additional retardation of the early breakthrough of transported radionu-

TR-10-50

27

clides. The fracture minerals that would be expected to contribute most to the enhanced retardation
are chlorite and other clay minerals, calcite, and (although to a lesser extent due to low abundance)
hematite.
Since the quantity of such minerals lining the fracture space is limited, however, the retention
capacity is small and only significant for flowpaths where the retardation effect arising due to matrix
diffusion and sorption on rock matrix microsurfaces is weak. On account of the fracture minerals
being distributed in a thin layer that is in direct contact with the flowing water, equilibrium sorption
can be reasonably assumed for ion-exchange and surface complexation reactions on the timescale oftransport.
Based on the statistical abundances of fracture minerals hosted in flow-bearing fractures at Forsmark/Löfgren and Sidborn 2010/, estimates have been made of the additional retardation effect arising
due to equilibrium sorption on fracture minerals. On average, there are about 6–14 g of calcite,
2–5 g of chlorite, and 1–2 g of clay minerals per square metre of fracture area in typical flow bearing
fractures at Forsmark. Given that the matrix retardation is approximately proportional to the squareof the F-factor, the additional retardation due to sorption on fracture minerals is mostly negligible
for flowpaths featuring F-factors greater than 104–105 yr/m. Although only an estimate, this range
may be considered to be an approximately representative transition region that depends additionallyon the strength of sorption both in the rock matrix and on fracture minerals. For flowpaths featuring
very low F-factors, on the other hand, nuclide retention on fracture minerals is expected to have amuch larger impact on the overall transport retardation (for details see Appendix B). For this reason,
the neglect of fracture mineral retention processes is considered a pessimistic assumption in thecentral case transport modelling for SR‑Site.
This reasoning assumes, however, that the evolving groundwater composition does not change insuch a way that might lead to a sudden pulse-like release of surface sorbed nuclides under elevatedflow conditions, which might occur periodically during a glacial cycle. In a model without explicit
consideration of fracture mineral retention, nuclides are sequestered to a greater extent in therock matrix rather than in association with the fracture minerals where they might be more easily
mobilised. For some nuclides this might lead to far-field dose rates being underestimated.
In order to address this issue, consideration has been given to the potential for remobilisation to
occur during the glacial IIa (saline upconing) and IVa (glacial meltwater penetration) time domains.
These events are thought to be representative of the largest deviations expected from the conditions
established during the temperate phase of repository evolution, which comprises the central case.
These time domains are also characterised by significantly higher flowrates and lower F-factors than
the temperate phase hydrogeological conditions. Cross plots of the main hydrochemical parameters
influencing sorption are shown in Figure 2‑9 as an aid to understanding relative changes in sorptivityof nuclides at different times in response to evolving groundwater chemistry.
Here, the impact of changing groundwater chemistry is considered simultaneously for phyllosilicate
fracture minerals (i.e. chlorite and clay) and the rock matrix since the primary sorption mechanismsof ion-exchange and surface complexation are the same in each case. A change in groundwater composition, for example, that gives rise to a decrease in rock matrix sorptivity might also be reasonably
inferred to give a similar although not necessarily proportionate decrease in sorptivity for fracture
filling minerals that feature similar sorption mechanisms.
Fracture calcite, on the other hand, must be considered separately since it may form solid solutions
with migrating nuclides. Since calcite does not typically occur within the rock matrix itself, thisprocess is not considered to be a relevant mechanism of nuclide retention in the rock matrix andis therefore not modelled. In order to properly account for the full range of retention processes
that might occur in association with fracture minerals, however, one would therefore also need toconsider the possible role of solid solution formation with calcite (and possibly barite in the case of
Ra-226). For this reason, detailed scoping calculations have been made on the impact of evolving
groundwater chemistry on retention by solid solution (see Appendix B).

28

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-2
-2.2

-2.4

-2.4

-2.4

-2.6

-2.6

-2.6

w

log 10CO2(mol/kgw)
3 total-2-2.2

log 10CO2(mol/kg )3 totallog 10CO2(mol/kgw)
3 total

-2
-2.2

-2.8
-3
-3.2
-3.4

-2.8
-3
-3.2
-3.4

-3.4

-3.6

-3.6

-3.8

-3.8

-3.8

-4

-4
-4

6

6.5

7

7.5

8

8.5

9

9.5

10

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

-4
-400

0

-2

-2

-2.2

-2.2

-2.4

-2.4

-2.4

-2.6

-2.6

-2.6

w

log 10CO2(mol/kgw)
3 total

-2

-2.8
-3
-3.2
-3.4

-2.8
-3
-3.2
-3.4

-3.6
-3.8

8

8.5

9

9.5

10

pH

-4
-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

-4
-400

0

-2
-2.2

-2.4

-2.4

-2.4

-2.6

-2.6

-2.6

-3.2
-3.4

log 10CO2(mol/kgw)
3 total-2-2.2

log 10CO2(mol/kgw)
3 total

-2

-3

-2.8
-3
-3.2
-3.4

-3.6
-3.8

-4
6

-4
-4

8.5

9

9.5

10

-3.5

-3

-2.5

-2

-1.5

log 10Ionic Strength (mol/kgw)

-200

-150

-100

-50

0

-150

-100

-50

0

-3.4

-3.8
8

-250

-3

-3.8

pH

-300

-3.2

-3.6

7.5

0

-2.8

-3.6

7

-50

Eh (mV)

-2.2

6.5

-350

log 10Ionic Strength (mol/kgw)

-2.8

-100

-3.4

-3.8
7.5

-150

-3

-3.8
7

-200

-3.2

-3.6

6.5

-250

-2.8

-3.6

6

-300

Eh (mV)

-2.2

-4

-350

log 10Ionic Strength (mol/kgw)

log 10CO2(mol/kg )3 totallog 10CO2(mol/kgw)
3 total

-3
-3.2

-3.6

pH

log 10CO2(mol/kgw)
3 total

-2.8

-1

-0.5

0

-4
-400

-350

-300

-250

-200
Eh (mV)

Figure 2‑9. Comparative plots of groundwater master variables influencing sorption. Data are shown forthe hydrochemical reference case at 3,000 years (bottom row), glacial IIa case (centre row), and glacial
IVa cases (top row) in the form of 2D histogram plots (log10 space). In each case the total carbonate
concentration is plotted versus pH (left), ionic strength (centre), and Eh (right). The plots correspond to
the data calculated by /­Salas et al. 2010/ and stored on SKB’s trac database.

Since the different sorption mechanisms respond in different ways to evolving groundwaterchemistry, they are each considered separately in the following discussions. The overall impact ofchanging groundwater chemistry on far-field dose rates, however, needs careful consideration of all
relevant sorption mechanisms simultaneously in the context of the prevailing hydrogeological situation. This must also be considered in the context of the inventory of nuclides that are actually sorbed
by fracture minerals relative to that sequestered in the rock matrix. Since the fracture minerals havea limited capacity for nuclide retention relative to the rock matrix, the impact of remobilisation is
generally not expected to be large even in cases where it might be reasonably expected to occur.

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29

Impact of evolving groundwater chemistry on ion-exchanging nuclides

For nuclides that sorb by an ion-exchange mechanism (or whose sorption is otherwise strongly
influenced by ionic strength), Kd values are chosen to reflect the most unfavourable groundwatercompositions expected. The groundwater compositions existing at 2,000–3,000 years during thetemperate time domain represent the peak groundwater salinity. Since sorption of these nuclides isnegatively affected by elevated ionic strength, the hydrochemical conditions existing at this time are
therefore used as a basis for the recommended rock matrix Kd values in the central case. For theseparticular solutes (Cs, Sr, and Ra), groundwater chemistry transfer factors are calculated with theaid of a simplified ion-exchange model to account for ionic strength effects during this time domain/Crawford 2010/. In the case of Ni, which exhibits a weak ionic strength dependency, groundwaterchemistry correction factors are calculated on the basis of a power law regression model relating
apparent Kd with ionic strength. Although slightly higher peak salinities are expected during theglacial IIa domain, this only occurs during brief transient periods and is not considered representative of the conditions prevailing during most of the repository evolution.
The correction implied by the chemistry transfer factor is very small relative to the level of overall
uncertainty in the uncorrected Kd data sets. Counterintuitively, the solutes that are most strongly
influenced by ionic strength on account of their weak sorptivity are also given smaller correction
factors than more strongly sorbing solutes that are less affected by ionic strength. This is due to thelarger underlying data uncertainty in the case of the more weakly sorbing solutes which tends todrown out the systematic trends that can be quantitatively related to evolving groundwater salinity.
This should not be taken to mean that ionic strength is less important for the weakly sorbing solutes,
but rather that the effect is more difficult to quantify for weakly sorbing solutes relative to the morestrongly sorbing solutes.
It must also be remembered that since the changes in groundwater composition are not resolved on
the level of individual migration paths, extrapolation to the groundwater situations existing at different times must consider the statistical distribution of spatially variable groundwater compositions
throughout the entire repository volume which, in itself, introduces additional statistical dispersion
in the calculation of Kd uncertainty ranges. It is therefore important when discussing the impactof evolving groundwater chemistry to distinguish between the true impact of ionic strength on thesorption process as it actually occurs from the impact that is statistically quantifiable for modelling
purposes. Changes in groundwater salinity are therefore likely to have a much more profound local
impact on sorptivity than has been quantified in the Kd recommendation. Since the Kd data arerecommended for relatively saline conditions, this means that the strength of sorption will be
pessimistically underestimated during the bulk of repository evolution.
Higher salinities encountered during the glacial IIa domain could result in a mobilisation of nuclides
that are sensitive to ionic strength and give far-field dose rates higher than predicted by the transportmodelling. Essentially, this would mean that radionuclide mass flux during the low-salinity phasesof repository groundwater evolution would be overestimated and the radionuclide mass flux during
the transitory saline glacial IIa phase would be underestimated. The nuclide most strongly influenced
by this (and which has the largest potential impact on far-field dose rates) is Ra-226. However,the landscape dose conversion factor for Ra-226 is almost 3 orders of magnitude lower during theglacial periods compared with the interglacial period /Avila et al. 2010/, thus easily overwhelming
any potential effects of underestimating salinity during the glacial IIa period.
Although not strictly considered to be an ion-exchanging solute, Ni-59 might also be affected by
evolving salinity on account of its apparent sensitivity to ionic strength. Given that Ni-59 contributes
much less to far-field dose rates, however, any variation in sorptive retention due to evolving
groundwater composition is not expected to make a meaningful contribution to the overall pictureof risk. Moreover, the landscape dose factor for Ni-59 is more than 3 orders of magnitude smaller
during the glacial period as compared with the interglacial period /Avila et al. 2010/.
During the glacial IVa period, decreased groundwater ionic strength would typically result inenhanced sorptivity both in the fracture minerals and in the rock matrix, which is pessimisticallyneglected.

30

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Impact of evolving groundwater chemistry on surface-complexing nuclides

For nuclides that sorb by way of a surface complexation mechanism, it was judged not feasible atthis time to make quantitative predictions of how changing groundwater chemistry might affectthe magnitude of sorption. This is largely due to a lack of suitable mechanistic models describing
the sorption of nuclides in association with granitic rock. At the same time, it is acknowledged that
relatively sophisticated surface complexation models do indeed exist for sorption of nuclides inassociation with fracture filling minerals such as illite and smectite. Similarly to the quantificationof ionic strength effects, however, even a very detailed mechanistic model would be unlikely togive a much reduced span of Kd uncertainty owing to the large spatial variability of groundwatercompositions existing throughout the repository volume at any given time. In spite of this, it is still
possible to make a relatively detailed qualitative account of how changes in groundwater chemistry
might affect sorptivity based upon the well-known behaviour of model systems comprised of single
minerals.
For surface complexing nuclides, groundwater pH, carbonate concentration (or pCO2), and redox
potential (Eh) are considered to be the most important master variables influencing sorption. In
general, lower pH levels and higher carbonate concentrations are expected to result in reduced
sorptivity of cationic nuclides by way of changes in the relative abundance of negatively charged
surface binding sites as well as increased aqueous phase complexation by carbonate. For anionicnuclides one would generally expect the opposite behaviour with regard to pH changes (although
this mostly concerns hematite, which has a relatively high point of zero charge). In most cases,
however, the sorption of anions is negligible owing to a higher abundance of negative surface charge
at prevailing groundwater pH and because their sorption is also subject to competition from otheranionic groundwater constituents.
Redox potential also has a very strong influence on the predominant state of the redox sensitive
nuclides that mostly sorb by surface complexation mechanisms. Higher Eh can imply a transition
from relatively immobile reduced forms to more mobile oxidised forms that, in some cases, could
imply the possibility of remobilisation during the glacial IVa period. Carbonate also plays animportant role in redox speciation by altering the threshold at which transitions between predomi­
nantly reduced and oxidised forms can take place. Of the redox sensitive solutes, Pu and Np are notexpected to be influenced by this on account of the Eh being well below their respective thresholds
for transition from reduced to oxidised speciation for all conceivable groundwater situations
predicted during the glacial cycle. U and Tc, on the other hand, may experience a transition to
predominantly oxidised speciation during the glacial IVa period. The predominant redox speciationof U, however, is sufficiently uncertain even during the temperate time period that both oxidised andreduced speciation cases are propagated in SR‑Site. This is due to the fact that the Eh and carbonate
concentration ranges predicted during the temperate phase are such that the predominance of the
U(IV) form cannot be strictly guaranteed at all times throughout the repository volume.
Although less mobile, the reduced U(IV) form is considered to be the more pessimistic assumption
in the central case since it represents a more concentrated secondary source of the Ra-226 daughter
nuclide. As already noted for Ra-226, any changes in the relative sorptivity of U which might giverise to remobilisation must also be considered in the context of the lower landscape dose factors
during the periods of remobilisation. For this reason remobilisation scenarios affecting U transport
in the far field are not considered to be of great significance to the overall picture of radiologicalrisk. Notwithstanding this, however, sensitivity calculations are made with low U sorptivity as
a variant of the central corrosion case in Section 4.5.4 and to assess the possible role of periodictransitions to low U sorptivity during the full glacial cycle in Section 4.5.7.
It should also be noted that the ranges of uncertainty recommended for Kd data implicitly include
the full range of spatial and temporal variability expected in groundwater compositions. Although
this means that nuclide dose rates are likely to be pessimistically overestimated during the temperate
time domain, this does not necessarily inform the discussion of possible remobilisation of nuclides
due to changing groundwater chemistry during the glacial IIa and IVa periods. Based on the relative
trends of pH and carbonate concentration depicted in Figure 2‑9, however, a decrease in sorptivity
is expected during the glacial IIa domain on account of higher carbonate concentrations and reduced
pH relative to the temperate time period. Groundwater conditions during the glacial IVa domain are

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31

more heterogeneous with a much broader range of pH and carbonate concentrations than are predicted to exist during the temperate time domain. On average, however, the carbonate concentration
is higher although the pH is also slightly higher implying a mixed impact on sorptivity.
Impact of evolving groundwater chemistry on retention by solid solution

In Appendix B, detailed scoping calculations have been made with the aim of approximately
quantifying retention by solid solution during the temperate time domain as well as likely impacts
that changes in groundwater chemistry might bring about. In these calculations, the retention of
nuclides as solid solutions in association with calcite (and barite in the case of Ra‑226) has beencast in a conditionally constant Kd framework. Although there are known situations in which a
conditionally constant Kd description may not be an appropriate means of modelling transport
retardation by solid solution, the approach is justified for the purpose of making scoping calculations
through the application of a series of simplifying assumptions that are considered reasonable for thephysicochemical boundary conditions describing the geosphere environment in SR‑Site. Although
only a small number of solutes (Ra, Am, Ni, U(IV), U(VI)) representing a range of different sorption
chemistries are considered in the calculations, more general conclusions concerning impacts on theretardation of other nuclides may then be drawn by invoking appropriate geochemical analogies.
In order to be consistent with the corresponding discussion for retention by ion-exchange andsurface complexation, equivalent Kd values are derived for the groundwater compositions existingat 3,000 years in the temperate time domain as a hydrochemical reference case.
The scoping calculations indicate that equilibrium retention by solid solutions with calcite varies
considerably amongst the different nuclides studied. In some cases the retention capacity is ofsimilar magnitude (Am and Ni) or larger (Ra) than that of the chlorite and clay minerals, althoughin other cases the retention by solid solution is estimated to be considerably smaller than that of thechlorite and clay minerals (U(IV) and U(VI)). Groundwater chemistry correction factors defined ina similar fashion to that outlined previously for ion-exchanging nuclides indicate that retention is
generally higher under most of the glacial cycle relative to the hydrochemical reference case withthe exception of the glacial IIa time domain where retention by calcite solid solution appears todecrease slightly relative to the hydrochemical reference case. On the other hand, retention appears
to be significantly enhanced during the glacial IVa time domain, which suggests that remobilisation
scenarios are unlikely for solid solutions involving calcite. The considerable increase in retention
by calcite during glacial IVa also suggests that possible decreases in sorptivity predicted for thesurface complexing nuclides in association with chlorite and other clay minerals may be at least
partially offset in some cases. This would certainly appear to be the case for trivalent actinides andlanthanides by way of geochemical analogy with Am.
Although barite has not been identified in quantifiable amounts in the fracture system at Forsmark
its presence might be reasonably inferred from the only slight oversaturation of barite apparent in
the groundwater compositions measured at the site /Crawford 2010/. Calculations indicate that aslittle as 1 mg/m2 of barite would be sufficient to represent a larger retention capacity for Ra than thatof the other fracture minerals. Calculation of chemistry correction factors for radiobarite indicate that
retention of Ra is considerably reduced during the glacial IIa and IVa time domains relative to thehydrochemical reference case. If barite were the only mineral likely to form solid solutions with Ra,
this would imply the potential for remobilisation during the glacial IIa and IVa periods. Interestingly,
the decrease in retention by barite is offset by a corresponding increase in retention by calcite andthe chlorite/clay mineral group during the glacial IVa period. If the amount of barite is much lessthan about 1 mg/m2, the net effect would be an increase in retention during glacial IVa althoughstill a slight decrease in retention during glacial IIa. As already noted, however, the landscape doseconversion factors are significantly lower during the glacial periods. The radiological consequencesof remobilisation scenarios of anthropogenic Ra‑226 therefore appear to be minor.
Although equilibrium sorption on fracture minerals can generally be assumed for ion-exchange andsurface complexation sorption mechanisms, this is not necessarily always the case for solid solution
retention processes on account of the kinetic effects related to the uptake process. In the scoping
calculations, both equilibrium sorption and kinetically limited modes of solute uptake are therefore
considered. It is concluded, however, that there is sufficient uncertainty concerning rates and actual
mechanisms of kinetic rates of solute uptake at this time that the notion of equilibrium sorption by

32

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solid solution formation is not a prudent assumption for safety assessment modelling. The retentionof radionuclides as solid solutions in association with calcite or barite may therefore be significantly
less than that estimated on the basis of the equilibrium assumption.

2.5

Summary of geosphere non-flow related data

The movement of solutes through fractured rock depends on several parameters, which are discussed
in detail in the Data report and supporting documents. Parameters related to the rock matrix – theeffective diffusivity, diffusion available porosity, and sorption partitioning coefficient – are summarised briefly here. These data are site specific, depending on the geological settings and groundwatercomposition.
Flow-related parameters (e.g. the F-factor) are specific to the modelling case addressed. Data for theflow triplet parameters (Qeq, tw, F) are therefore discussed on a case-by-case basis where appropriate
in Chapters 3 to 6. Near-field parameters related to the properties of buffer and backfill material canbe found in the Data report and supporting documents. Other parameters related to the conceptualisation of radionuclide release and conversion of radionuclide mass discharge to a radiological dose
rate are discussed in the following chapter.

2.5.1 Diffusion-available porosity
The diffusion available porosity is discussed in the Data Report. Based on consideration of thedominant rock type in the repository volume, a flowpath average porosity of 0.18% is recommended
for use in SR-Site calculations. This recommended value is reduced relative to the measured laboratory value to account for the possible biasing effect of mechanical damage incurred during drillingand core extraction. The applied scaling factor of 0.8 is based on comparison of water saturation
porosities with microcrack volume (porosity) measurements made in triaxial compression tests usingsite-specific rock samples.
2.5.2 Effective diffusivity
The handling of effective diffusivity and data used in SR-Site is discussed in the Data report. Basedon the analysis documented there, a flowpath average effective diffusivity is recommended for use intransport calculations. For the purposes of SR‑Site, the effective diffusivity recommended for cations
and neutral species is assumed to have a lognormally distributed uncertainty with the following
characteristics:

log10 De = −13.7 ± 0.25 								2‑2For anionic radionuclides, the recommended distribution is:

log10 De = −14.2 ± 0.25 								2‑3It should be noted that the standard error of the estimate given in Equations 2‑2 and 2‑3 relate touncertainty rather than spatial variability and the estimates are considered to be already averaged.
Since radionuclides may be present in a number of different speciated forms depending on ground­water chemistry, there is the possibility that cationic, anionic and neutral forms may exist contemporaneously. Because the safety assessment codes only allow for the assignment of a single effective
diffusivity per nuclide this means that a judgement must be made for which effective diffusivity is
to be used. Table 2‑3 summarises the assumed speciation of different elements and redox species ofimportance for SR‑Site.

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33

Table 2‑3. Dominant speciated forms estimated for elements and redox states at pH 8 and forsaline groundwater (5,190 mg/l Cl–, 22 mg/l HCO3–) approximately representative of current
con­ditions at repository depth. Carbonate complexed forms may take on greater significance ingroundwater of more meteoric character. In situations where there is doubt concerning the most
likely speciation, the anionic form might be considered a more cautious choice.
Element

Dominant species

StatusCs(I)Cs+

CationRa(II)

Ra2+

CationSr(II)

Sr2+

CationEu(III)

EuCO3+

CationHo(III)

HoCO3+

CationSm(III)

SmCO3+

CationAc(III)AcCO3+

CationAm(III)

AmCO3+

CationCm(III)

CmCO3+

CationNp(IV)

Np(OH)4

NeutralNp(V)NpO2+, NpO2CO3–

Cation/Anion (carbonate dependent)

Pa(IV)Pa(OH)4

NeutralPa(V)PaO2(OH)

NeutralPu(III)PuOH2+, Pu3+

CationPu(IV)

Pu(OH)4

Neutral

Pu(V)

PuO2+

CationPu(VI)

PuO2(CO3)22–, PuO2CO3

Anion

Th(IV)

Th(OH)3CO3–

Anion

U(IV)

U(OH)4

NeutralU(VI)UO2(CO3)34–, UO2(CO3)22–

Anion

Ni(II)

Ni2+, NiCl+

CationZr(IV)

Zr(OH)5–

Anion

Ag(I)

AgCl2–, AgCl43–, AgCl32–

Anion

Cd(II)

CdCl+, Cd2+, CdCl2

CationPb(II)

PbCO3, PbCl+, PbOH+, Pb2+

CationPd(II)

Pd(OH)2

NeutralMo(VI)MoO42–

Anion

Nb(V)

NbO3–, Nb(OH)5

Anion

Tc(IV)

TcO(OH)2

NeutralTc(VII)

TcO4–

Anion

C(IV)

HCO33–Anion

C(‑IV)

CH4 (or organic acids)

NeutralCl(‑I)

Cl–

Anion

I(‑I)

I–

Anion

Se(‑II)

HSe–

Anion

Se(IV)

HSeO3–, SeO32–

Anion

Se(VI)

SeO42–Anion

Sn(IV)

Sn(OH)2

Neutral34

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2.5.3 Rock matrix sorptivity
Kd data recommended for use in SR-Site are based in part on site specific data obtained during theForsmark and Laxemar site investigations, and in part on data contained in the open scientific literature. These data are documented in /Crawford 2010/ and the Data report. The data are corrected toaccount for biases due to differences in sorptive surface area and cation exchange capacity (CEC)of the crushed rock types used in laboratory investigations relative to the intact site specific rockassumed as a reference material for transport calculations (Forsmark metagranite).
In the small number of cases (Cs, Sr, Ra, Ni) where an ionic strength dependency has been quantified, data have been selected for the most unfavourable groundwater compositions expected whichcorresponds to roughly 2,000–3,000 years in the temperate case /Salas et al. 2010/. Generally, theoverall uncertainty of the underlying data sets dominate and the correction implied by temporalchanges in groundwater composition gives rise to only very small differences in the recommended
values. Although salinity is slightly less on average at 3,000 years than 2,000 years, the differenceis sufficiently small as to be statistically insignificant for the estimation of corrected Kd values. For
elements where it is not feasible to quantitatively estimate the impact of spatially and temporally
variable groundwater composition on sorptivity, Kd data representing a range of contact watercompositions are combined to give an uncertainty range that is thought to reasonably represent thediversity of hydrochemical conditions expected. The conditional Kd values recommended for use in
SR‑Site in most cases represent a relatively large span of contact water compositions and experimental conditions. Although there may be some bias in the sampled parameter space for certain nuclides,
the recommended data capture as much of the groundwater compositional uncertainty as is reasonably possible to achieve. In many cases it is likely that the uncertainty distributions represent a
broader parameter space than is predicted for SR‑Site groundwater compositions.
Recommended data for geosphere transport calculations

Sorption Kd data recommended for use in SR‑Site for radionuclide migration calculations in thegeosphere at the Forsmark site are summarised in Table 2‑4. The data are given in the form oflognormal distributions characterised by a mean (μ) and standard deviation (σ) and implicitly include
the combined impact of uncertainty as well as spatial and temporal variability. The median of theKd uncertainty distribution may be taken to be the best estimate value for central case deterministic
calculations. Since uncertainty rather than variability is expected to make the dominant contribution
to the statistical dispersion of the recommended Kd data ranges it is not possible to estimate ameaningful flowpath average for the geosphere. For stochastic simulations, it was recommended thatthe lognormal distributions be sampled uniformly between the 2.5% and 97.5% percentiles specified
as the lower and upper Kd limits in the table.
Kd values are given for the predominant redox species considered most likely for the ground­watercompositions existing during the temperate phase of groundwater evolution. For all redox sensitive
nuclides except U, the reduced species is predominant. Pu is assumed to be present in the trivalentstate even though a mixed Pu(III,IV) state is possible. Since Pu(III) is assigned a slightly lower Kd
interval than Pu(IV), this may be considered cautious with regard to model parameterisation. At latertimes during the temperate phase, reduced U(IV) speciation cannot be guaranteed and it is likely that
U(VI) is predominant in parts of the repository environment. Owing to this uncertainty, both U(IV)and U(VI) cases have been propagated forward in the transport calculations. For times greater than
9,000 y in the temperate case, the trend to increasing carbonate concentration and decreasing Ehowing to infiltration of meteoric water may give more weakly reducing conditions, although this isprincipally an issue for U redox speciation.

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35

Table 2‑4. Recommended sorption partitioning coefficient, Kd values for use in SR-Site simulations of the Forsmark site. The predominant species for redox sensitive elements are highlighted
in bold text. Values are given for the best estimate (median), parameters for the lognormal
distribution (μ and σ), as well as lower and upper limits corresponding to the 2.5% and 97.5%
percentiles, respectively.
Radionuclide(Redox State)

Best estimate
Kd (m3/kg)

log10Kd – μ

log10Kd – σLower Kd limit(m3/kg)Upper Kd limit(m3/kg)Ac(III)

1.48·10–2

–1.83

0.72

5.74·10–4

3.83·10–1

Ag(I)3.49·10

–4

–3.46

0.51

3.46·10–53.52·10–3

Am(III)

1.48·10

–2

–1.83

0.72

5.74·10–4

3.83·10–1

0.0

–

–

0.0

0.0

C, CH4

C, HCO3

0.0

–

–

0.0

0.0

C, -CO2H

0.0

–

–

0.0

0.0

Cd(II)

1.10·10–3

–2.96

0.65

5.97·10–5

2.04·10–2–

Cl(‑I)

0.0

–

–

0.0

0.0

Cm(III)

1.48·10–2

–1.83

0.72

5.74·10–4

3.83·10–1

Cs(I)3.49·10–4

–3.46

0.51

3.46·10–5

3.52·10–3

Eu(III)

1.48·10

–1.83

0.72

5.74·10–4

3.83·10–1

–2

H(I)

0.0

–

–

0.0

0.0

Ho(III)

1.48·10–2

–1.83

0.72

5.74·10–4

3.83·10–1

I(‑I)

0.0

–

–

0.0

0.0

Mo(VI)

0.0

–

–

0.0

0.0

Nb(V)

1.98·10–2

–1.70

0.64

1.11·10–3

3.53·10–1

Ni(II)

1.10·10

–3

–2.96

0.65

5.97·10–52.04·10–2

Np(IV)

5.29·10

–2

–1.28

0.65

2.84·10–3

9.84·10–1

Np(V)

4.13·10

–4

–3.38

0.74

1.48·10–5

1.15·10–2

Pa(IV)

5.92·10

–2

–1.23

0.48

6.76·10–3

5.18·10–1

Pa(V)5.92·10

–2

–1.23

0.48

6.76·10–3

5.18·10–1

Pb(II)

2.52·10

–2

–1.60

0.56

2.05·10–3

3.10·10–1

Pd(II)

5.20·10

–2

–1.28

0.83

1.22·10–3

2.21

Pu(III)

1.48·10–2

–1.83

0.72

5.74·10–4

3.83·10–1

Pu(IV)

5.29·10

–2

–1.28

0.65

2.84·10–3

9.84·10–1

Pu(V)9.14·10

–3

–2.04

0.60

6.19·10–4

1.35·10–1

Pu(VI)

9.14·10

–3

–2.04

0.60

6.19·10–4

1.35·10–1

Ra(II)

2.42·10

–4

–3.62

0.41

3.87·10–5

1.51·10–3

S(‑II)

0.0

–

–

0.0

0.0

Se(‑II)

2.95·10–4

–3.53

0.55

2.50·10–5

3.48·10–3

Se(IV)

2.95·10–4

–3.53

0.55

2.50·10–5

3.48·10–3

Se(VI)

2.95·10

–4

–3.53

0.55

2.50·10–5

3.48·10–3

Sm(III)

1.48·10

–2

–1.83

0.72

5.74·10–4

3.83·10–1

Sn(IV)

1.59·10

–1

–0.80

0.28

4.51·10–2

5.58·10–1

Sr(II)

3.42·10–6

–5.47

0.99

3.84·10–8

3.05·10–4

Tc(IV)

5.29·10–2

–1.28

0.65

2.84·10–3

9.84·10–1

Tc(VII)

0.0

–

–

0.0

0.0

Th(IV)

5.29·10–2

–1.28

0.65

2.84·10–3

9.84·10–1

U(IV)5.29·10–2

–1.28

0.65

2.84·10–3

9.84·10–1

U(VI)1.06·10–4

–3.97

0.66

5.53·10–6

2.05·10–3

Zr(IV)

2.13·10–2

–1.67

0.35

4.48·10–3

1.02·10–1

36

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3Conceptualisation of transport processes andconditions within SR-Site

The three hydrogeological models (semi-correlated, uncorrelated and fully correlated) describedby /­Joyce et al. 2010/ form the base for the calculations. The hydrogeological calculations are
performed for different climate conditions. Temperate conditions at the time 2000 AD are assumed
to provide adequate representations of near-field and far-field conditions at Forsmark for the purposeof estimating radionuclide release and transport. This approximation is relaxed in a few selectedvariant modelling cases to evaluate its adequacy.
The EFPC criterion has been applied for most of the calculation cases, i.e. canister positions intersected by fractures that also intersect the entire tunnel perimeter have been discarded. This meansthat those deposition holes have been filtered from the results of the transport calculations.

3.1

Selection of radionuclides

The selection of radionuclides is based on radiotoxicity, inventory, half-life and shared solubility.
The selection is further described in Appendix D. Some of the selected, short-lived nuclides wereomitted in cases where they would have decayed to insignificance at the time of the start of thecalculation.
The following 23 fission and activation products were selected: Ag-108m, C-14, Cd-113m, Cl‑36,
Cs-135, Cs-137, Eu-152, H-3, Ho-166m, I-129, Mo-93, Nb-93m, Nb-94, Ni-59, Ni-63, Pd-107,
Se-79, Sm-151, Sn-121m, Sn-126, Sr-90, Tc-99 and Zr-93.
The following 22 decay chain nuclides (ordered by chain) were selected: Pu-240, U-236, Th-232,
Cm-245, Am-241, Np-237, U-233, Th-229, Cm-246, Am-242m, Pu-242, Pu-238, U-238, U-234,
Th-230, Ra-226, Pb-210, Am-243, Pu-239, U-235, Pa-231 and Ac-227. Some nuclides with shorthalf-lives in comparison to their progeny were only included by adding their initial inventory to thatof their progen. This applies to e.g. Cm-244, Pu-241, Cm-243 and Pa-233.

3.2

Radionuclide release from the fuel

The following contributions to the outward transport from the fuel can be distinguished.
•

The instantaneously accessible fraction of radionuclides, IRF, that is assumed to rapidly dissolvein the water void volume and be subsequently released from the canister. This gives rise to apulse of uncertain duration, the uncertainty stemming from e.g. uncertainties in the detailed
development of the canister failure through which the IRF is made accessible.

•

A contribution from the corrosion of metal parts in the fuel assemblies and the congruent releaseof radionuclides embedded in the metal parts. These inventories are collectively called the corrosion release fraction, abbreviated CRF.

•

A contribution from fuel dissolution and the congruent release of radionuclides embedded in thefuel matrix.

•

Elemental solubilities as a limit for radionuclide release. If the solubility limit is reached, theconcentration of the dissolved nuclide in the water does not increase further.

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3.2.1 Release of instantaneous release fraction
As soon as a continuous water pathway has been formed the instant release fraction of the inventory
dissolves in the water in the canister void.
In the corrosion scenario the IRF is assumed to rapidly dissolve and be subsequently flushed fromthe canister. Since these nuclides are in general non-sorbing and since the flow related retardation
properties in the geosphere are poor for the flow paths associated with the deposition positions inquestion, they are generally released as pulses of durations of tens of years from the geosphere to
the biosphere. The release of the IRF is calculated separately, see Section 4.1.3.

3.2.2 Release of activation products in metal parts
The inventory of activation products in the metal parts of the fuel assemblies has normally been
assigned to the instantaneously accessible fraction (for example in SR-Can, SKB 2006a), since it
has been considered unnecessary to develop a model for the metal parts as nuclides in these aredispersed during transport through the near field and far field. However, in the corrosion scenario
this assumption would lead to unrealistically high peaks in the releases of e.g. Ni-59 and Nb-94.
Therefore, corrosion of metal parts of the fuel assemblies is included in the near-field model, withcorrosion rates given in the Data report, Section 3.2. The fraction of the inventory for which corrosion of metal parts determines the release rate is called the corrosion release fraction, CRF. The CRF
is given in the Data report, Section 3.2, in the same manner as other fractions of the inventory.

3.3

Near-field transport and retention

After failure the canister is not assumed to provide any transport resistance except in the growing
pinhole scenario.
There is no transport resistance at all in the near field in the corrosion scenario. The release isassumed to occur with the water flow in the deposition hole.
In all scenarios, but the corrosion scenario, the nuclides are sorbed with varying efficiency in thebuffer and the diffusion and sorption properties determine the time for diffusion through the buffer
to the rock at release path Q1, i.e. a fracture intersecting the deposition hole. In the shear load
scenario the shear is assumed to increase the fracture transmissivity significantly. The Qeq value forthe intersecting fracture is, therefore, assumed to be sufficiently high that it does not contribute to
the transport resistance in the near field. In the two hypothetical residual scenarios, isostatic load andgrowing pinhole, the limited flow in the fractures intersecting the deposition hole contributes to thetransport resistance through the Qeq value. Thermally induced spalling is assumed to have occurredin the wall of the deposition hole. This implies, that the transport resistance at the interface at Q1 islower than if spalling is not included.
In the growing pinhole scenario two additional exits from the near field are included: an excavation
damaged zone, EDZ, in the floor of the deposition tunnel (if such a zone is assumed to exist), Q2,
and a fracture intersecting the deposition tunnel, Q3. The radionuclide transport is assumed to occur
by diffusion in the buffer and backfill in the deposition hole and by diffusion and advection in thedeposition tunnel. The nuclides are sorbed with varying efficiency in the buffer and backfill andthe water flow, the diffusion and sorption properties in the backfill determine the time for diffusion
through the buffer and backfill to the rock at release paths Q1, Q2 and Q3. The advective flow in thedeposition tunnel and the boundary conditions for the near field at Q1, Q2 and Q3 are determined in
the hydrogeological calculations. In the section describing the near-field model COMP23 (Section
3.6.1) more details are given and in Figure 3‑1 the modelled system in the pinhole scenario including the three release paths Q1, Q2 and Q3 is shown. A detailed description of the discretisation,diffusion resistances and boundary conditions used in COMP23 in the different scenarios is given
in Appendix G.

38

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3.4

Geosphere transport and retention

In SR-Site, solute transport in the geosphere is conceptualised to occur by advective flow along
discrete migration paths where retention is caused by matrix diffusion and equilibrium sorption onrock matrix microsurfaces /Geosphere process report/. For modelling purposes these processes
are assumed to be reversible and linear thereby implying a Fickian formulation of matrix diffusion
characterised by an effective diffusivity, De, that can vary spatially along a flowpath depending
upon the local microstructural properties of the rock. The effective diffusivity of specific solutes in
the rock depends upon the geometric structure and connectivity of the rock matrix porosity, whichis conceptualised to consist of both microfractures and grain boundary porosity. The handling ofeffective diffusivity and data used in SR-Site are discussed in the Data report.
In a similar fashion, the sorptive properties of the rock are modelled based on the assumption of aconstant linear partitioning coefficient, Kd, which also can vary spatially along a flowpath dependingon the local mineralogy of the rock and porewater chemistry. The residence time distribution ofa solute subject to advective transport and retardation by matrix diffusion and linear sorption is afunction of the master variables De, Kd and the F-factor. In SR-Site, the diffusive mass transfer tothe rock matrix is furthermore assumed to be one-dimensional and perpendicular to the advective
flowpath along which the radionuclide is transported.

3.5

Biosphere representation

The biosphere is mainly represented by multiplying the radionuclide releases from the near field orfrom the geosphere by an appropriate dose conversion factor (LDF).
The so obtained doses, or, in the case of the near field, dose equivalent releases, are the main calculation end-points in the consequence calculations presented in this report. The conversion to dose isdone to obtain a convenient measure of the impact of the releases, where also a total measure is
obtained as the summed dose.
For the shear load scenario with early failure the use of LDF values overestimates the doses in thistime perspective since i) the LDF is a pessimistic upper bound on releases occurring continuously
over an entire interglacial period taking into account accumulation whereas a large part of theinterglacial period has elapsed without any releases when the repository is sealed and ii) it is notmeaningful to use the LDF concept for a radionuclide that decays to insignificance over an inter­glacial period, since the concept is based on a continuous releases over the period.
Basic Landscape Dose Conversion Factors (LDF)

The Basic Landscape Dose Conversion Factors, LDF, have been used for estimating doses for
scenarios characterised by nearly constant release rates during a long-term period. The LDF values
are therefore derived from simulations using constant unit release rates during the whole simulation
period. LDF values are calculated for the different climate conditions, e.g. interglacial, periglacial,glacial and submerged. The used values are the maximum values (over time and objects) obtained
from the transient modelling. For all radionuclide transport cases the values for interglacial con­ditions are used, except in the cases assessing influence of varying climate where also values for
periglacial, glacial and submerged conditions are used. The highest doses from a constant release
rate from the repository are expected under temperate conditions when humans are exposed toradionuclides that have accumulated in a wetland that has been converted to arable land, and whencontaminated well water is utilised by human inhabitants and livestock. Hence, the LDFs for theinterglacial period are the maximum values applicable during the reference glacial cycle. The interglacial period, i.e. the period from deglaciation to the onset of periglacial conditions, cf. Figure 4-35
in the Climate report, is represented by climate conditions similar to those of today and is, inaccordance with the reference glacial cycle, assumed to prevail for 18,400 years (i.e. from –9000 to
9400 AD) and include both submerged and temperate conditions. The LDF values used include theinfluence of exposure from a well. The details of how the LDF values have been derived are given in
the SR-Site Main report, Section 13.2 and in /Avila et al. 2010/. The interglacial-period LDF values
used are given in Table 3‑7; see the Data report for LDF values for other climate domains.

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Dose Conversion Factors for pulse releases (LDF pulse)

In the corrosion scenario the instant release fraction, IRF, are generally released as pulses of durations of tens of years from the geosphere to the biosphere, see further 4.1.3. The basic LDF values(previous section) are not applicable for pulse releases, since the former are derived from simulations
with a constant release rate during long-term periods, whereas pulse releases will, by definition, takeplace during a relatively short time period. Hence, the derivation of LDF pulse values has been doneby performing simulations for a release of 1Bq to the landscape during a short time period. The duration of the release period has been varied from 1 to 1,000 years and simulations have been carriedout for pulse releases occurring at different times within an interglacial period. Studies of the effectof the starting time of the releases and the duration of the pulse have shown very little influenceof these factors in the derived Dose Conversion Factors. In Table 3‑7 values of the LDF pulse arepresented for those radionuclides that occur in pulse releases. The values are the maximum annual
effective doses calculated for 1-year pulses released at 9000 BC, 3500 AD and 9400 AD.
Distributed LDF

There are also a few cases, calculated for illustrative purposes, see Section 6.2.3 and Section 6.5,
where a large number of canisters are assumed to fail. In such cases, LDF values calculated fora release spread over the landscape objects according to the distribution of release locations overtime during the modelled interglacial period are applied, rather than the basic LDF values where thelandscape object yielding the highest dose is pessimistically used to represent the biosphere. TheseLDF values are referred to as distributed LDF.
Time dependent biosphere

In a few cases of relatively early releases, the basic LDF values would represent an overestimationof the dose consequences, again since a steady state release situation is far from established. In someof these cases, time dependent releases are transferred to the same biosphere model as used for thederivation of LDF values and a time dependent dose, taking into account both the temporal variationof the release and the development of the landscape, is obtained.

3.6

Models used

Calculations of radionuclide release and transport rely on three primary computer codes COMP23,
FARF31 and MARFA. The codes are described in Section 3.6.1, 3.6.2 and 3.6.3, respectively. The
codes are further described in the SR-Site Model summary report. In addition, all three codes
require information derived from groundwater velocity fields calculated by the ConnectFlow code/­Joyce et al. 2010/. A summary of the transport model chain is given in Section 3.6.4.
In addition to the numerical codes an analytical model for both near-field and far-field calculations
is used. A short description of the model is given in Section 3.6.5 and a more detailed description is
given in the SR-Site Model summary report.

3.6.1 COMP23
COMP23 /Romero 1995, Cliffe and Kelly 2006, Kelly and Cliffe 2006/ is a compartment code used
for radionuclide migration calculations in the near field (the canister and the engineered systems).
The code was initially developed as NUCTRAN /Romero 1995/ and was subsequently incorporated
into the SKB safety assessment calculation framework Proper as the submodel COMP23. Proper isa collection of codes used for migration and consequence calculations through the near field, the far
field and the biosphere and uses standardised methods to transfer data and results between the different submodels. In SR-Site, an implementation of the COMP23 model written in Matlab/Simulink
is used for the near-field migration calculations. This implementation of COMP23 is also called
Compulink /Vahlund and Hermansson 2006/.

40

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COMP23 has been used by SKB in the SR 95 /SKB 1995/, the SR 97 /Lindgren and Lindström
1999, SKB 1999/, SR-Can interim /SKB 2004/ and the SR-Can /SKB 2006a/ assessments of a final
repository of the KBS-3 type. A closely related code, NUCTRAN/NUCFLOW, (which originate
from the same source but allows for multiple sources opposed to COMP23 which only handles
single sources) was used in the SAFE assessment of the SFR repository for operational waste/Lindgren et al. 2001/.
COMP23 models processes related to radionuclide release and transport in the canister interior, thebuffer and the deposition tunnel backfill. These incorporate the processes radioactive decay, metal
corrosion (modelled as a constant metal corrosion rate), fuel dissolution, dissolution of gap inventory(modelled as an instantaneous release), speciation of radionuclides (i.e. dissolution/precipitationof nuclides with shared elemental solubilities), diffusion and sorption in the buffer and advection,diffusion and sorption in the deposition tunnel backfill. It also handles the release of radionuclides
to different exit paths from the near field.
COMP23 is a multiple-path model that calculates transient nuclide transport in the near field of arepository by use of a network of coupled resistances and capacitances in analogy with an electricalcircuit network. Analytical solutions, instead of fine discretisation, at sensitive zones, for example
at the exit point of a small canister hole and at the entrance to fractures, are embedded to enhancecalculation speed.
Figure 3‑1 shows the canister, deposition hole and the deposition tunnel backfill and how these aremodelled by COMP23 in the growing pinhole scenario. Three exits from the near field are included:a fracture intersecting the deposition hole at the vertical position of the canister lid, denoted Q1,
an excavation damaged zone, EDZ, in the floor of the deposition tunnel (if such a zone is assumed
to exist), Q2, and a fracture intersecting the deposition tunnel, Q3. In the hydro­geological modelling,
the number of fractures intersecting a deposition hole and the properties of these fractures are determined statistically based on the DFN description of the rock. If more than one fracture intersects a
deposition hole, the transport capacity of the several fractures are added and pessimistically assigned
to the single fracture, Q1, modelled by COMP23. The equivalent flow rate through Q2 is also calculated as an integral part of the hydrogeological modelling. The flow rate in the deposition tunnel
and the distance to the nearest Q3 fracture through which radionuclides are released to the geospherefrom the tunnel are given by the hydrogeological modelling. Transport by advection and diffusionin the tunnel is included in the near-field simulations and the computational domain is extended in
the downstream direction to include the Q3 fracture. All needed results from the hydrogeologicalmodelling are transferred to COMP23 through the ptb-files from ConnectFlow.
Effects of spalling in deposition holes are treated by a modification of the equivalent flow rates forthe transport path Q1, see Appendix G.
Advective conditions in the buffer, as in the corrosion scenario, are simply treated by equating theoutflux from the canister interior compartment with the release to Q1. The release paths Q2 andQ3 are not modelled when advective conditions are assumed in the buffer since releases to Q1
completely dominate over those to Q2 and Q3 for such cases.
Further details of the discretisation, diffusion resistances and boundary conditions used in the different scenarios are described in Appendix G.

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41

Q3
Q2

4.8

Advection + diffusion
Backfill

1,25

1.25

E

2.75

Q2

Rock
fracture

8.1

Q1

Excavation
damaged 0.5
zone

4.8

Canister

0.5

C2

C1
Q1

0.5

Rock

B1-B6
D

BentonitebufferDimensions in m

0.5

C3

0.525 0.35

Ø 1.05
Ø 1.75Figure 3‑1. COMP23 model, for the growing pinhole scenario, with details of its model representationas com­partments B1–B6, C1–C3, D and E. The transport paths Q1, Q2 and Q3 to a fracture intersecting
the deposition hole, to the excavation damaged zone, and to a fracture intersecting the deposition tunnel,
respectively, are also shown.

3.6.2 FARF31
FARF31 /Norman and Kjellbert 1990, Lindgren et al. 2002, Elert et al. 2004/ is a code used forradionuclide migration calculations in the far field, i.e. the geosphere.
FARF31 has been employed already in earlier assessments, e.g. SR 97 /Lindgren and Lindström
1999/ and SR-Can /SKB 2006a/.
FARF31 is based on a model with a one-dimensional advection-dispersion equation along a, possibly
curved, stream tube coupled to a pure diffusion equation in the direction perpendicular to the centroid of the stream tube, for a number of radionuclides. Chain decay and in-growth are included in
the model. The concept of a stream tube can be compared to the combined effect of a large numberof individual fractures all sharing the same inlet and outlet.
The governing equations are solved in the Laplace domain using the advective travel time in thelongitudinal direction as the independent variable to obtain a unit response function, which issubsequently convoluted with the input function to obtain the output function. A detailed descriptionof the solution method can be found in /Norman and Kjellbert 1990/.
It is noted that the equations are expressed in terms of accumulated travel time rather than distancealong the flow path. This feature makes it easy to calculate travel times in a stand-alone groundwaterflow model, and subsequently radionuclide transport in a decoupled fashion.

42

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FARF31 was originally developed to be used with a groundwater flow model adopting a continuum
representation of the rock. In SR-Site, groundwater flow is primarily modelled through a discrete
fracture network (DFN) where individual fractures are represented explicitly. Here, the conceptualisation of a migration path is slightly different than in a continuum-based groundwater flow
model. Rather than macroscopic stream-tubes encompassing both rock and flow paths, the equation
now describes flow paths through the actual open pore space, i.e., through the connected fracture
network. However, the governing equations are identical for the two conceptualisations. The entities
calculated in the DFN-based groundwater flow models are the advective travel time (tw) and flowrelated transport resistance (F) along flow paths.

3.6.3 MARFAThe computer code MARFA /Painter and Mancillas 2009/ uses a particle-based Monte Carlo method
to simulate the transport of radionuclides in fractured or unfractured geologic media. MARFA was
specifically designed to integrate with the safety assessment workflow used by SKB. Version 3.2.2
and earlier versions accept pathline trajectories from the ConnectFlow code /Serco 2008/ in theform of ConnectFlow ptv-files. The pathline trajectories represent transport pathways. MARFA
then solves radionuclide transport along the pathways using a time-domain particle method. With
this method, particles are advanced along a pathway using deterministic spatial displacements andrandom transit times for each step. Testing and experience with the code demonstrate that the code iscomputationally efficient and extremely robust. Limited and unlimited matrix diffusion, equilibrium
sorption, longitudinal dispersion, decay, and in-growth are represented. MARFA supports full spatial
variability for all pathway properties, decay chains of any length, and full temporal variability inradionuclide source strength. The code reports radionuclide release rates (breakthrough) at thepathway endpoints.
Validation tests for MARFA are described in the MARFA Version 3.2.2 User’s Manual /Painter andMancillas 2009/. Additional comparisons between MARFA and FARF31 were also undertaken toprovide further confidence in the MARFA results for SR-Site parameter ranges (Appendix C).
Note that in a stochastic framework with multiple realisations, COMP23 and FARF31 must be
executed once for each realisation, but MARFA need to be run only once with parameters for all
pathway realisations as input. With multiple pathway realisations, MARFA calculates an ensemble
mean breakthrough. The Monte Carlo nature of the algorithm ensures that an unbiased statisticalestimate of the ensemble mean is obtained even when too few particles are used to accurately
calculate breakthrough for each pathway realisation. Moreover, the statistical uncertainty in theensemble mean is greatly reduced relative to that of individual realisations, a property of the methodwith significant advantages in terms of computational efficiency.

3.6.4 Summary of the transport model chain
Model linkages and data flows differ somewhat depending on whether far-field transport is modelledwith MARFA or FARF31. Data flows and model linkages for FARF31 and MARFA are shown in
Figure 3‑2 and Figure 3‑3, respectively.
FARF31, with its integrated description of the transport pathway, requires only global information
about each pathway from ConnectFlow. The required information – the flow-related transport
resistance factor F and advective travel time tw along each pathway – is contained in ConnectFlow
ptb-files. The ptb-files also contain the third component of the so-called flow triplets, the equivalent
flow rate Qeq at the canister. Qeq is required by COMP23.
MARFA accommodates a spatially resolved (segmented) description of the transport pathway andthus accepts ConnectFlow ptv-files, which contain F and tw parameters and a rocktype descriptor foreach segment in each segmented pathway.
MARFA and FARF31 both calculate radionuclide release rates in terms of moles of radio­nuclides
per time per each realisation. These release rates are then converted to effective doses by simply
multiplying with the Dose Conversion Factors (LDFs) and averaged to get mean annual releases.
A description of the work done for developing the LDFs is provided in /Avila et al. 2010/.

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43

CONNECTFLOWRadionuclide
inventory

ptb-file

COMP23Near-fieldtransport
parameters

Near-fieldreleases

Far-field
transport
parameters

FARF31

Far-field
releases

Figure 3‑2. Model linkages and data flows for radionuclide transport simulations using FARF31.

CONNECTFLOW

ptb-file
Radionuclide
inventory
COMP23Near-fieldtransport
parameters

Near-fieldreleases
ptv-file

Far-field
transport
parameters

MARFA

Far-field
releases

Figure 3‑3. Model linkages and data flows for radionuclide transport simulations using MARFA.

44

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The potential role of bentonite colloids in facilitating transport of certain radionuclides is addressedin variant modelling cases using MARFA. For those variants, the data flow shown in Figure 3‑3 ismodified slightly. Specifically, in the colloid-facilitated transport variant, the output of COMP23
is further processed to partition radionuclides between colloid-associated and dissolved states.
The model for that partitioning process is described later in this report. The implementation of thepartitioning model is not through compiled software but relies on Mathematica™ scripts.

3.6.5 Analytical models
Analytical simplified versions of the near-field and far-field transport models have been developed/Hedin 2002b/. These models use the same input data as the corresponding numerical models anddoses are calculated using the same LDF values as in the numerical approach. The models may be
executed probabilistically and yield results in good agreement with the deterministic and probabilistic calculation cases in the SR 97 assessment /Hedin 2002b, SKB 2004/. In the SR-Can assessment
they were shown to be in good agreement for the corrosion scenario, for the shear load scenario andfor releases from a pinhole failure of the canister /SKB 2006a/. A single realisation with the analytical models executes in around 0.1 second on a 2 GHz Personal Computer, making them well suitedfor probabilistic calculations. The corresponding calculation time for the numerical models is of theorder of 10 seconds.
The analytical models have been benchmarked against the numerical models for several calculation
cases in this report. The roles of the analytical models are to i) quickly and preliminarily evaluate
calculation cases to be used in the planning of the transport calculations, ii) serve as one of several
quality assurance measures of the numerical calculations by identifying potential differences inresults obtained with the analytical and numerical models and seeking explanations for these (arethey due to modelling errors or to differences in the nature of the models?), and iii) demonstrating
an understanding of the nature of the models facilitated by the simple nature of the analytic models.

3.6.6 Input data to the transport models
Detailed discussions of data sources and data qualification methods can be found in the Data report.
Unless otherwise noted, parameters required in the radionuclide transport calculations presented
in this Radionuclide transport report are taken from the Data report. Specific sections of theData report relevant to radionuclide transport calculations are as follows: parameters required tomodel spent fuel mobilisation are discussed in Chapter 3; buffer and backfill data required to model
radionuclide migration in the near field are described in Section 5.3; flow related and non-flow
related migration properties are found in Section 6.7 and 6.8, respectively; landscape dose factors
are discussed in Section 7.2. Additional discussions of parameters and parameter summaries are also
provided in this report, as needed, to facilitate a self-contained reading.
For some modelling cases, input parameters are required that are outside the scope of the Data
report. Input parameters required for those cases are documented here. The specific parameters are colloid concentrations for modelling cases that consider colloid-facilitated transport(Sections 4.5.6 and 4.5.8) and flow scaling factors for cases that considered the effects of unsteadyflow (Sections 4.5.7 and 4.5.8). In addition, one set of modelling cases (Section 6.4) that used ahypothetical residual scenario to illustrate certain barrier functions of the geosphere was completed
before SR-Site data were finalised. Assumed parameters for those modelling cases are summarisedin Appendix H.

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45

3.7

Summary of all data used

Hydrogeological data related to flow and transport, obtained from the modelling reported in /­Joyce
et al. 2010/ are transferred to the calculations through the ptb/ptv-files. Three fracture size/trans­missivity correlation functions are considered yielding three variants of the hydro­geological DFN
model. Several cases/realisations are available for each variant of the hydro­geological model, see
Table 3‑1. The ptb-files and ptv-files are archived at SKB, see Table 3-8. All hydrogeological cases
used in the radionuclide release calculations are for the time 2000 AD.
Almost all data are qualified in the SR-Site Data report and therefore is only a short summary of
the input given in this section. Table 3‑2 gives a summary of the data used.
The numerical dose estimates are dependent on the radionuclide inventory assumed. Sensitivity
to the assumed inventory and implications of using an average inventory in the calculations are
discussed in detail in Appendix E. The inventories for most nuclides that contribute significantly todose vary by less than a factor of 1.5. The exception is Ag-108m, which has negligible inventory in
BWR canisters and a PWR inventory that is a factor of 4 higher than the assumed average. However,Ag-108m contributes significantly to the total dose only in the shear failure case with early failure
and in hypothetical cases used to illustrate barrier function. Most of the dose-contributing radionuclides are single radionuclides and hence the doses are directly scaled to the inventories. Although
the dose from Ra-226 is dependent of the inventories of its precursor radionuclides, U-238, Pu-238,
U-234 and Th‑230, none of those radionuclides differ more than a factor of two between different
canisters.
Table 3‑1. Hydogeological realisations used in the radionuclide transport calculations /Joyce
et al. 2010/.
Hydrogeological DFN model

Realisations

Semi-correlated model

Base case and 10 additional realisations at 2000 AD
Crown space
No EDZEDZ with transmissivity of 10–7 m2/s
EDZ with transmissivity of 10–6 m2/s

Uncorrelated model

Base case and 5 additional realisations

Fully correlated model

Base case and 5 additional realisations46

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Table 3‑2. Input data for the probabilistic calculations for the corrosion, shear load, isostatic loadand pinhole scenarios.
Parameter
name

Parameter

Unit

Data

NF/
FF

Data reportsection andsymbolHALFLIFE

Half-life

yr

Constants

NF/
FF

3.1
t½

FPC, EFPC

Criteria for
exclusion ofdeposition holes

Corrosion: Used to select deposition holes, given in
ptb-files
Shear load: Not used
Isostatic load: same as corrosion
Pinhole: same as corrosion

NF/
FF

See Appendix G, Table G-1

NF

Near-field geometry
Number of failed canisters

See each case

NF

INVENTORY Radionuclide
inventorymolConstant. Data for average canister calculated from allfuel assemblies

NF

3.1

FDMC

Fuel conversion
time

yr

Log-triangular (106, 107,108 yr)

NF

3.3

IRF

Instant releasefraction of
inventory–

Data for average canister. Normal distributions for Cl, Cs, NF
I, Se. Triangular distributions for Sr, Ni, Nb, Mo Tc, Pd, Sn.
100% for H, Ag. Single value for Cd

3.2
IRF

CRF

Corrosion release –fraction of
inventory

Data for average canister. Double triangular distributions
for C, Cl, Ni, Se, Mo, Zr, Tc, Sn-121m, U-233. 100% for
Nb-94. Single value for Nb-93m

NF

3.2
CRF

TCORR

Corrosion timeyr

Log-triangular (102, 103, 104 yr)

NF

3.2
tcorr

TFAILURE

Time for failureyrCorrosion: As calculated with the corrosion model, seeeach case.
Shear load: See each case
Isostatic load: 10,000 years and 100,000 years(postulated)
Pinhole: Initial failure (postulated)

NF

TDELAY

Delay time
for onset ofradionuclidetransport*

yr

Corrosion: 0 years
Shear load: 100 years
Isostatic load: 0 years
Pinhole: 1,000 years

NF

4.2
tdelayTLARGETime for large
canister defectyrCorrosion: Same as time for failure
Shear load: Same as time for failure
Isostatic load: Same as time for failure
Pinhole: 10,000 yr (postulated)

NF

4.2
tlargeADELAY,ALARGE

Canister defect
sizes

m

Corrosion: Unlimited at the time for failure
Shear load: Unlimited at the time for failure
Isostatic load: Unlimited at the time for failure
Pinhole: Between onset and TLARGE: 2 mm radius
penetrating pinhole. After TLARGE: Unlimited.

NF

4.2
rdefect

CSOL

Solubility limits

mol/m3Calculated distributions based on distributions of several
groundwater compositions, see Appendix F
Corrosion: Not used (except in one alternative case“including solubility limits in the near field”)
Shear load: Calculated distributions
Isostatic load: Calculated distributions
Pinhole: Calculated distributions

NF

3.4

KDB

Buffer sorption
partitioning
coefficientsm3/kg

Corrosion: Not used
Shear load: Log triangular distributions
Isostatic load: Log triangular distributions
Pinhole: Log triangular distributions

NF

5.3
Kd

DEB

Buffer effective
diffusivities

m2/s

Corrosion: Not used
Shear load: Distributions
Isostatic load: Distributions
Pinhole: Distributions

NF

5.3
De

EPSB

Buffer porosities–(diffusion
available porosity)

Corrosion: Not used
Shear load: Anions: Triangular (0.13, 0.18, 0.24) Minorchanges in Data report; Cations: Triangular (0.43, 0.44,0.47) Minor changes in Data report
Isostatic load: same as shear loadPinhole: same as shear load

NF

5.3
ε

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47

RHO formaterial 2

Buffer density(density of thesolid particles)

kg/m3

Corrosion: Not used
Shear load: Constant = 2,780 kg/m3
Isostatic load: Constant = 2,780 kg/m3
Pinhole: Constant = 2,780 kg/m3

NF

5.1
ρs

KDBF

Backfill sorption
partitioning
coefficientsm3/kg

Corrosion: Not used
Shear load: Not used
Isostatic load: Log triangular distributions
Pinhole: Log triangular distributions

NF

5.3
Kd

DEBF

Backfill effective
diffusivities

m2/s

Corrosion: Not used
Shear load: Log triangular distributions
Isostatic load: Log triangular distributions
Pinhole: Log triangular distributions

NF

5.3
De

EPSBF

Backfill porosity–(diffusion
available porosity)

Corrosion: Not used
Shear load: Anions: triangular (0.13, 0.18, 0.26) Cations:triangular (0.44, 0.46, 0.48)
Isostatic load: same as shear loadPinhole: same as shear load

NF

5.3
ε

RHO formaterial 3

Backfill density(density of thesolid particles)

kg/m3

Corrosion: Not used
Shear load: Constant = 2,780 kg/m3
Isostatic load: Constant = 2,780 kg/m3
Pinhole: Constant = 2,780 kg/m3

NF

5.1
ρs

QEQ_1

Equivalent flowfrom deposition
hole to fracture(s)intersecting
deposition holem3/yrCorrosion: Not used
Shear load: 1 m3/yr
Isostatic load: given in ptb-files (QEQ)
Pinhole: given in ptb-files (QEQ)

NF

6.7
Qeq1

QEQ_2

Equivalent flow to
EDZ

m3/yr

Corrosion: Not used
Shear load: Not used
Isostatic load: given in ptb-files (QEQ)
Pinhole: given in ptb-files (QEQ)

NF

6.7
Qeq2

QEQ_3

Equivalent flow
to fracturesintersecting
deposition tunnel

m3/yr

Corrosion: Not used
Shear load: Not used
Isostatic load: given in ptb-files (QEQR)
Pinhole: given in ptb-files (QEQR)

NF

6.7
Qeq3

LR_TUN_3

Path length to thefirst fracture intunnelm

Corrosion: Not used
Shear load: Not used
Isostatic load: given in ptb-files (LR_TUN)
Pinhole: given in ptb-files (LR_TUN)

NF

TRAPP_3*
LR_TUN_3/
TR_TUN_3

Darcy flux in them/yrdeposition tunnel(Porosity*Pathlength/travel time)

Corrosion: Not used
Shear load: Not used
Isostatic load: Calculated from porosity (TRAPP), path
length (LR_TUN) and travel time (TR_TUN) given in
ptb-files
Pinhole: same as Isostatic load

NF

U0_1

Darcy flux at
deposition holem3/m2,yrCorrosion: Used to calculate the flow in the deposition
hole, given in ptb-files (U0)Shear load: Not used
Isostatic load: Used for spalling, given in ptb-files (U0)Pinhole: Used for spalling, given in ptb-files (U0)

NF

FLEN

Length oflargest fractureintersecting
deposition holemCorrosion: Not used
Shear load: Not used
Isostatic load: Used for spalling, given in ptb-files (FLEN)
Pinhole: Used for spalling, given in ptb-files (FLEN)

NF

Wzone

Width of spallingzonemCorrosion: Not used
Shear load: Not used
Isostatic load: Used for spalling, Constant = 0.5 m
Pinhole: Used for spalling, Constant = 0.5 m

NF

6.5
Wzone

Lzone

Length of spallingzonemCorrosion: Not used
Shear load: Not used
Isostatic load: Used for spalling, Constant = 8 m
Pinhole: Used for spalling, Constant = 8 m

NF

6.5
Lzone

dzone

Thickness of
spalling zonem

Corrosion: Not used
Shear load: Not used
Isostatic load: Used for spalling, Constant = 0.1 m
Pinhole: Used for spalling, Constant = 0.1 m

NF

6.5
dzone

48

6.7
q/U0

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epszone

Porosity ofspalling zone–

Corrosion: Not used
Shear load: Not used
Isostatic load: Used for spalling, Constant = 0.02
Pinhole: Used for spalling, Constant = 0.02

NF

6.5
εzone

Dp

Diffusioncoefficient inspalling zone
(damaged zone)m2/s

Corrosion: Not used
Shear load: Not used
Isostatic load: Used for spalling, Constant = 10–11 m2/s.
Calculated from Dp=Dw/τ2 according to /Neretnieks et al.
2010/. τ is given in the Data report.
Pinhole: same as isostatic load

NF

6.5

RHO formaterial 1

Water density

kg/m3

Constant = 1,000 kg/m3

NF

Dw

Diffusivity in water m2/s

Corrosion: Not used
Shear load: Not used
Isostatic load: Constant = 10–9 m2/s. Used for calculationof the diffusivity in spalling zone
Pinhole: Constant = 10–9 m2/s. Used for calculation of
the resistance in the hole in the pinhole scenario and for
calculation of the diffusivity in spalling zone

NF

6.8
Dw

KDR

Rock sorption
partitioning
coefficientsm3/kg

Corrosion: Truncated log-normal distributions
Shear load: Not used
Isostatic load: Truncated log-normal distributions
Pinhole: Truncated log-normal distributions

FF

6.8
Kd

DER

Rock effective
diffusivities

m2/s

Corrosion: Log normal distributions, mean values anions:2.1·10–7 m2/yr, cations: 6.6·10–7 m2/yr
Shear load: Not used
Isostatic load: same as corrosion
Pinhole: same as corrosion

FF

6.8
De

EPSR

Rock porosities–(diffusion
available porosity)

Corrosion: Constant = 0.0018
Shear load: Not used
Isostatic load: Constant = 0.0018
Pinhole: Constant = 0.0018

FF

6.8
ε

Rock density(solid density)

Corrosion: Constant = 2,700 kg/m3
Shear load: Not used
Isostatic load: Constant = 2,700 kg/m3
Pinhole: Constant = 2,700 kg/m3

FF

6.4
ρ

Corrosion: given in ptb-files (F)Shear load: Not used
Isostatic load: given in ptb-files (F)Pinhole: given in ptb-files (F)

FF

6.7
F

TW_1,
Rock advectiveyr
TW_2, TW_3 travel time forpaths beginning
at Q1, Q2 and Q3

Corrosion: given in ptb-files (TW)Shear load: Not used
Isostatic load: given in ptb-files (TW)
Pinhole: given in ptb-files (TW)

FF

6.7
tw

PE

Rock Peclet
number–Corrosion: Constant = 10
Shear load: Not used
Isostatic load: Constant = 10
Pinhole: Constant = 10

FF

6.7
Pe

DPEN

Max. penetration
depth in rockmatrixm

Corrosion: Constant = 12.5
Shear load: Not used
Isostatic load: Constant = 12.5
Pinhole: Constant = 12.5

FF

6.7
LD

LDF

Biosphere LDF
factors

Sv/y perBq/yConstant. Calculated LDF values, see Table 3‑7.

FF

7.2
LDF

KDC

Colloid sorption
coefficientsm3/kg

Corrosion: Only used in calculations including colloids
Buffer sorption coefficients, KDB, are used
Shear load: Not used
Isostatic load: Not used
Pinhole: Not usedFF

Concentrationof suspended
colloids

kg/m3

Corrosion: Only used in calculations including colloids
10 mg/litre and 10 g/litre
Shear load: Not used
Isostatic load: Not used
Pinhole: Not usedFF

F_1, F_2,
F_3

kg/m3

Rock transport
yr/mresistance forpaths beginning
at Q1, Q2 and Q3* Time between canister failure and the establishment of a continuous water pathway from the fuel to the exterior of thecanister.

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49

3.7.1 Probabilistic input data
The software @risk (the risk analysis add-in for excel, version 5.0.1, Palisade Corporation) wasused to generate input data to the transport calculations when the Data report recommended a
distribution. Also correlations recommended in the Data report were used. In all simulations Latin
hypercube was used as the sampling type and 6,916 iterations were run. Each data table from theData report was analysed separately with @risk. The simulation results were transferred to Matlab
files (.mat files) and these files were always used as input to COMP23 and FARF31. Each line
number in the .mat files forms a unique set of input data for a single calculation and in this section
it is called a realisation.
The variants of the corrosion case, including cases addressing best available technique (BAT),
had different numbers of realisations depending on how many possible failure times the case washolding. Each failure time was iterated 50 times (see Section 4.4.4 about convergence) so the total
number of realisations in each case was the number of failure times multiplied by 50. The input files
containing 6,916 realisations were always used starting from realisation 1 in the input file and endingat the realisation number. For corrosion variants with less than 6,916 realisations the procedure is not
fully consistent with Latin hypercube sampling, i.e. the advantage of the Latin hypercube is not fully
used. However, this is not expected to create any biases. In a few corrosion variants, the number ofrealisations was greater than 6,916 and in these calculations the input datasets were re-run from the
beginning as many times as needed to calculate up to the realisation number in demand. Again, thisprocedure is not fully consistent with Latin hypercube sampling but is not expected to create biases
in the results.
All variants of the shear load cases were run with exactly 6,916 realisations except for the case witha failure at 100,000 years, which was run with 1,000 realisations. This case had an input data set
with 1,000 simulations sampled by Latin hypercube.
All variants of the isostatic load case and the pinhole cases were run with exactly 6,916 realisations,i.e. the optimal spread of data sampled by Latin hypercube is used.

3.7.2 Deterministic input data
The deterministic input data set consists of median values from the probabilistic input data sets of
6,916 iterations, see Table 3‑3 and Table 3‑4. All variables were the same in all different calculation cases except for the transport parameters (U0, QEQ, FLEN, TW, F, TRAPP, LR_TUN and
TR_TUN). These parameters change with the hydrogeological case for the shear cases, the isostaticload cases and the pinhole cases. The semi-correlated base case is used for the shear load, isostaticload, the base case and the no spalling case of the pinhole scenario. The rest of the pinhole cases had
specific hydrogeological cases.
Near-field transport parameters are median values after excluding the special cases of OKFLAG=1,
FPC>0 and EFPC>4, see Table 3‑5. The only exception is in the shear load scenario where QEQ
always is assumed to be high and set to 1 m3/yr both in the probabilistic and deterministic calculations. OKFLAG=1 represents paths where the particle failed to start due to no fracture or low
velocity. Excluding FPC>0 means that deposition holes are excluded due to background fractures
or deformation zone fractures. Excluding EFPC>4 means that canister positions intersected byfractures that also intersect the entire tunnel perimeter have been discarded.
The far-field transport parameters are median values after excluding OKFLAG=1, 2, 3 and 4, FPC>0and EFPC>4, see Table 3‑6. OKFLAG 2, 3, 4 indicates that the particle tracing in the hydrogeological calculations failed to compleate.
For the corrosion scenario the transport parameters change with the hydrogeological case and theresults from the erosion/corrosion model and the parameters used in the deterministic calculations
are always those connected to the earliest failure time, see Section 4.3.
The LDF-values used for both deterministic and probabilistic calculations are given in Table 3‑7.

50

TR-10-50

Table 3‑3. Median values of De, Kd and ε used in the deterministic near-field and far-field calculations. ε rock is not in the table since it is constant, 1.80·10–3 (–), for all nuclides.
De buffer(m2/yr)De backfill(m2/yr)De rock(m2/yr)Kd buffer(m3/kg)Kd backfill(m3/kg)Kd rock(m3/kg)ε buffer(–)

ε backfill(–)

Ac-227

4.20·10–3

5.00·10–3

6.30·10–7

5.20

5.20

1.5·10–2

0.45

0.46

Ag-108m

4.20·10–3

5.00·10–3

6.30·10–7

0.00

0.00

3.5·10–4

0.45

0.46

Am-241

4.20·10–3

5.00·10–3

6.30·10–7

2.50·101

2.50·101

1.5·10–2

0.45

0.46

Am-242m

4.20·10–3

5.00·10–3

6.30·10–7

2.50·101

2.50·101

1.5·10–2

0.45

0.46

Am-243

4.20·10–3

5.00·10–3

6.30·10–7

2.50·101

2.50·101

1.5·10–2

0.45

0.46

C-14

4.20·10–3

5.00·10–3

6.30·10–7

0.00

0.00

0.0

0.45

0.46

Cd-113m

4.20·10–3

5.00·10–3

6.30·10–7

6.60·10–2

6.60·10–2

1.1·10–3

0.45

0.46

Cl-36

2.50·10–4

3.10·10–4

2.00·10–7

0.00

0.00

0.0

0.18

0.19

Cm-245

4.20·10–3

5.00·10–3

6.30·10–7

2.50·101

2.50·101

1.5·10–2

0.45

0.46

Cm-246

4.20·10–3

5.00·10–3

6.30·10–7

2.50·101

2.50·101

1.5·10–2

0.45

0.46

Cs-1358.40·10–3

9.90·10–3

6.30·10–7

3.10·10–2

3.10·10–2

3.5·10–4

0.45

0.46

Cs-1378.40·10–3

9.90·10–3

6.30·10–7

3.10·10–2

3.10·10–2

3.5·10–4

0.45

0.46

Eu-152

4.20·10–3

5.00·10–3

6.30·10–7

5.20

5.20

1.5·10–2

0.45

0.46

H-3

4.20·10–3

5.00·10–3

6.30·10–7

0.00

0.00

0.0

0.45

0.46

Ho-166m

4.20·10–3

5.00·10–3

6.30·10–7

5.20

5.20

1.5·10–2

0.45

0.46

I-129

2.50·10–4

3.10·10–4

2.00·10–7

0.00

0.00

0.0

0.18

0.19

Mo-93

2.50·10–4

3.10·10–4

2.00·10–7

0.00

0.00

0.0

0.18

0.19

Nb-93m

4.20·10–3

5.00·10–3

6.30·10–7

3.10

3.10

2.0·10–2

0.45

0.46

Nb-94

4.20·10–3

5.00·10–3

6.30·10–7

3.10

3.10

2.0·10–2

0.45

0.46

Ni-59

4.20·10–3

5.00·10–3

6.30·10–7

6.60·10–2

6.60·10–2

1.1·10–3

0.45

0.46

Ni-63

4.20·10–3

5.00·10–3

6.30·10–7

6.60·10–2

6.60·10–2

1.1·10–3

0.45

0.46

Np-237

4.20·10–3

5.00·10–3

6.30·10–7

3.90·101

3.90·101

5.3·10–2

0.45

0.46

Pa-231

4.20·10–3

5.00·10–3

6.30·10–7

3.10

3.10

5.9·10–2

0.45

0.46

Pb-2104.20·105.00·106.30·104.90·102.5·10

–2

0.45

0.46

Pd-107

4.20·10–3

5.00·10–3

6.30·10–7

5.10

5.10

5.2·10–2

0.45

0.46

Pu-2384.20·10–3

5.00·10–3

6.30·10–7

3.90·101

3.90·101

1.5·10–2

0.45

0.46

Pu-2394.20·10–3

5.00·10–3

6.30·10–7

3.90·101

3.90·101

1.5·10–2

0.45

0.46

Pu-2404.20·10–3

5.00·10–3

6.30·10–7

3.90·101

3.90·101

1.5·10–2

0.45

0.46

Pu-242

4.20·10–3

5.00·10–3

6.30·10–7

3.90·101

3.90·101

1.5·10–2

0.45

0.46

Ra-226

4.20·10–3

5.00·10–3

6.30·10–7

1.10·10–3

1.10·10–3

2.4·10–4

0.45

0.46

Se-79

2.50·10–4

3.10·10–4

2.00·10–7

0.00

0.00

3.0·10–4

0.18

0.19

Sm-151

4.20·10–3

5.00·10–3

6.30·10–7

5.20

5.20

1.5·10–2

0.45

0.46

Sn-121m

4.20·10–3

5.00·10–3

6.30·10–7

3.90·101

3.90·1011.6·10–1

0.45

0.46

Sn-126

4.20·10–3

5.00·10–3

6.30·10–7

3.90·101

3.90·1011.6·10–1

0.45

0.46

Sr-90

4.20·10–3

5.00·10–3

6.30·10–7

1.10·10–3

1.10·10–3

3.4·10–6

0.45

0.46

Tc-99

4.20·10–3

5.00·10–3

6.30·10–7

3.90·101

3.90·101

5.3·10–2

0.45

0.46

Th-2294.20·10–3

5.00·10–3

6.30·10–7

3.90·101

3.90·101

5.3·10–2

0.45

0.46

Th-2304.20·10–3

5.00·10–3

6.30·10–7

3.90·101

3.90·101

5.3·10–2

0.45

0.46

Th-232

4.20·10–3

5.00·10–3

6.30·10–7

3.90·101

3.90·101

5.3·10–2

0.45

0.46

U-233

4.20·10–3

5.00·10–3

6.30·10–7

3.90·101

3.90·101

5.3·10–2

0.45

0.46

U-234

4.20·10–3

5.00·10–3

6.30·10–7

3.90·101

3.90·101

5.3·10–2

0.45

0.46

U-235

4.20·10–3

5.00·10–3

6.30·10–7

3.90·101

3.90·101

5.3·10–2

0.45

0.46

U-236

4.20·10–3

5.00·10–3

6.30·10–7

3.90·101

3.90·101

5.3·10–2

0.45

0.46

U-238

4.20·10–3

5.00·10–3

6.30·10–7

3.90·101

3.90·101

5.3·10–2

0.45

0.46

Zr-93

4.20·10–3

5.00·10–3

6.30·10–7

4.70

4.70

2.1·10–2

0.45

0.46

TR-10-50

–3

–3

–7

1

4.90·101

51

Table 3‑4. Median values of solubilities (temperate conditions, see Appendix F), IRF and CRF
used in the deterministic near-field and far-field calculations. If IRF+CRF is greater than one CRF
is 1-IRF. The solubility, CSOL, 1.00·1017 corresponds to unlimited solubility.
CSOL (mol/dm3)

IRF (–)

CRF (–)

Ac-2271.00·1017

0.00

0.00

Ag-108m

1.10·10–5

1.00

0.00

Am-2412.50·10–6

0.00

0.00

Am-242m

2.50·10–6

0.00

0.00

Am-2432.50·10–6

0.00

0.00

C-14

1.00·1017

9.20·10–2

6.40·10–1

Cd-113m

1.00·1017

1.00

0.00

Cl-36

1.00·1017

8.60·10–2

1.50·10–2

Cm-2452.60·10

–6

0.00

0.00

Cm-2462.60·10–6

0.00

0.00

Cs-1351.00·1017

2.90·10–2

0.00

Cs-1371.00·1017

2.90·10–2

0.00

Eu-152

1.00·1017

0.00

0.00

H-3

1.00·1017

1.00

0.00

Ho-166m

4.10·10–6

0.00

0.00

I-129

1.00·1017

2.90·10–2

0.00

Mo-93

1.00·1017

1.20·10–2

8.10·10–1

1.70·10–2

1.00

Nb-93m

4.90·10Nb-94

4.90·10–5

1.80·10–2

1.00

Ni-59

3.00·10–4

1.20·10–2

9.60·10–1

Ni-63

3.00·10–4

1.20·109.70·10–1

Np-2371.00·10

–9

0.00

0.00

Pa-2313.30·10–7

0.00

0.00

Pb-2101.70·10–6

0.00

0.00

Pd-1073.90·10–6

2.00·10–3

0.00

Pu-2384.80·10–6

0.00

0.00

Pu-2394.80·10–6

0.00

0.00

Pu-2404.80·10–6

0.00

0.00

Pu-2424.80·10–6

0.00

0.00

Ra-2269.10·10–7

0.00

0.00

Se-79

6.70·10–9

4.20·10–3

1.30·10–4

0.00

0.00

–5

–2

Sm-1511.10·10

Sn-121m

9.00·10–8

1.90·10–4

5.20·10–1

3.00·10

–4

0.00

–7

Sn-1269.00·10

Sr-90

3.70·10–3

2.50·10–3

0.00

Tc-99

3.80·10–9

2.00·10–3

6.10·10–5

Th-2292.60·10

–9

0.00

0.00

Th-2302.60·10–9

0.00

0.00

Th-2322.60·10–9

0.00

0.00

U-233

9.50·10–10

0.00

2.50·10–1

U-234

9.50·10

–10

0.00

0.00

U-235

9.50·10–10

0.00

0.00

U-236

9.50·10–10

0.00

0.00

U-238

9.50·10–10

0.00

0.00

Zr-93

1.80·10–8

9.20·10–6

1.30·10–1

52–8

TR-10-50

Table 3‑5. Median values of transport parameters used as input data in the deterministic nearfield calculations.
Isostatic load,
pinhole base caseand no spalling

PinholeCrown space

Pinholeno EDZ

Pinholemax EDZ 6

Pinholemax EDZ 7

U0_1 (m/yr)

7.00·10–6

6.7·10–6

5.00·10–6

6.90·10–6

6.50·10–6

QEQ_1 (m3/yr)

4.20·10–6

4.2·10–6

4.50·10–6

4.30·10–6

4.20·10–6

FLEN (m)

6.00

6.20

1.60·101

5.90

6.00

TW_1 (yr)2.10·1021.20 ·102

4.70·102

1.30·102

1.60·102

F_1 (yr/m)

5.50·1063.20·1064.90·1072.60·1063.80·106

QEQ_2 (m3/yr)

9.30·10–5

9.50·10–5

0.00

6.00·10–4

2.20·10–4

TW_2 (yr)1.90·102

9.50·101

0.00

1.10·102

1.40·102

F_2 (yr/m)

63.50·101.2·100.00

1.60·106

QEQR_3 (m /yr)

1.20·10–469.20·1053.30·10–4

2.70·10–42.00·10–58.40·10–4

TW_3 (yr)21.70·108.00·1012.90·102

1.10·102

1.40·102

F_3 (yr/m)

2.40·106.00·105

1.10·1076.30·1051.30·106

TRAPP_3 (m)4.50·101.00

4.50·10–14.50·10–14.50·10–1

LR_TUN_3 (m)

5.10

118

1.80·10

5.00

5.30

TR_TUN_3 (yr)2.00·105890

1.20·1062.60·105

2.40·105

3

6
–1

1

Table 3‑6. Median values of transport parameters used as input data in the deterministic far-fieldcalculations.
Isostatic load,
pinhole base caseand no spalling

PinholeCrown space

Pinholeno EDZ

Pinholemax EDZ 6

Pinholemax EDZ 7

TW_1 (yr)1.80·1029.20·1012.10·102

1.06·102

1.35·102

F_1 (yr/m)

64.00·102.20·106

1.20·107

1.68·106

2.57·106

TW_2 (yr)21.60·107.90·1011.00·10–21

9.70·101

1.27·102

F_2 (yr/m)

62.30·107.50·105

1.00·10–21

6.19·105

1.12·106

TW_3 (yr)21.50·106.30·1012.00·102

9.60·101

1.26·102

F_3 (yr/m)

1.90·1063.20·1055.10·1065.08·105

1.01·106

TR-10-50

53

Table 3‑7. Basic Landscape Dose Factors (Sv/yr per Bq/yr), Dose Conversion Factors for pulse
releases and distributed Dose Conversion Factors /Avila et al. 2010/.
Radionuclide

Basic LDF
(Sv/yr per Bq/yr)

LDF pulse(Sv/yr per Bq/yr)

Distributed LDF(Sv/yr per Bq/yr)

Ag-108m

7.05·10–13

5.08·10–16

7.99·10–14

Ac-2271.30·10–11

Am-241

1.46·10–12

7.34·10–13

Am-243

1.53·10–12

7.57·10–13

C-14

5.44·10–12

Cl-36

5.84·10–13

Cm-2448.74·10–13

4.41·10–13

Cm-245

1.58·10–12

7.78·10–13

Cm-246

1.55·10–12

Cs-1353.96·10–14

Cs-137

1.20·10–13

Ho-166m

5.90·10–14

I-129

6.46·10–10

5.56·10–14

5.96·10–11

Nb-94

4.00·10–12

3.18·10–16

2.29·10–13

Ni-59

7.39·10–14

9.67·10–18

6.57·10–15

Ni-63

1.21·10–15

5.88·10–16

Np-237

4.83·10–11

2.48·10–11

Pa-2318.10·10–12

2.94·10–12

Pb-2105.07·10–12

2.56·10–12

Pd-107

6.73·10–15

2.00·10–15

Po-2108.86·10–12

4.47·10–12

Pu-2391.94·10–12

1.00·10–12

Pu-2401.88·10–12

9.54·10–13

Pu-242

1.89·10–12

1.03·10–12

Ra-2263.75·10

–12

Se-79

1.21·10–9

Sm-151

7.16·10–16

Sn-1262.47·10

–11

Sr-90

2.19·10

–13

Tc-99

8.98·10–13

Th-2293.61·10–121.80·10–12

Th-2301.31·10–11

3.48·10–12

Th-232

1.72·10–128.51·10–13

U-233

2.50·10–12

4.24·10–13

U-234

3.62·10–12

5.19·10–13

U-235

2.76·10–12

4.41·10–13

U-236

1.85·10–12

3.37·10–13

U-238

1.85·10–123.30·10–13

Zr-93

2.77·10–14

6.35·10–15

54

9.48·10–13
4.29·10–15

1.86·10–13

7.75·10–13
1.84·10–16

1.16·10–14
6.03·10–14
1.15·10–14

1.40·10–12
9.70

–14

2.31

–15

2.81

–15

1.50·10–10
3.61·10–16
2.58·10–12
1.10·10–13
2.03·10–13

TR-10-50

3.7.3 QA-related issues
Used scripts, input data and main results are archived at SKB, see Table 3-8.
During the work and final control of data according to the SR-Site quality assurance plan describedin Section 2.9 of the SR-Site Main report, some data have been changed or were identified as being
erroneous. The treatment of such data is as follows:•

The correlation groups for Kd in rock were changed at a late stage of the SR-Site project,when most of the cases had been calculated. The effects of the change were investigated in analternative calculation case of the central corrosion case, see Section 4.5.5. The conclusion isthat the correlation groups have negligible influence on the results. Hence, no other cases wererecalculated.

•

The radionuclide inventory for nuclides present in PWR control rods was changed when most of
the cases had been calculated. The changes in inventory were negligible for all nuclides except
Ag-108m. In calculation cases where Ag-108m contributes to the total dose, the results were
updated by scaling the old results to appropriately account for the corrected input. This is further
described in Appendix E. The solubility for Ag-108m has not been changed in the calculations
due to the changes in the inventory. This is a pessimistic approach.

•Minor changes of the probabilistic distributions for the porosity of the buffer bentonite in the
Data report. The Data report recommends a double triangular distribution (0.124, 0.174, 0.241)
for anions, while the calculations in this report use a triangular distribution (0.13, 0.18, 0.24).
For cations the Data report recommends a triangular distribution (0.41, 0.435, 0.46), while thecalculations in this report use a triangular distribution (0.43, 0.44, 0.47). Since these changes areminor and since the results are not sensitive to uncertainties in buffer porosity, it is concluded thatthe changes in input data would result in insignificant changes of the results if they were to be
implemented. No recalculations were, therefore, performed.

•

Some erroneous correlations between input data were identified when carrying out the sensitivity
analysis.
– One of these was a strong, positive correlation between the fuel dissolution rate and thecorrosion release rate, i.e. of two input data sets that are not correlated. The calculations forthe central corrosion case and the shear load case with failure during the period 1,000 years to
one million years were, therefore, recalculated, with the recalculated result being used in thisreport. The effect on the mean effective dose was negligible and hence no other cases wererecalculated.
– There are also erroneous input data correlations between Kd for buffer and Kd for backfill, Defor buffer and De for backfill and porosity for buffer and porosity for backfill. These correlations are only present in the hypothetical residual scenarios and hence no effort was made toinvestigate the effect of these unwanted correlations. Based on the low sensitivity of the resulton these input data uncertainties, these errors are, however, assessed to have a minor, if any,
impact on the resulting mean doses.

•

The solubility limits for plutonium are too high because of an incorrect value for the associatederror in an equilibrium constant used in the calculations. Figures in Appendix F have beencorrected but incorrect solubility limits for plutonium have been used in all calculation cases.
No recalculations were made since the fault was found at a very late stage of the SR-Site project,during the review of this report. Further, the approach used is pessimistic and does not affect the
total releases. Solubility limits are not included in the calculation cases where the canister fails
due to corrosion, except for the variant that includes solubility limits. The contribution fromplutonium is already low in this variant. In the cases where the canister fails due to shear load,
isostatic load or have a growing pinhole, solubility limits have been included in the calculations
but the contribution from plutonium is already several hundred times lower than the total release.

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55

Table 3-8. List of scripts, input data and main results are archived at SKB (access might be given
on request).
SKBdoc id, version

Title

Issuer, year

1256019 ver 1.0

Hydrogeological model data and results – Forsmark

SKB, 2010

1260107 ver 1.0

Supporting calculations related to radionuclide tramsport

SKB, 2010

1260295 ver 1.0

Results from radionuclide transport calculations with COMP23 andFARF31

SKB, 2010

1260297 ver 1.0

Scripts and input data used for radionuclide transport calculations
with COMP23

SKB, 2010

1265612 ver 1.0

Scripts and data used for Analytical erosion corrosion calculations

SKB, 2010

1266150 ver 1.0

Radionuclide transport calculations with MARFASKB, 2010

56

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4Canister failure due to corrosion

4.1

Introduction

In the ‘canister failure due to corrosion’ scenario (called briefly the corrosion scenario below)
canisters fail as a result of enhanced corrosion due to advective conditions in the deposition holefollowing the loss of buffer through erosion.
For this failure mode, both the canister and the buffer are bypassed, and the rock retention is small
since substantial copper corrosion after buffer erosion only occurs in deposition holes with high flow
rates, which in general are associated with flow paths to the surface of low geosphere retention.

4.1.1 Evolution of the canister after canister failure
According to the analysis of copper corrosion for advective conditions, a band, 0.35 m high andcovering half the circumference of the canister, is assumed to be evenly corroded /SKB 2010/. Thismeans that when penetration occurs, a large amount of damage must be assumed in the copper shell.
The time required to penetrate the cast iron insert is pessimistically neglected since it is difficult toestimate a reasonable development for this process for this failure mode. Also, because penetrationof the copper shell in general occurs after several hundred thousand years for the few canisters
exposed to the highest corrosion rates, the additional time to penetrate the cast iron insert is of lessimportance.
Once the copper canister and the cast iron insert have failed, the void in the insert is assumed to be
rapidly filled with water due to the high flow rate and the lack of transport resistances in the absenceof the buffer and with a large amount of damage also to the cast iron insert.

4.1.2 Radionuclide release
Advective conditions in the buffer must be assumed also for the consequence calculations for the
corrosion scenario. There is no buffer hindering the outward transport of radionuclides meaningthat this is controlled by the flow rate through the deposition hole, q (m3/yr). The following threecontributions to the outward transport can be distinguished.
•

The instantaneously accessible fraction of radionuclides, IRF, that is assumed to rapidly dissolvein the water in the void volume and be subsequently flushed from the canister. This gives rise
to a pulse of uncertain duration, the uncertainty stemming from e.g. uncertainties in the detailed
development of the canister failure through which the IRF is made accessible. The treatment of
the IRF pulse is further described below.

•

A contribution from the corrosion of metal parts in the fuel assemblies and the congruent releaseof radionuclides embedded in the metal parts. These inventories are collectively called the corrosion release fraction, abbreviated CRF.

•

A contribution from fuel dissolution and the congruent release of radionuclides embedded in thefuel matrix.

In a case where the buffer is severely eroded, a colloid filter /Buffer, backfill and closure processreport/ cannot be guaranteed. This means that the use of elemental solubilities as a limit for radio­
nuclide release could be questioned, since it cannot be excluded that the solid particles formed byvarious radionuclides reaching saturation would leave the canister and migrate further. In this case,however, this is of minor concern, since the flow through the deposition hole is often too high forsolid phases to precipitate (with the exception of uranium). This is demonstrated in Section 4.5.2
below by analysing a case where solubility limits are included.

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The release into the fracture is thus controlled by the corrosion rate and the fuel dissolution rate, withtwo exceptions:
1. For uranium, a concentration limit is still an effective constraint on release, due to the large
amount of U-238 present in the fuel. This limits the near-field releases of uranium isotopes,
but also leads to increased near-field releases of Th-230, Th-229 and Pa-231 generated by there-precipitated U-234, U-233 and U-235, respectively.
2. It cannot be excluded that co-precipitation processes and sorption/immobilisation in the remaining bentonite in the deposition hole could confine Th-230 to the near field. If this is the case, its
daughter nuclide, the considerably more mobile Ra-226, would be released. The so generated
Ra-226 is assumed to be released to the flowing groundwater in the fracture intersecting thedeposition hole. This causes higher releases of Ra-226, since there is a contribution not only
directly from the fuel dissolution, but also from the confined Th-230. Since Ra-226 is often themain contributor to dose, this also causes higher total doses. Sorption of thorium in the near fieldis thus assumed. The effect of disregarding thorium sorption is analysed as a separate calculation
case.
Furthermore, as the flow rate in the intersecting fracture is high, the retention in the rock is in
general limited for these deposition holes.
A description of the discretisation and boundary condition used in COMP23 is given in Appendix G,
Section G.6.

4.1.3 IRF-pulse
The fraction of the inventory assumed to be instantaneously released from the fuel upon watercontact is expected to be released to the geosphere in a matter of years in the corrosion scenario,
since the flow rates at the deposition positions with the eroded buffer and failed canister are high,see further Table 4‑3 below. Since these nuclides are in general non-sorbing and since the flow
related retardation properties in the geosphere are poor for the flow paths associated with the deposition positions in question, they are generally released as pulses of durations of tens of years from thegeosphere to the biosphere. In this case, the basic LDF values would yield overly pessimistic estimates of doses. Therefore, the calculations for the IRF are made separately. There are two reasons to
calculate them separately; one is the fact that the calculated basic LDF-values are not developed forpeak releases as described in Section 3.5 and the other is that it is not meaningful to present many
sharp peaks (up to almost 2,000 in one of the probabilistic cases) in a figure.
A number of nuclides with an IRF, and with half-lives up to 10,000 years (e.g. Sr-90, Cs-137,
Ag-108m and C-14,), were excluded from the analysis of the corrosion cases since they would decay
to insignificance before a failure would occur.
Tc-99

The release of the IRF part of Tc-99 has been calculated in two different ways for the near field
and for the far field. For the near field the dose equivalent release is calculated in the same way as
for all other IRF nuclides. The far-field pulse release is modelled with the far-field transport model
since sorption in the geosphere is considerable for Tc-99. To obtain the far-field annual effective
dose the IRF of Tc-99 was included in a separate calculation with COMP23 and transferred to the
FARF31 calculations. This means that the far-field annual effective dose of all Tc-99 (the IRF and
non IRF parts) is available when the figures for the far-field release are plotted, however the meanannual effective dose is lower than 10–3 µSv for all corrosion cases and therefore not visible in the
figures.

58

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Deterministic calculations

Deterministic calculations of the IRF-pulse from I-129, Se-79, Cs-135, Ni-59, Cl-36, Sn-126 andNb-94 are calculated as follows. The total dose associated with a pulse release, DTotPulse, is calculated
by taking the IRF inventory at 100,000 years multiplied by the pulse LDF-values, given in Table 3‑7,
to yield a total peak dose from the pulse release for one canister. The IRF inventory could be taken
at the actual failure time for the different cases, but this would not affect the result much since these
nuclides are long-lived in comparison to the failure times.
Note that it is also pessimistic to apply the pulse LDF approach because the maximum dose for agiven mass released to the biosphere is obtained when the entire mass is released at once, notingthat the LDF pulse values are by definition taken for the point in time in the landscape development
where the consequences are maximal.
Probabilistic calculations

The IRF pulses in the probabilistic cases are shown to give negligible contribution to the mean dose,
by applying the treatment for the central corrosion case, see Section 4.4.2. Therefore, the IRF-pulse
releases are not reported for the other cases. However, they are considered in the account of risk
dilution reported in the Main report Section 13.9.

4.2

Summary of calculation cases

There are three hydrogeological models (semi-correlated, uncorrelated and fully correlated),
described by /Joyce et al. 2010/ and summarised in the Data report, Section 6.7, that form the basefor the calculation cases. In Figure 4‑1 the hydrogeological models are indicated with blue boxes.
Three erosion cases (orange boxes in Figure 4‑1) are included yielding nine corrosion variants toconsider in the derivation of calculation cases for radionuclide transport and dose. Of these, the three‘no advection’ variants are not further treated as they do not lead to canister failures. A central corrosion variant base on the ‘SR-Site erosion model’ was identified as the one on which assessments ofradionuclide transport and dose should primarily be made. In addition the variant with initial advection was studied. The green boxes in Figure 4‑1 indicate all the calculation cases for radionuclidetransport and dose. The cases are reported in the same order as in the figure.
The central corrosion case consists of the semi-correlated hydrogeological DFN-model, the SR-Siteerosion model and base case transport assumptions. The following cases of alternative transportconditions are analysed for the central corrosion variant:
•
•
•
•
•
•
•
•

a case disregarding thorium sorption in the near field;
a case including solubility limits in the near field,
a case with decreased sorption of lead in the geosphere,a case with Kd for U(VI) instead of U(IV) in the geosphere,a case assessing the influence of correlation groups for Kd in the geosphere,cases with colloid facilitated transport in the geosphere,a case with varying climate conditions,a case with varying climate conditions and colloid facilitated transport in the geosphere.

The other five relevant corrosion cases are analysed with the base case transport assumption.

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59

Semicorrelatedhydro DFN

SR-Siteerosionmodel

Base case transport assumptions

Centralcorrosion
case

Disregarding thorium sorption in the near filed
Including solubility limits in the near field
Decreased sorption of lead in the geosphere
Kd for U(VI) instead of U(IV) in the geosphere
Influence of correlation groups for Kd in the geosphere
Initialadvection

Colloid-facilitated transport
Varying climate conditions
Varying climate conditions and colloid-facilitated transport

Uncorrelatedhydro DFN

No
advection

Base case transport assumptions

SR-Siteerosionmodel

Base case transport assumptions

Initialadvection

Base case transport assumptions

Noadvection
Fully
correlatedhydro DFN

SR-Siteerosionmodel

Base case transport assumptions

Initialadvection

Base case transport assumptions

Noadvection

Figure 4‑1. Overview of calculation cases for the corrosion scenario. Blue boxes indicate hydrogeological
DFN models, orange boxes indicate erosion/corrosion variants and green boxes indicate the calculation cases
for radionuclide transport and dose. The calculation cases are presented in the same order as in this figure.

4.3

Input data specific for the corrosion scenario

Most of the input data used in the corrosion scenario are given in Section 3.7 that summarises data
for all scenarios. In this section more details regarding the used hydrogeological calculations andfailure times are given.
The failure times are obtained as output from the erosion/corrosion calculations reported in /SKB
2010/ and the results are available in SKBdoc, see Table 3-8. The input to those calculations isqualified in the SR-Site Data report.
Several realisations of each of the three variants of the hydrogeological DFN model are propagatedto the corrosion scenario, see Table 4‑1. In all calculations for this scenario, deposition positions are
rejected according to the EFPC criterion (canister positions intersected by fractures that also intersect
the entire tunnel perimeter have been discarded) in the output from the hydrogeological modelling. In
the central corrosion case, data from the 10 realisations of the semi-correlated DFN model are used.

60

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Table 4‑1. Hydrogeological realisations used in the corrosion scenario /Joyce et al. 2010/.
Hydrogeological DFN model

Realisations

Semi-correlated model

Base case and 10 additional realisations

Uncorrelated model

Base case and 5 additional realisations

Fully correlated model

Base case and 5 additional realisations

The corrosion case is based on data for only the few deposition holes that experience canister failure
due to corrosion. This means that all deposition holes of relevance experience a high flow rate andin general also a low flow-related rock transport resistance, since these properties are strongly correlated. It is noted that the calculated hydraulic and transport properties of these deposition holes arefrom the extreme tails of distributions derived from a complex hydrogeological model with stochastic components (the generated fracture network). For the deterministic calculations of the corrosion
scenario the parameters used are those connected to the earliest failure time; these parameters are
summarised in Table 4-2. For probabilistic calculations, the ten realisations of the semi-correlated
model variant are used in order to obtain more reliable representations of these tails, see Table 4-3.
For the uncorrelated and fully correlated DFN model variants, for which consequences are analysedin Section 4.6 and 4.7, the five available realisations are used.
Table 4‑2. Data for the deposition holes where the first canister fails, used in deterministic
calculations.
Hydrogeological model/
Erosion modelTime of failure(yr)

Semi-correlated/SR-Site

114,485

53,6606

0.733

Uncorrelated/SR-Site

97,8155,757,000

292

0.641

Fully correlated/SR-Site

99,70045,60012

0.626

Semi-correlated/Initial advection

44,04953,6606

0.733

Uncorrelated/Initial advection

47,107

5,757,000

292

0.641

Fully correlated/Initial advection

47,65745,60012

0.626

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Rock transport
resistance,
F (yr/m)

Advective
travel time,tw (yr)Advective flow
through deposition
hole, q (m3/yr)

61

Table 4‑3. Data for the deposition holes where canisters fail due to corrosion for the ten realisations of the semi-correlated DFN model. Sorted by ascending time of failure.
Time of failure (yr)Rock transport resistance,
F (yr/m)

Advective travel time,tw (yr)Advective flow throughdeposition hole, q (m3/yr)

114,485
122,557
132,155
157,452
157,805
179,621201,037
230,828
305,884
313,807361,884
377,494
391,981402,471442,257
471,801
480,309504,166
521,967
526,759
531,274
569,225569,701
595,478
600,806
612,248612,252
644,354652,328
674,477
693,725705,692
714,768
750,814753,537
777,848
792,067
803,247
807,815
822,765
845,022845,360
849,820869,351885,650
889,770
891,310
893,681
901,874915,297
918,487
929,149
941,008
956,114956,944
978,463

53,660564,900
14,51026,260642,100
87,82089,910818,600
33,97033,140,000
2,184,000
38,17024,220,000
157,900
155,100
163,400
25,290,000
53,66024,830,000
116,600
53,66053,660564,900
53,660564,900
471,800
53,660564,900
211,100
564,900
564,900
1,710,000
26,260642,100
26,26014,510642,100
11,33026,26014,51087,82026,260642,100
26,26014,510642,100
87,82053,6609,083,000
642,100
2,008,000
14,51061,40087,82014,5103,845,000

6
61
23
7
78
14
17
38
16
2,501
124
14
2,021
19
19
29
2,070
6
1,994
241
6
6
61
6
61
31
6
61
20
61
61
99
7
78
7
23
78
20
7
23
14
7
78
7
23
78
14
6
601
78
135
23
18
14
23
91

0.733
0.557
0.267
0.358
0.316
0.251
0.144
0.148
0.082
0.079
0.083
0.095
0.060
0.086
0.075
0.067
0.047
0.733
0.042
0.050
0.733
0.733
0.557
0.733
0.557
0.048
0.733
0.557
0.044
0.557
0.557
0.033
0.358
0.316
0.358
0.267
0.316
0.035
0.358
0.267
0.251
0.358
0.316
0.358
0.267
0.316
0.251
0.733
0.026
0.316
0.024
0.267
0.032
0.251
0.267
0.033

62

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4.4

Central corrosion case

4.4.1

Deterministic calculations

Hydrogeological case:
Erosion/corrosion model:
Failure time:
Number of failed canisters:
Solubility limits:
Thorium sorption in near field:
Number of realisations:
Number of nuclides:

Semi-correlated, ten realisations
SR-Site model
114,485 years
1No
Yes (modelled as low solubility limit)
1
37

A deterministic calculation of the central corrosion case is performed for a canister taken from therealisation with the earliest failure time of the analysed realisations (114,485 years after deposition)with corresponding geosphere transport data, i.e. data used to calculate the corrosion time are fromthe same hydrogeological calculation as the geosphere transport data. Advection occurs in the buffer
void and the dose equivalent releases are primarily determined by the fuel dissolution rate set to 10−7/yr.
The contributions from the instantly released fraction of nuclides, IRF, are calculated separately.
Table 4‑4 shows peak annual doses from the pulse releases from the instantly released fraction, IRF.
The IRF inventory at 100,000 years has been multiplied by the pulse LDF-values given in Table 3‑7.
Figure 4‑2 shows the near-field releases converted to doses through multiplying the release rate by
the LDF-value. As mentioned in Section 3.5, the conversion to dose is done to obtain a convenientmetric of release consequence that can also be summed to obtain a metric that considers all nuclides.
The dose equivalent releases from the geosphere are shown in Figure 4‑3.
The dose equivalent release from the near field is dominated by Tc-99 (as IRF-pulse), Nb-94 andNi-59. The peak contributions from Nb-94 and Ni-59 are due to the relatively fast release of thepart of these nuclides embedded in the metal in the fuel assemblies. The time for metal corrosion isshort (log-triangular 102, 103, 104 yr) compared to the time scale for the release. The doses caused byreleases from the far field are dominated by I-129 (as IRF-pulse), Ra-226 and Se-79 (as IRF pulse).
The far-field pulse release for Tc-99 is modelled with the far-field transport model since sorption
in the geosphere is considerable for Tc-99. The pulse release of Tc-99 is thus included in the results
shown in Figure 4‑3.
Table 4‑4. Peak annual dose from the pulse releases from the instantly released fraction, IRF, fora deterministic calculation of the central corrosion case. The dose is calculated at 100,000 years.
NuclidePeak annual dose (µSv)

I-129

3.82

Se-79

1.72

Cs-135

0.21

Cl-36

0.12

Nb-94

0.026

Sn-126

0.019

Ni-59

0.012

Tc-99

6.81a)a)

The peak annual dose for Tc-99 is only valid for the near field.

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63

Annual effective dose [µSv]

102

101

100

10-1

Nb94
Ni59
Ra226
Se79
Zr93
Np237
Pb210
Pu239
I129
Tc99
Sn126
Pa231
Pu242
Ac227
Cl36
Total

(12)
(7.3)
(5.0)
(1.1)
(0.58)(0.45)(0.30)(0.17)(0.15)(0.11)(0.050)(0.030)(0.028)(0.0027)(0.0026)(22)

Dose corresponding
to risk limit

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑2. Near-field dose equivalent release for a deterministic calculation of the central corrosion case.
The legend is sorted by peak (in the one-million year period) of the annual effective dose. The values inbrackets are peak dose in units of µSv. The curves for Nb-94 and Ni-59 are hidden under the curve showing
the total dose equivalent release.

102

Annual effective dose [ µSv]

101

100

10-1

10-2

10-3
103

Ra226
Ni59
Se79
Np237
I129
Nb94
Pb210
Pu239
Tc99
Ac227
Pu242
Th229
Zr93
U233
Pa231
Sn126
Cl36
Total

(2.6)
(1.3)
(0.68)(0.24)(0.15)(0.11)(0.044)(0.024)(0.018)(0.014)(0.013)(0.0082)(0.0063)(0.0060)(0.0037)(0.0031)(0.0013)(3.2)

Dose corresponding to risk limit

104

105

106

Time [years]

Figure 4‑3. Far-field annual effective dose for a deterministic calculation of the central corrosion case.
The legend is sorted by peak (in the one-million year period) of the annual effective dose. The values inbrackets are peak dose in units of µSv.

64

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4.4.2

Probabilistic calculations

Hydrogeological case:
Erosion/corrosion model:
Failure time:
Average number of failed canisters:
Solubility limits:
Thorium sorption in near field:
Number of realisations:
Number of nuclides:

Semi-correlated, ten realisations
SR-Site model
56 times according to Table 4‑3
0.12NoYes (modelled as low solubility limit)
50 per canister failure time37

A probabilistic calculation of the central corrosion case is performed with failure times and geo­
sphere transport data from the ten realisations of the semi-correlated DFN model, see Table 4‑3.
The mean number of failed canisters, 0.12, is an outcome of the corrosion calculations /SKB 2010/.
The contributions from the instantly released fraction of nuclides, IRF, are calculated separately.
The contribution from the IRF pulse in the probabilistically calculated mean dose is treated as follows. The probability of canister failure, pFail, is determined for each 100,000 year interval from thecalculated distribution of canister failure times for the central corrosion case. The total probability
until one million years is the sum of all pFail, i.e. 0.12 for the central corrosion case. The width of thedose curves in the biosphere is typically 1,000 years. The likelihood that an exposure due to a pulse
release, pExpo, is present at a given point in time during the 100,000 year interval is thus 10−2 · pFail.
(The likelihood of overlaps between pulses is very small due to the low probabilities.) The total dose
associated with a pulse release DTotPulse is determined at the start of each 100,000 year interval (inthe same way as described for the deteministic case). The probabilistically calculated mean doseis then obtained as the probability of exposure multiplied with the total dose associated with thepulse release (pExpo·DTotPuls). The result of this procedure for the central corrosion case is shown in
Table 4‑5. As seen in the table, the highest mean dose is around 1·10−3 μSv, i.e. more than four ordersof magnitude below the dose corresponding to the risk limit. The pulse releases thus give negligible
contributions to the probabilistically calculated mean dose. It is also noted that this treatment
assumes that temperate conditions are prevailing. Including probabilities of periglacial and glacial
climate conditions would reduce the mean dose further. The IRF pulse of Tc-99 is modelled with the
far-field transport model since sorption in the geosphere is considerable for Tc-99. The pulse releaseof Tc-99 is thus included in the results shown in Figure 4‑5.
Figure 4‑4 shows near-field dose equivalent releases and Figure 4‑5 shows the corresponding
far-field dose equivalent releases. The failure times are reflected as distinct features in the release
curves, in particular for the near field. The pulse like features are due to release controlled bycorrosion of the metal parts of the fuel assemblies (e.g. Ni-59). The metal corrosion times (ranging
between 100 and 10,000 years) are such that the releases appear as pulses on the time scale of thedose curves. The first releases occur after around 110,000 years when the first canister fails.
Table 4‑5. Calculation of the total mean dose from release of the instant release fraction, IRF,
in the central corrosion case.
Time interval [yr]pFail

0–100,000

0

0

0

0

100,000–200,000

1.25·10–2

1.25·10–4

5.92

7.4·10–4

200,000–300,000

4.17·10–3

4.17·10–5

5.54

2.3·10–4

300,000–400,000

1.04·10–2

1.04·10–4

5.25

5.5·10–4

400,000–500,000

8.33·10–3

8.33·10–5

5.01

4.2·10–4

500,000–600,000

1.46·10–2

1.46·10–4

4.81

7.0·10–4

600,000–700,000

1.46·10–2

1.46·10–4

4.64

6.8·10–4

700,000–800,000

1.25·10–2

1.25·10–4

4.49

5.6·10–4

800,000–900,000

2.29·10–2

2.29·10–4

4.37

1.0·10–3

900,000–1,000,000

1.67·10–2

1.67·10–4

4.26

7.1·10–4

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pExpo

DTotPulse[µSv]

Mean dose
[µSv]

65

The doses caused by releases from the near field are dominated by Ra-226. Much of the Ra-226
released from the near field is transmitted through the geosphere since the failed canisters are locatedin deposition holes intersected by large, highly transmissive fractures with low retention. The releaseof Ra-226 from the geosphere is almost exclusively due to Ra released from the near field and not
to in-growth in the geosphere. This, in turn, is related to the fact that the parent nuclide Th-230
is assumed to be confined to the near field. Despite the fast release in the far field the dose from
Pb-210 decrease significantly due to its short half-life (22 years). The far field also significantly
influences nuclides controlled by corrosion with pulse like releases in the near field, for example
Ni-59. For Tc-99 the geosphere retention is significant and the dose is below 10–3 µSv/yr
Some statistics for the far-field release are shown in Figure 4‑6. Note that these are derived only forthe realisations of the failure times where failures actually occur in the corrosion calculations. Since
the mean number of failed canisters is about 0.12, the most likely outcome of the corrosion calculations is zero failures. This is not reflected in the percentiles in Figure 4‑6, other than for the meanvalue. Taking this into account would bring the 99th and 95th percentiles closer to the mean.

Mean annual effective dose [µSv]

102

101

100

Ra226

(0.38)

Pb210(0.095)

Np237(0.061)

I129(0.025)Se79(0.018)Nb94(0.016)Ni59(0.015)Pa231(0.0025)

Zr93(0.0016)

Tc99(0.0012)

Pu242(0.0010)Total(0.59)

Dose corresponding to risk limit

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑4. Near-field dose equivalent release for a probabilistic calculation of the central corrosion
case. The average number of failed canisters is 0.12. The legend is sorted by peak (in the one-million
year period) of the mean annual effective dose. The values in brackets are peak dose in units of µSv.

66

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102

Mean annual effective dose [µSv]

101

100

Ra226

(0.11)

I129(0.024)

Np237(0.019)Se79(0.013)Pb210(0.0059)

Ni59(0.0039)

Ac227(0.0031)

Nb94(0.0017)

Total(0.18)

Dose corresponding to risk limit

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑5. Far-field mean annual effective dose for a probabilistic calculation of the central corrosion
case. The legend is sorted by peak (in the one-million year period) of the mean annual effective dose.
The values in brackets are peak dose in units of µSv.

102
99:th percentile
95:th percentile
Mean

Annual effective dose [µSv]101

Dose corresponding to risk limit

Median

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑6. Far-field annual effective dose (mean, median, 95th and 99th percentiles) for the probabilistic
calculation of the central corrosion case.

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4.4.3

Sensitivity analysis

Introduction

This section presents results of sensitivity analyses of the results of the dose calculations, i.e. thesensitivity of the uncertainty in calculated dose to uncertainties in the input parameters is analysed.
All analyses concern the probabilistic calculation of the central corrosion case.
It is of interest to determine i) the variables that correlate with the dose over the entire dose range
and ii) the parameter values that are related to high and low doses. Ra-226 dominates the dose inmost of the realisations in the central corrosion case and it is thus of particular interest to clarify
sensitivities of the Ra-226 dose to input parameters.
Global sensitivity analysis

The first purpose is thus to perform a so-called global sensitivity analysis, i.e. to identify the input
parameters that have the greatest influence on the spread of the results. The contribution to output
spread depends on both the spread of the input parameter and the model’s sensitivity to variations inthat particular input parameter. A range of methods for this type of sensitivity analysis exists /­Saltelli
et al. 2000/. Several studies and reviews have demonstrated that standardised rank regression is asuitable method for sensitivity analysis of non-linear systems where the calculation end point is amonotonic function of the input variables /Saltelli et al. 1993, Helton 1993, Hamby 1994, Iman andConover 1979/. This applies to the present non-linear and monotonic system /Hedin 2003/, and thestandardised rank regression coefficient (SRRC) is, therefore, used for identifying the most importantvariables contributing to dose uncertainty.
A standardised rank regression analysis of the total dose at 106 years on the input variables yields,
in descending order, the fuel dissolution rate DFuel, the flow-related transport resistance along thegeosphere flow path, F, and the failure time tFailure as the input parameters most affecting dose results,
see Figure 4‑7. Regressing on Ra-226 dose at 106 years yields a similar result due to the dominanceof Ra-226. The ranking of the two most important variables is switched in this case. This switching of
the ranking is consistent with the fact that the fuel dissolution rate, DFuel, affects all nuclides whereas
the F parameter only affects sorbing nuclides. Thus F is relatively more important for the Ra-226 dosethan for the total dose, which is in some of the realisations dominated by the non-sorbing I-129. It is

F

DFuel
tFailure

Total dose @ 106 yearstwDe cations

R2 = 0.92

Ra-226 dose @ 106 years

F

R2 = 0.89

tw

DFuel

tFailure
Kd Ra
De cations
-1

-0.5

0

0.5

1

Standardised Rank Regression Coefficients
Figure 4‑7. Results of standardised rank regression for the central corrosion case. Regressing on total doseat 106 years and on Ra-226 dose at 106 years yields similar results due to the dominance of Ra-226.

68

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also noted that the three variables F, tw (advective travel time) and tFailure are correlated, meaning that
their significance is not necessarily as high as indicated by the SRRC method. This is further investigated with a tailored regression model, as descibed below. Standardised rank regression analysis on
maximum of total dose over time yields an almost identical result as regressing on total dose at one
million years (not shown in the figure). However, regressing on e.g. peak Ni-59 equivalent dose fromthe near field (not shown in the figure) identifies also the corrosion release rate, CRR, as a sensitive
input variable. This sensitivity to CRR is consistent with the fact that in some realisations of the central
corrosion case, the peak dose due to Ni-59 occurs shortly after canister failure and is then caused by
the releases congruent with the corrosion of the metal parts of the fuel assemblies.
Main risk contributors

The standardised rank regression analysis identifies the variables that co-vary with the dependent
variable, the total dose, over the entire dose range. To determine the variables that are related to thehighest doses, a conditional mean value analysis /Hedin 2002a/ was carried out. Here, the subsets
of input parameter values related to the top percentile of the dose are selected. For each such subset,
the mean value of the logarithmically transformed data was determined for each parameter and compared to the corresponding mean value of the entire input distribution. A dimensionless, normalised
measure, α99, is obtained by dividing the difference between the two mean values by the standard
deviation of the entire distribution.
The so determined conditional mean value identifies variables that take on significantly different
values in the top percentile realisations compared to the entire dose distribution. In descending order,
the tFailure, DFuel, F and tw parameters were identified as most significant, see Figure 4‑8. Similarly,
α1-values, relating to the lowest percentile of the dose distribution were determined. Also α99 − α1values were determined to distinguish extreme outcomes from others. The highest ranking variables
were, in descending order, DFuel, F, tw (tw is strongly correlated to F) and tFailure.

t Failure

DFuel

F
tw
Kd Ra
De cations

Ftwt Failure

-5

-4

-3

-2

α

99

DFuel

Kd Ra
De cations

-1

α −α
99

De anions
0

1

2

3

4

1

5

Conditional Mean Values
Figure 4‑8. Conditional mean values for the central corrosion case.

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Tailored regression model

The understanding and mathematical formulation of the transport models used in the dose calculations can be utilised to further explain the results. The release rate of Ra-226 is determined by theamount of its parent nuclide, Th-230, liberated from the fuel matrix and subsequently assumed tosorb in the near field. This amount is proportional to the product of the fuel dissolution rate, DFuel,and the time, t, elapsed between the canister failure and the point in time for which the dose is calculated, i.e. it is proportional to DFuel · t. In the studied case t = 106 – tFailure. It can further be shownthat the released Ra-226 is transported through the geosphere with a certain transmission efficiency,
θ, that in its full expression depends in a complex way on all the uncertain parameters relating togeosphere transport, see e.g. /Hedin 2002b/. However, it can also be demonstrated that most of thevariability of θ is captured by the simpler expression /Hedin 2003/:()

θ ∝ exp − cF 0.5 (K d De )0.25 							4‑1where c is a positive constant determined by well known properties like the density of the rock andthe half-life of Ra-226. This suggests that the Ra-226 dose varies according to:
0.25
log(DoseRa226) = Constant + log(DFuel t ) − cF 0.5 (K d De ) 				4‑2and that a tailored regression model according to the above expression could be successful inexplaining the calculated results. Figure 4‑9 shows how such a regression model is able to predictthe calculated results when successively more terms are included in the model. As seen in the figure,the agreement when all terms are included is good, with an R2-value of 0.99.

These expressions also reveal combinations of input variables of importance. Obviously, combinations of high DFuel and t values and combinations of low values of the three factors occurring in the
exponent of the first expression favour high doses. This result also illustrates that the variable tw,
identified as important for the Ra-226 dose by the SRRC method above is not needed to explain the
Ra-226 dose. It is concluded that tw is identified in the SRRC method only since it is correlated to
the F parameter. (This can be further analysed through use of partial rank correlations in the SRRC
method.)Regression model Ra-226 dose at 106 years [μSv]

A partition plot, Figure 4‑10, showing how high and low dose results relate to the variable groups
DFuel ·t and F 0.5(Kd ·De)0.25 confirms the explanatory power of these variable groups.
10

1

0.1

0.01

0.001

Blue: log(DFuel·t) + C
Green: log(DFuel·t) - cF0.5 + C
Red: log(DFuel·t) - cF0.5·Kd0.25 + C
Black: log(DFuel·t) - cF0.5·(Kd·De)0.25 + C

0.00010.00001
0.00001

0.0001

0.001

0.01

0.1
6
Calculated Ra-226 dose at 10 years [μSv]1

R2 = 0.13
R2 = 0.84
R2 = 0.94
R2 = 0.99
10

Figure 4‑9. Four tailored regression models, including successively more variables, for the Ra-226 dose at
one million years for the central corrosion case.

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1

DFuel·t

0.1

0.01

0.001
High; > 90:th percentile
Intermediate
Low; < 10:th percentile
0.0001
0.1

1

10

100

F 0.5(KdDe)0.25

Figure 4‑10. Partition plot demonstrating how the two groups of variables on the axes relate to high andlow dose results for Ra-226 for the central corrosion case.

Conclusions

The above analyses show that relatively simple methods can identify the uncertain input parameters
to which the probabilistic result is most sensitive. That sensitivities can be identified with relatively
simple methods is in part due to the nature of the conceptualisation of the calculation cases in the
corrosion scenario, where the buffer is omitted and the near-field release is essentially controlled
only by the fuel dissolution rate.
The fuel dissolution rate, DFuel, and the geosphere flow-related transport resistance, F, emerge
generally as the uncertain input parameters to which the result is most sensitive. The uncertainty incorrosion release rate, CRR, has a significant impact on the result of near-field releases immediately
after failure for nuclides that are released congruently with metal corrosion.
It is also noted that a number of different assumptions regarding transport conditions are analysedin Section 4.5, where it is found that the sensitivity to these assumptions is low, see Figure 4‑58
and Figure 4‑59. Similar results are expected for all corrosion variants since they differ from thecentral corrosion case only through somewhat altered input distributions for the failure times andthe hydrogeological transport parameters.

4.4.4

Issues related to the probabilistic nature of the calculations

Convergence

The number of canister failure times varies significantly in the different corrosion cases (from 56 in
the central corrosion case to 1,964 in a case that does not use best available technique BAT). Datain the Data report have distributions and these have been used to make input files to COMP23 andFARF31 for probabilistic calculations, see Section 3.7.1. To assure a correct use of the probabilistic
data, each canister failure time needs to be run several times with different sets of input (realisations). In Figure 4‑11 the near-field and far-field releases of Ni-59, in the central corrosion case, areshown for different numbers of realisations per canister failure time. Both curves converge rapidly;
50 realisations were judged to be adequate and this value was used for all the corrosion cases. The
choice of 50 realisations provides sufficient accuracy in the statistics without excessive total calculation times.

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102
Ni-59, nearfield
Ni-59, farfield
Dose corresponding to risk limit

Mean annual effective dose [ µSv]

101

100

10-1

10-2

10-3
0

50

100

150

200

250

Realisations

Figure 4‑11. Mean annual effective dose for Ni-59 as a function of the number of realisations in the central
corrosion case.

Risk dilution

The issue of risk dilution is discussed in the methodology Section 2.6.2 in the Main report andneeds to be addressed for the corrosion scenario. Doses are accounted for as a continuous contribution and as a relatively short pulse contribution.
In all probabilistic cases of the corrosion scenario, a fixed number of canisters, depending on thecase studied, were assumed to fail at a set of fixed times. Thus, this factor cannot give rise to risk
dilution. Regarding the pulse releases, these are given as peak doses for an assumed, single releaseof the entire IRF inventory and can thus not give rise to risk dilution.
The continuous contributions have, for a fixed failure time, an initial peak of limited duration
followed by an increasing dose that generally grows beyond the value of the initial peak. Because
this means that the maximum dose occurs at the end of the one million year assessment time, risk
dilution is not an issue for the continuous contributions; the maximum risk is experienced by thesame hypothetical generation living at the end of the assessment period irrespective of failure time.
This is verified by comparing the peak-of-the-mean value (0.177 μSv/yr) to the mean-of-the-peaks
value (0.179 μSv/yr) for the central corrosion case.
Risk dilution, including a treatment of the pulse releases, is further discussed in Section 13.9 in theMain report.

4.5

Alternative cases based on the semi-correlatedhydrogeological DFN model

In order to assess the sensitivity of the results to various assumptions, a set of alternative cases basedon the semi-correlated hydrogeological DFN model have been undertaken.

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4.5.1

Disregarding thorium sorption in the near field

Deterministic calculations
Hydrogeological case:
Erosion/corrosion model:
Failure time:
Number of failed canisters:
Solubility limits:
Thorium sorption in near field:
Number of realisations:
Number of nuclides:

Semi-correlated, ten realisations
SR-Site model
114,485 years
1
No
No
1
37

A deterministic calculation of the central corrosion case disregarding thorium sorption in the nearfield is performed to assess the sensitivity of the release of primarily Ra-226 due to alternativetransport conditions for thorium.
The calculation of the IRF-pulses for the deterministic central corrosion case is also valid for thecase disregarding thorium sorption in the near field. Hence, Table 4‑4 shows the peak annual doses
from the pulse releases from the instantly released fraction, IRF.
Figure 4‑12 and Figure 4‑13 show the deterministic near-field and far-field dose equivalent releases,
respectively, for the central corrosion case when disregarding thorium sorption in the near field. The
dose from thorium is obviously higher in this case compared to the central corrosion case. The dose
caused by the release of the dose-dominating Ra-226 is lower in this case compared to the central
corrosion case, showing that the assumption of thorium sorption in the near field made in the central
corrosion case is pessimistic.

102

Annual effective dose [µSv]

10

10

1

0

10-1

10-2

10-3

103

Nb94

(12)

Ni59

(7.3)

Se79

(1.1)

Th229

(0.61)

Zr93(0.58)

Np237(0.45)

Th230(0.37)

Pu239(0.17)

I129(0.15)

Tc99(0.11)

Pb210(0.056)Sn126(0.050)Ra226(0.041)

Pa231(0.030)Pu242(0.028)Ac227(0.0027)

Cl36(0.0026)

Total

(22)

Dose corresponding
to risk limit

104

105

106

Time [years]

Figure 4‑12. Near-field dose equivalent release for a deterministic calculation of the central corrosion
case, disregarding thorium sorption in the near field. The legend is sorted by peak (in the one-million year
period) of the annual effective dose. The values in brackets are peak dose in units of µSv.

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102

Annual effective dose [µSv]

101

10

0

10-1

10-2

Ra226

(1.6)

Ni59

(1.3)

Se79

(0.68)

Np237(0.24)

I129(0.15)

Nb94(0.11)

Th230(0.095)Pb210(0.028)Th229(0.024)

Pu239(0.024)Tc99(0.018)

Ac227(0.014)

Pu242(0.013)Zr93(0.0063)U233(0.0060)

Pa231(0.0037)

Sn126(0.0031)Cl36(0.0013)

Total

(2.4)

Dose corresponding to risk limit

10-3
103

104

105

106

Time [years]

Figure 4‑13. Far-field annual effective dose for a deterministic calculation of the central corrosion case,disregarding thorium sorption in the near field. The legend is sorted by peak (in the one-million year
period) of the annual effective dose. The values in brackets are peak dose in units of µSv.

Probabilistic calculations
Hydrogeological case:
Erosion/corrosion model:
Failure time:
Average number of failed canisters:
Solubility limits:
Thorium sorption in near field:
Number of realisations:
Number of nuclides:

Semi-correlated, ten realisations
SR-Site model
56 times according to Table 4‑3
0.12
No
No
50 per canister failure time37

The contributions from the instantly released fraction of nuclides, IRF, are not included in thecalculations except for Tc-99 that is included in the far-field calculations. The results for the IRF
presented for the central corrosion case is judged to be enough to conclude that their contribution
is negligible also in this case, see Section 4.4.2.
Figure 4‑14 and Figure 4‑15 show near-field and far-field dose equivalent releases, respectively,
for the central corrosion case when disregarding thorium sorption in the near field. Doses caused byrelease of Ra-226 and the total dose are both lower than in the central case, showing that the assumption of thorium sorption in the near field made in the central corrosion case is pessimistic.

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Mean annual effective dose [µSv]

102

10

1

100

10-1

Th229

(0.079)Np237(0.061)

Th230(0.033)

I129(0.025)Se79(0.018)Nb94(0.016)Ni59(0.015)Pb210(0.0032)

Pa231(0.0025)

Ra226(0.0024)

Zr93(0.0016)

Tc99(0.0012)

Pu242(0.0010)Total(0.22)

Dose corresponding to risk limit

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑14. Near-field dose equivalent release for the probabilistic central corrosion case, disregarding
thorium sorption in the near field. The legend is sorted by peak (in the one-million year period) of the meanannual effective dose. The values in brackets are peak dose in units of µSv.

Mean annual effective dose [µSv]

102

101

10

0

Ra226

(0.063)

I129(0.024)

Np237(0.019)Se79(0.016)Ni59(0.0071)

Th230(0.0058)

Th229(0.0054)

Ac227(0.0030)

Pb210(0.0027)

Nb94(0.0016)

Total(0.14)

Dose corresponding to risk limit

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑15. Far-field mean annual effective dose for the probabilistic central corrosion case, disregarding
thorium sorption in the near field. The legend is sorted by peak (in the one-million year period) of the meanannual effective dose. The values in brackets are peak dose in units of µSv.

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4.5.2

Including solubility limits in the near field

Deterministic calculations
Hydrogeological case:
Erosion/corrosion model:

Semi-correlated, ten realisations
SR-Site model

Failure time:
Number of failed canisters:
Solubility limits:
Thorium sorption in near field:
Number of realisations:
Number of nuclides:

114,485 years
1
Yes
Yes (modelled as low solubility limit)
1
37

The calculation of the IRF-pulses for the deterministic central corrosion case is also valid when
including solubility limits in the near field. Hence, Table 4‑4 shows the peak annual doses from thepulse releases from the instantly released fraction, IRF.
Figure 4‑16 and Figure 4‑17 show the deterministic near-field and far-field dose equivalent releases,
respectively, for the central corrosion case when including solubility limits in the near field. The
constant level of the doses caused by release of Np-237 and Zr-93 in Figure 4‑16 indicate that theyreach their solubility limits and hence the doses from these two nuclides are lower than in the central
corrosion case. The total dose is the same as in the deterministic calculation of the central corrosion
case.

102

Annual effective dose [µSv]

10

10

1

0

10-1

Nb94

(12)

Ni59

(7.3)

Ra226

(5.0)

Se79

(1.1)

Pb210

(0.30)

Np237(0.22)

Pu239(0.17)

I129(0.15)

Tc99(0.11)

Sn126(0.050)Pa231(0.030)Pu242(0.028)Zr93(0.0032)

Ac227(0.0027)

Cl36(0.0026)

Total

(21)

Dose corresponding
to risk limit

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑16. Near-field dose equivalent release for a deterministic calculation of the central corrosion
case, including solubility limits in the near field. The legend is sorted by peak (in the one-million year
period) of the annual effective dose. The values in brackets are peak dose in units of µSv.

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102

Annual effective dose [µSv]

101

100

10-1

10-2

Ra226

(2.6)

Ni59

(1.3)

Se79

(0.68)

I129(0.15)

Np237(0.14)

Nb94(0.11)

Pb210(0.044)

Pu239(0.024)Tc99(0.018)

Ac227(0.014)

Pu242(0.013)

Th229(0.0047)

Pa231(0.0037)

U233(0.0035)

Sn126(0.0031)

Zr93(0.0019)Cl36(0.0013)

Total

(3.0)

Dose corresponding to risk limit

10-3
103

104

105

106

Time [years]

Figure 4‑17. Far-field annual effective dose for a deterministic calculation of the central corrosion case,including solubility limits in the near field. The legend is sorted by peak (in the one-million year period)of the annual effective dose. The values in brackets are peak dose in units of µSv.

Probabilistic calculations
Hydrogeological case:
Erosion/corrosion model:
Failure time:
Average number of failed canisters:
Solubility limits:
Thorium sorption in near field:
Number of realisations:
Number of nuclides:

Semi-correlated, ten realisations
SR-Site model
56 times according to Table 4‑3
0.12
Yes
Yes (modelled as low solubility limit)
50 per canister failure time37

The contributions from the instantly released fraction of nuclides, IRF, are not included in thecalculations except for Tc-99 that is included in the far-field calculations. The results for the IRF
presented for the central corrosion case are judged to be sufficient to conclude that their contribution
is negligible also in this case, see Section 4.4.2.
Figure 4‑18 and Figure 4‑19 show near-field and far-field dose equivalent releases, respectively,
for the central corrosion case when including solubility limits in the near field. The near-field dose
caused by release of Pb-210 is considerably higher than for the central corrosion case. This is due to
Ra-226 reaching the solubility limit in some realisations and when Ra-226 is confined to the canisterinterior it generates Pb-210. The far-field doses are, however, similar to those of the central corrosion
case. Pb-210 decays considerably in the geosphere because of its short half-life.

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Mean annual effective dose [µSv]

102

101

100

Pb210

(5.9)

Ra226

(0.30)

I129(0.025)Se79(0.018)Nb94(0.016)

Np237(0.015)Ni59(0.015)Pa231(0.0025)

Pu242(0.0010)

Total

(6.2)

Dose corresponding to risk limit

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑18. Near-field dose equivalent release for the probabilistic central corrosion case, including
solubility limits in the near field. The legend is sorted by peak (in the one-million year period) of the meanannual effective dose. The values in brackets are peak dose in units of µSv.

102

Mean annual effective dose [µSv]

101

100

Ra226

(0.092)

I129(0.024)Se79(0.013)Pb210(0.0069)

Np237(0.0053)

Ni59(0.0039)

Ac227(0.0031)

Nb94(0.0017)

Total(0.15)

Dose corresponding to risk limit

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑19. Far-field mean annual effective dose for the probabilistic central corrosion case, including
solubility limits in the near field. The legend is sorted by peak (in the one-million year period) of the meanannual effective dose. The values in brackets are peak dose in units of µSv.

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4.5.3 Decreased sorption of lead in the geosphere
In the SR-Site Bedrock Kd data report /Crawford 2010, Section 5.2.6/ it is stated: “Due to the uncertainties outlined above, a case could be made for the use of the geochemical analogue Ni(II) as asensitivity case study in place of the data ranges given for Pb(II). It is possible, however, that the useof the Ni(II) analogue is overly pessimistic since Ni sorption appears to be more strongly influenced
by ionic strength. This may be attributable to the larger first hydrolysis constant for Pb(II) which
also implies stronger binding for inner sphere surface complexation. In this regard, the Kd for Pb(II)sorption is expected on theoretical grounds to be larger than that for Ni(II).” This consideration of
decreased sorption of Pb(II) has been addressed in a deterministic calculation and is presented in
Figure 4‑20.
In comparison with the results from the deterministic calculation for the central corrosion case,
Figure 4‑3, the increase in the effective dose from Pb-210 is almost 20 times. However, the increasein the total dose is only 20%.

102

Annual effective dose [µSv]

101

10

0

10-1

10-2

Ra226

(2.6)

Ni59

(1.3)

Pb210

(0.80)

Se79(0.68)

Np237(0.24)

I129(0.15)

Nb94(0.11)

Pu239(0.024)Tc99(0.018)

Ac227(0.014)

Pu242(0.013)

Th229(0.0082)

Zr93(0.0063)U233(0.0060)

Pa231(0.0037)

Sn126(0.0031)Cl36(0.0013)

Total

(3.9)

Dose corresponding to risk limit

10-3
103

104

105

106

Time [years]

Figure 4‑20. Far-field annual effective dose for a deterministic calculation of the central corrosion casewith decreased Kd for lead in the geosphere. The legend is sorted by peak (in the one-million year period)of the annual effective dose. The values in brackets are peak dose in units of µSv.

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79

4.5.4 Kd for U(VI) instead of U(IV) in the geosphere
All far-field calculations in SR-Site are done with Kd values for U(IV). According to /Crawford
2010/ and also described in Section 2.4.4, it cannot always be guaranteed that U(IV) is the dominant
redox species in the repository volume. Therefore, the Data report recommends calculations withboth U(IV) and U(VI). This statement only influences the Kd values in the rock.
Figure 4‑21shows the far-field effective dose for a probabilistic calculation of the central corrosion
case with Kd values for U(VI). Compared to the central corrosion case with Kd values for U(IV),
Figure 4‑5, the doses from the uranium isotopes are increased but no other nuclides are affected. The
increase in release of the uranium isotopes is not high enough to affect the total dose. U-233, which
increases almost 9 times to 0.0022 μSv, is the only uranium isotope that becomes high enough to be
seen in the main part of the figures in this report as they have a limit down to 0.001 μSv.
Figure 4‑22 shows a detailed comparison between far-field effective doses from the uranium
isotopes for the central corrosion case calculated with Kd values for U(IV) and U(VI). Due to thevery low releases of uranium, the limits on the y-axis have been changed in this figure.

102

Ra226 (0.11)
I129(0.024)
Np237 (0.019)
Se79 (0.013)
Pb210 (0.0059)
Ni59 (0.0033)
Ac227 (0.0031)
U233 (0.0022)
Nb94 (0.0017)
Total (0.18)

Annual effective dose [µSv]

101

100

Dose corresponding to risk limit

10-1

10-2

10-3

103

104

105

106

Time [years]

Figure 4‑21. Far-field annual effective dose for a probabilistic calculation of the central corrosion casewith Kd values for U(VI). The legend is sorted by peak (in the one-million year period) of the mean annual
effective dose. The values in brackets are peak dose in units of µSv.

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10–2

U233
U234
U236
U238
U235

Annual effective dose [µSv]

10–3

10–4

10–5

10–6

10–7

10–8

103

104

105

106

Time [years]

Figure 4‑22. Comparison between far-field annual effective doses from the uranium isotopes for probabilistic calculations of the central corrosion case with Kd values for U(IV) (solid lines) and U(VI) (dottedlines). Observe the change in y-axis limits.

4.5.5 Influence of correlation groups for Kd in the geospehere
All calculations in the SR-Site are done with five correlation groups for Kd in rock, according to
the data report for the SR-Can assessment /SKB 2006b/. Late in the SR-Site process, when most of
the calculations were done, the correlation groups were changed from five to two. The purpose of
the calculations presented in this section is to investigate whether the change has any considerable
influence on the releases from the far field.
Four cases are used to investigate the influence of correlation groups for Kd in rock. In all cases inthis investigation the same releases from the near field, the probabilistic calculation of the central
corrosion case, is used as input to the FARF31 calculation. The other input parameter that may influence the far-field releases is De for rock. De is always fully correlated in SR-Site and in all calculation cases in this comparison except for the case with no correlations, where De also is uncorrelated.
The following four cases are calculated:• without any correlation groups,• fully correlated case, i.e. one correlation group,• two correlation groups, (according to the Data report)• five correlation groups (according to the data report for SR-Can /SKB 2006b/.
It is not possible to see any differences between the four cases, see Figure 4‑23. The conclusion isthat the correlation groups have negligible influence on the results. Hence, no corrections have been
done to the calculations due to the change in correlation groups for Kd. In addition it is concluded
that the influence of correlations for De is negligible.

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102
No correlations
Fully correlated
2 correlation groups
101

Mean annual effective dose [µSv]

Dose corresponding to risk limit

5 correlation groups

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑23. Far-field mean annual effective dose for probabilistic calculations of the central corrosion
case with different correlations for Kd and De for rock.

4.5.6 Colloid-facilitated transport
The presence of bentonite material in tunnel backfill and borehole buffer is expected to result in bentonite colloids in the groundwater near deposition holes and along the geosphere transport pathways.
Radionuclides that have a strong affinity for bentonite will sorb onto bentonite colloids and may betransported through the geosphere with reduced interaction with the rock matrix, i.e., with a reduced
retention. Colloid facilitated transport involves a complicated combination of processes, many ofwhich can mitigate the transport. Mitigating processes include colloid retardation in fractures, physical filtration (straining) of colloids in fractures, colloid flocculation and sedimentation, saturationof sorption sites on colloids, and competition for sites on colloids. These processes are uncertain or
involve uncertain parameters that are difficult to quantify in short duration experiments. Rather thanattempting to develop detailed process models for colloid-facilitated transport, potential mitigatingprocesses are ignored so as to place an upper bound on the possible effect. Ignoring these potential
mitigating processes and taking into consideration that sorption of radionuclides onto bentonite isunderstood to be a reversible process on the time scale of geosphere transport /Buffer, backfill andclosure process report/, the effect of colloids in facilitating transport may be modelled through theintroduction of effective transport parameters as described in Appendix I. The effective parameters
depend on the colloid concentration and on the equilibrium partitioning coefficient for sorption onto
colloids.
Colloid concentrations that can be stably supported are highly sensitive to groundwater chemistry.
It has been determined /Wold 2010/ that 10 mg/l is a reasonably pessimistic value for colloid con­centrations for typical groundwater chemistries. However, this value may be higher during brief
periods when dilute glacial melt water enters the geosphere. A value of 10 g/l has been determined to
be a pessimistic value for colloid concentrations in very dilute waters /Buffer, backfill and closure
process report/.

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The partitioning coefficient for sorption onto bentonite colloids Kc may be related to the same
parameter for sorption onto bentonite buffer material Kd as Kc = γKd where γ is a ratio of specificsurface areas for colloidal and bulk bentonite. Given that bentonite is a fine-grained material and thatequilibrium partitioning coefficients for bentonite are typically measured using colloidal suspensions
with particle sizes less than 1 μm, γ ≈ 1 is a reasonable assumption. Thus, Kc distributions were takenfrom the Data report Section 5.3.
Using the MARFA transport code and the effective parameters derived in Appendix I, the effects ofcolloids are demonstrated in Figure 4‑24. Except for the effects of colloids, this modelling case isidentical to the central corrosion base case in Section 4.4.2. The dark blue curve is near-field meanannual release expressed as an effective dose, the black curve is the far-field mean-annual effective
dose without colloids. The green and pink curves are the far-field doses with colloid concentrationsof 10 mg/l and 10 g/l, respectively.

102

Dose corresponding to risk limit

Mean annual effective dose [µSv]

101

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑24. Mean annual effective dose for the probabilistic central corrosion case, with and without theeffects of bentonite colloids in facilitating transport. The black, green, and pink curves are far-field dosewith colloid concentrations of 0 mg/l, 10 mg/l, and 10 g/l, respectively. The dark blue curve is the near-fielddose equivalent release.

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83

4.5.7 Varying climate conditions
MARFA simulations are undertaken to address the corrosion scenario for a case with unsteady flowcaused by climate evolution.
The transport simulations are identical to the central corrosion case described in Section 4.4.2 except
for the use of the flow scaling factors shown in Figure 2-3 and the use of sorption Kd‑values foroxidising conditions for the redox sensitive elements during ice front passages (i.e., during the time
periods when flow scaling factors are 20 and 50, respectively). In addition, different dose conversion
factors (LDFs) are applied for different periods in the glacial cycle. The near-field release calculations used as input to the MARFA simulations do not take into consideration the changes in flow.
This simplification is based on the fact that releases of radioelements that are not solubility limited
will be limited by the rate of waste-form dissolution, which is independent of flow rate.
Mean annual effective dose versus time for this case is show in Figure 4‑25. Also shown is the casewithout flow changes, i.e., with temperate flow throughout the assessment period. The results are
based on 2,800 realisations where both near-field and far-field parameters follow distributions, as
described in Section 3.7.1.
The results in Figure 4‑25 indicate that the flow, Kd and LDF changes collectively cause a slightincrease in peak dose. However, the main effect is the sharp downward spikes in dose during
the time of glacial approach and retreat. Although the radionuclide discharge to the biosphere isincreased sharply during these periods due to changes in flow and, more importantly, changes in
Kd for redox-sensitive radionuclides, this increase is more than compensated by the greatly reduced
LDF factors during these periods.
The results without flow changes can also be compared to the corresponding case calculated using
FARF31, see Section 4.4.2, showing very similar total dose results.
102

Dose corresponding to risk limit

Mean annual effective dose [µSv]

101

100

10-1

10-2

10-3
0

200,000

400,000

600,000

800,000

1,000,000

Time [years]

Figure 4‑25. Far-field annual effective dose (green curve) for a probabilistic calculation of the central
corrosion case with varying climate conditions. For comparison the near-field dose equivalent release(blue curve) and also the far-field dose (black curve) without flow changes are given.

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4.5.8 Varying climate conditions and colloid-facilitated transport
MARFA calculations are undertaken to evaluate the simultaneous effects of varying climate conditions and colloid-facilitated transport. The simulations are identical to those in Section 4.5.7 except
for that the colloid facilitated transport model of Section 4.5.6 is used. As has been noted, 10 mg/l
has been determined to be a reasonable value for colloid concentration except during periods where
dilute groundwater is expected to contact clay minerals in buffer and backfill. During the periods ofdilute groundwater 10 g/l is used for the colloid concentration.
Results for a case with colloid concentration held constant at a high value of 10 g/l is shown in
Figure 4‑26. By comparing with Figure 4‑25 it can be seen that colloids enhance transport overthe colloid-free case and that the far-field dose approaches the near-field dose during the temperate
period. Mean annual dose is not significant increased in the other periods because the LDF factors
are lower then.
Results for a case with varying colloid concentration is shown in Figure 4‑27. In this case, thecolloid concentration is 10 g/l during periods of dilute groundwater and 10 mg/l otherwise. Dilute
groundwaters are assumed to exist during the brief periods of glacial retreat/advance and also
during the second halves of the glacial maximum and temperate periods /Climate report/. Results
are similar to those of Figure 4‑26 except that the period of colloid-enhanced dose is limited to thesecond half of the temperate period.
102

Dose corresponding to risk limit

Mean annual effective dose [µSv]

101

100

10-1

10-2

10-3
0

200,000

400,000

600,000

800,000

1,000,000

Time [years]

Figure 4‑26. Far-field annual effective dose (green curve) for a probabilistic calculation of the central
corrosion case with varying climate conditions and colloid-facilitated transport of actinides and transition
metals. For comparison the near-field dose (blue curve) is given. The colloid concentration is constant inthis case and has a value of 10 g/l.

TR-10-5085

102

Dose corresponding to risk limit

Mean annual effective dose [µSv]

101

100

10-1

10-2

10-3
0

200,000

400,000

600,000

800,000

1,000,000

Time [years]

Figure 4‑27. Far-field annual effective dose (green curve) for a probabilistic calculation of the central
corrosion case with varying climate conditions and colloid-facilitated transport of actinides and transition
metals. For comparison the near-field dose (blue curve) is given.

4.5.9

Initial advection

Deterministic calculations
Hydrogeological case:
Erosion/corrosion model:
Failure time:
Number of failed canisters:
Solubility limits:
Thorium sorption in near field:
Number of realisations:
Number of nuclides:

Semi-correlated, ten realisations
Initial advection
44,049 years, according to Table 4‑2
1No
Yes (modelled as low solubility limit)
1
37

A deterministic calculation of the semi-correlated case with initial advection is performed fora canister taken from the realisation with the earliest failure time of the analysed realisations,(44,049 years after deposition) with corresponding geosphere transport data, i.e. data used to calculate the corrosion time are from the same hydrogeological calculation as the geosphere transport
data. Advection occurs in the buffer void and the dose equivalent releases are primarily determinedby the fuel dissolution rate set to 10−7/yr. Table 4‑4 shows the peak annual doses from the pulse
releases from the instantly released fraction, IRF.
Figure 4‑28 and Figure 4‑29 show the deterministic near-field and far-field dose equivalent releases,
respectively, for the semi-correlated case with initial advection. Note that the peak in Figure 4‑28
reaches outside the figure (doses larger than 100 µSv) but the real maximum doses are given inbrackets in the figure legend. Doses from the near field are dominated by releases of Nb-94 andNi-59 shortly after canister failure and by Ra-226 in the longer term. Doses from the far field aredominated by releases of Ra-226.
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102

Annual effective dose [µSv]

101

100

10-1

Nb94

(135)

Ni59

(14)

Ra226

(5.6)

Pu239

(1.3)

Se79

(1.2)

C14

(1.0)

Zr93

(0.60)

Np237(0.46)

Pb210(0.34)

I129(0.15)

Tc99(0.14)

Sn126(0.082)

Pu240(0.074)Pa231(0.032)

Pu242(0.032)

Dose corresponding to risk limit

Am243 (0.0055)
Cl36
10

-2

(0.0031)Ac227(0.0028)

Total

(154)

10-3
103

104

105

106

Time [years]

Figure 4‑28. Near-field dose equivalent release for a deterministic calculation of the central corrosion
case, with initial advection in the erosion/corrosion model. The legend is sorted by peak (in the one-million
year period) of the annual effective dose. The values in brackets are peak dose in units of µSv. Note that thedose equivalent release for Nb-94 is 135 µSv/year, i.e. above the limit of the y-axis.
102

Annual effective dose [µSv]

101

10

0

10-1

10-2

Ra226

(2.8)

Ni59

(2.5)

Nb94

(1.2)

Se79

(0.76)

C14(0.57)

Np237(0.25)

Pu239(0.18)

I129(0.15)

Pb210(0.050)Tc99(0.022)

Ac227(0.016)

Pu242(0.015)

Th229(0.0086)

Zr93(0.0066)

U233(0.0062)

Sn126(0.0051)

Pa231(0.0040)Pu240(0.0032)

Cl36(0.0018)

Total

(3.6)

Dose corresponding to risk limit

10-3
103

104

105

106

Time [years]

Figure 4‑29. Far-field annual effective dose for a deterministic calculation of the central corrosion case,with initial advection in the erosion/corrosion model. The legend is sorted by peak (in the one-million year
period) of the annual effective dose. The values in brackets are peak dose in units of µSv.
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87

Probabilistic calculations
Semi-correlated, ten realisations
Initial advection
84 times according to the erosion/corrosion calculations
0.17
No
Yes (modelled as low solubility limit)
50 per canister failure time
37

Hydrogeological case:
Erosion/corrosion model:
Failure time:
Average number of failed canisters:
Solubility limits:
Thorium sorption in near field:
Number of realisations:
Number of nuclides:

A probabilistic calculation of the semi-correlated case with initial advection is performed with failure
times and geosphere transport data from the ten realisations of the semi-correlated DFN modeland failure times from the corrosion calculations with initial advection. The contributions from theinstantly released fraction of nuclides, IRF, are not included in the calculations except for Tc-99 thatis included in the far-field calculations. The results for the IRF presented for the central corrosion
case are judged to be sufficient to conclude that their contribution is negligible also in this case, see
Section 4.4.2.
Figure 4‑30 and Figure 4‑31 show the near-field and far-field dose equivalent releases, respectively,
for the semi-correlated case with initial advection. The total dose in the longer term is about 1.5 times
higher than in the central corrosion case and is dominating by Ra-226.
102

Mean annual effective dose [µSv]

101

10

0

10-1

Ra226

(0.62)

Nb94(0.37)

Pb210(0.22)

Np237(0.091)

I129(0.037)Ni59(0.037)Se79(0.027)

Pu239(0.0099)

Pa231(0.0040)

C14(0.0028)

Tc99(0.0022)Zr93(0.0016)

Pu242(0.0016)

Ac227(0.0013)Sn126(0.0012)

Total

(1.0)

Dose corresponding to risk limit

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑30. Near-field dose equivalent release for a probabilistic calculation of the central corrosion
case, with initial advection in the erosion/corrosion model. The legend is sorted by peak (in the one-million
year period) of the mean annual effective dose. The values in brackets are peak dose in units of µSv.

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102
Ra226 (0.17)
I129(0.036)

Mean annual effective dose [µSv]Np237 (0.026)
101

Se79

(0.020)Nb94(0.010)

Dose corresponding to risk limit

Pb210 (0.0092)
Ni59(0.0066)

Ac227 (0.0040)
Pu239 (0.0020)

100

Total

(0.27)

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑31. Far-field mean annual effective dose for a probabilistic calculation of the central corrosion
case, with initial advection in the erosion/corrosion model. The legend is sorted by peak (in the one-million
year period) of the mean annual effective dose. The values in brackets are peak dose in units of µSv.

4.6

Uncorrelated hydrogeological DFN model

4.6.1

Base case transport assumptions

Deterministic calculations
Hydrogeological case:
Erosion/corrosion model:
Failure time:
Number of failed canisters:
Solubility limits:
Thorium sorption in near field:
Number of realisations:
Number of nuclides:

Uncorrelated, five realisations
SR-Site model
97,815 years, according to Table 4‑2
1No
Yes (modelled as low solubility limit)
1
37

A deterministic calculation of the central corrosion case is performed for a canister taken from therealisations with the earliest failure time of the analysed realisation (97,815 years after deposition)with corresponding geosphere transport data, i.e. data used to calculate the corrosion time are fromthe same hydrogeological calculation as the geosphere transport data. Advection occurs in the buffer
void and the dose equivalent releases are primarily determined by the fuel dissolution rate set to10−7/yr. Table 4‑4 shows the peak annual doses from the pulse releases from the instantly released
fraction, IRF.
Figure 4‑32 and Figure 4‑33 show the deterministic near-field and far-field dose equivalent releases,
respectively, for the uncorrelated case. Doses caused by Nb-94 and Ni-59 are dominating the releases
from the near field and I-129 is dominating the far-field releases. The low releases of Ra-226 fromthe far field is an effect of the high F-factor, see Table 4-2.

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89

102

Annual effective dose [µSv]

10

1

100

10-1

Nb94

(22)

Ni59

(8.5)

Ra226

(5.1)

Se79

(1.1)

Zr93

(0.59)

Np237(0.46)

Pb210(0.35)

Pu239(0.28)

I129(0.15)

Tc99(0.12)

Sn126(0.056)

Pa231(0.031)

Pu242(0.029)Ac227(0.0029)Cl36(0.0027)

C14(0.0015)

Total

(33)

Dose corresponding
to risk limit

10-2

10-3
103

104

Time [years]

105

106

Figure 4‑32. Near-field dose equivalent release for a deterministic calculation of the corrosion scenario,
with hydrogeological data from the uncorrelated model. The legend is sorted by peak (in the one-million
year period) of the annual effective dose. The values in brackets are peak dose in units of µSv.

102
I129

(0.13)

Se79(0.016)Total(0.15)

Dose corresponding to risk limit

Annual effective dose [µSv]

101

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑33. Far-field annual effective dose for a deterministic calculation of the corrosion scenario, withhydrogeological data from the uncorrelated model. The legend is sorted by peak (in the one-million year
period) of the annual effective dose. The values in brackets are peak dose in units of µSv.

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Probabilistic calculations
Uncorrelated, five realisations
SR-Site model
154 times according to the erosion/corrosion calculations
0.65
No
Yes (modelled as low solubility limit)
50 per canister failure time
37

Hydrogeological case:
Erosion/corrosion model:
Failure time:
Average number of failed canisters:
Solubility limits:
Thorium sorption in near field:
Number of realisations:
Number of nuclides:

A probabilistic calculation of the central corrosion case is performed with failure times and geo­
sphere transport data from the five realisations of the uncorrelated DFN model. The contributions
from the instantly released fraction of nuclides, IRF, are not included in the calculations except for
Tc-99 that is included in the far-field calculations. The results for the IRF presented for the central
corrosion case are judged to be sufficient to conclude that their contribution is negligible also in thiscase, see Section 4.4.2.
Figure 4‑34 and Figure 4‑35 show the near-field and far-field dose equivalent releases, respectively,
for the uncorrelated case. The total doses from the near field and far field are about 5 times higher
and 2.5 times higher, respectively, compared to the central corrosion case, and are dominated by the
Ra-226 release.

102

Mean annual effective dose [µSv]

10

1

100

10-1

Ra226

(1.8)

Pb210

(0.69)

Np237(0.34)

I129(0.14)

Se79(0.093)

Nb94(0.074)Ni59(0.037)

Pa231(0.012)Zr93(0.0065)

Pu242(0.0055)

Tc99(0.0050)

Ac227(0.0044)

Pu239(0.0037)

Sn126(0.0017)

Total

(3.1)

Dose corresponding to riskl limit

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑34. Near-field dose equivalent release for the probabilistic calculation of the corrosion scenario,
with hydrogeological data from the uncorrelated model. The legend is sorted by peak (in the one-million
year period) of the mean annual effective dose. The values in brackets are peak dose in units of µSv.

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91

Mean annual effective dose [µSv]

102

101

Ra226

(0.22)

I129(0.13)

Se79(0.049)Np237(0.039)Pb210(0.0091)

Ni59(0.0045)

Ac227(0.0040)

Total(0.45)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑35. Far-field mean annual effective dose for the probabilistic calculation of the corrosion
scenario, with hydrogeological data from the uncorrelated model. The legend is sorted by peak (in the
one-million year period) of the mean annual effective dose. The values in brackets are peak dose in unitsof µSv.

4.6.2

Initial advection

Deterministic calculations
Hydrogeological case:
Erosion/corrosion model:
Failure time:
Number of failed canisters:
Solubility limits:
Thorium sorption in near field:
Number of realisations:
Number of nuclides:

Uncorrelated, five realisations
Initial advection
47,107 years, according to Table 4‑2
1No
Yes (modelled as low solubility limit)
1
37

A deterministic calculation of the uncorrelated case with initial advection is performed for a canister
taken from the realisation with the earliest failure time of the analysed realisations (47,107 years after
deposition) with corresponding geosphere transport data, i.e. data used to calculate the corrosion time
are from the same hydrogeological calculation as the geosphere transport data. Advection occurs
in the buffer void and the dose equivalent releases are primarily determined by the fuel dissolution
rate set to 10−7/yr. Table 4‑4 shows the peak annual doses from the pulse releases from the instantly
released fraction, IRF.
Figure 4‑36 and Figure 4‑37 show the deterministic near-field and far-field dose equivalent releases,
respectively, for the uncorrelated case with initial advection. Note that the peak in Figure 4‑36
reaches outside the figure (doses larger than 100 µSv) but the real maximum doses are given inbrackets in the figure legend. Doses from the near field are dominated by releases of Nb-94 andNi-59 shortly after canister failure and by Ra-226 in the longer term. Releases of I-129 are domi­
nating the doses from the far field. The high F-factor, see Table 4-2, implies that the far-field releasesof Ra-226 are low.
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102
Nb94

(122)

Ni59

(14)

Ra226 (5.5)
Se79

Annual effective dose [µSv]101

Dose corresponding to risk limit(1.2)

Pu239 (1.2)
C14(0.72)

Zr93(0.60)

Np237 (0.46)
Pb210 (0.38)

100

I129

(0.15)

Tc99(0.14)Sn126 (0.080)
Pu240 (0.054)

10-1

Pa231 (0.032)
Pu242 (0.032)
Am243 (0.0041)
Cl36

10-3

(0.0031)

Ac227 (0.0030)

10-2

Total

(140)

103

104

105

106

Time [years]

Figure 4‑36. Near-field dose equivalent release for a deterministic calculation of the corrosion scenario, withhydrogeological data from the uncorrelated model and initial advection in the erosion/corrosion model. The
legend is sorted by peak (in the one-million year period) of the annual effective dose. The values in brackets
are peak dose in units of µSv. Note that the dose equivalent release for Nb-94 is 122 µSv/year, i.e. above theend of the y-axis.
102

Annual effective dose [µSv]

10

1

I129

(0.14)

Se79(0.017)C14(0.014)Total(0.15)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑37. Far-field annual effective dose for a deterministic calculation of the corrosion scenario, withhydrogeological data from the uncorrelated model and initial advection in the erosion/corrosion model. The
legend is sorted by peak (in the one-million year period) of the annual effective dose. The values in brackets
are peak dose in units of µSv.
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Probabilistic calculations
Uncorrelated, five realisations
Initial advection
289 times according to the erosion/corrosion calculations
1.22
No
Yes (modelled as low solubility limit)
50 per canister failure time
37

Hydrogeological case:
Erosion/corrosion model:
Failure time:
Average number of failed canisters:
Solubility limits:
Thorium sorption in near field:
Number of realisations:
Number of nuclides:

A probabilistic calculation of the uncorrelated case with initial advection is performed with failure
times and geosphere transport data from the five realisations of the uncorrelated DFN model. The
average number of failed canisters is 1.22. The contributions from the instantly released fraction of
nuclides, IRF, are not included in the calculations except for Tc-99 that is included in the far-fieldcalculations. The results for the IRF presented for the central corrosion case is judged to be enoughto conclude that their contribution is negligible also in this case, see Section 4.4.2.
Figure 4‑38 and Figure 4‑39 show the near-field and far-field dose equivalent releases, respectively,
for the uncorrelated case with initial advection. Doses from the near field are dominated by releasesof Ra-226 and Pb-210 and from the far field by Ra-226 and I-129. The total doses from the nearfield and the far-field are about 12 times higher and 5 times higher, respectively, compared to thecentral corrosion case.
102

Mean annual effective dose [µSv]

101

10

0

10-1

Ra226

(3.9)

Pb210

(2.0)

Nb94

(0.77)

Np237(0.63)

I129(0.26)

Se79(0.17)

Ni59(0.13)

Pu239(0.031)

Pa231(0.025)

Ac227(0.011)

Tc99(0.011)

Pu242(0.010)Zr93(0.0070)

Sn126(0.0051)

C14(0.0045)

Total

(7.0)

Dose corresponding to risk limit

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑38. Near-field dose equivalent release for the probabilistic calculation of the corrosion scenario,
with hydrogeological data from the uncorrelated model and initial advection in the erosion/corrosion
model. The legend is sorted by peak (in the one-million year period) of the mean annual effective dose.
The values in brackets are peak dose in units of µSv.

94

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102

Mean annual effective dose [µSv]

10

1

100

10-1

Ra226

(0.41)

I129(0.24)

Se79(0.086)

Np237(0.062)

Pb210(0.021)

Nb94(0.011)

Ni59(0.010)Ac227(0.0081)

Pu239(0.0020)

Pu242(0.0016)

Th229(0.0015)

Tc99(0.0012)U233(0.0011)

Total(0.83)

Dose corresponding to risk limit

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑39. Far-field mean annual effective dose for the probabilistic calculation of the corrosion scenario,
with hydrogeological data from the uncorrelated model and initial advection in the erosion/corrosion
model. The legend is sorted by peak (in the one-million year period) of the mean annual effective dose.
The values in brackets are peak dose in units of µSv.

4.7

Fully correlated hydrogeological DFN model

4.7.1

Base case transport assumptions

Deterministic calculations
Hydrogeological case:
Erosion/corrosion model:
Failure time:
Number of failed canisters:
Solubility limits:
Thorium sorption in near field:
Number of realisations:
Number of nuclides:

Fully correlated, five realisations
SR-Site model
99,700 years, according to Table 4‑2
1No
Yes (modelled as low solubility limit)
1
37

A deterministic calculation of the fully correlated case is performed for a canister taken from therealisation with the earliest failure time of the analysed realisations (99,700 years after deposition)with corresponding geosphere transport data, i.e. data used to calculate the corrosion time are fromthe same hydrogeological calculation as the geosphere transport data. Advection occurs in the buffer
void and the dose equivalent releases are primarily determined by the fuel dissolution rate set to10−7/yr. Table 4‑4 shows the peak annual doses from the pulse releases from the instantly released
fraction, IRF.
Figure 4‑40 and Figure 4‑41 show the deterministic near-field and far-field dose equivalent releases,
respectively, for the fully correlated case. Doses caused by Nb-94 and Ni-59 are dominating thereleases from the near field shortly after canister failure and releases of Ra-226 are dominating in thelonger term in the near filed as well as in the far field.

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102

Annual effective dose [µSv]

10

1

100

10-1

Nb94

(20)

Ni59

(8.4)

Ra226

(5.1)

Se79

(1.1)

Zr93

(0.59)

Np237(0.45)

Pb210(0.35)

Pu239(0.27)

I129(0.15)

Tc99(0.12)

Sn126(0.056)

Pa231(0.031)

Pu242(0.029)Ac227(0.0029)Cl36(0.0027)

C14(0.0012)

Total

(31)

Dose corresponding
to risk limit

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑40. Near-field dose equivalent release for a deterministic calculation of the corrosion scenario,
with hydrogeological data from the fully correlated model. The legend is sorted by peak (in the one-million
year period) of the annual effective dose. The values in brackets are peak dose in units of µSv.
102

Annual effective dose [µSv]

101

100

10-1

10-2

10-3

103

Ra226

(2.9)

Ni59

(2.0)

Se79

(0.75)

Nb94(0.27)

Np237(0.26)

I129(0.15)

Pb210(0.064)

Pu239(0.045)

Tc99(0.022)

Ac227(0.019)Pu242(0.015)Zr93(0.0088)

Th229(0.0078)

U233(0.0058)

Pa231(0.0050)

Sn126(0.0047)

Cl36(0.0025)

Total

(3.5)

Dose corresponding to risk limit

104

105

106

Time [years]

Figure 4‑41. Far-field annual effective dose for a deterministic calculation of the corrosion scenario, withhydrogeological data from the fully correlated model. The legend is sorted by peak (in the one-million year
period) of the annual effective dose. The values in brackets are peak dose in units of µSv.

96

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Probabilistic calculations
Fully correlated, five realisations
SR-Site model
132 times according to the erosion/corrosion calculations
0.57
No
Yes (modelled as low solubility limit)
50 per canister failure time
37

Hydrogeological case:
Erosion/corrosion model:
Failure time:
Average number of failed canisters:
Solubility limits:
Thorium sorption in near field:
Number of realisations:
Number of nuclides:

A probabilistic calculation of the fully correlated case was performed with failure times and geo­
sphere transport data from the five realisations of the uncorrelated DFN model and the erosion/
corrosion calculations in SKBdoc, see Table 3-8. The average number of failed canisters is 0.57.
The contributions from the instantly released fraction of nuclides, IRF, are not included in thecalculations except for Tc-99 that is included in the far-field calculations. The results for the IRF
presented for the central corrosion case are judged to be sufficient to conclude that their contribution
is negligible also in this case, see Section 4.4.2.
Figure 4‑42 and Figure 4‑43 show the near-field and far-field dose equivalent releases, respectively,
for the fully correlated case. The near-field doses are dominated by Ra-226 and are about 5 times
higher than in the central corrosion case. The far-field doses are dominated by Ra-226 and I-129
and are about 3.5 times higher than in the central corrosion case.

102

Mean annual effective dose [µSv]

101

100

10-1

Ra226

(2.0)

Pb210

(0.68)

Np237(0.29)

I129(0.12)

Nb94(0.12)

Se79(0.094)Ni59(0.048)Pa231(0.013)

Tc99(0.0066)

Pu242(0.0055)

Ac227(0.0042)Zr93(0.0041)

Sn126(0.0019)

Pu239(0.0018)

Total

(3.2)

Dose corresponding to risk limit

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑42. Near-field dose equivalent release for the probabilistic calculation of the corrosion scenario,
with hydrogeological data from the fully correlated model. The legend is sorted by peak (in the one-million
year period) of the mean annual effective dose. The values in brackets are peak dose in units of µSv.

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102

Mean annual effective dose [µSv]

101

100

10-1

Ra226

(0.37)

I129(0.12)

Se79(0.068)Np237(0.056)

Pb210(0.012)

Ac227(0.0050)Ni59(0.0049)

Nb94(0.0022)Th229(0.0015)

Pu242(0.0014)U233(0.0011)

Tc99(0.0010)Total(0.63)

Dose corresponding to risk limit

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑43. Far-field mean annual effective dose for the probabilistic calculation of the corrosion scenario,
with hydrogeological data from the fully correlated model. The legend is sorted by peak (in the one-million
year period) of the mean annual effective dose. The values in brackets are peak dose in units of µSv.

4.7.2

Initial advection

Deterministic calculations
Hydrogeological case:
Erosion/corrosion model:
Failure time:
Number of failed canisters:
Solubility limits:
Thorium sorption in near field:
Number of realisations:
Number of nuclides:

Fully correlated, five realisations
Initial advection
47,657 years, according to Table 4‑2
1No
Yes (modelled as low solubility limit)
1
37

A deterministic calculation of the fully correlated case with initial advection is performed for a canister taken from the realisation with the earliest failure time of the analysed realisations (47,657 years
after deposition) with corresponding geosphere transport data, i.e. data used to calculate the corrosion time are from the same hydrogeological calculation as the geosphere transport data. Advection
occurs in the buffer void and the dose equivalent releases are primarily determined by the fueldissolution rate set to 10−7/yr. Table 4‑4 shows the peak annual doses from the pulse releases fromthe instantly released fraction, IRF.
Figure 4‑44 and Figure 4‑45 show the deterministic near-field and far-field dose equivalent releases,
respectively, for the fully correlated case with initial advection. Note that the peak in Figure 4‑44
reaches outside the figure (doses larger than 100 µSv) but the real maximum doses are given inbrackets in the figure legend. Doses from the near field are dominated by releases of Nb-94 andNi-59 shortly after canister failure and by Ra-226 in the longer term. The same nuclides are domi­
nating the doses from the far field.

98

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102

Annual effective dose [µSv]

10

1

100

10-1

Nb94

(120)

Ni59

(13)

Ra226

(5.5)

Se79

(1.2)

Pu239

(1.2)

C14

(0.67)

Zr93(0.60)

Np237(0.46)

Pb210(0.38)

I129(0.15)

Tc99(0.14)

Sn126(0.080)Pu240(0.051)

Pa231(0.032)

Pu242(0.032)

Dose corresponding to risk limit

Am243 (0.0039)
10-2

Cl36

(0.0031)Ac227(0.0030)

Total

(138)

10-3
103

104

105

106

Time [years]

Figure 4‑44. Near-field dose equivalent release for a deterministic calculation of the corrosion scenario,
with hydrogeological data from the fully correlated model and initial advection in the erosion/corrosion
model. The legend is sorted by peak (in the one-million year period) of the annual effective dose. The
values in brackets are peak dose in units of µSv. Note that the dose equivalent release forNb-94 is 120 µSv/
year, i.e. above the limit of the y-axis.
102

Annual effective dose [µSv]

101

100

10-1

10-2

Ni59

(3.1)

Ra226

(3.1)

Nb94

(1.6)

Se79

(0.82)

C14(0.40)

Np237(0.27)

Pu239(0.20)

I129(0.15)

Pb210(0.069)Tc99(0.024)

Ac227(0.020)Pu242(0.017)Zr93(0.0090)Th229(0.0080)Sn126(0.0067)

U233(0.0059)

Pa231(0.0052)

Pu240(0.0031)Cl36(0.0030)

Total

(4.5)

Dose corresponding to risk limit

10-3
103

104

105

106

Time [years]

Figure 4‑45. Far-field annual effective dose for a deterministic calculation of the corrosion scenario,
with hydrogeological data from the fully correlated model and initial advection in the erosion/corrosion
model. The legend is sorted by peak (in the one-million year period) of the annual effective dose. The
values in brackets are peak dose in units of µSv.
TR-10-50

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Probabilistic calculations
Fully correlated, five realisations
Initial advection
200 times according to the erosion/corrosion calculations
0.86
No
Yes (modelled as low solubility limit)
50 per canister failure time
37

Hydrogeological case:
Erosion/corrosion model:
Failure time:
Average number of failed canisters:
Solubility limits:
Thorium sorption in near field:
Number of realisations:
Number of nuclides:

A probabilistic calculation of the fully correlated case with initial advection was performed with failure times and geosphere transport data from the five realisations of the uncorrelated DFN model andthe erosion/corrosion calculations in SKBdoc, see Table 3-8. The average number of failed canisters
is 0.86. The contributions from the instantly released fraction of nuclides, IRF, are not included in
the calculations except for Tc-99 that is included in the far-field calculations. The results for the IRF
presented for the central corrosion case are judged to be sufficient to conclude that their contribution
is negligible also in this case, see Section 4.4.2.
Figure 4‑46 and Figure 4‑47 show the near-field and far-field dose equivalent releases, respectively,
for the fully correlated case with initial advection. Both near-and far-field doses are dominated byreleases of Ra-226 and the total doses are about 10 times higher and 5 times higher, respectively,
compared to the central corrosion case.

102

Mean annual effective dose [µSv]

10

1

100

10-1

Ra226

(3.6)

Pb210

(1.6)

Nb94

(0.93)

Np237(0.45)

I129(0.18)

Se79(0.18)

Ni59(0.11)

Pu239(0.023)Pa231(0.023)

Tc99(0.016)

Pu242(0.0094)

Ac227(0.0087)

Zr93(0.0081)Sn126(0.0074)C14(0.0048)

Total

(6.0)

Dose corresponding to risk limit

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑46. Near-field dose equivalent release for the probabilistic calculation of the corrosion scenario,
with hydrogeological data from the fully correlated model and initial advection in the erosion/corrosion
model. The legend is sorted by peak (in the one-million year period) of the mean annual effective dose. The
values in brackets are peak dose in units of µSv.

100

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102

Mean annual effective dose [µSv]

101

100

10-1

Ra226

(0.57)

I129(0.18)

Se79(0.11)

Np237(0.081)

Pb210(0.019)Ni59(0.014)Nb94(0.013)

Ac227(0.0082)

Pu239(0.0026)

Th229(0.0024)Pu242(0.0023)

Tc99(0.0019)U233(0.0018)

Total(0.96)

Dose corresponding to risk limit

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑47. Far-field mean annual effective dose for the probabilistic calculation of the corrosion
scenario, with hydrogeological data from the fully correlated model and initial advection in the corrosion
model. The legend is sorted by peak (in the one-million year period) of the mean annual effective dose.
The values in brackets are peak dose in units of µSv.

4.8

Cases addressing best available technique (BAT)

According to Swedish legislation, a licence application for a final repository needs to address theissues of best available technique (BAT). Factors considered in this section are:••

Alternative copper shell thickness, 25 mm and 100 mm, respectively.
Alternative deposition hole rejection criteria

These factors are implemented in the corrosion calculations and analysed as BAT-cases. The BAT
cases are variant cases that do not use best available technique.
Alternative copper shell thickness
Hydrogeological case:
Erosion/corrosion models:
Failure time:
Average number of failed canisters:
Solubility limits:
Thorium sorption in near field:
Number of realisations:
Number of nuclides:

TR-10-50

Semi-correlated, ten realisations
SR-Site model
107 times (25 mm)
21 times (100 mm)
0.22 (25 mm)
0.044 (100mm)
No
Yes (modelled as low solubility limit)
50 per canister failure time
37

101

Two probabilistic calculations of the corrosion case were performed with transport data from the ten
realisations of the semi-correlated DFN model and corrosion model for copper thicknesses of 25 mm
and 100 mm. In the reference design is the copper thickness 50 mm. The average number of failed
canisters is 0.22 and 0.044 for copper thickness of 25 mm and 100 mm, respectively. The contributions from the instantly released fraction of nuclides, IRF, are not included in the calculations.
Figure 4‑48 and Figure 4‑49 show the near- and far-field total dose equivalent releases, respectively,
for corrosion cases with copper thicknesses of 25 mm, 50 mm (central corrosion case) and 100 mm.
Doses both from the near-field and the far-field become about two times lower if the thickness of thecopper shell is doubled.

102
25 mm copper thickness(1.2)

50 mm copper thickness(0.59)

100 mm copper thickness (0.25)

Dose corresponding to risk limit

Mean annual effective dose [µSv]

101

100

10-1

10-2

10-3

102

103

104

105

106

Time [years]

Figure 4‑48. Near-field dose equivalent releases for probabilistic calculations of the cases with a copper
thickness of 25 mm, 50 mm (central corrosion case) and 100 mm. The legend is sorted by peak (in the onemillion year period) of the mean annual effective dose. The values in brackets are peak dose in units of µSv.

102

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102
25 mm copper thickness(0.36)

50 mm copper thickness(0.18)

100 mm copper thickness (0.078)
Dose corresponding to risk limit

Mean annual effective dose [µSv]

101

100

10-1

10-2

10-3
102

103

104

105

106

Time [years]

Figure 4‑49. Far-field mean annual effective dose for the probabilistic calculations of the cases with acopper thickness of 25 mm, 50 mm (central corrosion case) and 100 mm. The legend is sorted by peak(in the one-million year period) of the mean annual effective dose. The values in brackets are peak dosein units of µSv.

Alternative deposition hole rejection criteria
Hydrogeological case:
Erosion/corrosion models:
Failure time:
Average number of failed canisters:
Solubility limits:
Thorium sorption in near field:
Number of realisations:
Number of nuclides:

Semi-correlated, ten realisations
SR-Site model
126 times (no T/L-filtering)
1,964 times (neither T/L- nor EFPC-filtering)
0.26 (no T/L-filtering)
3.7 (neither T/L- nor EFPC-filtering)No
Yes (modelled as low solubility limit)
50 per canister failure time
37

The groundwater flow around and through deposition holes have a large impact on both the lossof bentonite which may potentially lead to advective conditions and on the rate of corrosion bysulphide in the groundwater. Applying the EFPC criterion means to avoid deposition holes with highgroundwater flow and it has been applied to all calculations. Furthermore, an additional deposition
hole rejection criterion related to the combination of a high transmissivity and length of the intersecting fracture (T/L-filtering) was assumed in all the calculations.
Two probabilistic calculations of the corrosion case were performed with transport data from the ten
realisations of the semi-correlated DFN model, without T/L-filtering and without both T/L-filteringand EFPC-filtering. The average number of failed canisters is 0.26 and 3.7 for no T/L-filtering andneither T/L- nor EFPC-filtering, respectively. The contributions from the instantly released fractionof nuclides, IRF, are not included in the calculations.
Figure 4‑50 and Figure 4‑51 show the near- and far-field total dose equivalent releases, respectively,
for corrosion cases with no T/L-filtering, neither T/L- nor EFPC-filtering and the central corrosion
case (T/L- and EFPC-filtering). Dose from the far field increases 67 times for the case without T/Lnor EFPC-filtering compared to the central corrosion case.
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102
Neither T/L- nor EFPC-filtering (20)
No T/L-filtering(1.3)

Central corrosion case(0.59)
Dose corresponding to risk limit

Mean annual effective dose [µSv]

101

100

10-1

10-2

10-3
102

103

104

105

106

Time [years]

Figure 4‑50. Near-field dose equivalent release for the probabilistic calculations of the cases with noT/L-filtering, neither T/L- nor EFPC-filtering and the central corrosion case (T/L- and EFPC-filtering).
The legend is sorted by peak (in the one-million year period) of the mean annual effective dose. The values
in brackets are peak dose in units of µSv.
102
Neither T/L- nor EFPC-filtering (12)Mean annual effective dose [µSv]10

No T/L-filtering(0.71)

Central corrosion case(0.18)
Dose corresponding to risk limit

1

100

10-1

10-2

10-3
102

103

104

105

106

Time [years]

Figure 4‑51. Far-field mean annual effective dose for the probabilistic calculations of the cases with noT/L-filtering, neither T/L- nor EFPC-filtering and the central corrosion case (T/L- and EFPC-filtering).
The legend is sorted by peak (in the one-million year period) of the mean annual effective dose. The values
in brackets are peak dose in units of µSv.

104

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4.9

Alternative safety indicators for the central corrosion case

Four alternative indicators to risk are used in SR-Site: release of activity from the geosphere,radiotoxicity flux from the geosphere, concentrations of radionuclides in ecosystems and naturalgeosphere fluxes of radionuclides. The following reference values are used when evaluating these
indicators.
•

The Finnish activity release constraints. These constraints are strictly applicable only in the
Finnish regulatory context, but are nevertheless deemed useful as reference values for SR-Site.

•

The reference value for radiotoxicity flux from the geosphere suggested by the EU SPIN project.

•

Measured concentrations of naturally occurring radionuclides in ecosystems at the Forsmark siteor other, comparable sites. Not further described here, see Main report Section 13.5.8.

•

Naturally occurring fluxes of radionuclides at the site.

4.9.1 Finnish activity release constraints
The Finnish Radiation and Nuclear Safety Authority STUK has issued activity release constraints tothe environment /STUK 2001/.
These nuclide specific constraints are defined for long-lived radionuclides only. The effects of theirshort-lived progeny have been taken into consideration in the constraints defined for the long-lived
parents. The nuclide-specific release rate constraints are:
•
•
•
•
•
•
•
•

0.03 GBq/yr for the long-lived α-emitting isotopes of Ra, Th, Pa, Pu, Am and Cm,
0.1 GBq/yr for Se-79, I-129, and Np-237,
0.3 GBq/yr for C-14, Cl-36, Cs-135, and the long-lived isotopes of U,
1 GBq/yr for Nb-94 and Sn-126,
3 GBq/yr for Tc-99,
10 GBq/yr for Zr-93,
30 GBq/yr for Ni-59,
100 GBq/yr for Pd-107 and Sm-151.

The constraints apply to activity releases that arise from the expected evolution scenarios and that
may enter the environment after several thousands of years, whereas dose rate constraints are appliedin the shorter term. In applying the above constraints, the activity releases can be averaged over
1,000 years at the most. The sum of the ratios between the nuclide-specific activity releases and therespective constraints shall be less than one. It should be noted that the Finnish regulator has derived
these constraints partly based on a set of reference biospheres considered possible in the future atthe planned disposal site, Olkiluoto at the coast of the Baltic Sea, and partly on natural fluxes ofradionuclides established for similar environments. The reference values of the Finnish regulatory
guide are thus not directly applicable for other disposal concepts and sites /EU 2002/. However, both
the disposal concept and the sites considered in Sweden are similar to those for which the Finnish
activity release constraints have been developed.
Figure 4‑52 shows the result of applying this activity constraint to releases calculated for the central
corrosion case. The releases from the geosphere are around two orders of magnitude lower than the
STUK constraint.
The pulses from IRF are not included in these calculations. But applying that the activity releases
can be averaged over 1,000 years, implies that the release of the IRF give a negligible contribution
to the calculated total activity release.

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101
Central corrosion, near field
Central corrosion, far field
STUK regulatory limit

Fraction of STUK release constraint[-]

100

10-1

10-2

10-3

10-4

103

104

105

106

Time [years]

Figure 4‑52. Releases as a fraction of the activity release constraint index adopted by the Finnish regulator.

4.9.2 Radiotoxicity flux from the geosphere – EU SPIN Project
An EU project /EU 2002/ concludes that two alternative indicators could preferably be used tocomplement the dose indicator. These are:•Radiotoxicity concentration in biosphere water: preference for medium time frames, i.e. several
thousand to several tens of thousands of years.

•

Radiotoxicity flux from the geosphere: preference for later time frames.

The project also reports on reference values that could tentatively be used for comparisons to
calculated concentrations and fluxes of radionuclides from the repository. Regarding radiotoxicity
flux from the geosphere, an indicative reference value of 60 Sv/yr for a typical area of 200 km2 wassuggested. The SPIN reference value was calculated from natural activity flux (Bq/year) converting
to radiotoxicity flux by using ingestion dose coefficients from ICRP72 /ICRP 1996/. It was assumed
that each daughter is in secular equilibrium with its parent, i.e. the dose coefficients of the daughter
nuclides (half-life >1 day) are added to the studied nuclide. For further details see the SPIN project
report /EU 2002/.
The same approach was used on the central corrosion case. The release rate (Bq/yr) is converted
to a radiotoxicity flux (Sv/yr) using the ICRP72 ingestion dose coefficients (Sv/Bq) /ICRP 1996/(the same values as reported by EU /EU 1996/ and also by IAEA /IAEA 1996/). Table 4‑6 show thenuclides that have daughters that are in secular equilibrium, i.e. the dose coefficients of the daughter
nuclides (half-life >1 day) are added to the studied parent nuclide. Note that shorter-lived progany
have small ingestion dose coefficients and their in-growth following ingestion of their parents is
explicitly addressed in the ICRP biokenetic and dosimetric models.
Figure 4‑53 shows the results for the central corrosion case. The releases from the geosphere,
0.011 Sv/year, are around four orders of magnitude lower than the SPIN reference value.

106

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102
SPIN reference value

Central corrosion, near field
Central corrosion, far field

Radiotoxicity flux [Sv/yr]

101

100

10-1

10-2

10-3

10-4
103

104

105

106

Time [years]

Figure 4‑53. Radiotoxicity flux in the central corrosion case compared to the SPIN reference value.
Table 4‑6. Parent nuclides and nuclides assumed to be in secular equilibrium.
Parent nuclide

Daughter in secular equilibrium (half-life >1 day)Th-232+ Ra-228 + Th-228 + Ra-224

Cm-245+ Pu-241

Np-237+ Pa-233

Th-229+ Ra-225 + Ac-225

U-238+ Th-234

Pb-210+ Bi-210 + Po-210

Am-242m+ Cm-242

Am-243+ Np-239

Ac-227+ Th-227 + Ra-223

4.9.3 Naturally occurring fluxes of radionuclides at the site
The last alternative indicator to risk used in SR-Site is naturally occurring fluxes of radionuclides atthe site. The naturally occurring fluxes of U-238, U-234 and Ra-226, are estimated based on measured activities during the site investigations, see Section 2.3. Figure 4‑54 shows the far-field release
rates of U-238, U-234 and Ra-226 in the central corrosion case compared to the naturally occurring
fluxes at Forsmark. The naturally occurring fluxes of U-238, U-234 and Ra-226 have also been con­verted to effective dose by using the basic LDF values, the obtained dose is shown in Figure 4‑55
together with the far-field annual effective dose in the central corrosion case and the case with Kd forU(VI) in the rock . It is noted that the releases from the repository could be concentrated to one ora few of the landscape objects in the release area. There are about ten objects in the area used in thederivation of the naturally occurring fluxes, suggesting that the natural fluxes would exceed those fromthe repository even if all the release from the repository were to occur to a single landscape object.
The repository-derived flux of Ra-226 is about two orders of magnitude below the naturally occurring
flux of Ra-226. For the U isotopes, the fluxes from the repository are about six orders of magnitude
below the natural fluxes, irrespective of whether rock Kd-distributions for U(IV) or U(VI) are used.
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Naturally occuring flux of Ra-226
106

Naturally occuring flux of U-234
Naturally occuring flux of U-238

Radionuclide flux [Bq/year]

105

104

103

102

101

100

10-1

10-2
103

Ra226
(29,000)
U(VI)234 (1.6)
U(VI)238 (1.1)
U(IV)234 (0.65)
U(IV)238 (0.46)
104

105

106

Time [years]

Figure 4‑54. Far-field release rates (Bq/year) of U-238, U-234 and Ra-226 in the central corrosion casecompared to the naturally occurring fluxes at Forsmark.

102

Mean annual effective dose [µSv]

101

100

Ra226

(0.11)

I129(0.024)

Np237(0.019)Se79(0.013)Pb210(0.0059)

Ni59(0.0039)

Ac227(0.0031)

Nb94(0.0017)

Total(0.18)

Dose corresponding to naturally occuring fluxes

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑55. Far-field annual effective dose in the central corrosion case compared to the naturally
occurring fluxes of U-238, U-234 and Ra-226 at Forsmark converted to dose using the basic LDF values.
The legend is sorted by peak (in the one-million year period) of the mean annual effective dose. The values
in brackets are peak dose in units of µSv.

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4.10

Calculation with analytical models

As mentioned in Section 3.6.5, simplified, analytical models are available for the modelling of radionuclide transport in the near field and the far field. The models are documented in /Hedin 2002b/.
The analytical models are applied to the six corrosion variants of the corrosion scenario.
Regarding the application of the models to the corrosion scenario, the following, further simplifying
conditions are noted. The near-field release is determined by the rate of radionuclide release to waterin the void space because the flow rate in the Q1 fracture is not a limitation (canister failures due tocorrosion only occur in the deposition holes with the highest flow rates). Therefore, the release ratefrom the near field is simply modelled as the dissolution rate of the fuel, alternatively the corrosion
rate of the metal parts, in both cases multiplied by the inventory. As in the numerical models, the IRF
is not included but handled separately.
The release rate from the far field is in most cases calculated as the release rate from the near fieldtimes a geosphere transmission factor /Hedin 2002b/. This yields a good approximation in cases of acontinuous release over long times.
However, in some cases of relatively short-duration releases caused by corrosion of the metal partsof the fuel, the treatment is overly pessimistic. In such cases the release of the entire inventory in themetal parts, M0, as a pulse to the geosphere is also considered. This yields a peak release rate fromthe geosphere of M0/τ where τ is obtained from /SKB 2006a, Appendix B/.
Hydrodynamic and molecular dispersion in the flowing fracture are pessimistically neglected when
this expression is used. Also, radioactive decay is neglected in the expression since no appreciable
decay will take place during the short transients of concern here.
Since both the above approaches overestimate the release rate from the far field, the smaller of thetwo is chosen in each realisation.
It is also noted that chain decay in the geosphere is not accounted for when applying the transmission factors for geosphere retention. The theory for a full, analytical treatment of chain decay intransmission factors has been developed, but is not yet implemented in the analytical model. Using
the numerical models, it has been demonstrated that chain decay of parent nuclides of Ra-226 in thefar field has a negligible impact on the releases of Ra-226 in the corrosion scenario.
The result of the analytical modelling of the probabilistic central corrosion case is shown in
Figure 4‑56. As seen by comparing the results in Figure 4‑56 with those of the corresponding
numerical case in Figure 4‑5, the agreement of the peak doses is very good for nuclides emerging
from the fuel matrix, whereas doses from nuclides embedded in metal parts (Ni-59 and Nb-94)
are somewhat overestimated with the analytical model. This is due to the pessimistic modelling of
nuclides released from corrosion of metal parts discussed above.
The modelling results of the six corrosion variants are shown in Figure 4‑57. Each case was modelled with 20,000 realisations using Latin Hypercube Sampling. As seen by comparing the results in
Figure 4‑57 with those in Figure 4‑59, which shows far-field annual effective dose for all corrosion
cases calculated with FARF31, the agreement between results obtained with the two sets of models
is good. All peak doses over one million years are the same to within less than a factor of 1.5.
That the numerical calculations are in good agreement with the analytical calculations significantly
enhances confidence in the dose equivalent releases provided here and in the Main report for two
reasons. First, the comparison provides an important quality assurance check on the numericalmodelling of dose equivalent releases. This check applies not only to the numerical calculations
but also to the data/parameter transfers, as the data for the analytical calculations were taken directlyfrom the Data report independently of the numerical calculations. Second, it demonstrates thatdose equivalent releases for the corrosion cases are controlled by relatively simple processes thatare straightforward to understand.

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100

Mean annual effective dose [µSv]

Dose corresponding to risk limit
10

Total

1

(0.187)

Ra-226 (0.119)
I-129(0.024)

Np-237 (0.028)

0.1

0.01

Se-79

(0.015)Ni-59(0.015)

Nb-94(0.004)

0.001
1,000

10,000100,000

1,000,000

Time [years]

Figure 4‑56. Far-field mean annual effective dose for the central corrosion case, obtained with analyticalmodels. The legend is sorted by peak (in the one-million year period) of the mean annual effective dose.
The values in brackets are peak dose in units of µSv.

100

Mean annual effective dose (µSv)

Dose corresponding to risk limit
101Correlated, initial advection (1.0)
0.1

Uncorrelated, initial advection (0.88)
Correlated (0.67)

0.01

Uncorrelated (0.49)
Semicorrelated, initial advection (0.28)
Semicorrelated (0.19)

0.001
1,000

10,000100,000

1,000,000

Time (years)

Figure 4‑57. Summary of far-field mean annual effective dose for analytical, probabilistic calculations of
the six corrosion variants of the corrosion scenario. These results can be compared to the corresponding
results obtained with numerical models in Figure 4‑59.

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4.11

Summary and conclusions for the corrosion scenario

Figure 4‑58 shows the total dose equivalent releases for cases calculated probabilistically with
COMP23 in Chapter 4. All other things being equal, the correlated and the uncorrelated cases produce larger dose equivalent releases from the near field as compared with the semi-correlated cases.
Cases with initial advection produce earlier and larger releases than the cases without. Disregarding
thorium sorption in the near field in the semi-correlated case results in significantly lower dose
equivalent releases. Thus the assumption of thorium sorption in the near field made in all othercorrosion cases should be pessimistic.
Figure 4‑59 shows the far-field total effective dose calculated with FARF31 for the same cases as
in Figure 4‑58. The modelling cases that have larger near-field dose equivalent releases experience
more attenuation in the far field, thereby reducing the variation among the cases. Significantly, thefar-field total effective doses are all at least an order of magnitude smaller than the dose corresponding to the risk limit. Moreover, peaks of the far-field total effective doses span a range of less than
one order of magnitude. This relatively tight clustering of results suggests relative insensitivity to themodelling assumptions.
Peak total effective dose for the corrosion cases that relied on COMP23 and MARFA are summarised in Table 4‑7. All of these cases used the semi-correlated DFN model. For comparison the peakof the mean annual dose equivalent near-field release is 0.59 µSv (see Figure 4‑4).
102

Mean annual effective dose [µSv]101

Uncorrelated, initial advection(7.0)

Including solubility limits in the nearfield(6.2)

Correlated, initial advection(6.0)

Correlated(3.2)

Uncorrelated(3.1)

Semicorrelated, initial advection(1.0)

Semicorrelated(0.59)

Disregarding Th sorption in the nearfield(0.22)

Dose corresponding
to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑58. Near-field dose equivalent release for probabilistic corrosion cases. The legend is sorted bypeak (in the one-million year period) of the mean annual effective dose. The values in brackets are peakdose in units of µSv.

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102

Mean annual effective dose [µSv]101

Correlated, initial advection(0.96)

Uncorrelated, initial advection(0.83)

Correlated(0.63)

Uncorrelated(0.45)

Semicorrelated, initial advection(0.27)

Semicorrelated(0.18)

Including solubilitiy limits in the nearfield(0.15)

Disregarding Th sorption in the nearfield(0.14)

Dose corresponding
to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 4‑59. Far-field annual effective dose for probabilistic corrosion cases calculated with FARF31.
The legend is sorted by peak (in the one-million year period) of the mean annual effective dose. The values
in brackets are peak dose in units of µSv.

Table 4‑7. Far-field peak of the mean annual effective dose for corrosion cases modelled with
COMP23 and MARFA.
Calculation caseFar-field peak annual effective dose (µSv)

Steady conditions, no colloids

0.15

Steady conditions, 10 mg/l colloids

0.19

Steady conditions, 10 g/l colloids

0.33

Varying climate, no colloids

0.19

Varying climate, steady colloid concentration of 10 g/l

0.41

Varying climate, unsteady colloid concentrations

0.35

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5Canister failure due to shear load

5.1

Introduction

In the ‘canister failure due to shear load’ scenario (called briefly the shear load scenario below), a
canister fails as a result of secondary rock movements induced by a large earthquake. It was demonstrated in the Main report to have a low probability in the reference evolution. Pessimistic estimatesof the extent of this failure mode indicate that the probability that one out of the 6,000 canisters has
failed at the end of the one million year assessment period is 0.079 /Main report Section 10.4.5/.
A failure frequency as a function of time is also provided in the Main report Section 10.4.5 and thisis used in the probabilistic assessment of the shear load scenario. For this failure mode, the canister
is bypassed, the thickness of the buffer is reduced and the rock retention is insignificant, since a
shearing fracture must have a considerable size with properties difficult to assess.

5.2

Calculation of doses for the shear load scenario

An earthquake can cause canister failure at any time after closure of the repository. The likelihood
is varying during different time periods. Three different cases of failure times have been consideredin the calculations: a postulated failure of one canister at 100,000 years, failure during the period
1,000 years to one million years and early failure. The following data and assumptions are used in
the calculation cases:•

In the affected deposition holes the faulting is supposed to be so large that it causes massive
failure of the canister, i.e. there will be no delay between failure and the onset of radionuclidetransport and no credit from limited transport resistance in the canister.

•

The shear movement will not affect the buffer to the extent that its protection against advective
flow will be impaired, but effective amount of buffer between the canister and the shearing
fracture is assumed to be reduced from 35 cm to 25 cm.

•

The canister failure location is assumed to fully coincide with the location of the shearing
fracture. Furthermore, the shear is assumed to increase the fracture transmissivity significantly.
The Qeq value for the intersecting fracture is, therefore, assumed to be sufficiently high (1 m3/yr)that it does not contribute to the transport resistance in the near field.

•

The shearing fracture is likely to be among the larger in the modelled fracture network and its
properties after shearing are difficult to assess. Therefore, no credit for radionuclide retention in
the geosphere is taken.

•

Solubility limits are included in the calculations, since, contrary to cases in the corrosion
scenario, the buffer is in place in the shear load scenario.

•

The contributions from the instantly released fraction of nuclides, IRF, are included in thecase with early release but not in the other cases. The contribution from the IRF is judged to be
negligible based on the low probability for this scenario and the low contribution shown in thecentral corrosion case in Section 4.4.2.

A detailed description of the discretisation, diffusion resistances and boundary conditions used in
COMP23 is given in Appendix G, section Canister failure due to shear load.

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5.2.1

Postulated failure of one canister at 100,000 years

Deterministic calculations
Hydrogeological case:
Failure time:
Number of failed canisters:
Solubility limits:
Number of realisations:
Number of nuclides:

Semi-correlated, base realisation
100,000 years
1
Yes
1
45

A deterministic calculation of the shear load case is performed for a postulated failure of one canisterat 100,000 years. No retention in the geosphere occurs and hence the release calculated for the nearfield is also valid for the far field. The contributions from the instantly released fraction of nuclides,
IRF, are not included in the calculations. Table 4‑4 shows the peak annual doses from pulse releasesof the instantly released fraction, IRF.
Figure 5‑1 show the deterministic near-field and far-field dose equivalent releases, for the shear loadcase with a postulated failure of one canister at 100,000 years. Shortly after the canister failure thedose is dominated by releases of Ni-59 and in the longer term the dose is dominated by Ra-226.
102
Ni59

(4.9)

Ra226 (1.8)

Annual effective dose [µSv]

101

Se79

(0.52)

Nb94(0.35)

I129(0.15)

Dose corresponding to risk limit

Th230 (0.021)
Pa231 (0.016)
Ac227 (0.0097)
Np237 (0.0082)

100

Pu242 (0.0081)
Sn126 (0.0037)

10-1

Tc99

(0.0034)

Cl36(0.0019)C14(0.0011)

Pu239 (0.0011)
Total

(5.6)

10-2

10-3
103

104

105

106

Time [years]

Figure 5‑1. Near-field and far-field annual effective dose for a deterministic calculation of the shear load
scenario, with a postulated failure of one canister at 100,000 years. The legend is sorted by peak (in the
one-million year period) of the annual effective dose. The values in brackets are peak dose in units of µSv.

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Probabilistic calculations
Hydrogeological case:
Failure time:
Number of failed canisters:
Solubility limits:
Number of realisations:
Number of nuclides:

Semi-correlated, base realisation
100,000 years
1 (postulated)
Yes
1,000
37

A probabilistic calculation of the shear load case is performed for a postulated failure time at
100,000 years and geosphere transport data from the base realisation of the semi-correlated DFN
model. The postulated number of failed canisters is 1. The contributions from the instantly released
fraction of nuclides, IRF, are not included in the calculations. Table 4‑4 shows the peak annual doses
from the pulse releases from the instantly released fraction, IRF. No retention in the geosphere occurs
and hence the release calculated for the near field is also valid for the far field.
Figure 5‑2 show the near-field and far-field dose equivalent releases for the shear load case witha postulated failure of one canister at 100,000 years. Shortly after the canister failure the dose isdominated by releases of Ni-59 and in the longer term the dose is dominated by releases of Ra-226.

102

Mean annual effective dose [µSv]

101

100

10-1

Ra226

(3.6)

Ni59

(3.4)

Nb94

(0.50)

Se79(0.46)

I129(0.23)

Th230(0.046)

Ac227(0.033)Pa231(0.024)

Np237(0.020)Pu242(0.012)

Sn126(0.010)Pu239(0.0095)

Th229(0.0058)

Tc99(0.0040)Cl36(0.0013)

Total

(4.2)

Dose corresponding to risk limit

10-2

10-3
103

104

105

106

Time [years]

Figure 5‑2. Near-field and far-field mean annual effective dose for the probabilistic calculation of theshear load scenario, with a postulated failure of one canister at 100,000 years. The legend is sorted bypeak (in the one-million year period) of the mean annual effective dose. The values in brackets are peakdose in units of µSv.

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5.2.2

Failure during the period 1,000 years to one million years

Probabilistic calculations
Hydrogeological case:
Failure time:
Average number of failed canisters:
Solubility limits:
Number of realisations:
Number of nuclides:

Semi-correlated, base realisation
1,000 to one million years
0.079
Yes
6,916
37

A probabilistic calculation of the shear load case is performed with failure during the period
1,000 years to one million years and geosphere transport data from the base realisation of thesemi-correlated DFN model. The average number of failed canisters is 0.079. The contributions
from the instantly released fraction of nuclides, IRF, are not included in the calculations, except for
Tc-99, which is included. The contribution from the IRF is judged to be negligible based on the low
probability for this scenario and the low contribution shown in the central corrosion case in Section
4.4.2. The influence is also shown to be small at early failure times, see 5.2.3. No retention in thegeosphere occurs and hence the release calculated for the near field is also valid for the far field.
Figure 5‑3 show the near-field and far-field dose equivalent releases for the shear load case with
failure during the period 1,000 years to one million years. For an early failure time, the dose isdominated by release of C-14, thereafter by Nb-94 and in the longer term the dose is dominatedby Ra-226. The dose at one million years in the present case is about 28 times lower than in thecase where one canister fails at 100,000 years, but in the former case the average number of failed
canisters is 0.079 compared to one in the latter.

102

Mean annual effective dose [µSv]

101

100

Ra226

(0.13)

I129(0.015)Se79(0.0076)

C14(0.0071)

Nb94(0.0058)

Th230(0.0011)

Np237(0.0010)

Ac227(0.0010)Total(0.15)

Dose corresponding to risk limit

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 5‑3. Near-field and far-field mean annual effective dose for the probabilistic calculation of theshear load scenario, with failure during the period 1,000 years to one million years. The legend is sorted
by peak (in the one-million year period) of the mean annual effective dose. The values in brackets are peakdose in units of µSv.

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Global sensitivity analysis

A global sensitivity analysis on the results of the probabilistic shear load case using the SRRC
method as for the central corrosion case yields results according to Figure 5‑4.
Regressing the total dose at 106 years on the input variables yields, in descending order, the fueldissolution rate DFuel, the solubilities of radium and thorium, and the failure time tFailure as the input
parameters most affecting dose results. Regressing on Ra-226 dose at 106 years yields a similar
result due to the dominance of Ra-226. The significance of the solubility of thorium is due to decayof Th-230 to Ra-226 in the buffer, where the release of Th-230 to the buffer is controlled by thesolubility of thorium. A further scrutiny of individual realisations reveals that the significance of thelimited solubility overall is due to a relatively limited number of realisations with low solubilities,
whereas the total dose is dominated by the larger number of realisations that have solubilities that are
sufficiently high so as to not limit the release. Solubilities of neither Th nor Ra (taking into accountco-precipitation with Ba) significantly limit the mean release rate of Ra-226. This conclusion iscorroborated by the fact that the case with the omitted buffer (Section 5.2.4), where neither sorption
in the buffer nor solubility limits are included, increases Ra-226 mean dose by only a factor of 2.
Regressing instead on the maximum of total dose over time yields the failure time and the corrosion
release rate, CRR, as significant variables. This is consistent with the fact that for early failures,the highest doses occur due to release of e.g. C-14 and Nb-94 congruently with the corrosion of
structural parts of the fuel elements.

Total dose @ 106 years
R2 = 0.76

DFuel
CSolRaCSolThtFailure

KdBuffTh
DeBuffCations
CSolRaDFuel

Ra-226 dose @ 106 years
R2 = 0.69

CSolThtFailure

KdBuffTh
DeBuffCations

tFailure

CRR

KdBuffNb-1-0.5

CSolRaDeBuffCations
0

0.5

Total dose
R2 = 0.94

1Standardised Rank Regression Coefficients
Figure 5‑4. Results of standardised rank regression for the probabilistic calculation of the shear load
scenario, with failure during the period 1,000 to one million years. Regressing on total dose at 106 years
and on Ra-226 dose at 106 years yields similar results due to the dominance of Ra-226. Regression on the
maximum of total dose over time identifies CRR as an additional sensitive input.

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Risk dilution

Risk dilution for the shear load scenario needs to be considered, because canisters fail at probabilistically determined times.
An illustration is obtained by comparing the results in Figure 5‑2 (postulated, deterministic failuretime) with those in Figure 5‑3 (distribution of failure times). If the result in Figure 5‑2 is multipliedby the overall probability of the event occurring during the assessment period, i.e. 0.079, thenthe dose at one million years (0.28 μSv) is relatively close to that obtained at one million years
in Figure 5‑3 (0.15 μSv). This small difference is because the consequences are determined i) by
in-growth of Ra-226 and ii) by the build-up of Th-230 released from the fuel and precipitated in thecanister interior or sorbed in the buffer, which in general occur long after the failure time. The ingrowth of Ra-226 is essentially controlled by the build-up of its parent nuclide Th-230, which occurs
on a time scale comparable to the half-life of Th-230 (approximately 75,000 years). The build-up of
Th-230 occurs on time scales determined by the fuel dissolution rate, which are of the order of one
million years.
Risk dilution, including a treatment of the pulse releases, is further discussed in Section 13.9 in theMain report.
Probabilistic calculations, disregarding co-precipitation of radium and barium
Hydrogeological case:
Failure time:
Average number of failed canisters:
Solubility limits:
Number of realisations:
Number of nuclides:

Semi-correlated, base realisation
1,000 to one million years
0.079
Yes, disregarding co-precipitation of radium and barium
6,916
37

Due to the assumed high equivalent flow rate in the Q1 buffer/rock interface, the release rate ofradionuclides from the near field is in general sufficiently high in comparison to the fuel dissolution
rate to render solubility limits inside the canister ineffective. As an illustration, a probabilistic casewhere no credit was taken for co-precipitation of Ra/Ba was calculated, i.e. where the solubility of
Ra was increased by a factor of 1,000. Figure 5‑5 show the near-field and far-field dose equivalentreleases for the shear load case with failure during the period 1,000 years to one million years anddisregarding co-precipitation of Ra/Ba. This assumption led to an increase of the release rate of Ra
by only a factor of about 1.5.

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102

Mean annual effective dose [µSv]

101

100

Ra226

(0.21)

I129(0.015)Se79(0.0076)

C14(0.0071)

Nb94(0.0058)

Th230(0.0011)

Np237(0.0010)

Ac227(0.0010)Total(0.24)

Dose corresponding to risk limit

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 5‑5. Near-field and far-field mean annual effective dose for the probabilistic calculation of
the shear load scenario, with failure during the period 1,000 years to one million years, disregarding
co‑precipitation of radium and barium. The legend is sorted by peak (in the one-million year period) of
the mean annual effective dose. The values in brackets are peak dose in units of µSv.

5.2.3

Early failure

Probabilistic calculations
Hydrogeological case:
Failure time:
Average number of failed canisters:
Solubility limits:
Number of realisations:
Number of nuclides:

Semi-correlated, base realisation
0–10,000 years
2.4·10–8/year
Yes
6,916
45

For times up to 1,000 years after closure, the frequency of earthquakes is assessed to be lower,with a probability of failure of one of the 6,000 canisters by the end of the initial 1,000 year period
being 2.4·10−5 or 2.4·10−8/year /Main report Section 10.4.5/. Also, the use of basic LDF-values
overestimates the doses in this time interval for two reasons. First, the basic LDF is a pessimistic
upper bound for releases occurring continuously over an entire interglacial period taking into
account accumulation because a large part of the interglacial period has elapsed without any releases
when the repository is sealed. Second, it is not meaningful to use the LDF concept for a radionuclide
that decays to insignificance over an interglacial period because the concept is based on a continuous
uniform release over the period.

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A more detailed calculation of the shear load scenario for the initial 10,000 years was done tofacilitate comparison with the results for the one million year time frame presented above. In thiscalculation, releases from the near field were determined as for all other cases; the IRF:s were also
included. Because no credit is taken for geosphere retention in the shear scenario, the near-fieldreleases are used as direct input to the biosphere modelling. In addition, because it is not possible
to determine a location of the releases among the identified potential landscape objects, the releaseis fed to each object and the time dependent development of radionuclide transport and dose in thelandscape is calculated for each object. The object giving the highest dose is then determined foreach point in time and for each radionuclide. This entity is pessimistically defined as the calculated
dose consequence for the case of a shear failure during the initial 10,000 years. A well is included ineach landscape object in the same way as for the LDF calculations.
The result of this calculation is that the peak dose is almost four orders of magnitude lower than that
corresponding to the regulatory risk limit, see Figure 5‑6. (Note the extended dose scale comparedto most other figures). Releases of Cs-137 and Sr-90 dominate in the beginning and thereafter C-14,
I-129, Ag-108m and Nb-94 dominate.
102

101

C14

(0.0027)

Nb94(0.00041)

Cs137(0.00028)

I129(0.00024)

Dose corresponding to risk limit

Mean annual effective dose [µSv]

Ag108m (0.00018)

10

0

Ni59

(0.00018)

Sr90(0.00016)

Total(0.0027)

10-1

10-2

10-3

10-4
102

103

104

Time [years]

Figure 5‑6. Near-field and far-field mean annual effective dose for the probabilistic calculation of theshear load scenario, with failure during the period up to 10,000 years. The legend is sorted by peak (in the
one-million year period) of the mean annual effective dose. The values in brackets are peak dose in unitsof µSv.

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5.2.4

Combination of shear load and buffer advection

Probabilistic calculations
Hydrogeological case:
Failure time:
Average number of failed canisters:
Solubility limits:
Thorium sorption in near field:
Number of realisations:
Number of nuclides:

Semi-correlated, base realisation
1,000 to one million years
0.079
No
Yes (modelled as low solubility limit)
6,916
37

In this case the combination of the shear load and the buffer advection scenarios /Main report
Section 12.9.3/ is addressed and the consequences of a shear failure followed by buffer erosion isconsidered, since it is reasonable to assume that the groundwater flow in a fracture that has undergone a major secondary shear movement could be high. Buffer erosion could then ultimately leadto loss of the buffer and its retardation function in the deposition hole with the canister failed due
to shearing. A similar situation could arise if the buffer material is transformed through interaction
with iron ions from the failed canister, as discussed in the Main report in the buffer transformation
scenario /Main report Section 12.4/.
The case with shear failures distributed between 1,000 and one million years was therefore calculated
also for near-field conditions with a missing buffer. The conceptualisation of the near field is thus
the same as in the corrosion scenario, but near-field flow data are stylised and geosphere retention isdisregarded as in other consequence calculations for the shear load scenario. The results are shownin Figure 5‑7.
102
Ra226 (0.25)
Np237 (0.041)

Mean annual effective dose [µSv]

101

Nb94

(0.030)I129(0.017)

Dose corresponding to risk limit

Pb210 (0.012)
Se79(0.011)C14(0.0070)

Pu239 (0.0043)
Pu240 (0.0019)

100

Pa231 (0.0017)
Ni59(0.0012)Total(0.34)

10-1

10-2

10-3

103

104

105

106

Time [years]

Figure 5‑7. Near-field and far-field mean annual effective dose for a probabilistic calculation of theshear load scenario, with advective conditions in the deposition hole, failure during the period between
1,000 years and one million years. The legend is sorted by peak (in the one-million year period) of themean annual effective dose. The values in brackets are peak dose in units of µSv.

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The result is similar to the situation where the buffer is present in Figure 5‑3 especially beyond
100,000 years. The peak annual effective dose from Ra-226 increases by about a factor of 2 from
0.13 µSv/yr to 0.25 µSv/yr. The retardation in the buffer and the limited solubility of the dose driving Ra-226, both of which contribute to retardation only when the buffer is present, are thus of minor
importance in the shear load scenario.
The main difference for the radionuclides contributing most to dose is for Nb-94, as this radionuclide
is significantly retained in the buffer when it is present. However, Nb-94 contributes to dose mainly
before 100,000 years. The above case is only relevant after the buffer has been eroded. Since thenear-field hydrogeological conditions are stylised with respect to radionuclide transport in the above
case, they are not necessarily relevant for estimating the time taken for buffer erosion to cause
advective conditions in the deposition hole. The first advective positions occur after several tens of
thousands of years in the buffer advection scenario. However, considering the unknown nature of thehydraulic conditions in the deposition hole after a shear failure, the results in Figure 5‑7 are seen as
cautiously representative of a combined scenario for times beyond 10,000 years.

5.3

Alternative safety indicators for shear load case 1,000 years
to one million years

Four alternative indicators to risk are used in SR-Site: release of activity from the geosphere,radiotoxicity flux from the geosphere, concentrations of radionuclides in ecosystems and naturalgeosphere fluxes of radionuclides. The following reference values are used when evaluating these
indicators.
•

The Finnish activity release constraints. These constraints are strictly applicable only in the
Finnish regulatory context, but are nevertheless deemed useful as reference values for SR-Site.

•

The reference value for radiotoxicity flux from the geosphere suggested by the EU SPIN project.

•

Measured concentrations of naturally occurring radionuclides in ecosystems at the Forsmark siteor other, comparable sites. Not further described here, see Main report Section 13.5.8.

•

Naturally occurring fluxes of radionuclides at the site.

For further descriptions of the indicators, see Alternative safety indicators for the central corrosion
case in Section 4.9.

5.3.1 Finnish activity release constraints
The activity release constraints issued by STUK, see Section 4.9.1, have been applied to releases
calculated for the shear load scenario, with failure during the period 1,000 years to one million years.
The releases are around three orders of magnitude lower than the STUK constraint, see Figure 5‑8.

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101
Failure during 1,000 to
one million years
STUK regulatory limit

Fraction of STUK release constraint[-]

100

10-1

10-2

10-3

10-4

10-5

10-6
103

105

104

106

Time [years]

Figure 5‑8. Releases as a fraction of the activity release constraint index adopted by the Finnish regulator
for the shear load case with failure during the period 1,000 years to one million years.

5.3.2 Radiotoxicity flux from the geosphere – EU SPIN Project
The EU SPIN project, see Section 4.9.2, approach was used on the releases calculated for the
shear load scenario, with failure during the period 1,000 years to one million years. The releases,
0.0096 Sv/year, are around four orders of magnitude lower than the SPIN reference value,
60 Sv/year, see Figure 5‑9.

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102
SPIN reference value

Failure during 1,000 to
one million years

Radiotoxicity flux [Sv/yr]

101

100

10-1

10-2

10-3

10-4
103

104

105

106

Time [years]

Figure 5‑9. Radiotoxicity flux in the shear load case with failure during the period 1,000 years to one
million years compared to the SPIN reference value.

5.3.3 Naturally occurring fluxes of radionuclides at the site
The last alternative indicator to risk used in SR-Site is naturally occurring fluxes of radionuclides
at the site. The naturally occurring fluxes of U-238, U-234 and Ra-226, are estimated based on measured activities during the site investigations, see Section 2.3. Figure 5‑10 shows the release rates of
U-238, U-234 and Ra-226 for the shear load scenario, with failure during the period 1,000 years to
one million years, compared to the naturally occurring fluxes at Forsmark. The naturally occurring
fluxes of U-238, U-234 and Ra-226 have been converted to effective dose by using the basic LDF
values, the obtained dose is shown together with the far-field annual effective dose in the shear loadcase 1,000 years to one million years in Figure 5‑11.

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Radionuclide flux [Bq/year]

10

6

Ra226

(33,000)

Naturally occuring flux of Ra-226

U234(0.078)Naturally occuring flux of U-234

U238(0.057)Naturally occuring flux of U-238

104

102

100

10-2

103

104

105

106

Time [years]

Figure 5‑10. Far-field release rates (Bq/year) of U-238, U-234 and Ra-226 in the shear load case
1,000 years to one million years compared to the naturally occurring fluxes at Forsmark. The legend
is sorted by peak (in the one-million year period) of the mean annual radionuclide flux. The values inbrackets are peak radionuclide fluxes in units of Bq/yr.
102
Ra226 (0.13)

Mean annual effective dose [µSv]

101

I129

(0.015)Se79(0.0076)

C14(0.0071)

Nb94(0.0058)

Dose corresponding to naturally occuring fluxes

Th230 (0.0011)
Np237 (0.0010)
Ac227 (0.0010)
100

Total

(0.15)

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 5‑11. Far-field annual effective dose in the shear load case 1,000 years to one million years
compared to the naturally occurring fluxes of U-238, U-234 and Ra-226 at Forsmark converted to doseusing the basic LDF values. The legend is sorted by peak (in the one-million year period) of the meanannual effective dose. The values in brackets are peak dose in units of µSv.
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5.4

Calculation with analytical models

For the shear load scenario, analytical models were applied to the variant with the combination ofshear load and buffer advection with failure during the period 1,000 years to one million years.
The result of the analytical modelling of the probabilistic shear load and buffer advection case isshown in Figure 5‑12. As seen by comparing the results in Figure 5‑12 with those of the corresponding numerical case in Figure 5‑7, the maximum total doses are almost identical. Together with thegood agreement obtained also for the corrosion scenario, Section 4.10, the analytical calculations
significantly enhances confidence in the dose equivalent releases provided here and in the Main
report.

Mean annual effective dose [µSv]102

Total (0.364)
Ra-226
I-129
Np-237
Se-79
Ni-59
Nb-94
Pu-239101

100

Dose corresponding to risk limit

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 5‑12. Near-field and far-field mean annual effective dose for the probabilistic calculation of the
combined shear load and buffer advection scenario, obtained with analytical models, with failure during
1,000 years to one million years.

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5.5

Summary and conclusions for the shear load scenario

Figure 5‑13 shows the total effective dose for early failure and for failure during the time period
1,000 years to one million years. No retention in the geosphere occurs and hence the release calculated for the near field is also valid for the far field. Note that the two cases have different probabilityof failure and that a more detailed calculation was performed for early failure (red curve) where the
COMP23 results were used as input to the biosphere modelling while for later failure (blue curve)
the COMP23 results were treated as in all other cases with basic LDF values.
It is seen that the early failure peak dose has it maximum of 0.0027 μSv after about 600 years.
For later failure the peak dose of 0.15 μSv occurs at one million years and is about two orders ofmagnitude below the dose corresponding to the regulatory risk limit, 14 μSv.

102
Failure during the priod 1000 to one million years (0.15)
Early failure(0.0027)
Dose corresponding to risk limit

Mean annual effective dose [µSv]

101

100

10-1

10-2

10-3

10-4
102

103

104

105

106

Time [years]

Figure 5‑13. Far-field annual effective dose for the shear load scenario. Note that the case for 1,000 to
one million years are calculated with basic LDF values, while the curve for early failure is calculated withtime a dependent biosphere model. The legend is sorted by peak (in the one-million year period) of themean annual effective dose. The values in brackets are peak dose in units of µSv.

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6

Hypothetical residual scenarios to illustratebarrier functions

6.1

Introduction

In this section, hypothetical, residual scenarios to illustrate barrier functions are analysed. They
encompass a) the scenario ‘canister failure due to isostatic load’, considered as residual according
to the analysis in Main report Section 12.8, b) a failure mode where a hypothetical initial defectin the form of a penetrating pinhole in the copper shell grows into a larger defect and c) a numberof additional cases where different barriers are assumed to be completely lost. The canister failure
due to isostatic load scenario is analysed in Section 6.2. The pinhole case is analysed in Section
6.3, using the model tools COMP23 and FARF31 and in Section 6.4 using the MARFA code for the
far-field transport. Hypothetical cases illustrating consequences of assumed barrier losses in addition
to the pinhole case are analysed in Section 6.5.

6.2

Canister failure due to isostatic load

In the ‘canister failure to due to isostatic load’ scenario (briefly called the isostatic load scenario
below) a canister fails due to isostatic collapse. It could occur as a consequence of the increased
isostatic pressure due to a glacial overburden. The likelihood for this failure mode is negligible.
For this failure mode the canister is bypassed, whereas the buffer and the geosphere are assumed tohave intact retention properties. It thus resembles the final state of the pinhole case, i.e. its state after
occurrence of a large failure (Section 6.3).
Three transport paths are modelled:•

Q1, a fracture intersecting the deposition hole at a vertical position of the canister lid. This
fracture is placed on the opposite side of the buffer to the canister defect, hence minimising thetransport distance and the diffusional transport resistance. Thermally induced spalling is assumed
to have occurred in the wall of the deposition hole meaning that the transport resistance at theinterface Q1 is decreased.

•

Q2, an excavation damage zone, EDZ, in the floor of the deposition tunnel. In the hydrogeological model, EDZ is treated as a thin conductive layer.

•

Q3, a fracture intersecting the deposition tunnel. The distance to Q3 is obtained in the hydrogeological model by tracing advectively transported particles released in the deposition tunnel justabove the deposition hole. As the distance from the deposition hole to Q3 differs, the longitudinal
dimensions of the modelled deposition tunnel are different for different deposition holes.

A detailed description of the discretisation, diffusion resistances and boundary conditions used in
COMP23 is given in Appendix G (section Growing pinhole – spalling, large hole).

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6.2.1

Postulated failure of one canister at 10,000 years

Deterministic calculations
Hydrogeological case:
Failure time:
Number of failed canisters:
Solubility limits:
Number of realisations:
Number of nuclides:

Semi-correlated, base realisation
10,000 years
1
Yes
1
45

A deterministic calculation of the isostatic load failure was performed with a postulated failure of
one canister at 10,000 years.
Figure 6‑1 and Figure 6‑2 show the deterministic near-field and far-field dose equivalent releases,
respectively, for the isostatic load case with a postulated failure of one canister at 10,000 years. The
doses from the near field are dominated by releases of I-129 and shortly after canister failure alsowith contribution of releases of C-14. The doses from the far field are dominated by releases ofI-129.
102

Annual effective dose [µSv]

101

I129
(4.6)
C14
(2.6)
Se79 (0.093)
Ni59(0.034)
Ra226 (0.016)
Nb94 (0.0070)
Cl36 (0.0022)
Total (7.0)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑1. Near-field dose equivalent release for a deterministic calculation of the isostatic load scenario,
with a postulated failure of one canister at 10,000 years. The legend is sorted by peak (in the one-million
year period) of the annual effective dose. The values in brackets are peak dose in units of µSv.

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102

Annual effective dose [µSv]101

I129 (1.3)
C14 (0.25)
Se79 (0.020)
Total (1.6)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑2. Far-field annual effective dose for a deterministic calculation of the isostatic load scenario,
with a postulated failure of one canister at 10,000 years. The legend is sorted by peak (in the one-million
year period) of the annual effective dose. The values in brackets are peak dose in units of µSv.

Probabilistic calculations
Hydrogeological case:
Failure time:
Number of failed canisters:
Solubility limits:
Number of realisations:
Number of nuclides:

Semi-correlated, base realisation
10,000 years
1 (postulated)
Yes
6,916
37

A probabilistic calculation of the isostatic load failure was performed with a postulated failure of one
canister at 10,000 years and geosphere transport data from the base realisation of the semi-correlated
DFN model.
Figure 6‑3 and Figure 6‑4 show the near-field and far-field dose equivalent releases, respectively,
for the isostatic load failure with a postulated failure of one canister at 10,000 years. Both near-field
and far-field doses are dominated by releases of I-129 and shortly after canister failure also with acontribution due to releases of C-14.

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102

Mean annual effective dose [µSv]

101

I129
(1.5)
C14
(0.99)
Se79 (0.10)
Ra226 (0.025)
Ni59 (0.0090)
Nb94 (0.0064)
Total (2.5)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑3. Near-field dose equivalent release for a probabilistic calculation of the isostatic load scenario,
with a postulated failure of one canister at 10,000 years. The legend is sorted by peak (in the one-million
year period) of the mean annual effective dose. The values in brackets are peak dose in units of µSv.

102

Mean annual effective dose [µSv]

101

I129
(0.42)
C14(0.20)
Se79 (0.026)
Ra226 (0.0011)
Total (0.63)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑4. Far-field mean annual effective dose for a probabilistic calculation of the isostatic load scenario,
with a postulated failure of one canister at 10,000 years. The legend is sorted by peak (in the one-million
year period) of the mean annual effective dose. The values in brackets are peak dose in units of µSv.

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6.2.2

Postulated failure of one canister at 100,000 years

Deterministic calculations
Hydrogeological case:
Failure time:
Number of failed canisters:
Solubility limits:
Number of realisations:
Number of nuclides:

Semi-correlated, base realisation
100,000 years
1
Yes
1
45

A deterministic calculation of the isostatic load failure was performed with a postulated failure of
one canister at 100,000 years.
Figure 6‑5 and Figure 6‑6 show the deterministic near-field and far-field dose equivalent releases,
respectively, for the isostatic load case with a postulated failure of one canister at 100,000 years.
Both near- and far-field doses are dominated by I-129. Compared to the failure at 10,000 years nopeak of C-14 appears shortly after canister failure.

102

Annual effective dose [µSv]

101

I129
(4.4)
Se79 (0.093)
Ra226 (0.015)
Ni59 (0.015)
Cl36 (0.0018)
Total (4.5)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑5. Near-field dose equivalent release for a deterministic calculation of the isostatic load scenario,
with a postulated failure of one canister at 100,000 years. The legend is sorted by peak (in the one-million
year period) of the annual effective dose. The values in brackets are peak dose in units of µSv.

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102

I129 (1.2)
Se79 (0.020)
Total (1.2)

Dose corresponding to risk limit

Annual effective dose [µSv]

101

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑6. Far-field annual effective dose for a deterministic calculation of the isostatic load scenario,
with a postulated failure of one canister at 100,000 years. The legend is sorted by peak (in the one-million
year period) of the annual effective dose. The values in brackets are peak dose in units of µSv.

Probabilistic calculations
Hydrogeological case:
Failure time:
Number of failed canisters:
Solubility limits:
Number of realisations:
Number of nuclides:

Semi-correlated, base realisation
100,000 years
1 (postulated)
Yes
6,916
37

A probabilistic calculation of the isostatic load failure was performed with a postulated failure of
one canister at 100,000 years and geosphere transport data from the base realisation of the semicorrelated DFN model. The postulated number of failed canisters is 1.
Figure 6‑7 and Figure 6‑8 show the near-field and far-field dose equivalent releases, respectively,
for the isostatic load failure with a postulated failure of one canister at 100,000 years. Both nearfield and far-field doses are dominated by releases of I-129. Compared to the case with failure at
10,000 years, the total doses are lower and the contributions to the dose of releases of C-14 are
negligible.

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Mean annual effective dose [µSv]

102

101

I129
(1.4)
Se79 (0.094)
Ra226 (0.023)
Ni59 (0.0043)
Total (1.5)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑7. Near-field dose equivalent release for a probabilistic calculation of the isostatic load scenario,
with a postulated failure of one canister at 100,000 years. The legend is sorted by peak (in the one-million
year period) of the mean annual effective dose. The values in brackets are peak dose in units of µSv.

102

Mean annual effective dose [µSv]

101

I129
(0.39)
Se79 (0.024)
Ra226 (0.0010)
Total (0.39)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑8. Far-field mean annual effective dose for a probabilistic calculation of the isostatic load scenario,
with a postulated failure of one canister at 100,000 years. The legend is sorted by peak (in the one-million
year period) of the mean annual effective dose. The values in brackets are peak dose in units of µSv.
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6.2.3 Summary and conclusions for the isostatic load scenario
The consequences of postulated failures of one canister due to isostatic collapse 10,000 years and100,000 years after repository closure are shown in Figure 6‑9 and Figure 6‑10 for the near field
and far field, respectively. Since both hypothetical global causes (glacial load) and local causes(deficient material properties, higher than intended buffer density) for this scenario can be envisaged,
simultaneous failure of more than one canister needs to be considered and would yield consequencesin proportion to the number of failed canisters, provided that all releases occur to the same biosphereobject. If a large number of canisters fail, it is more appropriate to use the LDF values for a distributed release when converting release to dose (see Table 3‑7), since the release can be expected to be
distributed over several landscape objects. Illustrations of consequences of extreme cases where allcanisters fail at 10,000 and 100,000 years are also shown in Figure 6‑9 and Figure 6‑10 for the nearfield and far field, respectively. It is noted that the cases where one canister fails yield lower doses at
one million years compared to single failures due both to corrosion where the buffer is eroded away(central corrosion case deterministic calculation, Figure 4‑3) and to shear load where geosphereretention is neglected (deterministic calculation with postulated failure at 100,000 years, Figure 5‑1).

Mean annual effective dose [µSv]

104

103

102

Dose corresponding to risk limit

101

100

10-1

10,000 years, 1 failed canister(2.5)
10,000 years, 6000 failed canisters (1898)
100,000 years, 1 failed canister(1.5)
100,000 years, 6000 failed canisters (821)
102

103

104

105

106

Time [years]

Figure 6‑9. Near-field dose equivalent release, for the isostatic load scenario. One failed canister (basicLDF) and 6,000 failed canisters (distributed LDF) at 10,000 years and 100,000 years. The values inbrackets in the legend are peak dose in units of µSv.

136

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104

Mean annual effective dose [µSv]103

10,000 years, 1 failed canister(0.63)
10,000 years, 6000 failed canisters (443)
100,000 years, 1 failed canister(0.39)
100,000 years, 6000 failed canisters (218)

102

101

Dose corresponding to risk limit

100

10-1
102

103

104

105

106

Time [years]

Figure 6‑10. Far-field mean annual effective dose, for the isostatic load scenario. One failed canister(basic LDF) and 6,000 failed canisters (distributed LDF) at 10,000 years and 100,000 years. The values
in brackets in the legend are peak dose in units of µSv.

6.3

The growing pinhole failure

A hypothetical, postulated failure mode where an initial defect in the form of a penetrating pinhole
in the copper shell grows over time into a larger defect is analysed. In the pinhole failure mode, apinhole in the canister wall initially offers considerable transport resistance that is subsequently lostas the defect expands with time, whereas the buffer and the geosphere have intact retention properties. It is, therefore, a convenient case for demonstrating the retarding capacity of the buffer and thegeosphere and for exploring uncertainties and sensitivities related to these repository subsystems.
Details of the pinhole scenario are as follows: One canister at an unknown location is assumed tohave a small defect. Transport is assumed to start 1,000 years after emplacement. Initially, transport
is through a hole with 2-mm radius. At 10,000 years after emplacement, complete loss of transport
resistance is assumed for the copper canister. This loss of transport resistance is modelled by allowing the water filled, nuclide containing canister void to directly contact bentonite in a 0.5-m-highregion next to the defect. The time-dependent release of radionuclides into the geosphere occurs
through the Q1, Q2 and Q3 release path. A more detailed description of the discretisation, diffusion
resistances and boundary conditions used in COMP23 is given in Appendix G.
As a base case for the analysis of the pinhole failure mode, the base case of the hydrogeologicalsemi-correlated DFN model was adopted. The EFPC criterion has been applied for the base case,i.e. canister positions intersected by fractures that also intersect the entire tunnel perimeter have been
discarded. This means that 612 deposition holes out of 6,916 have been filtered from the results of
the hydrogeological calculations. Furthermore, it was assumed that the equivalent flow rates for thepath Q1 are affected by spalling.

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The following is a brief description of the development of the system, driven by the processes thatare quantified in the transport models, as an introduction to the presentation of the results of thecalculations.
1. No releases occur from the canister before a continuous water pathway has been formed between
the fuel and the exterior of the failed canister, which could take thousands of years. In these cal­culations the delay time is assigned to be 1,000 years. Radioactive decay reduces the radionuclide
content and total radiotoxicity of the fuel.
2. As soon as a continuous water pathway has formed, the instant release fraction of the inventory
dissolves in the water in the canister void. If the solubility limit is reached, the concentration of the
dissolved nuclide in the water does not increase further. The nuclides dissolved in the water begin
to diffuse out of the canister. The release of nuclides embedded in the fuel is determined by the fueldissolution rate and the release of nuclides in metal parts is determined by the corrosion release rate.
Also in this case, the solubilities of the nuclides limit the concentrations that can occur in the water.
3. The nuclides are sorbed with varying efficiency in the buffer and the diffusion and sorption properties determine the time for diffusion through the buffer. If this time is shorter than a few half-livesof the nuclide, it passes out into the rock.
4. In the rock, the nuclide’s sorption properties, together with the rock’s transport properties, determine the time for transport through the rock to the biosphere. As in the buffer, the half-life of thenuclide determines whether it passes through the geosphere before decaying to a substantial degree.
5. In the biosphere, the nuclide gives rise to a dose that is dependent on its inherent radiotoxicity andits turnover in the biosphere type to which it is released. Both of these factors are included in the
LDF value used.
In general, nuclides with a relatively high instant release fraction also tend to be readily soluble andrelatively mobile in both buffer and rock. Several percent of the inventory of I-129, for example,
is instantly released; iodine has a very high solubility and is not sorbed in either buffer or rock.
Plutonium isotopes, on the other hand, lie completely embedded in the fuel matrix, have low solu­
bility and are sorbed strongly in both buffer and rock. Isotopes of uranium, thorium and americium
have similar properties to plutonium.

6.3.1

Base case, including the effect of spalling

Deterministic calculations
Hydrogeological case:
Failure time:
Number of failed canisters:
Solubility limits:
Spalling:
Number of realisations:
Number of nuclides:

Semi-correlated, base case
0 and 10,000 years
1
Yes
Yes
1
37

A deterministic calculation of the hypothetical pinhole failure mode including the effect of spalling
was performed for a canister with an initial penetrating pinhole that grows to a large hole after
10,000 years. Transport out of the canister is assumed to be established 1,000 years after deposition.
Median values of geosphere transport data from the base case of the semi-correlated DFN model areused. The number of failed canisters is 1.
Figure 6‑11 shows the deterministic near-field dose equivalent releases for the pinhole case including
the effect of spalling. Figure 6‑12 shows the same near-field dose equivalent releases decomposed
into Q1, Q2 and Q3. Doses from the near field are dominated by C-14 and I-129 and Q1 is thedominating release path. Figure 6‑13 shows the far-field dose equivalent releases for the pinhole caseincluding the effect of spalling and Figure 6‑14 shows the same releases decomposed into Q1, Q2
and Q3. Also the dose from the far field is dominated by I-129 and Q1 is again the dominating release
path.

138

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102

Annual effective dose [µSv]

101

C14

(5.6)

I129

(4.7)

Se79

(0.093)Ni59(0.037)

Ra226(0.017)Nb94(0.0071)

Cl36(0.0024)

Total

(9.5)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑11. Near-field dose equivalent release for a deterministic calculation of the pinhole case, including the effect of spalling. Summed doses for all release paths (Q1+Q2+Q3). The legend is sorted by peak(in the one-million year period) of the annual effective dose. The values in brackets are peak dose in unitsof µSv.
102

Annual effective dose [µSv]

101

Q1

(9.4)

Q2

(0.40)

Q3(0.23)

Total

(9.5)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑12. Near-field dose equivalent release for a deterministic calculation of the pinhole case, including
the effect of spalling. Doses decomposed into Q1, Q2 and Q3. The legend is sorted by peak (in the onemillion year period) of the annual effective dose. The values in brackets are peak dose in units of µSv.

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102

I129 (1.4)
C14 (0.26)
Se79 (0.020)
Total (1.6)

Annual effective dose [µSv]101

Dose corresponding to risk limit

100

10-1

10-2

10-3

103

104

105

106

Time [years]

Figure 6‑13. Far-field annual effective dose for a deterministic calculation of the pinhole case, including
the effect of spalling. Summed doses for all release paths (Q1+Q2+Q3). The legend is sorted by peak(in the one-million year period) of the annual effective dose. The values in brackets are peak dose in unitsof µSv.
102

Annual effective dose [µSv]101

Q1 (1.4)
Q2 (0.19)
Q3 (0.16)
Total (1.6)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑14. Far-field annual effective dose for a deterministic calculation of the pinhole case, including
the effect of spalling. Doses decomposed into Q1, Q2 and Q3. The legend is sorted by peak (in the onemillion year period) of the annual effective dose. The values in brackets are peak dose in units of µSv.

140

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Probabilistic calculations
Hydrogeological case:
Failure time:
Number of failed canisters:
Solubility limits:
Spalling:
Number of realisations:
Number of nuclides:

Semi-correlated, base case
0 and 10,000 years
1
Yes
Yes
6,916
37

A probabilistic calculation of the hypothetical pinhole failure mode including the effect of spalling
was performed for one canister with an initial penetrating pinhole that grows to a large hole after
10,000 years. Transport out of the canister is assumed to be established 1,000 years after deposition.
Geosphere transport parameters from the base realisation of the semi correlated DFN model areused. The number of failed canisters is 1. The calculation was run for each of the 6,916 positions
and a mean result was calculated over all positions.
Figure 6‑15 shows the near-field dose equivalent releases for the pinhole case including the effectof spalling and Figure 6‑16 shows the same releases decomposed into Q1, Q2 and Q3. Figure 6‑17shows the corresponding far-field dose equivalent releases and Figure 6‑18 shows the same releases
decomposed into Q1, Q2 and Q3. Doses from both the near field and the far field are dominated by
C-14 and I-129. Q1 is the dominating release path till shortly after the large hole in the canister has
developed. In the longer term Q3 becomes the dominating release path.

Mean annual effective dose [µSv]

102

101

C14

(2.3)

I129

(1.5)

Se79

(0.10)

Ra226(0.040)Ni59(0.011)

Nb94(0.0067)

Total

(3.7)

Dose corresponing to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑15. Near-field dose equivalent release for the probabilistic calculation of the pinhole case, including the effect of spalling. Summed doses for all release paths (Q1+Q2+Q3). The legend is sorted by peak(in the one-million year period) of the mean annual effective dose. The values in brackets are peak dose inunits of µSv.

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Mean annual effective dose [µSv]

102

101

Q1

(3.5)

Q2

(0.52)

Q3(0.37)

Total

(3.7)

Dose corresponding to risklimit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑16. Near-field dose equivalent release for the probabilistic calculation of the pinhole case, including
the effect of spalling. Doses decomposed into Q1, Q2 and Q3. The legend is sorted by peak (in the onemillion year period) of the mean annual effective dose. The values in brackets are peak dose in units of µSv.

Mean annual effective dose [µSv]

102

101

I129

(0.42)

C14(0.27)

Se79(0.026)

Ra226(0.0024)

Total(0.65)

Dose corresponing to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑17. Far-field mean annual mean effective dose for the probabilistic calculation of the pinhole
case, including the effect of spalling. Summed doses for all release paths (Q1+Q2+Q3). The legend issorted by peak (in the one-million year period) of the mean annual effective dose. The values in brackets
are peak dose in units of µSv.

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102

Mean annual effective dose [µSv]

101

Q1

(0.41)

Q2(0.20)

Q3(0.19)

Total(0.65)

Dose corresponing to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑18. Far-field mean annual effective dose for the probabilistic calculation of the pinhole case,including the effect of spalling. Doses decomposed into Q1, Q2 and Q3. The legend is sorted by peak(in the one-million year period) of the mean annual effective dose. The values in brackets are peak dosein units of µSv.

6.3.2

Disregarding the effect of spalling

Deterministic calculations
Hydrogeological case:
Failure time:
Number of failed canisters:
Solubility limits:
Spalling:
Number of realisations:
Number of nuclides:

Semi-correlated, base case
0 and 10,000 years
1
Yes
No
1
37

A deterministic calculation of the hypothetical pinhole failure mode disregarding the effect ofspalling was performed for a canister with an initial penetrating pinhole that grows to a large holeafter 10,000 years. Transport out of the canister is assumed to be established 1,000 years after
deposition. Median values of geosphere transport data from the base case of the semi correlated
DFN model are used. The number of failed canisters is 1.
Figure 6‑19 shows the deterministic near-field dose equivalent releases for the pinhole case disregarding the effect of spalling and Figure 6‑20 shows the same near-field dose equivalent releases
decomposed into Q1, Q2 and Q3. Disregarding spalling in the near-field results in doses about
13 times lower and release through Q3 are more dominating, compared to the pinhole case including
spalling. Figure 6‑21 shows the far-field dose equivalent releases for the pinhole case disregarding
the effect of spalling and Figure 6‑22 shows the same releases decomposed into Q1, Q2 and Q3.
Doses from the far field are about 4 times lower and releases through Q3 are dominating.

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102

Annual effective dose [µSv]

101

I129

(0.47)

C14(0.42)

Se79(0.036)

Ra226(0.0015)Total(0.72)

Dose corresponing to risk limit

100

10-1

10-2

10-3

103

104

105

106

Time [years]

Figure 6‑19. Near-field dose equivalent release for a deterministic calculation of the pinhole case, dis­regarding the effect of spalling. Summed doses for all release paths (Q1+Q2+Q3). The legend is sorted bypeak (in the one-million year period) of the annual effective dose. The values in brackets are peak dose inunits of µSv.

102

Annual effective dose [µSv]

10

1

Q1

(0.16)

Q2(0.46)

Q3(0.33)

Total(0.72)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑20. Near-field dose equivalent release for a deterministic calculation of the pinhole case, dis­­regarding the effect of spalling. Doses decomposed into Q1, Q2 and Q3. The legend is sorted by peak(in the one-million year period) of the annual effective dose. The values in brackets are peak dose in unitsof µSv.

144

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102
I129

(0.40)

C14(0.12)

Se79 (0.013)
Total

Annual effective dose [µSv]101

Dose corresponding to risk limit(0.41)

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑21. Far-field annual effective dose for a deterministic calculation of the pinhole case, disregarding the effect of spalling. Summed doses for all release paths (Q1+Q2+Q3). The legend is sorted by peak(in the one-million year period) of the annual effective dose. The values in brackets are peak dose in unitsof µSv.
102

Annual effective dose [µSv]

10

1

Q1

(0.029)Q2(0.23)

Q3(0.27)

Total(0.41)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑22. Far-field annual effective dose for a deterministic calculation of the pinhole case, disregarding the effect of spalling. Doses decomposed into Q1, Q2 and Q3. The legend is sorted by peak (in the
one-million year period) of the annual effective dose. The values in brackets are peak dose in units of µSv.

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Probabilistic calculations
Hydrogeological case:
Failure time:
Number of failed canisters:
Solubility limits:
Spalling:
Number of realisations:
Number of nuclides:

Semi-correlated, base case
0 and 10,000 years
1
Yes
No
6,916
37

A probabilistic calculation of the hypothetical pinhole failure mode disregarding the effect ofspalling was performed for one canister with an initial penetrating pinhole that grows to a largehole after 10,000 years. Transport out of the canister is assumed to be established 1,000 years after
deposition. Geosphere transport parameters from the base case of the semi correlated DFN model
are used. The number of failed canisters is 1. The calculation was run for each of the 6,916 positions
and a mean result was calculated over all positions.
Figure 6‑23 shows the near-field dose equivalent releases for the pinhole case disregarding the effectof spalling and Figure 6‑24 shows the same releases decomposed into Q1, Q2 and Q3. Disregarding
spalling in the near-field results in doses about 4 times lower and release through Q2 and Q3 arecompletely dominating, compared to the pinhole case including spalling. Figure 6‑25 shows the farfield dose equivalent releases for the pinhole case disregarding the effect of spalling and Figure 6‑26
shows the same releases decomposed into Q1, Q2 and Q3. Doses from the far field are similar tothe doses when the effect of spalling is included, but releases through Q2 and Q3 are completely
dominating over Q1.

Mean annual effective dose [µSv]

102

101

C14

(0.50)

I129(0.50)

Se79(0.079)Ra226(0.0063)

Total(0.85)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑23. Near-field dose equivalent release for the probabilistic calculation of the pinhole case, dis­regarding the effect of spalling. Summed doses for all release paths (Q1+Q2+Q3). The legend is sorted bypeak (in the one-million year period) of the mean annual effective dose. The values in brackets are peakdose in units of µSv.

146

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102

Mean annual effective dose [µSv]

101

Q1

(0.090)Q2(0.52)

Q3(0.39)

Total(0.85)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑24. Near-field dose equivalent release for the probabilistic calculation of the pinhole case, disregarding the effect of spalling. Doses decomposed into Q1, Q2 and Q3. The legend is sorted by peak (in the
one-million year period) of the mean annual effective dose. The values in brackets are peak dose in unitsof µSv.
102
I129(0.30)

C14(0.16)

Se79 (0.023)
Total

Mean annual effective dose [µSv]101

Dose corresponding to risk limit(0.41)

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑25. Far-field mean annual mean effective dose for the probabilistic calculation of the pinhole
case, disregarding the effect of spalling. Summed doses for all release paths (Q1+Q2+Q3). The legend issorted by peak (in the one-million year period) of the mean annual effective dose. The values in brackets
are peak dose in units of µSv.
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102

Mean annual effective dose [µSv]

101

Q1

(0.016)Q2(0.21)

Q3(0.20)

Total(0.41)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑26. Far-field mean annual effective dose for the probabilistic calculation of the pinhole case,disregarding the effect of spalling. Doses decomposed into Q1, Q2 and Q3. The legend is sorted by peak(in the one-million year period) of the mean annual effective dose. The values in brackets are peak dose inunits of µSv.

6.3.3

Lost swelling pressure in tunnel backfill, “Crown-space”

Deterministic calculations
Hydrogeological case:
Failure time:
Number of failed canisters:
Solubility limits:
Spalling:
Number of realisations:
Number of nuclides:

Semi-correlated, variant with crown space
0 and 10,000 years
1
Yes
Yes
1
37

A deterministic calculation of the hypothetical pinhole failure mode with lost swelling pressure in
the tunnel backfill (crown-space) was performed for a canister with an initial penetrating pinhole thatgrows to a large hole after 10,000 years. Transport out of the canister is assumed to be established
1,000 years after deposition. Median values of geosphere transport data from the variant with crownspace of the semi correlated DFN model are used. The number of failed canisters is 1.
Figure 6‑27 shows the deterministic near-field dose equivalent releases for the pinhole case with lost
swelling pressure in the tunnel backfill and Figure 6‑28 shows the same near-field dose equivalentreleases decomposed into Q1, Q2 and Q3. The early doses are 1–2 times higher and Q3 is more
dominating, as a release path, compared to the pinhole case with an intact tunnel backfill. The doses
are at about the same levels after one million years as the pinhole case with intact tunnel backfill(earlier called the pinhole case including the effect of spalling, see Section 6.2.1). Figure 6‑29 shows
the far-field dose equivalent releases for the pinhole case with lost swelling pressure in the tunnel
backfill and Figure 6‑30 shows the same releases decomposed into Q1, Q2 and Q3. Early releasesof C-14 are considerably higher and contribute more to the total peak dose than in the pinhole casewith an intact tunnel backfill.

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102

Annual effective dose [µSv]

10

1

100

C14

(11)

I129

(4.7)

Se79

(0.091)

Ni59(0.036)

Ra226(0.034)Nb94(0.0071)

Pb210(0.0066)

Cl36(0.0024)

Total

(16)

Dose corresponding to risk limit

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑27. Near-field dose equivalent release for a deterministic calculation of the pinhole case, withlost swelling pressure in tunnel backfill. Summed doses for all release paths (Q1+Q2+Q3). The legend issorted by peak (in the one-million year period) of the annual effective dose. The values in brackets are peakdose in units of µSv.
102

Annual effective dose [µSv]

10

1

Q1

(9.3)

Q2

(0.74)

Q3(9.5)
Dosecorresponding to risk limit

Total (16)

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑28. Near-field dose equivalent release for a deterministic calculation of the pinhole case, withlost swelling pressure in tunnel backfill. Doses decomposed into Q1, Q2 and Q3. The legend is sorted bypeak (in the one-million year period) of the annual effective dose. The values in brackets are peak dose inunits of µSv.
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102
C14

(7.9)

I129

(2.4)

Se79 (0.044)

Annual effective dose [µSv]

101

Cl36

(0.0012)

Total

(10)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑29. Far-field annual effective dose for a deterministic calculation of the pinhole case, with lost
swelling pressure in tunnel backfill. Summed doses for all release paths (Q1+Q2+Q3). The legend is sorted
by peak (in the one-million year period) of the annual effective dose. The values in brackets are peak dosein units of µSv.

102

Annual effective dose [µSv]

101

Q1

(2.4)

Q2

(0.56)

Q3(7.2)
Dose corresponing to risk limit

Total (10)

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑30. Far-field annual effective dose for a deterministic calculation of the pinhole case, with lost
swelling pressure in tunnel backfill. Doses decomposed into Q1, Q2 and Q3. The legend is sorted by peak(in the one-million year period) of the annual effective dose. The values in brackets are peak dose in unitsof µSv.

150

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Probabilistic calculations
Hydrogeological case:
Failure time:
Number of failed canisters:
Solubility limits:
Spalling:
Number of realisations:
Number of nuclides:

Semi-correlated, variant with crown space
0 and 10,000 years
1
Yes
Yes
6,916
37

A probabilistic calculation of the hypothetical pinhole failure mode with lost swelling pressure in
the tunnel backfill was performed for one canister with an initial penetrating pinhole that grows to alarge hole after 10,000 years. Transport out of the canister is assumed to be established 1,000 years
after deposition. Geosphere transport parameters from the variant with crown space of the semicorrelated DFN model are used. The number of failed canisters is 1. The calculation was run for
6,916 positions and a mean result was calculated over all positions.
Figure 6‑31 shows the near-field dose equivalent releases for the pinhole case with lost swellingpressure in the tunnel backfill and Figure 6‑32 shows the same near-field dose equivalent releases
decomposed into Q1, Q2 and Q3. Peak releases of C-14 are about 3 times higher compared to thepinhole case with an intact tunnel backfill, and Q3 is the dominating release path. In the longer
term I-129 and Ra-226 contributes considerably to the total dose. Figure 6‑33 shows the far-fielddose equivalent releases for the pinhole case with lost swelling pressure in the tunnel backfill andFigure 6‑34 shows the same releases decomposed into Q1, Q2 and Q3. Peak releases of C-14 areabout 8 times higher compared to the pinhole case with an intact tunnel backfill, and Q3 is thedominating release path. In the longer term, the total dose from the far field is at the same level
as in the pinhole case with an intact tunnel backfill.

Mean annual effective dose [µSv]

102

10

1

C14

(7.7)

I129

(1.8)

Ra226

(0.19)

Se79(0.16)

Pb210(0.051)

Ni59(0.011)

Nb94(0.0070)

Total

(9.5)

Dosecorresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑31. Near-field dose equivalent release for the probabilistic calculation of the pinhole case, withlost swelling pressure in tunnel backfill. Summed doses for all release paths (Q1+Q2+Q3). The legend issorted by peak (in the one-million year period) of the mean annual effective dose. The values in brackets
are peak dose in units of µSv.

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102

Mean annual effective dose [µSv]

101

Q1

(3.6)

Q2

(0.95)

Q3(6.9)
Dose corresponding to risk limit

Total (9.5)

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑32. Near-field dose equivalent release for the probabilistic calculation of the pinhole case, withlost swelling pressure in tunnel backfill. Doses decomposed into Q1, Q2 and Q3. The legend is sorted bypeak (in the one-million year period) of the mean annual effective dose. The values in brackets are peakdose in units of µSv.
102

Mean annual effective dose [µSv]

10

1

C14

(2.2)

I129

(0.75)

Se79(0.027)

Ra226(0.012)

Pb210(0.0015)

Total

(2.7)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑33. Far-field mean annual mean effective dose for the probabilistic calculation of the pinhole
case, with lost swelling pressure in tunnel backfill. Summed doses for all release paths (Q1+Q2+Q3). The
legend is sorted by peak (in the one-million year period) of the mean annual effective dose. The values inbrackets are peak dose in units of µSv.

152

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102

Mean annual effective dose [µSv]

101

Q1

(0.39)

Q2(0.36)

Q3(2.0)
Dose corresponding to risk limit

Total (2.7)

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑34. Far-field mean annual effective dose for the probabilistic calculation of the pinhole case,with lost swelling pressure in tunnel backfill. Doses decomposed into Q1, Q2 and Q3. The legend is sorted
by peak (in the one-million year period) of the mean annual effective dose. The values in brackets are peakdose in units of µSv.

6.3.4

Different assumptions regarding EDZ

Hydrogeological case:
Failure time:
Number of failed canisters:
Solubility limits:
Spalling:
Number of realisations:
Number of nuclides:

Semi-correlated, different variants of EDZ transmissivity
0 and 10,000 years
1
Yes
Yes
6,916
37

The excavation damage zone, EDZ, implies a possible release path located in the floor of the depo­
sition tunnel, see Figure 3‑1. In the base case (earlier called the pinhole case including the effectof spalling, see Section 6.3.1) is the EDZ transmissivity value 10–8 m2/s. The total near-field dose
equivalent releases for the pinhole cases with no EDZ, and EDZ transmissivities of 10–6 m2/s (EDZ
6), 10–7 m2/s (EDZ 7) and 10–8 m2/s (based case) are compared in Figure 6‑35 and Figure 6‑36 shows
the same dose equivalent releases decomposed into Q1, Q2 and Q3. Figure 6‑37 and Figure 6‑38
show the corresponding far-field dose equivalent releases. Eliminating the EDZ decreases the total
doses both from near field and far field. The Q2 and Q3 release paths follows the same pattern andthe changes are modest. An increase of the EDZ transmissivity above the base case value of 10–8 m2/s
does not increase the doses from Q1.

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102
EDZ 6

(5.8)

EDZ 7

(4.2)

Mean annual effective dose [µSv]

Base case (3.7)
101

No EDZ

Dose corresponding to risk limit

(2.5)

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑35. Near-field dose equivalent release for the probabilistic calculation of the pinhole case,comparison between different assumptions regarding EDZ transmissivity (EDZ 6, EDZ 7 and base casecorrespond to 10–6 m2/s, 10–7 m2/s and 10–8 m2/s, respectively). The legend is sorted by peak (in the onemillion year period) of the mean annual effective dose. The values in brackets are peak dose in units of µSv.
102

Mean annual effective dose [µSv]

101

EDZ 6

(5.8)

EDZ 7

(4.2)

Base case(3.7)

No EDZ(2.5)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑36. Near-field dose equivalent release for the probabilistic calculation of the pinhole case,comparison between different assumptions regarding EDZ transmissivity (EDZ 6, EDZ 7 and base casecorrespond to 10–6 m2/s, 10–7 m2/s and 10–8 m2/s, respectively). Doses decomposed into Q1 (dotted lines),
Q2 (dashed lines) and Q3 (solid lines). The legend is sorted by peak (in the one-million year period) of themean annual effective dose. The values in brackets are peak dose in units of µSv.

154

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102
EDZ 6

(2.0)

EDZ 7

(1.1)

Mean annual effective dose [µSv]

Base case (0.65)
101

No EDZ

Dose corresponding to risk limit(0.16)

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑37. Far-field mean annual effective dose for the probabilistic calculation of the pinhole case,comparison between different assumptions regarding EDZ transmissivity (EDZ 6, EDZ 7 and base casecorrespond to 10–6 m2/s, 10–7 m2/s and 10–8 m2/s, respectively). The legend is sorted by peak (in the onemillion year period) of the mean annual effective dose. The values in brackets are peak dose in units of µSv.

Mean annual effective dose [µSv]

102

101

EDZ 6

(2.0)

EDZ 7

(1.1)

Base case(0.65)No EDZ(0.16)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑38. Far-field mean annual effective dose for the probabilistic calculation of the pinhole case,comparison between different assumptions regarding EDZ transmissivity (EDZ 6, EDZ 7 and base casecorrespond to 10–6 m2/s, 10–7 m2/s and 10–8 m2/s, respectively). Doses decomposed into Q1 (dotted lines),
Q2 (dashed lines) and Q3 (solid lines). The legend is sorted by peak (in the one-million year period) of
the mean annual effective dose. The values in brackets are peak dose in units of µSv.
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6.3.5 Summary and conclusions for the growing pinhole scenario
Several variants of the growing pinhole scenario have been calculated to examine sensitivities tovarious transport conditions. The results are summarised in Figure 6‑39 and Figure 6‑40. The crownspace case, in which tunnel backfill has compacted with a resulting gap at the tunnel crown, dominates the releases. Comparing variants with different excavation damage zone (EDZ) transmissivity,
shows that the releases decrease with decreasing EDZ transmissivity. Thermally induced spallingis assumed to occur in the walls of the deposition holes and decrease the transport resistance in theinterface between the buffer and the rock. The effect of of spalling is assessed by a case that does
not include spalling. The maximum dose is about 4 times lower in the case that does not include
spalling.

Mean annual effective dose [µSv]102

Dose corresponding to risk limit

101

100

10-1

Crown space (9.5)
10

EDZ 6

-2

10-3
103

10

10

4

5

(5.8)

EDZ 7

(4.2)

Base case(3.7)

No EDZ(2.5)

No spalling(0.85)
106

Time [years]

Figure 6‑39. Near-field mean annual effective dose equivalent for the probabilistic calculations of thepinhole base case and cases with no spalling, with different assumptions regarding EDZ and with a crownspace in the deposition tunnel. The legend is sorted by peak (in the one-million year period) of the meanannual effective dose. The values in brackets are peak dose in units of µSv. (EDZ 6, EDZ 7 and base casecorrespond to a transmissivity of 10–6 m2/s, 10–7 m2/s and 10–8 m2/s, respectively).

156

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102
Crown space (2.7)

Mean annual effective dose [µSv]

101

EDZ 6

(2.0)

EDZ 7

(1.1)

Base case(0.65)

No spalling(0.41)No EDZ(0.16)

Dose corresponding to risk limit

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑40. Far-field mean annual effective dose for the probabilistic calculations of the pinhole basecase and cases with no spalling, with different assumptions regarding EDZ and with a crown space in thedeposition tunnel. The legend is sorted by peak (in the one-million year period) of the mean annual effective dose. The values in brackets are peak dose in units of µSv. (EDZ 6, EDZ 7 and base case correspondto a transmissivity of 10–6 m2/s, 10–7 m2/s and 10–8 m2/s, respectively).

6.4

Exploration of geosphere barrier performance using thegrowing pinhole case

The growing pinhole failure case provides a convenient hypothetical scenario to illustrate various
sensitivities related to the geosphere barrier. To that end, deterministic values are used for initialradionuclide inventories and for all near-field and far-field parameters not related to flow. However,
because the location of the defective canister is not known in this scenario, effective dose results arecalculated as mean values over all potential locations of the defective canister. That is, full spatial
variability in flow-related parameters is included.
COMP23 and MARFA are used here for the near-field and far-field transport. Recall that MARFA
supports spatial variability both along and among transport pathways, thus making it possible toaddress aspects of geosphere barrier performance that cannot be addressed with FARF31.
Specific sensitivities studied include:
•
•
•
•
•

The role of advective transport in tunnels and soils.
The role of sorption in tunnels and soils.
The effect of a crown space formed by compaction of backfill in repository tunnels.
Sensitivity to assumed fracture transmissivity in excavation damage zones.
Implications of assuming one or multiple transport pathways per deposition hole.

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6.4.1 Input parameters
The sensitivity study described in this section assumes steady groundwater flow corresponding to thetemperate period. ConnectFlow ptb- and ptv-files for the reference case flow model and key variants
provide the relevant information for use in COMP23 and MARFA, as shown in Table 6‑1. The semicorrelated DFN model is used.
Table 6-1. SR-Site temperate period flow fields used in this study. Unless otherwise noted, theptv-/ptb-files include all deposition holes with one pathway per hole.
ptv/ptb file

Description

fs_Qm_2000_pline_merged (with m = 1,2,3)Base cases

fs_crown_Q1_2000_pline_merged

Crown space variant, Q1 release

fs_crown_start_Q3_2000_pline_merged

Crown space variant, Q3 release*fs_maxedz_7_Qm_2000_pline_merged (m = 1,2,3)

EDZ transmissivity of 10–7 m2/s

fs_maxedz_6_Qm_2000_pline_merged (m = 1,2,3)

EDZ transmissivity of 10–6 m2/s

fs_noedz_Qm_2000_pline_merged (m = 1,3)

No EDZ

fs_newtop25_Q1_2000_pline10_merged

Q1 base case for top† 25% of deposition holes with
10 pathways per hole

* Q3 pathways for the crown space variant were defined by releasing particles into the crown space, to be consistent
with COMP23 definition of near-field release for that variant. For all other variants, Q3 pathways were defined by releasing particles in the tunnel 1 m above the deposition hole.
† Based on initial velocity.

The ptv-files provide by ConnectFlow were modified for two combinations of flow variants andtransport assumptions. The ConnectFlow ptv-files include pathline segments that pass throughtunnels and soils represented as Continuum Porous Medium (CPM) in addition to fractured rocksegments. The CPM segments contribute nothing to the flow-related transport resistance, F-factor,
but do contribute to the advective travel time tw. Thus, for variant modelling cases designed toquantify the contribution of tunnels and soils by neglecting travel distances in those regions, CPM
segments were removed to prepare new ptv-files. In addition, for Q3 cases that include the CPM
segments, the tunnel segments between the release point and the first fracture encountered were
removed to enforce consistency between the ptv-file and the near-field release calculation, which
defines Q3 release as flux into the fracture intersecting the tunnel nearest to the deposition hole.
The sensitivity studies described in this section were undertaken before SR-Site transport parameters
were finalised. Consequently, SR-Can or preliminary SR-Site values are used for radionuclide
inventories, near-field transport parameters, and far-field retention parameters. Details are provided inAppendix H.

6.4.2 Reference case
The reference case for this section assumes no sorption in the tunnels and no sorption in the soils.
The CPM parts of the pathway, however, are included in the travel time. It is important to note thatthe inclusion of the CPM parts of the pathway in the advective travel time is in contrast to calculations presented elsewhere in this report. The flow‑channelling factor is set to unity to represent nochannelling within individual fractures. Colloids are not included.
The pinhole release scenario considers failure of one canister at an unknown deposition hole. To
calculate the expected value of release, all canisters are forced to fail and an aggregate release iscalculated. The expectation value for release is then calculated by dividing the aggregate releaseby the number of emplaced canisters. Note that deposition holes that do not have a connected
pathway to the geosphere have zero release by definition. In addition, deposition holes for which a
ConnectFlow pathway could not be defined because of numerical failure in the ConnectFlow particle
tracking calculation (stuck particles, represented by OKFLAG > 0) are also assumed to result in no
release. This assumption is based on the observation that stuck particles in the ConnectFlow particle
tracking algorithm are caused by nearly stagnant pathways, and these pathways would not contribute

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significantly to the expected release. Deposition holes with the full perimeter criterion or effective
full perimeter criterion flags set (FPC = 1) or (EFPC > 5) were assumed to not have emplaced
canisters. That is, these contribute nothing to the aggregate release and were also not counted in
the number of canisters emplaced.
Comparison of release path

Far-field releases expressed as equivalent doses are shown in Figure 6‑41 for the three release
paths. The Q1 release path results in the largest peak release, followed by Q2 and Q3. Peak releaseis almost an order of magnitude larger for the Q1 path compared with the Q3 path. The Q2 and Q3
paths result in flatter release histories compared with the Q1 path. At late times, differences between
the release paths are much smaller, with the Q2 paths resulting in the largest releases.

Mean annual effective dose [µSv]

101

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑41. All-nuclides far-field releases expressed as effective dose for the pinhole scenario and different release paths. Expected values are shown for all deposition holes versus time for Q1 (blue), Q2 (green),and Q3 (black) release paths.

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Details for the Q1 release path

Total far-field and near-field releases expressed as effective doses for the Q1 release path are shown in
Figure 6‑42. The far-field geosphere reduces peak dose by a factor of approximately 20. The dose at
1 million years is reduced by a factor of approximately 4 by the geosphere. Observable in Figure 6‑42
is an increasing trend in the near-field release, which does not occur in the far field. This behaviour is
attributable to ingrowth of Ra-226 at near-field release, which is then retarded in the far field.

Mean annual effective dose [µSv]

101

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑42. All-nuclides near-field and far-field releases expressed as effective dose for the pinhole
scenario, Q1 release path. Expected values are shown for all deposition holes versus time: near-field dose
equivalent release (blue) and far-field mean annual effective dose (green).

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Trajectories for the 2% of pathways contributing the most by total instantaneous far-field release areshown in Figure 6‑43. Each trajectory is colour-coded by maximum all‑nuclides instan­taneous doseas shown in the figure legend. Canister locations are shown as red or green dots. Red signifies thatthe deposition hole is not connected to the biosphere by a Q1 pathway. Green dots represent holesthat contribute to transport through the Q1 pathway. It is noted that the majority of canisters have noconnected Q1 pathway. Among those with connected pathways, the majority of radionuclide dosecomes from a relatively small fraction of pathways.

Plot Color Legend
0 (Sv/yr)

2.99·10–6 (Sv/yr)

5.98·10–6 (Sv/yr)

8.97·10–6 (Sv/yr)

1.2·10–5 (Sv/yr)

1.5·10–5 (Sv/yr)

Radionuclide Source
Term Legend
Source does not havea pathway to biosphere
Source has a pathway
to biosphere

Figure 6‑43. Pathway trajectories for pinhole scenario, Q1 release path for the 2% of pathways contributing
the most to the ensemble release. The top image shows the entire repository. The bottom image is a detail fromthe larger image (rotated). Trajectories and starting locations are colour-coded as shown in the legend.

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161

Near-field and far-field releases for the 12 radionuclides contributing most to far-field release areshown in Figure 6‑44. It is clear that I-129, C-14, and Ra-226 account for almost all the far-fieldand near-field releases. Far-field attenuation factors range from about two orders of magnitude for
Th-230 and Pa-231 to less than an order of magnitude for Se‑79.

100
10

100

I129

-1

10

100

C14

-1

10-2

10-2

10-2

10

-3

10

-3

10-3

10

-4

10

-4

10-4

10

-5

10

-5

103

104

10-2
10

105

106

104

10-3

Ni59

-3

103

10

105

106

10-5
103

10-5

10-4

10

-5

10

-6

10-5

10

-6

10

-7

10-6

10

-7

10

-8

104

10-3

105

106

104

10-3

Cs135

10-4

103

105

106

10-5

10-5

10-6

10-6

10-6

10-7

10-7

10-7

10-8
103

10-8
103

10-4
10

105

106

10-4

Np237

-5

104

10

105

106

10-6

10-7

10

10

-7

10-8

10-8

10-8

10-9

10-9
103

10-9
103

104

105

106

104

105

106

10-10
103

105

106

105

106

Cl36

10-6

10-6
-7

104

10-5

Pu242

-5

10-8
103

106

Pa231

10-4

10-5

104

104

10-3

Th230

10-4

10-7
103

105

Nb94

10-3

10-4

103

104

10-2

Se79

-4

Ra226

10-1

104

105

106

Figure 6‑44. Near-field (blue) and far-field (green) releases for the 12 radionuclides contributing most to
the far-field release for the Q1 release path. Units are µSv/yr on the y-axis and year on the x-axis for eachplot. Note the scale on the y-axis is different for different radionuclides.

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Details for the Q2 release path

Total far-field and near-field releases expressed as effective dose in Sv/yr for the Q2 release path are
shown in Figure 6‑45. The far-field geosphere reduces peak dose by a factor of approximately 5. The
dose at 1 million years is reduced by a smaller factor. Near-field and far-field releases for the top six
contributors (by far-field release) are shown in Figure 6‑46. As is the case for the Q1 path, I-129,
C-14, and Ra-226 are the largest contributors. The geosphere attenuates the release by factors ofapproximately 5 for I‑129, 4.7 for C-14, and 40 for Ra-226.

Mean annual effective dose [µSv]

101

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑45. All-nuclides near-field and far-field releases expressed as effective dose for the pinhole
scenario, Q2 release path. Expected values are shown for all deposition holes versus time: near-field dose
equivalent release (blue) and far-field mean annual effective dose (green).

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100

10-1

I129

10-1

10-2

10-2

10-3

10-3

10-4

10-4

10-5

10-5
103

10-1

104

105

106

10-6

10-2

10-5

10-3

10-6

10-4

10-7

10-5

10-8

10-3

103

10-4

Ra226

10-6
103

C14

104

105

106

10-9

103

10-4

10-8

10-5

10-9

10-6

10-10

10-7

10-11

10-8
103

104

105

106

105

106

104

105

106

104

105

106

Ni59

10-7

Se79

104

10-12
103

Nb94

Figure 6‑46. Near-field (blue) and far-field (green) releases for the top six contributors (by far-fieldrelease) for the Q2 release path. Units are µSv/yr on the y-axis and year on the x-axis for each plot. Notethe scale on the y-axis is different for different radionuclides.

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Details for the Q3 release path

Total far-field and near-field releases expressed as effective dose for the Q3 release path are shownin Figure 6‑47. The far-field geosphere does not represent a significant barrier for this release path.
However, the near-field Q3 release is smaller than that of the Q1 and Q2 paths.
Trajectories for the 2% of pathways contributing the most by total instantaneous far-field release areshown in Figure 6‑48. Each trajectory is colour-coded by the maximum all-nuclides instantaneous
dose as shown in the figure legend. Canister locations are shown as red or green dots. Red signifies
that the deposition hole is not connected to the biosphere by a Q3 pathway or that the contribution
from that pathway is negligible. Green dots represent holes that contribute to transport through theQ3 pathway. It is noted that in contrast to the Q1 path, many pathways contribute to dose for the Q3
path, primarily because the repository tunnels provide pathways to the fracture network backbone(see detail in lower left of Figure 6‑48).

Mean annual effective dose [µSv]

101

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑47. All-nuclides near-field and far-field releases expressed as effective dose for the pinhole
scenario, Q3 release path. Expected values are shown for all deposition holes versus time near-field dose
equivalent release (blue) and far-field mean annual effective dose (green).

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Plot Color Legend
0 (Sv/yr)

1.28·10–7 (Sv/yr)

2.55·10–7 (Sv/yr)

3.83·10–7 (Sv/yr)

5.11·10–7 (Sv/yr)

6.39·10–7 (Sv/yr)

Radionuclide Source
Term Legend
Source does not havea pathway to biosphere
Source has a pathway
to biosphere

Figure 6‑48. Pathway trajectories for pinhole scenario, Q3 release path for top 2% of pathways by contribution to the all-nuclides release. The top image shows the entire repository. The bottom images are details
from the larger image. Trajectories and starting locations are colour-coded as shown in the legend. Notethe MARFA calculations used to calculate the dose rates shown in this figure used COMP23 outputs thatwere later found to be based on a ConnectFlow ptb-file that contained erroneous values for one parameter.
These results should be considered qualitative only.

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10-1

10-2

I129

10-2

10-3

10-3

10-4

10-4

10-5

10-5

10-6

10-6
103

104

105

106

10-3

C14

10-7
103

104

105

106

104

105

106

104

105

106

10-3
Ra226

Se79

10-4

10-4

10-5

10-5

10-6

10-6

10-7

10-7

10-8
103

104

105

106

10-4

10-8
103

10-6
Cs135

Cl36

10-5

10-7

10-6

10-8

10-7

10-9

10-8

10-10

10-9
103

104

105

106

10-11
103

Figure 6‑49. Near-field (blue) and far-field (green) releases for the top six contributors (by far-fieldrelease) for the Q3 release path. Units are µSv/yr on the y‑axis and year on the x-axis for each plot. Notethe scale on the y-axis is different for different radionuclides.

6.4.3

Issues related to the probabilistic nature of the calculations

Variability about the mean

The pinhole failure scenario presumes one failed canister at an unknown location. Results presented
thus far and elsewhere in this report have been for the expected value of discharge averaged overall starting locations. Some locations will contribute much to the expected value and some willcontribute little or nothing. For example, approximately 81% of deposition holes have no connected
pathway to the biosphere and thus contribute nothing to the mean value for the Q1 path. To understand the variability about the mean, selected percentiles in the discharge were calculated at eachtime. Results for the Q1 release path are shown in Figure 6‑50 (99th, 95th, 90th, and 85th percentiles
in green and mean curve in blue).
More than half of the trajectories have zero release because of no release path. Thus, the medianrelease is zero and is not shown. The peak of the 90th percentile is close to the peak of the mean,although the two peaks occur at different times. Thus, there is a less than 10% chance that thepinhole release scenario from one package will have a value greater than the peak of the mean.
As already noted, there is a greater than 80% chance that the release will be exactly zero.

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The shapes of the curves in Figure 6-50 are markedly different for the different percentiles. It isapparent that most of the deposition holes (90th and smaller percentiles) are either not connected topathway or are connected to a pathway that provides sufficient retardation to allow key radionuclides
to decay. Thus the peak of the mean is strongly influenced by the contributions from the few path­ways that exhibit little retardation.
Another way to analyse the range of possible doses delivered to the biosphere is to plot the exceedance probability versus dose (Figure 6‑51). This plot is based on a 1-million year interval. Thereis approximately a 2.7% probability that the maximum dose rate delivered to the biosphere will
exceed 10−6 Sv/yr at some time in the 1-million year interval. For 10−5 Sv/yr dose, the exceedance
probability is 4·10–4.

Mean annual effective dose [µSv]

101

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑50. Mean (blue curve) and selected percentiles (green curves) for pinhole Q1 release. Shown are
the 99th, 95th, 90th, and 85th percentiles.

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0.20

Exceedance probability [–]

0.15

0.10

0.05

0.00

10–4

10–3

10–2

10–1

100

101

Annual effective dose [µSv]

Figure 6‑51. Exceedance probability for a given dose rate (μSv/yr) for the pinhole Q1 release. A 1-million
year time window was used to calculate the exceedance probability. Thus, for a given dose rate, the exceedance probability is the probability that the dose rate exceeds that value at some time during the 1‑million
year period.

Multiple pathways for each deposition hole

The base case has one pathway per release point. The effect of this assumption was assessed byconsidering a variant case with 10 Q1 pathways per release point. This calculation was limited
to the 25 release points contributing most to the total dose in the base case. Results are shown in
Figure 6‑52. The blue curve is near-field release. The solid green curve is the base case far-fieldrelease. The dashed green curve is the far-field release for the case with 10 pathways per release
point. Although transport from any single release point may be different depending on whether
1 or 10 pathways are represented, these differences are averaged out in the ensemble.

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169

Mean annual effective dose [µSv]

101

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑52. Effect of having multiple Q1 pathways per release point. The blue curve is near-field release.
The solid green curve is the base case far-field release. The dashed green curve is the far-field release forthe case with 10 pathways per release point.

6.4.4

Exploration of barrier function of geosphere components

Transport and retention in soils and tunnels

The reference case includes soils and tunnel segments in the transport pathway, but assigns thesesegments zero equilibrium partitioning coefficients for all elements. Thus, the delay introduced
by a non-zero advective travel time through soils and tunnels is accounted for, but retardation ofsorbing elements is ignored. Effects of the soils and tunnels are summarised in Figure 6‑53 for theQ1 path. The blue curve is near-field release and the green curve is the base case. The pink curve
neglects the effect of the CPM parts of the pathways (i.e., tunnels and soils). In calculating the pink
curve, CPM segments were removed from the base case ptv-file and a new ptv-file was generated.
The black curve uses the base case ptv-file, but with sorption turned on in tunnels and soil layers.
There are two main conclusions to be drawn from Figure 6-53. First, the travel time in the CPM
part of the pathways decreases the peak dose by a factor of approximately 5 (compare pink to green
curves). This decrease is mostly due to the effect on the nonsorbing radionuclides I-129 and C-14.
Second, sorption in tunnels and soils has no significant effect on total dose. This lack of sensitivity
is a consequence of the dominant role that I-129 and C-14 play in determining the total dose. Indeed,examination of the far-field releases for individual nuclides (Figure 6‑54) reveals that releases ofsorbing radionuclides such as Ra-226 and Th-230 are significantly reduced by sorption in tunnels
and soils.
Effects of the soils and tunnels are summarised in Figure 6‑55 for the Q2 path. Without the delay
provided by soils and tunnels, the geosphere is not a major barrier to radionuclide transport for a Q2
release. Other sensitivities are similar to the Q1 path.

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Mean annual effective dose [µSv]

101

100

10-1

10-2

10-3
103

104

105

106

Time [years]

10-1
Ra226
10-2

10-3

10-4

10-5
103

104

105

Time [years]

106

Mean annual effective dose [µSv]

Mean annual effective dose [µSv]

Figure 6‑53. Expected values for all-nuclides releases for the Q1 pinhole release, expressed as equivalentdoses. The blue curve is near-field release and the other curves are far-field releases as follows: pink has
no CPM segments in the pathway, green curve is the base case (CPM included but with no sorption), black
has sorption in tunnels and soils.

10-4
Th230
10-5
10-6
10-7
10-8
10-9
103

104

105

106

Time [years]

Figure 6‑54. Expected Ra-226 and Th-230 releases for pinhole Q1 release path and different assumptions
about the role of tunnels and soils. The blue curve is near-field release and the other curves are far-fieldreleases as follows: pink has no CPM segments in the pathway, green curve is the base case (CPM included
but with no sorption), black has sorption in tunnels and soils.

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171

Mean annual effective dose [µSv]

101

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑55. Expected values for all-nuclides releases for the Q2 pinhole release, expressed as equivalentdoses. The blue curve is near-field release and the other curves are far-field releases as follows: pink has
no CPM segments in the pathway, green curve is the base case (CPM included but with no sorption), black
has sorption in tunnels and soils.

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Crown space in tunnels

A variant flow model is considered in which tunnel backfill has compacted thus allowing a gap toform at the tunnel crown. Note that the tunnel crown case has different near-field releases as well as
far-field releases, but the differences in near-field releases are small.
Results for the Q1 and Q3 release paths are shown in Figure 6‑56 and Figure 6‑57. In each figure,the green curve is the base case (i.e. no crown space). The black and pink curves have crown space.
For the black curve, matrix diffusion into the neighbouring backfill is allowed. For the pink curve,
this mitigating process is not active. Note that the differences between the crown space and no-crownspace are not due to differences in the near-field releases; the base case has slightly higher near-fieldreleases, but the differences are not large.

Mean annual effective dose [µSv]

100

10-1

10-2

10-3

10-4
103

104

105

106

Time [years]

Figure 6‑56. Expected far-field release as equivalent dose for pinhole Q1 release path and different
assumptions about the tunnel crown space. The green curve is the Q1 base case, which has no crown space
represented. The black and pink curves are for cases with crown space with and without retention in thecrown space.

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Mean annual effective dose [µSv]

101

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑57. Expected far-field release as equivalent dose for pinhole Q3 release path and different
assumptions about the tunnel crown space. The green curve is the Q3 base case, which has no crown space
represented. The black and pink curves are for cases with crown space with and without retention in thecrown space.

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EDZ transmissivity

The base case has an excavation damage zone (EDZ) transmissivity of 10−8 m2/s. The effects ofdifferent EDZ transmissivity for the Q1 release path are shown in Figure 6‑58. The blue curve is thebase case. The black curve is the case with no EDZ. The green and pink curves are results for EDZ
transmissivity of 10−6 m2/s and 10−7 m2/s. The no-EDZ case is lower than the others. The presence ofan EDZ increases the dose. Making the EDZ transmissivity larger than 10−8 m2/s, however, does notfurther increase the dose. Instead, the dose drops slightly when going from an EDZ transmissivity of
10−7 m2/s to 10−6 m2/s, most likely because of subtle changes in flow paths. It is noted that the basecase assumption for the uncertain EDZ transmissivity (10−8 m2/s) results in the largest dose.
Effects of EDZ transmissivity on the Q2 releases are shown in Figure 6‑59. Curves are coloured asin Figure 6‑58. Note that the no-EDZ variant is not meaningful for the Q2 release path. Increasing
the EDZ transmissivity above the base case value of 10−8 m2/s does increase the dose somewhat,
as expected. However, the effect is not large and quickly saturates; the doses for 10−7 m2/s and of
10−6 m2/s are not significantly different.

Mean annual effective dose [µSv]

101

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑58. Expected far-field release as equivalent dose for pinhole Q1 release path and different
assumptions about the EDZ. The blue curve is the Q1 base case, which has EDZ transmissivity of
10−8 m2/s. The black is the case for no EDZ. The green and pink curves are results for EDZ transmissivityof 10−6 m2/s and 10−7 m2/s, respectively.

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Mean annual effective dose [µSv]

101

100

10-1

10-2

10-3
103

104

105

106

Time [years]

Figure 6‑59. Expected far-field release as equivalent dose for pinhole Q2 release path and different
assumptions about the EDZ. The blue curve is the Q2 base case, which has EDZ transmissivity of 10−8 m2/s.
The green and pink curves are results for EDZ transmissivity of 10−6 m2/s and 10−7 m2/s.

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6.4.5 Colloid-facilitated transport assuming irreversible sorption
As discussed in Section 4.5.6, sorption onto mobile bentonite colloids has the potential to increase
the mobility of some radionuclides. Two limiting cases can be identified depending on the kinetics
of desorption: (i) radionuclide desorption from colloids is rapid relative to the advective travel time,and (ii) radionuclide desorption from colloids is slow compared to the advective travel time andmay thus be represented as irreversible. Sorption of radionuclides onto bentonite is understood to bereversible and rapid relative to the advective travel times of interest /Buffer, backfill and closure
process report/; thus, irreversible sorption is not considered plausible. Nevertheless, considerationof irreversible sorption to bentonite colloids can help understand how the engineered and naturalbarriers function.
Several processes help mitigate the potential effects of irreversible sorption to colloids. Thesemitigating processes include permanent filtration of the colloids, colloid retardation, the fact that permanent sorption onto bentonite would dramatically reduce near-field release, and limited availabilityof sorption sites on bentonite colloids. The last process is considered and other mitigating processes
neglected. The competitive Langmuir-type sorption model described in Appendix I.2 is used. In thismodel, radionuclides releases from the COMP23 code are partitioned between colloids and solution,
taking into account competition for the limited number of available sites on colloids. Once partitioned, MARFA is used to transport colloid-associated radionuclides without retention processes.
Radionuclides in solution are transported as in the reference case described in Section 6.4.2.
Dose-equivalent near-field releases based on the colloid-partitioning model are shown in Figure 6‑60
for the pinhole reference case, Q1 release path. In this calculation, actinide species and transition
metals were assumed to sorb irreversibly onto colloids that are present at a concentration of 10 mg/l.
The blue curve is dose equivalent near-field release for all radionuclides. The solid green curve isrelease for all actinides and transition metals including both the dissolved and colloid-associatedmass. The green dashed curve is the colloid-associated component. The actinide and transition
metal portions of the total release are an order of magnitude smaller than the total release in the time
period 20,000 to 50,000 years, and is even smaller before and after that time period. Moreover, when
the actinide/transition metal release is largest, the availability of sites limits the colloid-associatedrelease to even smaller fractions of the total release, mostly because Ni-59 and Nb-94 releases arelarge enough to saturate sorption sites. At late times, site limitations are less important, but the total
actinide/transition metal release is small and not a significant contribution to the total.
Far-field effective doses for the same cases with and without colloids are shown in Figure 6‑61.
At its largest, the colloid‑associated far-field release is approximately 1% of the total release.
Results in Figure 6‑60 and Figure 6‑61 are based on a colloid concentration of 10 mg/l. Although
this number is representative of clay colloid concentrations in waters that are not highly dilute, it isan uncertain parameter. As discussed in Section 4.5.8, colloid concentrations may be higher during
brief periods if dilute water reaches the repository horizon. An upper bound on colloid-facilitatedtransport for this situation can be established by allowing all actinides and transition metals tobe transported unretarded through the geosphere. This modelling case assumes that colloids aretransported unretarded through the geosphere, an unlimited supply of sorption sites on colloids,
and no desorption from colloids. Even with this extreme bounding approximation, colloids have nosignificant effect on the all-nuclides dose (Figure 6‑62). This lack of sensitivity is a consequenceof the dominant role that the three nuclides I-129, C-14, and Ra-226 play in controlling the overall
dose. I-129 and C-14 are already transported without sorbing in the MARFA far-field calculation,and their transport thus cannot be enhanced by colloids. Ra-226 sorbs by ion exchange, and is notexpected to irreversibly sorb.

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101

Mean dose–equivalent release [µSv]

100

10-1

10-2

10-3

10-4

10-5
103

104

105

106

Time [years]

Figure 6‑60. Mean dose-equivalent near-field release for pinhole Q1 release path with irreversible sorption to colloids. The blue curve is total release, the solid green curve is the actinide and transition metal
portion including the colloidal-associated and dissolved component, and the dashed green curve is thecolloid-associated release of actinides and transition metals.

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100

Mean annual effective dose [µSv]

10-1

10-2

10-3

10-4

10-5

10-6
103

104

105

106

Time [years]

Figure 6‑61. Mean far-field effective dose for pinhole Q1 release path with and without irreversible sorption
to colloids. The blue curve is total (all-nuclides) dose without colloids, while the pink curve is total dosewith irreversible sorption to colloids at a concentration of 10 mg/l. The green curve is the dose due to thecolloid-associated component.

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100

Mean annual effective dose [µSv]

10-1

10-2

10-3

10-4

10-5

10-6
103

104

105

106

Time [years]

Figure 6‑62. Mean far-field effective dose for pinhole Q1 release path with irreversible sorption to colloids
assuming unlimited sorption sites on colloids. The blue curve is total (all-nuclides) dose without colloids,
while the pink curve is total dose with irreversible sorption to colloids. The green curve is the dose due tothe colloid-associated component.

6.5

Additional cases to illustrate barrier function

Some conclusions regarding loss of barrier functions can be drawn from the analyses alreadypresented. In order to provide a fuller treatment, the following cases of barrier deficiencies are
postulated:
A. An initial absence of enough buffer to cause advective conditions in the deposition hole for all
deposition holes.
B. An initial pinhole in the copper shell for all canisters.
C. An initial, large opening in the copper shell and in the cast iron insert for all canisters.
D. A combination of cases A and C, i.e. an initial large opening in all canisters and advective conditions due to loss of buffer for all deposition holes.
E. A combination of case C with an assumption of fast fuel dissolution and fast corrosion of metalparts. An initial, large opening in every canister is combined with the assumption of complete
fuel dissolution and metal corrosion in only 100 years.
A loss of the radionuclide retention capability of the rock is combined with each of the five cases,
yielding a total of ten release situations. The cases without geosphere retention are denoted A*
through E*.

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In all cases it is assumed that the backfill and closure are installed and perform as expected. Also,
all aspects of the rock other than those related to retention, e.g. the near-field groundwater flow,which is generally low and with only about one sixth of the deposition holes connected to water
conducting fractures, as well as the stable and favourable groundwater composition in the near field,
are assumed to be present. Elemental solubilities are imposed on concentrations of radionuclides in
the canister void volume only if the buffer is in place.
Table 6‑2 gives an overview of the status of the retardation related safety functions.
The transport and dose calculations are probabilistic, since it is desirable to take into account both
uncertainties due to lack-of-knowledge in general and the spatial variability of the properties of thedeposition holes and their associated transport paths in the geosphere. The semi-correlated hydro­
geological DFN model is used for these stylised calculations. Except for the case specific assumptions
regarding failed barrier functions, all transport data are taken from the Data report. This applies toe.g. corrosion rates, fuel dissolution rate, sorption and diffusion data and LDF values.
Table 6‑2. Status of safety functions for the ten release situations. In cases denoted with anasterisk also geosphere retention is absent.

E*

E. Large canister defect, rapid fuel andmetal conversion

D*

D. Large canister defect and buffer missing

C*

C. Large canister defect

B*

B. Pinhole damage

A*

A. Buffer missing

Green: Safety function intact
Yellow: Safety function deteriorates over time
Red: Safety function absent initially

Limited fuel dissolution rate
Limited corrosion rate of metalparts
Limited solubilities
High transport resistance incanister/buffer interface
Retardation in bufferHigh transport resistance inbuffer/rock interface1)
Geosphere retention
1)
When this safety function is present, spalling is still pessimistically assumed in all deposition holes. When this safetyfunction is not present, i.e. when the buffer is missing, the groundwater turnover in the deposition hole is still limited by
the hydraulic properties of the rock.

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The biosphere is here represented by the constant LDF values obtained when the release is distributed in the landscape according to the time dependent distribution of release locations from therepository during an interglacial. Furthermore, since the LDF values are suited primarily to handle
releases that are constant over periods of time that are comparable to the duration of an interglacial,i.e. typically 10,000 years, the releases for these cases are, as a variant, also evaluated with fully
time dependent modelling of the biosphere. Here, the releases are distributed in the landscape andthe time dependent doses are presented, rather than a time dependent release converted to dose by
a constant LDF value.
In the following, each case is discussed briefly using distributed, constant LDFs. The section is
concluded with summarising accounts of all cases both with LDFs and with time dependent modelling of the biosphere.
Cases A and A*, initial absence of buffer

A 0.5 m high section of the bentonite buffer is assumed to be missing, leaving a void in the form of ahollow cylinder between the canister and the wall of the deposition hole. The Q1 fracture, if it exists,
intersects the deposition hole at the location of the void. The deposition hole is otherwise filled withbuffer and the deposition tunnel backfill is assumed to be intact. For most of the deposition holes,
the groundwater flow and sulphide concentrations are not sufficient to cause canister failure during
the one million year assessment period. The corrosion calculation takes both the natural variability offlow rates for the ensemble of 6,000 deposition holes and the distribution of sulphide concentrationsin the groundwater into account. This yields a calculated mean number of failed canisters of 0.17 at
one million years, used also here. Only the deposition holes with the highest flow rates in the Q1
fracture contribute. This also means that releases to Q2 and Q3 release paths are negligible for these
positions.
Radionuclide transport in the near field and far field is modelled as the semi-correlated case withinitial advection, see Section 4.5.9. The consequences are similar to those shown in Figure 4‑30
and Figure 4‑31. The only differences is that the distributed LDF values are applied and the results
are shown in Figure 6-69. Many of the radionuclides have decayed to insignificance when the first
failures occur after close to 50,000 years. Near-field release equivalent doses are dominated by
Nb-94 from metal parts of the fuel and Ra-226, Pb-210 and Np-237 from the fuel matrix. Far-field
doses are dominated by Nb-94, Ra-226, Se-79 and I-129.
Cases B and B*, initial, penetrating pinhole defect in all canisters

The canister defects are assumed to be the same as the growing pinhole failure. Near-field and far-fieldradionuclide transport is modelled as the probabilistic calculation of the hypothetical pinhole failuremode including the effect of spalling, see Section 6.3.1, but with growing holes in all canisters. The
deposition hole buffer and the deposition tunnel backfill are assumed to be intact. The dose consequences in the biosphere are calculated with the distributed LDF values since this is a more realistic
approach when releases occur from all over the repository.
The consequences are similar to those in the pinhole scenario, see Figure 6‑15 and Figure 6‑17
for the near field and the far field, respectively. The only difference is that all canisters are now
assumed to have defects, meaning that the probabilistic single-canister results should be multipliedby 6,000 and that the distributed LDF values are applied, leading to a reduction of the consequencesby typically one order of magnitude. The far-field results with all 6,000 canisters are shown in thesummary Figure 6‑69 later in this section.
Cases C and C*, initial, large opening in all canisters

The canister defects are assumed to be in the form of a large opening in the copper shell and the castiron insert. The deposition hole buffer and the deposition tunnel backfill are assumed to be intact.
In the reference evolution, some of the deposition holes are affected by buffer erosion to the extent
that advective conditions occur in the hole. For the stylised case considered here, no such erosion is,
however, assumed, in order to more clearly demonstrate the role of the canister if all other barriers areintact. Combinations of canister and buffer defects are analysed in one of the cases described below.
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The calculation case is similar to the failure due to isostatic load, see Section 6.2. Near-field andfar-field radionuclide transport is modelled as a probabilistic calculation case where the failure ispostulated at 100 years for all canisters.
The dose equivalent release from the near field is shown in Figure 6‑63. The dose is dominated theinitial 10,000 years by C-14, Cs-137, Sr-90, Ag-108m, I-129 and Se-79. After about 10,000 years
Se-79, C-14, Ra-226 and I-129 contribute most to the total dose. Releases of nuclides that sorb
strongly in the buffer, e.g. Pu-238 and Pu-239, are strongly reduced compared to case D* below
where the buffer is also assumed to be missing. There is a considerable reduction also of the releaseof Cs-137, Sr-90 and Ag-108m compared to the case in which the buffer is missing.
The dose from the far-field release is shown in Figure 6‑64. The peak total dose is reduced by lessthan an order of magnitude compared to the near-field release, whereas doses from many of theshort-lived or sorbing nuclides are considerably reduced.
It is noteworthy that this completely unrealistic case of initial loss of containment function for all
canisters in the repository yields far-field releases, converted to doses, which never exceed thebackground radiation. However, the containment function is required for a majority of the canisters
in order to fulfil the regulatory requirement on risk at Forsmark.
The long-term release rate of I-129 equals, to a good approximation, the release rate of this nuclide
from the fuel matrix. This is caused by the assumed absence of sorption and long half-life of I-129.
Regarding the calculated dose from I-129 for this and other hypothetical cases in this section,
it is noted that the mitigating effect of mixing of I-129 with naturally occurring stable iodine isdisregarded in the biosphere models.
10,000
Typical background radiation in Sweden

Mean annual effective dose [µSv]

1,000

Sum
Ag108m
C14
Cs137
Sr90
Ni63
Am241

100

I129
Se79
10

Dose corresponding to risk limit

1

0.1

0.01

0.001
100

1,000

10,000100,000

Nb94
Ni59
Ra226
Pb210
Np237
Pu239
Pu240
Tc99
Cs135
Sn126
Cl36
Pu242
Am243

1,000,000

Time [yr]Figure 6‑63. Near-field dose equivalent release for case C*, i.e. all canisters have an initial large defectand the buffer is intact.

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1,000Sum
Typical background radiation in Sweden

Ag108mMean annual effective dose [µSv]

C14
100

Cs137
Sr90
Dose corresponding to risk limit

10

Ni63
Am241
I129
Se79
Nb94

1

Ni59
Ra226
Pb210

0.1

Np237
Pu239
Pu240

0.01

Tc99
Cs135
Sn126

0.001
100

1,000

10,000Time [yr]100,000

1,000,000

Cl36
Pu242
Am243

Figure 6‑64. Far-field dose for case C, i.e. all canisters have an initial large defect and the buffer is intact.

Cases D and D*, initial large opening in all canisters and advective conditions due toloss of buffer for all deposition holes

The defects are assumed to be the same as those modelled in the corrosion scenario, i.e. a large
opening in the copper shell and the cast iron insert and a section of the bentonite buffer is missing
where the canister is damaged, leaving a void between the canister and the wall of the deposition
hole in the form of a hollow cylinder. The deposition hole is otherwise filled with buffer and thedeposition tunnel backfill is assumed to be intact. This means that releases occur predominantly to
the Q1 fracture, if it exists. Near-field and far-field radionuclide transport is modelled as a corrosion
case where all canisters fail after 100 years.
Only the Q1 release path is evaluated in detail, since releases from Q1 will dominate in this situation. In the base case realisation of the semi-correlated hydrogeological DFN model used, 1,169 outof the 6,000 deposition holes have a Q1 fracture. This means that virtually all radionuclides will
leave through Q1 from these deposition holes. The analysis is, for technical reasons, limited to
the 1,000 deposition holes with the lowest F values and hence lowest geosphere retention. For
the remaining 5,000 deposition holes, Q2 and Q3 releases need to be considered. The analysis of
the isostatic load scenario shows i) that the Q1 release path dominates the initial approximately
10,000 years even with the buffer in place, ii) that I-129 dominates the total release after approximately 10,000 years and iii) that the retention of I-129 is close to zero. Therefore, the calculated
release of I-129 from the 1,000 deposition holes with a Q1 path is multiplied by 6 to approximately
account for releases through Q2 and Q3 from the remaining deposition holes.
The dose equivalent release from the near field is shown in Figure 6‑65. The dose is dominated theinitial 10,000 years by the IRF and/or CRF of Ag-108m, Cs-137, Sr-90, C-14 and Nb-94. Note that
only the generally low flow rates at Forsmark limits the releases for the IRF/CRF. After about 10,000
years Nb-94, Pu-239, Pu-240, Np-237, Ra-226, Pb-210 and I-129 contribute most to the total dose.
The dose from the far-field release is shown in Figure 6‑66. The total dose is reduced by about afactor of 10 compared to the near-field release. For the earliest releases this is an effect of the travel
time in the geosphere. In the long term, strongly sorbing nuclides like Pu-239 and Pu-240 are
retained in the geosphere. It is noteworthy that this completely unrealistic case of initial absence of
all transport limitations in the engineered parts of the repository yields far-field releases, converted
to doses, that exceed the background radiation by a factor of about five initially and that in the longterm are less than a factor of ten above the risk limit.
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1,000,000

Sum
Ag108mC14

Mean annual effective dose [µSv]100,000

Cs137
Typical background radiation in Sweden

10,000Sr90
Ni63

Dose corresponding to risk limit

Am241

1,000

I129
Se79
Nb94

100

Ni59
Ra226

10

Pb210
Np237
Pu239

1

Pu240
Tc99

0.1

Cs135
Sn126

0.01

Cl36
Pu242

0.001

Am243
100

1,000

10,000100,000

1,000,000

Time [yr]Figure 6‑65. Near-field dose equivalent release for case D*, i.e. all canisters have an initial large defectand the buffer is missing between the defect in the canister and the wall of the deposition hole.

100,000

Sum
Ag108mC14

Mean annual effective dose [µSv]10,000

Cs137

Typical background radiation in Sweden

Sr90
Ni63

1,000
Dose corresponding to risk limit
100

Am241
I129
Se79
Nb94
Ni59

10

Ra226
Pb210
Np237

1

Pu239
Pu240

0.1

Tc99
Cs135
Sn126

0.01

Cl36
Pu242

0.001

Am243
100

1,000

10,000100,000

1,000,000

Time [yr]Figure 6‑66. Far-field dose for case D, i.e. all canisters have an initial large defect and the buffer ismissing between the defect in the canister and the wall of the deposition hole.

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Cases E and E*, initial, large opening in all canisters and rapid fuel dissolution andmetal corrosion

These cases are identical to cases C and C*, (all canisters have a large opening in the copper shelland the cast iron insert), except that for cases E and E* complete fuel dissolution and metal corrosion
is assumed to occur in 100 years after water contacts the fuel. The containment function of not
only the canister but also of the fuel matrix and the structural parts of the fuel is thus assumed to
be absent. The deposition hole buffer and the deposition tunnel backfill are assumed to be intact.
The near-field and far-field developments for these cases are identical to those for cases C and C*
with the exception of the fast conversion of the fuel and metal corrosion.
The dose equivalent release from the near field is shown in Figure 6‑67. The dose is dominated by
C-14, Cs-137, Sr-90 and I-129 for more than 10,000 years. In the longer term, Ra-226 and Se-79
together with I-129 contribute most to the total dose. Note that the release of Ag-108m is identicalto that in case C* since this release is controlled by the solubility of Ag and not by corrosion in themodel. The early releases of Sr-90, Cs-137 and I-129 have increased in inversed relation to the IRF
values for these nuclides; cases E and E* are similar to assuming 100% IRF for all nuclides. The
decrease of I-129 at very long times is caused by depletion of I-129 from the repository and the hostrock through outward transport and not through decay.
The dose from the far field release is shown in Figure 6‑68. The peak total dose is reduced by morethan an order of magnitude compared to the near field release, whereas doses from many of theshort-lived or sorbing nuclides are considerably reduced.
Sum

1000000

Ag108mC14

Mean annual effective dose [µSv]

100000
Typical background radiation in Sweden
10000

Sr90
Ni63
Am241

1000

I129
Se79

100
Dose corresponding to risk limit
10

Nb94
Ni59
Ra226
Pb210

1

Np237
Pu239

0.1

Pu240
Tc99

0.01
0.001
100

Cs137

Cs135
Sn126
1,000

10,000Time [yr]100,000

1,000,000

Cl36
Pu242
Am243

Figure 6‑67. Near-field dose equivalent release for case E*, i.e. all canisters have an initial large defect in
combination with a rapid fuel and metal conversion and the buffer is intact.

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100,000

Sum
Typical background radiation in Sweden

Ag108mC14

Mean annual effective dose [µSv]10,000

Cs137
Sr90

1,000

Ni63
Am241

100

I129
Se79

Dose corresponding to risk limit

10

Nb94
Ni59
Ra226

1

Pb210
Np237

0.1

Pu239
Pu240
Tc99

0.01

Cs135
0.001
100

Sn126
1,000

10,000100,000

1,000,000

Time [yr]

Cl36
Pu242
Am243

Figure 6‑68. Far-field dose for case E, i.e. all canisters have an initial large defect in combination witha rapid fuel and metal conversion and the buffer is intact.

Summary of results with distributed LDF values

The summed dose for each case discussed above is given in Figure 6‑69.

1,000,000

Mean annual effective dose [µSv]100,000
Typical background radiation in Sweden
10,000Omitted transport barriers"Rock" refers to retention only
E* Canisters, fuel, rockE. Canisters, fuel

1,000

D* Canisters, buffer, rockD. Canisters, buffer100

C* Canisters, rock10

C. Canisters
Dose corresponding to risk limit

1

B* Canisters (pinhole), rock
B. Canisters (pinhole)
A* Buffer, rock

0.1

A. Buffer

0.01
0.001
100

1,000

10,000100,000

1,000,000

Time [yr]Figure 6‑69. Results of stylised cases to illustrate loss of barrier functions. Note that an omission of the“rock” barrier in these cases refers to omission of retention of radionuclides in the rock fractures only,
whereas the favourable, low flow rate at repository depth and the favourable geochemical conditions arestill taken into account.
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The following are noted.
After about 10,000 years, the doses for all cases are below the dose caused by typical backgroundradiation in Sweden, except for the case in which retention properties of canisters, buffer androck are all disregarded (case D*) and those with rapid fuel dissolution in combination with failed
canisters (cases E and E*). The low flow and favourable groundwater chemistry of the rock and thepresence of backfill and closure of the repository tunnel thus provide substantial protection from afuel with unaltered dissolution rate.
If all canisters have large defects initially, but the barrier system is otherwise intact, case C, the peakannual dose to the most exposed individuals in the landscape does not exceed that caused by typicalbackground radiation in Sweden, i.e. 1 mSv. Beyond 10,000 years this annual dose is less than anorder of magnitude above the risk limit of 0.014 mSv.
If all canisters have large defects initially, and if also the buffer is assumed to be missing between
the canister damage and the wall of the deposition hole, case D, the dose is around ten times the
background radiation for the first few hundred years, but is after 1,000 years quite similar to the casewhere the buffer is in place, case C. This suggests that the buffer is, from the point of view of totaldose, not important as a retention barrier in this time perspective. However, a comparison between
Figure 6‑64 and Figure 6‑63 shows that the buffer has a considerable impact on near-field releases ofmany sorbing nuclides that do not dominate the dose.
With a large degree of damage to the canisters, the buffer missing and retention in the rock disregarded (case D*), the calculation results suggest annual doses in the Sievert range in the initial1,000 years. This is a demonstration of the necessity of properly protecting man and the environment from the spent nuclear fuel, in particular in the 1,000 year time frame. It is noted that a more
realistic treatment of corrosion of the AgInCd alloy of the PWR control rods would likely reduce thetotal dose, dominated by Ag-108m, by at least a factor of 10 the first 100 years and more between
100 and 1,000 years.
Beyond 10,000 years, the total dose is comparable to that caused by the background radiation evenwhen neglecting the retention properties of all three barriers, case D*.
As expected, the cases with initial pinhole defects, case B, and those with large initial defects, case C,
are quite similar beyond 10,000 years, when the pinhole defects are assumed to have grown intolarge defects. It is also noted that neglect of rock retention does not affect the total dose much forthese cases after about 1,000 years. However, a comparison between Figure 6‑66 and Figure 6‑64shows that the rock has a considerable impact on far-field releases of many sorbing nuclides that do
not dominate the dose.
A comparison of cases C and E shows the considerable containment function of the waste form for
more than 100,000 years.
Summary of results with time dependent modelling of the biosphere

As mentioned in the introduction, the LDF values are suited primarily to handle releases that are
constant over periods of time that are comparable to the duration of an interglacial, i.e. typically
10,000 years. Therefore, the releases for most of the above cases were also evaluated with a fully
time dependent modelling of the biosphere. Here, the releases are distributed in the landscapeaccording to the time dependent spatial distribution of release points from the repository and the timedependent doses are presented, rather than a time dependent release converted to dose by a constant
LDF value. This modelling was for assumed temperate conditions over a period of 60,000 years. The
results are given in Figure 6‑70. The solid curves are doses obtained with distributed LDF values(i.e. the same curves as in Figure 6‑69) and the dashed curves are the corresponding doses obtainedwith time dependent modelling of the biosphere.

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1,000,000

Mean annual effective dose [µSv]100,000
10,000

Typical background radiation in Sweden

Omitted transport barriers"Rock" refers to retention only
D* Canisters, buffer, rockD. Canisters, buffer

1,000

C* Canisters, rock
C. Canisters

100

B* Canisters (pinhole), rock
B. Canisters (pinhole)

10
Dose corresponding to risk limit

A* Buffer, rock
A. Buffer

1
0.1
0.01
0.001
100

1,000

10,000100,000

1,000,000

Time [yr]Figure 6‑70. Results of stylised cases to illustrate loss of barrier functions. Solid lines: Same as in
Figure 6‑69 (dose conversion through distributed LDF). Dashed lines: Corresponding cases with timedependent modelling of the biospehere.

The results from time dependent modelling of the biosphere (dashed curves) are generally within anorder of magnitude of, but below, the curves obtained with distributed LDF values. The one exception is the case where the retention properties of the canister, buffer and rock are all disregarded(case D*). In that case, the time dependent doses from Ag-108m around 1,000 years and from C-14
around 20,000 years exceed those obtained using the LDF. This exceedance is caused by accumulation and delay effects in the biosphere. The release of Ag-108m from the near field decreases rapidly
over the initial hundreds of years and hence so does the release multiplied by the LDF value. In thetime dependent case, some Ag-108m is accumulated in the landscape and this, in combination withthe development of landscape objects, leads to a delayed release and hence dose that exceeds thedose obtained with the LDF values.

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7

Summary and conclusions

Table 7‑1 shows a summary of near-field and far-field maximum dose-equivalent releases forprobabilistic numerical calculation cases discussed in this report. Contributions from the IRF are
not included in the table. The maximum doses do not appear at the same time in all cases. In the
corrosion cases and shear load cases the maximum normally appears at one million years whilepinhole cases and isostatic load cases in general have their maximum shortly after the large failurein the canister is postulated.
For all probabilistic cases considered, the maximum over the one million year assessment time of themean total far-field effective dose is smaller than the dose corresponding to the risk limit. Excluding
hypothetical cases (e.g. growing pinhole and postulated failure at 100,000 years due to shear load)
and the cases supporting the discussion of best available technique, the far-field effective dose is atleast one order of magnitude smaller than the dose corresponding to the risk limit. The two scenarios
contributing to the calculated risk, i.e. failure of the copper canister by corrosion and earthquakeinduced shear failure of the copper canister, the peak of the mean annual effective dose is estimated tobe 0.18 μSv/yr and 0.15 μSv/yr, respectively. These doses, which assume reference conditions, could
be compared with the dose corresponding to the risk limit of 14 μSv/yr and the dose corresponding totypical background radiation of approximately 1,000 μSv/yr. Further discussion of dose estimates associated with these and other scenarios and results of risk summation can be found in the Main report.
In the scenario of failure of the copper canister due to corrosion, the geosphere provides only amodest (factor of 3) attenuation of the dose-equivalent release for the central case. The annual
dose-equivalent release is relatively small because the geosphere provides benign geochemical andhydrological environments, thus limiting release from the waste form and engineered barriers. In
variant corrosion cases that result in higher near-field releases, the far-field attenuation is somewhat
stronger. This tendency to attenuate more strongly the larger near-field releases means that thegeosphere also tends to reduce uncertainty in the far-field dose-equivalent releases.
The detailed numerical calculations are in good agreement with an analytical calculation using
simplified modelling assumptions. This agreement significantly enhances confidence in the calculated dose-equivalent releases for two reasons. First, the comparison provides an important quality
assurance check on the numerical modelling of dose-equivalent releases. This check applies not only
to the numerical calculations but also to the data/parameter transfers, as the data for the analytical
calculations were taken directly from the Data report independently of the numerical calculations.
Second, it demonstrates that the effective dose for the corrosion cases and shear load case are controlled by relatively simple processes that are straightforward to understand.
Additional confidence in the calculated results is provided by extensive sensitivity analyses anddetailed calculations used to screen out certain neglected processes. Analyses of the potential effectof flow channelling within individual fractures because of aperture variability, Appendix A, showthat channelling is not sufficient to significantly alter the transport characteristics of the entire
pathway. Calculations detailed in Appendix B justify the neglect of fracture mineral retention pro­
cesses in the SR-Site transport calculations. The calculations in Appendix B indicate that sorption
on chlorite and other clay minerals should dominate fracture mineral retention, although minor
contributions from solid solutions involving calcite (and possibly barite) are feasible. These retention
processes are neglected in SR-Site, which is a pessimistic assumption provided changes in groundwater chemistry do not result in pulse remobilization of radionuclides. The analyses demonstrate that
pulse remobilization of radionuclides previously immobilized on fracture minerals is not expected tooccur to any great extent for the relevant ranges of groundwater compositions.

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Table 7‑1. Summary of the results for all numerical probabilistic calculation cases.
Calculation case

Maximum total
near-field dose
equivalent release(µSv/yr)

Maximum total
far-field meaneffective dose(µSv/yr)

Dose corresponding to background radiation

1,000

1,000

Dose corresponding to risk limit

14

14

Semi-correlated, central corrosion case

0.59

0.18

Semi-correlated, disregarding thorium in the near field

0.22

0.14

Semi-correlated including solubility limits

6.2

0.15

Semi-correlated, Kd for U(VI) instead of U(IV) in the geospehre

0.59

0.18

Semi-correlated, 10 mg/l colloids

0.59

0.19

Semi-correlated, 10 g/l colloids

0.59

0.33

Semi-correlated, varying climate, no colloids

0.59

0.19

Semi-correlated, varying climate, 10 g/l colloids

0.59

0.41

Semi-correlated, varying climate and colloid concentration

0.59

0.35

Semi-correlated with initial advection

1.0

0.27

Uncorrelated

3.1

0.45

Uncorrelated with initial advection

7.0

0.83

Fully correlated

3.2

0.63

Fully correlated with initial advection

6.0

0.96

Postulated failure of one canister at 100,000 years

4.2

4.2

Failure during the period 1,000 years to one million years

0.15

0.15

Early failure

0.00270.0027

Combination of shear load and buffer advection

0.34

0.34

Postulated failure of one canister at 10,000 years

2.5

0.63

Postulated failure of one canister at 100,000 years

1.5

0.39

Including the effect of spalling

3.7

0.65

Disregarding the effect of spalling

0.85

0.41

Lost swelling pressure in tunnel backfill, “Crown space”

9.5

2.7

EDZ with a transmissivity of 10–6 m2/s

5.8

2.0

EDZ with a transmissivity of 10–7 m2/s

4.2

1.1

No EDZ

2.5

0.16

Copper shell thickness 25 mm

1.2

0.36

Copper shell thickness 100 mm

0.25

0.078

No T/L-filtering

1.3

0.71

Neither T/L- nor EFPC-filtering

20

12Canister failure due to corrosion

Canister failure due to shear load

Canister failure due to isostatic load

The growing pinhole failure

Cases addressing best available technique (BAT)192

TR-10-50

8References

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